LMFDB - Embedded newform 861.2.cl.a.11.1

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			11.1
Character	$\chi$	$=$	861.11
Dual form			861.2.cl.a.548.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14683 + 1.73847i) q^{2} +(0.280422 + 1.70920i) q^{3} +(1.17079 - 5.50812i) q^{4} +(-0.113959 - 2.17447i) q^{5} +(-3.57341 - 3.18186i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(4.55397 + 8.93767i) q^{8} +(-2.84273 + 0.958594i) q^{9} +O(q^{10})$	\(q+(-2.14683 + 1.73847i) q^{2} +(0.280422 + 1.70920i) q^{3} +(1.17079 - 5.50812i) q^{4} +(-0.113959 - 2.17447i) q^{5} +(-3.57341 - 3.18186i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(4.55397 + 8.93767i) q^{8} +(-2.84273 + 0.958594i) q^{9} +(4.02491 + 4.47011i) q^{10} +(1.68453 + 4.75697i) q^{11} +(9.74280 + 0.456511i) q^{12} +(-2.02418 - 3.30316i) q^{13} +(5.10562 - 5.22981i) q^{14} +(3.68465 - 0.804549i) q^{15} +(-15.0258 - 6.68993i) q^{16} +(2.21736 - 4.64879i) q^{17} +(4.43637 - 6.99994i) q^{18} +(0.200649 + 0.00525417i) q^{19} +(-12.1107 - 1.91814i) q^{20} +(-1.26357 - 4.40493i) q^{21} +(-11.8863 - 7.28391i) q^{22} +(0.191198 - 1.81912i) q^{23} +(-13.9992 + 10.2900i) q^{24} +(0.257271 - 0.0270403i) q^{25} +(10.0880 + 3.57236i) q^{26} +(-2.43559 - 4.58998i) q^{27} +(-1.37919 + 14.8347i) q^{28} +(6.02991 + 0.474564i) q^{29} +(-6.51164 + 8.13289i) q^{30} +(1.45059 - 1.30612i) q^{31} +(24.5098 - 6.56739i) q^{32} +(-7.65823 + 4.21316i) q^{33} +(3.32149 + 13.8350i) q^{34} +(0.969523 + 5.67884i) q^{35} +(1.95183 + 16.7804i) q^{36} +(1.04235 - 1.15765i) q^{37} +(-0.439894 + 0.337542i) q^{38} +(5.07814 - 4.38601i) q^{39} +(18.9157 - 10.9210i) q^{40} +(-2.45695 + 5.91298i) q^{41} +(10.3705 + 7.25997i) q^{42} +(9.56729 - 1.51531i) q^{43} +(28.1742 - 3.70921i) q^{44} +(2.40839 + 6.07219i) q^{45} +(2.75203 + 4.23775i) q^{46} +(-6.93270 + 2.05356i) q^{47} +(7.22085 - 27.5581i) q^{48} +(6.81008 - 1.61949i) q^{49} +(-0.505309 + 0.505309i) q^{50} +(8.56751 + 2.48629i) q^{51} +(-20.5641 + 7.28213i) q^{52} +(1.69245 + 1.16319i) q^{53} +(13.2084 + 5.61971i) q^{54} +(10.1519 - 4.20507i) q^{55} +(-14.7208 - 22.0826i) q^{56} +(0.0472859 + 0.344422i) q^{57} +(-13.7702 + 9.46402i) q^{58} +(4.48835 + 10.0810i) q^{59} +(-0.117611 - 21.2375i) q^{60} +(-7.91348 + 3.03770i) q^{61} +(-0.843527 + 5.32582i) q^{62} +(7.17457 - 3.39493i) q^{63} +(-21.8658 + 30.0956i) q^{64} +(-6.95195 + 4.77795i) q^{65} +(9.11649 - 22.3586i) q^{66} +(5.27896 - 0.978398i) q^{67} +(-23.0101 - 17.6562i) q^{68} +(3.16286 - 0.183327i) q^{69} +(-11.9539 - 10.5060i) q^{70} +(7.24226 + 6.18547i) q^{71} +(-21.5133 - 21.0419i) q^{72} +(-0.816627 - 3.04769i) q^{73} +(-0.225216 + 4.29737i) q^{74} +(0.118362 + 0.432145i) q^{75} +(0.263858 - 1.09905i) q^{76} +(-5.89239 - 11.9810i) q^{77} +(-3.27697 + 18.2442i) q^{78} +(16.5581 - 2.17991i) q^{79} +(-12.8347 + 33.4356i) q^{80} +(7.16219 - 5.45004i) q^{81} +(-5.00488 - 16.9655i) q^{82} -2.15845i q^{83} +(-25.7423 + 1.80267i) q^{84} +(-10.3613 - 4.29181i) q^{85} +(-17.9051 + 19.8856i) q^{86} +(0.879794 + 10.4394i) q^{87} +(-34.8449 + 36.7189i) q^{88} +(-5.29703 + 5.02669i) q^{89} +(-15.7267 - 8.84906i) q^{90} +(6.33690 + 8.05611i) q^{91} +(-9.79611 - 3.18295i) q^{92} +(2.63919 + 2.11308i) q^{93} +(11.3133 - 16.4610i) q^{94} +(-0.0114407 - 0.436904i) q^{95} +(18.0981 + 40.0506i) q^{96} +(3.58219 - 3.05948i) q^{97} +(-11.8047 + 15.3159i) q^{98} +(-9.34867 - 11.9080i) 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	$0.714451\pi$
$2$	−2.14683	+	1.73847i	−1.51804	+	1.22929i	−0.894145	+	0.447777i	$0.852216\pi$
$3$	0.280422	+	1.70920i	0.161902	+	0.986807i
$3$	0.280422	+	1.70920i	0.161902	+	0.986807i
$4$	1.17079	−	5.50812i	0.585394	−	2.75406i
$5$	−0.113959	−	2.17447i	−0.0509641	−	0.972453i	−0.897746	−	0.440513i	$-0.854797\pi$
$5$	−0.113959	−	2.17447i	−0.0509641	−	0.972453i	0.846782	−	0.531940i	$-0.178537\pi$
$6$	−3.57341	−	3.18186i	−1.45884	−	1.29899i
$7$	−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
$9$	−2.84273	+	0.958594i	−0.947576	+	0.319531i
$10$	4.02491	+	4.47011i	1.27279	+	1.41357i
$11$	1.68453	+	4.75697i	0.507905	+	1.43428i	0.865739	+	0.500495i	$0.166849\pi$
$11$	1.68453	+	4.75697i	0.507905	+	1.43428i	−0.357834	+	0.933785i	$0.616485\pi$
$12$	9.74280	+	0.456511i	2.81250	+	0.131783i
$13$	−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
$15$	3.68465	−	0.804549i	0.951372	−	0.207734i
$16$	−15.0258	−	6.68993i	−3.75646	−	1.67248i
$17$	2.21736	−	4.64879i	0.537789	−	1.12750i	−0.435980	−	0.899956i	$-0.643598\pi$
$17$	2.21736	−	4.64879i	0.537789	−	1.12750i	0.973769	−	0.227541i	$-0.0730685\pi$
$18$	4.43637	−	6.99994i	1.04566	−	1.64990i
$19$	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
$21$	−1.26357	−	4.40493i	−0.275734	−	0.961234i
$22$	−11.8863	−	7.28391i	−2.53416	−	1.55294i
$23$	0.191198	−	1.81912i	0.0398675	−	0.379314i	−0.956337	−	0.292267i	$-0.905590\pi$
$23$	0.191198	−	1.81912i	0.0398675	−	0.379314i	0.996204	−	0.0870466i	$-0.0277429\pi$
$24$	−13.9992	+	10.2900i	−2.85758	+	2.10043i
$25$	0.257271	−	0.0270403i	0.0514542	−	0.00540806i
$26$	10.0880	+	3.57236i	1.97843	+	0.700597i
$27$	−2.43559	−	4.58998i	−0.468730	−	0.883342i
$28$	−1.37919	+	14.8347i	−0.260643	+	2.80350i
$29$	6.02991	+	0.474564i	1.11973	+	0.0881244i	0.624781	−	0.780800i	$-0.285188\pi$
$29$	6.02991	+	0.474564i	1.11973	+	0.0881244i	0.494945	+	0.868924i	$0.335188\pi$
$30$	−6.51164	+	8.13289i	−1.18886	+	1.48486i
$31$	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
$33$	−7.65823	+	4.21316i	−1.33313	+	0.733417i
$34$	3.32149	+	13.8350i	0.569631	+	2.37268i
$35$	0.969523	+	5.67884i	0.163879	+	0.959899i
$36$	1.95183	+	16.7804i	0.325304	+	2.79673i
$37$	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
$39$	5.07814	−	4.38601i	0.813153	−	0.702323i
$40$	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
$42$	10.3705	+	7.25997i	1.60021	+	1.12024i
$43$	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
$45$	2.40839	+	6.07219i	0.359022	+	0.905188i
$46$	2.75203	+	4.23775i	0.405764	+	0.624822i
$47$	−6.93270	+	2.05356i	−1.01124	+	0.299542i	−0.746935	−	0.664897i	$-0.768475\pi$
$47$	−6.93270	+	2.05356i	−1.01124	+	0.299542i	−0.264303	+	0.964440i	$0.585142\pi$
$48$	7.22085	−	27.5581i	1.04224	−	3.97768i
$49$	6.81008	−	1.61949i	0.972869	−	0.231356i
$50$	−0.505309	+	0.505309i	−0.0714615	+	0.0714615i
$51$	8.56751	+	2.48629i	1.19969	+	0.348150i
$52$	−20.5641	+	7.28213i	−2.85173	+	1.00985i
$53$	1.69245	+	1.16319i	0.232476	+	0.159777i	0.676982	−	0.735999i	$-0.263287\pi$
$53$	1.69245	+	1.16319i	0.232476	+	0.159777i	−0.444506	+	0.895776i	$0.646621\pi$
$54$	13.2084	+	5.61971i	1.79743	+	0.764746i
$55$	10.1519	−	4.20507i	1.36889	−	0.567011i
$56$	−14.7208	−	22.0826i	−1.96715	−	2.95091i
$57$	0.0472859	+	0.344422i	0.00626317	+	0.0456198i
$58$	−13.7702	+	9.46402i	−1.80812	+	1.24269i
$59$	4.48835	+	10.0810i	0.584333	+	1.31243i	0.927733	+	0.373244i	$0.121755\pi$
$59$	4.48835	+	10.0810i	0.584333	+	1.31243i	−0.343400	+	0.939189i	$0.611579\pi$
$60$	−0.117611	−	21.2375i	−0.0151835	−	2.74174i
$61$	−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
$63$	7.17457	−	3.39493i	0.903911	−	0.427721i
$64$	−21.8658	+	30.0956i	−2.73322	+	3.76195i
$65$	−6.95195	+	4.77795i	−0.862284	+	0.592631i
$66$	9.11649	−	22.3586i	1.12216	−	2.75215i
$67$	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
$69$	3.16286	−	0.183327i	0.380764	−	0.0220700i
$70$	−11.9539	−	10.5060i	−1.42876	−	1.25571i
$71$	7.24226	+	6.18547i	0.859498	+	0.734080i	0.965533	−	0.260282i	$-0.0838155\pi$
$71$	7.24226	+	6.18547i	0.859498	+	0.734080i	−0.106035	+	0.994362i	$0.533816\pi$
$72$	−21.5133	−	21.0419i	−2.53537	−	2.47982i
$73$	−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
$75$	0.118362	+	0.432145i	0.0136672	+	0.0498998i
$76$	0.263858	−	1.09905i	0.0302666	−	0.126069i
$77$	−5.89239	−	11.9810i	−0.671500	−	1.36536i
$78$	−3.27697	+	18.2442i	−0.371044	+	2.06575i
$79$	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
$81$	7.16219	−	5.45004i	0.795799	−	0.605560i
$82$	−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	$-0.0377959\pi$
$84$	−25.7423	+	1.80267i	−2.80871	+	0.196687i
$85$	−10.3613	−	4.29181i	−1.12385	−	0.465512i
$86$	−17.9051	+	19.8856i	−1.93075	+	2.14432i
$87$	0.879794	+	10.4394i	0.0943239	+	1.11922i
$88$	−34.8449	+	36.7189i	−3.71448	+	3.91425i
$89$	−5.29703	+	5.02669i	−0.561484	+	0.532828i	−0.915451	−	0.402430i	$-0.868166\pi$
$89$	−5.29703	+	5.02669i	−0.561484	+	0.532828i	0.353967	+	0.935258i	$0.384832\pi$
$90$	−15.7267	−	8.84906i	−1.65774	−	0.932773i
$91$	6.33690	+	8.05611i	0.664288	+	0.844510i
$92$	−9.79611	−	3.18295i	−1.02131	−	0.331845i
$93$	2.63919	+	2.11308i	0.273671	+	0.219116i
$94$	11.3133	−	16.4610i	1.16688	−	1.69782i
$95$	−0.0114407	−	0.436904i	−0.00117379	−	0.0448254i
$96$	18.0981	+	40.0506i	1.84713	+	4.08764i
$97$	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
$99$	−9.34867	−	11.9080i	−0.939577	−	1.19680i
$100$	0.152269	−	1.44874i	0.0152269	−	0.144874i
$101$	13.2289	−	7.18271i	1.31633	−	0.714706i	0.341968	−	0.939712i	$-0.388907\pi$
$101$	13.2289	−	7.18271i	1.31633	−	0.714706i	0.974357	+	0.225006i	$0.0722400\pi$
$102$	−22.7154	+	9.55672i	−2.24915	+	0.946257i
$103$	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
$105$	−9.43439	+	3.24958i	−0.920703	+	0.317126i
$106$	−5.65559	+	0.445105i	−0.549320	+	0.0432324i
$107$	12.7375	+	5.67111i	1.23138	+	0.548247i	0.916176	−	0.400776i	$-0.131259\pi$
$107$	12.7375	+	5.67111i	1.23138	+	0.548247i	0.315207	+	0.949023i	$0.397926\pi$
$108$	−28.1337	+	8.04165i	−2.70717	+	0.773809i
$109$	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
$111$	2.27095	+	1.45695i	0.215549	+	0.138288i
$112$	41.5456	+	12.9492i	3.92569	+	1.22358i
$113$	0.799144	−	2.45951i	0.0751771	−	0.231371i	−0.906406	−	0.422408i	$-0.861185\pi$
$113$	0.799144	−	2.45951i	0.0751771	−	0.231371i	0.981583	+	0.191037i	$0.0611849\pi$
$114$	−0.700283	−	0.657212i	−0.0655875	−	0.0615535i
$115$	−3.97742	−	0.208448i	−0.370896	−	0.0194379i
$116$	9.67370	−	32.6579i	0.898181	−	3.03221i
$117$	8.92058	+	7.44962i	0.824708	+	0.688717i
$118$	−27.1613	−	13.8394i	−2.50040	−	1.27402i
$119$	−4.39412	+	12.8991i	−0.402808	+	1.18246i
$120$	23.9706	+	29.2683i	2.18820	+	2.67182i
$121$	−11.2425	+	9.10401i	−1.02205	+	0.827637i
$122$	11.7080	−	20.2788i	1.05999	−	1.83596i
$123$	−10.7955	−	2.54129i	−0.973393	−	0.229141i
$124$	−5.49591	−	9.51920i	−0.493548	−	0.854850i
$125$	−1.79126	−	11.3096i	−0.160215	−	1.01156i
$126$	−9.50061	+	19.7611i	−0.846382	+	1.76046i
$127$	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
$129$	5.27285	+	15.9275i	0.464248	+	1.40234i
$130$	6.61837	−	22.3432i	0.580469	−	1.95963i
$131$	−0.314184	+	0.483801i	−0.0274504	+	0.0422699i	−0.852129	−	0.523331i	$-0.824689\pi$
$131$	−0.314184	+	0.483801i	−0.0274504	+	0.0422699i	0.824679	+	0.565601i	$0.191356\pi$
$132$	14.2404	+	47.1152i	1.23947	+	4.10085i
$133$	−0.528873	+	0.0480236i	−0.0458591	+	0.00416418i
$134$	−9.63214	+	11.2778i	−0.832090	+	0.974252i
$135$	−9.70322	+	5.81920i	−0.835120	+	0.500837i
$136$	51.6471	−	1.35243i	4.42871	−	0.115970i
$137$	−16.8239	−	2.21490i	−1.43736	−	0.189232i	−0.628763	−	0.777597i	$-0.716438\pi$
$137$	−16.8239	−	2.21490i	−1.43736	−	0.189232i	−0.808595	+	0.588365i	$0.799772\pi$
$138$	−6.47143	+	5.89212i	−0.550885	+	0.501570i
$139$	−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
$141$	−5.45403	−	11.2735i	−0.459312	−	0.949401i
$142$	−26.3012	−	0.688721i	−2.20715	−	0.0577962i
$143$	12.3032	−	15.1932i	1.02885	−	1.27052i
$144$	49.1273	+	4.61397i	4.09394	+	0.384498i
$145$	0.344762	−	13.1659i	0.0286310	−	1.09337i
$146$	7.05149	+	5.12321i	0.583586	+	0.424000i
$147$	4.67773	+	11.1857i	0.385812	+	0.922577i
$148$	−5.15609	−	7.09675i	−0.423828	−	0.583349i
$149$	18.1006	+	6.40976i	1.48286	+	0.525108i	0.947566	−	0.319559i	$-0.103535\pi$
$149$	18.1006	+	6.40976i	1.48286	+	0.525108i	0.535292	+	0.844667i	$0.320201\pi$
$150$	−1.00537	−	0.721975i	−0.0820885	−	0.0589490i
$151$	−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
$153$	−1.84704	+	15.3408i	−0.149325	+	1.24023i
$154$	33.4786	+	15.4775i	2.69778	+	1.24721i
$155$	−3.00542	−	3.00542i	−0.241401	−	0.241401i
$156$	−18.2132	−	33.1061i	−1.45823	−	2.65061i
$157$	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
$159$	−1.51352	+	3.21893i	−0.120030	+	0.255277i
$160$	−17.0737	−	52.5475i	−1.34980	−	4.15425i
$161$	0.0581478	+	4.83911i	0.00458269	+	0.381375i
$162$	−5.90129	+	24.1516i	−0.463649	+	1.89753i
$163$	−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
$165$	10.0341	+	16.1725i	0.781155	+	1.25903i
$166$	3.75241	+	4.63383i	0.291243	+	0.359655i
$167$	−0.574594	+	1.38719i	−0.0444634	+	0.107344i	−0.944551	−	0.328365i	$-0.893502\pi$
$167$	−0.574594	+	1.38719i	−0.0444634	+	0.107344i	0.900087	+	0.435709i	$0.143502\pi$
$168$	33.6155	−	31.3533i	2.59349	−	2.41896i
$169$	−0.911694	+	1.78930i	−0.0701303	+	0.137638i
$170$	29.7053	−	8.79911i	2.27829	−	0.674861i
$171$	−0.575426	+	0.177405i	−0.0440039	+	0.0135665i
$172$	2.85475	−	54.4719i	0.217673	−	4.15345i
$173$	−5.87304	−	1.57368i	−0.446519	−	0.119644i	0.0285511	−	0.999592i	$-0.490911\pi$
$173$	−5.87304	−	1.57368i	−0.446519	−	0.119644i	−0.475070	+	0.879948i	$0.657577\pi$
$174$	−20.0374	−	20.8822i	−1.51903	−	1.58307i
$175$	−0.667710	+	0.150334i	−0.0504741	+	0.0113641i
$176$	6.51232	−	82.7468i	0.490884	−	6.23728i
$177$	−15.9718	+	10.4984i	−1.20051	+	0.789109i
$178$	2.63308	−	20.0002i	0.197357	−	1.49908i
$179$	9.93636	−	1.84160i	0.742678	−	0.137647i	0.202599	−	0.979262i	$-0.435061\pi$
$179$	9.93636	−	1.84160i	0.742678	−	0.137647i	0.540079	+	0.841614i	$0.318394\pi$
$180$	36.2661	−	6.15647i	2.70311	−	0.458876i
$181$	−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
$183$	−7.41115	−	12.6739i	−0.547848	−	0.936880i
$184$	17.1294	−	6.57537i	1.26280	−	0.484743i
$185$	−2.63605	−	2.13463i	−0.193807	−	0.156941i
$186$	−9.33943	+	0.0517209i	−0.684800	+	0.00379236i
$187$	25.8494	+	2.71688i	1.89029	+	0.198678i
$188$	3.19454	+	40.5905i	0.232986	+	2.96036i
$189$	7.81452	+	11.3108i	0.568423	+	0.822736i
$190$	0.784106	+	0.918070i	0.0568850	+	0.0666038i
$191$	−11.0862	−	8.50677i	−0.802172	−	0.615528i	0.124149	−	0.992264i	$-0.460380\pi$
$191$	−11.0862	−	8.50677i	−0.802172	−	0.615528i	−0.926321	+	0.376735i	$0.877047\pi$
$192$	−57.5711	−	28.9335i	−4.15484	−	2.08809i
$193$	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
$195$	−10.1159	−	10.5424i	−0.724418	−	0.754960i
$196$	−0.947179	−	39.4069i	−0.0676557	−	2.81478i
$197$	−2.19649	+	1.11917i	−0.156494	+	0.0797376i	−0.530483	−	0.847695i	$-0.677990\pi$
$197$	−2.19649	+	1.11917i	−0.156494	+	0.0797376i	0.373990	+	0.927433i	$0.377990\pi$
$198$	40.7717	+	9.31207i	2.89752	+	0.661780i
$199$	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
$201$	3.15261	+	8.74844i	0.222368	+	0.617067i
$202$	−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
$207$	1.20028	+	5.35455i	0.0834252	+	0.372167i
$208$	8.31706	+	63.1744i	0.576684	+	4.38035i
$209$	0.313005	+	0.963331i	0.0216510	+	0.0666350i
$210$	14.6048	−	23.3777i	1.00783	−	1.61322i
$211$	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
$213$	−8.54132	+	14.1130i	−0.585241	+	0.967007i
$214$	−37.2044	+	9.96889i	−2.54324	+	0.681459i
$215$	−4.38528	−	20.6311i	−0.299074	−	1.40703i
$216$	29.9321	−	42.6711i	2.03662	−	2.90340i
$217$	−3.40929	+	3.87914i	−0.231438	+	0.263333i
$218$	−8.77157	+	5.37523i	−0.594086	+	0.364056i
$219$	4.98012	−	2.25042i	0.336525	−	0.152069i
$220$	−11.2763	−	60.8413i	−0.760246	−	4.10192i
$221$	−19.8440	+	2.08569i	−1.33485	+	0.140299i
$222$	−7.40822	+	0.820138i	−0.497207	+	0.0550441i
$223$	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
$225$	−0.705431	+	0.323487i	−0.0470287	+	0.0215658i
$226$	2.56016	+	6.66945i	0.170299	+	0.443645i
$227$	−3.17718	−	5.85165i	−0.210877	−	0.388387i	0.751654	−	0.659557i	$-0.229256\pi$
$227$	−3.17718	−	5.85165i	−0.210877	−	0.388387i	−0.962532	+	0.271170i	$0.912590\pi$
$228$	1.95248	+	0.142789i	0.129306	+	0.00945641i
$229$	−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
$231$	18.8256	−	13.4310i	1.23863	−	0.883695i
$232$	23.2185	+	56.0545i	1.52437	+	3.68016i
$233$	11.3419	−	20.8891i	0.743031	−	1.36849i	−0.179962	−	0.983674i	$-0.557597\pi$
$233$	11.3419	−	20.8891i	0.743031	−	1.36849i	0.922992	−	0.384819i	$-0.125736\pi$
$234$	−32.1020	−	0.484912i	−2.09857	−	0.0316997i
$235$	5.25545	+	14.8409i	0.342828	+	0.968116i
$236$	60.7823	−	12.9197i	3.95659	−	0.840999i
$237$	8.36915	+	27.6898i	0.543635	+	1.79864i
$238$	−12.9913	−	35.3313i	−0.842101	−	2.29019i
$239$	−7.50693	+	1.80225i	−0.485583	+	0.116578i	−0.468843	−	0.883282i	$-0.655329\pi$
$239$	−7.50693	+	1.80225i	−0.485583	+	0.116578i	−0.0167403	+	0.999860i	$0.505329\pi$
$240$	−60.7473	−	12.5610i	−3.92122	−	0.810811i
$241$	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
$243$	11.3237	+	10.7133i	0.726413	+	0.687259i
$244$	7.46702	+	47.1449i	0.478027	+	3.01815i
$245$	−4.29760	−	14.6238i	−0.274564	−	0.934279i
$246$	27.5940	−	13.3119i	1.75933	−	0.848733i
$247$	−0.388794	−	0.673410i	−0.0247384	−	0.0428481i
$248$	18.2796	+	7.01687i	1.16075	+	0.445571i
$249$	3.68922	−	0.605277i	0.233795	−	0.0383579i
$250$	23.5069	+	21.1657i	1.48671	+	1.33864i
$251$	−12.3464	−	6.29081i	−0.779298	−	0.397072i	0.0186286	−	0.999826i	$-0.494070\pi$
$251$	−12.3464	−	6.29081i	−0.779298	−	0.397072i	−0.797927	+	0.602754i	$0.794070\pi$
$252$	−10.2998	−	43.4932i	−0.648827	−	2.73981i
$253$	8.97560	−	2.15485i	0.564291	−	0.135474i
$254$	−3.23882	+	4.98734i	−0.203221	+	0.312934i
$255$	4.43001	−	18.9131i	0.277418	−	1.18439i
$256$	46.3637	+	51.4921i	2.89773	+	3.21826i
$257$	−3.79472	−	0.703309i	−0.236708	−	0.0438712i	0.0625565	−	0.998041i	$-0.480075\pi$
$257$	−3.79472	−	0.703309i	−0.236708	−	0.0438712i	−0.299265	+	0.954170i	$0.596741\pi$
$258$	−39.0094	−	25.0270i	−2.42862	−	1.55811i
$259$	−2.38230	+	3.36320i	−0.148029	+	0.208979i
$260$	18.1783	+	43.8862i	1.12737	+	2.72171i
$261$	−17.5963	+	4.43118i	−1.08918	+	0.274283i
$262$	−0.166574	−	1.58484i	−0.0102909	−	0.0979118i
$263$	0.684533	−	1.43515i	0.0422101	−	0.0884953i	−0.880395	−	0.474241i	$-0.842722\pi$
$263$	0.684533	−	1.43515i	0.0422101	−	0.0884953i	0.922605	+	0.385746i	$0.126056\pi$
$264$	−72.5312	−	49.2602i	−4.46399	−	3.03175i
$265$	2.33645	−	3.81275i	0.143527	−	0.234215i
$266$	1.05191	−	1.02253i	0.0644970	−	0.0626953i
$267$	−10.0770	−	7.64408i	−0.616704	−	0.467810i
$268$	0.791409	−	30.2227i	0.0483430	−	1.84614i
$269$	1.54434	−	0.687582i	0.0941598	−	0.0419226i	−0.359116	−	0.933293i	$-0.616922\pi$
$269$	1.54434	−	0.687582i	0.0941598	−	0.0419226i	0.453276	+	0.891370i	$0.350255\pi$
$270$	10.7147	−	29.3616i	0.652075	−	1.78689i
$271$	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
$273$	−11.9925	+	13.0901i	−0.725819	+	0.792251i
$274$	39.9686	−	24.4928i	2.41459	−	1.47966i
$275$	0.562011	+	1.17828i	0.0338905	+	0.0710530i
$276$	2.69325	−	17.6361i	0.162115	−	1.06157i
$277$	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
$279$	−2.87159	+	5.10345i	−0.171918	+	0.305536i
$280$	−46.3404	+	34.5265i	−2.76937	+	2.06336i
$281$	−16.2311	−	3.89674i	−0.968266	−	0.232460i	−0.281680	−	0.959508i	$-0.590892\pi$
$281$	−16.2311	−	3.89674i	−0.968266	−	0.232460i	−0.686586	+	0.727048i	$0.740892\pi$
$282$	31.3076	+	14.7207i	1.86434	+	0.876604i
$283$	−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
$285$	0.743547	−	0.142072i	0.0440439	−	0.00841561i
$286$			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
$291$	6.23378	+	5.26473i	0.365431	+	0.308624i
$292$	−17.7432	+	0.929880i	−1.03834	+	0.0544171i
$293$	3.22725	−	13.4424i	0.188538	−	0.785316i	−0.795294	−	0.606223i	$-0.792684\pi$
$293$	3.22725	−	13.4424i	0.188538	−	0.785316i	0.983832	−	0.179093i	$-0.0573163\pi$
$294$	−29.4882	−	15.8816i	−1.71979	−	0.926236i
$295$	21.4093	−	10.9086i	1.24650	−	0.635123i
$296$	15.0935	+	4.04429i	0.877291	+	0.235069i
$297$	17.7316	−	19.3180i	1.02889	−	1.12094i
$298$	−50.0022	+	17.7067i	−2.89655	+	1.02572i
$299$	−6.39588	+	3.05068i	−0.369883	+	0.176425i
$300$	2.51888	−	0.146001i	0.145428	−	0.00842936i
$301$	−24.6735	+	6.93003i	−1.42215	+	0.399440i
$302$	30.3402	+	35.5238i	1.74588	+	2.04416i
$303$	15.9864	+	20.5966i	0.918392	+	1.18325i
$304$	−2.97976	−	1.42127i	−0.170901	−	0.0815157i
$305$	7.50721	+	16.8615i	0.429861	+	0.965485i
$306$	−22.7042	−	36.1452i	−1.29791	−	2.06628i
$307$	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
$309$	−3.07645	+	1.79898i	−0.175013	+	0.102340i
$310$	11.6770	+	1.22730i	0.663207	+	0.0697059i
$311$	17.7134	+	8.44884i	1.00443	+	0.479089i	0.859928	−	0.510415i	$-0.170508\pi$
$311$	17.7134	+	8.44884i	1.00443	+	0.479089i	0.144504	+	0.989504i	$0.453841\pi$
$312$	62.3264	+	25.4130i	3.52854	+	1.43873i
$313$	−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
$315$	−8.19979	−	15.2140i	−0.462006	−	0.857212i
$316$	7.37877	−	93.7561i	0.415088	−	5.27420i
$317$	0.247338	−	1.33451i	0.0138919	−	0.0749538i	−0.975594	−	0.219580i	$-0.929531\pi$
$317$	0.247338	−	1.33451i	0.0138919	−	0.0749538i	0.989486	+	0.144626i	$0.0461980\pi$
$318$	−2.34672	−	9.54172i	−0.131598	−	0.535073i
$319$	7.90009	+	29.4835i	0.442320	+	1.65076i
$320$	67.9339	+	44.1168i	3.79762	+	2.46620i
$321$	−6.12118	+	23.3613i	−0.341651	+	1.30390i
$322$	−8.53749	−	10.2877i	−0.475776	−	0.573310i
$323$	0.469336	−	0.921123i	0.0261145	−	0.0512527i
$324$	−21.6341	−	45.8311i	−1.20189	−	2.54617i
$325$	−0.610081	−	0.795073i	−0.0338412	−	0.0441027i
$326$	8.05421	−	20.9819i	0.446082	−	1.16208i
$327$	0.204553	+	6.44700i	0.0113118	+	0.356520i
$328$	−64.0372	+	4.96811i	−3.53586	+	0.274318i
$329$	17.5846	−	7.53255i	0.969468	−	0.415283i
$330$	−49.6570	−	17.2756i	−2.73353	−	0.950990i
$331$	−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
$333$	−1.85340	+	4.29006i	−0.101566	+	0.235094i
$334$	−1.17804	−	3.97699i	−0.0644594	−	0.217611i
$335$	−2.72908	−	11.3675i	−0.149106	−	0.621070i
$336$	−10.4825	+	74.6409i	−0.571865	+	4.07199i
$337$	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
$339$	4.42789	+	0.676195i	0.240490	+	0.0367259i
$340$	−35.7708	+	52.0468i	−1.93994	+	2.82263i
$341$	8.65671	+	4.70021i	0.468787	+	0.254531i
$342$	0.926931	−	1.38122i	0.0501227	−	0.0746878i
$343$	−17.3961	+	6.35414i	−0.939302	+	0.343091i
$344$	57.1125	+	78.6086i	3.07930	+	4.23829i
$345$	−0.759077	−	6.85666i	−0.0408674	−	0.369150i
$346$	15.3442	−	6.83169i	0.824911	−	0.367274i
$347$	−9.44140	+	5.12626i	−0.506841	+	0.275192i	−0.710310	−	0.703889i	$-0.751445\pi$
$347$	−9.44140	+	5.12626i	−0.506841	+	0.275192i	0.203469	+	0.979081i	$0.434778\pi$
$348$	58.5316	+	7.37630i	3.13762	+	0.395411i
$349$	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
$351$	−10.2314	+	17.3361i	−0.546109	+	0.925332i
$352$	72.5285	+	105.530i	3.86578	+	5.62475i
$353$	0.655392	+	6.23564i	0.0348830	+	0.331889i	0.998021	+	0.0628816i	$0.0200291\pi$
$353$	0.655392	+	6.23564i	0.0348830	+	0.331889i	−0.963138	+	0.269008i	$0.913304\pi$
$354$	16.0376	−	50.3049i	0.852389	−	2.67367i
$355$	12.6248	−	16.4530i	0.670055	−	0.873233i
$356$	21.4859	+	35.0619i	1.13875	+	1.85828i
$357$	−23.2794	−	3.89323i	−1.23208	−	0.206052i
$358$	−18.1301	+	21.2277i	−0.958208	+	1.12192i
$359$	1.88270	−	0.400181i	0.0993653	−	0.0211208i	−0.157961	−	0.987445i	$-0.550492\pi$
$359$	1.88270	−	0.400181i	0.0993653	−	0.0211208i	0.257326	+	0.966325i	$0.417159\pi$
$360$	−43.3035	+	49.1780i	−2.28229	+	2.59191i
$361$	−18.9337	−	0.992275i	−0.996512	−	0.0522250i
$362$	8.01713	+	8.44829i	0.421371	+	0.444032i
$363$	−18.7132	−	16.6627i	−0.982189	−	0.874567i
$364$	51.7932	−	25.4725i	2.71470	−	1.33512i
$365$	−6.53406	+	2.12304i	−0.342008	+	0.111125i
$366$	37.9437	+	14.3246i	1.98335	+	0.748761i
$367$	−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
$369$	1.31629	−	19.1642i	0.0685236	−	0.997649i
$370$	9.37017			0.487132
$371$	−4.80577	−	2.53504i	−0.249503	−	0.131613i
$372$	14.7290	−	12.0630i	0.763665	−	0.625438i
$373$	−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
$375$	18.8280	−	6.23308i	0.972275	−	0.321875i
$376$	−49.9254	−	52.6103i	−2.57470	−	2.71317i
$377$	−10.6381	−	20.8784i	−0.547888	−	1.07529i
$378$	−36.4399	−	10.6970i	−1.87427	−	0.550193i
$379$	−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
$381$	1.71111	+	3.31276i	0.0876627	+	0.169718i
$382$	38.5891	−	1.01049i	1.97439	−	0.0517012i
$383$	21.3655	−	27.8441i	1.09173	−	1.42277i	0.194663	−	0.980870i	$-0.437639\pi$
$383$	21.3655	−	27.8441i	1.09173	−	1.42277i	0.897065	−	0.441898i	$-0.145695\pi$
$384$	88.0192	−	19.2191i	4.49171	−	0.980772i
$385$	−25.3809	+	14.1782i	−1.29353	+	0.722587i
$386$	−56.2338	+	4.42569i	−2.86222	+	0.225262i
$387$	−25.7446	+	13.4788i	−1.30867	+	0.685164i
$388$	−12.6580	−	23.3131i	−0.642612	−	1.18354i
$389$	0.665984	−	0.822422i	0.0337667	−	0.0416984i	−0.759983	−	0.649943i	$-0.774793\pi$
$389$	0.665984	−	0.822422i	0.0337667	−	0.0416984i	0.793750	+	0.608245i	$0.208126\pi$
$390$	40.0450	+	5.04658i	2.02776	+	0.255543i
$391$	−8.03277	−	4.92249i	−0.406235	−	0.248941i
$392$	45.4874	+	53.4912i	2.29746	+	2.70171i
$393$	−0.915017	−	0.401335i	−0.0461565	−	0.0202447i
$394$	2.76986	−	6.22122i	0.139544	−	0.313420i
$395$	−6.62710	−	35.7566i	−0.333446	−	1.79911i
$396$	−76.5360	+	37.5519i	−3.84608	+	1.88705i
$397$	−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
$399$	−0.230390	−	0.890482i	−0.0115339	−	0.0445799i
$400$	−4.04661	−	1.31482i	−0.202330	−	0.0657411i
$401$	−7.03385	+	26.2507i	−0.351254	+	1.31090i	0.533880	+	0.845560i	$0.320733\pi$
$401$	−7.03385	+	26.2507i	−0.351254	+	1.31090i	−0.885134	+	0.465337i	$0.845933\pi$
$402$	−21.9770	−	13.3007i	−1.09612	−	0.663379i
$403$	−7.25056	−	2.14771i	−0.361176	−	0.106985i
$404$	−24.0750	−	81.2759i	−1.19778	−	4.04363i
$405$	−12.6672	−	14.9529i	−0.629436	−	0.743016i
$406$	33.2683	−	29.1123i	1.65108	−	1.44482i
$407$	7.26276	+	3.00833i	0.360002	+	0.149118i
$408$	16.7946	+	87.8960i	0.831455	+	4.35150i
$409$	−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
$411$	−0.932068	−	29.3764i	−0.0459755	−	1.44903i
$412$	11.4439	−	1.81254i	0.563803	−	0.0892976i
$413$	−14.9007	−	25.1072i	−0.733216	−	1.23544i
$414$	−11.8855	−	9.40868i	−0.584142	−	0.462412i
$415$	−4.69349	+	0.245975i	−0.230394	+	0.0120745i
$416$	−71.3055	−	67.6664i	−3.49604	−	3.31762i
$417$	−5.21192	−	5.15451i	−0.255229	−	0.252417i
$418$	−2.34669	−	1.52396i	−0.114781	−	0.0745393i
$419$	3.99342	−	3.99342i	0.195091	−	0.195091i	−0.602801	−	0.797892i	$-0.705949\pi$
$419$	3.99342	−	3.99342i	0.195091	−	0.195091i	0.797892	+	0.602801i	$0.205949\pi$
$420$	6.85341	+	55.7704i	0.334412	+	2.72132i
$421$	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
$423$	17.7392	−	12.4834i	0.862512	−	0.606962i
$424$	−2.68883	+	20.4237i	−0.130581	+	0.991864i
$425$	0.444758	−	1.25596i	0.0215739	−	0.0609229i
$426$	−6.19827	−	45.1471i	−0.300307	−	2.18738i
$427$	19.8585	−	10.4209i	0.961022	−	0.504301i
$428$	46.1501	−	63.5202i	2.23075	−	3.07036i
$429$	29.4184	+	16.7682i	1.42033	+	0.809576i
$430$	45.2811	+	36.6679i	2.18365	+	1.76828i
$431$	−2.19464	−	1.77718i	−0.105712	−	0.0856040i	0.575007	−	0.818148i	$-0.304999\pi$
$431$	−2.19464	−	1.77718i	−0.105712	−	0.0856040i	−0.680719	+	0.732544i	$0.738333\pi$
$432$	5.89017	+	85.2622i	0.283391	+	4.10218i
$433$	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
$435$	22.5999	−	3.10275i	1.08358	−	0.148766i
$436$	7.00020	−	19.7679i	0.335249	−	0.946713i
$437$	0.0479215	−	0.364000i	0.00229240	−	0.0174125i
$438$	−6.77919	+	13.4891i	−0.323922	+	0.644533i
$439$	−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
$441$	−17.8068	+	11.1319i	−0.847942	+	0.530089i
$442$	38.9759	−	38.9759i	1.85390	−	1.85390i
$443$	11.1844	+	7.26325i	0.531388	+	0.345087i	0.782279	−	0.622928i	$-0.214057\pi$
$443$	11.1844	+	7.26325i	0.531388	+	0.345087i	−0.250891	+	0.968015i	$0.580724\pi$
$444$	10.6839	−	10.8029i	0.507034	−	0.512681i
$445$	11.5340	+	10.9454i	0.546766	+	0.518861i
$446$	−3.72790	+	0.195371i	−0.176521	+	0.00925108i
$447$	−5.87975	+	32.7350i	−0.278103	+	1.54831i
$448$	48.1836	−	85.8216i	2.27646	−	4.05469i
$449$	−27.2254	+	4.31209i	−1.28485	+	0.203500i	−0.761246	−	0.648463i	$-0.775412\pi$
$449$	−27.2254	+	4.31209i	−1.28485	+	0.203500i	−0.523602	+	0.851963i	$0.675412\pi$
$450$	0.952070	−	1.92084i	0.0448810	−	0.0905494i
$451$	−32.2667	−	1.72705i	−1.51938	−	0.0813235i
$452$	−12.6117	−	7.28135i	−0.593203	−	0.342486i
$453$	28.7708	−	5.49733i	1.35177	−	0.258287i
$454$	16.9938	+	7.03907i	0.797559	+	0.330360i
$455$	16.7956	−	14.6975i	0.787391	−	0.689029i
$456$	−2.86299	+	1.99111i	−0.134072	+	0.0932424i
$457$	−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
$459$	−26.7384	+	1.14493i	−1.24804	+	0.0534407i
$460$	−5.80487	+	21.6641i	−0.270654	+	1.01009i
$461$	−1.33331	−	0.433220i	−0.0620986	−	0.0201771i	0.277803	−	0.960638i	$-0.410394\pi$
$461$	−1.33331	−	0.433220i	−0.0620986	−	0.0201771i	−0.339902	+	0.940461i	$0.610394\pi$
$462$	−17.0660	+	61.5619i	−0.793981	+	2.86412i
$463$	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
$465$	4.29407	−	5.97964i	0.199133	−	0.277299i
$466$	11.9660	+	64.5630i	0.554316	+	2.99082i
$467$	−16.2495	+	36.4970i	−0.751937	+	1.68888i	−0.0274174	+	0.999624i	$0.508728\pi$
$467$	−16.2495	+	36.4970i	−0.751937	+	1.68888i	−0.724520	+	0.689254i	$0.757938\pi$
$468$	51.4775	−	40.4138i	2.37955	−	1.86813i
$469$	−13.5703	+	4.19770i	−0.626617	+	0.193832i
$470$	−37.0831	−	22.7246i	−1.71052	−	1.04821i
$471$	−0.112804	+	0.895112i	−0.00519775	+	0.0412446i
$472$	−69.6608	+	86.0239i	−3.20640	+	3.95957i
$473$	23.3247	+	42.9587i	1.07247	+	1.97524i
$474$	−66.1050	−	44.8958i	−3.03631	−	2.06213i
$475$	0.0517632	−	0.00407385i	0.00237506	−	0.000186921i
$476$	65.9054	+	39.3055i	3.02077	+	1.80156i
$477$	−5.92621	−	1.68426i	−0.271343	−	0.0771169i
$478$	12.9830	−	16.9197i	0.593827	−	0.773890i
$479$	26.3558	−	0.690150i	1.20423	−	0.0315337i	0.581217	−	0.813749i	$-0.302577\pi$
$479$	26.3558	−	0.690150i	1.20423	−	0.0315337i	0.623009	+	0.782215i	$0.285910\pi$
$480$	85.0264	−	43.9179i	3.88090	−	2.00457i
$481$	−5.93379	−	1.09976i	−0.270558	−	0.0501449i
$482$	−12.5089	+	38.4986i	−0.569767	+	1.75356i
$483$	−8.25470	+	1.45638i	−0.375602	+	0.0662675i
$484$	36.9834	+	72.5840i	1.68106	+	3.29927i
$485$	−7.06097	−	7.44071i	−0.320622	−	0.337865i
$486$	−42.9348	−	3.31384i	−1.94756	−	0.150319i
$487$	−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
$489$	−8.92861	−	10.9019i	−0.403766	−	0.493002i
$490$	34.6493	+	23.9236i	1.56529	+	1.08076i
$491$	21.7014			0.979372			0.489686	−	0.871899i	$-0.337111\pi$
$491$	21.7014			0.979372			0.489686	+	0.871899i	$0.337111\pi$
$492$	−26.6369	+	56.4874i	−1.20089	+	2.54665i
$493$	15.5766	−	26.9795i	0.701536	−	1.21510i
$494$	2.00538	+	0.769793i	0.0902263	+	0.0346346i
$495$	−24.8282	+	21.6854i	−1.11594	+	0.974688i
$496$	−30.5341	+	9.92113i	−1.37102	+	0.445472i
$497$	−20.9369	−	14.0221i	−0.939147	−	0.628978i
$498$	−6.86789	+	7.71304i	−0.307758	+	0.345630i
$499$	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
$501$	−2.53212	−	0.593097i	−0.113127	−	0.0264976i
$502$	37.4421	−	7.95856i	1.67112	−	0.355208i
$503$	20.8387	−	24.3989i	0.929150	−	1.08789i	−0.0667808	−	0.997768i	$-0.521273\pi$
$503$	20.8387	−	24.3989i	0.929150	−	1.08789i	0.995930	−	0.0901267i	$-0.0287272\pi$
$504$	63.0156	+	48.6635i	2.80694	+	2.16764i
$505$	−17.1261	−	27.9473i	−0.762104	−	1.24364i
$506$	−15.5230	+	20.2299i	−0.690080	+	0.899330i
$507$	−3.31393	−	1.05651i	−0.147177	−	0.0469211i
$508$	−1.26711	−	12.0558i	−0.0562191	−	0.534889i
$509$	21.9156	+	31.8874i	0.971391	+	1.41338i	0.909690	+	0.415288i	$0.136319\pi$
$509$	21.9156	+	31.8874i	0.971391	+	1.41338i	0.0617006	+	0.998095i	$0.480348\pi$
$510$	23.3694	+	48.3048i	1.03482	+	2.13897i
$511$	3.08504	+	7.75692i	0.136474	+	0.343146i
$512$	−86.3031	−	13.6691i	−3.81409	−	0.604093i
$513$	−0.464582	−	0.933770i	−0.0205118	−	0.0412270i
$514$	9.36931	−	5.08712i	0.413263	−	0.224383i
$515$	4.09295	−	1.82230i	0.180357	−	0.0803000i
$516$	93.9039	−	10.3958i	4.13389	−	0.457649i
$517$	−21.4471	−	29.5194i	−0.943241	−	1.29826i
$518$	−0.732433	−	11.3618i	−0.0321813	−	0.499208i
$519$	1.04280	−	10.4795i	0.0457737	−	0.459999i
$520$	−74.3627	−	40.3757i	−3.26102	−	1.77059i
$521$	14.9917	−	21.8130i	0.656798	−	0.955646i	−0.343069	−	0.939310i	$-0.611466\pi$
$521$	14.9917	−	21.8130i	0.656798	−	0.955646i	0.999867	−	0.0163362i	$-0.00520020\pi$
$522$	30.0729	−	40.1037i	1.31625	−	1.75529i
$523$	−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
$525$	−0.444191	−	1.09909i	−0.0193861	−	0.0479684i
$526$	1.02539	+	4.27108i	0.0447093	+	0.186228i
$527$	−2.85538	−	9.63961i	−0.124382	−	0.419908i
$528$	143.257	−	12.0732i	6.23446	−	0.525418i
$529$	19.2247	+	4.08634i	0.835858	+	0.177667i
$530$	1.61237	+	12.2472i	0.0700370	+	0.531984i
$531$	−22.4227	−	24.3550i	−0.973063	−	1.05692i
$532$	−0.354678	+	2.96932i	−0.0153772	+	0.128736i
$533$	24.5049	−	3.85323i	1.06142	−	0.166902i
$534$	34.9227	−	1.10804i	1.51125	−	0.0479497i
$535$	10.8801	−	28.3437i	0.470388	−	1.22540i
$536$	32.7848	+	42.7260i	1.41609	+	1.84548i
$537$	5.93403	+	16.4668i	0.256072	+	0.710595i
$538$	−2.12009	+	4.16091i	−0.0914035	+	0.179390i
$539$	19.1757	+	29.6673i	0.825954	+	1.27786i
$540$	20.6924	+	60.2596i	0.890461	+	2.59316i
$541$	−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
$543$	7.09118	−	1.74403i	0.304312	−	0.0748435i
$544$	23.8167	−	128.503i	1.02113	−	5.50954i
$545$	0.636221	−	8.08396i	0.0272527	−	0.346279i
$546$	2.98905	−	48.9510i	0.127919	−	2.09491i
$547$	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
$549$	19.5839	−	16.2212i	0.835822	−	0.692303i
$550$	−3.25495	−	1.55253i	−0.138792	−	0.0662002i
$551$	1.20740	+	0.126903i	0.0514370	+	0.00540624i
$552$	16.0421	+	27.4337i	0.682797	+	1.16766i
$553$	−42.8387	+	10.8307i	−1.82168	+	0.460566i
$554$	−8.26177	+	52.1628i	−0.351009	+	2.21618i
$555$	2.90931	−	5.10414i	0.123493	−	0.216659i
$556$	9.69332	+	21.7716i	0.411088	+	0.923320i
$557$	−20.0934	−	9.58406i	−0.851384	−	0.406089i	−0.0460705	−	0.998938i	$-0.514670\pi$
$557$	−20.0934	−	9.58406i	−0.851384	−	0.406089i	−0.805314	+	0.592849i	$0.798003\pi$
$558$	−2.70738	−	15.9484i	−0.114613	−	0.675152i
$559$	−24.3712	−	28.5350i	−1.03079	−	1.20690i
$560$	23.4231	−	91.8153i	0.989809	−	3.87990i
$561$	2.60504	+	44.9436i	0.109985	+	1.89752i
$562$	41.6198	−	19.8516i	1.75563	−	0.837391i
$563$	−26.4637	+	9.37130i	−1.11531	+	0.394953i	−0.826785	−	0.562518i	$-0.809833\pi$
$563$	−26.4637	+	9.37130i	−1.11531	+	0.394953i	−0.288528	+	0.957471i	$0.593166\pi$
$564$	−68.4814	+	16.8426i	−2.88359	+	0.709200i
$565$	−5.43921	−	1.45743i	−0.228829	−	0.0613146i
$566$	26.5806	−	13.5435i	1.11726	−	0.569275i
$567$	−17.1410	+	16.5284i	−0.719853	+	0.694126i
$568$	−22.3027	+	92.8974i	−0.935800	+	3.89789i
$569$	−33.4081	+	1.75084i	−1.40054	+	0.0733992i	−0.737582	−	0.675258i	$-0.764032\pi$
$569$	−33.4081	+	1.75084i	−1.40054	+	0.0733992i	−0.662958	+	0.748657i	$0.730699\pi$
$570$	−1.34928	+	1.59764i	−0.0565153	+	0.0669178i
$571$	−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
$576$	33.3089	−	106.514i	1.38787	−	4.43809i
$577$	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
$579$	−15.0490	+	32.0059i	−0.625417	+	1.33012i
$580$	−72.1160	−	17.3135i	−2.99445	−	0.718905i
$581$	0.665131	+	5.67186i	0.0275943	+	0.235308i
$582$	−22.5355	−	0.465245i	−0.934125	−	0.0192850i
$583$	−2.68227	+	10.0104i	−0.111088	+	0.414588i
$584$	23.5204	−	21.1778i	0.973280	−	0.876346i
$585$	15.1824	−	20.2465i	0.627715	−	0.837090i
$586$	16.4410	+	34.4692i	0.679170	+	1.42391i
$587$	−36.3968	+	22.3040i	−1.50226	+	0.920584i	−0.503872	+	0.863778i	$0.668092\pi$
$587$	−36.3968	+	22.3040i	−1.50226	+	0.920584i	−0.998385	+	0.0568062i	$0.981908\pi$
$588$	67.0886	−	12.6695i	2.76669	−	0.522480i
$589$	0.297921	−	0.254449i	0.0122756	−	0.0104844i
$590$	−26.9980	+	60.6385i	−1.11149	+	2.49645i
$591$	−2.52883	−	3.44041i	−0.104022	−	0.141519i
$592$	−23.4067	+	10.4213i	−0.962011	+	0.428315i
$593$	−0.890245	+	33.9971i	−0.0365580	+	1.39609i	0.697295	+	0.716784i	$0.254387\pi$
$593$	−0.890245	+	33.9971i	−0.0365580	+	1.39609i	−0.733853	+	0.679308i	$0.762280\pi$
$594$	−4.48290	+	72.2983i	−0.183936	+	2.96644i
$595$	28.5495	+	8.08492i	1.17042	+	0.331449i
$596$	56.4977	−	92.1959i	2.31424	−	3.77649i
$597$	−3.35482	+	4.93968i	−0.137304	+	0.202168i
$598$	8.42737	−	17.6683i	0.344621	−	0.722512i
$599$	2.05784	+	19.5790i	0.0840809	+	0.799976i	0.952581	+	0.304286i	$0.0984180\pi$
$599$	2.05784	+	19.5790i	0.0840809	+	0.799976i	−0.868500	+	0.495690i	$0.834915\pi$
$600$	−3.32335	+	3.02585i	−0.135675	+	0.123530i
$601$	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
$603$	−14.0688	+	7.84170i	−0.572924	+	0.319339i
$604$	−93.6361	−	17.3544i	−3.81000	−	0.706142i
$605$	21.0776	+	23.4090i	0.856926	+	0.951713i
$606$	−70.1267	−	16.4257i	−2.84870	−	0.667250i
$607$	−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
$609$	−5.52879	−	27.1610i	−0.224038	−	1.10062i
$610$	−45.4299	−	23.1477i	−1.83940	−	0.937223i
$611$	20.8163	+	18.7431i	0.842136	+	0.758263i
$612$	82.3365	+	28.1346i	3.32825	+	1.13727i
$613$	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
$615$	−4.29573	+	23.7640i	−0.173220	+	0.958257i
$616$	80.2486	−	107.225i	3.23331	−	4.32023i
$617$	−5.78169	−	36.5041i	−0.232762	−	1.46960i	−0.776378	−	0.630267i	$-0.782945\pi$
$617$	−5.78169	−	36.5041i	−0.232762	−	1.46960i	0.543616	−	0.839334i	$-0.317055\pi$
$618$	3.47716	−	9.21044i	0.139872	−	0.370498i
$619$	−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
$621$	−8.81542	+	3.55305i	−0.353750	+	0.142579i
$622$	−52.7157	+	12.6559i	−2.11371	+	0.507456i
$623$	12.3703	−	14.8411i	0.495604	−	0.594598i
$624$	−105.645	+	31.9310i	−4.22920	+	1.27826i
$625$	−23.1231	+	4.91496i	−0.924922	+	0.196598i
$626$	−31.1524	−	87.9716i	−1.24510	−	3.51605i
$627$	−1.55875	+	0.805128i	−0.0622505	+	0.0321537i
$628$	1.39959	−	2.57772i	0.0558497	−	0.102862i
$629$	−3.07039	−	7.41258i	−0.122425	−	0.295559i
$630$	44.0527	+	18.4068i	1.75510	+	0.733346i
$631$	−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
$633$	−0.222457	+	3.04185i	−0.00884186	+	0.120903i
$634$	1.78902	+	3.29497i	0.0710512	+	0.130860i
$635$	−1.67981	−	4.37606i	−0.0666612	−	0.173658i
$636$	15.9582	+	12.1054i	0.632785	+	0.480009i
$637$	−19.1343	−	19.2167i	−0.758127	−	0.761392i
$638$	−68.2164	−	49.5621i	−2.70071	−	1.96218i
$639$	−26.5171	−	10.6412i	−1.04900	−	0.420960i
$640$	−112.640	+	11.8390i	−4.45250	+	0.467977i
$641$	−2.14396	−	11.5678i	−0.0846813	−	0.456899i	−0.998688	−	0.0512010i	$-0.983695\pi$
$641$	−2.14396	−	11.5678i	−0.0846813	−	0.456899i	0.914007	−	0.405698i	$-0.132972\pi$
$642$	−27.4718	−	60.7943i	−1.08422	−	2.39936i
$643$	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
$645$	34.0330	−	13.2807i	1.34005	−	0.522928i
$646$	0.593761	+	2.79343i	0.0233612	+	0.109906i
$647$	−20.7552	+	5.56135i	−0.815973	+	0.218639i	−0.642585	−	0.766214i	$-0.722138\pi$
$647$	−20.7552	+	5.56135i	−0.815973	+	0.218639i	−0.173388	+	0.984854i	$0.555471\pi$
$648$	81.3271	+	39.1940i	3.19483	+	1.53969i
$649$	−40.3942	+	38.3327i	−1.58561	+	1.50469i
$650$	2.69196	+	0.646281i	0.105587	+	0.0253492i
$651$	−7.58626	−	4.73937i	−0.297329	−	0.185750i
$652$	14.1573	+	43.5716i	0.554442	+	1.70640i
$653$	−5.67470	−	43.1036i	−0.222068	−	1.68678i	−0.632244	−	0.774769i	$-0.717866\pi$
$653$	−5.67470	−	43.1036i	−0.222068	−	1.68678i	0.410176	−	0.912006i	$-0.365467\pi$
$654$	−11.6471	−	13.4850i	−0.455437	−	0.527307i
$655$	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	$-0.719068\pi$
$659$	9.24456	−	22.3184i	0.360117	−	0.869400i	0.995282	−	0.0970231i	$-0.0309321\pi$
$660$	100.828	−	36.3346i	3.92472	−	1.41432i
$661$	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
$663$	−9.12957	−	33.3325i	−0.354563	−	1.29453i
$664$	19.2915	−	9.82952i	0.748656	−	0.381459i
$665$	0.164696	+	1.14455i	0.00638664	+	0.0443836i
$666$	−3.47921	−	12.4321i	−0.134817	−	0.481735i
$667$	2.01620	−	10.8784i	0.0780674	−	0.421214i
$668$	6.96811	+	4.78905i	0.269604	+	0.185294i
$669$	−1.05104	+	2.09133i	−0.0406355	+	0.0808555i
$670$	25.6209	+	19.6596i	0.989821	+	0.759517i
$671$	−27.7808	−	32.5271i	−1.07246	−	1.25569i
$672$	−59.8988	−	99.6657i	−2.31065	−	3.84469i
$673$	−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
$675$	−0.750722	−	1.11501i	−0.0288953	−	0.0429167i
$676$	8.78828	+	7.11661i	0.338011	+	0.273716i
$677$	22.2465	−	8.53963i	0.855002	−	0.328205i	0.108914	−	0.994051i	$-0.465263\pi$
$677$	22.2465	−	8.53963i	0.855002	−	0.328205i	0.746089	+	0.665847i	$0.231929\pi$
$678$	−10.6815	+	6.24609i	−0.410220	+	0.239880i
$679$	−8.47029	+	9.14338i	−0.325060	+	0.350891i
$680$	−8.82648	−	112.151i	−0.338480	−	4.30080i
$681$	9.11068	−	7.07137i	0.349122	−	0.270976i
$682$	−26.7557	+	4.95888i	−1.02453	+	0.189885i
$683$	1.46565	−	11.1328i	0.0560817	−	0.425983i	−0.940255	−	0.340470i	$-0.889414\pi$
$683$	1.46565	−	11.1328i	0.0560817	−	0.425983i	0.996337	−	0.0855128i	$-0.0272529\pi$
$684$	0.303464	+	3.37722i	0.0116032	+	0.129131i
$685$	−2.89901	+	36.8354i	−0.110765	+	1.40741i
$686$	26.3001	−	43.8839i	1.00414	−	1.67550i
$687$	14.6966	−	14.1020i	0.560709	−	0.538025i
$688$	−153.894	−	41.2357i	−5.86715	−	1.57210i
$689$	0.416377	−	7.94495i	0.0158627	−	0.302679i
$690$	13.5497	+	13.4005i	0.515829	+	0.510147i
$691$	−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
$693$	28.2354	+	28.4103i	1.07257	+	1.07922i
$694$	11.3573	−	27.4189i	0.431116	−	1.04081i
$695$	5.79937	+	7.16163i	0.219983	+	0.271656i
$696$	−89.2973	+	55.4040i	−3.38481	+	2.10008i
$697$	22.0403	+	24.5331i	0.834835	+	0.929256i
$698$	−76.2363	+	44.0151i	−2.88559	+	1.66599i
$699$	38.8842	+	13.5277i	1.47074	+	0.511666i
$700$	0.0463086	+	3.85384i	0.00175030	+	0.145661i
$701$	15.0442	+	46.3014i	0.568213	+	1.74878i	0.658208	+	0.752836i	$0.271315\pi$
$701$	15.0442	+	46.3014i	0.568213	+	1.74878i	−0.0899951	+	0.995942i	$0.528685\pi$
$702$	−8.17328	−	55.0046i	−0.308481	−	2.07602i
$703$	0.215229	−	0.226804i	0.00811750	−	0.00855406i
$704$	−179.998	−	53.3177i	−6.78392	−	2.00949i
$705$	−23.8924	+	13.1443i	−0.899839	+	0.495044i
$706$	−12.2475	−	12.2475i	−0.460941	−	0.460941i
$707$	−32.5488	+	22.9508i	−1.22412	+	0.863155i
$708$	39.1270	+	100.266i	1.47048	+	3.76823i
$709$	−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
$711$	−44.9804	+	22.0694i	−1.68690	+	0.827666i
$712$	−69.0494	−	24.4517i	−2.58774	−	0.916365i
$713$	−2.09864	−	2.88853i	−0.0785945	−	0.108176i
$714$	56.7452	−	32.1124i	2.12364	−	1.20178i
$715$	−34.4393	−	25.0216i	−1.28796	−	0.935756i
$716$	1.48963	−	56.8868i	0.0556702	−	2.12596i
$717$	−5.18552	−	12.3254i	−0.193657	−	0.460302i
$718$	−3.34615	+	4.13215i	−0.124877	+	0.154210i
$719$	−7.10941	−	0.186167i	−0.265136	−	0.00694284i	−0.106622	−	0.994300i	$-0.534004\pi$
$719$	−7.10941	−	0.186167i	−0.265136	−	0.00694284i	−0.158514	+	0.987357i	$0.550670\pi$
$720$	4.43444	−	107.352i	0.165262	−	4.00076i
$721$	−2.52956	−	4.82045i	−0.0942056	−	0.179523i
$722$	42.3726	−	30.7855i	1.57695	−	1.14572i
$723$	17.0872	+	18.7672i	0.635479	+	0.697959i
$724$	−23.5385	−	3.09890i	−0.874801	−	0.115170i
$725$	1.56415	−	0.0409588i	0.0580912	−	0.00152117i
$726$	69.1419	+	3.23973i	2.56610	+	0.120238i
$727$	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
$729$	−15.1358	+	22.3586i	−0.560584	+	0.828097i
$730$	10.3367	−	15.9171i	0.382578	−	0.589118i
$731$	14.1698	−	47.8363i	0.524088	−	1.76929i
$732$	−78.4862	+	25.9831i	−2.90093	+	0.960363i
$733$	−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
$735$	23.7898	−	11.4463i	0.877501	−	0.422203i
$736$	−7.26068	−	45.8421i	−0.267632	−	1.68976i
$737$	13.5468	+	23.4637i	0.499002	+	0.864298i
$738$	30.4906	+	43.4307i	1.12237	+	1.59871i
$739$	−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
$741$	1.04197	−	0.853365i	0.0382776	−	0.0313492i
$742$	14.7243	−	2.91240i	0.540546	−	0.106918i
$743$	17.9100	+	9.12562i	0.657055	+	0.334786i	0.750531	−	0.660835i	$-0.229798\pi$
$743$	17.9100	+	9.12562i	0.657055	+	0.334786i	−0.0934757	+	0.995622i	$0.529798\pi$
$744$	−6.86724	+	33.2111i	−0.251765	+	1.21758i
$745$	11.8751	−	40.0897i	0.435070	−	1.46877i
$746$	7.41499	+	0.388603i	0.271482	+	0.0142278i
$747$	2.06908	+	6.13589i	0.0757036	+	0.224500i
$748$	45.2290	−	139.201i	1.65374	−	5.08968i
$749$	−35.2185	−	10.9771i	−1.28686	−	0.401096i
$750$	−29.5846	+	46.1134i	−1.08028	+	1.68382i
$751$	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
$753$	7.29004	−	22.8666i	0.265664	−	0.833304i
$754$	59.1346	+	26.3284i	2.15355	+	0.958824i
$755$	−36.7102	+	2.88915i	−1.33602	+	0.105147i
$756$	71.4502	−	29.8009i	2.59862	−	1.08385i
$757$	−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
$759$	6.20002	+	14.7368i	0.225047	+	0.534913i
$760$	3.85280	−	2.09190i	0.139756	−	0.0758812i
$761$	−1.13973	+	10.8438i	−0.0413153	+	0.393089i	0.954250	+	0.299011i	$0.0966568\pi$
$761$	−1.13973	+	10.8438i	−0.0413153	+	0.393089i	−0.995565	+	0.0940775i	$0.970010\pi$
$762$	−9.43260	−	4.13723i	−0.341707	−	0.149876i
$763$	−9.85193	−	0.139555i	−0.356664	−	0.00505223i
$764$	−59.8360	+	51.1048i	−2.16479	+	1.84890i
$765$	33.5686	+	2.26812i	1.21368	+	0.0820040i
$766$	2.53794	+	96.9201i	0.0916996	+	3.50187i
$767$	24.2139	−	35.2315i	0.874314	−	1.27213i
$768$	−75.0089	+	93.6844i	−2.70665	+	3.38054i
$769$	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
$771$	0.137974	−	6.68315i	0.00496901	−	0.240688i
$772$	83.4073	−	79.1505i	3.00189	−	2.84869i
$773$	−1.65694	+	1.74605i	−0.0595961	+	0.0628011i	−0.754492	−	0.656309i	$-0.772117\pi$
$773$	−1.65694	+	1.74605i	−0.0595961	+	0.0628011i	0.694896	+	0.719110i	$0.255450\pi$
$774$	31.8370	−	73.6930i	1.14436	−	2.64884i
$775$	0.337877	−	0.375250i	0.0121369	−	0.0134794i
$776$	43.6578	+	18.0836i	1.56722	+	0.649165i
$777$	−6.41643	−	3.12871i	−0.230188	−	0.112242i
$778$			2.92340i			0.104809i
$779$	−0.524052	+	1.17352i	−0.0187761	+	0.0420458i
$780$	−69.9127	+	43.3769i	−2.50328	+	1.55314i
$781$	−17.2243	+	44.8708i	−0.616334	+	1.60560i
$782$	25.8026	−	3.39698i	0.922700	−	0.121476i
$783$	−12.5082	−	28.8330i	−0.447005	−	1.03041i
$784$	−113.161	−	21.2248i	−4.04148	−	0.758030i
$785$	0.264772	−	1.10286i	0.00945013	−	0.0393626i
$786$	2.66210	−	0.729132i	0.0949539	−	0.0260073i
$787$	−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
$789$	2.64492	+	0.767555i	0.0941617	+	0.0273257i
$790$	76.3892	+	65.2425i	2.71781	+	2.32122i
$791$	−1.34204	+	6.70923i	−0.0477176	+	0.238553i
$792$	63.8561	−	137.784i	2.26903	−	4.89594i
$793$	26.0523	+	19.9906i	0.925145	+	0.709889i
$794$	10.4595	−	1.93855i	0.371192	−	0.0687964i
$795$	7.17194	+	2.92429i	0.254362	+	0.103714i
$796$	15.9990	−	10.9958i	0.567071	−	0.389737i
$797$	−9.54696	+	13.1403i	−0.338171	+	0.465452i	−0.943906	−	0.330214i	$-0.892879\pi$
$797$	−9.54696	+	13.1403i	−0.338171	+	0.465452i	0.605735	+	0.795666i	$0.292879\pi$
$798$	2.04269	+	1.51119i	0.0723103	+	0.0534956i
$799$	−5.82572	+	36.7822i	−0.206099	+	1.30126i
$800$	6.12809	−	2.35235i	0.216661	−	0.0831682i
$801$	10.2394	−	19.3672i	0.361793	−	0.684307i
$802$	−30.5356	−	68.5840i	−1.07825	−	2.42179i
$803$	13.1222	−	9.01861i	0.463071	−	0.318260i
$804$	51.8785	−	7.12243i	1.82961	−	0.251189i
$805$	10.5159	−	0.677902i	0.370636	−	0.0238929i
$806$	19.2995	−	7.99411i	0.679795	−	0.281580i
$807$	1.60828	+	2.44676i	0.0566142	+	0.0861302i
$808$	124.441	+	85.5257i	4.37781	+	3.00878i
$809$	−33.7010	+	11.9341i	−1.18486	+	0.419582i	−0.852075	−	0.523419i	$-0.824656\pi$
$809$	−33.7010	+	11.9341i	−1.18486	+	0.419582i	−0.332788	+	0.943002i	$0.607989\pi$
$810$	53.1895	+	10.0799i	1.86889	+	0.354171i
$811$	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
$813$	32.4024	+	8.49017i	1.13640	+	0.297763i
$814$	−20.8218	+	6.16771i	−0.729805	+	0.216178i
$815$	9.64842	+	14.8573i	0.337969	+	0.520427i
$816$	−112.101	−	94.6745i	−3.92431	−	3.31427i
$817$	1.92763	−	0.253777i	0.0674391	−	0.00887853i
$818$	73.5237	−	11.6450i	2.57070	−	0.407158i
$819$	−25.7366	−	16.8268i	−0.899311	−	0.587976i
$820$	41.0973	−	66.8975i	1.43518	−	2.33616i
$821$	12.6129	−	7.28203i	0.440192	−	0.254145i	−0.263487	−	0.964663i	$-0.584873\pi$
$821$	12.6129	−	7.28203i	0.440192	−	0.254145i	0.703679	+	0.710518i	$0.251539\pi$
$822$	53.0711	+	61.4459i	1.85107	+	2.14317i
$823$	−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
$825$	−1.85632	+	1.29100i	−0.0646287	+	0.0449470i
$826$	75.6375	+	27.9965i	2.63176	+	0.974122i
$827$	6.80495	+	28.3447i	0.236631	+	0.985640i	0.956547	+	0.291579i	$0.0941805\pi$
$827$	6.80495	+	28.3447i	0.236631	+	0.985640i	−0.719916	+	0.694062i	$0.755819\pi$
$828$	30.8988	−	0.342240i	1.07381	−	0.0118937i
$829$	−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
$831$	25.8491	+	20.6962i	0.896694	+	0.717943i
$832$	143.671	+	11.3071i	4.98089	+	0.392005i
$833$	7.57174	−	35.2496i	0.262345	−	1.22133i
$834$	20.1501	+	2.00510i	0.697740	+	0.0694310i
$835$	3.08189	+	1.09136i	0.106653	+	0.0377679i
$836$	5.67261	−	0.596215i	0.196191	−	0.0206205i
$837$	−9.52808	−	3.47700i	−0.329339	−	0.120183i
$838$	−1.63076	+	15.5157i	−0.0563337	+	0.535979i
$839$	10.3997	+	6.37296i	0.359039	+	0.220019i	0.690306	−	0.723518i	$-0.257476\pi$
$839$	10.3997	+	6.37296i	0.359039	+	0.220019i	−0.331267	+	0.943537i	$0.607476\pi$
$840$	−72.0076	−	69.5230i	−2.48450	−	2.39877i
$841$	7.49164	+	1.18656i	0.258332	+	0.0409158i
$842$	−36.7574	−	0.962525i	−1.26674	−	0.0331708i
$843$	2.10875	−	28.8349i	0.0726293	−	0.993127i
$844$	4.26894	−	8.95001i	0.146943	−	0.308072i
$845$	3.99468	+	1.77854i	0.137421	+	0.0611838i
$846$	−16.3812	+	57.6389i	−0.563199	+	1.98167i
$847$	26.7370	−	27.3874i	0.918696	−	0.941043i
$848$	−17.6488	−	28.8003i	−0.606064	−	0.989006i
$849$	0.875466	−	18.6841i	0.0300459	−	0.641236i
$850$	1.22863	+	3.46953i	0.0421415	+	0.119004i
$851$	−1.90661	−	2.11750i	−0.0653576	−	0.0725870i
$852$	67.7361	+	63.5700i	2.32060	+	2.17787i
$853$	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
$855$	0.451336	+	1.23103i	0.0154354	+	0.0421004i
$856$	7.31979	+	139.670i	0.250185	+	4.77382i
$857$	−6.23318	+	29.3248i	−0.212921	+	1.00172i	0.733726	+	0.679445i	$0.237779\pi$
$857$	−6.23318	+	29.3248i	−0.212921	+	1.00172i	−0.946648	+	0.322271i	$0.895554\pi$
$858$	−92.3074	+	15.1445i	−3.15132	+	0.517026i
$859$	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
$861$	29.1508	+	3.35123i	0.993457	+	0.114210i
$862$	7.80111			0.265707
$863$	−9.19400	+	7.44515i	−0.312967	+	0.253436i	−0.772914	−	0.634510i	$-0.781202\pi$
$863$	−9.19400	+	7.44515i	−0.312967	+	0.253436i	0.459947	+	0.887946i	$0.347868\pi$
$864$	−89.8402	−	96.5041i	−3.05642	−	3.28314i
$865$	−2.75263	+	12.9501i	−0.0935922	+	0.440316i
$866$	1.42957	+	27.2778i	0.0485788	+	0.926939i
$867$	10.9745	−	12.3250i	0.372713	−	0.418578i
$868$	17.3752	+	23.3205i	0.589753	+	0.791548i
$869$	38.2624	+	75.0941i	1.29796	+	2.54739i
$870$	−43.1242	+	45.9504i	−1.46205	+	1.55786i
$871$	−13.9174	−	15.4568i	−0.471572	−	0.523734i
$872$	12.4697	+	35.2132i	0.422276	+	1.19247i
$873$	−7.25038	+	12.1311i	−0.245388	+	0.410576i
$874$	0.529925	+	0.864758i	0.0179250	+	0.0292509i
$875$	8.19205	+	29.1667i	0.276942	+	0.986015i
$876$	−6.56493	−	30.0659i	−0.221808	−	1.01583i
$877$	−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
$879$	23.8808	+	1.74645i	0.805480	+	0.0589063i
$880$	−180.673	−	4.73108i	−6.09048	−	0.159485i
$881$	32.7878	+	5.19308i	1.10465	+	0.174959i	0.682013	−	0.731340i	$-0.261105\pi$
$881$	32.7878	+	5.19308i	1.10465	+	0.174959i	0.422637	+	0.906299i	$0.361105\pi$
$882$	18.8757	−	54.8549i	0.635580	−	1.84706i
$883$	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
$885$	24.6486	+	33.5338i	0.828555	+	1.12723i
$886$	−36.6380	+	3.85081i	−1.23088	+	0.129371i
$887$	−46.7973	−	16.5718i	−1.57130	−	0.556427i	−0.601193	−	0.799104i	$-0.705308\pi$
$887$	−46.7973	−	16.5718i	−1.57130	−	0.556427i	−0.970107	+	0.242677i	$0.921974\pi$
$888$	−2.67995	+	26.9319i	−0.0899332	+	0.903775i
$889$	−5.17488	+	2.37891i	−0.173560	+	0.0797862i
$890$	−43.7899	−	3.44634i	−1.46784	−	0.115522i
$891$	37.9906	+	24.8896i	1.27273	+	0.833832i
$892$	5.65505	−	5.09183i	0.189345	−	0.170487i
$893$	−1.40183	+	0.375618i	−0.0469104	+	0.0125696i
$894$	−44.2860	−	80.4983i	−1.48114	−	2.69227i
$895$	−5.13684	−	21.3965i	−0.171705	−	0.715205i
$896$	23.1601	+	135.657i	0.773723	+	4.53197i
$897$	−7.00776	−	10.0764i	−0.233982	−	0.336440i
$898$	50.9521	−	56.5880i	1.70029	−	1.88837i
$899$	9.36675	−	7.18736i	0.312399	−	0.239712i
$900$	0.955895	+	4.26433i	0.0318632	+	0.142144i
$901$	9.16021	−	5.28865i	0.305171	−	0.176190i
$902$	72.2737	−	52.3871i	2.40645	−	1.74430i
$903$	−18.7638	−	40.2285i	−0.624419	−	1.33872i
$904$	25.6216	−	4.05806i	0.852161	−	0.134969i
$905$	−9.10183	+	1.19828i	−0.302555	+	0.0398321i
$906$	−52.2092	+	61.8191i	−1.73453	+	2.05380i
$907$	−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
$909$	−30.7209	+	33.0996i	−1.01895	+	1.09785i
$910$	−10.5063	+	60.7518i	−0.348280	+	2.01390i
$911$	−6.83868	+	6.83868i	−0.226575	+	0.226575i	−0.811260	−	0.584685i	$-0.801218\pi$
$911$	−6.83868	+	6.83868i	−0.226575	+	0.226575i	0.584685	+	0.811260i	$0.301218\pi$
$912$	1.59365	−	5.49157i	0.0527710	−	0.181844i
$913$	10.2677	−	3.63598i	0.339811	−	0.120333i
$914$	41.4952	+	28.5189i	1.37254	+	0.943321i
$915$	−26.7144	+	17.5596i	−0.883151	+	0.580504i
$916$	−61.1790	+	25.3412i	−2.02141	+	0.837296i
$917$	0.676512	−	1.36812i	0.0223404	−	0.0451794i
$918$	55.4125	−	48.9420i	1.82889	−	1.61533i
$919$	−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
$921$	11.8228	−	0.0654736i	0.389574	−	0.00215743i
$922$	3.61554	−	1.38788i	0.119072	−	0.0457073i
$923$	5.77198	−	36.4428i	0.189987	−	1.19953i
$924$	−51.9389	−	119.419i	−1.70866	−	3.92858i
$925$	0.236863	−	0.326014i	0.00778802	−	0.0107193i
$926$	−42.6340	+	29.3016i	−1.40104	+	0.962909i
$927$	−3.93752	−	4.75380i	−0.129325	−	0.156135i
$928$	150.909	−	27.9693i	4.95382	−	0.918137i
$929$	36.5919	+	28.0779i	1.20054	+	0.921207i	0.998309	−	0.0581306i	$-0.0185140\pi$
$929$	36.5919	+	28.0779i	1.20054	+	0.921207i	0.202232	+	0.979338i	$0.435181\pi$
$930$	1.17678	+	20.3024i	0.0385881	+	0.665743i
$931$	1.37494	−	0.289167i	0.0450620	−	0.00947707i
$932$	−101.781	−	86.9292i	−3.33395	−	2.84746i
$933$	−9.47353	+	32.6449i	−0.310150	+	1.06875i
$934$	−28.5640	−	106.602i	−0.934642	−	3.48813i
$935$	2.96200	−	56.5183i	0.0968678	−	1.84835i
$936$	−25.9582	+	113.655i	−0.848469	+	3.71492i
$937$	−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
$939$	−57.5925	−	10.3446i	−1.87946	−	0.337583i
$940$	87.8987	−	11.5721i	2.86694	−	0.377440i
$941$	−14.4959	+	37.7632i	−0.472554	+	1.23105i	0.465652	+	0.884968i	$0.345820\pi$
$941$	−14.4959	+	37.7632i	−0.472554	+	1.23105i	−0.938206	+	0.346077i	$0.887513\pi$
$942$	−1.31395	−	2.11776i	−0.0428109	−	0.0690005i
$943$	10.2867	+	5.60005i	0.334981	+	0.182363i
$944$		−	181.502i		−	5.90739i
$945$	23.7044	−	18.2814i	0.771103	−	0.594695i
$946$	−124.757	−	51.6759i	−4.05619	−	1.68013i
$947$	−23.2232	+	25.7920i	−0.754652	+	0.838126i	−0.991045	−	0.133531i	$-0.957368\pi$
$947$	−23.2232	+	25.7920i	−0.754652	+	0.838126i	0.236392	+	0.971658i	$0.424035\pi$
$948$	162.317	−	13.6795i	5.27182	−	0.444289i
$949$	−8.41402	+	8.86653i	−0.273131	+	0.287820i
$950$	−0.104045	+	0.0987347i	−0.00337566	+	0.00320338i
$951$	2.35031	+	0.0485222i	0.0762140	+	0.00157344i
$952$	−135.299	+	19.4690i	−4.38506	+	0.630994i
$953$	31.2629	+	10.1579i	1.01271	+	0.329048i	0.767931	−	0.640532i	$-0.221286\pi$
$953$	31.2629	+	10.1579i	1.01271	+	0.329048i	0.244774	+	0.969580i	$0.421286\pi$
$954$	15.6506	−	6.68673i	0.506708	−	0.216491i
$955$	−17.2343	+	25.0761i	−0.557690	+	0.811445i
$956$	1.13802	+	43.4591i	0.0368061	+	1.40557i
$957$	−48.1779	+	21.7707i	−1.55737	+	0.703745i
$958$	−55.3816	+	47.3004i	−1.78930	+	1.52821i
$959$	44.8913	+	0.635897i	1.44962	+	0.0205342i
$960$	−56.3542	+	128.484i	−1.81883	+	4.14680i
$961$	−2.84211	+	27.0409i	−0.0916811	+	0.872287i
$962$	14.6508	−	7.95472i	0.472360	−	0.256471i
$963$	−41.6456	−	3.91130i	−1.34201	−	0.126040i
$964$	−29.5713	−	77.0359i	−0.952428	−	2.48116i
$965$	23.2315	−	37.9103i	0.747847	−	1.22038i
$966$	15.1896	−	17.4772i	0.488717	−	0.562319i
$967$	−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
$969$	1.70600	+	0.543885i	0.0548045	+	0.0174721i
$970$	28.0942	+	3.69867i	0.902050	+	0.118757i
$971$	−1.28871	+	2.37350i	−0.0413566	+	0.0761693i	−0.898670	−	0.438626i	$-0.855465\pi$
$971$	−1.28871	+	2.37350i	−0.0413566	+	0.0761693i	0.857313	+	0.514795i	$0.172132\pi$
$972$	72.2678	−	49.8291i	2.31799	−	1.59827i
$973$	8.23051	−	7.59182i	0.263858	−	0.243383i
$974$	14.6890	−	45.2081i	0.470665	−	1.44856i
$975$	1.18786	−	1.26571i	0.0380419	−	0.0405351i
$976$	139.229	+	7.29666i	4.45660	+	0.233560i
$977$	−0.152325	+	0.514241i	−0.00487331	+	0.0164520i	−0.961221	−	0.275779i	$-0.911064\pi$
$977$	−0.152325	+	0.514241i	−0.00487331	+	0.0164520i	0.956348	+	0.292231i	$0.0943976\pi$
$978$	38.1209	+	7.88246i	1.21897	+	0.252053i
$979$	−32.8348	−	16.7302i	−1.04941	−	0.534699i
$980$	−85.5812	+	6.55039i	−2.73379	+	0.209245i
$981$	−10.9619	+	2.15750i	−0.349985	+	0.0688838i
$982$	−46.5894	+	37.7273i	−1.48673	+	1.20393i
$983$	−9.05924	+	15.6911i	−0.288945	+	0.500467i	−0.973558	−	0.228439i	$-0.926638\pi$
$983$	−9.05924	+	15.6911i	−0.288945	+	0.500467i	0.684613	+	0.728906i	$0.259971\pi$
$984$	−26.4489	−	108.059i	−0.843161	−	3.44480i
$985$	2.68391	+	4.64868i	0.0855166	+	0.148119i
$986$	13.4627	+	85.0000i	0.428739	+	2.70695i
$987$	17.8057	+	27.9432i	0.566763	+	0.889443i
$988$	−4.16442	+	1.35310i	−0.132488	+	0.0430479i
$989$	−0.927293	−	17.6938i	−0.0294862	−	0.562630i
$990$	15.6025	−	89.7182i	0.495880	−	2.85143i
$991$	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
$993$	8.61159	−	2.60283i	0.273281	−	0.0825983i
$994$	69.3250	−	6.29498i	2.19886	−	0.199665i
$995$	4.87523	−	5.70816i	0.154555	−	0.180961i
$996$	0.985357	−	21.0293i	0.0312222	−	0.666340i
$997$	−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
$999$	−7.85231	−	1.96481i	−0.248436	−	0.0621637i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.14683 + 1.73847i) q^{2} +(0.280422 + 1.70920i) q^{3} +(1.17079 - 5.50812i) q^{4} +(-0.113959 - 2.17447i) q^{5} +(-3.57341 - 3.18186i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(4.55397 + 8.93767i) q^{8} +(-2.84273 + 0.958594i) q^{9} +O(q^{10})\)	\(q+(-2.14683 + 1.73847i) q^{2} +(0.280422 + 1.70920i) q^{3} +(1.17079 - 5.50812i) q^{4} +(-0.113959 - 2.17447i) q^{5} +(-3.57341 - 3.18186i) q^{6} +(-2.62774 + 0.308152i) q^{7} +(4.55397 + 8.93767i) q^{8} +(-2.84273 + 0.958594i) q^{9} +(4.02491 + 4.47011i) q^{10} +(1.68453 + 4.75697i) q^{11} +(9.74280 + 0.456511i) q^{12} +(-2.02418 - 3.30316i) q^{13} +(5.10562 - 5.22981i) q^{14} +(3.68465 - 0.804549i) q^{15} +(-15.0258 - 6.68993i) q^{16} +(2.21736 - 4.64879i) q^{17} +(4.43637 - 6.99994i) q^{18} +(0.200649 + 0.00525417i) q^{19} +(-12.1107 - 1.91814i) q^{20} +(-1.26357 - 4.40493i) q^{21} +(-11.8863 - 7.28391i) q^{22} +(0.191198 - 1.81912i) q^{23} +(-13.9992 + 10.2900i) q^{24} +(0.257271 - 0.0270403i) q^{25} +(10.0880 + 3.57236i) q^{26} +(-2.43559 - 4.58998i) q^{27} +(-1.37919 + 14.8347i) q^{28} +(6.02991 + 0.474564i) q^{29} +(-6.51164 + 8.13289i) q^{30} +(1.45059 - 1.30612i) q^{31} +(24.5098 - 6.56739i) q^{32} +(-7.65823 + 4.21316i) q^{33} +(3.32149 + 13.8350i) q^{34} +(0.969523 + 5.67884i) q^{35} +(1.95183 + 16.7804i) q^{36} +(1.04235 - 1.15765i) q^{37} +(-0.439894 + 0.337542i) q^{38} +(5.07814 - 4.38601i) q^{39} +(18.9157 - 10.9210i) q^{40} +(-2.45695 + 5.91298i) q^{41} +(10.3705 + 7.25997i) q^{42} +(9.56729 - 1.51531i) q^{43} +(28.1742 - 3.70921i) q^{44} +(2.40839 + 6.07219i) q^{45} +(2.75203 + 4.23775i) q^{46} +(-6.93270 + 2.05356i) q^{47} +(7.22085 - 27.5581i) q^{48} +(6.81008 - 1.61949i) q^{49} +(-0.505309 + 0.505309i) q^{50} +(8.56751 + 2.48629i) q^{51} +(-20.5641 + 7.28213i) q^{52} +(1.69245 + 1.16319i) q^{53} +(13.2084 + 5.61971i) q^{54} +(10.1519 - 4.20507i) q^{55} +(-14.7208 - 22.0826i) q^{56} +(0.0472859 + 0.344422i) q^{57} +(-13.7702 + 9.46402i) q^{58} +(4.48835 + 10.0810i) q^{59} +(-0.117611 - 21.2375i) q^{60} +(-7.91348 + 3.03770i) q^{61} +(-0.843527 + 5.32582i) q^{62} +(7.17457 - 3.39493i) q^{63} +(-21.8658 + 30.0956i) q^{64} +(-6.95195 + 4.77795i) q^{65} +(9.11649 - 22.3586i) q^{66} +(5.27896 - 0.978398i) q^{67} +(-23.0101 - 17.6562i) q^{68} +(3.16286 - 0.183327i) q^{69} +(-11.9539 - 10.5060i) q^{70} +(7.24226 + 6.18547i) q^{71} +(-21.5133 - 21.0419i) q^{72} +(-0.816627 - 3.04769i) q^{73} +(-0.225216 + 4.29737i) q^{74} +(0.118362 + 0.432145i) q^{75} +(0.263858 - 1.09905i) q^{76} +(-5.89239 - 11.9810i) q^{77} +(-3.27697 + 18.2442i) q^{78} +(16.5581 - 2.17991i) q^{79} +(-12.8347 + 33.4356i) q^{80} +(7.16219 - 5.45004i) q^{81} +(-5.00488 - 16.9655i) q^{82} -2.15845i q^{83} +(-25.7423 + 1.80267i) q^{84} +(-10.3613 - 4.29181i) q^{85} +(-17.9051 + 19.8856i) q^{86} +(0.879794 + 10.4394i) q^{87} +(-34.8449 + 36.7189i) q^{88} +(-5.29703 + 5.02669i) q^{89} +(-15.7267 - 8.84906i) q^{90} +(6.33690 + 8.05611i) q^{91} +(-9.79611 - 3.18295i) q^{92} +(2.63919 + 2.11308i) q^{93} +(11.3133 - 16.4610i) q^{94} +(-0.0114407 - 0.436904i) q^{95} +(18.0981 + 40.0506i) q^{96} +(3.58219 - 3.05948i) q^{97} +(-11.8047 + 15.3159i) q^{98} +(-9.34867 - 11.9080i) 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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