LMFDB - Embedded newform 861.2.cl.a.11.108

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(11,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(120))

chi = DirichletCharacter(H, H._module([60, 80, 9]))

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

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

chi := DirichletCharacter("861.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.cl (of order $120$, degree $32$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$3456$
Relative dimension:	$108$ over $\Q(\zeta_{120})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{120}]$

Embedding invariants

Embedding label			11.108
Character	$\chi$	$=$	861.11
Dual form			861.2.cl.a.548.108

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14683 - 1.73847i) q^{2} +(-1.57838 - 0.713240i) q^{3} +(1.17079 - 5.50812i) q^{4} +(0.113959 + 2.17447i) q^{5} +(-4.62847 + 1.21276i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(-4.55397 - 8.93767i) q^{8} +(1.98258 + 2.25153i) q^{9} +O(q^{10})$	\(q+(2.14683 - 1.73847i) q^{2} +(-1.57838 - 0.713240i) q^{3} +(1.17079 - 5.50812i) q^{4} +(0.113959 + 2.17447i) q^{5} +(-4.62847 + 1.21276i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(-4.55397 - 8.93767i) q^{8} +(1.98258 + 2.25153i) q^{9} +(4.02491 + 4.47011i) q^{10} +(-1.68453 - 4.75697i) q^{11} +(-5.77657 + 7.85887i) q^{12} +(-2.02418 - 3.30316i) q^{13} +(-5.10562 + 5.22981i) q^{14} +(1.37105 - 3.51343i) q^{15} +(-15.0258 - 6.68993i) q^{16} +(-2.21736 + 4.64879i) q^{17} +(8.17048 + 1.38701i) q^{18} +(0.200649 + 0.00525417i) q^{19} +(12.1107 + 1.91814i) q^{20} +(4.36737 + 1.38783i) q^{21} +(-11.8863 - 7.28391i) q^{22} +(-0.191198 + 1.81912i) q^{23} +(0.813197 + 17.3551i) q^{24} +(0.257271 - 0.0270403i) q^{25} +(-10.0880 - 3.57236i) q^{26} +(-1.52338 - 4.96783i) q^{27} +(-1.37919 + 14.8347i) q^{28} +(-6.02991 - 0.474564i) q^{29} +(-3.16458 - 9.92627i) q^{30} +(1.45059 - 1.30612i) q^{31} +(-24.5098 + 6.56739i) q^{32} +(-0.734029 + 8.70979i) q^{33} +(3.32149 + 13.8350i) q^{34} +(-0.969523 - 5.67884i) q^{35} +(14.7229 - 8.28421i) q^{36} +(1.04235 - 1.15765i) q^{37} +(0.439894 - 0.337542i) q^{38} +(0.838980 + 6.65738i) q^{39} +(18.9157 - 10.9210i) q^{40} +(2.45695 - 5.91298i) q^{41} +(11.7887 - 4.61310i) q^{42} +(9.56729 - 1.51531i) q^{43} +(-28.1742 + 3.70921i) q^{44} +(-4.66996 + 4.56764i) q^{45} +(2.75203 + 4.23775i) q^{46} +(6.93270 - 2.05356i) q^{47} +(18.9450 + 21.2763i) q^{48} +(6.81008 - 1.61949i) q^{49} +(0.505309 - 0.505309i) q^{50} +(6.81554 - 5.75605i) q^{51} +(-20.5641 + 7.28213i) q^{52} +(-1.69245 - 1.16319i) q^{53} +(-11.9069 - 8.01675i) q^{54} +(10.1519 - 4.20507i) q^{55} +(14.7208 + 22.0826i) q^{56} +(-0.312953 - 0.151404i) q^{57} +(-13.7702 + 9.46402i) q^{58} +(-4.48835 - 10.0810i) q^{59} +(-17.7472 - 11.6654i) q^{60} +(-7.91348 + 3.03770i) q^{61} +(0.843527 - 5.32582i) q^{62} +(-5.90352 - 5.30551i) q^{63} +(-21.8658 + 30.0956i) q^{64} +(6.95195 - 4.77795i) q^{65} +(13.5659 + 19.9746i) q^{66} +(5.27896 - 0.978398i) q^{67} +(23.0101 + 17.6562i) q^{68} +(1.59926 - 2.73490i) q^{69} +(-11.9539 - 10.5060i) q^{70} +(-7.24226 - 6.18547i) q^{71} +(11.0948 - 27.9730i) q^{72} +(-0.816627 - 3.04769i) q^{73} +(0.225216 - 4.29737i) q^{74} +(-0.425358 - 0.140816i) q^{75} +(0.263858 - 1.09905i) q^{76} +(5.89239 + 11.9810i) q^{77} +(13.3748 + 12.8337i) q^{78} +(16.5581 - 2.17991i) q^{79} +(12.8347 - 33.4356i) q^{80} +(-1.13878 + 8.92766i) q^{81} +(-5.00488 - 16.9655i) q^{82} +2.15845i q^{83} +(12.7576 - 22.4312i) q^{84} +(-10.3613 - 4.29181i) q^{85} +(17.9051 - 19.8856i) q^{86} +(9.17902 + 5.04982i) q^{87} +(-34.8449 + 36.7189i) q^{88} +(5.29703 - 5.02669i) q^{89} +(-2.08491 + 17.9245i) q^{90} +(6.33690 + 8.05611i) q^{91} +(9.79611 + 3.18295i) q^{92} +(-3.22116 + 1.02693i) q^{93} +(11.3133 - 16.4610i) q^{94} +(0.0114407 + 0.436904i) q^{95} +(43.3700 + 7.11555i) q^{96} +(3.58219 - 3.05948i) q^{97} +(11.8047 - 15.3159i) q^{98} +(7.37075 - 13.2238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9}+O(q^{10}) $ 3456 * q - 16 * q^3 - 40 * q^4 - 64 * q^6 - 64 * q^7 - 8 * q^9	$ 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9} - 24 q^{10} + 8 q^{12} - 128 q^{13} - 40 q^{15} - 408 q^{16} - 12 q^{18} - 32 q^{19} - 24 q^{21} - 48 q^{22} - 56 q^{24} - 40 q^{25} - 64 q^{27} - 32 q^{28} - 8 q^{30} - 40 q^{31} - 92 q^{33} - 128 q^{34} + 32 q^{36} - 24 q^{37} - 16 q^{39} - 192 q^{42} - 96 q^{43} - 20 q^{45} - 40 q^{46} + 104 q^{48} - 112 q^{49} + 24 q^{51} - 8 q^{52} - 136 q^{54} - 96 q^{55} - 64 q^{57} - 32 q^{58} - 48 q^{60} + 28 q^{63} - 160 q^{64} - 20 q^{66} - 16 q^{67} - 88 q^{69} - 184 q^{70} - 20 q^{72} - 32 q^{73} - 20 q^{75} - 640 q^{76} + 64 q^{78} - 16 q^{79} + 160 q^{82} + 32 q^{84} - 192 q^{85} - 36 q^{87} - 64 q^{88} - 112 q^{90} - 80 q^{91} + 48 q^{93} - 32 q^{94} + 96 q^{96} - 256 q^{97} - 192 q^{99}+O(q^{100}) $ 3456 * q - 16 * q^3 - 40 * q^4 - 64 * q^6 - 64 * q^7 - 8 * q^9 - 24 * q^10 + 8 * q^12 - 128 * q^13 - 40 * q^15 - 408 * q^16 - 12 * q^18 - 32 * q^19 - 24 * q^21 - 48 * q^22 - 56 * q^24 - 40 * q^25 - 64 * q^27 - 32 * q^28 - 8 * q^30 - 40 * q^31 - 92 * q^33 - 128 * q^34 + 32 * q^36 - 24 * q^37 - 16 * q^39 - 192 * q^42 - 96 * q^43 - 20 * q^45 - 40 * q^46 + 104 * q^48 - 112 * q^49 + 24 * q^51 - 8 * q^52 - 136 * q^54 - 96 * q^55 - 64 * q^57 - 32 * q^58 - 48 * q^60 + 28 * q^63 - 160 * q^64 - 20 * q^66 - 16 * q^67 - 88 * q^69 - 184 * q^70 - 20 * q^72 - 32 * q^73 - 20 * q^75 - 640 * q^76 + 64 * q^78 - 16 * q^79 + 160 * q^82 + 32 * q^84 - 192 * q^85 - 36 * q^87 - 64 * q^88 - 112 * q^90 - 80 * q^91 + 48 * q^93 - 32 * q^94 + 96 * q^96 - 256 * q^97 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.14683	−	1.73847i	1.51804	−	1.22929i	0.623896	−	0.781508i	$-0.285549\pi$
$2$	2.14683	−	1.73847i	1.51804	−	1.22929i	0.894145	−	0.447777i	$-0.147784\pi$
$3$	−1.57838	−	0.713240i	−0.911279	−	0.411789i
$3$	−1.57838	−	0.713240i	−0.911279	−	0.411789i
$4$	1.17079	−	5.50812i	0.585394	−	2.75406i
$5$	0.113959	+	2.17447i	0.0509641	+	0.972453i	0.897746	+	0.440513i	$0.145203\pi$
$5$	0.113959	+	2.17447i	0.0509641	+	0.972453i	−0.846782	+	0.531940i	$0.821463\pi$
$6$	−4.62847	+	1.21276i	−1.88957	+	0.495109i
$7$	−2.62774	+	0.308152i	−0.993194	+	0.116470i
$7$	−2.62774	+	0.308152i	−0.993194	+	0.116470i
$8$	−4.55397	−	8.93767i	−1.61007	−	3.15994i
$9$	1.98258	+	2.25153i	0.660859	+	0.750510i
$10$	4.02491	+	4.47011i	1.27279	+	1.41357i
$11$	−1.68453	−	4.75697i	−0.507905	−	1.43428i	−0.865739	−	0.500495i	$-0.833151\pi$
$11$	−1.68453	−	4.75697i	−0.507905	−	1.43428i	0.357834	−	0.933785i	$-0.383515\pi$
$12$	−5.77657	+	7.85887i	−1.66755	+	2.26866i
$13$	−2.02418	−	3.30316i	−0.561406	−	0.916132i	−0.999849	−	0.0173729i	$-0.994470\pi$
$13$	−2.02418	−	3.30316i	−0.561406	−	0.916132i	0.438443	−	0.898759i	$-0.355530\pi$
$14$	−5.10562	+	5.22981i	−1.36453	+	1.39773i
$15$	1.37105	−	3.51343i	0.354003	−	0.907163i
$16$	−15.0258	−	6.68993i	−3.75646	−	1.67248i
$17$	−2.21736	+	4.64879i	−0.537789	+	1.12750i	0.435980	+	0.899956i	$0.356402\pi$
$17$	−2.21736	+	4.64879i	−0.537789	+	1.12750i	−0.973769	+	0.227541i	$0.926931\pi$
$18$	8.17048	+	1.38701i	1.92580	+	0.326921i
$19$	0.200649	+	0.00525417i	0.0460320	+	0.00120539i	0.0491860	−	0.998790i	$-0.484337\pi$
$19$	0.200649	+	0.00525417i	0.0460320	+	0.00120539i	−0.00315402	+	0.999995i	$0.501004\pi$
$20$	12.1107	+	1.91814i	2.70803	+	0.428910i
$21$	4.36737	+	1.38783i	0.953038	+	0.302850i
$22$	−11.8863	−	7.28391i	−2.53416	−	1.55294i
$23$	−0.191198	+	1.81912i	−0.0398675	+	0.379314i	0.956337	+	0.292267i	$0.0944096\pi$
$23$	−0.191198	+	1.81912i	−0.0398675	+	0.379314i	−0.996204	+	0.0870466i	$0.972257\pi$
$24$	0.813197	+	17.3551i	0.165993	+	3.54260i
$25$	0.257271	−	0.0270403i	0.0514542	−	0.00540806i
$26$	−10.0880	−	3.57236i	−1.97843	−	0.700597i
$27$	−1.52338	−	4.96783i	−0.293175	−	0.956059i
$28$	−1.37919	+	14.8347i	−0.260643	+	2.80350i
$29$	−6.02991	−	0.474564i	−1.11973	−	0.0881244i	−0.494945	−	0.868924i	$-0.664812\pi$
$29$	−6.02991	−	0.474564i	−1.11973	−	0.0881244i	−0.624781	+	0.780800i	$0.714812\pi$
$30$	−3.16458	−	9.92627i	−0.577770	−	1.81228i
$31$	1.45059	−	1.30612i	0.260533	−	0.234585i	−0.528504	−	0.848931i	$-0.677247\pi$
$31$	1.45059	−	1.30612i	0.260533	−	0.234585i	0.789037	+	0.614346i	$0.210580\pi$
$32$	−24.5098	+	6.56739i	−4.33277	+	1.16096i
$33$	−0.734029	+	8.70979i	−0.127778	+	1.51618i
$34$	3.32149	+	13.8350i	0.569631	+	2.37268i
$35$	−0.969523	−	5.67884i	−0.163879	−	0.959899i
$36$	14.7229	−	8.28421i	2.45381	−	1.38070i
$37$	1.04235	−	1.15765i	0.171361	−	0.190316i	−0.651347	−	0.758780i	$-0.725796\pi$
$37$	1.04235	−	1.15765i	0.171361	−	0.190316i	0.822708	+	0.568464i	$0.192462\pi$
$38$	0.439894	−	0.337542i	0.0713602	−	0.0547566i
$39$	0.838980	+	6.65738i	0.134344	+	1.06603i
$40$	18.9157	−	10.9210i	2.99084	−	1.72676i
$41$	2.45695	−	5.91298i	0.383712	−	0.923453i
$41$	2.45695	−	5.91298i	0.383712	−	0.923453i
$42$	11.7887	−	4.61310i	1.81904	−	0.711817i
$43$	9.56729	−	1.51531i	1.45900	−	0.231083i	0.624038	−	0.781394i	$-0.285491\pi$
$43$	9.56729	−	1.51531i	1.45900	−	0.231083i	0.834960	+	0.550311i	$0.185491\pi$
$44$	−28.1742	+	3.70921i	−4.24742	+	0.559184i
$45$	−4.66996	+	4.56764i	−0.696156	+	0.680903i
$46$	2.75203	+	4.23775i	0.405764	+	0.624822i
$47$	6.93270	−	2.05356i	1.01124	−	0.299542i	0.264303	−	0.964440i	$-0.414858\pi$
$47$	6.93270	−	2.05356i	1.01124	−	0.299542i	0.746935	+	0.664897i	$0.231525\pi$
$48$	18.9450	+	21.2763i	2.73447	+	3.07097i
$49$	6.81008	−	1.61949i	0.972869	−	0.231356i
$50$	0.505309	−	0.505309i	0.0714615	−	0.0714615i
$51$	6.81554	−	5.75605i	0.954367	−	0.806009i
$52$	−20.5641	+	7.28213i	−2.85173	+	1.00985i
$53$	−1.69245	−	1.16319i	−0.232476	−	0.159777i	0.444506	−	0.895776i	$-0.353379\pi$
$53$	−1.69245	−	1.16319i	−0.232476	−	0.159777i	−0.676982	+	0.735999i	$0.736713\pi$
$54$	−11.9069	−	8.01675i	−1.62032	−	1.09094i
$55$	10.1519	−	4.20507i	1.36889	−	0.567011i
$56$	14.7208	+	22.0826i	1.96715	+	2.95091i
$57$	−0.312953	−	0.151404i	−0.0414516	−	0.0200539i
$58$	−13.7702	+	9.46402i	−1.80812	+	1.24269i
$59$	−4.48835	−	10.0810i	−0.584333	−	1.31243i	−0.927733	−	0.373244i	$-0.878245\pi$
$59$	−4.48835	−	10.0810i	−0.584333	−	1.31243i	0.343400	−	0.939189i	$-0.388421\pi$
$60$	−17.7472	−	11.6654i	−2.29115	−	1.50599i
$61$	−7.91348	+	3.03770i	−1.01322	+	0.388938i	−0.807623	−	0.589700i	$-0.799246\pi$
$61$	−7.91348	+	3.03770i	−1.01322	+	0.388938i	−0.205595	+	0.978637i	$0.565913\pi$
$62$	0.843527	−	5.32582i	0.107128	−	0.676380i
$63$	−5.90352	−	5.30551i	−0.743773	−	0.668432i
$64$	−21.8658	+	30.0956i	−2.73322	+	3.76195i
$65$	6.95195	−	4.77795i	0.862284	−	0.592631i
$66$	13.5659	+	19.9746i	1.66984	+	2.45870i
$67$	5.27896	−	0.978398i	0.644928	−	0.119530i	0.150307	−	0.988639i	$-0.451974\pi$
$67$	5.27896	−	0.978398i	0.644928	−	0.119530i	0.494621	+	0.869109i	$0.335307\pi$
$68$	23.0101	+	17.6562i	2.79038	+	2.14113i
$69$	1.59926	−	2.73490i	0.192528	−	0.329243i
$70$	−11.9539	−	10.5060i	−1.42876	−	1.25571i
$71$	−7.24226	−	6.18547i	−0.859498	−	0.734080i	0.106035	−	0.994362i	$-0.466184\pi$
$71$	−7.24226	−	6.18547i	−0.859498	−	0.734080i	−0.965533	+	0.260282i	$0.916184\pi$
$72$	11.0948	−	27.9730i	1.30754	−	3.29665i
$73$	−0.816627	−	3.04769i	−0.0955790	−	0.356706i	0.901528	−	0.432722i	$-0.142447\pi$
$73$	−0.816627	−	3.04769i	−0.0955790	−	0.356706i	−0.997107	+	0.0760160i	$0.975780\pi$
$74$	0.225216	−	4.29737i	0.0261808	−	0.499559i
$75$	−0.425358	−	0.140816i	−0.0491161	−	0.0162601i
$76$	0.263858	−	1.09905i	0.0302666	−	0.126069i
$77$	5.89239	+	11.9810i	0.671500	+	1.36536i
$78$	13.3748	+	12.8337i	1.51440	+	1.45313i
$79$	16.5581	−	2.17991i	1.86293	−	0.245259i	0.886754	−	0.462242i	$-0.152955\pi$
$79$	16.5581	−	2.17991i	1.86293	−	0.245259i	0.976175	+	0.216983i	$0.0696217\pi$
$80$	12.8347	−	33.4356i	1.43497	−	3.73821i
$81$	−1.13878	+	8.92766i	−0.126531	+	0.991963i
$82$	−5.00488	−	16.9655i	−0.552697	−	1.87353i
$83$			2.15845i			0.236921i	0.992959	+	0.118460i	$0.0377959\pi$
$83$			2.15845i			0.236921i	−0.992959	+	0.118460i	$0.962204\pi$
$84$	12.7576	−	22.4312i	1.39197	−	2.44744i
$85$	−10.3613	−	4.29181i	−1.12385	−	0.465512i
$86$	17.9051	−	19.8856i	1.93075	−	2.14432i
$87$	9.17902	+	5.04982i	0.984094	+	0.541397i
$88$	−34.8449	+	36.7189i	−3.71448	+	3.91425i
$89$	5.29703	−	5.02669i	0.561484	−	0.532828i	−0.353967	−	0.935258i	$-0.615168\pi$
$89$	5.29703	−	5.02669i	0.561484	−	0.532828i	0.915451	+	0.402430i	$0.131834\pi$
$90$	−2.08491	+	17.9245i	−0.219769	+	1.88941i
$91$	6.33690	+	8.05611i	0.664288	+	0.844510i
$92$	9.79611	+	3.18295i	1.02131	+	0.331845i
$93$	−3.22116	+	1.02693i	−0.334018	+	0.106488i
$94$	11.3133	−	16.4610i	1.16688	−	1.69782i
$95$	0.0114407	+	0.436904i	0.00117379	+	0.0448254i
$96$	43.3700	+	7.11555i	4.42643	+	0.726228i
$97$	3.58219	−	3.05948i	0.363716	−	0.310643i	−0.448743	−	0.893661i	$-0.648128\pi$
$97$	3.58219	−	3.05948i	0.363716	−	0.310643i	0.812459	+	0.583018i	$0.198128\pi$
$98$	11.8047	−	15.3159i	1.19245	−	1.54714i
$99$	7.37075	−	13.2238i	0.740788	−	1.32905i
$100$	0.152269	−	1.44874i	0.0152269	−	0.144874i
$101$	−13.2289	+	7.18271i	−1.31633	+	0.714706i	−0.974357	−	0.225006i	$-0.927760\pi$
$101$	−13.2289	+	7.18271i	−1.31633	+	0.714706i	−0.341968	+	0.939712i	$0.611093\pi$
$102$	4.62510	−	24.2059i	0.457953	−	2.39674i
$103$	0.737370	+	1.92092i	0.0726553	+	0.189273i	0.965099	−	0.261885i	$-0.0843442\pi$
$103$	0.737370	+	1.92092i	0.0726553	+	0.189273i	−0.892444	+	0.451159i	$0.851011\pi$
$104$	−20.3045	+	33.1340i	−1.99102	+	3.24905i
$105$	−2.52010	+	9.65488i	−0.245936	+	0.942220i
$106$	−5.65559	+	0.445105i	−0.549320	+	0.0432324i
$107$	−12.7375	−	5.67111i	−1.23138	−	0.548247i	−0.315207	−	0.949023i	$-0.602074\pi$
$107$	−12.7375	−	5.67111i	−1.23138	−	0.548247i	−0.916176	+	0.400776i	$0.868741\pi$
$108$	−29.1470	+	2.57469i	−2.80467	+	0.247750i
$109$	3.69219	+	0.486086i	0.353648	+	0.0465586i	0.305257	−	0.952270i	$-0.401257\pi$
$109$	3.69219	+	0.486086i	0.353648	+	0.0465586i	0.0483905	+	0.998828i	$0.484591\pi$
$110$	14.4841	−	26.6764i	1.38101	−	2.54350i
$111$	−2.47090	+	1.08376i	−0.234528	+	0.102866i
$112$	41.5456	+	12.9492i	3.92569	+	1.22358i
$113$	−0.799144	+	2.45951i	−0.0751771	+	0.231371i	−0.981583	−	0.191037i	$-0.938815\pi$
$113$	−0.799144	+	2.45951i	−0.0751771	+	0.231371i	0.906406	+	0.422408i	$0.138815\pi$
$114$	−0.935069	+	0.219021i	−0.0875772	+	0.0205132i
$115$	−3.97742	−	0.208448i	−0.370896	−	0.0194379i
$116$	−9.67370	+	32.6579i	−0.898181	+	3.03221i
$117$	3.42408	−	11.1063i	0.316556	−	1.02678i
$118$	−27.1613	−	13.8394i	−2.50040	−	1.27402i
$119$	4.39412	−	12.8991i	0.402808	−	1.18246i
$120$	−37.6456	+	3.74605i	−3.43655	+	0.341966i
$121$	−11.2425	+	9.10401i	−1.02205	+	0.827637i
$122$	−11.7080	+	20.2788i	−1.05999	+	1.83596i
$123$	−8.09539	+	7.58055i	−0.729937	+	0.683515i
$124$	−5.49591	−	9.51920i	−0.493548	−	0.854850i
$125$	1.79126	+	11.3096i	0.160215	+	1.01156i
$126$	−21.8974	−	1.12695i	−1.95077	−	0.100397i
$127$	2.04733	−	0.665218i	0.181671	−	0.0590286i	−0.216769	−	0.976223i	$-0.569552\pi$
$127$	2.04733	−	0.665218i	0.181671	−	0.0590286i	0.398440	+	0.917194i	$0.369552\pi$
$128$	2.72227	+	51.9440i	0.240617	+	4.59124i
$129$	−16.1816	−	4.43204i	−1.42471	−	0.390219i
$130$	6.61837	−	22.3432i	0.580469	−	1.95963i
$131$	0.314184	−	0.483801i	0.0274504	−	0.0422699i	−0.824679	−	0.565601i	$-0.808644\pi$
$131$	0.314184	−	0.483801i	0.0274504	−	0.0422699i	0.852129	+	0.523331i	$0.175311\pi$
$132$	47.1152	+	14.2404i	4.10085	+	1.23947i
$133$	−0.528873	+	0.0480236i	−0.0458591	+	0.00416418i
$134$	9.63214	−	11.2778i	0.832090	−	0.974252i
$135$	10.6288	−	3.87868i	0.914781	−	0.333823i
$136$	51.6471	−	1.35243i	4.42871	−	0.115970i
$137$	16.8239	+	2.21490i	1.43736	+	0.189232i	0.808595	−	0.588365i	$-0.200228\pi$
$137$	16.8239	+	2.21490i	1.43736	+	0.189232i	0.628763	+	0.777597i	$0.283562\pi$
$138$	−1.32121	−	8.65164i	−0.112469	−	0.736476i
$139$	−3.42387	+	2.48759i	−0.290409	+	0.210995i	−0.723445	−	0.690382i	$-0.757442\pi$
$139$	−3.42387	+	2.48759i	−0.290409	+	0.210995i	0.433036	+	0.901377i	$0.357442\pi$
$140$	−32.4149	−	1.30846i	−2.73956	−	0.110585i
$141$	−12.4071	−	1.70338i	−1.04487	−	0.143451i
$142$	−26.3012	−	0.688721i	−2.20715	−	0.0577962i
$143$	−12.3032	+	15.1932i	−1.02885	+	1.27052i
$144$	−14.7273	−	47.0944i	−1.22727	−	3.92453i
$145$	0.344762	−	13.1659i	0.0286310	−	1.09337i
$146$	−7.05149	−	5.12321i	−0.583586	−	0.424000i
$147$	−11.9040	−	2.30106i	−0.981825	−	0.189788i
$148$	−5.15609	−	7.09675i	−0.423828	−	0.583349i
$149$	−18.1006	−	6.40976i	−1.48286	−	0.525108i	−0.535292	−	0.844667i	$-0.679799\pi$
$149$	−18.1006	−	6.40976i	−1.48286	−	0.525108i	−0.947566	+	0.319559i	$0.896465\pi$
$150$	−1.15798	+	0.437164i	−0.0945485	+	0.0356943i
$151$	−0.442687	−	16.9055i	−0.0360254	−	1.37575i	−0.743368	−	0.668883i	$-0.766773\pi$
$151$	−0.442687	−	16.9055i	−0.0360254	−	1.37575i	0.707343	−	0.706871i	$-0.249894\pi$
$152$	−0.866788	−	1.81726i	−0.0703058	−	0.147399i
$153$	−14.8630	+	4.22413i	−1.20160	+	0.341501i
$154$	33.4786	+	15.4775i	2.69778	+	1.24721i
$155$	3.00542	+	3.00542i	0.241401	+	0.241401i
$156$	37.6519	+	3.17317i	3.01457	+	0.254057i
$157$	0.499431	+	0.147938i	0.0398589	+	0.0118067i	0.303883	−	0.952709i	$-0.401717\pi$
$157$	0.499431	+	0.147938i	0.0398589	+	0.0118067i	−0.264025	+	0.964516i	$0.585050\pi$
$158$	31.7577	−	33.4657i	2.52651	−	2.66238i
$159$	1.84170	+	3.04309i	0.146057	+	0.241332i
$160$	−17.0737	−	52.5475i	−1.34980	−	4.15425i
$161$	−0.0581478	−	4.83911i	−0.00458269	−	0.381375i
$162$	13.0757	+	21.1459i	1.02733	+	1.66138i
$163$	−7.04578	+	4.06788i	−0.551868	+	0.318621i	−0.749875	−	0.661580i	$-0.769886\pi$
$163$	−7.04578	+	4.06788i	−0.551868	+	0.318621i	0.198007	+	0.980201i	$0.436553\pi$
$164$	−29.6929	−	20.4561i	−2.31862	−	1.59735i
$165$	−19.0228	−	0.603565i	−1.48093	−	0.0469875i
$166$	3.75241	+	4.63383i	0.291243	+	0.359655i
$167$	0.574594	−	1.38719i	0.0444634	−	0.107344i	−0.900087	−	0.435709i	$-0.856498\pi$
$167$	0.574594	−	1.38719i	0.0444634	−	0.107344i	0.944551	+	0.328365i	$0.106498\pi$
$168$	−7.48489	−	45.3543i	−0.577472	−	3.49916i
$169$	−0.911694	+	1.78930i	−0.0701303	+	0.137638i
$170$	−29.7053	+	8.79911i	−2.27829	+	0.674861i
$171$	0.385972	+	0.462184i	0.0295160	+	0.0353441i
$172$	2.85475	−	54.4719i	0.217673	−	4.15345i
$173$	5.87304	+	1.57368i	0.446519	+	0.119644i	0.475070	−	0.879948i	$-0.342423\pi$
$173$	5.87304	+	1.57368i	0.446519	+	0.119644i	−0.0285511	+	0.999592i	$0.509089\pi$
$174$	28.4848	−	5.11635i	2.15943	−	0.387869i
$175$	−0.667710	+	0.150334i	−0.0504741	+	0.0113641i
$176$	−6.51232	+	82.7468i	−0.490884	+	6.23728i
$177$	−0.105846	+	19.1129i	−0.00795585	+	1.43662i
$178$	2.63308	−	20.0002i	0.197357	−	1.49908i
$179$	−9.93636	+	1.84160i	−0.742678	+	0.137647i	−0.540079	−	0.841614i	$-0.681606\pi$
$179$	−9.93636	+	1.84160i	−0.742678	+	0.137647i	−0.202599	+	0.979262i	$0.564939\pi$
$180$	19.6916	+	31.0704i	1.46772	+	2.31585i
$181$	−0.330791	−	4.20310i	−0.0245875	−	0.312414i	−0.996897	−	0.0787171i	$-0.974918\pi$
$181$	−0.330791	−	4.20310i	−0.0245875	−	0.312414i	0.972309	−	0.233697i	$-0.0750824\pi$
$182$	27.6096	+	6.27860i	2.04656	+	0.465401i
$183$	14.6571	+	0.849562i	1.08348	+	0.0628015i
$184$	17.1294	−	6.57537i	1.26280	−	0.484743i
$185$	2.63605	+	2.13463i	0.193807	+	0.156941i
$186$	−5.13000	+	7.80454i	−0.376150	+	0.572256i
$187$	25.8494	+	2.71688i	1.89029	+	0.198678i
$188$	−3.19454	−	40.5905i	−0.232986	−	2.96036i
$189$	5.53390	+	12.5848i	0.402532	+	0.915406i
$190$	0.784106	+	0.918070i	0.0568850	+	0.0666038i
$191$	11.0862	+	8.50677i	0.802172	+	0.615528i	0.926321	−	0.376735i	$-0.122953\pi$
$191$	11.0862	+	8.50677i	0.802172	+	0.615528i	−0.124149	+	0.992264i	$0.539620\pi$
$192$	55.9779	−	31.9069i	4.03986	−	2.30268i
$193$	16.8281	+	11.5657i	1.21132	+	0.832514i	0.989775	−	0.142637i	$-0.0455581\pi$
$193$	16.8281	+	11.5657i	1.21132	+	0.832514i	0.221541	+	0.975151i	$0.428891\pi$
$194$	2.37155	−	12.7957i	0.170267	−	0.918679i
$195$	−14.3807	+	2.58301i	−1.02982	+	0.184973i
$196$	−0.947179	−	39.4069i	−0.0676557	−	2.81478i
$197$	2.19649	−	1.11917i	0.156494	−	0.0797376i	−0.373990	−	0.927433i	$-0.622010\pi$
$197$	2.19649	−	1.11917i	0.156494	−	0.0797376i	0.530483	+	0.847695i	$0.322010\pi$
$198$	−7.16548	−	41.2032i	−0.509229	−	2.92818i
$199$	2.50071	+	2.37308i	0.177271	+	0.168224i	0.771832	−	0.635827i	$-0.219341\pi$
$199$	2.50071	+	2.37308i	0.177271	+	0.168224i	−0.594561	+	0.804050i	$0.702674\pi$
$200$	−1.41328	−	2.17626i	−0.0999341	−	0.153885i
$201$	−9.03005	−	2.22088i	−0.636931	−	0.156649i
$202$	−15.9133	+	38.4182i	−1.11966	+	2.70309i
$203$	15.9913	−	0.611094i	1.12237	−	0.0428904i
$204$	−23.7255	−	44.2800i	−1.66112	−	3.10022i
$205$	13.1376	+	4.66874i	0.917570	+	0.326079i
$206$	4.92247	+	2.84199i	0.342965	+	0.198011i
$207$	−4.47488	+	3.17606i	−0.311025	+	0.220752i
$208$	8.31706	+	63.1744i	0.576684	+	4.38035i
$209$	−0.313005	−	0.963331i	−0.0216510	−	0.0666350i
$210$	11.3745	+	25.1085i	0.784915	+	1.73265i
$211$	1.71225	+	0.411075i	0.117876	+	0.0282996i	0.291954	−	0.956432i	$-0.405694\pi$
$211$	1.71225	+	0.411075i	0.117876	+	0.0282996i	−0.174078	+	0.984732i	$0.555694\pi$
$212$	−8.38850	+	7.96039i	−0.576125	+	0.546722i
$213$	7.01932	+	14.9285i	0.480956	+	1.02288i
$214$	−37.2044	+	9.96889i	−2.54324	+	0.681459i
$215$	4.38528	+	20.6311i	0.299074	+	1.40703i
$216$	−37.4634	+	36.2388i	−2.54906	+	2.46574i
$217$	−3.40929	+	3.87914i	−0.231438	+	0.263333i
$218$	8.77157	−	5.37523i	0.594086	−	0.364056i
$219$	−0.884789	+	5.39287i	−0.0597885	+	0.364417i
$220$	−11.2763	−	60.8413i	−0.760246	−	4.10192i
$221$	19.8440	−	2.08569i	1.33485	−	0.140299i
$222$	−3.42053	+	6.62225i	−0.229571	+	0.444457i
$223$	1.09326	+	0.794297i	0.0732098	+	0.0531900i	0.623788	−	0.781593i	$-0.285593\pi$
$223$	1.09326	+	0.794297i	0.0732098	+	0.0531900i	−0.550578	+	0.834783i	$0.685593\pi$
$224$	62.3818	−	24.8102i	4.16806	−	1.65770i
$225$	0.570942	+	0.525644i	0.0380628	+	0.0350430i
$226$	2.56016	+	6.66945i	0.170299	+	0.443645i
$227$	3.17718	+	5.85165i	0.210877	+	0.388387i	0.962532	−	0.271170i	$-0.0874105\pi$
$227$	3.17718	+	5.85165i	0.210877	+	0.388387i	−0.751654	+	0.659557i	$0.770744\pi$
$228$	−1.20035	+	1.54652i	−0.0794953	+	0.102421i
$229$	−6.66064	−	9.69129i	−0.440147	−	0.640418i	0.539301	−	0.842113i	$-0.318689\pi$
$229$	−6.66064	−	9.69129i	−0.440147	−	0.640418i	−0.979448	+	0.201695i	$0.935355\pi$
$230$	−8.90124	+	6.46713i	−0.586930	+	0.426430i
$231$	−0.755096	−	23.1133i	−0.0496817	−	1.52074i
$232$	23.2185	+	56.0545i	1.52437	+	3.68016i
$233$	−11.3419	+	20.8891i	−0.743031	+	1.36849i	0.179962	+	0.983674i	$0.442403\pi$
$233$	−11.3419	+	20.8891i	−0.743031	+	1.36849i	−0.922992	+	0.384819i	$0.874264\pi$
$234$	−11.9570	−	29.7960i	−0.781655	−	1.94782i
$235$	5.25545	+	14.8409i	0.342828	+	0.968116i
$236$	−60.7823	+	12.9197i	−3.95659	+	0.840999i
$237$	−27.6898	−	8.36915i	−1.79864	−	0.543635i
$238$	−12.9913	−	35.3313i	−0.842101	−	2.29019i
$239$	7.50693	−	1.80225i	0.485583	−	0.116578i	0.0167403	−	0.999860i	$-0.494671\pi$
$239$	7.50693	−	1.80225i	0.485583	−	0.116578i	0.468843	+	0.883282i	$0.344671\pi$
$240$	−44.1057	+	43.6199i	−2.84701	+	2.81565i
$241$	12.2895	−	7.98089i	0.791635	−	0.514094i	−0.0843473	−	0.996436i	$-0.526881\pi$
$241$	12.2895	−	7.98089i	0.791635	−	0.514094i	0.875983	+	0.482342i	$0.160214\pi$
$242$	−8.30875	+	39.0896i	−0.534107	+	2.51277i
$243$	8.16500	−	13.2790i	0.523785	−	0.851851i
$244$	7.46702	+	47.1449i	0.478027	+	3.01815i
$245$	4.29760	+	14.6238i	0.274564	+	0.934279i
$246$	−4.20089	+	30.3478i	−0.267839	+	1.93490i
$247$	−0.388794	−	0.673410i	−0.0247384	−	0.0428481i
$248$	−18.2796	−	7.01687i	−1.16075	−	0.445571i
$249$	1.53949	−	3.40686i	0.0975615	−	0.215901i
$250$	23.5069	+	21.1657i	1.48671	+	1.33864i
$251$	12.3464	+	6.29081i	0.779298	+	0.397072i	0.797927	−	0.602754i	$-0.205930\pi$
$251$	12.3464	+	6.29081i	0.779298	+	0.397072i	−0.0186286	+	0.999826i	$0.505930\pi$
$252$	−36.1352	+	26.3057i	−2.27630	+	1.65710i
$253$	8.97560	−	2.15485i	0.564291	−	0.135474i
$254$	3.23882	−	4.98734i	0.203221	−	0.312934i
$255$	13.2931	+	14.1642i	0.832444	+	0.887000i
$256$	46.3637	+	51.4921i	2.89773	+	3.21826i
$257$	3.79472	+	0.703309i	0.236708	+	0.0438712i	0.299265	−	0.954170i	$-0.403259\pi$
$257$	3.79472	+	0.703309i	0.236708	+	0.0438712i	−0.0625565	+	0.998041i	$0.519925\pi$
$258$	−42.4442	+	18.6164i	−2.64246	+	1.15901i
$259$	−2.38230	+	3.36320i	−0.148029	+	0.208979i
$260$	−18.1783	−	43.8862i	−1.12737	−	2.72171i
$261$	−10.8863	−	14.5174i	−0.673843	−	0.898604i
$262$	−0.166574	−	1.58484i	−0.0102909	−	0.0979118i
$263$	−0.684533	+	1.43515i	−0.0422101	+	0.0884953i	−0.922605	−	0.385746i	$-0.873944\pi$
$263$	−0.684533	+	1.43515i	−0.0422101	+	0.0884953i	0.880395	+	0.474241i	$0.157278\pi$
$264$	81.1880	−	33.1036i	4.99677	−	2.03739i
$265$	2.33645	−	3.81275i	0.143527	−	0.234215i
$266$	−1.05191	+	1.02253i	−0.0644970	+	0.0626953i
$267$	−11.9460	+	4.15598i	−0.731081	+	0.254342i
$268$	0.791409	−	30.2227i	0.0483430	−	1.84614i
$269$	−1.54434	+	0.687582i	−0.0941598	+	0.0419226i	−0.453276	−	0.891370i	$-0.649745\pi$
$269$	−1.54434	+	0.687582i	−0.0941598	+	0.0419226i	0.359116	+	0.933293i	$0.383078\pi$
$270$	16.0753	−	26.8047i	0.978311	−	1.63128i
$271$	7.86592	−	17.6671i	0.477820	−	1.07320i	−0.500430	−	0.865777i	$-0.666825\pi$
$271$	7.86592	−	17.6671i	0.477820	−	1.07320i	0.978251	−	0.207425i	$-0.0665085\pi$
$272$	64.4177	−	55.0179i	3.90590	−	3.33595i
$273$	−4.25611	−	17.2353i	−0.257591	−	1.04313i
$274$	39.9686	−	24.4928i	2.41459	−	1.47966i
$275$	−0.562011	−	1.17828i	−0.0338905	−	0.0710530i
$276$	−13.1918	−	12.0109i	−0.794052	−	0.722970i
$277$	14.2075	−	12.7925i	0.853648	−	0.768628i	−0.120934	−	0.992661i	$-0.538589\pi$
$277$	14.2075	−	12.7925i	0.853648	−	0.768628i	0.974582	+	0.224033i	$0.0719223\pi$
$278$	−3.02588	+	11.2927i	−0.181480	+	0.677294i
$279$	5.81666	+	0.676570i	0.348234	+	0.0405052i
$280$	−46.3404	+	34.5265i	−2.76937	+	2.06336i
$281$	16.2311	+	3.89674i	0.968266	+	0.232460i	0.686586	−	0.727048i	$-0.259108\pi$
$281$	16.2311	+	3.89674i	0.968266	+	0.232460i	0.281680	+	0.959508i	$0.409108\pi$
$282$	−29.5973	+	17.9126i	−1.76249	+	1.06668i
$283$	−10.5631	−	2.24526i	−0.627912	−	0.133467i	−0.117045	−	0.993127i	$-0.537342\pi$
$283$	−10.5631	−	2.24526i	−0.627912	−	0.133467i	−0.510867	+	0.859660i	$0.670675\pi$
$284$	−42.5495	+	32.6494i	−2.52485	+	1.93738i
$285$	0.293559	−	0.697761i	0.0173890	−	0.0413318i
$286$			54.0062i			3.19345i
$287$	−4.63415	+	16.2949i	−0.273545	+	0.961859i
$288$	−63.3793	−	42.1643i	−3.73466	−	2.48456i
$289$	−5.99612	−	7.40459i	−0.352713	−	0.435564i
$290$	−22.1485	−	28.8645i	−1.30060	−	1.69498i
$291$	−7.83620	+	2.27406i	−0.459366	+	0.133308i
$292$	−17.7432	+	0.929880i	−1.03834	+	0.0544171i
$293$	−3.22725	+	13.4424i	−0.188538	+	0.785316i	0.795294	+	0.606223i	$0.207316\pi$
$293$	−3.22725	+	13.4424i	−0.188538	+	0.785316i	−0.983832	+	0.179093i	$0.942684\pi$
$294$	−29.5562	+	15.7548i	−1.72375	+	0.918837i
$295$	21.4093	−	10.9086i	1.24650	−	0.635123i
$296$	−15.0935	−	4.04429i	−0.877291	−	0.235069i
$297$	−21.0656	+	15.6151i	−1.22235	+	0.906082i
$298$	−50.0022	+	17.7067i	−2.89655	+	1.02572i
$299$	6.39588	−	3.05068i	0.369883	−	0.176425i
$300$	−1.27364	+	2.17806i	−0.0735335	+	0.125750i
$301$	−24.6735	+	6.93003i	−1.42215	+	0.399440i
$302$	−30.3402	−	35.5238i	−1.74588	−	2.04416i
$303$	26.0033	−	1.90167i	1.49385	−	0.109248i
$304$	−2.97976	−	1.42127i	−0.170901	−	0.0815157i
$305$	−7.50721	−	16.8615i	−0.429861	−	0.965485i
$306$	−24.5648	+	34.9074i	−1.40428	+	1.99552i
$307$	1.06782	−	6.74196i	0.0609438	−	0.384784i	−0.938297	−	0.345830i	$-0.887597\pi$
$307$	1.06782	−	6.74196i	0.0609438	−	0.384784i	0.999241	−	0.0389540i	$-0.0124026\pi$
$308$	72.8916	−	18.4288i	4.15339	−	1.05008i
$309$	0.206223	−	3.55786i	0.0117316	−	0.202400i
$310$	11.6770	+	1.22730i	0.663207	+	0.0697059i
$311$	−17.7134	−	8.44884i	−1.00443	−	0.479089i	−0.144504	−	0.989504i	$-0.546159\pi$
$311$	−17.7134	−	8.44884i	−1.00443	−	0.479089i	−0.859928	+	0.510415i	$0.829492\pi$
$312$	55.6807	−	37.8160i	3.15230	−	2.14091i
$313$	−11.2771	+	31.8454i	−0.637417	+	1.80001i	−0.0384146	+	0.999262i	$0.512231\pi$
$313$	−11.2771	+	31.8454i	−0.637417	+	1.80001i	−0.599002	+	0.800747i	$0.704436\pi$
$314$	1.32938	−	0.550648i	0.0750213	−	0.0310748i
$315$	10.8639	−	13.4416i	0.612113	−	0.757351i
$316$	7.37877	−	93.7561i	0.415088	−	5.27420i
$317$	−0.247338	+	1.33451i	−0.0138919	+	0.0749538i	−0.989486	−	0.144626i	$-0.953802\pi$
$317$	−0.247338	+	1.33451i	−0.0138919	+	0.0749538i	0.975594	+	0.219580i	$0.0704687\pi$
$318$	9.24415	+	3.33125i	0.518386	+	0.186807i
$319$	7.90009	+	29.4835i	0.442320	+	1.65076i
$320$	−67.9339	−	44.1168i	−3.79762	−	2.46620i
$321$	16.0598	+	18.0361i	0.896371	+	1.00668i
$322$	−8.53749	−	10.2877i	−0.475776	−	0.573310i
$323$	−0.469336	+	0.921123i	−0.0261145	+	0.0512527i
$324$	47.8414	+	16.7249i	2.65786	+	0.929163i
$325$	−0.610081	−	0.795073i	−0.0338412	−	0.0441027i
$326$	−8.05421	+	20.9819i	−0.446082	+	1.16208i
$327$	−5.48099	−	3.40065i	−0.303100	−	0.188056i
$328$	−64.0372	+	4.96811i	−3.53586	+	0.274318i
$329$	−17.5846	+	7.53255i	−0.969468	+	0.415283i
$330$	−41.8882	+	31.7749i	−2.30587	+	1.74915i
$331$	−0.677959	−	5.14961i	−0.0372640	−	0.283048i	−0.999924	−	0.0123345i	$-0.996074\pi$
$331$	−0.677959	−	5.14961i	−0.0372640	−	0.283048i	0.962660	−	0.270714i	$-0.0872596\pi$
$332$	11.8890	+	2.52709i	0.652494	+	0.138692i
$333$	4.67301	+	0.0517591i	0.256080	+	0.00283638i
$334$	−1.17804	−	3.97699i	−0.0644594	−	0.217611i
$335$	2.72908	+	11.3675i	0.149106	+	0.621070i
$336$	−56.3389	−	50.0707i	−3.07354	−	2.73158i
$337$	11.4810	+	11.4810i	0.625409	+	0.625409i	0.946909	−	0.321501i	$-0.104187\pi$
$337$	11.4810	+	11.4810i	0.625409	+	0.625409i	−0.321501	+	0.946909i	$0.604187\pi$
$338$	1.15339	+	5.42628i	0.0627362	+	0.295151i
$339$	3.01558	−	3.31207i	0.163784	−	0.179887i
$340$	−35.7708	+	52.0468i	−1.93994	+	2.82263i
$341$	−8.65671	−	4.70021i	−0.468787	−	0.254531i
$342$	1.63211	+	0.321231i	0.0882544	+	0.0173702i
$343$	−17.3961	+	6.35414i	−0.939302	+	0.343091i
$344$	−57.1125	−	78.6086i	−3.07930	−	4.23829i
$345$	6.12921	+	3.16587i	0.329986	+	0.170445i
$346$	15.3442	−	6.83169i	0.824911	−	0.367274i
$347$	9.44140	−	5.12626i	0.506841	−	0.275192i	−0.203469	−	0.979081i	$-0.565222\pi$
$347$	9.44140	−	5.12626i	0.506841	−	0.275192i	0.710310	+	0.703889i	$0.248555\pi$
$348$	38.5617	−	44.6469i	2.06712	−	2.39333i
$349$	31.4743	+	4.98503i	1.68478	+	0.266843i	0.924062	−	0.382242i	$-0.124848\pi$
$349$	31.4743	+	4.98503i	1.68478	+	0.266843i	0.760716	+	0.649085i	$0.224848\pi$
$350$	−1.17211	+	1.48354i	−0.0626520	+	0.0792984i
$351$	−13.3259	+	15.0877i	−0.711286	+	0.805324i
$352$	72.5285	+	105.530i	3.86578	+	5.62475i
$353$	−0.655392	−	6.23564i	−0.0348830	−	0.331889i	−0.998021	−	0.0628816i	$-0.979971\pi$
$353$	−0.655392	−	6.23564i	−0.0348830	−	0.331889i	0.963138	−	0.269008i	$-0.0866957\pi$
$354$	33.0000	+	41.2163i	1.75393	+	2.19062i
$355$	12.6248	−	16.4530i	0.670055	−	0.873233i
$356$	−21.4859	−	35.0619i	−1.13875	−	1.85828i
$357$	−16.1358	+	17.2257i	−0.853995	+	0.911679i
$358$	−18.1301	+	21.2277i	−0.958208	+	1.12192i
$359$	−1.88270	+	0.400181i	−0.0993653	+	0.0211208i	−0.257326	−	0.966325i	$-0.582841\pi$
$359$	−1.88270	+	0.400181i	−0.0993653	+	0.0211208i	0.157961	+	0.987445i	$0.449508\pi$
$360$	62.0909	+	20.9376i	3.27248	+	1.10351i
$361$	−18.9337	−	0.992275i	−0.996512	−	0.0522250i
$362$	−8.01713	−	8.44829i	−0.421371	−	0.444032i
$363$	24.2383	−	6.35099i	1.27218	−	0.333340i
$364$	51.7932	−	25.4725i	2.71470	−	1.33512i
$365$	6.53406	−	2.12304i	0.342008	−	0.111125i
$366$	32.9433	−	23.6571i	1.72197	−	1.23658i
$367$	−15.6993	−	6.02639i	−0.819496	−	0.314575i	−0.0877414	−	0.996143i	$-0.527965\pi$
$367$	−15.6993	−	6.02639i	−0.819496	−	0.314575i	−0.731755	+	0.681568i	$0.761298\pi$
$368$	15.0427	−	26.0547i	0.784156	−	1.35820i
$369$	18.1844	−	6.19104i	0.946640	−	0.322293i
$370$	9.37017			0.487132
$371$	4.80577	+	2.53504i	0.249503	+	0.131613i
$372$	1.88517	+	18.9448i	0.0977416	+	0.982244i
$373$	−1.99749	−	1.79855i	−0.103426	−	0.0931251i	0.615796	−	0.787906i	$-0.288835\pi$
$373$	−1.99749	−	1.79855i	−0.103426	−	0.0931251i	−0.719222	+	0.694781i	$0.755501\pi$
$374$	60.2175	−	39.1057i	3.11377	−	2.02211i
$375$	5.23916	−	19.1284i	0.270549	−	0.987788i
$376$	−49.9254	−	52.6103i	−2.57470	−	2.71317i
$377$	10.6381	+	20.8784i	0.547888	+	1.07529i
$378$	33.7586	+	17.3968i	1.73635	+	0.894797i
$379$	−4.78881	+	14.7384i	−0.245984	+	0.757062i	0.749489	+	0.662017i	$0.230299\pi$
$379$	−4.78881	+	14.7384i	−0.245984	+	0.757062i	−0.995473	+	0.0950449i	$0.969701\pi$
$380$	2.41991	+	0.448505i	0.124139	+	0.0230078i
$381$	−3.70593	−	0.410271i	−0.189861	−	0.0210188i
$382$	38.5891	−	1.01049i	1.97439	−	0.0517012i
$383$	−21.3655	+	27.8441i	−1.09173	+	1.42277i	−0.194663	+	0.980870i	$0.562361\pi$
$383$	−21.3655	+	27.8441i	−1.09173	+	1.42277i	−0.897065	+	0.441898i	$0.854305\pi$
$384$	32.7518	−	83.9290i	1.67136	−	4.28299i
$385$	−25.3809	+	14.1782i	−1.29353	+	0.722587i
$386$	56.2338	−	4.42569i	2.86222	−	0.225262i
$387$	22.3797	+	18.5368i	1.13762	+	0.942280i
$388$	−12.6580	−	23.3131i	−0.642612	−	1.18354i
$389$	−0.665984	+	0.822422i	−0.0337667	+	0.0416984i	−0.793750	−	0.608245i	$-0.791874\pi$
$389$	−0.665984	+	0.822422i	−0.0337667	+	0.0416984i	0.759983	+	0.649943i	$0.225207\pi$
$390$	−26.3824	+	30.5457i	−1.33592	+	1.54674i
$391$	−8.03277	−	4.92249i	−0.406235	−	0.248941i
$392$	−45.4874	−	53.4912i	−2.29746	−	2.70171i
$393$	−0.840969	+	0.539534i	−0.0424213	+	0.0272159i
$394$	2.76986	−	6.22122i	0.139544	−	0.313420i
$395$	6.62710	+	35.7566i	0.333446	+	1.79911i
$396$	−64.2089	−	56.0813i	−3.22662	−	2.81819i
$397$	−3.38412	−	1.83743i	−0.169844	−	0.0922178i	0.390004	−	0.920813i	$-0.372474\pi$
$397$	−3.38412	−	1.83743i	−0.169844	−	0.0922178i	−0.559848	+	0.828595i	$0.689140\pi$
$398$	9.49415	+	0.747206i	0.475899	+	0.0374540i
$399$	0.869015	+	0.301414i	0.0435052	+	0.0150896i
$400$	−4.04661	−	1.31482i	−0.202330	−	0.0657411i
$401$	7.03385	−	26.2507i	0.351254	−	1.31090i	−0.533880	−	0.845560i	$-0.679267\pi$
$401$	7.03385	−	26.2507i	0.351254	−	1.31090i	0.885134	−	0.465337i	$-0.154067\pi$
$402$	−23.2470	+	10.9306i	−1.15945	+	0.545170i
$403$	−7.25056	−	2.14771i	−0.361176	−	0.106985i
$404$	24.0750	+	81.2759i	1.19778	+	4.04363i
$405$	−19.5427	−	1.45885i	−0.971086	−	0.0724911i
$406$	33.2683	−	29.1123i	1.65108	−	1.44482i
$407$	−7.26276	−	3.00833i	−0.360002	−	0.149118i
$408$	−82.4835	−	34.7022i	−4.08354	−	1.71801i
$409$	−23.3369	−	13.4735i	−1.15393	−	0.666224i	−0.204091	−	0.978952i	$-0.565424\pi$
$409$	−23.3369	−	13.4735i	−1.15393	−	0.666224i	−0.949843	+	0.312728i	$0.898757\pi$
$410$	36.3207	−	12.8164i	1.79375	−	0.632955i
$411$	−24.9747	−	15.4954i	−1.23191	−	0.764332i
$412$	11.4439	−	1.81254i	0.563803	−	0.0892976i
$413$	14.9007	+	25.1072i	0.733216	+	1.23544i
$414$	−4.08532	+	14.5979i	−0.200782	+	0.717449i
$415$	−4.69349	+	0.245975i	−0.230394	+	0.0120745i
$416$	71.3055	+	67.6664i	3.49604	+	3.31762i
$417$	7.17843	−	1.48432i	0.351529	−	0.0726875i
$418$	−2.34669	−	1.52396i	−0.114781	−	0.0745393i
$419$	−3.99342	+	3.99342i	−0.195091	+	0.195091i	−0.797892	−	0.602801i	$-0.794051\pi$
$419$	−3.99342	+	3.99342i	−0.195091	+	0.195091i	0.602801	+	0.797892i	$0.294051\pi$
$420$	50.2298	+	25.1848i	2.45096	+	1.22889i
$421$	10.1215	+	8.64454i	0.493289	+	0.421309i	0.860980	−	0.508639i	$-0.169851\pi$
$421$	10.1215	+	8.64454i	0.493289	+	0.421309i	−0.367690	+	0.929948i	$0.619851\pi$
$422$	4.39056	−	2.09419i	0.213729	−	0.101944i
$423$	18.3683	+	11.5378i	0.893095	+	0.560989i
$424$	−2.68883	+	20.4237i	−0.130581	+	0.991864i
$425$	−0.444758	+	1.25596i	−0.0215739	+	0.0609229i
$426$	41.0221	+	19.8461i	1.98753	+	0.961548i
$427$	19.8585	−	10.4209i	0.961022	−	0.504301i
$428$	−46.1501	+	63.5202i	−2.23075	+	3.07036i
$429$	30.2556	−	15.2056i	1.46076	−	0.734132i
$430$	45.2811	+	36.6679i	2.18365	+	1.76828i
$431$	2.19464	+	1.77718i	0.105712	+	0.0856040i	0.680719	−	0.732544i	$-0.261667\pi$
$431$	2.19464	+	1.77718i	0.105712	+	0.0856040i	−0.575007	+	0.818148i	$0.695001\pi$
$432$	−10.3444	+	84.8370i	−0.497694	+	4.08172i
$433$	5.81204	−	7.99958i	0.279309	−	0.384435i	−0.646196	−	0.763171i	$-0.723641\pi$
$433$	5.81204	−	7.99958i	0.279309	−	0.384435i	0.925505	+	0.378736i	$0.123641\pi$
$434$	−0.575412	+	14.2548i	−0.0276207	+	0.684254i
$435$	−9.93465	+	20.5350i	−0.476330	+	0.984577i
$436$	7.00020	−	19.7679i	0.335249	−	0.946713i
$437$	−0.0479215	+	0.364000i	−0.00229240	+	0.0174125i
$438$	7.47586	+	13.1158i	0.357211	+	0.626696i
$439$	−26.8816	+	12.8219i	−1.28299	+	0.611955i	−0.944344	−	0.328958i	$-0.893302\pi$
$439$	−26.8816	+	12.8219i	−1.28299	+	0.611955i	−0.338647	+	0.940914i	$0.609969\pi$
$440$	−83.8151	−	71.5848i	−3.99573	−	3.41267i
$441$	17.1478	+	12.1224i	0.816564	+	0.577255i
$442$	38.9759	−	38.9759i	1.85390	−	1.85390i
$443$	−11.1844	−	7.26325i	−0.531388	−	0.345087i	0.250891	−	0.968015i	$-0.419276\pi$
$443$	−11.1844	−	7.26325i	−0.531388	−	0.345087i	−0.782279	+	0.622928i	$0.785943\pi$
$444$	3.07659	+	14.8789i	0.146008	+	0.706122i
$445$	11.5340	+	10.9454i	0.546766	+	0.518861i
$446$	3.72790	−	0.195371i	0.176521	−	0.00925108i
$447$	23.9980	+	23.0271i	1.13506	+	1.08915i
$448$	48.1836	−	85.8216i	2.27646	−	4.05469i
$449$	27.2254	−	4.31209i	1.28485	−	0.203500i	0.523602	−	0.851963i	$-0.324588\pi$
$449$	27.2254	−	4.31209i	1.28485	−	0.203500i	0.761246	+	0.648463i	$0.224588\pi$
$450$	2.13953	+	0.135905i	0.100859	+	0.00640662i
$451$	−32.2667	−	1.72705i	−1.51938	−	0.0813235i
$452$	12.6117	+	7.28135i	0.593203	+	0.342486i
$453$	−11.3590	+	26.9991i	−0.533692	+	1.26853i
$454$	16.9938	+	7.03907i	0.797559	+	0.330360i
$455$	−16.7956	+	14.6975i	−0.787391	+	0.689029i
$456$	0.0719800	+	3.48656i	0.00337077	+	0.163273i
$457$	−5.17667	−	17.4762i	−0.242154	−	0.817500i	−0.988406	−	0.151836i	$-0.951482\pi$
$457$	−5.17667	−	17.4762i	−0.242154	−	0.817500i	0.746251	−	0.665664i	$-0.231852\pi$
$458$	−31.1473	−	9.22626i	−1.45542	−	0.431115i
$459$	26.4723	+	3.93358i	1.23562	+	0.183604i
$460$	−5.80487	+	21.6641i	−0.270654	+	1.01009i
$461$	1.33331	+	0.433220i	0.0620986	+	0.0201771i	0.339902	−	0.940461i	$-0.389606\pi$
$461$	1.33331	+	0.433220i	0.0620986	+	0.0201771i	−0.277803	+	0.960638i	$0.589606\pi$
$462$	−41.8029	−	48.3077i	−1.94485	−	2.24748i
$463$	18.6692	+	1.46930i	0.867632	+	0.0682841i	0.504457	−	0.863437i	$-0.331693\pi$
$463$	18.6692	+	1.46930i	0.867632	+	0.0682841i	0.363175	+	0.931721i	$0.381693\pi$
$464$	87.4296	+	47.4704i	4.05882	+	2.20376i
$465$	−2.60011	−	6.88728i	−0.120577	−	0.319390i
$466$	11.9660	+	64.5630i	0.554316	+	2.99082i
$467$	16.2495	−	36.4970i	0.751937	−	1.68888i	0.0274174	−	0.999624i	$-0.491272\pi$
$467$	16.2495	−	36.4970i	0.751937	−	1.68888i	0.724520	−	0.689254i	$-0.242062\pi$
$468$	−57.1659	−	31.8633i	−2.64249	−	1.47288i
$469$	−13.5703	+	4.19770i	−0.626617	+	0.193832i
$470$	37.0831	+	22.7246i	1.71052	+	1.04821i
$471$	−0.682777	−	0.589717i	−0.0314607	−	0.0271727i
$472$	−69.6608	+	86.0239i	−3.20640	+	3.95957i
$473$	−23.3247	−	42.9587i	−1.07247	−	1.97524i
$474$	−73.9948	+	30.1707i	−3.39870	+	1.38579i
$475$	0.0517632	−	0.00407385i	0.00237506	−	0.000186921i
$476$	−65.9054	−	39.3055i	−3.02077	−	1.80156i
$477$	−0.736458	−	6.11673i	−0.0337201	−	0.280066i
$478$	12.9830	−	16.9197i	0.593827	−	0.773890i
$479$	−26.3558	+	0.690150i	−1.20423	+	0.0315337i	−0.623009	−	0.782215i	$-0.714090\pi$
$479$	−26.3558	+	0.690150i	−1.20423	+	0.0315337i	−0.581217	+	0.813749i	$0.697423\pi$
$480$	−10.5302	+	95.1177i	−0.480634	+	4.34151i
$481$	−5.93379	−	1.09976i	−0.270558	−	0.0501449i
$482$	12.5089	−	38.4986i	0.569767	−	1.75356i
$483$	−3.35967	+	7.67944i	−0.152870	+	0.349426i
$484$	36.9834	+	72.5840i	1.68106	+	3.29927i
$485$	7.06097	+	7.44071i	0.320622	+	0.337865i
$486$	−5.55633	−	42.7025i	−0.252040	−	1.93702i
$487$	−14.4313	+	9.37179i	−0.653944	+	0.424676i	−0.828514	−	0.559969i	$-0.810813\pi$
$487$	−14.4313	+	9.37179i	−0.653944	+	0.424676i	0.174570	+	0.984645i	$0.444147\pi$
$488$	63.1877	+	56.8945i	2.86037	+	2.57549i
$489$	14.0223	−	1.39534i	0.634110	−	0.0630993i
$490$	34.6493	+	23.9236i	1.56529	+	1.08076i
$491$	−21.7014			−0.979372			−0.489686	−	0.871899i	$-0.662889\pi$
$491$	−21.7014			−0.979372			−0.489686	+	0.871899i	$0.662889\pi$
$492$	32.2766	+	53.4656i	1.45514	+	2.41042i
$493$	15.5766	−	26.9795i	0.701536	−	1.21510i
$494$	−2.00538	−	0.769793i	−0.0902263	−	0.0346346i
$495$	29.5948	+	14.5205i	1.33019	+	0.652648i
$496$	−30.5341	+	9.92113i	−1.37102	+	0.445472i
$497$	20.9369	+	14.0221i	0.939147	+	0.628978i
$498$	−2.61769	−	9.99033i	−0.117301	−	0.447677i
$499$	9.86333	+	10.3938i	0.441543	+	0.465289i	0.907826	−	0.419346i	$-0.137741\pi$
$499$	9.86333	+	10.3938i	0.441543	+	0.465289i	−0.466283	+	0.884635i	$0.654407\pi$
$500$	64.3918	+	3.37463i	2.87969	+	0.150918i
$501$	−1.89633	+	1.77970i	−0.0847218	+	0.0795110i
$502$	37.4421	−	7.95856i	1.67112	−	0.355208i
$503$	−20.8387	+	24.3989i	−0.929150	+	1.08789i	0.0667808	+	0.997768i	$0.478727\pi$
$503$	−20.8387	+	24.3989i	−0.929150	+	1.08789i	−0.995930	+	0.0901267i	$0.971273\pi$
$504$	−20.5345	+	76.9249i	−0.914678	+	3.42651i
$505$	−17.1261	−	27.9473i	−0.762104	−	1.24364i
$506$	15.5230	−	20.2299i	0.690080	−	0.899330i
$507$	2.71520	−	2.17394i	0.120586	−	0.0965481i
$508$	−1.26711	−	12.0558i	−0.0562191	−	0.534889i
$509$	−21.9156	−	31.8874i	−0.971391	−	1.41338i	−0.909690	−	0.415288i	$-0.863681\pi$
$509$	−21.9156	−	31.8874i	−0.971391	−	1.41338i	−0.0617006	−	0.998095i	$-0.519652\pi$
$510$	53.1622	+	7.29866i	2.35406	+	0.323190i
$511$	3.08504	+	7.75692i	0.136474	+	0.343146i
$512$	86.3031	+	13.6691i	3.81409	+	0.604093i
$513$	−0.279562	−	1.00479i	−0.0123430	−	0.0443627i
$514$	9.36931	−	5.08712i	0.413263	−	0.224383i
$515$	−4.09295	+	1.82230i	−0.180357	+	0.0803000i
$516$	−43.3575	+	83.9414i	−1.90871	+	3.69531i
$517$	−21.4471	−	29.5194i	−0.943241	−	1.29826i
$518$	0.732433	+	11.3618i	0.0321813	+	0.499208i
$519$	−8.14749	−	6.67275i	−0.357635	−	0.292901i
$520$	−74.3627	−	40.3757i	−3.26102	−	1.77059i
$521$	−14.9917	+	21.8130i	−0.656798	+	0.955646i	0.343069	+	0.939310i	$0.388534\pi$
$521$	−14.9917	+	21.8130i	−0.656798	+	0.955646i	−0.999867	+	0.0163362i	$0.994800\pi$
$522$	−48.6091	−	12.2410i	−2.12756	−	0.535772i
$523$	−2.05384	−	9.66256i	−0.0898082	−	0.422514i	−0.999966	−	0.00825252i	$-0.997373\pi$
$523$	−2.05384	−	9.66256i	−0.0898082	−	0.422514i	0.910158	−	0.414262i	$-0.135960\pi$
$524$	−2.29699	−	2.29699i	−0.100345	−	0.100345i
$525$	1.16113	+	0.238954i	0.0506757	+	0.0104288i
$526$	1.02539	+	4.27108i	0.0447093	+	0.186228i
$527$	2.85538	+	9.63961i	0.124382	+	0.419908i
$528$	69.2973	−	125.961i	3.01578	−	5.48176i
$529$	19.2247	+	4.08634i	0.835858	+	0.177667i
$530$	−1.61237	−	12.2472i	−0.0700370	−	0.531984i
$531$	13.7992	−	30.0920i	0.598833	−	1.30588i
$532$	−0.354678	+	2.96932i	−0.0153772	+	0.128736i
$533$	−24.5049	+	3.85323i	−1.06142	+	0.166902i
$534$	−18.4209	+	29.6899i	−0.797152	+	1.28481i
$535$	10.8801	−	28.3437i	0.470388	−	1.22540i
$536$	−32.7848	−	42.7260i	−1.41609	−	1.84548i
$537$	16.9969	+	4.18027i	0.733469	+	0.180392i
$538$	−2.12009	+	4.16091i	−0.0914035	+	0.179390i
$539$	−19.1757	−	29.6673i	−0.825954	−	1.27786i
$540$	−8.92016	−	63.0858i	−0.383863	−	2.71478i
$541$	−12.5545	−	8.15301i	−0.539761	−	0.350525i	0.245788	−	0.969323i	$-0.420953\pi$
$541$	−12.5545	−	8.15301i	−0.539761	−	0.350525i	−0.785550	+	0.618798i	$0.787620\pi$
$542$	−13.8270	−	51.6031i	−0.593921	−	2.21654i
$543$	−2.47571	+	6.87003i	−0.106243	+	0.294821i
$544$	23.8167	−	128.503i	1.02113	−	5.50954i
$545$	−0.636221	+	8.08396i	−0.0272527	+	0.346279i
$546$	−39.1003	−	29.6023i	−1.67334	−	1.26686i
$547$	23.5849	−	9.76917i	1.00842	−	0.417700i	0.183539	−	0.983012i	$-0.441245\pi$
$547$	23.5849	−	9.76917i	1.00842	−	0.417700i	0.824877	+	0.565313i	$0.191245\pi$
$548$	31.8971	−	90.0747i	1.36258	−	3.84780i
$549$	−22.5286	−	11.7950i	−0.961495	−	0.503397i
$550$	−3.25495	−	1.55253i	−0.138792	−	0.0662002i
$551$	−1.20740	−	0.126903i	−0.0514370	−	0.00540624i
$552$	−31.7266	−	1.83895i	−1.35037	−	0.0782711i
$553$	−42.8387	+	10.8307i	−1.82168	+	0.460566i
$554$	8.26177	−	52.1628i	0.351009	−	2.21618i
$555$	−2.63819	−	5.24941i	−0.111985	−	0.222825i
$556$	9.69332	+	21.7716i	0.411088	+	0.923320i
$557$	20.0934	+	9.58406i	0.851384	+	0.406089i	0.805314	−	0.592849i	$-0.201997\pi$
$557$	20.0934	+	9.58406i	0.851384	+	0.406089i	0.0460705	+	0.998938i	$0.485330\pi$
$558$	13.6636	−	8.65962i	0.578426	−	0.366591i
$559$	−24.3712	−	28.5350i	−1.03079	−	1.20690i
$560$	−23.4231	+	91.8153i	−0.989809	+	3.87990i
$561$	−38.8624	−	22.7251i	−1.64077	−	0.959454i
$562$	41.6198	−	19.8516i	1.75563	−	0.837391i
$563$	26.4637	−	9.37130i	1.11531	−	0.394953i	0.288528	−	0.957471i	$-0.406834\pi$
$563$	26.4637	−	9.37130i	1.11531	−	0.394953i	0.826785	+	0.562518i	$0.190167\pi$
$564$	−23.9085	+	66.3457i	−1.00673	+	2.79366i
$565$	−5.43921	−	1.45743i	−0.228829	−	0.0613146i
$566$	−26.5806	+	13.5435i	−1.11726	+	0.569275i
$567$	0.241347	−	23.8105i	0.0101356	−	0.999949i
$568$	−22.3027	+	92.8974i	−0.935800	+	3.89789i
$569$	33.4081	−	1.75084i	1.40054	−	0.0733992i	0.662958	−	0.748657i	$-0.269301\pi$
$569$	33.4081	−	1.75084i	1.40054	−	0.0733992i	0.737582	+	0.675258i	$0.235968\pi$
$570$	−0.582814	−	2.00832i	−0.0244114	−	0.0841193i
$571$	−22.6208	−	29.4800i	−0.946651	−	1.23370i	−0.972230	−	0.234027i	$-0.924810\pi$
$571$	−22.6208	−	29.4800i	−0.946651	−	1.23370i	0.0255793	−	0.999673i	$-0.491857\pi$
$572$	69.2818	+	85.5559i	2.89682	+	3.57727i
$573$	−11.4309	−	21.3341i	−0.477534	−	0.891244i
$574$	18.3795	+	43.0388i	0.767146	+	1.79641i
$575$			0.473178i			0.0197329i
$576$	−111.112	+	10.4355i	−4.62966	+	0.434812i
$577$	8.46334	−	6.49415i	0.352333	−	0.270355i	−0.417397	−	0.908724i	$-0.637057\pi$
$577$	8.46334	−	6.49415i	0.352333	−	0.270355i	0.769730	+	0.638369i	$0.220391\pi$
$578$	−25.7454	−	5.47234i	−1.07087	−	0.227620i
$579$	−18.3121	−	30.2575i	−0.761026	−	1.25746i
$580$	−72.1160	−	17.3135i	−2.99445	−	0.718905i
$581$	−0.665131	−	5.67186i	−0.0275943	−	0.235308i
$582$	−12.8696	+	18.5050i	−0.533463	+	0.767059i
$583$	−2.68227	+	10.0104i	−0.111088	+	0.414588i
$584$	−23.5204	+	21.1778i	−0.973280	+	0.876346i
$585$	24.5405	+	6.17989i	1.01462	+	0.255507i
$586$	16.4410	+	34.4692i	0.679170	+	1.42391i
$587$	36.3968	−	22.3040i	1.50226	−	0.920584i	0.503872	−	0.863778i	$-0.331908\pi$
$587$	36.3968	−	22.3040i	1.50226	−	0.920584i	0.998385	−	0.0568062i	$-0.0180917\pi$
$588$	−26.6116	+	62.8746i	−1.09744	+	2.59291i
$589$	0.297921	−	0.254449i	0.0122756	−	0.0104844i
$590$	26.9980	−	60.6385i	1.11149	−	2.49645i
$591$	−4.26514	+	0.199849i	−0.175445	+	0.00822068i
$592$	−23.4067	+	10.4213i	−0.962011	+	0.428315i
$593$	0.890245	−	33.9971i	0.0365580	−	1.39609i	−0.697295	−	0.716784i	$-0.745613\pi$
$593$	0.890245	−	33.9971i	0.0365580	−	1.39609i	0.733853	−	0.679308i	$-0.237720\pi$
$594$	−18.0779	+	70.1451i	−0.741746	+	2.87809i
$595$	28.5495	+	8.08492i	1.17042	+	0.331449i
$596$	−56.4977	+	92.1959i	−2.31424	+	3.77649i
$597$	−2.25449	−	5.52924i	−0.0922703	−	0.226297i
$598$	8.42737	−	17.6683i	0.344621	−	0.722512i
$599$	−2.05784	−	19.5790i	−0.0840809	−	0.799976i	−0.952581	−	0.304286i	$-0.901582\pi$
$599$	−2.05784	−	19.5790i	−0.0840809	−	0.799976i	0.868500	−	0.495690i	$-0.165085\pi$
$600$	0.678500	+	4.44298i	0.0276996	+	0.181384i
$601$	10.8285	+	26.1422i	0.441702	+	1.06636i	0.975351	+	0.220658i	$0.0708204\pi$
$601$	10.8285	+	26.1422i	0.441702	+	1.06636i	−0.533649	+	0.845706i	$0.679180\pi$
$602$	−40.9221	+	57.7717i	−1.66786	+	2.35460i
$603$	12.6688	+	9.94600i	0.515915	+	0.405032i
$604$	−93.6361	−	17.3544i	−3.81000	−	0.706142i
$605$	−21.0776	−	23.4090i	−0.856926	−	0.951713i
$606$	52.5187	−	49.2885i	2.13342	−	2.00221i
$607$	−2.79906	+	4.31018i	−0.113610	+	0.174945i	−0.890902	−	0.454196i	$-0.849927\pi$
$607$	−2.79906	+	4.31018i	−0.113610	+	0.174945i	0.777291	+	0.629141i	$0.216593\pi$
$608$	−4.95237	+	1.18896i	−0.200845	+	0.0482187i
$609$	−25.6762	−	10.4411i	−1.04045	−	0.423095i
$610$	−45.4299	−	23.1477i	−1.83940	−	0.937223i
$611$	−20.8163	−	18.7431i	−0.842136	−	0.758263i
$612$	5.86564	+	86.8127i	0.237105	+	3.50919i
$613$	8.91029	+	3.42034i	0.359883	+	0.138146i	0.531590	−	0.847002i	$-0.321595\pi$
$613$	8.91029	+	3.42034i	0.359883	+	0.138146i	−0.171707	+	0.985148i	$0.554928\pi$
$614$	−9.42827	−	16.3302i	−0.380494	−	0.659035i
$615$	−17.4062	−	16.7393i	−0.701887	−	0.674994i
$616$	80.2486	−	107.225i	3.23331	−	4.32023i
$617$	5.78169	+	36.5041i	0.232762	+	1.46960i	0.776378	+	0.630267i	$0.217055\pi$
$617$	5.78169	+	36.5041i	0.232762	+	1.46960i	−0.543616	+	0.839334i	$0.682945\pi$
$618$	−5.74251	−	7.99665i	−0.230998	−	0.321672i
$619$	−3.48093	+	16.3765i	−0.139911	+	0.658227i	0.851162	+	0.524903i	$0.175898\pi$
$619$	−3.48093	+	16.3765i	−0.139911	+	0.658227i	−0.991072	+	0.133324i	$0.957435\pi$
$620$	20.0729	−	13.0355i	0.806148	−	0.523519i
$621$	9.32836	−	1.82138i	0.374334	−	0.0730895i
$622$	−52.7157	+	12.6559i	−2.11371	+	0.507456i
$623$	−12.3703	+	14.8411i	−0.495604	+	0.594598i
$624$	31.9310	−	105.645i	1.27826	−	4.22920i
$625$	−23.1231	+	4.91496i	−0.924922	+	0.196598i
$626$	31.1524	+	87.9716i	1.24510	+	3.51605i
$627$	−0.193045	+	1.74375i	−0.00770947	+	0.0696387i
$628$	1.39959	−	2.57772i	0.0558497	−	0.102862i
$629$	3.07039	+	7.41258i	0.122425	+	0.295559i
$630$	−0.0448754	−	47.7436i	−0.00178788	−	1.90215i
$631$	−30.8846	+	22.4390i	−1.22950	+	0.893282i	−0.996852	−	0.0792795i	$-0.974738\pi$
$631$	−30.8846	+	22.4390i	−1.22950	+	0.893282i	−0.232645	+	0.972562i	$0.574738\pi$
$632$	−94.8883	−	138.063i	−3.77445	−	5.49187i
$633$	−2.40939	−	1.87008i	−0.0957647	−	0.0743290i
$634$	1.78902	+	3.29497i	0.0710512	+	0.130860i
$635$	1.67981	+	4.37606i	0.0666612	+	0.173658i
$636$	18.9179	−	6.58152i	0.750145	−	0.260974i
$637$	−19.1343	−	19.2167i	−0.758127	−	0.761392i
$638$	68.2164	+	49.5621i	2.70071	+	1.96218i
$639$	−0.431551	−	28.5693i	−0.0170719	−	1.13019i
$640$	−112.640	+	11.8390i	−4.45250	+	0.467977i
$641$	2.14396	+	11.5678i	0.0846813	+	0.456899i	0.998688	+	0.0512010i	$0.0163049\pi$
$641$	2.14396	+	11.5678i	0.0846813	+	0.456899i	−0.914007	+	0.405698i	$0.867028\pi$
$642$	65.8330	+	10.8010i	2.59822	+	0.426280i
$643$	33.3008	−	20.4067i	1.31325	−	0.804763i	0.323320	−	0.946290i	$-0.395201\pi$
$643$	33.3008	−	20.4067i	1.31325	−	0.804763i	0.989935	+	0.141526i	$0.0452010\pi$
$644$	−26.7225	−	5.34529i	−1.05301	−	0.210634i
$645$	7.79330	−	35.6915i	0.306861	−	1.40535i
$646$	0.593761	+	2.79343i	0.0233612	+	0.109906i
$647$	20.7552	−	5.56135i	0.815973	−	0.218639i	0.173388	−	0.984854i	$-0.444529\pi$
$647$	20.7552	−	5.56135i	0.815973	−	0.218639i	0.642585	+	0.766214i	$0.277862\pi$
$648$	84.9785	−	30.4783i	3.33827	−	1.19730i
$649$	−40.3942	+	38.3327i	−1.58561	+	1.50469i
$650$	−2.69196	−	0.646281i	−0.105587	−	0.0253492i
$651$	8.14792	−	3.69112i	0.319342	−	0.144666i
$652$	14.1573	+	43.5716i	0.554442	+	1.70640i
$653$	5.67470	+	43.1036i	0.222068	+	1.68678i	0.632244	+	0.774769i	$0.282134\pi$
$653$	5.67470	+	43.1036i	0.222068	+	1.68678i	−0.410176	+	0.912006i	$0.634533\pi$
$654$	−17.6787	+	2.22792i	−0.691292	+	0.0871185i
$655$	1.08782	+	0.628051i	0.0425045	+	0.0245400i
$656$	−76.4752	+	72.4106i	−2.98586	+	2.82716i
$657$	5.24295	−	7.88095i	0.204547	−	0.307465i
$658$	−24.6560	+	46.7414i	−0.961191	+	1.82217i
$659$	−9.24456	+	22.3184i	−0.360117	+	0.869400i	0.635165	+	0.772376i	$0.280932\pi$
$659$	−9.24456	+	22.3184i	−0.360117	+	0.869400i	−0.995282	+	0.0970231i	$0.969068\pi$
$660$	−25.5962	+	104.074i	−0.996331	+	4.05106i
$661$	24.0308	+	37.0041i	0.934688	+	1.43929i	0.898015	+	0.439966i	$0.145009\pi$
$661$	24.0308	+	37.0041i	0.934688	+	1.43929i	0.0366734	+	0.999327i	$0.488324\pi$
$662$	−10.4079	−	9.87674i	−0.404515	−	0.383870i
$663$	−32.8091	−	10.8615i	−1.27420	−	0.421828i
$664$	19.2915	−	9.82952i	0.748656	−	0.381459i
$665$	−0.164696	−	1.14455i	−0.00638664	−	0.0443836i
$666$	10.1222	−	8.01278i	0.392226	−	0.310489i
$667$	2.01620	−	10.8784i	0.0780674	−	0.421214i
$668$	−6.96811	−	4.78905i	−0.269604	−	0.185294i
$669$	−1.15905	−	2.03346i	−0.0448115	−	0.0786180i
$670$	25.6209	+	19.6596i	0.989821	+	0.759517i
$671$	27.7808	+	32.5271i	1.07246	+	1.25569i
$672$	−116.158	−	5.33331i	−4.48089	−	0.205737i
$673$	−2.42063	−	30.7571i	−0.0933086	−	1.18560i	−0.848174	−	0.529718i	$-0.822298\pi$
$673$	−2.42063	−	30.7571i	−0.0933086	−	1.18560i	0.754865	−	0.655880i	$-0.227702\pi$
$674$	44.6071	+	4.68840i	1.71820	+	0.180590i
$675$	−0.526253	−	1.23689i	−0.0202555	−	0.0476078i
$676$	8.78828	+	7.11661i	0.338011	+	0.273716i
$677$	−22.2465	+	8.53963i	−0.855002	+	0.328205i	−0.746089	−	0.665847i	$-0.768071\pi$
$677$	−22.2465	+	8.53963i	−0.855002	+	0.328205i	−0.108914	+	0.994051i	$0.534737\pi$
$678$	0.716008	−	12.3530i	0.0274981	−	0.474412i
$679$	−8.47029	+	9.14338i	−0.325060	+	0.350891i
$680$	8.82648	+	112.151i	0.338480	+	4.30080i
$681$	−0.841180	−	11.5022i	−0.0322341	−	0.440766i
$682$	−26.7557	+	4.95888i	−1.02453	+	0.189885i
$683$	−1.46565	+	11.1328i	−0.0560817	+	0.425983i	0.940255	+	0.340470i	$0.110586\pi$
$683$	−1.46565	+	11.1328i	−0.0560817	+	0.425983i	−0.996337	+	0.0855128i	$0.972747\pi$
$684$	2.99766	−	1.58486i	0.114618	−	0.0605986i
$685$	−2.89901	+	36.8354i	−0.110765	+	1.40741i
$686$	−26.3001	+	43.8839i	−1.00414	+	1.67550i
$687$	3.60081	+	20.0472i	0.137380	+	0.764848i
$688$	−153.894	−	41.2357i	−5.86715	−	1.57210i
$689$	−0.416377	+	7.94495i	−0.0158627	+	0.302679i
$690$	18.6622	−	3.85888i	0.710457	−	0.146905i
$691$	−9.61042	+	2.84674i	−0.365598	+	0.108295i	−0.461605	−	0.887086i	$-0.652726\pi$
$691$	−9.61042	+	2.84674i	−0.365598	+	0.108295i	0.0960072	+	0.995381i	$0.469393\pi$
$692$	15.5441	−	30.5070i	0.590898	−	1.15970i
$693$	−15.2935	+	37.0202i	−0.580952	+	1.40628i
$694$	11.3573	−	27.4189i	0.431116	−	1.04081i
$695$	−5.79937	−	7.16163i	−0.219983	−	0.271656i
$696$	3.33262	−	105.036i	0.126323	−	3.98137i
$697$	22.0403	+	24.5331i	0.834835	+	0.929256i
$698$	76.2363	−	44.0151i	2.88559	−	1.66599i
$699$	32.8008	−	24.8815i	1.24064	−	0.941106i
$700$	0.0463086	+	3.85384i	0.00175030	+	0.145661i
$701$	−15.0442	−	46.3014i	−0.568213	−	1.74878i	−0.658208	−	0.752836i	$-0.728685\pi$
$701$	−15.0442	−	46.3014i	−0.568213	−	1.74878i	0.0899951	−	0.995942i	$-0.471315\pi$
$702$	−2.37896	+	55.5577i	−0.0897880	+	2.09689i
$703$	0.215229	−	0.226804i	0.00811750	−	0.00855406i
$704$	179.998	+	53.3177i	6.78392	+	2.00949i
$705$	2.29005	−	27.1731i	0.0862481	−	1.02340i
$706$	−12.2475	−	12.2475i	−0.460941	−	0.460941i
$707$	32.5488	−	22.9508i	1.22412	−	0.863155i
$708$	105.152	+	22.9602i	3.95187	+	0.862897i
$709$	−5.41721	−	11.3574i	−0.203448	−	0.426537i	0.775304	−	0.631589i	$-0.217597\pi$
$709$	−5.41721	−	11.3574i	−0.203448	−	0.426537i	−0.978751	+	0.205052i	$0.934264\pi$
$710$	−1.49966	−	57.2697i	−0.0562812	−	2.14929i
$711$	37.7358	+	32.9592i	1.41520	+	1.23607i
$712$	−69.0494	−	24.4517i	−2.58774	−	0.916365i
$713$	2.09864	+	2.88853i	0.0785945	+	0.108176i
$714$	−4.69448	+	65.0322i	−0.175687	+	2.43377i
$715$	−34.4393	−	25.0216i	−1.28796	−	0.935756i
$716$	−1.48963	+	56.8868i	−0.0556702	+	2.12596i
$717$	−13.1342	−	2.50960i	−0.490507	−	0.0937227i
$718$	−3.34615	+	4.13215i	−0.124877	+	0.154210i
$719$	7.10941	+	0.186167i	0.265136	+	0.00694284i	0.158514	−	0.987357i	$-0.449330\pi$
$719$	7.10941	+	0.186167i	0.265136	+	0.00694284i	0.106622	+	0.994300i	$0.465996\pi$
$720$	100.727	−	37.3909i	3.75388	−	1.39348i
$721$	−2.52956	−	4.82045i	−0.0942056	−	0.179523i
$722$	−42.3726	+	30.7855i	−1.57695	+	1.14572i
$723$	−25.0898	+	3.83153i	−0.933099	+	0.142496i
$724$	−23.5385	−	3.09890i	−0.874801	−	0.115170i
$725$	−1.56415	+	0.0409588i	−0.0580912	+	0.00152117i
$726$	40.9946	−	55.7722i	1.52145	−	2.06990i
$727$	24.6236	−	28.8305i	0.913238	−	1.06926i	−0.0841080	−	0.996457i	$-0.526804\pi$
$727$	24.6236	−	28.8305i	0.913238	−	1.06926i	0.997346	−	0.0728076i	$-0.0231959\pi$
$728$	43.1448	−	93.3244i	1.59905	−	3.45883i
$729$	−22.3586	+	15.1358i	−0.828097	+	0.560584i
$730$	10.3367	−	15.9171i	0.382578	−	0.589118i
$731$	−14.1698	+	47.8363i	−0.524088	+	1.76929i
$732$	21.8399	−	79.7385i	0.807224	−	2.94722i
$733$	−0.881898	−	16.8276i	−0.0325736	−	0.621542i	−0.965330	−	0.261034i	$-0.915937\pi$
$733$	−0.881898	−	16.8276i	−0.0325736	−	0.621542i	0.932756	−	0.360508i	$-0.117397\pi$
$734$	−44.1805	+	14.3551i	−1.63073	+	0.529856i
$735$	3.64701	−	26.1471i	0.134522	−	0.964451i
$736$	−7.26068	−	45.8421i	−0.267632	−	1.68976i
$737$	−13.5468	−	23.4637i	−0.499002	−	0.864298i
$738$	28.2759	−	44.9041i	1.04085	−	1.65294i
$739$	−3.39256	+	5.87609i	−0.124797	+	0.216155i	−0.921654	−	0.388013i	$-0.873161\pi$
$739$	−3.39256	+	5.87609i	−0.124797	+	0.216155i	0.796856	+	0.604169i	$0.206495\pi$
$740$	14.8441	−	12.0205i	0.545680	−	0.441883i
$741$	0.133361	+	1.34020i	0.00489915	+	0.0492335i
$742$	14.7243	−	2.91240i	0.540546	−	0.106918i
$743$	−17.9100	−	9.12562i	−0.657055	−	0.334786i	0.0934757	−	0.995622i	$-0.470202\pi$
$743$	−17.9100	−	9.12562i	−0.657055	−	0.334786i	−0.750531	+	0.660835i	$0.770202\pi$
$744$	23.8474	+	24.1130i	0.874289	+	0.884026i
$745$	11.8751	−	40.0897i	0.435070	−	1.46877i
$746$	−7.41499	−	0.388603i	−0.271482	−	0.0142278i
$747$	−4.85982	+	4.27929i	−0.177811	+	0.156571i
$748$	45.2290	−	139.201i	1.65374	−	5.08968i
$749$	35.2185	+	10.9771i	1.28686	+	0.401096i
$750$	−22.0067	−	50.1737i	−0.803569	−	1.83208i
$751$	21.5130	−	39.6220i	0.785021	−	1.44583i	−0.107204	−	0.994237i	$-0.534190\pi$
$751$	21.5130	−	39.6220i	0.785021	−	1.44583i	0.892225	−	0.451592i	$-0.149144\pi$
$752$	−117.908	−	15.5228i	−4.29965	−	0.566060i
$753$	−15.0005	−	18.7353i	−0.546648	−	0.682751i
$754$	59.1346	+	26.3284i	2.15355	+	0.958824i
$755$	36.7102	−	2.88915i	1.33602	−	0.105147i
$756$	75.7974	−	15.7473i	2.75672	−	0.572725i
$757$	−7.76503	+	12.6714i	−0.282225	+	0.460549i	−0.962069	−	0.272808i	$-0.912048\pi$
$757$	−7.76503	+	12.6714i	−0.282225	+	0.460549i	0.679844	+	0.733357i	$0.262048\pi$
$758$	15.3416	+	39.9662i	0.557231	+	1.45164i
$759$	−15.7038	−	3.00058i	−0.570013	−	0.108914i
$760$	3.85280	−	2.09190i	0.139756	−	0.0758812i
$761$	1.13973	−	10.8438i	0.0413153	−	0.393089i	−0.954250	−	0.299011i	$-0.903343\pi$
$761$	1.13973	−	10.8438i	0.0413153	−	0.393089i	0.995565	−	0.0940775i	$-0.0299902\pi$
$762$	−8.66926	+	5.56187i	−0.314054	+	0.201485i
$763$	−9.85193	−	0.139555i	−0.356664	−	0.00505223i
$764$	59.8360	−	51.1048i	2.16479	−	1.84890i
$765$	−10.8790	−	31.8377i	−0.393332	−	1.15110i
$766$	2.53794	+	96.9201i	0.0916996	+	3.50187i
$767$	−24.2139	+	35.2315i	−0.874314	+	1.27213i
$768$	−36.4534	−	114.343i	−1.31540	−	4.12599i
$769$	37.9907	+	12.3439i	1.36998	+	0.445133i	0.899362	−	0.437205i	$-0.144032\pi$
$769$	37.9907	+	12.3439i	1.36998	+	0.445133i	0.470616	+	0.882338i	$0.344032\pi$
$770$	−29.8402	+	74.5621i	−1.07536	+	2.68703i
$771$	−5.48788	−	3.81664i	−0.197641	−	0.137453i
$772$	83.4073	−	79.1505i	3.00189	−	2.84869i
$773$	1.65694	−	1.74605i	0.0595961	−	0.0628011i	−0.694896	−	0.719110i	$-0.744550\pi$
$773$	1.65694	−	1.74605i	0.0595961	−	0.0628011i	0.754492	+	0.656309i	$0.227883\pi$
$774$	80.2711	+	0.889096i	2.88529	+	0.0319579i
$775$	0.337877	−	0.375250i	0.0121369	−	0.0134794i
$776$	−43.6578	−	18.0836i	−1.56722	−	0.649165i
$777$	6.15894	−	3.60926i	0.220951	−	0.129482i
$778$			2.92340i			0.104809i
$779$	0.524052	−	1.17352i	0.0187761	−	0.0420458i
$780$	−2.60918	+	82.2346i	−0.0934235	+	2.94447i
$781$	−17.2243	+	44.8708i	−0.616334	+	1.60560i
$782$	−25.8026	+	3.39698i	−0.922700	+	0.121476i
$783$	6.82829	+	30.6785i	0.244023	+	1.09636i
$784$	−113.161	−	21.2248i	−4.04148	−	0.758030i
$785$	−0.264772	+	1.10286i	−0.00945013	+	0.0393626i
$786$	−0.867456	+	2.62029i	−0.0309411	+	0.0934627i
$787$	−0.636944	+	12.1536i	−0.0227046	+	0.433230i	0.963501	+	0.267705i	$0.0862652\pi$
$787$	−0.636944	+	12.1536i	−0.0227046	+	0.433230i	−0.986206	+	0.165525i	$0.947068\pi$
$788$	−3.59290	−	13.4089i	−0.127992	−	0.477671i
$789$	2.10406	−	1.77698i	0.0749066	−	0.0632623i
$790$	76.3892	+	65.2425i	2.71781	+	2.32122i
$791$	1.34204	−	6.70923i	0.0477176	−	0.238553i
$792$	−151.756	−	5.65640i	−5.39243	−	0.200991i
$793$	26.0523	+	19.9906i	0.925145	+	0.709889i
$794$	−10.4595	+	1.93855i	−0.371192	+	0.0687964i
$795$	−6.40722	+	4.35152i	−0.227241	+	0.154332i
$796$	15.9990	−	10.9958i	0.567071	−	0.389737i
$797$	9.54696	−	13.1403i	0.338171	−	0.465452i	−0.605735	−	0.795666i	$-0.707121\pi$
$797$	9.54696	−	13.1403i	0.338171	−	0.465452i	0.943906	+	0.330214i	$0.107121\pi$
$798$	2.38963	−	0.863673i	0.0845920	−	0.0305737i
$799$	−5.82572	+	36.7822i	−0.206099	+	1.30126i
$800$	−6.12809	+	2.35235i	−0.216661	+	0.0831682i
$801$	21.8195	+	1.96062i	0.770954	+	0.0692750i
$802$	−30.5356	−	68.5840i	−1.07825	−	2.42179i
$803$	−13.1222	+	9.01861i	−0.463071	+	0.318260i
$804$	−22.8052	+	47.1385i	−0.804277	+	1.66245i
$805$	10.5159	−	0.677902i	0.370636	−	0.0238929i
$806$	−19.2995	+	7.99411i	−0.679795	+	0.281580i
$807$	2.92796	+	0.0162148i	0.103069	+	0.000570788i
$808$	124.441	+	85.5257i	4.37781	+	3.00878i
$809$	33.7010	−	11.9341i	1.18486	−	0.419582i	0.332788	−	0.943002i	$-0.392011\pi$
$809$	33.7010	−	11.9341i	1.18486	−	0.419582i	0.852075	+	0.523419i	$0.175344\pi$
$810$	−44.4912	+	30.8426i	−1.56326	+	1.08370i
$811$	24.8123	−	24.8123i	0.871278	−	0.871278i	−0.121333	−	0.992612i	$-0.538717\pi$
$811$	24.8123	−	24.8123i	0.871278	−	0.871278i	0.992612	+	0.121333i	$0.0387170\pi$
$812$	15.3564	−	88.7975i	0.538905	−	3.11618i
$813$	−25.0163	+	22.2752i	−0.877361	+	0.781225i
$814$	−20.8218	+	6.16771i	−0.729805	+	0.216178i
$815$	−9.64842	−	14.8573i	−0.337969	−	0.520427i
$816$	−140.917	+	40.8940i	−4.93307	+	1.43158i
$817$	1.92763	−	0.253777i	0.0674391	−	0.00887853i
$818$	−73.5237	+	11.6450i	−2.57070	+	0.407158i
$819$	−5.57518	+	30.2396i	−0.194813	+	1.05666i
$820$	41.0973	−	66.8975i	1.43518	−	2.33616i
$821$	−12.6129	+	7.28203i	−0.440192	+	0.254145i	−0.703679	−	0.710518i	$-0.748461\pi$
$821$	−12.6129	+	7.28203i	−0.440192	+	0.254145i	0.263487	+	0.964663i	$0.415127\pi$
$822$	−80.5549	+	10.1517i	−2.80967	+	0.354083i
$823$	−18.0570	+	13.8556i	−0.629428	+	0.482977i	−0.873528	−	0.486773i	$-0.838174\pi$
$823$	−18.0570	+	13.8556i	−0.629428	+	0.482977i	0.244101	+	0.969750i	$0.421507\pi$
$824$	13.8105	−	15.3382i	0.481113	−	0.534330i
$825$	0.0466706	+	2.26063i	0.00162486	+	0.0787049i
$826$	75.6375	+	27.9965i	2.63176	+	0.974122i
$827$	−6.80495	−	28.3447i	−0.236631	−	0.985640i	−0.956547	−	0.291579i	$-0.905819\pi$
$827$	−6.80495	−	28.3447i	−0.236631	−	0.985640i	0.719916	−	0.694062i	$-0.244181\pi$
$828$	12.2550	+	28.3667i	0.425892	+	0.985810i
$829$	−7.82145	+	2.09575i	−0.271650	+	0.0727884i	−0.392073	−	0.919934i	$-0.628242\pi$
$829$	−7.82145	+	2.09575i	−0.271650	+	0.0727884i	0.120422	+	0.992723i	$0.461575\pi$
$830$	−9.64852	+	8.68757i	−0.334905	+	0.301550i
$831$	−31.5490	+	10.0581i	−1.09442	+	0.348911i
$832$	143.671	+	11.3071i	4.98089	+	0.392005i
$833$	−7.57174	+	35.2496i	−0.262345	+	1.22133i
$834$	12.8304	−	15.6661i	0.444282	−	0.542472i
$835$	3.08189	+	1.09136i	0.106653	+	0.0377679i
$836$	−5.67261	+	0.596215i	−0.196191	+	0.0206205i
$837$	−8.69835	−	5.21656i	−0.300659	−	0.180311i
$838$	−1.63076	+	15.5157i	−0.0563337	+	0.535979i
$839$	−10.3997	−	6.37296i	−0.359039	−	0.220019i	0.331267	−	0.943537i	$-0.392524\pi$
$839$	−10.3997	−	6.37296i	−0.359039	−	0.220019i	−0.690306	+	0.723518i	$0.742524\pi$
$840$	97.7686	−	21.4442i	3.37334	−	0.739895i
$841$	7.49164	+	1.18656i	0.258332	+	0.0409158i
$842$	36.7574	+	0.962525i	1.26674	+	0.0331708i
$843$	−22.8396	−	17.7272i	−0.786636	−	0.610558i
$844$	4.26894	−	8.95001i	0.146943	−	0.308072i
$845$	−3.99468	−	1.77854i	−0.137421	−	0.0611838i
$846$	59.4918	−	7.16286i	2.04537	−	0.246264i
$847$	26.7370	−	27.3874i	0.918696	−	0.941043i
$848$	17.6488	+	28.8003i	0.606064	+	0.989006i
$849$	15.0712	+	11.0779i	0.517243	+	0.380193i
$850$	1.22863	+	3.46953i	0.0421415	+	0.119004i
$851$	1.90661	+	2.11750i	0.0653576	+	0.0725870i
$852$	90.4462	−	21.1852i	3.09864	−	0.725792i
$853$	8.34841	+	16.3847i	0.285844	+	0.561001i	0.988624	−	0.150407i	$-0.0480582\pi$
$853$	8.34841	+	16.3847i	0.285844	+	0.561001i	−0.702780	+	0.711407i	$0.748058\pi$
$854$	24.5166	−	56.8953i	0.838941	−	1.94692i
$855$	−0.961020	+	0.891954i	−0.0328662	+	0.0305042i
$856$	7.31979	+	139.670i	0.250185	+	4.77382i
$857$	6.23318	−	29.3248i	0.212921	−	1.00172i	−0.733726	−	0.679445i	$-0.762221\pi$
$857$	6.23318	−	29.3248i	0.212921	−	1.00172i	0.946648	−	0.322271i	$-0.104446\pi$
$858$	38.5194	−	85.2424i	1.31503	−	2.91013i
$859$	15.1450	−	12.2642i	0.516742	−	0.418450i	−0.335152	−	0.942164i	$-0.608788\pi$
$859$	15.1450	−	12.2642i	0.516742	−	0.418450i	0.851894	+	0.523715i	$0.175454\pi$
$860$	118.773			4.05012
$861$	18.9367	−	22.4144i	0.645359	−	0.763879i
$862$	7.80111			0.265707
$863$	9.19400	−	7.44515i	0.312967	−	0.253436i	−0.459947	−	0.887946i	$-0.652132\pi$
$863$	9.19400	−	7.44515i	0.312967	−	0.253436i	0.772914	+	0.634510i	$0.218798\pi$
$864$	69.9635	+	111.756i	2.38021	+	3.80202i
$865$	−2.75263	+	12.9501i	−0.0935922	+	0.440316i
$866$	−1.42957	−	27.2778i	−0.0485788	−	0.926939i
$867$	4.18291	+	15.9640i	0.142059	+	0.542164i
$868$	17.3752	+	23.3205i	0.589753	+	0.791548i
$869$	−38.2624	−	75.0941i	−1.29796	−	2.54739i
$870$	14.3715	+	61.3563i	0.487238	+	2.08017i
$871$	−13.9174	−	15.4568i	−0.471572	−	0.523734i
$872$	−12.4697	−	35.2132i	−0.422276	−	1.19247i
$873$	13.9905	+	1.99976i	0.473505	+	0.0676815i
$874$	0.529925	+	0.864758i	0.0179250	+	0.0292509i
$875$	−8.19205	−	29.1667i	−0.276942	−	0.986015i
$876$	28.6687	+	11.1874i	0.968626	+	0.377988i
$877$	−40.4528	−	18.0107i	−1.36599	−	0.608179i	−0.412878	−	0.910786i	$-0.635476\pi$
$877$	−40.4528	−	18.0107i	−1.36599	−	0.608179i	−0.953115	+	0.302607i	$0.902143\pi$
$878$	−35.4199	+	74.2594i	−1.19536	+	2.50613i
$879$	14.6815	−	18.9155i	0.495195	−	0.638004i
$880$	−180.673	−	4.73108i	−6.09048	−	0.159485i
$881$	−32.7878	−	5.19308i	−1.10465	−	0.174959i	−0.422637	−	0.906299i	$-0.638895\pi$
$881$	−32.7878	−	5.19308i	−1.10465	−	0.174959i	−0.682013	+	0.731340i	$0.738895\pi$
$882$	57.8879	−	3.78636i	1.94919	−	0.127493i
$883$	40.3517	+	24.7275i	1.35794	+	0.832148i	0.995020	−	0.0996721i	$-0.0317794\pi$
$883$	40.3517	+	24.7275i	1.35794	+	0.832148i	0.362921	+	0.931820i	$0.381779\pi$
$884$	11.7449	−	111.745i	0.395024	−	3.75840i
$885$	−41.5726	+	1.94794i	−1.39745	+	0.0654791i
$886$	−36.6380	+	3.85081i	−1.23088	+	0.129371i
$887$	46.7973	+	16.5718i	1.57130	+	0.556427i	0.970107	−	0.242677i	$-0.0780255\pi$
$887$	46.7973	+	16.5718i	1.57130	+	0.556427i	0.601193	+	0.799104i	$0.294692\pi$
$888$	20.9387	+	17.1487i	0.702658	+	0.575473i
$889$	−5.17488	+	2.37891i	−0.173560	+	0.0797862i
$890$	43.7899	+	3.44634i	1.46784	+	0.115522i
$891$	44.3869	−	9.62179i	1.48702	−	0.322342i
$892$	5.65505	−	5.09183i	0.189345	−	0.170487i
$893$	1.40183	−	0.375618i	0.0469104	−	0.0125696i
$894$	91.5516	+	7.71564i	3.06194	+	0.258049i
$895$	−5.13684	−	21.3965i	−0.171705	−	0.715205i
$896$	−23.1601	−	135.657i	−0.773723	−	4.53197i
$897$	−12.2710	+	0.253335i	−0.409717	+	0.00845861i
$898$	50.9521	−	56.5880i	1.70029	−	1.88837i
$899$	−9.36675	+	7.18736i	−0.312399	+	0.239712i
$900$	3.56377	−	2.52940i	0.118792	−	0.0843133i
$901$	9.16021	−	5.28865i	0.305171	−	0.176190i
$902$	−72.2737	+	52.3871i	−2.40645	+	1.74430i
$903$	43.8869	+	6.65987i	1.46046	+	0.221627i
$904$	25.6216	−	4.05806i	0.852161	−	0.134969i
$905$	9.10183	−	1.19828i	0.302555	−	0.0398321i
$906$	22.5514	+	77.7099i	0.749220	+	2.58174i
$907$	−12.1253	−	18.6713i	−0.402614	−	0.619971i	0.577973	−	0.816056i	$-0.303844\pi$
$907$	−12.1253	−	18.6713i	−0.402614	−	0.619971i	−0.980587	+	0.196085i	$0.937177\pi$
$908$	35.9514	−	10.6493i	1.19309	−	0.353409i
$909$	−42.3994	−	15.5450i	−1.40630	−	0.515595i
$910$	−10.5063	+	60.7518i	−0.348280	+	2.01390i
$911$	6.83868	−	6.83868i	0.226575	−	0.226575i	−0.584685	−	0.811260i	$-0.698782\pi$
$911$	6.83868	−	6.83868i	0.226575	−	0.226575i	0.811260	+	0.584685i	$0.198782\pi$
$912$	3.68949	+	4.36860i	0.122171	+	0.144659i
$913$	10.2677	−	3.63598i	0.339811	−	0.120333i
$914$	−41.4952	−	28.5189i	−1.37254	−	0.943321i
$915$	−0.177037	+	31.9683i	−0.00585268	+	1.05684i
$916$	−61.1790	+	25.3412i	−2.02141	+	0.837296i
$917$	−0.676512	+	1.36812i	−0.0223404	+	0.0451794i
$918$	63.6700	−	37.5765i	2.10142	−	1.24021i
$919$	−4.46533	+	3.06894i	−0.147298	+	0.101235i	−0.637789	−	0.770211i	$-0.720151\pi$
$919$	−4.46533	+	3.06894i	−0.147298	+	0.101235i	0.490491	+	0.871446i	$0.336817\pi$
$920$	16.2500	+	36.4981i	0.535747	+	1.20331i
$921$	−6.49407	+	9.87977i	−0.213987	+	0.325549i
$922$	3.61554	−	1.38788i	0.119072	−	0.0457073i
$923$	−5.77198	+	36.4428i	−0.189987	+	1.19953i
$924$	−128.195	−	22.9016i	−4.21730	−	0.753408i
$925$	0.236863	−	0.326014i	0.00778802	−	0.0107193i
$926$	42.6340	−	29.3016i	1.40104	−	0.962909i
$927$	−2.86311	+	5.46858i	−0.0940368	+	0.179612i
$928$	150.909	−	27.9693i	4.95382	−	0.918137i
$929$	−36.5919	−	28.0779i	−1.20054	−	0.921207i	−0.202232	−	0.979338i	$-0.564819\pi$
$929$	−36.5919	−	28.0779i	−1.20054	−	0.921207i	−0.998309	+	0.0581306i	$0.981486\pi$
$930$	−17.5554	−	10.2656i	−0.575663	−	0.336623i
$931$	1.37494	−	0.289167i	0.0450620	−	0.00947707i
$932$	101.781	+	86.9292i	3.33395	+	2.84746i
$933$	21.9324	+	25.9694i	0.718034	+	0.850199i
$934$	−28.5640	−	106.602i	−0.934642	−	3.48813i
$935$	−2.96200	+	56.5183i	−0.0968678	+	1.84835i
$936$	−114.857	+	19.9744i	−3.75423	+	0.652883i
$937$	−0.473181	+	1.97094i	−0.0154582	+	0.0643879i	−0.979566	−	0.201123i	$-0.935541\pi$
$937$	−0.473181	+	1.97094i	−0.0154582	+	0.0643879i	0.964108	+	0.265511i	$0.0855408\pi$
$938$	−21.8355	+	32.6033i	−0.712955	+	1.06454i
$939$	40.5129	−	42.2210i	1.32209	−	1.37783i
$940$	87.8987	−	11.5721i	2.86694	−	0.377440i
$941$	14.4959	−	37.7632i	0.472554	−	1.23105i	−0.465652	−	0.884968i	$-0.654180\pi$
$941$	14.4959	−	37.7632i	0.472554	−	1.23105i	0.938206	−	0.346077i	$-0.112487\pi$
$942$	−2.49101	−	0.0790360i	−0.0811616	−	0.00257513i
$943$	10.2867	+	5.60005i	0.334981	+	0.182363i
$944$			181.502i			5.90739i
$945$	−26.7345	+	13.4675i	−0.869675	+	0.438096i
$946$	−124.757	−	51.6759i	−4.05619	−	1.68013i
$947$	23.2232	−	25.7920i	0.754652	−	0.838126i	−0.236392	−	0.971658i	$-0.575965\pi$
$947$	23.2232	−	25.7920i	0.754652	−	0.838126i	0.991045	+	0.133531i	$0.0426317\pi$
$948$	−78.5172	+	142.720i	−2.55012	+	4.63533i
$949$	−8.41402	+	8.86653i	−0.273131	+	0.287820i
$950$	0.104045	−	0.0987347i	0.00337566	−	0.00320338i
$951$	1.34222	−	1.92996i	0.0435246	−	0.0625833i
$952$	−135.299	+	19.4690i	−4.38506	+	0.630994i
$953$	−31.2629	−	10.1579i	−1.01271	−	0.329048i	−0.244774	−	0.969580i	$-0.578714\pi$
$953$	−31.2629	−	10.1579i	−1.01271	−	0.329048i	−0.767931	+	0.640532i	$0.778714\pi$
$954$	−12.2148	−	11.8513i	−0.395469	−	0.383699i
$955$	−17.2343	+	25.0761i	−0.557690	+	0.811445i
$956$	−1.13802	−	43.4591i	−0.0368061	−	1.40557i
$957$	8.55949	−	52.1709i	0.276689	−	1.68645i
$958$	−55.3816	+	47.3004i	−1.78930	+	1.52821i
$959$	−44.8913	−	0.635897i	−1.44962	−	0.0205342i
$960$	75.7597	+	118.086i	2.44513	+	3.81122i
$961$	−2.84211	+	27.0409i	−0.0916811	+	0.872287i
$962$	−14.6508	+	7.95472i	−0.472360	+	0.256471i
$963$	−12.4844	−	39.9223i	−0.402305	−	1.28648i
$964$	−29.5713	−	77.0359i	−0.952428	−	2.48116i
$965$	−23.2315	+	37.9103i	−0.747847	+	1.22038i
$966$	6.13783	+	22.3272i	0.197481	+	0.718365i
$967$	−13.5801	+	1.06878i	−0.436706	+	0.0343695i	−0.294907	−	0.955526i	$-0.595289\pi$
$967$	−13.5801	+	1.06878i	−0.436706	+	0.0343695i	−0.141799	+	0.989895i	$0.545289\pi$
$968$	132.567	+	59.0225i	4.26086	+	1.89706i
$969$	1.39777	−	1.11914i	0.0449029	−	0.0359518i
$970$	28.0942	+	3.69867i	0.902050	+	0.118757i
$971$	1.28871	−	2.37350i	0.0413566	−	0.0761693i	−0.857313	−	0.514795i	$-0.827868\pi$
$971$	1.28871	−	2.37350i	0.0413566	−	0.0761693i	0.898670	+	0.438626i	$0.144535\pi$
$972$	−63.5831	−	60.5208i	−2.03943	−	1.94120i
$973$	8.23051	−	7.59182i	0.263858	−	0.243383i
$974$	−14.6890	+	45.2081i	−0.470665	+	1.44856i
$975$	0.395863	+	1.69006i	0.0126778	+	0.0541254i
$976$	139.229	+	7.29666i	4.45660	+	0.233560i
$977$	0.152325	−	0.514241i	0.00487331	−	0.0164520i	−0.956348	−	0.292231i	$-0.905602\pi$
$977$	0.152325	−	0.514241i	0.00487331	−	0.0164520i	0.961221	+	0.275779i	$0.0889358\pi$
$978$	27.6778	−	27.3729i	0.885038	−	0.875290i
$979$	−32.8348	−	16.7302i	−1.04941	−	0.534699i
$980$	85.5812	−	6.55039i	2.73379	−	0.209245i
$981$	6.22562	+	9.27679i	0.198769	+	0.296185i
$982$	−46.5894	+	37.7273i	−1.48673	+	1.20393i
$983$	9.05924	−	15.6911i	0.288945	−	0.500467i	−0.684613	−	0.728906i	$-0.740029\pi$
$983$	9.05924	−	15.6911i	0.288945	−	0.500467i	0.973558	+	0.228439i	$0.0733622\pi$
$984$	104.619	+	37.8323i	3.33512	+	1.20605i
$985$	2.68391	+	4.64868i	0.0855166	+	0.148119i
$986$	−13.4627	−	85.0000i	−0.428739	−	2.70695i
$987$	33.1277	+	0.652771i	1.05447	+	0.0207779i
$988$	−4.16442	+	1.35310i	−0.132488	+	0.0430479i
$989$	0.927293	+	17.6938i	0.0294862	+	0.562630i
$990$	88.7786	−	20.2766i	2.82157	−	0.644433i
$991$	8.34029	−	28.1564i	0.264938	−	0.894416i	−0.715670	−	0.698438i	$-0.753879\pi$
$991$	8.34029	−	28.1564i	0.264938	−	0.894416i	0.980608	−	0.195978i	$-0.0627881\pi$
$992$	−26.9759	+	41.5393i	−0.856486	+	1.31887i
$993$	−2.60283	+	8.61159i	−0.0825983	+	0.273281i
$994$	69.3250	−	6.29498i	2.19886	−	0.199665i
$995$	−4.87523	+	5.70816i	−0.154555	+	0.180961i
$996$	−16.9630	−	12.4684i	−0.537493	−	0.395077i
$997$	−30.1308	+	0.789002i	−0.954252	+	0.0249880i	−0.500129	−	0.865951i	$-0.666714\pi$
$997$	−30.1308	+	0.789002i	−0.954252	+	0.0249880i	−0.454123	+	0.890939i	$0.650047\pi$
$998$	39.2442	+	5.16660i	1.24225	+	0.163546i
$999$	−7.33888	−	3.41468i	−0.232192	−	0.108036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.cl.a.11.108	yes	3456
3.2	odd	2	inner	861.2.cl.a.11.1	✓	3456
7.2	even	3	inner	861.2.cl.a.380.1	yes	3456
21.2	odd	6	inner	861.2.cl.a.380.108	yes	3456
41.15	odd	40	inner	861.2.cl.a.179.108	yes	3456
123.56	even	40	inner	861.2.cl.a.179.1	yes	3456
287.261	odd	120	inner	861.2.cl.a.548.1	yes	3456
861.548	even	120	inner	861.2.cl.a.548.108	yes	3456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.cl.a.11.1	✓	3456	3.2	odd	2	inner
861.2.cl.a.11.108	yes	3456	1.1	even	1	trivial
861.2.cl.a.179.1	yes	3456	123.56	even	40	inner
861.2.cl.a.179.108	yes	3456	41.15	odd	40	inner
861.2.cl.a.380.1	yes	3456	7.2	even	3	inner
861.2.cl.a.380.108	yes	3456	21.2	odd	6	inner
861.2.cl.a.548.1	yes	3456	287.261	odd	120	inner
861.2.cl.a.548.108	yes	3456	861.548	even	120	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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.cl (of order \(120\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14683 - 1.73847i) q^{2} +(-1.57838 - 0.713240i) q^{3} +(1.17079 - 5.50812i) q^{4} +(0.113959 + 2.17447i) q^{5} +(-4.62847 + 1.21276i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(-4.55397 - 8.93767i) q^{8} +(1.98258 + 2.25153i) q^{9} +O(q^{10})\)	\(q+(2.14683 - 1.73847i) q^{2} +(-1.57838 - 0.713240i) q^{3} +(1.17079 - 5.50812i) q^{4} +(0.113959 + 2.17447i) q^{5} +(-4.62847 + 1.21276i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(-4.55397 - 8.93767i) q^{8} +(1.98258 + 2.25153i) q^{9} +(4.02491 + 4.47011i) q^{10} +(-1.68453 - 4.75697i) q^{11} +(-5.77657 + 7.85887i) q^{12} +(-2.02418 - 3.30316i) q^{13} +(-5.10562 + 5.22981i) q^{14} +(1.37105 - 3.51343i) q^{15} +(-15.0258 - 6.68993i) q^{16} +(-2.21736 + 4.64879i) q^{17} +(8.17048 + 1.38701i) q^{18} +(0.200649 + 0.00525417i) q^{19} +(12.1107 + 1.91814i) q^{20} +(4.36737 + 1.38783i) q^{21} +(-11.8863 - 7.28391i) q^{22} +(-0.191198 + 1.81912i) q^{23} +(0.813197 + 17.3551i) q^{24} +(0.257271 - 0.0270403i) q^{25} +(-10.0880 - 3.57236i) q^{26} +(-1.52338 - 4.96783i) q^{27} +(-1.37919 + 14.8347i) q^{28} +(-6.02991 - 0.474564i) q^{29} +(-3.16458 - 9.92627i) q^{30} +(1.45059 - 1.30612i) q^{31} +(-24.5098 + 6.56739i) q^{32} +(-0.734029 + 8.70979i) q^{33} +(3.32149 + 13.8350i) q^{34} +(-0.969523 - 5.67884i) q^{35} +(14.7229 - 8.28421i) q^{36} +(1.04235 - 1.15765i) q^{37} +(0.439894 - 0.337542i) q^{38} +(0.838980 + 6.65738i) q^{39} +(18.9157 - 10.9210i) q^{40} +(2.45695 - 5.91298i) q^{41} +(11.7887 - 4.61310i) q^{42} +(9.56729 - 1.51531i) q^{43} +(-28.1742 + 3.70921i) q^{44} +(-4.66996 + 4.56764i) q^{45} +(2.75203 + 4.23775i) q^{46} +(6.93270 - 2.05356i) q^{47} +(18.9450 + 21.2763i) q^{48} +(6.81008 - 1.61949i) q^{49} +(0.505309 - 0.505309i) q^{50} +(6.81554 - 5.75605i) q^{51} +(-20.5641 + 7.28213i) q^{52} +(-1.69245 - 1.16319i) q^{53} +(-11.9069 - 8.01675i) q^{54} +(10.1519 - 4.20507i) q^{55} +(14.7208 + 22.0826i) q^{56} +(-0.312953 - 0.151404i) q^{57} +(-13.7702 + 9.46402i) q^{58} +(-4.48835 - 10.0810i) q^{59} +(-17.7472 - 11.6654i) q^{60} +(-7.91348 + 3.03770i) q^{61} +(0.843527 - 5.32582i) q^{62} +(-5.90352 - 5.30551i) q^{63} +(-21.8658 + 30.0956i) q^{64} +(6.95195 - 4.77795i) q^{65} +(13.5659 + 19.9746i) q^{66} +(5.27896 - 0.978398i) q^{67} +(23.0101 + 17.6562i) q^{68} +(1.59926 - 2.73490i) q^{69} +(-11.9539 - 10.5060i) q^{70} +(-7.24226 - 6.18547i) q^{71} +(11.0948 - 27.9730i) q^{72} +(-0.816627 - 3.04769i) q^{73} +(0.225216 - 4.29737i) q^{74} +(-0.425358 - 0.140816i) q^{75} +(0.263858 - 1.09905i) q^{76} +(5.89239 + 11.9810i) q^{77} +(13.3748 + 12.8337i) q^{78} +(16.5581 - 2.17991i) q^{79} +(12.8347 - 33.4356i) q^{80} +(-1.13878 + 8.92766i) q^{81} +(-5.00488 - 16.9655i) q^{82} +2.15845i q^{83} +(12.7576 - 22.4312i) q^{84} +(-10.3613 - 4.29181i) q^{85} +(17.9051 - 19.8856i) q^{86} +(9.17902 + 5.04982i) q^{87} +(-34.8449 + 36.7189i) q^{88} +(5.29703 - 5.02669i) q^{89} +(-2.08491 + 17.9245i) q^{90} +(6.33690 + 8.05611i) q^{91} +(9.79611 + 3.18295i) q^{92} +(-3.22116 + 1.02693i) q^{93} +(11.3133 - 16.4610i) q^{94} +(0.0114407 + 0.436904i) q^{95} +(43.3700 + 7.11555i) q^{96} +(3.58219 - 3.05948i) q^{97} +(11.8047 - 15.3159i) q^{98} +(7.37075 - 13.2238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9}+O(q^{10}) \) 3456 * q - 16 * q^3 - 40 * q^4 - 64 * q^6 - 64 * q^7 - 8 * q^9	\( 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9} - 24 q^{10} + 8 q^{12} - 128 q^{13} - 40 q^{15} - 408 q^{16} - 12 q^{18} - 32 q^{19} - 24 q^{21} - 48 q^{22} - 56 q^{24} - 40 q^{25} - 64 q^{27} - 32 q^{28} - 8 q^{30} - 40 q^{31} - 92 q^{33} - 128 q^{34} + 32 q^{36} - 24 q^{37} - 16 q^{39} - 192 q^{42} - 96 q^{43} - 20 q^{45} - 40 q^{46} + 104 q^{48} - 112 q^{49} + 24 q^{51} - 8 q^{52} - 136 q^{54} - 96 q^{55} - 64 q^{57} - 32 q^{58} - 48 q^{60} + 28 q^{63} - 160 q^{64} - 20 q^{66} - 16 q^{67} - 88 q^{69} - 184 q^{70} - 20 q^{72} - 32 q^{73} - 20 q^{75} - 640 q^{76} + 64 q^{78} - 16 q^{79} + 160 q^{82} + 32 q^{84} - 192 q^{85} - 36 q^{87} - 64 q^{88} - 112 q^{90} - 80 q^{91} + 48 q^{93} - 32 q^{94} + 96 q^{96} - 256 q^{97} - 192 q^{99}+O(q^{100}) \) 3456 * q - 16 * q^3 - 40 * q^4 - 64 * q^6 - 64 * q^7 - 8 * q^9 - 24 * q^10 + 8 * q^12 - 128 * q^13 - 40 * q^15 - 408 * q^16 - 12 * q^18 - 32 * q^19 - 24 * q^21 - 48 * q^22 - 56 * q^24 - 40 * q^25 - 64 * q^27 - 32 * q^28 - 8 * q^30 - 40 * q^31 - 92 * q^33 - 128 * q^34 + 32 * q^36 - 24 * q^37 - 16 * q^39 - 192 * q^42 - 96 * q^43 - 20 * q^45 - 40 * q^46 + 104 * q^48 - 112 * q^49 + 24 * q^51 - 8 * q^52 - 136 * q^54 - 96 * q^55 - 64 * q^57 - 32 * q^58 - 48 * q^60 + 28 * q^63 - 160 * q^64 - 20 * q^66 - 16 * q^67 - 88 * q^69 - 184 * q^70 - 20 * q^72 - 32 * q^73 - 20 * q^75 - 640 * q^76 + 64 * q^78 - 16 * q^79 + 160 * q^82 + 32 * q^84 - 192 * q^85 - 36 * q^87 - 64 * q^88 - 112 * q^90 - 80 * q^91 + 48 * q^93 - 32 * q^94 + 96 * q^96 - 256 * q^97 - 192 * q^99

Introduction

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