LMFDB - Embedded newform 675.2.ba.b.407.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			407.2
Character	$\chi$	$=$	675.407
Dual form			675.2.ba.b.68.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36466 - 1.94894i) q^{2} +(1.63096 - 0.583078i) q^{3} +(-1.25203 + 3.43992i) q^{4} +(-3.36209 - 2.38294i) q^{6} +(2.19758 + 1.02475i) q^{7} +(3.81650 - 1.02263i) q^{8} +(2.32004 - 1.90195i) q^{9} +(0.00275056 - 0.00327799i) q^{11} +(-0.0362633 + 6.34039i) q^{12} +(1.13206 + 0.792678i) q^{13} +(-1.00178 - 5.68139i) q^{14} +(-1.59279 - 1.33651i) q^{16} +(-1.90362 - 0.510074i) q^{17} +(-6.87287 - 1.92610i) q^{18} +(6.69182 + 3.86352i) q^{19} +(4.18166 + 0.389960i) q^{21} +(-0.0101422 - 0.000887327i) q^{22} +(3.12427 + 6.70002i) q^{23} +(5.62827 - 3.89318i) q^{24} -3.28806i q^{26} +(2.67490 - 4.45476i) q^{27} +(-6.27648 + 6.27648i) q^{28} +(1.74110 - 9.87424i) q^{29} +(-5.62932 - 2.04890i) q^{31} +(0.257571 - 2.94406i) q^{32} +(0.00257472 - 0.00695004i) q^{33} +(1.60370 + 4.40613i) q^{34} +(3.63779 + 10.3620i) q^{36} +(0.451272 - 1.68417i) q^{37} +(-1.60230 - 18.3144i) q^{38} +(2.30854 + 0.632743i) q^{39} +(-2.95191 + 0.520501i) q^{41} +(-4.94656 - 8.68198i) q^{42} +(7.18901 - 0.628957i) q^{43} +(0.00783223 + 0.0135658i) q^{44} +(8.79437 - 15.2323i) q^{46} +(0.871367 - 1.86865i) q^{47} +(-3.37706 - 1.25107i) q^{48} +(-0.720271 - 0.858385i) q^{49} +(-3.40214 + 0.278051i) q^{51} +(-4.14412 + 2.90174i) q^{52} +(1.25315 + 1.25315i) q^{53} +(-12.3324 + 0.866025i) q^{54} +(9.43499 + 1.66364i) q^{56} +(13.1668 + 2.39939i) q^{57} +(-21.6203 + 10.0817i) q^{58} +(-0.763311 + 0.640494i) q^{59} +(-6.39745 + 2.32848i) q^{61} +(3.68893 + 13.7673i) q^{62} +(7.04749 - 1.80223i) q^{63} +(-9.69063 + 5.59489i) q^{64} +(-0.0170589 + 0.00446650i) q^{66} +(-5.21964 + 7.45442i) q^{67} +(4.13800 - 5.90968i) q^{68} +(9.00219 + 9.10575i) q^{69} +(8.32564 - 4.80681i) q^{71} +(6.90944 - 9.63132i) q^{72} +(-0.744204 - 2.77741i) q^{73} +(-3.89819 + 1.41882i) q^{74} +(-21.6685 + 18.1821i) q^{76} +(0.00940367 - 0.00438501i) q^{77} +(-1.91719 - 5.36268i) q^{78} +(-6.95996 - 1.22723i) q^{79} +(1.76518 - 8.82520i) q^{81} +(5.04279 + 5.04279i) q^{82} +(-8.34640 + 5.84421i) q^{83} +(-6.57699 + 13.8963i) q^{84} +(-11.0364 - 13.1527i) q^{86} +(-2.91780 - 17.1197i) q^{87} +(0.00714534 - 0.0153232i) q^{88} +(-3.03785 + 5.26171i) q^{89} +(1.67550 + 2.90205i) q^{91} +(-26.9592 + 2.35862i) q^{92} +(-10.3758 - 0.0593438i) q^{93} +(-4.83102 + 0.851839i) q^{94} +(-1.29653 - 4.95181i) q^{96} +(-1.09824 - 12.5529i) q^{97} +(-0.690016 + 2.57517i) q^{98} +(0.000146839 - 0.0128365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.36466	−	1.94894i	−0.964963	−	1.37811i	−0.925441	−	0.378892i	$-0.876305\pi$
$2$	−1.36466	−	1.94894i	−0.964963	−	1.37811i	−0.0395221	−	0.999219i	$-0.512584\pi$
$3$	1.63096	−	0.583078i	0.941633	−	0.336640i
$3$	1.63096	−	0.583078i	0.941633	−	0.336640i
$4$	−1.25203	+	3.43992i	−0.626014	+	1.71996i
$5$		0			0
$5$		0			0
$6$	−3.36209	−	2.38294i	−1.37257	−	0.972829i
$7$	2.19758	+	1.02475i	0.830607	+	0.387318i	0.790939	−	0.611895i	$-0.209592\pi$
$7$	2.19758	+	1.02475i	0.830607	+	0.387318i	0.0396673	+	0.999213i	$0.487370\pi$
$8$	3.81650	−	1.02263i	1.34934	−	0.361553i
$9$	2.32004	−	1.90195i	0.773347	−	0.633983i
$10$		0			0
$11$	0.00275056	−	0.00327799i	0.000829324	−	0.000988350i	−0.765630	−	0.643282i	$-0.777572\pi$
$11$	0.00275056	−	0.00327799i	0.000829324	−	0.000988350i	0.766459	+	0.642293i	$0.222017\pi$
$12$	−0.0362633	+	6.34039i	−0.0104683	+	1.83031i
$13$	1.13206	+	0.792678i	0.313977	+	0.219849i	0.719933	−	0.694043i	$-0.244172\pi$
$13$	1.13206	+	0.792678i	0.313977	+	0.219849i	−0.405956	+	0.913893i	$0.633061\pi$
$14$	−1.00178	−	5.68139i	−0.267738	−	1.51842i
$15$		0			0
$16$	−1.59279	−	1.33651i	−0.398197	−	0.334127i
$17$	−1.90362	−	0.510074i	−0.461696	−	0.123711i	0.0204707	−	0.999790i	$-0.493484\pi$
$17$	−1.90362	−	0.510074i	−0.461696	−	0.123711i	−0.482167	+	0.876079i	$0.660150\pi$
$18$	−6.87287	−	1.92610i	−1.61995	−	0.453987i
$19$	6.69182	+	3.86352i	1.53521	+	0.886353i	0.999109	+	0.0421981i	$0.0134361\pi$
$19$	6.69182	+	3.86352i	1.53521	+	0.886353i	0.536099	+	0.844155i	$0.319897\pi$
$20$		0			0
$21$	4.18166	+	0.389960i	0.912514	+	0.0850962i
$22$	−0.0101422		0.000887327i	−0.00216232		0.000189179i
$23$	3.12427	+	6.70002i	0.651456	+	1.39705i	0.903184	+	0.429253i	$0.141223\pi$
$23$	3.12427	+	6.70002i	0.651456	+	1.39705i	−0.251729	+	0.967798i	$0.580999\pi$
$24$	5.62827	−	3.89318i	1.14887	−	0.794691i
$25$		0			0
$26$		−	3.28806i		−	0.644842i
$27$	2.67490	−	4.45476i	0.514785	−	0.857319i
$28$	−6.27648	+	6.27648i	−1.18614	+	1.18614i
$29$	1.74110	−	9.87424i	0.323313	−	1.83360i	−0.197959	−	0.980210i	$-0.563431\pi$
$29$	1.74110	−	9.87424i	0.323313	−	1.83360i	0.521272	−	0.853391i	$-0.325458\pi$
$30$		0			0
$31$	−5.62932	−	2.04890i	−1.01106	−	0.367994i	−0.217217	−	0.976123i	$-0.569698\pi$
$31$	−5.62932	−	2.04890i	−1.01106	−	0.367994i	−0.793838	+	0.608129i	$0.791920\pi$
$32$	0.257571	−	2.94406i	0.0455326	−	0.520440i
$33$	0.00257472	−	0.00695004i	0.000448201	−	0.00120985i
$34$	1.60370	+	4.40613i	0.275032	+	0.755645i
$35$		0			0
$36$	3.63779	+	10.3620i	0.606299	+	1.72701i
$37$	0.451272	−	1.68417i	0.0741887	−	0.276876i	−0.918859	−	0.394585i	$-0.870888\pi$
$37$	0.451272	−	1.68417i	0.0741887	−	0.276876i	0.993048	+	0.117709i	$0.0375550\pi$
$38$	−1.60230	−	18.3144i	−0.259927	−	2.97098i
$39$	2.30854	+	0.632743i	0.369661	+	0.101320i
$40$		0			0
$41$	−2.95191	+	0.520501i	−0.461011	+	0.0812887i	−0.399330	−	0.916807i	$-0.630757\pi$
$41$	−2.95191	+	0.520501i	−0.461011	+	0.0812887i	−0.0616809	+	0.998096i	$0.519646\pi$
$42$	−4.94656	−	8.68198i	−0.763270	−	1.33966i
$43$	7.18901	−	0.628957i	1.09631	−	0.0959151i	0.475382	−	0.879779i	$-0.342310\pi$
$43$	7.18901	−	0.628957i	1.09631	−	0.0959151i	0.620932	+	0.783864i	$0.286754\pi$
$44$	0.00783223	+	0.0135658i	0.00118075	+	0.00204512i
$45$		0			0
$46$	8.79437	−	15.2323i	1.29666	−	2.24588i
$47$	0.871367	−	1.86865i	0.127102	−	0.272571i	−0.832451	−	0.554098i	$-0.813063\pi$
$47$	0.871367	−	1.86865i	0.127102	−	0.272571i	0.959553	+	0.281527i	$0.0908410\pi$
$48$	−3.37706	−	1.25107i	−0.487436	−	0.180576i
$49$	−0.720271	−	0.858385i	−0.102896	−	0.122626i
$50$		0			0
$51$	−3.40214	+	0.278051i	−0.476395	+	0.0389350i
$52$	−4.14412	+	2.90174i	−0.574686	+	0.402399i
$53$	1.25315	+	1.25315i	0.172134	+	0.172134i	0.787916	−	0.615782i	$-0.211160\pi$
$53$	1.25315	+	1.25315i	0.172134	+	0.172134i	−0.615782	+	0.787916i	$0.711160\pi$
$54$	−12.3324	+	0.866025i	−1.67823	+	0.117851i
$55$		0			0
$56$	9.43499	+	1.66364i	1.26080	+	0.222314i
$57$	13.1668	+	2.39939i	1.74399	+	0.317807i
$58$	−21.6203	+	10.0817i	−2.83889	+	1.32380i
$59$	−0.763311	+	0.640494i	−0.0993747	+	0.0833853i	−0.691121	−	0.722739i	$-0.742883\pi$
$59$	−0.763311	+	0.640494i	−0.0993747	+	0.0833853i	0.591747	+	0.806124i	$0.298439\pi$
$60$		0			0
$61$	−6.39745	+	2.32848i	−0.819109	+	0.298131i	−0.717381	−	0.696681i	$-0.754659\pi$
$61$	−6.39745	+	2.32848i	−0.819109	+	0.298131i	−0.101728	+	0.994812i	$0.532437\pi$
$62$	3.68893	+	13.7673i	0.468495	+	1.74845i
$63$	7.04749	−	1.80223i	0.887900	−	0.227059i
$64$	−9.69063	+	5.59489i	−1.21133	+	0.699361i
$65$		0			0
$66$	−0.0170589	+	0.00446650i	−0.00209980	+	0.000549788i
$67$	−5.21964	+	7.45442i	−0.637680	+	0.910702i	−0.999770	−	0.0214414i	$-0.993174\pi$
$67$	−5.21964	+	7.45442i	−0.637680	+	0.910702i	0.362090	+	0.932143i	$0.382063\pi$
$68$	4.13800	−	5.90968i	0.501806	−	0.716654i
$69$	9.00219	+	9.10575i	1.08374	+	1.09620i
$70$		0			0
$71$	8.32564	−	4.80681i	0.988072	−	0.570464i	0.0833745	−	0.996518i	$-0.473430\pi$
$71$	8.32564	−	4.80681i	0.988072	−	0.570464i	0.904697	+	0.426055i	$0.140097\pi$
$72$	6.90944	−	9.63132i	0.814286	−	1.13506i
$73$	−0.744204	−	2.77741i	−0.0871025	−	0.325071i	0.908602	−	0.417664i	$-0.137151\pi$
$73$	−0.744204	−	2.77741i	−0.0871025	−	0.325071i	−0.995704	+	0.0925931i	$0.970484\pi$
$74$	−3.89819	+	1.41882i	−0.453155	+	0.164935i
$75$		0			0
$76$	−21.6685	+	18.1821i	−2.48555	+	2.08563i
$77$	0.00940367	−	0.00438501i	0.00107165	−	0.000499718i
$78$	−1.91719	−	5.36268i	−0.217080	−	0.607204i
$79$	−6.95996	−	1.22723i	−0.783057	−	0.138074i	−0.232194	−	0.972670i	$-0.574590\pi$
$79$	−6.95996	−	1.22723i	−0.783057	−	0.138074i	−0.550863	+	0.834595i	$0.685701\pi$
$80$		0			0
$81$	1.76518	−	8.82520i	0.196131	−	0.980578i
$82$	5.04279	+	5.04279i	0.556883	+	0.556883i
$83$	−8.34640	+	5.84421i	−0.916136	+	0.641485i	−0.933582	−	0.358363i	$-0.883335\pi$
$83$	−8.34640	+	5.84421i	−0.916136	+	0.641485i	0.0174466	+	0.999848i	$0.494446\pi$
$84$	−6.57699	+	13.8963i	−0.717608	+	1.51621i
$85$		0			0
$86$	−11.0364	−	13.1527i	−1.19008	−	1.41829i
$87$	−2.91780	−	17.1197i	−0.312821	−	1.83542i
$88$	0.00714534	−	0.0153232i	0.000761696	−	0.00163346i
$89$	−3.03785	+	5.26171i	−0.322012	+	0.557741i	−0.980903	−	0.194498i	$-0.937692\pi$
$89$	−3.03785	+	5.26171i	−0.322012	+	0.557741i	0.658891	+	0.752238i	$0.271026\pi$
$90$		0			0
$91$	1.67550	+	2.90205i	0.175640	+	0.304217i
$92$	−26.9592	+	2.35862i	−2.81069	+	0.245904i
$93$	−10.3758	−	0.0593438i	−1.07593	−	0.00615366i
$94$	−4.83102	+	0.851839i	−0.498281	+	0.0878604i
$95$		0			0
$96$	−1.29653	−	4.95181i	−0.132326	−	0.505392i
$97$	−1.09824	−	12.5529i	−0.111509	−	1.27456i	−0.821444	−	0.570289i	$-0.806831\pi$
$97$	−1.09824	−	12.5529i	−0.111509	−	1.27456i	0.709935	−	0.704267i	$-0.248724\pi$
$98$	−0.690016	+	2.57517i	−0.0697021	+	0.260132i
$99$	0.000146839	−	0.0128365i	1.47579e−5	−	0.00129012i
$100$		0			0
$101$	−1.67645	−	4.60600i	−0.166813	−	0.458314i	0.827916	−	0.560852i	$-0.189526\pi$
$101$	−1.67645	−	4.60600i	−0.166813	−	0.458314i	−0.994729	+	0.102537i	$0.967304\pi$
$102$	5.18468	+	6.25113i	0.513360	+	0.618954i
$103$	1.01013	−	11.5458i	0.0995307	−	1.13764i	−0.768066	−	0.640371i	$-0.778781\pi$
$103$	1.01013	−	11.5458i	0.0995307	−	1.13764i	0.867596	−	0.497269i	$-0.165664\pi$
$104$	5.13112	+	1.86758i	0.503148	+	0.183131i
$105$		0			0
$106$	0.732191	−	4.15246i	0.0711167	−	0.403323i
$107$	−3.31844	+	3.31844i	−0.320806	+	0.320806i	−0.849076	−	0.528270i	$-0.822841\pi$
$107$	−3.31844	+	3.31844i	−0.320806	+	0.320806i	0.528270	+	0.849076i	$0.322841\pi$
$108$	11.9750	+	14.7789i	1.15229	+	1.42210i
$109$			11.2538i			1.07792i	0.842332	+	0.538960i	$0.181182\pi$
$109$			11.2538i			1.07792i	−0.842332	+	0.538960i	$0.818818\pi$
$110$		0			0
$111$	−0.245997	−	3.00994i	−0.0233490	−	0.285691i
$112$	−2.13069	−	4.56928i	−0.201331	−	0.431757i
$113$	−1.87764	−	0.164272i	−0.176634	−	0.0154535i	−0.00150433	−	0.999999i	$-0.500479\pi$
$113$	−1.87764	−	0.164272i	−0.176634	−	0.0154535i	−0.175129	+	0.984545i	$0.556034\pi$
$114$	−13.2920	−	28.9357i	−1.24491	−	2.71008i
$115$		0			0
$116$	31.7867	+	18.3520i	2.95132	+	1.70394i
$117$	4.13406	−	0.314079i	0.382194	−	0.0290366i
$118$	2.28995	+	0.613590i	0.210807	+	0.0564856i
$119$	−3.66066	−	3.07166i	−0.335572	−	0.281579i
$120$		0			0
$121$	1.91013	+	10.8329i	0.173648	+	0.984806i
$122$	13.2684	+	9.29066i	1.20127	+	0.841137i
$123$	−4.51095	+	2.57011i	−0.406738	+	0.231739i
$124$	14.0961	−	16.7991i	1.26587	−	1.50860i
$125$		0			0
$126$	−13.1299	−	11.2757i	−1.16970	−	1.00452i
$127$	5.69522	−	1.52603i	0.505369	−	0.135413i	0.00287859	−	0.999996i	$-0.499084\pi$
$127$	5.69522	−	1.52603i	0.505369	−	0.135413i	0.502491	+	0.864583i	$0.332417\pi$
$128$	18.7718	+	8.75341i	1.65920	+	0.773700i
$129$	11.3582	−	5.21756i	1.00004	−	0.459380i
$130$		0			0
$131$	−5.29212	+	14.5400i	−0.462375	+	1.27036i	0.461320	+	0.887234i	$0.347376\pi$
$131$	−5.29212	+	14.5400i	−0.462375	+	1.27036i	−0.923694	+	0.383130i	$0.874846\pi$
$132$	0.0206840	+	0.0175585i	0.00180031	+	0.00152827i
$133$	10.7467	+	15.3478i	0.931854	+	1.33082i
$134$	21.6513			1.87039
$135$		0			0
$136$	−7.78679			−0.667712
$137$	2.24127	+	3.20087i	0.191485	+	0.273468i	0.903402	−	0.428795i	$-0.141062\pi$
$137$	2.24127	+	3.20087i	0.191485	+	0.273468i	−0.711917	+	0.702263i	$0.752173\pi$
$138$	5.46163	−	29.9710i	0.464924	−	2.55130i
$139$	1.85959	−	5.10917i	0.157728	−	0.433354i	−0.835506	−	0.549481i	$-0.814826\pi$
$139$	1.85959	−	5.10917i	0.157728	−	0.433354i	0.993234	+	0.116126i	$0.0370478\pi$
$140$		0			0
$141$	0.331592	−	3.55577i	0.0279251	−	0.299449i
$142$	−20.7299	−	9.66651i	−1.73961	−	0.811196i
$143$	0.00571218	−	0.00153058i	0.000477677	−	0.000127993i
$144$	−6.23730	−	0.0713498i	−0.519775	−	0.00594581i
$145$		0			0
$146$	−4.39742	+	5.24064i	−0.363933	+	0.433718i
$147$	−1.67524	−	0.980015i	−0.138171	−	0.0808303i
$148$	5.22840	+	3.66097i	0.429772	+	0.300930i
$149$	−1.59684	−	9.05612i	−0.130818	−	0.741907i	−0.977681	−	0.210095i	$-0.932623\pi$
$149$	−1.59684	−	9.05612i	−0.130818	−	0.741907i	0.846863	−	0.531811i	$-0.178488\pi$
$150$		0			0
$151$	8.68937	+	7.29124i	0.707131	+	0.593353i	0.923792	−	0.382894i	$-0.125072\pi$
$151$	8.68937	+	7.29124i	0.707131	+	0.593353i	−0.216662	+	0.976247i	$0.569517\pi$
$152$	29.4903	+	7.90189i	2.39198	+	0.640928i
$153$	−5.38662	+	2.43720i	−0.435482	+	0.197036i
$154$	−0.0213790	−	0.0123432i	−0.00172277	−	0.000994640i
$155$		0			0
$156$	−5.06693	+	7.14896i	−0.405679	+	0.572375i
$157$	0.876549	+	0.0766881i	0.0699562	+	0.00612037i	0.122080	−	0.992520i	$-0.461044\pi$
$157$	0.876549	+	0.0766881i	0.0699562	+	0.00612037i	−0.0521239	+	0.998641i	$0.516599\pi$
$158$	7.10621	+	15.2393i	0.565340	+	1.21238i
$159$	2.77453	+	1.31315i	0.220034	+	0.104140i
$160$		0			0
$161$			17.9254i			1.41272i
$162$	−19.6087	+	8.60321i	−1.54060	+	0.675932i
$163$	−4.75545	+	4.75545i	−0.372476	+	0.372476i	−0.868378	−	0.495902i	$-0.834837\pi$
$163$	−4.75545	+	4.75545i	−0.372476	+	0.372476i	0.495902	+	0.868378i	$0.334837\pi$
$164$	1.90539	−	10.8060i	0.148786	−	0.843808i
$165$		0			0
$166$	22.7800	+	8.29126i	1.76807	+	0.643527i
$167$	0.630926	−	7.21152i	0.0488226	−	0.558044i	−0.931910	−	0.362689i	$-0.881859\pi$
$167$	0.630926	−	7.21152i	0.0488226	−	0.558044i	0.980733	−	0.195355i	$-0.0625859\pi$
$168$	16.3581	−	2.78800i	1.26205	−	0.215099i
$169$	−3.79304	−	10.4213i	−0.291772	−	0.801637i
$170$		0			0
$171$	22.8735	−	3.76397i	1.74918	−	0.287838i
$172$	−6.83728	+	25.5171i	−0.521338	+	1.94566i
$173$	0.208175	+	2.37946i	0.0158273	+	0.180907i	0.999993	+	0.00365760i	$0.00116425\pi$
$173$	0.208175	+	2.37946i	0.0158273	+	0.180907i	−0.984166	+	0.177249i	$0.943280\pi$
$174$	−29.3834	+	29.0492i	−2.22755	+	2.20221i
$175$		0			0
$176$	−0.00876211	+	0.00154500i	−0.000660469	+	0.000116458i
$177$	−0.871470	+	1.48969i	−0.0655037	+	0.111972i
$178$	14.4004	−	1.25987i	1.07936	−	0.0944315i
$179$	8.41245	+	14.5708i	0.628776	+	1.08907i	0.987798	+	0.155743i	$0.0497772\pi$
$179$	8.41245	+	14.5708i	0.628776	+	1.08907i	−0.359021	+	0.933329i	$0.616889\pi$
$180$		0			0
$181$	3.54419	−	6.13871i	0.263437	−	0.456287i	−0.703716	−	0.710482i	$-0.748477\pi$
$181$	3.54419	−	6.13871i	0.263437	−	0.456287i	0.967153	+	0.254195i	$0.0818105\pi$
$182$	3.36943	−	7.22577i	0.249759	−	0.535610i
$183$	−9.07628	+	7.52786i	−0.670938	+	0.556476i
$184$	18.7754	+	22.3757i	1.38414	+	1.64955i
$185$		0			0
$186$	14.0439	+	20.3029i	1.02975	+	1.48868i
$187$	−0.00690804	+	0.00483706i	−0.000505166	+	0.000353721i
$188$	5.33703	+	5.33703i	0.389243	+	0.389243i
$189$	10.4433	−	7.04859i	0.759639	−	0.512709i
$190$		0			0
$191$	−7.71793	−	1.36088i	−0.558450	−	0.0984697i	−0.112703	−	0.993629i	$-0.535951\pi$
$191$	−7.71793	−	1.36088i	−0.558450	−	0.0984697i	−0.445747	+	0.895159i	$0.647062\pi$
$192$	−12.5427	+	14.7754i	−0.905195	+	1.06632i
$193$	16.8391	−	7.85219i	1.21210	−	0.565213i	0.291823	−	0.956472i	$-0.405738\pi$
$193$	16.8391	−	7.85219i	1.21210	−	0.565213i	0.920280	+	0.391259i	$0.127960\pi$
$194$	−22.9662	+	19.2709i	−1.64888	+	1.38357i
$195$		0			0
$196$	3.85457	−	1.40295i	0.275327	−	0.100211i
$197$	1.74344	+	6.50660i	0.124215	+	0.463576i	0.999810	−	0.0194688i	$-0.00619751\pi$
$197$	1.74344	+	6.50660i	0.124215	+	0.463576i	−0.875596	+	0.483045i	$0.839531\pi$
$198$	−0.0252180	+	0.0172313i	−0.00179216	+	0.00122458i
$199$	−7.81601	+	4.51257i	−0.554062	+	0.319888i	−0.750759	−	0.660576i	$-0.770312\pi$
$199$	−7.81601	+	4.51257i	−0.554062	+	0.319888i	0.196697	+	0.980464i	$0.436979\pi$
$200$		0			0
$201$	−4.16650	+	15.2013i	−0.293882	+	1.07222i
$202$	−6.68904	+	9.55295i	−0.470640	+	0.672143i
$203$	13.9448	−	19.9152i	0.978733	−	1.39778i
$204$	3.30310	−	12.0512i	0.231263	−	0.843753i
$205$		0			0
$206$	−23.8806	+	13.7874i	−1.66384	+	0.960617i
$207$	19.9915	+	9.60211i	1.38951	+	0.667393i
$208$	−0.743713	−	2.77557i	−0.0515672	−	0.192451i
$209$	0.0310708	−	0.0113089i	0.00214921	−	0.000782250i
$210$		0			0
$211$	4.86924	−	4.08578i	0.335213	−	0.281277i	−0.459607	−	0.888122i	$-0.652010\pi$
$211$	4.86924	−	4.08578i	0.335213	−	0.281277i	0.794820	+	0.606846i	$0.207565\pi$
$212$	−5.87973	+	2.74176i	−0.403822	+	0.188305i
$213$	10.7760	−	12.6942i	0.738361	−	0.869792i
$214$	10.9960	+	1.93889i	0.751672	+	0.132540i
$215$		0			0
$216$	5.65319	−	19.7370i	0.384651	−	1.34293i
$217$	−10.2713	−	10.2713i	−0.697258	−	0.697258i
$218$	21.9330	−	15.3577i	1.48549	−	1.04015i
$219$	−2.83321	−	4.09590i	−0.191451	−	0.276775i
$220$		0			0
$221$	−1.75069	−	2.08639i	−0.117764	−	0.140346i
$222$	−5.53049	+	4.58699i	−0.371182	+	0.307858i
$223$	−1.58829	+	3.40610i	−0.106360	+	0.228089i	−0.952284	−	0.305214i	$-0.901272\pi$
$223$	−1.58829	+	3.40610i	−0.106360	+	0.228089i	0.845924	+	0.533304i	$0.179050\pi$
$224$	3.58295	−	6.20585i	0.239396	−	0.414646i
$225$		0			0
$226$	2.24219	+	3.88359i	0.149149	+	0.258333i
$227$	−6.49455	+	0.568200i	−0.431059	+	0.0377127i	−0.300621	−	0.953744i	$-0.597194\pi$
$227$	−6.49455	+	0.568200i	−0.431059	+	0.0377127i	−0.130438	+	0.991456i	$0.541638\pi$
$228$	−24.7389	+	42.2886i	−1.63837	+	2.80063i
$229$	4.26742	−	0.752462i	0.281999	−	0.0497241i	−0.0308595	−	0.999524i	$-0.509824\pi$
$229$	4.26742	−	0.752462i	0.281999	−	0.0497241i	0.312859	+	0.949800i	$0.398713\pi$
$230$		0			0
$231$	0.0127802	−	0.0126348i	0.000840875	−	0.000831311i
$232$	−3.45279	−	39.4655i	−0.226687	−	2.59104i
$233$	−6.77460	+	25.2831i	−0.443818	+	1.65635i	0.275219	+	0.961382i	$0.411250\pi$
$233$	−6.77460	+	25.2831i	−0.443818	+	1.65635i	−0.719037	+	0.694972i	$0.755417\pi$
$234$	−6.25372	−	7.62843i	−0.408819	−	0.498686i
$235$		0			0
$236$	−1.24756	−	3.42764i	−0.0812093	−	0.223121i
$237$	−12.0670	+	2.05664i	−0.783834	+	0.133593i
$238$	−0.990915	+	11.3262i	−0.0642314	+	0.734169i
$239$	17.2215	+	6.26813i	1.11397	+	0.405452i	0.832448	−	0.554103i	$-0.186939\pi$
$239$	17.2215	+	6.26813i	1.11397	+	0.405452i	0.281521	+	0.959555i	$0.409161\pi$
$240$		0			0
$241$	−1.09892	+	6.23226i	−0.0707874	+	0.401455i	0.928740	+	0.370731i	$0.120893\pi$
$241$	−1.09892	+	6.23226i	−0.0707874	+	0.401455i	−0.999528	+	0.0307248i	$0.990218\pi$
$242$	18.5060	−	18.5060i	1.18961	−	1.18961i
$243$	−2.26685	−	15.4228i	−0.145419	−	0.989370i
$244$		−	24.9220i		−	1.59547i
$245$		0			0
$246$	11.1649	+	5.28424i	0.711849	+	0.336911i
$247$	4.51302	+	9.67820i	0.287156	+	0.615809i
$248$	−23.5795	−	2.06294i	−1.49730	−	0.130997i
$249$	−10.2050	+	14.3983i	−0.646714	+	0.912452i
$250$		0			0
$251$	−23.1604	−	13.3717i	−1.46187	−	0.844013i	−0.462775	−	0.886476i	$-0.653146\pi$
$251$	−23.1604	−	13.3717i	−1.46187	−	0.844013i	−0.999098	+	0.0424628i	$0.986480\pi$
$252$	−2.62414	+	26.4992i	−0.165305	+	1.66929i
$253$	0.0305561	+	0.00818747i	0.00192104	+	0.000514742i
$254$	−10.7462	−	9.01714i	−0.674277	−	0.565786i
$255$		0			0
$256$	−4.67107	−	26.4910i	−0.291942	−	1.65569i
$257$	3.21096	+	2.24834i	0.200294	+	0.140248i	0.669421	−	0.742883i	$-0.266542\pi$
$257$	3.21096	+	2.24834i	0.200294	+	0.140248i	−0.469127	+	0.883131i	$0.655431\pi$
$258$	−25.6689	−	15.0163i	−1.59808	−	0.934876i
$259$	2.71756	−	3.23866i	0.168861	−	0.201240i
$260$		0			0
$261$	−14.7409	−	26.2201i	−0.912439	−	1.62298i
$262$	35.5596	−	9.52815i	2.19688	−	0.588651i
$263$	−27.9551	−	13.0357i	−1.72379	−	0.803815i	−0.992571	−	0.121669i	$-0.961176\pi$
$263$	−27.9551	−	13.0357i	−1.72379	−	0.803815i	−0.731216	−	0.682146i	$-0.761047\pi$
$264$	0.00271910	−	0.0291578i	0.000167349	−	0.00179454i
$265$		0			0
$266$	15.2464	−	41.8892i	0.934819	−	2.56839i
$267$	−1.88662	+	10.3529i	−0.115459	+	0.633589i
$268$	−19.1074	−	27.2883i	−1.16717	−	1.66690i
$269$	−11.5179			−0.702257			−0.351128	−	0.936327i	$-0.614202\pi$
$269$	−11.5179			−0.702257			−0.351128	+	0.936327i	$0.614202\pi$
$270$		0			0
$271$	−6.78072			−0.411899			−0.205950	−	0.978563i	$-0.566028\pi$
$271$	−6.78072			−0.411899			−0.205950	+	0.978563i	$0.566028\pi$
$272$	2.35035	+	3.35665i	0.142511	+	0.203527i
$273$	4.42478	+	3.75617i	0.267800	+	0.227334i
$274$	3.17972	−	8.73621i	0.192094	−	0.527774i
$275$		0			0
$276$	−42.5940	+	19.5661i	−2.56386	+	1.17774i
$277$	−9.00402	−	4.19864i	−0.540999	−	0.252272i	0.132856	−	0.991135i	$-0.457585\pi$
$277$	−9.00402	−	4.19864i	−0.540999	−	0.252272i	−0.673855	+	0.738863i	$0.735363\pi$
$278$	−12.4952	+	3.34808i	−0.749412	+	0.200804i
$279$	−16.9572	+	5.95314i	−1.01520	+	0.356405i
$280$		0			0
$281$	−16.7510	+	19.9630i	−0.999280	+	1.19090i	−0.0177003	+	0.999843i	$0.505634\pi$
$281$	−16.7510	+	19.9630i	−0.999280	+	1.19090i	−0.981580	+	0.191052i	$0.938810\pi$
$282$	−7.38249	+	4.20617i	−0.439621	+	0.250474i
$283$	6.09224	+	4.26583i	0.362146	+	0.253577i	0.740461	−	0.672100i	$-0.234607\pi$
$283$	6.09224	+	4.26583i	0.362146	+	0.253577i	−0.378315	+	0.925677i	$0.623496\pi$
$284$	6.11110	+	34.6578i	0.362627	+	2.05656i
$285$		0			0
$286$	−0.0107782	−	0.00904400i	−0.000637329	−	0.000534783i
$287$	−7.02044	−	1.88112i	−0.414403	−	0.111039i
$288$	−5.00187	−	7.32021i	−0.294738	−	0.431348i
$289$	−11.3588	−	6.55802i	−0.668166	−	0.385766i
$290$		0			0
$291$	−9.11051	−	19.8329i	−0.534068	−	1.16263i
$292$	10.4858	+	0.917390i	0.613636	+	0.0536862i
$293$	3.52271	+	7.55448i	0.205799	+	0.441337i	0.981933	−	0.189231i	$-0.0605996\pi$
$293$	3.52271	+	7.55448i	0.205799	+	0.441337i	−0.776134	+	0.630568i	$0.782822\pi$
$294$	0.376141	+	4.60233i	0.0219370	+	0.268413i
$295$		0			0
$296$		−	6.88912i		−	0.400422i
$297$	−0.00724518	−	0.0210214i	−0.000420408	−	0.00121978i
$298$	−15.4707	+	15.4707i	−0.896194	+	0.896194i
$299$	−1.77409	+	10.0614i	−0.102598	+	0.581864i
$300$		0			0
$301$	16.4429	+	5.98474i	0.947755	+	0.344955i
$302$	2.35215	−	26.8852i	0.135351	−	1.54707i
$303$	−5.41987	−	6.53469i	−0.311363	−	0.375408i
$304$	−5.49502	−	15.0974i	−0.315161	−	0.865897i
$305$		0			0
$306$	12.1009	+	7.17224i	0.691762	+	0.410010i
$307$	−3.15476	+	11.7737i	−0.180052	+	0.671962i	0.815584	+	0.578638i	$0.196416\pi$
$307$	−3.15476	+	11.7737i	−0.180052	+	0.671962i	−0.995636	+	0.0933234i	$0.970251\pi$
$308$	0.00331040	+	0.0378380i	0.000188627	+	0.00215602i
$309$	−5.08462	−	19.4197i	−0.289254	−	1.10475i
$310$		0			0
$311$	19.9366	−	3.51536i	1.13050	−	0.199338i	0.423054	−	0.906104i	$-0.360958\pi$
$311$	19.9366	−	3.51536i	1.13050	−	0.199338i	0.707447	+	0.706767i	$0.249847\pi$
$312$	9.45758	+	0.0540918i	0.535430	+	0.00306235i
$313$	−7.21599	+	0.631317i	−0.407872	+	0.0356842i	−0.289246	−	0.957255i	$-0.593404\pi$
$313$	−7.21599	+	0.631317i	−0.407872	+	0.0356842i	−0.118626	+	0.992939i	$0.537849\pi$
$314$	−1.04673	−	1.81300i	−0.0590706	−	0.102313i
$315$		0			0
$316$	12.9356	−	22.4052i	0.727686	−	1.26039i
$317$	−2.07411	+	4.44794i	−0.116493	+	0.249821i	−0.955905	−	0.293675i	$-0.905122\pi$
$317$	−2.07411	+	4.44794i	−0.116493	+	0.249821i	0.839412	+	0.543496i	$0.182900\pi$
$318$	−1.22704	−	7.19941i	−0.0688088	−	0.403723i
$319$	−0.0275787	−	0.0328670i	−0.00154411	−	0.00184020i
$320$		0			0
$321$	−3.47733	+	7.34715i	−0.194085	+	0.410078i
$322$	34.9356	−	24.4622i	1.94688	−	1.36322i
$323$	−10.7680	−	10.7680i	−0.599148	−	0.599148i
$324$	28.1479	+	17.1215i	1.56377	+	0.951192i
$325$		0			0
$326$	15.7577	+	2.77851i	0.872739	+	0.153887i
$327$	6.56185	+	18.3545i	0.362871	+	1.01500i
$328$	−10.7337	+	5.00520i	−0.592668	+	0.276366i
$329$	3.82979	−	3.21358i	0.211143	−	0.177170i
$330$		0			0
$331$	−4.66635	+	1.69841i	−0.256486	+	0.0933531i	−0.467063	−	0.884224i	$-0.654688\pi$
$331$	−4.66635	+	1.69841i	−0.256486	+	0.0933531i	0.210577	+	0.977577i	$0.432466\pi$
$332$	−9.65368	−	36.0280i	−0.529814	−	1.97729i
$333$	−2.15624	−	4.76564i	−0.118161	−	0.261156i
$334$	−14.9158	+	8.61167i	−0.816159	+	0.471209i
$335$		0			0
$336$	−6.13932	−	6.20995i	−0.334927	−	0.338780i
$337$	12.5919	−	17.9831i	0.685925	−	0.979602i	−0.313624	−	0.949547i	$-0.601543\pi$
$337$	12.5919	−	17.9831i	0.685925	−	0.979602i	0.999548	−	0.0300546i	$-0.00956813\pi$
$338$	−15.1343	+	21.6140i	−0.823195	+	1.17564i
$339$	−3.15814	+	0.826891i	−0.171527	+	0.0449105i
$340$		0			0
$341$	−0.0222000	+	0.0128172i	−0.00120220	+	0.000694090i
$342$	−38.5504	−	39.4426i	−2.08457	−	2.13281i
$343$	−5.09624	−	19.0194i	−0.275171	−	1.02695i
$344$	26.7937	−	9.75210i	1.44462	−	0.525798i
$345$		0			0
$346$	4.35333	−	3.65288i	0.234037	−	0.196380i
$347$	−14.1467	+	6.59670i	−0.759433	+	0.354129i	−0.763454	−	0.645863i	$-0.776498\pi$
$347$	−14.1467	+	6.59670i	−0.759433	+	0.354129i	0.00402090	+	0.999992i	$0.498720\pi$
$348$	62.5434	+	11.3973i	3.35268	+	0.610959i
$349$	23.5190	+	4.14704i	1.25895	+	0.221986i	0.763017	−	0.646378i	$-0.223717\pi$
$349$	23.5190	+	4.14704i	1.25895	+	0.221986i	0.495928	+	0.868364i	$0.334828\pi$
$350$		0			0
$351$	6.55934	−	2.92273i	0.350112	−	0.156004i
$352$	−0.00894211	−	0.00894211i	−0.000476616	−	0.000476616i
$353$	−0.263489	+	0.184497i	−0.0140241	+	0.00981980i	−0.580567	−	0.814212i	$-0.697169\pi$
$353$	−0.263489	+	0.184497i	−0.0140241	+	0.00981980i	0.566543	+	0.824032i	$0.308280\pi$
$354$	4.09258	−	0.334480i	0.217518	−	0.0177774i
$355$		0			0
$356$	−14.2964	−	17.0378i	−0.757707	−	0.903000i
$357$	−7.76140	−	2.87529i	−0.410777	−	0.152177i
$358$	16.9175	−	36.2796i	0.894116	−	1.91744i
$359$	−2.09252	+	3.62435i	−0.110439	+	0.191286i	−0.915947	−	0.401298i	$-0.868559\pi$
$359$	−2.09252	+	3.62435i	−0.110439	+	0.191286i	0.805508	+	0.592585i	$0.201892\pi$
$360$		0			0
$361$	20.3536	+	35.2535i	1.07124	+	1.85545i
$362$	−16.8006	+	1.46986i	−0.883021	+	0.0772543i
$363$	9.43174	+	16.5542i	0.495038	+	0.868869i
$364$	−12.0806	+	2.13013i	−0.633194	+	0.111649i
$365$		0			0
$366$	27.0574	+	7.41614i	1.41431	+	0.387648i
$367$	1.16653	+	13.3335i	0.0608924	+	0.696004i	0.963880	+	0.266337i	$0.0858134\pi$
$367$	1.16653	+	13.3335i	0.0608924	+	0.696004i	−0.902988	+	0.429667i	$0.858631\pi$
$368$	3.97833	−	14.8473i	0.207385	−	0.773970i
$369$	−5.85858	+	6.82197i	−0.304986	+	0.355138i
$370$		0			0
$371$	1.46974	+	4.03807i	0.0763050	+	0.209646i
$372$	13.1950	−	35.6177i	0.684128	−	1.84669i
$373$	1.36803	−	15.6366i	0.0708338	−	0.809634i	−0.874818	−	0.484452i	$-0.839019\pi$
$373$	1.36803	−	15.6366i	0.0708338	−	0.809634i	0.945652	−	0.325182i	$-0.105425\pi$
$374$	0.0188543	+	0.00686241i	0.000974933	+	0.000354847i
$375$		0			0
$376$	1.41463	−	8.02279i	0.0729542	−	0.413744i
$377$	9.79812	−	9.79812i	0.504629	−	0.504629i
$378$	−27.9889	−	10.7345i	−1.43959	−	0.552121i
$379$		−	26.4477i		−	1.35853i	−0.733894	−	0.679264i	$-0.762299\pi$
$379$		−	26.4477i		−	1.35853i	0.733894	−	0.679264i	$-0.237701\pi$
$380$		0			0
$381$	8.39887	−	5.80965i	0.430287	−	0.297637i
$382$	7.88010	+	16.8989i	0.403181	+	0.864625i
$383$	−18.5309	−	1.62124i	−0.946883	−	0.0828415i	−0.396758	−	0.917923i	$-0.629865\pi$
$383$	−18.5309	−	1.62124i	−0.946883	−	0.0828415i	−0.550126	+	0.835082i	$0.685420\pi$
$384$	35.7198	+	3.33104i	1.82282	+	0.169987i
$385$		0			0
$386$	−38.2831	−	22.1028i	−1.94856	−	1.12500i
$387$	15.4826	−	15.1323i	0.787022	−	0.769220i
$388$	44.5560	+	11.9388i	2.26199	+	0.606098i
$389$	−25.4642	−	21.3670i	−1.29108	−	1.08335i	−0.991613	−	0.129243i	$-0.958745\pi$
$389$	−25.4642	−	21.3670i	−1.29108	−	1.08335i	−0.299472	−	0.954105i	$-0.596810\pi$
$390$		0			0
$391$	−2.52993	−	14.3479i	−0.127944	−	0.725606i
$392$	−3.62672	−	2.53946i	−0.183177	−	0.128262i
$393$	−0.153279	+	26.7998i	−0.00773191	+	1.35187i
$394$	10.3018	−	12.2772i	0.518996	−	0.618515i
$395$		0			0
$396$	0.0439726	+	0.0165767i	0.00220971	+	0.000833013i
$397$	−33.0030	+	8.84314i	−1.65637	+	0.443824i	−0.961388	−	0.275198i	$-0.911257\pi$
$397$	−33.0030	+	8.84314i	−1.65637	+	0.443824i	−0.694987	+	0.719022i	$0.744590\pi$
$398$	19.4610	+	9.07480i	0.975490	+	0.454879i
$399$	26.4763	+	18.7655i	1.32547	+	0.939450i
$400$		0			0
$401$	−3.56868	+	9.80487i	−0.178211	+	0.489632i	−0.996347	−	0.0853930i	$-0.972785\pi$
$401$	−3.56868	+	9.80487i	−0.178211	+	0.489632i	0.818136	+	0.575025i	$0.195008\pi$
$402$	35.3123	−	12.6244i	1.76122	−	0.629647i
$403$	−4.74861	−	6.78172i	−0.236545	−	0.337821i
$404$	17.9432			0.892709
$405$		0			0
$406$	−57.8436			−2.87073
$407$	−0.00427944	−	0.00611167i	−0.000212124	−	0.000302944i
$408$	−12.6999	+	4.54030i	−0.628740	+	0.224779i
$409$	−13.0223	+	35.7785i	−0.643911	+	1.76913i	−0.00483335	+	0.999988i	$0.501539\pi$
$409$	−13.0223	+	35.7785i	−0.643911	+	1.76913i	−0.639078	+	0.769142i	$0.720684\pi$
$410$		0			0
$411$	5.52177	+	3.91364i	0.272369	+	0.193046i
$412$	38.4519	+	17.9304i	1.89439	+	0.883367i
$413$	−2.33378	+	0.625335i	−0.114838	+	0.0307707i
$414$	−8.56777	−	52.0660i	−0.421083	−	2.55890i
$415$		0			0
$416$	2.62527	−	3.12868i	0.128715	−	0.153396i
$417$	0.0538605	−	9.41713i	0.00263756	−	0.461159i
$418$	−0.0644415	−	0.0451224i	−0.00315194	−	0.00220701i
$419$	−4.45593	−	25.2708i	−0.217686	−	1.23456i	−0.876184	−	0.481978i	$-0.839919\pi$
$419$	−4.45593	−	25.2708i	−0.217686	−	1.23456i	0.658497	−	0.752583i	$-0.271192\pi$
$420$		0			0
$421$	−18.3149	−	15.3680i	−0.892611	−	0.748990i	0.0761208	−	0.997099i	$-0.475747\pi$
$421$	−18.3149	−	15.3680i	−0.892611	−	0.748990i	−0.968732	+	0.248109i	$0.920191\pi$
$422$	−14.6078	−	3.91416i	−0.711098	−	0.190538i
$423$	−1.53248	−	5.99264i	−0.0745115	−	0.291372i
$424$	6.06417	+	3.50115i	0.294502	+	0.170031i
$425$		0			0
$426$	−39.4459	−	3.67852i	−1.91116	−	0.178225i
$427$	−16.4450	−	1.43875i	−0.795829	−	0.0696260i
$428$	−7.26039	−	15.5699i	−0.350944	−	0.752602i
$429$	0.00842388	−	0.00582695i	0.000406709	−	0.000281328i
$430$		0			0
$431$			15.6671i			0.754660i	0.926079	+	0.377330i	$0.123158\pi$
$431$			15.6671i			0.754660i	−0.926079	+	0.377330i	$0.876842\pi$
$432$	−10.2144	+	3.52046i	−0.491439	+	0.169378i
$433$	−10.5845	+	10.5845i	−0.508657	+	0.508657i	−0.914114	−	0.405457i	$-0.867112\pi$
$433$	−10.5845	+	10.5845i	−0.508657	+	0.508657i	0.405457	+	0.914114i	$0.367112\pi$
$434$	−6.00127	+	34.0349i	−0.288070	+	1.63373i
$435$		0			0
$436$	−38.7122	−	14.0901i	−1.85398	−	0.674792i
$437$	−4.97863	+	56.9060i	−0.238160	+	2.72218i
$438$	−4.11630	+	11.1113i	−0.196684	+	0.530918i
$439$	−7.09912	−	19.5047i	−0.338823	−	0.930907i	−0.985729	−	0.168338i	$-0.946160\pi$
$439$	−7.09912	−	19.5047i	−0.338823	−	0.930907i	0.646907	−	0.762569i	$-0.276062\pi$
$440$		0			0
$441$	−3.30366	−	0.621570i	−0.157317	−	0.0295986i
$442$	−1.67715	+	6.25923i	−0.0797741	+	0.297721i
$443$	−0.655331	−	7.49047i	−0.0311357	−	0.355883i	−0.995742	−	0.0921874i	$-0.970614\pi$
$443$	−0.655331	−	7.49047i	−0.0311357	−	0.355883i	0.964606	−	0.263696i	$-0.0849414\pi$
$444$	10.6619	+	2.92231i	0.505993	+	0.138687i
$445$		0			0
$446$	8.80576	−	1.55269i	0.416965	−	0.0735222i
$447$	−7.88480	−	13.8391i	−0.372938	−	0.654565i
$448$	−27.0293	+	2.36476i	−1.27701	+	0.111724i
$449$	2.66419	+	4.61452i	0.125731	+	0.217773i	0.922018	−	0.387146i	$-0.126539\pi$
$449$	2.66419	+	4.61452i	0.125731	+	0.217773i	−0.796287	+	0.604918i	$0.793206\pi$
$450$		0			0
$451$	−0.00641320	+	0.0111080i	−0.000301986	+	0.000523055i
$452$	2.91594	−	6.25326i	0.137154	−	0.294129i
$453$	18.4233	+	6.82513i	0.865604	+	0.320672i
$454$	9.97027	+	11.8821i	0.467928	+	0.557655i
$455$		0			0
$456$	52.7048	−	4.30747i	2.46813	−	0.201716i
$457$	−19.2609	+	13.4866i	−0.900988	+	0.630879i	−0.929543	−	0.368714i	$-0.879798\pi$
$457$	−19.2609	+	13.4866i	−0.900988	+	0.630879i	0.0285551	+	0.999592i	$0.490909\pi$
$458$	−7.29010	−	7.29010i	−0.340644	−	0.340644i
$459$	−7.36426	+	7.11579i	−0.343734	+	0.332137i
$460$		0			0
$461$	15.8701	+	2.79833i	0.739145	+	0.130331i	0.530529	−	0.847667i	$-0.321993\pi$
$461$	15.8701	+	2.79833i	0.739145	+	0.130331i	0.208615	+	0.977998i	$0.433104\pi$
$462$	−0.0420652	−	0.00766555i	−0.00195705	−	0.000356634i
$463$	13.5284	−	6.30838i	0.628716	−	0.293175i	−0.0820233	−	0.996630i	$-0.526138\pi$
$463$	13.5284	−	6.30838i	0.628716	−	0.293175i	0.710740	+	0.703455i	$0.248360\pi$
$464$	−15.9702	+	13.4006i	−0.741398	+	0.622106i
$465$		0			0
$466$	58.5204	−	21.2997i	2.71091	−	0.986689i
$467$	1.62693	+	6.07179i	0.0752854	+	0.280969i	0.993298	−	0.115583i	$-0.0368735\pi$
$467$	1.62693	+	6.07179i	0.0752854	+	0.280969i	−0.918012	+	0.396552i	$0.870207\pi$
$468$	−4.09555	+	14.6141i	−0.189317	+	0.675535i
$469$	−19.1095	+	11.0329i	−0.882393	+	0.509450i
$470$		0			0
$471$	1.47433	−	0.386021i	0.0679335	−	0.0177869i
$472$	−2.25819	+	3.22503i	−0.103942	+	0.148444i
$473$	0.0177121	−	0.0252955i	0.000814402	−	0.00116309i
$474$	20.4756	+	20.7112i	0.940477	+	0.951297i
$475$		0			0
$476$	15.1495	−	8.74657i	0.694377	−	0.400899i
$477$	5.29081	+	0.523933i	0.242249	+	0.0239892i
$478$	−11.2854	−	42.1177i	−0.516182	−	1.92642i
$479$	−6.42357	+	2.33799i	−0.293501	+	0.106825i	−0.484574	−	0.874750i	$-0.661025\pi$
$479$	−6.42357	+	2.33799i	−0.293501	+	0.106825i	0.191073	+	0.981576i	$0.438803\pi$
$480$		0			0
$481$	1.84587	−	1.54887i	0.0841645	−	0.0706224i
$482$	13.6460	−	6.36322i	0.621557	−	0.289837i
$483$	10.4519	+	29.2356i	0.475578	+	1.33026i
$484$	−39.6557	−	6.99237i	−1.80253	−	0.317835i
$485$		0			0
$486$	−26.9646	+	25.4648i	−1.22314	+	1.15511i
$487$	11.7403	+	11.7403i	0.532002	+	0.532002i	0.921168	−	0.389165i	$-0.127237\pi$
$487$	11.7403	+	11.7403i	0.532002	+	0.532002i	−0.389165	+	0.921168i	$0.627237\pi$
$488$	−22.0347	+	15.4289i	−0.997463	+	0.698431i
$489$	−4.98314	+	10.5287i	−0.225345	+	0.476126i
$490$		0			0
$491$	10.6951	+	12.7459i	0.482663	+	0.575215i	0.951336	−	0.308157i	$-0.0997121\pi$
$491$	10.6951	+	12.7459i	0.482663	+	0.575215i	−0.468673	+	0.883372i	$0.655268\pi$
$492$	−3.19313	−	18.7351i	−0.143958	−	0.844645i
$493$	−8.35099	+	17.9087i	−0.376109	+	0.806569i
$494$	12.7035	−	22.0031i	0.571557	−	0.989966i
$495$		0			0
$496$	6.22793	+	10.7871i	0.279642	+	0.484355i
$497$	23.2220	−	2.03166i	1.04165	−	0.0911326i
$498$	41.9877	+	0.240145i	1.88152	+	0.0107612i
$499$	27.4365	−	4.83779i	1.22823	−	0.216569i	0.478363	−	0.878162i	$-0.341230\pi$
$499$	27.4365	−	4.83779i	1.22823	−	0.216569i	0.749863	+	0.661593i	$0.230119\pi$
$500$		0			0
$501$	−3.17587	−	12.1296i	−0.141887	−	0.541909i
$502$	5.54557	+	63.3862i	0.247511	+	2.82906i
$503$	3.86525	−	14.4253i	0.172343	−	0.643192i	−0.824646	−	0.565649i	$-0.808626\pi$
$503$	3.86525	−	14.4253i	0.172343	−	0.643192i	0.996989	−	0.0775431i	$-0.0247075\pi$
$504$	25.0537	−	14.0852i	1.11598	−	0.627403i
$505$		0			0
$506$	−0.0257419	−	0.0707252i	−0.00114436	−	0.00314412i
$507$	−12.2627	−	14.7850i	−0.544606	−	0.656626i
$508$	−1.88116	+	21.5017i	−0.0834629	+	0.953985i
$509$	−5.75433	−	2.09440i	−0.255056	−	0.0928328i	0.211328	−	0.977415i	$-0.432221\pi$
$509$	−5.75433	−	2.09440i	−0.255056	−	0.0928328i	−0.466384	+	0.884582i	$0.654443\pi$
$510$		0			0
$511$	1.21069	−	6.86619i	0.0535580	−	0.303742i
$512$	−15.9632	+	15.9632i	−0.705482	+	0.705482i
$513$	35.1110	−	19.4759i	1.55019	−	0.859883i
$514$		−	9.32621i		−	0.411361i
$515$		0			0
$516$	3.72713	+	45.6039i	0.164078	+	2.00760i
$517$	−0.00372867	−	0.00799616i	−0.000163987	−	0.000351671i
$518$	−10.0205	−	0.876681i	−0.440276	−	0.0385191i
$519$	1.72693	+	3.75941i	0.0758039	+	0.165020i
$520$		0			0
$521$	19.3541	+	11.1741i	0.847920	+	0.489547i	0.859949	−	0.510381i	$-0.170495\pi$
$521$	19.3541	+	11.1741i	0.847920	+	0.489547i	−0.0120282	+	0.999928i	$0.503829\pi$
$522$	−30.9851	+	64.5108i	−1.35618	+	2.82356i
$523$	−3.27820	−	0.878392i	−0.143346	−	0.0384094i	0.186433	−	0.982468i	$-0.440307\pi$
$523$	−3.27820	−	0.878392i	−0.143346	−	0.0384094i	−0.329778	+	0.944058i	$0.606974\pi$
$524$	−43.3905	−	36.4089i	−1.89552	−	1.59053i
$525$		0			0
$526$	12.7435	+	72.2722i	0.555645	+	3.15122i
$527$	9.67101	+	6.77171i	0.421276	+	0.294980i
$528$	−0.0133898	+	0.00762881i	−0.000582715	+	0.000332001i
$529$	−20.3451	+	24.2463i	−0.884569	+	1.05419i
$530$		0			0
$531$	−0.552725	+	2.93775i	−0.0239862	+	0.127488i
$532$	−66.2503	+	17.7517i	−2.87232	+	0.769635i
$533$	−3.75433	−	1.75067i	−0.162618	−	0.0758301i
$534$	22.7519	−	10.4514i	0.984570	−	0.452275i
$535$		0			0
$536$	−12.2976	+	33.7875i	−0.531178	+	1.45940i
$537$	22.2163	+	18.8592i	0.958702	+	0.813836i
$538$	15.7180	+	22.4477i	0.677652	+	0.967787i
$539$	−0.00479492			−0.000206532
$540$		0			0
$541$	−32.7244			−1.40693			−0.703466	−	0.710729i	$-0.748365\pi$
$541$	−32.7244			−1.40693			−0.703466	+	0.710729i	$0.748365\pi$
$542$	9.25340	+	13.2152i	0.397467	+	0.567642i
$543$	2.20107	−	12.0785i	0.0944569	−	0.518338i
$544$	−1.99201	+	5.47299i	−0.0854065	+	0.234653i
$545$		0			0
$546$	1.28221	−	13.7496i	0.0548736	−	0.588427i
$547$	−25.9469	−	12.0993i	−1.10941	−	0.517327i	−0.220491	−	0.975389i	$-0.570766\pi$
$547$	−25.9469	−	12.0993i	−1.10941	−	0.517327i	−0.888920	+	0.458063i	$0.848544\pi$
$548$	−13.8168	+	3.70221i	−0.590226	+	0.158151i
$549$	−10.4137	+	17.5698i	−0.444445	+	0.749861i
$550$		0			0
$551$	49.8005	−	59.3499i	2.12157	−	2.52839i
$552$	43.6686	+	25.5462i	1.85866	+	1.08732i
$553$	−14.0375	−	9.82914i	−0.596934	−	0.417977i
$554$	4.10455	+	23.2780i	0.174385	+	0.988989i
$555$		0			0
$556$	15.2469	+	12.7937i	0.646612	+	0.542572i
$557$	−21.1671	−	5.67171i	−0.896879	−	0.240318i	−0.219203	−	0.975679i	$-0.570346\pi$
$557$	−21.1671	−	5.67171i	−0.896879	−	0.240318i	−0.677675	+	0.735361i	$0.737012\pi$
$558$	34.7431	+	24.9245i	1.47079	+	1.05514i
$559$	8.63696	+	4.98655i	0.365304	+	0.210909i
$560$		0			0
$561$	−0.00844633	+	0.0119170i	−0.000356604	+	0.000503135i
$562$	61.7663	+	5.40385i	2.60545	+	0.227948i
$563$	−4.57310	−	9.80704i	−0.192733	−	0.413317i	0.786065	−	0.618143i	$-0.212115\pi$
$563$	−4.57310	−	9.80704i	−0.192733	−	0.413317i	−0.978798	+	0.204826i	$0.934337\pi$
$564$	11.8164	+	5.59256i	0.497559	+	0.235489i
$565$		0			0
$566$		−	17.6948i		−	0.743770i
$567$	12.9227	−	17.5852i	0.542703	−	0.738509i
$568$	26.8592	−	26.8592i	1.12699	−	1.12699i
$569$	−2.29260	+	13.0020i	−0.0961109	+	0.545072i	0.898290	+	0.439402i	$0.144810\pi$
$569$	−2.29260	+	13.0020i	−0.0961109	+	0.545072i	−0.994401	+	0.105670i	$0.966301\pi$
$570$		0			0
$571$	−7.42564	−	2.70271i	−0.310753	−	0.113105i	0.181936	−	0.983310i	$-0.441764\pi$
$571$	−7.42564	−	2.70271i	−0.310753	−	0.113105i	−0.492689	+	0.870206i	$0.663986\pi$
$572$	−0.00188676	+	0.0215658i	−7.88894e−5	+	0.000901710i
$573$	−13.3811	+	2.28062i	−0.559004	+	0.0952742i
$574$	5.91434	+	16.2495i	0.246860	+	0.678242i
$575$		0			0
$576$	−11.8415	+	31.4115i	−0.493394	+	1.30881i
$577$	6.75192	−	25.1985i	0.281086	−	1.04903i	−0.670566	−	0.741850i	$-0.733949\pi$
$577$	6.75192	−	25.1985i	0.281086	−	1.04903i	0.951652	−	0.307178i	$-0.0993848\pi$
$578$	2.71978	+	31.0872i	0.113128	+	1.29306i
$579$	22.8854	−	22.6251i	0.951083	−	0.940266i
$580$		0			0
$581$	−24.3307	+	4.29016i	−1.00941	+	0.177986i
$582$	−26.2204	+	44.8211i	−1.08687	+	1.85790i
$583$	0.00755470		0.000660950i	0.000312884		2.73738e-5i
$584$	−5.68051	−	9.83893i	−0.235061	−	0.407138i
$585$		0			0
$586$	9.91592	−	17.1749i	0.409623	−	0.709488i
$587$	6.43160	−	13.7926i	0.265460	−	0.569282i	−0.727719	−	0.685875i	$-0.759420\pi$
$587$	6.43160	−	13.7926i	0.265460	−	0.569282i	0.993180	+	0.116593i	$0.0371974\pi$
$588$	5.46861	−	4.53567i	0.225522	−	0.187048i
$589$	−29.7544	−	35.4599i	−1.22601	−	1.46110i
$590$		0			0
$591$	6.63732	+	9.59542i	0.273023	+	0.394703i
$592$	−2.96969	+	2.07940i	−0.122053	+	0.0854627i
$593$	30.1991	+	30.1991i	1.24013	+	1.24013i	0.959947	+	0.280181i	$0.0903946\pi$
$593$	30.1991	+	30.1991i	1.24013	+	1.24013i	0.280181	+	0.959947i	$0.409605\pi$
$594$	−0.0310822	+	0.0428075i	−0.00127532	+	0.00175641i
$595$		0			0
$596$	33.1516	+	5.84552i	1.35794	+	0.239442i
$597$	−10.1164	+	11.9172i	−0.414036	+	0.487737i
$598$	22.0301	−	10.2728i	0.900876	−	0.420086i
$599$	−13.7064	+	11.5010i	−0.560028	+	0.469920i	−0.878320	−	0.478073i	$-0.841335\pi$
$599$	−13.7064	+	11.5010i	−0.560028	+	0.469920i	0.318292	+	0.947993i	$0.396891\pi$
$600$		0			0
$601$	−34.7520	+	12.6487i	−1.41757	+	0.515952i	−0.933341	−	0.358992i	$-0.883121\pi$
$601$	−34.7520	+	12.6487i	−1.41757	+	0.515952i	−0.484225	+	0.874944i	$0.660898\pi$
$602$	−10.7752	−	40.2135i	−0.439163	−	1.63898i
$603$	2.06815	+	27.2220i	0.0842216	+	1.10857i
$604$	−35.9606	+	20.7619i	−1.46322	+	0.844788i
$605$		0			0
$606$	−5.33943	+	19.4807i	−0.216900	+	0.791348i
$607$	24.8599	−	35.5036i	1.00903	−	1.44105i	0.114830	−	0.993385i	$-0.463368\pi$
$607$	24.8599	−	35.5036i	1.00903	−	1.44105i	0.894203	−	0.447663i	$-0.147743\pi$
$608$	13.0980	−	18.7059i	0.531196	−	0.758626i
$609$	11.1312	−	40.6118i	0.451060	−	1.64567i
$610$		0			0
$611$	2.46768	−	1.42471i	0.0998316	−	0.0576378i
$612$	−1.63958	−	21.5810i	−0.0662761	−	0.872359i
$613$	0.0568446	+	0.212147i	0.00229593	+	0.00856854i	0.967064	−	0.254532i	$-0.0819215\pi$
$613$	0.0568446	+	0.212147i	0.00229593	+	0.00856854i	−0.964768	+	0.263101i	$0.915255\pi$
$614$	27.2515	−	9.91873i	1.09978	−	0.400287i
$615$		0			0
$616$	0.0314049	−	0.0263518i	0.00126534	−	0.00106175i
$617$	−24.8316	+	11.5791i	−0.999681	+	0.466159i	−0.852374	−	0.522932i	$-0.824838\pi$
$617$	−24.8316	+	11.5791i	−0.999681	+	0.466159i	−0.147307	+	0.989091i	$0.547060\pi$
$618$	−30.9090	+	36.4110i	−1.24334	+	1.46466i
$619$	40.1687	+	7.08283i	1.61452	+	0.284683i	0.906720	−	0.421733i	$-0.138578\pi$
$619$	40.1687	+	7.08283i	1.61452	+	0.284683i	0.707797	+	0.706416i	$0.249689\pi$
$620$		0			0
$621$	38.2041	+	4.00401i	1.53308	+	0.160675i
$622$	−34.0580	−	34.0580i	−1.36560	−	1.36560i
$623$	−12.0678	+	8.45000i	−0.483488	+	0.338542i
$624$	−2.83134	−	4.09320i	−0.113344	−	0.163859i
$625$		0			0
$626$	11.0778	+	13.2020i	0.442758	+	0.527658i
$627$	0.0440812	−	0.0365609i	0.00176043	−	0.00146010i
$628$	−1.36126	+	2.91924i	−0.0543203	+	0.116490i
$629$	−1.71810	+	2.97584i	−0.0685053	+	0.118655i
$630$		0			0
$631$	−21.0645	−	36.4848i	−0.838565	−	1.45244i	−0.891095	−	0.453817i	$-0.850062\pi$
$631$	−21.0645	−	36.4848i	−0.838565	−	1.45244i	0.0525304	−	0.998619i	$-0.483271\pi$
$632$	−27.8177	+	2.43373i	−1.10653	+	0.0968087i
$633$	5.55920	−	9.50288i	0.220958	−	0.377706i
$634$	11.4992	−	2.02762i	0.456693	−	0.0805272i
$635$		0			0
$636$	−7.99093	+	7.90004i	−0.316861	+	0.313257i
$637$	−0.134968	−	1.54269i	−0.00534761	−	0.0611235i
$638$	−0.0264202	+	0.0986016i	−0.00104599	+	0.00390367i
$639$	10.1735	−	26.9869i	0.402458	−	1.06759i
$640$		0			0
$641$	−8.97472	−	24.6578i	−0.354480	−	0.973926i	−0.980912	−	0.194450i	$-0.937708\pi$
$641$	−8.97472	−	24.6578i	−0.354480	−	0.973926i	0.626432	−	0.779476i	$-0.284514\pi$
$642$	19.0645	−	3.24928i	0.752418	−	0.128239i
$643$	2.57976	−	29.4868i	0.101736	−	1.16284i	−0.758052	−	0.652194i	$-0.773849\pi$
$643$	2.57976	−	29.4868i	0.101736	−	1.16284i	0.859788	−	0.510651i	$-0.170596\pi$
$644$	−61.6619	−	22.4431i	−2.42982	−	0.884382i
$645$		0			0
$646$	−6.29152	+	35.6810i	−0.247536	+	1.40385i
$647$	3.41329	−	3.41329i	0.134190	−	0.134190i	−0.636821	−	0.771012i	$-0.719751\pi$
$647$	3.41329	−	3.41329i	0.134190	−	0.134190i	0.771012	+	0.636821i	$0.219751\pi$
$648$	−2.28810	−	35.4865i	−0.0898852	−	1.39404i
$649$			0.00426384i			0.000167370i
$650$		0			0
$651$	−22.7409	−	10.7630i	−0.891287	−	0.421837i
$652$	−10.4044	−	22.3123i	−0.407468	−	0.873818i
$653$	44.7996	+	3.91945i	1.75314	+	0.153380i	0.917981	−	0.396625i	$-0.129819\pi$
$653$	44.7996	+	3.91945i	1.75314	+	0.153380i	0.835161	+	0.550005i	$0.185374\pi$
$654$	26.8171	−	37.8364i	1.04863	−	1.47952i
$655$		0			0
$656$	5.39742	+	3.11620i	0.210734	+	0.121667i
$657$	−7.00907	−	5.02826i	−0.273450	−	0.196171i
$658$	−11.4895	−	3.07859i	−0.447906	−	0.120016i
$659$	31.0081	+	26.0189i	1.20790	+	1.01355i	0.999368	+	0.0355365i	$0.0113140\pi$
$659$	31.0081	+	26.0189i	1.20790	+	1.01355i	0.208535	+	0.978015i	$0.433130\pi$
$660$		0			0
$661$	−2.96480	−	16.8142i	−0.115318	−	0.653998i	−0.986593	−	0.163203i	$-0.947817\pi$
$661$	−2.96480	−	16.8142i	−0.115318	−	0.653998i	0.871275	−	0.490795i	$-0.163294\pi$
$662$	9.67810	+	6.77668i	0.376150	+	0.263383i
$663$	−4.07183	−	2.38203i	−0.158137	−	0.0925103i
$664$	−25.8776	+	30.8397i	−1.00424	+	1.19681i
$665$		0			0
$666$	−6.34542	+	10.7059i	−0.245880	+	0.414845i
$667$	71.5973	−	19.1844i	2.77226	−	0.742824i
$668$	24.0171	+	11.1994i	0.929250	+	0.433316i
$669$	−0.604411	+	6.48129i	−0.0233679	+	0.250581i
$670$		0			0
$671$	−0.00996382	+	0.0273754i	−0.000384649	+	0.00105681i
$672$	2.22514	−	12.2106i	0.0858367	−	0.471034i
$673$	17.5288	+	25.0337i	0.675685	+	0.964978i	0.999820	+	0.0189672i	$0.00603782\pi$
$673$	17.5288	+	25.0337i	0.675685	+	0.964978i	−0.324135	+	0.946011i	$0.605073\pi$
$674$	−52.2317			−2.01189
$675$		0			0
$676$	40.5973			1.56144
$677$	−12.3542	−	17.6437i	−0.474812	−	0.678102i	0.508284	−	0.861189i	$-0.330280\pi$
$677$	−12.3542	−	17.6437i	−0.474812	−	0.678102i	−0.983097	+	0.183087i	$0.941391\pi$
$678$	5.92136	+	5.02660i	0.227408	+	0.193045i
$679$	10.4501	−	28.7114i	0.401038	−	1.10184i
$680$		0			0
$681$	−10.2610	+	4.71354i	−0.393203	+	0.180623i
$682$	0.0552756	+	0.0257754i	0.00211661	+	0.000986992i
$683$	8.93120	−	2.39311i	0.341743	−	0.0915697i	−0.0838658	−	0.996477i	$-0.526727\pi$
$683$	8.93120	−	2.39311i	0.341743	−	0.0915697i	0.425609	+	0.904907i	$0.360060\pi$
$684$	−15.6905	+	83.3956i	−0.599942	+	3.18871i
$685$		0			0
$686$	−30.1131	+	35.8874i	−1.14972	+	1.37019i
$687$	6.52124	−	3.71547i	0.248801	−	0.141754i
$688$	−12.2912	−	8.60637i	−0.468597	−	0.328115i
$689$	0.425300	+	2.41199i	0.0162026	+	0.0918897i
$690$		0			0
$691$	15.9016	+	13.3430i	0.604925	+	0.507592i	0.893024	−	0.450008i	$-0.148579\pi$
$691$	15.9016	+	13.3430i	0.604925	+	0.507592i	−0.288099	+	0.957601i	$0.593023\pi$
$692$	−8.44577	−	2.26304i	−0.321060	−	0.0860278i
$693$	0.0134768	−	0.0280587i	0.000511943	−	0.00106586i
$694$	32.1620	+	18.5688i	1.22085	+	0.704860i
$695$		0			0
$696$	−28.6428	−	62.3533i	−1.08570	−	2.36350i
$697$	5.88482	+	0.514855i	0.222903	+	0.0195015i
$698$	−24.0132	−	51.4966i	−0.908915	−	1.94917i
$699$	3.69296	+	45.1858i	0.139681	+	1.70908i
$700$		0			0
$701$			5.94733i			0.224627i	0.993673	+	0.112314i	$0.0358262\pi$
$701$			5.94733i			0.224627i	−0.993673	+	0.112314i	$0.964174\pi$
$702$	−14.6475	−	8.79523i	−0.552835	−	0.331955i
$703$	9.52667	−	9.52667i	0.359305	−	0.359305i
$704$	−0.00831467	+	0.0471548i	−0.000313371	+	0.00177721i
$705$		0			0
$706$	0.719149	+	0.261749i	0.0270655	+	0.00985105i
$707$	1.03586	−	11.8400i	0.0389577	−	0.445289i
$708$	−4.03330	−	4.86292i	−0.151581	−	0.182760i
$709$	−0.0976022	−	0.268160i	−0.00366553	−	0.0100710i	0.937846	−	0.347051i	$-0.112817\pi$
$709$	−0.0976022	−	0.268160i	−0.00366553	−	0.0100710i	−0.941512	+	0.336980i	$0.890595\pi$
$710$		0			0
$711$	−18.4815	+	10.3903i	−0.693111	+	0.389666i
$712$	−6.21318	+	23.1879i	−0.232849	+	0.869004i
$713$	−3.85981	−	44.1179i	−0.144551	−	1.65223i
$714$	4.98792	+	19.0503i	0.186668	+	0.712941i
$715$		0			0
$716$	−60.6550	+	10.6951i	−2.26678	+	0.399695i
$717$	31.7424	+	0.181548i	1.18544	+	0.00678004i
$718$	9.91925	−	0.867822i	0.370183	−	0.0323868i
$719$	−13.3454	−	23.1148i	−0.497698	−	0.862038i	0.502299	−	0.864694i	$-0.332488\pi$
$719$	−13.3454	−	23.1148i	−0.497698	−	0.862038i	−0.999996	+	0.00265626i	$0.999154\pi$
$720$		0			0
$721$	14.0514	−	24.3377i	0.523300	−	0.906382i
$722$	40.9312	−	87.7772i	1.52330	−	3.26673i
$723$	1.84161	+	10.8053i	0.0684902	+	0.401854i
$724$	16.6792	+	19.8775i	0.619879	+	0.738743i
$725$		0			0
$726$	19.3920	−	40.9728i	0.719705	−	1.52064i
$727$	−41.3229	+	28.9346i	−1.53258	+	1.07313i	−0.563584	+	0.826059i	$0.690578\pi$
$727$	−41.3229	+	28.9346i	−1.53258	+	1.07313i	−0.968998	+	0.247067i	$0.920533\pi$
$728$	9.36225	+	9.36225i	0.346988	+	0.346988i
$729$	−12.6898	−	23.8321i	−0.469993	−	0.882670i
$730$		0			0
$731$	−14.0060	−	2.46963i	−0.518030	−	0.0913427i
$732$	−14.5315	−	40.6467i	−0.537099	−	1.50235i
$733$	−36.3592	+	16.9546i	−1.34296	+	0.626231i	−0.955318	−	0.295580i	$-0.904487\pi$
$733$	−36.3592	+	16.9546i	−1.34296	+	0.626231i	−0.387639	+	0.921811i	$0.626709\pi$
$734$	24.3943	−	20.4693i	0.900411	−	0.755535i
$735$		0			0
$736$	20.5300	−	7.47229i	0.756744	−	0.275432i
$737$	0.0100786	+	0.0376137i	0.000371249	+	0.00138552i
$738$	21.2906	+	2.10835i	0.783719	+	0.0776093i
$739$	−18.7080	+	10.8011i	−0.688186	+	0.397324i	−0.802932	−	0.596070i	$-0.796728\pi$
$739$	−18.7080	+	10.8011i	−0.688186	+	0.397324i	0.114746	+	0.993395i	$0.463395\pi$
$740$		0			0
$741$	13.0037	+	13.1533i	0.477702	+	0.483198i
$742$	5.86427	−	8.37505i	0.215284	−	0.307458i
$743$	−15.7534	+	22.4982i	−0.577937	+	0.825380i	−0.996568	−	0.0827765i	$-0.973621\pi$
$743$	−15.7534	+	22.4982i	−0.577937	+	0.825380i	0.418631	+	0.908156i	$0.362510\pi$
$744$	−39.6601	+	10.3841i	−1.45401	+	0.380701i
$745$		0			0
$746$	−32.3418	+	18.6725i	−1.18412	+	0.683650i
$747$	−8.24858	+	29.4332i	−0.301800	+	1.07691i
$748$	−0.00799004	−	0.0298192i	−0.000292145	−	0.00109030i
$749$	−10.6931	+	3.89197i	−0.390717	+	0.142210i
$750$		0			0
$751$	36.9715	−	31.0228i	1.34911	−	1.13204i	0.369926	−	0.929061i	$-0.379383\pi$
$751$	36.9715	−	31.0228i	1.34911	−	1.13204i	0.979184	−	0.202976i	$-0.0650615\pi$
$752$	−3.88537	+	1.81178i	−0.141685	+	0.0660687i
$753$	−45.5704	−	8.30430i	−1.66068	−	0.302625i
$754$	−32.4671	−	5.72483i	−1.18238	−	0.208486i
$755$		0			0
$756$	11.1713	+	44.7492i	0.406294	+	1.62751i
$757$	−25.7438	−	25.7438i	−0.935673	−	0.935673i	0.0623799	−	0.998052i	$-0.480131\pi$
$757$	−25.7438	−	25.7438i	−0.935673	−	0.935673i	−0.998052	+	0.0623799i	$0.980131\pi$
$758$	−51.5451	+	36.0923i	−1.87220	+	1.31093i
$759$	0.0546096	−	0.00446315i	0.00198220	−	0.000162002i
$760$		0			0
$761$	8.43284	+	10.0499i	0.305690	+	0.364308i	0.896918	−	0.442197i	$-0.145801\pi$
$761$	8.43284	+	10.0499i	0.305690	+	0.364308i	−0.591227	+	0.806505i	$0.701356\pi$
$762$	−22.7843	−	8.44069i	−0.825388	−	0.305774i
$763$	−11.5323	+	24.7311i	−0.417498	+	0.895327i
$764$	14.3444	−	24.8452i	0.518961	−	0.898867i
$765$		0			0
$766$	22.1287	+	38.3280i	0.799543	+	1.38485i
$767$	−1.37182	+	0.120019i	−0.0495336	+	0.00433362i
$768$	−23.0646	−	40.4820i	−0.832272	−	1.46077i
$769$	3.71767	−	0.655525i	0.134062	−	0.0236388i	−0.106214	−	0.994343i	$-0.533873\pi$
$769$	3.71767	−	0.655525i	0.134062	−	0.0236388i	0.240277	+	0.970704i	$0.422762\pi$
$770$		0			0
$771$	6.54790	+	1.79470i	0.235817	+	0.0646347i
$772$	5.92790	+	67.7562i	0.213350	+	2.43860i
$773$	6.14142	−	22.9201i	0.220892	−	0.824379i	−0.763117	−	0.646260i	$-0.776332\pi$
$773$	6.14142	−	22.9201i	0.220892	−	0.824379i	0.984009	−	0.178119i	$-0.0570012\pi$
$774$	−50.6206	−	9.52404i	−1.81952	−	0.342334i
$775$		0			0
$776$	−17.0284	−	46.7851i	−0.611284	−	1.67949i
$777$	2.54383	−	6.86666i	0.0912593	−	0.246340i
$778$	−6.89296	+	78.7869i	−0.247125	+	2.82465i
$779$	−21.7646	−	7.92167i	−0.779798	−	0.283823i
$780$		0			0
$781$	0.00714349	−	0.0405128i	0.000255614	−	0.00144966i
$782$	−24.5108	+	24.5108i	−0.876503	+	0.876503i
$783$	−39.3301	−	34.1688i	−1.40554	−	1.22109i
$784$			2.32987i			0.0832097i
$785$		0			0
$786$	52.4404	−	36.2740i	1.87049	−	1.29385i
$787$	1.00203	+	2.14886i	0.0357185	+	0.0765987i	0.923357	−	0.383941i	$-0.125434\pi$
$787$	1.00203	+	2.14886i	0.0357185	+	0.0765987i	−0.887639	+	0.460540i	$0.847656\pi$
$788$	−24.5650	−	2.14916i	−0.875092	−	0.0765606i
$789$	−53.1944	−	4.96063i	−1.89377	−	0.176603i
$790$		0			0
$791$	−3.95793	−	2.28511i	−0.140728	−	0.0812492i
$792$	−0.0125665	−	0.0491406i	−0.000446532	−	0.00174613i
$793$	−9.08804	−	2.43513i	−0.322726	−	0.0864741i
$794$	62.2728	+	52.2531i	2.20998	+	1.85439i
$795$		0			0
$796$	−5.73703	−	32.5363i	−0.203343	−	1.15322i
$797$	−15.7860	−	11.0535i	−0.559169	−	0.391534i	0.259549	−	0.965730i	$-0.416426\pi$
$797$	−15.7860	−	11.0535i	−0.559169	−	0.391534i	−0.818718	+	0.574196i	$0.805315\pi$
$798$	0.441593	−	77.2094i	0.0156322	−	2.73318i
$799$	−2.61190	+	3.11275i	−0.0924025	+	0.110121i
$800$		0			0
$801$	2.95958	+	17.9852i	0.104571	+	0.635477i
$802$	23.9792	−	6.42520i	0.846734	−	0.226882i
$803$	−0.0111513	−	0.00519993i	−0.000393520	−	0.000183501i
$804$	−47.0746	−	33.3648i	−1.66019	−	1.17669i
$805$		0			0
$806$	−6.73692	+	18.5095i	−0.237298	+	0.651971i
$807$	−18.7851	+	6.71581i	−0.661268	+	0.236408i
$808$	−11.1084	−	15.8644i	−0.390792	−	0.558108i
$809$	48.9190			1.71990			0.859951	−	0.510377i	$-0.170494\pi$
$809$	48.9190			1.71990			0.859951	+	0.510377i	$0.170494\pi$
$810$		0			0
$811$	11.0352			0.387500			0.193750	−	0.981051i	$-0.437935\pi$
$811$	11.0352			0.387500			0.193750	+	0.981051i	$0.437935\pi$
$812$	51.0475	+	72.9034i	1.79142	+	2.55841i
$813$	−11.0591	+	3.95368i	−0.387858	+	0.138662i
$814$	−0.00607130	+	0.0166808i	−0.000212799	+	0.000584660i
$815$		0			0
$816$	5.79050	+	4.10411i	0.202708	+	0.143673i
$817$	50.5376	+	23.5661i	1.76809	+	0.824472i
$818$	87.5012	−	23.4459i	3.05941	−	0.819766i
$819$	9.40677	+	3.54616i	0.328699	+	0.123913i
$820$		0			0
$821$	−7.94924	+	9.47354i	−0.277431	+	0.330629i	−0.886709	−	0.462327i	$-0.847015\pi$
$821$	−7.94924	+	9.47354i	−0.277431	+	0.330629i	0.609279	+	0.792956i	$0.291459\pi$
$822$	0.0920964	−	16.1024i	0.00321223	−	0.561636i
$823$	31.6390	+	22.1538i	1.10286	+	0.772234i	0.975583	−	0.219632i	$-0.0704858\pi$
$823$	31.6390	+	22.1538i	1.10286	+	0.772234i	0.127282	+	0.991867i	$0.459375\pi$
$824$	−7.95190	−	45.0975i	−0.277018	−	1.57104i
$825$		0			0
$826$	4.40357	+	3.69503i	0.153220	+	0.128567i
$827$	17.1270	+	4.58916i	0.595563	+	0.159581i	0.543994	−	0.839089i	$-0.316911\pi$
$827$	17.1270	+	4.58916i	0.595563	+	0.159581i	0.0515685	+	0.998669i	$0.483578\pi$
$828$	−58.0604	+	56.7471i	−2.01774	+	1.97210i
$829$	−20.1611	−	11.6400i	−0.700224	−	0.404275i	0.107207	−	0.994237i	$-0.465809\pi$
$829$	−20.1611	−	11.6400i	−0.700224	−	0.404275i	−0.807431	+	0.589962i	$0.799143\pi$
$830$		0			0
$831$	−17.1333	−	1.59776i	−0.594347	−	0.0554257i
$832$	−15.4053	−	1.34779i	−0.534084	−	0.0467263i
$833$	0.933284	+	2.00143i	0.0323364	+	0.0693455i
$834$	−18.4269	+	12.7462i	−0.638073	+	0.441366i
$835$		0			0
$836$			0.121040i			0.00418626i
$837$	−24.1853	+	19.5967i	−0.835965	+	0.677359i
$838$	−43.1705	+	43.1705i	−1.49130	+	1.49130i
$839$	0.280939	−	1.59329i	0.00969910	−	0.0550063i	−0.979574	−	0.201084i	$-0.935554\pi$
$839$	0.280939	−	1.59329i	0.00969910	−	0.0550063i	0.989273	+	0.146077i	$0.0466648\pi$
$840$		0			0
$841$	−67.2182	−	24.4654i	−2.31787	−	0.843635i
$842$	−4.95770	+	56.6667i	−0.170854	+	1.95286i
$843$	−15.6801	+	42.3260i	−0.540052	+	1.45778i
$844$	7.95832	+	21.8653i	0.273937	+	0.752635i
$845$		0			0
$846$	−9.58800	+	11.1647i	−0.329642	+	0.383849i
$847$	−6.90330	+	25.7635i	−0.237200	+	0.885243i
$848$	−0.321159	−	3.67086i	−0.0110286	−	0.126058i
$849$	12.4235	+	3.40514i	0.426373	+	0.116864i
$850$		0			0
$851$	12.6939	−	2.23827i	0.435141	−	0.0767270i
$852$	30.1751	+	52.9621i	1.03378	+	1.81445i
$853$	22.5084	−	1.96923i	0.770674	−	0.0674252i	0.304965	−	0.952363i	$-0.401355\pi$
$853$	22.5084	−	1.96923i	0.770674	−	0.0674252i	0.465708	+	0.884938i	$0.345800\pi$
$854$	19.6379	+	34.0138i	0.671994	+	1.16393i
$855$		0			0
$856$	−9.27130	+	16.0584i	−0.316886	+	0.548863i
$857$	13.0587	−	28.0044i	0.446076	−	0.956612i	−0.546778	−	0.837277i	$-0.684146\pi$
$857$	13.0587	−	28.0044i	0.446076	−	0.956612i	0.992854	−	0.119335i	$-0.0380762\pi$
$858$	−0.0228522	−	0.00846583i	−0.000780160	−	0.000289019i
$859$	−17.7378	−	21.1391i	−0.605205	−	0.721256i	0.373246	−	0.927732i	$-0.378245\pi$
$859$	−17.7378	−	21.1391i	−0.605205	−	0.721256i	−0.978452	+	0.206477i	$0.933800\pi$
$860$		0			0
$861$	−12.5469	+	1.02543i	−0.427596	+	0.0349467i
$862$	30.5344	−	21.3804i	1.04000	−	0.728219i
$863$	15.5004	+	15.5004i	0.527641	+	0.527641i	0.919868	−	0.392228i	$-0.128295\pi$
$863$	15.5004	+	15.5004i	0.527641	+	0.527641i	−0.392228	+	0.919868i	$0.628295\pi$
$864$	−12.4261	−	9.02248i	−0.422744	−	0.306951i
$865$		0			0
$866$	35.0727	+	6.18427i	1.19182	+	0.210150i
$867$	−22.3496	−	4.07277i	−0.759032	−	0.138319i
$868$	48.1922	−	22.4724i	1.63575	−	0.762762i
$869$	−0.0231666	+	0.0194391i	−0.000785874	+	0.000659426i
$870$		0			0
$871$	−11.8179	+	4.30136i	−0.400434	+	0.145746i
$872$	11.5085	+	42.9501i	0.389725	+	1.45448i
$873$	−26.4230	−	27.0345i	−0.894282	−	0.914979i
$874$	117.701	−	67.9545i	3.98129	−	2.29860i
$875$		0			0
$876$	17.6368	−	4.61782i	0.595893	−	0.156022i
$877$	1.56824	−	2.23967i	0.0529555	−	0.0756283i	−0.791801	−	0.610779i	$-0.790856\pi$
$877$	1.56824	−	2.23967i	0.0529555	−	0.0756283i	0.844757	+	0.535151i	$0.179745\pi$
$878$	−28.3256	+	40.4531i	−0.955942	+	1.36523i
$879$	10.1502	+	10.2670i	0.342359	+	0.346298i
$880$		0			0
$881$	38.0975	−	21.9956i	1.28354	−	0.741051i	0.306045	−	0.952017i	$-0.400994\pi$
$881$	38.0975	−	21.9956i	1.28354	−	0.741051i	0.977493	+	0.210966i	$0.0676609\pi$
$882$	3.29699	+	7.28688i	0.111015	+	0.245362i
$883$	−7.04478	−	26.2915i	−0.237076	−	0.884779i	−0.977202	−	0.212311i	$-0.931901\pi$
$883$	−7.04478	−	26.2915i	−0.237076	−	0.884779i	0.740126	−	0.672468i	$-0.234766\pi$
$884$	9.36894	−	3.41001i	0.315111	−	0.114691i
$885$		0			0
$886$	−13.7042	+	11.4992i	−0.460401	+	0.386322i
$887$	48.4940	−	22.6131i	1.62827	−	0.759274i	0.628442	−	0.777856i	$-0.283693\pi$
$887$	48.4940	−	22.6131i	1.62827	−	0.759274i	0.999827	+	0.0185820i	$0.00591519\pi$
$888$	−4.01689	−	11.2359i	−0.134798	−	0.377051i
$889$	14.0795	+	2.48260i	0.472211	+	0.0832636i
$890$		0			0
$891$	−0.0240737	−	0.0300604i	−0.000806498	−	0.00100706i
$892$	−9.72811	−	9.72811i	−0.325721	−	0.325721i
$893$	13.0506	−	9.13813i	0.436722	−	0.305796i
$894$	−16.2114	+	34.2527i	−0.542191	+	1.14558i
$895$		0			0
$896$	32.2824	+	38.4726i	1.07848	+	1.28528i
$897$	2.97310	+	17.4441i	0.0992688	+	0.582441i
$898$	5.35770	−	11.4896i	0.178789	−	0.383414i
$899$	−30.0326	+	52.0179i	−1.00164	+	1.73489i
$900$		0			0
$901$	−1.74633	−	3.02474i	−0.0581788	−	0.100769i
$902$	0.0304007	−	0.00265972i	0.00101223	−	8.85589e-5i
$903$	30.3073	+	0.173340i	1.00856	+	0.00576839i
$904$	−7.33401	+	1.29318i	−0.243926	+	0.0430107i
$905$		0			0
$906$	−11.8399	−	45.2200i	−0.393354	−	1.50234i
$907$	−4.20861	−	48.1046i	−0.139745	−	1.59729i	−0.665332	−	0.746548i	$-0.731710\pi$
$907$	−4.20861	−	48.1046i	−0.139745	−	1.59729i	0.525587	−	0.850740i	$-0.323846\pi$
$908$	6.17680	−	23.0521i	0.204984	−	0.765011i
$909$	−12.6498	−	7.49759i	−0.419568	−	0.248679i
$910$		0			0
$911$	−14.5674	−	40.0237i	−0.482640	−	1.32604i	−0.907221	−	0.420653i	$-0.861801\pi$
$911$	−14.5674	−	40.0237i	−0.482640	−	1.32604i	0.424581	−	0.905390i	$-0.360421\pi$
$912$	−17.7651	−	21.4192i	−0.588262	−	0.709262i
$913$	−0.00380000	+	0.0434342i	−0.000125762	+	0.00143746i
$914$	52.5694	+	19.1337i	1.73884	+	0.632886i
$915$		0			0
$916$	−2.75452	+	15.6217i	−0.0910121	+	0.516155i
$917$	−26.5297	+	26.5297i	−0.876087	+	0.876087i
$918$	23.9180	+	4.64186i	0.789412	+	0.153204i
$919$			29.7860i			0.982549i	0.871005	+	0.491274i	$0.163469\pi$
$919$			29.7860i			0.982549i	−0.871005	+	0.491274i	$0.836531\pi$
$920$		0			0
$921$	1.71972	+	21.0419i	0.0566667	+	0.693354i
$922$	−16.2036	−	34.7487i	−0.533637	−	1.14439i
$923$	13.2354	+	1.15795i	0.435648	+	0.0381143i
$924$	0.0274616	+	0.0597819i	0.000903421	+	0.00196668i
$925$		0			0
$926$	−30.7563	−	17.7572i	−1.01072	−	0.583537i
$927$	−19.6160	−	28.7079i	−0.644273	−	0.942892i
$928$	−28.6219	−	7.66920i	−0.939559	−	0.251754i
$929$	6.65219	+	5.58185i	0.218251	+	0.183135i	0.745358	−	0.666665i	$-0.232279\pi$
$929$	6.65219	+	5.58185i	0.218251	+	0.183135i	−0.527106	+	0.849799i	$0.676723\pi$
$930$		0			0
$931$	−1.50353	−	8.52694i	−0.0492762	−	0.279459i
$932$	−78.4899	−	54.9592i	−2.57102	−	1.80025i
$933$	30.4660	−	17.3580i	0.997412	−	0.568275i
$934$	9.61335	−	11.4567i	0.314559	−	0.374876i
$935$		0			0
$936$	15.4564	−	5.42628i	0.505210	−	0.177364i
$937$	−32.2615	+	8.64443i	−1.05394	+	0.282401i	−0.743877	−	0.668316i	$-0.767015\pi$
$937$	−32.2615	+	8.64443i	−1.05394	+	0.282401i	−0.310059	+	0.950717i	$0.600349\pi$
$938$	47.5804	+	22.1871i	1.55355	+	0.724434i
$939$	−11.4009	+	5.23713i	−0.372053	+	0.170907i
$940$		0			0
$941$	−2.59435	+	7.12792i	−0.0845735	+	0.232364i	−0.974769	−	0.223214i	$-0.928345\pi$
$941$	−2.59435	+	7.12792i	−0.0845735	+	0.232364i	0.890196	+	0.455578i	$0.150567\pi$
$942$	−2.76430	−	2.34659i	−0.0900656	−	0.0764561i
$943$	−12.7099	−	18.1517i	−0.413893	−	0.591100i
$944$	2.07182			0.0674319
$945$		0			0
$946$	−0.0734704			−0.00238873
$947$	11.8813	+	16.9682i	0.386089	+	0.551393i	0.964408	−	0.264418i	$-0.0851799\pi$
$947$	11.8813	+	16.9682i	0.386089	+	0.551393i	−0.578319	+	0.815811i	$0.696291\pi$
$948$	8.03350	−	44.0844i	0.260916	−	1.43179i
$949$	1.35910	−	3.73411i	0.0441184	−	0.121214i
$950$		0			0
$951$	−0.789285	+	8.46376i	−0.0255943	+	0.274456i
$952$	−17.1121	−	7.97949i	−0.554606	−	0.258617i
$953$	−32.1900	+	8.62530i	−1.04274	+	0.279401i	−0.739248	−	0.673434i	$-0.764819\pi$
$953$	−32.1900	+	8.62530i	−1.04274	+	0.279401i	−0.303490	+	0.952835i	$0.598152\pi$
$954$	−6.19906	−	11.0265i	−0.200702	−	0.356995i
$955$		0			0
$956$	−43.1237	+	51.3928i	−1.39472	+	1.66216i
$957$	−0.0641436	−	0.0375241i	−0.00207347	−	0.00121298i
$958$	13.3226	+	9.32860i	0.430435	+	0.301394i
$959$	1.64529	+	9.33089i	0.0531291	+	0.301310i
$960$		0			0
$961$	3.74384	+	3.14145i	0.120769	+	0.101337i
$962$	−5.53765	−	1.48381i	−0.178541	−	0.0478400i
$963$	−1.38741	+	14.0104i	−0.0447087	+	0.451480i
$964$	−20.0626	−	11.5831i	−0.646173	−	0.373068i
$965$		0			0
$966$	42.7151	−	60.2669i	1.37434	−	1.93906i
$967$	14.9736	+	1.31002i	0.481519	+	0.0421275i	0.325332	−	0.945600i	$-0.394524\pi$
$967$	14.9736	+	1.31002i	0.481519	+	0.0421275i	0.156188	+	0.987727i	$0.450080\pi$
$968$	18.3680	+	39.3903i	0.590369	+	1.26605i
$969$	−23.8408	−	11.2836i	−0.765876	−	0.362481i
$970$		0			0
$971$		−	29.8876i		−	0.959139i	−0.877504	−	0.479570i	$-0.840793\pi$
$971$		−	29.8876i		−	0.959139i	0.877504	−	0.479570i	$-0.159207\pi$
$972$	55.8912	+	11.5119i	1.79271	+	0.369245i
$973$	9.32220	−	9.32220i	0.298856	−	0.298856i
$974$	6.85958	−	38.9026i	0.219795	−	1.24652i
$975$		0			0
$976$	13.3018	+	4.84146i	0.425780	+	0.154971i
$977$	−3.39755	+	38.8342i	−0.108697	+	1.24242i	0.724435	+	0.689343i	$0.242101\pi$
$977$	−3.39755	+	38.8342i	−0.108697	+	1.24242i	−0.833132	+	0.553074i	$0.813455\pi$
$978$	27.3202	−	4.65634i	0.873604	−	0.148893i
$979$	0.00889204	+	0.0244307i	0.000284191	+	0.000780808i
$980$		0			0
$981$	21.4042	+	26.1093i	0.683383	+	0.833606i
$982$	10.2458	−	38.2380i	0.326958	−	1.22022i
$983$	−2.43483	−	27.8303i	−0.0776592	−	0.887648i	−0.930695	−	0.365796i	$-0.880797\pi$
$983$	−2.43483	−	27.8303i	−0.0776592	−	0.887648i	0.853036	−	0.521852i	$-0.174759\pi$
$984$	−14.5878	+	14.4218i	−0.465041	+	0.459751i
$985$		0			0
$986$	46.2994	−	8.16383i	1.47447	−	0.259989i
$987$	4.37246	−	7.47427i	0.139177	−	0.237909i
$988$	−38.9426	+	3.40704i	−1.23893	+	0.108392i
$989$	26.6744	+	46.2015i	0.848198	+	1.46912i
$990$		0			0
$991$	−19.0981	+	33.0789i	−0.606672	+	1.05079i	0.385113	+	0.922870i	$0.374163\pi$
$991$	−19.0981	+	33.0789i	−0.606672	+	1.05079i	−0.991785	+	0.127917i	$0.959171\pi$
$992$	−7.48204	+	16.0453i	−0.237555	+	0.509438i
$993$	−6.62030	+	5.49088i	−0.210089	+	0.174248i
$994$	−35.6498	−	42.4858i	−1.13074	−	1.34757i
$995$		0			0
$996$	−36.7519	−	53.1313i	−1.16453	−	1.68353i
$997$	−6.25727	+	4.38139i	−0.198170	+	0.138760i	−0.668450	−	0.743757i	$-0.733042\pi$
$997$	−6.25727	+	4.38139i	−0.198170	+	0.138760i	0.470280	+	0.882517i	$0.344153\pi$
$998$	−46.8702	−	46.8702i	−1.48365	−	1.48365i
$999$	−6.29547	−	6.51530i	−0.199180	−	0.206135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.407.2		192
5.2	odd	4		135.2.q.a.83.15	yes	192
5.3	odd	4	inner	675.2.ba.b.218.2		192
5.4	even	2		135.2.q.a.2.15	✓	192
15.2	even	4		405.2.r.a.8.2		192
15.14	odd	2		405.2.r.a.332.2		192
27.14	odd	18	inner	675.2.ba.b.257.2		192
135.14	odd	18		135.2.q.a.122.15	yes	192
135.67	odd	36		405.2.r.a.233.2		192
135.68	even	36	inner	675.2.ba.b.68.2		192
135.94	even	18		405.2.r.a.152.2		192
135.122	even	36		135.2.q.a.68.15	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.15	✓	192	5.4	even	2
135.2.q.a.68.15	yes	192	135.122	even	36
135.2.q.a.83.15	yes	192	5.2	odd	4
135.2.q.a.122.15	yes	192	135.14	odd	18
405.2.r.a.8.2		192	15.2	even	4
405.2.r.a.152.2		192	135.94	even	18
405.2.r.a.233.2		192	135.67	odd	36
405.2.r.a.332.2		192	15.14	odd	2
675.2.ba.b.68.2		192	135.68	even	36	inner
675.2.ba.b.218.2		192	5.3	odd	4	inner
675.2.ba.b.257.2		192	27.14	odd	18	inner
675.2.ba.b.407.2		192	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36466 - 1.94894i) q^{2} +(1.63096 - 0.583078i) q^{3} +(-1.25203 + 3.43992i) q^{4} +(-3.36209 - 2.38294i) q^{6} +(2.19758 + 1.02475i) q^{7} +(3.81650 - 1.02263i) q^{8} +(2.32004 - 1.90195i) q^{9} +(0.00275056 - 0.00327799i) q^{11} +(-0.0362633 + 6.34039i) q^{12} +(1.13206 + 0.792678i) q^{13} +(-1.00178 - 5.68139i) q^{14} +(-1.59279 - 1.33651i) q^{16} +(-1.90362 - 0.510074i) q^{17} +(-6.87287 - 1.92610i) q^{18} +(6.69182 + 3.86352i) q^{19} +(4.18166 + 0.389960i) q^{21} +(-0.0101422 - 0.000887327i) q^{22} +(3.12427 + 6.70002i) q^{23} +(5.62827 - 3.89318i) q^{24} -3.28806i q^{26} +(2.67490 - 4.45476i) q^{27} +(-6.27648 + 6.27648i) q^{28} +(1.74110 - 9.87424i) q^{29} +(-5.62932 - 2.04890i) q^{31} +(0.257571 - 2.94406i) q^{32} +(0.00257472 - 0.00695004i) q^{33} +(1.60370 + 4.40613i) q^{34} +(3.63779 + 10.3620i) q^{36} +(0.451272 - 1.68417i) q^{37} +(-1.60230 - 18.3144i) q^{38} +(2.30854 + 0.632743i) q^{39} +(-2.95191 + 0.520501i) q^{41} +(-4.94656 - 8.68198i) q^{42} +(7.18901 - 0.628957i) q^{43} +(0.00783223 + 0.0135658i) q^{44} +(8.79437 - 15.2323i) q^{46} +(0.871367 - 1.86865i) q^{47} +(-3.37706 - 1.25107i) q^{48} +(-0.720271 - 0.858385i) q^{49} +(-3.40214 + 0.278051i) q^{51} +(-4.14412 + 2.90174i) q^{52} +(1.25315 + 1.25315i) q^{53} +(-12.3324 + 0.866025i) q^{54} +(9.43499 + 1.66364i) q^{56} +(13.1668 + 2.39939i) q^{57} +(-21.6203 + 10.0817i) q^{58} +(-0.763311 + 0.640494i) q^{59} +(-6.39745 + 2.32848i) q^{61} +(3.68893 + 13.7673i) q^{62} +(7.04749 - 1.80223i) q^{63} +(-9.69063 + 5.59489i) q^{64} +(-0.0170589 + 0.00446650i) q^{66} +(-5.21964 + 7.45442i) q^{67} +(4.13800 - 5.90968i) q^{68} +(9.00219 + 9.10575i) q^{69} +(8.32564 - 4.80681i) q^{71} +(6.90944 - 9.63132i) q^{72} +(-0.744204 - 2.77741i) q^{73} +(-3.89819 + 1.41882i) q^{74} +(-21.6685 + 18.1821i) q^{76} +(0.00940367 - 0.00438501i) q^{77} +(-1.91719 - 5.36268i) q^{78} +(-6.95996 - 1.22723i) q^{79} +(1.76518 - 8.82520i) q^{81} +(5.04279 + 5.04279i) q^{82} +(-8.34640 + 5.84421i) q^{83} +(-6.57699 + 13.8963i) q^{84} +(-11.0364 - 13.1527i) q^{86} +(-2.91780 - 17.1197i) q^{87} +(0.00714534 - 0.0153232i) q^{88} +(-3.03785 + 5.26171i) q^{89} +(1.67550 + 2.90205i) q^{91} +(-26.9592 + 2.35862i) q^{92} +(-10.3758 - 0.0593438i) q^{93} +(-4.83102 + 0.851839i) q^{94} +(-1.29653 - 4.95181i) q^{96} +(-1.09824 - 12.5529i) q^{97} +(-0.690016 + 2.57517i) q^{98} +(0.000146839 - 0.0128365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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