LMFDB - Embedded newform 725.2.y.b.282.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(18,725)] 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("725.18"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.y (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [156] 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			282.9
Character	$\chi$	$=$	725.282
Dual form			725.2.y.b.18.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.920277 - 0.443182i) q^{2} +(1.22069 - 0.973467i) q^{3} +(-0.596480 + 0.747962i) q^{4} +(0.691949 - 1.43685i) q^{6} +(-0.359728 + 3.19267i) q^{7} +(-0.672023 + 2.94432i) q^{8} +(-0.125119 + 0.548181i) q^{9} +(-0.282265 - 0.177359i) q^{11} +1.49368i q^{12} +(-2.30460 + 3.66774i) q^{13} +(1.08389 + 3.09757i) q^{14} +(0.260662 + 1.14204i) q^{16} +7.42290 q^{17} +(0.127800 + 0.559929i) q^{18} +(-5.42486 + 0.611234i) q^{19} +(2.66885 + 4.24744i) q^{21} +(-0.338364 - 0.0381244i) q^{22} +(3.83282 - 1.34116i) q^{23} +(2.04587 + 4.24830i) q^{24} +(-0.495389 + 4.39670i) q^{26} +(2.41320 + 5.01106i) q^{27} +(-2.17343 - 2.17343i) q^{28} +(0.0218780 - 5.38512i) q^{29} +(0.716676 - 2.04814i) q^{31} +(-3.01992 - 3.78686i) q^{32} +(-0.517210 + 0.0582756i) q^{33} +(6.83113 - 3.28970i) q^{34} +(-0.335388 - 0.420563i) q^{36} +(-7.12342 - 1.62587i) q^{37} +(-4.72148 + 2.96670i) q^{38} +(0.757232 + 6.72062i) q^{39} +(1.70982 + 1.70982i) q^{41} +(4.33847 + 2.72604i) q^{42} +(2.98830 - 6.20526i) q^{43} +(0.301023 - 0.105332i) q^{44} +(2.93288 - 2.93288i) q^{46} +(9.47549 - 2.16272i) q^{47} +(1.42992 + 1.14032i) q^{48} +(-3.23926 - 0.739339i) q^{49} +(9.06106 - 7.22595i) q^{51} +(-1.36869 - 3.91149i) q^{52} +(-2.41210 + 6.89339i) q^{53} +(4.44163 + 3.54208i) q^{54} +(-9.15852 - 3.20470i) q^{56} +(-6.02705 + 6.02705i) q^{57} +(-2.36646 - 4.96550i) q^{58} -6.55260i q^{59} +(6.95855 + 0.784041i) q^{61} +(-0.248159 - 2.20248i) q^{62} +(-1.70515 - 0.596659i) q^{63} +(-6.56823 - 3.16309i) q^{64} +(-0.450150 + 0.282848i) q^{66} +(3.99208 + 6.35336i) q^{67} +(-4.42761 + 5.55205i) q^{68} +(3.37311 - 5.36827i) q^{69} +(-3.19119 + 0.728367i) q^{71} +(-1.52994 - 0.736780i) q^{72} +(3.80763 + 1.83366i) q^{73} +(-7.27608 + 1.66072i) q^{74} +(2.77864 - 4.42218i) q^{76} +(0.667786 - 0.837377i) q^{77} +(3.67532 + 5.84924i) q^{78} +(-1.68732 + 1.06021i) q^{79} +(6.30409 + 3.03589i) q^{81} +(2.33127 + 0.815745i) q^{82} +(-0.854097 - 7.58032i) q^{83} +(-4.76884 - 0.537319i) q^{84} -7.03492i q^{86} +(-5.21553 - 6.59486i) q^{87} +(0.711889 - 0.711889i) q^{88} +(9.71523 + 3.39950i) q^{89} +(-10.8809 - 8.67721i) q^{91} +(-1.28306 + 3.66678i) q^{92} +(-1.11896 - 3.19781i) q^{93} +(7.76160 - 6.18967i) q^{94} +(-7.37277 - 1.68279i) q^{96} +(-0.929141 - 0.740965i) q^{97} +(-3.30868 + 0.755184i) q^{98} +(0.132541 - 0.132541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 8 q^{2} + 14 q^{3} - 22 q^{4} - 28 q^{6} + 10 q^{7} - 4 q^{8} + 10 q^{9} - 20 q^{11} + 4 q^{14} - 34 q^{16} + 48 q^{17} + 94 q^{18} - 16 q^{21} + 6 q^{22} + 10 q^{23} + 56 q^{24} + 36 q^{26} + 56 q^{27}+ \cdots + 76 q^{99}+O(q^{100}) $ 156 * q + 8 * q^2 + 14 * q^3 - 22 * q^4 - 28 * q^6 + 10 * q^7 - 4 * q^8 + 10 * q^9 - 20 * q^11 + 4 * q^14 - 34 * q^16 + 48 * q^17 + 94 * q^18 - 16 * q^21 + 6 * q^22 + 10 * q^23 + 56 * q^24 + 36 * q^26 + 56 * q^27 - 8 * q^28 - 8 * q^31 - 28 * q^32 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 28 * q^37 - 92 * q^38 + 16 * q^39 - 22 * q^41 + 10 * q^42 + 42 * q^43 - 112 * q^44 + 4 * q^46 + 14 * q^47 - 154 * q^48 + 84 * q^49 - 28 * q^51 + 166 * q^52 - 14 * q^53 + 4 * q^56 - 12 * q^57 - 126 * q^58 - 46 * q^61 - 84 * q^62 - 38 * q^63 - 30 * q^64 - 48 * q^66 + 46 * q^67 + 44 * q^68 - 124 * q^69 - 28 * q^71 - 60 * q^72 - 130 * q^73 + 112 * q^74 - 48 * q^76 + 44 * q^77 + 210 * q^78 - 4 * q^79 + 58 * q^81 - 72 * q^82 - 46 * q^83 + 120 * q^84 + 144 * q^87 - 40 * q^88 + 46 * q^89 - 28 * q^91 + 14 * q^92 + 6 * q^93 - 84 * q^94 - 28 * q^96 - 154 * q^97 - 98 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.920277	−	0.443182i	0.650734	−	0.313377i	−0.0792362	−	0.996856i	$-0.525248\pi$
$2$	0.920277	−	0.443182i	0.650734	−	0.313377i	0.729970	+	0.683479i	$0.239534\pi$
$3$	1.22069	−	0.973467i	0.704765	−	0.562032i	−0.204187	−	0.978932i	$-0.565455\pi$
$3$	1.22069	−	0.973467i	0.704765	−	0.562032i	0.908952	+	0.416900i	$0.136884\pi$
$4$	−0.596480	+	0.747962i	−0.298240	+	0.373981i
$5$		0			0
$5$		0			0
$6$	0.691949	−	1.43685i	0.282487	−	0.586591i
$7$	−0.359728	+	3.19267i	−0.135964	+	1.20672i	0.721589	+	0.692322i	$0.243412\pi$
$7$	−0.359728	+	3.19267i	−0.135964	+	1.20672i	−0.857553	+	0.514395i	$0.828017\pi$
$8$	−0.672023	+	2.94432i	−0.237596	+	1.04098i
$9$	−0.125119	+	0.548181i	−0.0417063	+	0.182727i
$10$		0			0
$11$	−0.282265	−	0.177359i	−0.0851060	−	0.0534756i	0.488807	−	0.872392i	$-0.337432\pi$
$11$	−0.282265	−	0.177359i	−0.0851060	−	0.0534756i	−0.573913	+	0.818916i	$0.694575\pi$
$12$			1.49368i			0.431189i
$13$	−2.30460	+	3.66774i	−0.639180	+	1.01725i	0.357347	+	0.933972i	$0.383681\pi$
$13$	−2.30460	+	3.66774i	−0.639180	+	1.01725i	−0.996526	+	0.0832770i	$0.973461\pi$
$14$	1.08389	+	3.09757i	0.289681	+	0.827860i
$15$		0			0
$16$	0.260662	+	1.14204i	0.0651655	+	0.285509i
$17$	7.42290			1.80032			0.900159	−	0.435561i	$-0.143450\pi$
$17$	7.42290			1.80032			0.900159	+	0.435561i	$0.143450\pi$
$18$	0.127800	+	0.559929i	0.0301228	+	0.131977i
$19$	−5.42486	+	0.611234i	−1.24455	+	0.140227i	−0.709567	−	0.704638i	$-0.751110\pi$
$19$	−5.42486	+	0.611234i	−1.24455	+	0.140227i	−0.534980	+	0.844865i	$0.679681\pi$
$20$		0			0
$21$	2.66885	+	4.24744i	0.582390	+	0.926868i
$22$	−0.338364	−	0.0381244i	−0.0721394	−	0.00812816i
$23$	3.83282	−	1.34116i	0.799199	−	0.279652i	0.100379	−	0.994949i	$-0.467995\pi$
$23$	3.83282	−	1.34116i	0.799199	−	0.279652i	0.698820	+	0.715297i	$0.253709\pi$
$24$	2.04587	+	4.24830i	0.417612	+	0.867180i
$25$		0			0
$26$	−0.495389	+	4.39670i	−0.0971537	+	0.862263i
$27$	2.41320	+	5.01106i	0.464421	+	0.964379i
$28$	−2.17343	−	2.17343i	−0.410739	−	0.410739i
$29$	0.0218780	−	5.38512i	0.00406265	−	0.999992i
$29$	0.0218780	−	5.38512i	0.00406265	−	0.999992i
$30$		0			0
$31$	0.716676	−	2.04814i	0.128719	−	0.367857i	−0.861430	−	0.507876i	$-0.830431\pi$
$31$	0.716676	−	2.04814i	0.128719	−	0.367857i	0.990149	+	0.140019i	$0.0447164\pi$
$32$	−3.01992	−	3.78686i	−0.533852	−	0.669429i
$33$	−0.517210	+	0.0582756i	−0.0900347	+	0.0101445i
$34$	6.83113	−	3.28970i	1.17153	−	0.564178i
$35$		0			0
$36$	−0.335388	−	0.420563i	−0.0558980	−	0.0700939i
$37$	−7.12342	−	1.62587i	−1.17108	−	0.267292i	−0.407625	−	0.913149i	$-0.633643\pi$
$37$	−7.12342	−	1.62587i	−1.17108	−	0.267292i	−0.763458	+	0.645857i	$0.776500\pi$
$38$	−4.72148	+	2.96670i	−0.765926	+	0.481263i
$39$	0.757232	+	6.72062i	0.121254	+	1.07616i
$40$		0			0
$41$	1.70982	+	1.70982i	0.267029	+	0.267029i	0.827902	−	0.560873i	$-0.189534\pi$
$41$	1.70982	+	1.70982i	0.267029	+	0.267029i	−0.560873	+	0.827902i	$0.689534\pi$
$42$	4.33847	+	2.72604i	0.669440	+	0.420637i
$43$	2.98830	−	6.20526i	0.455711	−	0.946294i	−0.538876	−	0.842385i	$-0.681151\pi$
$43$	2.98830	−	6.20526i	0.455711	−	0.946294i	0.994587	−	0.103908i	$-0.0331349\pi$
$44$	0.301023	−	0.105332i	0.0453809	−	0.0158795i
$45$		0			0
$46$	2.93288	−	2.93288i	0.432430	−	0.432430i
$47$	9.47549	−	2.16272i	1.38214	−	0.315465i	0.534112	−	0.845414i	$-0.320646\pi$
$47$	9.47549	−	2.16272i	1.38214	−	0.315465i	0.848030	+	0.529949i	$0.177789\pi$
$48$	1.42992	+	1.14032i	0.206391	+	0.164592i
$49$	−3.23926	−	0.739339i	−0.462751	−	0.105620i
$50$		0			0
$51$	9.06106	−	7.22595i	1.26880	−	1.01184i
$52$	−1.36869	−	3.91149i	−0.189803	−	0.542425i
$53$	−2.41210	+	6.89339i	−0.331328	+	0.946880i	0.650896	+	0.759167i	$0.274393\pi$
$53$	−2.41210	+	6.89339i	−0.331328	+	0.946880i	−0.982224	+	0.187713i	$0.939892\pi$
$54$	4.44163	+	3.54208i	0.604429	+	0.482016i
$55$		0			0
$56$	−9.15852	−	3.20470i	−1.22386	−	0.428247i
$57$	−6.02705	+	6.02705i	−0.798302	+	0.798302i
$58$	−2.36646	−	4.96550i	−0.310731	−	0.652002i
$59$		−	6.55260i		−	0.853075i	−0.904470	−	0.426538i	$-0.859733\pi$
$59$		−	6.55260i		−	0.853075i	0.904470	−	0.426538i	$-0.140267\pi$
$60$		0			0
$61$	6.95855	+	0.784041i	0.890952	+	0.100386i	0.545559	−	0.838072i	$-0.316317\pi$
$61$	6.95855	+	0.784041i	0.890952	+	0.100386i	0.345392	+	0.938458i	$0.387746\pi$
$62$	−0.248159	−	2.20248i	−0.0315163	−	0.279715i
$63$	−1.70515	−	0.596659i	−0.214829	−	0.0751720i
$64$	−6.56823	−	3.16309i	−0.821029	−	0.395387i
$65$		0			0
$66$	−0.450150	+	0.282848i	−0.0554096	+	0.0348162i
$67$	3.99208	+	6.35336i	0.487710	+	0.776186i	0.996401	−	0.0847630i	$-0.0270133\pi$
$67$	3.99208	+	6.35336i	0.487710	+	0.776186i	−0.508691	+	0.860949i	$0.669870\pi$
$68$	−4.42761	+	5.55205i	−0.536927	+	0.673285i
$69$	3.37311	−	5.36827i	0.406075	−	0.646264i
$70$		0			0
$71$	−3.19119	+	0.728367i	−0.378724	+	0.0864413i	−0.407645	−	0.913140i	$-0.633650\pi$
$71$	−3.19119	+	0.728367i	−0.378724	+	0.0864413i	0.0289212	+	0.999582i	$0.490793\pi$
$72$	−1.52994	−	0.736780i	−0.180305	−	0.0868304i
$73$	3.80763	+	1.83366i	0.445650	+	0.214614i	0.643230	−	0.765673i	$-0.277594\pi$
$73$	3.80763	+	1.83366i	0.445650	+	0.214614i	−0.197580	+	0.980287i	$0.563308\pi$
$74$	−7.27608	+	1.66072i	−0.845827	+	0.193055i
$75$		0			0
$76$	2.77864	−	4.42218i	0.318732	−	0.507258i
$77$	0.667786	−	0.837377i	0.0761013	−	0.0954280i
$78$	3.67532	+	5.84924i	0.416148	+	0.662296i
$79$	−1.68732	+	1.06021i	−0.189838	+	0.119283i	−0.623598	−	0.781746i	$-0.714330\pi$
$79$	−1.68732	+	1.06021i	−0.189838	+	0.119283i	0.433760	+	0.901029i	$0.357187\pi$
$80$		0			0
$81$	6.30409	+	3.03589i	0.700454	+	0.337321i
$82$	2.33127	+	0.815745i	0.257445	+	0.0900840i
$83$	−0.854097	−	7.58032i	−0.0937493	−	0.832048i	−0.949309	−	0.314344i	$-0.898215\pi$
$83$	−0.854097	−	7.58032i	−0.0937493	−	0.832048i	0.855560	−	0.517704i	$-0.173213\pi$
$84$	−4.76884	−	0.537319i	−0.520323	−	0.0586264i
$85$		0			0
$86$		−	7.03492i		−	0.758595i
$87$	−5.21553	−	6.59486i	−0.559164	−	0.707043i
$88$	0.711889	−	0.711889i	0.0758877	−	0.0758877i
$89$	9.71523	+	3.39950i	1.02981	+	0.360347i	0.791712	−	0.610894i	$-0.209190\pi$
$89$	9.71523	+	3.39950i	1.02981	+	0.360347i	0.238100	+	0.971241i	$0.423476\pi$
$90$		0			0
$91$	−10.8809	−	8.67721i	−1.14063	−	0.909618i
$92$	−1.28306	+	3.66678i	−0.133769	+	0.382289i
$93$	−1.11896	−	3.19781i	−0.116031	−	0.331597i
$94$	7.76160	−	6.18967i	0.800547	−	0.638415i
$95$		0			0
$96$	−7.37277	−	1.68279i	−0.752480	−	0.171749i
$97$	−0.929141	−	0.740965i	−0.0943400	−	0.0752336i	0.575184	−	0.818024i	$-0.304930\pi$
$97$	−0.929141	−	0.740965i	−0.0943400	−	0.0752336i	−0.669524	+	0.742790i	$0.733502\pi$
$98$	−3.30868	+	0.755184i	−0.334227	+	0.0762851i
$99$	0.132541	−	0.132541i	0.0133209	−	0.0133209i
$100$		0			0
$101$	−8.62410	+	3.01770i	−0.858130	+	0.300273i	−0.723247	−	0.690589i	$-0.757351\pi$
$101$	−8.62410	+	3.01770i	−0.858130	+	0.300273i	−0.134882	+	0.990862i	$0.543066\pi$
$102$	5.13627	−	10.6656i	0.508567	−	1.05605i
$103$	8.94639	+	5.62139i	0.881514	+	0.553892i	0.895025	−	0.446017i	$-0.147158\pi$
$103$	8.94639	+	5.62139i	0.881514	+	0.553892i	−0.0135104	+	0.999909i	$0.504301\pi$
$104$	−9.25028	−	9.25028i	−0.907065	−	0.907065i
$105$		0			0
$106$	0.835225	+	7.41283i	0.0811242	+	0.719997i
$107$	−7.37505	+	4.63405i	−0.712973	+	0.447990i	−0.839067	−	0.544028i	$-0.816899\pi$
$107$	−7.37505	+	4.63405i	−0.712973	+	0.447990i	0.126094	+	0.992018i	$0.459756\pi$
$108$	−5.18751	−	1.18402i	−0.499168	−	0.113932i
$109$	3.50666	+	4.39721i	0.335877	+	0.421177i	0.920875	−	0.389858i	$-0.127476\pi$
$109$	3.50666	+	4.39721i	0.335877	+	0.421177i	−0.584998	+	0.811035i	$0.698905\pi$
$110$		0			0
$111$	−10.2782	+	4.94973i	−0.975566	+	0.469808i
$112$	−3.73991	+	0.421387i	−0.353388	+	0.0398173i
$113$	−0.145757	−	0.182774i	−0.0137117	−	0.0171939i	0.774928	−	0.632049i	$-0.217786\pi$
$113$	−0.145757	−	0.182774i	−0.0137117	−	0.0171939i	−0.788640	+	0.614855i	$0.789214\pi$
$114$	−2.87547	+	8.21763i	−0.269313	+	0.769652i
$115$		0			0
$116$	4.01482	+	3.22848i	0.372766	+	0.299757i
$117$	−1.72224	−	1.72224i	−0.159221	−	0.159221i
$118$	−2.90399	−	6.03020i	−0.267334	−	0.555125i
$119$	−2.67022	+	23.6989i	−0.244779	+	2.17247i
$120$		0			0
$121$	−4.72450	−	9.81053i	−0.429500	−	0.891867i
$122$	6.75127	−	2.36237i	0.611231	−	0.213879i
$123$	3.75161	+	0.422705i	0.338271	+	0.0381140i
$124$	1.10445	+	1.75772i	0.0991826	+	0.157848i
$125$		0			0
$126$	−1.83364	+	0.206602i	−0.163354	+	0.0184056i
$127$	−1.20212	−	5.26685i	−0.106671	−	0.467358i	−0.999844	−	0.0176444i	$-0.994383\pi$
$127$	−1.20212	−	5.26685i	−0.106671	−	0.467358i	0.893173	−	0.449713i	$-0.148474\pi$
$128$	2.24073			0.198055
$129$	−2.39284	−	10.4837i	−0.210678	−	0.923039i
$130$		0			0
$131$	2.90820	+	8.31115i	0.254091	+	0.726149i	0.998304	+	0.0582077i	$0.0185386\pi$
$131$	2.90820	+	8.31115i	0.254091	+	0.726149i	−0.744214	+	0.667941i	$0.767176\pi$
$132$	0.264918	−	0.421614i	0.0230581	−	0.0366968i
$133$		−	17.5397i		−	1.52088i
$134$	6.48951	+	4.07763i	0.560609	+	0.352254i
$135$		0			0
$136$	−4.98836	+	21.8554i	−0.427748	+	1.87409i
$137$	1.35489	−	5.93617i	0.115756	−	0.507161i	−0.883494	−	0.468443i	$-0.844815\pi$
$137$	1.35489	−	5.93617i	0.115756	−	0.507161i	0.999250	−	0.0387184i	$-0.0123275\pi$
$138$	0.725073	−	6.43520i	0.0617223	−	0.547801i
$139$	8.13195	−	16.8862i	0.689743	−	1.43227i	−0.201845	−	0.979418i	$-0.564694\pi$
$139$	8.13195	−	16.8862i	0.689743	−	1.43227i	0.891588	−	0.452848i	$-0.149592\pi$
$140$		0			0
$141$	9.46129	−	11.8641i	0.796784	−	0.999136i
$142$	−2.61398	+	2.08458i	−0.219360	+	0.174934i
$143$	1.30101	−	0.626534i	0.108796	−	0.0523934i
$144$	−0.658656			−0.0548880
$145$		0			0
$146$	4.31672			0.357255
$147$	−4.67385	+	2.25081i	−0.385493	+	0.185643i
$148$	5.46507	−	4.35825i	0.449226	−	0.358246i
$149$	12.0345	−	15.0908i	0.985904	−	1.23628i	0.0142448	−	0.999899i	$-0.495466\pi$
$149$	12.0345	−	15.0908i	0.985904	−	1.23628i	0.971659	−	0.236386i	$-0.0759630\pi$
$150$		0			0
$151$	−7.58945	+	15.7597i	−0.617621	+	1.28250i	0.324073	+	0.946032i	$0.394948\pi$
$151$	−7.58945	+	15.7597i	−0.617621	+	1.28250i	−0.941694	+	0.336471i	$0.890767\pi$
$152$	1.84595	−	16.3833i	0.149727	−	1.32886i
$153$	−0.928744	+	4.06909i	−0.0750845	+	0.328967i
$154$	0.243438	−	1.06657i	0.0196168	−	0.0859467i
$155$		0			0
$156$	−5.47845	−	3.44234i	−0.438627	−	0.275607i
$157$			18.5421i			1.47982i	0.672706	+	0.739910i	$0.265132\pi$
$157$			18.5421i			1.47982i	−0.672706	+	0.739910i	$0.734868\pi$
$158$	−1.08293	+	1.72348i	−0.0861534	+	0.137112i
$159$	3.76606	+	10.7628i	0.298668	+	0.853545i
$160$		0			0
$161$	2.90312	+	12.7194i	0.228798	+	1.00243i
$162$	7.14696			0.561518
$163$	0.438548	+	1.92140i	0.0343497	+	0.150496i	0.989195	−	0.146609i	$-0.0468360\pi$
$163$	0.438548	+	1.92140i	0.0343497	+	0.150496i	−0.954845	+	0.297105i	$0.903979\pi$
$164$	−2.29875	+	0.259007i	−0.179502	+	0.0202250i
$165$		0			0
$166$	−4.14547	−	6.59747i	−0.321751	−	0.512063i
$167$	−9.66345	−	1.08881i	−0.747780	−	0.0842546i	−0.270153	−	0.962817i	$-0.587074\pi$
$167$	−9.66345	−	1.08881i	−0.747780	−	0.0842546i	−0.477627	+	0.878563i	$0.658503\pi$
$168$	−14.2994	+	5.00357i	−1.10322	+	0.386034i
$169$	−2.50069	−	5.19273i	−0.192361	−	0.399441i
$170$		0			0
$171$	0.343684	−	3.05028i	0.0262822	−	0.233261i
$172$	2.85884	+	5.93645i	0.217985	+	0.452650i
$173$	0.563496	+	0.563496i	0.0428418	+	0.0428418i	0.728203	−	0.685361i	$-0.240356\pi$
$173$	0.563496	+	0.563496i	0.0428418	+	0.0428418i	−0.685361	+	0.728203i	$0.740356\pi$
$174$	−7.72246	−	3.75767i	−0.585438	−	0.284868i
$175$		0			0
$176$	0.128974	−	0.368587i	0.00972179	−	0.0277833i
$177$	−6.37874	−	7.99868i	−0.479455	−	0.601218i
$178$	10.4473	−	1.17713i	0.783058	−	0.0882295i
$179$	−1.04193	+	0.501769i	−0.0778778	+	0.0375040i	−0.472417	−	0.881375i	$-0.656618\pi$
$179$	−1.04193	+	0.501769i	−0.0778778	+	0.0375040i	0.394539	+	0.918879i	$0.370904\pi$
$180$		0			0
$181$	−8.53309	−	10.7002i	−0.634260	−	0.795337i	0.356012	−	0.934481i	$-0.384136\pi$
$181$	−8.53309	−	10.7002i	−0.634260	−	0.795337i	−0.990272	+	0.139145i	$0.955565\pi$
$182$	−13.8590	−	3.16323i	−1.02730	−	0.234474i
$183$	9.25747	−	5.81685i	0.684332	−	0.429994i
$184$	1.37307	+	12.1864i	0.101224	+	0.898391i
$185$		0			0
$186$	−2.44696	−	2.44696i	−0.179420	−	0.179420i
$187$	−2.09522	−	1.31652i	−0.153218	−	0.0962731i
$188$	−4.03431	+	8.37732i	−0.294232	+	0.610979i
$189$	−16.8668	+	5.90194i	−1.22688	+	0.429303i
$190$		0			0
$191$	10.1739	−	10.1739i	0.736156	−	0.736156i	−0.235676	−	0.971832i	$-0.575730\pi$
$191$	10.1739	−	10.1739i	0.736156	−	0.736156i	0.971832	+	0.235676i	$0.0757304\pi$
$192$	−11.0969	+	2.53280i	−0.800853	+	0.182789i
$193$	0.166154	+	0.132503i	0.0119600	+	0.00953779i	0.629452	−	0.777040i	$-0.283280\pi$
$193$	0.166154	+	0.132503i	0.0119600	+	0.00953779i	−0.617492	+	0.786578i	$0.711851\pi$
$194$	−1.18345	−	0.270115i	−0.0849667	−	0.0193931i
$195$		0			0
$196$	2.48515	−	1.98184i	0.177511	−	0.141560i
$197$	0.452582	+	1.29341i	0.0322452	+	0.0921514i	0.958881	−	0.283810i	$-0.0915984\pi$
$197$	0.452582	+	1.29341i	0.0322452	+	0.0921514i	−0.926635	+	0.375961i	$0.877313\pi$
$198$	0.0632348	−	0.180715i	0.00449390	−	0.0128428i
$199$	−16.6181	−	13.2525i	−1.17802	−	0.939443i	−0.179011	−	0.983847i	$-0.557290\pi$
$199$	−16.6181	−	13.2525i	−1.17802	−	0.939443i	−0.999014	+	0.0444042i	$0.985861\pi$
$200$		0			0
$201$	11.0579	+	3.86932i	0.779962	+	0.272921i
$202$	−6.59917	+	6.59917i	−0.464316	+	0.464316i
$203$	17.1851	+	2.00703i	1.20615	+	0.140866i
$204$			11.0875i			0.776278i
$205$		0			0
$206$	10.7245	+	1.20836i	0.747209	+	0.0841902i
$207$	0.255642	+	2.26889i	0.0177684	+	0.157699i
$208$	−4.78941	−	1.67589i	−0.332086	−	0.116202i
$209$	1.63965	+	0.789615i	0.113417	+	0.0546188i
$210$		0			0
$211$	0.0410704	−	0.0258062i	0.00282740	−	0.00177657i	−0.530618	−	0.847611i	$-0.678040\pi$
$211$	0.0410704	−	0.0258062i	0.00282740	−	0.00177657i	0.533445	+	0.845835i	$0.320897\pi$
$212$	−3.71722	−	5.91593i	−0.255300	−	0.406308i
$213$	−3.18640	+	3.99562i	−0.218329	+	0.273776i
$214$	−4.73336	+	7.53310i	−0.323566	+	0.514952i
$215$		0			0
$216$	−16.3759	+	3.73770i	−1.11424	+	0.254318i
$217$	6.28124	+	3.02488i	0.426398	+	0.205343i
$218$	5.17587	+	2.49257i	0.350554	+	0.168818i
$219$	6.43295	−	1.46828i	0.434698	−	0.0992170i
$220$		0			0
$221$	−17.1068	+	27.2253i	−1.15073	+	1.83137i
$222$	−7.26518	+	9.11025i	−0.487607	+	0.611440i
$223$	6.55891	+	10.4384i	0.439217	+	0.699010i	0.990834	−	0.135088i	$-0.0431316\pi$
$223$	6.55891	+	10.4384i	0.439217	+	0.699010i	−0.551616	+	0.834098i	$0.685989\pi$
$224$	13.1766	−	8.27938i	0.880396	−	0.553189i
$225$		0			0
$226$	−0.215139	−	0.103606i	−0.0143108	−	0.00689174i
$227$	−9.63473	−	3.37134i	−0.639480	−	0.223764i	−0.00898794	−	0.999960i	$-0.502861\pi$
$227$	−9.63473	−	3.37134i	−0.639480	−	0.223764i	−0.630492	+	0.776196i	$0.717147\pi$
$228$	−0.912991	−	8.10302i	−0.0604643	−	0.536635i
$229$	−20.6689	−	2.32882i	−1.36584	−	0.153893i	−0.601584	−	0.798810i	$-0.705463\pi$
$229$	−20.6689	−	2.32882i	−1.36584	−	0.153893i	−0.764253	+	0.644917i	$0.776892\pi$
$230$		0			0
$231$		−	1.67225i		−	0.110026i
$232$	15.8408	+	3.68334i	1.04000	+	0.241823i
$233$	15.9794	−	15.9794i	1.04684	−	1.04684i	0.0479964	−	0.998848i	$-0.484716\pi$
$233$	15.9794	−	15.9794i	1.04684	−	1.04684i	0.998848	−	0.0479964i	$-0.0152836\pi$
$234$	−2.34820	−	0.821672i	−0.153507	−	0.0537144i
$235$		0			0
$236$	4.90109	+	3.90849i	0.319034	+	0.254421i
$237$	−1.02761	+	2.93674i	−0.0667503	+	0.190761i
$238$	8.04558	+	22.9929i	0.521517	+	1.49041i
$239$	10.5217	−	8.39081i	0.680595	−	0.542757i	−0.221034	−	0.975266i	$-0.570943\pi$
$239$	10.5217	−	8.39081i	0.680595	−	0.542757i	0.901629	+	0.432509i	$0.142372\pi$
$240$		0			0
$241$	7.37877	+	1.68416i	0.475309	+	0.108486i	0.453463	−	0.891275i	$-0.350189\pi$
$241$	7.37877	+	1.68416i	0.475309	+	0.108486i	0.0218459	+	0.999761i	$0.493046\pi$
$242$	−8.69571	−	6.93459i	−0.558981	−	0.445773i
$243$	−5.61656	+	1.28194i	−0.360303	+	0.0822368i
$244$	−4.73707	+	4.73707i	−0.303260	+	0.303260i
$245$		0			0
$246$	3.63985	−	1.27364i	0.232069	−	0.0812043i
$247$	10.2602	−	21.3056i	0.652844	−	1.35564i
$248$	5.54877	+	3.48652i	0.352347	+	0.221395i
$249$	−8.42178	−	8.42178i	−0.533709	−	0.533709i
$250$		0			0
$251$	−2.50604	−	22.2418i	−0.158180	−	1.40389i	−0.782467	−	0.622692i	$-0.786039\pi$
$251$	−2.50604	−	22.2418i	−0.158180	−	1.40389i	0.624287	−	0.781195i	$-0.285390\pi$
$252$	1.46337	−	0.919496i	0.0921836	−	0.0579228i
$253$	−1.31974	−	0.301221i	−0.0829712	−	0.0189376i
$254$	−3.44046	−	4.31420i	−0.215874	−	0.270697i
$255$		0			0
$256$	15.1986	−	7.31924i	0.949910	−	0.457453i
$257$	−16.6517	+	1.87619i	−1.03870	+	0.117034i	−0.614807	−	0.788677i	$-0.710766\pi$
$257$	−16.6517	+	1.87619i	−1.03870	+	0.117034i	−0.423895	+	0.905711i	$0.639338\pi$
$258$	−6.84827	−	8.58745i	−0.426354	−	0.534632i
$259$	7.75338	−	22.1579i	0.481771	−	1.37682i
$260$		0			0
$261$	2.94928	+	0.685773i	0.182556	+	0.0424483i
$262$	6.35970	+	6.35970i	0.392904	+	0.392904i
$263$	3.95590	+	8.21450i	0.243931	+	0.506528i	0.986605	−	0.163125i	$-0.0521573\pi$
$263$	3.95590	+	8.21450i	0.243931	+	0.506528i	−0.742674	+	0.669653i	$0.766443\pi$
$264$	0.175995	−	1.56200i	0.0108317	−	0.0961343i
$265$		0			0
$266$	−7.77327	−	16.1414i	−0.476610	−	0.989690i
$267$	15.1686	−	5.30772i	0.928302	−	0.324827i
$268$	−7.13327	−	0.803726i	−0.435734	−	0.0490954i
$269$	−2.83114	−	4.50574i	−0.172618	−	0.274720i	0.749199	−	0.662344i	$-0.230438\pi$
$269$	−2.83114	−	4.50574i	−0.172618	−	0.274720i	−0.921817	+	0.387625i	$0.873296\pi$
$270$		0			0
$271$	1.33774	−	0.150727i	0.0812619	−	0.00915602i	−0.0712399	−	0.997459i	$-0.522696\pi$
$271$	1.33774	−	0.150727i	0.0812619	−	0.00915602i	0.152502	+	0.988303i	$0.451267\pi$
$272$	1.93487	+	8.47722i	0.117319	+	0.514007i
$273$	−21.7291			−1.31511
$274$	−1.38393	−	6.06338i	−0.0836061	−	0.366302i
$275$		0			0
$276$	2.00327	+	5.72503i	0.120583	+	0.344606i
$277$	11.8812	−	18.9088i	0.713871	−	1.13612i	−0.270958	−	0.962591i	$-0.587340\pi$
$277$	11.8812	−	18.9088i	0.713871	−	1.13612i	0.984829	−	0.173528i	$-0.0555168\pi$
$278$		−	19.1439i		−	1.14817i
$279$	1.03308	+	0.649129i	0.0618491	+	0.0388624i
$280$		0			0
$281$	−1.16627	+	5.10977i	−0.0695739	+	0.304823i	−0.997728	−	0.0673733i	$-0.978538\pi$
$281$	−1.16627	+	5.10977i	−0.0695739	+	0.304823i	0.928154	+	0.372197i	$0.121395\pi$
$282$	3.44906	−	15.1113i	0.205389	−	0.899866i
$283$	2.90239	−	25.7594i	0.172529	−	1.53124i	−0.547210	−	0.836995i	$-0.684310\pi$
$283$	2.90239	−	25.7594i	0.172529	−	1.53124i	0.719739	−	0.694244i	$-0.244261\pi$
$284$	1.35869	−	2.82134i	0.0806232	−	0.167416i
$285$		0			0
$286$	0.919622	−	1.15317i	0.0543784	−	0.0681884i
$287$	−6.07395	+	4.84382i	−0.358534	+	0.285921i
$288$	2.45373	−	1.18166i	0.144588	−	0.0696298i
$289$	38.0995			2.24115
$290$		0			0
$291$	−1.85550			−0.108771
$292$	−3.64269	+	1.75422i	−0.213172	+	0.102658i
$293$	−17.9259	+	14.2954i	−1.04724	+	0.835149i	−0.986624	−	0.163012i	$-0.947879\pi$
$293$	−17.9259	+	14.2954i	−1.04724	+	0.835149i	−0.0606195	+	0.998161i	$0.519308\pi$
$294$	−3.30372	+	4.14273i	−0.192677	+	0.241609i
$295$		0			0
$296$	9.57420	−	19.8810i	0.556489	−	1.15556i
$297$	0.207594	−	1.84245i	0.0120458	−	0.106910i
$298$	4.38711	−	19.2212i	0.254138	−	1.11345i
$299$	−3.91407	+	17.1487i	−0.226356	+	0.991732i
$300$		0			0
$301$	18.7364	+	11.7729i	1.07995	+	0.678576i
$302$			17.8668i			1.02812i
$303$	−7.58971	+	12.0790i	−0.436017	+	0.693918i
$304$	−2.11211	−	6.03605i	−0.121138	−	0.346191i
$305$		0			0
$306$	0.948648	+	4.15630i	0.0542306	+	0.237600i
$307$	31.7559			1.81240			0.906202	−	0.422844i	$-0.138968\pi$
$307$	31.7559			1.81240			0.906202	+	0.422844i	$0.138968\pi$
$308$	0.228006	+	0.998958i	0.0129918	+	0.0569209i
$309$	16.3930	−	1.84705i	0.932566	−	0.105075i
$310$		0			0
$311$	−1.19084	−	1.89521i	−0.0675263	−	0.107468i	0.811254	−	0.584693i	$-0.198785\pi$
$311$	−1.19084	−	1.89521i	−0.0675263	−	0.107468i	−0.878781	+	0.477226i	$0.841642\pi$
$312$	−20.2966	−	2.28687i	−1.14907	−	0.129469i
$313$	10.1055	−	3.53606i	0.571196	−	0.199870i	−0.0291992	−	0.999574i	$-0.509296\pi$
$313$	10.1055	−	3.53606i	0.571196	−	0.199870i	0.600395	+	0.799704i	$0.295010\pi$
$314$	8.21752	+	17.0639i	0.463741	+	0.962969i
$315$		0			0
$316$	0.213453	−	1.89444i	0.0120076	−	0.106571i
$317$	9.69299	+	20.1277i	0.544413	+	1.13048i	0.973809	+	0.227368i	$0.0730121\pi$
$317$	9.69299	+	20.1277i	0.544413	+	1.13048i	−0.429396	+	0.903116i	$0.641274\pi$
$318$	8.23570	+	8.23570i	0.461835	+	0.461835i
$319$	−0.961273	+	1.51615i	−0.0538209	+	0.0848880i
$320$		0			0
$321$	−4.49155	+	12.8361i	−0.250694	+	0.716441i
$322$	8.30869	+	10.4188i	0.463025	+	0.580615i
$323$	−40.2682	+	4.53713i	−2.24058	+	0.252453i
$324$	−6.03099	+	2.90437i	−0.335055	+	0.161354i
$325$		0			0
$326$	1.25512	+	1.57387i	0.0695146	+	0.0871685i
$327$	8.56109	+	1.95401i	0.473429	+	0.108057i
$328$	−6.18329	+	3.88522i	−0.341415	+	0.214525i
$329$	3.49625	+	31.0301i	0.192755	+	1.71075i
$330$		0			0
$331$	−8.77860	−	8.77860i	−0.482516	−	0.482516i	0.423418	−	0.905934i	$-0.360830\pi$
$331$	−8.77860	−	8.77860i	−0.482516	−	0.482516i	−0.905934	+	0.423418i	$0.860830\pi$
$332$	6.17924	+	3.88268i	0.339130	+	0.213090i
$333$	1.78255	−	3.70150i	0.0976830	−	0.202841i
$334$	−9.37559	+	3.28066i	−0.513009	+	0.179510i
$335$		0			0
$336$	−4.15506	+	4.15506i	−0.226677	+	0.226677i
$337$	−1.38871	+	0.316965i	−0.0756481	+	0.0172662i	−0.260177	−	0.965561i	$-0.583781\pi$
$337$	−1.38871	+	0.316965i	−0.0756481	+	0.0172662i	0.184529	+	0.982827i	$0.440924\pi$
$338$	−4.60265	−	3.67049i	−0.250351	−	0.199648i
$339$	−0.355849	−	0.0812201i	−0.0193270	−	0.00441127i
$340$		0			0
$341$	−0.565548	+	0.451009i	−0.0306261	+	0.0244235i
$342$	−1.03555	−	2.95942i	−0.0559959	−	0.160027i
$343$	−3.90230	+	11.1521i	−0.210704	+	0.602158i
$344$	16.2621	+	12.9686i	0.876794	+	0.699220i
$345$		0			0
$346$	0.768304	+	0.268841i	0.0413043	+	0.0144530i
$347$	14.4583	−	14.4583i	0.776163	−	0.776163i	−0.203013	−	0.979176i	$-0.565073\pi$
$347$	14.4583	−	14.4583i	0.776163	−	0.776163i	0.979176	+	0.203013i	$0.0650733\pi$
$348$	8.04366	+	0.0326789i	0.431186	+	0.00175177i
$349$			28.1957i			1.50928i	0.656138	+	0.754641i	$0.272189\pi$
$349$			28.1957i			1.50928i	−0.656138	+	0.754641i	$0.727811\pi$
$350$		0			0
$351$	−23.9407	−	2.69747i	−1.27786	−	0.143980i
$352$	0.180784	+	1.60451i	0.00963584	+	0.0855204i
$353$	−5.33528	−	1.86690i	−0.283968	−	0.0993648i	0.184537	−	0.982826i	$-0.440922\pi$
$353$	−5.33528	−	1.86690i	−0.283968	−	0.0993648i	−0.468505	+	0.883461i	$0.655207\pi$
$354$	−9.41508	−	4.53406i	−0.500406	−	0.240983i
$355$		0			0
$356$	−8.33764	+	5.23889i	−0.441894	+	0.277660i
$357$	19.8106	+	31.5284i	1.04849	+	1.66866i
$358$	−0.736493	+	0.923533i	−0.0389249	+	0.0488103i
$359$	0.405361	−	0.645128i	0.0213941	−	0.0340486i	−0.835856	−	0.548949i	$-0.815028\pi$
$359$	0.405361	−	0.645128i	0.0213941	−	0.0340486i	0.857250	+	0.514900i	$0.172171\pi$
$360$		0			0
$361$	10.5318	−	2.40382i	0.554307	−	0.126517i
$362$	−12.5949	−	6.06540i	−0.661975	−	0.318790i
$363$	−15.3174	−	7.37646i	−0.803954	−	0.387164i
$364$	12.9804	−	2.96270i	0.680360	−	0.155288i
$365$		0			0
$366$	5.94151	−	9.45586i	0.310568	−	0.494266i
$367$	−1.49125	+	1.86997i	−0.0778429	+	0.0976119i	−0.819228	−	0.573468i	$-0.805598\pi$
$367$	−1.49125	+	1.86997i	−0.0778429	+	0.0976119i	0.741385	+	0.671080i	$0.234169\pi$
$368$	2.53073	+	4.02763i	0.131923	+	0.209955i
$369$	−1.15122	+	0.723359i	−0.0599301	+	0.0376566i
$370$		0			0
$371$	−21.1406	−	10.1808i	−1.09757	−	0.528560i
$372$	3.05928	+	1.07049i	0.158616	+	0.0555022i
$373$	1.80161	+	15.9897i	0.0932837	+	0.827916i	0.950026	+	0.312171i	$0.101056\pi$
$373$	1.80161	+	15.9897i	0.0932837	+	0.827916i	−0.856742	+	0.515745i	$0.827515\pi$
$374$	−2.51164	−	0.282994i	−0.129874	−	0.0146333i
$375$		0			0
$376$			29.3523i			1.51373i
$377$	19.7008	+	12.4908i	1.01464	+	0.643307i
$378$	−12.9065	+	12.9065i	−0.663837	+	0.663837i
$379$	15.5819	+	5.45235i	0.800390	+	0.280069i	0.699318	−	0.714811i	$-0.253487\pi$
$379$	15.5819	+	5.45235i	0.800390	+	0.280069i	0.101072	+	0.994879i	$0.467773\pi$
$380$		0			0
$381$	−6.59453	−	5.25896i	−0.337848	−	0.269425i
$382$	4.85391	−	13.8717i	0.248347	−	0.709736i
$383$	−1.54379	−	4.41190i	−0.0788840	−	0.225437i	0.897687	−	0.440634i	$-0.145246\pi$
$383$	−1.54379	−	4.41190i	−0.0788840	−	0.225437i	−0.976571	+	0.215197i	$0.930961\pi$
$384$	2.73524	−	2.18128i	0.139582	−	0.111313i
$385$		0			0
$386$	0.211631	+	0.0483033i	0.0107717	+	0.00245857i
$387$	3.02772	+	2.41452i	0.153907	+	0.122737i
$388$	1.10843	−	0.252991i	0.0562719	−	0.0128437i
$389$	−26.3154	+	26.3154i	−1.33424	+	1.33424i	−0.432711	+	0.901533i	$0.642443\pi$
$389$	−26.3154	+	26.3154i	−1.33424	+	1.33424i	−0.901533	+	0.432711i	$0.857557\pi$
$390$		0			0
$391$	28.4507	−	9.95532i	1.43881	−	0.503462i
$392$	4.35371	−	9.04057i	0.219895	−	0.456618i
$393$	11.6406	+	7.31430i	0.587193	+	0.368958i
$394$	0.989716	+	0.989716i	0.0498612	+	0.0498612i
$395$		0			0
$396$	0.0200776	+	0.178194i	0.00100894	+	0.00895459i
$397$	−25.6132	+	16.0938i	−1.28549	+	0.807726i	−0.989086	−	0.147337i	$-0.952930\pi$
$397$	−25.6132	+	16.0938i	−1.28549	+	0.807726i	−0.296402	+	0.955063i	$0.595787\pi$
$398$	−21.1665	−	4.83111i	−1.06098	−	0.242162i
$399$	−17.0743	−	21.4105i	−0.854784	−	1.07186i
$400$		0			0
$401$	−2.42926	+	1.16987i	−0.121311	+	0.0584205i	−0.493555	−	0.869715i	$-0.664303\pi$
$401$	−2.42926	+	1.16987i	−0.121311	+	0.0584205i	0.372244	+	0.928135i	$0.378589\pi$
$402$	11.8911	−	1.33981i	0.593075	−	0.0668235i
$403$	5.86041	+	7.34872i	0.291928	+	0.366066i
$404$	2.88697	−	8.25050i	0.143632	−	0.410478i
$405$		0			0
$406$	16.7045	−	5.76909i	0.829030	−	0.286315i
$407$	1.72233	+	1.72233i	0.0853726	+	0.0853726i
$408$	15.1863	+	31.5347i	0.751834	+	1.56120i
$409$	1.94353	−	17.2493i	0.0961013	−	0.852922i	−0.849499	−	0.527591i	$-0.823095\pi$
$409$	1.94353	−	17.2493i	0.0961013	−	0.852922i	0.945600	−	0.325332i	$-0.105476\pi$
$410$		0			0
$411$	−4.12476	−	8.56516i	−0.203460	−	0.422488i
$412$	−9.54093	+	3.33852i	−0.470048	+	0.164477i
$413$	20.9203	+	2.35715i	1.02942	+	0.115988i
$414$	1.24079	+	1.97471i	0.0609816	+	0.0970516i
$415$		0			0
$416$	20.8489	−	2.34911i	1.02220	−	0.115175i
$417$	−6.51155	−	28.5290i	−0.318872	−	1.39707i
$418$	1.85888			0.0909207
$419$	−1.52289	−	6.67222i	−0.0743981	−	0.325960i	0.924010	−	0.382369i	$-0.124892\pi$
$419$	−1.52289	−	6.67222i	−0.0743981	−	0.325960i	−0.998408	+	0.0564098i	$0.982035\pi$
$420$		0			0
$421$	2.91469	+	8.32970i	0.142053	+	0.405965i	0.992826	−	0.119569i	$-0.0381513\pi$
$421$	2.91469	+	8.32970i	0.142053	+	0.405965i	−0.850773	+	0.525534i	$0.823866\pi$
$422$	0.0263593	−	0.0419505i	0.00128315	−	0.00204212i
$423$			5.46488i			0.265712i
$424$	−18.6754	−	11.7345i	−0.906957	−	0.569879i
$425$		0			0
$426$	−1.16159	+	5.08924i	−0.0562790	+	0.246574i
$427$	−5.00637	+	21.9343i	−0.242275	+	1.06148i
$428$	0.932974	−	8.28037i	0.0450970	−	0.400247i
$429$	0.978220	−	2.03130i	0.0472289	−	0.0980719i
$430$		0			0
$431$	10.0620	−	12.6174i	0.484671	−	0.607758i	−0.478024	−	0.878347i	$-0.658647\pi$
$431$	10.0620	−	12.6174i	0.484671	−	0.607758i	0.962695	+	0.270589i	$0.0872183\pi$
$432$	−5.09378	+	4.06215i	−0.245075	+	0.195440i
$433$	−3.68847	+	1.77627i	−0.177257	+	0.0853622i	−0.520408	−	0.853918i	$-0.674220\pi$
$433$	−3.68847	+	1.77627i	−0.177257	+	0.0853622i	0.343151	+	0.939280i	$0.388506\pi$
$434$	7.12105			0.341822
$435$		0			0
$436$	−5.38060			−0.257684
$437$	−19.9728	+	9.61837i	−0.955426	+	0.460109i
$438$	5.26938	−	4.20219i	0.251781	−	0.200788i
$439$	11.9256	−	14.9542i	0.569177	−	0.713725i	−0.411048	−	0.911614i	$-0.634837\pi$
$439$	11.9256	−	14.9542i	0.569177	−	0.713725i	0.980224	+	0.197889i	$0.0634085\pi$
$440$		0			0
$441$	0.810583	−	1.68319i	0.0385992	−	0.0801521i
$442$	−3.67722	+	32.6362i	−0.174908	+	1.55235i
$443$	−6.66320	+	29.1934i	−0.316578	+	1.38702i	0.526932	+	0.849908i	$0.323342\pi$
$443$	−6.66320	+	29.1934i	−0.316578	+	1.38702i	−0.843510	+	0.537113i	$0.819515\pi$
$444$	2.42854	−	10.6401i	0.115254	−	0.504959i
$445$		0			0
$446$	10.6621	+	6.69947i	0.504867	+	0.317229i
$447$		−	30.1363i		−	1.42540i
$448$	12.4615	−	19.8324i	0.588750	−	0.936991i
$449$	−0.137280	−	0.392324i	−0.00647865	−	0.0185149i	0.940599	−	0.339521i	$-0.110265\pi$
$449$	−0.137280	−	0.392324i	−0.00647865	−	0.0185149i	−0.947077	+	0.321006i	$0.895979\pi$
$450$		0			0
$451$	−0.179370	−	0.785871i	−0.00844621	−	0.0370052i
$452$	0.223649			0.0105196
$453$	6.07715	+	26.6257i	0.285529	+	1.25099i
$454$	−10.3607	+	1.16738i	−0.486254	+	0.0547876i
$455$		0			0
$456$	−13.6953	−	21.7959i	−0.641340	−	1.02069i
$457$	28.0159	+	3.15663i	1.31053	+	0.147661i	0.739437	−	0.673226i	$-0.235092\pi$
$457$	28.0159	+	3.15663i	1.31053	+	0.147661i	0.571091	+	0.820887i	$0.306520\pi$
$458$	−20.0532	+	7.01691i	−0.937023	+	0.327879i
$459$	17.9129	+	37.1966i	0.836105	+	1.73619i
$460$		0			0
$461$	−1.94340	+	17.2482i	−0.0905133	+	0.803328i	0.863660	+	0.504074i	$0.168166\pi$
$461$	−1.94340	+	17.2482i	−0.0905133	+	0.803328i	−0.954174	+	0.299254i	$0.903262\pi$
$462$	−0.741109	−	1.53893i	−0.0344795	−	0.0715975i
$463$	10.1426	+	10.1426i	0.471365	+	0.471365i	0.902356	−	0.430991i	$-0.141836\pi$
$463$	10.1426	+	10.1426i	0.471365	+	0.471365i	−0.430991	+	0.902356i	$0.641836\pi$
$464$	6.15570	−	1.37871i	0.285771	−	0.0640051i
$465$		0			0
$466$	7.62368	−	21.7872i	0.353160	−	1.00927i
$467$	3.38662	+	4.24669i	0.156714	+	0.196513i	0.853990	−	0.520290i	$-0.174176\pi$
$467$	3.38662	+	4.24669i	0.156714	+	0.196513i	−0.697276	+	0.716803i	$0.745605\pi$
$468$	2.31545	−	0.260889i	0.107032	−	0.0120596i
$469$	−21.7202	+	10.4599i	−1.00295	+	0.482994i
$470$		0			0
$471$	18.0501	+	22.6341i	0.831705	+	1.04293i
$472$	19.2930	+	4.40349i	0.888031	+	0.202687i
$473$	−1.94405	+	1.22153i	−0.0893874	+	0.0561658i
$474$	0.355824	+	3.15803i	0.0163436	+	0.145053i
$475$		0			0
$476$	−16.1331	−	16.1331i	−0.739461	−	0.739461i
$477$	−3.47703	−	2.18476i	−0.159202	−	0.100033i
$478$	5.96427	−	12.3849i	0.272799	−	0.566473i
$479$	7.85928	−	2.75008i	0.359100	−	0.125654i	−0.144698	−	0.989476i	$-0.546221\pi$
$479$	7.85928	−	2.75008i	0.359100	−	0.125654i	0.503798	+	0.863821i	$0.331936\pi$
$480$		0			0
$481$	22.3799	−	22.3799i	1.02044	−	1.02044i
$482$	7.53690	−	1.72025i	0.343297	−	0.0783552i
$483$	15.9257	+	12.7003i	0.724646	+	0.577886i
$484$	10.1560	+	2.31804i	0.461635	+	0.105365i
$485$		0			0
$486$	−4.60066	+	3.66890i	−0.208690	+	0.166425i
$487$	−6.34097	−	18.1215i	−0.287337	−	0.821161i	−0.993574	−	0.113186i	$-0.963894\pi$
$487$	−6.34097	−	18.1215i	−0.287337	−	0.821161i	0.706237	−	0.707975i	$-0.250391\pi$
$488$	−6.98478	+	19.9613i	−0.316186	+	0.903608i
$489$	2.40576	+	1.91853i	0.108792	+	0.0867588i
$490$		0			0
$491$	9.42610	+	3.29834i	0.425394	+	0.148852i	0.534481	−	0.845180i	$-0.320507\pi$
$491$	9.42610	+	3.29834i	0.425394	+	0.148852i	−0.109087	+	0.994032i	$0.534793\pi$
$492$	−2.55393	+	2.55393i	−0.115140	+	0.115140i
$493$	0.162399	−	39.9732i	0.00731406	−	1.80030i
$494$		−	24.1542i		−	1.08675i
$495$		0			0
$496$	2.52586	+	0.284596i	0.113415	+	0.0127787i
$497$	−1.17748	−	10.4504i	−0.0528172	−	0.468766i
$498$	−11.4828	−	4.01799i	−0.514555	−	0.180050i
$499$	−6.72572	−	3.23894i	−0.301085	−	0.144995i	0.277242	−	0.960800i	$-0.410580\pi$
$499$	−6.72572	−	3.23894i	−0.301085	−	0.144995i	−0.578326	+	0.815805i	$0.696294\pi$
$500$		0			0
$501$	−12.8560	+	8.07795i	−0.574363	+	0.360896i
$502$	−12.1634	−	19.3579i	−0.542879	−	0.863987i
$503$	23.7256	−	29.7509i	1.05787	−	1.32653i	0.115001	−	0.993365i	$-0.463313\pi$
$503$	23.7256	−	29.7509i	1.05787	−	1.32653i	0.942869	−	0.333163i	$-0.108116\pi$
$504$	2.90266	−	4.61956i	0.129295	−	0.205771i
$505$		0			0
$506$	−1.34802	+	0.307677i	−0.0599268	+	0.0136779i
$507$	−8.10752	−	3.90438i	−0.360068	−	0.173399i
$508$	4.65645	+	2.24243i	0.206597	+	0.0994917i
$509$	−17.5133	+	3.99729i	−0.776263	+	0.177177i	−0.592258	−	0.805748i	$-0.701763\pi$
$509$	−17.5133	+	3.99729i	−0.776263	+	0.177177i	−0.184005	+	0.982925i	$0.558906\pi$
$510$		0			0
$511$	−7.22399	+	11.4969i	−0.319570	+	0.508593i
$512$	7.94898	−	9.96771i	0.351299	−	0.440515i
$513$	−16.1542	−	25.7093i	−0.713225	−	1.13509i
$514$	−14.4927	+	9.10634i	−0.639244	+	0.401663i
$515$		0			0
$516$	9.26870	+	4.46357i	0.408032	+	0.196498i
$517$	−3.05817	−	1.07010i	−0.134498	−	0.0470630i
$518$	−2.68472	−	23.8275i	−0.117960	−	1.04692i
$519$	1.23640	+	0.139309i	0.0542719	+	0.00611498i
$520$		0			0
$521$		−	15.7501i		−	0.690024i	−0.938598	−	0.345012i	$-0.887875\pi$
$521$		−	15.7501i		−	0.690024i	0.938598	−	0.345012i	$-0.112125\pi$
$522$	3.01808	−	0.675969i	0.132098	−	0.0295864i
$523$	8.21538	−	8.21538i	0.359233	−	0.359233i	−0.504297	−	0.863530i	$-0.668248\pi$
$523$	8.21538	−	8.21538i	0.359233	−	0.359233i	0.863530	+	0.504297i	$0.168248\pi$
$524$	−7.95111	−	2.78221i	−0.347346	−	0.121542i
$525$		0			0
$526$	7.28104	+	5.80644i	0.317468	+	0.253173i
$527$	5.31982	−	15.2032i	0.231735	−	0.662260i
$528$	−0.201370	−	0.575482i	−0.00876350	−	0.0250446i
$529$	−5.09030	+	4.05938i	−0.221318	+	0.176495i
$530$		0			0
$531$	3.59201	+	0.819853i	0.155880	+	0.0355786i
$532$	13.1190	+	10.4621i	0.568781	+	0.453588i
$533$	−10.2116	+	2.33073i	−0.442314	+	0.100955i
$534$	11.6070	−	11.6070i	0.502285	−	0.502285i
$535$		0			0
$536$	−21.3891	+	7.48437i	−0.923869	+	0.323276i
$537$	−0.783422	+	1.62679i	−0.0338072	+	0.0702013i
$538$	−4.60230	−	2.89181i	−0.198419	−	0.124675i
$539$	0.783199	+	0.783199i	0.0337348	+	0.0337348i
$540$		0			0
$541$	3.67537	+	32.6198i	0.158016	+	1.40243i	0.783109	+	0.621884i	$0.213633\pi$
$541$	3.67537	+	32.6198i	0.158016	+	1.40243i	−0.625093	+	0.780551i	$0.714939\pi$
$542$	1.16429	−	0.731573i	0.0500106	−	0.0314238i
$543$	−20.8325	−	4.75488i	−0.894009	−	0.204052i
$544$	−22.4166	−	28.1095i	−0.961103	−	1.20518i
$545$		0			0
$546$	−19.9968	+	9.62997i	−0.855786	+	0.412125i
$547$	−9.99406	+	1.12606i	−0.427315	+	0.0481468i	−0.323003	−	0.946398i	$-0.604693\pi$
$547$	−9.99406	+	1.12606i	−0.427315	+	0.0481468i	−0.104312	+	0.994545i	$0.533264\pi$
$548$	3.63186	+	4.55421i	0.155145	+	0.194546i
$549$	−1.30044	+	3.71645i	−0.0555015	+	0.158614i
$550$		0			0
$551$	3.17289	+	29.2269i	0.135169	+	1.24511i
$552$	13.5391	+	13.5391i	0.576264	+	0.576264i
$553$	−2.77793	−	5.76843i	−0.118130	−	0.245299i
$554$	2.55394	−	22.6669i	0.108507	−	0.963023i
$555$		0			0
$556$	7.77967	+	16.1547i	0.329931	+	0.685110i
$557$	−35.6586	+	12.4775i	−1.51090	+	0.528688i	−0.953458	−	0.301525i	$-0.902504\pi$
$557$	−35.6586	+	12.4775i	−1.51090	+	0.528688i	−0.557446	+	0.830213i	$0.688219\pi$
$558$	1.23841	+	0.139535i	0.0524259	+	0.00590698i
$559$	15.8725	+	25.2609i	0.671335	+	1.06842i
$560$		0			0
$561$	−3.83920	+	0.432574i	−0.162091	+	0.0182633i
$562$	1.19127	+	5.21927i	0.0502505	+	0.220162i
$563$	0.0469315			0.00197793			0.000988963	−	1.00000i	$-0.499685\pi$
$563$	0.0469315			0.00197793			0.000988963		1.00000i	$0.499685\pi$
$564$	3.23042	+	14.1534i	0.136025	+	0.595965i
$565$		0			0
$566$	−8.74512	−	24.9921i	−0.367585	−	1.05050i
$567$	−11.9603	+	19.0348i	−0.502287	+	0.799386i
$568$		−	9.88536i		−	0.414781i
$569$	24.4344	+	15.3531i	1.02434	+	0.643637i	0.935835	−	0.352438i	$-0.114647\pi$
$569$	24.4344	+	15.3531i	1.02434	+	0.643637i	0.0885075	+	0.996076i	$0.471790\pi$
$570$		0			0
$571$	9.57895	−	41.9681i	0.400867	−	1.75631i	−0.223036	−	0.974810i	$-0.571597\pi$
$571$	9.57895	−	41.9681i	0.400867	−	1.75631i	0.623903	−	0.781502i	$-0.285546\pi$
$572$	−0.307403	+	1.34682i	−0.0128532	+	0.0563135i
$573$	2.51521	−	22.3231i	0.105074	−	0.932560i
$574$	−3.44303	+	7.14952i	−0.143709	+	0.298415i
$575$		0			0
$576$	2.55576	−	3.20482i	0.106490	−	0.133534i
$577$	−21.3823	+	17.0518i	−0.890155	+	0.709875i	−0.957678	−	0.287843i	$-0.907062\pi$
$577$	−21.3823	+	17.0518i	−0.890155	+	0.709875i	0.0675225	+	0.997718i	$0.478491\pi$
$578$	35.0621	−	16.8850i	1.45839	−	0.702324i
$579$	0.331810			0.0137895
$580$		0			0
$581$	24.5087			1.01679
$582$	−1.70757	+	0.822324i	−0.0707812	+	0.0340864i
$583$	1.90345	−	1.51795i	0.0788329	−	0.0628672i
$584$	−7.95770	+	9.97865i	−0.329292	+	0.412919i
$585$		0			0
$586$	−10.1613	+	21.1002i	−0.419761	+	0.871642i
$587$	−0.247035	+	2.19250i	−0.0101962	+	0.0904941i	−0.997780	−	0.0666013i	$-0.978784\pi$
$587$	−0.247035	+	2.19250i	−0.0101962	+	0.0904941i	0.987583	+	0.157095i	$0.0502130\pi$
$588$	1.10434	−	4.83842i	0.0455422	−	0.199533i
$589$	−2.63597	+	11.5489i	−0.108613	+	0.475866i
$590$		0			0
$591$	1.81155	+	1.13827i	0.0745173	+	0.0468223i
$592$		−	8.55900i		−	0.351773i
$593$	−0.841384	+	1.33905i	−0.0345515	+	0.0549884i	−0.863553	−	0.504257i	$-0.831766\pi$
$593$	−0.841384	+	1.33905i	−0.0345515	+	0.0549884i	0.829002	+	0.559246i	$0.188909\pi$
$594$	−0.625496	−	1.78756i	−0.0256644	−	0.0733446i
$595$		0			0
$596$	4.10900	+	18.0027i	0.168311	+	0.737419i
$597$	−33.1864			−1.35823
$598$	3.99795	+	17.5162i	0.163488	+	0.716289i
$599$	−25.1241	+	2.83081i	−1.02654	+	0.115664i	−0.609144	−	0.793060i	$-0.708487\pi$
$599$	−25.1241	+	2.83081i	−1.02654	+	0.115664i	−0.417399	+	0.908723i	$0.637058\pi$
$600$		0			0
$601$	−14.9382	−	23.7740i	−0.609342	−	0.969762i	−0.998812	−	0.0487229i	$-0.984485\pi$
$601$	−14.9382	−	23.7740i	−0.609342	−	0.969762i	0.389471	−	0.921039i	$-0.372658\pi$
$602$	22.4602	+	2.53066i	0.915409	+	0.103142i
$603$	−3.98227	+	1.39346i	−0.162171	+	0.0567460i
$604$	−7.26068	−	15.0769i	−0.295433	−	0.613472i
$605$		0			0
$606$	−1.63146	+	14.4796i	−0.0662735	+	0.588194i
$607$	−14.6311	−	30.3818i	−0.593859	−	1.23316i	−0.953872	−	0.300213i	$-0.902942\pi$
$607$	−14.6311	−	30.3818i	−0.593859	−	1.23316i	0.360013	−	0.932947i	$-0.382772\pi$
$608$	18.6973	+	18.6973i	0.758276	+	0.758276i
$609$	22.9314	−	14.2791i	0.929227	−	0.578620i
$610$		0			0
$611$	−13.9049	+	39.7378i	−0.562531	+	1.60762i
$612$	−2.48955	−	3.12180i	−0.100634	−	0.126191i
$613$	36.8524	−	4.15227i	1.48846	−	0.167709i	0.670036	−	0.742329i	$-0.266279\pi$
$613$	36.8524	−	4.15227i	1.48846	−	0.167709i	0.818420	+	0.574620i	$0.194850\pi$
$614$	29.2242	−	14.0736i	1.17939	−	0.567966i
$615$		0			0
$616$	2.01674	+	2.52892i	0.0812569	+	0.101893i
$617$	23.6532	+	5.39870i	0.952243	+	0.217343i	0.670302	−	0.742088i	$-0.266165\pi$
$617$	23.6532	+	5.39870i	0.952243	+	0.217343i	0.281941	+	0.959432i	$0.409022\pi$
$618$	14.2675	−	8.96488i	0.573924	−	0.360621i
$619$	−4.24442	−	37.6702i	−0.170598	−	1.51410i	−0.728994	−	0.684521i	$-0.760012\pi$
$619$	−4.24442	−	37.6702i	−0.170598	−	1.51410i	0.558396	−	0.829574i	$-0.311417\pi$
$620$		0			0
$621$	15.9700	+	15.9700i	0.640855	+	0.640855i
$622$	−1.93583	−	1.21636i	−0.0776195	−	0.0487716i
$623$	−14.3483	+	29.7946i	−0.574854	+	1.19370i
$624$	−7.47781	+	2.61660i	−0.299352	+	0.104748i
$625$		0			0
$626$	7.73273	−	7.73273i	0.309062	−	0.309062i
$627$	2.77017	−	0.632273i	0.110630	−	0.0252506i
$628$	−13.8688	−	11.0600i	−0.553424	−	0.441341i
$629$	−52.8765	−	12.0687i	−2.10832	−	0.481211i
$630$		0			0
$631$	15.9303	−	12.7040i	0.634175	−	0.505737i	−0.252822	−	0.967513i	$-0.581359\pi$
$631$	15.9303	−	12.7040i	0.634175	−	0.505737i	0.886997	+	0.461775i	$0.152787\pi$
$632$	−1.98769	−	5.68049i	−0.0790661	−	0.225958i
$633$	0.0250127	−	0.0714821i	0.000994164	−	0.00284116i
$634$	17.8405	+	14.2273i	0.708536	+	0.565038i
$635$		0			0
$636$	−10.2965	−	3.60291i	−0.408284	−	0.142865i
$637$	10.1769	−	10.1769i	0.403223	−	0.403223i
$638$	−0.212707	+	1.82130i	−0.00842117	+	0.0721058i
$639$		−	1.84048i		−	0.0728083i
$640$		0			0
$641$	−20.0334	−	2.25723i	−0.791273	−	0.0891550i	−0.292929	−	0.956134i	$-0.594630\pi$
$641$	−20.0334	−	2.25723i	−0.791273	−	0.0891550i	−0.498344	+	0.866979i	$0.666058\pi$
$642$	1.55526	+	13.8033i	0.0613813	+	0.544775i
$643$	−41.5577	−	14.5417i	−1.63887	−	0.573467i	−0.655522	−	0.755176i	$-0.727551\pi$
$643$	−41.5577	−	14.5417i	−1.63887	−	0.573467i	−0.983352	+	0.181709i	$0.941837\pi$
$644$	−11.2453	−	5.41544i	−0.443126	−	0.213398i
$645$		0			0
$646$	−35.0471	+	22.0216i	−1.37891	+	0.866426i
$647$	−21.7375	−	34.5951i	−0.854591	−	1.36007i	−0.931767	−	0.363056i	$-0.881733\pi$
$647$	−21.7375	−	34.5951i	−0.854591	−	1.36007i	0.0771768	−	0.997017i	$-0.475409\pi$
$648$	−13.1751	+	16.5211i	−0.517568	+	0.649010i
$649$	−1.16216	+	1.84957i	−0.0456187	+	0.0726018i
$650$		0			0
$651$	10.6121	−	2.42214i	0.415920	−	0.0949310i
$652$	−1.69872	−	0.818062i	−0.0665271	−	0.0320378i
$653$	−38.3770	−	18.4814i	−1.50181	−	0.723233i	−0.511137	−	0.859499i	$-0.670776\pi$
$653$	−38.3770	−	18.4814i	−1.50181	−	0.723233i	−0.990672	+	0.136266i	$0.956490\pi$
$654$	8.74456	−	1.99589i	0.341939	−	0.0780454i
$655$		0			0
$656$	−1.50699	+	2.39836i	−0.0588379	+	0.0936401i
$657$	−1.48158	+	1.85785i	−0.0578021	+	0.0724815i
$658$	16.9695	+	27.0068i	0.661540	+	1.05284i
$659$	−29.0653	+	18.2629i	−1.13222	+	0.711423i	−0.961747	−	0.273939i	$-0.911673\pi$
$659$	−29.0653	+	18.2629i	−1.13222	+	0.711423i	−0.170476	+	0.985362i	$0.554530\pi$
$660$		0			0
$661$	−42.5571	−	20.4944i	−1.65528	−	0.797141i	−0.999095	−	0.0425427i	$-0.986454\pi$
$661$	−42.5571	−	20.4944i	−1.65528	−	0.797141i	−0.656187	−	0.754599i	$-0.727832\pi$
$662$	−11.9693	−	4.18823i	−0.465199	−	0.162780i
$663$	5.62086	+	49.8865i	0.218296	+	1.93743i
$664$	22.8929	+	2.57941i	0.888417	+	0.100100i
$665$		0			0
$666$		−	4.19640i		−	0.162607i
$667$	−7.13847	−	20.6696i	−0.276403	−	0.800329i
$668$	6.57844	−	6.57844i	0.254528	−	0.254528i
$669$	18.1679	+	6.35722i	0.702411	+	0.245784i
$670$		0			0
$671$	−1.82510	−	1.45547i	−0.0704571	−	0.0561877i
$672$	8.02478	−	22.9335i	0.309563	−	0.884679i
$673$	−12.1061	−	34.5971i	−0.466654	−	1.33362i	−0.901368	−	0.433053i	$-0.857436\pi$
$673$	−12.1061	−	34.5971i	−0.466654	−	1.33362i	0.434714	−	0.900569i	$-0.356849\pi$
$674$	−1.13753	+	0.907149i	−0.0438160	+	0.0349421i
$675$		0			0
$676$	5.37558	+	1.22694i	0.206753	+	0.0471900i
$677$	21.1078	+	16.8329i	0.811240	+	0.646942i	0.938636	−	0.344910i	$-0.112090\pi$
$677$	21.1078	+	16.8329i	0.811240	+	0.646942i	−0.127396	+	0.991852i	$0.540662\pi$
$678$	−0.363475	+	0.0829607i	−0.0139592	+	0.00318609i
$679$	2.69990	−	2.69990i	0.103613	−	0.103613i
$680$		0			0
$681$	−15.0429	+	5.26374i	−0.576445	+	0.201707i
$682$	−0.320581	+	0.665694i	−0.0122757	+	0.0254908i
$683$	−9.70047	−	6.09521i	−0.371178	−	0.233227i	0.333506	−	0.942748i	$-0.391768\pi$
$683$	−9.70047	−	6.09521i	−0.371178	−	0.233227i	−0.704684	+	0.709521i	$0.748911\pi$
$684$	2.07649	+	2.07649i	0.0793967	+	0.0793967i
$685$		0			0
$686$	1.35123	+	11.9925i	0.0515901	+	0.457875i
$687$	−27.4973	+	17.2777i	−1.04909	+	0.659185i
$688$	7.86556	+	1.79526i	0.299872	+	0.0684438i
$689$	−19.7243	−	24.7334i	−0.751434	−	0.942269i
$690$		0			0
$691$	−15.3535	+	7.39386i	−0.584075	+	0.281276i	−0.702496	−	0.711688i	$-0.747931\pi$
$691$	−15.3535	+	7.39386i	−0.584075	+	0.281276i	0.118421	+	0.992964i	$0.462217\pi$
$692$	−0.757588	+	0.0853597i	−0.0287992	+	0.00324489i
$693$	0.375482	+	0.470839i	0.0142634	+	0.0178857i
$694$	6.89799	−	19.7133i	0.261844	−	0.748308i
$695$		0			0
$696$	22.9224	−	10.9243i	0.868870	−	0.414085i
$697$	12.6918	+	12.6918i	0.480736	+	0.480736i
$698$	12.4958	+	25.9479i	0.472974	+	0.982141i
$699$	3.95046	−	35.0613i	0.149420	−	1.32614i
$700$		0			0
$701$	−9.35305	−	19.4218i	−0.353260	−	0.733552i	0.646304	−	0.763080i	$-0.276314\pi$
$701$	−9.35305	−	19.4218i	−0.353260	−	0.733552i	−0.999564	+	0.0295282i	$0.990600\pi$
$702$	−23.2276	+	8.12768i	−0.876669	+	0.306760i
$703$	39.6373	+	4.46605i	1.49495	+	0.168440i
$704$	1.29298	+	2.05776i	0.0487309	+	0.0775548i
$705$		0			0
$706$	−5.73731	+	0.646440i	−0.215927	+	0.0243291i
$707$	−6.53221	−	28.6195i	−0.245669	−	1.07635i
$708$	9.78750			0.367837
$709$	5.43528	+	23.8135i	0.204126	+	0.894336i	0.968392	+	0.249434i	$0.0802445\pi$
$709$	5.43528	+	23.8135i	0.204126	+	0.894336i	−0.764266	+	0.644902i	$0.776898\pi$
$710$		0			0
$711$	−0.370073	−	1.05761i	−0.0138788	−	0.0396634i
$712$	−16.5381	+	26.3202i	−0.619791	+	0.986392i
$713$		−	8.81135i		−	0.329988i
$714$	32.2040	+	20.2351i	1.20521	+	0.757281i
$715$		0			0
$716$	0.246189	−	1.07862i	0.00920050	−	0.0403100i
$717$	4.67560	−	20.4852i	0.174614	−	0.765032i
$718$	0.0871351	−	0.773345i	0.00325185	−	0.0288610i
$719$	−12.1135	+	25.1540i	−0.451758	+	0.938086i	0.543369	+	0.839494i	$0.317148\pi$
$719$	−12.1135	+	25.1540i	−0.451758	+	0.938086i	−0.995128	+	0.0985924i	$0.968566\pi$
$720$		0			0
$721$	−21.1655	+	26.5407i	−0.788245	+	0.988428i
$722$	8.62687	−	6.87970i	0.321059	−	0.256036i
$723$	10.6467	−	5.12716i	0.395954	−	0.190681i
$724$	13.0931			0.486602
$725$		0			0
$726$	−17.3654			−0.644489
$727$	3.96162	−	1.90781i	0.146928	−	0.0707569i	−0.358975	−	0.933347i	$-0.616874\pi$
$727$	3.96162	−	1.90781i	0.146928	−	0.0707569i	0.505903	+	0.862590i	$0.331159\pi$
$728$	32.8607	−	26.2055i	1.21790	−	0.971242i
$729$	−18.6958	+	23.4438i	−0.692438	+	0.868290i
$730$		0			0
$731$	22.1818	−	46.0611i	0.820425	−	1.70363i
$732$	−1.17111	+	10.3939i	−0.0432854	+	0.384169i
$733$	−5.79725	+	25.3994i	−0.214126	+	0.938149i	0.747603	+	0.664146i	$0.231205\pi$
$733$	−5.79725	+	25.3994i	−0.214126	+	0.938149i	−0.961729	+	0.274003i	$0.911652\pi$
$734$	−0.543629	+	2.38179i	−0.0200657	+	0.0879136i
$735$		0			0
$736$	−16.6536	−	10.4642i	−0.613861	−	0.385714i
$737$		−	2.50136i		−	0.0921387i
$738$	−0.738861	+	1.17589i	−0.0271979	+	0.0432851i
$739$	−1.95496	−	5.58694i	−0.0719142	−	0.205519i	0.902316	−	0.431075i	$-0.141866\pi$
$739$	−1.95496	−	5.58694i	−0.0719142	−	0.205519i	−0.974230	+	0.225556i	$0.927580\pi$
$740$		0			0
$741$	−8.21575	−	35.9956i	−0.301813	−	1.32233i
$742$	−23.9672			−0.879863
$743$	1.56594	+	6.86085i	0.0574489	+	0.251700i	0.995495	−	0.0948090i	$-0.0302241\pi$
$743$	1.56594	+	6.86085i	0.0574489	+	0.251700i	−0.938047	+	0.346509i	$0.887367\pi$
$744$	10.1673	−	1.14558i	0.372753	−	0.0419992i
$745$		0			0
$746$	8.74433	+	13.9165i	0.320153	+	0.509520i
$747$	4.26225	+	0.480240i	0.155948	+	0.0175711i
$748$	2.23446	−	0.781872i	0.0817000	−	0.0285881i
$749$	−12.1420	−	25.2131i	−0.443659	−	0.921267i
$750$		0			0
$751$	5.32203	−	47.2343i	0.194203	−	1.72360i	−0.397632	−	0.917545i	$-0.630168\pi$
$751$	5.32203	−	47.2343i	0.194203	−	1.72360i	0.591836	−	0.806059i	$-0.298403\pi$
$752$	4.93980	+	10.2576i	0.180136	+	0.374056i
$753$	−24.7107	−	24.7107i	−0.900509	−	0.900509i
$754$	23.6659	+	2.76392i	0.861861	+	0.100656i
$755$		0			0
$756$	5.64626	−	16.1361i	0.205353	−	0.586864i
$757$	−11.4688	−	14.3815i	−0.416842	−	0.522704i	0.528434	−	0.848974i	$-0.322779\pi$
$757$	−11.4688	−	14.3815i	−0.416842	−	0.522704i	−0.945276	+	0.326271i	$0.894208\pi$
$758$	16.7561	−	1.88796i	0.608608	−	0.0685737i
$759$	−1.90422	+	0.917023i	−0.0691188	+	0.0332858i
$760$		0			0
$761$	−12.2089	−	15.3094i	−0.442571	−	0.554966i	0.509648	−	0.860383i	$-0.329776\pi$
$761$	−12.2089	−	15.3094i	−0.442571	−	0.554966i	−0.952219	+	0.305417i	$0.901204\pi$
$762$	−8.39947	−	1.91713i	−0.304281	−	0.0694501i
$763$	−15.3003	+	9.61382i	−0.553908	+	0.348044i
$764$	1.54116	+	13.6782i	0.0557573	+	0.494860i
$765$		0			0
$766$	−3.37599	−	3.37599i	−0.121979	−	0.121979i
$767$	24.0332	+	15.1011i	0.867790	+	0.545268i
$768$	11.4277	−	23.7298i	0.412361	−	0.856276i
$769$	−15.5886	+	5.45470i	−0.562141	+	0.196702i	−0.596366	−	0.802713i	$-0.703389\pi$
$769$	−15.5886	+	5.45470i	−0.562141	+	0.196702i	0.0342253	+	0.999414i	$0.489104\pi$
$770$		0			0
$771$	−18.5001	+	18.5001i	−0.666265	+	0.666265i
$772$	−0.198215	+	0.0452412i	−0.00713391	+	0.00162827i
$773$	16.0469	+	12.7969i	0.577166	+	0.460274i	0.868045	−	0.496486i	$-0.165376\pi$
$773$	16.0469	+	12.7969i	0.577166	+	0.460274i	−0.290879	+	0.956760i	$0.593948\pi$
$774$	3.85641	+	0.880201i	0.138616	+	0.0316382i
$775$		0			0
$776$	2.80605	−	2.23775i	0.100731	−	0.0803304i
$777$	−12.1055	−	34.5956i	−0.434283	−	1.24111i
$778$	−12.5549	+	35.8800i	−0.450117	+	1.28636i
$779$	−10.3206	−	8.23041i	−0.369774	−	0.294885i
$780$		0			0
$781$	1.02994	+	0.360392i	0.0368542	+	0.0128958i
$782$	21.7705	−	21.7705i	0.778511	−	0.778511i
$783$	27.0380	−	12.8857i	0.966258	−	0.460499i
$784$		−	3.89206i		−	0.139002i
$785$		0			0
$786$	13.9542	+	1.57226i	0.497729	+	0.0560806i
$787$	−3.84619	−	34.1359i	−0.137102	−	1.21681i	−0.854239	−	0.519880i	$-0.825977\pi$
$787$	−3.84619	−	34.1359i	−0.137102	−	1.21681i	0.717137	−	0.696932i	$-0.245452\pi$
$788$	−1.23738	−	0.432976i	−0.0440797	−	0.0154241i
$789$	12.8255	+	6.17642i	0.456599	+	0.219886i
$790$		0			0
$791$	0.635969	−	0.399606i	0.0226125	−	0.0142084i
$792$	0.301174	+	0.479315i	0.0107017	+	0.0170317i
$793$	−18.9123	+	23.7153i	−0.671596	+	0.842155i
$794$	−16.4387	+	26.1621i	−0.583388	+	0.928457i
$795$		0			0
$796$	19.8247	−	4.52486i	0.702668	−	0.160379i
$797$	12.4319	+	5.98688i	0.440360	+	0.212066i	0.640908	−	0.767618i	$-0.278558\pi$
$797$	12.4319	+	5.98688i	0.440360	+	0.212066i	−0.200548	+	0.979684i	$0.564272\pi$
$798$	−25.2018	−	12.1366i	−0.892135	−	0.429630i
$799$	70.3356	−	16.0536i	2.48829	−	0.567937i
$800$		0			0
$801$	−3.07910	+	4.90036i	−0.108795	+	0.173146i
$802$	−1.71713	+	2.15321i	−0.0606338	+	0.0760324i
$803$	−0.749545	−	1.19289i	−0.0264509	−	0.0420963i
$804$	−9.48990	+	5.96290i	−0.334683	+	0.210295i
$805$		0			0
$806$	8.65002	+	4.16563i	0.304684	+	0.146728i
$807$	−7.84213	−	2.74408i	−0.276056	−	0.0965962i
$808$	−3.08950	−	27.4201i	−0.108688	−	0.964636i
$809$	19.1241	+	2.15477i	0.672367	+	0.0757576i	0.441546	−	0.897239i	$-0.354430\pi$
$809$	19.1241	+	2.15477i	0.672367	+	0.0757576i	0.230821	+	0.972996i	$0.425859\pi$
$810$		0			0
$811$			46.6872i			1.63941i	0.572787	+	0.819704i	$0.305862\pi$
$811$			46.6872i			1.63941i	−0.572787	+	0.819704i	$0.694138\pi$
$812$	−11.7517	+	11.6566i	−0.412405	+	0.409067i
$813$	1.48624	−	1.48624i	0.0521246	−	0.0521246i
$814$	2.34832	+	0.821714i	0.0823087	+	0.0288010i
$815$		0			0
$816$	10.6142	+	8.46452i	0.371570	+	0.296317i
$817$	−12.4182	+	35.4892i	−0.434458	+	1.24161i
$818$	−5.85599	−	16.7355i	−0.204750	−	0.585142i
$819$	6.11808	−	4.87901i	0.213783	−	0.170486i
$820$		0			0
$821$	−8.38107	−	1.91292i	−0.292501	−	0.0667615i	0.0737522	−	0.997277i	$-0.476503\pi$
$821$	−8.38107	−	1.91292i	−0.292501	−	0.0667615i	−0.366254	+	0.930515i	$0.619360\pi$
$822$	−7.59185	−	6.05430i	−0.264796	−	0.211168i
$823$	−16.7204	+	3.81633i	−0.582838	+	0.133029i	−0.503766	−	0.863840i	$-0.668053\pi$
$823$	−16.7204	+	3.81633i	−0.582838	+	0.133029i	−0.0790717	+	0.996869i	$0.525196\pi$
$824$	−22.5634	+	22.5634i	−0.786033	+	0.786033i
$825$		0			0
$826$	20.2971	−	7.10227i	0.706227	−	0.247119i
$827$	−11.2519	+	23.3648i	−0.391267	+	0.812474i	0.608553	+	0.793513i	$0.291750\pi$
$827$	−11.2519	+	23.3648i	−0.391267	+	0.812474i	−0.999820	+	0.0189613i	$0.993964\pi$
$828$	−1.84953	−	1.16213i	−0.0642755	−	0.0403870i
$829$	−8.01072	−	8.01072i	−0.278224	−	0.278224i	0.554176	−	0.832400i	$-0.313034\pi$
$829$	−8.01072	−	8.01072i	−0.278224	−	0.278224i	−0.832400	+	0.554176i	$0.813034\pi$
$830$		0			0
$831$	−3.90386	−	34.6477i	−0.135423	−	1.20192i
$832$	26.7385	−	16.8009i	0.926992	−	0.582468i
$833$	−24.0447	−	5.48804i	−0.833099	−	0.190149i
$834$	−18.6359	−	23.3687i	−0.645310	−	0.809193i
$835$		0			0
$836$	−1.56862	+	0.755409i	−0.0542519	+	0.0261264i
$837$	11.9928	−	1.35127i	0.414533	−	0.0467067i
$838$	−4.35849	−	5.46538i	−0.150562	−	0.188798i
$839$	−1.26460	+	3.61402i	−0.0436588	+	0.124770i	−0.963649	−	0.267172i	$-0.913911\pi$
$839$	−1.26460	+	3.61402i	−0.0436588	+	0.124770i	0.919990	+	0.391942i	$0.128197\pi$
$840$		0			0
$841$	−28.9990	−	0.235632i	−0.999967	−	0.00812523i
$842$	6.37389	+	6.37389i	0.219659	+	0.219659i
$843$	3.55054	+	7.37277i	0.122287	+	0.253932i
$844$	−0.00519557	+	0.0461120i	−0.000178839	+	0.00158724i
$845$		0			0
$846$	2.42194	+	5.02920i	0.0832679	+	0.172908i
$847$	33.0214	−	11.5547i	1.13463	−	0.397023i
$848$	−8.50124	−	0.957859i	−0.291934	−	0.0328930i
$849$	−21.5331	−	34.2697i	−0.739013	−	1.17613i
$850$		0			0
$851$	−29.4834	+	3.32198i	−1.01068	+	0.113876i
$852$	−1.08795	−	4.76662i	−0.0372726	−	0.163302i
$853$	−39.2828			−1.34502			−0.672509	−	0.740089i	$-0.734783\pi$
$853$	−39.2828			−1.34502			−0.672509	+	0.740089i	$0.734783\pi$
$854$	5.11366	+	22.4044i	0.174986	+	0.766663i
$855$		0			0
$856$	−8.68794	−	24.8287i	−0.296948	−	0.848628i
$857$	−29.7994	+	47.4255i	−1.01793	+	1.62002i	−0.262341	+	0.964975i	$0.584495\pi$
$857$	−29.7994	+	47.4255i	−1.01793	+	1.62002i	−0.755587	+	0.655048i	$0.772648\pi$
$858$		−	2.30288i		−	0.0786192i
$859$	−3.31692	−	2.08416i	−0.113172	−	0.0711105i	0.474257	−	0.880387i	$-0.342717\pi$
$859$	−3.31692	−	2.08416i	−0.113172	−	0.0711105i	−0.587429	+	0.809276i	$0.699860\pi$
$860$		0			0
$861$	−2.69911	+	11.8256i	−0.0919856	+	0.403015i
$862$	3.66805	−	16.0708i	0.124934	−	0.547374i
$863$	3.91273	−	34.7264i	0.133191	−	1.18210i	−0.732231	−	0.681057i	$-0.761521\pi$
$863$	3.91273	−	34.7264i	0.133191	−	1.18210i	0.865421	−	0.501045i	$-0.167051\pi$
$864$	11.6885	−	24.2715i	0.397652	−	0.825732i
$865$		0			0
$866$	−2.60720	+	3.26933i	−0.0885963	+	0.111096i
$867$	46.5076	−	37.0886i	1.57948	−	1.25959i
$868$	−6.00913	+	2.89385i	−0.203963	+	0.0982235i
$869$	0.664307			0.0225351
$870$		0			0
$871$	−32.5026			−1.10131
$872$	−15.3034	+	7.36972i	−0.518238	+	0.249570i
$873$	0.522436	−	0.416629i	0.0176818	−	0.0141008i
$874$	−14.1178	+	17.7031i	−0.477541	+	0.598817i
$875$		0			0
$876$	−2.73891	+	5.68740i	−0.0925391	+	0.192159i
$877$	1.13966	−	10.1148i	0.0384837	−	0.341553i	−0.959686	−	0.281075i	$-0.909309\pi$
$877$	1.13966	−	10.1148i	0.0384837	−	0.341553i	0.998170	−	0.0604776i	$-0.0192624\pi$
$878$	4.34740	−	19.0472i	0.146718	−	0.642812i
$879$	−7.96583	+	34.9006i	−0.268681	+	1.17717i
$880$		0			0
$881$	−10.5567	−	6.63321i	−0.355664	−	0.223479i	0.342334	−	0.939578i	$-0.388783\pi$
$881$	−10.5567	−	6.63321i	−0.355664	−	0.223479i	−0.697998	+	0.716100i	$0.745925\pi$
$882$		−	1.90824i		−	0.0642538i
$883$	5.60565	−	8.92134i	0.188645	−	0.300227i	−0.738989	−	0.673718i	$-0.764696\pi$
$883$	5.60565	−	8.92134i	0.188645	−	0.300227i	0.927634	+	0.373491i	$0.121839\pi$
$884$	−10.1596	−	29.0346i	−0.341706	−	0.976538i
$885$		0			0
$886$	6.80600	+	29.8190i	0.228652	+	1.00179i
$887$	10.4690			0.351515			0.175758	−	0.984433i	$-0.443763\pi$
$887$	10.4690			0.351515			0.175758	+	0.984433i	$0.443763\pi$
$888$	−7.66641	−	33.5888i	−0.257268	−	1.12716i
$889$	17.2478	−	1.94336i	0.578472	−	0.0651781i
$890$		0			0
$891$	−1.24098	−	1.97501i	−0.0415744	−	0.0661652i
$892$	−11.7198	−	1.32051i	−0.392409	−	0.0442138i
$893$	−50.0812	+	17.5242i	−1.67590	+	0.586424i
$894$	−13.3559	−	27.7338i	−0.446688	−	0.927556i
$895$		0			0
$896$	−0.806054	+	7.15393i	−0.0269284	+	0.238996i
$897$	11.9158	+	24.7434i	0.397857	+	0.826158i
$898$	−0.300207	−	0.300207i	−0.0100180	−	0.0100180i
$899$	−11.0138	−	3.90420i	−0.367331	−	0.130212i
$900$		0			0
$901$	−17.9048	+	51.1689i	−0.596495	+	1.70468i
$902$	−0.513354	−	0.643726i	−0.0170928	−	0.0214337i
$903$	34.3318	−	3.86827i	1.14249	−	0.128728i
$904$	0.636097	−	0.306328i	0.0211563	−	0.0101883i
$905$		0			0
$906$	17.3927	+	21.8098i	0.577834	+	0.724581i
$907$	36.6334	+	8.36134i	1.21639	+	0.277634i	0.782109	−	0.623142i	$-0.214144\pi$
$907$	36.6334	+	8.36134i	1.21639	+	0.277634i	0.434284	+	0.900776i	$0.357001\pi$
$908$	8.26856	−	5.19548i	0.274402	−	0.172418i
$909$	−0.575211	−	5.10514i	−0.0190785	−	0.169327i
$910$		0			0
$911$	27.7673	+	27.7673i	0.919972	+	0.919972i	0.997027	−	0.0770545i	$-0.0245516\pi$
$911$	27.7673	+	27.7673i	0.919972	+	0.919972i	−0.0770545	+	0.997027i	$0.524552\pi$
$912$	−8.45412	−	5.31208i	−0.279944	−	0.175900i
$913$	−1.10335	+	2.29114i	−0.0365157	+	0.0758256i
$914$	27.1813	−	9.51116i	0.899079	−	0.314601i
$915$		0			0
$916$	14.0704	−	14.0704i	0.464900	−	0.464900i
$917$	−27.5810	+	6.29517i	−0.910803	+	0.207885i
$918$	32.9697	+	26.2925i	1.08816	+	0.867782i
$919$	26.5398	+	6.05753i	0.875466	+	0.199819i	0.636564	−	0.771224i	$-0.280355\pi$
$919$	26.5398	+	6.05753i	0.875466	+	0.199819i	0.238902	+	0.971044i	$0.423212\pi$
$920$		0			0
$921$	38.7641	−	30.9133i	1.27732	−	1.01863i
$922$	5.85561	+	16.7344i	0.192844	+	0.551118i
$923$	4.68293	−	13.3830i	0.154140	−	0.440508i
$924$	1.25078	+	0.997461i	0.0411475	+	0.0328141i
$925$		0			0
$926$	13.8290	+	4.83896i	0.454448	+	0.159018i
$927$	−4.20090	+	4.20090i	−0.137976	+	0.137976i
$928$	−20.4588	+	16.1798i	−0.671592	+	0.531128i
$929$		−	42.3538i		−	1.38958i	−0.719211	−	0.694792i	$-0.755496\pi$
$929$		−	42.3538i		−	1.38958i	0.719211	−	0.694792i	$-0.244504\pi$
$930$		0			0
$931$	18.0244	+	2.03086i	0.590726	+	0.0665588i
$932$	2.42059	+	21.4834i	0.0792891	+	0.703711i
$933$	−3.29857	−	1.15422i	−0.107990	−	0.0377875i
$934$	4.99869	+	2.40724i	0.163562	+	0.0787674i
$935$		0			0
$936$	6.22821	−	3.91345i	0.203576	−	0.127915i
$937$	−3.38468	−	5.38668i	−0.110573	−	0.175975i	0.786854	−	0.617139i	$-0.211709\pi$
$937$	−3.38468	−	5.38668i	−0.110573	−	0.175975i	−0.897426	+	0.441164i	$0.854566\pi$
$938$	−15.3530	+	19.2521i	−0.501293	+	0.628602i
$939$	8.89342	−	14.1538i	0.290226	−	0.461892i
$940$		0			0
$941$	43.5932	−	9.94986i	1.42110	−	0.324356i	0.558188	−	0.829715i	$-0.311497\pi$
$941$	43.5932	−	9.94986i	1.42110	−	0.324356i	0.862910	+	0.505358i	$0.168640\pi$
$942$	26.6421	+	12.8302i	0.868048	+	0.418030i
$943$	8.84657	+	4.26028i	0.288084	+	0.138734i
$944$	7.48330	−	1.70801i	0.243561	−	0.0555911i
$945$		0			0
$946$	−1.24770	+	1.98571i	−0.0405663	+	0.0645610i
$947$	−12.6098	+	15.8121i	−0.409762	+	0.513825i	−0.943296	−	0.331954i	$-0.892292\pi$
$947$	−12.6098	+	15.8121i	−0.409762	+	0.513825i	0.533534	+	0.845779i	$0.320864\pi$
$948$	−1.58362	−	2.52032i	−0.0514336	−	0.0818561i
$949$	−15.5004	+	9.73958i	−0.503166	+	0.316160i
$950$		0			0
$951$	31.4258	+	15.1339i	1.01905	+	0.490749i
$952$	−67.9828	−	23.7882i	−2.20333	−	0.770980i
$953$	4.17513	+	37.0553i	0.135246	+	1.20034i	0.859621	+	0.510933i	$0.170700\pi$
$953$	4.17513	+	37.0553i	0.135246	+	1.20034i	−0.724375	+	0.689406i	$0.757872\pi$
$954$	−4.16807	−	0.469629i	−0.134946	−	0.0152048i
$955$		0			0
$956$			12.8748i			0.416402i
$957$	0.302506	+	2.78651i	0.00977862	+	0.0900752i
$958$	6.01393	−	6.01393i	0.194301	−	0.194301i
$959$	18.4648	+	6.46113i	0.596261	+	0.208641i
$960$		0			0
$961$	20.5555	+	16.3925i	0.663081	+	0.528790i
$962$	10.6773	−	30.5141i	0.344251	−	0.983813i
$963$	−1.61754	−	4.62267i	−0.0521245	−	0.148963i
$964$	−5.66098	+	4.51448i	−0.182328	+	0.145402i
$965$		0			0
$966$	20.2847	+	4.62984i	0.652648	+	0.148963i
$967$	−29.4946	−	23.5211i	−0.948482	−	0.756389i	0.0214491	−	0.999770i	$-0.493172\pi$
$967$	−29.4946	−	23.5211i	−0.948482	−	0.756389i	−0.969931	+	0.243381i	$0.921743\pi$
$968$	32.0604	−	7.31757i	1.03046	−	0.235196i
$969$	−44.7382	+	44.7382i	−1.43720	+	1.43720i
$970$		0			0
$971$	−37.0487	+	12.9639i	−1.18895	+	0.416031i	−0.851016	−	0.525139i	$-0.824013\pi$
$971$	−37.0487	+	12.9639i	−1.18895	+	0.416031i	−0.337933	+	0.941170i	$0.609728\pi$
$972$	2.39132	−	4.96563i	0.0767017	−	0.159273i
$973$	50.9867	+	32.0371i	1.63456	+	1.02706i
$974$	−13.8666	−	13.8666i	−0.444313	−	0.444313i
$975$		0			0
$976$	0.918429	+	8.15128i	0.0293982	+	0.260916i
$977$	−16.5196	+	10.3799i	−0.528508	+	0.332083i	−0.769712	−	0.638391i	$-0.779600\pi$
$977$	−16.5196	+	10.3799i	−0.528508	+	0.332083i	0.241205	+	0.970474i	$0.422457\pi$
$978$	3.06422	+	0.699388i	0.0979829	+	0.0223640i
$979$	−2.13933	−	2.68264i	−0.0683734	−	0.0857375i
$980$		0			0
$981$	−2.84922	+	1.37211i	−0.0909686	+	0.0438081i
$982$	10.1364	−	1.14210i	0.323465	−	0.0364458i
$983$	−10.5042	−	13.1719i	−0.335033	−	0.420118i	0.585568	−	0.810624i	$-0.300872\pi$
$983$	−10.5042	−	13.1719i	−0.335033	−	0.420118i	−0.920601	+	0.390505i	$0.872300\pi$
$984$	−3.76574	+	10.7619i	−0.120048	+	0.343076i
$985$		0			0
$986$	−17.5660	−	36.8584i	−0.559414	−	1.17381i
$987$	34.4746	+	34.4746i	1.09734	+	1.09734i
$988$	9.81577	+	20.3827i	0.312281	+	0.648459i
$989$	3.13135	−	27.7915i	0.0995710	−	0.883717i
$990$		0			0
$991$	−1.37219	−	2.84939i	−0.0435892	−	0.0905139i	0.878037	−	0.478593i	$-0.158853\pi$
$991$	−1.37219	−	2.84939i	−0.0435892	−	0.0905139i	−0.921626	+	0.388079i	$0.873139\pi$
$992$	−9.92033	+	3.47128i	−0.314971	+	0.110213i
$993$	−19.2616	−	2.17026i	−0.611249	−	0.0688713i
$994$	−5.71505	−	9.09545i	−0.181270	−	0.288490i
$995$		0			0
$996$	11.3226	−	1.27575i	0.358770	−	0.0404237i
$997$	3.17575	+	13.9139i	0.100577	+	0.440657i	0.999994	+	0.00356433i	$0.00113456\pi$
$997$	3.17575	+	13.9139i	0.100577	+	0.440657i	−0.899417	+	0.437092i	$0.856008\pi$
$998$	−7.62497			−0.241364
$999$	−9.04288	−	39.6195i	−0.286104	−	1.25350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.y.b.282.9		156
5.2	odd	4		145.2.t.a.108.9	yes	156
5.3	odd	4		725.2.bd.b.543.5		156
5.4	even	2		145.2.o.a.137.5	yes	156
29.18	odd	28		725.2.bd.b.482.5		156
145.18	even	28	inner	725.2.y.b.18.9		156
145.47	even	28		145.2.o.a.18.5	✓	156
145.134	odd	28		145.2.t.a.47.9	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.5	✓	156	145.47	even	28
145.2.o.a.137.5	yes	156	5.4	even	2
145.2.t.a.47.9	yes	156	145.134	odd	28
145.2.t.a.108.9	yes	156	5.2	odd	4
725.2.y.b.18.9		156	145.18	even	28	inner
725.2.y.b.282.9		156	1.1	even	1	trivial
725.2.bd.b.482.5		156	29.18	odd	28
725.2.bd.b.543.5		156	5.3	odd	4

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.y (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.920277 - 0.443182i) q^{2} +(1.22069 - 0.973467i) q^{3} +(-0.596480 + 0.747962i) q^{4} +(0.691949 - 1.43685i) q^{6} +(-0.359728 + 3.19267i) q^{7} +(-0.672023 + 2.94432i) q^{8} +(-0.125119 + 0.548181i) q^{9} +(-0.282265 - 0.177359i) q^{11} +1.49368i q^{12} +(-2.30460 + 3.66774i) q^{13} +(1.08389 + 3.09757i) q^{14} +(0.260662 + 1.14204i) q^{16} +7.42290 q^{17} +(0.127800 + 0.559929i) q^{18} +(-5.42486 + 0.611234i) q^{19} +(2.66885 + 4.24744i) q^{21} +(-0.338364 - 0.0381244i) q^{22} +(3.83282 - 1.34116i) q^{23} +(2.04587 + 4.24830i) q^{24} +(-0.495389 + 4.39670i) q^{26} +(2.41320 + 5.01106i) q^{27} +(-2.17343 - 2.17343i) q^{28} +(0.0218780 - 5.38512i) q^{29} +(0.716676 - 2.04814i) q^{31} +(-3.01992 - 3.78686i) q^{32} +(-0.517210 + 0.0582756i) q^{33} +(6.83113 - 3.28970i) q^{34} +(-0.335388 - 0.420563i) q^{36} +(-7.12342 - 1.62587i) q^{37} +(-4.72148 + 2.96670i) q^{38} +(0.757232 + 6.72062i) q^{39} +(1.70982 + 1.70982i) q^{41} +(4.33847 + 2.72604i) q^{42} +(2.98830 - 6.20526i) q^{43} +(0.301023 - 0.105332i) q^{44} +(2.93288 - 2.93288i) q^{46} +(9.47549 - 2.16272i) q^{47} +(1.42992 + 1.14032i) q^{48} +(-3.23926 - 0.739339i) q^{49} +(9.06106 - 7.22595i) q^{51} +(-1.36869 - 3.91149i) q^{52} +(-2.41210 + 6.89339i) q^{53} +(4.44163 + 3.54208i) q^{54} +(-9.15852 - 3.20470i) q^{56} +(-6.02705 + 6.02705i) q^{57} +(-2.36646 - 4.96550i) q^{58} -6.55260i q^{59} +(6.95855 + 0.784041i) q^{61} +(-0.248159 - 2.20248i) q^{62} +(-1.70515 - 0.596659i) q^{63} +(-6.56823 - 3.16309i) q^{64} +(-0.450150 + 0.282848i) q^{66} +(3.99208 + 6.35336i) q^{67} +(-4.42761 + 5.55205i) q^{68} +(3.37311 - 5.36827i) q^{69} +(-3.19119 + 0.728367i) q^{71} +(-1.52994 - 0.736780i) q^{72} +(3.80763 + 1.83366i) q^{73} +(-7.27608 + 1.66072i) q^{74} +(2.77864 - 4.42218i) q^{76} +(0.667786 - 0.837377i) q^{77} +(3.67532 + 5.84924i) q^{78} +(-1.68732 + 1.06021i) q^{79} +(6.30409 + 3.03589i) q^{81} +(2.33127 + 0.815745i) q^{82} +(-0.854097 - 7.58032i) q^{83} +(-4.76884 - 0.537319i) q^{84} -7.03492i q^{86} +(-5.21553 - 6.59486i) q^{87} +(0.711889 - 0.711889i) q^{88} +(9.71523 + 3.39950i) q^{89} +(-10.8809 - 8.67721i) q^{91} +(-1.28306 + 3.66678i) q^{92} +(-1.11896 - 3.19781i) q^{93} +(7.76160 - 6.18967i) q^{94} +(-7.37277 - 1.68279i) q^{96} +(-0.929141 - 0.740965i) q^{97} +(-3.30868 + 0.755184i) q^{98} +(0.132541 - 0.132541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 8 q^{2} + 14 q^{3} - 22 q^{4} - 28 q^{6} + 10 q^{7} - 4 q^{8} + 10 q^{9} - 20 q^{11} + 4 q^{14} - 34 q^{16} + 48 q^{17} + 94 q^{18} - 16 q^{21} + 6 q^{22} + 10 q^{23} + 56 q^{24} + 36 q^{26} + 56 q^{27}+ \cdots + 76 q^{99}+O(q^{100}) \) 156 * q + 8 * q^2 + 14 * q^3 - 22 * q^4 - 28 * q^6 + 10 * q^7 - 4 * q^8 + 10 * q^9 - 20 * q^11 + 4 * q^14 - 34 * q^16 + 48 * q^17 + 94 * q^18 - 16 * q^21 + 6 * q^22 + 10 * q^23 + 56 * q^24 + 36 * q^26 + 56 * q^27 - 8 * q^28 - 8 * q^31 - 28 * q^32 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 28 * q^37 - 92 * q^38 + 16 * q^39 - 22 * q^41 + 10 * q^42 + 42 * q^43 - 112 * q^44 + 4 * q^46 + 14 * q^47 - 154 * q^48 + 84 * q^49 - 28 * q^51 + 166 * q^52 - 14 * q^53 + 4 * q^56 - 12 * q^57 - 126 * q^58 - 46 * q^61 - 84 * q^62 - 38 * q^63 - 30 * q^64 - 48 * q^66 + 46 * q^67 + 44 * q^68 - 124 * q^69 - 28 * q^71 - 60 * q^72 - 130 * q^73 + 112 * q^74 - 48 * q^76 + 44 * q^77 + 210 * q^78 - 4 * q^79 + 58 * q^81 - 72 * q^82 - 46 * q^83 + 120 * q^84 + 144 * q^87 - 40 * q^88 + 46 * q^89 - 28 * q^91 + 14 * q^92 + 6 * q^93 - 84 * q^94 - 28 * q^96 - 154 * q^97 - 98 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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