LMFDB - Embedded newform 861.2.cl.a.548.108

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			548.108
Character	$\chi$	$=$	861.548
Dual form			861.2.cl.a.11.108

$q$-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 $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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	0.894145	+	0.447777i	$0.147784\pi$
$2$	2.14683	+	1.73847i	1.51804	+	1.22929i	0.623896	+	0.781508i	$0.285549\pi$
$3$	−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	−0.846782	−	0.531940i	$-0.821463\pi$
$5$	0.113959	−	2.17447i	0.0509641	−	0.972453i	0.897746	−	0.440513i	$-0.145203\pi$
$6$	−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	0.357834	+	0.933785i	$0.383515\pi$
$11$	−1.68453	+	4.75697i	−0.507905	+	1.43428i	−0.865739	+	0.500495i	$0.833151\pi$
$12$	−5.77657	−	7.85887i	−1.66755	−	2.26866i
$13$	−2.02418	+	3.30316i	−0.561406	+	0.916132i	0.438443	+	0.898759i	$0.355530\pi$
$13$	−2.02418	+	3.30316i	−0.561406	+	0.916132i	−0.999849	+	0.0173729i	$0.994470\pi$
$14$	−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	−0.973769	−	0.227541i	$-0.926931\pi$
$17$	−2.21736	−	4.64879i	−0.537789	−	1.12750i	0.435980	−	0.899956i	$-0.356402\pi$
$18$	8.17048	−	1.38701i	1.92580	−	0.326921i
$19$	0.200649	−	0.00525417i	0.0460320	−	0.00120539i	−0.00315402	−	0.999995i	$-0.501004\pi$
$19$	0.200649	−	0.00525417i	0.0460320	−	0.00120539i	0.0491860	+	0.998790i	$0.484337\pi$
$20$	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	−0.996204	−	0.0870466i	$-0.972257\pi$
$23$	−0.191198	−	1.81912i	−0.0398675	−	0.379314i	0.956337	−	0.292267i	$-0.0944096\pi$
$24$	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	−0.624781	−	0.780800i	$-0.714812\pi$
$29$	−6.02991	+	0.474564i	−1.11973	+	0.0881244i	−0.494945	+	0.868924i	$0.664812\pi$
$30$	−3.16458	+	9.92627i	−0.577770	+	1.81228i
$31$	1.45059	+	1.30612i	0.260533	+	0.234585i	0.789037	−	0.614346i	$-0.210580\pi$
$31$	1.45059	+	1.30612i	0.260533	+	0.234585i	−0.528504	+	0.848931i	$0.677247\pi$
$32$	−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	0.822708	−	0.568464i	$-0.192462\pi$
$37$	1.04235	+	1.15765i	0.171361	+	0.190316i	−0.651347	+	0.758780i	$0.725796\pi$
$38$	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	0.834960	−	0.550311i	$-0.185491\pi$
$43$	9.56729	+	1.51531i	1.45900	+	0.231083i	0.624038	+	0.781394i	$0.285491\pi$
$44$	−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	0.746935	−	0.664897i	$-0.231525\pi$
$47$	6.93270	+	2.05356i	1.01124	+	0.299542i	0.264303	+	0.964440i	$0.414858\pi$
$48$	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	−0.676982	−	0.735999i	$-0.736713\pi$
$53$	−1.69245	+	1.16319i	−0.232476	+	0.159777i	0.444506	+	0.895776i	$0.353379\pi$
$54$	−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	0.343400	+	0.939189i	$0.388421\pi$
$59$	−4.48835	+	10.0810i	−0.584333	+	1.31243i	−0.927733	+	0.373244i	$0.878245\pi$
$60$	−17.7472	+	11.6654i	−2.29115	+	1.50599i
$61$	−7.91348	−	3.03770i	−1.01322	−	0.388938i	−0.205595	−	0.978637i	$-0.565913\pi$
$61$	−7.91348	−	3.03770i	−1.01322	−	0.388938i	−0.807623	+	0.589700i	$0.799246\pi$
$62$	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	0.494621	−	0.869109i	$-0.335307\pi$
$67$	5.27896	+	0.978398i	0.644928	+	0.119530i	0.150307	+	0.988639i	$0.451974\pi$
$68$	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	−0.965533	−	0.260282i	$-0.916184\pi$
$71$	−7.24226	+	6.18547i	−0.859498	+	0.734080i	0.106035	+	0.994362i	$0.466184\pi$
$72$	11.0948	+	27.9730i	1.30754	+	3.29665i
$73$	−0.816627	+	3.04769i	−0.0955790	+	0.356706i	−0.997107	−	0.0760160i	$-0.975780\pi$
$73$	−0.816627	+	3.04769i	−0.0955790	+	0.356706i	0.901528	+	0.432722i	$0.142447\pi$
$74$	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	0.976175	−	0.216983i	$-0.0696217\pi$
$79$	16.5581	+	2.17991i	1.86293	+	0.245259i	0.886754	+	0.462242i	$0.152955\pi$
$80$	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	$-0.962204\pi$
$83$		−	2.15845i		−	0.236921i	0.992959	−	0.118460i	$-0.0377959\pi$
$84$	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	0.915451	−	0.402430i	$-0.131834\pi$
$89$	5.29703	+	5.02669i	0.561484	+	0.532828i	−0.353967	+	0.935258i	$0.615168\pi$
$90$	−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	0.812459	−	0.583018i	$-0.198128\pi$
$97$	3.58219	+	3.05948i	0.363716	+	0.310643i	−0.448743	+	0.893661i	$0.648128\pi$
$98$	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	−0.341968	−	0.939712i	$-0.611093\pi$
$101$	−13.2289	−	7.18271i	−1.31633	−	0.714706i	−0.974357	+	0.225006i	$0.927760\pi$
$102$	4.62510	+	24.2059i	0.457953	+	2.39674i
$103$	0.737370	−	1.92092i	0.0726553	−	0.189273i	−0.892444	−	0.451159i	$-0.851011\pi$
$103$	0.737370	−	1.92092i	0.0726553	−	0.189273i	0.965099	+	0.261885i	$0.0843442\pi$
$104$	−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	−0.916176	−	0.400776i	$-0.868741\pi$
$107$	−12.7375	+	5.67111i	−1.23138	+	0.548247i	−0.315207	+	0.949023i	$0.602074\pi$
$108$	−29.1470	−	2.57469i	−2.80467	−	0.247750i
$109$	3.69219	−	0.486086i	0.353648	−	0.0465586i	0.0483905	−	0.998828i	$-0.484591\pi$
$109$	3.69219	−	0.486086i	0.353648	−	0.0465586i	0.305257	+	0.952270i	$0.401257\pi$
$110$	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	0.906406	−	0.422408i	$-0.138815\pi$
$113$	−0.799144	−	2.45951i	−0.0751771	−	0.231371i	−0.981583	+	0.191037i	$0.938815\pi$
$114$	−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	0.398440	−	0.917194i	$-0.369552\pi$
$127$	2.04733	+	0.665218i	0.181671	+	0.0590286i	−0.216769	+	0.976223i	$0.569552\pi$
$128$	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	0.852129	−	0.523331i	$-0.175311\pi$
$131$	0.314184	+	0.483801i	0.0274504	+	0.0422699i	−0.824679	+	0.565601i	$0.808644\pi$
$132$	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	0.628763	−	0.777597i	$-0.283562\pi$
$137$	16.8239	−	2.21490i	1.43736	−	0.189232i	0.808595	+	0.588365i	$0.200228\pi$
$138$	−1.32121	+	8.65164i	−0.112469	+	0.736476i
$139$	−3.42387	−	2.48759i	−0.290409	−	0.210995i	0.433036	−	0.901377i	$-0.357442\pi$
$139$	−3.42387	−	2.48759i	−0.290409	−	0.210995i	−0.723445	+	0.690382i	$0.757442\pi$
$140$	−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	−0.947566	−	0.319559i	$-0.896465\pi$
$149$	−18.1006	+	6.40976i	−1.48286	+	0.525108i	−0.535292	+	0.844667i	$0.679799\pi$
$150$	−1.15798	−	0.437164i	−0.0945485	−	0.0356943i
$151$	−0.442687	+	16.9055i	−0.0360254	+	1.37575i	0.707343	+	0.706871i	$0.249894\pi$
$151$	−0.442687	+	16.9055i	−0.0360254	+	1.37575i	−0.743368	+	0.668883i	$0.766773\pi$
$152$	−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	−0.264025	−	0.964516i	$-0.585050\pi$
$157$	0.499431	−	0.147938i	0.0398589	−	0.0118067i	0.303883	+	0.952709i	$0.401717\pi$
$158$	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	0.198007	−	0.980201i	$-0.436553\pi$
$163$	−7.04578	−	4.06788i	−0.551868	−	0.318621i	−0.749875	+	0.661580i	$0.769886\pi$
$164$	−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	0.944551	−	0.328365i	$-0.106498\pi$
$167$	0.574594	+	1.38719i	0.0444634	+	0.107344i	−0.900087	+	0.435709i	$0.856498\pi$
$168$	−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	−0.0285511	−	0.999592i	$-0.509089\pi$
$173$	5.87304	−	1.57368i	0.446519	−	0.119644i	0.475070	+	0.879948i	$0.342423\pi$
$174$	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	−0.202599	−	0.979262i	$-0.564939\pi$
$179$	−9.93636	−	1.84160i	−0.742678	−	0.137647i	−0.540079	+	0.841614i	$0.681606\pi$
$180$	19.6916	−	31.0704i	1.46772	−	2.31585i
$181$	−0.330791	+	4.20310i	−0.0245875	+	0.312414i	0.972309	+	0.233697i	$0.0750824\pi$
$181$	−0.330791	+	4.20310i	−0.0245875	+	0.312414i	−0.996897	+	0.0787171i	$0.974918\pi$
$182$	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	−0.124149	−	0.992264i	$-0.539620\pi$
$191$	11.0862	−	8.50677i	0.802172	−	0.615528i	0.926321	+	0.376735i	$0.122953\pi$
$192$	55.9779	+	31.9069i	4.03986	+	2.30268i
$193$	16.8281	−	11.5657i	1.21132	−	0.832514i	0.221541	−	0.975151i	$-0.428891\pi$
$193$	16.8281	−	11.5657i	1.21132	−	0.832514i	0.989775	+	0.142637i	$0.0455581\pi$
$194$	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	0.530483	−	0.847695i	$-0.322010\pi$
$197$	2.19649	+	1.11917i	0.156494	+	0.0797376i	−0.373990	+	0.927433i	$0.622010\pi$
$198$	−7.16548	+	41.2032i	−0.509229	+	2.92818i
$199$	2.50071	−	2.37308i	0.177271	−	0.168224i	−0.594561	−	0.804050i	$-0.702674\pi$
$199$	2.50071	−	2.37308i	0.177271	−	0.168224i	0.771832	+	0.635827i	$0.219341\pi$
$200$	−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	−0.174078	−	0.984732i	$-0.555694\pi$
$211$	1.71225	−	0.411075i	0.117876	−	0.0282996i	0.291954	+	0.956432i	$0.405694\pi$
$212$	−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	−0.550578	−	0.834783i	$-0.685593\pi$
$223$	1.09326	−	0.794297i	0.0732098	−	0.0531900i	0.623788	+	0.781593i	$0.285593\pi$
$224$	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	−0.751654	−	0.659557i	$-0.770744\pi$
$227$	3.17718	−	5.85165i	0.210877	−	0.388387i	0.962532	+	0.271170i	$0.0874105\pi$
$228$	−1.20035	−	1.54652i	−0.0794953	−	0.102421i
$229$	−6.66064	+	9.69129i	−0.440147	+	0.640418i	−0.979448	−	0.201695i	$-0.935355\pi$
$229$	−6.66064	+	9.69129i	−0.440147	+	0.640418i	0.539301	+	0.842113i	$0.318689\pi$
$230$	−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	−0.922992	−	0.384819i	$-0.874264\pi$
$233$	−11.3419	−	20.8891i	−0.743031	−	1.36849i	0.179962	−	0.983674i	$-0.442403\pi$
$234$	−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	0.468843	−	0.883282i	$-0.344671\pi$
$239$	7.50693	+	1.80225i	0.485583	+	0.116578i	0.0167403	+	0.999860i	$0.494671\pi$
$240$	−44.1057	−	43.6199i	−2.84701	−	2.81565i
$241$	12.2895	+	7.98089i	0.791635	+	0.514094i	0.875983	−	0.482342i	$-0.160214\pi$
$241$	12.2895	+	7.98089i	0.791635	+	0.514094i	−0.0843473	+	0.996436i	$0.526881\pi$
$242$	−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	−0.0186286	−	0.999826i	$-0.505930\pi$
$251$	12.3464	−	6.29081i	0.779298	−	0.397072i	0.797927	+	0.602754i	$0.205930\pi$
$252$	−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	−0.0625565	−	0.998041i	$-0.519925\pi$
$257$	3.79472	−	0.703309i	0.236708	−	0.0438712i	0.299265	+	0.954170i	$0.403259\pi$
$258$	−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	0.880395	−	0.474241i	$-0.157278\pi$
$263$	−0.684533	−	1.43515i	−0.0422101	−	0.0884953i	−0.922605	+	0.385746i	$0.873944\pi$
$264$	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	0.359116	−	0.933293i	$-0.383078\pi$
$269$	−1.54434	−	0.687582i	−0.0941598	−	0.0419226i	−0.453276	+	0.891370i	$0.649745\pi$
$270$	16.0753	+	26.8047i	0.978311	+	1.63128i
$271$	7.86592	+	17.6671i	0.477820	+	1.07320i	0.978251	+	0.207425i	$0.0665085\pi$
$271$	7.86592	+	17.6671i	0.477820	+	1.07320i	−0.500430	+	0.865777i	$0.666825\pi$
$272$	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	0.974582	−	0.224033i	$-0.0719223\pi$
$277$	14.2075	+	12.7925i	0.853648	+	0.768628i	−0.120934	+	0.992661i	$0.538589\pi$
$278$	−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	0.281680	−	0.959508i	$-0.409108\pi$
$281$	16.2311	−	3.89674i	0.968266	−	0.232460i	0.686586	+	0.727048i	$0.259108\pi$
$282$	−29.5973	−	17.9126i	−1.76249	−	1.06668i
$283$	−10.5631	+	2.24526i	−0.627912	+	0.133467i	−0.510867	−	0.859660i	$-0.670675\pi$
$283$	−10.5631	+	2.24526i	−0.627912	+	0.133467i	−0.117045	+	0.993127i	$0.537342\pi$
$284$	−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	−0.983832	−	0.179093i	$-0.942684\pi$
$293$	−3.22725	−	13.4424i	−0.188538	−	0.785316i	0.795294	−	0.606223i	$-0.207316\pi$
$294$	−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	0.999241	+	0.0389540i	$0.0124026\pi$
$307$	1.06782	+	6.74196i	0.0609438	+	0.384784i	−0.938297	+	0.345830i	$0.887597\pi$
$308$	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	−0.859928	−	0.510415i	$-0.829492\pi$
$311$	−17.7134	+	8.44884i	−1.00443	+	0.479089i	−0.144504	+	0.989504i	$0.546159\pi$
$312$	55.6807	+	37.8160i	3.15230	+	2.14091i
$313$	−11.2771	−	31.8454i	−0.637417	−	1.80001i	−0.599002	−	0.800747i	$-0.704436\pi$
$313$	−11.2771	−	31.8454i	−0.637417	−	1.80001i	−0.0384146	−	0.999262i	$-0.512231\pi$
$314$	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	0.975594	−	0.219580i	$-0.0704687\pi$
$317$	−0.247338	−	1.33451i	−0.0138919	−	0.0749538i	−0.989486	+	0.144626i	$0.953802\pi$
$318$	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	0.962660	+	0.270714i	$0.0872596\pi$
$331$	−0.677959	+	5.14961i	−0.0372640	+	0.283048i	−0.999924	+	0.0123345i	$0.996074\pi$
$332$	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	−0.321501	−	0.946909i	$-0.604187\pi$
$337$	11.4810	−	11.4810i	0.625409	−	0.625409i	0.946909	+	0.321501i	$0.104187\pi$
$338$	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	0.710310	−	0.703889i	$-0.248555\pi$
$347$	9.44140	+	5.12626i	0.506841	+	0.275192i	−0.203469	+	0.979081i	$0.565222\pi$
$348$	38.5617	+	44.6469i	2.06712	+	2.39333i
$349$	31.4743	−	4.98503i	1.68478	−	0.266843i	0.760716	−	0.649085i	$-0.224848\pi$
$349$	31.4743	−	4.98503i	1.68478	−	0.266843i	0.924062	+	0.382242i	$0.124848\pi$
$350$	−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	0.963138	+	0.269008i	$0.0866957\pi$
$353$	−0.655392	+	6.23564i	−0.0348830	+	0.331889i	−0.998021	+	0.0628816i	$0.979971\pi$
$354$	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	0.157961	−	0.987445i	$-0.449508\pi$
$359$	−1.88270	−	0.400181i	−0.0993653	−	0.0211208i	−0.257326	+	0.966325i	$0.582841\pi$
$360$	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	−0.731755	−	0.681568i	$-0.761298\pi$
$367$	−15.6993	+	6.02639i	−0.819496	+	0.314575i	−0.0877414	+	0.996143i	$0.527965\pi$
$368$	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	−0.719222	−	0.694781i	$-0.755501\pi$
$373$	−1.99749	+	1.79855i	−0.103426	+	0.0931251i	0.615796	+	0.787906i	$0.288835\pi$
$374$	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	−0.995473	−	0.0950449i	$-0.969701\pi$
$379$	−4.78881	−	14.7384i	−0.245984	−	0.757062i	0.749489	−	0.662017i	$-0.230299\pi$
$380$	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	−0.897065	−	0.441898i	$-0.854305\pi$
$383$	−21.3655	−	27.8441i	−1.09173	−	1.42277i	−0.194663	−	0.980870i	$-0.562361\pi$
$384$	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	0.759983	−	0.649943i	$-0.225207\pi$
$389$	−0.665984	−	0.822422i	−0.0337667	−	0.0416984i	−0.793750	+	0.608245i	$0.791874\pi$
$390$	−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	−0.559848	−	0.828595i	$-0.689140\pi$
$397$	−3.38412	+	1.83743i	−0.169844	+	0.0922178i	0.390004	+	0.920813i	$0.372474\pi$
$398$	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	0.885134	+	0.465337i	$0.154067\pi$
$401$	7.03385	+	26.2507i	0.351254	+	1.31090i	−0.533880	+	0.845560i	$0.679267\pi$
$402$	−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	−0.949843	−	0.312728i	$-0.898757\pi$
$409$	−23.3369	+	13.4735i	−1.15393	+	0.666224i	−0.204091	+	0.978952i	$0.565424\pi$
$410$	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	0.602801	−	0.797892i	$-0.294051\pi$
$419$	−3.99342	−	3.99342i	−0.195091	−	0.195091i	−0.797892	+	0.602801i	$0.794051\pi$
$420$	50.2298	−	25.1848i	2.45096	−	1.22889i
$421$	10.1215	−	8.64454i	0.493289	−	0.421309i	−0.367690	−	0.929948i	$-0.619851\pi$
$421$	10.1215	−	8.64454i	0.493289	−	0.421309i	0.860980	+	0.508639i	$0.169851\pi$
$422$	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	−0.575007	−	0.818148i	$-0.695001\pi$
$431$	2.19464	−	1.77718i	0.105712	−	0.0856040i	0.680719	+	0.732544i	$0.261667\pi$
$432$	−10.3444	−	84.8370i	−0.497694	−	4.08172i
$433$	5.81204	+	7.99958i	0.279309	+	0.384435i	0.925505	−	0.378736i	$-0.123641\pi$
$433$	5.81204	+	7.99958i	0.279309	+	0.384435i	−0.646196	+	0.763171i	$0.723641\pi$
$434$	−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	−0.338647	−	0.940914i	$-0.609969\pi$
$439$	−26.8816	−	12.8219i	−1.28299	−	0.611955i	−0.944344	+	0.328958i	$0.893302\pi$
$440$	−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	−0.782279	−	0.622928i	$-0.785943\pi$
$443$	−11.1844	+	7.26325i	−0.531388	+	0.345087i	0.250891	+	0.968015i	$0.419276\pi$
$444$	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	0.761246	−	0.648463i	$-0.224588\pi$
$449$	27.2254	+	4.31209i	1.28485	+	0.203500i	0.523602	+	0.851963i	$0.324588\pi$
$450$	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	0.746251	+	0.665664i	$0.231852\pi$
$457$	−5.17667	+	17.4762i	−0.242154	+	0.817500i	−0.988406	+	0.151836i	$0.951482\pi$
$458$	−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	−0.277803	−	0.960638i	$-0.589606\pi$
$461$	1.33331	−	0.433220i	0.0620986	−	0.0201771i	0.339902	+	0.940461i	$0.389606\pi$
$462$	−41.8029	+	48.3077i	−1.94485	+	2.24748i
$463$	18.6692	−	1.46930i	0.867632	−	0.0682841i	0.363175	−	0.931721i	$-0.381693\pi$
$463$	18.6692	−	1.46930i	0.867632	−	0.0682841i	0.504457	+	0.863437i	$0.331693\pi$
$464$	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	0.724520	+	0.689254i	$0.242062\pi$
$467$	16.2495	+	36.4970i	0.751937	+	1.68888i	0.0274174	+	0.999624i	$0.491272\pi$
$468$	−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	−0.581217	−	0.813749i	$-0.697423\pi$
$479$	−26.3558	−	0.690150i	−1.20423	−	0.0315337i	−0.623009	+	0.782215i	$0.714090\pi$
$480$	−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	0.174570	−	0.984645i	$-0.444147\pi$
$487$	−14.4313	−	9.37179i	−0.653944	−	0.424676i	−0.828514	+	0.559969i	$0.810813\pi$
$488$	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	−0.466283	−	0.884635i	$-0.654407\pi$
$499$	9.86333	−	10.3938i	0.441543	−	0.465289i	0.907826	+	0.419346i	$0.137741\pi$
$500$	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	−0.995930	−	0.0901267i	$-0.971273\pi$
$503$	−20.8387	−	24.3989i	−0.929150	−	1.08789i	0.0667808	−	0.997768i	$-0.478727\pi$
$504$	−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	−0.0617006	+	0.998095i	$0.519652\pi$
$509$	−21.9156	+	31.8874i	−0.971391	+	1.41338i	−0.909690	+	0.415288i	$0.863681\pi$
$510$	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	−0.999867	−	0.0163362i	$-0.994800\pi$
$521$	−14.9917	−	21.8130i	−0.656798	−	0.955646i	0.343069	−	0.939310i	$-0.388534\pi$
$522$	−48.6091	+	12.2410i	−2.12756	+	0.535772i
$523$	−2.05384	+	9.66256i	−0.0898082	+	0.422514i	0.910158	+	0.414262i	$0.135960\pi$
$523$	−2.05384	+	9.66256i	−0.0898082	+	0.422514i	−0.999966	+	0.00825252i	$0.997373\pi$
$524$	−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	−0.785550	−	0.618798i	$-0.787620\pi$
$541$	−12.5545	+	8.15301i	−0.539761	+	0.350525i	0.245788	+	0.969323i	$0.420953\pi$
$542$	−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	0.824877	−	0.565313i	$-0.191245\pi$
$547$	23.5849	+	9.76917i	1.00842	+	0.417700i	0.183539	+	0.983012i	$0.441245\pi$
$548$	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	0.0460705	−	0.998938i	$-0.485330\pi$
$557$	20.0934	−	9.58406i	0.851384	−	0.406089i	0.805314	+	0.592849i	$0.201997\pi$
$558$	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	0.826785	−	0.562518i	$-0.190167\pi$
$563$	26.4637	+	9.37130i	1.11531	+	0.394953i	0.288528	+	0.957471i	$0.406834\pi$
$564$	−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	0.737582	−	0.675258i	$-0.235968\pi$
$569$	33.4081	+	1.75084i	1.40054	+	0.0733992i	0.662958	+	0.748657i	$0.269301\pi$
$570$	−0.582814	+	2.00832i	−0.0244114	+	0.0841193i
$571$	−22.6208	+	29.4800i	−0.946651	+	1.23370i	0.0255793	+	0.999673i	$0.491857\pi$
$571$	−22.6208	+	29.4800i	−0.946651	+	1.23370i	−0.972230	+	0.234027i	$0.924810\pi$
$572$	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	0.769730	−	0.638369i	$-0.220391\pi$
$577$	8.46334	+	6.49415i	0.352333	+	0.270355i	−0.417397	+	0.908724i	$0.637057\pi$
$578$	−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	0.998385	+	0.0568062i	$0.0180917\pi$
$587$	36.3968	+	22.3040i	1.50226	+	0.920584i	0.503872	+	0.863778i	$0.331908\pi$
$588$	−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	0.733853	+	0.679308i	$0.237720\pi$
$593$	0.890245	+	33.9971i	0.0365580	+	1.39609i	−0.697295	+	0.716784i	$0.745613\pi$
$594$	−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	0.868500	+	0.495690i	$0.165085\pi$
$599$	−2.05784	+	19.5790i	−0.0840809	+	0.799976i	−0.952581	+	0.304286i	$0.901582\pi$
$600$	0.678500	−	4.44298i	0.0276996	−	0.181384i
$601$	10.8285	−	26.1422i	0.441702	−	1.06636i	−0.533649	−	0.845706i	$-0.679180\pi$
$601$	10.8285	−	26.1422i	0.441702	−	1.06636i	0.975351	−	0.220658i	$-0.0708204\pi$
$602$	−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	0.777291	−	0.629141i	$-0.216593\pi$
$607$	−2.79906	−	4.31018i	−0.113610	−	0.174945i	−0.890902	+	0.454196i	$0.849927\pi$
$608$	−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	−0.171707	−	0.985148i	$-0.554928\pi$
$613$	8.91029	−	3.42034i	0.359883	−	0.138146i	0.531590	+	0.847002i	$0.321595\pi$
$614$	−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	−0.543616	−	0.839334i	$-0.682945\pi$
$617$	5.78169	−	36.5041i	0.232762	−	1.46960i	0.776378	−	0.630267i	$-0.217055\pi$
$618$	−5.74251	+	7.99665i	−0.230998	+	0.321672i
$619$	−3.48093	−	16.3765i	−0.139911	−	0.658227i	−0.991072	−	0.133324i	$-0.957435\pi$
$619$	−3.48093	−	16.3765i	−0.139911	−	0.658227i	0.851162	−	0.524903i	$-0.175898\pi$
$620$	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	−0.232645	−	0.972562i	$-0.574738\pi$
$631$	−30.8846	−	22.4390i	−1.22950	−	0.893282i	−0.996852	+	0.0792795i	$0.974738\pi$
$632$	−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	−0.914007	−	0.405698i	$-0.867028\pi$
$641$	2.14396	−	11.5678i	0.0846813	−	0.456899i	0.998688	−	0.0512010i	$-0.0163049\pi$
$642$	65.8330	−	10.8010i	2.59822	−	0.426280i
$643$	33.3008	+	20.4067i	1.31325	+	0.804763i	0.989935	−	0.141526i	$-0.0452010\pi$
$643$	33.3008	+	20.4067i	1.31325	+	0.804763i	0.323320	+	0.946290i	$0.395201\pi$
$644$	−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	0.642585	−	0.766214i	$-0.277862\pi$
$647$	20.7552	+	5.56135i	0.815973	+	0.218639i	0.173388	+	0.984854i	$0.444529\pi$
$648$	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	−0.410176	−	0.912006i	$-0.634533\pi$
$653$	5.67470	−	43.1036i	0.222068	−	1.68678i	0.632244	−	0.774769i	$-0.282134\pi$
$654$	−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	−0.995282	−	0.0970231i	$-0.969068\pi$
$659$	−9.24456	−	22.3184i	−0.360117	−	0.869400i	0.635165	−	0.772376i	$-0.280932\pi$
$660$	−25.5962	−	104.074i	−0.996331	−	4.05106i
$661$	24.0308	−	37.0041i	0.934688	−	1.43929i	0.0366734	−	0.999327i	$-0.488324\pi$
$661$	24.0308	−	37.0041i	0.934688	−	1.43929i	0.898015	−	0.439966i	$-0.145009\pi$
$662$	−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	0.754865	+	0.655880i	$0.227702\pi$
$673$	−2.42063	+	30.7571i	−0.0933086	+	1.18560i	−0.848174	+	0.529718i	$0.822298\pi$
$674$	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	−0.108914	−	0.994051i	$-0.534737\pi$
$677$	−22.2465	−	8.53963i	−0.855002	−	0.328205i	−0.746089	+	0.665847i	$0.768071\pi$
$678$	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	−0.996337	−	0.0855128i	$-0.972747\pi$
$683$	−1.46565	−	11.1328i	−0.0560817	−	0.425983i	0.940255	−	0.340470i	$-0.110586\pi$
$684$	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	0.0960072	−	0.995381i	$-0.469393\pi$
$691$	−9.61042	−	2.84674i	−0.365598	−	0.108295i	−0.461605	+	0.887086i	$0.652726\pi$
$692$	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	0.0899951	+	0.995942i	$0.471315\pi$
$701$	−15.0442	+	46.3014i	−0.568213	+	1.74878i	−0.658208	+	0.752836i	$0.728685\pi$
$702$	−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	−0.978751	−	0.205052i	$-0.934264\pi$
$709$	−5.41721	+	11.3574i	−0.203448	+	0.426537i	0.775304	+	0.631589i	$0.217597\pi$
$710$	−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	0.106622	−	0.994300i	$-0.465996\pi$
$719$	7.10941	−	0.186167i	0.265136	−	0.00694284i	0.158514	+	0.987357i	$0.449330\pi$
$720$	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	0.997346	+	0.0728076i	$0.0231959\pi$
$727$	24.6236	+	28.8305i	0.913238	+	1.06926i	−0.0841080	+	0.996457i	$0.526804\pi$
$728$	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	0.932756	+	0.360508i	$0.117397\pi$
$733$	−0.881898	+	16.8276i	−0.0325736	+	0.621542i	−0.965330	+	0.261034i	$0.915937\pi$
$734$	−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	0.796856	−	0.604169i	$-0.206495\pi$
$739$	−3.39256	−	5.87609i	−0.124797	−	0.216155i	−0.921654	+	0.388013i	$0.873161\pi$
$740$	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	−0.750531	−	0.660835i	$-0.770202\pi$
$743$	−17.9100	+	9.12562i	−0.657055	+	0.334786i	0.0934757	+	0.995622i	$0.470202\pi$
$744$	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	0.892225	+	0.451592i	$0.149144\pi$
$751$	21.5130	+	39.6220i	0.785021	+	1.44583i	−0.107204	+	0.994237i	$0.534190\pi$
$752$	−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	0.679844	−	0.733357i	$-0.262048\pi$
$757$	−7.76503	−	12.6714i	−0.282225	−	0.460549i	−0.962069	+	0.272808i	$0.912048\pi$
$758$	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	0.995565	+	0.0940775i	$0.0299902\pi$
$761$	1.13973	+	10.8438i	0.0413153	+	0.393089i	−0.954250	+	0.299011i	$0.903343\pi$
$762$	−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	0.470616	−	0.882338i	$-0.344032\pi$
$769$	37.9907	−	12.3439i	1.36998	−	0.445133i	0.899362	+	0.437205i	$0.144032\pi$
$770$	−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	0.754492	−	0.656309i	$-0.227883\pi$
$773$	1.65694	+	1.74605i	0.0595961	+	0.0628011i	−0.694896	+	0.719110i	$0.744550\pi$
$774$	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	−0.986206	−	0.165525i	$-0.947068\pi$
$787$	−0.636944	−	12.1536i	−0.0227046	−	0.433230i	0.963501	−	0.267705i	$-0.0862652\pi$
$788$	−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	0.943906	−	0.330214i	$-0.107121\pi$
$797$	9.54696	+	13.1403i	0.338171	+	0.465452i	−0.605735	+	0.795666i	$0.707121\pi$
$798$	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	0.852075	−	0.523419i	$-0.175344\pi$
$809$	33.7010	+	11.9341i	1.18486	+	0.419582i	0.332788	+	0.943002i	$0.392011\pi$
$810$	−44.4912	−	30.8426i	−1.56326	−	1.08370i
$811$	24.8123	+	24.8123i	0.871278	+	0.871278i	0.992612	−	0.121333i	$-0.0387170\pi$
$811$	24.8123	+	24.8123i	0.871278	+	0.871278i	−0.121333	+	0.992612i	$0.538717\pi$
$812$	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	0.263487	−	0.964663i	$-0.415127\pi$
$821$	−12.6129	−	7.28203i	−0.440192	−	0.254145i	−0.703679	+	0.710518i	$0.748461\pi$
$822$	−80.5549	−	10.1517i	−2.80967	−	0.354083i
$823$	−18.0570	−	13.8556i	−0.629428	−	0.482977i	0.244101	−	0.969750i	$-0.421507\pi$
$823$	−18.0570	−	13.8556i	−0.629428	−	0.482977i	−0.873528	+	0.486773i	$0.838174\pi$
$824$	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	0.719916	+	0.694062i	$0.244181\pi$
$827$	−6.80495	+	28.3447i	−0.236631	+	0.985640i	−0.956547	+	0.291579i	$0.905819\pi$
$828$	12.2550	−	28.3667i	0.425892	−	0.985810i
$829$	−7.82145	−	2.09575i	−0.271650	−	0.0727884i	0.120422	−	0.992723i	$-0.461575\pi$
$829$	−7.82145	−	2.09575i	−0.271650	−	0.0727884i	−0.392073	+	0.919934i	$0.628242\pi$
$830$	−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	−0.690306	−	0.723518i	$-0.742524\pi$
$839$	−10.3997	+	6.37296i	−0.359039	+	0.220019i	0.331267	+	0.943537i	$0.392524\pi$
$840$	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	−0.702780	−	0.711407i	$-0.748058\pi$
$853$	8.34841	−	16.3847i	0.285844	−	0.561001i	0.988624	+	0.150407i	$0.0480582\pi$
$854$	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	0.946648	+	0.322271i	$0.104446\pi$
$857$	6.23318	+	29.3248i	0.212921	+	1.00172i	−0.733726	+	0.679445i	$0.762221\pi$
$858$	38.5194	+	85.2424i	1.31503	+	2.91013i
$859$	15.1450	+	12.2642i	0.516742	+	0.418450i	0.851894	−	0.523715i	$-0.175454\pi$
$859$	15.1450	+	12.2642i	0.516742	+	0.418450i	−0.335152	+	0.942164i	$0.608788\pi$
$860$	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	0.772914	−	0.634510i	$-0.218798\pi$
$863$	9.19400	+	7.44515i	0.312967	+	0.253436i	−0.459947	+	0.887946i	$0.652132\pi$
$864$	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	−0.953115	−	0.302607i	$-0.902143\pi$
$877$	−40.4528	+	18.0107i	−1.36599	+	0.608179i	−0.412878	+	0.910786i	$0.635476\pi$
$878$	−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	−0.682013	−	0.731340i	$-0.738895\pi$
$881$	−32.7878	+	5.19308i	−1.10465	+	0.174959i	−0.422637	+	0.906299i	$0.638895\pi$
$882$	57.8879	+	3.78636i	1.94919	+	0.127493i
$883$	40.3517	−	24.7275i	1.35794	−	0.832148i	0.362921	−	0.931820i	$-0.381779\pi$
$883$	40.3517	−	24.7275i	1.35794	−	0.832148i	0.995020	+	0.0996721i	$0.0317794\pi$
$884$	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	0.601193	−	0.799104i	$-0.294692\pi$
$887$	46.7973	−	16.5718i	1.57130	−	0.556427i	0.970107	+	0.242677i	$0.0780255\pi$
$888$	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	−0.980587	−	0.196085i	$-0.937177\pi$
$907$	−12.1253	+	18.6713i	−0.402614	+	0.619971i	0.577973	+	0.816056i	$0.303844\pi$
$908$	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	0.811260	−	0.584685i	$-0.198782\pi$
$911$	6.83868	+	6.83868i	0.226575	+	0.226575i	−0.584685	+	0.811260i	$0.698782\pi$
$912$	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	0.490491	−	0.871446i	$-0.336817\pi$
$919$	−4.46533	−	3.06894i	−0.147298	−	0.101235i	−0.637789	+	0.770211i	$0.720151\pi$
$920$	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	−0.998309	−	0.0581306i	$-0.981486\pi$
$929$	−36.5919	+	28.0779i	−1.20054	+	0.921207i	−0.202232	+	0.979338i	$0.564819\pi$
$930$	−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	0.964108	−	0.265511i	$-0.0855408\pi$
$937$	−0.473181	−	1.97094i	−0.0154582	−	0.0643879i	−0.979566	+	0.201123i	$0.935541\pi$
$938$	−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	0.938206	+	0.346077i	$0.112487\pi$
$941$	14.4959	+	37.7632i	0.472554	+	1.23105i	−0.465652	+	0.884968i	$0.654180\pi$
$942$	−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	0.991045	−	0.133531i	$-0.0426317\pi$
$947$	23.2232	+	25.7920i	0.754652	+	0.838126i	−0.236392	+	0.971658i	$0.575965\pi$
$948$	−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	−0.767931	−	0.640532i	$-0.778714\pi$
$953$	−31.2629	+	10.1579i	−1.01271	+	0.329048i	−0.244774	+	0.969580i	$0.578714\pi$
$954$	−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	−0.141799	−	0.989895i	$-0.545289\pi$
$967$	−13.5801	−	1.06878i	−0.436706	−	0.0343695i	−0.294907	+	0.955526i	$0.595289\pi$
$968$	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	0.898670	−	0.438626i	$-0.144535\pi$
$971$	1.28871	+	2.37350i	0.0413566	+	0.0761693i	−0.857313	+	0.514795i	$0.827868\pi$
$972$	−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	0.961221	−	0.275779i	$-0.0889358\pi$
$977$	0.152325	+	0.514241i	0.00487331	+	0.0164520i	−0.956348	+	0.292231i	$0.905602\pi$
$978$	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	0.973558	−	0.228439i	$-0.0733622\pi$
$983$	9.05924	+	15.6911i	0.288945	+	0.500467i	−0.684613	+	0.728906i	$0.740029\pi$
$984$	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	0.980608	+	0.195978i	$0.0627881\pi$
$991$	8.34029	+	28.1564i	0.264938	+	0.894416i	−0.715670	+	0.698438i	$0.753879\pi$
$992$	−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	−0.454123	−	0.890939i	$-0.650047\pi$
$997$	−30.1308	−	0.789002i	−0.954252	−	0.0249880i	−0.500129	+	0.865951i	$0.666714\pi$
$998$	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.548.108	yes	3456
3.2	odd	2	inner	861.2.cl.a.548.1	yes	3456
7.4	even	3	inner	861.2.cl.a.179.1	yes	3456
21.11	odd	6	inner	861.2.cl.a.179.108	yes	3456
41.11	odd	40	inner	861.2.cl.a.380.108	yes	3456
123.11	even	40	inner	861.2.cl.a.380.1	yes	3456
287.11	odd	120	inner	861.2.cl.a.11.1	✓	3456
861.11	even	120	inner	861.2.cl.a.11.108	yes	3456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.cl.a.11.1	✓	3456	287.11	odd	120	inner
861.2.cl.a.11.108	yes	3456	861.11	even	120	inner
861.2.cl.a.179.1	yes	3456	7.4	even	3	inner
861.2.cl.a.179.108	yes	3456	21.11	odd	6	inner
861.2.cl.a.380.1	yes	3456	123.11	even	40	inner
861.2.cl.a.380.108	yes	3456	41.11	odd	40	inner
861.2.cl.a.548.1	yes	3456	3.2	odd	2	inner
861.2.cl.a.548.108	yes	3456	1.1	even	1	trivial

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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