LMFDB - Embedded newform 189.2.ba.a.101.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.159953 + 0.190625i) q^{2} +(-0.234154 + 1.71615i) q^{3} +(0.336544 + 1.90863i) q^{4} +(1.62936 - 1.36719i) q^{5} +(-0.289688 - 0.319140i) q^{6} +(2.64099 - 0.158668i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(-2.89034 - 0.803688i) q^{9} +O(q^{10})$	\(q+(-0.159953 + 0.190625i) q^{2} +(-0.234154 + 1.71615i) q^{3} +(0.336544 + 1.90863i) q^{4} +(1.62936 - 1.36719i) q^{5} +(-0.289688 - 0.319140i) q^{6} +(2.64099 - 0.158668i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(-2.89034 - 0.803688i) q^{9} +0.529283i q^{10} +(-0.919336 + 1.09562i) q^{11} +(-3.35430 + 0.130644i) q^{12} +(-1.30709 + 3.59121i) q^{13} +(-0.392189 + 0.528818i) q^{14} +(1.96479 + 3.11635i) q^{15} +(-3.41324 + 1.24232i) q^{16} +0.218194 q^{17} +(0.615524 - 0.422419i) q^{18} -2.96748i q^{19} +(3.15782 + 2.64972i) q^{20} +(-0.346102 + 4.56949i) q^{21} +(-0.0618021 - 0.350497i) q^{22} +(2.64486 - 7.26669i) q^{23} +(1.03960 - 1.34172i) q^{24} +(-0.0826545 + 0.468757i) q^{25} +(-0.475500 - 0.823590i) q^{26} +(2.05604 - 4.77208i) q^{27} +(1.19165 + 4.98728i) q^{28} +(-1.78349 - 4.90009i) q^{29} +(-0.908329 - 0.123934i) q^{30} +(3.81477 - 0.672647i) q^{31} +(0.979478 - 2.69109i) q^{32} +(-1.66498 - 1.83426i) q^{33} +(-0.0349009 + 0.0415932i) q^{34} +(4.08618 - 3.86926i) q^{35} +(0.561220 - 5.78708i) q^{36} +(-3.00625 + 5.20699i) q^{37} +(0.565677 + 0.474659i) q^{38} +(-5.85699 - 3.08406i) q^{39} +(-2.05269 + 0.361945i) q^{40} +(10.0627 + 3.66253i) q^{41} +(-0.815699 - 0.796881i) q^{42} +(1.29579 - 7.34878i) q^{43} +(-2.40054 - 1.38595i) q^{44} +(-5.80819 + 2.64216i) q^{45} +(0.962159 + 1.66651i) q^{46} +(-1.01967 + 5.78285i) q^{47} +(-1.33278 - 6.14853i) q^{48} +(6.94965 - 0.838080i) q^{49} +(-0.0761360 - 0.0907353i) q^{50} +(-0.0510911 + 0.374453i) q^{51} +(-7.29419 - 1.28616i) q^{52} +(-12.1036 - 6.98800i) q^{53} +(0.580807 + 1.15524i) q^{54} +3.04206i q^{55} +(-2.31908 - 1.15938i) q^{56} +(5.09265 + 0.694850i) q^{57} +(1.21936 + 0.443809i) q^{58} +(-1.48515 - 0.540550i) q^{59} +(-5.28674 + 4.79884i) q^{60} +(4.18950 + 0.738722i) q^{61} +(-0.481963 + 0.834784i) q^{62} +(-7.76089 - 1.66393i) q^{63} +(-3.27598 - 5.67416i) q^{64} +(2.78015 + 7.63839i) q^{65} +(0.615977 - 0.0239912i) q^{66} +(11.4276 - 9.58891i) q^{67} +(0.0734317 + 0.416452i) q^{68} +(11.8514 + 6.24050i) q^{69} +(0.0839802 + 1.39783i) q^{70} +(-4.29452 + 2.47944i) q^{71} +(2.05917 + 2.09829i) q^{72} +(-2.13740 + 1.23403i) q^{73} +(-0.511721 - 1.40594i) q^{74} +(-0.785104 - 0.251609i) q^{75} +(5.66384 - 0.998688i) q^{76} +(-2.25412 + 3.03939i) q^{77} +(1.52475 - 0.623182i) q^{78} +(-2.98202 - 2.50221i) q^{79} +(-3.86290 + 6.69073i) q^{80} +(7.70817 + 4.64587i) q^{81} +(-2.30773 + 1.33237i) q^{82} +(0.141502 - 0.0515026i) q^{83} +(-8.83795 + 0.877250i) q^{84} +(0.355515 - 0.298313i) q^{85} +(1.19360 + 1.42247i) q^{86} +(8.82691 - 1.91335i) q^{87} +(1.31705 - 0.479367i) q^{88} +6.80542 q^{89} +(0.425379 - 1.52981i) q^{90} +(-2.88221 + 9.69173i) q^{91} +(14.7595 + 2.60251i) q^{92} +(0.261118 + 6.70423i) q^{93} +(-0.939256 - 1.11936i) q^{94} +(-4.05712 - 4.83509i) q^{95} +(4.38897 + 2.31106i) q^{96} +(-12.2644 - 2.16255i) q^{97} +(-0.951861 + 1.45883i) q^{98} +(3.53773 - 2.42786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.159953	+	0.190625i	−0.113104	+	0.134792i	−0.819626	−	0.572899i	$-0.805819\pi$
$2$	−0.159953	+	0.190625i	−0.113104	+	0.134792i	0.706522	+	0.707691i	$0.250263\pi$
$3$	−0.234154	+	1.71615i	−0.135189	+	0.990820i
$3$	−0.234154	+	1.71615i	−0.135189	+	0.990820i
$4$	0.336544	+	1.90863i	0.168272	+	0.954317i
$5$	1.62936	−	1.36719i	0.728670	−	0.611427i	−0.201099	−	0.979571i	$-0.564451\pi$
$5$	1.62936	−	1.36719i	0.728670	−	0.611427i	0.929769	+	0.368144i	$0.120007\pi$
$6$	−0.289688	−	0.319140i	−0.118264	−	0.130288i
$7$	2.64099	−	0.158668i	0.998200	−	0.0599708i
$7$	2.64099	−	0.158668i	0.998200	−	0.0599708i
$8$	−0.848674	−	0.489982i	−0.300052	−	0.173235i
$9$	−2.89034	−	0.803688i	−0.963448	−	0.267896i
$10$			0.529283i			0.167374i
$11$	−0.919336	+	1.09562i	−0.277190	+	0.330342i	−0.886621	−	0.462497i	$-0.846954\pi$
$11$	−0.919336	+	1.09562i	−0.277190	+	0.330342i	0.609431	+	0.792839i	$0.291398\pi$
$12$	−3.35430	+	0.130644i	−0.968304	+	0.0377138i
$13$	−1.30709	+	3.59121i	−0.362522	+	0.996021i	0.615613	+	0.788049i	$0.288909\pi$
$13$	−1.30709	+	3.59121i	−0.362522	+	0.996021i	−0.978135	+	0.207972i	$0.933314\pi$
$14$	−0.392189	+	0.528818i	−0.104817	+	0.141333i
$15$	1.96479	+	3.11635i	0.507305	+	0.804639i
$16$	−3.41324	+	1.24232i	−0.853310	+	0.310580i
$17$	0.218194			0.0529198			0.0264599	−	0.999650i	$-0.491577\pi$
$17$	0.218194			0.0529198			0.0264599	+	0.999650i	$0.491577\pi$
$18$	0.615524	−	0.422419i	0.145080	−	0.0995652i
$19$		−	2.96748i		−	0.680788i	−0.940283	−	0.340394i	$-0.889440\pi$
$19$		−	2.96748i		−	0.680788i	0.940283	−	0.340394i	$-0.110560\pi$
$20$	3.15782	+	2.64972i	0.706109	+	0.592496i
$21$	−0.346102	+	4.56949i	−0.0755256	+	0.997144i
$22$	−0.0618021	−	0.350497i	−0.0131762	−	0.0747262i
$23$	2.64486	−	7.26669i	0.551491	−	1.51521i	−0.280184	−	0.959946i	$-0.590396\pi$
$23$	2.64486	−	7.26669i	0.551491	−	1.51521i	0.831675	−	0.555262i	$-0.187382\pi$
$24$	1.03960	−	1.34172i	0.212208	−	0.273878i
$25$	−0.0826545	+	0.468757i	−0.0165309	+	0.0937514i
$26$	−0.475500	−	0.823590i	−0.0932532	−	0.161519i
$27$	2.05604	−	4.77208i	0.395684	−	0.918387i
$28$	1.19165	+	4.98728i	0.225200	+	0.942508i
$29$	−1.78349	−	4.90009i	−0.331185	−	0.909924i	−0.987804	−	0.155702i	$-0.950236\pi$
$29$	−1.78349	−	4.90009i	−0.331185	−	0.909924i	0.656619	−	0.754223i	$-0.271986\pi$
$30$	−0.908329	−	0.123934i	−0.165837	−	0.0226271i
$31$	3.81477	−	0.672647i	0.685153	−	0.120811i	0.179774	−	0.983708i	$-0.442463\pi$
$31$	3.81477	−	0.672647i	0.685153	−	0.120811i	0.505380	+	0.862897i	$0.331352\pi$
$32$	0.979478	−	2.69109i	0.173149	−	0.475723i
$33$	−1.66498	−	1.83426i	−0.289837	−	0.319304i
$34$	−0.0349009	+	0.0415932i	−0.00598545	+	0.00713318i
$35$	4.08618	−	3.86926i	0.690691	−	0.654025i
$36$	0.561220	−	5.78708i	0.0935367	−	0.964514i
$37$	−3.00625	+	5.20699i	−0.494225	+	0.856023i	−0.999978	−	0.00665534i	$-0.997882\pi$
$37$	−3.00625	+	5.20699i	−0.494225	+	0.856023i	0.505753	+	0.862679i	$0.331215\pi$
$38$	0.565677	+	0.474659i	0.0917649	+	0.0769999i
$39$	−5.85699	−	3.08406i	−0.937868	−	0.493845i
$40$	−2.05269	+	0.361945i	−0.324559	+	0.0572285i
$41$	10.0627	+	3.66253i	1.57153	+	0.571990i	0.973341	−	0.229364i	$-0.0736646\pi$
$41$	10.0627	+	3.66253i	1.57153	+	0.571990i	0.598190	+	0.801354i	$0.295887\pi$
$42$	−0.815699	−	0.796881i	−0.125865	−	0.122961i
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	−0.711053	−	0.703139i	$-0.751781\pi$
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	0.908659	−	0.417540i	$-0.137108\pi$
$44$	−2.40054	−	1.38595i	−0.361894	−	0.208940i
$45$	−5.80819	+	2.64216i	−0.865834	+	0.393870i
$46$	0.962159	+	1.66651i	0.141863	+	0.245713i
$47$	−1.01967	+	5.78285i	−0.148735	+	0.843515i	0.815558	+	0.578675i	$0.196430\pi$
$47$	−1.01967	+	5.78285i	−0.148735	+	0.843515i	−0.964292	+	0.264840i	$0.914681\pi$
$48$	−1.33278	−	6.14853i	−0.192370	−	0.887464i
$49$	6.94965	−	0.838080i	0.992807	−	0.119726i
$50$	−0.0761360	−	0.0907353i	−0.0107673	−	0.0128319i
$51$	−0.0510911	+	0.374453i	−0.00715418	+	0.0524340i
$52$	−7.29419	−	1.28616i	−1.01152	−	0.178359i
$53$	−12.1036	−	6.98800i	−1.66255	−	0.959875i	−0.971490	−	0.237080i	$-0.923810\pi$
$53$	−12.1036	−	6.98800i	−1.66255	−	0.959875i	−0.691063	−	0.722795i	$-0.742857\pi$
$54$	0.580807	+	1.15524i	0.0790379	+	0.157209i
$55$			3.04206i			0.410192i
$56$	−2.31908	−	1.15938i	−0.309901	−	0.154929i
$57$	5.09265	+	0.694850i	0.674538	+	0.0920351i
$58$	1.21936	+	0.443809i	0.160109	+	0.0582750i
$59$	−1.48515	−	0.540550i	−0.193350	−	0.0703736i	0.243530	−	0.969893i	$-0.421694\pi$
$59$	−1.48515	−	0.540550i	−0.193350	−	0.0703736i	−0.436880	+	0.899520i	$0.643917\pi$
$60$	−5.28674	+	4.79884i	−0.682515	+	0.619528i
$61$	4.18950	+	0.738722i	0.536410	+	0.0945836i	0.435290	−	0.900291i	$-0.356646\pi$
$61$	4.18950	+	0.738722i	0.536410	+	0.0945836i	0.101121	+	0.994874i	$0.467757\pi$
$62$	−0.481963	+	0.834784i	−0.0612093	+	0.106018i
$63$	−7.76089	−	1.66393i	−0.977780	−	0.209635i
$64$	−3.27598	−	5.67416i	−0.409497	−	0.709270i
$65$	2.78015	+	7.63839i	0.344835	+	0.947426i
$66$	0.615977	−	0.0239912i	0.0758215	−	0.00295311i
$67$	11.4276	−	9.58891i	1.39611	−	1.17147i	0.433308	−	0.901246i	$-0.357346\pi$
$67$	11.4276	−	9.58891i	1.39611	−	1.17147i	0.962797	−	0.270226i	$-0.0870983\pi$
$68$	0.0734317	+	0.416452i	0.00890490	+	0.0505022i
$69$	11.8514	+	6.24050i	1.42674	+	0.751268i
$70$	0.0839802	+	1.39783i	0.0100376	+	0.167073i
$71$	−4.29452	+	2.47944i	−0.509666	+	0.294256i	−0.732696	−	0.680556i	$-0.761738\pi$
$71$	−4.29452	+	2.47944i	−0.509666	+	0.294256i	0.223031	+	0.974811i	$0.428405\pi$
$72$	2.05917	+	2.09829i	0.242675	+	0.247285i
$73$	−2.13740	+	1.23403i	−0.250164	+	0.144432i	−0.619839	−	0.784729i	$-0.712802\pi$
$73$	−2.13740	+	1.23403i	−0.250164	+	0.144432i	0.369676	+	0.929161i	$0.379469\pi$
$74$	−0.511721	−	1.40594i	−0.0594864	−	0.163438i
$75$	−0.785104	−	0.251609i	−0.0906560	−	0.0290533i
$76$	5.66384	−	0.998688i	0.649687	−	0.114557i
$77$	−2.25412	+	3.03939i	−0.256880	+	0.346371i
$78$	1.52475	−	0.623182i	0.172643	−	0.0705615i
$79$	−2.98202	−	2.50221i	−0.335503	−	0.281521i	0.459435	−	0.888212i	$-0.348052\pi$
$79$	−2.98202	−	2.50221i	−0.335503	−	0.281521i	−0.794938	+	0.606691i	$0.792497\pi$
$80$	−3.86290	+	6.69073i	−0.431885	+	0.748047i
$81$	7.70817	+	4.64587i	0.856463	+	0.516208i
$82$	−2.30773	+	1.33237i	−0.254847	+	0.147136i
$83$	0.141502	−	0.0515026i	0.0155319	−	0.00565315i	−0.334243	−	0.942487i	$-0.608480\pi$
$83$	0.141502	−	0.0515026i	0.0155319	−	0.00565315i	0.349774	+	0.936834i	$0.386258\pi$
$84$	−8.83795	+	0.877250i	−0.964300	+	0.0957159i
$85$	0.355515	−	0.298313i	0.0385610	−	0.0323566i
$86$	1.19360	+	1.42247i	0.128709	+	0.153389i
$87$	8.82691	−	1.91335i	0.946344	−	0.205133i
$88$	1.31705	−	0.479367i	0.140398	−	0.0511007i
$89$	6.80542			0.721373			0.360686	−	0.932687i	$-0.382542\pi$
$89$	6.80542			0.721373			0.360686	+	0.932687i	$0.382542\pi$
$90$	0.425379	−	1.52981i	0.0448388	−	0.161256i
$91$	−2.88221	+	9.69173i	−0.302137	+	1.01597i
$92$	14.7595	+	2.60251i	1.53879	+	0.271330i
$93$	0.261118	+	6.70423i	0.0270767	+	0.695196i
$94$	−0.939256	−	1.11936i	−0.0968769	−	0.115453i
$95$	−4.05712	−	4.83509i	−0.416252	−	0.496069i
$96$	4.38897	+	2.31106i	0.447948	+	0.235872i
$97$	−12.2644	−	2.16255i	−1.24526	−	0.219573i	−0.488092	−	0.872792i	$-0.662307\pi$
$97$	−12.2644	−	2.16255i	−1.24526	−	0.219573i	−0.757169	+	0.653219i	$0.773418\pi$
$98$	−0.951861	+	1.45883i	−0.0961525	+	0.147364i
$99$	3.53773	−	2.42786i	0.355556	−	0.244009i
$100$	−0.922502			−0.0922502
$101$	−7.87176	+	2.86509i	−0.783269	+	0.285087i	−0.702535	−	0.711649i	$-0.747949\pi$
$101$	−7.87176	+	2.86509i	−0.783269	+	0.285087i	−0.0807341	+	0.996736i	$0.525726\pi$
$102$	−0.0632080	−	0.0696344i	−0.00625853	−	0.00689483i
$103$	0.137771	+	0.164189i	0.0135750	+	0.0161781i	0.772789	−	0.634663i	$-0.218861\pi$
$103$	0.137771	+	0.164189i	0.0135750	+	0.0161781i	−0.759214	+	0.650841i	$0.774417\pi$
$104$	2.86892	−	2.40731i	0.281321	−	0.236056i
$105$	5.68344	+	7.91851i	0.554647	+	0.772767i
$106$	3.26809	−	1.18949i	0.317425	−	0.115533i
$107$	−15.3166	+	8.84302i	−1.48071	+	0.854887i	−0.999761	−	0.0218632i	$-0.993040\pi$
$107$	−15.3166	+	8.84302i	−1.48071	+	0.854887i	−0.480946	+	0.876750i	$0.659707\pi$
$108$	9.80009	+	2.31821i	0.943014	+	0.223070i
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	−0.887936	−	0.459967i	$-0.847861\pi$
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	0.842311	+	0.538992i	$0.181195\pi$
$110$	−0.579894	−	0.486589i	−0.0552907	−	0.0463944i
$111$	−8.23204	−	6.37842i	−0.781351	−	0.605413i
$112$	−8.81722	+	3.82252i	−0.833149	+	0.361194i
$113$	−13.8921	+	2.44955i	−1.30686	+	0.230434i	−0.783346	−	0.621586i	$-0.786489\pi$
$113$	−13.8921	+	2.44955i	−1.30686	+	0.230434i	−0.523510	+	0.852020i	$0.675378\pi$
$114$	−0.947043	+	0.859643i	−0.0886987	+	0.0805130i
$115$	−5.62554	−	15.4560i	−0.524584	−	1.44128i
$116$	8.75226	−	5.05312i	0.812627	−	0.469170i
$117$	6.66415	−	9.32932i	0.616101	−	0.862496i
$118$	0.340597	−	0.196644i	0.0313545	−	0.0181025i
$119$	0.576248	−	0.0346203i	0.0528245	−	0.00317364i
$120$	−0.140505	−	3.60748i	−0.0128263	−	0.329316i
$121$	1.55492	+	8.81840i	0.141356	+	0.801673i
$122$	−0.810944	+	0.680463i	−0.0734194	+	0.0616062i
$123$	−8.64167	+	16.4115i	−0.779193	+	1.47978i
$124$	2.56767	+	7.05463i	0.230584	+	0.633524i
$125$	5.82364	+	10.0868i	0.520882	+	0.902194i
$126$	1.55857	−	1.21327i	0.138848	−	0.108087i
$127$	−2.41898	+	4.18980i	−0.214650	+	0.371785i	−0.953164	−	0.302453i	$-0.902194\pi$
$127$	−2.41898	+	4.18980i	−0.214650	+	0.371785i	0.738514	+	0.674238i	$0.235528\pi$
$128$	7.24623	+	1.27771i	0.640482	+	0.112934i
$129$	12.3082	+	3.94452i	1.08368	+	0.347295i
$130$	−1.90076	−	0.691822i	−0.166708	−	0.0606768i
$131$	3.37090	+	1.22691i	0.294517	+	0.107195i	0.485053	−	0.874485i	$-0.338800\pi$
$131$	3.37090	+	1.22691i	0.294517	+	0.107195i	−0.190536	+	0.981680i	$0.561023\pi$
$132$	2.94059	−	3.79515i	0.255946	−	0.330326i
$133$	−0.470844	−	7.83709i	−0.0408274	−	0.679562i
$134$			3.71217i			0.320683i
$135$	−3.17433	−	10.5864i	−0.273203	−	0.911133i
$136$	−0.185175	−	0.106911i	−0.0158787	−	0.00916755i
$137$	−3.52128	−	0.620896i	−0.300843	−	0.0530467i	0.0211891	−	0.999775i	$-0.493255\pi$
$137$	−3.52128	−	0.620896i	−0.300843	−	0.0530467i	−0.322032	+	0.946729i	$0.604366\pi$
$138$	−3.08527	+	1.26099i	−0.262636	+	0.107342i
$139$	3.85722	+	4.59686i	0.327165	+	0.389900i	0.904405	−	0.426674i	$-0.140315\pi$
$139$	3.85722	+	4.59686i	0.327165	+	0.389900i	−0.577240	+	0.816574i	$0.695870\pi$
$140$	8.76018	+	6.49684i	0.740371	+	0.549084i
$141$	−9.68548	−	3.10399i	−0.815664	−	0.261403i
$142$	0.214279	−	1.21524i	0.0179819	−	0.101981i
$143$	−2.73295	−	4.73360i	−0.228540	−	0.395844i
$144$	10.8639	−	0.847544i	0.905323	−	0.0706287i
$145$	−9.60530	−	5.54562i	−0.797677	−	0.460539i
$146$	0.106648	−	0.604829i	0.00882623	−	0.0500560i
$147$	−0.189020	+	12.1229i	−0.0155901	+	0.999878i
$148$	−10.9500	−	3.98546i	−0.900081	−	0.327603i
$149$	−5.49324	+	0.968607i	−0.450024	+	0.0793514i	−0.394067	−	0.919082i	$-0.628932\pi$
$149$	−5.49324	+	0.968607i	−0.450024	+	0.0793514i	−0.0559572	+	0.998433i	$0.517821\pi$
$150$	0.173543	−	0.109415i	0.0141697	−	0.00893367i
$151$	1.21887	+	1.02275i	0.0991903	+	0.0832306i	0.691034	−	0.722822i	$-0.257155\pi$
$151$	1.21887	+	1.02275i	0.0991903	+	0.0832306i	−0.591844	+	0.806053i	$0.701600\pi$
$152$	−1.45401	+	2.51843i	−0.117936	+	0.204271i
$153$	−0.630655	−	0.175360i	−0.0509854	−	0.0141770i
$154$	−0.218831	−	0.915852i	−0.0176339	−	0.0738015i
$155$	5.29598	−	6.31151i	0.425384	−	0.506952i
$156$	3.91521	−	12.2168i	0.313468	−	0.978124i
$157$	8.46292	−	23.2517i	0.675414	−	1.85569i	0.188947	−	0.981987i	$-0.439493\pi$
$157$	8.46292	−	23.2517i	0.675414	−	1.85569i	0.486467	−	0.873699i	$-0.338285\pi$
$158$	0.953968	−	0.168210i	0.0758936	−	0.0133821i
$159$	14.8266	−	19.1353i	1.17582	−	1.51753i
$160$	−2.08332	−	5.72388i	−0.164701	−	0.452513i
$161$	5.83205	−	19.6109i	0.459630	−	1.54555i
$162$	−2.11857	+	0.726248i	−0.166450	+	0.0570594i
$163$	−6.48707	−	11.2359i	−0.508107	−	0.880066i	−0.999956	−	0.00938604i	$-0.997012\pi$
$163$	−6.48707	−	11.2359i	−0.508107	−	0.880066i	0.491849	−	0.870680i	$-0.336321\pi$
$164$	−3.60388	+	20.4386i	−0.281416	+	1.59599i
$165$	−5.22064	−	0.712313i	−0.406426	−	0.0554535i
$166$	−0.0128161	+	0.0352119i	−0.000994721	+	0.00273297i
$167$	−1.43124	−	8.11696i	−0.110753	−	0.628110i	−0.988766	−	0.149473i	$-0.952242\pi$
$167$	−1.43124	−	8.11696i	−0.110753	−	0.628110i	0.878013	−	0.478637i	$-0.158869\pi$
$168$	2.53270	−	3.70842i	0.195402	−	0.286111i
$169$	−1.22969	−	1.03183i	−0.0945915	−	0.0793717i
$170$			0.115486i			0.00885740i
$171$	−2.38493	+	8.57705i	−0.182380	+	0.655903i
$172$	14.4622			1.10273
$173$	−22.1228	+	8.05204i	−1.68197	+	0.612186i	−0.993577	−	0.113156i	$-0.963904\pi$
$173$	−22.1228	+	8.05204i	−1.68197	+	0.612186i	−0.688389	+	0.725342i	$0.741682\pi$
$174$	−1.04716	+	1.98868i	−0.0793851	+	0.150761i
$175$	−0.143913	+	1.25110i	−0.0108788	+	0.0945740i
$176$	1.77680	−	4.88173i	0.133932	−	0.367974i
$177$	1.27542	−	2.42217i	0.0958663	−	0.182061i
$178$	−1.08855	+	1.29728i	−0.0815903	+	0.0972355i
$179$			8.34763i			0.623931i	0.950093	+	0.311965i	$0.100987\pi$
$179$			8.34763i			0.623931i	−0.950093	+	0.311965i	$0.899013\pi$
$180$	−6.99762	−	10.1965i	−0.521572	−	0.760003i
$181$	3.60525	+	2.08149i	0.267976	+	0.154716i	0.627967	−	0.778240i	$-0.283887\pi$
$181$	3.60525	+	2.08149i	0.267976	+	0.154716i	−0.359992	+	0.932956i	$0.617220\pi$
$182$	−1.38647	−	2.09965i	−0.102772	−	0.155636i
$183$	−2.24875	+	7.01684i	−0.166232	+	0.518699i
$184$	−5.80517	+	4.87111i	−0.427963	+	0.359103i
$185$	2.22069	+	12.5942i	0.163268	+	0.925941i
$186$	−1.31976	−	1.02259i	−0.0967696	−	0.0749798i
$187$	−0.200593	+	0.239058i	−0.0146688	+	0.0174816i
$188$	−11.3805			−0.830009
$189$	4.67280	−	12.9292i	0.339896	−	0.940463i
$190$	1.57064			0.113946
$191$	0.621752	−	0.740976i	0.0449884	−	0.0536151i	−0.743081	−	0.669201i	$-0.766636\pi$
$191$	0.621752	−	0.740976i	0.0449884	−	0.0536151i	0.788069	+	0.615586i	$0.211081\pi$
$192$	10.5048	−	4.29344i	0.758118	−	0.309852i
$193$	−1.25034	−	7.09105i	−0.0900017	−	0.510425i	−0.996165	−	0.0874966i	$-0.972113\pi$
$193$	−1.25034	−	7.09105i	−0.0900017	−	0.510425i	0.906163	−	0.422928i	$-0.138998\pi$
$194$	2.37397	−	1.99200i	0.170441	−	0.143017i
$195$	−13.7596	+	2.98259i	−0.985347	+	0.213588i
$196$	3.93845	+	12.9823i	0.281318	+	0.927306i
$197$	6.90426	+	3.98617i	0.491908	+	0.284003i	0.725366	−	0.688364i	$-0.241671\pi$
$197$	6.90426	+	3.98617i	0.491908	+	0.284003i	−0.233458	+	0.972367i	$0.575004\pi$
$198$	−0.103061	+	1.06273i	−0.00732423	+	0.0755246i
$199$		−	4.27232i		−	0.302857i	−0.988468	−	0.151428i	$-0.951613\pi$
$199$		−	4.27232i		−	0.302857i	0.988468	−	0.151428i	$-0.0483873\pi$
$200$	0.299829	−	0.357323i	0.0212011	−	0.0252665i
$201$	13.7802	+	21.8568i	0.971979	+	1.54166i
$202$	0.712958	−	1.95884i	0.0501635	−	0.137823i
$203$	−5.48766	−	12.6581i	−0.385158	−	0.888425i
$204$	−0.731889	+	0.0285058i	−0.0512424	+	0.00199580i
$205$	21.4031	−	7.79009i	1.49486	−	0.544084i
$206$	−0.0533356			−0.00371607
$207$	−13.4847	+	18.8776i	−0.937251	+	1.31208i
$208$		−	13.8815i		−	0.962507i
$209$	3.25124	+	2.72811i	0.224893	+	0.188708i
$210$	−2.41855	−	0.183186i	−0.166896	−	0.0126410i
$211$	3.70699	+	21.0234i	0.255199	+	1.44731i	0.795560	+	0.605875i	$0.207177\pi$
$211$	3.70699	+	21.0234i	0.255199	+	1.44731i	−0.540361	+	0.841433i	$0.681712\pi$
$212$	9.26415	−	25.4530i	0.636264	−	1.74812i
$213$	−3.24951	−	7.95061i	−0.222653	−	0.544767i
$214$	0.764235	−	4.33419i	0.0522420	−	0.296279i
$215$	−7.93589	−	13.7454i	−0.541223	−	0.937426i
$216$	−4.08314	+	3.04252i	−0.277822	+	0.207017i
$217$	9.96805	−	2.38174i	0.676675	−	0.161683i
$218$	−0.0810826	−	0.222773i	−0.00549161	−	0.0150881i
$219$	−1.61730	−	3.95705i	−0.109287	−	0.267393i
$220$	−5.80618	+	1.02379i	−0.391453	+	0.0690237i
$221$	−0.285199	+	0.783579i	−0.0191846	+	0.0527092i
$222$	2.53263	−	0.548983i	0.169979	−	0.0368453i
$223$	−7.92110	+	9.44000i	−0.530436	+	0.632149i	−0.963015	−	0.269447i	$-0.913159\pi$
$223$	−7.92110	+	9.44000i	−0.530436	+	0.632149i	0.432579	+	0.901596i	$0.357604\pi$
$224$	2.15980	−	7.26256i	0.144308	−	0.485250i
$225$	0.615635	−	1.28844i	0.0410423	−	0.0858960i
$226$	1.75514	−	3.03999i	0.116750	−	0.202217i
$227$	−14.3018	−	12.0006i	−0.949245	−	0.796511i	0.0299253	−	0.999552i	$-0.490473\pi$
$227$	−14.3018	−	12.0006i	−0.949245	−	0.796511i	−0.979170	+	0.203041i	$0.934917\pi$
$228$	0.387685	+	9.95385i	0.0256751	+	0.659210i
$229$	−19.1244	+	3.37215i	−1.26378	+	0.222838i	−0.765078	−	0.643937i	$-0.777300\pi$
$229$	−19.1244	+	3.37215i	−1.26378	+	0.222838i	−0.498699	+	0.866775i	$0.666189\pi$
$230$	3.84613	+	1.39988i	0.253607	+	0.0923052i
$231$	−4.68824	−	4.58009i	−0.308464	−	0.301348i
$232$	−0.887358	+	5.03246i	−0.0582579	+	0.330397i
$233$	11.4205	+	6.59360i	0.748179	+	0.431961i	0.825036	−	0.565081i	$-0.191155\pi$
$233$	11.4205	+	6.59360i	0.748179	+	0.431961i	−0.0768565	+	0.997042i	$0.524488\pi$
$234$	0.712449	+	2.76261i	0.0465742	+	0.180598i
$235$	6.24485	+	10.8164i	0.407369	+	0.705584i
$236$	0.531894	−	3.01652i	0.0346234	−	0.196359i
$237$	4.99242	−	4.53169i	0.324293	−	0.294365i
$238$	−0.0855733	+	0.115385i	−0.00554689	+	0.00747929i
$239$	10.0464	+	11.9729i	0.649849	+	0.774460i	0.985891	−	0.167387i	$-0.0535330\pi$
$239$	10.0464	+	11.9729i	0.649849	+	0.774460i	−0.336043	+	0.941847i	$0.609089\pi$
$240$	−10.5778	−	8.19598i	−0.682793	−	0.529048i
$241$	6.39561	+	1.12772i	0.411978	+	0.0726428i	0.375796	−	0.926702i	$-0.377369\pi$
$241$	6.39561	+	1.12772i	0.411978	+	0.0726428i	0.0361818	+	0.999345i	$0.488480\pi$
$242$	−1.92972	−	1.11413i	−0.124047	−	0.0716187i
$243$	−9.77791	+	12.1405i	−0.627254	+	0.778815i
$244$			8.24483i			0.527821i
$245$	10.1776	−	10.8670i	0.650225	−	0.694269i
$246$	−1.74618	−	4.27240i	−0.111333	−	0.272398i
$247$	10.6568	+	3.87877i	0.678079	+	0.246801i
$248$	−3.56708	−	1.29831i	−0.226510	−	0.0824429i
$249$	0.0552528	+	0.254899i	0.00350151	+	0.0161535i
$250$	−2.85432	−	0.503293i	−0.180523	−	0.0318310i
$251$	11.9045	−	20.6191i	0.751403	−	1.30147i	−0.195740	−	0.980656i	$-0.562711\pi$
$251$	11.9045	−	20.6191i	0.751403	−	1.30147i	0.947143	−	0.320812i	$-0.103956\pi$
$252$	0.563952	−	15.3727i	0.0355257	−	0.968387i
$253$	5.53002	+	9.57828i	0.347670	+	0.602182i
$254$	−0.411757	−	1.13129i	−0.0258359	−	0.0709836i
$255$	0.428704	+	0.679969i	0.0268465	+	0.0425813i
$256$	8.63555	−	7.24609i	0.539722	−	0.452881i
$257$	5.27488	+	29.9153i	0.329038	+	1.86607i	0.479631	+	0.877470i	$0.340770\pi$
$257$	5.27488	+	29.9153i	0.329038	+	1.86607i	−0.150594	+	0.988596i	$0.548119\pi$
$258$	−2.72066	+	1.71531i	−0.169381	+	0.106791i
$259$	−7.11331	+	14.2286i	−0.441999	+	0.884122i
$260$	−13.6433	+	7.87694i	−0.846119	+	0.488507i
$261$	1.21674	+	15.5963i	0.0753146	+	0.965388i
$262$	−0.773067	+	0.446330i	−0.0477602	+	0.0275744i
$263$	−5.29060	−	14.5358i	−0.326232	−	0.896316i	−0.989056	−	0.147540i	$-0.952864\pi$
$263$	−5.29060	−	14.5358i	−0.326232	−	0.896316i	0.662824	−	0.748775i	$-0.269358\pi$
$264$	0.514273	+	2.37250i	0.0316513	+	0.146018i
$265$	−29.2749	+	5.16196i	−1.79835	+	0.317097i
$266$	1.56926	+	1.16382i	0.0962175	+	0.0713581i
$267$	−1.59352	+	11.6791i	−0.0975217	+	0.714750i
$268$	22.1476	+	18.5840i	1.35288	+	1.13520i
$269$	−0.343714	+	0.595329i	−0.0209566	+	0.0362979i	−0.876314	−	0.481741i	$-0.840005\pi$
$269$	−0.343714	+	0.595329i	−0.0209566	+	0.0362979i	0.855357	+	0.518039i	$0.173338\pi$
$270$	2.52578	+	1.08823i	0.153714	+	0.0662273i
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	−0.298131	−	0.954525i	$-0.596363\pi$
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	0.677578	+	0.735451i	$0.263030\pi$
$272$	−0.744748	+	0.271066i	−0.0451570	+	0.0164358i
$273$	−15.9576	−	7.21566i	−0.965797	−	0.436712i
$274$	0.681599	−	0.571929i	0.0411769	−	0.0345515i
$275$	−0.437593	−	0.521503i	−0.0263879	−	0.0314478i
$276$	−7.92231	+	24.7202i	−0.476867	+	1.48798i
$277$	−11.6791	+	4.25083i	−0.701727	+	0.255408i	−0.668148	−	0.744028i	$-0.732913\pi$
$277$	−11.6791	+	4.25083i	−0.701727	+	0.255408i	−0.0335789	+	0.999436i	$0.510691\pi$
$278$	−1.49325			−0.0895593
$279$	−11.5666	−	1.12171i	−0.692474	−	0.0671548i
$280$	−5.36371	+	1.28159i	−0.320543	+	0.0765896i
$281$	2.05517	+	0.362382i	0.122601	+	0.0216179i	0.234612	−	0.972089i	$-0.424618\pi$
$281$	2.05517	+	0.362382i	0.122601	+	0.0216179i	−0.112011	+	0.993707i	$0.535729\pi$
$282$	2.14092	−	1.34980i	0.127490	−	0.0803795i
$283$	13.0108	+	15.5056i	0.773410	+	0.921714i	0.998616	−	0.0525970i	$-0.0167499\pi$
$283$	13.0108	+	15.5056i	0.773410	+	0.921714i	−0.225206	+	0.974311i	$0.572305\pi$
$284$	−6.17764	−	7.36222i	−0.366575	−	0.436867i
$285$	9.24773	−	5.83047i	0.547788	−	0.345367i
$286$	1.33949	+	0.236188i	0.0792055	+	0.0139661i
$287$	27.1566	+	8.07606i	1.60301	+	0.476715i
$288$	−4.99383	+	6.99099i	−0.294264	+	0.411948i
$289$	−16.9524			−0.997199
$290$	2.59354	−	0.943970i	0.152298	−	0.0554318i
$291$	6.58302	−	20.5412i	0.385903	−	1.20415i
$292$	−3.07464	−	3.66421i	−0.179929	−	0.214432i
$293$	−21.6520	+	18.1682i	−1.26493	+	1.06140i	−0.269786	+	0.962920i	$0.586953\pi$
$293$	−21.6520	+	18.1682i	−1.26493	+	1.06140i	−0.995139	+	0.0984780i	$0.968603\pi$
$294$	−2.28069	−	1.97513i	−0.133013	−	0.115192i
$295$	−3.15887	+	1.14973i	−0.183916	+	0.0669401i
$296$	5.10266	−	2.94602i	0.296586	−	0.171234i
$297$	3.33820	+	6.63978i	0.193702	+	0.385279i
$298$	0.694022	−	1.20208i	0.0402036	−	0.0696347i
$299$	22.6391	+	18.9965i	1.30925	+	1.09859i
$300$	0.216008	−	1.58315i	0.0124712	−	0.0914033i
$301$	2.25615	−	19.6136i	0.130042	−	1.13051i
$302$	−0.389925	+	0.0687543i	−0.0224377	+	0.00395637i
$303$	−3.07371	−	14.1800i	−0.176580	−	0.814619i
$304$	3.68656	+	10.1287i	0.211439	+	0.580923i
$305$	7.83616	−	4.52421i	0.448697	−	0.259055i
$306$	0.134303	−	0.0921693i	0.00767762	−	0.00526897i
$307$	1.71807	−	0.991927i	0.0980553	−	0.0566122i	−0.450170	−	0.892943i	$-0.648637\pi$
$307$	1.71807	−	0.991927i	0.0980553	−	0.0566122i	0.548226	+	0.836330i	$0.315303\pi$
$308$	−6.55969	−	3.27939i	−0.373773	−	0.186861i
$309$	−0.314034	+	0.197991i	−0.0178647	+	0.0112633i
$310$	0.356021	+	2.01909i	0.0202206	+	0.114677i
$311$	10.4064	−	8.73204i	0.590095	−	0.495149i	−0.298150	−	0.954519i	$-0.596369\pi$
$311$	10.4064	−	8.73204i	0.590095	−	0.495149i	0.888245	+	0.459371i	$0.151925\pi$
$312$	3.45954	+	5.48718i	0.195858	+	0.310651i
$313$	5.00633	+	13.7548i	0.282974	+	0.777466i	0.997004	+	0.0773503i	$0.0246460\pi$
$313$	5.00633	+	13.7548i	0.282974	+	0.777466i	−0.714030	+	0.700116i	$0.753132\pi$
$314$	3.07868	+	5.33243i	0.173740	+	0.300927i
$315$	−14.9201	+	7.89949i	−0.840655	+	0.445086i
$316$	3.77222	−	6.53368i	0.212204	−	0.367548i
$317$	18.6192	+	3.28307i	1.04576	+	0.184395i	0.670029	−	0.742335i	$-0.266281\pi$
$317$	18.6192	+	3.28307i	1.04576	+	0.184395i	0.375728	+	0.926730i	$0.377393\pi$
$318$	1.27610	+	5.88707i	0.0715603	+	0.330130i
$319$	7.00827	+	2.55080i	0.392388	+	0.142817i
$320$	−13.0954	−	4.76633i	−0.732055	−	0.266446i
$321$	−11.5895	−	28.3561i	−0.646863	−	1.58269i
$322$	2.80547	+	4.24857i	0.156343	+	0.236763i
$323$		−	0.647487i		−	0.0360271i
$324$	−6.27313	+	16.2756i	−0.348507	+	0.904200i
$325$	−1.57537	−	0.909538i	−0.0873856	−	0.0504521i
$326$	3.17948	+	0.560628i	0.176095	+	0.0310503i
$327$	−1.30437	−	1.01067i	−0.0721320	−	0.0558899i
$328$	−6.74539	−	8.03884i	−0.372452	−	0.443871i
$329$	−1.77539	+	15.4342i	−0.0978805	+	0.850917i
$330$	0.970844	−	0.881248i	0.0534432	−	0.0485111i
$331$	2.05674	−	11.6643i	0.113049	−	0.641130i	−0.874649	−	0.484756i	$-0.838908\pi$
$331$	2.05674	−	11.6643i	0.113049	−	0.641130i	0.987698	−	0.156374i	$-0.0499806\pi$
$332$	0.145921	+	0.252743i	0.00800847	+	0.0138711i
$333$	12.8739	−	12.6339i	0.705486	−	0.692333i
$334$	1.77623	+	1.02551i	0.0971909	+	0.0561132i
$335$	5.50977	−	31.2475i	0.301031	−	1.70723i
$336$	−4.49543	−	16.0267i	−0.245246	−	0.874330i
$337$	19.6990	+	7.16984i	1.07307	+	0.390566i	0.817324	−	0.576178i	$-0.195456\pi$
$337$	19.6990	+	7.16984i	1.07307	+	0.390566i	0.255747	+	0.966744i	$0.417679\pi$
$338$	0.393386	−	0.0693646i	0.0213974	−	0.00377294i
$339$	−0.950901	−	24.4145i	−0.0516458	−	1.32601i
$340$	0.689016	+	0.578153i	0.0373671	+	0.0313548i
$341$	−2.77009	+	4.79794i	−0.150009	+	0.259823i
$342$	−1.25352	−	1.82656i	−0.0677827	−	0.0987689i
$343$	18.2210	−	3.31605i	0.983840	−	0.179050i
$344$	−4.70047	+	5.60181i	−0.253433	+	0.302029i
$345$	27.8421	−	6.03517i	1.49897	−	0.324923i
$346$	2.00370	−	5.50512i	0.107719	−	0.295957i
$347$	−30.1613	+	5.31825i	−1.61914	+	0.285499i	−0.908447	−	0.418000i	$-0.862731\pi$
$347$	−30.1613	+	5.31825i	−1.61914	+	0.285499i	−0.710697	+	0.703499i	$0.751620\pi$
$348$	6.62253	+	16.2034i	0.355005	+	0.868593i
$349$	6.58819	+	18.1009i	0.352658	+	0.968919i	0.981513	+	0.191397i	$0.0613017\pi$
$349$	6.58819	+	18.1009i	0.352658	+	0.968919i	−0.628855	+	0.777523i	$0.716476\pi$
$350$	−0.215471	−	0.227551i	−0.0115174	−	0.0121631i
$351$	14.4501	+	13.6212i	0.771288	+	0.727045i
$352$	2.04795	+	3.54715i	0.109156	+	0.189064i
$353$	3.20406	−	18.1711i	0.170535	−	0.967152i	−0.772637	−	0.634848i	$-0.781063\pi$
$353$	3.20406	−	18.1711i	0.170535	−	0.967152i	0.943172	−	0.332304i	$-0.107826\pi$
$354$	0.257718	+	0.630560i	0.0136976	+	0.0335139i
$355$	−3.60743	+	9.91132i	−0.191462	+	0.526038i
$356$	2.29032	+	12.9890i	0.121387	+	0.688418i
$357$	−0.0755172	+	0.997034i	−0.00399680	+	0.0527686i
$358$	−1.59127	−	1.33523i	−0.0841011	−	0.0705692i
$359$		−	0.779690i		−	0.0411504i	−0.999788	−	0.0205752i	$-0.993450\pi$
$359$		−	0.779690i		−	0.0411504i	0.999788	−	0.0205752i	$-0.00654976\pi$
$360$	6.22387	+	0.603579i	0.328027	+	0.0318114i
$361$	10.1940			0.536528
$362$	−0.973456	+	0.354309i	−0.0511637	+	0.0186221i
$363$	−15.4978	+	0.603612i	−0.813423	+	0.0316814i
$364$	−19.4679	−	2.23939i	−1.02040	−	0.117376i
$365$	−1.79543	+	4.93291i	−0.0939771	+	0.258200i
$366$	−0.977890	−	1.55103i	−0.0511151	−	0.0810739i
$367$	15.9909	−	19.0572i	0.834717	−	0.994777i	−0.165247	−	0.986252i	$-0.552842\pi$
$367$	15.9909	−	19.0572i	0.834717	−	0.994777i	0.999964	−	0.00852445i	$-0.00271345\pi$
$368$			28.0887i			1.46423i
$369$	−26.1411	−	18.6732i	−1.36085	−	0.972090i
$370$	−2.75597	−	1.59116i	−0.143276	−	0.0827205i
$371$	−33.0742	−	16.5348i	−1.71712	−	0.858443i
$372$	−12.7080	+	2.75464i	−0.658881	+	0.142822i
$373$	−18.4215	+	15.4574i	−0.953827	+	0.800356i	−0.979938	−	0.199303i	$-0.936132\pi$
$373$	−18.4215	+	15.4574i	−0.953827	+	0.800356i	0.0261111	+	0.999659i	$0.491688\pi$
$374$	−0.0134848	−	0.0764763i	−0.000697284	−	0.00395449i
$375$	−18.6742	+	7.63236i	−0.964329	+	0.394133i
$376$	3.69886	−	4.40813i	0.190754	−	0.227332i
$377$	19.9284			1.02637
$378$	1.71721	+	2.95883i	0.0883235	+	0.152186i
$379$	−30.5872			−1.57116			−0.785579	−	0.618761i	$-0.787635\pi$
$379$	−30.5872			−1.57116			−0.785579	+	0.618761i	$0.787635\pi$
$380$	7.86301	−	9.37077i	0.403364	−	0.480710i
$381$	−6.62391	−	5.13240i	−0.339353	−	0.262941i
$382$	0.0417971	+	0.237043i	0.00213853	+	0.0121282i
$383$	27.5758	−	23.1388i	1.40906	−	1.18234i	0.452149	−	0.891942i	$-0.350658\pi$
$383$	27.5758	−	23.1388i	1.40906	−	1.18234i	0.956907	−	0.290396i	$-0.0937869\pi$
$384$	−3.88947	+	12.1364i	−0.198484	+	0.619335i
$385$	0.482678	+	8.03406i	0.0245995	+	0.409454i
$386$	1.55173	+	0.895891i	0.0789809	+	0.0455997i
$387$	−9.65140	+	20.1991i	−0.490608	+	1.02678i
$388$		−	24.1360i		−	1.22532i
$389$	15.6823	−	18.6895i	0.795125	−	0.947593i	−0.204385	−	0.978891i	$-0.565519\pi$
$389$	15.6823	−	18.6895i	0.795125	−	0.947593i	0.999510	+	0.0312973i	$0.00996386\pi$
$390$	1.63234	−	3.10000i	0.0826569	−	0.156975i
$391$	0.577092	−	1.58555i	0.0291848	−	0.0801845i
$392$	−6.30863	−	2.69395i	−0.318634	−	0.136065i
$393$	−2.89487	+	5.49769i	−0.146027	+	0.277322i
$394$	−1.86422	+	0.678522i	−0.0939183	+	0.0341835i
$395$	−8.27977			−0.416600
$396$	5.82450	+	5.93515i	0.292692	+	0.298253i
$397$		−	6.76334i		−	0.339443i	−0.985492	−	0.169721i	$-0.945713\pi$
$397$		−	6.76334i		−	0.339443i	0.985492	−	0.169721i	$-0.0542867\pi$
$398$	0.814412	+	0.683373i	0.0408228	+	0.0342544i
$399$	13.5599	+	1.02705i	0.678843	+	0.0514169i
$400$	−0.300226	−	1.70266i	−0.0150113	−	0.0851332i
$401$	0.329299	−	0.904741i	0.0164444	−	0.0451806i	−0.931199	−	0.364512i	$-0.881236\pi$
$401$	0.329299	−	0.904741i	0.0164444	−	0.0451806i	0.947643	+	0.319331i	$0.103458\pi$
$402$	−6.37064	−	0.869221i	−0.317739	−	0.0433528i
$403$	−2.57064	+	14.5788i	−0.128053	+	0.726224i
$404$	−8.11759	−	14.0601i	−0.403865	−	0.699515i
$405$	18.9111	−	2.96877i	0.939702	−	0.147519i
$406$	3.29072	+	0.978623i	0.163316	+	0.0485682i
$407$	−2.94113	−	8.08068i	−0.145786	−	0.400545i
$408$	0.226835	−	0.292755i	0.0112300	−	0.0144935i
$409$	−28.6167	+	5.04589i	−1.41500	+	0.249503i	−0.828294	−	0.560294i	$-0.810688\pi$
$409$	−28.6167	+	5.04589i	−1.41500	+	0.249503i	−0.586709	+	0.809798i	$0.699577\pi$
$410$	−1.93851	+	5.32602i	−0.0957363	+	0.263033i
$411$	1.89007	−	5.89765i	0.0932304	−	0.290910i
$412$	−0.267011	+	0.318212i	−0.0131547	+	0.0156772i
$413$	−4.00803	−	1.19194i	−0.197222	−	0.0586516i
$414$	−1.44162	−	5.59006i	−0.0708516	−	0.274736i
$415$	0.160144	−	0.277377i	0.00786114	−	0.0136159i
$416$	8.38400	+	7.03501i	0.411060	+	0.344920i
$417$	−8.79208	+	5.54320i	−0.430550	+	0.271452i
$418$	−1.04009	+	0.183397i	−0.0508727	+	0.00897022i
$419$	−22.8869	−	8.33016i	−1.11810	−	0.406955i	−0.284141	−	0.958782i	$-0.591708\pi$
$419$	−22.8869	−	8.33016i	−1.11810	−	0.406955i	−0.833958	+	0.551828i	$0.813931\pi$
$420$	−13.2008	+	13.5125i	−0.644133	+	0.659344i
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	−0.894155	−	0.447758i	$-0.852223\pi$
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	0.993373	−	0.114936i	$-0.0366663\pi$
$422$	−4.60053	−	2.65611i	−0.223950	−	0.129298i
$423$	7.59481	−	15.8949i	0.369272	−	0.772838i
$424$	6.84799	+	11.8611i	0.332568	+	0.576024i
$425$	−0.0180347	+	0.102280i	−0.000874812	+	0.00496130i
$426$	2.03536	+	0.652289i	0.0986134	+	0.0316035i
$427$	11.1816	+	1.28622i	0.541117	+	0.0622444i
$428$	−22.0328	−	26.2576i	−1.06499	−	1.26921i
$429$	8.76350	−	3.58175i	0.423106	−	0.172929i
$430$	3.88958	+	0.685839i	0.187572	+	0.0330741i
$431$	22.9443	+	13.2469i	1.10519	+	0.638082i	0.937579	−	0.347772i	$-0.113062\pi$
$431$	22.9443	+	13.2469i	1.10519	+	0.638082i	0.167610	+	0.985853i	$0.446395\pi$
$432$	−1.08931	+	18.8425i	−0.0524096	+	0.906560i
$433$		−	23.5474i		−	1.13161i	−0.824538	−	0.565807i	$-0.808565\pi$
$433$		−	23.5474i		−	1.13161i	0.824538	−	0.565807i	$-0.191435\pi$
$434$	−1.14040	+	2.28113i	−0.0547412	+	0.109498i
$435$	11.7662	−	15.1856i	0.564148	−	0.728094i
$436$	−1.73503	−	0.631499i	−0.0830928	−	0.0302433i
$437$	−21.5638	−	7.84857i	−1.03154	−	0.375448i
$438$	1.01301	+	0.324647i	0.0484033	+	0.0155122i
$439$	4.11182	+	0.725025i	0.196247	+	0.0346036i	0.270907	−	0.962605i	$-0.412676\pi$
$439$	4.11182	+	0.725025i	0.196247	+	0.0346036i	−0.0746608	+	0.997209i	$0.523787\pi$
$440$	1.49056	−	2.58172i	0.0710595	−	0.123079i
$441$	−20.7604	−	3.16301i	−0.988592	−	0.150620i
$442$	−0.103751	−	0.179702i	−0.00493494	−	0.00854757i
$443$	0.830398	+	2.28150i	0.0394534	+	0.108397i	0.957855	−	0.287252i	$-0.0927417\pi$
$443$	0.830398	+	2.28150i	0.0394534	+	0.108397i	−0.918402	+	0.395649i	$0.870520\pi$
$444$	9.40363	−	17.8586i	0.446277	−	0.847530i
$445$	11.0884	−	9.30431i	0.525643	−	0.441066i
$446$	−0.532494	−	3.01992i	−0.0252143	−	0.142997i
$447$	−0.376008	−	9.65403i	−0.0177846	−	0.456620i
$448$	−9.55213	−	14.4656i	−0.451296	−	0.683435i
$449$	10.0967	−	5.82936i	0.476495	−	0.275104i	−0.242460	−	0.970161i	$-0.577954\pi$
$449$	10.0967	−	5.82936i	0.476495	−	0.275104i	0.718955	+	0.695057i	$0.244621\pi$
$450$	0.147136	+	0.323446i	0.00693607	+	0.0152474i
$451$	−13.2637	+	7.65783i	−0.624565	+	0.360593i
$452$	−9.35057	−	25.6905i	−0.439814	−	1.20838i
$453$	−2.04060	+	1.85228i	−0.0958759	+	0.0870279i
$454$	4.57525	−	0.806740i	0.214727	−	0.0378622i
$455$	8.55431	+	19.7318i	0.401032	+	0.925041i
$456$	−3.98154	−	3.08501i	−0.186452	−	0.144469i
$457$	−16.2729	−	13.6546i	−0.761213	−	0.638734i	0.177229	−	0.984170i	$-0.443287\pi$
$457$	−16.2729	−	13.6546i	−0.761213	−	0.638734i	−0.938442	+	0.345436i	$0.887731\pi$
$458$	2.41620	−	4.18498i	0.112902	−	0.195551i
$459$	0.448615	−	1.04124i	0.0209395	−	0.0486008i
$460$	27.6067	−	15.9387i	1.28717	−	0.743147i
$461$	−25.2929	+	9.20586i	−1.17801	+	0.428760i	−0.855498	−	0.517806i	$-0.826749\pi$
$461$	−25.2929	+	9.20586i	−1.17801	+	0.428760i	−0.322510	+	0.946566i	$0.604527\pi$
$462$	1.62298	−	0.161096i	0.0755079	−	0.00749487i
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	−0.106424	−	0.994321i	$-0.533940\pi$
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	0.960735	+	0.277469i	$0.0894956\pi$
$464$	12.1749	+	14.5095i	0.565208	+	0.673588i
$465$	9.59142	+	10.5666i	0.444791	+	0.490013i
$466$	−3.08365	+	1.12236i	−0.142847	+	0.0519922i
$467$	6.18976			0.286428			0.143214	−	0.989692i	$-0.454256\pi$
$467$	6.18976			0.286428			0.143214	+	0.989692i	$0.454256\pi$
$468$	20.0490	+	9.57970i	0.926767	+	0.442822i
$469$	28.6588	−	27.1374i	1.32334	−	1.25309i
$470$	−3.06076	−	0.539695i	−0.141183	−	0.0248943i
$471$	37.9217	+	19.9681i	1.74734	+	0.920083i
$472$	0.995547	+	1.18645i	0.0458238	+	0.0546106i
$473$	6.86022	+	8.17569i	0.315433	+	0.375918i
$474$	0.0652983	+	1.67654i	0.00299925	+	0.0770060i
$475$	1.39103	+	0.245276i	0.0638248	+	0.0112540i
$476$	0.260010	+	1.08819i	0.0119175	+	0.0498773i
$477$	29.3673	+	29.9252i	1.34464	+	1.37018i
$478$	−3.88929			−0.177892
$479$	15.1479	−	5.51338i	0.692124	−	0.251913i	0.0280796	−	0.999606i	$-0.491061\pi$
$479$	15.1479	−	5.51338i	0.692124	−	0.251913i	0.664044	+	0.747693i	$0.268839\pi$
$480$	10.3109	−	2.23502i	0.470624	−	0.102014i
$481$	−14.7699	−	17.6021i	−0.673450	−	0.802586i
$482$	−1.23797	+	1.03878i	−0.0563881	+	0.0473152i
$483$	32.2896	+	14.6007i	1.46923	+	0.664353i
$484$	−16.3078	+	5.93555i	−0.741263	+	0.269798i
$485$	−22.9397	+	13.2442i	−1.04164	+	0.601390i
$486$	−0.750278	−	3.80584i	−0.0340333	−	0.172636i
$487$	−13.0260	+	22.5617i	−0.590265	+	1.02237i	0.403931	+	0.914789i	$0.367643\pi$
$487$	−13.0260	+	22.5617i	−0.590265	+	1.02237i	−0.994196	+	0.107580i	$0.965690\pi$
$488$	−3.19356	−	2.67971i	−0.144566	−	0.121305i
$489$	20.8015	−	8.50184i	0.940678	−	0.384467i
$490$	0.443582	+	3.67833i	0.0200390	+	0.166170i
$491$	10.3899	−	1.83203i	0.468892	−	0.0826783i	0.0657902	−	0.997833i	$-0.479043\pi$
$491$	10.3899	−	1.83203i	0.468892	−	0.0826783i	0.403102	+	0.915155i	$0.367932\pi$
$492$	−34.2319	−	10.9706i	−1.54329	−	0.494592i
$493$	−0.389146	−	1.06917i	−0.0175263	−	0.0481530i
$494$	−2.44399	+	1.41104i	−0.109960	+	0.0634857i
$495$	2.44487	−	8.79261i	0.109889	−	0.395198i
$496$	−12.1851	+	7.03507i	−0.547127	+	0.315884i
$497$	−10.9484	+	7.22958i	−0.491101	+	0.324291i
$498$	−0.0574280	−	0.0302393i	−0.00257341	−	0.00135506i
$499$	−1.40174	−	7.94964i	−0.0627503	−	0.355875i	−0.999974	−	0.00714726i	$-0.997725\pi$
$499$	−1.40174	−	7.94964i	−0.0627503	−	0.355875i	0.937224	−	0.348728i	$-0.113386\pi$
$500$	−17.2922	+	14.5098i	−0.773329	+	0.648900i
$501$	14.2651	−	0.555599i	0.637316	−	0.0248223i
$502$	2.02637	+	5.56739i	0.0904411	+	0.248485i
$503$	15.6629	+	27.1289i	0.698373	+	1.20962i	0.969030	+	0.246941i	$0.0794255\pi$
$503$	15.6629	+	27.1289i	0.698373	+	1.20962i	−0.270658	+	0.962676i	$0.587241\pi$
$504$	5.77117	+	5.21483i	0.257068	+	0.232287i
$505$	−8.90877	+	15.4304i	−0.396435	+	0.686646i
$506$	−2.71041	−	0.477918i	−0.120492	−	0.0212460i
$507$	2.05872	−	1.86872i	0.0914308	−	0.0829929i
$508$	−8.81089	−	3.20690i	−0.390920	−	0.142283i
$509$	38.0919	+	13.8643i	1.68840	+	0.614526i	0.994422	−	0.105474i	$-0.0336361\pi$
$509$	38.0919	+	13.8643i	1.68840	+	0.614526i	0.693974	+	0.720000i	$0.255858\pi$
$510$	−0.198192	−	0.0270416i	−0.00877608	−	0.00119742i
$511$	−5.44905	+	3.59819i	−0.241052	+	0.159175i
$512$			17.5212i			0.774336i
$513$	−14.1611	−	6.10126i	−0.625226	−	0.269377i
$514$	−6.54634	−	3.77953i	−0.288747	−	0.166708i
$515$	0.448957	+	0.0791632i	0.0197834	+	0.00348835i
$516$	−3.38639	+	24.8193i	−0.149078	+	1.09261i
$517$	−5.39839	−	6.43355i	−0.237421	−	0.282947i
$518$	−1.57453	−	3.63189i	−0.0691808	−	0.159576i
$519$	−8.63836	−	39.8515i	−0.379182	−	1.74929i
$520$	1.38324	−	7.84473i	0.0606590	−	0.344014i
$521$	11.7007	+	20.2662i	0.512616	+	0.887878i	0.999893	+	0.0146299i	$0.00465701\pi$
$521$	11.7007	+	20.2662i	0.512616	+	0.887878i	−0.487277	+	0.873248i	$0.662010\pi$
$522$	−3.16767	−	2.26274i	−0.138645	−	0.0990376i
$523$	12.1378	+	7.00778i	0.530751	+	0.306429i	0.741322	−	0.671149i	$-0.234199\pi$
$523$	12.1378	+	7.00778i	0.530751	+	0.306429i	−0.210571	+	0.977578i	$0.567532\pi$
$524$	−1.20726	+	6.84672i	−0.0527395	+	0.299100i
$525$	−2.11337	−	0.539926i	−0.0922351	−	0.0235643i
$526$	3.61714	+	1.31653i	0.157715	+	0.0574035i
$527$	0.832360	−	0.146768i	0.0362582	−	0.00639329i
$528$	7.96173	+	4.19234i	0.346490	+	0.182448i
$529$	−28.1904	−	23.6546i	−1.22567	−	1.02846i
$530$	3.69863	−	6.40621i	0.160658	−	0.278268i
$531$	3.85815	+	2.75597i	0.167430	+	0.119599i
$532$	14.7997	−	3.53619i	0.641647	−	0.153313i
$533$	−26.3058	+	31.3500i	−1.13943	+	1.35792i
$534$	−1.97144	−	2.17188i	−0.0853127	−	0.0939864i
$535$	−12.8660	+	35.3491i	−0.556246	+	1.52827i
$536$	−14.3967	+	2.53853i	−0.621843	+	0.109648i
$537$	−14.3258	−	1.95463i	−0.618203	−	0.0843487i
$538$	−0.0585066	−	0.160745i	−0.00252240	−	0.00693023i
$539$	−5.47084	+	8.38466i	−0.235646	+	0.361153i
$540$	19.1373	−	9.62141i	0.823537	−	0.414040i
$541$	−11.9247	−	20.6542i	−0.512683	−	0.887993i	−0.999892	−	0.0147075i	$-0.995318\pi$
$541$	−11.9247	−	20.6542i	−0.512683	−	0.887993i	0.487209	−	0.873285i	$-0.338015\pi$
$542$	−0.311675	+	1.76759i	−0.0133876	+	0.0759247i
$543$	−4.41633	+	5.69975i	−0.189523	+	0.244600i
$544$	0.213716	−	0.587180i	0.00916300	−	0.0251751i
$545$	0.351870	+	1.99555i	0.0150724	+	0.0854801i
$546$	3.92796	−	1.88775i	0.168101	−	0.0807881i
$547$	−0.534982	−	0.448903i	−0.0228742	−	0.0191937i	0.631279	−	0.775556i	$-0.282530\pi$
$547$	−0.534982	−	0.448903i	−0.0228742	−	0.0191937i	−0.654153	+	0.756362i	$0.726975\pi$
$548$		−	6.92978i		−	0.296026i
$549$	−11.5154	−	5.50221i	−0.491465	−	0.234829i
$550$	0.169406			0.00722350
$551$	−14.5409	+	5.29247i	−0.619465	+	0.225467i
$552$	−7.00026	−	11.1031i	−0.297951	−	0.472581i
$553$	−8.27250	−	6.13516i	−0.351782	−	0.260894i
$554$	1.05779	−	2.90626i	0.0449413	−	0.123475i
$555$	−22.1334	+	0.862059i	−0.939513	+	0.0365924i
$556$	−7.47559	+	8.90906i	−0.317036	+	0.377828i
$557$		−	11.1225i		−	0.471276i	−0.971841	−	0.235638i	$-0.924282\pi$
$557$		−	11.1225i		−	0.471276i	0.971841	−	0.235638i	$-0.0757180\pi$
$558$	2.06394	−	2.02546i	0.0873737	−	0.0857447i
$559$	24.6973	+	14.2590i	1.04458	+	0.603090i
$560$	−9.14027	+	18.2831i	−0.386247	+	0.772601i
$561$	−0.363289	−	0.400225i	−0.0153381	−	0.0168975i
$562$	−0.397811	+	0.333803i	−0.0167806	+	0.0140806i
$563$	1.95102	+	11.0648i	0.0822256	+	0.466325i	0.997921	+	0.0644512i	$0.0205297\pi$
$563$	1.95102	+	11.0648i	0.0822256	+	0.466325i	−0.915695	+	0.401873i	$0.868359\pi$
$564$	2.66480	−	19.5307i	0.112208	−	0.822389i
$565$	−19.2861	+	22.9843i	−0.811373	+	0.966957i
$566$	−5.03688			−0.211716
$567$	21.0943	+	11.0467i	0.885879	+	0.463916i
$568$	4.85953			0.203901
$569$	−23.2352	+	27.6906i	−0.974069	+	1.16085i	0.0128961	+	0.999917i	$0.495895\pi$
$569$	−23.2352	+	27.6906i	−0.974069	+	1.16085i	−0.986965	+	0.160934i	$0.948550\pi$
$570$	−0.367772	+	2.69545i	−0.0154043	+	0.112900i
$571$	3.46989	+	19.6787i	0.145210	+	0.823528i	0.967198	+	0.254023i	$0.0817540\pi$
$571$	3.46989	+	19.6787i	0.145210	+	0.823528i	−0.821988	+	0.569505i	$0.807135\pi$
$572$	8.11495	−	6.80925i	0.339303	−	0.284709i
$573$	1.12604	+	1.24052i	0.0470410	+	0.0518236i
$574$	−5.88330	+	3.88494i	−0.245564	+	0.162154i
$575$	3.18770	+	1.84042i	0.132936	+	0.0767508i
$576$	4.90844	+	19.0331i	0.204518	+	0.793047i
$577$			30.5734i			1.27279i	0.771365	+	0.636393i	$0.219574\pi$
$577$			30.5734i			1.27279i	−0.771365	+	0.636393i	$0.780426\pi$
$578$	2.71159	−	3.23155i	0.112787	−	0.134415i
$579$	12.4621	−	0.485376i	0.517906	−	0.0201716i
$580$	7.35196	−	20.1993i	0.305273	−	0.838732i
$581$	0.365534	−	0.158470i	0.0151649	−	0.00657443i
$582$	2.86269	+	4.54052i	0.118662	+	0.188211i
$583$	18.7834	−	6.83661i	0.777930	−	0.283144i
$584$	2.41861			0.100083
$585$	−1.89669	−	24.3120i	−0.0784187	−	1.00518i
$586$		−	7.03349i		−	0.290551i
$587$	23.6386	+	19.8352i	0.975671	+	0.818685i	0.983431	−	0.181285i	$-0.0580257\pi$
$587$	23.6386	+	19.8352i	0.975671	+	0.818685i	−0.00775999	+	0.999970i	$0.502470\pi$
$588$	−23.2017	+	3.71911i	−0.956824	+	0.153373i
$589$	−1.99607	−	11.3203i	−0.0822467	−	0.466444i
$590$	0.286104	−	0.786064i	0.0117787	−	0.0323617i
$591$	−8.45754	+	10.9154i	−0.347897	+	0.448998i
$592$	3.79234	−	21.5074i	0.155864	−	0.883950i
$593$	−15.8362	−	27.4292i	−0.650316	−	1.12638i	−0.983046	−	0.183358i	$-0.941303\pi$
$593$	−15.8362	−	27.4292i	−0.650316	−	1.12638i	0.332730	−	0.943022i	$-0.392030\pi$
$594$	−1.79967	−	0.425710i	−0.0738412	−	0.0174671i
$595$	0.891579	−	0.844250i	0.0365512	−	0.0346109i
$596$	−3.69743	−	10.1586i	−0.151453	−	0.416113i
$597$	7.33194	+	1.00038i	0.300077	+	0.0409429i
$598$	−7.24240	+	1.27703i	−0.296164	+	0.0522217i
$599$	−5.08335	+	13.9664i	−0.207700	+	0.570651i	−0.999178	−	0.0405469i	$-0.987090\pi$
$599$	−5.08335	+	13.9664i	−0.207700	+	0.570651i	0.791478	+	0.611198i	$0.209312\pi$
$600$	0.543013	+	0.598221i	0.0221684	+	0.0244223i
$601$	11.0892	−	13.2156i	0.452338	−	0.539075i	−0.490890	−	0.871221i	$-0.663328\pi$
$601$	11.0892	−	13.2156i	0.452338	−	0.539075i	0.943228	+	0.332146i	$0.107773\pi$
$602$	3.37798	+	3.56735i	0.137676	+	0.145394i
$603$	−40.7362	+	18.5310i	−1.65891	+	0.754640i
$604$	−1.54186	+	2.67058i	−0.0627374	+	0.108664i
$605$	14.5900	+	12.2424i	0.593166	+	0.497726i
$606$	3.19471	+	1.68221i	0.129776	+	0.0683352i
$607$	−40.0370	+	7.05960i	−1.62505	+	0.286540i	−0.910645	−	0.413191i	$-0.864414\pi$
$607$	−40.0370	+	7.05960i	−1.62505	+	0.286540i	−0.714406	+	0.699731i	$0.753303\pi$
$608$	−7.98578	−	2.90659i	−0.323866	−	0.117878i
$609$	23.0082	−	6.45369i	0.932338	−	0.261517i
$610$	−0.390993	+	2.21743i	−0.0158308	+	0.0897812i
$611$	−19.4346	−	11.2206i	−0.786240	−	0.453936i
$612$	0.122455	−	1.26271i	0.00494994	−	0.0510418i
$613$	−14.0624	−	24.3568i	−0.567975	−	0.983761i	−0.996766	−	0.0803574i	$-0.974394\pi$
$613$	−14.0624	−	24.3568i	−0.567975	−	0.983761i	0.428792	−	0.903403i	$-0.358939\pi$
$614$	−0.0857247	+	0.486169i	−0.00345957	+	0.0196202i
$615$	8.35734	+	38.5550i	0.337000	+	1.55469i
$616$	3.40226	−	1.47498i	0.137081	−	0.0594286i
$617$	2.77984	+	3.31289i	0.111912	+	0.133372i	0.819092	−	0.573661i	$-0.194477\pi$
$617$	2.77984	+	3.31289i	0.111912	+	0.133372i	−0.707180	+	0.707033i	$0.750033\pi$
$618$	0.0124888	−	0.0915320i	0.000502372	−	0.00368196i
$619$	15.2309	+	2.68562i	0.612182	+	0.107944i	0.471139	−	0.882059i	$-0.343843\pi$
$619$	15.2309	+	2.68562i	0.612182	+	0.107944i	0.141044	+	0.990003i	$0.454954\pi$
$620$	13.8287	+	7.98399i	0.555373	+	0.320645i
$621$	−29.2393	−	27.5620i	−1.17333	−	1.10603i
$622$			3.38045i			0.135544i
$623$	17.9730	−	1.07980i	0.720074	−	0.0432613i
$624$	23.8227	+	3.25041i	0.953671	+	0.130121i
$625$	21.0430	+	7.65903i	0.841720	+	0.306361i
$626$	−3.42279	−	1.24579i	−0.136802	−	0.0497919i
$627$	−5.44315	+	4.94082i	−0.217378	+	0.197317i
$628$	47.2271	+	8.32741i	1.88457	+	0.332300i
$629$	−0.655946	+	1.13613i	−0.0261543	+	0.0453006i
$630$	0.880689	−	4.10771i	0.0350875	−	0.163655i
$631$	−17.0661	−	29.5593i	−0.679389	−	1.17674i	−0.975165	−	0.221479i	$-0.928911\pi$
$631$	−17.0661	−	29.5593i	−0.679389	−	1.17674i	0.295776	−	0.955257i	$-0.404422\pi$
$632$	1.30472	+	3.58470i	0.0518991	+	0.142592i
$633$	−36.9473	+	1.43903i	−1.46852	+	0.0571964i
$634$	−3.60404	+	3.02415i	−0.143135	+	0.120104i
$635$	1.78688	+	10.1339i	0.0709101	+	0.402151i
$636$	41.5120	+	21.8586i	1.64606	+	0.866750i
$637$	−6.07411	+	26.0531i	−0.240665	+	1.03226i
$638$	−1.60724	+	0.927943i	−0.0636314	+	0.0367376i
$639$	14.4053	−	3.71498i	0.569866	−	0.146962i
$640$	13.5536	−	7.82515i	0.535751	−	0.309316i
$641$	−1.13498	−	3.11832i	−0.0448289	−	0.123166i	0.915258	−	0.402868i	$-0.131987\pi$
$641$	−1.13498	−	3.11832i	−0.0448289	−	0.123166i	−0.960087	+	0.279702i	$0.909764\pi$
$642$	7.25918	+	2.32641i	0.286497	+	0.0918162i
$643$	24.9953	−	4.40734i	0.985717	−	0.173808i	0.342521	−	0.939510i	$-0.388719\pi$
$643$	24.9953	−	4.40734i	0.985717	−	0.173808i	0.643196	+	0.765702i	$0.277608\pi$
$644$	39.3927	+	4.53133i	1.55229	+	0.178559i
$645$	25.4473	−	10.4006i	1.00199	−	0.409525i
$646$	0.123427	+	0.103568i	0.00485618	+	0.00407482i
$647$	−0.170073	+	0.294574i	−0.00668625	+	0.0115809i	−0.869349	−	0.494198i	$-0.835462\pi$
$647$	−0.170073	+	0.294574i	−0.00668625	+	0.0115809i	0.862663	+	0.505779i	$0.168795\pi$
$648$	−4.26533	−	7.71970i	−0.167558	−	0.303258i
$649$	1.95759	−	1.13021i	0.0768420	−	0.0443648i
$650$	0.425366	−	0.154821i	0.0166842	−	0.00607256i
$651$	1.75335	+	17.6644i	0.0687194	+	0.692321i
$652$	19.2621	−	16.1628i	0.754362	−	0.632985i
$653$	−18.0690	−	21.5337i	−0.707093	−	0.842680i	0.286217	−	0.958165i	$-0.407602\pi$
$653$	−18.0690	−	21.5337i	−0.707093	−	0.842680i	−0.993309	+	0.115485i	$0.963158\pi$
$654$	0.401297	−	0.0869867i	0.0156920	−	0.00340145i
$655$	7.16981	−	2.60960i	0.280148	−	0.101965i
$656$	−38.8965			−1.51865
$657$	7.16959	−	1.84896i	0.279712	−	0.0721349i
$658$	−2.65817	−	2.80719i	−0.103626	−	0.109436i
$659$	29.0041	+	5.11420i	1.12984	+	0.199221i	0.707157	−	0.707057i	$-0.249978\pi$
$659$	29.0041	+	5.11420i	1.12984	+	0.199221i	0.422682	+	0.906278i	$0.361089\pi$
$660$	−0.397428	−	10.2040i	−0.0154699	−	0.397191i
$661$	−0.521355	−	0.621326i	−0.0202783	−	0.0241668i	0.755810	−	0.654791i	$-0.227243\pi$
$661$	−0.521355	−	0.621326i	−0.0202783	−	0.0241668i	−0.776088	+	0.630624i	$0.782799\pi$
$662$	1.89453	+	2.25782i	0.0736332	+	0.0877526i
$663$	−1.27796	−	0.672923i	−0.0496318	−	0.0261342i
$664$	−0.145325	−	0.0256247i	−0.00563969	−	0.000994430i
$665$	−11.4820	−	12.1257i	−0.445252	−	0.470214i
$666$	0.349111	+	4.47492i	0.0135278	+	0.173400i
$667$	−40.3245			−1.56137
$668$	15.0106	−	5.46342i	0.580779	−	0.211386i
$669$	−14.3457	−	15.8042i	−0.554637	−	0.611027i
$670$	5.07525	+	6.04844i	0.196074	+	0.233672i
$671$	−4.66091	+	3.91097i	−0.179933	+	0.150981i
$672$	11.9579	+	5.40710i	0.461287	+	0.208584i
$673$	12.2309	−	4.45168i	0.471466	−	0.171600i	−0.0953502	−	0.995444i	$-0.530397\pi$
$673$	12.2309	−	4.45168i	0.471466	−	0.171600i	0.566816	+	0.823844i	$0.308175\pi$
$674$	−4.51767	+	2.60828i	−0.174014	+	0.100467i
$675$	2.06700	+	1.35822i	0.0795590	+	0.0522777i
$676$	1.55554	−	2.69428i	0.0598286	−	0.103626i
$677$	−10.0934	−	8.46940i	−0.387922	−	0.325506i	0.427881	−	0.903835i	$-0.359260\pi$
$677$	−10.0934	−	8.46940i	−0.387922	−	0.325506i	−0.815803	+	0.578330i	$0.803705\pi$
$678$	4.80611	+	3.72391i	0.184577	+	0.143016i
$679$	−32.7333	−	3.76529i	−1.25619	−	0.144499i
$680$	−0.447885	+	0.0789741i	−0.0171756	+	0.00302852i
$681$	23.9437	−	21.7341i	0.917526	−	0.832851i
$682$	−0.471522	−	1.29550i	−0.0180555	−	0.0496071i
$683$	−5.41536	+	3.12656i	−0.207213	+	0.119635i	−0.600016	−	0.799988i	$-0.704839\pi$
$683$	−5.41536	+	3.12656i	−0.207213	+	0.119635i	0.392802	+	0.919623i	$0.371506\pi$
$684$	−17.1731	−	1.66541i	−0.656629	−	0.0636786i
$685$	−6.58629	+	3.80260i	−0.251649	+	0.145290i
$686$	−2.28239	+	4.00379i	−0.0871419	+	0.152865i
$687$	−1.30905	−	33.6100i	−0.0499434	−	1.28230i
$688$	4.70669	+	26.6929i	0.179441	+	1.01766i
$689$	40.9158	−	34.3324i	1.55877	−	1.30796i
$690$	−3.30299	+	6.27276i	−0.125743	+	0.238800i
$691$	1.78729	+	4.91054i	0.0679918	+	0.186806i	0.969035	−	0.246923i	$-0.0794196\pi$
$691$	1.78729	+	4.91054i	0.0679918	+	0.186806i	−0.901043	+	0.433729i	$0.857197\pi$
$692$	−22.8137	−	39.5145i	−0.867246	−	1.50211i
$693$	8.95789	−	6.97328i	0.340282	−	0.264893i
$694$	3.81061	−	6.60018i	0.144649	−	0.250539i
$695$	12.5696	+	2.21635i	0.476791	+	0.0840711i
$696$	−8.42868	−	2.70121i	−0.319488	−	0.102389i
$697$	2.19562	+	0.799141i	0.0831651	+	0.0302696i
$698$	−4.50429	−	1.63943i	−0.170490	−	0.0620533i
$699$	−13.9898	+	18.0553i	−0.529142	+	0.682914i
$700$	−2.43632	+	0.146371i	−0.0920842	+	0.00553232i
$701$		−	21.7945i		−	0.823166i	−0.911372	−	0.411583i	$-0.864976\pi$
$701$		−	21.7945i		−	0.823166i	0.911372	−	0.411583i	$-0.135024\pi$
$702$	−4.90788	+	0.575791i	−0.185236	+	0.0217318i
$703$	15.4517	+	8.92101i	0.582770	+	0.336462i
$704$	9.22845	+	1.62723i	0.347810	+	0.0613284i
$705$	−20.0248	+	8.18440i	−0.754179	+	0.308242i
$706$	2.95137	+	3.51731i	0.111076	+	0.132376i
$707$	−20.3346	+	8.81566i	−0.764763	+	0.331547i
$708$	5.05226	+	1.61914i	0.189876	+	0.0608511i
$709$	3.00042	−	17.0162i	0.112683	−	0.639059i	−0.875188	−	0.483783i	$-0.839262\pi$
$709$	3.00042	−	17.0162i	0.112683	−	0.639059i	0.987871	−	0.155276i	$-0.0496265\pi$
$710$	−1.31233	−	2.27302i	−0.0492507	−	0.0853048i
$711$	6.60806	+	9.62886i	0.247822	+	0.361110i
$712$	−5.77558	−	3.33453i	−0.216449	−	0.124967i
$713$	5.20161	−	29.4998i	0.194802	−	1.10478i
$714$	−0.177980	−	0.173875i	−0.00666075	−	0.00650709i
$715$	−10.9247	−	3.97626i	−0.408560	−	0.148704i
$716$	−15.9326	+	2.80934i	−0.595428	+	0.104990i
$717$	−22.8996	+	14.4377i	−0.855202	+	0.539184i
$718$	0.148628	+	0.124714i	0.00554676	+	0.00465429i
$719$	12.1162	−	20.9858i	0.451857	−	0.782639i	−0.546645	−	0.837365i	$-0.684095\pi$
$719$	12.1162	−	20.9858i	0.451857	−	0.782639i	0.998501	+	0.0547260i	$0.0174285\pi$
$720$	16.5424	−	16.2340i	0.616497	−	0.605004i
$721$	0.389904	+	0.411763i	0.0145208	+	0.0153348i
$722$	−1.63057	+	1.94324i	−0.0606836	+	0.0723199i
$723$	−3.43290	+	10.7118i	−0.127671	+	0.398375i
$724$	−2.75948	+	7.58160i	−0.102555	+	0.281768i
$725$	2.44437	−	0.431008i	0.0907815	−	0.0160072i
$726$	2.36386	−	3.05082i	0.0877311	−	0.113226i
$727$	−4.28953	−	11.7854i	−0.159090	−	0.437095i	0.834380	−	0.551189i	$-0.185826\pi$
$727$	−4.28953	−	11.7854i	−0.159090	−	0.437095i	−0.993470	+	0.114094i	$0.963604\pi$
$728$	7.19483	−	6.81289i	0.266658	−	0.252502i
$729$	−18.5454	−	19.6231i	−0.686868	−	0.726783i
$730$	−0.653150	−	1.13129i	−0.0241742	−	0.0418709i
$731$	0.282733	−	1.60346i	0.0104573	−	0.0593060i
$732$	−14.1494	−	1.93056i	−0.522976	−	0.0713557i
$733$	−6.22901	+	17.1141i	−0.230074	+	0.632123i	−0.999982	−	0.00603225i	$-0.998080\pi$
$733$	−6.22901	+	17.1141i	−0.230074	+	0.632123i	0.769908	+	0.638155i	$0.220302\pi$
$734$	1.07498	+	6.09652i	0.0396783	+	0.225027i
$735$	16.2663	+	20.0109i	0.599992	+	0.738114i
$736$	−16.9648	−	14.2351i	−0.625329	−	0.524713i
$737$			21.3358i			0.785913i
$738$	7.74096	−	1.99631i	0.284949	−	0.0734852i
$739$	−48.3570			−1.77884			−0.889420	−	0.457092i	$-0.848891\pi$
$739$	−48.3570			−1.77884			−0.889420	+	0.457092i	$0.848891\pi$
$740$	−23.2903	+	8.47696i	−0.856167	+	0.311619i
$741$	−9.15191	+	17.3805i	−0.336204	+	0.638489i
$742$	8.44227	−	3.65997i	0.309925	−	0.134362i
$743$	11.3965	−	31.3117i	0.418098	−	1.14872i	−0.534682	−	0.845053i	$-0.679569\pi$
$743$	11.3965	−	31.3117i	0.418098	−	1.14872i	0.952780	−	0.303662i	$-0.0982092\pi$
$744$	3.06335	−	5.81765i	0.112308	−	0.213285i
$745$	−7.62617	+	9.08852i	−0.279401	+	0.332978i
$746$		−	5.98406i		−	0.219092i
$747$	−0.450382	+	0.0351365i	−0.0164786	+	0.00128558i
$748$	−0.523782	−	0.302406i	−0.0191514	−	0.0110570i
$749$	−39.0478	+	25.7846i	−1.42677	+	0.942147i
$750$	1.53208	−	4.78059i	0.0559435	−	0.174562i
$751$	25.3577	−	21.2776i	0.925314	−	0.776430i	−0.0496563	−	0.998766i	$-0.515813\pi$
$751$	25.3577	−	21.2776i	0.925314	−	0.776430i	0.974970	+	0.222336i	$0.0713682\pi$
$752$	−3.70375	−	21.0050i	−0.135062	−	0.765974i
$753$	32.5981	+	25.2579i	1.18794	+	0.920449i
$754$	−3.18762	+	3.79886i	−0.116086	+	0.138346i
$755$	3.38427			0.123166
$756$	26.2498	+	4.56741i	0.954694	+	0.166115i
$757$	37.7148			1.37077			0.685384	−	0.728182i	$-0.259635\pi$
$757$	37.7148			1.37077			0.685384	+	0.728182i	$0.259635\pi$
$758$	4.89253	−	5.83069i	0.177705	−	0.211780i
$759$	−17.7327	+	7.24756i	−0.643655	+	0.263070i
$760$	1.07407	+	6.09133i	0.0389605	+	0.220956i
$761$	4.49229	−	3.76948i	0.162845	−	0.136644i	−0.557724	−	0.830027i	$-0.688325\pi$
$761$	4.49229	−	3.76948i	0.162845	−	0.136644i	0.720569	+	0.693383i	$0.243881\pi$
$762$	2.03788	−	0.441739i	0.0738247	−	0.0160025i
$763$	−1.12711	+	2.25453i	−0.0408040	+	0.0816194i
$764$	1.62350	+	0.937327i	0.0587361	+	0.0339113i
$765$	−1.26731	+	0.576503i	−0.0458198	+	0.0208435i
$766$			8.95777i			0.323657i
$767$	3.88245	−	4.62692i	0.140187	−	0.167069i
$768$	10.4133	+	16.5166i	0.375759	+	0.595992i
$769$	6.33820	−	17.4141i	0.228561	−	0.627967i	−0.771404	−	0.636346i	$-0.780445\pi$
$769$	6.33820	−	17.4141i	0.228561	−	0.627967i	0.999965	+	0.00837935i	$0.00266726\pi$
$770$	−1.60870	−	1.19307i	−0.0579735	−	0.0429951i
$771$	−52.5743	+	2.04768i	−1.89342	+	0.0737453i
$772$	13.1134	−	4.77289i	0.471962	−	0.171780i
$773$	−6.32723			−0.227575			−0.113787	−	0.993505i	$-0.536298\pi$
$773$	−6.32723			−0.227575			−0.113787	+	0.993505i	$0.536298\pi$
$774$	−2.30668	−	5.07071i	−0.0829118	−	0.182263i
$775$			1.84380i			0.0662312i
$776$	9.34888	+	7.84464i	0.335605	+	0.281606i
$777$	−22.7528	−	15.5392i	−0.816252	−	0.557465i
$778$	1.05424	+	5.97889i	0.0377963	+	0.214354i
$779$	10.8685	−	29.8609i	0.389404	−	1.06988i
$780$	−10.3234	−	25.2583i	−0.369636	−	0.904392i
$781$	1.23157	−	6.98460i	0.0440692	−	0.249929i
$782$	0.209937	+	0.363622i	0.00750733	+	0.0130031i
$783$	−27.0505	−	1.56383i	−0.966707	−	0.0558867i
$784$	−22.6797	+	11.4942i	−0.809988	+	0.410509i
$785$	−18.0004	−	49.4557i	−0.642462	−	1.76515i
$786$	−0.584953	−	1.43121i	−0.0208646	−	0.0510495i
$787$	46.5890	−	8.21490i	1.66072	−	0.292830i	0.736998	−	0.675895i	$-0.236243\pi$
$787$	46.5890	−	8.21490i	1.66072	−	0.292830i	0.923721	+	0.383065i	$0.125132\pi$
$788$	−5.28456	+	14.5192i	−0.188255	+	0.517226i
$789$	26.1844	−	5.67584i	0.932190	−	0.202065i
$790$	1.32438	−	1.57833i	0.0471192	−	0.0561545i
$791$	−36.3002	+	8.67345i	−1.29068	+	0.308392i
$792$	−4.19199	+	0.327038i	−0.148956	+	0.0116208i
$793$	−8.12896	+	14.0798i	−0.288668	+	0.499987i
$794$	1.28926	+	1.08182i	0.0457542	+	0.0383924i
$795$	−2.00384	−	51.4489i	−0.0710691	−	1.82470i
$796$	8.15429	−	1.43782i	0.289021	−	0.0509622i
$797$	14.8436	+	5.40264i	0.525788	+	0.191371i	0.591257	−	0.806483i	$-0.298632\pi$
$797$	14.8436	+	5.40264i	0.525788	+	0.191371i	−0.0654686	+	0.997855i	$0.520854\pi$
$798$	−2.36473	+	2.42057i	−0.0837106	+	0.0856874i
$799$	−0.222486	+	1.26178i	−0.00787100	+	0.0446386i
$800$	1.18051	+	0.681568i	0.0417374	+	0.0240971i
$801$	−19.6700	−	5.46943i	−0.695005	−	0.193253i
$802$	0.119794	+	0.207489i	0.00423007	+	0.00732669i
$803$	0.612960	−	3.47627i	0.0216309	−	0.122675i
$804$	−37.0790	+	33.6571i	−1.30767	+	1.18699i
$805$	−17.3094	−	39.9266i	−0.610075	−	1.40723i
$806$	−2.36791	−	2.82197i	−0.0834061	−	0.0993995i
$807$	−0.941193	−	0.729263i	−0.0331316	−	0.0256713i
$808$	8.08440	+	1.42550i	0.284408	+	0.0501488i
$809$	43.3139	+	25.0073i	1.52284	+	0.879210i	0.999635	+	0.0269998i	$0.00859536\pi$
$809$	43.3139	+	25.0073i	1.52284	+	0.879210i	0.523200	+	0.852210i	$0.324738\pi$
$810$	−2.45898	+	4.07980i	−0.0863998	+	0.143350i
$811$			43.1499i			1.51520i	0.652720	+	0.757600i	$0.273628\pi$
$811$			43.1499i			1.51520i	−0.652720	+	0.757600i	$0.726372\pi$
$812$	22.3129	−	14.7339i	0.783028	−	0.517060i
$813$	4.72650	+	11.5644i	0.165766	+	0.405580i
$814$	2.01083	+	0.731880i	0.0704794	+	0.0256524i
$815$	−25.9314	−	9.43826i	−0.908338	−	0.330608i
$816$	−0.290804	−	1.34157i	−0.0101802	−	0.0469644i
$817$	−21.8074	−	3.84523i	−0.762944	−	0.134528i
$818$	3.61546	−	6.26216i	0.126412	−	0.218951i
$819$	16.1197	−	25.6960i	0.563268	−	0.897892i
$820$	22.0715	+	38.2290i	0.770770	+	1.33501i
$821$	10.3629	+	28.4718i	0.361667	+	0.993671i	0.978440	+	0.206531i	$0.0662173\pi$
$821$	10.3629	+	28.4718i	0.361667	+	0.993671i	−0.616773	+	0.787141i	$0.711560\pi$
$822$	0.821917	+	1.30365i	0.0286677	+	0.0454699i
$823$	16.6545	−	13.9748i	0.580539	−	0.487130i	−0.304585	−	0.952485i	$-0.598518\pi$
$823$	16.6545	−	13.9748i	0.580539	−	0.487130i	0.885124	+	0.465355i	$0.154073\pi$
$824$	−0.0364730	−	0.206849i	−0.00127060	−	0.00720592i
$825$	0.997442	−	0.628863i	0.0347265	−	0.0218942i
$826$	0.868312	−	0.573376i	0.0302124	−	0.0199503i
$827$	6.80237	−	3.92735i	0.236541	−	0.136567i	−0.377045	−	0.926195i	$-0.623060\pi$
$827$	6.80237	−	3.92735i	0.236541	−	0.136567i	0.613586	+	0.789628i	$0.289726\pi$
$828$	−40.5686	−	19.3842i	−1.40985	−	0.673648i
$829$	−3.51679	+	2.03042i	−0.122143	+	0.0705193i	−0.559827	−	0.828610i	$-0.689132\pi$
$829$	−3.51679	+	2.03042i	−0.122143	+	0.0705193i	0.437684	+	0.899129i	$0.355799\pi$
$830$	0.0272595	+	0.0748947i	0.000946190	+	0.00259963i
$831$	−4.56036	−	21.0384i	−0.158197	−	0.729813i
$832$	24.6591	−	4.34806i	0.854900	−	0.150742i
$833$	1.51637	−	0.182864i	0.0525391	−	0.00633586i
$834$	0.349652	−	2.56265i	0.0121074	−	0.0887372i
$835$	−13.4294	−	11.2686i	−0.464745	−	0.389967i
$836$	−4.11279	+	7.12355i	−0.142244	+	0.246373i
$837$	4.63339	−	19.5874i	0.160153	−	0.677039i
$838$	5.24878	−	3.03038i	0.181316	−	0.104683i
$839$	−16.0171	+	5.82975i	−0.552971	+	0.201265i	−0.603366	−	0.797464i	$-0.706174\pi$
$839$	−16.0171	+	5.82975i	−0.552971	+	0.201265i	0.0503948	+	0.998729i	$0.483952\pi$
$840$	−0.943463	−	9.50502i	−0.0325526	−	0.327954i
$841$	1.38521	−	1.16233i	0.0477660	−	0.0400804i
$842$	1.87523	+	2.23482i	0.0646248	+	0.0770169i
$843$	−1.10313	+	3.44213i	−0.0379938	+	0.118553i
$844$	−38.8783	+	14.1506i	−1.33825	+	0.487082i
$845$	−3.41431			−0.117456
$846$	1.81515	+	3.99021i	0.0624063	+	0.137186i
$847$	5.50573	+	23.0426i	0.189179	+	0.791752i
$848$	49.9937	+	8.81524i	1.71679	+	0.302717i
$849$	−29.6565	+	18.6977i	−1.01781	+	0.641704i
$850$	−0.0166124	−	0.0197979i	−0.000569801	−	0.000679062i
$851$	29.8864	+	35.6172i	1.02449	+	1.22094i
$852$	14.0812	−	8.87786i	0.482414	−	0.304150i
$853$	23.9922	+	4.23048i	0.821478	+	0.144849i	0.568563	−	0.822640i	$-0.307500\pi$
$853$	23.9922	+	4.23048i	0.821478	+	0.144849i	0.252915	+	0.967488i	$0.418611\pi$
$854$	−2.03373	+	1.92577i	−0.0695927	+	0.0658983i
$855$	7.84057	+	17.2357i	0.268142	+	0.589449i
$856$	17.3317			0.592385
$857$	50.7585	−	18.4746i	1.73388	−	0.631079i	0.734982	−	0.678087i	$-0.237191\pi$
$857$	50.7585	−	18.4746i	1.73388	−	0.631079i	0.998895	+	0.0470070i	$0.0149683\pi$
$858$	−0.718981	+	2.24346i	−0.0245456	+	0.0765904i
$859$	17.6336	+	21.0149i	0.601652	+	0.717021i	0.977800	−	0.209539i	$-0.0671962\pi$
$859$	17.6336	+	21.0149i	0.601652	+	0.717021i	−0.376149	+	0.926559i	$0.622752\pi$
$860$	23.5641	−	19.7726i	0.803529	−	0.674241i
$861$	−20.2186	+	44.7138i	−0.689047	+	1.52384i
$862$	−6.19522	+	2.25488i	−0.211010	+	0.0768014i
$863$	−13.4069	+	7.74047i	−0.456376	+	0.263489i	−0.710519	−	0.703678i	$-0.751540\pi$
$863$	−13.4069	+	7.74047i	−0.456376	+	0.263489i	0.254143	+	0.967167i	$0.418207\pi$
$864$	−10.8283	−	10.2071i	−0.368385	−	0.347254i
$865$	−25.0372	+	43.3658i	−0.851292	+	1.47448i
$866$	4.48872	+	3.76648i	0.152533	+	0.127990i
$867$	3.96948	−	29.0929i	0.134811	−	0.988045i
$868$	7.90054	+	18.2238i	0.268162	+	0.618556i
$869$	5.48295	−	0.966792i	0.185996	−	0.0327962i
$870$	1.01271	+	4.67193i	0.0343340	+	0.158393i
$871$	19.4988	+	53.5725i	0.660691	+	1.81523i
$872$	0.808520	−	0.466799i	0.0273799	−	0.0158078i
$873$	33.7103	+	16.1073i	1.14092	+	0.545148i
$874$	4.94534	−	2.85519i	0.167278	−	0.0965783i
$875$	16.9806	+	25.7152i	0.574050	+	0.869333i
$876$	7.00827	−	4.41855i	0.236788	−	0.149289i
$877$	6.31884	+	35.8359i	0.213372	+	1.21009i	0.883709	+	0.468036i	$0.155038\pi$
$877$	6.31884	+	35.8359i	0.213372	+	1.21009i	−0.670337	+	0.742057i	$0.733851\pi$
$878$	−0.795908	+	0.667846i	−0.0268606	+	0.0225387i
$879$	−26.1095	−	41.4123i	−0.880650	−	1.39680i
$880$	−3.77921	−	10.3833i	−0.127397	−	0.350021i
$881$	−16.4076	−	28.4188i	−0.552787	−	0.957455i	−0.998072	−	0.0620663i	$-0.980231\pi$
$881$	−16.4076	−	28.4188i	−0.552787	−	0.957455i	0.445285	−	0.895389i	$-0.353102\pi$
$882$	3.92365	−	3.45152i	0.132116	−	0.116219i
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	−0.928633	−	0.370999i	$-0.879015\pi$
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	0.785611	+	0.618720i	$0.212349\pi$
$884$	−1.59155	−	0.280633i	−0.0535295	−	0.00943870i
$885$	−1.23345	−	5.69031i	−0.0414621	−	0.191278i
$886$	−0.567736	−	0.206639i	−0.0190735	−	0.00694218i
$887$	−7.44027	−	2.70804i	−0.249820	−	0.0909270i	0.214075	−	0.976817i	$-0.431326\pi$
$887$	−7.44027	−	2.70804i	−0.249820	−	0.0909270i	−0.463895	+	0.885890i	$0.653548\pi$
$888$	3.86101	+	9.44676i	0.129567	+	0.317012i
$889$	−5.72372	+	11.4490i	−0.191967	+	0.383988i
$890$			3.60199i			0.120739i
$891$	−12.1765	+	4.17412i	−0.407928	+	0.139838i
$892$	−20.6833	−	11.9415i	−0.692528	−	0.399831i
$893$	17.1605	+	3.02586i	0.574255	+	0.101257i
$894$	1.90044	+	1.47252i	0.0635604	+	0.0492484i
$895$	11.4128	+	13.6012i	0.381488	+	0.454640i
$896$	19.3399	+	2.22466i	0.646102	+	0.0743208i
$897$	−37.9018	+	34.4040i	−1.26550	+	1.14872i
$898$	−0.503787	+	2.85712i	−0.0168116	+	0.0953433i
$899$	−10.0996	−	17.4931i	−0.336842	−	0.583427i
$900$	2.66635	+	0.741404i	0.0888783	+	0.0247135i
$901$	−2.64092	−	1.52474i	−0.0879819	−	0.0507964i
$902$	0.661808	−	3.75330i	0.0220358	−	0.124971i
$903$	33.1317	+	8.46451i	1.10255	+	0.281681i
$904$	12.9901	+	4.72800i	0.432044	+	0.157251i
$905$	8.72002	−	1.53758i	0.289863	−	0.0511107i
$906$	−0.0266901	−	0.685270i	−0.000886718	−	0.0227666i
$907$	−28.2444	−	23.6999i	−0.937840	−	0.786941i	0.0393684	−	0.999225i	$-0.487465\pi$
$907$	−28.2444	−	23.6999i	−0.937840	−	0.786941i	−0.977208	+	0.212284i	$0.931910\pi$
$908$	18.0917	−	31.3357i	0.600393	−	1.03991i
$909$	25.0547	−	1.95464i	0.831013	−	0.0648313i
$910$	−5.12967	−	1.52550i	−0.170047	−	0.0505699i
$911$	−3.62967	+	4.32568i	−0.120256	+	0.143316i	−0.822814	−	0.568311i	$-0.807597\pi$
$911$	−3.62967	+	4.32568i	−0.120256	+	0.143316i	0.702557	+	0.711627i	$0.252041\pi$
$912$	−18.2457	+	3.95500i	−0.604174	+	0.130963i
$913$	−0.0736607	+	0.202381i	−0.00243781	+	0.00669784i
$914$	5.20581	−	0.917924i	0.172193	−	0.0303622i
$915$	5.92935	+	14.5074i	0.196018	+	0.479599i
$916$	−12.8724	−	35.3666i	−0.425316	−	1.16855i
$917$	9.09719	+	2.70540i	0.300416	+	0.0893401i
$918$	0.126729	+	0.252067i	0.00418267	+	0.00831944i
$919$	10.6179	+	18.3908i	0.350253	+	0.606655i	0.986294	−	0.165000i	$-0.0527624\pi$
$919$	10.6179	+	18.3908i	0.350253	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$920$	−2.79894	+	15.8736i	−0.0922782	+	0.523336i
$921$	1.30000	+	3.18073i	0.0428365	+	0.104808i
$922$	2.29082	−	6.29397i	0.0754441	−	0.207281i
$923$	−3.29085	−	18.6634i	−0.108320	−	0.614312i
$924$	7.16391	−	10.4895i	0.235675	−	0.345080i
$925$	−2.19233	−	1.83958i	−0.0720834	−	0.0604851i
$926$			5.97143i			0.196233i
$927$	−0.266249	−	0.585289i	−0.00874477	−	0.0192234i
$928$	−14.9335			−0.490216
$929$	−37.4072	+	13.6151i	−1.22729	+	0.446697i	−0.872668	−	0.488314i	$-0.837612\pi$
$929$	−37.4072	+	13.6151i	−1.22729	+	0.446697i	−0.354621	+	0.935010i	$0.615390\pi$
$930$	−3.54843	+	0.138205i	−0.116358	+	0.00453193i
$931$	−2.48699	−	20.6230i	−0.0815078	−	0.675891i
$932$	−8.74129	+	24.0165i	−0.286331	+	0.786687i
$933$	12.5488	+	19.9037i	0.410829	+	0.651617i
$934$	−0.990073	+	1.17992i	−0.0323962	+	0.0386083i
$935$			0.663760i			0.0217073i
$936$	−10.2269	+	4.65224i	−0.334277	+	0.152063i
$937$	−2.26157	−	1.30572i	−0.0738824	−	0.0426560i	0.462604	−	0.886565i	$-0.346915\pi$
$937$	−2.26157	−	1.30572i	−0.0738824	−	0.0426560i	−0.536486	+	0.843909i	$0.680249\pi$
$938$	0.589002	+	9.80380i	0.0192316	+	0.320105i
$939$	−24.7775	+	5.37087i	−0.808584	+	0.175272i
$940$	−18.5429	+	15.5593i	−0.604802	+	0.507489i
$941$	−5.15868	−	29.2563i	−0.168168	−	0.953730i	−0.945737	−	0.324932i	$-0.894659\pi$
$941$	−5.15868	−	29.2563i	−0.168168	−	0.953730i	0.777569	−	0.628798i	$-0.216453\pi$
$942$	−9.87214	+	4.03487i	−0.321652	+	0.131463i
$943$	53.2288	−	63.4357i	1.73337	−	2.06575i
$944$	5.74070			0.186844
$945$	−10.0631	−	27.4549i	−0.327352	−	0.893109i
$946$	−2.65581			−0.0863477
$947$	−11.1333	+	13.2682i	−0.361784	+	0.431158i	−0.915977	−	0.401231i	$-0.868583\pi$
$947$	−11.1333	+	13.2682i	−0.361784	+	0.431158i	0.554193	+	0.832388i	$0.313027\pi$
$948$	10.3295	+	8.00359i	0.335486	+	0.259945i
$949$	−1.63787	−	9.28883i	−0.0531676	−	0.301528i
$950$	−0.269256	+	0.225932i	−0.00873581	+	0.00733021i
$951$	−9.99400	+	31.1846i	−0.324078	+	1.01123i
$952$	−0.506010	−	0.252970i	−0.0163999	−	0.00819880i
$953$	−16.8568	−	9.73226i	−0.546044	−	0.315259i	0.201481	−	0.979492i	$-0.435425\pi$
$953$	−16.8568	−	9.73226i	−0.546044	−	0.315259i	−0.747525	+	0.664234i	$0.768758\pi$
$954$	−10.4019	+	0.811502i	−0.336774	+	0.0262734i
$955$		−	2.05737i		−	0.0665748i
$956$	−19.4707	+	23.2043i	−0.629728	+	0.750481i
$957$	−6.01858	+	11.4300i	−0.194553	+	0.369478i
$958$	−1.37197	+	3.76945i	−0.0443262	+	0.121785i
$959$	−9.39817	−	1.08107i	−0.303483	−	0.0349095i
$960$	11.2461	−	21.3576i	0.362966	−	0.689314i
$961$	−15.0304	+	5.47063i	−0.484853	+	0.176472i
$962$	5.71790			0.184352
$963$	51.3771	−	13.2496i	1.65561	−	0.426963i
$964$			12.5864i			0.405381i
$965$	−11.7321	−	9.84438i	−0.377669	−	0.316902i
$966$	−7.94809	+	3.81979i	−0.255726	+	0.122900i
$967$	3.08674	+	17.5057i	0.0992627	+	0.562947i	0.993357	+	0.115069i	$0.0367089\pi$
$967$	3.08674	+	17.5057i	0.0992627	+	0.562947i	−0.894095	+	0.447878i	$0.852180\pi$
$968$	3.00124	−	8.24583i	0.0964634	−	0.265031i
$969$	1.11118	+	0.151612i	0.0356964	+	0.00487048i
$970$	1.14460	−	6.49134i	0.0367509	−	0.208424i
$971$	15.6634	+	27.1298i	0.502662	+	0.870636i	0.999995	+	0.00307625i	$0.000979204\pi$
$971$	15.6634	+	27.1298i	0.502662	+	0.870636i	−0.497334	+	0.867559i	$0.665687\pi$
$972$	−26.4625	−	14.5766i	−0.848785	−	0.467546i
$973$	10.9163	+	11.5282i	0.349959	+	0.369578i
$974$	−2.21727	−	6.09191i	−0.0710461	−	0.195197i
$975$	1.92978	−	2.49059i	0.0618025	−	0.0797628i
$976$	−15.2175	+	2.68326i	−0.487100	+	0.0858889i
$977$	−0.0731353	+	0.200938i	−0.00233980	+	0.00642856i	−0.940857	−	0.338804i	$-0.889978\pi$
$977$	−0.0731353	+	0.200938i	−0.00233980	+	0.00642856i	0.938517	+	0.345232i	$0.112200\pi$
$978$	−1.70661	+	5.32519i	−0.0545714	+	0.170281i
$979$	−6.25646	+	7.45616i	−0.199957	+	0.238300i
$980$	24.1664	+	15.7681i	0.771967	+	0.503695i
$981$	2.03988	−	2.00185i	0.0651283	−	0.0639141i
$982$	−1.31268	+	2.27362i	−0.0418892	+	0.0725543i
$983$	−14.8906	−	12.4947i	−0.474935	−	0.398518i	0.373656	−	0.927568i	$-0.378104\pi$
$983$	−14.8906	−	12.4947i	−0.474935	−	0.398518i	−0.848591	+	0.529049i	$0.822549\pi$
$984$	15.3753	−	9.69377i	0.490147	−	0.309026i
$985$	16.6994	−	2.94455i	0.532086	−	0.0938210i
$986$	0.266056	+	0.0968364i	0.00847295	+	0.00308390i
$987$	−26.0717	−	6.66083i	−0.829873	−	0.212017i
$988$	−3.81667	+	21.6454i	−0.121424	+	0.688632i
$989$	−49.9741	−	28.8526i	−1.58908	−	0.917458i
$990$	1.28503	+	1.87246i	0.0408408	+	0.0595108i
$991$	14.0834	+	24.3931i	0.447373	+	0.774872i	0.998214	−	0.0597375i	$-0.0190264\pi$
$991$	14.0834	+	24.3931i	0.447373	+	0.774872i	−0.550841	+	0.834610i	$0.685693\pi$
$992$	1.92633	−	10.9248i	0.0611610	−	0.346861i
$993$	19.5362	+	6.26093i	0.619962	+	0.198685i
$994$	0.373090	−	3.24343i	0.0118337	−	0.102875i
$995$	−5.84108	−	6.96113i	−0.185175	−	0.220683i
$996$	−0.467913	+	0.191242i	−0.0148264	+	0.00605973i
$997$	−32.9869	−	5.81648i	−1.04471	−	0.184210i	−0.375144	−	0.926966i	$-0.622407\pi$
$997$	−32.9869	−	5.81648i	−1.04471	−	0.184210i	−0.669561	+	0.742757i	$0.733518\pi$
$998$	1.73961	+	1.00437i	0.0550665	+	0.0317927i
$999$	18.6672	+	25.0518i	0.590603	+	0.792605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.10	✓	132
3.2	odd	2		567.2.ba.a.143.13		132
7.5	odd	6		189.2.bd.a.47.13	yes	132
21.5	even	6		567.2.bd.a.467.10		132
27.4	even	9		567.2.bd.a.17.10		132
27.23	odd	18		189.2.bd.a.185.13	yes	132
189.131	even	18	inner	189.2.ba.a.131.10	yes	132
189.166	odd	18		567.2.ba.a.341.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.10	✓	132	1.1	even	1	trivial
189.2.ba.a.131.10	yes	132	189.131	even	18	inner
189.2.bd.a.47.13	yes	132	7.5	odd	6
189.2.bd.a.185.13	yes	132	27.23	odd	18
567.2.ba.a.143.13		132	3.2	odd	2
567.2.ba.a.341.13		132	189.166	odd	18
567.2.bd.a.17.10		132	27.4	even	9
567.2.bd.a.467.10		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.159953 + 0.190625i) q^{2} +(-0.234154 + 1.71615i) q^{3} +(0.336544 + 1.90863i) q^{4} +(1.62936 - 1.36719i) q^{5} +(-0.289688 - 0.319140i) q^{6} +(2.64099 - 0.158668i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(-2.89034 - 0.803688i) q^{9} +O(q^{10})\)	\(q+(-0.159953 + 0.190625i) q^{2} +(-0.234154 + 1.71615i) q^{3} +(0.336544 + 1.90863i) q^{4} +(1.62936 - 1.36719i) q^{5} +(-0.289688 - 0.319140i) q^{6} +(2.64099 - 0.158668i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(-2.89034 - 0.803688i) q^{9} +0.529283i q^{10} +(-0.919336 + 1.09562i) q^{11} +(-3.35430 + 0.130644i) q^{12} +(-1.30709 + 3.59121i) q^{13} +(-0.392189 + 0.528818i) q^{14} +(1.96479 + 3.11635i) q^{15} +(-3.41324 + 1.24232i) q^{16} +0.218194 q^{17} +(0.615524 - 0.422419i) q^{18} -2.96748i q^{19} +(3.15782 + 2.64972i) q^{20} +(-0.346102 + 4.56949i) q^{21} +(-0.0618021 - 0.350497i) q^{22} +(2.64486 - 7.26669i) q^{23} +(1.03960 - 1.34172i) q^{24} +(-0.0826545 + 0.468757i) q^{25} +(-0.475500 - 0.823590i) q^{26} +(2.05604 - 4.77208i) q^{27} +(1.19165 + 4.98728i) q^{28} +(-1.78349 - 4.90009i) q^{29} +(-0.908329 - 0.123934i) q^{30} +(3.81477 - 0.672647i) q^{31} +(0.979478 - 2.69109i) q^{32} +(-1.66498 - 1.83426i) q^{33} +(-0.0349009 + 0.0415932i) q^{34} +(4.08618 - 3.86926i) q^{35} +(0.561220 - 5.78708i) q^{36} +(-3.00625 + 5.20699i) q^{37} +(0.565677 + 0.474659i) q^{38} +(-5.85699 - 3.08406i) q^{39} +(-2.05269 + 0.361945i) q^{40} +(10.0627 + 3.66253i) q^{41} +(-0.815699 - 0.796881i) q^{42} +(1.29579 - 7.34878i) q^{43} +(-2.40054 - 1.38595i) q^{44} +(-5.80819 + 2.64216i) q^{45} +(0.962159 + 1.66651i) q^{46} +(-1.01967 + 5.78285i) q^{47} +(-1.33278 - 6.14853i) q^{48} +(6.94965 - 0.838080i) q^{49} +(-0.0761360 - 0.0907353i) q^{50} +(-0.0510911 + 0.374453i) q^{51} +(-7.29419 - 1.28616i) q^{52} +(-12.1036 - 6.98800i) q^{53} +(0.580807 + 1.15524i) q^{54} +3.04206i q^{55} +(-2.31908 - 1.15938i) q^{56} +(5.09265 + 0.694850i) q^{57} +(1.21936 + 0.443809i) q^{58} +(-1.48515 - 0.540550i) q^{59} +(-5.28674 + 4.79884i) q^{60} +(4.18950 + 0.738722i) q^{61} +(-0.481963 + 0.834784i) q^{62} +(-7.76089 - 1.66393i) q^{63} +(-3.27598 - 5.67416i) q^{64} +(2.78015 + 7.63839i) q^{65} +(0.615977 - 0.0239912i) q^{66} +(11.4276 - 9.58891i) q^{67} +(0.0734317 + 0.416452i) q^{68} +(11.8514 + 6.24050i) q^{69} +(0.0839802 + 1.39783i) q^{70} +(-4.29452 + 2.47944i) q^{71} +(2.05917 + 2.09829i) q^{72} +(-2.13740 + 1.23403i) q^{73} +(-0.511721 - 1.40594i) q^{74} +(-0.785104 - 0.251609i) q^{75} +(5.66384 - 0.998688i) q^{76} +(-2.25412 + 3.03939i) q^{77} +(1.52475 - 0.623182i) q^{78} +(-2.98202 - 2.50221i) q^{79} +(-3.86290 + 6.69073i) q^{80} +(7.70817 + 4.64587i) q^{81} +(-2.30773 + 1.33237i) q^{82} +(0.141502 - 0.0515026i) q^{83} +(-8.83795 + 0.877250i) q^{84} +(0.355515 - 0.298313i) q^{85} +(1.19360 + 1.42247i) q^{86} +(8.82691 - 1.91335i) q^{87} +(1.31705 - 0.479367i) q^{88} +6.80542 q^{89} +(0.425379 - 1.52981i) q^{90} +(-2.88221 + 9.69173i) q^{91} +(14.7595 + 2.60251i) q^{92} +(0.261118 + 6.70423i) q^{93} +(-0.939256 - 1.11936i) q^{94} +(-4.05712 - 4.83509i) q^{95} +(4.38897 + 2.31106i) q^{96} +(-12.2644 - 2.16255i) q^{97} +(-0.951861 + 1.45883i) q^{98} +(3.53773 - 2.42786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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