LMFDB - Embedded newform 270.2.k.e.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(31,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("270.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.k (of order $9$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	270.211
Dual form			270.2.k.e.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.67972 + 0.422540i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(1.01514 - 1.40339i) q^{6} +(0.192018 + 1.08899i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.64292 - 1.41950i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67972 + 0.422540i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(1.01514 - 1.40339i) q^{6} +(0.192018 + 1.08899i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.64292 - 1.41950i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.27093 - 0.826550i) q^{11} +(0.124440 + 1.72757i) q^{12} +(4.17017 + 3.49919i) q^{13} +(-0.847083 - 0.710787i) q^{14} +(-1.43390 + 0.971556i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.850824 + 1.47367i) q^{17} +(-1.11216 + 2.78623i) q^{18} +(3.10949 + 5.38579i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(-0.782677 - 1.74806i) q^{21} +(2.27093 - 0.826550i) q^{22} +(-1.57099 + 8.90951i) q^{23} +(-1.20579 - 1.24341i) q^{24} +(0.766044 - 0.642788i) q^{25} -5.44377 q^{26} +(-3.83957 + 3.50110i) q^{27} +1.10579 q^{28} +(-1.04331 + 0.875444i) q^{29} +(0.473930 - 1.66595i) q^{30} +(0.817858 - 4.63830i) q^{31} +(0.939693 - 0.342020i) q^{32} +(4.16377 + 0.428816i) q^{33} +(-0.295488 - 1.67580i) q^{34} +(0.552894 + 0.957640i) q^{35} +(-0.938993 - 2.84926i) q^{36} +(-0.0721794 + 0.125018i) q^{37} +(-5.84393 - 2.12702i) q^{38} +(-8.48326 - 4.11559i) q^{39} +(0.766044 + 0.642788i) q^{40} +(3.79786 + 3.18678i) q^{41} +(1.72320 + 0.835997i) q^{42} +(5.56236 + 2.02453i) q^{43} +(-1.20833 + 2.09290i) q^{44} +(1.99804 - 2.23782i) q^{45} +(-4.52347 - 7.83489i) q^{46} +(-2.35553 - 13.3589i) q^{47} +(1.72294 + 0.177441i) q^{48} +(5.42882 - 1.97593i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(0.806462 - 2.83486i) q^{51} +(4.17017 - 3.49919i) q^{52} +0.597985 q^{53} +(0.690822 - 5.15003i) q^{54} -2.41667 q^{55} +(-0.847083 + 0.710787i) q^{56} +(-7.49879 - 7.73275i) q^{57} +(0.236500 - 1.34126i) q^{58} +(8.69592 - 3.16505i) q^{59} +(0.707801 + 1.58083i) q^{60} +(1.17167 + 6.64487i) q^{61} +(2.35493 + 4.07886i) q^{62} +(2.05330 + 2.60554i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.11547 + 1.86188i) q^{65} +(-3.46527 + 2.34793i) q^{66} +(-1.95962 - 1.64432i) q^{67} +(1.30354 + 1.09380i) q^{68} +(-1.12580 - 15.6293i) q^{69} +(-1.03910 - 0.378202i) q^{70} +(0.681582 - 1.18054i) q^{71} +(2.55078 + 1.57909i) q^{72} +(-4.53509 - 7.85501i) q^{73} +(-0.0250677 - 0.142166i) q^{74} +(-1.01514 + 1.40339i) q^{75} +(5.84393 - 2.12702i) q^{76} +(0.464044 - 2.63173i) q^{77} +(9.14401 - 2.30021i) q^{78} +(-11.5492 + 9.69094i) q^{79} -1.00000 q^{80} +(4.97006 - 7.50323i) q^{81} -4.95776 q^{82} +(-10.7089 + 8.98582i) q^{83} +(-1.85741 + 0.467239i) q^{84} +(-0.295488 + 1.67580i) q^{85} +(-5.56236 + 2.02453i) q^{86} +(1.38256 - 1.91134i) q^{87} +(-0.419650 - 2.37995i) q^{88} +(-1.26685 - 2.19424i) q^{89} +(-0.0921398 + 2.99858i) q^{90} +(-3.00983 + 5.21317i) q^{91} +(8.50135 + 3.09424i) q^{92} +(0.586095 + 8.13663i) q^{93} +(10.3914 + 8.71939i) q^{94} +(4.76402 + 3.99748i) q^{95} +(-1.43390 + 0.971556i) q^{96} +(-8.68688 - 3.16176i) q^{97} +(-2.88862 + 5.00323i) q^{98} +(-7.17516 + 1.03907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9	$ 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9} - 12 q^{10} + 9 q^{13} - 3 q^{14} + 15 q^{17} - 12 q^{18} - 9 q^{19} + 24 q^{21} - 12 q^{23} + 3 q^{24} - 12 q^{26} - 3 q^{27} + 6 q^{28} - 33 q^{29} + 6 q^{30} - 21 q^{31} + 6 q^{33} - 15 q^{34} + 3 q^{35} - 6 q^{36} - 12 q^{37} + 12 q^{38} - 36 q^{39} + 21 q^{41} + 15 q^{42} + 12 q^{43} + 9 q^{44} - 12 q^{45} - 15 q^{46} - 21 q^{47} + 27 q^{49} + 3 q^{51} + 9 q^{52} - 60 q^{53} + 36 q^{54} + 18 q^{55} - 3 q^{56} - 24 q^{57} - 21 q^{58} + 36 q^{59} + 33 q^{61} + 18 q^{62} + 39 q^{63} - 12 q^{64} - 9 q^{66} - 12 q^{67} - 3 q^{68} - 48 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{74} - 12 q^{76} - 60 q^{77} - 36 q^{78} - 15 q^{79} - 24 q^{80} - 15 q^{81} + 6 q^{82} - 27 q^{83} + 3 q^{84} - 15 q^{85} - 12 q^{86} + 78 q^{87} - 9 q^{88} + 30 q^{89} - 9 q^{90} - 9 q^{91} + 6 q^{92} - 30 q^{93} + 12 q^{94} - 15 q^{95} + 3 q^{97} + 27 q^{98} - 111 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9 - 12 * q^10 + 9 * q^13 - 3 * q^14 + 15 * q^17 - 12 * q^18 - 9 * q^19 + 24 * q^21 - 12 * q^23 + 3 * q^24 - 12 * q^26 - 3 * q^27 + 6 * q^28 - 33 * q^29 + 6 * q^30 - 21 * q^31 + 6 * q^33 - 15 * q^34 + 3 * q^35 - 6 * q^36 - 12 * q^37 + 12 * q^38 - 36 * q^39 + 21 * q^41 + 15 * q^42 + 12 * q^43 + 9 * q^44 - 12 * q^45 - 15 * q^46 - 21 * q^47 + 27 * q^49 + 3 * q^51 + 9 * q^52 - 60 * q^53 + 36 * q^54 + 18 * q^55 - 3 * q^56 - 24 * q^57 - 21 * q^58 + 36 * q^59 + 33 * q^61 + 18 * q^62 + 39 * q^63 - 12 * q^64 - 9 * q^66 - 12 * q^67 - 3 * q^68 - 48 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^74 - 12 * q^76 - 60 * q^77 - 36 * q^78 - 15 * q^79 - 24 * q^80 - 15 * q^81 + 6 * q^82 - 27 * q^83 + 3 * q^84 - 15 * q^85 - 12 * q^86 + 78 * q^87 - 9 * q^88 + 30 * q^89 - 9 * q^90 - 9 * q^91 + 6 * q^92 - 30 * q^93 + 12 * q^94 - 15 * q^95 + 3 * q^97 + 27 * q^98 - 111 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.67972	+	0.422540i	−0.969787	+	0.243953i
$3$	−1.67972	+	0.422540i	−0.969787	+	0.243953i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	1.01514	−	1.40339i	0.414428	−	0.572931i
$7$	0.192018	+	1.08899i	0.0725760	+	0.411599i	0.999352	+	0.0359852i	$0.0114569\pi$
$7$	0.192018	+	1.08899i	0.0725760	+	0.411599i	−0.926776	+	0.375614i	$0.877432\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.64292	−	1.41950i	0.880973	−	0.473166i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.27093	−	0.826550i	−0.684710	−	0.249214i	−0.0238415	−	0.999716i	$-0.507590\pi$
$11$	−2.27093	−	0.826550i	−0.684710	−	0.249214i	−0.660869	+	0.750502i	$0.729812\pi$
$12$	0.124440	+	1.72757i	0.0359227	+	0.498708i
$13$	4.17017	+	3.49919i	1.15660	+	0.970500i	0.999853	−	0.0171395i	$-0.00545593\pi$
$13$	4.17017	+	3.49919i	1.15660	+	0.970500i	0.156744	+	0.987639i	$0.449900\pi$
$14$	−0.847083	−	0.710787i	−0.226392	−	0.189966i
$15$	−1.43390	+	0.971556i	−0.370232	+	0.250855i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.850824	+	1.47367i	−0.206355	+	0.357418i	−0.950564	−	0.310530i	$-0.899494\pi$
$17$	−0.850824	+	1.47367i	−0.206355	+	0.357418i	0.744209	+	0.667947i	$0.232827\pi$
$18$	−1.11216	+	2.78623i	−0.262138	+	0.656722i
$19$	3.10949	+	5.38579i	0.713366	+	1.23559i	0.963586	+	0.267397i	$0.0861636\pi$
$19$	3.10949	+	5.38579i	0.713366	+	1.23559i	−0.250220	+	0.968189i	$0.580503\pi$
$20$	−0.173648	−	0.984808i	−0.0388289	−	0.220210i
$21$	−0.782677	−	1.74806i	−0.170794	−	0.381458i
$22$	2.27093	−	0.826550i	0.484163	−	0.176221i
$23$	−1.57099	+	8.90951i	−0.327573	+	1.85776i	0.163365	+	0.986566i	$0.447765\pi$
$23$	−1.57099	+	8.90951i	−0.327573	+	1.85776i	−0.490938	+	0.871195i	$0.663346\pi$
$24$	−1.20579	−	1.24341i	−0.246131	−	0.253810i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−5.44377			−1.06761
$27$	−3.83957	+	3.50110i	−0.738926	+	0.673786i
$28$	1.10579			0.208974
$29$	−1.04331	+	0.875444i	−0.193738	+	0.162566i	−0.734497	−	0.678612i	$-0.762582\pi$
$29$	−1.04331	+	0.875444i	−0.193738	+	0.162566i	0.540758	+	0.841178i	$0.318137\pi$
$30$	0.473930	−	1.66595i	0.0865274	−	0.304160i
$31$	0.817858	−	4.63830i	0.146892	−	0.833064i	−0.818937	−	0.573883i	$-0.805436\pi$
$31$	0.817858	−	4.63830i	0.146892	−	0.833064i	0.965829	−	0.259181i	$-0.0834526\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	4.16377	+	0.428816i	0.724820	+	0.0746472i
$34$	−0.295488	−	1.67580i	−0.0506758	−	0.287397i
$35$	0.552894	+	0.957640i	0.0934561	+	0.161871i
$36$	−0.938993	−	2.84926i	−0.156499	−	0.474877i
$37$	−0.0721794	+	0.125018i	−0.0118662	+	0.0205529i	−0.871898	−	0.489688i	$-0.837111\pi$
$37$	−0.0721794	+	0.125018i	−0.0118662	+	0.0205529i	0.860031	+	0.510241i	$0.170444\pi$
$38$	−5.84393	−	2.12702i	−0.948011	−	0.345048i
$39$	−8.48326	−	4.11559i	−1.35841	−	0.659022i
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	3.79786	+	3.18678i	0.593126	+	0.497692i	0.889228	−	0.457464i	$-0.151242\pi$
$41$	3.79786	+	3.18678i	0.593126	+	0.497692i	−0.296102	+	0.955156i	$0.595687\pi$
$42$	1.72320	+	0.835997i	0.265895	+	0.128997i
$43$	5.56236	+	2.02453i	0.848252	+	0.308738i	0.729327	−	0.684165i	$-0.239833\pi$
$43$	5.56236	+	2.02453i	0.848252	+	0.308738i	0.118925	+	0.992903i	$0.462055\pi$
$44$	−1.20833	+	2.09290i	−0.182163	+	0.315516i
$45$	1.99804	−	2.23782i	0.297850	−	0.333595i
$46$	−4.52347	−	7.83489i	−0.666950	−	1.15519i
$47$	−2.35553	−	13.3589i	−0.343590	−	1.94859i	−0.315296	−	0.948993i	$-0.602104\pi$
$47$	−2.35553	−	13.3589i	−0.343590	−	1.94859i	−0.0282938	−	0.999600i	$-0.509007\pi$
$48$	1.72294	+	0.177441i	0.248685	+	0.0256114i
$49$	5.42882	−	1.97593i	0.775546	−	0.282276i
$50$	−0.173648	+	0.984808i	−0.0245576	+	0.139273i
$51$	0.806462	−	2.83486i	0.112927	−	0.396960i
$52$	4.17017	−	3.49919i	0.578298	−	0.485250i
$53$	0.597985			0.0821396			0.0410698	−	0.999156i	$-0.486923\pi$
$53$	0.597985			0.0821396			0.0410698	+	0.999156i	$0.486923\pi$
$54$	0.690822	−	5.15003i	0.0940090	−	0.700830i
$55$	−2.41667			−0.325864
$56$	−0.847083	+	0.710787i	−0.113196	+	0.0949829i
$57$	−7.49879	−	7.73275i	−0.993238	−	1.02423i
$58$	0.236500	−	1.34126i	0.0310540	−	0.176116i
$59$	8.69592	−	3.16505i	1.13211	−	0.412055i	0.293053	−	0.956096i	$-0.405329\pi$
$59$	8.69592	−	3.16505i	1.13211	−	0.412055i	0.839059	+	0.544041i	$0.183106\pi$
$60$	0.707801	+	1.58083i	0.0913767	+	0.204084i
$61$	1.17167	+	6.64487i	0.150017	+	0.850788i	0.963201	+	0.268782i	$0.0866210\pi$
$61$	1.17167	+	6.64487i	0.150017	+	0.850788i	−0.813184	+	0.582006i	$0.802268\pi$
$62$	2.35493	+	4.07886i	0.299076	+	0.518015i
$63$	2.05330	+	2.60554i	0.258692	+	0.328267i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.11547	+	1.86188i	0.634496	+	0.230938i
$66$	−3.46527	+	2.34793i	−0.426545	+	0.289010i
$67$	−1.95962	−	1.64432i	−0.239406	−	0.200885i	0.515189	−	0.857077i	$-0.327722\pi$
$67$	−1.95962	−	1.64432i	−0.239406	−	0.200885i	−0.754594	+	0.656192i	$0.772166\pi$
$68$	1.30354	+	1.09380i	0.158077	+	0.132643i
$69$	−1.12580	−	15.6293i	−0.135531	−	1.88154i
$70$	−1.03910	−	0.378202i	−0.124196	−	0.0452038i
$71$	0.681582	−	1.18054i	0.0808889	−	0.140104i	−0.822743	−	0.568413i	$-0.807557\pi$
$71$	0.681582	−	1.18054i	0.0808889	−	0.140104i	0.903632	+	0.428310i	$0.140891\pi$
$72$	2.55078	+	1.57909i	0.300612	+	0.186097i
$73$	−4.53509	−	7.85501i	−0.530792	−	0.919359i	−0.999354	−	0.0359284i	$-0.988561\pi$
$73$	−4.53509	−	7.85501i	−0.530792	−	0.919359i	0.468562	−	0.883430i	$-0.344772\pi$
$74$	−0.0250677	−	0.142166i	−0.00291406	−	0.0165264i
$75$	−1.01514	+	1.40339i	−0.117218	+	0.162049i
$76$	5.84393	−	2.12702i	0.670345	−	0.243986i
$77$	0.464044	−	2.63173i	0.0528827	−	0.299913i
$78$	9.14401	−	2.30021i	1.03536	−	0.260447i
$79$	−11.5492	+	9.69094i	−1.29939	+	1.09032i	−0.309137	+	0.951018i	$0.600040\pi$
$79$	−11.5492	+	9.69094i	−1.29939	+	1.09032i	−0.990251	+	0.139298i	$0.955515\pi$
$80$	−1.00000			−0.111803
$81$	4.97006	−	7.50323i	0.552229	−	0.833693i
$82$	−4.95776			−0.547493
$83$	−10.7089	+	8.98582i	−1.17545	+	0.986322i	−0.175455	+	0.984488i	$0.556140\pi$
$83$	−10.7089	+	8.98582i	−1.17545	+	0.986322i	−0.999998	+	0.00183470i	$0.999416\pi$
$84$	−1.85741	+	0.467239i	−0.202661	+	0.0509800i
$85$	−0.295488	+	1.67580i	−0.0320502	+	0.181766i
$86$	−5.56236	+	2.02453i	−0.599805	+	0.218311i
$87$	1.38256	−	1.91134i	0.148226	−	0.204917i
$88$	−0.419650	−	2.37995i	−0.0447349	−	0.253704i
$89$	−1.26685	−	2.19424i	−0.134285	−	0.232589i	0.791039	−	0.611766i	$-0.209541\pi$
$89$	−1.26685	−	2.19424i	−0.134285	−	0.232589i	−0.925324	+	0.379177i	$0.876207\pi$
$90$	−0.0921398	+	2.99858i	−0.00971239	+	0.316079i
$91$	−3.00983	+	5.21317i	−0.315516	+	0.546489i
$92$	8.50135	+	3.09424i	0.886327	+	0.322597i
$93$	0.586095	+	8.13663i	0.0607752	+	0.843729i
$94$	10.3914	+	8.71939i	1.07179	+	0.899336i
$95$	4.76402	+	3.99748i	0.488778	+	0.410133i
$96$	−1.43390	+	0.971556i	−0.146347	+	0.0991590i
$97$	−8.68688	−	3.16176i	−0.882019	−	0.321029i	−0.138995	−	0.990293i	$-0.544387\pi$
$97$	−8.68688	−	3.16176i	−0.882019	−	0.321029i	−0.743024	+	0.669265i	$0.766609\pi$
$98$	−2.88862	+	5.00323i	−0.291794	+	0.505403i
$99$	−7.17516	+	1.03907i	−0.721131	+	0.104430i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.63260	−	9.25896i	−0.162450	−	0.921301i	−0.951655	−	0.307170i	$-0.900618\pi$
$101$	−1.63260	−	9.25896i	−0.162450	−	0.921301i	0.789204	−	0.614131i	$-0.210493\pi$
$102$	1.20443	+	2.69001i	0.119256	+	0.266351i
$103$	8.55088	−	3.11226i	0.842543	−	0.306661i	0.115547	−	0.993302i	$-0.463138\pi$
$103$	8.55088	−	3.11226i	0.842543	−	0.306661i	0.726996	+	0.686642i	$0.240916\pi$
$104$	−0.945300	+	5.36107i	−0.0926943	+	0.525696i
$105$	−1.33335	−	1.37495i	−0.130121	−	0.134181i
$106$	−0.458083	+	0.384378i	−0.0444930	+	0.0373340i
$107$	1.77202			0.171307			0.0856536	−	0.996325i	$-0.472702\pi$
$107$	1.77202			0.171307			0.0856536	+	0.996325i	$0.472702\pi$
$108$	2.78117	+	4.38920i	0.267618	+	0.422351i
$109$	−2.62614			−0.251539			−0.125769	−	0.992060i	$-0.540140\pi$
$109$	−2.62614			−0.251539			−0.125769	+	0.992060i	$0.540140\pi$
$110$	1.85128	−	1.55341i	0.176512	−	0.148111i
$111$	0.0684160	−	0.240495i	0.00649376	−	0.0228267i
$112$	0.192018	−	1.08899i	0.0181440	−	0.102900i
$113$	5.63339	−	2.05039i	0.529945	−	0.192884i	−0.0631688	−	0.998003i	$-0.520121\pi$
$113$	5.63339	−	2.05039i	0.529945	−	0.192884i	0.593114	+	0.805119i	$0.297898\pi$
$114$	10.7149	+	1.10350i	1.00354	+	0.103352i
$115$	1.57099	+	8.90951i	0.146495	+	0.830816i
$116$	0.680974	+	1.17948i	0.0632269	+	0.109512i
$117$	15.9885	+	3.32853i	1.47814	+	0.307723i
$118$	−4.62700	+	8.01420i	−0.425950	+	0.737767i
$119$	−1.76818	−	0.643566i	−0.162089	−	0.0589956i
$120$	−1.55834	−	0.756019i	−0.142257	−	0.0690148i
$121$	−3.95257	−	3.31660i	−0.359324	−	0.301509i
$122$	−5.16879	−	4.33713i	−0.467960	−	0.392665i
$123$	−7.72589	−	3.74816i	−0.696620	−	0.337960i
$124$	−4.42582	−	1.61087i	−0.397450	−	0.144660i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−3.24773	−	0.676122i	−0.289331	−	0.0602337i
$127$	−8.64771	−	14.9783i	−0.767360	−	1.32911i	−0.938990	−	0.343945i	$-0.888236\pi$
$127$	−8.64771	−	14.9783i	−0.767360	−	1.32911i	0.171629	−	0.985162i	$-0.445097\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−10.1987	−	1.05033i	−0.897942	−	0.0924766i
$130$	−5.11547	+	1.86188i	−0.448656	+	0.163298i
$131$	−0.0158044	+	0.0896311i	−0.00138083	+	0.00783110i	−0.985490	−	0.169731i	$-0.945710\pi$
$131$	−0.0158044	+	0.0896311i	−0.00138083	+	0.00783110i	0.984110	+	0.177562i	$0.0568211\pi$
$132$	1.14533	−	4.02605i	0.0996884	−	0.350423i
$133$	−5.26799	+	4.42037i	−0.456793	+	0.383295i
$134$	2.55810			0.220986
$135$	−2.41057	+	4.60317i	−0.207469	+	0.396177i
$136$	−1.70165			−0.145915
$137$	1.74853	−	1.46719i	0.149387	−	0.125350i	−0.565031	−	0.825069i	$-0.691136\pi$
$137$	1.74853	−	1.46719i	0.149387	−	0.125350i	0.714418	+	0.699719i	$0.246692\pi$
$138$	10.9087	+	11.2491i	0.928612	+	0.957585i
$139$	−1.21559	+	6.89397i	−0.103105	+	0.584739i	0.888855	+	0.458189i	$0.151502\pi$
$139$	−1.21559	+	6.89397i	−0.103105	+	0.584739i	−0.991960	+	0.126550i	$0.959609\pi$
$140$	1.03910	−	0.378202i	0.0878200	−	0.0319639i
$141$	9.60129	+	21.4439i	0.808575	+	1.80590i
$142$	0.236711	+	1.34245i	0.0198643	+	0.112656i
$143$	−6.57789	−	11.3932i	−0.550071	−	0.952751i
$144$	−2.96903	+	0.429959i	−0.247419	+	0.0358299i
$145$	−0.680974	+	1.17948i	−0.0565518	+	0.0979506i
$146$	8.52318	+	3.10218i	0.705383	+	0.256739i
$147$	−8.28400	+	5.61290i	−0.683252	+	0.462944i
$148$	0.110585	+	0.0927921i	0.00909006	+	0.00762746i
$149$	15.5244	+	13.0265i	1.27181	+	1.06718i	0.994318	+	0.106447i	$0.0339475\pi$
$149$	15.5244	+	13.0265i	1.27181	+	1.06718i	0.277492	+	0.960728i	$0.410497\pi$
$150$	−0.124440	−	1.72757i	−0.0101605	−	0.141056i
$151$	7.90720	+	2.87798i	0.643479	+	0.234207i	0.643087	−	0.765793i	$-0.277653\pi$
$151$	7.90720	+	2.87798i	0.643479	+	0.234207i	0.000391268		1.00000i	$0.499875\pi$
$152$	−3.10949	+	5.38579i	−0.252213	+	0.436846i
$153$	−0.156789	+	5.10254i	−0.0126757	+	0.412516i
$154$	1.33616	+	2.31430i	0.107671	+	0.186492i
$155$	−0.817858	−	4.63830i	−0.0656920	−	0.372558i
$156$	−5.52617	+	7.63972i	−0.442448	+	0.611667i
$157$	−10.7011	+	3.89488i	−0.854040	+	0.310845i	−0.731686	−	0.681642i	$-0.761266\pi$
$157$	−10.7011	+	3.89488i	−0.854040	+	0.310845i	−0.122353	+	0.992487i	$0.539044\pi$
$158$	2.61799	−	14.8474i	0.208276	−	1.18119i
$159$	−1.00445	+	0.252673i	−0.0796579	+	0.0200382i
$160$	0.766044	−	0.642788i	0.0605611	−	0.0508168i
$161$	−10.0040			−0.788426
$162$	1.01570	+	8.94250i	0.0798011	+	0.702589i
$163$	11.4431			0.896291			0.448145	−	0.893961i	$-0.352085\pi$
$163$	11.4431			0.896291			0.448145	+	0.893961i	$0.352085\pi$
$164$	3.79786	−	3.18678i	0.296563	−	0.248846i
$165$	4.05933	−	1.02114i	0.316018	−	0.0794955i
$166$	2.42751	−	13.7671i	0.188411	−	1.06853i
$167$	4.90570	−	1.78553i	0.379615	−	0.138169i	−0.145163	−	0.989408i	$-0.546371\pi$
$167$	4.90570	−	1.78553i	0.379615	−	0.138169i	0.524778	+	0.851239i	$0.324148\pi$
$168$	1.12253	−	1.55185i	0.0866048	−	0.119728i
$169$	2.88857	+	16.3819i	0.222198	+	1.26015i
$170$	−0.850824	−	1.47367i	−0.0652552	−	0.113025i
$171$	15.8633	+	9.82032i	1.21309	+	0.750978i
$172$	2.95967	−	5.12630i	0.225673	−	0.390877i
$173$	1.45413	+	0.529261i	0.110556	+	0.0402390i	0.396706	−	0.917946i	$-0.370153\pi$
$173$	1.45413	+	0.529261i	0.110556	+	0.0402390i	−0.286150	+	0.958185i	$0.592376\pi$
$174$	0.169481	+	2.35287i	0.0128483	+	0.178370i
$175$	0.847083	+	0.710787i	0.0640334	+	0.0537304i
$176$	1.85128	+	1.55341i	0.139545	+	0.117092i
$177$	−13.2693	+	8.99078i	−0.997385	+	0.675788i
$178$	2.38089	+	0.866573i	0.178455	+	0.0649524i
$179$	3.44877	−	5.97345i	0.257773	−	0.446476i	−0.707872	−	0.706341i	$-0.750345\pi$
$179$	3.44877	−	5.97345i	0.257773	−	0.446476i	0.965645	+	0.259865i	$0.0836779\pi$
$180$	−1.85687	−	2.35628i	−0.138403	−	0.175626i
$181$	−7.14229	−	12.3708i	−0.530882	−	0.919515i	−0.999351	−	0.0360344i	$-0.988527\pi$
$181$	−7.14229	−	12.3708i	−0.530882	−	0.919515i	0.468469	−	0.883480i	$-0.344806\pi$
$182$	−1.04530	−	5.92820i	−0.0774829	−	0.439427i
$183$	−4.77580	−	10.6664i	−0.353037	−	0.788486i
$184$	−8.50135	+	3.09424i	−0.626728	+	0.228110i
$185$	−0.0250677	+	0.142166i	−0.00184301	+	0.0104522i
$186$	−5.67910	−	5.85629i	−0.416412	−	0.429404i
$187$	3.15022	−	2.64335i	0.230367	−	0.193301i
$188$	−13.5650			−0.989327
$189$	−4.54992	−	3.50898i	−0.330958	−	0.255241i
$190$	−6.21898			−0.451172
$191$	5.12623	−	4.30142i	0.370921	−	0.311240i	−0.438205	−	0.898875i	$-0.644386\pi$
$191$	5.12623	−	4.30142i	0.370921	−	0.311240i	0.809126	+	0.587636i	$0.199941\pi$
$192$	0.473930	−	1.66595i	0.0342030	−	0.120230i
$193$	4.02374	−	22.8198i	0.289635	−	1.64260i	−0.398606	−	0.917122i	$-0.630506\pi$
$193$	4.02374	−	22.8198i	0.289635	−	1.64260i	0.688241	−	0.725482i	$-0.258383\pi$
$194$	8.68688	−	3.16176i	0.623681	−	0.227001i
$195$	−9.37927	−	0.965946i	−0.671664	−	0.0691729i
$196$	−1.00321	−	5.68946i	−0.0716576	−	0.406390i
$197$	11.8290	+	20.4885i	0.842783	+	1.45974i	0.887533	+	0.460744i	$0.152417\pi$
$197$	11.8290	+	20.4885i	0.842783	+	1.45974i	−0.0447503	+	0.998998i	$0.514249\pi$
$198$	4.82859	−	5.40808i	0.343153	−	0.384335i
$199$	−6.80087	+	11.7795i	−0.482101	+	0.835023i	−0.999789	−	0.0205463i	$-0.993459\pi$
$199$	−6.80087	+	11.7795i	−0.482101	+	0.835023i	0.517688	+	0.855569i	$0.326793\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	3.98640	+	1.93397i	0.281179	+	0.136412i
$202$	7.20219	+	6.04335i	0.506744	+	0.425209i
$203$	−1.15368	−	0.968055i	−0.0809727	−	0.0679441i
$204$	−2.65175	−	1.28648i	−0.185660	−	0.0900715i
$205$	4.65877	+	1.69565i	0.325382	+	0.118430i
$206$	−4.54983	+	7.88053i	−0.317001	+	0.549063i
$207$	8.49502	+	25.7771i	0.590445	+	1.79163i
$208$	−2.72188	−	4.71444i	−0.188729	−	0.326888i
$209$	−2.60980	−	14.8009i	−0.180523	−	1.02380i
$210$	1.90520	+	0.196212i	0.131472	+	0.0135399i
$211$	14.5452	−	5.29401i	1.00133	−	0.364455i	0.211233	−	0.977436i	$-0.432252\pi$
$211$	14.5452	−	5.29401i	1.00133	−	0.364455i	0.790098	+	0.612981i	$0.210030\pi$
$212$	0.103839	−	0.588901i	0.00713170	−	0.0404459i
$213$	−0.646045	+	2.27096i	−0.0442662	+	0.155604i
$214$	−1.35744	+	1.13903i	−0.0927929	+	0.0778625i
$215$	5.91934			0.403696
$216$	−4.95183	−	1.57462i	−0.336929	−	0.107139i
$217$	5.20810			0.353549
$218$	2.01174	−	1.68805i	0.136252	−	0.114329i
$219$	10.9367	+	11.2780i	0.739036	+	0.762094i
$220$	−0.419650	+	2.37995i	−0.0282928	+	0.160457i
$221$	−8.70473	+	3.16826i	−0.585543	+	0.213120i
$222$	0.102177	+	0.228207i	0.00685769	+	0.0153162i
$223$	−4.21099	−	23.8817i	−0.281989	−	1.59924i	−0.715847	−	0.698257i	$-0.753959\pi$
$223$	−4.21099	−	23.8817i	−0.281989	−	1.59924i	0.433859	−	0.900981i	$-0.357152\pi$
$224$	0.552894	+	0.957640i	0.0369418	+	0.0639850i
$225$	1.11216	−	2.78623i	0.0741440	−	0.185749i
$226$	−2.99747	+	5.19176i	−0.199388	+	0.345351i
$227$	−3.77381	−	1.37356i	−0.250477	−	0.0911661i	0.213731	−	0.976893i	$-0.431439\pi$
$227$	−3.77381	−	1.37356i	−0.250477	−	0.0911661i	−0.464207	+	0.885727i	$0.653661\pi$
$228$	−8.91742	+	6.04209i	−0.590570	+	0.400147i
$229$	−21.5224	−	18.0594i	−1.42224	−	1.19340i	−0.950128	−	0.311861i	$-0.899048\pi$
$229$	−21.5224	−	18.0594i	−1.42224	−	1.19340i	−0.472111	−	0.881539i	$-0.656508\pi$
$230$	−6.93037	−	5.81527i	−0.456975	−	0.383447i
$231$	0.332544	+	4.61664i	0.0218798	+	0.303753i
$232$	−1.27981	−	0.465814i	−0.0840238	−	0.0305822i
$233$	−2.11716	+	3.66703i	−0.138700	+	0.240235i	−0.927005	−	0.375050i	$-0.877626\pi$
$233$	−2.11716	+	3.66703i	−0.138700	+	0.240235i	0.788305	+	0.615285i	$0.210959\pi$
$234$	−14.3874	+	7.72741i	−0.940537	+	0.505157i
$235$	−6.78248	−	11.7476i	−0.442440	−	0.766329i
$236$	−1.60694	−	9.11341i	−0.104603	−	0.593233i
$237$	15.3046	−	21.1581i	0.994143	−	1.37436i
$238$	1.76818	−	0.643566i	0.114614	−	0.0417162i
$239$	2.70454	−	15.3382i	0.174942	−	0.992147i	−0.763268	−	0.646082i	$-0.776406\pi$
$239$	2.70454	−	15.3382i	0.174942	−	0.992147i	0.938210	−	0.346065i	$-0.112482\pi$
$240$	1.67972	−	0.422540i	0.108425	−	0.0272748i
$241$	−16.0118	+	13.4355i	−1.03141	+	0.865457i	−0.991018	−	0.133727i	$-0.957305\pi$
$241$	−16.0118	+	13.4355i	−1.03141	+	0.865457i	−0.0403929	+	0.999184i	$0.512861\pi$
$242$	5.15971			0.331679
$243$	−5.17789	+	14.7034i	−0.332162	+	0.943222i
$244$	6.74737			0.431956
$245$	4.42562	−	3.71353i	0.282742	−	0.237249i
$246$	8.32765	−	2.09485i	0.530951	−	0.133563i
$247$	−5.87881	+	33.3404i	−0.374059	+	2.12140i
$248$	4.42582	−	1.61087i	0.281040	−	0.102290i
$249$	14.1911	−	19.6186i	0.899322	−	1.24328i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−14.3223	−	24.8070i	−0.904016	−	1.56580i	−0.822232	−	0.569152i	$-0.807272\pi$
$251$	−14.3223	−	24.8070i	−0.904016	−	1.56580i	−0.0817841	−	0.996650i	$-0.526062\pi$
$252$	2.92251	−	1.56966i	0.184101	−	0.0988794i
$253$	10.9317	−	18.9343i	0.687273	−	1.19039i
$254$	16.2524	+	5.91538i	1.01977	+	0.371164i
$255$	−0.211753	−	2.93972i	−0.0132605	−	0.184093i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−20.6807	−	17.3531i	−1.29002	−	1.08246i	−0.991778	−	0.127969i	$-0.959154\pi$
$257$	−20.6807	−	17.3531i	−1.29002	−	1.08246i	−0.298246	−	0.954489i	$-0.596401\pi$
$258$	8.48776	−	5.75097i	0.528425	−	0.358040i
$259$	−0.150003	−	0.0545968i	−0.00932076	−	0.00339248i
$260$	2.72188	−	4.71444i	0.168804	−	0.292377i
$261$	−1.51470	+	3.79471i	−0.0937578	+	0.234887i
$262$	−0.0455069	−	0.0788202i	−0.00281142	−	0.00486953i
$263$	−2.40382	−	13.6327i	−0.148226	−	0.840630i	−0.964720	−	0.263277i	$-0.915197\pi$
$263$	−2.40382	−	13.6327i	−0.148226	−	0.840630i	0.816495	−	0.577353i	$-0.195914\pi$
$264$	1.71052	+	3.82034i	0.105275	+	0.235126i
$265$	0.561922	−	0.204523i	0.0345186	−	0.0125637i
$266$	1.19416	−	6.77240i	0.0732184	−	0.415242i
$267$	3.05510	+	3.15042i	0.186969	+	0.192802i
$268$	−1.95962	+	1.64432i	−0.119703	+	0.100443i
$269$	20.4100			1.24442			0.622210	−	0.782851i	$-0.286235\pi$
$269$	20.4100			1.24442			0.622210	+	0.782851i	$0.286235\pi$
$270$	−1.11225	−	5.07572i	−0.0676895	−	0.308898i
$271$	18.5732			1.12824			0.564122	−	0.825691i	$-0.309215\pi$
$271$	18.5732			1.12824			0.564122	+	0.825691i	$0.309215\pi$
$272$	1.30354	−	1.09380i	0.0790386	−	0.0663213i
$273$	2.85289	−	10.0284i	0.172665	−	0.606949i
$274$	−0.396359	+	2.24786i	−0.0239449	+	0.135798i
$275$	−2.27093	+	0.826550i	−0.136942	+	0.0498428i
$276$	−15.5873	−	1.60530i	−0.938247	−	0.0966276i
$277$	1.75744	+	9.96692i	0.105594	+	0.598854i	0.990981	+	0.134000i	$0.0427822\pi$
$277$	1.75744	+	9.96692i	0.105594	+	0.598854i	−0.885387	+	0.464854i	$0.846107\pi$
$278$	−3.50016	−	6.06246i	−0.209926	−	0.363602i
$279$	−4.42252	−	13.4196i	−0.264770	−	0.803411i
$280$	−0.552894	+	0.957640i	−0.0330417	+	0.0572300i
$281$	20.1374	+	7.32940i	1.20129	+	0.437236i	0.863676	−	0.504047i	$-0.168156\pi$
$281$	20.1374	+	7.32940i	1.20129	+	0.437236i	0.337619	+	0.941283i	$0.390379\pi$
$282$	−21.1389	−	10.2554i	−1.25880	−	0.610699i
$283$	−10.8122	−	9.07252i	−0.642719	−	0.539306i	0.262133	−	0.965032i	$-0.415574\pi$
$283$	−10.8122	−	9.07252i	−0.642719	−	0.539306i	−0.904852	+	0.425726i	$0.860019\pi$
$284$	−1.04424	−	0.876225i	−0.0619645	−	0.0519944i
$285$	−9.69131	−	4.70167i	−0.574064	−	0.278503i
$286$	12.3624	+	4.49955i	0.731004	+	0.266064i
$287$	−2.74111	+	4.74775i	−0.161803	+	0.280251i
$288$	1.99804	−	2.23782i	0.117735	−	0.131865i
$289$	7.05220	+	12.2148i	0.414835	+	0.718516i
$290$	−0.236500	−	1.34126i	−0.0138878	−	0.0787613i
$291$	15.9275	+	1.64033i	0.933686	+	0.0961579i
$292$	−8.52318	+	3.10218i	−0.498781	+	0.181542i
$293$	−5.40990	+	30.6810i	−0.316050	+	1.79241i	0.250223	+	0.968188i	$0.419496\pi$
$293$	−5.40990	+	30.6810i	−0.316050	+	1.79241i	−0.566273	+	0.824218i	$0.691615\pi$
$294$	2.73800	−	9.62458i	0.159684	−	0.561317i
$295$	7.08898	−	5.94836i	0.412736	−	0.346327i
$296$	−0.144359			−0.00839069
$297$	11.6132	−	4.77714i	0.673867	−	0.277197i
$298$	−20.2657			−1.17396
$299$	−37.7273	+	31.6570i	−2.18183	+	1.83077i
$300$	1.20579	+	1.24341i	0.0696163	+	0.0717883i
$301$	−1.13662	+	6.44609i	−0.0655137	+	0.371547i
$302$	−7.90720	+	2.87798i	−0.455008	+	0.165609i
$303$	6.65459	+	14.8626i	0.382296	+	0.853835i
$304$	−1.07991	−	6.12450i	−0.0619374	−	0.351264i
$305$	3.37369	+	5.84340i	0.193177	+	0.334592i
$306$	−3.15974	−	4.00955i	−0.180630	−	0.229211i
$307$	15.1421	−	26.2270i	0.864208	−	1.49685i	−0.00362421	−	0.999993i	$-0.501154\pi$
$307$	15.1421	−	26.2270i	0.864208	−	1.49685i	0.867832	−	0.496858i	$-0.165513\pi$
$308$	−2.51116	−	0.913989i	−0.143087	−	0.0520793i
$309$	−13.0480	+	8.84082i	−0.742276	+	0.502937i
$310$	3.60796	+	3.02744i	0.204918	+	0.171947i
$311$	10.0007	+	8.39159i	0.567088	+	0.475843i	0.880678	−	0.473715i	$-0.157087\pi$
$311$	10.0007	+	8.39159i	0.567088	+	0.475843i	−0.313590	+	0.949558i	$0.601532\pi$
$312$	−0.677423	−	9.40452i	−0.0383515	−	0.532426i
$313$	−15.5334	−	5.65368i	−0.877997	−	0.319565i	−0.136596	−	0.990627i	$-0.543616\pi$
$313$	−15.5334	−	5.65368i	−0.877997	−	0.319565i	−0.741401	+	0.671062i	$0.765838\pi$
$314$	5.69393	−	9.86217i	0.321327	−	0.556555i
$315$	2.82062	+	1.74614i	0.158924	+	0.0983836i
$316$	7.53821	+	13.0566i	0.424057	+	0.734489i
$317$	2.53003	+	14.3485i	0.142101	+	0.805892i	0.969650	+	0.244499i	$0.0786235\pi$
$317$	2.53003	+	14.3485i	0.142101	+	0.805892i	−0.827549	+	0.561394i	$0.810265\pi$
$318$	0.607037	−	0.839205i	0.0340409	−	0.0470603i
$319$	3.09288	−	1.12572i	0.173168	−	0.0630281i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	−2.97649	+	0.748747i	−0.166131	+	0.0417910i
$322$	7.66351	−	6.43045i	0.427071	−	0.358355i
$323$	−10.5825			−0.588827
$324$	−6.52620	−	6.19747i	−0.362567	−	0.344304i
$325$	5.44377			0.301966
$326$	−8.76590	+	7.35547i	−0.485499	+	0.407382i
$327$	4.41118	−	1.10965i	0.243939	−	0.0613637i
$328$	−0.860905	+	4.88244i	−0.0475356	+	0.269588i
$329$	14.0954	−	5.13029i	0.777102	−	0.282842i
$330$	−2.45325	+	3.39152i	−0.135047	+	0.186697i
$331$	1.85134	+	10.4995i	0.101759	+	0.577104i	0.992465	+	0.122525i	$0.0390992\pi$
$331$	1.85134	+	10.4995i	0.101759	+	0.577104i	−0.890706	+	0.454579i	$0.849790\pi$
$332$	6.98973	+	12.1066i	0.383611	+	0.664434i
$333$	−0.0133012	+	0.432872i	−0.000728901	+	0.0237213i
$334$	−2.61027	+	4.52112i	−0.142828	+	0.247385i
$335$	−2.40383	−	0.874922i	−0.131335	−	0.0478021i
$336$	0.137604	+	1.91033i	0.00750693	+	0.104217i
$337$	−7.43351	−	6.23746i	−0.404929	−	0.339776i	0.417466	−	0.908693i	$-0.362918\pi$
$337$	−7.43351	−	6.23746i	−0.404929	−	0.339776i	−0.822395	+	0.568917i	$0.807363\pi$
$338$	−12.7429	−	10.6925i	−0.693120	−	0.581597i
$339$	−8.59615	+	5.82441i	−0.466879	+	0.316339i
$340$	1.59903	+	0.581998i	0.0867194	+	0.0315633i
$341$	−5.69108	+	9.85725i	−0.308190	+	0.533800i
$342$	−18.4643	+	2.67391i	−0.998437	+	0.144588i
$343$	7.06445	+	12.2360i	0.381445	+	0.660682i
$344$	1.02788	+	5.82941i	0.0554197	+	0.314301i
$345$	−6.40344	−	14.3017i	−0.344749	−	0.769976i
$346$	−1.45413	+	0.529261i	−0.0781746	+	0.0284532i
$347$	2.47225	−	14.0208i	0.132718	−	0.752679i	−0.843704	−	0.536808i	$-0.819630\pi$
$347$	2.47225	−	14.0208i	0.132718	−	0.752679i	0.976422	−	0.215871i	$-0.0692589\pi$
$348$	−1.64222	−	1.69346i	−0.0880325	−	0.0907790i
$349$	0.544905	−	0.457230i	0.0291681	−	0.0244750i	−0.628087	−	0.778143i	$-0.716162\pi$
$349$	0.544905	−	0.457230i	0.0291681	−	0.0244750i	0.657255	+	0.753668i	$0.271717\pi$
$350$	−1.10579			−0.0591068
$351$	−28.2627	+	1.16478i	−1.50855	+	0.0621713i
$352$	−2.41667			−0.128809
$353$	−25.3085	+	21.2364i	−1.34704	+	1.13030i	−0.367280	+	0.930110i	$0.619711\pi$
$353$	−25.3085	+	21.2364i	−1.34704	+	1.13030i	−0.979757	+	0.200188i	$0.935845\pi$
$354$	4.38575	−	15.4167i	0.233100	−	0.819389i
$355$	0.236711	−	1.34245i	0.0125633	−	0.0712501i
$356$	−2.38089	+	0.866573i	−0.126187	+	0.0459283i
$357$	3.24199	+	0.333883i	0.171584	+	0.0176710i
$358$	1.19775	+	6.79275i	0.0633028	+	0.359008i
$359$	−1.93105	−	3.34468i	−0.101917	−	0.176525i	0.810557	−	0.585659i	$-0.199164\pi$
$359$	−1.93105	−	3.34468i	−0.101917	−	0.176525i	−0.912474	+	0.409134i	$0.865831\pi$
$360$	2.93703	+	0.611439i	0.154795	+	0.0322257i
$361$	−9.83786	+	17.0397i	−0.517782	+	0.896825i
$362$	13.4231	+	4.88561i	0.705503	+	0.256782i
$363$	8.04060	+	3.90084i	0.422022	+	0.204741i
$364$	4.61132	+	3.86936i	0.241699	+	0.202809i
$365$	−6.94816	−	5.83020i	−0.363683	−	0.305167i
$366$	10.5147	+	5.10114i	0.549614	+	0.266641i
$367$	31.8305	+	11.5854i	1.66154	+	0.604751i	0.990604	−	0.136764i	$-0.0436703\pi$
$367$	31.8305	+	11.5854i	1.66154	+	0.604751i	0.670936	+	0.741515i	$0.265893\pi$
$368$	4.52347	−	7.83489i	0.235802	−	0.408422i
$369$	14.5611	+	3.03136i	0.758020	+	0.157807i
$370$	−0.0721794	−	0.125018i	−0.00375243	−	0.00649940i
$371$	0.114824	+	0.651199i	0.00596136	+	0.0338086i
$372$	8.11479	+	0.835721i	0.420732	+	0.0433301i
$373$	−10.6475	+	3.87536i	−0.551305	+	0.200659i	−0.602626	−	0.798024i	$-0.705879\pi$
$373$	−10.6475	+	3.87536i	−0.551305	+	0.200659i	0.0513213	+	0.998682i	$0.483657\pi$
$374$	−0.714097	+	4.04985i	−0.0369251	+	0.209413i
$375$	−0.473930	+	1.66595i	−0.0244736	+	0.0860293i
$376$	10.3914	−	8.71939i	0.535894	−	0.449668i
$377$	−7.41413			−0.381847
$378$	5.74097	−	0.236600i	0.295284	−	0.0121694i
$379$	7.59611			0.390186			0.195093	−	0.980785i	$-0.437499\pi$
$379$	7.59611			0.390186			0.195093	+	0.980785i	$0.437499\pi$
$380$	4.76402	−	3.99748i	0.244389	−	0.205067i
$381$	20.8547	+	21.5053i	1.06842	+	1.10175i
$382$	−1.16202	+	6.59015i	−0.0594542	+	0.337181i
$383$	9.36563	−	3.40881i	0.478562	−	0.174182i	−0.0914652	−	0.995808i	$-0.529155\pi$
$383$	9.36563	−	3.40881i	0.478562	−	0.174182i	0.570027	+	0.821626i	$0.306933\pi$
$384$	0.707801	+	1.58083i	0.0361198	+	0.0806713i
$385$	−0.464044	−	2.63173i	−0.0236499	−	0.134125i
$386$	11.5859	+	20.0674i	0.589707	+	1.02140i
$387$	17.5747	−	2.54507i	0.893372	−	0.129373i
$388$	−4.62219	+	8.00587i	−0.234656	+	0.406436i
$389$	15.1281	+	5.50616i	0.767023	+	0.279173i	0.695751	−	0.718284i	$-0.255072\pi$
$389$	15.1281	+	5.50616i	0.767023	+	0.279173i	0.0712721	+	0.997457i	$0.477294\pi$
$390$	7.80584	−	5.28892i	0.395264	−	0.267815i
$391$	−11.7930	−	9.89554i	−0.596400	−	0.500439i
$392$	4.42562	+	3.71353i	0.223527	+	0.187562i
$393$	−0.0113258	−	0.157233i	−0.000571309	−	0.00793136i
$394$	−22.2313	−	8.09153i	−1.12000	−	0.407645i
$395$	−7.53821	+	13.0566i	−0.379288	+	0.656947i
$396$	−0.222671	+	7.24659i	−0.0111897	+	0.364155i
$397$	12.8152	+	22.1965i	0.643174	+	1.11401i	0.984720	+	0.174145i	$0.0557162\pi$
$397$	12.8152	+	22.1965i	0.643174	+	1.11401i	−0.341546	+	0.939865i	$0.610950\pi$
$398$	−2.36192	−	13.3951i	−0.118392	−	0.671436i
$399$	6.98097	−	9.65092i	0.349486	−	0.483150i
$400$	−0.939693	+	0.342020i	−0.0469846	+	0.0171010i
$401$	−1.61117	+	9.13738i	−0.0804579	+	0.456299i	0.917787	+	0.397074i	$0.129974\pi$
$401$	−1.61117	+	9.13738i	−0.0804579	+	0.456299i	−0.998245	+	0.0592256i	$0.981137\pi$
$402$	−4.29689	+	1.08090i	−0.214310	+	0.0539103i
$403$	19.6409	−	16.4807i	0.978383	−	0.820961i
$404$	−9.40179			−0.467757
$405$	2.10407	−	8.75059i	0.104552	−	0.434821i
$406$	1.50603			0.0747428
$407$	0.267248	−	0.224248i	0.0132470	−	0.0111156i
$408$	2.85829	−	0.719014i	0.141507	−	0.0355965i
$409$	5.25723	−	29.8152i	0.259953	−	1.47427i	−0.523077	−	0.852285i	$-0.675216\pi$
$409$	5.25723	−	29.8152i	0.259953	−	1.47427i	0.783030	−	0.621983i	$-0.213673\pi$
$410$	−4.65877	+	1.69565i	−0.230080	+	0.0837423i
$411$	−2.31709	+	3.20329i	−0.114294	+	0.158006i
$412$	−1.58014	−	8.96141i	−0.0778478	−	0.441497i
$413$	5.11648	+	8.86200i	0.251766	+	0.436071i
$414$	−23.0768	−	14.2859i	−1.13416	−	0.702115i
$415$	−6.98973	+	12.1066i	−0.343112	+	0.594288i
$416$	5.11547	+	1.86188i	0.250807	+	0.0912861i
$417$	−0.871120	−	12.0936i	−0.0426589	−	0.592225i
$418$	11.5131	+	9.66060i	0.563122	+	0.472515i
$419$	11.6147	+	9.74592i	0.567417	+	0.476119i	0.880788	−	0.473512i	$-0.157014\pi$
$419$	11.6147	+	9.74592i	0.567417	+	0.476119i	−0.313371	+	0.949631i	$0.601458\pi$
$420$	−1.58559	+	1.07433i	−0.0773690	+	0.0524221i
$421$	−8.17198	−	2.97436i	−0.398278	−	0.144961i	0.135113	−	0.990830i	$-0.456860\pi$
$421$	−8.17198	−	2.97436i	−0.398278	−	0.144961i	−0.533391	+	0.845869i	$0.679082\pi$
$422$	−7.73933	+	13.4049i	−0.376745	+	0.652541i
$423$	−25.1884	−	31.9628i	−1.22470	−	1.55408i
$424$	0.298993	+	0.517870i	0.0145204	+	0.0251500i
$425$	0.295488	+	1.67580i	0.0143333	+	0.0812880i
$426$	−0.964849	−	2.15493i	−0.0467471	−	0.104407i
$427$	−7.01120	+	2.55187i	−0.339296	+	0.123494i
$428$	0.307707	−	1.74509i	0.0148736	−	0.0843523i
$429$	15.8631	+	16.3580i	0.765879	+	0.789774i
$430$	−4.53448	+	3.80488i	−0.218672	+	0.183488i
$431$	7.84929			0.378087			0.189043	−	0.981969i	$-0.439461\pi$
$431$	7.84929			0.378087			0.189043	+	0.981969i	$0.439461\pi$
$432$	4.80546	−	1.97674i	0.231203	−	0.0951061i
$433$	20.9067			1.00471			0.502356	−	0.864661i	$-0.332467\pi$
$433$	20.9067			1.00471			0.502356	+	0.864661i	$0.332467\pi$
$434$	−3.98964	+	3.34770i	−0.191509	+	0.160695i
$435$	0.645468	−	2.26894i	0.0309478	−	0.108787i
$436$	−0.456024	+	2.58624i	−0.0218396	+	0.123859i
$437$	−52.8697	+	19.2430i	−2.52910	+	0.920518i
$438$	−15.6274	−	1.60942i	−0.746704	−	0.0769010i
$439$	0.375049	+	2.12701i	0.0179001	+	0.101517i	0.992449	−	0.122659i	$-0.0391422\pi$
$439$	0.375049	+	2.12701i	0.0179001	+	0.101517i	−0.974549	+	0.224176i	$0.928031\pi$
$440$	−1.20833	−	2.09290i	−0.0576051	−	0.0997750i
$441$	11.5431	−	12.9284i	0.549672	−	0.615639i
$442$	4.63169	−	8.02232i	0.220307	−	0.381583i
$443$	25.2759	+	9.19969i	1.20090	+	0.437091i	0.863537	−	0.504285i	$-0.168244\pi$
$443$	25.2759	+	9.19969i	1.20090	+	0.437091i	0.337359	+	0.941376i	$0.390466\pi$
$444$	−0.224961	−	0.109138i	−0.0106762	−	0.00517946i
$445$	−1.94092	−	1.62863i	−0.0920084	−	0.0772042i
$446$	18.5767	+	15.5877i	0.879631	+	0.738098i
$447$	−31.5809	−	15.3212i	−1.49373	−	0.724670i
$448$	−1.03910	−	0.378202i	−0.0490929	−	0.0178684i
$449$	6.14684	−	10.6466i	0.290088	−	0.502446i	−0.683743	−	0.729723i	$-0.739649\pi$
$449$	6.14684	−	10.6466i	0.290088	−	0.502446i	0.973830	+	0.227277i	$0.0729822\pi$
$450$	0.938993	+	2.84926i	0.0442646	+	0.134315i
$451$	−5.99063	−	10.3761i	−0.282088	−	0.488590i
$452$	−1.04101	−	5.90386i	−0.0489649	−	0.277694i
$453$	−14.4979	−	1.49310i	−0.681173	−	0.0701522i
$454$	3.77381	−	1.37356i	0.177114	−	0.0644642i
$455$	−1.04530	+	5.92820i	−0.0490045	+	0.277918i
$456$	2.94736	−	10.3605i	0.138023	−	0.485175i
$457$	17.5405	−	14.7182i	0.820510	−	0.688489i	−0.132582	−	0.991172i	$-0.542327\pi$
$457$	17.5405	−	14.7182i	0.820510	−	0.688489i	0.953091	+	0.302683i	$0.0978823\pi$
$458$	28.0955			1.31282
$459$	−1.89266	−	8.63708i	−0.0883419	−	0.403144i
$460$	9.04695			0.421816
$461$	−16.5154	+	13.8580i	−0.769198	+	0.645433i	−0.940503	−	0.339784i	$-0.889646\pi$
$461$	−16.5154	+	13.8580i	−0.769198	+	0.645433i	0.171306	+	0.985218i	$0.445201\pi$
$462$	−3.22226	−	3.32280i	−0.149913	−	0.154590i
$463$	−3.49904	+	19.8440i	−0.162614	+	0.922230i	0.788876	+	0.614552i	$0.210663\pi$
$463$	−3.49904	+	19.8440i	−0.162614	+	0.922230i	−0.951490	+	0.307678i	$0.900448\pi$
$464$	1.27981	−	0.465814i	0.0594138	−	0.0216249i
$465$	3.33364	+	7.44548i	0.154594	+	0.345276i
$466$	−0.735281	−	4.16999i	−0.0340612	−	0.193171i
$467$	3.49724	+	6.05740i	0.161833	+	0.280303i	0.935526	−	0.353258i	$-0.114926\pi$
$467$	3.49724	+	6.05740i	0.161833	+	0.280303i	−0.773693	+	0.633561i	$0.781593\pi$
$468$	6.05434	−	15.1676i	0.279862	−	0.701123i
$469$	1.41436	−	2.44974i	0.0653090	−	0.113118i
$470$	12.7469	+	4.63949i	0.587970	+	0.214004i
$471$	16.3291	−	11.0639i	0.752405	−	0.509799i
$472$	7.08898	+	5.94836i	0.326297	+	0.273795i
$473$	−10.9583	−	9.19513i	−0.503865	−	0.422793i
$474$	1.87611	+	26.0456i	0.0861726	+	1.19632i
$475$	5.84393	+	2.12702i	0.268138	+	0.0975942i
$476$	−0.940831	+	1.62957i	−0.0431229	+	0.0746911i
$477$	1.58043	−	0.848838i	0.0723628	−	0.0388656i
$478$	7.78742	+	13.4882i	0.356188	+	0.616936i
$479$	0.911856	+	5.17139i	0.0416637	+	0.236287i	0.998527	−	0.0542507i	$-0.0172770\pi$
$479$	0.911856	+	5.17139i	0.0416637	+	0.236287i	−0.956864	+	0.290538i	$0.906166\pi$
$480$	−1.01514	+	1.40339i	−0.0463345	+	0.0640556i
$481$	−0.738463	+	0.268779i	−0.0336710	+	0.0122553i
$482$	3.62958	−	20.5844i	0.165323	−	0.937593i
$483$	16.8039	−	4.22709i	0.764605	−	0.192339i
$484$	−3.95257	+	3.31660i	−0.179662	+	0.150754i
$485$	−9.24438			−0.419766
$486$	−5.48466	−	14.5917i	−0.248789	−	0.661894i
$487$	−26.9170			−1.21973			−0.609864	−	0.792506i	$-0.708776\pi$
$487$	−26.9170			−1.21973			−0.609864	+	0.792506i	$0.708776\pi$
$488$	−5.16879	+	4.33713i	−0.233980	+	0.196333i
$489$	−19.2212	+	4.83515i	−0.869211	+	0.218653i
$490$	−1.00321	+	5.68946i	−0.0453202	+	0.257024i
$491$	−40.8302	+	14.8610i	−1.84264	+	0.670667i	−0.854021	+	0.520239i	$0.825843\pi$
$491$	−40.8302	+	14.8610i	−1.84264	+	0.670667i	−0.988621	+	0.150428i	$0.951935\pi$
$492$	−5.03280	+	6.95765i	−0.226896	+	0.313675i
$493$	−0.402440	−	2.28235i	−0.0181250	−	0.102792i
$494$	−16.9273	−	29.3190i	−0.761597	−	1.31913i
$495$	−6.38707	+	3.43045i	−0.287077	+	0.154187i
$496$	−2.35493	+	4.07886i	−0.105739	+	0.183146i
$497$	1.41647	+	0.515551i	0.0635371	+	0.0231256i
$498$	1.73960	+	24.1506i	0.0779535	+	1.08221i
$499$	14.1763	+	11.8954i	0.634620	+	0.532509i	0.902361	−	0.430982i	$-0.141833\pi$
$499$	14.1763	+	11.8954i	0.634620	+	0.532509i	−0.267741	+	0.963491i	$0.586277\pi$
$500$	−0.766044	−	0.642788i	−0.0342585	−	0.0287463i
$501$	−7.48575	+	5.07205i	−0.334439	+	0.226602i
$502$	26.9171	+	9.79704i	1.20137	+	0.437263i
$503$	17.9235	−	31.0444i	0.799170	−	1.38420i	−0.120987	−	0.992654i	$-0.538606\pi$
$503$	17.9235	−	31.0444i	0.799170	−	1.38420i	0.920157	−	0.391549i	$-0.128061\pi$
$504$	−1.22981	+	3.08098i	−0.0547802	+	0.137238i
$505$	−4.70090	−	8.14219i	−0.209187	−	0.362323i
$506$	3.79655	+	21.5313i	0.168777	+	0.957184i
$507$	−11.7740	−	26.2965i	−0.522901	−	1.16787i
$508$	−16.2524	+	5.91538i	−0.721083	+	0.262453i
$509$	3.98714	−	22.6122i	0.176727	−	1.00227i	−0.759405	−	0.650618i	$-0.774510\pi$
$509$	3.98714	−	22.6122i	0.176727	−	1.00227i	0.936132	−	0.351649i	$-0.114379\pi$
$510$	2.05183	+	2.11585i	0.0908566	+	0.0936913i
$511$	7.68319	−	6.44696i	0.339884	−	0.285197i
$512$	−1.00000			−0.0441942
$513$	−30.7953	−	9.79253i	−1.35965	−	0.432351i
$514$	26.9967			1.19077
$515$	6.97074	−	5.84914i	0.307167	−	0.257744i
$516$	−2.80535	+	9.86133i	−0.123499	+	0.434121i
$517$	−5.69254	+	32.2840i	−0.250358	+	1.41985i
$518$	0.150003	−	0.0545968i	0.00659077	−	0.00239884i
$519$	−2.66617	−	0.274582i	−0.117032	−	0.0120528i
$520$	0.945300	+	5.36107i	0.0414542	+	0.235098i
$521$	−8.32895	−	14.4262i	−0.364898	−	0.632022i	0.623862	−	0.781535i	$-0.285563\pi$
$521$	−8.32895	−	14.4262i	−0.364898	−	0.632022i	−0.988760	+	0.149513i	$0.952229\pi$
$522$	−1.27886	−	3.88055i	−0.0559742	−	0.169847i
$523$	11.5959	−	20.0848i	0.507055	−	0.878245i	−0.492912	−	0.870079i	$-0.664067\pi$
$523$	11.5959	−	20.0848i	0.507055	−	0.878245i	0.999967	−	0.00816576i	$-0.00259927\pi$
$524$	0.0855250	+	0.0311285i	0.00373618	+	0.00135986i
$525$	−1.72320	−	0.835997i	−0.0752065	−	0.0364859i
$526$	10.6044	+	8.89813i	0.462373	+	0.387977i
$527$	6.13948	+	5.15163i	0.267440	+	0.224409i
$528$	−3.76600	−	1.82705i	−0.163894	−	0.0795121i
$529$	−55.2984	−	20.1270i	−2.40428	−	0.875085i
$530$	−0.298993	+	0.517870i	−0.0129874	+	0.0224949i
$531$	18.4898	−	20.7088i	0.802390	−	0.898686i
$532$	3.43844	+	5.95555i	0.149075	+	0.258206i
$533$	4.68657	+	26.5789i	0.202998	+	1.15126i
$534$	−4.36539	−	0.449580i	−0.188909	−	0.0194552i
$535$	1.66515	−	0.606065i	0.0719907	−	0.0262025i
$536$	0.444210	−	2.51924i	0.0191869	−	0.108814i
$537$	−3.26895	+	11.4910i	−0.141066	+	0.495872i
$538$	−15.6350	+	13.1193i	−0.674071	+	0.565613i
$539$	−13.9617			−0.601371
$540$	4.11464	+	3.17328i	0.177066	+	0.136556i
$541$	−0.936892			−0.0402801			−0.0201401	−	0.999797i	$-0.506411\pi$
$541$	−0.936892			−0.0402801			−0.0201401	+	0.999797i	$0.506411\pi$
$542$	−14.2279	+	11.9387i	−0.611142	+	0.512809i
$543$	17.2242	+	17.7616i	0.739161	+	0.762223i
$544$	−0.295488	+	1.67580i	−0.0126689	+	0.0718492i
$545$	−2.46776	+	0.898193i	−0.105707	+	0.0384744i
$546$	4.26071	+	9.51604i	0.182342	+	0.407249i
$547$	−7.91491	−	44.8877i	−0.338417	−	1.91926i	−0.390472	−	0.920615i	$-0.627688\pi$
$547$	−7.91491	−	44.8877i	−0.338417	−	1.91926i	0.0520544	−	0.998644i	$-0.483423\pi$
$548$	−1.14127	−	1.97674i	−0.0487526	−	0.0844420i
$549$	12.5290	+	15.8987i	0.534725	+	0.678539i
$550$	1.20833	−	2.09290i	0.0515236	−	0.0892414i
$551$	−7.95913	−	2.89689i	−0.339070	−	0.123412i
$552$	12.9725	−	8.78961i	0.552144	−	0.374111i
$553$	−12.7710	−	10.7161i	−0.543077	−	0.455696i
$554$	−7.75289	−	6.50545i	−0.329389	−	0.276390i
$555$	−0.0179640	−	0.249391i	−0.000762530	−	0.0105860i
$556$	6.57815	+	2.39425i	0.278976	+	0.101539i
$557$	3.37069	−	5.83821i	0.142821	−	0.247373i	−0.785737	−	0.618561i	$-0.787716\pi$
$557$	3.37069	−	5.83821i	0.142821	−	0.247373i	0.928558	+	0.371188i	$0.121049\pi$
$558$	12.0138	+	7.43728i	0.508585	+	0.314845i
$559$	16.1118	+	27.9064i	0.681455	+	1.18031i
$560$	−0.192018	−	1.08899i	−0.00811424	−	0.0460182i
$561$	−4.17457	+	5.77118i	−0.176250	+	0.243659i
$562$	−20.1374	+	7.32940i	−0.849444	+	0.309172i
$563$	−0.541770	+	3.07253i	−0.0228329	+	0.129492i	−0.994094	−	0.108527i	$-0.965387\pi$
$563$	−0.541770	+	3.07253i	−0.0228329	+	0.129492i	0.971261	+	0.238018i	$0.0764978\pi$
$564$	22.7853	−	5.73174i	0.959436	−	0.241350i
$565$	4.59238	−	3.85347i	0.193203	−	0.162117i
$566$	14.1143			0.593270
$567$	9.12528	+	3.97158i	0.383226	+	0.166791i
$568$	1.36316			0.0571971
$569$	−6.44610	+	5.40892i	−0.270235	+	0.226754i	−0.767827	−	0.640657i	$-0.778662\pi$
$569$	−6.44610	+	5.40892i	−0.270235	+	0.226754i	0.497592	+	0.867411i	$0.334218\pi$
$570$	10.4461	−	2.62777i	0.437541	−	0.110065i
$571$	−2.77424	+	15.7335i	−0.116098	+	0.658427i	0.870102	+	0.492872i	$0.164053\pi$
$571$	−2.77424	+	15.7335i	−0.116098	+	0.658427i	−0.986200	+	0.165556i	$0.947058\pi$
$572$	−12.3624	+	4.49955i	−0.516898	+	0.188135i
$573$	−6.79311	+	9.39121i	−0.283786	+	0.392323i
$574$	−0.951979	−	5.39894i	−0.0397348	−	0.225347i
$575$	4.52347	+	7.83489i	0.188642	+	0.326737i
$576$	−0.0921398	+	2.99858i	−0.00383916	+	0.124941i
$577$	7.32778	−	12.6921i	0.305059	−	0.528378i	−0.672215	−	0.740356i	$-0.734657\pi$
$577$	7.32778	−	12.6921i	0.305059	−	0.528378i	0.977275	+	0.211977i	$0.0679903\pi$
$578$	−13.2538	−	4.82399i	−0.551285	−	0.200651i
$579$	2.88350	+	40.0311i	0.119834	+	1.66363i
$580$	1.04331	+	0.875444i	0.0433212	+	0.0363508i
$581$	−11.8418	−	9.93641i	−0.491279	−	0.412232i
$582$	−13.2556	+	8.98143i	−0.549460	+	0.372292i
$583$	−1.35798	−	0.494265i	−0.0562418	−	0.0204703i
$584$	4.53509	−	7.85501i	0.187663	−	0.325042i
$585$	16.1627	−	2.34060i	0.668246	−	0.0967717i
$586$	−15.5772	−	26.9805i	−0.643487	−	1.11455i
$587$	−4.34601	−	24.6474i	−0.179379	−	1.01731i	−0.932967	−	0.359962i	$-0.882790\pi$
$587$	−4.34601	−	24.6474i	−0.179379	−	1.01731i	0.753588	−	0.657347i	$-0.228321\pi$
$588$	4.08913	+	9.13281i	0.168633	+	0.376631i
$589$	27.5241	−	10.0179i	1.13411	−	0.412782i
$590$	−1.60694	+	9.11341i	−0.0661567	+	0.375193i
$591$	−28.5266	−	29.4167i	−1.17343	−	1.21004i
$592$	0.110585	−	0.0927921i	0.00454503	−	0.00381373i
$593$	4.41639			0.181360			0.0906798	−	0.995880i	$-0.471096\pi$
$593$	4.41639			0.181360			0.0906798	+	0.995880i	$0.471096\pi$
$594$	−5.82556	+	11.1243i	−0.239026	+	0.456437i
$595$	−1.88166			−0.0771406
$596$	15.5244	−	13.0265i	0.635905	−	0.533588i
$597$	6.44627	−	22.6598i	0.263828	−	0.927405i
$598$	8.55209	−	48.5013i	0.349721	−	1.98337i
$599$	−7.92869	+	2.88581i	−0.323958	+	0.117911i	−0.498879	−	0.866671i	$-0.666255\pi$
$599$	−7.92869	+	2.88581i	−0.323958	+	0.117911i	0.174922	+	0.984582i	$0.444033\pi$
$600$	−1.72294	−	0.177441i	−0.0703386	−	0.00724399i
$601$	−4.72665	−	26.8062i	−0.192804	−	1.09345i	−0.915512	−	0.402292i	$-0.868214\pi$
$601$	−4.72665	−	26.8062i	−0.192804	−	1.09345i	0.722708	−	0.691154i	$-0.242897\pi$
$602$	−3.27277	−	5.66860i	−0.133388	−	0.231035i
$603$	−7.51322	−	1.56412i	−0.305962	−	0.0636960i
$604$	4.20733	−	7.28731i	0.171194	−	0.296517i
$605$	−4.84854	−	1.76472i	−0.197121	−	0.0717462i
$606$	−14.6512	−	7.10793i	−0.595165	−	0.288740i
$607$	15.0683	+	12.6438i	0.611602	+	0.513195i	0.895151	−	0.445763i	$-0.147067\pi$
$607$	15.0683	+	12.6438i	0.611602	+	0.513195i	−0.283549	+	0.958958i	$0.591512\pi$
$608$	4.76402	+	3.99748i	0.193206	+	0.162119i
$609$	2.34691	+	1.13858i	0.0951014	+	0.0461378i
$610$	−6.34046	−	2.30774i	−0.256718	−	0.0934376i
$611$	36.9223	−	63.9512i	1.49371	−	2.58719i
$612$	4.99779	+	1.04045i	0.202024	+	0.0420578i
$613$	24.0019	+	41.5725i	0.969428	+	1.67910i	0.697215	+	0.716862i	$0.254422\pi$
$613$	24.0019	+	41.5725i	0.969428	+	1.67910i	0.272214	+	0.962237i	$0.412244\pi$
$614$	5.25881	+	29.8242i	0.212228	+	1.20361i
$615$	−8.54191	−	0.879708i	−0.344443	−	0.0354733i
$616$	2.51116	−	0.913989i	0.101178	−	0.0368256i
$617$	−0.882271	+	5.00361i	−0.0355189	+	0.201438i	−0.997403	−	0.0720188i	$-0.977056\pi$
$617$	−0.882271	+	5.00361i	−0.0355189	+	0.201438i	0.961884	+	0.273456i	$0.0881670\pi$
$618$	4.31260	−	15.1596i	0.173478	−	0.609807i
$619$	22.2980	−	18.7102i	0.896231	−	0.752027i	−0.0732194	−	0.997316i	$-0.523327\pi$
$619$	22.2980	−	18.7102i	0.896231	−	0.752027i	0.969450	+	0.245289i	$0.0788829\pi$
$620$	−4.70986			−0.189152
$621$	−25.1611	−	39.7089i	−1.00968	−	1.59346i
$622$	−13.0550			−0.523458
$623$	2.14625	−	1.80091i	0.0859875	−	0.0721521i
$624$	6.56404	+	6.76884i	0.262772	+	0.270970i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	15.5334	−	5.65368i	0.620838	−	0.225966i
$627$	10.6377	+	23.7586i	0.424829	+	0.948828i
$628$	1.97748	+	11.2149i	0.0789101	+	0.447521i
$629$	−0.122824	−	0.212737i	−0.00489731	−	0.00848240i
$630$	−3.28312	+	0.475443i	−0.130802	+	0.0189421i
$631$	−11.3406	+	19.6425i	−0.451463	+	0.781957i	−0.998477	−	0.0551665i	$-0.982431\pi$
$631$	−11.3406	+	19.6425i	−0.451463	+	0.781957i	0.547014	+	0.837123i	$0.315764\pi$
$632$	−14.1672	−	5.15644i	−0.563541	−	0.205112i
$633$	−22.1949	+	15.0384i	−0.882168	+	0.597722i
$634$	−11.1612	−	9.36532i	−0.443266	−	0.371944i
$635$	−13.2491	−	11.1173i	−0.525773	−	0.441176i
$636$	0.0744133	+	1.03306i	0.00295068	+	0.0409637i
$637$	29.5533	+	10.7565i	1.17094	+	0.426188i
$638$	−1.64569	+	2.85042i	−0.0651535	+	0.112849i
$639$	0.125602	−	4.08756i	0.00496873	−	0.161702i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−5.63454	−	31.9551i	−0.222551	−	1.26215i	−0.867312	−	0.497766i	$-0.834154\pi$
$641$	−5.63454	−	31.9551i	−0.222551	−	1.26215i	0.644761	−	0.764385i	$-0.276957\pi$
$642$	1.79884	−	2.48682i	0.0709945	−	0.0981471i
$643$	24.0518	−	8.75416i	0.948512	−	0.345230i	0.178990	−	0.983851i	$-0.442717\pi$
$643$	24.0518	−	8.75416i	0.948512	−	0.345230i	0.769522	+	0.638621i	$0.220495\pi$
$644$	−1.73718	+	9.85202i	−0.0684544	+	0.388224i
$645$	−9.94284	+	2.50116i	−0.391499	+	0.0984829i
$646$	8.10668	−	6.80231i	0.318953	−	0.267633i
$647$	31.9250			1.25510			0.627550	−	0.778577i	$-0.284058\pi$
$647$	31.9250			1.25510			0.627550	+	0.778577i	$0.284058\pi$
$648$	8.98302	+	0.552578i	0.352886	+	0.0217073i
$649$	−22.3639			−0.877858
$650$	−4.17017	+	3.49919i	−0.163567	+	0.137249i
$651$	−8.74816	+	2.20063i	−0.342867	+	0.0862495i
$652$	1.98707	−	11.2692i	0.0778196	−	0.441337i
$653$	14.2402	−	5.18302i	0.557263	−	0.202827i	−0.0480073	−	0.998847i	$-0.515287\pi$
$653$	14.2402	−	5.18302i	0.557263	−	0.202827i	0.605271	+	0.796020i	$0.293065\pi$
$654$	−2.66589	+	3.68549i	−0.104245	+	0.144114i
$655$	0.0158044	+	0.0896311i	0.000617528	+	0.00350218i
$656$	−2.47888	−	4.29354i	−0.0967839	−	0.167635i
$657$	−23.1360	−	14.3226i	−0.902623	−	0.558778i
$658$	−7.49999	+	12.9904i	−0.292380	+	0.506417i
$659$	−37.2771	−	13.5678i	−1.45211	−	0.528525i	−0.508930	−	0.860808i	$-0.669959\pi$
$659$	−37.2771	−	13.5678i	−1.45211	−	0.528525i	−0.943180	+	0.332283i	$0.892181\pi$
$660$	−0.300730	−	4.17498i	−0.0117059	−	0.162511i
$661$	−11.5028	−	9.65196i	−0.447406	−	0.375418i	0.391066	−	0.920362i	$-0.372106\pi$
$661$	−11.5028	−	9.65196i	−0.447406	−	0.375418i	−0.838472	+	0.544945i	$0.816551\pi$
$662$	−8.16716	−	6.85306i	−0.317426	−	0.266352i
$663$	13.2828	−	8.99989i	0.515861	−	0.349527i
$664$	−13.1364	−	4.78126i	−0.509791	−	0.185549i
$665$	−3.43844	+	5.95555i	−0.133337	+	0.230946i
$666$	−0.268056	−	0.340149i	−0.0103869	−	0.0131805i
$667$	−6.16074	−	10.6707i	−0.238545	−	0.413172i
$668$	−0.906538	−	5.14123i	−0.0350750	−	0.198920i
$669$	17.1643	+	38.3353i	0.663608	+	1.48213i
$670$	2.40383	−	0.874922i	0.0928680	−	0.0338012i
$671$	2.83154	−	16.0584i	0.109310	−	0.619929i
$672$	−1.33335	−	1.37495i	−0.0514350	−	0.0530398i
$673$	−33.1307	+	27.8000i	−1.27710	+	1.07161i	−0.283458	+	0.958985i	$0.591482\pi$
$673$	−33.1307	+	27.8000i	−1.27710	+	1.07161i	−0.993638	+	0.112625i	$0.964074\pi$
$674$	9.70376			0.373775
$675$	−0.690822	+	5.15003i	−0.0265898	+	0.198225i
$676$	16.6346			0.639793
$677$	23.8551	−	20.0168i	0.916826	−	0.769308i	−0.0565795	−	0.998398i	$-0.518019\pi$
$677$	23.8551	−	20.0168i	0.916826	−	0.769308i	0.973405	+	0.229090i	$0.0735750\pi$
$678$	2.84118	−	9.98726i	0.109115	−	0.383558i
$679$	1.77509	−	10.0670i	0.0681216	−	0.386337i
$680$	−1.59903	+	0.581998i	−0.0613198	+	0.0223186i
$681$	6.91933	+	0.712604i	0.265149	+	0.0273070i
$682$	−1.97649	−	11.2092i	−0.0756838	−	0.429224i
$683$	−5.42129	−	9.38994i	−0.207440	−	0.359296i	0.743468	−	0.668772i	$-0.233180\pi$
$683$	−5.42129	−	9.38994i	−0.207440	−	0.359296i	−0.950907	+	0.309476i	$0.899846\pi$
$684$	12.4257	−	13.9170i	0.475110	−	0.532129i
$685$	1.14127	−	1.97674i	0.0436057	−	0.0755272i
$686$	−13.2768	−	4.83237i	−0.506912	−	0.184501i
$687$	43.7824	+	21.2407i	1.67040	+	0.810384i
$688$	−4.53448	−	3.80488i	−0.172875	−	0.145060i
$689$	2.49370	+	2.09246i	0.0950024	+	0.0797165i
$690$	14.0983	+	6.83967i	0.536711	+	0.260382i
$691$	−27.1683	−	9.88846i	−1.03353	−	0.376175i	−0.231107	−	0.972928i	$-0.574235\pi$
$691$	−27.1683	−	9.88846i	−1.03353	−	0.376175i	−0.802424	+	0.596754i	$0.796457\pi$
$692$	0.773728	−	1.34014i	0.0294127	−	0.0509443i
$693$	−2.50929	−	7.61415i	−0.0953202	−	0.289238i
$694$	7.11857	+	12.3297i	0.270217	+	0.468030i
$695$	1.21559	+	6.89397i	0.0461101	+	0.261503i
$696$	2.34655	+	0.241665i	0.0889458	+	0.00916029i
$697$	−7.92758	+	2.88540i	−0.300279	+	0.109292i
$698$	−0.123520	+	0.700517i	−0.00467530	+	0.0265150i
$699$	2.00677	−	7.05416i	0.0759030	−	0.266813i
$700$	0.847083	−	0.710787i	0.0320167	−	0.0268652i
$701$	4.61819			0.174427			0.0872133	−	0.996190i	$-0.472204\pi$
$701$	4.61819			0.174427			0.0872133	+	0.996190i	$0.472204\pi$
$702$	20.9017	−	19.0592i	0.788886	−	0.719342i
$703$	−0.897765			−0.0338599
$704$	1.85128	−	1.55341i	0.0697726	−	0.0585462i
$705$	16.3565	+	16.8668i	0.616021	+	0.635241i
$706$	5.73698	−	32.5360i	0.215914	−	1.22451i
$707$	9.76941	−	3.55577i	0.367416	−	0.133729i
$708$	6.54999	+	14.6290i	0.246164	+	0.549791i
$709$	−0.531894	−	3.01652i	−0.0199757	−	0.113288i	0.973190	−	0.230005i	$-0.0738741\pi$
$709$	−0.531894	−	3.01652i	−0.0199757	−	0.113288i	−0.993165	+	0.116717i	$0.962763\pi$
$710$	0.681582	+	1.18054i	0.0255793	+	0.0443047i
$711$	−16.7674	+	42.0064i	−0.628826	+	1.57536i
$712$	1.26685	−	2.19424i	0.0474770	−	0.0822326i
$713$	40.0402	+	14.5734i	1.49952	+	0.545779i
$714$	−2.69812	+	1.82814i	−0.100975	+	0.0684164i
$715$	−10.0779	−	8.45638i	−0.376893	−	0.316251i
$716$	−5.28382	−	4.43365i	−0.197466	−	0.165693i
$717$	1.93813	+	26.9067i	0.0723809	+	1.00485i
$718$	3.62919	+	1.32092i	0.135440	+	0.0492962i
$719$	7.33137	−	12.6983i	0.273414	−	0.473567i	−0.696320	−	0.717732i	$-0.745181\pi$
$719$	7.33137	−	12.6983i	0.273414	−	0.473567i	0.969734	+	0.244165i	$0.0785138\pi$
$720$	−2.64292	+	1.41950i	−0.0984958	+	0.0529015i
$721$	5.03114	+	8.71419i	0.187370	+	0.324534i
$722$	−3.41665	−	19.3768i	−0.127155	−	0.721130i
$723$	21.2183	−	29.3335i	0.789118	−	1.09092i
$724$	−13.4231	+	4.88561i	−0.498866	+	0.181572i
$725$	−0.236500	+	1.34126i	−0.00878338	+	0.0498131i
$726$	−8.66687	+	2.18018i	−0.321658	+	0.0809141i
$727$	−16.5126	+	13.8557i	−0.612417	+	0.513879i	−0.895410	−	0.445243i	$-0.853117\pi$
$727$	−16.5126	+	13.8557i	−0.612417	+	0.513879i	0.282993	+	0.959122i	$0.408673\pi$
$728$	−6.01965			−0.223103
$729$	2.48465	−	26.8854i	0.0920239	−	0.995757i
$730$	9.07018			0.335702
$731$	−7.71608	+	6.47456i	−0.285390	+	0.239470i
$732$	−11.3337	+	2.85103i	−0.418906	+	0.105377i
$733$	−7.67766	+	43.5422i	−0.283581	+	1.60827i	0.426731	+	0.904379i	$0.359665\pi$
$733$	−7.67766	+	43.5422i	−0.283581	+	1.60827i	−0.710312	+	0.703887i	$0.751446\pi$
$734$	−31.8305	+	11.5854i	−1.17489	+	0.427624i
$735$	−5.86468	+	8.10770i	−0.216322	+	0.299057i
$736$	1.57099	+	8.90951i	0.0579073	+	0.328409i
$737$	3.09104	+	5.35384i	0.113860	+	0.197211i
$738$	−13.1030	+	7.03752i	−0.482327	+	0.259055i
$739$	−1.56196	+	2.70539i	−0.0574576	+	0.0995196i	−0.893324	−	0.449414i	$-0.851633\pi$
$739$	−1.56196	+	2.70539i	−0.0574576	+	0.0995196i	0.835866	+	0.548934i	$0.184966\pi$
$740$	0.135653	+	0.0493736i	0.00498670	+	0.00181501i
$741$	−4.21288	−	58.4865i	−0.154764	−	2.14856i
$742$	−0.506543	−	0.425040i	−0.0185958	−	0.0156037i
$743$	15.0511	+	12.6293i	0.552170	+	0.463326i	0.875675	−	0.482901i	$-0.160417\pi$
$743$	15.0511	+	12.6293i	0.552170	+	0.463326i	−0.323505	+	0.946226i	$0.604861\pi$
$744$	−6.75348	+	4.57589i	−0.247595	+	0.167760i
$745$	19.0435	+	6.93127i	0.697701	+	0.253942i
$746$	5.66540	−	9.81276i	0.207425	−	0.359271i
$747$	−15.5474	+	38.9500i	−0.568849	+	1.42511i
$748$	−2.05616	−	3.56137i	−0.0751807	−	0.130217i
$749$	0.340259	+	1.92970i	0.0124328	+	0.0705099i
$750$	−0.707801	−	1.58083i	−0.0258452	−	0.0577237i
$751$	−23.5872	+	8.58503i	−0.860708	+	0.313272i	−0.734398	−	0.678719i	$-0.762536\pi$
$751$	−23.5872	+	8.58503i	−0.860708	+	0.313272i	−0.126310	+	0.991991i	$0.540313\pi$
$752$	−2.35553	+	13.3589i	−0.0858974	+	0.487148i
$753$	34.5394	+	35.6170i	1.25869	+	1.29796i
$754$	5.67955	−	4.76571i	0.206837	−	0.173557i
$755$	8.41466			0.306241
$756$	−4.24575	+	3.87147i	−0.154417	+	0.140804i
$757$	−19.1051			−0.694388			−0.347194	−	0.937793i	$-0.612866\pi$
$757$	−19.1051			−0.694388			−0.347194	+	0.937793i	$0.612866\pi$
$758$	−5.81896	+	4.88268i	−0.211354	+	0.177347i
$759$	−10.3618	+	36.4235i	−0.376108	+	1.32209i
$760$	−1.07991	+	6.12450i	−0.0391726	+	0.222159i
$761$	41.2518	−	15.0144i	1.49538	−	0.544272i	0.540517	−	0.841333i	$-0.318229\pi$
$761$	41.2518	−	15.0144i	1.49538	−	0.544272i	0.954859	+	0.297061i	$0.0960064\pi$
$762$	−29.7989	−	3.06891i	−1.07950	−	0.111175i
$763$	−0.504266	−	2.85984i	−0.0182557	−	0.103533i
$764$	−3.34591	−	5.79528i	−0.121051	−	0.209666i
$765$	1.59784	+	4.84844i	0.0577699	+	0.175296i
$766$	−4.98335	+	8.63142i	−0.180056	+	0.311866i
$767$	47.3386	+	17.2298i	1.70930	+	0.622133i
$768$	−1.55834	−	0.756019i	−0.0562319	−	0.0272805i
$769$	−23.0081	−	19.3061i	−0.829693	−	0.696195i	0.125527	−	0.992090i	$-0.459938\pi$
$769$	−23.0081	−	19.3061i	−0.829693	−	0.696195i	−0.955220	+	0.295895i	$0.904382\pi$
$770$	2.04712	+	1.71774i	0.0737730	+	0.0619029i
$771$	42.0701	+	20.4100i	1.51512	+	0.735048i
$772$	−21.7744	−	7.92523i	−0.783677	−	0.285235i
$773$	−1.49443	+	2.58843i	−0.0537508	+	0.0930992i	−0.891649	−	0.452728i	$-0.850451\pi$
$773$	−1.49443	+	2.58843i	−0.0537508	+	0.0930992i	0.837898	+	0.545827i	$0.183784\pi$
$774$	−11.8271	+	13.2464i	−0.425115	+	0.476133i
$775$	−2.35493	−	4.07886i	−0.0845915	−	0.146517i
$776$	−1.60527	−	9.10394i	−0.0576258	−	0.326812i
$777$	0.275033	+	0.0283249i	0.00986676	+	0.00101615i
$778$	−15.1281	+	5.50616i	−0.542367	+	0.197405i
$779$	−5.35395	+	30.3638i	−0.191825	+	1.08790i
$780$	−2.57997	+	9.06905i	−0.0923776	+	0.324724i
$781$	−2.52359	+	2.11755i	−0.0903013	+	0.0757718i
$782$	15.3947			0.550514
$783$	0.940864	−	7.01407i	0.0336237	−	0.250662i
$784$	−5.77723			−0.206330
$785$	−8.72361	+	7.31997i	−0.311359	+	0.261261i
$786$	0.109744	+	0.113167i	0.00391442	+	0.00403655i
$787$	−0.306496	+	1.73823i	−0.0109254	+	0.0619611i	−0.989783	−	0.142582i	$-0.954460\pi$
$787$	−0.306496	+	1.73823i	−0.0109254	+	0.0619611i	0.978858	+	0.204543i	$0.0655707\pi$
$788$	22.2313	−	8.09153i	0.791957	−	0.288249i
$789$	9.79810	+	21.8834i	0.348822	+	0.779071i
$790$	−2.61799	−	14.8474i	−0.0931440	−	0.528246i
$791$	3.31456	+	5.74099i	0.117852	+	0.204126i
$792$	−4.48744	−	5.69434i	−0.159454	−	0.202340i
$793$	−18.3656	+	31.8101i	−0.652181	+	1.12961i
$794$	−24.0846	−	8.76608i	−0.854731	−	0.311097i
$795$	−0.857453	+	0.580976i	−0.0304107	+	0.0206051i
$796$	10.4195	+	8.74303i	0.369311	+	0.309888i
$797$	−18.3778	−	15.4208i	−0.650975	−	0.546233i	0.256392	−	0.966573i	$-0.417466\pi$
$797$	−18.3778	−	15.4208i	−0.650975	−	0.546233i	−0.907367	+	0.420340i	$0.861911\pi$
$798$	0.855758	+	11.8803i	0.0302935	+	0.420558i
$799$	21.6907	+	7.89478i	0.767363	+	0.279297i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−6.46289	−	4.00092i	−0.228355	−	0.141366i
$802$	−4.63917	−	8.03528i	−0.163815	−	0.283736i
$803$	3.80630	+	21.5866i	0.134322	+	0.761775i
$804$	2.59682	−	3.59001i	0.0915829	−	0.126610i
$805$	−9.40069	+	3.42157i	−0.331331	+	0.120595i
$806$	−4.45223	+	25.2499i	−0.156823	+	0.889388i
$807$	−34.2831	+	8.62403i	−1.20682	+	0.303580i
$808$	7.20219	−	6.04335i	0.253372	−	0.212604i
$809$	−5.31068			−0.186714			−0.0933568	−	0.995633i	$-0.529760\pi$
$809$	−5.31068			−0.186714			−0.0933568	+	0.995633i	$0.529760\pi$
$810$	4.01296	+	8.05581i	0.141001	+	0.283052i
$811$	−17.3673			−0.609850			−0.304925	−	0.952376i	$-0.598631\pi$
$811$	−17.3673			−0.609850			−0.304925	+	0.952376i	$0.598631\pi$
$812$	−1.15368	+	0.968055i	−0.0404863	+	0.0339721i
$813$	−31.1979	+	7.84793i	−1.09416	+	0.275239i
$814$	−0.0605802	+	0.343568i	−0.00212334	+	0.0120420i
$815$	10.7530	−	3.91376i	0.376660	−	0.137093i
$816$	−1.72741	+	2.38807i	−0.0604713	+	0.0835992i
$817$	6.39238	+	36.2530i	0.223641	+	1.26833i
$818$	15.1376	+	26.2191i	0.529274	+	0.916729i
$819$	−0.554650	+	18.0504i	−0.0193810	+	0.630733i
$820$	2.47888	−	4.29354i	0.0865662	−	0.149937i
$821$	23.2687	+	8.46911i	0.812083	+	0.295574i	0.714484	−	0.699652i	$-0.246661\pi$
$821$	23.2687	+	8.46911i	0.812083	+	0.295574i	0.0975991	+	0.995226i	$0.468884\pi$
$822$	−0.284039	−	3.94326i	−0.00990700	−	0.137537i
$823$	19.2028	+	16.1130i	0.669366	+	0.561665i	0.912878	−	0.408233i	$-0.133855\pi$
$823$	19.2028	+	16.1130i	0.669366	+	0.561665i	−0.243512	+	0.969898i	$0.578299\pi$
$824$	6.97074	+	5.84914i	0.242837	+	0.203765i
$825$	3.46527	−	2.34793i	0.120645	−	0.0817444i
$826$	−9.61584	−	3.49988i	−0.334578	−	0.121776i
$827$	−12.8054	+	22.1796i	−0.445287	+	0.771260i	−0.998072	−	0.0620636i	$-0.980232\pi$
$827$	−12.8054	+	22.1796i	−0.445287	+	0.771260i	0.552785	+	0.833324i	$0.313565\pi$
$828$	26.8607	−	3.88982i	0.933472	−	0.135180i
$829$	6.10184	+	10.5687i	0.211926	+	0.367066i	0.952317	−	0.305110i	$-0.0986932\pi$
$829$	6.10184	+	10.5687i	0.211926	+	0.367066i	−0.740391	+	0.672176i	$0.765360\pi$
$830$	−2.42751	−	13.7671i	−0.0842600	−	0.477862i
$831$	−7.16342	−	15.9991i	−0.248496	−	0.555001i
$832$	−5.11547	+	1.86188i	−0.177347	+	0.0645490i
$833$	−1.70710	+	9.68146i	−0.0591476	+	0.335443i
$834$	8.44092	+	8.70428i	0.292285	+	0.301405i
$835$	3.99917	−	3.35570i	0.138397	−	0.116129i
$836$	−15.0292			−0.519796
$837$	13.0989	+	20.6725i	0.452765	+	0.714546i
$838$	−15.1620			−0.523761
$839$	−28.7654	+	24.1370i	−0.993091	+	0.833302i	−0.986012	−	0.166673i	$-0.946698\pi$
$839$	−28.7654	+	24.1370i	−0.993091	+	0.833302i	−0.00707874	+	0.999975i	$0.502253\pi$
$840$	0.524066	−	1.84219i	0.0180820	−	0.0635615i
$841$	−4.71370	+	26.7327i	−0.162541	+	0.921817i
$842$	8.17198	−	2.97436i	0.281625	−	0.102503i
$843$	−36.9221	−	3.80251i	−1.27166	−	0.130965i
$844$	−2.68784	−	15.2435i	−0.0925193	−	0.524703i
$845$	8.31731	+	14.4060i	0.286124	+	0.495581i
$846$	39.8407	+	8.29414i	1.36975	+	0.285159i
$847$	2.85277	−	4.94115i	0.0980224	−	0.169780i
$848$	−0.561922	−	0.204523i	−0.0192965	−	0.00702335i
$849$	21.9950	+	10.6707i	0.754866	+	0.366218i
$850$	−1.30354	−	1.09380i	−0.0447110	−	0.0375170i
$851$	−1.00046	−	0.839485i	−0.0342953	−	0.0287772i
$852$	2.12428	+	1.03058i	0.0727766	+	0.0353070i
$853$	−40.2839	−	14.6621i	−1.37929	−	0.502022i	−0.457330	−	0.889297i	$-0.651194\pi$
$853$	−40.2839	−	14.6621i	−1.37929	−	0.502022i	−0.921964	+	0.387275i	$0.873416\pi$
$854$	3.73058	−	6.46156i	0.127658	−	0.221110i
$855$	18.2653	+	3.80253i	0.624661	+	0.130044i
$856$	0.886008	+	1.53461i	0.0302831	+	0.0524519i
$857$	−2.38915	−	13.5495i	−0.0816117	−	0.462843i	−0.998036	−	0.0626360i	$-0.980049\pi$
$857$	−2.38915	−	13.5495i	−0.0816117	−	0.462843i	0.916425	−	0.400207i	$-0.131062\pi$
$858$	−22.6666	−	2.33437i	−0.773825	−	0.0796942i
$859$	2.95244	−	1.07460i	0.100736	−	0.0366649i	−0.291160	−	0.956674i	$-0.594041\pi$
$859$	2.95244	−	1.07460i	0.100736	−	0.0366649i	0.391896	+	0.920009i	$0.371819\pi$
$860$	1.02788	−	5.82941i	0.0350505	−	0.198781i
$861$	2.59819	−	9.13312i	0.0885462	−	0.311256i
$862$	−6.01290	+	5.04543i	−0.204800	+	0.171848i
$863$	34.6106			1.17816			0.589079	−	0.808076i	$-0.299491\pi$
$863$	34.6106			1.17816			0.589079	+	0.808076i	$0.299491\pi$
$864$	−2.41057	+	4.60317i	−0.0820094	+	0.156603i
$865$	1.54746			0.0526151
$866$	−16.0155	+	13.4386i	−0.544227	+	0.456661i
$867$	−17.0069	−	17.5376i	−0.577586	−	0.595607i
$868$	0.904378	−	5.12898i	0.0306966	−	0.174089i
$869$	34.2374	−	12.4614i	1.16143	−	0.422724i
$870$	0.963988	+	2.15301i	0.0326823	+	0.0729938i
$871$	−2.41817	−	13.7141i	−0.0819367	−	0.464686i
$872$	−1.31307	−	2.27430i	−0.0444662	−	0.0770177i
$873$	−27.4468	+	3.97470i	−0.928935	+	0.134523i
$874$	28.1314	−	48.7250i	0.951559	−	1.64815i
$875$	1.03910	+	0.378202i	0.0351280	+	0.0127856i
$876$	13.0058	−	8.81218i	0.439424	−	0.297736i
$877$	−5.64019	−	4.73268i	−0.190456	−	0.159811i	0.542574	−	0.840008i	$-0.317450\pi$
$877$	−5.64019	−	4.73268i	−0.190456	−	0.159811i	−0.733030	+	0.680197i	$0.761894\pi$
$878$	−1.65452	−	1.38831i	−0.0558373	−	0.0468531i
$879$	−3.87685	−	53.8215i	−0.130763	−	1.81535i
$880$	2.27093	+	0.826550i	0.0765529	+	0.0278630i
$881$	−22.9013	+	39.6661i	−0.771563	+	1.33639i	0.165143	+	0.986270i	$0.447191\pi$
$881$	−22.9013	+	39.6661i	−0.771563	+	1.33639i	−0.936706	+	0.350116i	$0.886142\pi$
$882$	−0.532313	+	17.3235i	−0.0179239	+	0.583313i
$883$	2.08549	+	3.61218i	0.0701825	+	0.121560i	0.898981	−	0.437987i	$-0.144309\pi$
$883$	2.08549	+	3.61218i	0.0701825	+	0.121560i	−0.828799	+	0.559547i	$0.810975\pi$
$884$	1.60857	+	9.12265i	0.0541020	+	0.306828i
$885$	−9.39408	+	12.9869i	−0.315779	+	0.436551i
$886$	−25.2759	+	9.19969i	−0.849162	+	0.309070i
$887$	3.98347	−	22.5914i	0.133752	−	0.758545i	−0.841969	−	0.539526i	$-0.818603\pi$
$887$	3.98347	−	22.5914i	0.133752	−	0.758545i	0.975721	−	0.219019i	$-0.0702856\pi$
$888$	0.242483	−	0.0609974i	0.00813718	−	0.00204694i
$889$	14.6507	−	12.2934i	0.491367	−	0.412306i
$890$	2.53369			0.0849295
$891$	−17.4884	+	12.9313i	−0.585884	+	0.433215i
$892$	−24.2501			−0.811954
$893$	64.6237	−	54.2257i	2.16255	−	1.81459i
$894$	34.0407	−	8.56306i	1.13849	−	0.286391i
$895$	1.19775	−	6.79275i	0.0400362	−	0.227057i
$896$	1.03910	−	0.378202i	0.0347139	−	0.0126348i
$897$	49.9950	−	69.1161i	1.66928	−	2.30772i
$898$	2.13478	+	12.1069i	0.0712384	+	0.404013i
$899$	3.20729	+	5.55519i	0.106969	+	0.185276i
$900$	−2.55078	−	1.57909i	−0.0850260	−	0.0526363i
$901$	−0.508780	+	0.881233i	−0.0169499	+	0.0293581i
$902$	11.2587	+	4.09783i	0.374874	+	0.136443i
$903$	−0.814526	−	11.3079i	−0.0271057	−	0.376303i
$904$	4.59238	+	3.85347i	0.152740	+	0.128164i
$905$	−10.9426	−	9.18195i	−0.363745	−	0.305218i
$906$	12.0658	−	8.17531i	0.400860	−	0.271607i
$907$	−11.9421	−	4.34659i	−0.396532	−	0.144326i	0.136054	−	0.990701i	$-0.456558\pi$
$907$	−11.9421	−	4.34659i	−0.396532	−	0.144326i	−0.532587	+	0.846375i	$0.678780\pi$
$908$	−2.00800	+	3.47797i	−0.0666380	+	0.115420i
$909$	−17.4579	−	22.1532i	−0.579042	−	0.734776i
$910$	−3.00983	−	5.21317i	−0.0997748	−	0.172815i
$911$	8.10354	+	45.9575i	0.268482	+	1.52264i	0.758932	+	0.651170i	$0.225721\pi$
$911$	8.10354	+	45.9575i	0.268482	+	1.52264i	−0.490450	+	0.871469i	$0.663167\pi$
$912$	4.40180	+	9.83114i	0.145758	+	0.325542i
$913$	31.7463	−	11.5547i	1.05065	−	0.382405i
$914$	−3.97611	+	22.5496i	−0.131518	+	0.745875i
$915$	−8.13592	−	8.38976i	−0.268965	−	0.277357i
$916$	−21.5224	+	18.0594i	−0.711119	+	0.596700i
$917$	−0.100642			−0.00332349
$918$	7.00167	+	5.39981i	0.231090	+	0.178220i
$919$	−35.2401			−1.16246			−0.581232	−	0.813738i	$-0.697429\pi$
$919$	−35.2401			−1.16246			−0.581232	+	0.813738i	$0.697429\pi$
$920$	−6.93037	+	5.81527i	−0.228487	+	0.191724i
$921$	−14.3526	+	50.4521i	−0.472935	+	1.66245i
$922$	3.74373	−	21.2318i	0.123293	−	0.699231i
$923$	6.97323	−	2.53805i	0.229527	−	0.0835408i
$924$	4.60425	+	0.474179i	0.151469	+	0.0155993i
$925$	0.0250677	+	0.142166i	0.000824219	+	0.00467438i
$926$	−10.0751	−	17.4505i	−0.331088	−	0.573461i
$927$	18.1814	−	20.3634i	0.597157	−	0.668822i
$928$	−0.680974	+	1.17948i	−0.0223541	+	0.0387184i
$929$	−28.6634	−	10.4326i	−0.940414	−	0.342283i	−0.174085	−	0.984731i	$-0.555697\pi$
$929$	−28.6634	−	10.4326i	−0.940414	−	0.342283i	−0.766329	+	0.642448i	$0.777919\pi$
$930$	−7.33958	−	3.56074i	−0.240674	−	0.116761i
$931$	27.5228	+	23.0944i	0.902024	+	0.756888i
$932$	3.24367	+	2.72177i	0.106250	+	0.0891544i
$933$	−20.3442	−	9.86983i	−0.666038	−	0.323124i
$934$	−6.57266	−	2.39225i	−0.215064	−	0.0782770i
$935$	2.05616	−	3.56137i	0.0672436	−	0.116469i
$936$	5.11166	+	15.5107i	0.167080	+	0.506984i
$937$	11.7766	+	20.3977i	0.384725	+	0.666364i	0.991731	−	0.128334i	$-0.0409628\pi$
$937$	11.7766	+	20.3977i	0.384725	+	0.666364i	−0.607006	+	0.794697i	$0.707629\pi$
$938$	0.491201	+	2.78574i	0.0160383	+	0.0909577i
$939$	28.4806	+	2.93314i	0.929429	+	0.0957194i
$940$	−12.7469	+	4.63949i	−0.415758	+	0.151324i
$941$	8.59070	−	48.7203i	0.280049	−	1.58824i	−0.442405	−	0.896816i	$-0.645874\pi$
$941$	8.59070	−	48.7203i	0.280049	−	1.58824i	0.722453	−	0.691420i	$-0.243014\pi$
$942$	−5.39705	+	18.9716i	−0.175845	+	0.618128i
$943$	−34.3591	+	28.8307i	−1.11889	+	0.938856i
$944$	−9.25400			−0.301192
$945$	−5.47567	−	1.74120i	−0.178123	−	0.0566411i
$946$	14.3051			0.465099
$947$	29.5816	−	24.8219i	0.961273	−	0.806604i	−0.0198864	−	0.999802i	$-0.506330\pi$
$947$	29.5816	−	24.8219i	0.961273	−	0.806604i	0.981160	+	0.193198i	$0.0618860\pi$
$948$	−18.1790	−	18.7462i	−0.590426	−	0.608848i
$949$	8.57404	−	48.6258i	0.278325	−	1.57846i
$950$	−5.84393	+	2.12702i	−0.189602	+	0.0690095i
$951$	−10.3126	−	23.0324i	−0.334407	−	0.746878i
$952$	−0.326747	−	1.85307i	−0.0105899	−	0.0600585i
$953$	−0.839338	−	1.45378i	−0.0271888	−	0.0470924i	0.852111	−	0.523361i	$-0.175322\pi$
$953$	−0.839338	−	1.45378i	−0.0271888	−	0.0470924i	−0.879300	+	0.476269i	$0.841989\pi$
$954$	−0.665055	+	1.66613i	−0.0215320	+	0.0539429i
$955$	3.34591	−	5.79528i	0.108271	−	0.187531i
$956$	−14.6356	−	5.32691i	−0.473348	−	0.172285i
$957$	−4.71952	+	3.19776i	−0.152560	+	0.103369i
$958$	−4.02263	−	3.37539i	−0.129965	−	0.109054i
$959$	1.93350	+	1.62240i	0.0624359	+	0.0523900i
$960$	−0.124440	−	1.72757i	−0.00401628	−	0.0557572i
$961$	8.28550	+	3.01567i	0.267274	+	0.0972798i
$962$	0.392928	−	0.680572i	0.0126685	−	0.0219425i
$963$	4.68330	−	2.51537i	0.150917	−	0.0810567i
$964$	10.4510	+	18.1016i	0.336603	+	0.583013i
$965$	−4.02374	−	22.8198i	−0.129529	−	0.734595i
$966$	−10.1554	+	14.0395i	−0.326746	+	0.451713i
$967$	−15.3981	+	5.60445i	−0.495170	+	0.180227i	−0.577520	−	0.816376i	$-0.695980\pi$
$967$	−15.3981	+	5.60445i	−0.495170	+	0.180227i	0.0823504	+	0.996603i	$0.473757\pi$
$968$	0.895974	−	5.08132i	0.0287977	−	0.163320i
$969$	17.7757	−	4.47153i	0.571037	−	0.143646i
$970$	7.08161	−	5.94217i	0.227377	−	0.190792i
$971$	−15.8066			−0.507258			−0.253629	−	0.967302i	$-0.581624\pi$
$971$	−15.8066			−0.507258			−0.253629	+	0.967302i	$0.581624\pi$
$972$	13.5809	+	7.65244i	0.435607	+	0.245452i
$973$	−7.74087			−0.248161
$974$	20.6197	−	17.3019i	0.660696	−	0.554390i
$975$	−9.14401	+	2.30021i	−0.292843	+	0.0736656i
$976$	1.17167	−	6.64487i	0.0375042	−	0.212697i
$977$	−17.1508	+	6.24238i	−0.548702	+	0.199711i	−0.601470	−	0.798895i	$-0.705418\pi$
$977$	−17.1508	+	6.24238i	−0.548702	+	0.199711i	0.0527674	+	0.998607i	$0.483196\pi$
$978$	11.6163	−	16.0591i	0.371448	−	0.513512i
$979$	1.06326	+	6.03007i	0.0339821	+	0.192722i
$980$	−2.88862	−	5.00323i	−0.0922735	−	0.159822i
$981$	−6.94068	+	3.72780i	−0.221599	+	0.119019i
$982$	21.7253	−	37.6293i	0.693282	−	1.20080i
$983$	−27.5329	−	10.0212i	−0.878164	−	0.319625i	−0.136695	−	0.990613i	$-0.543648\pi$
$983$	−27.5329	−	10.0212i	−0.878164	−	0.319625i	−0.741468	+	0.670988i	$0.765870\pi$
$984$	−0.616943	−	8.56490i	−0.0196674	−	0.273039i
$985$	18.1231	+	15.2071i	0.577450	+	0.484538i
$986$	1.77535	+	1.48970i	0.0565387	+	0.0474416i
$987$	−21.5085	+	14.5733i	−0.684624	+	0.463873i
$988$	31.8130	+	11.5790i	1.01211	+	0.368377i
$989$	−26.7760	+	46.3774i	−0.851427	+	1.47471i
$990$	2.68772	−	6.73341i	0.0854214	−	0.214002i
$991$	−16.2160	−	28.0869i	−0.515118	−	0.892210i	−0.999846	−	0.0175454i	$-0.994415\pi$
$991$	−16.2160	−	28.0869i	−0.515118	−	0.892210i	0.484728	−	0.874665i	$-0.338918\pi$
$992$	−0.817858	−	4.63830i	−0.0259670	−	0.147266i
$993$	−7.54619	−	16.8539i	−0.239471	−	0.534844i
$994$	−1.41647	+	0.515551i	−0.0449275	+	0.0163523i
$995$	−2.36192	+	13.3951i	−0.0748778	+	0.424653i
$996$	−16.8563	−	17.3822i	−0.534112	−	0.550776i
$997$	24.3658	−	20.4453i	0.771672	−	0.647510i	−0.169464	−	0.985536i	$-0.554204\pi$
$997$	24.3658	−	20.4453i	0.771672	−	0.647510i	0.941137	+	0.338026i	$0.109759\pi$
$998$	−18.5059			−0.585794
$999$	−0.160563	−	0.732725i	−0.00508000	−	0.0231824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.k.e.211.1	yes	24
3.2	odd	2		810.2.k.e.361.3		24
27.4	even	9		7290.2.a.s.1.7		12
27.11	odd	18		810.2.k.e.451.3		24
27.16	even	9	inner	270.2.k.e.151.1	✓	24
27.23	odd	18		7290.2.a.v.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.k.e.151.1	✓	24	27.16	even	9	inner
270.2.k.e.211.1	yes	24	1.1	even	1	trivial
810.2.k.e.361.3		24	3.2	odd	2
810.2.k.e.451.3		24	27.11	odd	18
7290.2.a.s.1.7		12	27.4	even	9
7290.2.a.v.1.7		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67972 + 0.422540i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(1.01514 - 1.40339i) q^{6} +(0.192018 + 1.08899i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.64292 - 1.41950i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67972 + 0.422540i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} +(1.01514 - 1.40339i) q^{6} +(0.192018 + 1.08899i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.64292 - 1.41950i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.27093 - 0.826550i) q^{11} +(0.124440 + 1.72757i) q^{12} +(4.17017 + 3.49919i) q^{13} +(-0.847083 - 0.710787i) q^{14} +(-1.43390 + 0.971556i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.850824 + 1.47367i) q^{17} +(-1.11216 + 2.78623i) q^{18} +(3.10949 + 5.38579i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(-0.782677 - 1.74806i) q^{21} +(2.27093 - 0.826550i) q^{22} +(-1.57099 + 8.90951i) q^{23} +(-1.20579 - 1.24341i) q^{24} +(0.766044 - 0.642788i) q^{25} -5.44377 q^{26} +(-3.83957 + 3.50110i) q^{27} +1.10579 q^{28} +(-1.04331 + 0.875444i) q^{29} +(0.473930 - 1.66595i) q^{30} +(0.817858 - 4.63830i) q^{31} +(0.939693 - 0.342020i) q^{32} +(4.16377 + 0.428816i) q^{33} +(-0.295488 - 1.67580i) q^{34} +(0.552894 + 0.957640i) q^{35} +(-0.938993 - 2.84926i) q^{36} +(-0.0721794 + 0.125018i) q^{37} +(-5.84393 - 2.12702i) q^{38} +(-8.48326 - 4.11559i) q^{39} +(0.766044 + 0.642788i) q^{40} +(3.79786 + 3.18678i) q^{41} +(1.72320 + 0.835997i) q^{42} +(5.56236 + 2.02453i) q^{43} +(-1.20833 + 2.09290i) q^{44} +(1.99804 - 2.23782i) q^{45} +(-4.52347 - 7.83489i) q^{46} +(-2.35553 - 13.3589i) q^{47} +(1.72294 + 0.177441i) q^{48} +(5.42882 - 1.97593i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(0.806462 - 2.83486i) q^{51} +(4.17017 - 3.49919i) q^{52} +0.597985 q^{53} +(0.690822 - 5.15003i) q^{54} -2.41667 q^{55} +(-0.847083 + 0.710787i) q^{56} +(-7.49879 - 7.73275i) q^{57} +(0.236500 - 1.34126i) q^{58} +(8.69592 - 3.16505i) q^{59} +(0.707801 + 1.58083i) q^{60} +(1.17167 + 6.64487i) q^{61} +(2.35493 + 4.07886i) q^{62} +(2.05330 + 2.60554i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.11547 + 1.86188i) q^{65} +(-3.46527 + 2.34793i) q^{66} +(-1.95962 - 1.64432i) q^{67} +(1.30354 + 1.09380i) q^{68} +(-1.12580 - 15.6293i) q^{69} +(-1.03910 - 0.378202i) q^{70} +(0.681582 - 1.18054i) q^{71} +(2.55078 + 1.57909i) q^{72} +(-4.53509 - 7.85501i) q^{73} +(-0.0250677 - 0.142166i) q^{74} +(-1.01514 + 1.40339i) q^{75} +(5.84393 - 2.12702i) q^{76} +(0.464044 - 2.63173i) q^{77} +(9.14401 - 2.30021i) q^{78} +(-11.5492 + 9.69094i) q^{79} -1.00000 q^{80} +(4.97006 - 7.50323i) q^{81} -4.95776 q^{82} +(-10.7089 + 8.98582i) q^{83} +(-1.85741 + 0.467239i) q^{84} +(-0.295488 + 1.67580i) q^{85} +(-5.56236 + 2.02453i) q^{86} +(1.38256 - 1.91134i) q^{87} +(-0.419650 - 2.37995i) q^{88} +(-1.26685 - 2.19424i) q^{89} +(-0.0921398 + 2.99858i) q^{90} +(-3.00983 + 5.21317i) q^{91} +(8.50135 + 3.09424i) q^{92} +(0.586095 + 8.13663i) q^{93} +(10.3914 + 8.71939i) q^{94} +(4.76402 + 3.99748i) q^{95} +(-1.43390 + 0.971556i) q^{96} +(-8.68688 - 3.16176i) q^{97} +(-2.88862 + 5.00323i) q^{98} +(-7.17516 + 1.03907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - 3 q^{3} + 3 q^{7} + 12 q^{8} + 9 q^{9} - 12 q^{10} + 9 q^{13} - 3 q^{14} + 15 q^{17} - 12 q^{18} - 9 q^{19} + 24 q^{21} - 12 q^{23} + 3 q^{24} - 12 q^{26} - 3 q^{27} + 6 q^{28} - 33 q^{29} + 6 q^{30} - 21 q^{31} + 6 q^{33} - 15 q^{34} + 3 q^{35} - 6 q^{36} - 12 q^{37} + 12 q^{38} - 36 q^{39} + 21 q^{41} + 15 q^{42} + 12 q^{43} + 9 q^{44} - 12 q^{45} - 15 q^{46} - 21 q^{47} + 27 q^{49} + 3 q^{51} + 9 q^{52} - 60 q^{53} + 36 q^{54} + 18 q^{55} - 3 q^{56} - 24 q^{57} - 21 q^{58} + 36 q^{59} + 33 q^{61} + 18 q^{62} + 39 q^{63} - 12 q^{64} - 9 q^{66} - 12 q^{67} - 3 q^{68} - 48 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{74} - 12 q^{76} - 60 q^{77} - 36 q^{78} - 15 q^{79} - 24 q^{80} - 15 q^{81} + 6 q^{82} - 27 q^{83} + 3 q^{84} - 15 q^{85} - 12 q^{86} + 78 q^{87} - 9 q^{88} + 30 q^{89} - 9 q^{90} - 9 q^{91} + 6 q^{92} - 30 q^{93} + 12 q^{94} - 15 q^{95} + 3 q^{97} + 27 q^{98} - 111 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^7 + 12 * q^8 + 9 * q^9 - 12 * q^10 + 9 * q^13 - 3 * q^14 + 15 * q^17 - 12 * q^18 - 9 * q^19 + 24 * q^21 - 12 * q^23 + 3 * q^24 - 12 * q^26 - 3 * q^27 + 6 * q^28 - 33 * q^29 + 6 * q^30 - 21 * q^31 + 6 * q^33 - 15 * q^34 + 3 * q^35 - 6 * q^36 - 12 * q^37 + 12 * q^38 - 36 * q^39 + 21 * q^41 + 15 * q^42 + 12 * q^43 + 9 * q^44 - 12 * q^45 - 15 * q^46 - 21 * q^47 + 27 * q^49 + 3 * q^51 + 9 * q^52 - 60 * q^53 + 36 * q^54 + 18 * q^55 - 3 * q^56 - 24 * q^57 - 21 * q^58 + 36 * q^59 + 33 * q^61 + 18 * q^62 + 39 * q^63 - 12 * q^64 - 9 * q^66 - 12 * q^67 - 3 * q^68 - 48 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^74 - 12 * q^76 - 60 * q^77 - 36 * q^78 - 15 * q^79 - 24 * q^80 - 15 * q^81 + 6 * q^82 - 27 * q^83 + 3 * q^84 - 15 * q^85 - 12 * q^86 + 78 * q^87 - 9 * q^88 + 30 * q^89 - 9 * q^90 - 9 * q^91 + 6 * q^92 - 30 * q^93 + 12 * q^94 - 15 * q^95 + 3 * q^97 + 27 * q^98 - 111 * q^99

Introduction

L-functions

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