LMFDB - Embedded newform 125.2.h.a.39.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			39.8
Character	$\chi$	$=$	125.39
Dual form			125.2.h.a.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.161861 + 1.28126i) q^{2} +(-1.71483 - 1.41863i) q^{3} +(0.321728 - 0.0826056i) q^{4} +(0.720344 + 2.11686i) q^{5} +(1.54008 - 2.42678i) q^{6} +(2.27945 + 0.740638i) q^{7} +(1.10874 + 2.80036i) q^{8} +(0.365988 + 1.91858i) q^{9} +O(q^{10})$	\(q+(0.161861 + 1.28126i) q^{2} +(-1.71483 - 1.41863i) q^{3} +(0.321728 - 0.0826056i) q^{4} +(0.720344 + 2.11686i) q^{5} +(1.54008 - 2.42678i) q^{6} +(2.27945 + 0.740638i) q^{7} +(1.10874 + 2.80036i) q^{8} +(0.365988 + 1.91858i) q^{9} +(-2.59566 + 1.26559i) q^{10} +(4.57197 - 0.577574i) q^{11} +(-0.668897 - 0.314759i) q^{12} +(-5.66906 + 1.08143i) q^{13} +(-0.579998 + 3.04046i) q^{14} +(1.76778 - 4.65197i) q^{15} +(-2.82639 + 1.55382i) q^{16} +(1.07959 - 4.20471i) q^{17} +(-2.39897 + 0.779471i) q^{18} +(-3.02560 - 3.65732i) q^{19} +(0.406619 + 0.621549i) q^{20} +(-2.85818 - 4.50378i) q^{21} +(1.48005 + 5.76442i) q^{22} +(-0.551231 - 0.587001i) q^{23} +(2.07138 - 6.37505i) q^{24} +(-3.96221 + 3.04974i) q^{25} +(-2.30320 - 7.08852i) q^{26} +(-1.12238 + 2.04161i) q^{27} +(0.794543 + 0.0499884i) q^{28} +(0.0122026 - 0.193954i) q^{29} +(6.24654 + 1.51202i) q^{30} +(0.935449 + 0.240183i) q^{31} +(1.09233 + 1.50346i) q^{32} +(-8.65953 - 5.49551i) q^{33} +(5.56208 + 0.702655i) q^{34} +(0.0741581 + 5.35880i) q^{35} +(0.276234 + 0.587027i) q^{36} +(-3.98946 - 7.25681i) q^{37} +(4.19627 - 4.46857i) q^{38} +(11.2556 + 6.18784i) q^{39} +(-5.12931 + 4.36428i) q^{40} +(0.442053 + 0.415115i) q^{41} +(5.30790 - 4.39107i) q^{42} +(6.60429 - 9.09003i) q^{43} +(1.42322 - 0.563492i) q^{44} +(-3.79773 + 2.15678i) q^{45} +(0.662880 - 0.801285i) q^{46} +(-1.47059 + 3.71428i) q^{47} +(7.05108 + 1.34507i) q^{48} +(-1.01577 - 0.738000i) q^{49} +(-4.54885 - 4.58300i) q^{50} +(-7.81625 + 5.67884i) q^{51} +(-1.73456 + 0.816222i) q^{52} +(-6.95421 + 4.41327i) q^{53} +(-2.79751 - 1.10761i) q^{54} +(4.51604 + 9.26218i) q^{55} +(0.453266 + 7.20446i) q^{56} +10.5639i q^{57} +(0.250482 - 0.0157590i) q^{58} +(2.33894 - 4.97049i) q^{59} +(0.184466 - 1.64270i) q^{60} +(-8.65640 + 8.12890i) q^{61} +(-0.156324 + 1.23743i) q^{62} +(-0.586720 + 4.64437i) q^{63} +(-6.45186 + 6.05870i) q^{64} +(-6.37291 - 11.2216i) q^{65} +(5.63955 - 11.9847i) q^{66} +(-1.08702 + 0.0683896i) q^{67} -1.44195i q^{68} +(0.112529 + 1.78860i) q^{69} +(-6.85403 + 0.962398i) q^{70} +(0.401350 + 0.158906i) q^{71} +(-4.96693 + 3.15211i) q^{72} +(13.2717 - 6.24516i) q^{73} +(8.65215 - 6.28615i) q^{74} +(11.1210 + 0.391136i) q^{75} +(-1.27554 - 0.926731i) q^{76} +(10.8494 + 2.06963i) q^{77} +(-6.10641 + 15.4230i) q^{78} +(0.594972 - 0.719197i) q^{79} +(-5.32519 - 4.86379i) q^{80} +(10.2690 - 4.06580i) q^{81} +(-0.460321 + 0.633577i) q^{82} +(-1.41326 + 1.16915i) q^{83} +(-1.29159 - 1.21289i) q^{84} +(9.67846 - 0.743500i) q^{85} +(12.7157 + 6.99052i) q^{86} +(-0.296076 + 0.315288i) q^{87} +(6.68655 + 12.1628i) q^{88} +(-1.00941 - 2.14511i) q^{89} +(-3.37811 - 4.51679i) q^{90} +(-13.7233 - 1.73365i) q^{91} +(-0.225836 - 0.143320i) q^{92} +(-1.26341 - 1.73893i) q^{93} +(-4.99700 - 1.28301i) q^{94} +(5.56258 - 9.03931i) q^{95} +(0.259698 - 4.12779i) q^{96} +(7.38421 + 0.464575i) q^{97} +(0.781159 - 1.42092i) q^{98} +(2.78141 + 8.56030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{50}\right)$

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 $

$2$	0.161861	+	1.28126i	0.114453	+	0.905991i	0.939886	+	0.341489i	$0.110931\pi$
$2$	0.161861	+	1.28126i	0.114453	+	0.905991i	−0.825432	+	0.564501i	$0.809069\pi$
$3$	−1.71483	−	1.41863i	−0.990059	−	0.819048i	−0.00656345	−	0.999978i	$-0.502089\pi$
$3$	−1.71483	−	1.41863i	−0.990059	−	0.819048i	−0.983496	+	0.180930i	$0.942089\pi$
$4$	0.321728	−	0.0826056i	0.160864	−	0.0413028i
$5$	0.720344	+	2.11686i	0.322147	+	0.946690i
$5$	0.720344	+	2.11686i	0.322147	+	0.946690i
$6$	1.54008	−	2.42678i	0.628735	−	0.990727i
$7$	2.27945	+	0.740638i	0.861551	+	0.279935i	0.706276	−	0.707936i	$-0.250374\pi$
$7$	2.27945	+	0.740638i	0.861551	+	0.279935i	0.155275	+	0.987871i	$0.450374\pi$
$8$	1.10874	+	2.80036i	0.391999	+	0.990078i
$9$	0.365988	+	1.91858i	0.121996	+	0.639526i
$10$	−2.59566	+	1.26559i	−0.820821	+	0.400214i
$11$	4.57197	−	0.577574i	1.37850	−	0.174145i	0.599102	−	0.800673i	$-0.295524\pi$
$11$	4.57197	−	0.577574i	1.37850	−	0.174145i	0.779399	+	0.626528i	$0.215524\pi$
$12$	−0.668897	−	0.314759i	−0.193094	−	0.0908631i
$13$	−5.66906	+	1.08143i	−1.57231	+	0.299935i	−0.898502	−	0.438969i	$-0.855344\pi$
$13$	−5.66906	+	1.08143i	−1.57231	+	0.299935i	−0.673811	+	0.738903i	$0.735344\pi$
$14$	−0.579998	+	3.04046i	−0.155011	+	0.812597i
$15$	1.76778	−	4.65197i	0.456439	−	1.20113i
$16$	−2.82639	+	1.55382i	−0.706597	+	0.388455i
$17$	1.07959	−	4.20471i	0.261838	−	1.01979i	−0.692586	−	0.721336i	$-0.743528\pi$
$17$	1.07959	−	4.20471i	0.261838	−	1.01979i	0.954423	−	0.298456i	$-0.0964715\pi$
$18$	−2.39897	+	0.779471i	−0.565442	+	0.183723i
$19$	−3.02560	−	3.65732i	−0.694120	−	0.839048i	0.299230	−	0.954181i	$-0.403270\pi$
$19$	−3.02560	−	3.65732i	−0.694120	−	0.839048i	−0.993350	+	0.115134i	$0.963270\pi$
$20$	0.406619	+	0.621549i	0.0909228	+	0.138983i
$21$	−2.85818	−	4.50378i	−0.623707	−	0.982804i
$22$	1.48005	+	5.76442i	0.315548	+	1.22898i
$23$	−0.551231	−	0.587001i	−0.114940	−	0.122398i	0.668925	−	0.743330i	$-0.266755\pi$
$23$	−0.551231	−	0.587001i	−0.114940	−	0.122398i	−0.783865	+	0.620931i	$0.786755\pi$
$24$	2.07138	−	6.37505i	0.422819	−	1.30130i
$25$	−3.96221	+	3.04974i	−0.792442	+	0.609947i
$26$	−2.30320	−	7.08852i	−0.451695	−	1.39017i
$27$	−1.12238	+	2.04161i	−0.216003	+	0.392908i
$28$	0.794543	+	0.0499884i	0.150155	+	0.00944693i
$29$	0.0122026	−	0.193954i	0.00226596	−	0.0360164i	−0.996731	−	0.0807885i	$-0.974256\pi$
$29$	0.0122026	−	0.193954i	0.00226596	−	0.0360164i	0.998997	+	0.0447721i	$0.0142562\pi$
$30$	6.24654	+	1.51202i	1.14046	+	0.276056i
$31$	0.935449	+	0.240183i	0.168012	+	0.0431381i	0.331759	−	0.943364i	$-0.392358\pi$
$31$	0.935449	+	0.240183i	0.168012	+	0.0431381i	−0.163747	+	0.986502i	$0.552358\pi$
$32$	1.09233	+	1.50346i	0.193098	+	0.265776i
$33$	−8.65953	−	5.49551i	−1.50743	−	0.956645i
$34$	5.56208	+	0.702655i	0.953890	+	0.120504i
$35$	0.0741581	+	5.35880i	0.0125350	+	0.905802i
$36$	0.276234	+	0.587027i	0.0460390	+	0.0978378i
$37$	−3.98946	−	7.25681i	−0.655864	−	1.19301i	−0.969877	−	0.243593i	$-0.921674\pi$
$37$	−3.98946	−	7.25681i	−0.655864	−	1.19301i	0.314014	−	0.949418i	$-0.398326\pi$
$38$	4.19627	−	4.46857i	0.680725	−	0.724898i
$39$	11.2556	+	6.18784i	1.80235	+	0.990848i
$40$	−5.12931	+	4.36428i	−0.811015	+	0.690053i
$41$	0.442053	+	0.415115i	0.0690370	+	0.0648301i	0.718298	−	0.695736i	$-0.244922\pi$
$41$	0.442053	+	0.415115i	0.0690370	+	0.0648301i	−0.649261	+	0.760566i	$0.724922\pi$
$42$	5.30790	−	4.39107i	0.819026	−	0.677557i
$43$	6.60429	−	9.09003i	1.00715	−	1.38622i	0.0863081	−	0.996268i	$-0.472493\pi$
$43$	6.60429	−	9.09003i	1.00715	−	1.38622i	0.920837	−	0.389948i	$-0.127507\pi$
$44$	1.42322	−	0.563492i	0.214558	−	0.0849497i
$45$	−3.79773	+	2.15678i	−0.566132	+	0.321514i
$46$	0.662880	−	0.801285i	0.0977364	−	0.118143i
$47$	−1.47059	+	3.71428i	−0.214507	+	0.541783i	−0.996693	−	0.0812622i	$-0.974105\pi$
$47$	−1.47059	+	3.71428i	−0.214507	+	0.541783i	0.782186	+	0.623046i	$0.214105\pi$
$48$	7.05108	+	1.34507i	1.01774	+	0.194144i
$49$	−1.01577	−	0.738000i	−0.145110	−	0.105429i
$50$	−4.54885	−	4.58300i	−0.643304	−	0.648135i
$51$	−7.81625	+	5.67884i	−1.09449	+	0.795196i
$52$	−1.73456	+	0.816222i	−0.240540	+	0.113190i
$53$	−6.95421	+	4.41327i	−0.955234	+	0.606210i	−0.919474	−	0.393151i	$-0.871385\pi$
$53$	−6.95421	+	4.41327i	−0.955234	+	0.606210i	−0.0357596	+	0.999360i	$0.511385\pi$
$54$	−2.79751	−	1.10761i	−0.380693	−	0.150727i
$55$	4.51604	+	9.26218i	0.608942	+	1.24891i
$56$	0.453266	+	7.20446i	0.0605703	+	0.962737i
$57$			10.5639i			1.39923i
$58$	0.250482	−	0.0157590i	0.0328899	−	0.00206926i
$59$	2.33894	−	4.97049i	0.304504	−	0.647103i	−0.692749	−	0.721179i	$-0.743601\pi$
$59$	2.33894	−	4.97049i	0.304504	−	0.647103i	0.997253	+	0.0740756i	$0.0236006\pi$
$60$	0.184466	−	1.64270i	0.0238144	−	0.212071i
$61$	−8.65640	+	8.12890i	−1.10834	+	1.04080i	−0.109434	+	0.993994i	$0.534904\pi$
$61$	−8.65640	+	8.12890i	−1.10834	+	1.04080i	−0.998904	+	0.0468051i	$0.985096\pi$
$62$	−0.156324	+	1.23743i	−0.0198532	+	0.157154i
$63$	−0.586720	+	4.64437i	−0.0739198	+	0.585135i
$64$	−6.45186	+	6.05870i	−0.806483	+	0.757338i
$65$	−6.37291	−	11.2216i	−0.790462	−	1.39187i
$66$	5.63955	−	11.9847i	0.694181	−	1.47521i
$67$	−1.08702	+	0.0683896i	−0.132801	+	0.00835511i	−0.129052	−	0.991638i	$-0.541193\pi$
$67$	−1.08702	+	0.0683896i	−0.132801	+	0.00835511i	−0.00374898	+	0.999993i	$0.501193\pi$
$68$		−	1.44195i		−	0.174862i
$69$	0.112529	+	1.78860i	0.0135469	+	0.215322i
$70$	−6.85403	+	0.962398i	−0.819213	+	0.115029i
$71$	0.401350	+	0.158906i	0.0476315	+	0.0188587i	0.391820	−	0.920042i	$-0.371846\pi$
$71$	0.401350	+	0.158906i	0.0476315	+	0.0188587i	−0.344188	+	0.938901i	$0.611846\pi$
$72$	−4.96693	+	3.15211i	−0.585358	+	0.371479i
$73$	13.2717	−	6.24516i	1.55333	−	0.730941i	0.558217	−	0.829695i	$-0.311486\pi$
$73$	13.2717	−	6.24516i	1.55333	−	0.730941i	0.995112	+	0.0987536i	$0.0314856\pi$
$74$	8.65215	−	6.28615i	1.00579	−	0.730750i
$75$	11.1210	+	0.391136i	1.28414	+	0.0451645i
$76$	−1.27554	−	0.926731i	−0.146314	−	0.106303i
$77$	10.8494	+	2.06963i	1.23640	+	0.235856i
$78$	−6.10641	+	15.4230i	−0.691414	+	1.74631i
$79$	0.594972	−	0.719197i	0.0669396	−	0.0809160i	−0.735981	−	0.677003i	$-0.763279\pi$
$79$	0.594972	−	0.719197i	0.0669396	−	0.0809160i	0.802920	+	0.596087i	$0.203279\pi$
$80$	−5.32519	−	4.86379i	−0.595375	−	0.543788i
$81$	10.2690	−	4.06580i	1.14100	−	0.451756i
$82$	−0.460321	+	0.633577i	−0.0508339	+	0.0699669i
$83$	−1.41326	+	1.16915i	−0.155125	+	0.128331i	−0.711749	−	0.702434i	$-0.752097\pi$
$83$	−1.41326	+	1.16915i	−0.155125	+	0.128331i	0.556624	+	0.830765i	$0.312097\pi$
$84$	−1.29159	−	1.21289i	−0.140924	−	0.132337i
$85$	9.67846	−	0.743500i	1.04978	−	0.0806439i
$86$	12.7157	+	6.99052i	1.37117	+	0.753807i
$87$	−0.296076	+	0.315288i	−0.0317426	+	0.0338025i
$88$	6.68655	+	12.1628i	0.712789	+	1.29656i
$89$	−1.00941	−	2.14511i	−0.106998	−	0.227381i	0.844157	−	0.536096i	$-0.180101\pi$
$89$	−1.00941	−	2.14511i	−0.106998	−	0.227381i	−0.951155	+	0.308714i	$0.900101\pi$
$90$	−3.37811	−	4.51679i	−0.356084	−	0.476112i
$91$	−13.7233	−	1.73365i	−1.43859	−	0.181736i
$92$	−0.225836	−	0.143320i	−0.0235450	−	0.0149421i
$93$	−1.26341	−	1.73893i	−0.131009	−	0.180319i
$94$	−4.99700	−	1.28301i	−0.515402	−	0.132333i
$95$	5.56258	−	9.03931i	0.570708	−	0.927414i
$96$	0.259698	−	4.12779i	0.0265053	−	0.421290i
$97$	7.38421	+	0.464575i	0.749753	+	0.0471705i	0.433069	−	0.901361i	$-0.357431\pi$
$97$	7.38421	+	0.464575i	0.749753	+	0.0471705i	0.316684	+	0.948531i	$0.397431\pi$
$98$	0.781159	−	1.42092i	0.0789090	−	0.143535i
$99$	2.78141	+	8.56030i	0.279542	+	0.860342i
$100$	−1.02283	+	1.30849i	−0.102283	+	0.130849i
$101$	−3.00233	+	9.24022i	−0.298743	+	0.919436i	0.683195	+	0.730236i	$0.260590\pi$
$101$	−3.00233	+	9.24022i	−0.298743	+	0.919436i	−0.981938	+	0.189201i	$0.939410\pi$
$102$	−8.54124	−	9.09549i	−0.845708	−	0.900588i
$103$	−1.69208	−	6.59022i	−0.166726	−	0.649353i	−0.995908	−	0.0903749i	$-0.971193\pi$
$103$	−1.69208	−	6.59022i	−0.166726	−	0.649353i	0.829182	−	0.558978i	$-0.188807\pi$
$104$	−9.31392	−	14.6764i	−0.913305	−	1.43914i
$105$	7.47500	−	9.29464i	0.729485	−	0.907064i
$106$	−6.78019	−	8.19584i	−0.658550	−	0.796050i
$107$	10.6456	−	3.45898i	1.02915	−	0.334392i	0.254697	−	0.967021i	$-0.418024\pi$
$107$	10.6456	−	3.45898i	1.02915	−	0.334392i	0.774455	+	0.632629i	$0.218024\pi$
$108$	−0.192454	+	0.749557i	−0.0185189	+	0.0721262i
$109$	−10.8208	+	5.94880i	−1.03645	+	0.569791i	−0.906709	−	0.421757i	$-0.861414\pi$
$109$	−10.8208	+	5.94880i	−1.03645	+	0.569791i	−0.129738	+	0.991548i	$0.541414\pi$
$110$	−11.1363	+	7.28542i	−1.06181	+	0.694638i
$111$	−3.45348	+	18.1038i	−0.327790	+	1.71834i
$112$	−7.59343	+	1.44852i	−0.717512	+	0.136873i
$113$	13.4749	+	6.34083i	1.26762	+	0.596495i	0.937677	−	0.347507i	$-0.112972\pi$
$113$	13.4749	+	6.34083i	1.26762	+	0.596495i	0.329939	+	0.944002i	$0.392972\pi$
$114$	−13.5352	+	1.70989i	−1.26768	+	0.160146i
$115$	0.845525	−	1.58972i	0.0788456	−	0.148242i
$116$	−0.0120958	−	0.0634085i	−0.00112307	−	0.00588733i
$117$	−4.14962	−	10.4807i	−0.383632	−	0.968944i
$118$	6.74710	+	2.19227i	0.621121	+	0.201814i
$119$	5.57503	−	8.78484i	0.511062	−	0.805305i
$120$	14.9872	−	0.207402i	1.36814	−	0.0189331i
$121$	9.91492	−	2.54572i	0.901356	−	0.231429i
$122$	−11.8164	−	9.77538i	−1.06981	−	0.885021i
$123$	−0.169150	−	1.33896i	−0.0152518	−	0.120730i
$124$	0.320800			0.0288087
$125$	−9.31002	−	6.19060i	−0.832714	−	0.553704i
$126$	−6.04563			−0.538587
$127$	0.195688	+	1.54903i	0.0173645	+	0.137454i	0.998414	−	0.0563052i	$-0.0179320\pi$
$127$	0.195688	+	1.54903i	0.0173645	+	0.137454i	−0.981049	+	0.193759i	$0.937932\pi$
$128$	−5.94330	−	4.91673i	−0.525319	−	0.434581i
$129$	−24.2207	+	6.21881i	−2.13251	+	0.547536i
$130$	13.3463	−	9.98172i	1.17055	−	0.875455i
$131$	−1.25967	+	1.98492i	−0.110058	+	0.173423i	−0.894892	−	0.446282i	$-0.852748\pi$
$131$	−1.25967	+	1.98492i	−0.110058	+	0.173423i	0.784835	+	0.619705i	$0.212748\pi$
$132$	−3.23997	−	1.05273i	−0.282003	−	0.0916285i
$133$	−4.18795	−	10.5776i	−0.363142	−	0.917191i
$134$	−0.263572	−	1.38169i	−0.0227691	−	0.119360i
$135$	−5.13031	−	0.905272i	−0.441546	−	0.0779134i
$136$	12.9717	−	1.63871i	1.11231	−	0.140518i
$137$	−6.73554	−	3.16951i	−0.575456	−	0.270789i	0.115950	−	0.993255i	$-0.463009\pi$
$137$	−6.73554	−	3.16951i	−0.575456	−	0.270789i	−0.691407	+	0.722466i	$0.743009\pi$
$138$	−2.27346	+	0.433685i	−0.193530	+	0.0369177i
$139$	−1.36337	+	7.14706i	−0.115640	+	0.606206i	0.876534	+	0.481340i	$0.159850\pi$
$139$	−1.36337	+	7.14706i	−0.115640	+	0.606206i	−0.992174	+	0.124865i	$0.960150\pi$
$140$	0.466526	+	1.71795i	0.0394286	+	0.145193i
$141$	7.79101	−	4.28315i	0.656122	−	0.360706i
$142$	−0.138637	+	0.539957i	−0.0116342	+	0.0453121i
$143$	−25.2942	+	8.21857i	−2.11520	+	0.687272i
$144$	−4.01555	−	4.85396i	−0.334629	−	0.404497i
$145$	0.419365	−	0.113883i	0.0348263	−	0.00945744i
$146$	10.1499	+	15.9936i	0.840009	+	1.32364i
$147$	0.694925	+	2.70655i	0.0573164	+	0.223233i
$148$	−1.88297	−	2.00516i	−0.154780	−	0.164823i
$149$	−6.51667	+	20.0563i	−0.533867	+	1.64307i	0.212219	+	0.977222i	$0.431931\pi$
$149$	−6.51667	+	20.0563i	−0.533867	+	1.64307i	−0.746085	+	0.665850i	$0.768069\pi$
$150$	1.29891	+	14.3122i	0.106055	+	1.16859i
$151$	−1.38145	−	4.25168i	−0.112421	−	0.345997i	0.878979	−	0.476860i	$-0.158225\pi$
$151$	−1.38145	−	4.25168i	−0.112421	−	0.345997i	−0.991400	+	0.130863i	$0.958225\pi$
$152$	6.88722	−	12.5278i	0.558627	−	1.01614i
$153$	8.46217	+	0.532395i	0.684126	+	0.0430416i
$154$	−0.895646	+	14.2359i	−0.0721732	+	1.14716i
$155$	0.165411	+	2.15323i	0.0132862	+	0.172952i
$156$	4.13240	+	1.06102i	0.330857	+	0.0849497i
$157$	2.95670	+	4.06955i	0.235971	+	0.324786i	0.910536	−	0.413429i	$-0.135669\pi$
$157$	2.95670	+	4.06955i	0.235971	+	0.324786i	−0.674566	+	0.738215i	$0.735669\pi$
$158$	1.01778	+	0.645906i	0.0809706	+	0.0513855i
$159$	18.1861	+	2.29744i	1.44225	+	0.182199i
$160$	−2.39576	+	3.39531i	−0.189402	+	0.268423i
$161$	−0.821747	−	1.74630i	−0.0647628	−	0.137628i
$162$	6.87152	+	12.4993i	0.539878	+	0.982034i
$163$	−3.40852	+	3.62971i	−0.266976	+	0.284301i	−0.848463	−	0.529255i	$-0.822471\pi$
$163$	−3.40852	+	3.62971i	−0.266976	+	0.284301i	0.581486	+	0.813556i	$0.302471\pi$
$164$	0.176511	+	0.0970380i	0.0137832	+	0.00757739i
$165$	5.39539	−	22.2897i	0.420031	−	1.73525i
$166$	−1.72674	−	1.62152i	−0.134021	−	0.125854i
$167$	−5.90320	+	4.88355i	−0.456803	+	0.377901i	−0.837177	−	0.546932i	$-0.815795\pi$
$167$	−5.90320	+	4.88355i	−0.456803	+	0.377901i	0.380373	+	0.924833i	$0.375795\pi$
$168$	9.44322	−	12.9975i	0.728560	−	1.00278i
$169$	18.8816	−	7.47577i	1.45243	−	0.575059i
$170$	2.51919	+	12.2803i	0.193213	+	0.941857i
$171$	5.90952	−	7.14339i	0.451913	−	0.546269i
$172$	1.37390	−	3.47007i	0.104759	−	0.264590i
$173$	1.31096	+	0.250079i	0.0996704	+	0.0190132i	0.236975	−	0.971516i	$-0.423844\pi$
$173$	1.31096	+	0.250079i	0.0996704	+	0.0190132i	−0.137305	+	0.990529i	$0.543844\pi$
$174$	−0.451891	−	0.328318i	−0.0342578	−	0.0248897i
$175$	−11.2904	+	4.01716i	−0.853475	+	0.303668i
$176$	−12.0247	+	8.73647i	−0.906397	+	0.658536i
$177$	−11.0622	+	5.20547i	−0.831485	+	0.391267i
$178$	2.58507	−	1.64053i	0.193759	−	0.122963i
$179$	13.7021	+	5.42503i	1.02414	+	0.405486i	0.819334	−	0.573317i	$-0.194344\pi$
$179$	13.7021	+	5.42503i	1.02414	+	0.405486i	0.204806	+	0.978803i	$0.434344\pi$
$180$	−1.04367	+	1.00761i	−0.0777907	+	0.0751028i
$181$	−0.0768556	−	1.22159i	−0.00571263	−	0.0907997i	0.994137	−	0.108125i	$-0.0344848\pi$
$181$	−0.0768556	−	1.22159i	−0.00571263	−	0.0907997i	−0.999850	+	0.0173257i	$0.994485\pi$
$182$		−	17.8638i		−	1.32415i
$183$	26.3762	−	1.65945i	1.94979	−	0.122670i
$184$	1.03264	−	2.19448i	0.0761274	−	0.161779i
$185$	12.4879	−	13.6725i	0.918127	−	1.00522i
$186$	2.02354	−	1.90023i	0.148373	−	0.139331i
$187$	2.50730	−	19.8473i	0.183352	−	1.45138i
$188$	−0.166308	+	1.31647i	−0.0121293	+	0.0960131i
$189$	−4.07051	+	3.82247i	−0.296086	+	0.278043i
$190$	12.4821	+	5.66402i	0.905547	+	0.410911i
$191$	−2.92625	+	6.21860i	−0.211736	+	0.449962i	−0.982279	−	0.187426i	$-0.939985\pi$
$191$	−2.92625	+	6.21860i	−0.211736	+	0.449962i	0.770542	+	0.637389i	$0.219985\pi$
$192$	19.6590	−	1.23684i	1.41876	−	0.0892610i
$193$			22.1313i			1.59304i	0.604609	+	0.796522i	$0.293329\pi$
$193$			22.1313i			1.59304i	−0.604609	+	0.796522i	$0.706671\pi$
$194$	0.599975	+	9.53632i	0.0430757	+	0.684668i
$195$	−4.99088	+	28.2840i	−0.357404	+	2.02546i
$196$	−0.387764	−	0.153527i	−0.0276975	−	0.0109662i
$197$	−9.09001	+	5.76869i	−0.647636	+	0.411002i	−0.818671	−	0.574263i	$-0.805289\pi$
$197$	−9.09001	+	5.76869i	−0.647636	+	0.411002i	0.171035	+	0.985265i	$0.445289\pi$
$198$	−10.5178	+	4.94930i	−0.747467	+	0.351731i
$199$	5.76789	−	4.19062i	0.408875	−	0.297065i	−0.364271	−	0.931293i	$-0.618682\pi$
$199$	5.76789	−	4.19062i	0.408875	−	0.297065i	0.773146	+	0.634228i	$0.218682\pi$
$200$	−12.9334	−	7.71426i	−0.914532	−	0.545480i
$201$	1.96108	+	1.42481i	0.138324	+	0.100498i
$202$	−12.3251	−	2.35114i	−0.867193	−	0.165426i
$203$	0.171465	−	0.433072i	0.0120345	−	0.0303957i
$204$	−2.04560	+	2.47271i	−0.143221	+	0.173124i
$205$	−0.560312	+	1.23479i	−0.0391339	+	0.0862415i
$206$	8.16992	−	3.23470i	0.569226	−	0.225372i
$207$	0.924463	−	1.27241i	0.0642546	−	0.0884389i
$208$	14.3426	−	11.8652i	0.994481	−	0.822706i
$209$	−15.9453	−	14.9737i	−1.10296	−	1.03575i
$210$	13.1188	+	8.07300i	0.905284	+	0.557090i
$211$	−23.5752	−	12.9606i	−1.62298	−	0.892243i	−0.993322	−	0.115374i	$-0.963193\pi$
$211$	−23.5752	−	12.9606i	−1.62298	−	0.892243i	−0.629662	−	0.776869i	$-0.716807\pi$
$212$	−1.87280	+	1.99433i	−0.128624	+	0.136971i
$213$	−0.462820	−	0.841866i	−0.0317119	−	0.0576837i
$214$	6.15498	+	13.0800i	0.420746	+	0.894130i
$215$	23.9997	+	7.43243i	1.63677	+	0.506888i
$216$	−6.96168	−	0.879465i	−0.473682	−	0.0598400i
$217$	1.95442	+	1.24031i	0.132675	+	0.0841980i
$218$	−9.37345	−	12.9014i	−0.634850	−	0.873796i
$219$	−31.6183	−	8.11819i	−2.13656	−	0.548577i
$220$	2.21804	+	2.60685i	0.149540	+	0.175754i
$221$	−1.57313	+	25.0042i	−0.105820	+	1.68197i
$222$	−23.7547	−	1.49452i	−1.59431	−	0.100306i
$223$	6.24793	−	11.3649i	0.418393	−	0.761053i	−0.580179	−	0.814489i	$-0.697017\pi$
$223$	6.24793	−	11.3649i	0.418393	−	0.761053i	0.998571	+	0.0534360i	$0.0170173\pi$
$224$	1.37638	+	4.23607i	0.0919635	+	0.283034i
$225$	−7.30128	−	6.48564i	−0.486752	−	0.432376i
$226$	−5.94320	+	18.2913i	−0.395336	+	1.21672i
$227$	−15.2390	−	16.2278i	−1.01144	−	1.07708i	−0.997017	−	0.0771834i	$-0.975407\pi$
$227$	−15.2390	−	16.2278i	−1.01144	−	1.07708i	−0.0144279	−	0.999896i	$-0.504593\pi$
$228$	0.872639	+	3.39871i	0.0577920	+	0.225085i
$229$	0.467076	+	0.735995i	0.0308653	+	0.0486359i	0.859410	−	0.511287i	$-0.170831\pi$
$229$	0.467076	+	0.735995i	0.0308653	+	0.0486359i	−0.828545	+	0.559922i	$0.810831\pi$
$230$	2.17371	+	0.826026i	0.143330	+	0.0544665i
$231$	−15.6688	−	18.9403i	−1.03093	−	1.24618i
$232$	0.556672	−	0.180874i	0.0365473	−	0.0118749i
$233$	−4.27122	+	16.6353i	−0.279817	+	1.08981i	0.660860	+	0.750509i	$0.270192\pi$
$233$	−4.27122	+	16.6353i	−0.279817	+	1.08981i	−0.940677	+	0.339305i	$0.889808\pi$
$234$	12.7569	−	7.01318i	0.833947	−	0.458466i
$235$	−8.92195	−	0.437473i	−0.582004	−	0.0285376i
$236$	0.341910	−	1.79236i	0.0222564	−	0.116672i
$237$	−2.04055	+	0.389257i	−0.132548	+	0.0252849i
$238$	12.1581	+	5.72116i	0.788091	+	0.370848i
$239$	26.2269	−	3.31323i	1.69648	−	0.214315i	0.783234	−	0.621727i	$-0.213569\pi$
$239$	26.2269	−	3.31323i	1.69648	−	0.214315i	0.913244	+	0.407412i	$0.133569\pi$
$240$	2.23188	+	15.8951i	0.144067	+	1.02602i
$241$	−0.0299061	−	0.156773i	−0.00192642	−	0.0100987i	0.981311	−	0.192428i	$-0.0616362\pi$
$241$	−0.0299061	−	0.156773i	−0.00192642	−	0.0100987i	−0.983237	+	0.182330i	$0.941636\pi$
$242$	4.86658	+	12.2916i	0.312835	+	0.790132i
$243$	−16.7303	−	5.43600i	−1.07325	−	0.348720i
$244$	−2.11351	+	3.33036i	−0.135304	+	0.213204i
$245$	0.830541	−	2.68186i	0.0530613	−	0.171338i
$246$	1.68819	−	0.433453i	0.107635	−	0.0276359i
$247$	21.1074	+	17.4616i	1.34303	+	1.11106i
$248$	0.364574	+	2.88590i	0.0231505	+	0.183255i
$249$	4.08210			0.258692
$250$	6.42486	−	12.9306i	0.406344	−	0.817804i
$251$	23.7462			1.49885			0.749423	−	0.662091i	$-0.230331\pi$
$251$	23.7462			1.49885			0.749423	+	0.662091i	$0.230331\pi$
$252$	0.194887	+	1.54269i	0.0122767	+	0.0971802i
$253$	−2.85925	−	2.36537i	−0.179759	−	0.148710i
$254$	−1.95304	+	0.501455i	−0.122545	+	0.0314641i
$255$	−17.6517	−	12.4552i	−1.10539	−	0.779975i
$256$	−4.14722	+	6.53498i	−0.259201	+	0.408436i
$257$	25.4457	+	8.26780i	1.58726	+	0.515731i	0.963913	−	0.266216i	$-0.0857734\pi$
$257$	25.4457	+	8.26780i	1.58726	+	0.515731i	0.623345	+	0.781947i	$0.285773\pi$
$258$	−11.8883	−	30.0265i	−0.740135	−	1.86937i
$259$	−3.71911	−	19.4963i	−0.231095	−	1.21144i
$260$	−2.97731	−	3.08387i	−0.184645	−	0.191253i
$261$	0.376582	−	0.0475734i	0.0233099	−	0.00294472i
$262$	−2.74710	−	1.29269i	−0.169716	−	0.0798624i
$263$	−23.3890	+	4.46169i	−1.44223	+	0.275120i	−0.848350	−	0.529435i	$-0.822404\pi$
$263$	−23.3890	+	4.46169i	−1.44223	+	0.275120i	−0.593878	+	0.804555i	$0.702404\pi$
$264$	5.78822	−	30.3429i	0.356241	−	1.86748i
$265$	−14.3517	−	11.5420i	−0.881618	−	0.709021i
$266$	12.8748	−	7.07797i	0.789404	−	0.433978i
$267$	−1.31215	+	5.11049i	−0.0803024	+	0.312757i
$268$	−0.344075	+	0.111797i	−0.0210178	+	0.00682908i
$269$	1.43803	+	1.73828i	0.0876782	+	0.105985i	0.812528	−	0.582922i	$-0.198091\pi$
$269$	1.43803	+	1.73828i	0.0876782	+	0.105985i	−0.724850	+	0.688907i	$0.758091\pi$
$270$	0.329495	−	6.71981i	0.0200524	−	0.408954i
$271$	7.43111	+	11.7096i	0.451408	+	0.711305i	0.991472	−	0.130319i	$-0.0416001\pi$
$271$	7.43111	+	11.7096i	0.451408	+	0.711305i	−0.540064	+	0.841624i	$0.681600\pi$
$272$	3.48203	+	13.5616i	0.211129	+	0.822294i
$273$	21.0737	+	22.4412i	1.27544	+	1.35821i
$274$	2.97075	−	9.14303i	0.179470	−	0.552351i
$275$	−16.3537	+	16.2318i	−0.986163	+	0.978813i
$276$	0.183952	+	0.566148i	0.0110726	+	0.0340781i
$277$	12.9346	−	23.5279i	0.777164	−	1.41366i	−0.129403	−	0.991592i	$-0.541306\pi$
$277$	12.9346	−	23.5279i	0.777164	−	1.41366i	0.906566	−	0.422063i	$-0.138694\pi$
$278$	−9.37795	−	0.590010i	−0.562452	−	0.0353865i
$279$	−0.118445	+	1.88264i	−0.00709114	+	0.112710i
$280$	−14.9244	+	6.14919i	−0.891901	+	0.367485i
$281$	−19.9870	−	5.13179i	−1.19232	−	0.306137i	−0.400160	−	0.916445i	$-0.631045\pi$
$281$	−19.9870	−	5.13179i	−1.19232	−	0.306137i	−0.792164	+	0.610309i	$0.791045\pi$
$282$	6.74890	+	9.28907i	0.401891	+	0.553156i
$283$	2.32715	+	1.47686i	0.138335	+	0.0877900i	0.603193	−	0.797595i	$-0.293895\pi$
$283$	2.32715	+	1.47686i	0.138335	+	0.0877900i	−0.464858	+	0.885385i	$0.653895\pi$
$284$	0.142252	+	0.0179706i	0.00844111	+	0.00106636i
$285$	−22.3624	+	7.60965i	−1.32463	+	0.450757i
$286$	−14.6243	−	31.0782i	−0.864753	−	1.83769i
$287$	0.700187	+	1.27364i	0.0413307	+	0.0751803i
$288$	−2.48472	+	2.64596i	−0.146414	+	0.155915i
$289$	−1.61685	−	0.888870i	−0.0951087	−	0.0522864i
$290$	0.213793	+	0.518884i	0.0125543	+	0.0304699i
$291$	−12.0036	−	11.2722i	−0.703665	−	0.660786i
$292$	3.75397	−	3.10556i	0.219685	−	0.181739i
$293$	−1.38920	+	1.91207i	−0.0811581	+	0.111704i	−0.847666	−	0.530531i	$-0.821993\pi$
$293$	−1.38920	+	1.91207i	−0.0811581	+	0.111704i	0.766508	+	0.642235i	$0.221993\pi$
$294$	−3.35533	+	1.32847i	−0.195687	+	0.0774778i
$295$	12.2067	+	1.37074i	0.710701	+	0.0798078i
$296$	15.8984	−	19.2179i	0.924076	−	1.11702i
$297$	−3.95233	+	9.98244i	−0.229337	+	0.579240i
$298$	−26.7522	−	5.10325i	−1.54971	−	0.295623i
$299$	3.75976	+	2.73162i	0.217432	+	0.157974i
$300$	3.61024	−	0.792817i	0.208437	−	0.0457733i
$301$	21.7866	−	15.8289i	1.25576	−	0.912361i
$302$	5.22392	−	2.45819i	0.300603	−	0.141453i
$303$	18.2570	−	11.5862i	1.04884	−	0.665612i
$304$	14.2343	+	5.63578i	0.816396	+	0.323234i
$305$	−23.4433	−	12.4688i	−1.34236	−	0.713962i
$306$	0.687560	+	10.9285i	0.0393052	+	0.624738i
$307$			15.4005i			0.878950i	0.898255	+	0.439475i	$0.144836\pi$
$307$			15.4005i			0.878950i	−0.898255	+	0.439475i	$0.855164\pi$
$308$	3.66150	−	0.230362i	0.208633	−	0.0131261i
$309$	−6.44746	+	13.7016i	−0.366783	+	0.779455i
$310$	−2.73208	+	0.560461i	−0.155172	+	0.0318320i
$311$	1.28486	−	1.20657i	0.0728579	−	0.0684182i	−0.647263	−	0.762267i	$-0.724086\pi$
$311$	1.28486	−	1.20657i	0.0728579	−	0.0684182i	0.720121	+	0.693849i	$0.244086\pi$
$312$	−4.84860	+	38.3806i	−0.274498	+	2.17287i
$313$	3.72758	−	29.5069i	0.210695	−	1.66783i	−0.432129	−	0.901812i	$-0.642237\pi$
$313$	3.72758	−	29.5069i	0.210695	−	1.66783i	0.642824	−	0.766014i	$-0.277763\pi$
$314$	−4.73560	+	4.44702i	−0.267245	+	0.250960i
$315$	−10.2541	+	2.10353i	−0.577755	+	0.118521i
$316$	0.132009	−	0.280534i	0.00742610	−	0.0157813i
$317$	−6.17143	+	0.388273i	−0.346622	+	0.0218076i	−0.235147	−	0.971960i	$-0.575557\pi$
$317$	−6.17143	+	0.388273i	−0.346622	+	0.0218076i	−0.111474	+	0.993767i	$0.535557\pi$
$318$			23.6731i			1.32752i
$319$	−0.0562332	−	0.893802i	−0.00314846	−	0.0500433i
$320$	−17.4730	−	9.29336i	−0.976770	−	0.519515i
$321$	−23.1625	−	9.17069i	−1.29281	−	0.511858i
$322$	2.10446	−	1.33553i	0.117277	−	0.0744264i
$323$	−18.6444	+	8.77337i	−1.03740	+	0.488164i
$324$	2.96798	−	2.15636i	0.164888	−	0.119798i
$325$	19.1639	−	21.5740i	1.06302	−	1.19671i
$326$	−5.20232	−	3.77971i	−0.288130	−	0.209339i
$327$	26.9951	+	5.14958i	1.49283	+	0.284773i
$328$	−0.672350	+	1.69816i	−0.0371243	+	0.0937654i
$329$	−6.10307	+	7.37734i	−0.336473	+	0.406726i
$330$	29.4323	+	3.30508i	1.62019	+	0.181939i
$331$	27.4519	−	10.8690i	1.50889	−	0.597413i	0.539295	−	0.842117i	$-0.318691\pi$
$331$	27.4519	−	10.8690i	1.50889	−	0.597413i	0.969598	+	0.244704i	$0.0786907\pi$
$332$	−0.358106	+	0.492891i	−0.0196536	+	0.0270509i
$333$	12.4627	−	10.3100i	0.682949	−	0.564985i
$334$	−7.21262	−	6.77310i	−0.394657	−	0.370608i
$335$	−0.927800	−	2.25181i	−0.0506911	−	0.123029i
$336$	15.0764	+	8.28832i	0.822484	+	0.452165i
$337$	−13.7470	+	14.6391i	−0.748848	+	0.797442i	−0.984684	−	0.174351i	$-0.944217\pi$
$337$	−13.7470	+	14.6391i	−0.748848	+	0.797442i	0.235836	+	0.971793i	$0.424217\pi$
$338$	12.6346	+	22.9823i	0.687234	+	1.25007i
$339$	−14.1120	−	29.9895i	−0.766457	−	1.62880i
$340$	3.05241	−	1.03870i	0.165540	−	0.0563314i
$341$	4.41557	+	0.557816i	0.239117	+	0.0302074i
$342$	10.1091	+	6.41542i	0.546637	+	0.346906i
$343$	−11.6303	−	16.0077i	−0.627975	−	0.864333i
$344$	32.7778	+	8.41592i	1.76726	+	0.453756i
$345$	−3.70517	+	1.52662i	−0.199479	+	0.0821903i
$346$	−0.108224	+	1.72016i	−0.00581813	+	0.0924766i
$347$	11.0779	+	0.696960i	0.594690	+	0.0374148i	0.357284	−	0.933996i	$-0.383703\pi$
$347$	11.0779	+	0.696960i	0.594690	+	0.0374148i	0.237406	+	0.971410i	$0.423703\pi$
$348$	−0.0692111	+	0.125895i	−0.00371010	+	0.00674866i
$349$	4.53597	+	13.9603i	0.242805	+	0.747276i	0.995990	+	0.0894676i	$0.0285165\pi$
$349$	4.53597	+	13.9603i	0.242805	+	0.747276i	−0.753185	+	0.657809i	$0.771483\pi$
$350$	−6.97452	−	13.8158i	−0.372804	−	0.738484i
$351$	4.15500	−	12.7878i	0.221778	−	0.682561i
$352$	5.86244	+	6.24286i	0.312469	+	0.332746i
$353$	2.11645	+	8.24304i	0.112647	+	0.438733i	0.999739	−	0.0228614i	$-0.00727766\pi$
$353$	2.11645	+	8.24304i	0.112647	+	0.438733i	−0.887091	+	0.461594i	$0.847278\pi$
$354$	−8.46013	−	13.3310i	−0.449651	−	0.708536i
$355$	−0.0472716	+	0.964070i	−0.00250892	+	0.0511675i
$356$	−0.501954	−	0.606759i	−0.0266035	−	0.0321581i
$357$	−22.0227	+	7.15561i	−1.16557	+	0.378715i
$358$	−4.73306	+	18.4341i	−0.250150	+	0.974270i
$359$	23.5213	−	12.9310i	1.24141	−	0.682469i	0.280637	−	0.959814i	$-0.409454\pi$
$359$	23.5213	−	12.9310i	1.24141	−	0.682469i	0.960771	+	0.277345i	$0.0894544\pi$
$360$	−10.2505	−	8.24370i	−0.540247	−	0.434481i
$361$	−0.661508	+	3.46774i	−0.0348162	+	0.182513i
$362$	1.55273	−	0.296200i	0.0816099	−	0.0155679i
$363$	−20.6139	−	9.70015i	−1.08195	−	0.509126i
$364$	−4.55837	+	0.575856i	−0.238924	+	0.0301831i
$365$	22.7803	+	23.5956i	1.19238	+	1.23505i
$366$	6.39548	+	33.5263i	0.334297	+	1.75245i
$367$	5.53176	+	13.9716i	0.288755	+	0.729313i	0.999661	+	0.0260258i	$0.00828520\pi$
$367$	5.53176	+	13.9716i	0.288755	+	0.729313i	−0.710906	+	0.703287i	$0.751715\pi$
$368$	2.47008	+	0.802579i	0.128762	+	0.0418373i
$369$	−0.634644	+	1.00004i	−0.0330383	+	0.0520600i
$370$	19.5394	+	13.7872i	1.01581	+	0.716763i
$371$	−19.1204	+	4.90929i	−0.992682	+	0.254877i
$372$	−0.550119	−	0.455098i	−0.0285224	−	0.0235957i
$373$	0.549001	+	4.34579i	0.0284262	+	0.225017i	0.999928	−	0.0120164i	$-0.00382503\pi$
$373$	0.549001	+	4.34579i	0.0284262	+	0.225017i	−0.971502	+	0.237033i	$0.923825\pi$
$374$	25.8355			1.33592
$375$	7.18295	+	23.8233i	0.370926	+	1.23023i
$376$	−12.0318			−0.620494
$377$	0.140571	+	1.11273i	0.00723978	+	0.0573088i
$378$	−5.55645	−	4.59669i	−0.285793	−	0.236428i
$379$	−4.75810	+	1.22167i	−0.244407	+	0.0627531i	−0.368906	−	0.929467i	$-0.620268\pi$
$379$	−4.75810	+	1.22167i	−0.244407	+	0.0627531i	0.124499	+	0.992220i	$0.460268\pi$
$380$	1.04294	−	3.36770i	0.0535016	−	0.172759i
$381$	1.86193	−	2.93393i	0.0953896	−	0.150310i
$382$	−8.44132	−	2.74275i	−0.431896	−	0.140331i
$383$	9.91036	+	25.0307i	0.506396	+	1.27901i	0.928119	+	0.372285i	$0.121426\pi$
$383$	9.91036	+	25.0307i	0.506396	+	1.27901i	−0.421723	+	0.906725i	$0.638574\pi$
$384$	3.21674	+	16.8627i	0.164154	+	0.860523i
$385$	3.43415	+	24.4574i	0.175021	+	1.24647i
$386$	−28.3560	+	3.58220i	−1.44328	+	0.182329i
$387$	19.8570	+	9.34400i	1.00939	+	0.474982i
$388$	2.41408	−	0.460511i	0.122557	−	0.0233789i
$389$	2.32366	−	12.1810i	0.117814	−	0.617603i	−0.873579	−	0.486683i	$-0.838207\pi$
$389$	2.32366	−	12.1810i	0.117814	−	0.617603i	0.991393	−	0.130920i	$-0.0417932\pi$
$390$	−37.0471	−	1.81655i	−1.87595	−	0.0919844i
$391$	−3.06327	+	1.68405i	−0.154916	+	0.0851658i
$392$	0.940441	−	3.66278i	0.0474995	−	0.184998i
$393$	4.97599	−	1.61680i	0.251006	−	0.0815567i
$394$	−8.86254	−	10.7130i	−0.446488	−	0.539712i
$395$	1.95103	+	0.741404i	0.0981667	+	0.0373041i
$396$	1.60199	+	2.52432i	0.0805028	+	0.126852i
$397$	−8.19202	−	31.9058i	−0.411146	−	1.60131i	−0.750649	−	0.660701i	$-0.770259\pi$
$397$	−8.19202	−	31.9058i	−0.411146	−	1.60131i	0.339503	−	0.940605i	$-0.389741\pi$
$398$	6.30288	+	6.71189i	0.315935	+	0.336437i
$399$	−7.82404	+	24.0799i	−0.391692	+	1.20550i
$400$	6.46000	−	14.7763i	0.323000	−	0.738815i
$401$	2.45252	+	7.54808i	0.122473	+	0.376933i	0.993432	−	0.114422i	$-0.0365016\pi$
$401$	2.45252	+	7.54808i	0.122473	+	0.376933i	−0.870959	+	0.491355i	$0.836502\pi$
$402$	−1.50813	+	2.74328i	−0.0752188	+	0.136822i
$403$	−5.56286	−	0.349985i	−0.277106	−	0.0174340i
$404$	−0.202638	+	3.22084i	−0.0100816	+	0.160243i
$405$	16.0040	+	18.8094i	0.795244	+	0.934645i
$406$	0.582633	+	0.149595i	0.0289156	+	0.00742426i
$407$	−22.4311	−	30.8737i	−1.11187	−	1.53035i
$408$	−24.5690	−	15.5920i	−1.21635	−	0.771917i
$409$	−3.01037	−	0.380298i	−0.148853	−	0.0188045i	0.0505535	−	0.998721i	$-0.483901\pi$
$409$	−3.01037	−	0.380298i	−0.148853	−	0.0188045i	−0.199407	+	0.979917i	$0.563901\pi$
$410$	−1.67278	−	0.518042i	−0.0826129	−	0.0255843i
$411$	7.05397	+	14.9904i	0.347946	+	0.739424i
$412$	−1.08878	−	1.98048i	−0.0536402	−	0.0975712i
$413$	9.01283	−	9.59769i	0.443492	−	0.472271i
$414$	1.77993	+	0.978526i	0.0874789	+	0.0480920i
$415$	−3.49296	−	2.14948i	−0.171463	−	0.105514i
$416$	−7.81834	−	7.34191i	−0.383326	−	0.359967i
$417$	12.4770	−	10.3219i	0.611002	−	0.505465i
$418$	16.6043	−	22.8538i	0.812142	−	1.11782i
$419$	−7.19409	+	2.84834i	−0.351454	+	0.139151i	−0.537217	−	0.843444i	$-0.680524\pi$
$419$	−7.19409	+	2.84834i	−0.351454	+	0.139151i	0.185763	+	0.982595i	$0.440524\pi$
$420$	1.63712	−	3.60782i	0.0798835	−	0.176044i
$421$	16.1357	−	19.5047i	0.786405	−	0.950600i	−0.213247	−	0.976998i	$-0.568404\pi$
$421$	16.1357	−	19.5047i	0.786405	−	0.950600i	0.999651	+	0.0263985i	$0.00840387\pi$
$422$	12.7900	−	32.3039i	0.622608	−	1.57253i
$423$	−7.66435	−	1.46205i	−0.372654	−	0.0710875i
$424$	−20.0692	−	14.5811i	−0.974646	−	0.708122i
$425$	8.54570	+	19.9524i	0.414527	+	0.967833i
$426$	1.00374	−	0.729260i	0.0486314	−	0.0353328i
$427$	−25.7524	+	12.1182i	−1.24625	+	0.586439i
$428$	3.13927	−	1.99224i	0.151742	−	0.0962985i
$429$	55.0344	+	21.7897i	2.65709	+	1.05201i
$430$	−5.63829	+	31.9530i	−0.271902	+	1.54091i
$431$	−1.77100	−	28.1492i	−0.0853061	−	1.35590i	−0.775074	−	0.631871i	$-0.782287\pi$
$431$	−1.77100	−	28.1492i	−0.0853061	−	1.35590i	0.689768	−	0.724031i	$-0.257713\pi$
$432$		−	7.51436i		−	0.361535i
$433$	−9.53198	+	0.599701i	−0.458078	+	0.0288198i	−0.290153	−	0.956980i	$-0.593706\pi$
$433$	−9.53198	+	0.599701i	−0.458078	+	0.0288198i	−0.167924	+	0.985800i	$0.553706\pi$
$434$	−1.27282	+	2.70489i	−0.0610975	+	0.129839i
$435$	−0.880698	−	0.399635i	−0.0422262	−	0.0191610i
$436$	−2.98995	+	2.80775i	−0.143193	+	0.134467i
$437$	−0.479048	+	3.79206i	−0.0229160	+	0.181399i
$438$	5.28377	−	41.8254i	0.252468	−	1.99849i
$439$	−22.0611	+	20.7167i	−1.05292	+	0.988756i	−0.999952	−	0.00984037i	$-0.996868\pi$
$439$	−22.0611	+	20.7167i	−1.05292	+	0.988756i	−0.0529665	+	0.998596i	$0.516868\pi$
$440$	−20.9303	+	22.9159i	−0.997815	+	1.09247i
$441$	1.04415	−	2.21893i	0.0497215	−	0.105663i
$442$	−32.2916	+	2.03162i	−1.53596	+	0.0966342i
$443$			19.6665i			0.934382i	0.884156	+	0.467191i	$0.154734\pi$
$443$			19.6665i			0.934382i	−0.884156	+	0.467191i	$0.845266\pi$
$444$	0.384394	+	6.10977i	0.0182425	+	0.289957i
$445$	3.81378	−	3.68200i	0.180791	−	0.174544i
$446$	15.5728	+	6.16571i	0.737393	+	0.291955i
$447$	39.6275	−	25.1484i	1.87432	−	1.18948i
$448$	−19.1940	+	9.03202i	−0.906832	+	0.426723i
$449$	−10.1828	+	7.39826i	−0.480558	+	0.349146i	−0.801542	−	0.597939i	$-0.795986\pi$
$449$	−10.1828	+	7.39826i	−0.480558	+	0.349146i	0.320984	+	0.947085i	$0.395986\pi$
$450$	7.12802	−	10.4046i	0.336018	−	0.490479i
$451$	2.26081	+	1.64258i	0.106457	+	0.0773459i
$452$	4.85905	+	0.926914i	0.228551	+	0.0435984i
$453$	−3.66261	+	9.25070i	−0.172084	+	0.434636i
$454$	18.3255	−	22.1518i	0.860061	−	1.03963i
$455$	−6.21557	−	30.2991i	−0.291391	−	1.42045i
$456$	−29.5828	+	11.7127i	−1.38534	+	0.548496i
$457$	−9.95236	+	13.6982i	−0.465552	+	0.640777i	−0.975648	−	0.219340i	$-0.929610\pi$
$457$	−9.95236	+	13.6982i	−0.465552	+	0.640777i	0.510097	+	0.860117i	$0.329610\pi$
$458$	−0.867402	+	0.717577i	−0.0405310	+	0.0335302i
$459$	7.37266	+	6.92339i	0.344126	+	0.323156i
$460$	0.140709	−	0.581303i	0.00656058	−	0.0271034i
$461$	7.03750	+	3.86890i	0.327769	+	0.180193i	0.637138	−	0.770749i	$-0.280118\pi$
$461$	7.03750	+	3.86890i	0.327769	+	0.180193i	−0.309369	+	0.950942i	$0.600118\pi$
$462$	21.7314	−	23.1416i	1.01104	−	1.07664i
$463$	0.658259	+	1.19737i	0.0305919	+	0.0556464i	0.891161	−	0.453688i	$-0.149892\pi$
$463$	0.658259	+	1.19737i	0.0305919	+	0.0556464i	−0.860569	+	0.509334i	$0.829892\pi$
$464$	0.266881	+	0.567151i	0.0123896	+	0.0263293i
$465$	2.77099	−	3.92709i	0.128502	−	0.182114i
$466$	−22.0055	−	2.77995i	−1.01939	−	0.128779i
$467$	−23.8417	−	15.1304i	−1.10326	−	0.700152i	−0.145975	−	0.989288i	$-0.546632\pi$
$467$	−23.8417	−	15.1304i	−1.10326	−	0.700152i	−0.957288	+	0.289136i	$0.906632\pi$
$468$	−2.20082	−	3.02916i	−0.101733	−	0.140023i
$469$	−2.52846	−	0.649199i	−0.116754	−	0.0299772i
$470$	−0.883599	−	11.5022i	−0.0407574	−	0.530556i
$471$	0.702951	−	11.1731i	0.0323903	−	0.514829i
$472$	16.5125	+	1.03888i	0.760048	+	0.0478181i
$473$	24.9445	−	45.3738i	1.14695	−	2.08629i
$474$	−0.829027	−	2.55148i	−0.0380785	−	0.117194i
$475$	23.1419	+	5.26380i	1.06182	+	0.241520i
$476$	1.06796	−	3.28686i	0.0489501	−	0.150653i
$477$	−11.0124	−	11.7270i	−0.504222	−	0.536941i
$478$	8.49025	+	33.0673i	0.388335	+	1.51246i
$479$	−21.3622	−	33.6614i	−0.976062	−	1.53803i	−0.836610	−	0.547799i	$-0.815466\pi$
$479$	−21.3622	−	33.6614i	−0.976062	−	1.53803i	−0.139452	−	0.990229i	$-0.544534\pi$
$480$	8.92503	−	2.42368i	0.407370	−	0.110625i
$481$	30.4642	+	36.8249i	1.38905	+	1.67907i
$482$	0.196027	−	0.0636932i	0.00892881	−	0.00290115i
$483$	−1.06820	+	4.16037i	−0.0486049	+	0.189304i
$484$	2.97961	−	1.63806i	0.135437	−	0.0744571i
$485$	4.33573	+	15.9660i	0.196875	+	0.724979i
$486$	4.25697	−	22.3158i	0.193100	−	1.01227i
$487$	10.0166	−	1.91076i	0.453893	−	0.0865848i	0.0446350	−	0.999003i	$-0.485788\pi$
$487$	10.0166	−	1.91076i	0.453893	−	0.0865848i	0.409258	+	0.912419i	$0.365788\pi$
$488$	−32.3616	−	15.2282i	−1.46494	−	0.689349i
$489$	10.9943	−	1.38890i	0.497178	−	0.0628082i
$490$	3.57060	+	0.630053i	0.161303	+	0.0284629i
$491$	0.157079	+	0.823439i	0.00708889	+	0.0371613i	0.985656	−	0.168767i	$-0.0539786\pi$
$491$	0.157079	+	0.823439i	0.00708889	+	0.0371613i	−0.978567	+	0.205928i	$0.933979\pi$
$492$	−0.165026	−	0.416809i	−0.00743996	−	0.0187912i
$493$	−0.802348	−	0.260699i	−0.0361359	−	0.0117413i
$494$	−18.9564	+	29.8706i	−0.852891	+	1.34394i
$495$	−16.1174	+	12.0542i	−0.724423	+	0.541797i
$496$	−3.01714	+	0.774671i	−0.135474	+	0.0347837i
$497$	0.797166	+	0.659473i	0.0357578	+	0.0295814i
$498$	0.660733	+	5.23024i	0.0296082	+	0.234373i
$499$	−21.9417			−0.982246			−0.491123	−	0.871090i	$-0.663414\pi$
$499$	−21.9417			−0.982246			−0.491123	+	0.871090i	$0.663414\pi$
$500$	−3.50667	−	1.22263i	−0.156823	−	0.0546775i
$501$	17.0510			0.761781
$502$	3.84359	+	30.4252i	0.171548	+	1.35794i
$503$	−10.7232	−	8.87103i	−0.478125	−	0.395540i	0.366905	−	0.930259i	$-0.380417\pi$
$503$	−10.7232	−	8.87103i	−0.478125	−	0.395540i	−0.845030	+	0.534719i	$0.820417\pi$
$504$	−13.6564	+	3.50638i	−0.608306	+	0.156186i
$505$	−21.7230	+	0.300615i	−0.966660	+	0.0133772i
$506$	2.56787	−	4.04631i	0.114156	−	0.179881i
$507$	−42.9842	−	13.9664i	−1.90900	−	0.620270i
$508$	0.190917	+	0.482200i	0.00847055	+	0.0213942i
$509$	−1.37195	−	7.19204i	−0.0608108	−	0.318782i	0.938864	−	0.344289i	$-0.111880\pi$
$509$	−1.37195	−	7.19204i	−0.0608108	−	0.318782i	−0.999675	+	0.0255072i	$0.991880\pi$
$510$	13.1013	−	24.6325i	0.580134	−	1.09075i
$511$	34.8775	−	4.40605i	1.54289	−	0.194912i
$512$	−23.0030	−	10.8244i	−1.01660	−	0.478374i
$513$	10.8627	−	2.07217i	0.479600	−	0.0914887i
$514$	−6.47457	+	33.9409i	−0.285581	+	1.49707i
$515$	12.7317	−	8.32912i	0.561026	−	0.367025i
$516$	−7.27875	+	4.00153i	−0.320429	+	0.176158i
$517$	−4.57821	+	17.8310i	−0.201349	+	0.784204i
$518$	24.3779	−	7.92086i	1.07110	−	0.348023i
$519$	−1.89331	−	2.28862i	−0.0831070	−	0.100459i
$520$	24.3587	−	30.2883i	1.06820	−	1.32823i
$521$	2.92542	+	4.60972i	0.128165	+	0.201956i	0.902350	−	0.431003i	$-0.141840\pi$
$521$	2.92542	+	4.60972i	0.128165	+	0.201956i	−0.774185	+	0.632959i	$0.781840\pi$
$522$	0.121908	+	0.474801i	0.00533578	+	0.0207815i
$523$	14.0955	+	15.0102i	0.616353	+	0.656349i	0.959096	−	0.283080i	$-0.0913561\pi$
$523$	14.0955	+	15.0102i	0.616353	+	0.656349i	−0.342743	+	0.939429i	$0.611356\pi$
$524$	−0.241305	+	0.742659i	−0.0105414	+	0.0324432i
$525$	25.0600	+	9.12820i	1.09371	+	0.398387i
$526$	−9.50238	−	29.2453i	−0.414324	−	1.27516i
$527$	2.01979	−	3.67399i	0.0879836	−	0.160042i
$528$	33.0142	+	2.07708i	1.43676	+	0.0903933i
$529$	1.40347	−	22.3075i	0.0610203	−	0.969890i
$530$	12.4654	−	20.2565i	0.541462	−	0.879888i
$531$	10.3923	+	2.66829i	0.450987	+	0.115794i
$532$	−2.22115	−	3.05715i	−0.0962990	−	0.132544i
$533$	−2.95494	−	1.87526i	−0.127993	−	0.0812266i
$534$	−6.76028	−	0.854022i	−0.292546	−	0.0369571i
$535$	14.9907	+	20.0437i	0.648104	+	0.866564i
$536$	−1.39674	−	2.96823i	−0.0603300	−	0.128208i
$537$	−15.8006	−	28.7412i	−0.681847	−	1.24027i
$538$	−1.99443	+	2.12386i	−0.0859861	+	0.0915659i
$539$	−5.07032	−	2.78743i	−0.218394	−	0.120063i
$540$	−1.72534	+	0.132541i	−0.0742469	+	0.00570366i
$541$	17.5737	+	16.5028i	0.755553	+	0.709511i	0.963228	−	0.268687i	$-0.0865896\pi$
$541$	17.5737	+	16.5028i	0.755553	+	0.709511i	−0.207675	+	0.978198i	$0.566590\pi$
$542$	−13.8002	+	11.4165i	−0.592770	+	0.490382i
$543$	−1.60119	+	2.20385i	−0.0687135	+	0.0945761i
$544$	7.50085	−	2.96980i	0.321596	−	0.127329i
$545$	−20.3875	−	18.6210i	−0.873304	−	0.797636i
$546$	−25.3421	+	30.6334i	−1.08454	+	1.31099i
$547$	−15.1488	+	38.2616i	−0.647717	+	1.63595i	0.118186	+	0.992991i	$0.462292\pi$
$547$	−15.1488	+	38.2616i	−0.647717	+	1.63595i	−0.765904	+	0.642955i	$0.777708\pi$
$548$	−2.42883	−	0.463324i	−0.103754	−	0.0197922i
$549$	−18.7641	−	13.6329i	−0.800831	−	0.581838i
$550$	−23.4442	−	18.3261i	−0.999665	−	0.781426i
$551$	−0.746274	+	0.542200i	−0.0317923	+	0.0230985i
$552$	−4.88397	+	2.29822i	−0.207876	+	0.0978188i
$553$	1.88887	−	1.19872i	0.0803231	−	0.0509746i
$554$	32.2391	+	12.7644i	1.36971	+	0.542306i
$555$	−40.8109	+	5.73040i	−1.73233	+	0.243242i
$556$	0.151752	+	2.41203i	0.00643572	+	0.102293i
$557$		−	11.6966i		−	0.495599i	−0.968811	−	0.247799i	$-0.920293\pi$
$557$		−	11.6966i		−	0.495599i	0.968811	−	0.247799i	$-0.0797074\pi$
$558$	−2.43133	+	0.152966i	−0.102926	+	0.00647557i
$559$	−27.6099	+	58.6740i	−1.16777	+	2.48164i
$560$	−8.53620	−	15.0308i	−0.360720	−	0.635168i
$561$	−32.4557	+	30.4779i	−1.37028	+	1.28678i
$562$	3.34005	−	26.4392i	0.140892	−	1.11527i
$563$	−3.23546	+	25.6113i	−0.136359	+	1.07939i	0.764300	+	0.644861i	$0.223085\pi$
$563$	−3.23546	+	25.6113i	−0.136359	+	1.07939i	−0.900658	+	0.434528i	$0.856915\pi$
$564$	2.15277	−	2.02159i	0.0906481	−	0.0851242i
$565$	−3.71607	+	33.0922i	−0.156336	+	1.39220i
$566$	−1.51557	+	3.22074i	−0.0637040	+	0.135378i
$567$	26.4191	−	1.66215i	1.10950	−	0.0698036i
$568$			1.30011i			0.0545515i
$569$	1.08886	+	17.3070i	0.0456476	+	0.725548i	0.952583	+	0.304278i	$0.0984153\pi$
$569$	1.08886	+	17.3070i	0.0456476	+	0.725548i	−0.906936	+	0.421269i	$0.861585\pi$
$570$	−13.3696	−	27.4204i	−0.559990	−	1.14851i
$571$	−36.6876	−	14.5256i	−1.53533	−	0.607879i	−0.559970	−	0.828513i	$-0.689188\pi$
$571$	−36.6876	−	14.5256i	−1.53533	−	0.607879i	−0.975357	+	0.220634i	$0.929188\pi$
$572$	−7.45893	+	4.73358i	−0.311874	+	0.197921i
$573$	13.8400	−	6.51259i	0.578172	−	0.272067i
$574$	−1.51853	+	1.10328i	−0.0633822	+	0.0460499i
$575$	3.97429	+	0.644714i	0.165739	+	0.0268864i
$576$	−13.9854	−	10.1610i	−0.582725	−	0.423375i
$577$	−3.81334	−	0.727434i	−0.158751	−	0.0302835i	0.107393	−	0.994217i	$-0.465750\pi$
$577$	−3.81334	−	0.727434i	−0.158751	−	0.0302835i	−0.266144	+	0.963933i	$0.585750\pi$
$578$	0.877172	−	2.21548i	0.0364855	−	0.0921519i
$579$	31.3962	−	37.9515i	1.30478	−	1.57721i
$580$	0.125514	−	0.0712811i	0.00521168	−	0.00295979i
$581$	−4.08737	+	1.61830i	−0.169573	+	0.0671385i
$582$	12.4997	−	17.2044i	0.518129	−	0.713143i
$583$	−29.2454	+	24.1939i	−1.21122	+	1.00201i
$584$	32.2036	+	30.2412i	1.33259	+	1.25139i
$585$	19.1971	−	16.3339i	0.793703	−	0.675324i
$586$	−2.67473	−	1.47044i	−0.110492	−	0.0607435i
$587$	8.71404	−	9.27951i	0.359667	−	0.383006i	−0.523531	−	0.852007i	$-0.675386\pi$
$587$	8.71404	−	9.27951i	0.359667	−	0.383006i	0.883198	+	0.469000i	$0.155386\pi$
$588$	0.447153	+	0.813368i	0.0184403	+	0.0335427i
$589$	−1.95187	−	4.14794i	−0.0804254	−	0.170913i
$590$	0.219506	+	15.8619i	0.00903690	+	0.653022i
$591$	23.7715	+	3.00304i	0.977829	+	0.123529i
$592$	22.5515	+	14.3116i	0.926863	+	0.588205i
$593$	17.4831	+	24.0634i	0.717945	+	0.988166i	0.999590	+	0.0286475i	$0.00912004\pi$
$593$	17.4831	+	24.0634i	0.717945	+	0.988166i	−0.281645	+	0.959519i	$0.590880\pi$
$594$	−13.4299	−	3.44820i	−0.551034	−	0.141482i
$595$	22.6122	+	5.47347i	0.927011	+	0.224390i
$596$	−0.439834	+	6.99097i	−0.0180163	+	0.286361i
$597$	−15.8359	−	0.996311i	−0.648121	−	0.0407763i
$598$	−2.89137	+	5.25939i	−0.118237	+	0.215072i
$599$	−12.5249	−	38.5477i	−0.511754	−	1.57502i	−0.789112	−	0.614250i	$-0.789459\pi$
$599$	−12.5249	−	38.5477i	−0.511754	−	1.57502i	0.277358	−	0.960767i	$-0.410541\pi$
$600$	11.2350	+	31.5765i	0.458666	+	1.28910i
$601$	−4.17440	+	12.8475i	−0.170277	+	0.524059i	−0.999386	−	0.0350274i	$-0.988848\pi$
$601$	−4.17440	+	12.8475i	−0.170277	+	0.524059i	0.829109	+	0.559087i	$0.188848\pi$
$602$	23.8074	+	25.3523i	0.970316	+	1.03328i
$603$	−0.529048	−	2.06050i	−0.0215445	−	0.0839102i
$604$	−0.795665	−	1.25377i	−0.0323751	−	0.0510151i
$605$	12.5311	+	19.1547i	0.509461	+	0.778750i
$606$	17.8001	+	21.5166i	0.723080	+	0.874054i
$607$	−7.82677	+	2.54307i	−0.317679	+	0.103220i	−0.463516	−	0.886089i	$-0.653412\pi$
$607$	−7.82677	+	2.54307i	−0.317679	+	0.103220i	0.145837	+	0.989309i	$0.453412\pi$
$608$	2.19369	−	8.54385i	0.0889657	−	0.346499i
$609$	−0.908404	+	0.499399i	−0.0368104	+	0.0202367i
$610$	12.1813	−	32.0553i	0.493205	−	1.29788i
$611$	4.32011	−	22.6468i	0.174773	−	0.916192i
$612$	2.76649	−	0.527737i	0.111829	−	0.0213325i
$613$	−11.7422	−	5.52546i	−0.474263	−	0.223171i	0.173766	−	0.984787i	$-0.444406\pi$
$613$	−11.7422	−	5.52546i	−0.474263	−	0.223171i	−0.648029	+	0.761616i	$0.724406\pi$
$614$	−19.7320	+	2.49274i	−0.796320	+	0.100599i
$615$	2.71255	−	1.32258i	0.109381	−	0.0533316i
$616$	6.23343	+	32.6768i	0.251152	+	1.31659i
$617$	−4.91066	−	12.4029i	−0.197696	−	0.499322i	0.796782	−	0.604266i	$-0.206534\pi$
$617$	−4.91066	−	12.4029i	−0.197696	−	0.499322i	−0.994478	+	0.104944i	$0.966534\pi$
$618$	−18.5989	−	6.04315i	−0.748158	−	0.243091i
$619$	12.2030	−	19.2288i	0.490480	−	0.772872i	−0.505464	−	0.862847i	$-0.668679\pi$
$619$	12.2030	−	19.2288i	0.490480	−	0.772872i	0.995944	+	0.0899752i	$0.0286788\pi$
$620$	0.231087	+	0.679090i	0.00928066	+	0.0272729i
$621$	1.81712	−	0.466557i	0.0729185	−	0.0187223i
$622$	1.75390	+	1.45095i	0.0703250	+	0.0581779i
$623$	−0.712155	−	5.63728i	−0.0285319	−	0.225853i
$624$	−41.4276			−1.65843
$625$	6.39822	−	24.1674i	0.255929	−	0.966696i
$626$	38.4094			1.53515
$627$	6.10145	+	48.2979i	0.243668	+	1.92883i
$628$	1.28742	+	1.06505i	0.0513737	+	0.0425000i
$629$	−34.8197	+	8.94018i	−1.38835	+	0.356468i
$630$	−4.35493	−	12.7978i	−0.173505	−	0.509875i
$631$	3.01367	−	4.74878i	0.119972	−	0.189046i	−0.779034	−	0.626981i	$-0.784290\pi$
$631$	3.01367	−	4.74878i	0.119972	−	0.189046i	0.899006	+	0.437936i	$0.144290\pi$
$632$	2.67368	+	0.868732i	0.106353	+	0.0345563i
$633$	22.0412	+	55.6698i	0.876060	+	2.21268i
$634$	−1.49640	−	7.84438i	−0.0594295	−	0.311540i
$635$	−3.13812	+	1.53008i	−0.124532	+	0.0607192i
$636$	6.04076	−	0.763126i	0.239532	−	0.0302599i
$637$	6.55656	+	3.08528i	0.259780	+	0.122243i
$638$	1.13609	−	0.216722i	0.0449784	−	0.00858009i
$639$	−0.157984	+	0.828180i	−0.00624974	+	0.0327623i
$640$	6.12681	−	16.1229i	0.242184	−	0.637313i
$641$	7.06472	−	3.88386i	0.279040	−	0.153403i	−0.336089	−	0.941830i	$-0.609104\pi$
$641$	7.06472	−	3.88386i	0.279040	−	0.153403i	0.615128	+	0.788427i	$0.289104\pi$
$642$	8.00096	−	31.1617i	0.315773	−	1.22985i
$643$	31.2243	−	10.1454i	1.23137	−	0.400095i	0.380157	−	0.924922i	$-0.375870\pi$
$643$	31.2243	−	10.1454i	1.23137	−	0.400095i	0.851209	+	0.524827i	$0.175870\pi$
$644$	−0.408633	−	0.493953i	−0.0161024	−	0.0194645i
$645$	−30.6116	−	46.7921i	−1.20533	−	1.84244i
$646$	−14.2588	−	22.4683i	−0.561005	−	0.884003i
$647$	−6.90254	−	26.8836i	−0.271367	−	1.05690i	−0.947405	−	0.320037i	$-0.896305\pi$
$647$	−6.90254	−	26.8836i	−0.271367	−	1.05690i	0.676038	−	0.736866i	$-0.263695\pi$
$648$	22.7714	+	24.2491i	0.894546	+	0.952595i
$649$	7.82272	−	24.0759i	0.307069	−	0.945060i
$650$	30.7439	+	21.0621i	1.20587	+	0.826122i
$651$	−1.59196	−	4.89954i	−0.0623937	−	0.192028i
$652$	−0.796782	+	1.44934i	−0.0312044	+	0.0567606i
$653$	16.2141	+	1.02010i	0.634507	+	0.0399198i	0.376787	−	0.926300i	$-0.377029\pi$
$653$	16.2141	+	1.02010i	0.634507	+	0.0399198i	0.257720	+	0.966220i	$0.417029\pi$
$654$	−2.22852	+	35.4213i	−0.0871421	+	1.38508i
$655$	−5.10919	−	1.23672i	−0.199633	−	0.0483226i
$656$	−1.89443	−	0.486406i	−0.0739649	−	0.0189910i
$657$	16.8391	+	23.1770i	0.656956	+	0.904222i
$658$	−10.4402	−	6.62554i	−0.407000	−	0.258290i
$659$	−15.2615	−	1.92797i	−0.594503	−	0.0751032i	−0.177676	−	0.984089i	$-0.556858\pi$
$659$	−15.2615	−	1.92797i	−0.594503	−	0.0751032i	−0.416827	+	0.908986i	$0.636858\pi$
$660$	−0.105407	−	7.61690i	−0.00410297	−	0.296488i
$661$	8.75412	+	18.6034i	0.340496	+	0.723590i	0.999595	−	0.0284660i	$-0.00906223\pi$
$661$	8.75412	+	18.6034i	0.340496	+	0.723590i	−0.659099	+	0.752056i	$0.729062\pi$
$662$	18.3694	+	33.4139i	0.713948	+	1.29867i
$663$	38.1695	−	40.6464i	1.48238	−	1.57857i
$664$	−4.84098	−	2.66135i	−0.187866	−	0.103280i
$665$	19.3745	−	16.4848i	0.751310	−	0.639253i
$666$	15.2271	+	14.2992i	0.590036	+	0.554081i
$667$	−0.120578	+	0.0997506i	−0.00466879	+	0.00386236i
$668$	−1.49581	+	2.05881i	−0.0578748	+	0.0796578i
$669$	−26.8369	+	10.6255i	−1.03757	+	0.410804i
$670$	2.73499	−	1.55324i	0.105662	−	0.0600068i
$671$	−34.8818	+	42.1648i	−1.34660	+	1.62775i
$672$	3.64917	−	9.21674i	0.140770	−	0.355543i
$673$	−21.3524	−	4.07318i	−0.823073	−	0.157010i	−0.241393	−	0.970427i	$-0.577604\pi$
$673$	−21.3524	−	4.07318i	−0.823073	−	0.157010i	−0.581680	+	0.813418i	$0.697604\pi$
$674$	−20.9816	−	15.2441i	−0.808183	−	0.587179i
$675$	−1.77925	−	11.5123i	−0.0684832	−	0.443107i
$676$	5.45720	−	3.96489i	0.209892	−	0.152496i
$677$	6.53506	−	3.07517i	0.251163	−	0.118188i	−0.296077	−	0.955164i	$-0.595679\pi$
$677$	6.53506	−	3.07517i	0.251163	−	0.118188i	0.547240	+	0.836976i	$0.315679\pi$
$678$	36.1403	−	22.9353i	1.38796	−	0.880825i
$679$	16.4879	+	6.52801i	0.632746	+	0.250522i
$680$	12.8130	+	26.2788i	0.491356	+	1.00775i
$681$	3.11091	+	49.4465i	0.119210	+	1.89479i
$682$			5.74780i			0.220095i
$683$	25.9627	−	1.63344i	0.993436	−	0.0625017i	0.442257	−	0.896888i	$-0.354178\pi$
$683$	25.9627	−	1.63344i	0.993436	−	0.0625017i	0.551179	+	0.834387i	$0.314178\pi$
$684$	1.31117	−	2.78639i	0.0501340	−	0.106540i
$685$	1.85750	−	16.5413i	0.0709715	−	0.632012i
$686$	18.6276	−	17.4924i	0.711204	−	0.667865i
$687$	0.243148	−	1.92472i	0.00927669	−	0.0734326i
$688$	−4.54202	+	35.9538i	−0.173163	+	1.37073i
$689$	34.6511	−	32.5396i	1.32010	−	1.23966i
$690$	−2.55572	−	4.50019i	−0.0972947	−	0.171319i
$691$	−12.4999	+	26.5637i	−0.475520	+	1.01053i	0.512853	+	0.858477i	$0.328589\pi$
$691$	−12.4999	+	26.5637i	−0.475520	+	1.01053i	−0.988372	+	0.152054i	$0.951411\pi$
$692$	0.442430	−	0.0278353i	0.0168187	−	0.00105814i
$693$			21.5728i			0.819482i
$694$	0.900087	+	14.3065i	0.0341668	+	0.543066i
$695$	−16.1114	+	2.26226i	−0.611141	+	0.0858125i
$696$	−1.21119	−	0.479545i	−0.0459102	−	0.0181771i
$697$	2.22267	−	1.41055i	0.0841897	−	0.0534284i
$698$	−17.1526	+	8.07140i	−0.649236	+	0.305507i
$699$	30.9238	−	22.4675i	1.16965	−	0.849797i
$700$	−3.30060	+	2.22508i	−0.124751	+	0.0841002i
$701$	8.21119	+	5.96578i	0.310132	+	0.225324i	0.731953	−	0.681355i	$-0.238609\pi$
$701$	8.21119	+	5.96578i	0.310132	+	0.225324i	−0.421821	+	0.906679i	$0.638609\pi$
$702$	17.0571	+	3.25381i	0.643777	+	0.122807i
$703$	−14.4700	+	36.5470i	−0.545745	+	1.37839i
$704$	−25.9984	+	31.4267i	−0.979851	+	1.18444i
$705$	14.6790	+	13.4072i	0.552844	+	0.504943i
$706$	−10.2189	+	4.04596i	−0.384595	+	0.152272i
$707$	−13.6873	+	18.8390i	−0.514765	+	0.708513i
$708$	−3.12901	+	2.58855i	−0.117596	+	0.0972835i
$709$	−34.1604	−	32.0788i	−1.28292	−	1.20474i	−0.966658	−	0.256072i	$-0.917571\pi$
$709$	−34.1604	−	32.0788i	−1.28292	−	1.20474i	−0.316264	−	0.948671i	$-0.602429\pi$
$710$	−1.24288	+	0.0954782i	−0.0466445	+	0.00358323i
$711$	1.59759	+	0.878282i	0.0599142	+	0.0329381i
$712$	4.88791	−	5.20510i	0.183182	−	0.195069i
$713$	−0.374661	−	0.681506i	−0.0140312	−	0.0255226i
$714$	−12.7329	−	27.0587i	−0.476515	−	1.01265i
$715$	−35.6181	−	47.6241i	−1.33204	−	1.78104i
$716$	4.85647	+	0.613515i	0.181495	+	0.0229281i
$717$	−49.6751	−	31.5247i	−1.85515	−	1.17731i
$718$	20.3752	+	28.0440i	0.760394	+	1.04659i
$719$	22.1441	+	5.68564i	0.825835	+	0.212038i	0.637877	−	0.770138i	$-0.279813\pi$
$719$	22.1441	+	5.68564i	0.825835	+	0.212038i	0.187959	+	0.982177i	$0.439813\pi$
$720$	7.38260	−	11.9969i	0.275133	−	0.447098i
$721$	1.02395	−	16.2753i	0.0381341	−	0.606123i
$722$	−4.55017	−	0.286272i	−0.169340	−	0.0106540i
$723$	−0.171120	+	0.311266i	−0.00636402	+	0.0115761i
$724$	−0.125636	−	0.386669i	−0.00466924	−	0.0143704i
$725$	0.543160	+	0.805703i	0.0201725	+	0.0299230i
$726$	9.09187	−	27.9819i	0.337431	−	1.03851i
$727$	−7.99505	−	8.51386i	−0.296520	−	0.315762i	0.563406	−	0.826180i	$-0.309491\pi$
$727$	−7.99505	−	8.51386i	−0.296520	−	0.315762i	−0.859926	+	0.510418i	$0.829491\pi$
$728$	−10.3607	−	40.3524i	−0.383994	−	1.49556i
$729$	3.22394	+	5.08011i	0.119405	+	0.188152i
$730$	−26.5449	+	33.0068i	−0.982472	+	1.22164i
$731$	−31.0910	−	37.5826i	−1.14994	−	1.39004i
$732$	8.34888	−	2.71272i	0.308583	−	0.100265i
$733$	4.34718	−	16.9311i	0.160567	−	0.625366i	−0.836441	−	0.548058i	$-0.815367\pi$
$733$	4.34718	−	16.9311i	0.160567	−	0.625366i	0.997007	−	0.0773083i	$-0.0246326\pi$
$734$	−17.0060	+	9.34911i	−0.627702	+	0.345082i
$735$	−5.22881	+	3.42071i	−0.192868	+	0.126175i
$736$	0.280407	−	1.46995i	0.0103360	−	0.0541830i
$737$	−4.93033	+	0.940510i	−0.181611	+	0.0346441i
$738$	−1.38404	−	0.651279i	−0.0509472	−	0.0239739i
$739$	11.5925	−	1.46448i	0.426439	−	0.0538717i	0.0908148	−	0.995868i	$-0.471053\pi$
$739$	11.5925	−	1.46448i	0.426439	−	0.0538717i	0.335624	+	0.941996i	$0.391053\pi$
$740$	2.88827	−	5.43040i	0.106175	−	0.199626i
$741$	−11.4241	−	59.8875i	−0.419676	−	2.20002i
$742$	−9.38495	−	23.7037i	−0.344532	−	0.870189i
$743$	−20.9821	−	6.81750i	−0.769759	−	0.250110i	−0.102297	−	0.994754i	$-0.532619\pi$
$743$	−20.9821	−	6.81750i	−0.769759	−	0.250110i	−0.667462	+	0.744644i	$0.732619\pi$
$744$	3.46885	−	5.46603i	0.127174	−	0.200394i
$745$	−47.1506	+	0.652497i	−1.72746	+	0.0239056i
$746$	−5.47925	+	1.40683i	−0.200609	+	0.0515078i
$747$	−2.76034	−	2.28355i	−0.100996	−	0.0835508i
$748$	−0.832834	−	6.59256i	−0.0304514	−	0.241048i
$749$	26.8281			0.980276
$750$	−29.3614	+	13.0593i	−1.07213	+	0.476859i
$751$	−21.3393			−0.778684			−0.389342	−	0.921093i	$-0.627298\pi$
$751$	−21.3393			−0.778684			−0.389342	+	0.921093i	$0.627298\pi$
$752$	−1.61487	−	12.7830i	−0.0588883	−	0.466149i
$753$	−40.7208	−	33.6872i	−1.48395	−	1.22763i
$754$	−1.40295	+	0.360217i	−0.0510926	+	0.0131183i
$755$	8.00510	−	5.98702i	0.291335	−	0.217890i
$756$	−0.993840	+	1.56604i	−0.0361456	+	0.0569563i
$757$	−2.23164	−	0.725104i	−0.0811104	−	0.0263544i	0.268181	−	0.963369i	$-0.413578\pi$
$757$	−2.23164	−	0.725104i	−0.0811104	−	0.0263544i	−0.349291	+	0.937014i	$0.613578\pi$
$758$	−2.33544	−	5.89864i	−0.0848269	−	0.214248i
$759$	1.54753	+	8.11245i	0.0561718	+	0.294463i
$760$	31.4808	+	5.55497i	1.14193	+	0.201500i
$761$	−37.4792	+	4.73473i	−1.35862	+	0.171634i	−0.770656	−	0.637252i	$-0.780071\pi$
$761$	−37.4792	+	4.73473i	−1.35862	+	0.171634i	−0.587966	+	0.808886i	$0.700071\pi$
$762$	4.06052	+	1.91073i	0.147097	+	0.0692186i
$763$	−29.0714	+	5.54567i	−1.05246	+	0.200767i
$764$	−0.427765	+	2.24242i	−0.0154760	+	0.0811280i
$765$	4.96867	+	18.2968i	0.179642	+	0.661521i
$766$	−30.4668	+	16.7493i	−1.10081	+	0.605176i
$767$	−7.88432	+	30.7074i	−0.284686	+	1.10878i
$768$	16.3825	−	5.32301i	0.591154	−	0.192077i
$769$	14.5843	+	17.6294i	0.525924	+	0.635732i	0.964853	−	0.262789i	$-0.0846423\pi$
$769$	14.5843	+	17.6294i	0.525924	+	0.635732i	−0.438930	+	0.898521i	$0.644642\pi$
$770$	−30.7806	+	8.35877i	−1.10925	+	0.301229i
$771$	−31.9061	−	50.2760i	−1.14907	−	1.81065i
$772$	1.82817	+	7.12025i	0.0657972	+	0.256263i
$773$	−16.1842	−	17.2344i	−0.582106	−	0.619880i	0.368744	−	0.929531i	$-0.379788\pi$
$773$	−16.1842	−	17.2344i	−0.582106	−	0.619880i	−0.950850	+	0.309651i	$0.899788\pi$
$774$	−8.75805	+	26.9545i	−0.314802	+	0.968860i
$775$	−4.43894	+	1.90122i	−0.159451	+	0.0682938i
$776$	6.88621	+	21.1936i	0.247200	+	0.760805i
$777$	−21.2804	+	38.7089i	−0.763431	+	1.38868i
$778$	15.9832	+	1.00558i	0.573027	+	0.0360518i
$779$	0.180735	−	2.87270i	0.00647551	−	0.102925i
$780$	0.730715	+	9.51203i	0.0261638	+	0.340585i
$781$	1.92674	+	0.494703i	0.0689443	+	0.0177019i
$782$	−2.65353	−	3.65227i	−0.0948901	−	0.130605i
$783$	0.382283	+	0.242604i	0.0136617	+	0.00866996i
$784$	4.01768	+	0.507551i	0.143489	+	0.0181268i
$785$	−6.48484	+	9.19041i	−0.231454	+	0.328020i
$786$	2.87697	+	6.11387i	0.102618	+	0.218074i
$787$	3.99766	+	7.27172i	0.142501	+	0.259209i	0.937920	−	0.346851i	$-0.112749\pi$
$787$	3.99766	+	7.27172i	0.142501	+	0.259209i	−0.795419	+	0.606060i	$0.792749\pi$
$788$	−2.44798	+	2.60683i	−0.0872057	+	0.0928646i
$789$	46.4378	+	25.5294i	1.65323	+	0.908870i
$790$	−0.634139	+	2.61978i	−0.0225616	+	0.0932077i
$791$	26.0192	+	24.4337i	0.925137	+	0.868761i
$792$	−20.8881	+	17.2801i	−0.742225	+	0.614022i
$793$	40.2828	−	55.4445i	1.43048	−	1.96889i
$794$	39.5538	−	15.6604i	1.40371	−	0.555769i
$795$	8.23689	+	40.1525i	0.292132	+	1.42406i
$796$	1.50952	−	1.82470i	0.0535036	−	0.0646747i
$797$	4.83404	−	12.2094i	0.171231	−	0.432479i	−0.818666	−	0.574270i	$-0.805286\pi$
$797$	4.83404	−	12.2094i	0.171231	−	0.432479i	0.989897	+	0.141791i	$0.0452860\pi$
$798$	−32.1192	−	6.12706i	−1.13701	−	0.216895i
$799$	14.0298	+	10.1933i	0.496340	+	0.360612i
$800$	−8.91317	−	2.62571i	−0.315128	−	0.0928328i
$801$	3.74613	−	2.72172i	0.132363	−	0.0961673i
$802$	−9.27412	+	4.36407i	−0.327481	+	0.154101i
$803$	57.0706	−	36.2181i	2.01398	−	1.27811i
$804$	0.748631	+	0.296404i	0.0264022	+	0.0104534i
$805$	3.10474	−	2.99746i	0.109428	−	0.105647i
$806$	−0.451988	−	7.18414i	−0.0159206	−	0.253050i
$807$		−	5.02090i		−	0.176744i
$808$	−29.2048	+	1.83741i	−1.02742	+	0.0646398i
$809$	−12.0325	+	25.5705i	−0.423042	+	0.899009i	0.573755	+	0.819027i	$0.305486\pi$
$809$	−12.0325	+	25.5705i	−0.423042	+	0.899009i	−0.996796	+	0.0799821i	$0.974514\pi$
$810$	−21.5093	+	23.5498i	−0.755761	+	0.827457i
$811$	40.0019	−	37.5643i	1.40466	−	1.31906i	0.518956	−	0.854801i	$-0.326321\pi$
$811$	40.0019	−	37.5643i	1.40466	−	1.31906i	0.885700	−	0.464259i	$-0.153679\pi$
$812$	0.0193909	−	0.153495i	0.000680489	−	0.00538662i
$813$	3.86845	−	30.6220i	0.135673	−	1.07396i
$814$	35.9266	−	33.7374i	1.25923	−	1.18249i
$815$	−10.1389	−	4.60073i	−0.355150	−	0.161157i
$816$	13.2679	−	28.1956i	0.464468	−	0.987045i
$817$	−53.2271	+	3.34877i	−1.86218	+	0.117159i
$818$		−	3.91863i		−	0.137012i
$819$	−1.69641	−	26.9637i	−0.0592774	−	0.942187i
$820$	−0.0782672	+	0.443551i	−0.00273321	+	0.0154895i
$821$	8.58760	+	3.40007i	0.299709	+	0.118663i	0.513166	−	0.858289i	$-0.328472\pi$
$821$	8.58760	+	3.40007i	0.299709	+	0.118663i	−0.213457	+	0.976952i	$0.568472\pi$
$822$	−18.0649	+	11.4644i	−0.630087	+	0.399866i
$823$	−31.1123	+	14.6404i	−1.08451	+	0.510331i	−0.883104	−	0.469178i	$-0.844550\pi$
$823$	−31.1123	+	14.6404i	−1.08451	+	0.510331i	−0.201404	+	0.979508i	$0.564550\pi$
$824$	16.5789	−	12.0453i	0.577554	−	0.419617i
$825$	51.0707	−	4.63493i	1.77806	−	0.161368i
$826$	13.7560	+	9.99432i	0.478632	+	0.347747i
$827$	6.44636	+	1.22971i	0.224162	+	0.0427612i	0.298238	−	0.954491i	$-0.403601\pi$
$827$	6.44636	+	1.22971i	0.224162	+	0.0427612i	−0.0740766	+	0.997253i	$0.523601\pi$
$828$	0.192317	−	0.485737i	0.00668347	−	0.0168805i
$829$	28.4362	−	34.3734i	0.987629	−	1.19384i	0.00659956	−	0.999978i	$-0.497899\pi$
$829$	28.4362	−	34.3734i	0.987629	−	1.19384i	0.981029	−	0.193860i	$-0.0621007\pi$
$830$	2.18868	−	4.82332i	0.0759703	−	0.167420i
$831$	−55.5581	+	21.9970i	−1.92729	+	0.763068i
$832$	30.0239	−	41.3244i	1.04089	−	1.43267i
$833$	−4.19969	+	3.47428i	−0.145510	+	0.120377i
$834$	15.2446	+	14.3156i	0.527877	+	0.495710i
$835$	−14.5901	−	8.97842i	−0.504912	−	0.310711i
$836$	−6.36697	−	3.50027i	−0.220206	−	0.121059i
$837$	−1.54029	+	1.64024i	−0.0532403	+	0.0566951i
$838$	−4.81392	−	8.75649i	−0.166294	−	0.302488i
$839$	6.30331	+	13.3952i	0.217615	+	0.462454i	0.983591	−	0.180415i	$-0.0577439\pi$
$839$	6.30331	+	13.3952i	0.217615	+	0.462454i	−0.765976	+	0.642869i	$0.777744\pi$
$840$	34.3162	+	10.6273i	1.18402	+	0.366678i
$841$	28.7339	+	3.62993i	0.990823	+	0.125170i
$842$	27.6024	+	17.5170i	0.951241	+	0.603676i
$843$	26.9942	+	37.1544i	0.929731	+	1.27966i
$844$	−8.65541	−	2.22233i	−0.297932	−	0.0764958i
$845$	29.4264	+	34.5847i	1.01230	+	1.18975i
$846$	0.632714	−	10.0567i	0.0217532	−	0.345757i
$847$	24.4860	+	1.54053i	0.841349	+	0.0529332i
$848$	12.7979	−	23.2792i	0.439480	−	0.799411i
$849$	−1.89556	−	5.83394i	−0.0650555	−	0.200220i
$850$	−24.1811	+	14.1788i	−0.829403	+	0.486330i
$851$	−2.06064	+	6.34199i	−0.0706378	+	0.217401i
$852$	−0.218445	−	0.232620i	−0.00748380	−	0.00796944i
$853$	1.21604	+	4.73615i	0.0416363	+	0.162163i	0.986002	−	0.166736i	$-0.0533226\pi$
$853$	1.21604	+	4.73615i	0.0416363	+	0.162163i	−0.944365	+	0.328898i	$0.893323\pi$
$854$	−19.6949	−	31.0342i	−0.673945	−	1.06197i
$855$	19.3785	+	7.36395i	0.662729	+	0.251842i
$856$	21.4897	+	25.9765i	0.734501	+	0.887860i
$857$	22.5168	−	7.31615i	0.769159	−	0.249915i	0.101954	−	0.994789i	$-0.467490\pi$
$857$	22.5168	−	7.31615i	0.769159	−	0.249915i	0.667205	+	0.744874i	$0.267490\pi$
$858$	−19.0104	+	74.0405i	−0.649003	+	2.52770i
$859$	−12.2950	+	6.75925i	−0.419501	+	0.230623i	−0.677500	−	0.735522i	$-0.736937\pi$
$859$	−12.2950	+	6.75925i	−0.419501	+	0.230623i	0.257999	+	0.966145i	$0.416937\pi$
$860$	8.33533	+	0.408710i	0.284232	+	0.0139369i
$861$	0.606118	−	3.17738i	0.0206564	−	0.108285i
$862$	35.7800	−	6.82539i	1.21867	−	0.232474i
$863$	22.1702	+	10.4325i	0.754683	+	0.355127i	0.764329	−	0.644827i	$-0.223070\pi$
$863$	22.1702	+	10.4325i	0.754683	+	0.355127i	−0.00964574	+	0.999953i	$0.503070\pi$
$864$	−4.29548	+	0.542645i	−0.146135	+	0.0184612i
$865$	0.414959	+	2.95526i	0.0141090	+	0.100482i
$866$	−2.31123	−	12.1159i	−0.0785389	−	0.411715i
$867$	1.51164	+	3.81798i	0.0513381	+	0.129665i
$868$	0.731249	+	0.237597i	0.0248202	+	0.00806457i
$869$	2.30480	−	3.63179i	0.0781851	−	0.123200i
$870$	0.369487	−	1.19309i	0.0125268	−	0.0404496i
$871$	6.08843	−	1.56324i	0.206298	−	0.0529684i
$872$	−28.6563	−	23.7065i	−0.970424	−	0.802805i
$873$	1.81121	+	14.3372i	0.0613002	+	0.485241i
$874$	−4.93617			−0.166968
$875$	−16.6367	−	21.0065i	−0.562425	−	0.710150i
$876$	−10.8431			−0.366354
$877$	−6.94538	−	54.9784i	−0.234529	−	1.85649i	−0.467485	−	0.884001i	$-0.654840\pi$
$877$	−6.94538	−	54.9784i	−0.234529	−	1.85649i	0.232956	−	0.972487i	$-0.425160\pi$
$878$	−30.1144	−	24.9128i	−1.01631	−	0.840768i
$879$	5.09478	−	1.30812i	0.171843	−	0.0441217i
$880$	−27.1558	−	19.1614i	−0.915423	−	0.645931i
$881$	−29.0306	+	45.7449i	−0.978065	+	1.54118i	−0.143956	+	0.989584i	$0.545982\pi$
$881$	−29.0306	+	45.7449i	−0.978065	+	1.54118i	−0.834109	+	0.551600i	$0.814018\pi$
$882$	3.01205	+	0.978673i	0.101421	+	0.0329536i
$883$	−3.90775	−	9.86984i	−0.131506	−	0.332147i	0.849071	−	0.528278i	$-0.177162\pi$
$883$	−3.90775	−	9.86984i	−0.131506	−	0.332147i	−0.980578	+	0.196131i	$0.937162\pi$
$884$	1.55937	+	8.17450i	0.0524473	+	0.274938i
$885$	−18.9879	−	19.6674i	−0.638270	−	0.661113i
$886$	−25.1979	+	3.18324i	−0.846542	+	0.106943i
$887$	42.8609	+	20.1688i	1.43913	+	0.677202i	0.977706	−	0.209978i	$-0.0673393\pi$
$887$	42.8609	+	20.1688i	1.43913	+	0.677202i	0.461422	+	0.887181i	$0.347339\pi$
$888$	−54.5262	+	10.4014i	−1.82978	+	0.349049i
$889$	−0.701209	+	3.67587i	−0.0235178	+	0.123285i
$890$	5.33492	+	4.29049i	0.178827	+	0.143817i
$891$	44.6015	−	24.5199i	1.49421	−	0.821446i
$892$	1.07132	−	4.17253i	0.0358706	−	0.139707i
$893$	18.0337	−	5.85951i	0.603476	−	0.196081i
$894$	38.6358	+	46.7027i	1.29218	+	1.56197i
$895$	−1.61385	+	32.9132i	−0.0539450	+	1.10017i
$896$	−9.90595	−	15.6093i	−0.330934	−	0.521469i
$897$	−2.57218	−	10.0180i	−0.0858828	−	0.334491i
$898$	−11.1273	−	11.8494i	−0.371324	−	0.395420i
$899$	0.0579993	−	0.178504i	0.00193439	−	0.00595343i
$900$	−2.88477	−	1.48348i	−0.0961591	−	0.0494495i
$901$	11.0489	+	34.0049i	0.368091	+	1.13287i
$902$	−1.73864	+	3.16257i	−0.0578902	+	0.105302i
$903$	−59.8157	−	3.76329i	−1.99054	−	0.125234i
$904$	−2.81638	+	44.7651i	−0.0936714	+	1.48886i
$905$	2.53057	−	1.04265i	0.0841188	−	0.0346590i
$906$	−12.4454	−	3.19544i	−0.413471	−	0.106161i
$907$	17.4766	+	24.0545i	0.580300	+	0.798715i	0.993728	−	0.111822i	$-0.0356686\pi$
$907$	17.4766	+	24.0545i	0.580300	+	0.798715i	−0.413428	+	0.910537i	$0.635669\pi$
$908$	−6.24330	−	3.96212i	−0.207191	−	0.131488i
$909$	−18.8269	−	2.37839i	−0.624449	−	0.0788862i
$910$	37.8151	−	12.8680i	1.25356	−	0.426572i
$911$	−11.0778	−	23.5416i	−0.367025	−	0.779968i	−0.999983	−	0.00578219i	$-0.998159\pi$
$911$	−11.0778	−	23.5416i	−0.367025	−	0.779968i	0.632958	−	0.774186i	$-0.281841\pi$
$912$	−16.4144	−	29.8577i	−0.543536	−	0.988688i
$913$	−5.78611	+	6.16158i	−0.191492	+	0.203918i
$914$	−19.1620	−	10.5344i	−0.633822	−	0.348446i
$915$	22.5128	+	54.6394i	0.744249	+	1.80632i
$916$	0.211069	+	0.198207i	0.00697391	+	0.00654893i
$917$	−4.34146	+	3.59157i	−0.143368	+	0.118604i
$918$	−7.67734	+	10.5670i	−0.253390	+	0.348761i
$919$	25.5410	−	10.1124i	0.842521	−	0.333577i	0.0930878	−	0.995658i	$-0.470326\pi$
$919$	25.5410	−	10.1124i	0.842521	−	0.333577i	0.749433	+	0.662080i	$0.230326\pi$
$920$	5.38926	+	0.605185i	0.177679	+	0.0199523i
$921$	21.8476	−	26.4092i	0.719903	−	0.870213i
$922$	−3.81798	+	9.64312i	−0.125739	+	0.317579i
$923$	−2.44712	−	0.466814i	−0.0805481	−	0.0153654i
$924$	−6.60566	−	4.79930i	−0.217310	−	0.157885i
$925$	37.9384	+	16.5862i	1.24741	+	0.545350i
$926$	−1.42760	+	1.03721i	−0.0469138	+	0.0340849i
$927$	12.0246	−	5.65833i	0.394938	−	0.185844i
$928$	0.304931	−	0.193515i	0.0100099	−	0.00635245i
$929$	−39.3131	−	15.5652i	−1.28982	−	0.510677i	−0.379735	−	0.925095i	$-0.623985\pi$
$929$	−39.3131	−	15.5652i	−1.28982	−	0.510677i	−0.910086	+	0.414419i	$0.863985\pi$
$930$	5.48016	+	2.91473i	0.179701	+	0.0955777i
$931$	0.374210	+	5.94789i	0.0122642	+	0.194934i
$932$			5.70486i			0.186869i
$933$	−3.91500	+	0.246311i	−0.128171	+	0.00806386i
$934$	15.5270	−	32.9966i	0.508059	−	1.07968i
$935$	43.8202	−	8.98929i	1.43307	−	0.293981i
$936$	24.7490	−	23.2409i	0.808947	−	0.759651i
$937$	3.10338	−	24.5658i	0.101383	−	0.802528i	−0.856656	−	0.515889i	$-0.827462\pi$
$937$	3.10338	−	24.5658i	0.101383	−	0.802528i	0.958038	−	0.286640i	$-0.0925382\pi$
$938$	0.422535	−	3.34471i	0.0137963	−	0.109209i
$939$	−48.2516	+	45.3113i	−1.57463	+	1.47868i
$940$	−2.90658	+	0.596256i	−0.0948020	+	0.0194477i
$941$	7.92949	−	16.8510i	0.258494	−	0.549328i	−0.732885	−	0.680353i	$-0.761827\pi$
$941$	7.92949	−	16.8510i	0.258494	−	0.549328i	0.991379	+	0.131025i	$0.0418267\pi$
$942$	14.4295	−	0.907824i	0.470137	−	0.0295785i
$943$		−	0.488309i		−	0.0159015i
$944$	1.11251	+	17.6828i	0.0362091	+	0.575527i
$945$	−11.0238	−	5.86322i	−0.358604	−	0.190731i
$946$	62.1734	+	24.6162i	2.02143	+	0.800341i
$947$	−13.4663	+	8.54599i	−0.437597	+	0.277707i	−0.736321	−	0.676632i	$-0.763439\pi$
$947$	−13.4663	+	8.54599i	−0.437597	+	0.277707i	0.298725	+	0.954339i	$0.403439\pi$
$948$	−0.624348	+	0.293796i	−0.0202779	+	0.00954205i
$949$	−68.4840	+	49.7566i	−2.22309	+	1.61517i
$950$	−2.99853	+	30.5029i	−0.0972853	+	0.989646i
$951$	11.1338	+	8.08917i	0.361038	+	0.262309i
$952$	30.7820	+	5.87198i	0.997651	+	0.190312i
$953$	−3.20786	+	8.10213i	−0.103913	+	0.262454i	−0.972426	−	0.233213i	$-0.925076\pi$
$953$	−3.20786	+	8.10213i	−0.103913	+	0.262454i	0.868513	+	0.495667i	$0.165076\pi$
$954$	13.2429	−	16.0079i	0.428754	−	0.518275i
$955$	−15.2718	−	1.71494i	−0.494185	−	0.0554943i
$956$	8.16424	−	3.23245i	0.264050	−	0.104545i
$957$	−1.17155	+	1.61250i	−0.0378707	+	0.0521246i
$958$	39.6714	−	32.8191i	1.28173	−	1.06034i
$959$	−13.0059	−	12.2133i	−0.419982	−	0.394389i
$960$	16.7794	+	40.7243i	0.541553	+	1.31437i
$961$	−26.3481	−	14.4850i	−0.849940	−	0.467258i
$962$	−42.2515	+	44.9933i	−1.36224	+	1.45064i
$963$	10.5325	+	19.1585i	0.339405	+	0.617375i
$964$	−0.0225720	−	0.0479679i	−0.000726995	−	0.00154494i
$965$	−46.8489	+	15.9421i	−1.50812	+	0.513195i
$966$	−5.50344	−	0.695246i	−0.177070	−	0.0223692i
$967$	24.4753	+	15.5325i	0.787072	+	0.499491i	0.867601	−	0.497261i	$-0.165661\pi$
$967$	24.4753	+	15.5325i	0.787072	+	0.499491i	−0.0805287	+	0.996752i	$0.525661\pi$
$968$	18.1220	+	24.9428i	0.582464	+	0.801692i
$969$	44.4182	+	11.4047i	1.42692	+	0.366370i
$970$	−19.7549	+	8.13949i	−0.634292	+	0.261343i
$971$	2.08524	−	33.1440i	0.0669187	−	1.06364i	−0.811067	−	0.584954i	$-0.801113\pi$
$971$	2.08524	−	33.1440i	0.0669187	−	1.06364i	0.877985	−	0.478688i	$-0.158887\pi$
$972$	−5.83164	−	0.366896i	−0.187050	−	0.0117682i
$973$	−8.40113	+	15.2816i	−0.269328	+	0.489905i
$974$	4.06948	+	12.5246i	0.130395	+	0.401313i
$975$	−63.4685	+	9.80920i	−2.03262	+	0.314146i
$976$	11.8355	−	36.4259i	0.378845	−	1.16597i
$977$	10.4289	+	11.1057i	0.333651	+	0.355303i	0.873816	−	0.486257i	$-0.161638\pi$
$977$	10.4289	+	11.1057i	0.333651	+	0.355303i	−0.540165	+	0.841559i	$0.681638\pi$
$978$	3.55909	+	13.8618i	0.113807	+	0.443250i
$979$	−5.85397	−	9.22437i	−0.187094	−	0.294812i
$980$	0.0456715	−	0.931436i	0.00145892	−	0.0297536i
$981$	−15.3735	−	18.5834i	−0.490839	−	0.593322i
$982$	−1.02962	+	0.334543i	−0.0328564	+	0.0106757i
$983$	−11.7957	+	45.9413i	−0.376225	+	1.46530i	0.445431	+	0.895316i	$0.353050\pi$
$983$	−11.7957	+	45.9413i	−0.376225	+	1.46530i	−0.821656	+	0.569984i	$0.806950\pi$
$984$	3.56204	−	1.95825i	0.113554	−	0.0624267i
$985$	−18.7595	−	15.0868i	−0.597726	−	0.480707i
$986$	0.204155	−	1.07022i	0.00650161	−	0.0340826i
$987$	20.9315	−	3.99290i	0.666257	−	0.127095i
$988$	8.23328	+	3.87429i	0.261936	+	0.123257i
$989$	−8.97634	+	1.13398i	−0.285431	+	0.0360583i
$990$	−18.0534	−	18.6995i	−0.573775	−	0.594310i
$991$	−4.14836	−	21.7465i	−0.131777	−	0.690800i	−0.985447	−	0.169985i	$-0.945628\pi$
$991$	−4.14836	−	21.7465i	−0.131777	−	0.690800i	0.853670	−	0.520815i	$-0.174372\pi$
$992$	0.660711	+	1.66876i	0.0209776	+	0.0529833i
$993$	−62.4945	−	20.3057i	−1.98320	−	0.644382i
$994$	−0.715929	+	1.12812i	−0.0227079	+	0.0357819i
$995$	13.0258	+	9.19114i	0.412946	+	0.291379i
$996$	1.31332	−	0.337204i	0.0416142	−	0.0106847i
$997$	25.5832	+	21.1642i	0.810227	+	0.670278i	0.947323	−	0.320279i	$-0.103777\pi$
$997$	25.5832	+	21.1642i	0.810227	+	0.670278i	−0.137096	+	0.990558i	$0.543777\pi$
$998$	−3.55152	−	28.1131i	−0.112421	−	0.889906i
$999$	19.2933			0.610412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.39.8	✓	240
5.2	odd	4		625.2.g.b.176.8		480
5.3	odd	4		625.2.g.b.176.17		480
5.4	even	2		625.2.h.a.449.5		240
125.16	even	25		625.2.h.a.174.5		240
125.37	odd	100		625.2.g.b.451.8		480
125.88	odd	100		625.2.g.b.451.17		480
125.109	even	50	inner	125.2.h.a.109.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.8	✓	240	1.1	even	1	trivial
125.2.h.a.109.8	yes	240	125.109	even	50	inner
625.2.g.b.176.8		480	5.2	odd	4
625.2.g.b.176.17		480	5.3	odd	4
625.2.g.b.451.8		480	125.37	odd	100
625.2.g.b.451.17		480	125.88	odd	100
625.2.h.a.174.5		240	125.16	even	25
625.2.h.a.449.5		240	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.161861 + 1.28126i) q^{2} +(-1.71483 - 1.41863i) q^{3} +(0.321728 - 0.0826056i) q^{4} +(0.720344 + 2.11686i) q^{5} +(1.54008 - 2.42678i) q^{6} +(2.27945 + 0.740638i) q^{7} +(1.10874 + 2.80036i) q^{8} +(0.365988 + 1.91858i) q^{9} +O(q^{10})\)	\(q+(0.161861 + 1.28126i) q^{2} +(-1.71483 - 1.41863i) q^{3} +(0.321728 - 0.0826056i) q^{4} +(0.720344 + 2.11686i) q^{5} +(1.54008 - 2.42678i) q^{6} +(2.27945 + 0.740638i) q^{7} +(1.10874 + 2.80036i) q^{8} +(0.365988 + 1.91858i) q^{9} +(-2.59566 + 1.26559i) q^{10} +(4.57197 - 0.577574i) q^{11} +(-0.668897 - 0.314759i) q^{12} +(-5.66906 + 1.08143i) q^{13} +(-0.579998 + 3.04046i) q^{14} +(1.76778 - 4.65197i) q^{15} +(-2.82639 + 1.55382i) q^{16} +(1.07959 - 4.20471i) q^{17} +(-2.39897 + 0.779471i) q^{18} +(-3.02560 - 3.65732i) q^{19} +(0.406619 + 0.621549i) q^{20} +(-2.85818 - 4.50378i) q^{21} +(1.48005 + 5.76442i) q^{22} +(-0.551231 - 0.587001i) q^{23} +(2.07138 - 6.37505i) q^{24} +(-3.96221 + 3.04974i) q^{25} +(-2.30320 - 7.08852i) q^{26} +(-1.12238 + 2.04161i) q^{27} +(0.794543 + 0.0499884i) q^{28} +(0.0122026 - 0.193954i) q^{29} +(6.24654 + 1.51202i) q^{30} +(0.935449 + 0.240183i) q^{31} +(1.09233 + 1.50346i) q^{32} +(-8.65953 - 5.49551i) q^{33} +(5.56208 + 0.702655i) q^{34} +(0.0741581 + 5.35880i) q^{35} +(0.276234 + 0.587027i) q^{36} +(-3.98946 - 7.25681i) q^{37} +(4.19627 - 4.46857i) q^{38} +(11.2556 + 6.18784i) q^{39} +(-5.12931 + 4.36428i) q^{40} +(0.442053 + 0.415115i) q^{41} +(5.30790 - 4.39107i) q^{42} +(6.60429 - 9.09003i) q^{43} +(1.42322 - 0.563492i) q^{44} +(-3.79773 + 2.15678i) q^{45} +(0.662880 - 0.801285i) q^{46} +(-1.47059 + 3.71428i) q^{47} +(7.05108 + 1.34507i) q^{48} +(-1.01577 - 0.738000i) q^{49} +(-4.54885 - 4.58300i) q^{50} +(-7.81625 + 5.67884i) q^{51} +(-1.73456 + 0.816222i) q^{52} +(-6.95421 + 4.41327i) q^{53} +(-2.79751 - 1.10761i) q^{54} +(4.51604 + 9.26218i) q^{55} +(0.453266 + 7.20446i) q^{56} +10.5639i q^{57} +(0.250482 - 0.0157590i) q^{58} +(2.33894 - 4.97049i) q^{59} +(0.184466 - 1.64270i) q^{60} +(-8.65640 + 8.12890i) q^{61} +(-0.156324 + 1.23743i) q^{62} +(-0.586720 + 4.64437i) q^{63} +(-6.45186 + 6.05870i) q^{64} +(-6.37291 - 11.2216i) q^{65} +(5.63955 - 11.9847i) q^{66} +(-1.08702 + 0.0683896i) q^{67} -1.44195i q^{68} +(0.112529 + 1.78860i) q^{69} +(-6.85403 + 0.962398i) q^{70} +(0.401350 + 0.158906i) q^{71} +(-4.96693 + 3.15211i) q^{72} +(13.2717 - 6.24516i) q^{73} +(8.65215 - 6.28615i) q^{74} +(11.1210 + 0.391136i) q^{75} +(-1.27554 - 0.926731i) q^{76} +(10.8494 + 2.06963i) q^{77} +(-6.10641 + 15.4230i) q^{78} +(0.594972 - 0.719197i) q^{79} +(-5.32519 - 4.86379i) q^{80} +(10.2690 - 4.06580i) q^{81} +(-0.460321 + 0.633577i) q^{82} +(-1.41326 + 1.16915i) q^{83} +(-1.29159 - 1.21289i) q^{84} +(9.67846 - 0.743500i) q^{85} +(12.7157 + 6.99052i) q^{86} +(-0.296076 + 0.315288i) q^{87} +(6.68655 + 12.1628i) q^{88} +(-1.00941 - 2.14511i) q^{89} +(-3.37811 - 4.51679i) q^{90} +(-13.7233 - 1.73365i) q^{91} +(-0.225836 - 0.143320i) q^{92} +(-1.26341 - 1.73893i) q^{93} +(-4.99700 - 1.28301i) q^{94} +(5.56258 - 9.03931i) q^{95} +(0.259698 - 4.12779i) q^{96} +(7.38421 + 0.464575i) q^{97} +(0.781159 - 1.42092i) q^{98} +(2.78141 + 8.56030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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