LMFDB - Embedded newform 322.2.i.d.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.2
Character	$\chi$	$=$	322.141
Dual form			322.2.i.d.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.182677 + 0.400008i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.48992 - 2.87352i) q^{5} +(0.421934 + 0.123891i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.83795 + 2.12110i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.182677 + 0.400008i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.48992 - 2.87352i) q^{5} +(0.421934 + 0.123891i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.83795 + 2.12110i) q^{9} +(-3.19863 - 2.05563i) q^{10} +(0.610212 - 4.24412i) q^{11} +(0.0625825 - 0.435271i) q^{12} +(-2.14909 - 1.38114i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.694579 + 1.52092i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.58064 + 1.05137i) q^{17} +(1.83795 - 2.12110i) q^{18} +(-1.18781 + 0.348774i) q^{19} +(-1.57950 + 3.45862i) q^{20} +(-0.0625825 - 0.435271i) q^{21} -4.28776 q^{22} +(-1.68058 - 4.49173i) q^{23} -0.439747 q^{24} +(-1.34585 - 9.36058i) q^{25} +(-1.06123 + 2.32377i) q^{26} +(-2.45001 + 0.719388i) q^{27} +(0.654861 - 0.755750i) q^{28} +(5.13929 + 1.50903i) q^{29} +(1.40659 - 0.903958i) q^{30} +(-2.97598 - 6.51650i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.58621 + 1.01939i) q^{33} +(0.531091 - 3.69382i) q^{34} +(-0.541112 + 3.76351i) q^{35} +(-2.36108 - 1.51737i) q^{36} +(5.05639 + 5.83538i) q^{37} +(0.514267 + 1.12609i) q^{38} +(0.945056 - 0.607351i) q^{39} +(3.64820 + 1.07121i) q^{40} +(0.147899 - 0.170685i) q^{41} +(-0.421934 + 0.123891i) q^{42} +(-3.98270 + 8.72090i) q^{43} +(0.610212 + 4.24412i) q^{44} +10.6714 q^{45} +(-4.20684 + 2.30271i) q^{46} +0.240829 q^{47} +(0.0625825 + 0.435271i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-9.07377 + 2.66430i) q^{50} +(-1.07466 + 1.24022i) q^{51} +(2.45115 + 0.719723i) q^{52} +(-8.72405 + 5.60661i) q^{53} +(1.06074 + 2.32269i) q^{54} +(-10.6762 - 12.3210i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(0.0774746 - 0.538848i) q^{57} +(0.762274 - 5.30173i) q^{58} +(6.17963 + 3.97141i) q^{59} +(-1.09493 - 1.26362i) q^{60} +(3.72155 + 8.14906i) q^{61} +(-6.02664 + 3.87309i) q^{62} +(-2.69293 - 0.790717i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-9.31980 + 2.73654i) q^{65} +(0.783276 - 1.71514i) q^{66} +(1.83706 + 12.7770i) q^{67} -3.73181 q^{68} +(2.10373 + 0.148294i) q^{69} +3.80222 q^{70} +(1.00016 + 6.95624i) q^{71} +(-1.16591 + 2.55299i) q^{72} +(2.22598 - 0.653608i) q^{73} +(5.05639 - 5.83538i) q^{74} +(3.99016 + 1.17162i) q^{75} +(1.04144 - 0.669292i) q^{76} +(1.78120 + 3.90028i) q^{77} +(-0.735664 - 0.849002i) q^{78} +(4.54548 + 2.92120i) q^{79} +(0.541112 - 3.76351i) q^{80} +(-1.03847 + 7.22273i) q^{81} +(-0.189996 - 0.122103i) q^{82} +(-1.65605 - 1.91119i) q^{83} +(0.182677 + 0.400008i) q^{84} +(11.9367 - 7.67122i) q^{85} +(9.19893 + 2.70105i) q^{86} +(-1.54246 + 1.78009i) q^{87} +(4.11407 - 1.20800i) q^{88} +(-1.27490 + 2.79164i) q^{89} +(-1.51870 - 10.5628i) q^{90} +2.55463 q^{91} +(2.87797 + 3.83631i) q^{92} +3.15029 q^{93} +(-0.0342736 - 0.238378i) q^{94} +(-1.95536 + 4.28163i) q^{95} +(0.421934 - 0.123891i) q^{96} +(8.97403 - 10.3566i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(10.1237 - 6.50614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.182677	+	0.400008i	−0.105469	+	0.230945i	−0.955007	−	0.296582i	$-0.904153\pi$
$3$	−0.182677	+	0.400008i	−0.105469	+	0.230945i	0.849539	+	0.527527i	$0.176880\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.48992	−	2.87352i	1.11353	−	1.28508i	0.158893	−	0.987296i	$-0.449208\pi$
$5$	2.48992	−	2.87352i	1.11353	−	1.28508i	0.954634	−	0.297782i	$-0.0962470\pi$
$6$	0.421934	+	0.123891i	0.172254	+	0.0505783i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	1.83795	+	2.12110i	0.612649	+	0.707035i
$10$	−3.19863	−	2.05563i	−1.01149	−	0.650048i
$11$	0.610212	−	4.24412i	0.183986	−	1.27965i	−0.663236	−	0.748410i	$-0.730818\pi$
$11$	0.610212	−	4.24412i	0.183986	−	1.27965i	0.847222	−	0.531239i	$-0.178273\pi$
$12$	0.0625825	−	0.435271i	0.0180660	−	0.125652i
$13$	−2.14909	−	1.38114i	−0.596051	−	0.383059i	0.207552	−	0.978224i	$-0.433450\pi$
$13$	−2.14909	−	1.38114i	−0.596051	−	0.383059i	−0.803603	+	0.595165i	$0.797087\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	0.694579	+	1.52092i	0.179339	+	0.392699i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	3.58064	+	1.05137i	0.868433	+	0.254995i	0.685449	−	0.728121i	$-0.259606\pi$
$17$	3.58064	+	1.05137i	0.868433	+	0.254995i	0.182984	+	0.983116i	$0.441424\pi$
$18$	1.83795	−	2.12110i	0.433208	−	0.499949i
$19$	−1.18781	+	0.348774i	−0.272503	+	0.0800142i	−0.415129	−	0.909762i	$-0.636264\pi$
$19$	−1.18781	+	0.348774i	−0.272503	+	0.0800142i	0.142626	+	0.989777i	$0.454445\pi$
$20$	−1.57950	+	3.45862i	−0.353186	+	0.773370i
$21$	−0.0625825	−	0.435271i	−0.0136566	−	0.0949839i
$22$	−4.28776			−0.914153
$23$	−1.68058	−	4.49173i	−0.350425	−	0.936591i
$23$	−1.68058	−	4.49173i	−0.350425	−	0.936591i
$24$	−0.439747			−0.0897629
$25$	−1.34585	−	9.36058i	−0.269170	−	1.87212i
$26$	−1.06123	+	2.32377i	−0.208125	+	0.455730i
$27$	−2.45001	+	0.719388i	−0.471505	+	0.138446i
$28$	0.654861	−	0.755750i	0.123757	−	0.142823i
$29$	5.13929	+	1.50903i	0.954342	+	0.280220i	0.721593	−	0.692317i	$-0.243410\pi$
$29$	5.13929	+	1.50903i	0.954342	+	0.280220i	0.232748	+	0.972537i	$0.425228\pi$
$30$	1.40659	−	0.903958i	0.256806	−	0.165039i
$31$	−2.97598	−	6.51650i	−0.534503	−	1.17040i	−0.963651	−	0.267164i	$-0.913914\pi$
$31$	−2.97598	−	6.51650i	−0.534503	−	1.17040i	0.429149	−	0.903234i	$-0.358814\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.58621	+	1.01939i	0.276123	+	0.177454i
$34$	0.531091	−	3.69382i	0.0910814	−	0.633485i
$35$	−0.541112	+	3.76351i	−0.0914646	+	0.636150i
$36$	−2.36108	−	1.51737i	−0.393514	−	0.252896i
$37$	5.05639	+	5.83538i	0.831265	+	0.959331i	0.999652	−	0.0263898i	$-0.00840110\pi$
$37$	5.05639	+	5.83538i	0.831265	+	0.959331i	−0.168386	+	0.985721i	$0.553856\pi$
$38$	0.514267	+	1.12609i	0.0834252	+	0.182676i
$39$	0.945056	−	0.607351i	0.151330	−	0.0972540i
$40$	3.64820	+	1.07121i	0.576831	+	0.169373i
$41$	0.147899	−	0.170685i	0.0230980	−	0.0266565i	−0.744083	−	0.668087i	$-0.767113\pi$
$41$	0.147899	−	0.170685i	0.0230980	−	0.0266565i	0.767181	+	0.641431i	$0.221659\pi$
$42$	−0.421934	+	0.123891i	−0.0651058	+	0.0191168i
$43$	−3.98270	+	8.72090i	−0.607356	+	1.32992i	0.317011	+	0.948422i	$0.397321\pi$
$43$	−3.98270	+	8.72090i	−0.607356	+	1.32992i	−0.924368	+	0.381503i	$0.875407\pi$
$44$	0.610212	+	4.24412i	0.0919929	+	0.639824i
$45$	10.6714			1.59080
$46$	−4.20684	+	2.30271i	−0.620265	+	0.339516i
$47$	0.240829			0.0351285			0.0175643	−	0.999846i	$-0.494409\pi$
$47$	0.240829			0.0351285			0.0175643	+	0.999846i	$0.494409\pi$
$48$	0.0625825	+	0.435271i	0.00903300	+	0.0628259i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−9.07377	+	2.66430i	−1.28322	+	0.376789i
$51$	−1.07466	+	1.24022i	−0.150482	+	0.173666i
$52$	2.45115	+	0.719723i	0.339913	+	0.0998076i
$53$	−8.72405	+	5.60661i	−1.19834	+	0.770127i	−0.978668	−	0.205447i	$-0.934135\pi$
$53$	−8.72405	+	5.60661i	−1.19834	+	0.770127i	−0.219673	+	0.975574i	$0.570499\pi$
$54$	1.06074	+	2.32269i	0.144348	+	0.316079i
$55$	−10.6762	−	12.3210i	−1.43958	−	1.66136i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	0.0774746	−	0.538848i	0.0102618	−	0.0713721i
$58$	0.762274	−	5.30173i	0.100092	−	0.696152i
$59$	6.17963	+	3.97141i	0.804520	+	0.517033i	0.877088	−	0.480330i	$-0.159483\pi$
$59$	6.17963	+	3.97141i	0.804520	+	0.517033i	−0.0725682	+	0.997363i	$0.523120\pi$
$60$	−1.09493	−	1.26362i	−0.141355	−	0.163133i
$61$	3.72155	+	8.14906i	0.476496	+	1.04338i	0.983412	+	0.181385i	$0.0580581\pi$
$61$	3.72155	+	8.14906i	0.476496	+	1.04338i	−0.506916	+	0.861995i	$0.669215\pi$
$62$	−6.02664	+	3.87309i	−0.765384	+	0.491883i
$63$	−2.69293	−	0.790717i	−0.339278	−	0.0996210i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−9.31980	+	2.73654i	−1.15598	+	0.339426i
$66$	0.783276	−	1.71514i	0.0964147	−	0.211119i
$67$	1.83706	+	12.7770i	0.224432	+	1.56096i	0.720984	+	0.692952i	$0.243690\pi$
$67$	1.83706	+	12.7770i	0.224432	+	1.56096i	−0.496552	+	0.868007i	$0.665401\pi$
$68$	−3.73181			−0.452548
$69$	2.10373	+	0.148294i	0.253259	+	0.0178525i
$70$	3.80222			0.454452
$71$	1.00016	+	6.95624i	0.118697	+	0.825553i	0.958994	+	0.283427i	$0.0914714\pi$
$71$	1.00016	+	6.95624i	0.118697	+	0.825553i	−0.840297	+	0.542126i	$0.817619\pi$
$72$	−1.16591	+	2.55299i	−0.137404	+	0.300873i
$73$	2.22598	−	0.653608i	0.260532	−	0.0764990i	−0.148858	−	0.988859i	$-0.547560\pi$
$73$	2.22598	−	0.653608i	0.260532	−	0.0764990i	0.409390	+	0.912360i	$0.365742\pi$
$74$	5.05639	−	5.83538i	0.587793	−	0.678350i
$75$	3.99016	+	1.17162i	0.460744	+	0.135287i
$76$	1.04144	−	0.669292i	0.119461	−	0.0767731i
$77$	1.78120	+	3.90028i	0.202986	+	0.444478i
$78$	−0.735664	−	0.849002i	−0.0832976	−	0.0961306i
$79$	4.54548	+	2.92120i	0.511406	+	0.328661i	0.770764	−	0.637120i	$-0.219875\pi$
$79$	4.54548	+	2.92120i	0.511406	+	0.328661i	−0.259358	+	0.965781i	$0.583511\pi$
$80$	0.541112	−	3.76351i	0.0604981	−	0.420774i
$81$	−1.03847	+	7.22273i	−0.115386	+	0.802525i
$82$	−0.189996	−	0.122103i	−0.0209815	−	0.0134840i
$83$	−1.65605	−	1.91119i	−0.181775	−	0.209780i	0.657548	−	0.753413i	$-0.271594\pi$
$83$	−1.65605	−	1.91119i	−0.181775	−	0.209780i	−0.839323	+	0.543633i	$0.817048\pi$
$84$	0.182677	+	0.400008i	0.0199317	+	0.0436444i
$85$	11.9367	−	7.67122i	1.29471	−	0.832061i
$86$	9.19893	+	2.70105i	0.991946	+	0.291262i
$87$	−1.54246	+	1.78009i	−0.165369	+	0.190846i
$88$	4.11407	−	1.20800i	0.438562	−	0.128773i
$89$	−1.27490	+	2.79164i	−0.135139	+	0.295913i	−0.965088	−	0.261926i	$-0.915642\pi$
$89$	−1.27490	+	2.79164i	−0.135139	+	0.295913i	0.829949	+	0.557840i	$0.188370\pi$
$90$	−1.51870	−	10.5628i	−0.160085	−	1.11341i
$91$	2.55463			0.267798
$92$	2.87797	+	3.83631i	0.300049	+	0.399963i
$93$	3.15029			0.326670
$94$	−0.0342736	−	0.238378i	−0.00353505	−	0.0245868i
$95$	−1.95536	+	4.28163i	−0.200615	+	0.439286i
$96$	0.421934	−	0.123891i	0.0430634	−	0.0126446i
$97$	8.97403	−	10.3566i	0.911175	−	1.05155i	−0.0872911	−	0.996183i	$-0.527821\pi$
$97$	8.97403	−	10.3566i	0.911175	−	1.05155i	0.998466	−	0.0553690i	$-0.0176335\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	10.1237	−	6.50614i	1.01747	−	0.653891i
$100$	3.92851	+	8.60224i	0.392851	+	0.860224i
$101$	−6.41582	−	7.40425i	−0.638398	−	0.736750i	0.340693	−	0.940175i	$-0.389338\pi$
$101$	−6.41582	−	7.40425i	−0.638398	−	0.736750i	−0.979091	+	0.203424i	$0.934793\pi$
$102$	1.38054	+	0.887218i	0.136694	+	0.0878477i
$103$	1.70033	−	11.8260i	0.167538	−	1.16525i	−0.716414	−	0.697676i	$-0.754218\pi$
$103$	1.70033	−	11.8260i	0.167538	−	1.16525i	0.883952	−	0.467578i	$-0.154873\pi$
$104$	0.363562	−	2.52863i	0.0356502	−	0.247952i
$105$	−1.40659	−	0.903958i	−0.137269	−	0.0882172i
$106$	6.79110	+	7.83735i	0.659610	+	0.761231i
$107$	7.22800	+	15.8271i	0.698757	+	1.53006i	0.841472	+	0.540300i	$0.181689\pi$
$107$	7.22800	+	15.8271i	0.698757	+	1.53006i	−0.142716	+	0.989764i	$0.545583\pi$
$108$	2.14809	−	1.38050i	0.206700	−	0.132838i
$109$	−16.2235	−	4.76365i	−1.55393	−	0.456275i	−0.611657	−	0.791123i	$-0.709497\pi$
$109$	−16.2235	−	4.76365i	−1.55393	−	0.456275i	−0.942272	+	0.334848i	$0.891315\pi$
$110$	−10.6762	+	12.3210i	−1.01793	+	1.17476i
$111$	−3.25789	+	0.956602i	−0.309225	+	0.0907966i
$112$	−0.415415	+	0.909632i	−0.0392530	+	0.0859521i
$113$	0.228774	+	1.59116i	0.0215212	+	0.149683i	0.997749	−	0.0670658i	$-0.0213637\pi$
$113$	0.228774	+	1.59116i	0.0215212	+	0.149683i	−0.976227	+	0.216749i	$0.930455\pi$
$114$	−0.544389			−0.0509867
$115$	−17.0916	−	6.35488i	−1.59380	−	0.592596i
$116$	−5.35625			−0.497316
$117$	−1.02038	−	7.09691i	−0.0943343	−	0.656109i
$118$	3.05153	−	6.68192i	0.280916	−	0.615121i
$119$	−3.58064	+	1.05137i	−0.328237	+	0.0963790i
$120$	−1.09493	+	1.26362i	−0.0999534	+	0.115352i
$121$	−7.08573	−	2.08056i	−0.644157	−	0.189142i
$122$	7.53649	−	4.84341i	0.682321	−	0.438501i
$123$	0.0412574	+	0.0903410i	0.00372005	+	0.00814577i
$124$	4.69135	+	5.41410i	0.421295	+	0.486201i
$125$	−14.2558	−	9.16162i	−1.27507	−	0.819441i
$126$	−0.399424	+	2.77806i	−0.0355835	+	0.247489i
$127$	−0.455821	+	3.17030i	−0.0404475	+	0.281319i	−1.00000		0.000211113i	$-0.999933\pi$
$127$	−0.455821	+	3.17030i	−0.0404475	+	0.281319i	0.959552	+	0.281530i	$0.0908419\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−2.76088	−	3.18622i	−0.243082	−	0.280531i
$130$	4.03503	+	8.83549i	0.353896	+	0.774924i
$131$	−7.91646	+	5.08760i	−0.691664	+	0.444506i	−0.838677	−	0.544629i	$-0.816671\pi$
$131$	−7.91646	+	5.08760i	−0.691664	+	0.444506i	0.147013	+	0.989135i	$0.453034\pi$
$132$	−1.80915	−	0.531214i	−0.157466	−	0.0462363i
$133$	0.810692	−	0.935588i	0.0702959	−	0.0811258i
$134$	12.3855	−	3.63671i	1.06995	−	0.314164i
$135$	−4.03316	+	8.83138i	−0.347119	+	0.760084i
$136$	0.531091	+	3.69382i	0.0455407	+	0.316743i
$137$	−14.4038			−1.23060			−0.615298	−	0.788295i	$-0.710964\pi$
$137$	−14.4038			−1.23060			−0.615298	+	0.788295i	$0.710964\pi$
$138$	−0.152608	−	2.10342i	−0.0129908	−	0.179055i
$139$	14.8220			1.25719			0.628593	−	0.777734i	$-0.283631\pi$
$139$	14.8220			1.25719			0.628593	+	0.777734i	$0.283631\pi$
$140$	−0.541112	−	3.76351i	−0.0457323	−	0.318075i
$141$	−0.0439940	+	0.0963335i	−0.00370497	+	0.00811274i
$142$	6.74310	−	1.97995i	0.565868	−	0.166154i
$143$	−7.17311	+	8.27821i	−0.599846	+	0.692259i
$144$	2.69293	+	0.790717i	0.224411	+	0.0658931i
$145$	17.1327	−	11.0105i	1.42279	−	0.914371i
$146$	−0.963745	−	2.11031i	−0.0797601	−	0.174650i
$147$	0.287973	+	0.332338i	0.0237516	+	0.0274108i
$148$	−6.49559	−	4.17446i	−0.533934	−	0.343139i
$149$	2.16746	−	15.0750i	0.177566	−	1.23500i	−0.684808	−	0.728723i	$-0.740114\pi$
$149$	2.16746	−	15.0750i	0.177566	−	1.23500i	0.862374	−	0.506272i	$-0.168977\pi$
$150$	0.591832	−	4.11628i	0.0483229	−	0.336093i
$151$	0.0956825	+	0.0614914i	0.00778653	+	0.00500410i	0.544528	−	0.838742i	$-0.316709\pi$
$151$	0.0956825	+	0.0614914i	0.00778653	+	0.00500410i	−0.536742	+	0.843747i	$0.680345\pi$
$152$	−0.810692	−	0.935588i	−0.0657558	−	0.0758862i
$153$	4.35096	+	9.52728i	0.351754	+	0.770235i
$154$	3.60709	−	2.31814i	0.290668	−	0.186801i
$155$	−26.1353	−	7.67401i	−2.09924	−	0.616391i
$156$	−0.735664	+	0.849002i	−0.0589003	+	0.0679746i
$157$	−22.5944	+	6.63433i	−1.80323	+	0.529477i	−0.997984	−	0.0634609i	$-0.979786\pi$
$157$	−22.5944	+	6.63433i	−1.80323	+	0.529477i	−0.805248	+	0.592938i	$0.797968\pi$
$158$	2.24458	−	4.91494i	0.178569	−	0.391012i
$159$	−0.648999	−	4.51389i	−0.0514690	−	0.357975i
$160$	−3.80222			−0.300591
$161$	3.84221	+	2.87010i	0.302808	+	0.226195i
$162$	7.29700			0.573307
$163$	0.937386	+	6.51966i	0.0734217	+	0.510659i	0.993034	+	0.117831i	$0.0375942\pi$
$163$	0.937386	+	6.51966i	0.0734217	+	0.510659i	−0.919612	+	0.392828i	$0.871497\pi$
$164$	−0.0938207	+	0.205439i	−0.00732617	+	0.0160421i
$165$	6.87878	−	2.01979i	0.535512	−	0.157241i
$166$	−1.65605	+	1.91119i	−0.128535	+	0.148337i
$167$	−16.0657	−	4.71733i	−1.24320	−	0.365038i	−0.406986	−	0.913434i	$-0.633420\pi$
$167$	−16.0657	−	4.71733i	−1.24320	−	0.365038i	−0.836218	+	0.548397i	$0.815238\pi$
$168$	0.369938	−	0.237745i	0.0285414	−	0.0183424i
$169$	−2.68934	−	5.88883i	−0.206872	−	0.452987i
$170$	−9.29190	−	10.7234i	−0.712656	−	0.822449i
$171$	−2.92293	−	1.87845i	−0.223522	−	0.143649i
$172$	1.36441	−	9.48970i	0.104036	−	0.723583i
$173$	−1.28658	+	8.94836i	−0.0978169	+	0.680331i	0.880626	+	0.473813i	$0.157123\pi$
$173$	−1.28658	+	8.94836i	−0.0978169	+	0.680331i	−0.978443	+	0.206519i	$0.933787\pi$
$174$	1.98148	+	1.27342i	0.150216	+	0.0965379i
$175$	6.19291	+	7.14700i	0.468140	+	0.540263i
$176$	−1.78120	−	3.90028i	−0.134263	−	0.293995i
$177$	−2.71747	+	1.74641i	−0.204258	+	0.131268i
$178$	2.94466	+	0.864631i	0.220712	+	0.0648068i
$179$	11.0862	−	12.7941i	0.828620	−	0.956278i	−0.170960	−	0.985278i	$-0.554687\pi$
$179$	11.0862	−	12.7941i	0.828620	−	0.956278i	0.999579	+	0.0289998i	$0.00923223\pi$
$180$	−10.2391	+	3.00648i	−0.763179	+	0.224090i
$181$	8.97288	−	19.6479i	0.666949	−	1.46042i	−0.208953	−	0.977926i	$-0.567005\pi$
$181$	8.97288	−	19.6479i	0.666949	−	1.46042i	0.875902	−	0.482489i	$-0.160267\pi$
$182$	−0.363562	−	2.52863i	−0.0269490	−	0.187434i
$183$	−3.93953			−0.291219
$184$	3.38769	−	3.39464i	0.249744	−	0.250256i
$185$	29.3581			2.15845
$186$	−0.448334	−	3.11823i	−0.0328734	−	0.228640i
$187$	6.64709	−	14.5551i	0.486083	−	1.06437i
$188$	−0.231074	+	0.0678494i	−0.0168528	+	0.00494843i
$189$	1.67215	−	1.92976i	0.121631	−	0.140370i
$190$	4.51633	+	1.32611i	0.327649	+	0.0962063i
$191$	6.02669	−	3.87312i	0.436076	−	0.280249i	−0.304128	−	0.952631i	$-0.598365\pi$
$191$	6.02669	−	3.87312i	0.436076	−	0.280249i	0.740204	+	0.672382i	$0.234729\pi$
$192$	−0.182677	−	0.400008i	−0.0131836	−	0.0288681i
$193$	0.845872	+	0.976188i	0.0608872	+	0.0702676i	0.785376	−	0.619019i	$-0.212470\pi$
$193$	0.845872	+	0.976188i	0.0608872	+	0.0702676i	−0.724489	+	0.689286i	$0.757924\pi$
$194$	−11.5283	−	7.40879i	−0.827684	−	0.531920i
$195$	0.607880	−	4.22790i	0.0435312	−	0.302766i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	16.8927	+	10.8563i	1.20355	+	0.773478i	0.979568	−	0.201115i	$-0.0644564\pi$
$197$	16.8927	+	10.8563i	1.20355	+	0.773478i	0.223987	+	0.974592i	$0.428093\pi$
$198$	−7.88067	−	9.09478i	−0.560055	−	0.646338i
$199$	−4.69059	−	10.2710i	−0.332507	−	0.728089i	0.667354	−	0.744740i	$-0.267427\pi$
$199$	−4.69059	−	10.2710i	−0.332507	−	0.728089i	−0.999861	+	0.0166514i	$0.994699\pi$
$200$	7.95560	−	5.11275i	0.562546	−	0.361526i
$201$	−5.44649	−	1.59923i	−0.384166	−	0.112801i
$202$	−6.41582	+	7.40425i	−0.451415	+	0.520961i
$203$	−5.13929	+	1.50903i	−0.360707	+	0.105913i
$204$	0.681717	−	1.49275i	0.0477297	−	0.104513i
$205$	−0.122209	−	0.849983i	−0.00853545	−	0.0593654i
$206$	−11.9476			−0.832432
$207$	6.43862	−	11.8202i	0.447515	−	0.821564i
$208$	−2.55463			−0.177132
$209$	0.755418	+	5.25405i	0.0522533	+	0.363430i
$210$	−0.694579	+	1.52092i	−0.0479305	+	0.104953i
$211$	−12.7039	+	3.73019i	−0.874569	+	0.256797i	−0.688058	−	0.725656i	$-0.741536\pi$
$211$	−12.7039	+	3.73019i	−0.874569	+	0.256797i	−0.186512	+	0.982453i	$0.559718\pi$
$212$	6.79110	−	7.83735i	0.466415	−	0.538272i
$213$	−2.96525	−	0.870677i	−0.203176	−	0.0596578i
$214$	14.6374	−	9.40686i	1.00059	−	0.643040i
$215$	15.1431	+	33.1587i	1.03275	+	2.26141i
$216$	−1.67215	−	1.92976i	−0.113775	−	0.131304i
$217$	6.02664	+	3.87309i	0.409115	+	0.262922i
$218$	−2.40632	+	16.7363i	−0.162976	+	1.13353i
$219$	−0.145189	+	1.00981i	−0.00981094	+	0.0682366i
$220$	13.7149	+	8.81406i	0.924661	+	0.594244i
$221$	−6.24304	−	7.20486i	−0.419952	−	0.484651i
$222$	1.41051	+	3.08859i	0.0946673	+	0.207292i
$223$	−2.01942	+	1.29780i	−0.135230	+	0.0869071i	−0.606507	−	0.795078i	$-0.707430\pi$
$223$	−2.01942	+	1.29780i	−0.135230	+	0.0869071i	0.471277	+	0.881985i	$0.343793\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	17.3812	−	20.0589i	1.15874	−	1.33726i
$226$	1.54240	−	0.452890i	0.102599	−	0.0301258i
$227$	−7.06356	+	15.4670i	−0.468825	+	1.02658i	0.516562	+	0.856250i	$0.327212\pi$
$227$	−7.06356	+	15.4670i	−0.468825	+	1.02658i	−0.985387	+	0.170333i	$0.945516\pi$
$228$	0.0774746	+	0.538848i	0.00513088	+	0.0356861i
$229$	18.3918			1.21536			0.607681	−	0.794181i	$-0.292100\pi$
$229$	18.3918			1.21536			0.607681	+	0.794181i	$0.292100\pi$
$230$	−3.85781	+	17.8220i	−0.254377	+	1.17515i
$231$	−1.88553			−0.124059
$232$	0.762274	+	5.30173i	0.0500458	+	0.348076i
$233$	−2.75255	+	6.02725i	−0.180326	+	0.394858i	−0.978111	−	0.208083i	$-0.933278\pi$
$233$	−2.75255	+	6.02725i	−0.180326	+	0.394858i	0.797785	+	0.602942i	$0.206005\pi$
$234$	−6.87946	+	2.01999i	−0.449724	+	0.132051i
$235$	0.599646	−	0.692028i	0.0391166	−	0.0451429i
$236$	−7.04819	−	2.06953i	−0.458798	−	0.134715i
$237$	−1.99886	+	1.28459i	−0.129840	+	0.0834430i
$238$	1.55025	+	3.39457i	0.100488	+	0.220037i
$239$	5.32188	+	6.14178i	0.344244	+	0.397279i	0.901300	−	0.433196i	$-0.142614\pi$
$239$	5.32188	+	6.14178i	0.344244	+	0.397279i	−0.557055	+	0.830475i	$0.688069\pi$
$240$	1.40659	+	0.903958i	0.0907947	+	0.0583502i
$241$	−3.30424	+	22.9815i	−0.212845	+	1.48037i	0.550747	+	0.834672i	$0.314343\pi$
$241$	−3.30424	+	22.9815i	−0.212845	+	1.48037i	−0.763593	+	0.645698i	$0.776566\pi$
$242$	−1.05098	+	7.30970i	−0.0675593	+	0.469886i
$243$	−9.14372	−	5.87631i	−0.586570	−	0.376966i
$244$	−5.86666	−	6.77049i	−0.375574	−	0.433436i
$245$	−1.57950	−	3.45862i	−0.100910	−	0.220963i
$246$	0.0835499	−	0.0536943i	0.00532695	−	0.00342342i
$247$	3.03443	+	0.890988i	0.193076	+	0.0566922i
$248$	4.69135	−	5.41410i	0.297901	−	0.343796i
$249$	1.06701	−	0.313303i	0.0676191	−	0.0198548i
$250$	−7.03956	+	15.4145i	−0.445221	+	0.974898i
$251$	−0.915136	−	6.36491i	−0.0577629	−	0.401750i	−0.998106	−	0.0615214i	$-0.980405\pi$
$251$	−0.915136	−	6.36491i	−0.0577629	−	0.401750i	0.940343	−	0.340228i	$-0.110504\pi$
$252$	2.80662			0.176801
$253$	−20.0889	+	4.39166i	−1.26298	+	0.276101i
$254$	3.20290			0.200968
$255$	0.887991	+	6.17611i	0.0556081	+	0.386763i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	15.8952	−	4.66726i	0.991517	−	0.291136i	0.254546	−	0.967061i	$-0.418074\pi$
$257$	15.8952	−	4.66726i	0.991517	−	0.291136i	0.736971	+	0.675925i	$0.236256\pi$
$258$	−2.76088	+	3.18622i	−0.171885	+	0.198366i
$259$	−7.40855	−	2.17535i	−0.460345	−	0.135170i
$260$	8.17131	−	5.25138i	0.506763	−	0.325677i
$261$	6.24493	+	13.6745i	0.386551	+	0.846429i
$262$	6.16245	+	7.11184i	0.380717	+	0.439371i
$263$	−12.0555	−	7.74762i	−0.743376	−	0.477739i	0.113321	−	0.993558i	$-0.463851\pi$
$263$	−12.0555	−	7.74762i	−0.743376	−	0.477739i	−0.856697	+	0.515820i	$0.827487\pi$
$264$	−0.268339	+	1.86634i	−0.0165151	+	0.114865i
$265$	−5.61149	+	39.0288i	−0.344711	+	2.39752i
$266$	−1.04144	−	0.669292i	−0.0638547	−	0.0410369i
$267$	−0.883782	−	1.01994i	−0.0540866	−	0.0624193i
$268$	−5.36234	−	11.7419i	−0.327557	−	0.717250i
$269$	−2.06191	+	1.32511i	−0.125717	+	0.0807934i	−0.601988	−	0.798505i	$-0.705624\pi$
$269$	−2.06191	+	1.32511i	−0.125717	+	0.0807934i	0.476271	+	0.879299i	$0.341988\pi$
$270$	9.31547	+	2.73527i	0.566921	+	0.166463i
$271$	12.8139	−	14.7880i	0.778387	−	0.898306i	−0.218605	−	0.975813i	$-0.570151\pi$
$271$	12.8139	−	14.7880i	0.778387	−	0.898306i	0.996992	+	0.0775072i	$0.0246961\pi$
$272$	3.58064	−	1.05137i	0.217108	−	0.0637487i
$273$	−0.466673	+	1.02187i	−0.0282444	+	0.0618465i
$274$	2.04987	+	14.2571i	0.123837	+	0.861305i
$275$	−40.5486			−2.44517
$276$	−2.06029	+	0.450402i	−0.124015	+	0.0271110i
$277$	−12.1410			−0.729480			−0.364740	−	0.931109i	$-0.618842\pi$
$277$	−12.1410			−0.729480			−0.364740	+	0.931109i	$0.618842\pi$
$278$	−2.10939	−	14.6711i	−0.126513	−	0.879916i
$279$	8.35247	−	18.2894i	0.500049	−	1.09495i
$280$	−3.64820	+	1.07121i	−0.218022	+	0.0640169i
$281$	−5.62276	+	6.48902i	−0.335426	+	0.387102i	−0.898258	−	0.439469i	$-0.855167\pi$
$281$	−5.62276	+	6.48902i	−0.335426	+	0.387102i	0.562832	+	0.826572i	$0.309712\pi$
$282$	0.101614	+	0.0298366i	0.00605102	+	0.00177674i
$283$	0.886531	−	0.569739i	0.0526988	−	0.0338675i	−0.514026	−	0.857775i	$-0.671847\pi$
$283$	0.886531	−	0.569739i	0.0526988	−	0.0338675i	0.566725	+	0.823907i	$0.308210\pi$
$284$	−2.91944	−	6.39268i	−0.173237	−	0.379336i
$285$	−1.35549	−	1.56431i	−0.0802920	−	0.0926620i
$286$	9.21479	+	5.92199i	0.544882	+	0.350174i
$287$	−0.0321416	+	0.223549i	−0.00189726	+	0.0131957i
$288$	0.399424	−	2.77806i	0.0235363	−	0.163698i
$289$	−2.58570	−	1.66173i	−0.152100	−	0.0977486i
$290$	−13.3366	−	15.3913i	−0.783155	−	0.903809i
$291$	2.50336	+	5.48159i	0.146750	+	0.321337i
$292$	−1.95167	+	1.25426i	−0.114213	+	0.0734002i
$293$	30.9426	+	9.08556i	1.80768	+	0.530784i	0.998395	−	0.0566280i	$-0.0180349\pi$
$293$	30.9426	+	9.08556i	1.80768	+	0.530784i	0.809288	+	0.587412i	$0.199853\pi$
$294$	0.287973	−	0.332338i	0.0167949	−	0.0193824i
$295$	26.7987	−	7.86882i	1.56028	−	0.458140i
$296$	−3.20755	+	7.02356i	−0.186435	+	0.408236i
$297$	1.55814	+	10.8371i	0.0904125	+	0.628833i
$298$	−15.2301			−0.882254
$299$	−2.59199	+	11.9743i	−0.149898	+	0.692489i
$300$	−4.15861			−0.240098
$301$	−1.36441	−	9.48970i	−0.0786434	−	0.546977i
$302$	0.0472485	−	0.103460i	0.00271884	−	0.00595344i
$303$	4.13378	−	1.21379i	0.237479	−	0.0697303i
$304$	−0.810692	+	0.935588i	−0.0464964	+	0.0536597i
$305$	32.6829	+	9.59656i	1.87142	+	0.549498i
$306$	8.81110	−	5.66255i	0.503697	−	0.323706i
$307$	−0.477718	−	1.04606i	−0.0272648	−	0.0597016i	0.895510	−	0.445042i	$-0.146811\pi$
$307$	−0.477718	−	1.04606i	−0.0272648	−	0.0597016i	−0.922774	+	0.385340i	$0.874084\pi$
$308$	−2.80788	−	3.24047i	−0.159994	−	0.184643i
$309$	4.41989	+	2.84049i	0.251439	+	0.161590i
$310$	−3.87646	+	26.9614i	−0.220168	+	1.53130i
$311$	2.28844	−	15.9165i	0.129766	−	0.902539i	−0.816084	−	0.577934i	$-0.803859\pi$
$311$	2.28844	−	15.9165i	0.129766	−	0.902539i	0.945849	−	0.324606i	$-0.105232\pi$
$312$	0.945056	+	0.607351i	0.0535033	+	0.0343845i
$313$	−19.2512	−	22.2171i	−1.08814	−	1.25578i	−0.964677	−	0.263434i	$-0.915145\pi$
$313$	−19.2512	−	22.2171i	−1.08814	−	1.25578i	−0.123464	−	0.992349i	$-0.539401\pi$
$314$	9.78232	+	21.4203i	0.552048	+	1.20882i
$315$	−8.97734	+	5.76939i	−0.505816	+	0.325068i
$316$	−5.18435	−	1.52226i	−0.291643	−	0.0856340i
$317$	14.6904	−	16.9536i	0.825093	−	0.952208i	−0.174379	−	0.984679i	$-0.555792\pi$
$317$	14.6904	−	16.9536i	0.825093	−	0.952208i	0.999473	+	0.0324702i	$0.0103374\pi$
$318$	−4.37558	+	1.28479i	−0.245370	+	0.0720473i
$319$	9.54055	−	20.8909i	0.534168	−	1.16967i
$320$	0.541112	+	3.76351i	0.0302491	+	0.210387i
$321$	−7.65135			−0.427057
$322$	2.29408	−	4.21155i	0.127844	−	0.234701i
$323$	−4.61983			−0.257054
$324$	−1.03847	−	7.22273i	−0.0576929	−	0.401263i
$325$	−10.0359	+	21.9756i	−0.556692	+	1.21898i
$326$	6.31990	−	1.85569i	0.350027	−	0.102777i
$327$	4.86916	−	5.61931i	0.269265	−	0.310749i
$328$	0.216700	+	0.0636288i	0.0119652	+	0.00351331i
$329$	−0.202598	+	0.130202i	−0.0111696	+	0.00717827i
$330$	−2.97819	−	6.52132i	−0.163944	−	0.358987i
$331$	0.529583	+	0.611171i	0.0291085	+	0.0335930i	0.770117	−	0.637902i	$-0.220198\pi$
$331$	0.529583	+	0.611171i	0.0291085	+	0.0335930i	−0.741009	+	0.671495i	$0.765652\pi$
$332$	2.12741	+	1.36721i	0.116757	+	0.0750351i
$333$	−3.08408	+	21.4503i	−0.169007	+	1.17547i
$334$	−2.38292	+	16.5736i	−0.130387	+	0.906865i
$335$	41.2891	+	26.5349i	2.25587	+	1.44976i
$336$	−0.287973	−	0.332338i	−0.0157102	−	0.0181305i
$337$	−5.20583	−	11.3992i	−0.283580	−	0.620953i	0.713216	−	0.700945i	$-0.247238\pi$
$337$	−5.20583	−	11.3992i	−0.283580	−	0.620953i	−0.996796	+	0.0799915i	$0.974511\pi$
$338$	−5.44616	+	3.50003i	−0.296232	+	0.190377i
$339$	−0.678266	−	0.199157i	−0.0368384	−	0.0108167i
$340$	−9.29190	+	10.7234i	−0.503924	+	0.581560i
$341$	−29.4727	+	8.65398i	−1.59604	+	0.468639i
$342$	−1.44335	+	3.16051i	−0.0780477	+	0.170901i
$343$	0.142315	+	0.989821i	0.00768428	+	0.0534453i
$344$	−9.58728			−0.516912
$345$	5.66425	−	5.67588i	0.304953	−	0.305579i
$346$	9.04038			0.486014
$347$	1.88192	+	13.0890i	0.101027	+	0.702657i	0.975886	+	0.218280i	$0.0700446\pi$
$347$	1.88192	+	13.0890i	0.101027	+	0.702657i	−0.874859	+	0.484377i	$0.839046\pi$
$348$	0.978466	−	2.14254i	0.0524513	−	0.114852i
$349$	−13.6938	+	4.02085i	−0.733010	+	0.215231i	−0.626874	−	0.779120i	$-0.715666\pi$
$349$	−13.6938	+	4.02085i	−0.733010	+	0.215231i	−0.106136	+	0.994352i	$0.533848\pi$
$350$	6.19291	−	7.14700i	0.331025	−	0.382023i
$351$	6.25887	+	1.83777i	0.334074	+	0.0980930i
$352$	−3.60709	+	2.31814i	−0.192259	+	0.123557i
$353$	−12.1392	−	26.5812i	−0.646107	−	1.41478i	−0.894921	−	0.446225i	$-0.852768\pi$
$353$	−12.1392	−	26.5812i	−0.646107	−	1.41478i	0.248814	−	0.968551i	$-0.419959\pi$
$354$	2.11537	+	2.44127i	0.112431	+	0.129752i
$355$	22.4792	+	14.4465i	1.19307	+	0.766741i
$356$	0.436761	−	3.03774i	0.0231483	−	0.161000i
$357$	0.233546	−	1.62435i	0.0123605	−	0.0859695i
$358$	−14.2416	−	9.15254i	−0.752694	−	0.483727i
$359$	8.13187	+	9.38468i	0.429184	+	0.495305i	0.928613	−	0.371050i	$-0.121002\pi$
$359$	8.13187	+	9.38468i	0.429184	+	0.495305i	−0.499429	+	0.866355i	$0.666457\pi$
$360$	4.43305	+	9.70703i	0.233642	+	0.511606i
$361$	−14.6946	+	9.44362i	−0.773398	+	0.497033i
$362$	−20.7249	−	6.08537i	−1.08927	−	0.319840i
$363$	2.12664	−	2.45428i	0.111620	−	0.128816i
$364$	−2.45115	+	0.719723i	−0.128475	+	0.0377237i
$365$	3.66437	−	8.02384i	0.191802	−	0.419987i
$366$	0.560654	+	3.89943i	0.0293058	+	0.203827i
$367$	−35.1509			−1.83486			−0.917432	−	0.397894i	$-0.869741\pi$
$367$	−35.1509			−1.83486			−0.917432	+	0.397894i	$0.869741\pi$
$368$	−3.84221	−	2.87010i	−0.200289	−	0.149614i
$369$	0.633871			0.0329980
$370$	−4.17810	−	29.0593i	−0.217209	−	1.51072i
$371$	4.30798	−	9.43316i	0.223659	−	0.489745i
$372$	−3.02268	+	0.887540i	−0.156719	+	0.0460168i
$373$	6.22461	−	7.18359i	0.322298	−	0.371952i	−0.571360	−	0.820699i	$-0.693584\pi$
$373$	6.22461	−	7.18359i	0.322298	−	0.371952i	0.893659	+	0.448747i	$0.148130\pi$
$374$	−15.3529	−	4.50803i	−0.793881	−	0.233104i
$375$	6.26893	−	4.02879i	0.323726	−	0.208046i
$376$	0.100044	+	0.219066i	0.00515938	+	0.0112975i
$377$	−8.96063	−	10.3411i	−0.461496	−	0.532594i
$378$	−2.14809	−	1.38050i	−0.110486	−	0.0710050i
$379$	−4.81172	+	33.4663i	−0.247162	+	1.71905i	0.367302	+	0.930102i	$0.380282\pi$
$379$	−4.81172	+	33.4663i	−0.247162	+	1.71905i	−0.614463	+	0.788945i	$0.710627\pi$
$380$	0.669875	−	4.65908i	0.0343639	−	0.239006i
$381$	−1.18488	−	0.761474i	−0.0607031	−	0.0390115i
$382$	−4.69138	−	5.41414i	−0.240032	−	0.277012i
$383$	4.08289	+	8.94028i	0.208626	+	0.456827i	0.984800	−	0.173692i	$-0.0555696\pi$
$383$	4.08289	+	8.94028i	0.208626	+	0.456827i	−0.776174	+	0.630518i	$0.782842\pi$
$384$	−0.369938	+	0.237745i	−0.0188783	+	0.0121324i
$385$	15.6426	+	4.59308i	0.797220	+	0.234085i
$386$	0.845872	−	0.976188i	0.0430537	−	0.0496867i
$387$	−25.8179	+	7.58083i	−1.31240	+	0.385355i
$388$	−5.69273	+	12.4653i	−0.289005	+	0.632832i
$389$	3.58228	+	24.9153i	0.181629	+	1.26326i	0.852912	+	0.522055i	$0.174834\pi$
$389$	3.58228	+	24.9153i	0.181629	+	1.26326i	−0.671283	+	0.741201i	$0.734256\pi$
$390$	−4.27137			−0.216289
$391$	−1.29507	−	17.8502i	−0.0654944	−	0.902723i
$392$	1.00000			0.0505076
$393$	−0.588921	−	4.09603i	−0.0297071	−	0.206618i
$394$	8.34169	−	18.2658i	0.420248	−	0.920216i
$395$	19.7120	−	5.78797i	0.991819	−	0.291224i
$396$	−7.88067	+	9.09478i	−0.396019	+	0.457030i
$397$	−19.1924	−	5.63539i	−0.963239	−	0.282832i	−0.237950	−	0.971277i	$-0.576475\pi$
$397$	−19.1924	−	5.63539i	−0.963239	−	0.282832i	−0.725289	+	0.688445i	$0.758294\pi$
$398$	−9.49888	+	6.10456i	−0.476136	+	0.305994i
$399$	0.226147	+	0.495194i	0.0113215	+	0.0247907i
$400$	−6.19291	−	7.14700i	−0.309646	−	0.357350i
$401$	−17.9661	−	11.5461i	−0.897184	−	0.576585i	0.00877009	−	0.999962i	$-0.497208\pi$
$401$	−17.9661	−	11.5461i	−0.897184	−	0.576585i	−0.905954	+	0.423377i	$0.860845\pi$
$402$	−0.807839	+	5.61864i	−0.0402913	+	0.280232i
$403$	−2.60452	+	18.1148i	−0.129740	+	0.902363i
$404$	8.24195	+	5.29678i	0.410052	+	0.263525i
$405$	18.1690	+	20.9681i	0.902823	+	1.04191i
$406$	2.22507	+	4.87222i	0.110428	+	0.241804i
$407$	27.8515	−	17.8991i	1.38055	−	0.887224i
$408$	−1.57458	−	0.462337i	−0.0779531	−	0.0228891i
$409$	23.0332	−	26.5817i	1.13892	−	1.31438i	0.196288	−	0.980546i	$-0.437111\pi$
$409$	23.0332	−	26.5817i	1.13892	−	1.31438i	0.942631	−	0.333836i	$-0.108343\pi$
$410$	−0.823939	+	0.241930i	−0.0406915	+	0.0119481i
$411$	2.63124	−	5.76161i	0.129789	−	0.284199i
$412$	1.70033	+	11.8260i	0.0837691	+	0.582627i
$413$	−7.34574			−0.361460
$414$	−12.6162	−	4.69089i	−0.620055	−	0.230544i
$415$	−9.61527			−0.471995
$416$	0.363562	+	2.52863i	0.0178251	+	0.123976i
$417$	−2.70764	+	5.92891i	−0.132594	+	0.290340i
$418$	5.09306	−	1.49546i	0.249110	−	0.0731452i
$419$	3.08597	−	3.56140i	0.150760	−	0.173986i	−0.675346	−	0.737501i	$-0.736006\pi$
$419$	3.08597	−	3.56140i	0.150760	−	0.173986i	0.826106	+	0.563515i	$0.190551\pi$
$420$	1.60428	+	0.471060i	0.0782810	+	0.0229854i
$421$	27.8440	−	17.8942i	1.35703	−	0.872111i	0.358910	−	0.933372i	$-0.383148\pi$
$421$	27.8440	−	17.8942i	1.35703	−	0.872111i	0.998122	+	0.0612607i	$0.0195121\pi$
$422$	5.50017	+	12.0437i	0.267744	+	0.586277i
$423$	0.442631	+	0.510824i	0.0215215	+	0.0248371i
$424$	−8.72405	−	5.60661i	−0.423678	−	0.272281i
$425$	5.02245	−	34.9319i	0.243624	−	1.69444i
$426$	−0.439815	+	3.05898i	−0.0213091	+	0.148208i
$427$	−7.53649	−	4.84341i	−0.364716	−	0.234389i
$428$	−11.3942	−	13.1496i	−0.550761	−	0.635612i
$429$	−2.00098	−	4.38154i	−0.0966084	−	0.211543i
$430$	30.6661	−	19.7079i	1.47885	−	0.950401i
$431$	18.1549	+	5.33076i	0.874490	+	0.256774i	0.688024	−	0.725688i	$-0.258478\pi$
$431$	18.1549	+	5.33076i	0.874490	+	0.256774i	0.186466	+	0.982461i	$0.440296\pi$
$432$	−1.67215	+	1.92976i	−0.0804513	+	0.0928458i
$433$	−30.6863	+	9.01032i	−1.47469	+	0.433008i	−0.917621	−	0.397457i	$-0.869893\pi$
$433$	−30.6863	+	9.01032i	−1.47469	+	0.433008i	−0.557070	+	0.830466i	$0.688075\pi$
$434$	2.97598	−	6.51650i	0.142852	−	0.312802i
$435$	1.27453	+	8.86456i	0.0611091	+	0.425023i
$436$	16.9084			0.809766
$437$	3.56281	+	4.74920i	0.170432	+	0.227185i
$438$	1.02019			0.0487467
$439$	4.02758	+	28.0124i	0.192226	+	1.33696i	0.826100	+	0.563523i	$0.190555\pi$
$439$	4.02758	+	28.0124i	0.192226	+	1.33696i	−0.633874	+	0.773436i	$0.718536\pi$
$440$	6.77250	−	14.8297i	0.322866	−	0.706979i
$441$	2.69293	−	0.790717i	0.128235	−	0.0376532i
$442$	−6.24304	+	7.20486i	−0.296951	+	0.342700i
$443$	−2.58577	−	0.759250i	−0.122854	−	0.0360731i	0.219728	−	0.975561i	$-0.429483\pi$
$443$	−2.58577	−	0.759250i	−0.122854	−	0.0360731i	−0.342581	+	0.939488i	$0.611301\pi$
$444$	2.85641	−	1.83571i	0.135559	−	0.0871187i
$445$	4.84744	+	10.6144i	0.229791	+	0.503172i
$446$	1.57198	+	1.81417i	0.0744356	+	0.0859032i
$447$	5.63419	+	3.62087i	0.266488	+	0.171261i
$448$	0.142315	−	0.989821i	0.00672374	−	0.0467647i
$449$	−1.00346	+	6.97920i	−0.0473561	+	0.329369i	0.952347	+	0.305016i	$0.0986617\pi$
$449$	−1.00346	+	6.97920i	−0.0473561	+	0.329369i	−0.999703	+	0.0243531i	$0.992247\pi$
$450$	−22.3284	−	14.3496i	−1.05257	−	0.676445i
$451$	−0.634156	−	0.731855i	−0.0298612	−	0.0344617i
$452$	−0.667787	−	1.46225i	−0.0314101	−	0.0687784i
$453$	−0.0420761	+	0.0270406i	−0.00197691	+	0.00127048i
$454$	16.3148	+	4.79047i	0.765694	+	0.224828i
$455$	6.36083	−	7.34079i	0.298200	−	0.344142i
$456$	0.522337	−	0.153372i	0.0244607	−	0.00718231i
$457$	−12.4276	+	27.2127i	−0.581341	+	1.27296i	0.359195	+	0.933263i	$0.383051\pi$
$457$	−12.4276	+	27.2127i	−0.581341	+	1.27296i	−0.940535	+	0.339696i	$0.889676\pi$
$458$	−2.61742	−	18.2046i	−0.122304	−	0.850644i
$459$	−9.52895			−0.444774
$460$	18.1896	+	1.28221i	0.848097	+	0.0597831i
$461$	−2.09849			−0.0977366			−0.0488683	−	0.998805i	$-0.515561\pi$
$461$	−2.09849			−0.0977366			−0.0488683	+	0.998805i	$0.515561\pi$
$462$	0.268339	+	1.86634i	0.0124842	+	0.0868298i
$463$	13.5838	−	29.7444i	0.631293	−	1.38234i	−0.275720	−	0.961238i	$-0.588916\pi$
$463$	13.5838	−	29.7444i	0.631293	−	1.38234i	0.907014	−	0.421102i	$-0.138356\pi$
$464$	5.13929	−	1.50903i	0.238585	−	0.0700550i
$465$	7.84398	−	9.05244i	0.363756	−	0.419797i
$466$	6.35763	+	1.86677i	0.294512	+	0.0864764i
$467$	−23.4194	+	15.0507i	−1.08372	+	0.696466i	−0.955414	−	0.295269i	$-0.904591\pi$
$467$	−23.4194	+	15.0507i	−1.08372	+	0.696466i	−0.128307	+	0.991734i	$0.540954\pi$
$468$	2.97848	+	6.52196i	0.137680	+	0.301478i
$469$	−8.45320	−	9.75551i	−0.390332	−	0.450468i
$470$	−0.770323	−	0.495056i	−0.0355323	−	0.0228352i
$471$	1.47371	−	10.2499i	0.0679050	−	0.472290i
$472$	−1.04541	+	7.27097i	−0.0481188	+	0.334674i
$473$	34.5822	+	22.2246i	1.59009	+	1.02189i
$474$	1.55598	+	1.79570i	0.0714686	+	0.0824791i
$475$	4.86334	+	10.6492i	0.223146	+	0.488620i
$476$	3.13940	−	2.01757i	0.143894	−	0.0924750i
$477$	−27.9266	−	8.19998i	−1.27867	−	0.375451i
$478$	5.32188	−	6.14178i	0.243417	−	0.280919i
$479$	41.1636	−	12.0867i	1.88081	−	0.552257i	0.884494	−	0.466552i	$-0.154504\pi$
$479$	41.1636	−	12.0867i	1.88081	−	0.552257i	0.996321	−	0.0857044i	$-0.0273141\pi$
$480$	0.694579	−	1.52092i	0.0317030	−	0.0694200i
$481$	−2.80718	−	19.5244i	−0.127996	−	0.890234i
$482$	23.2179			1.05754
$483$	−1.84994	+	1.01261i	−0.0841754	+	0.0460753i
$484$	7.38487			0.335676
$485$	−7.41524	−	51.5742i	−0.336709	−	2.34186i
$486$	−4.51521	+	9.88694i	−0.204814	+	0.448481i
$487$	−4.79761	+	1.40871i	−0.217401	+	0.0638346i	−0.388619	−	0.921399i	$-0.627048\pi$
$487$	−4.79761	+	1.40871i	−0.217401	+	0.0638346i	0.171219	+	0.985233i	$0.445230\pi$
$488$	−5.86666	+	6.77049i	−0.265571	+	0.306486i
$489$	−2.77915	−	0.816033i	−0.125678	−	0.0369023i
$490$	−3.19863	+	2.05563i	−0.144499	+	0.0928640i
$491$	−14.6997	−	32.1878i	−0.663387	−	1.45261i	−0.879332	−	0.476209i	$-0.842011\pi$
$491$	−14.6997	−	32.1878i	−0.663387	−	1.45261i	0.215945	−	0.976405i	$-0.430717\pi$
$492$	−0.0650382	−	0.0750580i	−0.00293215	−	0.00338388i
$493$	16.8154	+	10.8066i	0.757327	+	0.486705i
$494$	0.450075	−	3.13034i	0.0202498	−	0.140841i
$495$	6.51180	−	45.2906i	0.292684	−	2.03566i
$496$	−6.02664	−	3.87309i	−0.270604	−	0.173907i
$497$	−4.60221	−	5.31123i	−0.206437	−	0.238241i
$498$	−0.461966	−	1.01156i	−0.0207012	−	0.0453292i
$499$	28.5547	−	18.3510i	1.27828	−	0.821502i	0.287607	−	0.957748i	$-0.407140\pi$
$499$	28.5547	−	18.3510i	1.27828	−	0.821502i	0.990675	+	0.136247i	$0.0435039\pi$
$500$	16.2594	+	4.77420i	0.727144	+	0.213509i
$501$	4.82181	−	5.56467i	0.215423	−	0.248611i
$502$	−6.16989	+	1.81164i	−0.275376	+	0.0808576i
$503$	0.393231	−	0.861055i	0.0175333	−	0.0383926i	−0.900663	−	0.434519i	$-0.856918\pi$
$503$	0.393231	−	0.861055i	0.0175333	−	0.0383926i	0.918196	+	0.396126i	$0.129646\pi$
$504$	−0.399424	−	2.77806i	−0.0177918	−	0.123744i
$505$	−37.2512			−1.65765
$506$	7.20591	+	19.2595i	0.320342	+	0.856188i
$507$	2.84686			0.126433
$508$	−0.455821	−	3.17030i	−0.0202238	−	0.140659i
$509$	2.32687	−	5.09514i	0.103137	−	0.225838i	−0.851028	−	0.525121i	$-0.824020\pi$
$509$	2.32687	−	5.09514i	0.103137	−	0.225838i	0.954164	+	0.299283i	$0.0967473\pi$
$510$	5.98687	−	1.75790i	0.265103	−	0.0778413i
$511$	−1.51925	+	1.75331i	−0.0672076	+	0.0775617i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	2.65925	−	1.70900i	0.117409	−	0.0754541i
$514$	−6.88188	−	15.0692i	−0.303547	−	0.664675i
$515$	−29.7487	−	34.3318i	−1.31088	−	1.51284i
$516$	3.54670	+	2.27933i	0.156135	+	0.100342i
$517$	0.146957	−	1.02211i	0.00646315	−	0.0449522i
$518$	−1.09886	+	7.64273i	−0.0482811	+	0.335802i
$519$	−3.34438	−	2.14931i	−0.146802	−	0.0943440i
$520$	−6.36083	−	7.34079i	−0.278941	−	0.321915i
$521$	−3.50020	−	7.66438i	−0.153347	−	0.335782i	0.817331	−	0.576169i	$-0.195453\pi$
$521$	−3.50020	−	7.66438i	−0.153347	−	0.335782i	−0.970677	+	0.240387i	$0.922726\pi$
$522$	12.6466	−	8.12744i	0.553524	−	0.355729i
$523$	−27.5626	−	8.09310i	−1.20523	−	0.353886i	−0.383377	−	0.923592i	$-0.625239\pi$
$523$	−27.5626	−	8.09310i	−1.20523	−	0.353886i	−0.821849	+	0.569705i	$0.807057\pi$
$524$	6.16245	−	7.11184i	0.269208	−	0.310682i
$525$	−3.99016	+	1.17162i	−0.174145	+	0.0511335i
$526$	−5.95308	+	13.0354i	−0.259567	+	0.568371i
$527$	−3.80468	−	26.4621i	−0.165734	−	1.15271i
$528$	1.88553			0.0820570
$529$	−17.3513	+	15.0974i	−0.754405	+	0.656409i
$530$	39.4301			1.71274
$531$	2.93407	+	20.4069i	0.127328	+	0.885583i
$532$	−0.514267	+	1.12609i	−0.0222963	+	0.0488221i
$533$	−0.553588	+	0.162548i	−0.0239786	+	0.00704074i
$534$	−0.883782	+	1.01994i	−0.0382450	+	0.0441371i
$535$	63.4767	+	18.6384i	2.74434	+	0.805810i
$536$	−10.8592	+	6.97880i	−0.469047	+	0.301438i
$537$	3.09256	+	6.77175i	0.133454	+	0.292223i
$538$	1.60506	+	1.85234i	0.0691992	+	0.0798601i
$539$	−3.60709	−	2.31814i	−0.155368	−	0.0998492i
$540$	1.38170	−	9.60992i	0.0594588	−	0.413545i
$541$	−1.34749	+	9.37198i	−0.0579330	+	0.402933i	0.940135	+	0.340802i	$0.110699\pi$
$541$	−1.34749	+	9.37198i	−0.0579330	+	0.402933i	−0.998068	+	0.0621308i	$0.980210\pi$
$542$	−16.4611	−	10.5789i	−0.707063	−	0.454402i
$543$	6.22016	+	7.17844i	0.266933	+	0.308057i
$544$	−1.55025	−	3.39457i	−0.0664663	−	0.145541i
$545$	−54.0837	+	34.7575i	−2.31669	+	1.48885i
$546$	1.07789	+	0.316496i	0.0461292	+	0.0135448i
$547$	15.8839	−	18.3309i	0.679145	−	0.783775i	−0.306633	−	0.951828i	$-0.599203\pi$
$547$	15.8839	−	18.3309i	0.679145	−	0.783775i	0.985778	+	0.168053i	$0.0537480\pi$
$548$	13.8203	−	4.05801i	0.590374	−	0.173349i
$549$	−10.4450	+	22.8713i	−0.445782	+	0.976125i
$550$	5.77067	+	40.1359i	0.246062	+	1.71140i
$551$	−6.63083			−0.282483
$552$	0.739028	+	1.97522i	0.0314551	+	0.0840711i
$553$	−5.40322			−0.229768
$554$	1.72784	+	12.0174i	0.0734089	+	0.510570i
$555$	−5.36306	+	11.7435i	−0.227649	+	0.498483i
$556$	−14.2216	+	4.17584i	−0.603131	+	0.177095i
$557$	−2.88607	+	3.33071i	−0.122287	+	0.141127i	−0.813592	−	0.581437i	$-0.802491\pi$
$557$	−2.88607	+	3.33071i	−0.122287	+	0.141127i	0.691305	+	0.722563i	$0.257036\pi$
$558$	−19.2919	−	5.66460i	−0.816690	−	0.239802i
$559$	20.6040	−	13.2414i	0.871455	−	0.560050i
$560$	1.57950	+	3.45862i	0.0667459	+	0.146153i
$561$	4.60788	+	5.31777i	0.194545	+	0.224517i
$562$	7.22317	+	4.64205i	0.304691	+	0.195813i
$563$	−0.451143	+	3.13777i	−0.0190134	+	0.132241i	−0.997117	−	0.0758764i	$-0.975825\pi$
$563$	−0.451143	+	3.13777i	−0.0190134	+	0.132241i	0.978104	+	0.208117i	$0.0667336\pi$
$564$	0.0150717	−	0.104826i	0.000634632	−	0.00441396i
$565$	5.14185	+	3.30447i	0.216319	+	0.139020i
$566$	−0.690106	−	0.796425i	−0.0290073	−	0.0334762i
$567$	−3.03128	−	6.63759i	−0.127302	−	0.278752i
$568$	−5.91214	+	3.79950i	−0.248068	+	0.159423i
$569$	−7.90865	−	2.32219i	−0.331548	−	0.0973512i	0.111722	−	0.993740i	$-0.464363\pi$
$569$	−7.90865	−	2.32219i	−0.331548	−	0.0973512i	−0.443270	+	0.896388i	$0.646182\pi$
$570$	−1.35549	+	1.56431i	−0.0567750	+	0.0655219i
$571$	−0.221343	+	0.0649922i	−0.00926292	+	0.00271984i	−0.286361	−	0.958122i	$-0.592446\pi$
$571$	−0.221343	+	0.0649922i	−0.00926292	+	0.00271984i	0.277098	+	0.960842i	$0.410627\pi$
$572$	4.55031	−	9.96378i	0.190258	−	0.416607i
$573$	0.448337	+	3.11825i	0.0187296	+	0.130267i
$574$	0.225848			0.00942672
$575$	−39.7834	+	21.7764i	−1.65908	+	0.908138i
$576$	−2.80662			−0.116943
$577$	0.747804	+	5.20109i	0.0311315	+	0.216524i	0.999449	−	0.0331989i	$-0.0105695\pi$
$577$	0.747804	+	5.20109i	0.0311315	+	0.216524i	−0.968317	+	0.249723i	$0.919660\pi$
$578$	−1.27683	+	2.79587i	−0.0531091	+	0.116293i
$579$	−0.545004	+	0.160028i	−0.0226496	+	0.00665053i
$580$	−13.3366	+	15.3913i	−0.553774	+	0.639090i
$581$	2.42642	+	0.712462i	0.100665	+	0.0295579i
$582$	5.06953	−	3.25799i	0.210139	−	0.135048i
$583$	18.4716	+	40.4471i	0.765014	+	1.67515i
$584$	1.51925	+	1.75331i	0.0628670	+	0.0725524i
$585$	−22.9338	−	14.7387i	−0.948196	−	0.609368i
$586$	4.58949	−	31.9206i	0.189590	−	1.31863i
$587$	2.47005	−	17.1796i	0.101950	−	0.709078i	−0.873173	−	0.487411i	$-0.837941\pi$
$587$	2.47005	−	17.1796i	0.101950	−	0.709078i	0.975123	−	0.221667i	$-0.0711496\pi$
$588$	−0.369938	−	0.237745i	−0.0152560	−	0.00980444i
$589$	5.80770	+	6.70244i	0.239302	+	0.276169i
$590$	−11.6026	−	25.4061i	−0.477671	−	1.04595i
$591$	−7.42851	+	4.77401i	−0.305568	+	0.196377i
$592$	7.40855	+	2.17535i	0.304490	+	0.0894062i
$593$	−14.7402	+	17.0111i	−0.605306	+	0.698561i	−0.972848	−	0.231446i	$-0.925654\pi$
$593$	−14.7402	+	17.0111i	−0.605306	+	0.698561i	0.367541	+	0.930007i	$0.380200\pi$
$594$	10.5051	−	3.08456i	0.431028	−	0.126561i
$595$	−5.89438	+	12.9069i	−0.241646	+	0.529131i
$596$	2.16746	+	15.0750i	0.0887828	+	0.617498i
$597$	4.96533			0.203217
$598$	12.2213	+	0.861488i	0.499764	+	0.0352289i
$599$	21.4950			0.878260			0.439130	−	0.898424i	$-0.355287\pi$
$599$	21.4950			0.878260			0.439130	+	0.898424i	$0.355287\pi$
$600$	0.591832	+	4.11628i	0.0241615	+	0.168047i
$601$	−3.90022	+	8.54028i	−0.159093	+	0.348365i	−0.972346	−	0.233545i	$-0.924967\pi$
$601$	−3.90022	+	8.54028i	−0.159093	+	0.348365i	0.813253	+	0.581911i	$0.197695\pi$
$602$	−9.19893	+	2.70105i	−0.374920	+	0.110087i
$603$	−23.7249	+	27.3800i	−0.966154	+	1.11500i
$604$	−0.109131	−	0.0320437i	−0.00444047	−	0.00130384i
$605$	−23.6214	+	15.1806i	−0.960348	+	0.617178i
$606$	−1.78973	−	3.91896i	−0.0727029	−	0.159197i
$607$	−25.2888	−	29.1848i	−1.02644	−	1.18458i	−0.982638	−	0.185535i	$-0.940598\pi$
$607$	−25.2888	−	29.1848i	−1.02644	−	1.18458i	−0.0438027	−	0.999040i	$-0.513947\pi$
$608$	1.04144	+	0.669292i	0.0422359	+	0.0271434i
$609$	0.335208	−	2.33142i	0.0135833	−	0.0944739i
$610$	4.84762	−	33.7160i	0.196275	−	1.36512i
$611$	−0.517564	−	0.332618i	−0.0209384	−	0.0134563i
$612$	−6.85886	−	7.91555i	−0.277253	−	0.319967i
$613$	−11.0494	−	24.1948i	−0.446281	−	0.977220i	−0.990403	−	0.138213i	$-0.955864\pi$
$613$	−11.0494	−	24.1948i	−0.446281	−	0.977220i	0.544121	−	0.839007i	$-0.316863\pi$
$614$	−0.967423	+	0.621725i	−0.0390420	+	0.0250908i
$615$	0.362325	+	0.106388i	0.0146103	+	0.00428998i
$616$	−2.80788	+	3.24047i	−0.113133	+	0.130562i
$617$	2.98626	−	0.876846i	0.120222	−	0.0353005i	−0.221068	−	0.975258i	$-0.570954\pi$
$617$	2.98626	−	0.876846i	0.120222	−	0.0353005i	0.341290	+	0.939958i	$0.389136\pi$
$618$	2.18256	−	4.77915i	0.0877956	−	0.192246i
$619$	1.87839	+	13.0645i	0.0754989	+	0.525106i	0.992114	+	0.125336i	$0.0400009\pi$
$619$	1.87839	+	13.0645i	0.0754989	+	0.525106i	−0.916615	+	0.399770i	$0.869090\pi$
$620$	27.2386			1.09393
$621$	7.34873	+	9.79580i	0.294894	+	0.393092i
$622$	−16.0801			−0.644754
$623$	−0.436761	−	3.03774i	−0.0174985	−	0.121704i
$624$	0.466673	−	1.02187i	0.0186819	−	0.0409076i
$625$	−16.4530	+	4.83104i	−0.658120	+	0.193242i
$626$	−19.2512	+	22.2171i	−0.769433	+	0.887973i
$627$	−2.23966	−	0.657622i	−0.0894433	−	0.0262629i
$628$	19.8101	−	12.7312i	0.790509	−	0.508029i
$629$	11.9700	+	26.2106i	0.477274	+	1.04508i
$630$	6.98827	+	8.06489i	0.278419	+	0.321313i
$631$	−7.79426	−	5.00907i	−0.310285	−	0.199408i	0.376225	−	0.926528i	$-0.377222\pi$
$631$	−7.79426	−	5.00907i	−0.310285	−	0.199408i	−0.686510	+	0.727120i	$0.740858\pi$
$632$	−0.768958	+	5.34822i	−0.0305875	+	0.212741i
$633$	0.828603	−	5.76306i	0.0329340	−	0.229061i
$634$	−18.8717	−	12.1281i	−0.749490	−	0.481668i
$635$	7.97498	+	9.20362i	0.316477	+	0.365234i
$636$	1.89442	+	4.14820i	0.0751186	+	0.164487i
$637$	−2.14909	+	1.38114i	−0.0851502	+	0.0547227i
$638$	−22.0360	−	6.47036i	−0.872415	−	0.256164i
$639$	−12.9167	+	14.9066i	−0.510975	+	0.589697i
$640$	3.64820	−	1.07121i	0.144208	−	0.0423432i
$641$	4.85712	−	10.6356i	0.191845	−	0.420081i	−0.789128	−	0.614229i	$-0.789467\pi$
$641$	4.85712	−	10.6356i	0.191845	−	0.420081i	0.980972	+	0.194148i	$0.0621943\pi$
$642$	1.08890	+	7.57347i	0.0429755	+	0.298901i
$643$	35.1178			1.38491			0.692456	−	0.721460i	$-0.256529\pi$
$643$	35.1178			1.38491			0.692456	+	0.721460i	$0.256529\pi$
$644$	−4.49517	−	1.67136i	−0.177134	−	0.0658609i
$645$	−16.0300			−0.631183
$646$	0.657470	+	4.57281i	0.0258678	+	0.179915i
$647$	7.35869	−	16.1133i	0.289300	−	0.633478i	−0.708056	−	0.706157i	$-0.750427\pi$
$647$	7.35869	−	16.1133i	0.289300	−	0.633478i	0.997355	+	0.0726783i	$0.0231546\pi$
$648$	−7.00142	+	2.05580i	−0.275042	+	0.0807596i
$649$	20.6260	−	23.8037i	0.809641	−	0.934376i
$650$	23.1801	+	6.80630i	0.909200	+	0.266965i
$651$	−2.65020	+	1.70318i	−0.103869	+	0.0667528i
$652$	−2.73622	−	5.99148i	−0.107159	−	0.234644i
$653$	−2.26079	−	2.60909i	−0.0884717	−	0.102102i	0.709788	−	0.704416i	$-0.248791\pi$
$653$	−2.26079	−	2.60909i	−0.0884717	−	0.102102i	−0.798259	+	0.602314i	$0.794245\pi$
$654$	−6.25507	−	4.01989i	−0.244593	−	0.157190i
$655$	−5.09203	+	35.4158i	−0.198962	+	1.38381i
$656$	0.0321416	−	0.223549i	0.00125492	−	0.00872814i
$657$	5.47761	+	3.52025i	0.213702	+	0.137338i
$658$	0.157710	+	0.182007i	0.00614816	+	0.00709535i
$659$	−5.49015	−	12.0218i	−0.213866	−	0.468301i	0.772046	−	0.635567i	$-0.219234\pi$
$659$	−5.49015	−	12.0218i	−0.213866	−	0.468301i	−0.985912	+	0.167266i	$0.946506\pi$
$660$	−6.03110	+	3.87595i	−0.234760	+	0.150871i
$661$	−36.0372	−	10.5815i	−1.40168	−	0.411571i	−0.508421	−	0.861108i	$-0.669771\pi$
$661$	−36.0372	−	10.5815i	−1.40168	−	0.411571i	−0.893262	+	0.449537i	$0.851589\pi$
$662$	0.529583	−	0.611171i	0.0205828	−	0.0237538i
$663$	4.02246	−	1.18110i	0.156219	−	0.0458702i
$664$	1.05053	−	2.30033i	0.0407683	−	0.0892702i
$665$	−0.669875	−	4.65908i	−0.0259766	−	0.180671i
$666$	21.6708			0.839728
$667$	−1.85881	−	25.6203i	−0.0719734	−	0.992024i
$668$	16.7440			0.647844
$669$	−0.150228	−	1.04486i	−0.00580816	−	0.0403967i
$670$	20.3888	−	44.6452i	0.787687	−	1.72479i
$671$	36.8565	−	10.8220i	1.42283	−	0.417780i
$672$	−0.287973	+	0.332338i	−0.0111088	+	0.0128202i
$673$	29.3857	+	8.62842i	1.13274	+	0.332601i	0.793782	−	0.608202i	$-0.208109\pi$
$673$	29.3857	+	8.62842i	1.13274	+	0.332601i	0.338953	+	0.940803i	$0.389927\pi$
$674$	−10.5423	+	6.77512i	−0.406074	+	0.260968i
$675$	10.0312	+	21.9653i	0.386102	+	0.845446i
$676$	4.23948	+	4.89262i	0.163057	+	0.188178i
$677$	40.4539	+	25.9981i	1.55477	+	0.999190i	0.984018	+	0.178067i	$0.0569844\pi$
$677$	40.4539	+	25.9981i	1.55477	+	0.999190i	0.570751	+	0.821123i	$0.306652\pi$
$678$	−0.100602	+	0.699705i	−0.00386361	+	0.0268720i
$679$	−1.95024	+	13.5642i	−0.0748435	+	0.520548i
$680$	11.9367	+	7.67122i	0.457750	+	0.294178i
$681$	−4.89658	−	5.65095i	−0.187637	−	0.216545i
$682$	12.7603	+	27.9412i	0.488617	+	1.06992i
$683$	−9.93674	+	6.38596i	−0.380219	+	0.244352i	−0.716765	−	0.697315i	$-0.754378\pi$
$683$	−9.93674	+	6.38596i	−0.380219	+	0.244352i	0.336546	+	0.941667i	$0.390741\pi$
$684$	3.33375	+	0.978876i	0.127469	+	0.0374283i
$685$	−35.8642	+	41.3895i	−1.37030	+	1.58141i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	−3.35976	+	7.35685i	−0.128183	+	0.280681i
$688$	1.36441	+	9.48970i	0.0520178	+	0.361791i
$689$	26.4923			1.00928
$690$	−6.42421	−	4.79883i	−0.244566	−	0.182689i
$691$	−31.7389			−1.20740			−0.603702	−	0.797210i	$-0.706308\pi$
$691$	−31.7389			−1.20740			−0.603702	+	0.797210i	$0.706308\pi$
$692$	−1.28658	−	8.94836i	−0.0489084	−	0.340166i
$693$	−4.99915	+	10.9466i	−0.189902	+	0.415828i
$694$	12.6880	−	3.72553i	0.481630	−	0.141419i
$695$	36.9056	−	42.5914i	1.39991	−	1.61558i
$696$	−2.25998	−	0.663591i	−0.0856645	−	0.0251534i
$697$	0.709027	−	0.455664i	0.0268563	−	0.0172595i
$698$	5.92875	+	12.9822i	0.224406	+	0.491382i
$699$	−1.90812	−	2.20209i	−0.0721717	−	0.0832905i
$700$	−7.95560	−	5.11275i	−0.300693	−	0.193244i
$701$	4.79036	−	33.3177i	0.180929	−	1.25839i	−0.673643	−	0.739057i	$-0.735271\pi$
$701$	4.79036	−	33.3177i	0.180929	−	1.25839i	0.854572	−	0.519333i	$-0.173820\pi$
$702$	0.928335	−	6.45671i	0.0350377	−	0.243693i
$703$	−8.04128	−	5.16782i	−0.303283	−	0.194908i
$704$	2.80788	+	3.24047i	0.105826	+	0.122130i
$705$	0.167275	+	0.366281i	0.00629993	+	0.0137949i
$706$	−24.5831	+	15.7986i	−0.925196	+	0.594588i
$707$	9.40037	+	2.76020i	0.353537	+	0.103808i
$708$	2.11537	−	2.44127i	0.0795006	−	0.0917486i
$709$	−7.45871	+	2.19007i	−0.280118	+	0.0822499i	−0.418774	−	0.908091i	$-0.637540\pi$
$709$	−7.45871	+	2.19007i	−0.280118	+	0.0822499i	0.138656	+	0.990341i	$0.455722\pi$
$710$	11.1003	−	24.3064i	0.416588	−	0.912201i
$711$	2.15818	+	15.0104i	0.0809379	+	0.562936i
$712$	−3.06898			−0.115015
$713$	−24.2690	+	24.3188i	−0.908881	+	0.910746i
$714$	−1.64105			−0.0614147
$715$	5.92714	+	41.2242i	0.221663	+	1.54170i
$716$	−7.03259	+	15.3992i	−0.262820	+	0.575496i
$717$	−3.42895	+	1.00683i	−0.128056	+	0.0376007i
$718$	8.13187	−	9.38468i	0.303479	−	0.350233i
$719$	−5.27753	−	1.54962i	−0.196818	−	0.0577911i	0.181838	−	0.983329i	$-0.441795\pi$
$719$	−5.27753	−	1.54962i	−0.196818	−	0.0577911i	−0.378656	+	0.925537i	$0.623614\pi$
$720$	8.97734	−	5.76939i	0.334566	−	0.215012i
$721$	4.96323	+	10.8680i	0.184840	+	0.404744i
$722$	11.4387	+	13.2010i	0.425706	+	0.491291i
$723$	−8.58918	−	5.51993i	−0.319435	−	0.205288i
$724$	−3.07397	+	21.3800i	−0.114243	+	0.794580i
$725$	7.20871	−	50.1376i	0.267725	−	1.86207i
$726$	−2.73195	−	1.75572i	−0.101392	−	0.0651607i
$727$	−8.00871	−	9.24254i	−0.297027	−	0.342787i	0.587545	−	0.809192i	$-0.300095\pi$
$727$	−8.00871	−	9.24254i	−0.297027	−	0.342787i	−0.884572	+	0.466405i	$0.845549\pi$
$728$	1.06123	+	2.32377i	0.0393319	+	0.0861248i
$729$	−14.3950	+	9.25108i	−0.533147	+	0.342633i
$730$	−8.46367	−	2.48516i	−0.313254	−	0.0919798i
$731$	−23.4295	+	27.0391i	−0.866573	+	1.00008i
$732$	3.77995	−	1.10989i	0.139711	−	0.0410229i
$733$	−13.5041	+	29.5698i	−0.498784	+	1.09218i	0.478078	+	0.878317i	$0.341333\pi$
$733$	−13.5041	+	29.5698i	−0.498784	+	1.09218i	−0.976863	+	0.213868i	$0.931394\pi$
$734$	5.00250	+	34.7931i	0.184646	+	1.28424i
$735$	1.67201			0.0616731
$736$	−2.29408	+	4.21155i	−0.0845609	+	0.155240i
$737$	55.3481			2.03877
$738$	−0.0902092	−	0.627419i	−0.00332065	−	0.0230956i
$739$	14.5375	−	31.8327i	0.534771	−	1.17098i	−0.428768	−	0.903415i	$-0.641052\pi$
$739$	14.5375	−	31.8327i	0.534771	−	1.17098i	0.963539	−	0.267570i	$-0.0862205\pi$
$740$	−28.1689	+	8.27114i	−1.03551	+	0.304053i
$741$	−0.910724	+	1.05103i	−0.0334563	+	0.0386106i
$742$	−9.95023	−	2.92165i	−0.365285	−	0.107257i
$743$	−16.7227	+	10.7470i	−0.613497	+	0.394271i	−0.810167	−	0.586199i	$-0.800624\pi$
$743$	−16.7227	+	10.7470i	−0.613497	+	0.394271i	0.196670	+	0.980470i	$0.436987\pi$
$744$	1.30868	+	2.86561i	0.0479785	+	0.105058i
$745$	−37.9217	−	43.7639i	−1.38934	−	1.60339i
$746$	−7.99632	−	5.13893i	−0.292766	−	0.188149i
$747$	1.01009	−	7.02531i	0.0369572	−	0.257043i
$748$	−2.27719	+	15.8382i	−0.0832624	+	0.579102i
$749$	−14.6374	−	9.40686i	−0.534837	−	0.343719i
$750$	−4.87995	−	5.63176i	−0.178190	−	0.205643i
$751$	−1.26369	−	2.76710i	−0.0461127	−	0.100973i	0.885174	−	0.465261i	$-0.154040\pi$
$751$	−1.26369	−	2.76710i	−0.0461127	−	0.100973i	−0.931286	+	0.364288i	$0.881312\pi$
$752$	0.202598	−	0.130202i	0.00738800	−	0.00474798i
$753$	2.71319	+	0.796664i	0.0988741	+	0.0290320i
$754$	−8.96063	+	10.3411i	−0.326327	+	0.376601i
$755$	0.414939	−	0.121837i	0.0151012	−	0.00443410i
$756$	−1.06074	+	2.32269i	−0.0385787	+	0.0844755i
$757$	−5.28968	−	36.7905i	−0.192257	−	1.33717i	−0.826017	−	0.563645i	$-0.809399\pi$
$757$	−5.28968	−	36.7905i	−0.192257	−	1.33717i	0.633761	−	0.773529i	$-0.281510\pi$
$758$	33.8104			1.22805
$759$	1.91310	−	8.83798i	0.0694410	−	0.320799i
$760$	−4.70699			−0.170741
$761$	4.23404	+	29.4484i	0.153484	+	1.06750i	0.910322	+	0.413901i	$0.135834\pi$
$761$	4.23404	+	29.4484i	0.153484	+	1.06750i	−0.756838	+	0.653603i	$0.773257\pi$
$762$	−0.585098	+	1.28119i	−0.0211959	+	0.0464125i
$763$	16.2235	−	4.76365i	0.587330	−	0.172456i
$764$	−4.69138	+	5.41414i	−0.169728	+	0.195877i
$765$	38.2104	+	11.2196i	1.38150	+	0.405645i
$766$	8.26822	−	5.31366i	0.298743	−	0.191991i
$767$	−7.79554	−	17.0698i	−0.281481	−	0.616357i
$768$	0.287973	+	0.332338i	0.0103913	+	0.0119922i
$769$	1.30834	+	0.840821i	0.0471801	+	0.0303208i	0.564018	−	0.825762i	$-0.309255\pi$
$769$	1.30834	+	0.840821i	0.0471801	+	0.0303208i	−0.516838	+	0.856083i	$0.672891\pi$
$770$	2.32016	−	16.1370i	0.0836126	−	0.581538i
$771$	−1.03676	+	7.21081i	−0.0373380	+	0.259691i
$772$	−1.08663	−	0.698336i	−0.0391087	−	0.0251337i
$773$	15.8280	+	18.2665i	0.569293	+	0.656999i	0.965268	−	0.261262i	$-0.0841388\pi$
$773$	15.8280	+	18.2665i	0.569293	+	0.656999i	−0.395975	+	0.918261i	$0.629593\pi$
$774$	11.1779	+	24.4763i	0.401783	+	0.879782i
$775$	−56.9930	+	36.6272i	−2.04725	+	1.31569i
$776$	13.1486	+	3.86079i	0.472008	+	0.138594i
$777$	2.22353	−	2.56609i	0.0797687	−	0.0920580i
$778$	24.1519	−	7.09164i	0.865887	−	0.254247i
$779$	−0.116146	+	0.254325i	−0.00416138	+	0.00911214i
$780$	0.607880	+	4.22790i	0.0217656	+	0.151383i
$781$	30.1334			1.07826
$782$	−17.4842	+	3.82223i	−0.625234	+	0.136683i
$783$	−13.6769			−0.488772
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	−37.1945	+	81.4446i	−1.32753	+	2.90688i
$786$	−3.97053	+	1.16585i	−0.141624	+	0.0415846i
$787$	10.8369	−	12.5065i	0.386295	−	0.445808i	−0.528982	−	0.848633i	$-0.677426\pi$
$787$	10.8369	−	12.5065i	0.386295	−	0.445808i	0.915277	+	0.402825i	$0.131972\pi$
$788$	−19.2670	−	5.65730i	−0.686358	−	0.201533i
$789$	5.30138	−	3.40699i	0.188734	−	0.121292i
$790$	−8.53437	−	18.6877i	−0.303639	−	0.664877i
$791$	−1.05270	−	1.21488i	−0.0374297	−	0.0431962i
$792$	10.1237	+	6.50614i	0.359732	+	0.231186i
$793$	3.25702	−	22.6531i	0.115660	−	0.804434i
$794$	−2.84667	+	19.7990i	−0.101025	+	0.702642i
$795$	−14.5867	−	9.37431i	−0.517338	−	0.332473i
$796$	7.39425	+	8.53342i	0.262082	+	0.302459i
$797$	9.32796	+	20.4254i	0.330413	+	0.723504i	0.999812	−	0.0193994i	$-0.00617540\pi$
$797$	9.32796	+	20.4254i	0.330413	+	0.723504i	−0.669399	+	0.742903i	$0.733448\pi$
$798$	0.457969	−	0.294319i	0.0162119	−	0.0104188i
$799$	0.862323	+	0.253201i	0.0305068	+	0.00895760i
$800$	−6.19291	+	7.14700i	−0.218953	+	0.252685i
$801$	−8.26456	+	2.42669i	−0.292014	+	0.0857430i
$802$	−8.87174	+	19.4264i	−0.313272	+	0.685970i
$803$	−1.41567	−	9.84617i	−0.0499577	−	0.347464i
$804$	5.67642			0.200192
$805$	17.8141	−	3.89435i	0.627864	−	0.137258i
$806$	18.3011			0.644628
$807$	−0.153390	−	1.06685i	−0.00539957	−	0.0375548i
$808$	4.06991	−	8.91187i	0.143179	−	0.313518i
$809$	2.32433	−	0.682486i	0.0817192	−	0.0239949i	−0.240617	−	0.970620i	$-0.577350\pi$
$809$	2.32433	−	0.682486i	0.0817192	−	0.0239949i	0.322337	+	0.946625i	$0.395532\pi$
$810$	18.1690	−	20.9681i	0.638392	−	0.736744i
$811$	9.97934	+	2.93020i	0.350422	+	0.102893i	0.452206	−	0.891913i	$-0.350637\pi$
$811$	9.97934	+	2.93020i	0.350422	+	0.102893i	−0.101785	+	0.994806i	$0.532455\pi$
$812$	4.50597	−	2.89581i	0.158128	−	0.101623i
$813$	3.57450	+	7.82707i	0.125363	+	0.274507i
$814$	−21.6806	−	25.0207i	−0.759904	−	0.876976i
$815$	21.0684	+	13.5398i	0.737994	+	0.474280i
$816$	−0.233546	+	1.62435i	−0.00817573	+	0.0568635i
$817$	1.68909	−	11.7479i	0.0590937	−	0.411006i
$818$	−29.5891	−	19.0158i	−1.03456	−	0.664872i
$819$	4.69528	+	5.41864i	0.164066	+	0.189343i
$820$	0.356727	+	0.781122i	0.0124574	+	0.0272780i
$821$	31.6708	−	20.3536i	1.10532	−	0.710344i	0.145049	−	0.989424i	$-0.453666\pi$
$821$	31.6708	−	20.3536i	1.10532	−	0.710344i	0.960268	+	0.279080i	$0.0900295\pi$
$822$	−6.07743	−	1.78449i	−0.211975	−	0.0622414i
$823$	3.79232	−	4.37657i	0.132192	−	0.152557i	−0.685794	−	0.727795i	$-0.740545\pi$
$823$	3.79232	−	4.37657i	0.132192	−	0.152557i	0.817986	+	0.575238i	$0.195091\pi$
$824$	11.4637	−	3.36604i	0.399356	−	0.117262i
$825$	7.40732	−	16.2198i	0.257890	−	0.564700i
$826$	1.04541	+	7.27097i	0.0363744	+	0.252990i
$827$	8.90654			0.309711			0.154855	−	0.987937i	$-0.450509\pi$
$827$	8.90654			0.309711			0.154855	+	0.987937i	$0.450509\pi$
$828$	−2.84766	+	13.1554i	−0.0989631	+	0.457182i
$829$	−48.2830			−1.67694			−0.838468	−	0.544950i	$-0.816549\pi$
$829$	−48.2830			−1.67694			−0.838468	+	0.544950i	$0.816549\pi$
$830$	1.36840	+	9.51740i	0.0474977	+	0.330354i
$831$	2.21788	−	4.85648i	0.0769374	−	0.168469i
$832$	2.45115	−	0.719723i	0.0849784	−	0.0249519i
$833$	2.44381	−	2.82031i	0.0846731	−	0.0977180i
$834$	6.25390	+	1.83631i	0.216555	+	0.0635863i
$835$	−53.5578	+	34.4195i	−1.85344	+	1.19114i
$836$	−2.20505	−	4.82839i	−0.0762634	−	0.166994i
$837$	11.9791	+	13.8246i	0.414058	+	0.477848i
$838$	−3.96433	−	2.54772i	−0.136945	−	0.0880095i
$839$	1.61591	−	11.2389i	0.0557874	−	0.388010i	−0.942729	−	0.333559i	$-0.891750\pi$
$839$	1.61591	−	11.2389i	0.0557874	−	0.388010i	0.998516	−	0.0544505i	$-0.0173407\pi$
$840$	0.237952	−	1.65499i	0.00821013	−	0.0571027i
$841$	−0.261250	−	0.167895i	−0.00900862	−	0.00578949i
$842$	−21.6747	−	25.0139i	−0.746960	−	0.862037i
$843$	−1.56850	−	3.43455i	−0.0540222	−	0.118292i
$844$	11.1383	−	7.15818i	0.383397	−	0.246395i
$845$	−23.6179	−	6.93485i	−0.812481	−	0.238566i
$846$	0.442631	−	0.510824i	0.0152180	−	0.0175625i
$847$	7.08573	−	2.08056i	0.243469	−	0.0714888i
$848$	−4.30798	+	9.43316i	−0.147937	+	0.323936i
$849$	0.0659508	+	0.458698i	0.00226342	+	0.0157425i
$850$	−35.2911			−1.21047
$851$	17.7133	−	32.5188i	0.607205	−	1.11473i
$852$	3.09044			0.105877
$853$	−4.76916	−	33.1702i	−0.163293	−	1.13573i	−0.892373	−	0.451298i	$-0.850961\pi$
$853$	−4.76916	−	33.1702i	−0.163293	−	1.13573i	0.729080	−	0.684428i	$-0.239948\pi$
$854$	−3.72155	+	8.14906i	−0.127349	+	0.278855i
$855$	−12.6756	+	3.72190i	−0.433497	+	0.127286i
$856$	−11.3942	+	13.1496i	−0.389446	+	0.449445i
$857$	29.2046	+	8.57524i	0.997609	+	0.292925i	0.739475	−	0.673184i	$-0.235074\pi$
$857$	29.2046	+	8.57524i	0.997609	+	0.292925i	0.258135	+	0.966109i	$0.416892\pi$
$858$	−4.05217	+	2.60417i	−0.138339	+	0.0889050i
$859$	16.1557	+	35.3761i	0.551225	+	1.20702i	0.956207	+	0.292691i	$0.0945506\pi$
$859$	16.1557	+	35.3761i	0.551225	+	1.20702i	−0.404982	+	0.914325i	$0.632722\pi$
$860$	−23.8716	−	27.5493i	−0.814014	−	0.939422i
$861$	−0.0835499	−	0.0536943i	−0.00284737	−	0.00182990i
$862$	2.69279	−	18.7287i	0.0917167	−	0.637904i
$863$	−6.09037	+	42.3594i	−0.207319	+	1.44193i	0.574540	+	0.818476i	$0.305181\pi$
$863$	−6.09037	+	42.3594i	−0.207319	+	1.44193i	−0.781859	+	0.623456i	$0.785728\pi$
$864$	2.14809	+	1.38050i	0.0730796	+	0.0469654i
$865$	22.5098	+	25.9777i	0.765357	+	0.883270i
$866$	13.2857	+	29.0917i	0.451467	+	0.988576i
$867$	1.13705	−	0.730739i	0.0386163	−	0.0248172i
$868$	−6.87370	−	2.01830i	−0.233308	−	0.0685055i
$869$	15.1716	−	17.5090i	0.514662	−	0.593952i
$870$	8.59295	−	2.52312i	0.291328	−	0.0855417i
$871$	13.6988	−	29.9962i	0.464166	−	1.01638i
$872$	−2.40632	−	16.7363i	−0.0814882	−	0.566763i
$873$	38.4612			1.30171
$874$	4.19382	−	4.20243i	0.141858	−	0.142149i
$875$	16.9459			0.572875
$876$	−0.145189	−	1.00981i	−0.00490547	−	0.0341183i
$877$	−6.18556	+	13.5445i	−0.208872	+	0.457365i	−0.984853	−	0.173391i	$-0.944528\pi$
$877$	−6.18556	+	13.5445i	−0.208872	+	0.457365i	0.775982	+	0.630756i	$0.217255\pi$
$878$	27.1541	−	7.97316i	0.916407	−	0.269081i
$879$	−9.28680	+	10.7175i	−0.313236	+	0.361493i
$880$	−15.6426	−	4.59308i	−0.527312	−	0.154833i
$881$	13.3025	−	8.54901i	0.448173	−	0.288023i	−0.297021	−	0.954871i	$-0.595993\pi$
$881$	13.3025	−	8.54901i	0.448173	−	0.288023i	0.745194	+	0.666848i	$0.232357\pi$
$882$	−1.16591	−	2.55299i	−0.0392583	−	0.0859638i
$883$	30.8267	+	35.5759i	1.03740	+	1.19723i	0.980025	+	0.198873i	$0.0637281\pi$
$883$	30.8267	+	35.5759i	1.03740	+	1.19723i	0.0573764	+	0.998353i	$0.481726\pi$
$884$	8.02000	+	5.15414i	0.269742	+	0.173352i
$885$	−1.74793	+	12.1572i	−0.0587562	+	0.408658i
$886$	−0.383529	+	2.66750i	−0.0128849	+	0.0896165i
$887$	28.3804	+	18.2389i	0.952919	+	0.612404i	0.922030	−	0.387119i	$-0.126530\pi$
$887$	28.3804	+	18.2389i	0.952919	+	0.612404i	0.0308893	+	0.999523i	$0.490166\pi$
$888$	−2.22353	−	2.56609i	−0.0746168	−	0.0861124i
$889$	−1.33053	−	2.91346i	−0.0446247	−	0.0977144i
$890$	9.81652	−	6.30869i	0.329050	−	0.211468i
$891$	30.0204	+	8.81478i	1.00572	+	0.295306i
$892$	1.57198	−	1.81417i	0.0526339	−	0.0607428i
$893$	−0.286060	+	0.0839949i	−0.00957264	+	0.00281078i
$894$	2.78219	−	6.09214i	0.0930503	−	0.203752i
$895$	−9.16051	−	63.7128i	−0.306202	−	2.12968i
$896$	−1.00000			−0.0334077
$897$	−4.31630	−	3.22424i	−0.144117	−	0.107654i
$898$	7.05097			0.235294
$899$	−5.46084	−	37.9810i	−0.182129	−	1.26674i
$900$	−11.0259	+	24.1433i	−0.367528	+	0.804775i
$901$	−37.1323	+	10.9030i	−1.23706	+	0.363233i
$902$	−0.634156	+	0.731855i	−0.0211151	+	0.0243681i
$903$	4.04520	+	1.18778i	0.134616	+	0.0395268i
$904$	−1.35233	+	0.869090i	−0.0449778	+	0.0289055i
$905$	−34.1168	−	74.7055i	−1.13408	−	2.48329i
$906$	0.0327534	+	0.0377995i	0.00108816	+	0.00125580i
$907$	8.35111	+	5.36693i	0.277294	+	0.178206i	0.671895	−	0.740647i	$-0.265481\pi$
$907$	8.35111	+	5.36693i	0.277294	+	0.178206i	−0.394601	+	0.918853i	$0.629117\pi$
$908$	2.41987	−	16.8305i	0.0803061	−	0.558541i
$909$	3.91325	−	27.2172i	0.129794	−	0.902739i
$910$	−8.17131	−	5.25138i	−0.270876	−	0.174082i
$911$	−11.5254	−	13.3010i	−0.381854	−	0.440683i	0.531989	−	0.846752i	$-0.321445\pi$
$911$	−11.5254	−	13.3010i	−0.381854	−	0.440683i	−0.913843	+	0.406068i	$0.866899\pi$
$912$	−0.226147	−	0.495194i	−0.00748849	−	0.0163975i
$913$	−9.12183	+	5.86225i	−0.301889	+	0.194012i
$914$	28.7044	+	8.42837i	0.949457	+	0.278786i
$915$	−9.80912	+	11.3203i	−0.324280	+	0.374239i
$916$	−17.6468	+	5.18156i	−0.583066	+	0.171204i
$917$	3.90919	−	8.55992i	0.129093	−	0.282674i
$918$	1.35611	+	9.43196i	0.0447584	+	0.311301i
$919$	−25.0757			−0.827171			−0.413586	−	0.910465i	$-0.635724\pi$
$919$	−25.0757			−0.827171			−0.413586	+	0.910465i	$0.635724\pi$
$920$	−1.31950	−	18.1870i	−0.0435027	−	0.599607i
$921$	0.505699			0.0166633
$922$	0.298647	+	2.07713i	0.00983541	+	0.0684067i
$923$	7.45810	−	16.3310i	0.245486	−	0.537540i
$924$	1.80915	−	0.531214i	0.0595167	−	0.0174757i
$925$	47.8175	−	55.1843i	1.57223	−	1.81445i
$926$	−31.3748	−	9.21248i	−1.03104	−	0.302741i
$927$	28.2094	−	18.1291i	0.926517	−	0.595436i
$928$	−2.22507	−	4.87222i	−0.0730414	−	0.159938i
$929$	15.4581	+	17.8396i	0.507164	+	0.585299i	0.950370	−	0.311121i	$-0.100704\pi$
$929$	15.4581	+	17.8396i	0.507164	+	0.585299i	−0.443206	+	0.896420i	$0.646159\pi$
$930$	−10.0766	−	6.47585i	−0.330425	−	0.212351i
$931$	−0.176180	+	1.22536i	−0.00577407	+	0.0401595i
$932$	0.942983	−	6.55859i	0.0308884	−	0.214834i
$933$	5.94866	+	3.82297i	0.194750	+	0.125158i
$934$	18.2305	+	21.0391i	0.596520	+	0.688420i
$935$	−25.2737	−	55.3416i	−0.826537	−	1.80986i
$936$	6.03169	−	3.87633i	0.197152	−	0.126702i
$937$	−27.9336	−	8.20205i	−0.912552	−	0.267949i	−0.208437	−	0.978036i	$-0.566838\pi$
$937$	−27.9336	−	8.20205i	−0.912552	−	0.267949i	−0.704115	+	0.710086i	$0.748656\pi$
$938$	−8.45320	+	9.75551i	−0.276007	+	0.318529i
$939$	12.4038	−	3.64207i	0.404781	−	0.118854i
$940$	−0.380389	+	0.832936i	−0.0124069	+	0.0271674i
$941$	4.67804	+	32.5365i	0.152500	+	1.06066i	0.912011	+	0.410165i	$0.134529\pi$
$941$	4.67804	+	32.5365i	0.152500	+	1.06066i	−0.759512	+	0.650494i	$0.774562\pi$
$942$	−10.3553			−0.337394
$943$	−1.01523	−	0.377474i	−0.0330603	−	0.0122923i
$944$	7.34574			0.239084
$945$	−1.38170	−	9.60992i	−0.0449466	−	0.312611i
$946$	17.0769	−	37.3931i	0.555217	−	1.21575i
$947$	13.3533	−	3.92089i	0.433924	−	0.127412i	−0.0574733	−	0.998347i	$-0.518304\pi$
$947$	13.3533	−	3.92089i	0.433924	−	0.127412i	0.491398	+	0.870935i	$0.336486\pi$
$948$	1.55598	−	1.79570i	0.0505359	−	0.0583215i
$949$	−5.68657	−	1.66973i	−0.184594	−	0.0542016i
$950$	9.84872	−	6.32939i	0.319535	−	0.205352i
$951$	4.09797	+	8.97330i	0.132886	+	0.290979i
$952$	−2.44381	−	2.82031i	−0.0792044	−	0.0914068i
$953$	−2.13951	−	1.37498i	−0.0693055	−	0.0445400i	0.505529	−	0.862810i	$-0.331297\pi$
$953$	−2.13951	−	1.37498i	−0.0693055	−	0.0445400i	−0.574835	+	0.818270i	$0.694934\pi$
$954$	−4.14215	+	28.8093i	−0.134107	+	0.932735i
$955$	3.87649	−	26.9616i	0.125440	−	0.872456i
$956$	−6.83665	−	4.39365i	−0.221113	−	0.142101i
$957$	6.61368	+	7.63259i	0.213790	+	0.246727i
$958$	−17.8219	−	39.0245i	−0.575799	−	1.26083i
$959$	12.1172	−	7.78726i	0.391285	−	0.251464i
$960$	−1.60428	−	0.471060i	−0.0517780	−	0.0152034i
$961$	−13.3076	+	15.3578i	−0.429277	+	0.495412i
$962$	−18.9261	+	5.55721i	−0.610203	+	0.179172i
$963$	−20.2863	+	44.4207i	−0.653716	+	1.43144i
$964$	−3.30424	−	22.9815i	−0.106423	−	0.740185i
$965$	4.91125			0.158099
$966$	1.26558	+	1.68701i	0.0407193	+	0.0542785i
$967$	20.3330			0.653865			0.326932	−	0.945048i	$-0.393985\pi$
$967$	20.3330			0.653865			0.326932	+	0.945048i	$0.393985\pi$
$968$	−1.05098	−	7.30970i	−0.0337797	−	0.234943i
$969$	0.843938	−	1.84797i	0.0271112	−	0.0593652i
$970$	−49.9939	+	14.6795i	−1.60521	+	0.471332i
$971$	8.21403	−	9.47949i	0.263601	−	0.304211i	−0.608484	−	0.793566i	$-0.708222\pi$
$971$	8.21403	−	9.47949i	0.263601	−	0.304211i	0.872085	+	0.489355i	$0.162768\pi$
$972$	10.4289	+	3.06220i	0.334507	+	0.0982200i
$973$	−12.4691	+	8.01338i	−0.399740	+	0.256897i
$974$	2.07714	+	4.54830i	0.0665558	+	0.145737i
$975$	−6.95706	−	8.02888i	−0.222804	−	0.257130i
$976$	7.53649	+	4.84341i	0.241237	+	0.155034i
$977$	−2.49301	+	17.3392i	−0.0797583	+	0.554731i	0.910287	+	0.413979i	$0.135861\pi$
$977$	−2.49301	+	17.3392i	−0.0797583	+	0.554731i	−0.990045	+	0.140752i	$0.955048\pi$
$978$	−0.412212	+	2.86700i	−0.0131811	+	0.0916766i
$979$	11.0701	+	7.11431i	0.353801	+	0.227374i
$980$	2.48992	+	2.87352i	0.0795376	+	0.0917913i
$981$	−19.7137	−	43.1671i	−0.629411	−	1.37822i
$982$	−29.7682	+	19.1308i	−0.949941	+	0.610490i
$983$	0.875916	+	0.257192i	0.0279374	+	0.00820316i	0.295671	−	0.955290i	$-0.404457\pi$
$983$	0.875916	+	0.257192i	0.0279374	+	0.00820316i	−0.267734	+	0.963493i	$0.586275\pi$
$984$	−0.0650382	+	0.0750580i	−0.00207334	+	0.00239276i
$985$	73.2572	−	21.5103i	2.33417	−	0.685374i
$986$	8.30352	−	18.1822i	0.264438	−	0.579039i
$987$	−0.0150717	−	0.104826i	−0.000479737	−	0.00333664i
$988$	−3.16253			−0.100614
$989$	45.8652	+	3.23308i	1.45843	+	0.102806i
$990$	−45.7563			−1.45423
$991$	−4.14034	−	28.7967i	−0.131522	−	0.914757i	−0.943572	−	0.331168i	$-0.892557\pi$
$991$	−4.14034	−	28.7967i	−0.131522	−	0.914757i	0.812049	−	0.583589i	$-0.198352\pi$
$992$	−2.97598	+	6.51650i	−0.0944876	+	0.206899i
$993$	−0.341216	+	0.100190i	−0.0108282	+	0.00317943i
$994$	−4.60221	+	5.31123i	−0.145973	+	0.168462i
$995$	−41.1930	−	12.0954i	−1.30591	−	0.383449i
$996$	−0.935523	+	0.601224i	−0.0296432	+	0.0190505i
$997$	−17.7604	−	38.8898i	−0.562477	−	1.23165i	−0.950707	−	0.310090i	$-0.899641\pi$
$997$	−17.7604	−	38.8898i	−0.562477	−	1.23165i	0.388230	−	0.921562i	$-0.373087\pi$
$998$	−22.2279	−	25.6524i	−0.703613	−	0.812012i
$999$	−16.5861	−	10.6592i	−0.524761	−	0.337244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.141.2	✓	40
23.8	even	11	inner	322.2.i.d.169.2	yes	40
23.10	odd	22		7406.2.a.bv.1.7		20
23.13	even	11		7406.2.a.bu.1.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.141.2	✓	40	1.1	even	1	trivial
322.2.i.d.169.2	yes	40	23.8	even	11	inner
7406.2.a.bu.1.7		20	23.13	even	11
7406.2.a.bv.1.7		20	23.10	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.182677 + 0.400008i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.48992 - 2.87352i) q^{5} +(0.421934 + 0.123891i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.83795 + 2.12110i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.182677 + 0.400008i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.48992 - 2.87352i) q^{5} +(0.421934 + 0.123891i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.83795 + 2.12110i) q^{9} +(-3.19863 - 2.05563i) q^{10} +(0.610212 - 4.24412i) q^{11} +(0.0625825 - 0.435271i) q^{12} +(-2.14909 - 1.38114i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.694579 + 1.52092i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.58064 + 1.05137i) q^{17} +(1.83795 - 2.12110i) q^{18} +(-1.18781 + 0.348774i) q^{19} +(-1.57950 + 3.45862i) q^{20} +(-0.0625825 - 0.435271i) q^{21} -4.28776 q^{22} +(-1.68058 - 4.49173i) q^{23} -0.439747 q^{24} +(-1.34585 - 9.36058i) q^{25} +(-1.06123 + 2.32377i) q^{26} +(-2.45001 + 0.719388i) q^{27} +(0.654861 - 0.755750i) q^{28} +(5.13929 + 1.50903i) q^{29} +(1.40659 - 0.903958i) q^{30} +(-2.97598 - 6.51650i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.58621 + 1.01939i) q^{33} +(0.531091 - 3.69382i) q^{34} +(-0.541112 + 3.76351i) q^{35} +(-2.36108 - 1.51737i) q^{36} +(5.05639 + 5.83538i) q^{37} +(0.514267 + 1.12609i) q^{38} +(0.945056 - 0.607351i) q^{39} +(3.64820 + 1.07121i) q^{40} +(0.147899 - 0.170685i) q^{41} +(-0.421934 + 0.123891i) q^{42} +(-3.98270 + 8.72090i) q^{43} +(0.610212 + 4.24412i) q^{44} +10.6714 q^{45} +(-4.20684 + 2.30271i) q^{46} +0.240829 q^{47} +(0.0625825 + 0.435271i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-9.07377 + 2.66430i) q^{50} +(-1.07466 + 1.24022i) q^{51} +(2.45115 + 0.719723i) q^{52} +(-8.72405 + 5.60661i) q^{53} +(1.06074 + 2.32269i) q^{54} +(-10.6762 - 12.3210i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(0.0774746 - 0.538848i) q^{57} +(0.762274 - 5.30173i) q^{58} +(6.17963 + 3.97141i) q^{59} +(-1.09493 - 1.26362i) q^{60} +(3.72155 + 8.14906i) q^{61} +(-6.02664 + 3.87309i) q^{62} +(-2.69293 - 0.790717i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-9.31980 + 2.73654i) q^{65} +(0.783276 - 1.71514i) q^{66} +(1.83706 + 12.7770i) q^{67} -3.73181 q^{68} +(2.10373 + 0.148294i) q^{69} +3.80222 q^{70} +(1.00016 + 6.95624i) q^{71} +(-1.16591 + 2.55299i) q^{72} +(2.22598 - 0.653608i) q^{73} +(5.05639 - 5.83538i) q^{74} +(3.99016 + 1.17162i) q^{75} +(1.04144 - 0.669292i) q^{76} +(1.78120 + 3.90028i) q^{77} +(-0.735664 - 0.849002i) q^{78} +(4.54548 + 2.92120i) q^{79} +(0.541112 - 3.76351i) q^{80} +(-1.03847 + 7.22273i) q^{81} +(-0.189996 - 0.122103i) q^{82} +(-1.65605 - 1.91119i) q^{83} +(0.182677 + 0.400008i) q^{84} +(11.9367 - 7.67122i) q^{85} +(9.19893 + 2.70105i) q^{86} +(-1.54246 + 1.78009i) q^{87} +(4.11407 - 1.20800i) q^{88} +(-1.27490 + 2.79164i) q^{89} +(-1.51870 - 10.5628i) q^{90} +2.55463 q^{91} +(2.87797 + 3.83631i) q^{92} +3.15029 q^{93} +(-0.0342736 - 0.238378i) q^{94} +(-1.95536 + 4.28163i) q^{95} +(0.421934 - 0.123891i) q^{96} +(8.97403 - 10.3566i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(10.1237 - 6.50614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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Database

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