LMFDB - Embedded newform 225.2.q.a.106.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.6
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68376 - 0.357895i) q^{2} +(-0.402409 - 1.68466i) q^{3} +(0.879882 + 0.391749i) q^{4} +(1.96791 + 1.06176i) q^{5} +(0.0746324 + 2.98058i) q^{6} +(-2.11497 + 3.66323i) q^{7} +(1.44394 + 1.04909i) q^{8} +(-2.67613 + 1.35584i) q^{9} +O(q^{10})$	\(q+(-1.68376 - 0.357895i) q^{2} +(-0.402409 - 1.68466i) q^{3} +(0.879882 + 0.391749i) q^{4} +(1.96791 + 1.06176i) q^{5} +(0.0746324 + 2.98058i) q^{6} +(-2.11497 + 3.66323i) q^{7} +(1.44394 + 1.04909i) q^{8} +(-2.67613 + 1.35584i) q^{9} +(-2.93350 - 2.49206i) q^{10} +(5.35421 + 1.13807i) q^{11} +(0.305889 - 1.63994i) q^{12} +(-2.27272 + 0.483081i) q^{13} +(4.87216 - 5.41109i) q^{14} +(0.996792 - 3.74251i) q^{15} +(-3.34474 - 3.71472i) q^{16} +(-1.13466 - 0.824379i) q^{17} +(4.99123 - 1.32515i) q^{18} +(4.74872 + 3.45015i) q^{19} +(1.31559 + 1.70515i) q^{20} +(7.02237 + 2.08888i) q^{21} +(-8.60791 - 3.83249i) q^{22} +(2.33826 - 2.59691i) q^{23} +(1.18629 - 2.85471i) q^{24} +(2.74534 + 4.17889i) q^{25} +3.99961 q^{26} +(3.36103 + 3.96276i) q^{27} +(-3.29599 + 2.39468i) q^{28} +(0.451070 + 4.29164i) q^{29} +(-3.01779 + 5.94476i) q^{30} +(0.330923 - 3.14852i) q^{31} +(2.51747 + 4.36039i) q^{32} +(-0.237324 - 9.47797i) q^{33} +(1.61546 + 1.79415i) q^{34} +(-8.05154 + 4.96333i) q^{35} +(-2.88583 + 0.144610i) q^{36} +(0.930443 - 2.86361i) q^{37} +(-6.76093 - 7.50877i) q^{38} +(1.72839 + 3.63435i) q^{39} +(1.72767 + 3.59763i) q^{40} +(-4.52265 + 0.961319i) q^{41} +(-11.0764 - 6.03045i) q^{42} +(-2.17619 + 3.76927i) q^{43} +(4.26523 + 3.09887i) q^{44} +(-6.70597 - 0.173229i) q^{45} +(-4.86650 + 3.53572i) q^{46} +(0.300021 + 2.85451i) q^{47} +(-4.91206 + 7.12958i) q^{48} +(-5.44619 - 9.43308i) q^{49} +(-3.12690 - 8.01881i) q^{50} +(-0.932197 + 2.24325i) q^{51} +(-2.18897 - 0.465280i) q^{52} +(4.61926 - 3.35609i) q^{53} +(-4.24093 - 7.87525i) q^{54} +(9.32824 + 7.92450i) q^{55} +(-6.89694 + 3.07072i) q^{56} +(3.90138 - 9.38833i) q^{57} +(0.776463 - 7.38755i) q^{58} +(11.3426 - 2.41094i) q^{59} +(2.34318 - 2.90248i) q^{60} +(-10.6036 - 2.25387i) q^{61} +(-1.68404 + 5.18293i) q^{62} +(0.693168 - 12.6709i) q^{63} +(0.411065 + 1.26513i) q^{64} +(-4.98542 - 1.46242i) q^{65} +(-2.99252 + 16.0436i) q^{66} +(-1.17916 + 11.2190i) q^{67} +(-0.675418 - 1.16986i) q^{68} +(-5.31583 - 2.89415i) q^{69} +(15.3332 - 5.47547i) q^{70} +(-5.34318 + 3.88205i) q^{71} +(-5.28658 - 0.849733i) q^{72} +(1.20170 + 3.69845i) q^{73} +(-2.59152 + 4.48864i) q^{74} +(5.93524 - 6.30658i) q^{75} +(2.82672 + 4.89603i) q^{76} +(-15.4930 + 17.2067i) q^{77} +(-1.60948 - 6.73797i) q^{78} +(0.299995 + 2.85427i) q^{79} +(-2.63803 - 10.8615i) q^{80} +(5.32338 - 7.25683i) q^{81} +7.95913 q^{82} +(6.23662 - 2.77672i) q^{83} +(5.36055 + 4.58897i) q^{84} +(-1.35762 - 2.82704i) q^{85} +(5.01319 - 5.56772i) q^{86} +(7.04843 - 2.48690i) q^{87} +(6.53724 + 7.26034i) q^{88} +(-1.41471 - 4.35403i) q^{89} +(11.2293 + 2.69171i) q^{90} +(3.03709 - 9.34720i) q^{91} +(3.07473 - 1.36896i) q^{92} +(-5.43734 + 0.709504i) q^{93} +(0.516451 - 4.91370i) q^{94} +(5.68183 + 11.8316i) q^{95} +(6.33270 - 5.99573i) q^{96} +(-1.44531 - 13.7512i) q^{97} +(5.79405 + 17.8322i) q^{98} +(-15.8716 + 4.21384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.68376	−	0.357895i	−1.19060	−	0.253070i	−0.430327	−	0.902673i	$-0.641602\pi$
$2$	−1.68376	−	0.357895i	−1.19060	−	0.253070i	−0.760274	+	0.649603i	$0.774935\pi$
$3$	−0.402409	−	1.68466i	−0.232331	−	0.972637i
$3$	−0.402409	−	1.68466i	−0.232331	−	0.972637i
$4$	0.879882	+	0.391749i	0.439941	+	0.195874i
$5$	1.96791	+	1.06176i	0.880076	+	0.474833i
$5$	1.96791	+	1.06176i	0.880076	+	0.474833i
$6$	0.0746324	+	2.98058i	0.0304686	+	1.21682i
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	0.120635	+	0.992697i	$0.461507\pi$
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	−0.920018	+	0.391876i	$0.871826\pi$
$8$	1.44394	+	1.04909i	0.510511	+	0.370908i
$9$	−2.67613	+	1.35584i	−0.892044	+	0.451948i
$10$	−2.93350	−	2.49206i	−0.927654	−	0.788057i
$11$	5.35421	+	1.13807i	1.61435	+	0.343142i	0.924611	−	0.380912i	$-0.124390\pi$
$11$	5.35421	+	1.13807i	1.61435	+	0.343142i	0.689743	+	0.724054i	$0.257723\pi$
$12$	0.305889	−	1.63994i	0.0883026	−	0.473411i
$13$	−2.27272	+	0.483081i	−0.630338	+	0.133983i	−0.511992	−	0.858990i	$-0.671092\pi$
$13$	−2.27272	+	0.483081i	−0.630338	+	0.133983i	−0.118346	+	0.992972i	$0.537759\pi$
$14$	4.87216	−	5.41109i	1.30214	−	1.44617i
$15$	0.996792	−	3.74251i	0.257371	−	0.966313i
$16$	−3.34474	−	3.71472i	−0.836186	−	0.928679i
$17$	−1.13466	−	0.824379i	−0.275195	−	0.199941i	0.441624	−	0.897200i	$-0.354403\pi$
$17$	−1.13466	−	0.824379i	−0.275195	−	0.199941i	−0.716819	+	0.697259i	$0.754403\pi$
$18$	4.99123	−	1.32515i	1.17644	−	0.312340i
$19$	4.74872	+	3.45015i	1.08943	+	0.791518i	0.979303	−	0.202400i	$-0.0648740\pi$
$19$	4.74872	+	3.45015i	1.08943	+	0.791518i	0.110128	+	0.993917i	$0.464874\pi$
$20$	1.31559	+	1.70515i	0.294174	+	0.381283i
$21$	7.02237	+	2.08888i	1.53241	+	0.455830i
$22$	−8.60791	−	3.83249i	−1.83521	−	0.817090i
$23$	2.33826	−	2.59691i	0.487562	−	0.541492i	−0.448289	−	0.893889i	$-0.647966\pi$
$23$	2.33826	−	2.59691i	0.487562	−	0.541492i	0.935851	+	0.352396i	$0.114633\pi$
$24$	1.18629	−	2.85471i	0.242151	−	0.582715i
$25$	2.74534	+	4.17889i	0.549068	+	0.835778i
$26$	3.99961			0.784388
$27$	3.36103	+	3.96276i	0.646831	+	0.762634i
$28$	−3.29599	+	2.39468i	−0.622884	+	0.452552i
$29$	0.451070	+	4.29164i	0.0837616	+	0.796938i	0.953087	+	0.302698i	$0.0978872\pi$
$29$	0.451070	+	4.29164i	0.0837616	+	0.796938i	−0.869325	+	0.494241i	$0.835446\pi$
$30$	−3.01779	+	5.94476i	−0.550971	+	1.08536i
$31$	0.330923	−	3.14852i	0.0594355	−	0.565491i	−0.923765	−	0.382961i	$-0.874904\pi$
$31$	0.330923	−	3.14852i	0.0594355	−	0.565491i	0.983200	−	0.182531i	$-0.0584289\pi$
$32$	2.51747	+	4.36039i	0.445030	+	0.770815i
$33$	−0.237324	−	9.47797i	−0.0413128	−	1.64990i
$34$	1.61546	+	1.79415i	0.277049	+	0.307694i
$35$	−8.05154	+	4.96333i	−1.36096	+	0.838956i
$36$	−2.88583	+	0.144610i	−0.480972	+	0.0241017i
$37$	0.930443	−	2.86361i	0.152964	−	0.470775i	−0.844985	−	0.534790i	$-0.820391\pi$
$37$	0.930443	−	2.86361i	0.152964	−	0.470775i	0.997949	+	0.0640154i	$0.0203907\pi$
$38$	−6.76093	−	7.50877i	−1.09677	−	1.21808i
$39$	1.72839	+	3.63435i	0.276764	+	0.581962i
$40$	1.72767	+	3.59763i	0.273169	+	0.568835i
$41$	−4.52265	+	0.961319i	−0.706319	+	0.150133i	−0.547047	−	0.837102i	$-0.684248\pi$
$41$	−4.52265	+	0.961319i	−0.706319	+	0.150133i	−0.159272	+	0.987235i	$0.550915\pi$
$42$	−11.0764	−	6.03045i	−1.70913	−	0.930518i
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	−0.982878	−	0.184259i	$-0.941011\pi$
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	0.651012	+	0.759068i	$0.274345\pi$
$44$	4.26523	+	3.09887i	0.643008	+	0.467173i
$45$	−6.70597	−	0.173229i	−0.999667	−	0.0258235i
$46$	−4.86650	+	3.53572i	−0.717527	+	0.521314i
$47$	0.300021	+	2.85451i	0.0437626	+	0.416374i	0.994369	+	0.105974i	$0.0337961\pi$
$47$	0.300021	+	2.85451i	0.0437626	+	0.416374i	−0.950606	+	0.310399i	$0.899537\pi$
$48$	−4.91206	+	7.12958i	−0.708995	+	1.02907i
$49$	−5.44619	−	9.43308i	−0.778027	−	1.34758i
$50$	−3.12690	−	8.01881i	−0.442210	−	1.13403i
$51$	−0.932197	+	2.24325i	−0.130534	+	0.314118i
$52$	−2.18897	−	0.465280i	−0.303555	−	0.0645227i
$53$	4.61926	−	3.35609i	0.634504	−	0.460994i	−0.223454	−	0.974715i	$-0.571733\pi$
$53$	4.61926	−	3.35609i	0.634504	−	0.460994i	0.857958	+	0.513720i	$0.171733\pi$
$54$	−4.24093	−	7.87525i	−0.577118	−	1.07169i
$55$	9.32824	+	7.92450i	1.25782	+	1.06854i
$56$	−6.89694	+	3.07072i	−0.921643	+	0.410342i
$57$	3.90138	−	9.38833i	0.516750	−	1.24351i
$58$	0.776463	−	7.38755i	0.101955	−	0.970033i
$59$	11.3426	−	2.41094i	1.47668	−	0.313877i	0.601966	−	0.798522i	$-0.294384\pi$
$59$	11.3426	−	2.41094i	1.47668	−	0.313877i	0.874711	+	0.484645i	$0.161051\pi$
$60$	2.34318	−	2.90248i	0.302504	−	0.374708i
$61$	−10.6036	−	2.25387i	−1.35766	−	0.288579i	−0.529136	−	0.848537i	$-0.677484\pi$
$61$	−10.6036	−	2.25387i	−1.35766	−	0.288579i	−0.828521	+	0.559958i	$0.810817\pi$
$62$	−1.68404	+	5.18293i	−0.213873	+	0.658233i
$63$	0.693168	−	12.6709i	0.0873309	−	1.59638i
$64$	0.411065	+	1.26513i	0.0513831	+	0.158141i
$65$	−4.98542	−	1.46242i	−0.618365	−	0.181390i
$66$	−2.99252	+	16.0436i	−0.368354	+	1.97483i
$67$	−1.17916	+	11.2190i	−0.144058	+	1.37062i	0.648683	+	0.761059i	$0.275320\pi$
$67$	−1.17916	+	11.2190i	−0.144058	+	1.37062i	−0.792741	+	0.609559i	$0.791347\pi$
$68$	−0.675418	−	1.16986i	−0.0819064	−	0.141866i
$69$	−5.31583	−	2.89415i	−0.639951	−	0.348415i
$70$	15.3332	−	5.47547i	1.83267	−	0.654444i
$71$	−5.34318	+	3.88205i	−0.634119	+	0.460714i	−0.857825	−	0.513942i	$-0.828184\pi$
$71$	−5.34318	+	3.88205i	−0.634119	+	0.460714i	0.223706	+	0.974657i	$0.428184\pi$
$72$	−5.28658	−	0.849733i	−0.623030	−	0.100142i
$73$	1.20170	+	3.69845i	0.140648	+	0.432871i	0.996426	−	0.0844731i	$-0.0269207\pi$
$73$	1.20170	+	3.69845i	0.140648	+	0.432871i	−0.855777	+	0.517344i	$0.826921\pi$
$74$	−2.59152	+	4.48864i	−0.301258	+	0.521794i
$75$	5.93524	−	6.30658i	0.685343	−	0.728221i
$76$	2.82672	+	4.89603i	0.324247	+	0.561613i
$77$	−15.4930	+	17.2067i	−1.76559	+	1.96089i
$78$	−1.60948	−	6.73797i	−0.182238	−	0.762925i
$79$	0.299995	+	2.85427i	0.0337521	+	0.321130i	0.998351	+	0.0574078i	$0.0182835\pi$
$79$	0.299995	+	2.85427i	0.0337521	+	0.321130i	−0.964599	+	0.263722i	$0.915050\pi$
$80$	−2.63803	−	10.8615i	−0.294940	−	1.21436i
$81$	5.32338	−	7.25683i	0.591486	−	0.806315i
$82$	7.95913			0.878938
$83$	6.23662	−	2.77672i	0.684558	−	0.304785i	−0.0348298	−	0.999393i	$-0.511089\pi$
$83$	6.23662	−	2.77672i	0.684558	−	0.304785i	0.719388	+	0.694608i	$0.244422\pi$
$84$	5.36055	+	4.58897i	0.584884	+	0.500698i
$85$	−1.35762	−	2.82704i	−0.147254	−	0.306635i
$86$	5.01319	−	5.56772i	0.540587	−	0.600382i
$87$	7.04843	−	2.48690i	0.755671	−	0.266623i
$88$	6.53724	+	7.26034i	0.696872	+	0.773955i
$89$	−1.41471	−	4.35403i	−0.149959	−	0.461526i	0.847656	−	0.530545i	$-0.178013\pi$
$89$	−1.41471	−	4.35403i	−0.149959	−	0.461526i	−0.997615	+	0.0690197i	$0.978013\pi$
$90$	11.2293	+	2.69171i	1.18367	+	0.283731i
$91$	3.03709	−	9.34720i	0.318373	−	0.979852i
$92$	3.07473	−	1.36896i	0.320563	−	0.142724i
$93$	−5.43734	+	0.709504i	−0.563826	+	0.0735721i
$94$	0.516451	−	4.91370i	0.0532679	−	0.506810i
$95$	5.68183	+	11.8316i	0.582943	+	1.21389i
$96$	6.33270	−	5.99573i	0.646328	−	0.611937i
$97$	−1.44531	−	13.7512i	−0.146749	−	1.39623i	−0.781691	−	0.623666i	$-0.785643\pi$
$97$	−1.44531	−	13.7512i	−0.146749	−	1.39623i	0.634942	−	0.772560i	$-0.281024\pi$
$98$	5.79405	+	17.8322i	0.585287	+	1.80133i
$99$	−15.8716	+	4.21384i	−1.59516	+	0.423506i
$100$	0.778500	+	4.75241i	0.0778500	+	0.475241i
$101$	−4.29330	+	7.43621i	−0.427199	+	0.739930i	−0.996623	−	0.0821135i	$-0.973833\pi$
$101$	−4.29330	+	7.43621i	−0.427199	+	0.739930i	0.569424	+	0.822044i	$0.307166\pi$
$102$	2.37245	−	3.44348i	0.234907	−	0.340955i
$103$	0.0160907	+	0.00716406i	0.00158547	+	0.000705896i	0.407529	−	0.913192i	$-0.366390\pi$
$103$	0.0160907	+	0.00716406i	0.00158547	+	0.000705896i	−0.405944	+	0.913898i	$0.633057\pi$
$104$	−3.78847	−	1.68673i	−0.371490	−	0.165398i
$105$	11.6015	+	11.5668i	1.13219	+	1.12880i
$106$	−8.97887	+	3.99765i	−0.872105	+	0.388286i
$107$	3.33334			0.322246			0.161123	−	0.986934i	$-0.448488\pi$
$107$	3.33334			0.322246			0.161123	+	0.986934i	$0.448488\pi$
$108$	1.40490	+	4.80344i	0.135187	+	0.462211i
$109$	0.885216	−	2.72442i	0.0847883	−	0.260952i	−0.899670	−	0.436571i	$-0.856193\pi$
$109$	0.885216	−	2.72442i	0.0847883	−	0.260952i	0.984458	+	0.175619i	$0.0561928\pi$
$110$	−12.8704	−	16.6815i	−1.22715	−	1.59052i
$111$	−5.19862	−	0.415133i	−0.493431	−	0.0394027i
$112$	20.6819	−	4.39607i	1.95426	−	0.415390i
$113$	7.87550	−	1.67399i	0.740864	−	0.157476i	0.178007	−	0.984029i	$-0.443035\pi$
$113$	7.87550	−	1.67399i	0.740864	−	0.157476i	0.562858	+	0.826554i	$0.309702\pi$
$114$	−9.92904	+	14.4114i	−0.929940	+	1.34976i
$115$	7.35878	−	2.62780i	0.686210	−	0.245044i
$116$	−1.28436	+	3.95285i	−0.119250	+	0.367013i
$117$	5.42711	−	4.37424i	0.501737	−	0.404398i
$118$	−19.9611			−1.83757
$119$	5.41966	−	2.41299i	0.496820	−	0.221198i
$120$	5.36553	−	4.35826i	0.489804	−	0.397852i
$121$	17.3233	+	7.71285i	1.57485	+	0.701168i
$122$	17.0474	+	7.58998i	1.54340	+	0.687165i
$123$	3.43945	+	7.23227i	0.310125	+	0.652111i
$124$	1.52460	−	2.64069i	0.136913	−	0.237141i
$125$	0.965608	+	11.1386i	0.0863666	+	0.996263i
$126$	−5.70197	+	21.0867i	−0.507972	+	1.87855i
$127$	−1.46943	−	4.52243i	−0.130391	−	0.401301i	0.864454	−	0.502712i	$-0.167664\pi$
$127$	−1.46943	−	4.52243i	−0.130391	−	0.401301i	−0.994845	+	0.101411i	$0.967664\pi$
$128$	−1.29194	−	12.2920i	−0.114193	−	1.08647i
$129$	7.22565	+	2.14934i	0.636183	+	0.189239i
$130$	7.87087	+	4.24662i	0.690321	+	0.372453i
$131$	1.92495	−	18.3147i	0.168184	−	1.60016i	−0.506623	−	0.862168i	$-0.669106\pi$
$131$	1.92495	−	18.3147i	0.168184	−	1.60016i	0.674807	−	0.737995i	$-0.264227\pi$
$132$	3.50417	−	8.43247i	0.304999	−	0.733952i
$133$	−22.6821	+	10.0987i	−1.96679	+	0.875670i
$134$	6.00065	−	18.4681i	0.518377	−	1.59540i
$135$	2.40671	+	11.3670i	0.207137	+	0.978312i
$136$	−0.773540	−	2.38071i	−0.0663305	−	0.204144i
$137$	−11.0852	−	12.3114i	−0.947074	−	1.05183i	−0.998586	−	0.0531595i	$-0.983071\pi$
$137$	−11.0852	−	12.3114i	−0.947074	−	1.05183i	0.0515124	−	0.998672i	$-0.483596\pi$
$138$	7.91481	+	6.77558i	0.673753	+	0.576776i
$139$	−7.23633	+	8.03676i	−0.613778	+	0.681669i	−0.967265	−	0.253770i	$-0.918329\pi$
$139$	−7.23633	+	8.03676i	−0.613778	+	0.681669i	0.353487	+	0.935440i	$0.384996\pi$
$140$	−9.02878	+	1.21296i	−0.763071	+	0.102514i
$141$	4.68814	−	1.65412i	0.394813	−	0.139302i
$142$	10.3860	−	4.62415i	0.871575	−	0.388050i
$143$	−12.7184			−1.06356
$144$	13.9876	+	5.40612i	1.16563	+	0.450510i
$145$	−3.66902	+	8.92450i	−0.304696	+	0.741139i
$146$	−0.699721	−	6.65740i	−0.0579094	−	0.550971i
$147$	−13.6999	+	12.9709i	−1.12995	+	1.06982i
$148$	1.94050	−	2.15514i	0.159508	−	0.177151i
$149$	−4.92744	−	8.53458i	−0.403672	−	0.699180i	0.590494	−	0.807042i	$-0.298933\pi$
$149$	−4.92744	−	8.53458i	−0.403672	−	0.699180i	−0.994166	+	0.107862i	$0.965600\pi$
$150$	−12.2506	+	8.49459i	−1.00026	+	0.693581i
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	−0.214994	−	0.976615i	$-0.568973\pi$
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	0.953271	−	0.302117i	$-0.0976934\pi$
$152$	3.23738	+	9.96363i	0.262586	+	0.808157i
$153$	4.15423	+	0.667726i	0.335850	+	0.0539825i
$154$	32.2448	−	23.4272i	2.59836	−	1.88782i
$155$	3.99420	−	5.84465i	0.320822	−	0.469453i
$156$	0.0970255	+	3.87489i	0.00776826	+	0.310240i
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	0.808010	−	0.589169i	$-0.200545\pi$
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	−0.914240	+	0.405172i	$0.867212\pi$
$158$	0.516406	−	4.91328i	0.0410831	−	0.390879i
$159$	−7.51269	−	6.43134i	−0.595795	−	0.510038i
$160$	0.324478	+	11.2538i	0.0256522	+	0.889691i
$161$	4.56772	+	14.0580i	0.359986	+	1.10792i
$162$	−11.5605	+	10.3136i	−0.908279	+	0.810312i
$163$	1.19215	−	3.66905i	0.0933761	−	0.287382i	−0.893451	−	0.449161i	$-0.851723\pi$
$163$	1.19215	−	3.66905i	0.0933761	−	0.287382i	0.986827	+	0.161779i	$0.0517230\pi$
$164$	−4.35599	−	0.925895i	−0.340146	−	0.0723003i
$165$	9.59628	−	18.9038i	0.747070	−	1.47166i
$166$	−11.4948	+	2.44329i	−0.892168	+	0.189636i
$167$	1.09890	−	10.4554i	0.0850358	−	0.809061i	−0.866013	−	0.500021i	$-0.833326\pi$
$167$	1.09890	−	10.4554i	0.0850358	−	0.809061i	0.951049	−	0.309040i	$-0.100008\pi$
$168$	7.94850	+	10.3833i	0.613240	+	0.801089i
$169$	−6.94422	+	3.09176i	−0.534170	+	0.237828i
$170$	1.27412	+	5.24595i	0.0977209	+	0.402346i
$171$	−17.3861	−	2.79453i	−1.32955	−	0.213703i
$172$	−3.39140	+	2.46399i	−0.258592	+	0.187878i
$173$	−6.01334	−	1.27818i	−0.457186	−	0.0971779i	−0.0264386	−	0.999650i	$-0.508417\pi$
$173$	−6.01334	−	1.27818i	−0.457186	−	0.0971779i	−0.430747	+	0.902473i	$0.641750\pi$
$174$	−12.7579	+	1.66475i	−0.967177	+	0.126204i
$175$	−21.1146	+	1.21860i	−1.59611	+	0.0921172i
$176$	−13.6808	−	23.6959i	−1.03123	−	1.78615i
$177$	−8.62596	−	18.1381i	−0.648367	−	1.36335i
$178$	0.823751	+	7.83747i	0.0617428	+	0.587443i
$179$	5.82725	−	4.23375i	0.435549	−	0.316445i	−0.348315	−	0.937378i	$-0.613246\pi$
$179$	5.82725	−	4.23375i	0.435549	−	0.316445i	0.783864	+	0.620933i	$0.213246\pi$
$180$	−5.83260	−	2.77948i	−0.434736	−	0.207170i
$181$	−18.3734	−	13.3490i	−1.36568	−	0.992226i	−0.998061	−	0.0622510i	$-0.980172\pi$
$181$	−18.3734	−	13.3490i	−1.36568	−	0.992226i	−0.367622	−	0.929975i	$-0.619828\pi$
$182$	−8.45906	+	14.6515i	−0.627027	+	1.08604i
$183$	0.470004	+	18.7705i	0.0347437	+	1.38755i
$184$	6.10070	−	1.29674i	0.449749	−	0.0955972i
$185$	4.87149	−	4.64742i	0.358159	−	0.341685i
$186$	9.40913	+	0.751362i	0.689911	+	0.0550925i
$187$	−5.13700	−	5.70522i	−0.375655	−	0.417207i
$188$	−0.854269	+	2.62917i	−0.0623039	+	0.191752i
$189$	−21.6250	+	3.93113i	−1.57299	+	0.285948i
$190$	−5.33240	−	21.9551i	−0.386853	−	1.59279i
$191$	−7.18086	−	7.97515i	−0.519589	−	0.577062i	0.425052	−	0.905169i	$-0.360256\pi$
$191$	−7.18086	−	7.97515i	−0.519589	−	0.577062i	−0.944641	+	0.328107i	$0.893589\pi$
$192$	1.96589	−	1.20160i	0.141876	−	0.0867182i
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	0.998930	+	0.0462566i	$0.0147292\pi$
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	−0.459405	+	0.888227i	$0.651937\pi$
$194$	−2.48793	+	23.6711i	−0.178623	+	1.69949i
$195$	−0.457490	+	8.98720i	−0.0327615	+	0.643587i
$196$	−1.09661	−	10.4335i	−0.0783292	−	0.745253i
$197$	6.42527	−	4.66823i	0.457782	−	0.332598i	−0.334879	−	0.942261i	$-0.608695\pi$
$197$	6.42527	−	4.66823i	0.457782	−	0.332598i	0.792660	+	0.609663i	$0.208695\pi$
$198$	28.2322	−	1.41473i	2.00637	−	0.100540i
$199$	−14.1116			−1.00034			−0.500172	−	0.865926i	$-0.666730\pi$
$199$	−14.1116			−1.00034			−0.500172	+	0.865926i	$0.666730\pi$
$200$	−0.419902	+	8.91418i	−0.0296916	+	0.630327i
$201$	19.3746	−	2.52814i	1.36658	−	0.178321i
$202$	9.89028	−	10.9843i	0.695878	−	0.772851i
$203$	−16.6753	−	7.42432i	−1.17038	−	0.521085i
$204$	−1.69901	+	1.60861i	−0.118955	+	0.112625i
$205$	−9.92085	−	2.91017i	−0.692903	−	0.203255i
$206$	−0.0245290	−	0.0178214i	−0.00170902	−	0.00124167i
$207$	−2.73651	+	10.1200i	−0.190201	+	0.703387i
$208$	9.39616	+	6.82671i	0.651507	+	0.473347i
$209$	21.4991	+	23.8772i	1.48712	+	1.65162i
$210$	−15.3945	−	23.6279i	−1.06232	−	1.63048i
$211$	4.89947	−	5.44141i	0.337293	−	0.374602i	−0.550507	−	0.834830i	$-0.685566\pi$
$211$	4.89947	−	5.44141i	0.337293	−	0.374602i	0.887801	+	0.460228i	$0.152232\pi$
$212$	5.37915	−	1.14337i	0.369441	−	0.0785272i
$213$	8.69006	+	7.43925i	0.595433	+	0.509729i
$214$	−5.61255	−	1.19299i	−0.383666	−	0.0815508i
$215$	−8.28460	+	5.10700i	−0.565005	+	0.348294i
$216$	0.695861	+	9.24801i	0.0473474	+	0.629247i
$217$	10.8339	+	7.87128i	0.735452	+	0.534337i
$218$	−2.46555	+	4.27046i	−0.166988	+	0.289232i
$219$	5.74705	−	3.51274i	0.388349	−	0.237369i
$220$	5.10334	+	10.6270i	0.344067	+	0.716469i
$221$	2.97700	+	1.32545i	0.200255	+	0.0891592i
$222$	8.60467	+	2.55955i	0.577508	+	0.171786i
$223$	19.8964	+	4.22911i	1.33236	+	0.283202i	0.818419	−	0.574622i	$-0.194851\pi$
$223$	19.8964	+	4.22911i	1.33236	+	0.283202i	0.513943	+	0.857825i	$0.328184\pi$
$224$	−21.2975			−1.42300
$225$	−13.0128	−	7.46102i	−0.867521	−	0.497401i
$226$	−13.8596			−0.921926
$227$	21.2885	+	4.52501i	1.41297	+	0.300335i	0.850278	−	0.526333i	$-0.176434\pi$
$227$	21.2885	+	4.52501i	1.41297	+	0.300335i	0.562689	+	0.826669i	$0.309767\pi$
$228$	7.11062	−	6.73226i	0.470912	−	0.445855i
$229$	−17.1567	−	7.63866i	−1.13375	−	0.504777i	−0.247915	−	0.968782i	$-0.579745\pi$
$229$	−17.1567	−	7.63866i	−1.13375	−	0.504777i	−0.885833	+	0.464005i	$0.846412\pi$
$230$	−13.3309	+	1.79093i	−0.879015	+	0.118091i
$231$	35.2220	+	19.1762i	2.31744	+	1.26170i
$232$	−3.85098	+	6.67010i	−0.252830	+	0.437914i
$233$	−5.17867	−	3.76252i	−0.339266	−	0.246491i	0.405086	−	0.914279i	$-0.367242\pi$
$233$	−5.17867	−	3.76252i	−0.339266	−	0.246491i	−0.744352	+	0.667787i	$0.767242\pi$
$234$	−10.7035	+	5.42285i	−0.699709	+	0.354503i
$235$	−2.44039	+	5.93598i	−0.159193	+	0.387220i
$236$	10.9246	+	2.32210i	0.711131	+	0.151156i
$237$	4.68773	−	1.65397i	0.304501	−	0.107437i
$238$	−9.98903	+	2.12323i	−0.647493	+	0.137629i
$239$	−11.7685	+	13.0702i	−0.761238	+	0.845440i	−0.991824	−	0.127612i	$-0.959269\pi$
$239$	−11.7685	+	13.0702i	−0.761238	+	0.845440i	0.230586	+	0.973052i	$0.425936\pi$
$240$	−17.2364	+	8.81495i	−1.11260	+	0.569003i
$241$	5.08374	+	5.64606i	0.327472	+	0.363695i	0.884289	−	0.466941i	$-0.154644\pi$
$241$	5.08374	+	5.64606i	0.327472	+	0.363695i	−0.556816	+	0.830636i	$0.687977\pi$
$242$	−26.4080	−	19.1866i	−1.69757	−	1.23336i
$243$	−14.3674	−	6.04784i	−0.921672	−	0.387969i
$244$	−8.44700	−	6.13711i	−0.540764	−	0.392888i
$245$	−0.701962	−	24.3460i	−0.0448467	−	1.55541i
$246$	−3.20283	−	13.4084i	−0.204205	−	0.854888i
$247$	−12.4592	−	5.54719i	−0.792759	−	0.352959i
$248$	3.78091	−	4.19912i	0.240088	−	0.266644i
$249$	−7.18750	−	9.38919i	−0.455489	−	0.595016i
$250$	2.36058	−	19.1003i	0.149296	−	1.20801i
$251$	25.9812			1.63992			0.819959	−	0.572422i	$-0.193996\pi$
$251$	25.9812			1.63992			0.819959	+	0.572422i	$0.193996\pi$
$252$	5.57370	−	10.8773i	0.351110	−	0.685207i
$253$	15.4750	−	11.2433i	0.972906	−	0.706858i
$254$	0.855612	+	8.14061i	0.0536859	+	0.510787i
$255$	−4.21627	+	3.42475i	−0.264033	+	0.214466i
$256$	−1.94583	+	18.5133i	−0.121614	+	1.15708i
$257$	0.478674	+	0.829088i	0.0298589	+	0.0517171i	0.880569	−	0.473919i	$-0.157161\pi$
$257$	0.478674	+	0.829088i	0.0298589	+	0.0517171i	−0.850710	+	0.525636i	$0.823828\pi$
$258$	−11.3970	−	6.20501i	−0.709549	−	0.386307i
$259$	8.52222	+	9.46488i	0.529545	+	0.588119i
$260$	−3.81368	−	3.23978i	−0.236514	−	0.200923i
$261$	−7.02592	−	10.8734i	−0.434894	−	0.673048i
$262$	−9.79591	+	30.1487i	−0.605193	+	1.86259i
$263$	−3.53512	−	3.92615i	−0.217985	−	0.242097i	0.624227	−	0.781243i	$-0.285414\pi$
$263$	−3.53512	−	3.92615i	−0.217985	−	0.242097i	−0.842213	+	0.539146i	$0.818747\pi$
$264$	9.60053	−	13.9346i	0.590872	−	0.857617i
$265$	12.6536	−	1.69994i	0.777307	−	0.104427i
$266$	41.8056	−	8.88605i	2.56326	−	0.544838i
$267$	−6.76574	+	4.13540i	−0.414057	+	0.253082i
$268$	−5.43255	+	9.40945i	−0.331846	+	0.574774i
$269$	14.1657	+	10.2920i	0.863699	+	0.627514i	0.928889	−	0.370359i	$-0.120765\pi$
$269$	14.1657	+	10.2920i	0.863699	+	0.627514i	−0.0651897	+	0.997873i	$0.520765\pi$
$270$	0.0158415	−	20.0006i	0.000964082	−	1.21720i
$271$	−10.8922	+	7.91361i	−0.661651	+	0.480718i	−0.867220	−	0.497925i	$-0.834096\pi$
$271$	−10.8922	+	7.91361i	−0.661651	+	0.480718i	0.205569	+	0.978643i	$0.434096\pi$
$272$	0.732816	+	6.97227i	0.0444335	+	0.422756i
$273$	−16.9690	−	1.35505i	−1.02701	−	0.0820113i
$274$	14.2587	+	24.6968i	0.861400	+	1.49199i
$275$	9.94324	+	25.4990i	0.599600	+	1.53765i
$276$	−3.54353	−	4.62898i	−0.213295	−	0.278632i
$277$	25.7950	+	5.48290i	1.54987	+	0.329436i	0.901804	−	0.432146i	$-0.142244\pi$
$277$	25.7950	+	5.48290i	1.54987	+	0.329436i	0.648069	+	0.761582i	$0.275577\pi$
$278$	15.0606	−	10.9422i	0.903274	−	0.656267i
$279$	3.38331	+	8.87454i	0.202553	+	0.531305i
$280$	−16.8329	−	1.27999i	−1.00596	−	0.0764942i
$281$	22.9358	−	10.2117i	1.36823	−	0.609176i	0.414559	−	0.910022i	$-0.363936\pi$
$281$	22.9358	−	10.2117i	1.36823	−	0.609176i	0.953673	+	0.300846i	$0.0972690\pi$
$282$	−8.48573	+	1.10728i	−0.505318	+	0.0659375i
$283$	1.50697	−	14.3378i	0.0895798	−	0.852295i	−0.853805	−	0.520593i	$-0.825711\pi$
$283$	1.50697	−	14.3378i	0.0895798	−	0.852295i	0.943385	−	0.331701i	$-0.107623\pi$
$284$	−6.22215	+	1.32256i	−0.369217	+	0.0784795i
$285$	17.6457	−	14.3331i	1.04524	−	0.849017i
$286$	21.4148	+	4.55185i	1.26628	+	0.269156i
$287$	6.04373	−	18.6007i	0.356750	−	1.09796i
$288$	−12.6491	−	8.25568i	−0.745355	−	0.486471i
$289$	−4.64544	−	14.2972i	−0.273261	−	0.841011i
$290$	9.37180	−	13.7136i	0.550331	−	0.805292i
$291$	−22.5845	+	7.96848i	−1.32393	+	0.467120i
$292$	−0.391510	+	3.72497i	−0.0229114	+	0.217987i
$293$	3.34662	+	5.79652i	0.195512	+	0.338636i	0.947068	−	0.321033i	$-0.104030\pi$
$293$	3.34662	+	5.79652i	0.195512	+	0.338636i	−0.751556	+	0.659669i	$0.770697\pi$
$294$	27.7096	−	16.9368i	1.61606	−	0.987777i
$295$	24.8810	+	7.29856i	1.44863	+	0.424939i
$296$	4.34768	−	3.15878i	0.252704	−	0.183600i
$297$	13.4858	+	25.0425i	0.782523	+	1.45312i
$298$	5.24217	+	16.1337i	0.303671	+	0.934602i
$299$	−4.05970	+	7.03160i	−0.234778	+	0.406648i
$300$	7.69291	−	3.22392i	0.444150	−	0.186133i
$301$	−9.20515	−	15.9438i	−0.530576	−	0.918985i
$302$	−20.8990	+	23.2107i	−1.20260	+	1.33562i
$303$	14.2551	+	4.24033i	0.818935	+	0.243601i
$304$	−3.06694	−	29.1800i	−0.175901	−	1.67359i
$305$	−18.4739	−	15.6939i	−1.05781	−	0.898631i
$306$	−6.75577	−	2.61107i	−0.386202	−	0.149265i
$307$	3.26128			0.186131			0.0930657	−	0.995660i	$-0.470333\pi$
$307$	3.26128			0.186131			0.0930657	+	0.995660i	$0.470333\pi$
$308$	−20.3727	+	9.07053i	−1.16084	+	0.516841i
$309$	0.00559391	−	0.0299903i	0.000318226	−	0.00170609i
$310$	−8.81706	+	8.41151i	−0.500775	+	0.477741i
$311$	−21.5663	+	23.9518i	−1.22291	+	1.35818i	−0.309629	+	0.950858i	$0.600205\pi$
$311$	−21.5663	+	23.9518i	−1.22291	+	1.35818i	−0.913284	+	0.407324i	$0.866462\pi$
$312$	−1.31705	+	7.06102i	−0.0745634	+	0.399752i
$313$	−13.7340	−	15.2532i	−0.776292	−	0.862159i	0.217193	−	0.976129i	$-0.430310\pi$
$313$	−13.7340	−	15.2532i	−0.776292	−	0.862159i	−0.993484	+	0.113969i	$0.963643\pi$
$314$	1.41608	+	4.35826i	0.0799142	+	0.245951i
$315$	14.8175	−	24.1992i	0.834871	−	1.36347i
$316$	−0.854194	+	2.62894i	−0.0480522	+	0.147889i
$317$	−3.65413	+	1.62692i	−0.205236	+	0.0913771i	−0.506781	−	0.862075i	$-0.669165\pi$
$317$	−3.65413	+	1.62692i	−0.205236	+	0.0913771i	0.301544	+	0.953452i	$0.402498\pi$
$318$	10.3478	+	13.5176i	0.580279	+	0.758030i
$319$	−2.46908	+	23.4917i	−0.138242	+	1.31528i
$320$	−0.534321	+	2.92611i	−0.0298695	+	0.163575i
$321$	−1.34137	−	5.61553i	−0.0748678	−	0.313428i
$322$	−2.65967	−	25.3051i	−0.148218	−	1.41020i
$323$	−2.54395	−	7.82948i	−0.141549	−	0.435644i
$324$	7.52680	−	4.29973i	0.418156	−	0.238874i
$325$	−8.25812	−	8.17121i	−0.458078	−	0.453257i
$326$	−3.32043	+	5.75115i	−0.183902	+	0.318527i
$327$	−4.94592	−	0.394954i	−0.273510	−	0.0218410i
$328$	−7.53895	−	3.35656i	−0.416269	−	0.185335i
$329$	−11.0913	−	4.93816i	−0.611483	−	0.272250i
$330$	−22.9234	+	28.3950i	−1.26189	+	1.56310i
$331$	1.34664	−	0.599564i	0.0740181	−	0.0329550i	−0.369394	−	0.929273i	$-0.620435\pi$
$331$	1.34664	−	0.599564i	0.0740181	−	0.0329550i	0.443412	+	0.896318i	$0.353768\pi$
$332$	6.57527			0.360865
$333$	1.39262	+	8.92494i	0.0763149	+	0.489084i
$334$	−5.59222	+	17.2111i	−0.305993	+	0.941749i
$335$	−14.2323	+	20.8260i	−0.777596	+	1.13784i
$336$	−15.7285	−	33.0729i	−0.858058	−	1.80427i
$337$	9.11619	−	1.93771i	0.496590	−	0.105554i	0.0471935	−	0.998886i	$-0.484972\pi$
$337$	9.11619	−	1.93771i	0.496590	−	0.105554i	0.449397	+	0.893332i	$0.351639\pi$
$338$	12.7990	−	2.72050i	0.696171	−	0.147976i
$339$	−5.98927	−	12.5939i	−0.325292	−	0.684005i
$340$	−0.0870549	−	3.01930i	−0.00472122	−	0.163745i
$341$	5.35508	−	16.4812i	0.289994	−	0.892509i
$342$	28.2739	+	10.9277i	1.52888	+	0.590903i
$343$	16.4645			0.889001
$344$	−7.09658	+	3.15960i	−0.382622	+	0.170354i
$345$	−7.38819	−	11.3396i	−0.397767	−	0.610501i
$346$	9.66760	+	4.30429i	0.519733	+	0.231400i
$347$	−6.09966	−	2.71574i	−0.327447	−	0.145789i	0.236428	−	0.971649i	$-0.424023\pi$
$347$	−6.09966	−	2.71574i	−0.327447	−	0.145789i	−0.563875	+	0.825860i	$0.690690\pi$
$348$	7.17603	+	0.573038i	0.384675	+	0.0307181i
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	−0.802019	−	0.597299i	$-0.796241\pi$
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	0.918285	+	0.395919i	$0.129574\pi$
$350$	35.9881	+	5.50497i	1.92364	+	0.294253i
$351$	−9.55301	−	7.38258i	−0.509902	−	0.394053i
$352$	8.51663	+	26.2115i	0.453938	+	1.39708i
$353$	0.483612	+	4.60126i	0.0257401	+	0.244900i	0.999825	+	0.0187171i	$0.00595818\pi$
$353$	0.483612	+	4.60126i	0.0257401	+	0.244900i	−0.974085	+	0.226183i	$0.927375\pi$
$354$	8.03253	+	33.6276i	0.426924	+	1.78728i
$355$	−14.6367	+	1.96635i	−0.776835	+	0.104363i
$356$	0.460907	−	4.38524i	0.0244280	−	0.232417i
$357$	−6.24598	−	8.15926i	−0.330572	−	0.431834i
$358$	−11.3270	+	5.04309i	−0.598648	+	0.266535i
$359$	−2.78646	+	8.57585i	−0.147064	+	0.452616i	−0.997271	−	0.0738329i	$-0.976477\pi$
$359$	−2.78646	+	8.57585i	−0.147064	+	0.452616i	0.850207	+	0.526449i	$0.176477\pi$
$360$	−9.50130	−	7.28527i	−0.500763	−	0.383967i
$361$	4.77550	+	14.6975i	0.251342	+	0.773551i
$362$	26.1589	+	29.0524i	1.37488	+	1.52696i
$363$	6.02242	−	32.2876i	0.316095	−	1.69466i
$364$	6.33403	−	7.03465i	0.331993	−	0.368716i
$365$	−1.56203	+	8.55414i	−0.0817601	+	0.447744i
$366$	5.92648	−	31.7733i	0.309782	−	1.66081i
$367$	−8.45692	+	3.76527i	−0.441448	+	0.196545i	−0.615410	−	0.788207i	$-0.711010\pi$
$367$	−8.45692	+	3.76527i	−0.441448	+	0.196545i	0.173962	+	0.984752i	$0.444343\pi$
$368$	−17.4677			−0.910565
$369$	10.7998	−	8.70462i	0.562216	−	0.453144i
$370$	−9.86573	+	6.08168i	−0.512895	+	0.316171i
$371$	2.52455	+	24.0194i	0.131068	+	1.24703i
$372$	−5.06217	−	1.50579i	−0.262461	−	0.0780717i
$373$	−3.62568	+	4.02673i	−0.187731	+	0.208496i	−0.829662	−	0.558266i	$-0.811467\pi$
$373$	−3.62568	+	4.02673i	−0.187731	+	0.208496i	0.641931	+	0.766762i	$0.278133\pi$
$374$	6.60763	+	11.4448i	0.341673	+	0.591794i
$375$	18.3761	−	6.10898i	0.948937	−	0.315466i
$376$	−2.56142	+	4.43650i	−0.132095	+	0.228795i
$377$	−3.09837	−	9.53579i	−0.159574	−	0.491118i
$378$	37.8183	+	1.12039i	1.94516	+	0.0576265i
$379$	7.21488	−	5.24191i	0.370603	−	0.269259i	−0.386858	−	0.922139i	$-0.626440\pi$
$379$	7.21488	−	5.24191i	0.370603	−	0.269259i	0.757461	+	0.652880i	$0.226440\pi$
$380$	0.364338	+	12.6362i	0.0186901	+	0.648225i
$381$	−7.02743	+	4.29535i	−0.360026	+	0.220057i
$382$	9.23661	+	15.9983i	0.472586	+	0.818543i
$383$	1.92865	−	18.3499i	0.0985493	−	0.937634i	−0.827814	−	0.561003i	$-0.810416\pi$
$383$	1.92865	−	18.3499i	0.0985493	−	0.937634i	0.926363	−	0.376631i	$-0.122918\pi$
$384$	−20.1879	+	7.12290i	−1.03021	+	0.363489i
$385$	−48.7582	+	17.4115i	−2.48495	+	0.887370i
$386$	−7.97405	−	24.5416i	−0.405868	−	1.24913i
$387$	0.713232	−	13.0376i	0.0362556	−	0.662741i
$388$	4.11532	−	12.6657i	0.208924	−	0.643001i
$389$	12.3953	+	2.63469i	0.628465	+	0.133584i	0.511123	−	0.859507i	$-0.329230\pi$
$389$	12.3953	+	2.63469i	0.628465	+	0.133584i	0.117341	+	0.993092i	$0.462563\pi$
$390$	3.98678	−	14.9686i	0.201879	−	0.757964i
$391$	−4.79397	+	1.01899i	−0.242441	+	0.0515325i
$392$	2.03212	−	19.3344i	0.102638	−	0.976532i
$393$	−31.6286	+	4.12712i	−1.59545	+	0.208186i
$394$	−12.4894	+	5.56063i	−0.629206	+	0.280140i
$395$	−2.44018	+	5.93546i	−0.122779	+	0.298645i
$396$	−15.6159	−	2.51001i	−0.784730	−	0.126133i
$397$	5.05655	−	3.67380i	0.253781	−	0.184383i	−0.453620	−	0.891195i	$-0.649868\pi$
$397$	5.05655	−	3.67380i	0.253781	−	0.184383i	0.707401	+	0.706813i	$0.249868\pi$
$398$	23.7606	+	5.05047i	1.19101	+	0.253157i
$399$	26.1403	+	34.1477i	1.30865	+	1.70952i
$400$	6.34093	−	24.1755i	0.317046	−	1.20877i
$401$	13.3637	+	23.1466i	0.667352	+	1.15589i	0.978642	+	0.205572i	$0.0659056\pi$
$401$	13.3637	+	23.1466i	0.667352	+	1.15589i	−0.311290	+	0.950315i	$0.600761\pi$
$402$	−33.5271	−	2.67729i	−1.67218	−	0.133531i
$403$	0.768897	+	7.31556i	0.0383015	+	0.364414i
$404$	−6.69072	+	4.86109i	−0.332876	+	0.241848i
$405$	18.1809	−	8.62866i	0.903418	−	0.428761i
$406$	25.4201	+	18.4688i	1.26158	+	0.916592i
$407$	8.24078	−	14.2735i	0.408480	−	0.707509i
$408$	−3.69940	+	2.26117i	−0.183148	+	0.111945i
$409$	−23.4005	+	4.97392i	−1.15708	+	0.245945i	−0.746185	−	0.665739i	$-0.768117\pi$
$409$	−23.4005	+	4.97392i	−1.15708	+	0.245945i	−0.410893	+	0.911683i	$0.634783\pi$
$410$	15.6628	+	8.45067i	0.773533	+	0.417349i
$411$	−16.2796	+	23.6290i	−0.803016	+	1.16553i
$412$	0.0113514	+	0.0126071i	0.000559246	+	0.000621105i
$413$	−15.1574	+	46.6496i	−0.745845	+	2.29547i
$414$	8.22953	−	16.0603i	0.404459	−	0.789320i
$415$	15.2213	+	1.15744i	0.747185	+	0.0568167i
$416$	−7.82792	−	8.69378i	−0.383795	−	0.426248i
$417$	16.4511	+	8.95666i	0.805616	+	0.438610i
$418$	−27.6539	−	47.8980i	−1.35260	−	2.34277i
$419$	1.31148	−	12.4779i	0.0640699	−	0.609584i	−0.914631	−	0.404291i	$-0.867518\pi$
$419$	1.31148	−	12.4779i	0.0640699	−	0.609584i	0.978700	−	0.205294i	$-0.0658150\pi$
$420$	5.67670	+	14.7223i	0.276994	+	0.718374i
$421$	0.123363	+	1.17372i	0.00601232	+	0.0572034i	0.997117	−	0.0758835i	$-0.0241777\pi$
$421$	0.123363	+	1.17372i	0.00601232	+	0.0572034i	−0.991104	+	0.133087i	$0.957511\pi$
$422$	−10.1970	+	7.40856i	−0.496382	+	0.360643i
$423$	−4.67317	−	7.23228i	−0.227217	−	0.351645i
$424$	10.1908			0.494908
$425$	0.329962	−	7.00482i	0.0160055	−	0.339784i
$426$	−11.9695	−	15.6361i	−0.579926	−	0.757570i
$427$	30.6828	−	34.0767i	1.48485	−	1.64909i
$428$	2.93294	+	1.30583i	0.141769	+	0.0631197i
$429$	5.11800	+	21.4261i	0.247099	+	1.03446i
$430$	15.7771	−	5.63396i	0.760839	−	0.271694i
$431$	−20.3282	−	14.7693i	−0.979174	−	0.711412i	−0.0216502	−	0.999766i	$-0.506892\pi$
$431$	−20.3282	−	14.7693i	−0.979174	−	0.711412i	−0.957524	+	0.288354i	$0.906892\pi$
$432$	3.47873	−	25.7397i	0.167371	−	1.23840i
$433$	16.1875	+	11.7609i	0.777922	+	0.565193i	0.904355	−	0.426782i	$-0.140353\pi$
$433$	16.1875	+	11.7609i	0.777922	+	0.565193i	−0.126433	+	0.991975i	$0.540353\pi$
$434$	−15.4246	−	17.1308i	−0.740405	−	0.822303i
$435$	16.5112	+	2.58974i	0.791649	+	0.124169i
$436$	1.84617	−	2.05038i	0.0884156	−	0.0981955i
$437$	20.0635	−	4.26462i	0.959765	−	0.204004i
$438$	−10.9339	+	3.85779i	−0.522440	+	0.184332i
$439$	22.1767	+	4.71380i	1.05844	+	0.224977i	0.704071	−	0.710130i	$-0.251364\pi$
$439$	22.1767	+	4.71380i	1.05844	+	0.224977i	0.354365	+	0.935107i	$0.384697\pi$
$440$	5.15597	+	21.2287i	0.245801	+	1.01204i
$441$	27.3645	+	17.8600i	1.30307	+	0.850476i
$442$	−4.53820	−	3.29719i	−0.215860	−	0.156832i
$443$	2.48298	−	4.30064i	0.117970	−	0.204330i	−0.800993	−	0.598673i	$-0.795695\pi$
$443$	2.48298	−	4.30064i	0.117970	−	0.204330i	0.918963	+	0.394344i	$0.129028\pi$
$444$	−4.41154	−	2.40182i	−0.209363	−	0.113985i
$445$	1.83890	−	10.0704i	0.0871724	−	0.477383i
$446$	−31.9873	−	14.2416i	−1.51464	−	0.674362i
$447$	−12.3950	+	11.7354i	−0.586263	+	0.555067i
$448$	−5.50385	−	1.16988i	−0.260032	−	0.0552716i
$449$	17.7685			0.838548			0.419274	−	0.907860i	$-0.362285\pi$
$449$	17.7685			0.838548			0.419274	+	0.907860i	$0.362285\pi$
$450$	19.2402	+	17.2198i	0.906994	+	0.811750i
$451$	−25.3093			−1.19177
$452$	7.58529	+	1.61230i	0.356782	+	0.0758364i
$453$	−30.1222	−	8.96017i	−1.41527	−	0.420985i
$454$	−34.2253	−	15.2381i	−1.60627	−	0.715159i
$455$	15.9012	−	15.1698i	0.745459	−	0.711170i
$456$	15.4825	−	9.46333i	0.725036	−	0.443161i
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	−0.999355	−	0.0359099i	$-0.988567\pi$
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	0.530776	+	0.847512i	$0.321900\pi$
$458$	26.1540	+	19.0020i	1.22210	+	0.887906i
$459$	−0.546812	−	7.26715i	−0.0255230	−	0.339201i
$460$	7.50430	+	0.570634i	0.349890	+	0.0266060i
$461$	12.3278	+	2.62035i	0.574161	+	0.122042i	0.485836	−	0.874050i	$-0.338515\pi$
$461$	12.3278	+	2.62035i	0.574161	+	0.122042i	0.0883252	+	0.996092i	$0.471849\pi$
$462$	−52.4424	−	44.8940i	−2.43984	−	2.08866i
$463$	24.3569	−	5.17722i	1.13196	−	0.240606i	0.396409	−	0.918074i	$-0.370256\pi$
$463$	24.3569	−	5.17722i	1.13196	−	0.240606i	0.735552	+	0.677469i	$0.236923\pi$
$464$	14.4335	−	16.0300i	0.670059	−	0.744176i
$465$	−11.4535	−	4.37691i	−0.531145	−	0.202974i
$466$	7.37307	+	8.18862i	0.341551	+	0.379331i
$467$	−29.6418	−	21.5361i	−1.37166	−	0.996570i	−0.997605	−	0.0691640i	$-0.977967\pi$
$467$	−29.6418	−	21.5361i	−1.37166	−	0.996570i	−0.374056	−	0.927406i	$-0.622033\pi$
$468$	6.48882	−	1.72275i	0.299946	−	0.0796341i
$469$	−38.6039	−	28.0474i	−1.78256	−	1.29511i
$470$	6.23350	−	9.12138i	0.287530	−	0.420738i
$471$	−3.34830	+	3.17013i	−0.154281	+	0.146072i
$472$	18.9073	+	8.41808i	0.870279	+	0.387473i
$473$	−15.9415	+	17.7048i	−0.732990	+	0.814068i
$474$	−8.48499	+	1.10718i	−0.389728	+	0.0508546i
$475$	−1.38094	+	29.3162i	−0.0633618	+	1.34512i
$476$	5.71395			0.261899
$477$	−7.81142	+	15.2443i	−0.357660	+	0.697990i
$478$	24.4931	−	17.7952i	1.12029	−	0.813936i
$479$	−0.763778	−	7.26686i	−0.0348979	−	0.332031i	−0.998016	−	0.0629539i	$-0.979948\pi$
$479$	−0.763778	−	7.26686i	−0.0348979	−	0.332031i	0.963119	−	0.269078i	$-0.0867188\pi$
$480$	18.8282	−	5.07527i	0.859386	−	0.231653i
$481$	−0.731279	+	6.95766i	−0.0333435	+	0.317242i
$482$	−6.53911	−	11.3261i	−0.297849	−	0.515889i
$483$	21.8448	−	13.3521i	0.993972	−	0.607541i
$484$	12.2210	+	13.5728i	0.555500	+	0.616945i
$485$	11.7562	−	28.5957i	0.533823	−	1.29847i
$486$	22.0269	+	15.3252i	0.999161	+	0.695164i
$487$	−7.65681	+	23.5652i	−0.346963	+	1.06784i	0.613561	+	0.789647i	$0.289736\pi$
$487$	−7.65681	+	23.5652i	−0.346963	+	1.06784i	−0.960524	+	0.278195i	$0.910264\pi$
$488$	−12.9465	−	14.3786i	−0.586063	−	0.650889i
$489$	−6.66082	−	0.531897i	−0.301213	−	0.0240532i
$490$	−7.53137	+	41.2441i	−0.340233	+	1.86322i
$491$	19.9579	−	4.24219i	0.900690	−	0.191447i	0.265780	−	0.964034i	$-0.414371\pi$
$491$	19.9579	−	4.24219i	0.900690	−	0.191447i	0.634910	+	0.772586i	$0.281037\pi$
$492$	0.193078	+	7.71094i	0.00870465	+	0.347636i
$493$	3.02613	−	5.24141i	0.136290	−	0.236061i
$494$	18.9930	+	13.7992i	0.854537	+	0.620857i
$495$	−35.7080	−	8.55938i	−1.60496	−	0.384715i
$496$	−12.8027	+	9.30172i	−0.574859	+	0.417659i
$497$	−2.92019	−	27.7837i	−0.130988	−	1.24627i
$498$	8.74171	+	18.3815i	0.391726	+	0.823697i
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	0.519355	−	0.854559i	$-0.326172\pi$
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	−0.999747	+	0.0224950i	$0.992839\pi$
$500$	−3.51390	+	10.1789i	−0.157146	+	0.455214i
$501$	−18.0559	+	2.35607i	−0.806679	+	0.105261i
$502$	−43.7462	−	9.29854i	−1.95249	−	0.415014i
$503$	−8.58020	+	6.23388i	−0.382572	+	0.277955i	−0.762405	−	0.647100i	$-0.775981\pi$
$503$	−8.58020	+	6.23388i	−0.382572	+	0.277955i	0.379833	+	0.925055i	$0.375981\pi$
$504$	14.2937	−	17.5688i	0.636693	−	0.782578i
$505$	−16.3443	+	10.0753i	−0.727311	+	0.448347i
$506$	−30.0802	+	13.3926i	−1.33723	+	0.595372i
$507$	8.00298	+	10.4545i	0.355425	+	0.464299i
$508$	0.478734	−	4.55485i	0.0212404	−	0.202089i
$509$	−4.48811	+	0.953978i	−0.198932	+	0.0422843i	−0.306300	−	0.951935i	$-0.599091\pi$
$509$	−4.48811	+	0.953978i	−0.198932	+	0.0422843i	0.107368	+	0.994219i	$0.465758\pi$
$510$	8.32490	−	4.25748i	0.368633	−	0.188524i
$511$	−16.0899	−	3.42000i	−0.711773	−	0.151292i
$512$	2.26343	−	6.96611i	0.100030	−	0.307861i
$513$	2.28849	+	30.4141i	0.101039	+	1.34281i
$514$	−0.509248	−	1.56730i	−0.0224620	−	0.0691308i
$515$	0.0240586	+	0.0311827i	0.00106015	+	0.00137407i
$516$	5.51571	+	4.72180i	0.242816	+	0.207866i
$517$	−1.64226	+	15.6251i	−0.0722267	+	0.687191i
$518$	−10.9620	−	18.9867i	−0.481641	−	0.834227i
$519$	0.266540	+	10.6448i	0.0116998	+	0.467253i
$520$	−5.66446	−	7.34178i	−0.248403	−	0.321958i
$521$	9.38013	−	6.81506i	0.410951	−	0.298573i	−0.363036	−	0.931775i	$-0.618260\pi$
$521$	9.38013	−	6.81506i	0.410951	−	0.298573i	0.773987	+	0.633202i	$0.218260\pi$
$522$	7.93844	+	20.8228i	0.347456	+	0.911391i
$523$	−2.58596	−	7.95877i	−0.113076	−	0.348013i	0.878465	−	0.477807i	$-0.158568\pi$
$523$	−2.58596	−	7.95877i	−0.113076	−	0.348013i	−0.991541	+	0.129794i	$0.958568\pi$
$524$	8.86849	−	15.3607i	0.387422	−	0.671034i
$525$	10.5496	+	35.0804i	0.460423	+	1.53103i
$526$	4.54717	+	7.87592i	0.198266	+	0.343407i
$527$	−2.97106	+	3.29970i	−0.129421	+	0.143737i
$528$	−34.4142	+	32.5830i	−1.49768	+	1.41799i
$529$	1.12772	+	10.7295i	0.0490311	+	0.466500i
$530$	−21.9141	−	1.66637i	−0.951890	−	0.0723827i
$531$	−27.0854	+	21.8307i	−1.17541	+	0.947373i
$532$	−23.9137			−1.03679
$533$	9.81431	−	4.36961i	0.425105	−	0.189269i
$534$	12.8720	−	4.54161i	0.557024	−	0.196535i
$535$	6.55971	+	3.53920i	0.283601	+	0.153013i
$536$	−13.4723	+	14.9625i	−0.581916	+	0.646283i
$537$	−9.47735	−	8.11322i	−0.408978	−	0.350111i
$538$	−20.1683	−	22.3991i	−0.869516	−	0.965695i
$539$	−18.4245	−	56.7048i	−0.793600	−	2.44245i
$540$	−2.33537	+	10.9444i	−0.100498	+	0.470972i
$541$	6.73533	−	20.7292i	0.289575	−	0.891219i	−0.695416	−	0.718608i	$-0.744780\pi$
$541$	6.73533	−	20.7292i	0.289575	−	0.891219i	0.984990	−	0.172611i	$-0.0552203\pi$
$542$	21.1721	−	9.42641i	0.909418	−	0.404899i
$543$	−15.0949	+	36.3246i	−0.647785	+	1.55884i
$544$	0.738137	−	7.02291i	0.0316474	−	0.301105i
$545$	4.63470	−	4.42152i	0.198529	−	0.189397i
$546$	28.0868	+	8.35469i	1.20200	+	0.357548i
$547$	−3.48938	−	33.1992i	−0.149195	−	1.41950i	−0.771255	−	0.636526i	$-0.780371\pi$
$547$	−3.48938	−	33.1992i	−0.149195	−	1.41950i	0.622060	−	0.782969i	$-0.286296\pi$
$548$	−4.93071	−	15.1752i	−0.210630	−	0.648251i
$549$	31.4327	−	8.34521i	1.34151	−	0.356165i
$550$	−7.61609	−	46.4930i	−0.324751	−	1.98247i
$551$	−12.6648	+	21.9361i	−0.539538	+	0.934508i
$552$	−4.63955	−	9.75576i	−0.197472	−	0.415233i
$553$	−11.0903	−	4.93773i	−0.471609	−	0.209974i
$554$	−41.4704	−	18.4638i	−1.76191	−	0.784453i
$555$	−9.78964	−	6.33662i	−0.415547	−	0.268975i
$556$	−9.51551	+	4.23658i	−0.403548	+	0.179671i
$557$	0.351013			0.0148729			0.00743646	−	0.999972i	$-0.497633\pi$
$557$	0.351013			0.0148729			0.00743646	+	0.999972i	$0.497633\pi$
$558$	−2.52054	−	16.1535i	−0.106703	−	0.683833i
$559$	3.12500	−	9.61776i	0.132173	−	0.406788i
$560$	45.3677	+	13.3081i	1.91713	+	0.562370i
$561$	−7.54416	+	10.9499i	−0.318515	+	0.462306i
$562$	−42.2731	+	8.98542i	−1.78318	+	0.379027i
$563$	−6.71206	+	1.42669i	−0.282879	+	0.0601279i	−0.347166	−	0.937804i	$-0.612856\pi$
$563$	−6.71206	+	1.42669i	−0.282879	+	0.0601279i	0.0642869	+	0.997931i	$0.479523\pi$
$564$	4.77301	+	0.381147i	0.200980	+	0.0160492i
$565$	17.2756	+	5.06762i	0.726792	+	0.213196i
$566$	−7.66881	+	23.6022i	−0.322344	+	0.992073i
$567$	15.3247	+	34.8488i	0.643577	+	1.46351i
$568$	−11.7878			−0.494607
$569$	13.8450	−	6.16417i	0.580411	−	0.258416i	−0.0954629	−	0.995433i	$-0.530433\pi$
$569$	13.8450	−	6.16417i	0.580411	−	0.258416i	0.675874	+	0.737017i	$0.263766\pi$
$570$	−34.8409	+	17.8182i	−1.45933	+	0.746322i
$571$	36.1997	+	16.1171i	1.51491	+	0.674481i	0.984839	−	0.173473i	$-0.0554989\pi$
$571$	36.1997	+	16.1171i	1.51491	+	0.674481i	0.530070	+	0.847954i	$0.322166\pi$
$572$	−11.1907	−	4.98241i	−0.467906	−	0.208325i
$573$	−10.5457	+	15.3066i	−0.440555	+	0.639441i
$574$	−16.8333	+	29.1561i	−0.702609	+	1.21695i
$575$	17.2715	+	2.64196i	0.720272	+	0.110177i
$576$	−2.81538	−	2.82831i	−0.117308	−	0.117846i
$577$	−3.56209	−	10.9630i	−0.148292	−	0.456396i	0.849128	−	0.528188i	$-0.177128\pi$
$577$	−3.56209	−	10.9630i	−0.148292	−	0.456396i	−0.997420	+	0.0717920i	$0.977128\pi$
$578$	2.70493	+	25.7357i	0.112510	+	1.07046i
$579$	18.8545	−	17.8512i	0.783564	−	0.741871i
$580$	−6.72447	+	6.41517i	−0.279218	+	0.266375i
$581$	−3.01848	+	28.7189i	−0.125228	+	1.19146i
$582$	40.8788	−	5.33416i	1.69448	−	0.221108i
$583$	28.5519	−	12.7121i	1.18250	−	0.526483i
$584$	−2.14481	+	6.60104i	−0.0887528	+	0.273153i
$585$	15.3244	−	2.84582i	0.633588	−	0.117660i
$586$	−3.56038	−	10.9577i	−0.147078	−	0.452659i
$587$	−26.2637	−	29.1688i	−1.08402	−	1.20393i	−0.977791	−	0.209583i	$-0.932789\pi$
$587$	−26.2637	−	29.1688i	−1.08402	−	1.20393i	−0.106228	−	0.994342i	$-0.533877\pi$
$588$	−17.1356	+	6.04596i	−0.706662	+	0.249331i
$589$	12.4343	−	13.8097i	0.512347	−	0.569019i
$590$	−39.2816	−	21.1938i	−1.61720	−	0.872537i
$591$	−10.4500	−	8.94583i	−0.429854	−	0.367982i
$592$	−13.7496	+	6.12171i	−0.565105	+	0.251601i
$593$	−2.11729			−0.0869465			−0.0434733	−	0.999055i	$-0.513842\pi$
$593$	−2.11729			−0.0869465			−0.0434733	+	0.999055i	$0.513842\pi$
$594$	−13.7442	−	46.9922i	−0.563933	−	1.92811i
$595$	13.2274	+	1.00583i	0.542271	+	0.0412349i
$596$	−0.992157	−	9.43975i	−0.0406403	−	0.386667i
$597$	5.67863	+	23.7732i	0.232411	+	0.972971i
$598$	9.35215	−	10.3866i	0.382438	−	0.424740i
$599$	−1.13371	−	1.96364i	−0.0463219	−	0.0802320i	0.841935	−	0.539579i	$-0.181417\pi$
$599$	−1.13371	−	1.96364i	−0.0463219	−	0.0802320i	−0.888257	+	0.459347i	$0.848083\pi$
$600$	15.1863	−	2.87976i	0.619978	−	0.117566i
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	−0.230985	−	0.972957i	$-0.574195\pi$
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	0.958098	−	0.286440i	$-0.0924718\pi$
$602$	9.79310	+	30.1401i	0.399137	+	1.22842i
$603$	−12.0556	−	31.6223i	−0.490942	−	1.28776i
$604$	14.1380	−	10.2719i	0.575269	−	0.417957i
$605$	25.9016	+	33.5714i	1.05305	+	1.36487i
$606$	−22.4847	−	12.2416i	−0.913377	−	0.497279i
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	−0.999915	−	0.0130175i	$-0.995856\pi$
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	0.488684	−	0.872461i	$-0.337477\pi$
$608$	−3.08921	+	29.3919i	−0.125284	+	1.19200i
$609$	−5.79713	+	31.0798i	−0.234912	+	1.25942i
$610$	25.4890	+	33.0366i	1.03202	+	1.33761i
$611$	−2.06082	−	6.34257i	−0.0833720	−	0.256593i
$612$	3.39365	+	2.21493i	0.137180	+	0.0895334i
$613$	−13.2971	+	40.9242i	−0.537063	+	1.65291i	0.202085	+	0.979368i	$0.435228\pi$
$613$	−13.2971	+	40.9242i	−0.537063	+	1.65291i	−0.739148	+	0.673543i	$0.764772\pi$
$614$	−5.49123	−	1.16720i	−0.221608	−	0.0471043i
$615$	−0.910393	+	17.8843i	−0.0367106	+	0.721165i
$616$	−40.4224	+	8.59204i	−1.62866	+	0.346183i
$617$	−3.34729	+	31.8474i	−0.134757	+	1.28213i	0.692958	+	0.720978i	$0.256307\pi$
$617$	−3.34729	+	31.8474i	−0.134757	+	1.28213i	−0.827715	+	0.561149i	$0.810360\pi$
$618$	−0.0201522	+	0.0484945i	−0.000810640	+	0.00195073i
$619$	−11.9559	+	5.32313i	−0.480550	+	0.213955i	−0.632691	−	0.774404i	$-0.718050\pi$
$619$	−11.9559	+	5.32313i	−0.480550	+	0.213955i	0.152141	+	0.988359i	$0.451383\pi$
$620$	5.80406	−	3.57788i	0.233096	−	0.143691i
$621$	18.1499	+	0.537700i	0.728330	+	0.0215771i
$622$	44.8848	−	32.6107i	1.79972	−	1.30757i
$623$	18.9419	+	4.02622i	0.758890	+	0.161307i
$624$	7.71956	−	18.5764i	0.309030	−	0.743653i
$625$	−9.92623	+	22.9449i	−0.397049	+	0.917797i
$626$	17.6658	+	30.5980i	0.706067	+	1.22294i
$627$	31.5734	−	45.8270i	1.26092	−	1.83015i
$628$	−0.268015	−	2.54999i	−0.0106949	−	0.101756i
$629$	−3.41644	+	2.48219i	−0.136222	+	0.0989713i
$630$	−33.6099	+	35.4426i	−1.33905	+	1.41207i
$631$	34.4722	+	25.0455i	1.37232	+	0.997047i	0.997552	+	0.0699268i	$0.0222766\pi$
$631$	34.4722	+	25.0455i	1.37232	+	0.997047i	0.374765	+	0.927120i	$0.377723\pi$
$632$	−2.56119	+	4.43612i	−0.101879	+	0.176459i
$633$	−11.1385	−	6.06424i	−0.442716	−	0.241032i
$634$	6.73496	−	1.43156i	0.267479	−	0.0568545i
$635$	1.91003	−	10.4599i	0.0757972	−	0.415089i
$636$	−4.09081	−	8.60191i	−0.162211	−	0.341088i
$637$	16.9346	+	18.8078i	0.670973	+	0.745191i
$638$	12.5649	−	38.6708i	0.497450	−	1.53099i
$639$	9.03561	−	17.6334i	0.357443	−	0.697566i
$640$	10.5087	−	25.5613i	0.415394	−	1.01040i
$641$	−1.78356	−	1.98084i	−0.0704464	−	0.0782386i	0.706891	−	0.707322i	$-0.250097\pi$
$641$	−1.78356	−	1.98084i	−0.0704464	−	0.0782386i	−0.777338	+	0.629084i	$0.783430\pi$
$642$	0.248775	+	9.93529i	0.00981837	+	0.392115i
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	0.945505	+	0.325607i	$0.105569\pi$
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	−0.190769	+	0.981635i	$0.561098\pi$
$644$	−1.48815	+	14.1588i	−0.0586412	+	0.557934i
$645$	11.9373	+	11.9016i	0.470032	+	0.468625i
$646$	1.48128	+	14.0935i	0.0582803	+	0.554500i
$647$	29.1546	−	21.1821i	1.14619	−	0.832753i	0.158217	−	0.987404i	$-0.449425\pi$
$647$	29.1546	−	21.1821i	1.14619	−	0.832753i	0.987969	+	0.154651i	$0.0494254\pi$
$648$	15.2997	−	4.89378i	0.601029	−	0.192246i
$649$	63.4743			2.49158
$650$	10.9803	+	16.7139i	0.430682	+	0.655574i
$651$	8.90074	−	21.4188i	0.348847	−	0.839471i
$652$	2.48629	−	2.76131i	0.0973708	−	0.108141i
$653$	25.9936	+	11.5731i	1.01721	+	0.452890i	0.846476	−	0.532428i	$-0.178720\pi$
$653$	25.9936	+	11.5731i	1.01721	+	0.452890i	0.170732	+	0.985318i	$0.445387\pi$
$654$	8.18642	+	2.43513i	0.320114	+	0.0952212i
$655$	23.2339	−	33.9978i	0.907824	−	1.32841i
$656$	18.6981	+	13.5850i	0.730039	+	0.530405i
$657$	−8.23043	−	8.26823i	−0.321100	−	0.322575i
$658$	16.9078	+	12.2842i	0.659134	+	0.478889i
$659$	−21.6918	−	24.0912i	−0.844993	−	0.938460i	0.153774	−	0.988106i	$-0.450857\pi$
$659$	−21.6918	−	24.0912i	−0.844993	−	0.938460i	−0.998767	+	0.0496464i	$0.984191\pi$
$660$	15.8491	−	12.8738i	0.616926	−	0.501110i
$661$	31.0769	−	34.5144i	1.20875	−	1.34245i	0.285443	−	0.958396i	$-0.407859\pi$
$661$	31.0769	−	34.5144i	1.20875	−	1.34245i	0.923309	−	0.384059i	$-0.125474\pi$
$662$	−2.48201	+	0.527567i	−0.0964660	+	0.0205045i
$663$	1.03495	−	5.54860i	0.0401941	−	0.215490i
$664$	11.9184	+	2.53332i	0.462522	+	0.0983120i
$665$	−55.3587	−	4.20953i	−2.14672	−	0.163239i
$666$	0.849354	−	15.5259i	0.0329118	−	0.601617i
$667$	12.1997	+	8.86361i	0.472375	+	0.343200i
$668$	5.06279	−	8.76900i	0.195885	−	0.339283i
$669$	−0.881903	−	35.2204i	−0.0340963	−	1.36170i
$670$	31.4174	−	29.9723i	1.21376	−	1.15793i
$671$	−54.2090	−	24.1354i	−2.09272	−	0.931737i
$672$	8.57031	+	35.8790i	0.330607	+	1.38406i
$673$	−5.72623	−	1.21715i	−0.220730	−	0.0469176i	0.0962191	−	0.995360i	$-0.469325\pi$
$673$	−5.72623	−	1.21715i	−0.220730	−	0.0469176i	−0.316949	+	0.948443i	$0.602658\pi$
$674$	−16.0430			−0.617953
$675$	−7.33277	+	24.9245i	−0.282238	+	0.959344i
$676$	−7.32129			−0.281588
$677$	−19.4462	−	4.13342i	−0.747379	−	0.158860i	−0.181549	−	0.983382i	$-0.558111\pi$
$677$	−19.4462	−	4.13342i	−0.747379	−	0.158860i	−0.565830	+	0.824522i	$0.691444\pi$
$678$	5.57723	+	23.3486i	0.214192	+	0.896699i
$679$	53.4307	+	23.7889i	2.05048	+	0.912934i
$680$	1.00548	−	5.50634i	0.0385585	−	0.211158i
$681$	−0.943608	−	37.6847i	−0.0361591	−	1.44408i
$682$	−14.9152	+	25.8340i	−0.571134	+	0.989233i
$683$	−36.4251	−	26.4644i	−1.39377	−	1.01263i	−0.995440	−	0.0953885i	$-0.969591\pi$
$683$	−36.4251	−	26.4644i	−1.39377	−	1.01263i	−0.398328	−	0.917243i	$-0.630409\pi$
$684$	−14.2029	−	9.26982i	−0.543063	−	0.354441i
$685$	−8.74299	−	35.9975i	−0.334053	−	1.37539i
$686$	−27.7224	−	5.89258i	−1.05845	−	0.224980i
$687$	−5.96450	+	31.9770i	−0.227560	+	1.22000i
$688$	21.2806	−	4.52332i	0.811314	−	0.172450i
$689$	−8.87700	+	9.85891i	−0.338187	+	0.375595i
$690$	8.38160	+	21.7373i	0.319082	+	0.827526i
$691$	0.672969	+	0.747407i	0.0256009	+	0.0284327i	0.755809	−	0.654792i	$-0.227244\pi$
$691$	0.672969	+	0.747407i	0.0256009	+	0.0284327i	−0.730208	+	0.683225i	$0.760577\pi$
$692$	−4.79031	−	3.48036i	−0.182100	−	0.132304i
$693$	18.1317	−	67.0536i	0.688767	−	2.54716i
$694$	9.29844	+	6.75571i	0.352964	+	0.256443i
$695$	−22.7735	+	8.13239i	−0.863850	+	0.308479i
$696$	12.7865	+	3.80347i	0.484671	+	0.144170i
$697$	5.92416	+	2.63761i	0.224394	+	0.0999065i
$698$	−5.00364	+	5.55710i	−0.189390	+	0.210339i
$699$	−4.25461	+	10.2384i	−0.160924	+	0.387250i
$700$	−19.0557	−	7.19938i	−0.720238	−	0.272111i
$701$	−8.14396			−0.307593			−0.153797	−	0.988103i	$-0.549150\pi$
$701$	−8.14396			−0.307593			−0.153797	+	0.988103i	$0.549150\pi$
$702$	13.4428	+	15.8495i	0.507367	+	0.598201i
$703$	14.2983	−	10.3883i	0.539270	−	0.391803i
$704$	0.761121	+	7.24158i	0.0286858	+	0.272927i
$705$	10.9821	+	1.72252i	0.413610	+	0.0648739i
$706$	0.832480	−	7.92052i	0.0313308	−	0.298093i
$707$	−18.1604	−	31.4547i	−0.682992	−	1.18298i
$708$	−0.484231	−	19.3386i	−0.0181985	−	0.726791i
$709$	27.5012	+	30.5431i	1.03283	+	1.14707i	0.988982	+	0.148033i	$0.0472941\pi$
$709$	27.5012	+	30.5431i	1.03283	+	1.14707i	0.0438449	+	0.999038i	$0.486039\pi$
$710$	25.3485	+	1.92752i	0.951312	+	0.0723387i
$711$	−4.67276	−	7.23165i	−0.175242	−	0.271208i
$712$	2.52499	−	7.77112i	0.0946279	−	0.291235i
$713$	−7.40263	−	8.22145i	−0.277231	−	0.307896i
$714$	7.59660	+	15.9737i	0.284296	+	0.597800i
$715$	−25.0286	−	13.5038i	−0.936018	−	0.505015i
$716$	6.78586	−	1.44238i	0.253600	−	0.0539042i
$717$	26.7545	+	14.5662i	0.999166	+	0.543986i
$718$	7.76100	−	13.4424i	0.289638	−	0.501668i
$719$	39.3653	+	28.6006i	1.46808	+	1.06662i	0.981165	+	0.193173i	$0.0618779\pi$
$719$	39.3653	+	28.6006i	1.46808	+	1.06662i	0.486915	+	0.873449i	$0.338122\pi$
$720$	21.7862	+	25.4902i	0.811926	+	0.949962i
$721$	−0.0602751	+	0.0437924i	−0.00224476	+	0.00163091i
$722$	−2.78066	−	26.4562i	−0.103485	−	0.984597i
$723$	7.46593	−	10.8364i	0.277661	−	0.403009i
$724$	−10.9369	−	18.9433i	−0.406468	−	0.704023i
$725$	−16.6960	+	13.6670i	−0.620073	+	0.507579i
$726$	−21.6959	+	52.2093i	−0.805211	+	1.93767i
$727$	−38.1966	−	8.11893i	−1.41663	−	0.301115i	−0.564929	−	0.825139i	$-0.691097\pi$
$727$	−38.1966	−	8.11893i	−1.41663	−	0.301115i	−0.851703	+	0.524025i	$0.824430\pi$
$728$	14.1914	−	10.3107i	0.525968	−	0.382138i
$729$	−4.40694	+	26.6379i	−0.163220	+	0.986590i
$730$	5.69157	−	13.8441i	0.210654	−	0.512393i
$731$	5.57654	−	2.48284i	0.206256	−	0.0918310i
$732$	−6.93976	+	16.6999i	−0.256501	+	0.617247i
$733$	−0.0804066	+	0.765018i	−0.00296989	+	0.0282566i	−0.995906	−	0.0903896i	$-0.971189\pi$
$733$	−0.0804066	+	0.765018i	−0.00296989	+	0.0282566i	0.992937	+	0.118646i	$0.0378554\pi$
$734$	15.5870	−	3.31313i	0.575328	−	0.122290i
$735$	−40.7321	+	10.9796i	−1.50243	+	0.404989i
$736$	17.2100	+	3.65810i	0.634370	+	0.134839i
$737$	−19.0815	+	58.7268i	−0.702876	+	2.16323i
$738$	−21.2997	+	10.7913i	−0.784052	+	0.397234i
$739$	16.0888	+	49.5162i	0.591835	+	1.82148i	0.569888	+	0.821723i	$0.306987\pi$
$739$	16.0888	+	49.5162i	0.591835	+	1.82148i	0.0219476	+	0.999759i	$0.493013\pi$
$740$	6.10696	−	2.18078i	0.224496	−	0.0801672i
$741$	−4.33141	+	23.2217i	−0.159118	+	0.853070i
$742$	4.34570	−	41.3466i	0.159536	−	1.51788i
$743$	19.6551	+	34.0437i	0.721076	+	1.24894i	0.960569	+	0.278043i	$0.0896857\pi$
$743$	19.6551	+	34.0437i	0.721076	+	1.24894i	−0.239492	+	0.970898i	$0.576981\pi$
$744$	−8.59555	−	4.67976i	−0.315128	−	0.171568i
$745$	−0.635101	−	22.0270i	−0.0232683	−	0.807008i
$746$	7.54594	−	5.48244i	0.276276	−	0.200727i
$747$	−12.9252	+	15.8868i	−0.472910	+	0.581266i
$748$	−2.28494	−	7.03234i	−0.0835458	−	0.257128i
$749$	−7.04991	+	12.2108i	−0.257598	+	0.446173i
$750$	−33.1274	+	3.70938i	−1.20964	+	0.135447i
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	0.959149	+	0.282903i	$0.0912973\pi$
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	−0.234573	+	0.972098i	$0.575369\pi$
$752$	9.60021	−	10.6621i	0.350084	−	0.388807i
$753$	−10.4551	−	43.7694i	−0.381004	−	1.59504i
$754$	1.80410	+	17.1649i	0.0657016	+	0.625109i
$755$	34.5368	−	21.2900i	1.25692	−	0.774824i
$756$	−20.5675	−	5.01264i	−0.748031	−	0.182308i
$757$	−30.6481			−1.11392			−0.556961	−	0.830538i	$-0.688033\pi$
$757$	−30.6481			−1.11392			−0.556961	+	0.830538i	$0.688033\pi$
$758$	−14.0242	+	6.24398i	−0.509382	+	0.226792i
$759$	−25.1683	−	21.5457i	−0.913552	−	0.782059i
$760$	−4.20809	+	23.0448i	−0.152644	+	0.835924i
$761$	−12.5617	+	13.9511i	−0.455360	+	0.505729i	−0.926482	−	0.376340i	$-0.877183\pi$
$761$	−12.5617	+	13.9511i	−0.455360	+	0.505729i	0.471122	+	0.882068i	$0.343849\pi$
$762$	13.3698	−	4.71727i	0.484337	−	0.170889i
$763$	8.10797	+	9.00481i	0.293528	+	0.325996i
$764$	−3.19405	−	9.83029i	−0.115557	−	0.355647i
$765$	7.46619	+	5.72481i	0.269941	+	0.206981i
$766$	−9.81472	+	30.2066i	−0.354620	+	1.09141i
$767$	−24.6138	+	10.9588i	−0.888752	+	0.395698i
$768$	31.9716	−	4.17189i	1.15368	−	0.150540i
$769$	3.95016	−	37.5833i	0.142446	−	1.35529i	−0.656700	−	0.754152i	$-0.728048\pi$
$769$	3.95016	−	37.5833i	0.142446	−	1.35529i	0.799147	−	0.601136i	$-0.205285\pi$
$770$	88.3289	−	11.8665i	3.18315	−	0.427638i
$771$	1.20411	−	1.14003i	0.0433648	−	0.0410574i
$772$	1.50921	+	14.3591i	0.0543175	+	0.516796i
$773$	−8.44199	−	25.9818i	−0.303637	−	0.934500i	−0.980182	−	0.198098i	$-0.936524\pi$
$773$	−8.44199	−	25.9818i	−0.303637	−	0.934500i	0.676545	−	0.736401i	$-0.263476\pi$
$774$	−5.86702	+	21.6971i	−0.210886	+	0.779885i
$775$	14.0658	−	7.26087i	0.505259	−	0.260818i
$776$	12.3393	−	21.3722i	0.442954	−	0.767219i
$777$	12.5157	−	18.1658i	0.448996	−	0.651693i
$778$	−19.9278	−	8.87241i	−0.714445	−	0.318091i
$779$	−24.7935	−	11.0388i	−0.888318	−	0.395505i
$780$	−3.92326	+	7.72846i	−0.140475	+	0.276723i
$781$	−33.0265	+	14.7044i	−1.18178	+	0.526164i
$782$	8.43660			0.301692
$783$	−15.4907	+	16.2118i	−0.553592	+	0.579364i
$784$	−16.8251	+	51.7823i	−0.600896	+	1.84937i
$785$	−0.171562	−	5.95023i	−0.00612330	−	0.212373i
$786$	54.7322	+	4.37061i	1.95223	+	0.155895i
$787$	15.6555	−	3.32767i	0.558057	−	0.118619i	0.0797556	−	0.996814i	$-0.474586\pi$
$787$	15.6555	−	3.32767i	0.558057	−	0.118619i	0.478301	+	0.878196i	$0.341253\pi$
$788$	7.48226	−	1.59040i	0.266544	−	0.0566557i
$789$	−5.19165	+	7.53539i	−0.184828	+	0.268267i
$790$	6.23295	−	9.12059i	0.221759	−	0.324496i
$791$	−10.5242	+	32.3902i	−0.374198	+	1.15166i
$792$	−27.3384	−	10.5662i	−0.971428	−	0.375452i
$793$	25.1879			0.894448
$794$	−9.82887	+	4.37610i	−0.348814	+	0.155302i
$795$	−7.95576	−	20.6330i	−0.282162	−	0.731776i
$796$	−12.4165	−	5.52819i	−0.440092	−	0.195942i
$797$	−15.8206	−	7.04381i	−0.560396	−	0.249504i	0.106934	−	0.994266i	$-0.465897\pi$
$797$	−15.8206	−	7.04381i	−0.560396	−	0.249504i	−0.667331	+	0.744762i	$0.732563\pi$
$798$	−31.7929	−	66.8522i	−1.12546	−	2.36654i
$799$	2.01278	−	3.48623i	0.0712070	−	0.123334i
$800$	−11.3103	+	22.4910i	−0.399878	+	0.795176i
$801$	9.68932	+	9.73383i	0.342355	+	0.343928i
$802$	−14.2173	−	43.7563i	−0.502029	−	1.54509i
$803$	2.22505	+	21.1699i	0.0785202	+	0.747070i
$804$	18.0378	+	5.36552i	0.636144	+	0.189227i
$805$	−5.93733	+	32.5147i	−0.209263	+	1.14599i
$806$	1.32356	−	12.5929i	0.0466205	−	0.443565i
$807$	11.6381	−	28.0060i	0.409679	−	0.985857i
$808$	−14.0005	+	6.23342i	−0.492536	+	0.219291i
$809$	3.76845	−	11.5981i	0.132492	−	0.407767i	−0.862700	−	0.505716i	$-0.831228\pi$
$809$	3.76845	−	11.5981i	0.132492	−	0.407767i	0.995191	+	0.0979492i	$0.0312283\pi$
$810$	−33.7006	+	8.02176i	−1.18412	+	0.281856i
$811$	1.10851	+	3.41163i	0.0389249	+	0.119799i	0.968631	−	0.248504i	$-0.0799390\pi$
$811$	1.10851	+	3.41163i	0.0389249	+	0.119799i	−0.929706	+	0.368303i	$0.879939\pi$
$812$	−11.7638	−	13.0651i	−0.412829	−	0.458493i
$813$	17.7148	+	15.1650i	0.621286	+	0.531860i
$814$	−18.9839	+	21.0838i	−0.665387	+	0.738987i
$815$	6.24168	−	5.95459i	0.218637	−	0.208580i
$816$	11.4510	−	4.04025i	0.400865	−	0.141437i
$817$	−23.3386	+	10.3910i	−0.816516	+	0.363536i
$818$	41.1810			1.43986
$819$	4.54568	+	29.1322i	0.158839	+	1.01796i
$820$	−7.58913	−	6.44709i	−0.265024	−	0.225142i
$821$	0.975788	+	9.28401i	0.0340552	+	0.324014i	0.998265	+	0.0588748i	$0.0187513\pi$
$821$	0.975788	+	9.28401i	0.0340552	+	0.324014i	−0.964210	+	0.265139i	$0.914582\pi$
$822$	35.8678	−	33.9592i	1.25103	−	1.18446i
$823$	−32.2029	+	35.7650i	−1.12252	+	1.24669i	−0.156656	+	0.987653i	$0.550071\pi$
$823$	−32.2029	+	35.7650i	−1.12252	+	1.24669i	−0.965868	+	0.259035i	$0.916595\pi$
$824$	0.0157184	+	0.0272251i	0.000547576	+	0.000948430i
$825$	38.9559	−	27.0120i	1.35627	−	0.940437i
$826$	42.2171	−	73.1221i	1.46892	−	2.54424i
$827$	8.29286	+	25.5228i	0.288371	+	0.887515i	0.985368	+	0.170441i	$0.0545191\pi$
$827$	8.29286	+	25.5228i	0.288371	+	0.887515i	−0.696997	+	0.717074i	$0.745481\pi$
$828$	−6.37230	+	7.83237i	−0.221453	+	0.272194i
$829$	−27.4122	+	19.9161i	−0.952065	+	0.691716i	−0.951294	−	0.308284i	$-0.900245\pi$
$829$	−27.4122	+	19.9161i	−0.952065	+	0.691716i	−0.000770971		1.00000i	$0.500245\pi$
$830$	−25.2149	−	7.39650i	−0.875221	−	0.256736i
$831$	−1.14336	−	45.6621i	−0.0396627	−	1.58400i
$832$	−1.54539	−	2.67670i	−0.0535769	−	0.0927979i
$833$	−1.59686	+	15.1931i	−0.0553278	+	0.526408i
$834$	−24.4943	−	20.9687i	−0.848169	−	0.726086i
$835$	13.2636	−	19.4085i	0.459007	−	0.671658i
$836$	9.56283	+	29.4314i	0.330737	+	1.01790i
$837$	13.5891	−	9.27091i	0.469707	−	0.320450i
$838$	−6.67399	+	20.5404i	−0.230549	+	0.709558i
$839$	17.6290	+	3.74715i	0.608620	+	0.129366i	0.501904	−	0.864923i	$-0.332633\pi$
$839$	17.6290	+	3.74715i	0.608620	+	0.129366i	0.106716	+	0.994290i	$0.465966\pi$
$840$	4.61738	+	28.8728i	0.159315	+	0.996205i
$841$	10.1515	−	2.15778i	0.350053	−	0.0744061i
$842$	0.212354	−	2.02041i	0.00731820	−	0.0696280i
$843$	−26.4327	−	34.5296i	−0.910390	−	1.18926i
$844$	6.44262	−	2.86844i	0.221764	−	0.0987358i
$845$	−16.9483	−	1.28877i	−0.583039	−	0.0443349i
$846$	5.28012	+	13.8500i	0.181534	+	0.476171i
$847$	−64.8923	+	47.1470i	−2.22973	+	1.61999i
$848$	−27.9171	−	5.93397i	−0.958679	−	0.203773i
$849$	−24.7607	+	3.23095i	−0.849785	+	0.110886i
$850$	−3.06257	+	11.6764i	−0.105045	+	0.400496i
$851$	−5.26090	−	9.11215i	−0.180341	−	0.312361i
$852$	4.73191	+	9.94998i	0.162113	+	0.340881i
$853$	−4.26725	−	40.6001i	−0.146108	−	1.39012i	−0.784365	−	0.620299i	$-0.787011\pi$
$853$	−4.26725	−	40.6001i	−0.146108	−	1.39012i	0.638257	−	0.769823i	$-0.279656\pi$
$854$	−63.8586	+	46.3960i	−2.18520	+	1.58764i
$855$	−31.2471	−	23.9592i	−1.06863	−	0.819387i
$856$	4.81315	+	3.49696i	0.164510	+	0.119524i
$857$	−0.284511	+	0.492787i	−0.00971870	+	0.0168333i	−0.870844	−	0.491560i	$-0.836427\pi$
$857$	−0.284511	+	0.492787i	−0.00971870	+	0.0168333i	0.861125	+	0.508393i	$0.169760\pi$
$858$	−0.949204	−	37.9082i	−0.0324053	−	1.29416i
$859$	−34.4947	+	7.33208i	−1.17695	+	0.250167i	−0.754549	−	0.656244i	$-0.772144\pi$
$859$	−34.4947	+	7.33208i	−1.17695	+	0.250167i	−0.422396	+	0.906411i	$0.638811\pi$
$860$	−9.29013	+	1.24807i	−0.316791	+	0.0425590i
$861$	−33.7678	−	2.69651i	−1.15080	−	0.0918969i
$862$	28.9420	+	32.1434i	0.985769	+	1.09481i
$863$	7.48769	−	23.0447i	0.254884	−	0.784452i	−0.738968	−	0.673740i	$-0.764687\pi$
$863$	7.48769	−	23.0447i	0.254884	−	0.784452i	0.993852	−	0.110712i	$-0.0353132\pi$
$864$	−8.81787	+	24.6315i	−0.299990	+	0.837982i
$865$	−10.4766	−	8.90005i	−0.356215	−	0.302611i
$866$	−23.0468	−	25.5960i	−0.783161	−	0.869789i
$867$	−22.2165	+	13.5793i	−0.754511	+	0.461177i
$868$	6.44898	+	11.1700i	0.218893	+	0.379133i
$869$	−1.64212	+	15.6237i	−0.0557052	+	0.529999i
$870$	−26.8740	−	10.2698i	−0.911115	−	0.348178i
$871$	−2.73977	−	26.0672i	−0.0928337	−	0.883254i
$872$	4.13635	−	3.00523i	0.140074	−	0.101770i
$873$	22.5124	+	34.8405i	0.761928	+	1.17917i
$874$	−35.3084			−1.19433
$875$	−42.8454	−	20.0205i	−1.44844	−	0.676815i
$876$	6.43284	−	0.839403i	0.217345	−	0.0283608i
$877$	−32.8680	+	36.5036i	−1.10987	+	1.23264i	−0.139710	+	0.990193i	$0.544617\pi$
$877$	−32.8680	+	36.5036i	−1.10987	+	1.23264i	−0.970165	+	0.242448i	$0.922050\pi$
$878$	−35.6533	−	15.8739i	−1.20324	−	0.535717i
$879$	8.41843	−	7.97048i	0.283947	−	0.268838i
$880$	−1.76333	−	61.1572i	−0.0594419	−	2.06161i
$881$	−9.93477	−	7.21804i	−0.334711	−	0.243182i	0.407716	−	0.913109i	$-0.366325\pi$
$881$	−9.93477	−	7.21804i	−0.334711	−	0.243182i	−0.742427	+	0.669927i	$0.766325\pi$
$882$	−39.6834	−	39.8656i	−1.33621	−	1.34235i
$883$	−40.0558	−	29.1022i	−1.34798	−	0.979367i	−0.999109	−	0.0421976i	$-0.986564\pi$
$883$	−40.0558	−	29.1022i	−1.34798	−	0.979367i	−0.348874	−	0.937170i	$-0.613436\pi$
$884$	2.10017	+	2.33247i	0.0706363	+	0.0784496i
$885$	2.28322	−	44.8529i	0.0767495	−	1.50771i
$886$	−5.71992	+	6.35262i	−0.192165	+	0.213420i
$887$	46.9880	−	9.98760i	1.57770	−	0.335351i	0.665919	−	0.746024i	$-0.268040\pi$
$887$	46.9880	−	9.98760i	1.57770	−	0.335351i	0.911783	+	0.410673i	$0.134706\pi$
$888$	−7.07100	−	6.05323i	−0.237287	−	0.203133i
$889$	19.6745	+	4.18195i	0.659862	+	0.140258i
$890$	−6.70043	+	16.2981i	−0.224599	+	0.546312i
$891$	36.7613	−	32.7962i	1.23155	−	1.09871i
$892$	15.8497	+	11.5155i	0.530688	+	0.385568i
$893$	−8.42377	+	14.5904i	−0.281891	+	0.488249i
$894$	25.0703	−	15.3236i	0.838476	−	0.512498i
$895$	15.9627	−	2.14450i	0.533575	−	0.0716827i
$896$	47.7609	+	21.2645i	1.59558	+	0.710399i
$897$	13.4795	+	4.00961i	0.450067	+	0.133877i
$898$	−29.9180	−	6.35927i	−0.998376	−	0.212211i
$899$	13.6616			0.455640
$900$	−8.52690	−	11.6626i	−0.284230	−	0.388752i
$901$	−8.00797			−0.266784
$902$	42.6148	+	9.05806i	1.41892	+	0.301600i
$903$	−23.1556	+	21.9234i	−0.770569	+	0.729567i
$904$	13.1279	+	5.84493i	0.436628	+	0.194399i
$905$	−21.9837	−	45.7778i	−0.730763	−	1.52171i
$906$	47.5120	+	25.8674i	1.57848	+	0.859387i
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	−0.931553	−	0.363607i	$-0.881545\pi$
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	0.780669	+	0.624945i	$0.214879\pi$
$908$	16.9587	+	12.3212i	0.562794	+	0.408894i
$909$	1.40710	−	25.7213i	0.0466706	−	0.853123i
$910$	−32.2030	+	19.8514i	−1.06752	+	0.658067i
$911$	−2.29989	−	0.488856i	−0.0761987	−	0.0161965i	0.169655	−	0.985504i	$-0.445735\pi$
$911$	−2.29989	−	0.488856i	−0.0761987	−	0.0161965i	−0.245853	+	0.969307i	$0.579068\pi$
$912$	−47.9241	+	16.9090i	−1.58693	+	0.559914i
$913$	36.5523	−	7.76943i	1.20970	−	0.257131i
$914$	23.0759	−	25.6284i	0.763282	−	0.847711i
$915$	−19.0048	+	37.4376i	−0.628279	+	1.23765i
$916$	−12.1035	−	13.4422i	−0.399909	−	0.444144i
$917$	63.0198	+	45.7866i	2.08110	+	1.51201i
$918$	−1.68017	+	12.4319i	−0.0554540	+	0.410313i
$919$	−35.1878	−	25.5654i	−1.16074	−	0.843325i	−0.170866	−	0.985294i	$-0.554657\pi$
$919$	−35.1878	−	25.5654i	−1.16074	−	0.843325i	−0.989871	+	0.141969i	$0.954657\pi$
$920$	13.3825	+	3.92559i	0.441206	+	0.129423i
$921$	−1.31237	−	5.49414i	−0.0432441	−	0.181038i
$922$	−19.8192	−	8.82409i	−0.652712	−	0.290606i
$923$	10.2682	−	11.4040i	0.337982	−	0.375367i
$924$	23.4789	+	30.6710i	0.772399	+	1.00900i
$925$	14.5211	−	3.97336i	0.477451	−	0.130643i
$926$	−42.8642			−1.40860
$927$	−0.0527743	+	0.00264455i	−0.00173334	+	8.68583e-5i
$928$	−17.5777	+	12.7709i	−0.577015	+	0.419226i
$929$	−5.37815	−	51.1697i	−0.176451	−	1.67882i	−0.621576	−	0.783354i	$-0.713507\pi$
$929$	−5.37815	−	51.1697i	−0.176451	−	1.67882i	0.445125	−	0.895469i	$-0.353159\pi$
$930$	17.7186	+	11.4688i	0.581015	+	0.376078i
$931$	6.68307	−	63.5852i	0.219029	−	2.08392i
$932$	−3.08265	−	5.33931i	−0.100976	−	0.174895i
$933$	49.0290	+	26.6934i	1.60514	+	0.873901i
$934$	42.2022	+	46.8703i	1.38090	+	1.53364i
$935$	−4.05159	−	16.6816i	−0.132501	−	0.545547i
$936$	12.4254	−	0.622642i	0.406137	−	0.0203517i
$937$	−1.71388	+	5.27478i	−0.0559900	+	0.172320i	−0.975141	−	0.221587i	$-0.928876\pi$
$937$	−1.71388	+	5.27478i	−0.0559900	+	0.172320i	0.919151	+	0.393906i	$0.128876\pi$
$938$	54.9618	+	61.0413i	1.79457	+	1.99307i
$939$	−20.1696	+	29.2751i	−0.658211	+	0.955356i
$940$	−4.47267	+	4.26694i	−0.145882	+	0.139172i
$941$	−34.3030	+	7.29133i	−1.11825	+	0.237691i	−0.729720	−	0.683746i	$-0.760349\pi$
$941$	−34.3030	+	7.29133i	−1.11825	+	0.237691i	−0.388527	+	0.921437i	$0.627016\pi$
$942$	6.77232	−	4.13942i	0.220654	−	0.134869i
$943$	−8.07869	+	13.9927i	−0.263078	+	0.455665i
$944$	−46.8939	−	34.0704i	−1.52627	−	1.10890i
$945$	−46.7300	−	15.2244i	−1.52013	−	0.495250i
$946$	33.1782	−	24.1053i	1.07871	−	0.783732i
$947$	5.85222	+	55.6801i	0.190172	+	1.80936i	0.508155	+	0.861265i	$0.330328\pi$
$947$	5.85222	+	55.6801i	0.190172	+	1.80936i	−0.317984	+	0.948096i	$0.603006\pi$
$948$	4.77260	+	0.381113i	0.155007	+	0.0123780i
$949$	−4.51778	−	7.82502i	−0.146653	−	0.254011i
$950$	12.8173	−	48.8673i	0.415848	−	1.58546i
$951$	4.21126	+	5.50126i	0.136559	+	0.178391i
$952$	10.3571	+	2.20147i	0.335676	+	0.0713502i
$953$	−5.24619	+	3.81158i	−0.169941	+	0.123469i	−0.669505	−	0.742808i	$-0.733494\pi$
$953$	−5.24619	+	3.81158i	−0.169941	+	0.123469i	0.499564	+	0.866277i	$0.333494\pi$
$954$	18.6085	−	22.8722i	0.602471	−	0.740514i
$955$	−5.66360	−	23.3187i	−0.183270	−	0.754576i
$956$	−15.4751	+	6.88995i	−0.500500	+	0.222837i
$957$	40.5690	−	5.29374i	1.31141	−	0.171122i
$958$	−1.31475	+	12.5090i	−0.0424777	+	0.404149i
$959$	68.5443	−	14.5696i	2.21341	−	0.470475i
$960$	5.14450	−	0.277347i	0.166038	−	0.00895132i
$961$	20.5189	+	4.36143i	0.661900	+	0.140691i
$962$	3.72141	−	11.4533i	0.119983	−	0.369270i
$963$	−8.92045	+	4.51948i	−0.287458	+	0.145638i
$964$	2.26125	+	6.95941i	0.0728300	+	0.224148i
$965$	0.966074	+	33.5061i	0.0310990	+	1.07860i
$966$	−41.5601	+	14.6636i	−1.33717	+	0.471795i
$967$	−0.523420	+	4.98001i	−0.0168321	+	0.160146i	−0.999709	−	0.0241160i	$-0.992323\pi$
$967$	−0.523420	+	4.98001i	−0.0168321	+	0.160146i	0.982877	+	0.184262i	$0.0589896\pi$
$968$	16.9225	+	29.3106i	0.543909	+	0.942078i
$969$	−12.1663	+	7.43635i	−0.390837	+	0.238890i
$970$	−30.0290	+	43.9410i	−0.964173	+	1.41086i
$971$	−40.8653	+	29.6904i	−1.31143	+	0.952810i	−0.311434	+	0.950268i	$0.600809\pi$
$971$	−40.8653	+	29.6904i	−1.31143	+	0.952810i	−0.999997	+	0.00254202i	$0.999191\pi$
$972$	−10.2724	−	10.9498i	−0.329488	−	0.351216i
$973$	−14.1359	−	43.5059i	−0.453177	−	1.39473i
$974$	21.3261	−	36.9380i	0.683333	−	1.18357i
$975$	−10.4425	+	17.2003i	−0.334429	+	0.550849i
$976$	27.0940	+	46.9281i	0.867257	+	1.50213i
$977$	15.9615	−	17.7270i	0.510653	−	0.567138i	−0.431589	−	0.902070i	$-0.642047\pi$
$977$	15.9615	−	17.7270i	0.510653	−	0.567138i	0.942242	+	0.334933i	$0.108714\pi$
$978$	11.0249	+	3.27946i	0.352537	+	0.104866i
$979$	−2.61945	−	24.9224i	−0.0837180	−	0.796523i
$980$	8.91987	−	21.6966i	0.284935	−	0.693072i
$981$	1.32492	+	8.49111i	0.0423016	+	0.271100i
$982$	−35.1227			−1.12081
$983$	8.65772	−	3.85467i	0.276138	−	0.122945i	−0.263995	−	0.964524i	$-0.585040\pi$
$983$	8.65772	−	3.85467i	0.276138	−	0.122945i	0.540134	+	0.841579i	$0.318374\pi$
$984$	−2.62090	+	14.0513i	−0.0835513	+	0.447938i
$985$	17.6009	−	2.36458i	0.560811	−	0.0753417i
$986$	−6.97116	+	7.74226i	−0.222007	+	0.246564i
$987$	−3.85586	+	20.6722i	−0.122733	+	0.658002i
$988$	−8.78951	−	9.76174i	−0.279632	−	0.310562i
$989$	4.69993	+	14.4649i	0.149449	+	0.459957i
$990$	57.0605	+	27.1917i	1.81350	+	0.864209i
$991$	8.47195	−	26.0740i	0.269120	−	0.828268i	−0.721595	−	0.692316i	$-0.756591\pi$
$991$	8.47195	−	26.0740i	0.269120	−	0.828268i	0.990715	−	0.135952i	$-0.0434093\pi$
$992$	14.5619	−	6.48336i	0.462340	−	0.205847i
$993$	−1.55196	−	2.02736i	−0.0492500	−	0.0643363i
$994$	−5.02675	+	47.8264i	−0.159439	+	1.51696i
$995$	−27.7703	−	14.9831i	−0.880378	−	0.474996i
$996$	−2.64595	−	11.0771i	−0.0838402	−	0.350990i
$997$	−2.65815	−	25.2906i	−0.0841844	−	0.800961i	−0.952416	−	0.304802i	$-0.901410\pi$
$997$	−2.65815	−	25.2906i	−0.0841844	−	0.800961i	0.868232	−	0.496159i	$-0.165257\pi$
$998$	11.4166	+	35.1366i	0.361385	+	1.11223i
$999$	14.4751	−	5.93756i	0.457970	−	0.187856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.6	yes	224
3.2	odd	2		675.2.r.a.181.23		224
9.4	even	3	inner	225.2.q.a.31.23	✓	224
9.5	odd	6		675.2.r.a.631.6		224
25.21	even	5	inner	225.2.q.a.196.23	yes	224
75.71	odd	10		675.2.r.a.46.6		224
225.121	even	15	inner	225.2.q.a.121.6	yes	224
225.221	odd	30		675.2.r.a.496.23		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.23	✓	224	9.4	even	3	inner
225.2.q.a.106.6	yes	224	1.1	even	1	trivial
225.2.q.a.121.6	yes	224	225.121	even	15	inner
225.2.q.a.196.23	yes	224	25.21	even	5	inner
675.2.r.a.46.6		224	75.71	odd	10
675.2.r.a.181.23		224	3.2	odd	2
675.2.r.a.496.23		224	225.221	odd	30
675.2.r.a.631.6		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68376 - 0.357895i) q^{2} +(-0.402409 - 1.68466i) q^{3} +(0.879882 + 0.391749i) q^{4} +(1.96791 + 1.06176i) q^{5} +(0.0746324 + 2.98058i) q^{6} +(-2.11497 + 3.66323i) q^{7} +(1.44394 + 1.04909i) q^{8} +(-2.67613 + 1.35584i) q^{9} +O(q^{10})\)	\(q+(-1.68376 - 0.357895i) q^{2} +(-0.402409 - 1.68466i) q^{3} +(0.879882 + 0.391749i) q^{4} +(1.96791 + 1.06176i) q^{5} +(0.0746324 + 2.98058i) q^{6} +(-2.11497 + 3.66323i) q^{7} +(1.44394 + 1.04909i) q^{8} +(-2.67613 + 1.35584i) q^{9} +(-2.93350 - 2.49206i) q^{10} +(5.35421 + 1.13807i) q^{11} +(0.305889 - 1.63994i) q^{12} +(-2.27272 + 0.483081i) q^{13} +(4.87216 - 5.41109i) q^{14} +(0.996792 - 3.74251i) q^{15} +(-3.34474 - 3.71472i) q^{16} +(-1.13466 - 0.824379i) q^{17} +(4.99123 - 1.32515i) q^{18} +(4.74872 + 3.45015i) q^{19} +(1.31559 + 1.70515i) q^{20} +(7.02237 + 2.08888i) q^{21} +(-8.60791 - 3.83249i) q^{22} +(2.33826 - 2.59691i) q^{23} +(1.18629 - 2.85471i) q^{24} +(2.74534 + 4.17889i) q^{25} +3.99961 q^{26} +(3.36103 + 3.96276i) q^{27} +(-3.29599 + 2.39468i) q^{28} +(0.451070 + 4.29164i) q^{29} +(-3.01779 + 5.94476i) q^{30} +(0.330923 - 3.14852i) q^{31} +(2.51747 + 4.36039i) q^{32} +(-0.237324 - 9.47797i) q^{33} +(1.61546 + 1.79415i) q^{34} +(-8.05154 + 4.96333i) q^{35} +(-2.88583 + 0.144610i) q^{36} +(0.930443 - 2.86361i) q^{37} +(-6.76093 - 7.50877i) q^{38} +(1.72839 + 3.63435i) q^{39} +(1.72767 + 3.59763i) q^{40} +(-4.52265 + 0.961319i) q^{41} +(-11.0764 - 6.03045i) q^{42} +(-2.17619 + 3.76927i) q^{43} +(4.26523 + 3.09887i) q^{44} +(-6.70597 - 0.173229i) q^{45} +(-4.86650 + 3.53572i) q^{46} +(0.300021 + 2.85451i) q^{47} +(-4.91206 + 7.12958i) q^{48} +(-5.44619 - 9.43308i) q^{49} +(-3.12690 - 8.01881i) q^{50} +(-0.932197 + 2.24325i) q^{51} +(-2.18897 - 0.465280i) q^{52} +(4.61926 - 3.35609i) q^{53} +(-4.24093 - 7.87525i) q^{54} +(9.32824 + 7.92450i) q^{55} +(-6.89694 + 3.07072i) q^{56} +(3.90138 - 9.38833i) q^{57} +(0.776463 - 7.38755i) q^{58} +(11.3426 - 2.41094i) q^{59} +(2.34318 - 2.90248i) q^{60} +(-10.6036 - 2.25387i) q^{61} +(-1.68404 + 5.18293i) q^{62} +(0.693168 - 12.6709i) q^{63} +(0.411065 + 1.26513i) q^{64} +(-4.98542 - 1.46242i) q^{65} +(-2.99252 + 16.0436i) q^{66} +(-1.17916 + 11.2190i) q^{67} +(-0.675418 - 1.16986i) q^{68} +(-5.31583 - 2.89415i) q^{69} +(15.3332 - 5.47547i) q^{70} +(-5.34318 + 3.88205i) q^{71} +(-5.28658 - 0.849733i) q^{72} +(1.20170 + 3.69845i) q^{73} +(-2.59152 + 4.48864i) q^{74} +(5.93524 - 6.30658i) q^{75} +(2.82672 + 4.89603i) q^{76} +(-15.4930 + 17.2067i) q^{77} +(-1.60948 - 6.73797i) q^{78} +(0.299995 + 2.85427i) q^{79} +(-2.63803 - 10.8615i) q^{80} +(5.32338 - 7.25683i) q^{81} +7.95913 q^{82} +(6.23662 - 2.77672i) q^{83} +(5.36055 + 4.58897i) q^{84} +(-1.35762 - 2.82704i) q^{85} +(5.01319 - 5.56772i) q^{86} +(7.04843 - 2.48690i) q^{87} +(6.53724 + 7.26034i) q^{88} +(-1.41471 - 4.35403i) q^{89} +(11.2293 + 2.69171i) q^{90} +(3.03709 - 9.34720i) q^{91} +(3.07473 - 1.36896i) q^{92} +(-5.43734 + 0.709504i) q^{93} +(0.516451 - 4.91370i) q^{94} +(5.68183 + 11.8316i) q^{95} +(6.33270 - 5.99573i) q^{96} +(-1.44531 - 13.7512i) q^{97} +(5.79405 + 17.8322i) q^{98} +(-15.8716 + 4.21384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

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