LMFDB - Embedded newform 483.2.q.d.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	483.169
Dual form			483.2.q.d.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.275145 + 1.91367i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-1.66745 - 0.489608i) q^{4} +(-1.20808 - 1.39419i) q^{5} +(1.85504 - 0.544688i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.210547 + 0.461033i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.275145 + 1.91367i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-1.66745 - 0.489608i) q^{4} +(-1.20808 - 1.39419i) q^{5} +(1.85504 - 0.544688i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.210547 + 0.461033i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(3.00043 - 1.92826i) q^{10} +(-0.691395 - 4.80876i) q^{11} +(0.247321 + 1.72016i) q^{12} +(-5.09940 + 3.27718i) q^{13} +(-1.26608 + 1.46113i) q^{14} +(-0.766351 + 1.67807i) q^{15} +(-3.74827 - 2.40887i) q^{16} +(-6.18009 + 1.81464i) q^{17} +(-1.26608 - 1.46113i) q^{18} +(0.373684 + 0.109723i) q^{19} +(1.33180 + 2.91623i) q^{20} +(0.142315 - 0.989821i) q^{21} +9.39262 q^{22} +(-0.428202 - 4.77668i) q^{23} +0.506835 q^{24} +(0.227245 - 1.58052i) q^{25} +(-4.86838 - 10.6603i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-1.13805 - 1.31338i) q^{28} +(-0.921113 + 0.270463i) q^{29} +(-3.00043 - 1.92826i) q^{30} +(0.399100 - 0.873907i) q^{31} +(4.97729 - 5.74410i) q^{32} +(-4.08698 + 2.62655i) q^{33} +(-1.77220 - 12.3260i) q^{34} +(-0.262540 - 1.82601i) q^{35} +(1.46197 - 0.939551i) q^{36} +(-0.0741282 + 0.0855485i) q^{37} +(-0.312792 + 0.684918i) q^{38} +(5.09940 + 3.27718i) q^{39} +(0.897126 - 0.263420i) q^{40} +(-5.82688 - 6.72457i) q^{41} +(1.85504 + 0.544688i) q^{42} +(4.69251 + 10.2752i) q^{43} +(-1.20154 + 8.35688i) q^{44} +1.84478 q^{45} +(9.25881 + 0.494839i) q^{46} -10.6332 q^{47} +(-0.634096 + 4.41023i) q^{48} +(0.415415 + 0.909632i) q^{49} +(2.96208 + 0.869744i) q^{50} +(4.21796 + 4.86778i) q^{51} +(10.1075 - 2.96784i) q^{52} +(1.27137 + 0.817059i) q^{53} +(-0.803143 + 1.75864i) q^{54} +(-5.86908 + 6.77328i) q^{55} +(-0.426377 + 0.274016i) q^{56} +(-0.0554259 - 0.385495i) q^{57} +(-0.264139 - 1.83713i) q^{58} +(7.68380 - 4.93808i) q^{59} +(2.09945 - 2.42290i) q^{60} +(1.20419 - 2.63680i) q^{61} +(1.56256 + 1.00420i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(3.78728 + 4.37076i) q^{64} +(10.7295 + 3.15046i) q^{65} +(-3.90184 - 8.54383i) q^{66} +(0.257551 - 1.79130i) q^{67} +11.1935 q^{68} +(-4.16714 + 2.37381i) q^{69} +3.56661 q^{70} +(0.141644 - 0.985153i) q^{71} +(-0.210547 - 0.461033i) q^{72} +(0.383307 + 0.112549i) q^{73} +(-0.143316 - 0.165395i) q^{74} +(-1.53210 + 0.449864i) q^{75} +(-0.569378 - 0.365917i) q^{76} +(2.01817 - 4.41918i) q^{77} +(-7.67453 + 8.85688i) q^{78} +(-2.28897 + 1.47103i) q^{79} +(1.16977 + 8.13592i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(14.4719 - 9.30050i) q^{82} +(-9.69155 + 11.1846i) q^{83} +(-0.721928 + 1.58080i) q^{84} +(9.99598 + 6.42402i) q^{85} +(-20.9544 + 6.15277i) q^{86} +(0.628666 + 0.725519i) q^{87} +(2.36257 + 0.693713i) q^{88} +(7.74611 + 16.9616i) q^{89} +(-0.507582 + 3.53031i) q^{90} -6.06166 q^{91} +(-1.62469 + 8.17453i) q^{92} -0.960726 q^{93} +(2.92568 - 20.3485i) q^{94} +(-0.298462 - 0.653542i) q^{95} +(-7.29266 - 2.14132i) q^{96} +(0.977938 + 1.12860i) q^{97} +(-1.85504 + 0.544688i) q^{98} +(4.08698 + 2.62655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.275145	+	1.91367i	−0.194557	+	1.35317i	0.625203	+	0.780462i	$0.285016\pi$
$2$	−0.275145	+	1.91367i	−0.194557	+	1.35317i	−0.819759	+	0.572708i	$0.805893\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−1.66745	−	0.489608i	−0.833726	−	0.244804i
$5$	−1.20808	−	1.39419i	−0.540268	−	0.623502i	0.418320	−	0.908300i	$-0.362619\pi$
$5$	−1.20808	−	1.39419i	−0.540268	−	0.623502i	−0.958588	+	0.284797i	$0.908074\pi$
$6$	1.85504	−	0.544688i	0.757316	−	0.222368i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$8$	−0.210547	+	0.461033i	−0.0744395	+	0.163000i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	3.00043	−	1.92826i	0.948818	−	0.609768i
$11$	−0.691395	−	4.80876i	−0.208463	−	1.44989i	−0.778174	−	0.628049i	$-0.783854\pi$
$11$	−0.691395	−	4.80876i	−0.208463	−	1.44989i	0.569710	−	0.821846i	$-0.307055\pi$
$12$	0.247321	+	1.72016i	0.0713955	+	0.496567i
$13$	−5.09940	+	3.27718i	−1.41432	+	0.908927i	−0.999999	−	0.00120466i	$-0.999617\pi$
$13$	−5.09940	+	3.27718i	−1.41432	+	0.908927i	−0.414319	+	0.910132i	$0.635980\pi$
$14$	−1.26608	+	1.46113i	−0.338373	+	0.390503i
$15$	−0.766351	+	1.67807i	−0.197871	+	0.433277i
$16$	−3.74827	−	2.40887i	−0.937069	−	0.602217i
$17$	−6.18009	+	1.81464i	−1.49889	+	0.440114i	−0.925367	−	0.379073i	$-0.876243\pi$
$17$	−6.18009	+	1.81464i	−1.49889	+	0.440114i	−0.573525	+	0.819188i	$0.694425\pi$
$18$	−1.26608	−	1.46113i	−0.298417	−	0.344391i
$19$	0.373684	+	0.109723i	0.0857289	+	0.0251723i	0.324316	−	0.945949i	$-0.394866\pi$
$19$	0.373684	+	0.109723i	0.0857289	+	0.0251723i	−0.238587	+	0.971121i	$0.576684\pi$
$20$	1.33180	+	2.91623i	0.297799	+	0.652090i
$21$	0.142315	−	0.989821i	0.0310556	−	0.215997i
$22$	9.39262			2.00251
$23$	−0.428202	−	4.77668i	−0.0892862	−	0.996006i
$23$	−0.428202	−	4.77668i	−0.0892862	−	0.996006i
$24$	0.506835			0.103457
$25$	0.227245	−	1.58052i	0.0454490	−	0.316105i
$26$	−4.86838	−	10.6603i	−0.954769	−	2.09065i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	−1.13805	−	1.31338i	−0.215071	−	0.248205i
$29$	−0.921113	+	0.270463i	−0.171046	+	0.0502238i	−0.366134	−	0.930562i	$-0.619319\pi$
$29$	−0.921113	+	0.270463i	−0.171046	+	0.0502238i	0.195088	+	0.980786i	$0.437501\pi$
$30$	−3.00043	−	1.92826i	−0.547800	−	0.352050i
$31$	0.399100	−	0.873907i	0.0716805	−	0.156958i	−0.870400	−	0.492345i	$-0.836140\pi$
$31$	0.399100	−	0.873907i	0.0716805	−	0.156958i	0.942080	+	0.335387i	$0.108867\pi$
$32$	4.97729	−	5.74410i	0.879869	−	1.01542i
$33$	−4.08698	+	2.62655i	−0.711453	+	0.457223i
$34$	−1.77220	−	12.3260i	−0.303931	−	2.11388i
$35$	−0.262540	−	1.82601i	−0.0443774	−	0.308651i
$36$	1.46197	−	0.939551i	0.243662	−	0.156592i
$37$	−0.0741282	+	0.0855485i	−0.0121866	+	0.0140641i	−0.761810	−	0.647800i	$-0.775689\pi$
$37$	−0.0741282	+	0.0855485i	−0.0121866	+	0.0140641i	0.749624	+	0.661864i	$0.230235\pi$
$38$	−0.312792	+	0.684918i	−0.0507415	+	0.111108i
$39$	5.09940	+	3.27718i	0.816557	+	0.524769i
$40$	0.897126	−	0.263420i	0.141848	−	0.0416504i
$41$	−5.82688	−	6.72457i	−0.910005	−	1.05020i	−0.998534	−	0.0541282i	$-0.982762\pi$
$41$	−5.82688	−	6.72457i	−0.910005	−	1.05020i	0.0885290	−	0.996074i	$-0.471783\pi$
$42$	1.85504	+	0.544688i	0.286238	+	0.0840472i
$43$	4.69251	+	10.2752i	0.715600	+	1.56695i	0.819969	+	0.572408i	$0.193990\pi$
$43$	4.69251	+	10.2752i	0.715600	+	1.56695i	−0.104369	+	0.994539i	$0.533282\pi$
$44$	−1.20154	+	8.35688i	−0.181139	+	1.25985i
$45$	1.84478			0.275004
$46$	9.25881	+	0.494839i	1.36514	+	0.0729600i
$47$	−10.6332			−1.55102			−0.775509	−	0.631337i	$-0.782507\pi$
$47$	−10.6332			−1.55102			−0.775509	+	0.631337i	$0.782507\pi$
$48$	−0.634096	+	4.41023i	−0.0915238	+	0.636562i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	2.96208	+	0.869744i	0.418901	+	0.123000i
$51$	4.21796	+	4.86778i	0.590632	+	0.681625i
$52$	10.1075	−	2.96784i	1.40166	−	0.411565i
$53$	1.27137	+	0.817059i	0.174636	+	0.112232i	0.625039	−	0.780594i	$-0.285083\pi$
$53$	1.27137	+	0.817059i	0.174636	+	0.112232i	−0.450403	+	0.892826i	$0.648720\pi$
$54$	−0.803143	+	1.75864i	−0.109294	+	0.239320i
$55$	−5.86908	+	6.77328i	−0.791387	+	0.913309i
$56$	−0.426377	+	0.274016i	−0.0569770	+	0.0366169i
$57$	−0.0554259	−	0.385495i	−0.00734133	−	0.0510601i
$58$	−0.264139	−	1.83713i	−0.0346831	−	0.241226i
$59$	7.68380	−	4.93808i	1.00035	−	0.642883i	0.0654686	−	0.997855i	$-0.479146\pi$
$59$	7.68380	−	4.93808i	1.00035	−	0.642883i	0.934877	+	0.354971i	$0.115509\pi$
$60$	2.09945	−	2.42290i	0.271038	−	0.312794i
$61$	1.20419	−	2.63680i	0.154180	−	0.337608i	−0.816742	−	0.577003i	$-0.804222\pi$
$61$	1.20419	−	2.63680i	0.154180	−	0.337608i	0.970922	+	0.239396i	$0.0769493\pi$
$62$	1.56256	+	1.00420i	0.198446	+	0.127533i
$63$	−0.959493	+	0.281733i	−0.120885	+	0.0354950i
$64$	3.78728	+	4.37076i	0.473410	+	0.546344i
$65$	10.7295	+	3.15046i	1.33083	+	0.390767i
$66$	−3.90184	−	8.54383i	−0.480283	−	1.05167i
$67$	0.257551	−	1.79130i	0.0314648	−	0.218843i	−0.968022	−	0.250864i	$-0.919285\pi$
$67$	0.257551	−	1.79130i	0.0314648	−	0.218843i	0.999487	+	0.0320213i	$0.0101944\pi$
$68$	11.1935			1.35741
$69$	−4.16714	+	2.37381i	−0.501664	+	0.285773i
$70$	3.56661			0.426292
$71$	0.141644	−	0.985153i	0.0168100	−	0.116916i	−0.979689	−	0.200524i	$-0.935735\pi$
$71$	0.141644	−	0.985153i	0.0168100	−	0.116916i	0.996499	+	0.0836084i	$0.0266445\pi$
$72$	−0.210547	−	0.461033i	−0.0248132	−	0.0543333i
$73$	0.383307	+	0.112549i	0.0448627	+	0.0131729i	0.304087	−	0.952644i	$-0.401649\pi$
$73$	0.383307	+	0.112549i	0.0448627	+	0.0131729i	−0.259224	+	0.965817i	$0.583467\pi$
$74$	−0.143316	−	0.165395i	−0.0166601	−	0.0192268i
$75$	−1.53210	+	0.449864i	−0.176911	+	0.0519458i
$76$	−0.569378	−	0.365917i	−0.0653121	−	0.0419735i
$77$	2.01817	−	4.41918i	0.229992	−	0.503612i
$78$	−7.67453	+	8.85688i	−0.868969	+	1.00284i
$79$	−2.28897	+	1.47103i	−0.257530	+	0.165504i	−0.663035	−	0.748588i	$-0.730732\pi$
$79$	−2.28897	+	1.47103i	−0.257530	+	0.165504i	0.405505	+	0.914093i	$0.367096\pi$
$80$	1.16977	+	8.13592i	0.130784	+	0.909623i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	14.4719	−	9.30050i	1.59815	−	1.02707i
$83$	−9.69155	+	11.1846i	−1.06379	+	1.22767i	−0.0910286	+	0.995848i	$0.529015\pi$
$83$	−9.69155	+	11.1846i	−1.06379	+	1.22767i	−0.972757	+	0.231826i	$0.925530\pi$
$84$	−0.721928	+	1.58080i	−0.0787687	+	0.172480i
$85$	9.99598	+	6.42402i	1.08422	+	0.696783i
$86$	−20.9544	+	6.15277i	−2.25957	+	0.663470i
$87$	0.628666	+	0.725519i	0.0674001	+	0.0777838i
$88$	2.36257	+	0.693713i	0.251851	+	0.0739500i
$89$	7.74611	+	16.9616i	0.821086	+	1.79793i	0.549447	+	0.835529i	$0.314839\pi$
$89$	7.74611	+	16.9616i	0.821086	+	1.79793i	0.271639	+	0.962399i	$0.412434\pi$
$90$	−0.507582	+	3.53031i	−0.0535038	+	0.372127i
$91$	−6.06166			−0.635435
$92$	−1.62469	+	8.17453i	−0.169386	+	0.852253i
$93$	−0.960726			−0.0996227
$94$	2.92568	−	20.3485i	0.301761	−	2.09879i
$95$	−0.298462	−	0.653542i	−0.0306216	−	0.0670520i
$96$	−7.29266	−	2.14132i	−0.744304	−	0.218547i
$97$	0.977938	+	1.12860i	0.0992946	+	0.114592i	0.803222	−	0.595680i	$-0.203117\pi$
$97$	0.977938	+	1.12860i	0.0992946	+	0.114592i	−0.703927	+	0.710272i	$0.748572\pi$
$98$	−1.85504	+	0.544688i	−0.187387	+	0.0550218i
$99$	4.08698	+	2.62655i	0.410757	+	0.263978i
$100$	−1.15276	+	2.52418i	−0.115276	+	0.252418i
$101$	−1.91834	+	2.21388i	−0.190882	+	0.220290i	−0.843121	−	0.537724i	$-0.819284\pi$
$101$	−1.91834	+	2.21388i	−0.190882	+	0.220290i	0.652239	+	0.758013i	$0.273830\pi$
$102$	−10.4759	+	6.73244i	−1.03727	+	0.666611i
$103$	−1.50379	−	10.4591i	−0.148173	−	1.03056i	−0.919208	−	0.393771i	$-0.871170\pi$
$103$	−1.50379	−	10.4591i	−0.148173	−	1.03056i	0.771036	−	0.636792i	$-0.219739\pi$
$104$	−0.437229	−	3.04099i	−0.0428738	−	0.298194i
$105$	−1.55193	+	0.997365i	−0.151453	+	0.0973329i
$106$	−1.91339	+	2.20817i	−0.185845	+	0.214477i
$107$	−7.16082	+	15.6800i	−0.692263	+	1.51584i	0.156844	+	0.987623i	$0.449868\pi$
$107$	−7.16082	+	15.6800i	−0.692263	+	1.51584i	−0.849107	+	0.528221i	$0.822859\pi$
$108$	−1.46197	−	0.939551i	−0.140678	−	0.0904083i
$109$	−1.01571	+	0.298239i	−0.0972871	+	0.0285661i	−0.330014	−	0.943976i	$-0.607053\pi$
$109$	−1.01571	+	0.298239i	−0.0972871	+	0.0285661i	0.232727	+	0.972542i	$0.425235\pi$
$110$	−11.3470	−	13.0951i	−1.08189	−	1.24857i
$111$	0.108612	+	0.0318912i	0.0103090	+	0.00302698i
$112$	−1.85092	−	4.05294i	−0.174895	−	0.382967i
$113$	2.97222	−	20.6722i	0.279603	−	1.94468i	−0.0454055	−	0.998969i	$-0.514458\pi$
$113$	2.97222	−	20.6722i	0.279603	−	1.94468i	0.325008	−	0.945711i	$-0.394633\pi$
$114$	0.752962			0.0705213
$115$	−6.14231	+	6.36758i	−0.572774	+	0.593780i
$116$	1.66833			0.154901
$117$	0.862665	−	5.99997i	0.0797534	−	0.554697i
$118$	7.33571	+	16.0630i	0.675307	+	1.47872i
$119$	−6.18009	−	1.81464i	−0.566528	−	0.166348i
$120$	−0.612295	−	0.706626i	−0.0558946	−	0.0645058i
$121$	−12.0917	+	3.55044i	−1.09925	+	0.322768i
$122$	4.71465	+	3.02992i	0.426844	+	0.274316i
$123$	−3.69631	+	8.09380i	−0.333285	+	0.729793i
$124$	−1.09335	+	1.26180i	−0.0981859	+	0.113313i
$125$	−10.2377	+	6.57939i	−0.915691	+	0.588479i
$126$	−0.275145	−	1.91367i	−0.0245118	−	0.170483i
$127$	−2.29246	−	15.9444i	−0.203423	−	1.41484i	−0.794031	−	0.607878i	$-0.792021\pi$
$127$	−2.29246	−	15.9444i	−0.203423	−	1.41484i	0.590608	−	0.806959i	$-0.298888\pi$
$128$	3.38171	−	2.17329i	0.298904	−	0.192094i
$129$	7.39727	−	8.53691i	0.651293	−	0.751633i
$130$	−8.98111	+	19.6659i	−0.787696	+	1.72481i
$131$	−1.41759	−	0.911029i	−0.123855	−	0.0795970i	0.477246	−	0.878770i	$-0.341635\pi$
$131$	−1.41759	−	0.911029i	−0.123855	−	0.0795970i	−0.601102	+	0.799173i	$0.705271\pi$
$132$	8.10082	−	2.37862i	0.705086	−	0.207032i
$133$	0.255042	+	0.294334i	0.0221149	+	0.0255220i
$134$	3.35711	+	0.985735i	0.290010	+	0.0851545i
$135$	−0.766351	−	1.67807i	−0.0659570	−	0.144426i
$136$	0.464590	−	3.23129i	0.0398382	−	0.277081i
$137$	15.2237			1.30065			0.650323	−	0.759658i	$-0.274633\pi$
$137$	15.2237			1.30065			0.650323	+	0.759658i	$0.274633\pi$
$138$	−3.39613	−	8.62768i	−0.289098	−	0.734436i
$139$	9.99899			0.848103			0.424052	−	0.905638i	$-0.360608\pi$
$139$	9.99899			0.848103			0.424052	+	0.905638i	$0.360608\pi$
$140$	−0.456254	+	3.17332i	−0.0385605	+	0.268194i
$141$	4.41721	+	9.67234i	0.371996	+	0.814558i
$142$	1.84629	+	0.542119i	0.154937	+	0.0454936i
$143$	19.2849	+	22.2559i	1.61268	+	1.86113i
$144$	4.27510	−	1.25528i	0.356258	−	0.104607i
$145$	1.48985	+	0.957470i	0.123726	+	0.0795136i
$146$	−0.320847	+	0.702557i	−0.0265535	+	0.0581441i
$147$	0.654861	−	0.755750i	0.0540120	−	0.0623332i
$148$	0.165490	−	0.106354i	0.0136032	−	0.00874226i
$149$	−0.267311	−	1.85919i	−0.0218990	−	0.152311i	0.975938	−	0.218048i	$-0.0699690\pi$
$149$	−0.267311	−	1.85919i	−0.0218990	−	0.152311i	−0.997837	+	0.0657377i	$0.979060\pi$
$150$	−0.439344	−	3.05571i	−0.0358723	−	0.249497i
$151$	−18.2574	+	11.7333i	−1.48576	+	0.954842i	−0.489185	+	0.872180i	$0.662706\pi$
$151$	−18.2574	+	11.7333i	−1.48576	+	0.954842i	−0.996578	+	0.0826614i	$0.973658\pi$
$152$	−0.129264	+	0.149179i	−0.0104847	+	0.0121000i
$153$	2.67569	−	5.85894i	0.216316	−	0.473667i
$154$	7.90157	+	5.07803i	0.636727	+	0.409200i
$155$	−1.70054	+	0.499323i	−0.136591	+	0.0401066i
$156$	−6.89846	−	7.96125i	−0.552319	−	0.637410i
$157$	−12.5482	−	3.68450i	−1.00146	−	0.294055i	−0.260404	−	0.965500i	$-0.583856\pi$
$157$	−12.5482	−	3.68450i	−1.00146	−	0.294055i	−0.741055	+	0.671445i	$0.765674\pi$
$158$	−2.18528	−	4.78510i	−0.173852	−	0.380682i
$159$	0.215077	−	1.49590i	0.0170568	−	0.118632i
$160$	−14.0213			−1.10848
$161$	2.22224	−	4.24990i	0.175137	−	0.334939i
$162$	1.93335			0.151898
$163$	−2.26108	+	15.7262i	−0.177101	+	1.23177i	0.686326	+	0.727294i	$0.259222\pi$
$163$	−2.26108	+	15.7262i	−0.177101	+	1.23177i	−0.863427	+	0.504474i	$0.831687\pi$
$164$	6.42363	+	14.0658i	0.501601	+	1.09835i
$165$	8.59930	+	2.52498i	0.669455	+	0.196570i
$166$	−18.7372	−	21.6238i	−1.45429	−	1.67834i
$167$	11.1037	−	3.26034i	0.859231	−	0.252293i	0.177702	−	0.984084i	$-0.443134\pi$
$167$	11.1037	−	3.26034i	0.859231	−	0.252293i	0.681529	+	0.731791i	$0.261315\pi$
$168$	0.426377	+	0.274016i	0.0328957	+	0.0211408i
$169$	9.86352	−	21.5981i	0.758732	−	1.66139i
$170$	−15.0438	+	17.3615i	−1.15381	+	1.33157i
$171$	−0.327634	+	0.210558i	−0.0250548	+	0.0161017i
$172$	−2.79373	−	19.4308i	−0.213020	−	1.48159i
$173$	2.13182	+	14.8271i	0.162079	+	1.12728i	0.894706	+	0.446655i	$0.147385\pi$
$173$	2.13182	+	14.8271i	0.162079	+	1.12728i	−0.732627	+	0.680630i	$0.761706\pi$
$174$	−1.56138	+	1.00344i	−0.118368	+	0.0760705i
$175$	1.04567	−	1.20676i	0.0790449	−	0.0912227i
$176$	−8.99213	+	19.6900i	−0.677808	+	1.48419i
$177$	−7.68380	−	4.93808i	−0.577550	−	0.371169i
$178$	−34.5903	+	10.1566i	−2.59265	+	0.761271i
$179$	0.131730	+	0.152024i	0.00984593	+	0.0113628i	0.760651	−	0.649161i	$-0.224880\pi$
$179$	0.131730	+	0.152024i	0.00984593	+	0.0113628i	−0.750805	+	0.660524i	$0.770334\pi$
$180$	−3.07609	−	0.903220i	−0.229278	−	0.0673221i
$181$	1.53546	+	3.36218i	0.114130	+	0.249909i	0.958074	−	0.286522i	$-0.0924993\pi$
$181$	1.53546	+	3.36218i	0.114130	+	0.249909i	−0.843944	+	0.536431i	$0.819772\pi$
$182$	1.66783	−	11.6000i	0.123628	−	0.859852i
$183$	−2.89875			−0.214282
$184$	2.29236	+	0.808299i	0.168995	+	0.0595886i
$185$	0.208824			0.0153530
$186$	0.264339	−	1.83852i	0.0193822	−	0.134806i
$187$	12.9990	+	28.4639i	0.950584	+	2.08149i
$188$	17.7304	+	5.20612i	1.29312	+	0.379695i
$189$	0.654861	+	0.755750i	0.0476341	+	0.0549727i
$190$	1.33278	−	0.391341i	0.0966904	−	0.0283909i
$191$	4.97154	+	3.19501i	0.359728	+	0.231183i	0.708003	−	0.706209i	$-0.249596\pi$
$191$	4.97154	+	3.19501i	0.359728	+	0.231183i	−0.348275	+	0.937392i	$0.613233\pi$
$192$	2.40249	−	5.26071i	0.173384	−	0.379659i
$193$	1.23175	−	1.42152i	0.0886637	−	0.102323i	−0.709684	−	0.704520i	$-0.751162\pi$
$193$	1.23175	−	1.42152i	0.0886637	−	0.102323i	0.798348	+	0.602197i	$0.205708\pi$
$194$	−2.42885	+	1.56092i	−0.174381	+	0.112068i
$195$	−1.59143	−	11.0686i	−0.113965	−	0.792641i
$196$	−0.247321	−	1.72016i	−0.0176658	−	0.122868i
$197$	13.3049	−	8.55056i	0.947937	−	0.609202i	0.0273023	−	0.999627i	$-0.491308\pi$
$197$	13.3049	−	8.55056i	0.947937	−	0.609202i	0.920635	+	0.390425i	$0.127672\pi$
$198$	−6.15086	+	7.09847i	−0.437122	+	0.504466i
$199$	4.33903	−	9.50115i	0.307586	−	0.673519i	−0.691206	−	0.722657i	$-0.742920\pi$
$199$	4.33903	−	9.50115i	0.307586	−	0.673519i	0.998792	+	0.0491389i	$0.0156477\pi$
$200$	0.680828	+	0.437541i	0.0481418	+	0.0309389i
$201$	−1.73642	+	0.509858i	−0.122477	+	0.0359626i
$202$	−3.70883	−	4.28022i	−0.260952	−	0.301155i
$203$	−0.921113	−	0.270463i	−0.0646495	−	0.0189828i
$204$	−4.64993	−	10.1819i	−0.325560	−	0.712878i
$205$	−2.33605	+	16.2476i	−0.163157	+	1.13478i
$206$	20.4290			1.42336
$207$	3.89038	+	2.80444i	0.270400	+	0.194922i
$208$	27.0082			1.87269
$209$	0.269270	−	1.87282i	0.0186258	−	0.129545i
$210$	−1.48162	−	3.24431i	−0.102242	−	0.223878i
$211$	10.6483	+	3.12662i	0.733059	+	0.215245i	0.626896	−	0.779103i	$-0.284325\pi$
$211$	10.6483	+	3.12662i	0.733059	+	0.215245i	0.106163	+	0.994349i	$0.466143\pi$
$212$	−1.71991	−	1.98488i	−0.118124	−	0.136322i
$213$	−0.954968	+	0.280404i	−0.0654333	+	0.0192129i
$214$	−28.0361	−	18.0177i	−1.91651	−	1.23167i
$215$	8.65665	−	18.9554i	0.590379	−	1.29275i
$216$	−0.331906	+	0.383040i	−0.0225834	+	0.0260626i
$217$	0.808214	−	0.519408i	0.0548652	−	0.0352597i
$218$	−0.291265	−	2.02579i	−0.0197269	−	0.137204i
$219$	−0.0568533	−	0.395423i	−0.00384179	−	0.0267202i
$220$	13.1027	−	8.42057i	0.883381	−	0.567715i
$221$	25.5678	−	29.5068i	1.71988	−	1.98485i
$222$	−0.0909133	+	0.199072i	−0.00610170	+	0.0133609i
$223$	−18.3310	−	11.7806i	−1.22753	−	0.788889i	−0.244029	−	0.969768i	$-0.578469\pi$
$223$	−18.3310	−	11.7806i	−1.22753	−	0.788889i	−0.983505	+	0.180879i	$0.942106\pi$
$224$	7.29266	−	2.14132i	0.487261	−	0.143073i
$225$	1.04567	+	1.20676i	0.0697110	+	0.0804508i
$226$	38.7421	+	11.3757i	2.57709	+	0.756700i
$227$	−7.12856	−	15.6094i	−0.473139	−	1.03603i	−0.984293	−	0.176541i	$-0.943509\pi$
$227$	−7.12856	−	15.6094i	−0.473139	−	1.03603i	0.511154	−	0.859489i	$-0.329218\pi$
$228$	−0.0963216	+	0.669932i	−0.00637906	+	0.0443673i
$229$	10.0979			0.667291			0.333645	−	0.942699i	$-0.391721\pi$
$229$	10.0979			0.667291			0.333645	+	0.942699i	$0.391721\pi$
$230$	−10.4954	−	13.5064i	−0.692049	−	0.890585i
$231$	−4.85821			−0.319647
$232$	0.0692449	−	0.481609i	0.00454615	−	0.0316192i
$233$	−8.60475	−	18.8418i	−0.563716	−	1.23437i	−0.950076	−	0.312018i	$-0.898995\pi$
$233$	−8.60475	−	18.8418i	−0.563716	−	1.23437i	0.386360	−	0.922348i	$-0.373732\pi$
$234$	11.2446	+	3.30172i	0.735083	+	0.215840i
$235$	12.8458	+	14.8248i	0.837965	+	0.967064i
$236$	−15.2301	+	4.47196i	−0.991394	+	0.291100i
$237$	2.28897	+	1.47103i	0.148685	+	0.0955540i
$238$	5.17304	−	11.3274i	0.335318	−	0.734245i
$239$	−15.4092	+	17.7832i	−0.996738	+	1.15030i	−0.00810255	+	0.999967i	$0.502579\pi$
$239$	−15.4092	+	17.7832i	−0.996738	+	1.15030i	−0.988636	+	0.150330i	$0.951966\pi$
$240$	6.91475	−	4.44384i	0.446345	−	0.286849i
$241$	−4.07003	−	28.3077i	−0.262174	−	1.82346i	−0.516438	−	0.856324i	$-0.672742\pi$
$241$	−4.07003	−	28.3077i	−0.262174	−	1.82346i	0.254265	−	0.967135i	$-0.418167\pi$
$242$	−3.46742	−	24.1164i	−0.222894	−	1.55026i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−3.29892	+	3.80716i	−0.211192	+	0.243728i
$245$	0.766351	−	1.67807i	0.0489603	−	0.107208i
$246$	−14.4719	−	9.30050i	−0.922692	−	0.592978i
$247$	−2.26514	+	0.665106i	−0.144128	+	0.0423197i
$248$	0.318871	+	0.367997i	0.0202483	+	0.0233678i
$249$	14.1999	+	4.16947i	0.899884	+	0.264230i
$250$	−9.77395	−	21.4020i	−0.618159	−	1.35358i
$251$	0.773971	−	5.38309i	0.0488526	−	0.339777i	−0.950707	−	0.310092i	$-0.899640\pi$
$251$	0.773971	−	5.38309i	0.0488526	−	0.339777i	0.999559	−	0.0296857i	$-0.00945065\pi$
$252$	1.73785			0.109474
$253$	−22.6738	+	5.36169i	−1.42549	+	0.337086i
$254$	31.1431			1.95409
$255$	1.69102	−	11.7613i	0.105896	−	0.736521i
$256$	8.03348	+	17.5909i	0.502093	+	1.09943i
$257$	12.1530	+	3.56843i	0.758080	+	0.222592i	0.637857	−	0.770154i	$-0.279821\pi$
$257$	12.1530	+	3.56843i	0.758080	+	0.222592i	0.120223	+	0.992747i	$0.461639\pi$
$258$	14.3015	+	16.5048i	0.890374	+	1.02755i
$259$	−0.108612	+	0.0318912i	−0.00674880	+	0.00198163i
$260$	−16.3484	−	10.5065i	−1.01389	−	0.651585i
$261$	0.398798	−	0.873247i	0.0246850	−	0.0540526i
$262$	2.13345	−	2.46214i	0.131805	−	0.152111i
$263$	−1.26778	+	0.814753i	−0.0781747	+	0.0502398i	−0.579144	−	0.815225i	$-0.696613\pi$
$263$	−1.26778	+	0.814753i	−0.0781747	+	0.0502398i	0.500970	+	0.865465i	$0.332977\pi$
$264$	−0.350423	−	2.43725i	−0.0215670	−	0.150002i
$265$	−0.396771	−	2.75960i	−0.0243735	−	0.169521i
$266$	−0.633432	+	0.407082i	−0.0388382	+	0.0249598i
$267$	12.2110	−	14.0922i	0.747300	−	0.862430i
$268$	−1.30649	+	2.86081i	−0.0798066	+	0.174752i
$269$	−18.4285	−	11.8433i	−1.12361	−	0.722099i	−0.159392	−	0.987215i	$-0.550953\pi$
$269$	−18.4285	−	11.8433i	−1.12361	−	0.722099i	−0.964216	+	0.265116i	$0.914590\pi$
$270$	3.42214	−	1.00483i	0.208265	−	0.0611521i
$271$	−4.85892	−	5.60749i	−0.295158	−	0.340631i	0.588729	−	0.808330i	$-0.299628\pi$
$271$	−4.85892	−	5.60749i	−0.295158	−	0.340631i	−0.883888	+	0.467699i	$0.845083\pi$
$272$	27.5359	+	8.08527i	1.66961	+	0.490242i
$273$	2.51811	+	5.51388i	0.152403	+	0.333715i
$274$	−4.18871	+	29.1331i	−0.253049	+	1.76000i
$275$	−7.75747			−0.467793
$276$	8.11073	−	1.91795i	0.488209	−	0.115447i
$277$	−8.80155			−0.528834			−0.264417	−	0.964408i	$-0.585179\pi$
$277$	−8.80155			−0.528834			−0.264417	+	0.964408i	$0.585179\pi$
$278$	−2.75117	+	19.1348i	−0.165004	+	1.14763i
$279$	0.399100	+	0.873907i	0.0238935	+	0.0523195i
$280$	0.897126	+	0.263420i	0.0536135	+	0.0157424i
$281$	−14.5301	−	16.7686i	−0.866792	−	1.00033i	−0.999957	−	0.00923788i	$-0.997059\pi$
$281$	−14.5301	−	16.7686i	−0.866792	−	1.00033i	0.133165	−	0.991094i	$-0.457486\pi$
$282$	−19.7251	+	5.79180i	−1.17461	+	0.344897i
$283$	14.6656	+	9.42504i	0.871782	+	0.560260i	0.898297	−	0.439388i	$-0.144805\pi$
$283$	14.6656	+	9.42504i	0.871782	+	0.560260i	−0.0265154	+	0.999648i	$0.508441\pi$
$284$	−0.718523	+	1.57334i	−0.0426365	+	0.0933608i
$285$	−0.470497	+	0.542982i	−0.0278698	+	0.0321635i
$286$	−47.8967	+	30.7813i	−2.83219	+	1.82014i
$287$	−1.26630	−	8.80732i	−0.0747474	−	0.519879i
$288$	1.08167	+	7.52317i	0.0637380	+	0.443307i
$289$	20.5993	−	13.2384i	1.21172	−	0.778727i
$290$	−2.24221	+	2.58765i	−0.131667	+	0.151952i
$291$	0.620361	−	1.35840i	0.0363662	−	0.0796309i
$292$	−0.584042	−	0.375341i	−0.0341784	−	0.0219652i
$293$	−5.98339	+	1.75688i	−0.349553	+	0.102638i	−0.451796	−	0.892121i	$-0.649216\pi$
$293$	−5.98339	+	1.75688i	−0.349553	+	0.102638i	0.102243	+	0.994760i	$0.467398\pi$
$294$	1.26608	+	1.46113i	0.0738390	+	0.0852148i
$295$	−16.1673	−	4.74713i	−0.941294	−	0.276389i
$296$	−0.0238332	−	0.0521875i	−0.00138528	−	0.00303334i
$297$	0.691395	−	4.80876i	0.0401188	−	0.279032i
$298$	3.63143			0.210363
$299$	17.8376	+	22.9549i	1.03158	+	1.32751i
$300$	2.77495			0.160212
$301$	−1.60758	+	11.1810i	−0.0926594	+	0.644460i
$302$	−17.4303	−	38.1669i	−1.00300	−	2.19626i
$303$	2.81073	+	0.825304i	0.161472	+	0.0474125i
$304$	−1.13636	−	1.31143i	−0.0651747	−	0.0752156i
$305$	−5.13096	+	1.50659i	−0.293798	+	0.0862668i
$306$	10.4759	+	6.73244i	0.598866	+	0.384868i
$307$	3.95772	−	8.66619i	0.225879	−	0.494606i	−0.762430	−	0.647071i	$-0.775994\pi$
$307$	3.95772	−	8.66619i	0.225879	−	0.494606i	0.988309	+	0.152465i	$0.0487211\pi$
$308$	−5.52887	+	6.38066i	−0.315037	+	0.363572i
$309$	−8.88921	+	5.71275i	−0.505689	+	0.324987i
$310$	−0.487647	−	3.39166i	−0.0276965	−	0.192633i
$311$	1.48935	+	10.3587i	0.0844534	+	0.587386i	0.987473	+	0.157787i	$0.0504360\pi$
$311$	1.48935	+	10.3587i	0.0844534	+	0.587386i	−0.903020	+	0.429599i	$0.858655\pi$
$312$	−2.58455	+	1.66099i	−0.146321	+	0.0940351i
$313$	−3.80779	+	4.39442i	−0.215229	+	0.248387i	−0.853090	−	0.521764i	$-0.825274\pi$
$313$	−3.80779	+	4.39442i	−0.215229	+	0.248387i	0.637861	+	0.770152i	$0.279819\pi$
$314$	10.5035	−	22.9995i	0.592747	−	1.29793i
$315$	1.55193	+	0.997365i	0.0874414	+	0.0561952i
$316$	4.53698	−	1.33218i	0.255225	−	0.0749409i
$317$	0.223371	+	0.257784i	0.0125458	+	0.0144786i	0.761988	−	0.647591i	$-0.224224\pi$
$317$	0.223371	+	0.257784i	0.0125458	+	0.0144786i	−0.749442	+	0.662070i	$0.769678\pi$
$318$	2.80348	+	0.823175i	0.157211	+	0.0461614i
$319$	1.93744	+	4.24241i	0.108476	+	0.237530i
$320$	1.51836	−	10.5604i	0.0848788	−	0.590345i
$321$	17.2378			0.962118
$322$	7.52148	+	5.42198i	0.419156	+	0.302155i
$323$	−2.50851			−0.139577
$324$	−0.247321	+	1.72016i	−0.0137401	+	0.0955643i
$325$	4.02085	+	8.80444i	0.223037	+	0.488382i
$326$	−29.4726	−	8.65393i	−1.63234	−	0.479297i
$327$	0.693227	+	0.800027i	0.0383356	+	0.0442416i
$328$	4.32708	−	1.27055i	0.238923	−	0.0701541i
$329$	−8.94525	−	5.74877i	−0.493168	−	0.316940i
$330$	−7.19804	+	15.7615i	−0.396239	+	0.867642i
$331$	17.9364	−	20.6997i	0.985871	−	1.13776i	−0.00459380	−	0.999989i	$-0.501462\pi$
$331$	17.9364	−	20.6997i	0.985871	−	1.13776i	0.990465	−	0.137766i	$-0.0439923\pi$
$332$	21.6363	−	13.9048i	1.18745	−	0.763125i
$333$	−0.0161096	−	0.112045i	−0.000882800	−	0.00614001i
$334$	3.18410	+	22.1459i	0.174226	+	1.21177i
$335$	−2.80857	+	1.80496i	−0.153448	+	0.0986153i
$336$	−2.91779	+	3.36730i	−0.159178	+	0.183702i
$337$	−7.90640	+	17.3126i	−0.430689	+	0.943078i	0.562525	+	0.826780i	$0.309830\pi$
$337$	−7.90640	+	17.3126i	−0.430689	+	0.943078i	−0.993214	+	0.116298i	$0.962897\pi$
$338$	38.6178	+	24.8181i	2.10053	+	1.34993i
$339$	−20.0388	+	5.88393i	−1.08836	+	0.319571i
$340$	−13.5226	−	15.6059i	−0.733363	−	0.846346i
$341$	−4.47834	−	1.31496i	−0.242516	−	0.0712091i
$342$	−0.312792	−	0.684918i	−0.0169138	−	0.0370361i
$343$	−0.142315	+	0.989821i	−0.00768428	+	0.0534453i
$344$	−5.72518			−0.308681
$345$	8.34377	+	2.94206i	0.449213	+	0.158395i
$346$	−28.9608			−1.55694
$347$	−0.991405	+	6.89537i	−0.0532214	+	0.370163i	0.945753	+	0.324886i	$0.105326\pi$
$347$	−0.991405	+	6.89537i	−0.0532214	+	0.370163i	−0.998974	+	0.0452767i	$0.985583\pi$
$348$	−0.693050	−	1.51757i	−0.0371514	−	0.0813502i
$349$	−26.3276	−	7.73049i	−1.40929	−	0.413804i	−0.513424	−	0.858135i	$-0.671623\pi$
$349$	−26.3276	−	7.73049i	−1.40929	−	0.413804i	−0.895862	+	0.444332i	$0.853441\pi$
$350$	2.02164	+	2.33310i	0.108061	+	0.124709i
$351$	−5.81612	+	1.70777i	−0.310442	+	0.0911539i
$352$	−31.0633	−	19.9632i	−1.65568	−	1.06404i
$353$	6.95861	−	15.2372i	0.370369	−	0.810996i	−0.629065	−	0.777353i	$-0.716562\pi$
$353$	6.95861	−	15.2372i	0.370369	−	0.810996i	0.999434	−	0.0336426i	$-0.0107108\pi$
$354$	11.5640	−	13.3456i	0.614621	−	0.709310i
$355$	−1.54461	+	0.992661i	−0.0819794	+	0.0526850i
$356$	−4.61172	−	32.0752i	−0.244421	−	1.69998i
$357$	0.916649	+	6.37544i	0.0485142	+	0.337424i
$358$	−0.327169	+	0.210259i	−0.0172914	+	0.0111125i
$359$	−15.5639	+	17.9617i	−0.821430	+	0.947981i	−0.999349	−	0.0360643i	$-0.988518\pi$
$359$	−15.5639	+	17.9617i	−0.821430	+	0.947981i	0.177920	+	0.984045i	$0.443063\pi$
$360$	−0.388413	+	0.850506i	−0.0204712	+	0.0448256i
$361$	−15.8562	−	10.1902i	−0.834538	−	0.536325i
$362$	−6.85658	+	2.01327i	−0.360374	+	0.105815i
$363$	8.25267	+	9.52409i	0.433153	+	0.499885i
$364$	10.1075	+	2.96784i	0.529779	+	0.155557i
$365$	−0.306149	−	0.670373i	−0.0160246	−	0.0350889i
$366$	0.797577	−	5.54727i	0.0416900	−	0.289960i
$367$	8.51080			0.444260			0.222130	−	0.975017i	$-0.428699\pi$
$367$	8.51080			0.444260			0.222130	+	0.975017i	$0.428699\pi$
$368$	−9.90138	+	18.9358i	−0.516145	+	0.987096i
$369$	8.89788			0.463205
$370$	−0.0574567	+	0.399620i	−0.00298703	+	0.0207753i
$371$	0.627808	+	1.37471i	0.0325942	+	0.0713713i
$372$	1.60196	+	0.470379i	0.0830580	+	0.0243880i
$373$	−0.473693	−	0.546671i	−0.0245269	−	0.0283056i	0.743354	−	0.668899i	$-0.233234\pi$
$373$	−0.473693	−	0.546671i	−0.0245269	−	0.0283056i	−0.767881	+	0.640593i	$0.778689\pi$
$374$	−58.0472	+	17.0442i	−3.00155	+	0.881335i
$375$	10.2377	+	6.57939i	0.528674	+	0.339758i
$376$	2.23880	−	4.90228i	0.115457	−	0.252816i
$377$	3.81076	−	4.39786i	0.196264	−	0.226501i
$378$	−1.62644	+	1.04525i	−0.0836550	+	0.0537618i
$379$	1.11925	+	7.78458i	0.0574922	+	0.399867i	0.998165	+	0.0605522i	$0.0192862\pi$
$379$	1.11925	+	7.78458i	0.0574922	+	0.399867i	−0.940673	+	0.339315i	$0.889805\pi$
$380$	0.177692	+	1.23588i	0.00911543	+	0.0633992i
$381$	−13.5512	+	8.70884i	−0.694250	+	0.446167i
$382$	−7.48210	+	8.63480i	−0.382818	+	0.441795i
$383$	−0.482277	+	1.05604i	−0.0246432	+	0.0539611i	−0.921553	−	0.388252i	$-0.873079\pi$
$383$	−0.482277	+	1.05604i	−0.0246432	+	0.0539611i	0.896910	+	0.442213i	$0.145806\pi$
$384$	−3.38171	−	2.17329i	−0.172572	−	0.110905i
$385$	−8.59930	+	2.52498i	−0.438261	+	0.128685i
$386$	2.38141	+	2.74830i	0.121211	+	0.139885i
$387$	−10.8384	−	3.18244i	−0.550946	−	0.161772i
$388$	−1.07809	−	2.36069i	−0.0547319	−	0.119846i
$389$	0.534235	−	3.71569i	0.0270868	−	0.188393i	−0.971786	−	0.235865i	$-0.924208\pi$
$389$	0.534235	−	3.71569i	0.0270868	−	0.188393i	0.998873	+	0.0474725i	$0.0151166\pi$
$390$	21.6196			1.09475
$391$	11.3143	+	28.7433i	0.572187	+	1.45361i
$392$	−0.506835			−0.0255990
$393$	−0.239813	+	1.66794i	−0.0120970	+	0.0841364i
$394$	12.7022	+	27.8139i	0.639927	+	1.40124i
$395$	4.81616	+	1.41415i	0.242327	+	0.0711538i
$396$	−5.52887	−	6.38066i	−0.277836	−	0.320640i
$397$	13.0465	−	3.83079i	0.654783	−	0.192262i	0.0625669	−	0.998041i	$-0.480071\pi$
$397$	13.0465	−	3.83079i	0.654783	−	0.192262i	0.592216	+	0.805779i	$0.298253\pi$
$398$	16.9882	+	10.9177i	0.851543	+	0.547253i
$399$	0.161787	−	0.354265i	0.00809950	−	0.0177354i
$400$	−4.65905	+	5.37683i	−0.232952	+	0.268842i
$401$	−14.0294	+	9.01616i	−0.700596	+	0.450246i	−0.841839	−	0.539729i	$-0.818527\pi$
$401$	−14.0294	+	9.01616i	−0.700596	+	0.450246i	0.141243	+	0.989975i	$0.454890\pi$
$402$	−0.497936	−	3.46322i	−0.0248348	−	0.172730i
$403$	0.828785	+	5.76432i	0.0412847	+	0.287141i
$404$	4.28268	−	2.75231i	0.213071	−	0.136932i
$405$	−1.20808	+	1.39419i	−0.0600298	+	0.0692781i
$406$	0.771017	−	1.68829i	0.0382649	−	0.0837885i
$407$	0.462634	+	0.297317i	0.0229319	+	0.0147374i
$408$	−3.13228	+	0.919722i	−0.155071	+	0.0455330i
$409$	−20.2410	−	23.3593i	−1.00085	−	1.15504i	−0.987894	−	0.155129i	$-0.950421\pi$
$409$	−20.2410	−	23.3593i	−1.00085	−	1.15504i	−0.0129578	−	0.999916i	$-0.504125\pi$
$410$	−30.4498	−	8.94087i	−1.50381	−	0.441558i
$411$	−6.32414	−	13.8479i	−0.311947	−	0.683069i
$412$	−2.61335	+	18.1763i	−0.128751	+	0.895480i
$413$	9.13375			0.449443
$414$	−6.43721	+	6.67329i	−0.316371	+	0.327974i
$415$	27.3017			1.34019
$416$	−6.55671	+	45.6030i	−0.321469	+	2.23587i
$417$	−4.15373	−	9.09540i	−0.203409	−	0.445404i
$418$	3.50987	+	1.03059i	0.171673	+	0.0504078i
$419$	−0.415907	−	0.479982i	−0.0203184	−	0.0234487i	0.745499	−	0.666506i	$-0.232211\pi$
$419$	−0.415907	−	0.479982i	−0.0203184	−	0.0234487i	−0.765818	+	0.643058i	$0.777666\pi$
$420$	3.07609	−	0.903220i	0.150098	−	0.0440726i
$421$	−32.1275	−	20.6471i	−1.56580	−	1.00628i	−0.980747	−	0.195283i	$-0.937437\pi$
$421$	−32.1275	−	20.6471i	−1.56580	−	1.00628i	−0.585053	−	0.810995i	$-0.698926\pi$
$422$	−8.91315	+	19.5171i	−0.433885	+	0.950076i
$423$	6.96329	−	8.03607i	0.338567	−	0.390727i
$424$	−0.644374	+	0.414114i	−0.0312936	+	0.0201112i
$425$	1.46368	+	10.1801i	0.0709991	+	0.493809i
$426$	−0.273847	−	1.90465i	−0.0132679	−	0.0922804i
$427$	2.43859	−	1.56719i	0.118012	−	0.0758414i
$428$	19.6174	−	22.6397i	0.948242	−	1.09433i
$429$	12.2335	−	26.7876i	0.590638	−	1.29332i
$430$	33.8926	+	21.7815i	1.63445	+	1.05040i
$431$	−5.75696	+	1.69040i	−0.277303	+	0.0814235i	−0.417427	−	0.908710i	$-0.637068\pi$
$431$	−5.75696	+	1.69040i	−0.277303	+	0.0814235i	0.140124	+	0.990134i	$0.455250\pi$
$432$	−2.91779	−	3.36730i	−0.140382	−	0.162010i
$433$	−22.6194	−	6.64166i	−1.08702	−	0.319178i	−0.311337	−	0.950300i	$-0.600777\pi$
$433$	−22.6194	−	6.64166i	−1.08702	−	0.319178i	−0.775684	+	0.631122i	$0.782595\pi$
$434$	0.771601	+	1.68957i	0.0370380	+	0.0811019i
$435$	0.252038	−	1.75297i	0.0120843	−	0.0840482i
$436$	1.83966			0.0881039
$437$	0.364101	−	1.83195i	0.0174173	−	0.0876340i
$438$	0.772354			0.0369045
$439$	−2.20280	+	15.3208i	−0.105134	+	0.731222i	0.867256	+	0.497862i	$0.165881\pi$
$439$	−2.20280	+	15.3208i	−0.105134	+	0.731222i	−0.972390	+	0.233360i	$0.925028\pi$
$440$	−1.88699	−	4.13194i	−0.0899588	−	0.196982i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	49.4316	+	57.0471i	2.35122	+	2.71345i
$443$	−18.9417	+	5.56178i	−0.899947	+	0.264248i	−0.698804	−	0.715313i	$-0.746284\pi$
$443$	−18.9417	+	5.56178i	−0.899947	+	0.264248i	−0.201143	+	0.979562i	$0.564466\pi$
$444$	−0.165490	−	0.106354i	−0.00785382	−	0.00504735i
$445$	14.2899	−	31.2905i	0.677406	−	1.48331i
$446$	27.5879	−	31.8382i	1.30633	−	1.50758i
$447$	−1.58013	+	1.01549i	−0.0747377	+	0.0480310i
$448$	0.823055	+	5.72447i	0.0388857	+	0.270456i
$449$	−3.56947	−	24.8262i	−0.168454	−	1.17162i	−0.882082	−	0.471097i	$-0.843858\pi$
$449$	−3.56947	−	24.8262i	−0.168454	−	1.17162i	0.713628	−	0.700525i	$-0.247051\pi$
$450$	−2.59706	+	1.66903i	−0.122426	+	0.0786787i
$451$	−28.3082	+	32.6694i	−1.33298	+	1.53834i
$452$	−15.0773	+	33.0147i	−0.709177	+	1.55288i
$453$	18.2574	+	11.7333i	0.857805	+	0.551278i
$454$	31.8326	−	9.34689i	1.49398	−	0.438671i
$455$	7.32295	+	8.45114i	0.343305	+	0.396195i
$456$	0.189396	+	0.0556116i	0.00886927	+	0.00260425i
$457$	10.8865	+	23.8382i	0.509251	+	1.11510i	0.973351	+	0.229321i	$0.0736506\pi$
$457$	10.8865	+	23.8382i	0.509251	+	1.11510i	−0.464100	+	0.885783i	$0.653622\pi$
$458$	−2.77839	+	19.3242i	−0.129826	+	0.902958i
$459$	−6.44100			−0.300640
$460$	13.3596	−	7.61031i	0.622896	−	0.354833i
$461$	14.7242			0.685774			0.342887	−	0.939377i	$-0.388595\pi$
$461$	14.7242			0.685774			0.342887	+	0.939377i	$0.388595\pi$
$462$	1.33671	−	9.29702i	0.0621893	−	0.432536i
$463$	−13.4662	−	29.4869i	−0.625828	−	1.37037i	−0.911204	−	0.411956i	$-0.864846\pi$
$463$	−13.4662	−	29.4869i	−0.625828	−	1.37037i	0.285376	−	0.958416i	$-0.407881\pi$
$464$	4.10410	+	1.20507i	0.190528	+	0.0559440i
$465$	1.16063	+	1.33944i	0.0538229	+	0.0621150i
$466$	38.4246	−	11.2825i	1.77998	−	0.522650i
$467$	−21.2019	−	13.6256i	−0.981105	−	0.630518i	−0.0513437	−	0.998681i	$-0.516350\pi$
$467$	−21.2019	−	13.6256i	−0.981105	−	0.630518i	−0.929761	+	0.368163i	$0.879987\pi$
$468$	−4.37608	+	9.58228i	−0.202284	+	0.442941i
$469$	1.18512	−	1.36770i	0.0547236	−	0.0631544i
$470$	−31.9043	+	20.5036i	−1.47163	+	0.945762i
$471$	1.86119	+	12.9449i	0.0857593	+	0.596469i
$472$	0.658819	+	4.58218i	0.0303246	+	0.210912i
$473$	46.1664	−	29.6693i	2.12273	−	1.36420i
$474$	−3.44488	+	3.97560i	−0.158228	+	0.182605i
$475$	0.258338	−	0.565681i	0.0118534	−	0.0259552i
$476$	9.41654	+	6.05164i	0.431606	+	0.277377i
$477$	−1.45006	+	0.425777i	−0.0663938	+	0.0194950i
$478$	−29.7914	−	34.3811i	−1.36263	−	1.57256i
$479$	−0.371717	−	0.109146i	−0.0169842	−	0.00498700i	0.273229	−	0.961949i	$-0.411908\pi$
$479$	−0.371717	−	0.109146i	−0.0169842	−	0.00498700i	−0.290214	+	0.956962i	$0.593726\pi$
$480$	5.82467	+	12.7543i	0.265859	+	0.582150i
$481$	0.0976510	−	0.679177i	0.00445250	−	0.0309678i
$482$	55.2915			2.51846
$483$	−4.78900	−	0.255949i	−0.217907	−	0.0116461i
$484$	21.9006			0.995484
$485$	0.392065	−	2.72687i	0.0178027	−	0.123821i
$486$	−0.803143	−	1.75864i	−0.0364313	−	0.0797734i
$487$	13.1468	+	3.86024i	0.595737	+	0.174924i	0.565681	−	0.824624i	$-0.308613\pi$
$487$	13.1468	+	3.86024i	0.595737	+	0.174924i	0.0300561	+	0.999548i	$0.490431\pi$
$488$	0.962115	+	1.11034i	0.0435529	+	0.0502627i
$489$	15.2443	−	4.47613i	0.689371	−	0.202418i
$490$	3.00043	+	1.92826i	0.135545	+	0.0871098i
$491$	6.20084	−	13.5779i	0.279840	−	0.612764i	−0.716562	−	0.697524i	$-0.754285\pi$
$491$	6.20084	−	13.5779i	0.279840	−	0.612764i	0.996401	+	0.0847602i	$0.0270124\pi$
$492$	10.1262	−	11.6863i	0.456525	−	0.526858i
$493$	5.20177	−	3.34297i	0.234276	−	0.150560i
$494$	−0.649554	−	4.51774i	−0.0292248	−	0.203263i
$495$	−1.27547	−	8.87111i	−0.0573283	−	0.398727i
$496$	−3.60107	+	2.31426i	−0.161693	+	0.103914i
$497$	0.651772	−	0.752185i	0.0292360	−	0.0337401i
$498$	−11.8860	+	26.0268i	−0.532626	+	1.16629i
$499$	−27.1936	−	17.4763i	−1.21735	−	0.782345i	−0.235478	−	0.971880i	$-0.575666\pi$
$499$	−27.1936	−	17.4763i	−1.21735	−	0.782345i	−0.981874	+	0.189535i	$0.939302\pi$
$500$	20.2923	−	5.95834i	0.907497	−	0.266465i
$501$	−7.57836	−	8.74590i	−0.338576	−	0.390738i
$502$	10.0885	+	2.96225i	0.450272	+	0.132212i
$503$	5.48768	+	12.0163i	0.244684	+	0.535782i	0.991632	−	0.129100i	$-0.0412089\pi$
$503$	5.48768	+	12.0163i	0.244684	+	0.535782i	−0.746948	+	0.664882i	$0.768482\pi$
$504$	0.0721301	−	0.501676i	0.00321293	−	0.0223464i
$505$	5.40409			0.240479
$506$	−4.02194	−	44.8655i	−0.178797	−	1.99452i
$507$	−23.7438			−1.05450
$508$	−3.98394	+	27.7089i	−0.176759	+	1.22938i
$509$	−3.65752	−	8.00884i	−0.162117	−	0.354986i	0.811089	−	0.584923i	$-0.198875\pi$
$509$	−3.65752	−	8.00884i	−0.162117	−	0.354986i	−0.973205	+	0.229937i	$0.926148\pi$
$510$	22.0420	+	6.47211i	0.976036	+	0.286590i
$511$	0.261610	+	0.301914i	0.0115729	+	0.0133559i
$512$	−28.1595	+	8.26838i	−1.24449	+	0.365414i
$513$	0.327634	+	0.210558i	0.0144654	+	0.00929635i
$514$	−10.1726	+	22.2749i	−0.448695	+	0.982505i
$515$	−12.7653	+	14.7319i	−0.562506	+	0.649166i
$516$	−16.5143	+	10.6131i	−0.727003	+	0.467216i
$517$	7.35177	+	51.1327i	0.323331	+	2.24881i
$518$	−0.0311455	−	0.216622i	−0.00136845	−	0.00951781i
$519$	12.6016	−	8.09858i	0.553150	−	0.355488i
$520$	−3.71153	+	4.28333i	−0.162761	+	0.187836i
$521$	−4.85935	+	10.6405i	−0.212892	+	0.466169i	−0.985708	−	0.168461i	$-0.946120\pi$
$521$	−4.85935	+	10.6405i	−0.212892	+	0.466169i	0.772816	+	0.634630i	$0.218847\pi$
$522$	1.56138	+	1.00344i	0.0683398	+	0.0439193i
$523$	−16.4576	+	4.83240i	−0.719643	+	0.211306i	−0.620993	−	0.783816i	$-0.713270\pi$
$523$	−16.4576	+	4.83240i	−0.719643	+	0.211306i	−0.0986496	+	0.995122i	$0.531452\pi$
$524$	1.91771	+	2.21316i	0.0837757	+	0.0966823i
$525$	−1.53210	−	0.449864i	−0.0668661	−	0.0196337i
$526$	−1.21035	−	2.65029i	−0.0527736	−	0.115558i
$527$	−0.880649	+	6.12505i	−0.0383617	+	0.266811i
$528$	21.6461			0.942027
$529$	−22.6333	+	4.09076i	−0.984056	+	0.177859i
$530$	5.39015			0.234133
$531$	−1.29987	+	9.04078i	−0.0564095	+	0.392337i
$532$	−0.281161	−	0.615658i	−0.0121899	−	0.0266921i
$533$	51.7512	+	15.1955i	2.24159	+	0.658191i
$534$	23.6081	+	27.2452i	1.02162	+	1.17902i
$535$	30.5118	−	8.95907i	1.31914	−	0.387334i
$536$	0.771624	+	0.495893i	0.0333291	+	0.0214193i
$537$	0.0835634	−	0.182978i	0.00360603	−	0.00789610i
$538$	27.7347	−	32.0076i	1.19573	−	1.37994i
$539$	4.08698	−	2.62655i	0.176039	−	0.113133i
$540$	0.456254	+	3.17332i	0.0196341	+	0.136558i
$541$	−1.99577	−	13.8809i	−0.0858049	−	0.596786i	−0.986676	−	0.162699i	$-0.947980\pi$
$541$	−1.99577	−	13.8809i	−0.0858049	−	0.596786i	0.900871	−	0.434087i	$-0.142929\pi$
$542$	12.0678	−	7.75551i	0.518357	−	0.333128i
$543$	2.42049	−	2.79340i	0.103873	−	0.119876i
$544$	−20.3366	+	44.5311i	−0.871927	+	1.90925i
$545$	1.64285	+	1.05580i	0.0703721	+	0.0452254i
$546$	−11.2446	+	3.30172i	−0.481225	+	0.141300i
$547$	6.87817	+	7.93783i	0.294089	+	0.339397i	0.883496	−	0.468440i	$-0.155184\pi$
$547$	6.87817	+	7.93783i	0.294089	+	0.339397i	−0.589406	+	0.807837i	$0.700638\pi$
$548$	−25.3847	−	7.45363i	−1.08438	−	0.318403i
$549$	1.20419	+	2.63680i	0.0513934	+	0.112536i
$550$	2.13442	−	14.8453i	0.0910122	−	0.633004i
$551$	−0.373881			−0.0159279
$552$	−0.217028	−	2.42099i	−0.00923731	−	0.103044i
$553$	−2.72091			−0.115705
$554$	2.42170	−	16.8433i	0.102888	−	0.715602i
$555$	−0.0867485	−	0.189953i	−0.00368227	−	0.00806304i
$556$	−16.6728	−	4.89558i	−0.707085	−	0.207619i
$557$	8.42296	+	9.72062i	0.356892	+	0.411876i	0.905596	−	0.424141i	$-0.139424\pi$
$557$	8.42296	+	9.72062i	0.356892	+	0.411876i	−0.548704	+	0.836017i	$0.684878\pi$
$558$	−1.78218	+	0.523296i	−0.0754458	+	0.0221529i
$559$	−57.6025	−	37.0189i	−2.43633	−	1.56573i
$560$	−3.41454	+	7.47680i	−0.144291	+	0.315952i
$561$	20.4917	−	23.6487i	0.865160	−	0.998448i
$562$	36.0875	−	23.1920i	1.52226	−	0.978297i
$563$	−3.74781	−	26.0666i	−0.157951	−	1.09858i	−0.902401	−	0.430897i	$-0.858197\pi$
$563$	−3.74781	−	26.0666i	−0.157951	−	1.09858i	0.744450	−	0.667678i	$-0.232712\pi$
$564$	−2.62983	−	18.2909i	−0.110736	−	0.770184i
$565$	−32.4118	+	20.8298i	−1.36357	+	0.876315i
$566$	−22.0716	+	25.4720i	−0.927739	+	1.07067i
$567$	0.415415	−	0.909632i	0.0174458	−	0.0382010i
$568$	0.424366	+	0.272723i	0.0178060	+	0.0114432i
$569$	12.9605	−	3.80554i	0.543332	−	0.159537i	0.00146172	−	0.999999i	$-0.499535\pi$
$569$	12.9605	−	3.80554i	0.543332	−	0.159537i	0.541870	+	0.840462i	$0.317717\pi$
$570$	−0.909635	−	1.04977i	−0.0381004	−	0.0439702i
$571$	−3.10563	−	0.911897i	−0.129967	−	0.0381617i	0.216102	−	0.976371i	$-0.430666\pi$
$571$	−3.10563	−	0.911897i	−0.129967	−	0.0381617i	−0.346069	+	0.938209i	$0.612484\pi$
$572$	−21.2599	−	46.5527i	−0.888922	−	1.94647i
$573$	0.841035	−	5.84953i	0.0351347	−	0.244367i
$574$	17.2027			0.718028
$575$	−7.64695	−	0.408693i	−0.318900	−	0.0170437i
$576$	−5.78334			−0.240972
$577$	2.37207	−	16.4981i	0.0987506	−	0.686825i	−0.878964	−	0.476888i	$-0.841765\pi$
$577$	2.37207	−	16.4981i	0.0987506	−	0.686825i	0.977715	−	0.209938i	$-0.0673261\pi$
$578$	19.6661	+	43.0628i	0.818002	+	1.79117i
$579$	−1.80475	−	0.529923i	−0.0750029	−	0.0220228i
$580$	−2.01547	−	2.32598i	−0.0836879	−	0.0965810i
$581$	−14.1999	+	4.16947i	−0.589112	+	0.172979i
$582$	2.42885	+	1.56092i	0.100679	+	0.0647024i
$583$	3.05002	−	6.67862i	0.126319	−	0.276600i
$584$	−0.132593	+	0.153021i	−0.00548674	+	0.00633204i
$585$	−9.40728	+	6.04569i	−0.388943	+	0.249959i
$586$	−1.71580	−	11.9336i	−0.0708790	−	0.492974i
$587$	0.628905	+	4.37413i	0.0259577	+	0.180540i	0.998675	−	0.0514520i	$-0.0163849\pi$
$587$	0.628905	+	4.37413i	0.0259577	+	0.180540i	−0.972718	+	0.231992i	$0.925476\pi$
$588$	−1.46197	+	0.939551i	−0.0602906	+	0.0387464i
$589$	0.245025	−	0.282774i	0.0100961	−	0.0116515i
$590$	13.5328	−	29.6327i	0.557136	−	1.21996i
$591$	−13.3049	−	8.55056i	−0.547292	−	0.351723i
$592$	0.483928	−	0.142094i	0.0198893	−	0.00584003i
$593$	27.3543	+	31.5685i	1.12330	+	1.29636i	0.950263	+	0.311448i	$0.100814\pi$
$593$	27.3543	+	31.5685i	1.12330	+	1.29636i	0.173041	+	0.984915i	$0.444641\pi$
$594$	9.01215	+	2.64621i	0.369773	+	0.108575i
$595$	4.93606	+	10.8085i	0.202359	+	0.443104i
$596$	−0.464545	+	3.23098i	−0.0190285	+	0.132346i
$597$	−10.4450			−0.427487
$598$	−48.8360	+	27.8194i	−1.99705	+	1.13762i
$599$	−3.48278			−0.142302			−0.0711512	−	0.997466i	$-0.522667\pi$
$599$	−3.48278			−0.142302			−0.0711512	+	0.997466i	$0.522667\pi$
$600$	0.115176	−	0.801064i	0.00470203	−	0.0327033i
$601$	−8.76703	−	19.1971i	−0.357614	−	0.783066i	−0.999863	−	0.0165697i	$-0.994725\pi$
$601$	−8.76703	−	19.1971i	−0.357614	−	0.783066i	0.642248	−	0.766497i	$-0.278002\pi$
$602$	−20.9544	−	6.15277i	−0.854037	−	0.250768i
$603$	1.18512	+	1.36770i	0.0482617	+	0.0556970i
$604$	36.1880	−	10.6257i	1.47247	−	0.432355i
$605$	19.5577	+	12.5690i	0.795134	+	0.511001i
$606$	−2.35272	+	5.15173i	−0.0955726	+	0.209275i
$607$	11.0728	−	12.7786i	0.449429	−	0.518669i	−0.485147	−	0.874433i	$-0.661234\pi$
$607$	11.0728	−	12.7786i	0.449429	−	0.518669i	0.934576	+	0.355764i	$0.115779\pi$
$608$	2.49019	−	1.60035i	0.100991	−	0.0649028i
$609$	0.136622	+	0.950228i	0.00553621	+	0.0385052i
$610$	−1.47136	−	10.2335i	−0.0595735	−	0.414342i
$611$	54.2231	−	34.8471i	2.19363	−	1.40976i
$612$	−7.33016	+	8.45945i	−0.296304	+	0.341953i
$613$	0.208225	−	0.455949i	0.00841013	−	0.0184156i	−0.905380	−	0.424602i	$-0.860414\pi$
$613$	0.208225	−	0.455949i	0.00841013	−	0.0184156i	0.913790	+	0.406186i	$0.133141\pi$
$614$	15.4953	+	9.95823i	0.625340	+	0.401882i
$615$	15.7498	−	4.62455i	0.635092	−	0.186480i
$616$	1.61247	+	1.86089i	0.0649682	+	0.0749773i
$617$	13.7578	+	4.03965i	0.553868	+	0.162630i	0.546676	−	0.837344i	$-0.315893\pi$
$617$	13.7578	+	4.03965i	0.553868	+	0.162630i	0.00719113	+	0.999974i	$0.497711\pi$
$618$	−8.48651	−	18.5829i	−0.341378	−	0.747513i
$619$	−0.404178	+	2.81112i	−0.0162453	+	0.112988i	−0.996331	−	0.0855886i	$-0.972723\pi$
$619$	−0.404178	+	2.81112i	−0.0162453	+	0.112988i	0.980085	+	0.198577i	$0.0636320\pi$
$620$	3.08004			0.123697
$621$	0.934889	−	4.70383i	0.0375158	−	0.188758i
$622$	−20.2329			−0.811265
$623$	−2.65370	+	18.4569i	−0.106318	+	0.739459i
$624$	−11.2196	−	24.5676i	−0.449145	−	0.983490i
$625$	13.8804	+	4.07566i	0.555217	+	0.163027i
$626$	−7.36179	−	8.49595i	−0.294236	−	0.339567i
$627$	−1.81543	+	0.533059i	−0.0725014	+	0.0212883i
$628$	19.1196	+	12.2874i	0.762956	+	0.490322i
$629$	0.302879	−	0.663213i	0.0120766	−	0.0264440i
$630$	−2.33563	+	2.69547i	−0.0930539	+	0.107390i
$631$	25.5967	−	16.4500i	1.01899	−	0.654864i	0.0792839	−	0.996852i	$-0.474737\pi$
$631$	25.5967	−	16.4500i	1.01899	−	0.654864i	0.939704	+	0.341988i	$0.111100\pi$
$632$	−0.196260	−	1.36502i	−0.00780679	−	0.0542974i
$633$	−1.57939	−	10.9849i	−0.0627750	−	0.436610i
$634$	−0.554773	+	0.356531i	−0.0220328	+	0.0141596i
$635$	−19.4601	+	22.4582i	−0.772251	+	0.891226i
$636$	−1.09103	+	2.38903i	−0.0432623	+	0.0947312i
$637$	−5.09940	−	3.27718i	−0.202045	−	0.129847i
$638$	−8.65167	+	2.54036i	−0.342523	+	0.100574i
$639$	0.651772	+	0.752185i	0.0257837	+	0.0297560i
$640$	−7.11536	−	2.08926i	−0.281259	−	0.0825851i
$641$	−3.37836	−	7.39757i	−0.133437	−	0.292186i	0.831105	−	0.556116i	$-0.187709\pi$
$641$	−3.37836	−	7.39757i	−0.133437	−	0.292186i	−0.964542	+	0.263929i	$0.914982\pi$
$642$	−4.74287	+	32.9874i	−0.187186	+	1.30191i
$643$	−12.4490			−0.490939			−0.245470	−	0.969404i	$-0.578942\pi$
$643$	−12.4490			−0.490939			−0.245470	+	0.969404i	$0.578942\pi$
$644$	−5.78626	+	5.99848i	−0.228011	+	0.236373i
$645$	−20.8386			−0.820518
$646$	0.690202	−	4.80046i	0.0271556	−	0.188872i
$647$	0.0678380	+	0.148545i	0.00266699	+	0.00583989i	0.910961	−	0.412493i	$-0.135342\pi$
$647$	0.0678380	+	0.148545i	0.00266699	+	0.00583989i	−0.908294	+	0.418333i	$0.862615\pi$
$648$	0.486304	+	0.142792i	0.0191038	+	0.00560939i
$649$	−29.0586	−	33.5354i	−1.14065	−	1.31638i
$650$	−17.9551	+	5.27210i	−0.704258	+	0.206789i
$651$	−0.808214	−	0.519408i	−0.0316764	−	0.0203572i
$652$	11.4699	−	25.1156i	0.449196	−	0.983601i
$653$	−29.2821	+	33.7934i	−1.14590	+	1.32244i	−0.206961	+	0.978349i	$0.566357\pi$
$653$	−29.2821	+	33.7934i	−1.14590	+	1.32244i	−0.938937	+	0.344088i	$0.888188\pi$
$654$	−1.72173	+	1.10649i	−0.0673249	+	0.0432671i
$655$	0.442404	+	3.07699i	0.0172861	+	0.120228i
$656$	5.64211	+	39.2417i	0.220287	+	1.53213i
$657$	−0.336072	+	0.215980i	−0.0131114	+	0.00842620i
$658$	13.4625	−	15.5365i	0.524823	−	0.605678i
$659$	−9.25850	+	20.2733i	−0.360660	+	0.789735i	0.639127	+	0.769101i	$0.279296\pi$
$659$	−9.25850	+	20.2733i	−0.360660	+	0.789735i	−0.999787	+	0.0206340i	$0.993432\pi$
$660$	−13.1027	−	8.42057i	−0.510021	−	0.327770i
$661$	16.1400	−	4.73913i	0.627773	−	0.184331i	0.0476558	−	0.998864i	$-0.484825\pi$
$661$	16.1400	−	4.73913i	0.627773	−	0.184331i	0.580117	+	0.814533i	$0.303007\pi$
$662$	34.6773	+	40.0197i	1.34777	+	1.55541i
$663$	−37.4616	−	10.9997i	−1.45489	−	0.427194i
$664$	−3.11597	−	6.82302i	−0.120923	−	0.264784i
$665$	0.102249	−	0.711155i	0.00396503	−	0.0275774i
$666$	0.218849			0.00848024
$667$	1.68634	+	4.28405i	0.0652952	+	0.165879i
$668$	−20.1112			−0.778125
$669$	−3.10105	+	21.5683i	−0.119894	+	0.833879i
$670$	−2.68133	−	5.87130i	−0.103589	−	0.226828i
$671$	−13.5123	−	3.96757i	−0.521637	−	0.153166i
$672$	−4.97729	−	5.74410i	−0.192003	−	0.221584i
$673$	−9.49904	+	2.78917i	−0.366161	+	0.107515i	−0.459637	−	0.888107i	$-0.652020\pi$
$673$	−9.49904	+	2.78917i	−0.366161	+	0.107515i	0.0934757	+	0.995622i	$0.470202\pi$
$674$	−30.9553	−	19.8937i	−1.19235	−	0.766278i
$675$	0.663325	−	1.45248i	0.0255314	−	0.0559059i
$676$	−27.0215	+	31.1845i	−1.03929	+	1.19940i
$677$	−2.38491	+	1.53269i	−0.0916597	+	0.0589061i	−0.585668	−	0.810551i	$-0.699168\pi$
$677$	−2.38491	+	1.53269i	−0.0916597	+	0.0589061i	0.494008	+	0.869457i	$0.335531\pi$
$678$	−5.74634	−	39.9667i	−0.220687	−	1.53491i
$679$	0.212526	+	1.47815i	0.00815601	+	0.0567263i
$680$	−5.06631	+	3.25592i	−0.194284	+	0.124859i
$681$	−11.2375	+	12.9687i	−0.430621	+	0.496963i
$682$	3.74860	−	8.20828i	0.143541	−	0.314311i
$683$	−25.3432	−	16.2871i	−0.969732	−	0.623209i	−0.0430572	−	0.999073i	$-0.513710\pi$
$683$	−25.3432	−	16.2871i	−0.969732	−	0.623209i	−0.926675	+	0.375864i	$0.877346\pi$
$684$	0.649405	−	0.190682i	0.0248306	−	0.00729092i
$685$	−18.3914	−	21.2248i	−0.702698	−	0.810956i
$686$	−1.85504	−	0.544688i	−0.0708256	−	0.0207963i
$687$	−4.19484	−	9.18541i	−0.160043	−	0.350445i
$688$	7.16271	−	49.8177i	0.273076	−	1.89928i
$689$	−9.16087			−0.349001
$690$	−7.92587	+	15.1577i	−0.301733	+	0.577046i
$691$	42.1737			1.60436			0.802182	−	0.597079i	$-0.203672\pi$
$691$	42.1737			1.60436			0.802182	+	0.597079i	$0.203672\pi$
$692$	3.70477	−	25.7673i	0.140834	−	0.979524i
$693$	2.01817	+	4.41918i	0.0766640	+	0.167871i
$694$	−12.9227	−	3.79445i	−0.490539	−	0.144035i
$695$	−12.0795	−	13.9405i	−0.458203	−	0.528794i
$696$	−0.466852	+	0.137080i	−0.0176960	+	0.00519601i
$697$	48.2133	+	30.9848i	1.82621	+	1.17363i
$698$	22.0375	−	48.2555i	0.834133	−	1.82650i
$699$	−13.5645	+	15.6543i	−0.513058	+	0.592101i
$700$	−2.33444	+	1.50025i	−0.0882334	+	0.0567042i
$701$	5.75402	+	40.0201i	0.217326	+	1.51154i	0.747850	+	0.663867i	$0.231086\pi$
$701$	5.75402	+	40.0201i	0.217326	+	1.51154i	−0.530524	+	0.847670i	$0.678005\pi$
$702$	−1.66783	−	11.6000i	−0.0629483	−	0.437815i
$703$	−0.0370872	+	0.0238345i	−0.00139877	+	0.000898934i
$704$	18.3994	−	21.2340i	0.693453	−	0.800288i
$705$	8.14879	−	17.8434i	0.306901	−	0.672020i
$706$	27.2444	+	17.5089i	1.02536	+	0.658957i
$707$	−2.81073	+	0.825304i	−0.105708	+	0.0310388i
$708$	10.3946	+	11.9961i	0.390655	+	0.450839i
$709$	50.4498	+	14.8134i	1.89468	+	0.556328i	0.992038	+	0.125936i	$0.0401933\pi$
$709$	50.4498	+	14.8134i	1.89468	+	0.556328i	0.902642	+	0.430393i	$0.141625\pi$
$710$	−1.47464	−	3.22900i	−0.0553421	−	0.121182i
$711$	0.387226	−	2.69321i	0.0145221	−	0.101003i
$712$	−9.45079			−0.354183
$713$	−4.34527	−	1.53216i	−0.162732	−	0.0573800i
$714$	−12.4527			−0.466031
$715$	7.73149	−	53.7737i	0.289141	−	2.01102i
$716$	−0.145220	−	0.317988i	−0.00542714	−	0.0118838i
$717$	22.5774	+	6.62931i	0.843167	+	0.247576i
$718$	−30.0904	−	34.7262i	−1.12297	−	1.29597i
$719$	−40.1087	+	11.7770i	−1.49580	+	0.439207i	−0.924388	−	0.381454i	$-0.875423\pi$
$719$	−40.1087	+	11.7770i	−1.49580	+	0.439207i	−0.571415	+	0.820661i	$0.693605\pi$
$720$	−6.91475	−	4.44384i	−0.257698	−	0.165612i
$721$	4.38953	−	9.61174i	0.163475	−	0.357960i
$722$	23.8634	−	27.5398i	0.888104	−	1.02493i
$723$	−24.0588	+	15.4617i	−0.894758	+	0.575026i
$724$	−0.914149	−	6.35804i	−0.0339741	−	0.236295i
$725$	0.218155	+	1.51730i	0.00810207	+	0.0563512i
$726$	−20.4967	+	13.1724i	−0.760703	+	0.488874i
$727$	−25.6568	+	29.6096i	−0.951559	+	1.09816i	0.0435182	+	0.999053i	$0.486143\pi$
$727$	−25.6568	+	29.6096i	−0.951559	+	1.09816i	−0.995077	+	0.0991048i	$0.968402\pi$
$728$	1.27626	−	2.79463i	0.0473015	−	0.103576i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	1.36711	−	0.401419i	0.0505990	−	0.0148572i
$731$	−47.6458	−	54.9862i	−1.76224	−	2.03374i
$732$	4.83353	+	1.41925i	0.178653	+	0.0524571i
$733$	−7.18572	−	15.7345i	−0.265411	−	0.581168i	0.729264	−	0.684232i	$-0.239863\pi$
$733$	−7.18572	−	15.7345i	−0.265411	−	0.581168i	−0.994675	+	0.103064i	$0.967135\pi$
$734$	−2.34170	+	16.2869i	−0.0864338	+	0.601160i
$735$	−1.84478			−0.0680458
$736$	−29.5690	−	21.3153i	−1.08993	−	0.785692i
$737$	−8.79202			−0.323858
$738$	−2.44820	+	17.0276i	−0.0901197	+	0.626796i
$739$	9.19395	+	20.1319i	0.338205	+	0.740566i	0.999958	−	0.00915617i	$-0.00291454\pi$
$739$	9.19395	+	20.1319i	0.338205	+	0.740566i	−0.661753	+	0.749722i	$0.730187\pi$
$740$	−0.348203	−	0.102242i	−0.0128002	−	0.00375848i
$741$	1.54598	+	1.78415i	0.0567929	+	0.0655425i
$742$	−2.80348	+	0.823175i	−0.102919	+	0.0302197i
$743$	19.3367	+	12.4269i	0.709395	+	0.455900i	0.844933	−	0.534872i	$-0.179640\pi$
$743$	19.3367	+	12.4269i	0.709395	+	0.455900i	−0.135538	+	0.990772i	$0.543276\pi$
$744$	0.202278	−	0.442927i	0.00741587	−	0.0162385i
$745$	−2.26914	+	2.61872i	−0.0831347	+	0.0959426i
$746$	1.17648	−	0.756080i	0.0430741	−	0.0276821i
$747$	−2.10618	−	14.6488i	−0.0770609	−	0.535970i
$748$	−7.73910	−	53.8266i	−0.282970	−	1.96810i
$749$	−14.5013	+	9.31943i	−0.529867	+	0.340525i
$750$	−15.4077	+	17.7814i	−0.562608	+	0.649284i
$751$	3.61620	−	7.91836i	0.131957	−	0.288945i	−0.832107	−	0.554615i	$-0.812866\pi$
$751$	3.61620	−	7.91836i	0.131957	−	0.288945i	0.964064	+	0.265669i	$0.0855930\pi$
$752$	39.8563	+	25.6141i	1.45341	+	0.934050i
$753$	−5.21815	+	1.53219i	−0.190160	+	0.0558360i
$754$	7.36754	+	8.50260i	0.268310	+	0.309646i
$755$	38.4148	+	11.2796i	1.39806	+	0.410506i
$756$	−0.721928	−	1.58080i	−0.0262562	−	0.0574932i
$757$	−5.16195	+	35.9021i	−0.187614	+	1.30489i	0.650548	+	0.759465i	$0.274539\pi$
$757$	−5.16195	+	35.9021i	−0.187614	+	1.30489i	−0.838163	+	0.545421i	$0.816370\pi$
$758$	−15.2051			−0.552274
$759$	14.2962	+	18.3975i	0.518920	+	0.667787i
$760$	0.364145			0.0132089
$761$	−4.26735	+	29.6800i	−0.154691	+	1.07590i	0.753531	+	0.657412i	$0.228349\pi$
$761$	−4.26735	+	29.6800i	−0.154691	+	1.07590i	−0.908222	+	0.418488i	$0.862560\pi$
$762$	−12.9373	−	28.3288i	−0.468670	−	1.02624i
$763$	−1.01571	−	0.298239i	−0.0367711	−	0.0107970i
$764$	−6.72549	−	7.76163i	−0.243320	−	0.280806i
$765$	−11.4009	+	3.34761i	−0.412201	+	0.121033i
$766$	−1.88822	−	1.21348i	−0.0682240	−	0.0438449i
$767$	−22.9998	+	50.3625i	−0.830473	+	1.81848i
$768$	12.6640	−	14.6150i	0.456973	−	0.527374i
$769$	22.2627	−	14.3074i	0.802814	−	0.515937i	−0.0737187	−	0.997279i	$-0.523487\pi$
$769$	22.2627	−	14.3074i	0.802814	−	0.515937i	0.876533	+	0.481342i	$0.159850\pi$
$770$	−2.46594	−	17.1510i	−0.0888663	−	0.618078i
$771$	−1.80256	−	12.5371i	−0.0649177	−	0.451512i
$772$	−2.74988	+	1.76724i	−0.0989703	+	0.0636044i
$773$	18.3777	−	21.2090i	0.661001	−	0.762836i	−0.321939	−	0.946760i	$-0.604335\pi$
$773$	18.3777	−	21.2090i	0.661001	−	0.762836i	0.982940	+	0.183924i	$0.0588802\pi$
$774$	9.07226	−	19.8655i	0.326096	−	0.714050i
$775$	−1.29054	−	0.829378i	−0.0463575	−	0.0297921i
$776$	−0.726224	+	0.213239i	−0.0260699	+	0.00765482i
$777$	0.0741282	+	0.0855485i	0.00265933	+	0.00306903i
$778$	6.96362	+	2.04470i	0.249658	+	0.0733061i
$779$	−1.43956	−	3.15221i	−0.0515778	−	0.112940i
$780$	−2.76566	+	19.2356i	−0.0990265	+	0.688745i
$781$	−4.83529			−0.173020
$782$	−58.1182	+	13.7432i	−2.07830	+	0.491457i
$783$	−0.960000			−0.0343076
$784$	0.634096	−	4.41023i	0.0226463	−	0.157508i
$785$	10.0223	+	21.9458i	0.357712	+	0.783281i
$786$	−3.12591	−	0.917849i	−0.111497	−	0.0327386i
$787$	−0.859488	−	0.991902i	−0.0306374	−	0.0353575i	0.740224	−	0.672360i	$-0.234719\pi$
$787$	−0.859488	−	0.991902i	−0.0306374	−	0.0353575i	−0.770861	+	0.637003i	$0.780174\pi$
$788$	−26.3717	+	7.74344i	−0.939455	+	0.275849i
$789$	1.26778	+	0.814753i	0.0451342	+	0.0290060i
$790$	−4.03137	+	8.82746i	−0.143430	+	0.314067i
$791$	13.6766	−	15.7837i	0.486285	−	0.561203i
$792$	−2.07143	+	1.33122i	−0.0736049	+	0.0473030i
$793$	2.50065	+	17.3924i	0.0888008	+	0.617623i
$794$	3.74121	+	26.0207i	0.132770	+	0.923439i
$795$	−2.34540	+	1.50730i	−0.0831828	+	0.0534583i
$796$	−11.8870	+	13.7183i	−0.421322	+	0.486232i
$797$	13.1317	−	28.7543i	0.465147	−	1.01853i	−0.521137	−	0.853473i	$-0.674492\pi$
$797$	13.1317	−	28.7543i	0.465147	−	1.01853i	0.986284	−	0.165057i	$-0.0527808\pi$
$798$	0.633432	+	0.407082i	0.0224232	+	0.0144105i
$799$	65.7144	−	19.2955i	2.32481	−	0.682625i
$800$	−7.94762	−	9.17204i	−0.280991	−	0.324281i
$801$	−17.8914	−	5.25338i	−0.632160	−	0.185619i
$802$	−13.3939	−	29.3285i	−0.472954	−	1.03562i
$803$	0.276205	−	1.92105i	0.00974706	−	0.0677923i
$804$	3.14502			0.110916
$805$	−8.60982	+	2.03597i	−0.303456	+	0.0717584i
$806$	−11.2591			−0.396584
$807$	−3.11756	+	21.6831i	−0.109743	+	0.763281i
$808$	−0.616773	−	1.35055i	−0.0216980	−	0.0475120i
$809$	38.2677	+	11.2364i	1.34542	+	0.395051i	0.873601	−	0.486643i	$-0.161779\pi$
$809$	38.2677	+	11.2364i	1.34542	+	0.395051i	0.471820	+	0.881695i	$0.343597\pi$
$810$	−2.33563	−	2.69547i	−0.0820658	−	0.0947090i
$811$	34.9495	−	10.2621i	1.22724	−	0.360351i	0.397034	−	0.917804i	$-0.370039\pi$
$811$	34.9495	−	10.2621i	1.22724	−	0.360351i	0.830209	+	0.557453i	$0.188221\pi$
$812$	1.40349	+	0.901968i	0.0492529	+	0.0316529i
$813$	−3.08229	+	6.74926i	−0.108100	+	0.236707i
$814$	−0.696258	+	0.803524i	−0.0244038	+	0.0281635i
$815$	24.6569	−	15.8460i	0.863693	−	0.555062i
$816$	−4.08421	−	28.4063i	−0.142976	−	0.994419i
$817$	0.626087	+	4.35453i	0.0219040	+	0.152346i
$818$	50.2713	−	32.3074i	1.75770	−	1.12960i
$819$	3.96955	−	4.58110i	0.138707	−	0.160077i
$820$	11.8502	−	25.9483i	0.413827	−	0.906155i
$821$	−22.7184	−	14.6002i	−0.792877	−	0.509551i	0.0804075	−	0.996762i	$-0.474378\pi$
$821$	−22.7184	−	14.6002i	−0.792877	−	0.509551i	−0.873284	+	0.487211i	$0.838014\pi$
$822$	28.2405	−	8.29215i	0.985000	−	0.289222i
$823$	5.58253	+	6.44258i	0.194595	+	0.224574i	0.844659	−	0.535305i	$-0.179803\pi$
$823$	5.58253	+	6.44258i	0.194595	+	0.224574i	−0.650064	+	0.759879i	$0.725258\pi$
$824$	5.13860	+	1.50883i	0.179011	+	0.0525625i
$825$	3.22257	+	7.05644i	0.112195	+	0.245674i
$826$	−2.51310	+	17.4790i	−0.0874420	+	0.608173i
$827$	26.6089			0.925282			0.462641	−	0.886546i	$-0.346902\pi$
$827$	26.6089			0.925282			0.462641	+	0.886546i	$0.346902\pi$
$828$	−5.11395	−	6.58104i	−0.177722	−	0.228707i
$829$	9.89782			0.343766			0.171883	−	0.985117i	$-0.445015\pi$
$829$	9.89782			0.343766			0.171883	+	0.985117i	$0.445015\pi$
$830$	−7.51191	+	52.2465i	−0.260742	+	1.81350i
$831$	3.65629	+	8.00617i	0.126835	+	0.277731i
$832$	−33.6366	−	9.87660i	−1.16614	−	0.342410i
$833$	−4.21796	−	4.86778i	−0.146143	−	0.168659i
$834$	18.5485	−	5.44633i	0.642282	−	0.188591i
$835$	−17.9597	−	11.5420i	−0.621520	−	0.399427i
$836$	−1.36594	+	2.99099i	−0.0472420	+	0.103446i
$837$	0.629142	−	0.726068i	0.0217463	−	0.0250966i
$838$	1.03296	−	0.663845i	0.0356831	−	0.0229322i
$839$	6.56767	+	45.6791i	0.226741	+	1.57702i	0.711701	+	0.702483i	$0.247925\pi$
$839$	6.56767	+	45.6791i	0.226741	+	1.57702i	−0.484960	+	0.874537i	$0.661166\pi$
$840$	−0.133064	−	0.925483i	−0.00459116	−	0.0319322i
$841$	−23.6211	+	15.1803i	−0.814519	+	0.523460i
$842$	48.3515	−	55.8006i	1.66630	−	1.92302i
$843$	−9.21725	+	20.1830i	−0.317459	+	0.695138i
$844$	−16.2247	−	10.4270i	−0.558477	−	0.358911i
$845$	−42.0278	+	12.3405i	−1.44580	+	0.424526i
$846$	13.4625	+	15.5365i	0.462850	+	0.534157i
$847$	−12.0917	−	3.55044i	−0.415476	−	0.121995i
$848$	−2.79725	−	6.12512i	−0.0960580	−	0.210338i
$849$	2.48099	−	17.2556i	0.0851472	−	0.592212i
$850$	−19.8842			−0.682022
$851$	0.440379	+	0.317454i	0.0150960	+	0.0108822i
$852$	1.72965			0.0592568
$853$	−2.12568	+	14.7844i	−0.0727818	+	0.506208i	0.920523	+	0.390688i	$0.127763\pi$
$853$	−2.12568	+	14.7844i	−0.0727818	+	0.506208i	−0.993305	+	0.115521i	$0.963146\pi$
$854$	2.32811	+	5.09786i	0.0796664	+	0.174445i
$855$	0.689365	+	0.202416i	0.0235758	+	0.00692248i
$856$	−5.72132	−	6.60275i	−0.195551	−	0.225677i
$857$	13.1685	−	3.86661i	0.449826	−	0.132081i	−0.0489698	−	0.998800i	$-0.515594\pi$
$857$	13.1685	−	3.86661i	0.449826	−	0.132081i	0.498796	+	0.866719i	$0.333776\pi$
$858$	47.8967	+	30.7813i	1.63517	+	1.05086i
$859$	8.87395	−	19.4312i	0.302775	−	0.662985i	−0.695692	−	0.718341i	$-0.744902\pi$
$859$	8.87395	−	19.4312i	0.302775	−	0.662985i	0.998467	+	0.0553556i	$0.0176292\pi$
$860$	−23.7153	+	27.3689i	−0.808684	+	0.933271i
$861$	−7.48538	+	4.81056i	−0.255101	+	0.163943i
$862$	−1.65087	−	11.4820i	−0.0562288	−	0.391080i
$863$	−5.31206	−	36.9462i	−0.180825	−	1.25766i	−0.854819	−	0.518926i	$-0.826332\pi$
$863$	−5.31206	−	36.9462i	−0.180825	−	1.25766i	0.673994	−	0.738736i	$-0.264577\pi$
$864$	6.39398	−	4.10916i	0.217528	−	0.139796i
$865$	18.0965	−	20.8845i	0.615299	−	0.710093i
$866$	18.9336	−	41.4588i	0.643389	−	1.40883i
$867$	−20.5993	−	13.2384i	−0.699589	−	0.449598i
$868$	−1.60196	+	0.470379i	−0.0543742	+	0.0159657i
$869$	8.65644	+	9.99006i	0.293649	+	0.338890i
$870$	3.28525	+	0.964638i	0.111381	+	0.0327043i
$871$	4.55708	+	9.97861i	0.154411	+	0.338112i
$872$	0.0763561	−	0.531068i	0.00258574	−	0.0179842i
$873$	−1.49335			−0.0505423
$874$	3.40557	+	1.20082i	0.115195	+	0.0406184i
$875$	−12.1696			−0.411408
$876$	−0.0988023	+	0.687185i	−0.00333822	+	0.0232178i
$877$	−5.77652	−	12.6488i	−0.195059	−	0.427120i	0.786678	−	0.617364i	$-0.211799\pi$
$877$	−5.77652	−	12.6488i	−0.195059	−	0.427120i	−0.981737	+	0.190244i	$0.939072\pi$
$878$	−28.7129	−	8.43087i	−0.969014	−	0.284528i
$879$	4.08370	+	4.71285i	0.137740	+	0.158960i
$880$	38.3149	−	11.2503i	1.29159	−	0.379246i
$881$	−13.9856	−	8.98799i	−0.471186	−	0.302813i	0.283414	−	0.958998i	$-0.408533\pi$
$881$	−13.9856	−	8.98799i	−0.471186	−	0.302813i	−0.754600	+	0.656185i	$0.772169\pi$
$882$	0.803143	−	1.75864i	0.0270432	−	0.0592164i
$883$	33.7425	−	38.9409i	1.13553	−	1.31047i	0.191164	−	0.981558i	$-0.438774\pi$
$883$	33.7425	−	38.9409i	1.13553	−	1.31047i	0.944362	−	0.328909i	$-0.106681\pi$
$884$	−57.0799	+	36.6830i	−1.91980	+	1.23378i
$885$	2.39798	+	16.6783i	0.0806071	+	0.560634i
$886$	−5.43173	−	37.7785i	−0.182482	−	1.26919i
$887$	−20.6376	+	13.2630i	−0.692941	+	0.445326i	−0.839130	−	0.543930i	$-0.816936\pi$
$887$	−20.6376	+	13.2630i	−0.692941	+	0.445326i	0.146189	+	0.989257i	$0.453299\pi$
$888$	−0.0375707	+	0.0433590i	−0.00126079	+	0.00145503i
$889$	6.69165	−	14.6527i	0.224431	−	0.491435i
$890$	55.9480	+	35.9556i	1.87538	+	1.20523i
$891$	−4.66142	+	1.36872i	−0.156163	+	0.0458537i
$892$	24.7982	+	28.6186i	0.830304	+	0.958222i
$893$	−3.97347	−	1.16672i	−0.132967	−	0.0390426i
$894$	−1.50855	−	3.30326i	−0.0504534	−	0.110478i
$895$	0.0528116	−	0.367313i	0.00176530	−	0.0122779i
$896$	4.01985			0.134294
$897$	13.4705	−	25.7615i	0.449766	−	0.860150i
$898$	48.4914			1.61818
$899$	−0.131257	+	0.912909i	−0.00437765	+	0.0304472i
$900$	−1.15276	−	2.52418i	−0.0384252	−	0.0841395i
$901$	−9.33984	−	2.74242i	−0.311155	−	0.0913634i
$902$	−54.7296	−	63.1614i	−1.82230	−	2.10304i
$903$	10.8384	−	3.18244i	0.360679	−	0.105905i
$904$	8.90479	+	5.72276i	0.296169	+	0.190336i
$905$	2.83258	−	6.20249i	0.0941583	−	0.206178i
$906$	−27.4771	+	31.7102i	−0.912865	+	1.05350i
$907$	−28.3308	+	18.2071i	−0.940709	+	0.604557i	−0.918596	−	0.395198i	$-0.870676\pi$
$907$	−28.3308	+	18.2071i	−0.940709	+	0.604557i	−0.0221133	+	0.999755i	$0.507039\pi$
$908$	4.24406	+	29.5181i	0.140844	+	0.979591i
$909$	−0.416895	−	2.89957i	−0.0138275	−	0.0961727i
$910$	−18.1876	+	11.6884i	−0.602912	+	0.387468i
$911$	−19.8711	+	22.9325i	−0.658360	+	0.759788i	−0.982508	−	0.186218i	$-0.940377\pi$
$911$	−19.8711	+	22.9325i	−0.658360	+	0.759788i	0.324148	+	0.946006i	$0.394922\pi$
$912$	−0.720857	+	1.57846i	−0.0238699	+	0.0522679i
$913$	60.4849	+	38.8713i	2.00176	+	1.28645i
$914$	−48.6139	+	14.2743i	−1.60800	+	0.472153i
$915$	3.50192	+	4.04143i	0.115770	+	0.133605i
$916$	−16.8378	−	4.94403i	−0.556337	−	0.163355i
$917$	−0.700012	−	1.53281i	−0.0231164	−	0.0506179i
$918$	1.77220	−	12.3260i	0.0584915	−	0.406817i
$919$	−34.5350			−1.13921			−0.569603	−	0.821920i	$-0.692903\pi$
$919$	−34.5350			−1.13921			−0.569603	+	0.821920i	$0.692903\pi$
$920$	−1.64242	−	4.17249i	−0.0541491	−	0.137563i
$921$	−9.52714			−0.313930
$922$	−4.05128	+	28.1773i	−0.133422	+	0.927969i
$923$	2.50623	+	5.48788i	0.0824936	+	0.180636i
$924$	8.10082	+	2.37862i	0.266498	+	0.0782507i
$925$	0.118366	+	0.136602i	0.00389185	+	0.00449144i
$926$	60.1334	−	17.6568i	1.97611	−	0.580237i
$927$	8.88921	+	5.71275i	0.291960	+	0.187631i
$928$	−3.03108	+	6.63714i	−0.0995001	+	0.217875i
$929$	−2.49559	+	2.88006i	−0.0818775	+	0.0944917i	−0.795210	−	0.606334i	$-0.792639\pi$
$929$	−2.49559	+	2.88006i	−0.0818775	+	0.0944917i	0.713333	+	0.700826i	$0.247185\pi$
$930$	−2.88259	+	1.85253i	−0.0945238	+	0.0607467i
$931$	0.0554259	+	0.385495i	0.00181651	+	0.0126341i
$932$	5.12292	+	35.6307i	0.167807	+	1.16712i
$933$	8.80387	−	5.65791i	0.288226	−	0.185232i
$934$	31.9085	−	36.8244i	1.04408	−	1.20493i
$935$	23.9804	−	52.5098i	0.784243	−	1.71725i
$936$	2.58455	+	1.66099i	0.0844787	+	0.0542912i
$937$	8.85372	−	2.59969i	0.289238	−	0.0849281i	−0.133895	−	0.990996i	$-0.542748\pi$
$937$	8.85372	−	2.59969i	0.289238	−	0.0849281i	0.423133	+	0.906067i	$0.360930\pi$
$938$	2.29125	+	2.64424i	0.0748119	+	0.0863375i
$939$	5.57912	+	1.63818i	0.182068	+	0.0534599i
$940$	−14.1613	−	31.0090i	−0.461892	−	1.01140i
$941$	−3.12399	+	21.7278i	−0.101839	+	0.708307i	0.873376	+	0.487047i	$0.161926\pi$
$941$	−3.12399	+	21.7278i	−0.101839	+	0.708307i	−0.975215	+	0.221260i	$0.928983\pi$
$942$	−25.2844			−0.823809
$943$	−29.6260	+	30.7126i	−0.964756	+	1.00014i
$944$	−40.6962			−1.32455
$945$	0.262540	−	1.82601i	0.00854043	−	0.0594000i
$946$	44.0749	+	96.5106i	1.43300	+	3.13783i
$947$	42.7586	+	12.5551i	1.38947	+	0.407985i	0.889054	−	0.457802i	$-0.151363\pi$
$947$	42.7586	+	12.5551i	1.38947	+	0.407985i	0.500414	+	0.865786i	$0.333181\pi$
$948$	−3.09652	−	3.57358i	−0.100570	−	0.116064i
$949$	−2.32348	+	0.682236i	−0.0754234	+	0.0221463i
$950$	1.01145	+	0.650018i	0.0328157	+	0.0210894i
$951$	0.141697	−	0.310272i	0.00459483	−	0.0100613i
$952$	2.13781	−	2.46716i	0.0692867	−	0.0799611i
$953$	−2.60147	+	1.67186i	−0.0842698	+	0.0541569i	−0.582097	−	0.813119i	$-0.697768\pi$
$953$	−2.60147	+	1.67186i	−0.0842698	+	0.0541569i	0.497827	+	0.867276i	$0.334131\pi$
$954$	−0.415820	−	2.89209i	−0.0134627	−	0.0936350i
$955$	−1.55153	−	10.7911i	−0.0502062	−	0.349192i
$956$	34.4009	−	22.1081i	1.11260	−	0.715027i
$957$	3.05419	−	3.52472i	0.0987280	−	0.113938i
$958$	0.311145	−	0.681313i	0.0100526	−	0.0220122i
$959$	12.8070	+	8.23054i	0.413559	+	0.265778i
$960$	−10.2368	+	3.00581i	−0.330392	+	0.0970120i
$961$	19.6962	+	22.7307i	0.635363	+	0.733248i
$962$	1.27285	+	0.373744i	0.0410385	+	0.0120500i
$963$	−7.16082	−	15.6800i	−0.230754	−	0.505281i
$964$	−7.07309	+	49.1944i	−0.227809	+	1.58445i
$965$	−3.46993			−0.111701
$966$	1.80747	−	9.09415i	0.0581543	−	0.292599i
$967$	0.671295			0.0215874			0.0107937	−	0.999942i	$-0.496564\pi$
$967$	0.671295			0.0215874			0.0107937	+	0.999942i	$0.496564\pi$
$968$	0.908997	−	6.32221i	0.0292163	−	0.203204i
$969$	1.04207	+	2.28182i	0.0334762	+	0.0733025i
$970$	5.11046	+	1.50057i	0.164087	+	0.0481803i
$971$	23.9918	+	27.6880i	0.769932	+	0.888549i	0.996340	−	0.0854834i	$-0.0272434\pi$
$971$	23.9918	+	27.6880i	0.769932	+	0.888549i	−0.226407	+	0.974033i	$0.572698\pi$
$972$	1.66745	−	0.489608i	0.0534835	−	0.0157042i
$973$	8.41168	+	5.40586i	0.269666	+	0.173304i
$974$	−11.0045	+	24.0965i	−0.352607	+	0.772102i
$975$	6.33847	−	7.31499i	0.202994	−	0.234267i
$976$	−10.8653	+	6.98272i	−0.347791	+	0.223512i
$977$	5.96752	+	41.5050i	0.190918	+	1.32786i	0.829586	+	0.558380i	$0.188577\pi$
$977$	5.96752	+	41.5050i	0.190918	+	1.32786i	−0.638668	+	0.769483i	$0.720514\pi$
$978$	4.37146	+	30.4042i	0.139784	+	0.972219i
$979$	76.2087	−	48.9763i	2.43564	−	1.56529i
$980$	−2.09945	+	2.42290i	−0.0670645	+	0.0773965i
$981$	0.439753	−	0.962925i	0.0140402	−	0.0307438i
$982$	24.2776	+	15.6023i	0.774729	+	0.497888i
$983$	13.0438	−	3.83000i	0.416032	−	0.122158i	−0.0670161	−	0.997752i	$-0.521348\pi$
$983$	13.0438	−	3.83000i	0.416032	−	0.122158i	0.483048	+	0.875594i	$0.339530\pi$
$984$	−2.95326	−	3.40825i	−0.0941466	−	0.108651i
$985$	−27.9945	−	8.21993i	−0.891979	−	0.261909i
$986$	4.96612	+	10.8743i	0.158153	+	0.346308i
$987$	−1.51327	+	10.5250i	−0.0481679	+	0.335015i
$988$	4.10266			0.130523
$989$	47.0718	−	26.8144i	1.49679	−	0.852649i
$990$	17.3273			0.550699
$991$	−6.59528	+	45.8711i	−0.209506	+	1.45715i	0.565268	+	0.824907i	$0.308773\pi$
$991$	−6.59528	+	45.8711i	−0.209506	+	1.45715i	−0.774774	+	0.632238i	$0.782136\pi$
$992$	−3.03337	−	6.64216i	−0.0963097	−	0.210889i
$993$	−26.2801	−	7.71653i	−0.833974	−	0.244877i
$994$	1.26010	+	1.45424i	0.0399681	+	0.0461256i
$995$	−18.4883	+	5.42866i	−0.586119	+	0.172100i
$996$	−21.6363	−	13.9048i	−0.685572	−	0.440590i
$997$	−3.34897	+	7.33321i	−0.106063	+	0.232245i	−0.955221	−	0.295894i	$-0.904383\pi$
$997$	−3.34897	+	7.33321i	−0.106063	+	0.232245i	0.849158	+	0.528139i	$0.177110\pi$
$998$	40.9260	−	47.2311i	1.29549	−	1.49507i
$999$	−0.0952273	+	0.0611988i	−0.00301286	+	0.00193625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.169.2	✓	60
23.3	even	11	inner	483.2.q.d.463.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.169.2	✓	60	1.1	even	1	trivial
483.2.q.d.463.2	yes	60	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.275145 + 1.91367i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-1.66745 - 0.489608i) q^{4} +(-1.20808 - 1.39419i) q^{5} +(1.85504 - 0.544688i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.210547 + 0.461033i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.275145 + 1.91367i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-1.66745 - 0.489608i) q^{4} +(-1.20808 - 1.39419i) q^{5} +(1.85504 - 0.544688i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.210547 + 0.461033i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(3.00043 - 1.92826i) q^{10} +(-0.691395 - 4.80876i) q^{11} +(0.247321 + 1.72016i) q^{12} +(-5.09940 + 3.27718i) q^{13} +(-1.26608 + 1.46113i) q^{14} +(-0.766351 + 1.67807i) q^{15} +(-3.74827 - 2.40887i) q^{16} +(-6.18009 + 1.81464i) q^{17} +(-1.26608 - 1.46113i) q^{18} +(0.373684 + 0.109723i) q^{19} +(1.33180 + 2.91623i) q^{20} +(0.142315 - 0.989821i) q^{21} +9.39262 q^{22} +(-0.428202 - 4.77668i) q^{23} +0.506835 q^{24} +(0.227245 - 1.58052i) q^{25} +(-4.86838 - 10.6603i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-1.13805 - 1.31338i) q^{28} +(-0.921113 + 0.270463i) q^{29} +(-3.00043 - 1.92826i) q^{30} +(0.399100 - 0.873907i) q^{31} +(4.97729 - 5.74410i) q^{32} +(-4.08698 + 2.62655i) q^{33} +(-1.77220 - 12.3260i) q^{34} +(-0.262540 - 1.82601i) q^{35} +(1.46197 - 0.939551i) q^{36} +(-0.0741282 + 0.0855485i) q^{37} +(-0.312792 + 0.684918i) q^{38} +(5.09940 + 3.27718i) q^{39} +(0.897126 - 0.263420i) q^{40} +(-5.82688 - 6.72457i) q^{41} +(1.85504 + 0.544688i) q^{42} +(4.69251 + 10.2752i) q^{43} +(-1.20154 + 8.35688i) q^{44} +1.84478 q^{45} +(9.25881 + 0.494839i) q^{46} -10.6332 q^{47} +(-0.634096 + 4.41023i) q^{48} +(0.415415 + 0.909632i) q^{49} +(2.96208 + 0.869744i) q^{50} +(4.21796 + 4.86778i) q^{51} +(10.1075 - 2.96784i) q^{52} +(1.27137 + 0.817059i) q^{53} +(-0.803143 + 1.75864i) q^{54} +(-5.86908 + 6.77328i) q^{55} +(-0.426377 + 0.274016i) q^{56} +(-0.0554259 - 0.385495i) q^{57} +(-0.264139 - 1.83713i) q^{58} +(7.68380 - 4.93808i) q^{59} +(2.09945 - 2.42290i) q^{60} +(1.20419 - 2.63680i) q^{61} +(1.56256 + 1.00420i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(3.78728 + 4.37076i) q^{64} +(10.7295 + 3.15046i) q^{65} +(-3.90184 - 8.54383i) q^{66} +(0.257551 - 1.79130i) q^{67} +11.1935 q^{68} +(-4.16714 + 2.37381i) q^{69} +3.56661 q^{70} +(0.141644 - 0.985153i) q^{71} +(-0.210547 - 0.461033i) q^{72} +(0.383307 + 0.112549i) q^{73} +(-0.143316 - 0.165395i) q^{74} +(-1.53210 + 0.449864i) q^{75} +(-0.569378 - 0.365917i) q^{76} +(2.01817 - 4.41918i) q^{77} +(-7.67453 + 8.85688i) q^{78} +(-2.28897 + 1.47103i) q^{79} +(1.16977 + 8.13592i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(14.4719 - 9.30050i) q^{82} +(-9.69155 + 11.1846i) q^{83} +(-0.721928 + 1.58080i) q^{84} +(9.99598 + 6.42402i) q^{85} +(-20.9544 + 6.15277i) q^{86} +(0.628666 + 0.725519i) q^{87} +(2.36257 + 0.693713i) q^{88} +(7.74611 + 16.9616i) q^{89} +(-0.507582 + 3.53031i) q^{90} -6.06166 q^{91} +(-1.62469 + 8.17453i) q^{92} -0.960726 q^{93} +(2.92568 - 20.3485i) q^{94} +(-0.298462 - 0.653542i) q^{95} +(-7.29266 - 2.14132i) q^{96} +(0.977938 + 1.12860i) q^{97} +(-1.85504 + 0.544688i) q^{98} +(4.08698 + 2.62655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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