LMFDB - Embedded newform 125.2.h.a.4.4

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			4.4
Character	$\chi$	$=$	125.4
Dual form			125.2.h.a.94.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58276 - 0.0995789i) q^{2} +(0.718817 + 0.338250i) q^{3} +(0.510990 + 0.0645531i) q^{4} +(-1.79303 - 1.33605i) q^{5} +(-1.10403 - 0.606948i) q^{6} +(2.20198 - 3.03077i) q^{7} +(2.31325 + 0.441277i) q^{8} +(-1.50999 - 1.82526i) q^{9} +O(q^{10})$	\(q+(-1.58276 - 0.0995789i) q^{2} +(0.718817 + 0.338250i) q^{3} +(0.510990 + 0.0645531i) q^{4} +(-1.79303 - 1.33605i) q^{5} +(-1.10403 - 0.606948i) q^{6} +(2.20198 - 3.03077i) q^{7} +(2.31325 + 0.441277i) q^{8} +(-1.50999 - 1.82526i) q^{9} +(2.70490 + 2.29320i) q^{10} +(-0.102822 + 1.63430i) q^{11} +(0.345473 + 0.219244i) q^{12} +(3.74074 - 3.09461i) q^{13} +(-3.78702 + 4.57771i) q^{14} +(-0.836943 - 1.56687i) q^{15} +(-4.61513 - 1.18496i) q^{16} +(-0.665246 - 5.26597i) q^{17} +(2.20819 + 3.03932i) q^{18} +(-0.185629 - 0.394481i) q^{19} +(-0.829976 - 0.798455i) q^{20} +(2.60798 - 1.43375i) q^{21} +(0.325484 - 2.57647i) q^{22} +(-2.57076 + 6.49301i) q^{23} +(1.51354 + 1.09965i) q^{24} +(1.42993 + 4.79117i) q^{25} +(-6.22885 + 4.52553i) q^{26} +(-1.06071 - 4.13118i) q^{27} +(1.32084 - 1.40655i) q^{28} +(2.89224 + 2.71600i) q^{29} +(1.16866 + 2.56332i) q^{30} +(-1.10019 + 0.138987i) q^{31} +(2.70724 + 0.879636i) q^{32} +(-0.626712 + 1.13999i) q^{33} +(0.528547 + 8.40102i) q^{34} +(-7.99749 + 2.49231i) q^{35} +(-0.653763 - 1.03016i) q^{36} +(-2.58301 + 10.0602i) q^{37} +(0.254524 + 0.642854i) q^{38} +(3.73565 - 0.959153i) q^{39} +(-3.55817 - 3.88185i) q^{40} +(-5.16095 + 2.04336i) q^{41} +(-4.27058 + 2.00958i) q^{42} +(11.4034 - 3.70519i) q^{43} +(-0.158040 + 0.828476i) q^{44} +(0.268814 + 5.29017i) q^{45} +(4.71547 - 10.0209i) q^{46} +(7.20980 - 1.37534i) q^{47} +(-2.91662 - 2.41284i) q^{48} +(-2.17371 - 6.69001i) q^{49} +(-1.78614 - 7.72567i) q^{50} +(1.30302 - 4.01029i) q^{51} +(2.11125 - 1.33984i) q^{52} +(-3.57311 - 6.49946i) q^{53} +(1.26747 + 6.64430i) q^{54} +(2.36788 - 2.79298i) q^{55} +(6.43115 - 6.03925i) q^{56} -0.346348i q^{57} +(-4.30728 - 4.58678i) q^{58} +(3.36914 - 5.30892i) q^{59} +(-0.326524 - 0.854682i) q^{60} +(3.85850 + 1.52769i) q^{61} +(1.75519 - 0.110427i) q^{62} +(-8.85691 + 0.557229i) q^{63} +(4.66312 + 1.84626i) q^{64} +(-10.8418 + 0.550914i) q^{65} +(1.10546 - 1.74192i) q^{66} +(0.0597187 + 0.0635939i) q^{67} -2.73380i q^{68} +(-4.04416 + 3.79772i) q^{69} +(12.9063 - 3.14835i) q^{70} +(0.733649 + 3.84592i) q^{71} +(-2.68754 - 4.88861i) q^{72} +(-4.28008 + 2.71622i) q^{73} +(5.09007 - 15.6656i) q^{74} +(-0.592750 + 3.92765i) q^{75} +(-0.0693894 - 0.213559i) q^{76} +(4.72679 + 3.91034i) q^{77} +(-6.00816 + 1.14612i) q^{78} +(-0.764053 + 1.62370i) q^{79} +(6.69191 + 8.29073i) q^{80} +(-0.696741 + 3.65244i) q^{81} +(8.37202 - 2.72024i) q^{82} +(9.72636 - 4.57688i) q^{83} +(1.42520 - 0.564278i) q^{84} +(-5.84280 + 10.3309i) q^{85} +(-18.4178 + 4.72890i) q^{86} +(1.16031 + 2.93061i) q^{87} +(-0.959033 + 3.73519i) q^{88} +(1.02704 + 1.61836i) q^{89} +(0.101321 - 8.39985i) q^{90} +(-1.14200 - 18.1516i) q^{91} +(-1.73278 + 3.15191i) q^{92} +(-0.837850 - 0.272234i) q^{93} +(-11.5484 + 1.45890i) q^{94} +(-0.194208 + 0.955326i) q^{95} +(1.64847 + 1.54802i) q^{96} +(-6.52045 + 6.94357i) q^{97} +(2.77429 + 10.8051i) q^{98} +(3.13829 - 2.28010i) 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 $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{50}\right)$

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 $

$2$	−1.58276	−	0.0995789i	−1.11918	−	0.0704129i	−0.507599	−	0.861593i	$-0.669467\pi$
$2$	−1.58276	−	0.0995789i	−1.11918	−	0.0704129i	−0.611583	+	0.791180i	$0.709467\pi$
$3$	0.718817	+	0.338250i	0.415009	+	0.195288i	0.621936	−	0.783068i	$-0.286346\pi$
$3$	0.718817	+	0.338250i	0.415009	+	0.195288i	−0.206927	+	0.978356i	$0.566346\pi$
$4$	0.510990	+	0.0645531i	0.255495	+	0.0322765i
$5$	−1.79303	−	1.33605i	−0.801869	−	0.597500i
$5$	−1.79303	−	1.33605i	−0.801869	−	0.597500i
$6$	−1.10403	−	0.606948i	−0.450720	−	0.247785i
$7$	2.20198	−	3.03077i	0.832271	−	1.14552i	−0.155225	−	0.987879i	$-0.549610\pi$
$7$	2.20198	−	3.03077i	0.832271	−	1.14552i	0.987496	−	0.157644i	$-0.0503898\pi$
$8$	2.31325	+	0.441277i	0.817859	+	0.156015i
$9$	−1.50999	−	1.82526i	−0.503329	−	0.608420i
$10$	2.70490	+	2.29320i	0.855365	+	0.725173i
$11$	−0.102822	+	1.63430i	−0.0310019	+	0.492761i	0.951636	+	0.307228i	$0.0994013\pi$
$11$	−0.102822	+	1.63430i	−0.0310019	+	0.492761i	−0.982638	+	0.185533i	$0.940599\pi$
$12$	0.345473	+	0.219244i	0.0997296	+	0.0632903i
$13$	3.74074	−	3.09461i	1.03749	−	0.858289i	0.0474249	−	0.998875i	$-0.484899\pi$
$13$	3.74074	−	3.09461i	1.03749	−	0.858289i	0.990069	+	0.140586i	$0.0448985\pi$
$14$	−3.78702	+	4.57771i	−1.01212	+	1.22345i
$15$	−0.836943	−	1.56687i	−0.216098	−	0.404564i
$16$	−4.61513	−	1.18496i	−1.15378	−	0.296241i
$17$	−0.665246	−	5.26597i	−0.161346	−	1.27718i	−0.839943	−	0.542674i	$-0.817412\pi$
$17$	−0.665246	−	5.26597i	−0.161346	−	1.27718i	0.678597	−	0.734511i	$-0.262588\pi$
$18$	2.20819	+	3.03932i	0.520476	+	0.716374i
$19$	−0.185629	−	0.394481i	−0.0425861	−	0.0905001i	0.882402	−	0.470497i	$-0.155925\pi$
$19$	−0.185629	−	0.394481i	−0.0425861	−	0.0905001i	−0.924988	+	0.379996i	$0.875925\pi$
$20$	−0.829976	−	0.798455i	−0.185588	−	0.178540i
$21$	2.60798	−	1.43375i	0.569108	−	0.312870i
$22$	0.325484	−	2.57647i	0.0693935	−	0.549306i
$23$	−2.57076	+	6.49301i	−0.536041	+	1.35389i	0.369344	+	0.929293i	$0.379583\pi$
$23$	−2.57076	+	6.49301i	−0.536041	+	1.35389i	−0.905385	+	0.424592i	$0.860417\pi$
$24$	1.51354	+	1.09965i	0.308951	+	0.224466i
$25$	1.42993	+	4.79117i	0.285987	+	0.958234i
$26$	−6.22885	+	4.52553i	−1.22158	+	0.887529i
$27$	−1.06071	−	4.13118i	−0.204133	−	0.795046i
$28$	1.32084	−	1.40655i	0.249615	−	0.265813i
$29$	2.89224	+	2.71600i	0.537076	+	0.504348i	0.904944	−	0.425530i	$-0.139912\pi$
$29$	2.89224	+	2.71600i	0.537076	+	0.504348i	−0.367868	+	0.929878i	$0.619912\pi$
$30$	1.16866	+	2.56332i	0.213366	+	0.467997i
$31$	−1.10019	+	0.138987i	−0.197601	+	0.0249628i	−0.223511	−	0.974702i	$-0.571752\pi$
$31$	−1.10019	+	0.138987i	−0.197601	+	0.0249628i	0.0259098	+	0.999664i	$0.491752\pi$
$32$	2.70724	+	0.879636i	0.478577	+	0.155499i
$33$	−0.626712	+	1.13999i	−0.109097	+	0.198446i
$34$	0.528547	+	8.40102i	0.0906451	+	1.44076i
$35$	−7.99749	+	2.49231i	−1.35182	+	0.421277i
$36$	−0.653763	−	1.03016i	−0.108960	−	0.171694i
$37$	−2.58301	+	10.0602i	−0.424644	+	1.65388i	0.291984	+	0.956423i	$0.405685\pi$
$37$	−2.58301	+	10.0602i	−0.424644	+	1.65388i	−0.716628	+	0.697456i	$0.754315\pi$
$38$	0.254524	+	0.642854i	0.0412892	+	0.104285i
$39$	3.73565	−	0.959153i	0.598183	−	0.153587i
$40$	−3.55817	−	3.88185i	−0.562596	−	0.613774i
$41$	−5.16095	+	2.04336i	−0.806004	+	0.319120i	−0.734750	−	0.678339i	$-0.762700\pi$
$41$	−5.16095	+	2.04336i	−0.806004	+	0.319120i	−0.0712547	+	0.997458i	$0.522700\pi$
$42$	−4.27058	+	2.00958i	−0.658965	+	0.310085i
$43$	11.4034	−	3.70519i	1.73900	−	0.565037i	0.744303	−	0.667843i	$-0.232782\pi$
$43$	11.4034	−	3.70519i	1.73900	−	0.565037i	0.994701	+	0.102806i	$0.0327820\pi$
$44$	−0.158040	+	0.828476i	−0.0238255	+	0.124897i
$45$	0.268814	+	5.29017i	0.0400724	+	0.788612i
$46$	4.71547	−	10.0209i	0.695258	−	1.47750i
$47$	7.20980	−	1.37534i	1.05166	−	0.200615i	0.367556	−	0.930001i	$-0.380194\pi$
$47$	7.20980	−	1.37534i	1.05166	−	0.200615i	0.684102	+	0.729387i	$0.260194\pi$
$48$	−2.91662	−	2.41284i	−0.420978	−	0.348263i
$49$	−2.17371	−	6.69001i	−0.310531	−	0.955715i
$50$	−1.78614	−	7.72567i	−0.252599	−	1.09257i
$51$	1.30302	−	4.01029i	0.182459	−	0.561552i
$52$	2.11125	−	1.33984i	0.292777	−	0.185802i
$53$	−3.57311	−	6.49946i	−0.490804	−	0.892769i	−0.999494	−	0.0318190i	$-0.989870\pi$
$53$	−3.57311	−	6.49946i	−0.490804	−	0.892769i	0.508690	−	0.860950i	$-0.330130\pi$
$54$	1.26747	+	6.64430i	0.172481	+	0.904174i
$55$	2.36788	−	2.79298i	0.319284	−	0.376606i
$56$	6.43115	−	6.03925i	0.859399	−	0.807029i
$57$		−	0.346348i		−	0.0458749i
$58$	−4.30728	−	4.58678i	−0.565573	−	0.602274i
$59$	3.36914	−	5.30892i	0.438625	−	0.691162i	−0.551053	−	0.834470i	$-0.685774\pi$
$59$	3.36914	−	5.30892i	0.438625	−	0.691162i	0.989678	+	0.143308i	$0.0457739\pi$
$60$	−0.326524	−	0.854682i	−0.0421540	−	0.110339i
$61$	3.85850	+	1.52769i	0.494031	+	0.195601i	0.601911	−	0.798563i	$-0.294406\pi$
$61$	3.85850	+	1.52769i	0.494031	+	0.195601i	−0.107880	+	0.994164i	$0.534406\pi$
$62$	1.75519	−	0.110427i	0.222909	−	0.0140242i
$63$	−8.85691	+	0.557229i	−1.11587	+	0.0702043i
$64$	4.66312	+	1.84626i	0.582890	+	0.230782i
$65$	−10.8418	+	0.550914i	−1.34476	+	0.0683325i
$66$	1.10546	−	1.74192i	0.136072	−	0.214415i
$67$	0.0597187	+	0.0635939i	0.00729579	+	0.00776923i	0.732606	−	0.680653i	$-0.238304\pi$
$67$	0.0597187	+	0.0635939i	0.00729579	+	0.00776923i	−0.725310	+	0.688422i	$0.758304\pi$
$68$		−	2.73380i		−	0.331522i
$69$	−4.04416	+	3.79772i	−0.486860	+	0.457192i
$70$	12.9063	−	3.14835i	1.54260	−	0.376299i
$71$	0.733649	+	3.84592i	0.0870681	+	0.456427i	0.998943	+	0.0459594i	$0.0146345\pi$
$71$	0.733649	+	3.84592i	0.0870681	+	0.456427i	−0.911875	+	0.410468i	$0.865366\pi$
$72$	−2.68754	−	4.88861i	−0.316729	−	0.576129i
$73$	−4.28008	+	2.71622i	−0.500945	+	0.317910i	−0.762179	−	0.647366i	$-0.775871\pi$
$73$	−4.28008	+	2.71622i	−0.500945	+	0.317910i	0.261234	+	0.965276i	$0.415871\pi$
$74$	5.09007	−	15.6656i	0.591708	−	1.82109i
$75$	−0.592750	+	3.92765i	−0.0684449	+	0.453526i
$76$	−0.0693894	−	0.213559i	−0.00795951	−	0.0244969i
$77$	4.72679	+	3.91034i	0.538667	+	0.445624i
$78$	−6.00816	+	1.14612i	−0.680290	+	0.129772i
$79$	−0.764053	+	1.62370i	−0.0859627	+	0.182680i	−0.943186	−	0.332264i	$-0.892187\pi$
$79$	−0.764053	+	1.62370i	−0.0859627	+	0.182680i	0.857224	+	0.514944i	$0.172187\pi$
$80$	6.69191	+	8.29073i	0.748178	+	0.926932i
$81$	−0.696741	+	3.65244i	−0.0774157	+	0.405827i
$82$	8.37202	−	2.72024i	0.924535	−	0.300400i
$83$	9.72636	−	4.57688i	1.06761	−	0.502378i	0.190012	−	0.981782i	$-0.439147\pi$
$83$	9.72636	−	4.57688i	1.06761	−	0.502378i	0.877594	+	0.479404i	$0.159147\pi$
$84$	1.42520	−	0.564278i	0.155503	−	0.0615678i
$85$	−5.84280	+	10.3309i	−0.633740	+	1.12054i
$86$	−18.4178	+	4.72890i	−1.98605	+	0.509930i
$87$	1.16031	+	2.93061i	0.124398	+	0.314194i
$88$	−0.959033	+	3.73519i	−0.102233	+	0.398172i
$89$	1.02704	+	1.61836i	0.108866	+	0.171546i	0.894393	−	0.447282i	$-0.147608\pi$
$89$	1.02704	+	1.61836i	0.108866	+	0.171546i	−0.785527	+	0.618828i	$0.787608\pi$
$90$	0.101321	−	8.39985i	0.0106802	−	0.885422i
$91$	−1.14200	−	18.1516i	−0.119714	−	1.90280i
$92$	−1.73278	+	3.15191i	−0.180655	+	0.328610i
$93$	−0.837850	−	0.272234i	−0.0868810	−	0.0282294i
$94$	−11.5484	+	1.45890i	−1.19112	+	0.150474i
$95$	−0.194208	+	0.955326i	−0.0199254	+	0.0980144i
$96$	1.64847	+	1.54802i	0.168247	+	0.157994i
$97$	−6.52045	+	6.94357i	−0.662051	+	0.705013i	−0.969096	−	0.246682i	$-0.920660\pi$
$97$	−6.52045	+	6.94357i	−0.662051	+	0.705013i	0.307045	+	0.951695i	$0.400660\pi$
$98$	2.77429	+	10.8051i	0.280246	+	1.09148i
$99$	3.13829	−	2.28010i	0.315410	−	0.229159i
$100$	0.421397	+	2.54055i	0.0421397	+	0.254055i
$101$	13.9677	+	10.1481i	1.38984	+	1.00978i	0.995883	+	0.0906493i	$0.0288942\pi$
$101$	13.9677	+	10.1481i	1.38984	+	1.00978i	0.393957	+	0.919129i	$0.371106\pi$
$102$	−2.46171	+	6.21758i	−0.243746	+	0.615632i
$103$	0.0975555	−	0.772232i	0.00961243	−	0.0760902i	−0.986579	−	0.163286i	$-0.947791\pi$
$103$	0.0975555	−	0.772232i	0.00961243	−	0.0760902i	0.996191	+	0.0871959i	$0.0277906\pi$
$104$	10.0188	−	5.50791i	0.982429	−	0.540095i
$105$	−6.59175	−	0.913636i	−0.643289	−	0.0891617i
$106$	5.00817	+	10.6429i	0.486436	+	1.03373i
$107$	1.13197	+	1.55802i	0.109431	+	0.150619i	0.860220	−	0.509923i	$-0.170326\pi$
$107$	1.13197	+	1.55802i	0.109431	+	0.150619i	−0.750789	+	0.660543i	$0.770326\pi$
$108$	−0.275330	−	2.17946i	−0.0264937	−	0.209719i
$109$	−5.15405	−	1.32334i	−0.493668	−	0.126753i	−0.00635531	−	0.999980i	$-0.502023\pi$
$109$	−5.15405	−	1.32334i	−0.493668	−	0.126753i	−0.487313	+	0.873227i	$0.662023\pi$
$110$	−4.02591	+	4.18484i	−0.383855	+	0.399009i
$111$	−5.25955	+	6.35771i	−0.499215	+	0.603447i
$112$	−13.7538	+	11.3781i	−1.29961	+	1.07513i
$113$	3.04873	+	1.93478i	0.286800	+	0.182009i	0.671442	−	0.741057i	$-0.265675\pi$
$113$	3.04873	+	1.93478i	0.286800	+	0.182009i	−0.384642	+	0.923066i	$0.625675\pi$
$114$	−0.0344890	+	0.548187i	−0.00323019	+	0.0513424i
$115$	13.2845	−	8.20750i	1.23878	−	0.765353i
$116$	1.30258	+	1.57455i	0.120942	+	0.146193i
$117$	−11.2969	−	2.15500i	−1.04440	−	0.199230i
$118$	−5.86121	+	8.06726i	−0.539568	+	0.742651i
$119$	−17.4248	−	9.57936i	−1.59733	−	0.878139i
$120$	−1.24464	−	3.99389i	−0.113620	−	0.364591i
$121$	8.25289	+	1.04258i	0.750262	+	0.0947802i
$122$	−5.95497	−	2.80219i	−0.539137	−	0.253699i
$123$	−4.40094	−	0.276884i	−0.396819	−	0.0249658i
$124$	−0.571161			−0.0512917
$125$	3.83733	−	10.5012i	0.343221	−	0.939255i
$126$	14.0739			1.25380
$127$	7.76357	+	0.488442i	0.688905	+	0.0433423i	0.403385	−	0.915030i	$-0.367834\pi$
$127$	7.76357	+	0.488442i	0.688905	+	0.0433423i	0.285520	+	0.958373i	$0.407834\pi$
$128$	−12.3481	−	5.81055i	−1.09142	−	0.513585i
$129$	9.45024	+	1.19384i	0.832048	+	0.105112i
$130$	17.2149	+	0.207650i	1.50984	+	0.0182121i
$131$	−0.255694	−	0.140569i	−0.0223401	−	0.0122816i	0.470544	−	0.882376i	$-0.344058\pi$
$131$	−0.255694	−	0.140569i	−0.0223401	−	0.0122816i	−0.492885	+	0.870095i	$0.664058\pi$
$132$	−0.393834	+	0.542065i	−0.0342788	+	0.0471807i
$133$	−1.60433	−	0.306042i	−0.139113	−	0.0265372i
$134$	−0.0881878	−	0.106601i	−0.00761827	−	0.00920890i
$135$	−3.61759	+	8.82450i	−0.311352	+	0.759492i
$136$	0.784865	−	12.4751i	0.0673017	−	1.06973i
$137$	4.39283	+	2.78778i	0.375305	+	0.238176i	0.710078	−	0.704123i	$-0.248660\pi$
$137$	4.39283	+	2.78778i	0.375305	+	0.238176i	−0.334773	+	0.942299i	$0.608660\pi$
$138$	6.77912	−	5.60818i	0.577077	−	0.477400i
$139$	−3.39652	+	4.10569i	−0.288089	+	0.348240i	−0.894626	−	0.446815i	$-0.852558\pi$
$139$	−3.39652	+	4.10569i	−0.288089	+	0.348240i	0.606537	+	0.795055i	$0.292558\pi$
$140$	−4.24753	+	0.757282i	−0.358981	+	0.0640020i
$141$	5.64774	+	1.45009i	0.475625	+	0.122120i
$142$	−0.778219	−	6.16024i	−0.0653067	−	0.516955i
$143$	4.67290	+	6.43169i	0.390767	+	0.537845i
$144$	4.80592	+	10.2131i	0.400493	+	0.851091i
$145$	−1.55718	−	8.73406i	−0.129316	−	0.725324i
$146$	7.04483	−	3.87293i	0.583034	−	0.320526i
$147$	0.700389	−	5.54415i	0.0577671	−	0.457273i
$148$	−1.96931	+	4.97390i	−0.161876	+	0.408852i
$149$	−7.48887	−	5.44098i	−0.613512	−	0.445742i	0.237137	−	0.971476i	$-0.423791\pi$
$149$	−7.48887	−	5.44098i	−0.613512	−	0.445742i	−0.850649	+	0.525734i	$0.823791\pi$
$150$	1.32929	−	6.15750i	0.108536	−	0.502758i
$151$	−15.8128	+	11.4887i	−1.28683	+	0.934937i	−0.999736	−	0.0229652i	$-0.992689\pi$
$151$	−15.8128	+	11.4887i	−1.28683	+	0.934937i	−0.287094	+	0.957902i	$0.592689\pi$
$152$	−0.255331	−	0.994448i	−0.0207101	−	0.0806604i
$153$	−8.60725	+	9.16579i	−0.695855	+	0.741010i
$154$	−7.09199	−	6.65982i	−0.571489	−	0.536664i
$155$	2.15838	+	1.22071i	0.173365	+	0.0980496i
$156$	1.97080	−	0.248970i	0.157790	−	0.0199335i
$157$	−6.09456	−	1.98024i	−0.486399	−	0.158041i	0.0555434	−	0.998456i	$-0.482311\pi$
$157$	−6.09456	−	1.98024i	−0.486399	−	0.158041i	−0.541942	+	0.840416i	$0.682311\pi$
$158$	1.37100	−	2.49384i	0.109071	−	0.198399i
$159$	−0.369971	−	5.88052i	−0.0293406	−	0.466356i
$160$	−3.67893	−	5.19423i	−0.290845	−	0.410640i
$161$	14.0180	+	22.0889i	1.10478	+	1.74085i
$162$	1.46648	−	5.71157i	0.115218	−	0.448743i
$163$	−6.67153	−	16.8504i	−0.522554	−	1.31982i	−0.916260	−	0.400585i	$-0.868807\pi$
$163$	−6.67153	−	16.8504i	−0.522554	−	1.31982i	0.393705	−	0.919237i	$-0.371193\pi$
$164$	−2.76910	+	0.710984i	−0.216230	+	0.0555185i
$165$	2.64680	−	1.20671i	0.206053	−	0.0939424i
$166$	−15.8503	+	6.27557i	−1.23022	+	0.487079i
$167$	−5.48373	+	2.58045i	−0.424344	+	0.199681i	−0.626080	−	0.779759i	$-0.715342\pi$
$167$	−5.48373	+	2.58045i	−0.424344	+	0.199681i	0.201736	+	0.979440i	$0.435342\pi$
$168$	6.66560	−	2.16578i	0.514262	−	0.167094i
$169$	1.98056	−	10.3825i	0.152351	−	0.798652i
$170$	10.2765	−	15.7695i	0.788171	−	1.20946i
$171$	−0.439734	+	0.934481i	−0.0336273	+	0.0714616i
$172$	6.06621	−	1.15719i	0.462545	−	0.0882351i
$173$	7.12989	+	5.89836i	0.542076	+	0.448444i	0.867724	−	0.497047i	$-0.165582\pi$
$173$	7.12989	+	5.89836i	0.542076	+	0.448444i	−0.325648	+	0.945491i	$0.605582\pi$
$174$	−1.54467	−	4.75399i	−0.117101	−	0.360399i
$175$	17.6696	+	6.21627i	1.33570	+	0.469906i
$176$	2.41113	−	7.42068i	0.181745	−	0.559355i
$177$	4.21754	−	2.67653i	0.317009	−	0.201180i
$178$	−1.46441	−	2.66375i	−0.109762	−	0.199657i
$179$	−0.465096	−	2.43812i	−0.0347629	−	0.182233i	0.960671	−	0.277690i	$-0.0895689\pi$
$179$	−0.465096	−	2.43812i	−0.0347629	−	0.182233i	−0.995434	+	0.0954567i	$0.969569\pi$
$180$	−0.204136	+	2.72058i	−0.0152154	+	0.202780i
$181$	−16.7517	+	15.7309i	−1.24515	+	1.16927i	−0.266476	+	0.963842i	$0.585859\pi$
$181$	−16.7517	+	15.7309i	−1.24515	+	1.16927i	−0.978672	+	0.205430i	$0.934141\pi$
$182$			28.8433i			2.13801i
$183$	2.25682	+	2.40327i	0.166829	+	0.177655i
$184$	−8.81204	+	13.8856i	−0.649632	+	1.02366i
$185$	18.0723	−	14.5872i	1.32870	−	1.07247i
$186$	1.29901	+	0.514314i	0.0952480	+	0.0377113i
$187$	8.67459	−	0.545759i	0.634349	−	0.0399099i
$188$	3.77292	−	0.237372i	0.275169	−	0.0173121i
$189$	−14.8563	−	5.88203i	−1.08064	−	0.427855i
$190$	0.402516	−	1.49271i	0.0292016	−	0.108293i
$191$	2.51076	−	3.95632i	0.181672	−	0.286269i	−0.741271	−	0.671206i	$-0.765777\pi$
$191$	2.51076	−	3.95632i	0.181672	−	0.286269i	0.922943	+	0.384937i	$0.125777\pi$
$192$	2.72743	+	2.90442i	0.196835	+	0.209609i
$193$		−	0.862682i		−	0.0620972i	−0.999518	−	0.0310486i	$-0.990115\pi$
$193$		−	0.862682i		−	0.0620972i	0.999518	−	0.0310486i	$-0.00988467\pi$
$194$	11.0117	−	10.3407i	0.790597	−	0.742420i
$195$	−7.97963	−	3.27123i	−0.571433	−	0.234258i
$196$	−0.678886	−	3.55885i	−0.0484919	−	0.254203i
$197$	−1.84717	−	3.35998i	−0.131605	−	0.239389i	0.802291	−	0.596933i	$-0.203614\pi$
$197$	−1.84717	−	3.35998i	−0.131605	−	0.239389i	−0.933896	+	0.357544i	$0.883614\pi$
$198$	−5.19422	+	3.29635i	−0.369137	+	0.234261i
$199$	−6.20579	+	19.0994i	−0.439917	+	1.35392i	0.448047	+	0.894010i	$0.352120\pi$
$199$	−6.20579	+	19.0994i	−0.439917	+	1.35392i	−0.887963	+	0.459914i	$0.847880\pi$
$200$	1.19357	+	11.7142i	0.0843980	+	0.828318i
$201$	0.0214162	+	0.0659122i	0.00151058	+	0.00464909i
$202$	−21.0970	−	17.4530i	−1.48438	−	1.22799i
$203$	14.6002	−	2.78514i	1.02474	−	0.195479i
$204$	0.924707	−	1.96510i	0.0647425	−	0.137585i
$205$	11.9838	+	3.23147i	0.836984	+	0.225696i
$206$	−0.231305	+	1.21254i	−0.0161158	+	0.0844820i
$207$	15.7332	−	5.11204i	1.09354	−	0.355311i
$208$	−20.9310	+	9.84937i	−1.45130	+	0.682931i
$209$	0.663788	−	0.262812i	0.0459152	−	0.0181791i
$210$	10.3422	+	2.10247i	0.713679	+	0.145084i
$211$	1.71080	−	0.439260i	0.117777	−	0.0302399i	−0.189341	−	0.981911i	$-0.560635\pi$
$211$	1.71080	−	0.439260i	0.117777	−	0.0302399i	0.307118	+	0.951671i	$0.400635\pi$
$212$	−1.40626	−	3.55181i	−0.0965825	−	0.243940i
$213$	−0.773522	+	3.01267i	−0.0530009	+	0.206425i
$214$	−1.63649	−	2.57869i	−0.111868	−	0.176276i
$215$	−25.3970	−	8.59201i	−1.73206	−	0.585970i
$216$	−0.630690	−	10.0245i	−0.0429130	−	0.682083i
$217$	−2.00137	+	3.64048i	−0.135862	+	0.247132i
$218$	8.02586	+	2.60776i	0.543580	+	0.176620i
$219$	−3.99535	+	0.504731i	−0.269981	+	0.0341065i
$220$	1.39026	−	1.27433i	0.0937311	−	0.0859156i
$221$	−18.7846	−	17.6399i	−1.26359	−	1.18659i
$222$	8.95771	−	9.53899i	0.601202	−	0.640215i
$223$	−3.61016	−	14.0607i	−0.241755	−	0.941572i	−0.967349	−	0.253449i	$-0.918435\pi$
$223$	−3.61016	−	14.0607i	−0.241755	−	0.941572i	0.725594	−	0.688123i	$-0.241565\pi$
$224$	8.62727	−	6.26808i	0.576434	−	0.418804i
$225$	6.58595	−	9.84460i	0.439063	−	0.656307i
$226$	−4.63275	−	3.36589i	−0.308166	−	0.223895i
$227$	7.92083	−	20.0057i	0.525724	−	1.32783i	−0.388063	−	0.921633i	$-0.626856\pi$
$227$	7.92083	−	20.0057i	0.525724	−	1.32783i	0.913787	−	0.406195i	$-0.133144\pi$
$228$	0.0223578	−	0.176981i	0.00148068	−	0.0117208i
$229$	9.57469	−	5.26373i	0.632713	−	0.347837i	−0.132908	−	0.991128i	$-0.542432\pi$
$229$	9.57469	−	5.26373i	0.632713	−	0.347837i	0.765622	+	0.643291i	$0.222432\pi$
$230$	−21.8434	+	11.6677i	−1.44031	+	0.769343i
$231$	2.07502	+	4.40965i	0.136527	+	0.290134i
$232$	5.49199	+	7.55907i	0.360567	+	0.496277i
$233$	−1.27891	−	10.1236i	−0.0837840	−	0.663218i	−0.976946	−	0.213484i	$-0.931519\pi$
$233$	−1.27891	−	10.1236i	−0.0837840	−	0.663218i	0.893163	−	0.449734i	$-0.148481\pi$
$234$	17.6658	+	4.53579i	1.15485	+	0.296514i
$235$	−14.7649	−	7.16663i	−0.963159	−	0.467500i
$236$	2.06431	−	2.49532i	0.134375	−	0.162431i
$237$	−1.09843	+	0.908699i	−0.0713506	+	0.0590264i
$238$	26.6254	+	16.8970i	1.72587	+	1.09527i
$239$	−0.619428	+	9.84553i	−0.0400675	+	0.636854i	0.925832	+	0.377936i	$0.123366\pi$
$239$	−0.619428	+	9.84553i	−0.0400675	+	0.636854i	−0.965899	+	0.258918i	$0.916634\pi$
$240$	2.00592	+	8.22305i	0.129482	+	0.530796i
$241$	3.07677	+	3.71918i	0.198192	+	0.239573i	0.860241	−	0.509887i	$-0.170313\pi$
$241$	3.07677	+	3.71918i	0.198192	+	0.239573i	−0.662049	+	0.749461i	$0.730313\pi$
$242$	−12.9585	−	2.47197i	−0.833006	−	0.158904i
$243$	−9.25729	+	12.7416i	−0.593856	+	0.817372i
$244$	1.87304	+	1.02971i	0.119909	+	0.0659206i
$245$	−5.04065	+	14.8996i	−0.322035	+	0.951900i
$246$	6.93807	+	0.876482i	0.442355	+	0.0558825i
$247$	−1.91515	−	0.901201i	−0.121858	−	0.0573420i
$248$	−2.60636	−	0.163978i	−0.165504	−	0.0104126i
$249$	8.53960			0.541175
$250$	−7.11928	+	16.2388i	−0.450263	+	1.02703i
$251$	17.2875			1.09117			0.545587	−	0.838054i	$-0.316307\pi$
$251$	17.2875			1.09117			0.545587	+	0.838054i	$0.316307\pi$
$252$	−4.56177	−	0.287002i	−0.287364	−	0.0180794i
$253$	−10.3472	−	4.86903i	−0.650524	−	0.306113i
$254$	−12.2392	−	1.54618i	−0.767959	−	0.0970157i
$255$	−7.69431	+	5.44967i	−0.481836	+	0.341272i
$256$	10.1755	+	5.59404i	0.635970	+	0.349627i
$257$	2.50137	−	3.44284i	0.156031	−	0.214758i	−0.723844	−	0.689964i	$-0.757626\pi$
$257$	2.50137	−	3.44284i	0.156031	−	0.214758i	0.879875	+	0.475206i	$0.157626\pi$
$258$	−14.8386	−	2.83062i	−0.923811	−	0.176226i
$259$	24.8023	+	29.9808i	1.54114	+	1.86291i
$260$	−5.57563	−	0.418361i	−0.345786	−	0.0259456i
$261$	0.590153	−	9.38022i	0.0365296	−	0.580621i
$262$	0.390705	+	0.247949i	0.0241378	+	0.0153183i
$263$	23.7113	−	19.6157i	1.46210	−	1.20955i	0.529669	−	0.848204i	$-0.322316\pi$
$263$	23.7113	−	19.6157i	1.46210	−	1.20955i	0.932430	−	0.361349i	$-0.117684\pi$
$264$	−1.95279	+	2.36052i	−0.120186	+	0.145280i
$265$	−2.27691	+	16.4276i	−0.139870	+	1.00914i
$266$	2.50880	+	0.644150i	0.153824	+	0.0394954i
$267$	0.190846	+	1.51070i	0.0116796	+	0.0924536i
$268$	0.0264105	+	0.0363509i	0.00161328	+	0.00222048i
$269$	−6.52068	−	13.8572i	−0.397573	−	0.844885i	−0.998945	−	0.0459166i	$-0.985379\pi$
$269$	−6.52068	−	13.8572i	−0.397573	−	0.844885i	0.601372	−	0.798969i	$-0.294621\pi$
$270$	6.60451	−	13.6068i	0.401938	−	0.828086i
$271$	5.01067	−	2.75464i	0.304376	−	0.167332i	−0.322245	−	0.946656i	$-0.604437\pi$
$271$	5.01067	−	2.75464i	0.304376	−	0.167332i	0.626621	+	0.779324i	$0.284437\pi$
$272$	−3.16978	+	25.0914i	−0.192196	+	1.52139i
$273$	5.31887	−	13.4339i	0.321913	−	0.813059i
$274$	−6.67520	−	4.84982i	−0.403264	−	0.292988i
$275$	−7.97725	+	1.84431i	−0.481046	+	0.111216i
$276$	−2.31168	+	1.67954i	−0.139147	+	0.101096i
$277$	7.88237	+	30.6998i	0.473606	+	1.84457i	0.532677	+	0.846318i	$0.321186\pi$
$277$	7.88237	+	30.6998i	0.473606	+	1.84457i	−0.0590717	+	0.998254i	$0.518814\pi$
$278$	5.78473	−	6.16011i	0.346945	−	0.369459i
$279$	1.91497	+	1.79827i	0.114646	+	0.107660i
$280$	−19.6000	+	2.23623i	−1.17133	+	0.133640i
$281$	−25.6560	+	3.24111i	−1.53051	+	0.193349i	−0.845021	−	0.534733i	$-0.820412\pi$
$281$	−25.6560	+	3.24111i	−1.53051	+	0.193349i	−0.685490	+	0.728082i	$0.740412\pi$
$282$	−8.79463	−	2.85755i	−0.523712	−	0.170164i
$283$	7.47103	−	13.5897i	0.444106	−	0.807826i	−0.555615	−	0.831440i	$-0.687517\pi$
$283$	7.47103	−	13.5897i	0.444106	−	0.807826i	0.999721	+	0.0236134i	$0.00751707\pi$
$284$	0.126621	+	2.01259i	0.00751359	+	0.119425i
$285$	−0.462739	+	0.621014i	−0.0274103	+	0.0367857i
$286$	−6.75562	−	10.6452i	−0.399468	−	0.629461i
$287$	−5.17135	+	20.1411i	−0.305255	+	1.18889i
$288$	−2.48233	−	6.26966i	−0.146273	−	0.369443i
$289$	−10.8220	+	2.77861i	−0.636586	+	0.163447i
$290$	1.59491	+	13.9790i	0.0936563	+	0.820875i
$291$	−7.03567	+	2.78562i	−0.412438	+	0.163296i
$292$	−2.36242	+	1.11167i	−0.138250	+	0.0650556i
$293$	−26.4403	+	8.59099i	−1.54466	+	0.501891i	−0.952658	−	0.304045i	$-0.901663\pi$
$293$	−26.4403	+	8.59099i	−1.54466	+	0.501891i	−0.592003	+	0.805936i	$0.701663\pi$
$294$	−1.66063	+	8.70532i	−0.0968498	+	0.507705i
$295$	−13.1340	+	5.01772i	−0.764689	+	0.292143i
$296$	−10.4145	+	22.1319i	−0.605328	+	1.28639i
$297$	6.86067	−	1.30874i	0.398096	−	0.0759409i
$298$	11.3113	+	9.35751i	0.655245	+	0.542066i
$299$	10.4767	+	32.2441i	0.605886	+	1.86473i
$300$	−0.556431	+	1.96873i	−0.0321256	+	0.113664i
$301$	13.8805	−	42.7199i	0.800060	−	2.46233i
$302$	26.1720	−	16.6093i	1.50603	−	0.955755i
$303$	6.60763	+	12.0192i	0.379598	+	0.690487i
$304$	0.389254	+	2.04054i	0.0223253	+	0.117033i
$305$	−4.87735	−	7.89436i	−0.279276	−	0.452029i
$306$	14.5360	−	13.6502i	0.830965	−	0.780328i
$307$		−	5.48805i		−	0.313220i	−0.987661	−	0.156610i	$-0.949944\pi$
$307$		−	5.48805i		−	0.313220i	0.987661	−	0.156610i	$-0.0500565\pi$
$308$	2.16292	+	2.30327i	0.123244	+	0.131241i
$309$	0.331332	−	0.522095i	0.0188488	−	0.0297009i
$310$	−3.29464	−	2.14702i	−0.187123	−	0.121943i
$311$	−21.7517	−	8.61209i	−1.23342	−	0.488347i	−0.341221	−	0.939983i	$-0.610840\pi$
$311$	−21.7517	−	8.61209i	−1.23342	−	0.488347i	−0.892202	+	0.451636i	$0.850840\pi$
$312$	9.06477	−	0.570307i	0.513191	−	0.0322873i
$313$	−13.8523	+	0.871512i	−0.782978	+	0.0492608i	−0.449247	−	0.893408i	$-0.648308\pi$
$313$	−13.8523	+	0.871512i	−0.782978	+	0.0492608i	−0.333731	+	0.942668i	$0.608308\pi$
$314$	9.44905	+	3.74114i	0.533241	+	0.211125i
$315$	16.6252	+	10.8342i	0.936725	+	0.610435i
$316$	−0.495238	+	0.780371i	−0.0278593	+	0.0438993i
$317$	14.3344	+	15.2646i	0.805099	+	0.857343i	0.992156	−	0.125006i	$-0.0398949\pi$
$317$	14.3344	+	15.2646i	0.805099	+	0.857343i	−0.187057	+	0.982349i	$0.559895\pi$
$318$			9.34431i			0.524003i
$319$	−4.73615	+	4.44754i	−0.265174	+	0.249015i
$320$	−5.89443	−	9.54057i	−0.329509	−	0.533334i
$321$	0.286677	+	1.50282i	0.0160008	+	0.0838790i
$322$	−19.9876	−	36.3573i	−1.11387	−	2.02611i
$323$	−1.95383	+	1.23994i	−0.108714	+	0.0689922i
$324$	−0.591805	+	1.82139i	−0.0328780	+	0.101188i
$325$	20.1758	+	13.4974i	1.11915	+	0.748702i
$326$	8.88150	+	27.3344i	0.491901	+	1.51391i
$327$	−3.25720	−	2.69459i	−0.180124	−	0.149011i
$328$	−12.8403	+	2.44941i	−0.708985	+	0.135246i
$329$	11.7075	−	24.8797i	0.645456	−	1.37166i
$330$	−4.30941	+	1.64637i	−0.237225	+	0.0906298i
$331$	4.31832	−	22.6375i	0.237357	−	1.24427i	−0.641478	−	0.767141i	$-0.721679\pi$
$331$	4.31832	−	22.6375i	0.237357	−	1.24427i	0.878835	−	0.477126i	$-0.158321\pi$
$332$	5.26553	−	1.71087i	0.288983	−	0.0938964i
$333$	22.2627	−	10.4760i	1.21999	−	0.574083i
$334$	8.93640	−	3.53817i	0.488978	−	0.193600i
$335$	−0.0221128	−	0.193813i	−0.00120815	−	0.0105891i
$336$	−13.7351	+	3.52657i	−0.749311	+	0.192390i
$337$	−10.7437	−	27.1355i	−0.585248	−	1.47817i	−0.856752	−	0.515729i	$-0.827521\pi$
$337$	−10.7437	−	27.1355i	−0.585248	−	1.47817i	0.271504	−	0.962437i	$-0.412479\pi$
$338$	−4.16863	+	16.2358i	−0.226744	+	0.883109i
$339$	1.53704	+	2.42198i	0.0834804	+	0.131544i
$340$	−3.65250	+	4.90180i	−0.198085	+	0.265837i
$341$	−0.114023	−	1.81234i	−0.00617469	−	0.0981438i
$342$	0.789048	−	1.43527i	0.0426668	−	0.0776107i
$343$	−0.122163	−	0.0396931i	−0.00659617	−	0.00214322i
$344$	28.0140	−	3.53899i	1.51041	−	0.190810i
$345$	12.3253	−	1.40623i	0.663570	−	0.0757089i
$346$	−10.6976	−	10.0457i	−0.575105	−	0.540060i
$347$	−20.6817	+	22.0237i	−1.11025	+	1.18230i	−0.128581	+	0.991699i	$0.541042\pi$
$347$	−20.6817	+	22.0237i	−1.11025	+	1.18230i	−0.981668	+	0.190597i	$0.938958\pi$
$348$	0.403727	+	1.57241i	0.0216420	+	0.0842902i
$349$	1.94621	−	1.41401i	0.104178	−	0.0756900i	−0.534476	−	0.845183i	$-0.679491\pi$
$349$	1.94621	−	1.41401i	0.104178	−	0.0756900i	0.638655	+	0.769493i	$0.279491\pi$
$350$	−27.3478	−	11.5984i	−1.46180	−	0.619960i
$351$	−16.7522	−	12.1712i	−0.894166	−	0.649650i
$352$	−1.71596	+	4.33401i	−0.0914607	+	0.231003i
$353$	−2.59280	+	20.5241i	−0.138001	+	1.09239i	0.759229	+	0.650823i	$0.225576\pi$
$353$	−2.59280	+	20.5241i	−0.138001	+	1.09239i	−0.897230	+	0.441564i	$0.854424\pi$
$354$	−6.94188	+	3.81633i	−0.368957	+	0.202836i
$355$	3.82289	−	7.87606i	0.202898	−	0.418018i
$356$	0.420339	+	0.893266i	0.0222779	+	0.0473430i
$357$	−9.28502	−	12.7797i	−0.491415	−	0.676375i
$358$	0.493351	+	3.90527i	0.0260744	+	0.206400i
$359$	−22.1504	−	5.68726i	−1.16905	−	0.300162i	−0.386228	−	0.922403i	$-0.626222\pi$
$359$	−22.1504	−	5.68726i	−1.16905	−	0.300162i	−0.782825	+	0.622241i	$0.786222\pi$
$360$	−1.71260	+	12.3561i	−0.0902617	+	0.651225i
$361$	11.9899	−	14.4933i	0.631047	−	0.762805i
$362$	28.0805	−	23.2302i	1.47588	−	1.22095i
$363$	5.57966	+	3.54096i	0.292856	+	0.185852i
$364$	0.588189	−	9.34900i	0.0308295	−	0.490021i
$365$	11.3033	+	0.848133i	0.591643	+	0.0443933i
$366$	−3.33269	−	4.02853i	−0.174202	−	0.210575i
$367$	21.3212	+	4.06723i	1.11296	+	0.212308i	0.710891	−	0.703303i	$-0.248292\pi$
$367$	21.3212	+	4.06723i	1.11296	+	0.212308i	0.402066	+	0.915611i	$0.368292\pi$
$368$	19.5584	−	26.9198i	1.01955	−	1.40329i
$369$	11.5226	+	6.33462i	0.599844	+	0.329767i
$370$	−30.0567	+	21.2884i	−1.56257	+	1.10673i
$371$	−27.5663	−	3.48243i	−1.43117	−	0.180799i
$372$	−0.410560	−	0.193195i	−0.0212865	−	0.0100167i
$373$	14.5139	+	0.913140i	0.751503	+	0.0472806i	0.433922	−	0.900950i	$-0.357129\pi$
$373$	14.5139	+	0.913140i	0.751503	+	0.0472806i	0.317581	+	0.948231i	$0.397129\pi$
$374$	−13.7842			−0.712762
$375$	6.31036	−	6.25045i	0.325866	−	0.322772i
$376$	17.2850			0.891407
$377$	19.2241	+	1.20948i	0.990090	+	0.0622912i
$378$	22.9283	+	10.7892i	1.17930	+	0.554938i
$379$	−0.775252	−	0.0979371i	−0.0398220	−	0.00503069i	0.105397	−	0.994430i	$-0.466389\pi$
$379$	−0.775252	−	0.0979371i	−0.0398220	−	0.00503069i	−0.145219	+	0.989400i	$0.546389\pi$
$380$	−0.160908	+	0.475626i	−0.00825440	+	0.0243991i
$381$	5.41537	+	2.97712i	0.277438	+	0.152523i
$382$	−4.36789	+	6.01189i	−0.223481	+	0.307595i
$383$	4.18359	+	0.798063i	0.213771	+	0.0407791i	0.293154	−	0.956065i	$-0.405295\pi$
$383$	4.18359	+	0.798063i	0.213771	+	0.0407791i	−0.0793829	+	0.996844i	$0.525295\pi$
$384$	−6.91057	−	8.35345i	−0.352654	−	0.426285i
$385$	−3.25087	−	13.3266i	−0.165680	−	0.679186i
$386$	−0.0859050	+	1.36542i	−0.00437245	+	0.0694981i
$387$	−23.9819	−	15.2194i	−1.21907	−	0.773646i
$388$	−3.78011	+	3.12718i	−0.191906	+	0.158759i
$389$	9.72727	−	11.7583i	0.493192	−	0.596167i	−0.463923	−	0.885876i	$-0.653558\pi$
$389$	9.72727	−	11.7583i	0.493192	−	0.596167i	0.957115	+	0.289709i	$0.0935584\pi$
$390$	12.3041	+	5.97218i	0.623042	+	0.302413i
$391$	35.9022	+	9.21811i	1.81565	+	0.466180i
$392$	−2.07621	−	16.4349i	−0.104864	−	0.830087i
$393$	−0.136250	−	0.187532i	−0.00687289	−	0.00945972i
$394$	2.58904	+	5.50199i	0.130434	+	0.277186i
$395$	3.53931	−	1.89053i	0.178082	−	0.0951227i
$396$	1.75082	−	0.962523i	0.0879822	−	0.0483686i
$397$	1.16648	−	9.23363i	0.0585439	−	0.463423i	−0.935405	−	0.353578i	$-0.884965\pi$
$397$	1.16648	−	9.23363i	0.0585439	−	0.463423i	0.993949	−	0.109844i	$-0.0350352\pi$
$398$	11.7242	−	29.6119i	0.587680	−	1.48431i
$399$	−1.04970	−	0.762653i	−0.0525508	−	0.0381804i
$400$	−0.921967	−	23.8063i	−0.0460983	−	1.19031i
$401$	−10.2190	+	7.42456i	−0.510314	+	0.370765i	−0.812943	−	0.582344i	$-0.802136\pi$
$401$	−10.2190	+	7.42456i	−0.510314	+	0.370765i	0.302629	+	0.953109i	$0.402136\pi$
$402$	−0.0273332	−	0.106456i	−0.00136326	−	0.00530954i
$403$	−3.68543	+	3.92458i	−0.183584	+	0.195497i
$404$	6.48228	+	6.08726i	0.322505	+	0.302853i
$405$	6.12913	−	5.61807i	0.304559	−	0.279164i
$406$	−23.3860	+	2.95434i	−1.16063	+	0.146622i
$407$	−16.1758	−	5.25582i	−0.801802	−	0.260521i
$408$	4.78386	−	8.70182i	0.236837	−	0.430804i
$409$	0.450866	+	7.16632i	0.0222939	+	0.354352i	0.993321	+	0.115383i	$0.0368094\pi$
$409$	0.450866	+	7.16632i	0.0222939	+	0.354352i	−0.971027	+	0.238969i	$0.923191\pi$
$410$	−18.6457	−	6.30798i	−0.920845	−	0.311529i
$411$	2.21468	+	3.48977i	0.109242	+	0.172138i
$412$	0.0996999	−	0.388305i	0.00491186	−	0.0191304i
$413$	−8.67131	−	21.9012i	−0.426687	−	1.07769i
$414$	−25.4110	+	6.52445i	−1.24888	+	0.320659i
$415$	−23.5546	−	4.78843i	−1.15625	−	0.235055i
$416$	12.8492	−	5.08736i	0.629984	−	0.249428i
$417$	−3.83023	+	1.80237i	−0.187567	+	0.0882623i
$418$	−1.07679	+	0.349870i	−0.0526675	+	0.0171127i
$419$	−0.193367	+	1.01367i	−0.00944662	+	0.0495209i	−0.986698	−	0.162561i	$-0.948024\pi$
$419$	−0.193367	+	1.01367i	−0.00944662	+	0.0495209i	0.977252	+	0.212082i	$0.0680245\pi$
$420$	−3.30934	−	0.892377i	−0.161479	−	0.0435435i
$421$	−7.29011	+	15.4923i	−0.355298	+	0.755047i	−0.999956	−	0.00942476i	$-0.997000\pi$
$421$	−7.29011	+	15.4923i	−0.355298	+	0.755047i	0.644658	+	0.764471i	$0.277000\pi$
$422$	−2.75154	+	0.524884i	−0.133943	+	0.0255510i
$423$	−13.3971	−	11.0830i	−0.651388	−	0.538875i
$424$	−5.39744	−	16.6116i	−0.262123	−	0.806732i
$425$	24.2789	−	10.7173i	1.17770	−	0.519865i
$426$	1.52430	−	4.69131i	0.0738526	−	0.227295i
$427$	13.1264	−	8.33029i	0.635232	−	0.403131i
$428$	0.477849	+	0.869203i	0.0230977	+	0.0420145i
$429$	1.18344	+	6.20381i	0.0571371	+	0.299523i
$430$	39.3419	+	16.1281i	1.89723	+	0.777767i
$431$	−1.38168	+	1.29749i	−0.0665533	+	0.0624977i	−0.717110	−	0.696960i	$-0.754536\pi$
$431$	−1.38168	+	1.29749i	−0.0665533	+	0.0624977i	0.650557	+	0.759458i	$0.274536\pi$
$432$			20.3228i			0.977782i
$433$	−7.02584	−	7.48176i	−0.337640	−	0.359550i	0.537633	−	0.843179i	$-0.319319\pi$
$433$	−7.02584	−	7.48176i	−0.337640	−	0.359550i	−0.875273	+	0.483629i	$0.839319\pi$
$434$	3.53021	−	5.56272i	0.169456	−	0.267019i
$435$	1.83497	−	6.80490i	0.0879800	−	0.326270i
$436$	−2.54824	−	1.00892i	−0.122039	−	0.0483186i
$437$	3.03857	−	0.191171i	0.145355	−	0.00914494i
$438$	6.37395	−	0.401015i	0.304559	−	0.0191612i
$439$	24.3264	+	9.63150i	1.16104	+	0.459687i	0.868073	−	0.496437i	$-0.165359\pi$
$439$	24.3264	+	9.63150i	1.16104	+	0.459687i	0.292963	+	0.956124i	$0.405359\pi$
$440$	6.70998	−	5.41599i	0.319886	−	0.258197i
$441$	−8.92872	+	14.0694i	−0.425177	+	0.669972i
$442$	27.9750	+	29.7903i	1.33064	+	1.41698i
$443$			13.4089i			0.637078i	0.947910	+	0.318539i	$0.103192\pi$
$443$			13.4089i			0.637078i	−0.947910	+	0.318539i	$0.896808\pi$
$444$	−3.09799	+	2.90921i	−0.147024	+	0.138065i
$445$	0.320692	−	4.27396i	0.0152022	−	0.202605i
$446$	4.31389	+	22.6142i	0.204268	+	1.07081i
$447$	−3.54271	−	6.44417i	−0.167565	−	0.304799i
$448$	15.8637	−	10.0674i	0.749489	−	0.475640i
$449$	−9.56982	+	29.4529i	−0.451628	+	1.38997i	0.423421	+	0.905933i	$0.360829\pi$
$449$	−9.56982	+	29.4529i	−0.451628	+	1.38997i	−0.875049	+	0.484035i	$0.839171\pi$
$450$	−11.4043	+	14.9258i	−0.537604	+	0.703611i
$451$	−2.80882	−	8.64465i	−0.132262	−	0.407061i
$452$	1.43297	+	1.18546i	0.0674014	+	0.0557593i
$453$	−15.2526	+	2.90959i	−0.716629	+	0.136704i
$454$	−14.5289	+	30.8756i	−0.681877	+	1.44906i
$455$	−22.2038	+	34.0721i	−1.04093	+	1.59733i
$456$	0.152835	−	0.801191i	0.00715717	−	0.0375192i
$457$	−32.8045	+	10.6588i	−1.53453	+	0.498599i	−0.949861	−	0.312673i	$-0.898776\pi$
$457$	−32.8045	+	10.6588i	−1.53453	+	0.498599i	−0.584669	+	0.811272i	$0.698776\pi$
$458$	−15.6786	+	7.37779i	−0.732613	+	0.344742i
$459$	−21.0490	+	8.33390i	−0.982485	+	0.388993i
$460$	7.31805	−	3.33640i	0.341206	−	0.155561i
$461$	−19.5777	+	5.02669i	−0.911823	+	0.234116i	−0.675329	−	0.737516i	$-0.735998\pi$
$461$	−19.5777	+	5.02669i	−0.911823	+	0.234116i	−0.236494	+	0.971633i	$0.575998\pi$
$462$	−2.84516	−	7.18605i	−0.132369	−	0.334325i
$463$	−9.75154	+	37.9798i	−0.453193	+	1.76507i	0.172511	+	0.985008i	$0.444812\pi$
$463$	−9.75154	+	37.9798i	−0.453193	+	1.76507i	−0.625703	+	0.780061i	$0.715188\pi$
$464$	−10.1297	−	15.9619i	−0.470260	−	0.741012i
$465$	1.13857	+	1.60754i	0.0528001	+	0.0745477i
$466$	1.01611	+	16.1506i	0.0470703	+	0.748161i
$467$	10.3790	−	18.8794i	0.480283	−	0.873632i	−0.519533	−	0.854451i	$-0.673894\pi$
$467$	10.3790	−	18.8794i	0.480283	−	0.873632i	0.999816	−	0.0191816i	$-0.00610606\pi$
$468$	−5.63351	−	1.83044i	−0.260409	−	0.0846120i
$469$	0.324238	−	0.0409608i	0.0149719	−	0.00189139i
$470$	22.6558	+	12.8134i	1.04503	+	0.591036i
$471$	−3.71106	−	3.48491i	−0.170996	−	0.160576i
$472$	10.1364	−	10.7942i	0.466565	−	0.496841i
$473$	4.88289	+	19.0176i	0.224516	+	0.874431i
$474$	1.82904	−	1.32887i	0.0840105	−	0.0610372i
$475$	1.62459	−	1.45346i	0.0745412	−	0.0666893i
$476$	−8.28552	−	6.01979i	−0.379766	−	0.275916i
$477$	−6.46786	+	16.3359i	−0.296143	+	0.747972i
$478$	1.96081	−	15.5214i	0.0896856	−	0.709934i
$479$	−14.1800	+	7.79550i	−0.647899	+	0.356185i	−0.771576	−	0.636137i	$-0.780531\pi$
$479$	−14.1800	+	7.79550i	−0.647899	+	0.356185i	0.123677	+	0.992322i	$0.460531\pi$
$480$	−0.887534	−	4.97810i	−0.0405102	−	0.227218i
$481$	21.4699	+	45.6258i	0.978941	+	2.08036i
$482$	−4.49945	−	6.19296i	−0.204944	−	0.282081i
$483$	2.60484	+	20.6194i	0.118524	+	0.938217i
$484$	4.14984	+	1.06550i	0.188629	+	0.0484318i
$485$	20.9683	−	3.73840i	0.952123	−	0.169752i
$486$	15.9209	−	19.2450i	0.722186	−	0.872973i
$487$	−17.2523	+	14.2724i	−0.781777	+	0.646742i	−0.940198	−	0.340630i	$-0.889360\pi$
$487$	−17.2523	+	14.2724i	−0.781777	+	0.646742i	0.158421	+	0.987372i	$0.449360\pi$
$488$	8.25156	+	5.23660i	0.373531	+	0.237050i
$489$	0.904018	−	14.3690i	0.0408811	−	0.649787i
$490$	9.46183	−	23.0806i	0.427442	−	1.04267i
$491$	0.305052	+	0.368745i	0.0137668	+	0.0166412i	0.777352	−	0.629066i	$-0.216563\pi$
$491$	0.305052	+	0.368745i	0.0137668	+	0.0166412i	−0.763585	+	0.645707i	$0.776563\pi$
$492$	−2.23096	−	0.425579i	−0.100580	−	0.0191866i
$493$	12.3783	−	17.0373i	0.557491	−	0.767320i
$494$	2.94149	+	1.61710i	0.132344	+	0.0727566i
$495$	−8.67339	−	0.104621i	−0.389840	−	0.00470234i
$496$	5.24223	+	0.662248i	0.235383	+	0.0297358i
$497$	13.2716	+	6.24513i	0.595312	+	0.280132i
$498$	−13.5162	−	0.850364i	−0.605673	−	0.0381057i
$499$	10.7937			0.483191			0.241595	−	0.970377i	$-0.422329\pi$
$499$	10.7937			0.483191			0.241595	+	0.970377i	$0.422329\pi$
$500$	2.63872	−	5.11829i	0.118007	−	0.228897i
$501$	−4.81463			−0.215102
$502$	−27.3619	−	1.72147i	−1.22122	−	0.0768328i
$503$	26.4240	+	12.4342i	1.17819	+	0.554413i	0.912273	−	0.409583i	$-0.134326\pi$
$503$	26.4240	+	12.4342i	1.17819	+	0.554413i	0.265915	+	0.963996i	$0.414326\pi$
$504$	−20.7342	−	2.61934i	−0.923573	−	0.116674i
$505$	−11.4861	−	36.8575i	−0.511127	−	1.64014i
$506$	15.8923	+	8.73688i	0.706500	+	0.388402i
$507$	4.93553	−	6.79317i	0.219195	−	0.301695i
$508$	3.93558	+	0.750752i	0.174613	+	0.0333092i
$509$	−8.06998	−	9.75492i	−0.357695	−	0.432379i	0.560715	−	0.828009i	$-0.310526\pi$
$509$	−8.06998	−	9.75492i	−0.357695	−	0.432379i	−0.918410	+	0.395630i	$0.870526\pi$
$510$	12.7209	−	7.85934i	0.563292	−	0.348018i
$511$	−1.19242	+	18.9530i	−0.0527496	+	0.838431i
$512$	7.49649	+	4.75741i	0.331301	+	0.210250i
$513$	−1.43277	+	1.18529i	−0.0632585	+	0.0523320i
$514$	−4.30190	+	5.20011i	−0.189749	+	0.229367i
$515$	−1.20666	+	1.25430i	−0.0531718	+	0.0552709i
$516$	4.75192	+	1.22008i	0.209191	+	0.0537112i
$517$	1.50641	+	11.9244i	0.0662516	+	0.524436i
$518$	−36.2706	−	49.9222i	−1.59364	−	2.19346i
$519$	3.12997	+	6.65152i	0.137390	+	0.291970i
$520$	−25.3230	−	3.50984i	−1.11049	−	0.153916i
$521$	29.7214	−	16.3395i	1.30212	−	0.715845i	0.328602	−	0.944469i	$-0.393423\pi$
$521$	29.7214	−	16.3395i	1.30212	−	0.715845i	0.973515	+	0.228624i	$0.0734226\pi$
$522$	−1.86815	+	14.7879i	−0.0817665	+	0.647248i
$523$	−10.7160	+	27.0655i	−0.468577	+	1.18349i	0.482874	+	0.875690i	$0.339593\pi$
$523$	−10.7160	+	27.0655i	−0.468577	+	1.18349i	−0.951451	+	0.307800i	$0.900407\pi$
$524$	−0.121583	−	0.0883352i	−0.00531138	−	0.00385894i
$525$	10.5986	+	10.4451i	0.462559	+	0.455861i
$526$	−39.4826	+	28.6858i	−1.72152	+	1.25076i
$527$	1.46380	+	5.70113i	0.0637642	+	0.248345i
$528$	4.24320	−	4.51855i	0.184662	−	0.196645i
$529$	−18.7840	−	17.6394i	−0.816697	−	0.766929i
$530$	5.23965	−	25.7742i	0.227596	−	1.11956i
$531$	−14.7775	+	1.86684i	−0.641290	+	0.0810137i
$532$	−0.800041	−	0.259949i	−0.0346862	−	0.0112702i
$533$	−12.9823	+	23.6148i	−0.562327	+	1.02287i
$534$	−0.151630	−	2.41009i	−0.00656167	−	0.104295i
$535$	0.0519393	−	4.30594i	0.00224553	−	0.186162i
$536$	0.110082	+	0.173461i	0.00475481	+	0.00749239i
$537$	0.490373	−	1.90988i	0.0211612	−	0.0824173i
$538$	8.94081	+	22.5819i	0.385465	+	0.973575i
$539$	11.1570	−	2.86463i	0.480566	−	0.123388i
$540$	−2.41820	+	4.27571i	−0.104063	+	0.183997i
$541$	21.8137	−	8.63664i	0.937842	−	0.371318i	0.151043	−	0.988527i	$-0.451737\pi$
$541$	21.8137	−	8.63664i	0.937842	−	0.371318i	0.786799	+	0.617209i	$0.211737\pi$
$542$	−8.20499	+	3.86098i	−0.352435	+	0.165843i
$543$	−17.3624	+	5.64139i	−0.745093	+	0.242095i
$544$	2.83115	−	14.8414i	0.121385	−	0.636321i
$545$	7.47334	+	9.25886i	0.320123	+	0.396606i
$546$	−9.75625	+	20.7331i	−0.417529	+	0.887294i
$547$	5.23110	−	0.997886i	0.223666	−	0.0426665i	−0.0743301	−	0.997234i	$-0.523682\pi$
$547$	5.23110	−	0.997886i	0.223666	−	0.0426665i	0.297996	+	0.954567i	$0.403682\pi$
$548$	2.06473	+	1.70810i	0.0882011	+	0.0729663i
$549$	−3.03786	−	9.34957i	−0.129653	−	0.399030i
$550$	12.8097	−	2.12474i	0.546209	−	0.0905991i
$551$	0.534526	−	1.64510i	0.0227716	−	0.0700837i
$552$	−11.0310	+	7.00050i	−0.469512	+	0.297961i
$553$	3.23862	+	5.89102i	0.137720	+	0.250512i
$554$	−9.41886	−	49.3754i	−0.400169	−	2.09776i
$555$	17.9248	−	4.37254i	0.760864	−	0.185604i
$556$	−2.00062	+	1.87871i	−0.0848454	+	0.0796751i
$557$			3.58777i			0.152019i	0.997107	+	0.0760094i	$0.0242179\pi$
$557$			3.58777i			0.152019i	−0.997107	+	0.0760094i	$0.975782\pi$
$558$	−2.85187	−	3.03693i	−0.120729	−	0.128563i
$559$	31.1910	−	49.1492i	1.31924	−	2.07879i
$560$	39.8627	−	2.02558i	1.68451	−	0.0855964i
$561$	6.42005	+	2.54188i	0.271055	+	0.107318i
$562$	40.9302	−	2.57511i	1.72653	−	0.108624i
$563$	−17.8192	+	1.12109i	−0.750989	+	0.0472482i	−0.433671	−	0.901071i	$-0.642782\pi$
$563$	−17.8192	+	1.12109i	−0.750989	+	0.0472482i	−0.317318	+	0.948319i	$0.602782\pi$
$564$	2.79233	+	1.10556i	0.117578	+	0.0465526i
$565$	−2.88150	−	7.54238i	−0.121226	−	0.317310i
$566$	−13.1781	+	20.7654i	−0.553917	+	0.872834i
$567$	9.53550	+	10.1543i	0.400454	+	0.426440i
$568$			9.22034i			0.386877i
$569$	−4.87389	+	4.57689i	−0.204324	+	0.191873i	−0.779953	−	0.625838i	$-0.784757\pi$
$569$	−4.87389	+	4.57689i	−0.204324	+	0.191873i	0.575629	+	0.817711i	$0.304757\pi$
$570$	0.794246	−	0.936838i	0.0332673	−	0.0392398i
$571$	−0.853824	−	4.47590i	−0.0357314	−	0.187311i	0.959947	−	0.280183i	$-0.0903952\pi$
$571$	−0.853824	−	4.47590i	−0.0357314	−	0.187311i	−0.995678	+	0.0928723i	$0.970395\pi$
$572$	1.97262	+	3.58818i	0.0824794	+	0.150029i
$573$	3.14300	−	1.99461i	0.131301	−	0.0833258i
$574$	10.1906	−	31.3636i	0.425349	−	1.30909i
$575$	−34.7851	−	3.03239i	−1.45064	−	0.126459i
$576$	−3.67134	−	11.2992i	−0.152973	−	0.470802i
$577$	−29.6508	−	24.5293i	−1.23438	−	1.02117i	−0.998783	−	0.0493174i	$-0.984295\pi$
$577$	−29.6508	−	24.5293i	−1.23438	−	1.02117i	−0.235597	−	0.971851i	$-0.575705\pi$
$578$	17.4053	−	3.32023i	0.723964	−	0.138103i
$579$	0.291802	−	0.620110i	0.0121269	−	0.0257709i
$580$	−0.231891	−	4.56354i	−0.00962875	−	0.189491i
$581$	7.54582	−	39.5566i	0.313053	−	1.64108i
$582$	11.4132	−	3.70837i	0.473091	−	0.153717i
$583$	10.9895	−	5.17126i	0.455138	−	0.214172i
$584$	−11.0995	+	4.39461i	−0.459301	+	0.181850i
$585$	17.3766	+	18.9573i	0.718432	+	0.783786i
$586$	42.7042	−	10.9646i	1.76410	−	0.452943i
$587$	−2.87548	−	7.26263i	−0.118684	−	0.299761i	0.858275	−	0.513190i	$-0.171537\pi$
$587$	−2.87548	−	7.26263i	−0.118684	−	0.299761i	−0.976958	+	0.213430i	$0.931537\pi$
$588$	0.715784	−	2.78779i	0.0295184	−	0.114967i
$589$	0.259055	+	0.408205i	0.0106742	+	0.0168198i
$590$	21.2876	−	6.63399i	0.876397	−	0.273117i
$591$	−0.191261	−	3.04001i	−0.00786745	−	0.125049i
$592$	23.8418	−	43.3681i	0.979893	−	1.78242i
$593$	−20.5908	−	6.69036i	−0.845563	−	0.274740i	−0.145976	−	0.989288i	$-0.546632\pi$
$593$	−20.5908	−	6.69036i	−0.845563	−	0.274740i	−0.699586	+	0.714548i	$0.746632\pi$
$594$	−10.9891	+	1.38825i	−0.450889	+	0.0569606i
$595$	18.4447	+	40.4565i	0.756159	+	1.65856i
$596$	−3.47551	−	3.26372i	−0.142362	−	0.133687i
$597$	−10.9212	+	11.6299i	−0.446975	+	0.475980i
$598$	−13.3714	−	52.0780i	−0.546796	−	2.12963i
$599$	−28.1939	+	20.4841i	−1.15197	+	0.836956i	−0.988742	−	0.149632i	$-0.952191\pi$
$599$	−28.1939	+	20.4841i	−1.15197	+	0.836956i	−0.163229	+	0.986588i	$0.552191\pi$
$600$	−3.10436	+	8.82408i	−0.126735	+	0.360241i
$601$	−12.1456	−	8.82430i	−0.495430	−	0.359951i	0.311839	−	0.950135i	$-0.399055\pi$
$601$	−12.1456	−	8.82430i	−0.495430	−	0.359951i	−0.807269	+	0.590184i	$0.799055\pi$
$602$	−26.2236	+	66.2332i	−1.06879	+	2.69946i
$603$	0.0259011	−	0.205028i	0.00105477	−	0.00834939i
$604$	−8.82184	+	4.84985i	−0.358956	+	0.197337i
$605$	−13.4048	−	12.8957i	−0.544981	−	0.524283i
$606$	−9.26144	−	19.6816i	−0.376220	−	0.799509i
$607$	−18.8113	−	25.8915i	−0.763527	−	1.05091i	−0.996912	−	0.0785207i	$-0.974980\pi$
$607$	−18.8113	−	25.8915i	−0.763527	−	1.05091i	0.233385	−	0.972384i	$-0.425020\pi$
$608$	−0.155542	−	1.23124i	−0.00630805	−	0.0499334i
$609$	11.4370	+	2.93651i	0.463449	+	0.118994i
$610$	6.93357	+	12.9806i	0.280732	+	0.525568i
$611$	22.7138	−	27.4563i	0.918903	−	1.11076i
$612$	−4.98990	+	4.12801i	−0.201705	+	0.166865i
$613$	−30.4319	−	19.3127i	−1.22913	−	0.780031i	−0.247145	−	0.968978i	$-0.579493\pi$
$613$	−30.4319	−	19.3127i	−1.22913	−	0.780031i	−0.981987	+	0.188947i	$0.939493\pi$
$614$	−0.546494	+	8.68628i	−0.0220547	+	0.350550i
$615$	7.52110	+	6.37634i	0.303280	+	0.257119i
$616$	9.20871	+	11.1314i	0.371030	+	0.448498i
$617$	−30.1916	−	5.75936i	−1.21547	−	0.231863i	−0.460522	−	0.887648i	$-0.652338\pi$
$617$	−30.1916	−	5.75936i	−1.21547	−	0.231863i	−0.754948	+	0.655785i	$0.772338\pi$
$618$	−0.576409	+	0.793358i	−0.0231866	+	0.0319136i
$619$	31.8966	+	17.5353i	1.28203	+	0.704803i	0.969497	−	0.245104i	$-0.0788220\pi$
$619$	31.8966	+	17.5353i	1.28203	+	0.704803i	0.312534	+	0.949906i	$0.398822\pi$
$620$	1.02411	+	0.763100i	0.0411292	+	0.0306468i
$621$	29.5506	+	3.73311i	1.18582	+	0.149804i
$622$	33.5701	+	15.7969i	1.34604	+	0.633398i
$623$	7.16642	+	0.450873i	0.287116	+	0.0180638i
$624$	−18.3771			−0.735672
$625$	−20.9106	+	13.7021i	−0.836423	+	0.548084i
$626$	22.0117			0.879763
$627$	0.566038	+	0.0356121i	0.0226054	+	0.00142221i
$628$	−2.98643	−	1.40531i	−0.119172	−	0.0560779i
$629$	54.6948	+	6.90956i	2.18082	+	0.275502i
$630$	−25.2349	−	18.8034i	−1.00538	−	0.749146i
$631$	−6.62858	−	3.64409i	−0.263880	−	0.145069i	0.344322	−	0.938852i	$-0.388109\pi$
$631$	−6.62858	−	3.64409i	−0.263880	−	0.145069i	−0.608202	+	0.793783i	$0.708109\pi$
$632$	−2.48395	+	3.41886i	−0.0988062	+	0.135995i
$633$	1.37833	+	0.262931i	0.0547839	+	0.0104506i
$634$	−21.1679	−	25.5876i	−0.840684	−	1.01621i
$635$	−13.2678	−	11.2483i	−0.526515	−	0.446376i
$636$	0.190554	−	3.02877i	0.00755596	−	0.120099i
$637$	−28.8342	−	18.2988i	−1.14245	−	0.725023i
$638$	7.93908	−	6.56778i	0.314311	−	0.260021i
$639$	5.91201	−	7.14639i	0.233876	−	0.282707i
$640$	14.3773	+	26.9161i	0.568311	+	1.06395i
$641$	−4.23592	−	1.08760i	−0.167309	−	0.0429576i	0.164106	−	0.986443i	$-0.447526\pi$
$641$	−4.23592	−	1.08760i	−0.167309	−	0.0429576i	−0.331415	+	0.943485i	$0.607526\pi$
$642$	−0.304093	−	2.40715i	−0.0120016	−	0.0950025i
$643$	13.9519	+	19.2032i	0.550210	+	0.757300i	0.990041	−	0.140781i	$-0.0449614\pi$
$643$	13.9519	+	19.2032i	0.550210	+	0.757300i	−0.439830	+	0.898081i	$0.644961\pi$
$644$	5.73717	+	12.1921i	0.226076	+	0.480436i
$645$	−15.3496	−	14.7666i	−0.604388	−	0.581435i
$646$	3.21593	−	1.76797i	0.126529	−	0.0695599i
$647$	−4.88669	+	38.6821i	−0.192116	+	1.52075i	0.541218	+	0.840882i	$0.317963\pi$
$647$	−4.88669	+	38.6821i	−0.192116	+	1.52075i	−0.733334	+	0.679869i	$0.762037\pi$
$648$	−3.22348	+	8.14158i	−0.126630	+	0.319831i
$649$	8.32996	+	6.05207i	0.326980	+	0.237565i
$650$	−30.5894	−	23.3723i	−1.19981	−	0.916736i
$651$	−2.67001	+	1.93988i	−0.104646	+	0.0760297i
$652$	−2.32134	−	9.04103i	−0.0909108	−	0.354074i
$653$	11.7924	−	12.5576i	0.461471	−	0.491417i	−0.455575	−	0.890197i	$-0.650566\pi$
$653$	11.7924	−	12.5576i	0.461471	−	0.491417i	0.917046	+	0.398780i	$0.130566\pi$
$654$	4.88705	+	4.58924i	0.191099	+	0.179454i
$655$	0.270660	+	0.593665i	0.0105756	+	0.0231964i
$656$	26.2397	−	3.31485i	1.02449	−	0.129423i
$657$	11.4207	+	3.71080i	0.445563	+	0.144772i
$658$	−21.0077	+	38.2129i	−0.818966	+	1.48969i
$659$	−1.76196	−	28.0055i	−0.0686360	−	1.09094i	−0.870094	−	0.492887i	$-0.835942\pi$
$659$	−1.76196	−	28.0055i	−0.0686360	−	1.09094i	0.801457	−	0.598052i	$-0.204058\pi$
$660$	1.43038	−	0.445759i	0.0556776	−	0.0173512i
$661$	20.4925	+	32.2910i	0.797065	+	1.25597i	0.962910	+	0.269821i	$0.0869647\pi$
$661$	20.4925	+	32.2910i	0.797065	+	1.25597i	−0.165846	+	0.986152i	$0.553035\pi$
$662$	−9.08909	+	35.3997i	−0.353258	+	1.37585i
$663$	−7.53600	−	19.0338i	−0.292674	−	0.739210i
$664$	24.5192	−	6.29546i	0.951530	−	0.244311i
$665$	2.46773	+	2.69221i	0.0956944	+	0.104400i
$666$	−36.2798	+	14.3642i	−1.40581	+	0.556600i
$667$	−25.0703	+	11.7972i	−0.970724	+	0.456788i
$668$	−2.96871	+	0.964592i	−0.114863	+	0.0373212i
$669$	2.16097	−	11.3282i	0.0835478	−	0.437973i
$670$	0.0156996	+	0.308962i	0.000606527	+	0.0119362i
$671$	−2.89345	+	6.14889i	−0.111700	+	0.237375i
$672$	8.32160	−	1.58743i	0.321013	−	0.0612365i
$673$	−25.2491	−	20.8879i	−0.973282	−	0.805169i	0.00756073	−	0.999971i	$-0.497593\pi$
$673$	−25.2491	−	20.8879i	−0.973282	−	0.805169i	−0.980842	+	0.194803i	$0.937593\pi$
$674$	14.3026	+	44.0189i	0.550916	+	1.69555i
$675$	18.2764	−	10.9893i	0.703460	−	0.422980i
$676$	1.68227	−	5.17749i	0.0647026	−	0.199134i
$677$	2.22025	−	1.40901i	0.0853311	−	0.0541528i	−0.492477	−	0.870326i	$-0.663908\pi$
$677$	2.22025	−	1.40901i	0.0853311	−	0.0541528i	0.577808	+	0.816173i	$0.303908\pi$
$678$	−2.19159	−	3.98648i	−0.0841673	−	0.153100i
$679$	6.68645	+	35.0516i	0.256602	+	1.34516i
$680$	−18.0746	+	21.3196i	−0.693131	+	0.817570i
$681$	12.4606	−	11.7012i	0.477490	−	0.448393i
$682$			2.87986i			0.110276i
$683$	9.48547	+	10.1010i	0.362951	+	0.386504i	0.884362	−	0.466802i	$-0.154594\pi$
$683$	9.48547	+	10.1010i	0.362951	+	0.386504i	−0.521410	+	0.853306i	$0.674594\pi$
$684$	−0.285023	+	0.449125i	−0.0108981	+	0.0171727i
$685$	−4.15188	−	10.8676i	−0.158635	−	0.415230i
$686$	0.189402	+	0.0749895i	0.00723140	+	0.00286311i
$687$	8.66290	−	0.545024i	0.330510	−	0.0207939i
$688$	−57.0187	+	3.58732i	−2.17382	+	0.136765i
$689$	−33.4793	−	13.2554i	−1.27546	−	0.504990i
$690$	−19.6480	+	0.998391i	−0.747987	+	0.0380081i
$691$	3.11718	−	4.91188i	0.118583	−	0.186857i	−0.779851	−	0.625965i	$-0.784705\pi$
$691$	3.11718	−	4.91188i	0.118583	−	0.186857i	0.898434	+	0.439108i	$0.144705\pi$
$692$	3.26255	+	3.47426i	0.124023	+	0.132072i
$693$		−	14.5322i		−	0.552032i
$694$	34.9272	−	32.7989i	1.32582	−	1.24503i
$695$	11.5755	−	2.82371i	0.439083	−	0.107109i
$696$	1.39088	+	7.29125i	0.0527212	+	0.276374i
$697$	14.1936	+	25.8180i	0.537620	+	0.977928i
$698$	−3.22119	+	2.04423i	−0.121924	+	0.0773753i
$699$	2.50500	−	7.70960i	0.0947478	−	0.291604i
$700$	8.62772	+	4.31708i	0.326097	+	0.163170i
$701$	12.6718	+	38.9997i	0.478606	+	1.47300i	0.841033	+	0.540984i	$0.181948\pi$
$701$	12.6718	+	38.9997i	0.478606	+	1.47300i	−0.362427	+	0.932012i	$0.618052\pi$
$702$	25.3027	+	20.9323i	0.954991	+	0.790037i
$703$	4.44802	−	0.848504i	0.167760	−	0.0320020i
$704$	−3.49682	+	7.43112i	−0.131791	+	0.280071i
$705$	−8.18918	−	10.1457i	−0.308422	−	0.382110i
$706$	6.14755	−	32.2266i	0.231366	−	1.21286i
$707$	61.5134	−	19.9869i	2.31345	−	0.751685i
$708$	2.32790	−	1.09543i	0.0874878	−	0.0411686i
$709$	8.35740	−	3.30893i	0.313869	−	0.124269i	−0.205909	−	0.978571i	$-0.566015\pi$
$709$	8.35740	−	3.30893i	0.313869	−	0.124269i	0.519777	+	0.854302i	$0.326015\pi$
$710$	−6.83502	+	12.0852i	−0.256514	+	0.453551i
$711$	4.11738	−	1.05716i	0.154414	−	0.0396467i
$712$	1.66167	+	4.19689i	0.0622736	+	0.157285i
$713$	1.92590	−	7.50087i	0.0721254	−	0.280910i
$714$	13.4234	+	21.1519i	0.502358	+	0.791589i
$715$	0.214412	−	17.7755i	0.00801855	−	0.664765i
$716$	−0.0802714	−	1.27588i	−0.00299988	−	0.0476818i
$717$	−3.77550	+	6.86761i	−0.140999	+	0.256476i
$718$	34.4925	+	11.2073i	1.28725	+	0.418252i
$719$	−8.94289	+	1.12975i	−0.333514	+	0.0421326i	−0.290307	−	0.956934i	$-0.593757\pi$
$719$	−8.94289	+	1.12975i	−0.333514	+	0.0421326i	−0.0432066	+	0.999066i	$0.513757\pi$
$720$	5.02805	−	24.7334i	0.187384	−	0.921758i
$721$	−2.12564	−	1.99611i	−0.0791630	−	0.0743390i
$722$	−20.4204	+	21.7455i	−0.759968	+	0.809284i
$723$	0.953625	+	3.71412i	0.0354657	+	0.138130i
$724$	−9.57546	+	6.95698i	−0.355869	+	0.258554i
$725$	−8.87709	+	17.7409i	−0.329687	+	0.658881i
$726$	−8.47867	−	6.16011i	−0.314673	−	0.228623i
$727$	1.04957	−	2.65091i	0.0389263	−	0.0983167i	−0.909013	−	0.416768i	$-0.863163\pi$
$727$	1.04957	−	2.65091i	0.0389263	−	0.0983167i	0.947939	+	0.318451i	$0.103163\pi$
$728$	5.36813	−	42.4931i	0.198956	−	1.57490i
$729$	−1.18900	+	0.653658i	−0.0440370	+	0.0242095i
$730$	−17.8060	−	2.46797i	−0.659031	−	0.0913435i
$731$	−27.0975	−	57.5851i	−1.00224	−	2.12986i
$732$	0.998073	+	1.37373i	0.0368898	+	0.0507745i
$733$	0.849650	+	6.72567i	0.0313825	+	0.248418i	1.00000		0.000137896i	$-4.38935e-5\pi$
$733$	0.849650	+	6.72567i	0.0313825	+	0.248418i	−0.968617	+	0.248556i	$0.920044\pi$
$734$	−33.3414	−	8.56061i	−1.23065	−	0.315978i
$735$	−8.66308	+	9.00508i	−0.319543	+	0.332157i
$736$	−12.6712	+	15.3168i	−0.467065	+	0.564585i
$737$	−0.110072	+	0.0910596i	−0.00405456	+	0.00335422i
$738$	−17.6068	−	11.1736i	−0.648115	−	0.411306i
$739$	2.30263	−	36.5993i	0.0847036	−	1.34633i	−0.694472	−	0.719520i	$-0.744362\pi$
$739$	2.30263	−	36.5993i	0.0847036	−	1.34633i	0.779175	−	0.626806i	$-0.215638\pi$
$740$	10.1764	−	6.28727i	0.374092	−	0.231125i
$741$	−1.07181	−	1.29560i	−0.0393740	−	0.0475949i
$742$	43.2841	+	8.25688i	1.58901	+	0.303119i
$743$	−2.23125	+	3.07105i	−0.0818567	+	0.112666i	−0.847982	−	0.530026i	$-0.822182\pi$
$743$	−2.23125	+	3.07105i	−0.0818567	+	0.112666i	0.766125	+	0.642692i	$0.222182\pi$
$744$	−1.81803	−	0.999471i	−0.0666522	−	0.0366424i
$745$	6.15835	+	19.7614i	0.225625	+	0.724000i
$746$	−22.8812	−	2.89057i	−0.837740	−	0.105831i
$747$	−23.0407	−	10.8421i	−0.843014	−	0.396692i
$748$	4.46786	+	0.281094i	0.163361	+	0.0102778i
$749$	7.21456			0.263614
$750$	−10.6102	+	9.26460i	−0.387430	+	0.338295i
$751$	−20.4608			−0.746625			−0.373312	−	0.927706i	$-0.621778\pi$
$751$	−20.4608			−0.746625			−0.373312	+	0.927706i	$0.621778\pi$
$752$	−34.9039	−	2.19597i	−1.27281	−	0.0800787i
$753$	12.4265	+	5.84747i	0.452847	+	0.213094i
$754$	−30.3067	−	3.82862i	−1.10370	−	0.139430i
$755$	43.7024	+	0.527149i	1.59049	+	0.0191849i
$756$	−7.21173	−	3.96468i	−0.262288	−	0.144194i
$757$	−2.84250	+	3.91236i	−0.103312	+	0.142197i	−0.857543	−	0.514412i	$-0.828010\pi$
$757$	−2.84250	+	3.91236i	−0.103312	+	0.142197i	0.754231	+	0.656610i	$0.228010\pi$
$758$	1.21729	+	0.232210i	0.0442138	+	0.00843424i
$759$	−5.79080	−	6.99988i	−0.210193	−	0.254080i
$760$	−0.870817	+	2.12421i	−0.0315878	+	0.0770533i
$761$	−0.150666	+	2.39477i	−0.00546163	+	0.0868102i	−0.999813	−	0.0193260i	$-0.993848\pi$
$761$	−0.150666	+	2.39477i	−0.00546163	+	0.0868102i	0.994352	+	0.106136i	$0.0338480\pi$
$762$	−8.27478	−	5.25134i	−0.299764	−	0.190236i
$763$	−15.3599	+	12.7068i	−0.556064	+	0.460016i
$764$	1.53836	−	1.85956i	0.0556561	−	0.0672766i
$765$	27.6791	−	4.93484i	1.00074	−	0.178419i
$766$	−6.54216	−	1.67974i	−0.236378	−	0.0606915i
$767$	−3.82594	−	30.2854i	−0.138147	−	1.09354i
$768$	5.42215	+	7.46295i	0.195655	+	0.269296i
$769$	−9.06335	−	19.2606i	−0.326833	−	0.694555i	0.672114	−	0.740448i	$-0.265387\pi$
$769$	−9.06335	−	19.2606i	−0.326833	−	0.694555i	−0.998946	+	0.0458933i	$0.985387\pi$
$770$	3.81831	+	21.4165i	0.137602	+	0.771798i
$771$	2.96256	−	1.62868i	0.106694	−	0.0586556i
$772$	0.0556888	−	0.440822i	0.00200428	−	0.0158655i
$773$	−9.75638	+	24.6418i	−0.350913	+	0.886304i	0.641918	+	0.766773i	$0.278139\pi$
$773$	−9.75638	+	24.6418i	−0.350913	+	0.886304i	−0.992831	+	0.119531i	$0.961861\pi$
$774$	36.4422	+	26.4768i	1.30989	+	0.951689i
$775$	−2.23911	−	5.07247i	−0.0804313	−	0.182209i
$776$	−18.1475	+	13.1849i	−0.651457	+	0.473311i
$777$	7.68730	+	29.9400i	0.275780	+	1.07409i
$778$	−16.5668	+	17.6419i	−0.593950	+	0.632492i
$779$	1.76409	+	1.65659i	0.0632049	+	0.0593534i
$780$	−3.86634	−	2.18668i	−0.138437	−	0.0782956i
$781$	−6.36084	+	0.803561i	−0.227609	+	0.0287537i
$782$	−55.9066	−	18.1652i	−1.99922	−	0.649585i
$783$	8.15245	−	14.8293i	0.291345	−	0.529954i
$784$	2.10456	+	33.4510i	0.0751628	+	1.19468i
$785$	8.28204	+	11.6933i	0.295599	+	0.417351i
$786$	0.196977	+	0.310386i	0.00702593	+	0.0110711i
$787$	0.191699	−	0.746617i	0.00683332	−	0.0266140i	−0.965075	−	0.261973i	$-0.915627\pi$
$787$	0.191699	−	0.746617i	0.00683332	−	0.0266140i	0.971908	+	0.235359i	$0.0756267\pi$
$788$	−0.726986	−	1.83616i	−0.0258978	−	0.0654104i
$789$	23.6791	−	6.07975i	0.842997	−	0.216445i
$790$	−5.79015	+	2.63981i	−0.206004	+	0.0939203i
$791$	12.5771	−	4.97963i	0.447191	−	0.177055i
$792$	8.26582	−	3.88960i	0.293713	−	0.138211i
$793$	19.1612	−	6.22586i	0.680435	−	0.221087i
$794$	−2.76573	+	14.4985i	−0.0981522	+	0.514532i
$795$	−7.19331	+	11.0383i	−0.255120	+	0.391487i
$796$	−4.40403	+	9.35903i	−0.156097	+	0.331722i
$797$	49.6233	−	9.46614i	1.75775	−	0.335308i	0.795184	−	0.606369i	$-0.207374\pi$
$797$	49.6233	−	9.46614i	1.75775	−	0.335308i	0.962562	+	0.271061i	$0.0873744\pi$
$798$	1.58548	+	1.31163i	0.0561255	+	0.0464310i
$799$	−12.0388	−	37.0517i	−0.425903	−	1.31079i
$800$	−0.343309	+	14.2287i	−0.0121378	+	0.503059i
$801$	1.40311	−	4.31833i	0.0495765	−	0.152581i
$802$	16.9136	−	10.7337i	0.597241	−	0.379021i
$803$	−3.99904	−	7.27424i	−0.141123	−	0.256702i
$804$	0.00668862	+	0.0350630i	0.000235889	+	0.00123658i
$805$	4.37709	−	58.3349i	0.154272	−	2.05603i
$806$	6.22396	−	5.84469i	0.219230	−	0.205870i
$807$		−	12.1664i		−	0.428277i
$808$	27.8327	+	29.6389i	0.979153	+	1.04269i
$809$	−22.8048	+	35.9346i	−0.801773	+	1.26339i	0.159336	+	0.987224i	$0.449065\pi$
$809$	−22.8048	+	35.9346i	−0.801773	+	1.26339i	−0.961109	+	0.276168i	$0.910935\pi$
$810$	−10.2604	+	8.28174i	−0.360514	+	0.290991i
$811$	51.0633	+	20.2174i	1.79308	+	0.709929i	0.994087	+	0.108583i	$0.0346313\pi$
$811$	51.0633	+	20.2174i	1.79308	+	0.709929i	0.798989	+	0.601346i	$0.205369\pi$
$812$	7.64037	−	0.480691i	0.268124	−	0.0168690i
$813$	4.53351	−	0.285224i	0.158997	−	0.0100032i
$814$	25.0790	+	9.92948i	0.879018	+	0.348028i
$815$	−10.5507	+	39.1267i	−0.369574	+	1.37055i
$816$	−10.7657	+	16.9640i	−0.376873	+	0.593857i
$817$	−3.57843	−	3.81064i	−0.125193	−	0.133317i
$818$		−	11.3875i		−	0.398154i
$819$	−31.4070	+	29.4931i	−1.09745	+	1.03057i
$820$	5.91499	+	2.42484i	0.206561	+	0.0846791i
$821$	−2.57897	−	13.5195i	−0.0900068	−	0.471832i	−0.998540	−	0.0540193i	$-0.982797\pi$
$821$	−2.57897	−	13.5195i	−0.0900068	−	0.471832i	0.908533	−	0.417813i	$-0.137203\pi$
$822$	−3.15780	−	5.74402i	−0.110141	−	0.200346i
$823$	22.5126	−	14.2869i	0.784740	−	0.498011i	−0.0820840	−	0.996625i	$-0.526158\pi$
$823$	22.5126	−	14.2869i	0.784740	−	0.498011i	0.866824	+	0.498614i	$0.166158\pi$
$824$	0.566439	−	1.74332i	0.0197328	−	0.0607314i
$825$	−6.35802	−	1.37258i	−0.221358	−	0.0477871i
$826$	11.5437	+	35.5279i	0.401658	+	1.23617i
$827$	−28.8574	−	23.8729i	−1.00347	−	0.830142i	−0.0179731	−	0.999838i	$-0.505721\pi$
$827$	−28.8574	−	23.8729i	−1.00347	−	0.830142i	−0.985496	+	0.169696i	$0.945721\pi$
$828$	8.36953	−	1.59657i	0.290861	−	0.0554848i
$829$	−21.6993	+	46.1133i	−0.753647	+	1.60158i	0.0444208	+	0.999013i	$0.485856\pi$
$829$	−21.6993	+	46.1133i	−0.753647	+	1.60158i	−0.798068	+	0.602568i	$0.794144\pi$
$830$	36.8045	+	9.92448i	1.27750	+	0.344484i
$831$	−4.71821	+	24.7337i	−0.163673	+	0.858004i
$832$	23.1569	−	7.52415i	0.802823	−	0.260853i
$833$	−33.7833	+	15.8972i	−1.17052	+	0.550806i
$834$	6.24181	−	2.47131i	0.216136	−	0.0855744i
$835$	13.2801	+	2.69972i	0.459578	+	0.0934276i
$836$	0.356155	−	0.0914449i	0.0123179	−	0.00316269i
$837$	1.74116	+	4.39768i	0.0601834	+	0.152006i
$838$	0.406995	−	1.58514i	0.0140594	−	0.0547577i
$839$	−3.41971	−	5.38860i	−0.118061	−	0.186035i	0.780158	−	0.625583i	$-0.215139\pi$
$839$	−3.41971	−	5.38860i	−0.118061	−	0.186035i	−0.898219	+	0.439548i	$0.855139\pi$
$840$	−14.8452	−	5.02226i	−0.512209	−	0.173284i
$841$	−0.832494	−	13.2321i	−0.0287067	−	0.456280i
$842$	13.0812	−	23.7946i	0.450808	−	0.820017i
$843$	−19.5383	−	6.34838i	−0.672935	−	0.218650i
$844$	0.902560	−	0.114020i	0.0310674	−	0.00392473i
$845$	−17.4227	+	15.9700i	−0.599360	+	0.549384i
$846$	20.1007	+	18.8759i	0.691078	+	0.648965i
$847$	21.3325	−	22.7168i	0.732995	−	0.780560i
$848$	8.78873	+	34.2298i	0.301806	+	1.17546i
$849$	9.96702	−	7.24147i	0.342067	−	0.248526i
$850$	−39.4949	+	14.5453i	−1.35466	+	0.498898i
$851$	−58.6803	−	42.6337i	−2.01154	−	1.46147i
$852$	−0.589739	+	1.48951i	−0.0202041	+	0.0510298i
$853$	−1.88567	+	14.9266i	−0.0645642	+	0.511078i	0.926358	+	0.376644i	$0.122922\pi$
$853$	−1.88567	+	14.9266i	−0.0645642	+	0.511078i	−0.990922	+	0.134435i	$0.957078\pi$
$854$	−21.6055	+	11.8777i	−0.739326	+	0.406448i
$855$	2.03697	−	1.08805i	0.0696630	−	0.0372105i
$856$	1.93101	+	4.10360i	0.0660005	+	0.140258i
$857$	−14.0377	−	19.3212i	−0.479519	−	0.660001i	0.498894	−	0.866663i	$-0.333740\pi$
$857$	−14.0377	−	19.3212i	−0.479519	−	0.660001i	−0.978412	+	0.206663i	$0.933740\pi$
$858$	−1.25534	−	9.93701i	−0.0428565	−	0.339244i
$859$	13.1164	+	3.36771i	0.447525	+	0.114905i	0.465725	−	0.884929i	$-0.345794\pi$
$859$	13.1164	+	3.36771i	0.447525	+	0.114905i	−0.0182001	+	0.999834i	$0.505794\pi$
$860$	−12.4230	−	6.02989i	−0.423620	−	0.205618i
$861$	−10.5300	+	12.7285i	−0.358860	+	0.433788i
$862$	2.31608	−	1.91602i	0.0788859	−	0.0652601i
$863$	48.9684	+	31.0763i	1.66690	+	1.05785i	0.919177	+	0.393844i	$0.128855\pi$
$863$	48.9684	+	31.0763i	1.66690	+	1.05785i	0.747727	+	0.664006i	$0.231145\pi$
$864$	0.762345	−	12.1171i	0.0259355	−	0.412233i
$865$	−4.90362	−	20.1019i	−0.166728	−	0.683484i
$866$	10.3752	+	12.5415i	0.352564	+	0.426176i
$867$	−8.71887	−	1.66321i	−0.296108	−	0.0564857i
$868$	−1.25769	+	1.73106i	−0.0426886	+	0.0587559i
$869$	−2.57505	−	1.41565i	−0.0873526	−	0.0480225i
$870$	−3.58194	+	10.5878i	−0.121439	+	0.358961i
$871$	0.420190	+	0.0530823i	0.0142376	+	0.00179863i
$872$	−11.3387	−	5.33557i	−0.383976	−	0.180685i
$873$	22.5196	+	1.41681i	0.762174	+	0.0479519i
$874$	−4.82837			−0.163322
$875$	−23.3769	−	34.7535i	−0.790285	−	1.17488i
$876$	−2.07417			−0.0700797
$877$	−21.1541	−	1.33091i	−0.714324	−	0.0449415i	−0.298530	−	0.954400i	$-0.596496\pi$
$877$	−21.1541	−	1.33091i	−0.714324	−	0.0449415i	−0.415794	+	0.909459i	$0.636496\pi$
$878$	−37.5438	−	17.6668i	−1.26704	−	0.596225i
$879$	−21.9117	−	2.76809i	−0.739062	−	0.0933652i
$880$	−14.2376	+	10.0841i	−0.479951	+	0.339936i
$881$	−10.6633	−	5.86221i	−0.359257	−	0.197503i	0.291896	−	0.956450i	$-0.405714\pi$
$881$	−10.6633	−	5.86221i	−0.359257	−	0.197503i	−0.651152	+	0.758947i	$0.725714\pi$
$882$	15.5331	−	21.3794i	0.523025	−	0.719883i
$883$	30.4356	+	5.80591i	1.02424	+	0.195384i	0.672020	−	0.740533i	$-0.265427\pi$
$883$	30.4356	+	5.80591i	1.02424	+	0.195384i	0.352221	+	0.935917i	$0.385427\pi$
$884$	−8.46004	−	10.2264i	−0.284542	−	0.343952i
$885$	−11.1382	−	0.835739i	−0.374405	−	0.0280931i
$886$	1.33525	−	21.2232i	0.0448585	−	0.713006i
$887$	33.2318	+	21.0895i	1.11581	+	0.708117i	0.960092	−	0.279684i	$-0.0902298\pi$
$887$	33.2318	+	21.0895i	1.11581	+	0.708117i	0.155721	+	0.987801i	$0.450230\pi$
$888$	−14.9722	+	12.3861i	−0.502434	+	0.415649i
$889$	18.5756	−	22.4540i	0.623006	−	0.753085i
$890$	−0.933175	+	6.73273i	−0.0312801	+	0.225682i
$891$	−5.89756	−	1.51424i	−0.197576	−	0.0507288i
$892$	−0.937100	−	7.41791i	−0.0313764	−	0.248370i
$893$	−1.88089	−	2.58883i	−0.0629417	−	0.0866318i
$894$	4.96557	+	10.5524i	0.166073	+	0.352924i
$895$	−2.42352	+	4.99302i	−0.0810093	+	0.166898i
$896$	−44.8006	+	24.6294i	−1.49668	+	0.822809i
$897$	−3.37569	+	26.7214i	−0.112711	+	0.892201i
$898$	18.0796	−	45.6640i	0.603325	−	1.52383i
$899$	−3.55952	−	2.58614i	−0.118717	−	0.0862526i
$900$	4.00086	−	4.60535i	0.133362	−	0.153512i
$901$	−31.8489	+	23.1396i	−1.06104	+	0.770892i
$902$	3.58487	+	13.9621i	0.119363	+	0.464888i
$903$	24.4275	−	26.0127i	0.812898	−	0.865648i
$904$	6.19870	+	5.82097i	0.206166	+	0.193603i
$905$	51.0538	−	5.82489i	1.69709	−	0.193626i
$906$	24.4309	−	3.08635i	0.811664	−	0.102537i
$907$	−31.4009	−	10.2028i	−1.04265	−	0.338777i	−0.262869	−	0.964831i	$-0.584669\pi$
$907$	−31.4009	−	10.2028i	−1.04265	−	0.338777i	−0.779779	+	0.626054i	$0.784669\pi$
$908$	5.33890	−	9.71142i	0.177178	−	0.322285i
$909$	−2.56807	−	40.8183i	−0.0851775	−	1.35386i
$910$	38.5362	−	51.7171i	1.27746	−	1.71440i
$911$	−0.363149	−	0.572232i	−0.0120317	−	0.0189589i	0.838259	−	0.545272i	$-0.183574\pi$
$911$	−0.363149	−	0.572232i	−0.0120317	−	0.0189589i	−0.850291	+	0.526314i	$0.823574\pi$
$912$	−0.410410	+	1.59844i	−0.0135900	+	0.0529297i
$913$	6.47993	+	16.3664i	0.214454	+	0.541650i
$914$	52.9831	−	13.6037i	1.75253	−	0.449972i
$915$	−0.835660	−	7.32436i	−0.0276261	−	0.242136i
$916$	5.23236	−	2.07164i	0.172882	−	0.0684489i
$917$	−0.989066	+	0.465419i	−0.0326618	+	0.0153695i
$918$	34.1455	−	11.0945i	1.12697	−	0.366174i
$919$	−11.1072	+	58.2262i	−0.366394	+	1.92070i	0.0232296	+	0.999730i	$0.492605\pi$
$919$	−11.1072	+	58.2262i	−0.366394	+	1.92070i	−0.389624	+	0.920974i	$0.627395\pi$
$920$	34.3521	−	13.1239i	1.13255	−	0.432683i
$921$	1.85633	−	3.94490i	0.0611682	−	0.129989i
$922$	31.4874	−	6.00654i	1.03698	−	0.197815i
$923$	14.6460	+	12.1162i	0.482079	+	0.398810i
$924$	0.775660	+	2.38724i	0.0255174	+	0.0785343i
$925$	−51.8934	+	2.00972i	−1.70624	+	0.0660792i
$926$	19.2164	−	59.1419i	0.631489	−	1.94352i
$927$	−1.55683	+	0.987995i	−0.0511331	+	0.0324500i
$928$	5.44091	+	9.89698i	0.178607	+	0.324884i
$929$	6.09364	+	31.9440i	0.199926	+	1.04805i	0.930798	+	0.365533i	$0.119113\pi$
$929$	6.09364	+	31.9440i	0.199926	+	1.04805i	−0.730873	+	0.682514i	$0.760887\pi$
$930$	−1.64202	−	2.65772i	−0.0538438	−	0.0871502i
$931$	−2.23557	+	2.09934i	−0.0732680	+	0.0688032i
$932$		−	5.25561i		−	0.172153i
$933$	−12.7224	−	13.5480i	−0.416513	−	0.443542i
$934$	−18.3075	+	28.8480i	−0.599039	+	0.943935i
$935$	−16.2830	−	10.6111i	−0.532511	−	0.347021i
$936$	−25.1817	−	9.97014i	−0.823090	−	0.325884i
$937$	12.3065	−	0.774262i	0.402037	−	0.0252941i	0.139515	−	0.990220i	$-0.455446\pi$
$937$	12.3065	−	0.774262i	0.402037	−	0.0252941i	0.262522	+	0.964926i	$0.415446\pi$
$938$	−0.517270	+	0.0325439i	−0.0168895	+	0.00106260i
$939$	−10.2521	−	4.05907i	−0.334563	−	0.132463i
$940$	−7.08212	−	4.61520i	−0.230993	−	0.150531i
$941$	14.2265	−	22.4175i	0.463772	−	0.730788i	−0.529282	−	0.848446i	$-0.677539\pi$
$941$	14.2265	−	22.4175i	0.463772	−	0.730788i	0.993054	+	0.117658i	$0.0375386\pi$
$942$	5.52670	+	5.88533i	0.180070	+	0.191755i
$943$		−	38.7630i		−	1.26230i
$944$	−21.8399	+	20.5090i	−0.710828	+	0.667512i
$945$	18.7792	+	30.3955i	0.610886	+	0.988764i
$946$	−5.83470	−	30.5866i	−0.189703	−	0.994456i
$947$	−3.06771	−	5.58015i	−0.0996873	−	0.181331i	0.821760	−	0.569834i	$-0.192992\pi$
$947$	−3.06771	−	5.58015i	−0.0996873	−	0.181331i	−0.921447	+	0.388503i	$0.872992\pi$
$948$	−0.619946	+	0.393430i	−0.0201349	+	0.0127780i
$949$	−7.60501	+	23.4058i	−0.246869	+	0.759785i
$950$	−2.71607	+	2.13870i	−0.0881209	+	0.0693887i
$951$	5.14056	+	15.8210i	0.166694	+	0.513032i
$952$	−36.0808	−	29.8487i	−1.16939	−	0.967400i
$953$	48.6970	−	9.28945i	1.57745	−	0.300915i	0.677037	−	0.735949i	$-0.263264\pi$
$953$	48.6970	−	9.28945i	1.57745	−	0.300915i	0.900414	+	0.435034i	$0.143264\pi$
$954$	11.8638	−	25.2119i	0.384105	−	0.816264i
$955$	−9.78771	+	3.73931i	−0.316723	+	0.121001i
$956$	−0.952081	+	4.99098i	−0.0307925	+	0.161420i
$957$	−4.90880	+	1.59497i	−0.158679	+	0.0515580i
$958$	23.2198	−	10.9264i	0.750196	−	0.353016i
$959$	18.1220	−	7.17502i	0.585191	−	0.231694i
$960$	−1.00992	−	8.85171i	−0.0325951	−	0.285688i
$961$	−28.8350	+	7.40356i	−0.930160	+	0.238825i
$962$	−29.4383	−	74.3527i	−0.949129	−	2.39723i
$963$	1.13453	−	4.41872i	0.0365598	−	0.142391i
$964$	1.33212	+	2.09908i	0.0429046	+	0.0676068i
$965$	−1.15259	+	1.54682i	−0.0371031	+	0.0497938i
$966$	−2.06958	−	32.8951i	−0.0665877	−	1.05838i
$967$	−3.47255	+	6.31654i	−0.111670	+	0.203126i	−0.926236	−	0.376944i	$-0.876975\pi$
$967$	−3.47255	+	6.31654i	−0.111670	+	0.203126i	0.814566	+	0.580070i	$0.196975\pi$
$968$	18.6310	+	6.05356i	0.598822	+	0.194569i
$969$	−1.82386	+	0.230407i	−0.0585908	+	0.00740174i
$970$	−33.5602	+	3.82899i	−1.07755	+	0.122941i
$971$	17.0128	+	15.9760i	0.545965	+	0.512695i	0.907719	−	0.419578i	$-0.137822\pi$
$971$	17.0128	+	15.9760i	0.545965	+	0.512695i	−0.361754	+	0.932274i	$0.617822\pi$
$972$	−5.55289	+	5.91323i	−0.178109	+	0.189667i
$973$	4.96432	+	19.3347i	0.159149	+	0.619843i
$974$	28.7275	−	20.8718i	0.920489	−	0.668775i
$975$	9.93720	+	16.5266i	0.318245	+	0.529275i
$976$	−15.9972	−	11.6227i	−0.512059	−	0.372033i
$977$	11.9918	−	30.2877i	0.383650	−	0.968991i	−0.601742	−	0.798691i	$-0.705526\pi$
$977$	11.9918	−	30.2877i	0.383650	−	0.968991i	0.985392	−	0.170300i	$-0.0544736\pi$
$978$	−2.86169	+	22.6526i	−0.0915068	+	0.724351i
$979$	−2.75050	+	1.51210i	−0.0879063	+	0.0483269i
$980$	−3.53754	+	7.28816i	−0.113002	+	0.232812i
$981$	5.36712	+	11.4057i	0.171359	+	0.364156i
$982$	−0.446106	−	0.614013i	−0.0142358	−	0.0195939i
$983$	1.51399	+	11.9845i	0.0482888	+	0.382245i	0.997676	+	0.0681370i	$0.0217055\pi$
$983$	1.51399	+	11.9845i	0.0482888	+	0.382245i	−0.949387	+	0.314108i	$0.898294\pi$
$984$	−10.0583	−	2.58254i	−0.320647	−	0.0823282i
$985$	−1.17708	+	8.49246i	−0.0375049	+	0.270592i
$986$	−21.2885	+	25.7333i	−0.677963	+	0.819516i
$987$	16.8311	−	13.9239i	0.535740	−	0.443203i
$988$	−0.920448	−	0.584134i	−0.0292833	−	0.0185838i
$989$	−5.25763	+	83.5676i	−0.167183	+	2.65729i
$990$	13.7175	+	1.02928i	0.435970	+	0.0327125i
$991$	−6.75076	−	8.16027i	−0.214445	−	0.259219i	0.652312	−	0.757951i	$-0.273799\pi$
$991$	−6.75076	−	8.16027i	−0.214445	−	0.259219i	−0.866757	+	0.498732i	$0.833799\pi$
$992$	−3.10075	−	0.591499i	−0.0984489	−	0.0187801i
$993$	10.7612	−	14.8115i	0.341496	−	0.470029i
$994$	−20.3839	−	11.2061i	−0.646537	−	0.355437i
$995$	36.6450	−	25.9547i	1.16173	−	0.822819i
$996$	4.36365	+	0.551257i	0.138268	+	0.0174673i
$997$	−10.5782	−	4.97772i	−0.335015	−	0.157646i	0.250912	−	0.968010i	$-0.419269\pi$
$997$	−10.5782	−	4.97772i	−0.335015	−	0.157646i	−0.585927	+	0.810364i	$0.699269\pi$
$998$	−17.0838	−	1.07482i	−0.540778	−	0.0340229i
$999$	44.3001			1.40159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.4.4	✓	240
5.2	odd	4		625.2.g.b.226.19		480
5.3	odd	4		625.2.g.b.226.6		480
5.4	even	2		625.2.h.a.399.9		240
125.17	odd	100		625.2.g.b.401.19		480
125.31	even	25		625.2.h.a.224.9		240
125.94	even	50	inner	125.2.h.a.94.4	yes	240
125.108	odd	100		625.2.g.b.401.6		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.4.4	✓	240	1.1	even	1	trivial
125.2.h.a.94.4	yes	240	125.94	even	50	inner
625.2.g.b.226.6		480	5.3	odd	4
625.2.g.b.226.19		480	5.2	odd	4
625.2.g.b.401.6		480	125.108	odd	100
625.2.g.b.401.19		480	125.17	odd	100
625.2.h.a.224.9		240	125.31	even	25
625.2.h.a.399.9		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)

\(f(q)\)	\(=\)	\(q+(-1.58276 - 0.0995789i) q^{2} +(0.718817 + 0.338250i) q^{3} +(0.510990 + 0.0645531i) q^{4} +(-1.79303 - 1.33605i) q^{5} +(-1.10403 - 0.606948i) q^{6} +(2.20198 - 3.03077i) q^{7} +(2.31325 + 0.441277i) q^{8} +(-1.50999 - 1.82526i) q^{9} +O(q^{10})\)	\(q+(-1.58276 - 0.0995789i) q^{2} +(0.718817 + 0.338250i) q^{3} +(0.510990 + 0.0645531i) q^{4} +(-1.79303 - 1.33605i) q^{5} +(-1.10403 - 0.606948i) q^{6} +(2.20198 - 3.03077i) q^{7} +(2.31325 + 0.441277i) q^{8} +(-1.50999 - 1.82526i) q^{9} +(2.70490 + 2.29320i) q^{10} +(-0.102822 + 1.63430i) q^{11} +(0.345473 + 0.219244i) q^{12} +(3.74074 - 3.09461i) q^{13} +(-3.78702 + 4.57771i) q^{14} +(-0.836943 - 1.56687i) q^{15} +(-4.61513 - 1.18496i) q^{16} +(-0.665246 - 5.26597i) q^{17} +(2.20819 + 3.03932i) q^{18} +(-0.185629 - 0.394481i) q^{19} +(-0.829976 - 0.798455i) q^{20} +(2.60798 - 1.43375i) q^{21} +(0.325484 - 2.57647i) q^{22} +(-2.57076 + 6.49301i) q^{23} +(1.51354 + 1.09965i) q^{24} +(1.42993 + 4.79117i) q^{25} +(-6.22885 + 4.52553i) q^{26} +(-1.06071 - 4.13118i) q^{27} +(1.32084 - 1.40655i) q^{28} +(2.89224 + 2.71600i) q^{29} +(1.16866 + 2.56332i) q^{30} +(-1.10019 + 0.138987i) q^{31} +(2.70724 + 0.879636i) q^{32} +(-0.626712 + 1.13999i) q^{33} +(0.528547 + 8.40102i) q^{34} +(-7.99749 + 2.49231i) q^{35} +(-0.653763 - 1.03016i) q^{36} +(-2.58301 + 10.0602i) q^{37} +(0.254524 + 0.642854i) q^{38} +(3.73565 - 0.959153i) q^{39} +(-3.55817 - 3.88185i) q^{40} +(-5.16095 + 2.04336i) q^{41} +(-4.27058 + 2.00958i) q^{42} +(11.4034 - 3.70519i) q^{43} +(-0.158040 + 0.828476i) q^{44} +(0.268814 + 5.29017i) q^{45} +(4.71547 - 10.0209i) q^{46} +(7.20980 - 1.37534i) q^{47} +(-2.91662 - 2.41284i) q^{48} +(-2.17371 - 6.69001i) q^{49} +(-1.78614 - 7.72567i) q^{50} +(1.30302 - 4.01029i) q^{51} +(2.11125 - 1.33984i) q^{52} +(-3.57311 - 6.49946i) q^{53} +(1.26747 + 6.64430i) q^{54} +(2.36788 - 2.79298i) q^{55} +(6.43115 - 6.03925i) q^{56} -0.346348i q^{57} +(-4.30728 - 4.58678i) q^{58} +(3.36914 - 5.30892i) q^{59} +(-0.326524 - 0.854682i) q^{60} +(3.85850 + 1.52769i) q^{61} +(1.75519 - 0.110427i) q^{62} +(-8.85691 + 0.557229i) q^{63} +(4.66312 + 1.84626i) q^{64} +(-10.8418 + 0.550914i) q^{65} +(1.10546 - 1.74192i) q^{66} +(0.0597187 + 0.0635939i) q^{67} -2.73380i q^{68} +(-4.04416 + 3.79772i) q^{69} +(12.9063 - 3.14835i) q^{70} +(0.733649 + 3.84592i) q^{71} +(-2.68754 - 4.88861i) q^{72} +(-4.28008 + 2.71622i) q^{73} +(5.09007 - 15.6656i) q^{74} +(-0.592750 + 3.92765i) q^{75} +(-0.0693894 - 0.213559i) q^{76} +(4.72679 + 3.91034i) q^{77} +(-6.00816 + 1.14612i) q^{78} +(-0.764053 + 1.62370i) q^{79} +(6.69191 + 8.29073i) q^{80} +(-0.696741 + 3.65244i) q^{81} +(8.37202 - 2.72024i) q^{82} +(9.72636 - 4.57688i) q^{83} +(1.42520 - 0.564278i) q^{84} +(-5.84280 + 10.3309i) q^{85} +(-18.4178 + 4.72890i) q^{86} +(1.16031 + 2.93061i) q^{87} +(-0.959033 + 3.73519i) q^{88} +(1.02704 + 1.61836i) q^{89} +(0.101321 - 8.39985i) q^{90} +(-1.14200 - 18.1516i) q^{91} +(-1.73278 + 3.15191i) q^{92} +(-0.837850 - 0.272234i) q^{93} +(-11.5484 + 1.45890i) q^{94} +(-0.194208 + 0.955326i) q^{95} +(1.64847 + 1.54802i) q^{96} +(-6.52045 + 6.94357i) q^{97} +(2.77429 + 10.8051i) q^{98} +(3.13829 - 2.28010i) 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

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