LMFDB - Embedded newform 225.2.u.a.169.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(4,225)]

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([10, 3]))

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

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

chi := DirichletCharacter("225.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.u (of order $30$, 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 $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			169.20
Character	$\chi$	$=$	225.169
Dual form			225.2.u.a.4.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.250369 - 1.17789i) q^{2} +(-1.73132 - 0.0503723i) q^{3} +(0.502342 + 0.223657i) q^{4} +(-1.04324 + 1.97779i) q^{5} +(-0.492802 + 2.02670i) q^{6} +(2.32094 + 1.33999i) q^{7} +(1.80485 - 2.48416i) q^{8} +(2.99493 + 0.174421i) q^{9} +O(q^{10})$	\(q+(0.250369 - 1.17789i) q^{2} +(-1.73132 - 0.0503723i) q^{3} +(0.502342 + 0.223657i) q^{4} +(-1.04324 + 1.97779i) q^{5} +(-0.492802 + 2.02670i) q^{6} +(2.32094 + 1.33999i) q^{7} +(1.80485 - 2.48416i) q^{8} +(2.99493 + 0.174421i) q^{9} +(2.06843 + 1.72401i) q^{10} +(1.37561 + 0.292396i) q^{11} +(-0.858447 - 0.412525i) q^{12} +(-0.0338103 - 0.159065i) q^{13} +(2.15946 - 2.39833i) q^{14} +(1.90581 - 3.37163i) q^{15} +(-1.73831 - 1.93059i) q^{16} +(0.113531 - 0.156262i) q^{17} +(0.955286 - 3.48403i) q^{18} +(6.07397 + 4.41300i) q^{19} +(-0.966411 + 0.760196i) q^{20} +(-3.95079 - 2.43687i) q^{21} +(0.688822 - 1.54712i) q^{22} +(-4.38392 - 3.94730i) q^{23} +(-3.24990 + 4.20996i) q^{24} +(-2.82328 - 4.12663i) q^{25} -0.195827 q^{26} +(-5.17638 - 0.452840i) q^{27} +(0.866205 + 1.19223i) q^{28} +(0.636956 + 6.06023i) q^{29} +(-3.49426 - 3.08900i) q^{30} +(0.0629147 - 0.598594i) q^{31} +(2.60917 - 1.50640i) q^{32} +(-2.36690 - 0.575523i) q^{33} +(-0.155636 - 0.172851i) q^{34} +(-5.07153 + 3.19238i) q^{35} +(1.46547 + 0.757455i) q^{36} +(0.888903 + 0.288822i) q^{37} +(6.71878 - 6.04962i) q^{38} +(0.0505239 + 0.277095i) q^{39} +(3.03024 + 6.16119i) q^{40} +(-5.53191 + 1.17584i) q^{41} +(-3.85953 + 4.04349i) q^{42} +(5.91893 + 3.41730i) q^{43} +(0.625632 + 0.454548i) q^{44} +(-3.46941 + 5.74136i) q^{45} +(-5.74710 + 4.17551i) q^{46} +(-0.217685 + 0.0228796i) q^{47} +(2.91232 + 3.43003i) q^{48} +(0.0911727 + 0.157916i) q^{49} +(-5.56760 + 2.29234i) q^{50} +(-0.204430 + 0.264821i) q^{51} +(0.0185917 - 0.0874669i) q^{52} +(-7.64631 - 10.5242i) q^{53} +(-1.82940 + 5.98385i) q^{54} +(-2.01340 + 2.41563i) q^{55} +(7.51770 - 3.34710i) q^{56} +(-10.2937 - 7.94626i) q^{57} +(7.29779 + 0.767028i) q^{58} +(5.81390 - 1.23578i) q^{59} +(1.71146 - 1.26746i) q^{60} +(-13.7973 - 2.93271i) q^{61} +(-0.689328 - 0.223976i) q^{62} +(6.71732 + 4.41801i) q^{63} +(-2.72670 - 8.39191i) q^{64} +(0.349869 + 0.0990742i) q^{65} +(-1.27050 + 2.64386i) q^{66} +(-6.42391 - 0.675180i) q^{67} +(0.0919806 - 0.0531050i) q^{68} +(7.39113 + 7.05486i) q^{69} +(2.49053 + 6.77300i) q^{70} +(2.90460 - 2.11032i) q^{71} +(5.83867 - 7.12507i) q^{72} +(-11.0652 + 3.59530i) q^{73} +(0.562756 - 0.974721i) q^{74} +(4.68013 + 7.28673i) q^{75} +(2.06421 + 3.57532i) q^{76} +(2.80091 + 2.52195i) q^{77} +(0.339038 + 0.00986425i) q^{78} +(-1.42166 - 13.5262i) q^{79} +(5.63178 - 1.42393i) q^{80} +(8.93915 + 1.04476i) q^{81} +6.81040i q^{82} +(5.96001 + 13.3864i) q^{83} +(-1.43962 - 2.10776i) q^{84} +(0.190613 + 0.387560i) q^{85} +(5.50713 - 6.11629i) q^{86} +(-0.797506 - 10.5243i) q^{87} +(3.20913 - 2.88951i) q^{88} +(-3.38521 - 10.4186i) q^{89} +(5.89408 + 5.52405i) q^{90} +(0.134675 - 0.414486i) q^{91} +(-1.31938 - 2.96339i) q^{92} +(-0.139078 + 1.03319i) q^{93} +(-0.0275518 + 0.262138i) q^{94} +(-15.0646 + 7.40918i) q^{95} +(-4.59318 + 2.47663i) q^{96} +(3.08167 - 0.323896i) q^{97} +(0.208835 - 0.0678546i) q^{98} +(4.06886 + 1.11564i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.250369	−	1.17789i	0.177038	−	0.832897i	−0.796548	−	0.604575i	$-0.793343\pi$
$2$	0.250369	−	1.17789i	0.177038	−	0.832897i	0.973586	−	0.228322i	$-0.0733238\pi$
$3$	−1.73132	−	0.0503723i	−0.999577	−	0.0290825i
$3$	−1.73132	−	0.0503723i	−0.999577	−	0.0290825i
$4$	0.502342	+	0.223657i	0.251171	+	0.111828i
$5$	−1.04324	+	1.97779i	−0.466553	+	0.884493i
$5$	−1.04324	+	1.97779i	−0.466553	+	0.884493i
$6$	−0.492802	+	2.02670i	−0.201185	+	0.827396i
$7$	2.32094	+	1.33999i	0.877233	+	0.506470i	0.869745	−	0.493501i	$-0.164283\pi$
$7$	2.32094	+	1.33999i	0.877233	+	0.506470i	0.00748764	+	0.999972i	$0.497617\pi$
$8$	1.80485	−	2.48416i	0.638110	−	0.878283i
$9$	2.99493	+	0.174421i	0.998308	+	0.0581403i
$10$	2.06843	+	1.72401i	0.654094	+	0.545179i
$11$	1.37561	+	0.292396i	0.414763	+	0.0881606i	0.410567	−	0.911831i	$-0.365331\pi$
$11$	1.37561	+	0.292396i	0.414763	+	0.0881606i	0.00419636	+	0.999991i	$0.498664\pi$
$12$	−0.858447	−	0.412525i	−0.247812	−	0.119086i
$13$	−0.0338103	−	0.159065i	−0.00937729	−	0.0441167i	0.973210	−	0.229917i	$-0.0738455\pi$
$13$	−0.0338103	−	0.159065i	−0.00937729	−	0.0441167i	−0.982587	+	0.185800i	$0.940512\pi$
$14$	2.15946	−	2.39833i	0.577141	−	0.640980i
$15$	1.90581	−	3.37163i	0.492079	−	0.870550i
$16$	−1.73831	−	1.93059i	−0.434578	−	0.482648i
$17$	0.113531	−	0.156262i	0.0275354	−	0.0378992i	−0.795027	−	0.606574i	$-0.792544\pi$
$17$	0.113531	−	0.156262i	0.0275354	−	0.0378992i	0.822563	+	0.568674i	$0.192544\pi$
$18$	0.955286	−	3.48403i	0.225163	−	0.821195i
$19$	6.07397	+	4.41300i	1.39346	+	1.01241i	0.995475	+	0.0950213i	$0.0302919\pi$
$19$	6.07397	+	4.41300i	1.39346	+	1.01241i	0.397989	+	0.917390i	$0.369708\pi$
$20$	−0.966411	+	0.760196i	−0.216096	+	0.169985i
$21$	−3.95079	−	2.43687i	−0.862132	−	0.531768i
$22$	0.688822	−	1.54712i	0.146857	−	0.329847i
$23$	−4.38392	−	3.94730i	−0.914110	−	0.823069i	0.0705575	−	0.997508i	$-0.477522\pi$
$23$	−4.38392	−	3.94730i	−0.914110	−	0.823069i	−0.984668	+	0.174439i	$0.944189\pi$
$24$	−3.24990	+	4.20996i	−0.663383	+	0.859354i
$25$	−2.82328	−	4.12663i	−0.564656	−	0.825326i
$26$	−0.195827			−0.0384048
$27$	−5.17638	−	0.452840i	−0.996195	−	0.0871490i
$28$	0.866205	+	1.19223i	0.163697	+	0.225310i
$29$	0.636956	+	6.06023i	0.118280	+	1.12536i	0.879180	+	0.476489i	$0.158091\pi$
$29$	0.636956	+	6.06023i	0.118280	+	1.12536i	−0.760901	+	0.648868i	$0.775243\pi$
$30$	−3.49426	−	3.08900i	−0.637962	−	0.563971i
$31$	0.0629147	−	0.598594i	0.0112998	−	0.107511i	−0.987418	−	0.158131i	$-0.949453\pi$
$31$	0.0629147	−	0.598594i	0.0112998	−	0.107511i	0.998718	+	0.0506203i	$0.0161198\pi$
$32$	2.60917	−	1.50640i	0.461240	−	0.266297i
$33$	−2.36690	−	0.575523i	−0.412024	−	0.100186i
$34$	−0.155636	−	0.172851i	−0.0266913	−	0.0296437i
$35$	−5.07153	+	3.19238i	−0.857245	+	0.539611i
$36$	1.46547	+	0.757455i	0.244244	+	0.126242i
$37$	0.888903	+	0.288822i	0.146135	+	0.0474821i	0.381171	−	0.924505i	$-0.375521\pi$
$37$	0.888903	+	0.288822i	0.146135	+	0.0474821i	−0.235036	+	0.971987i	$0.575521\pi$
$38$	6.71878	−	6.04962i	1.08993	−	0.981377i
$39$	0.0505239	+	0.277095i	0.00809031	+	0.0443708i
$40$	3.03024	+	6.16119i	0.479123	+	0.974169i
$41$	−5.53191	+	1.17584i	−0.863940	+	0.183636i	−0.618509	−	0.785778i	$-0.712263\pi$
$41$	−5.53191	+	1.17584i	−0.863940	+	0.183636i	−0.245431	+	0.969414i	$0.578929\pi$
$42$	−3.85953	+	4.04349i	−0.595538	+	0.623924i
$43$	5.91893	+	3.41730i	0.902629	+	0.521133i	0.878052	−	0.478565i	$-0.158843\pi$
$43$	5.91893	+	3.41730i	0.902629	+	0.521133i	0.0245768	+	0.999698i	$0.492176\pi$
$44$	0.625632	+	0.454548i	0.0943175	+	0.0685257i
$45$	−3.46941	+	5.74136i	−0.517189	+	0.855871i
$46$	−5.74710	+	4.17551i	−0.847363	+	0.615645i
$47$	−0.217685	+	0.0228796i	−0.0317525	+	0.00333733i	−0.120391	−	0.992727i	$-0.538415\pi$
$47$	−0.217685	+	0.0228796i	−0.0317525	+	0.00333733i	0.0886389	+	0.996064i	$0.471748\pi$
$48$	2.91232	+	3.43003i	0.420358	+	0.495082i
$49$	0.0911727	+	0.157916i	0.0130247	+	0.0225594i
$50$	−5.56760	+	2.29234i	−0.787377	+	0.324186i
$51$	−0.204430	+	0.264821i	−0.0286259	+	0.0370823i
$52$	0.0185917	−	0.0874669i	0.00257820	−	0.0121295i
$53$	−7.64631	−	10.5242i	−1.05030	−	1.44562i	−0.888547	−	0.458785i	$-0.848285\pi$
$53$	−7.64631	−	10.5242i	−1.05030	−	1.44562i	−0.161754	−	0.986831i	$-0.551715\pi$
$54$	−1.82940	+	5.98385i	−0.248950	+	0.814299i
$55$	−2.01340	+	2.41563i	−0.271486	+	0.325723i
$56$	7.51770	−	3.34710i	1.00460	−	0.447275i
$57$	−10.2937	−	7.94626i	−1.36343	−	1.05251i
$58$	7.29779	+	0.767028i	0.958246	+	0.100716i
$59$	5.81390	−	1.23578i	0.756905	−	0.160885i	0.186733	−	0.982411i	$-0.440210\pi$
$59$	5.81390	−	1.23578i	0.756905	−	0.160885i	0.570172	+	0.821525i	$0.306877\pi$
$60$	1.71146	−	1.26746i	0.220948	−	0.163628i
$61$	−13.7973	−	2.93271i	−1.76656	−	0.375495i	−0.793961	−	0.607969i	$-0.791984\pi$
$61$	−13.7973	−	2.93271i	−1.76656	−	0.375495i	−0.972602	+	0.232475i	$0.925318\pi$
$62$	−0.689328	−	0.223976i	−0.0875447	−	0.0284450i
$63$	6.71732	+	4.41801i	0.846302	+	0.556616i
$64$	−2.72670	−	8.39191i	−0.340837	−	1.04899i
$65$	0.349869	+	0.0990742i	0.0433959	+	0.0122886i
$66$	−1.27050	+	2.64386i	−0.156388	+	0.325436i
$67$	−6.42391	−	0.675180i	−0.784805	−	0.0824863i	−0.296355	−	0.955078i	$-0.595771\pi$
$67$	−6.42391	−	0.675180i	−0.784805	−	0.0824863i	−0.488450	+	0.872592i	$0.662438\pi$
$68$	0.0919806	−	0.0531050i	0.0111543	−	0.00643993i
$69$	7.39113	+	7.05486i	0.889787	+	0.849305i
$70$	2.49053	+	6.77300i	0.297675	+	0.809528i
$71$	2.90460	−	2.11032i	0.344713	−	0.250449i	−0.401935	−	0.915668i	$-0.631662\pi$
$71$	2.90460	−	2.11032i	0.344713	−	0.250449i	0.746648	+	0.665220i	$0.231662\pi$
$72$	5.83867	−	7.12507i	0.688094	−	0.839697i
$73$	−11.0652	+	3.59530i	−1.29508	+	0.420798i	−0.873868	−	0.486163i	$-0.838396\pi$
$73$	−11.0652	+	3.59530i	−1.29508	+	0.420798i	−0.421215	+	0.906961i	$0.638396\pi$
$74$	0.562756	−	0.974721i	0.0654190	−	0.113309i
$75$	4.68013	+	7.28673i	0.540415	+	0.841399i
$76$	2.06421	+	3.57532i	0.236781	+	0.410117i
$77$	2.80091	+	2.52195i	0.319193	+	0.287403i
$78$	0.339038	+	0.00986425i	0.0383885	+	0.00111691i
$79$	−1.42166	−	13.5262i	−0.159950	−	1.52182i	−0.720357	−	0.693603i	$-0.756022\pi$
$79$	−1.42166	−	13.5262i	−0.159950	−	1.52182i	0.560407	−	0.828217i	$-0.310645\pi$
$80$	5.63178	−	1.42393i	0.629653	−	0.159200i
$81$	8.93915	+	1.04476i	0.993239	+	0.116084i
$82$			6.81040i			0.752083i
$83$	5.96001	+	13.3864i	0.654196	+	1.46935i	0.870071	+	0.492927i	$0.164073\pi$
$83$	5.96001	+	13.3864i	0.654196	+	1.46935i	−0.215875	+	0.976421i	$0.569260\pi$
$84$	−1.43962	−	2.10776i	−0.157076	−	0.229976i
$85$	0.190613	+	0.387560i	0.0206748	+	0.0420368i
$86$	5.50713	−	6.11629i	0.593849	−	0.659537i
$87$	−0.797506	−	10.5243i	−0.0855016	−	1.12832i
$88$	3.20913	−	2.88951i	0.342094	−	0.308023i
$89$	−3.38521	−	10.4186i	−0.358831	−	1.10437i	−0.953754	−	0.300587i	$-0.902817\pi$
$89$	−3.38521	−	10.4186i	−0.358831	−	1.10437i	0.594923	−	0.803783i	$-0.297183\pi$
$90$	5.89408	+	5.52405i	0.621291	+	0.582286i
$91$	0.134675	−	0.414486i	0.0141177	−	0.0434499i
$92$	−1.31938	−	2.96339i	−0.137555	−	0.308954i
$93$	−0.139078	+	1.03319i	−0.0144217	+	0.107137i
$94$	−0.0275518	+	0.262138i	−0.00284175	+	0.0270374i
$95$	−15.0646	+	7.40918i	−1.54560	+	0.760166i
$96$	−4.59318	+	2.47663i	−0.468789	+	0.252770i
$97$	3.08167	−	0.323896i	0.312896	−	0.0328867i	0.0532209	−	0.998583i	$-0.483051\pi$
$97$	3.08167	−	0.323896i	0.312896	−	0.0328867i	0.259675	+	0.965696i	$0.416385\pi$
$98$	0.208835	−	0.0678546i	0.0210955	−	0.00685435i
$99$	4.06886	+	1.11564i	0.408936	+	0.112126i
$100$	−0.495302	−	2.70443i	−0.0495302	−	0.270443i
$101$	4.01857	−	6.96037i	0.399863	−	0.692583i	−0.593846	−	0.804579i	$-0.702391\pi$
$101$	4.01857	−	6.96037i	0.399863	−	0.692583i	0.993709	+	0.111996i	$0.0357244\pi$
$102$	0.260748	+	0.307100i	0.0258179	+	0.0304074i
$103$	0.219557	−	0.493132i	0.0216336	−	0.0485898i	−0.902406	−	0.430888i	$-0.858201\pi$
$103$	0.219557	−	0.493132i	0.0216336	−	0.0485898i	0.924039	+	0.382298i	$0.124867\pi$
$104$	−0.456165	−	0.203098i	−0.0447307	−	0.0199154i
$105$	8.94124	−	5.27156i	0.872576	−	0.514452i
$106$	−14.3108	+	6.37160i	−1.38999	+	0.618864i
$107$		−	0.671621i		−	0.0649281i	−0.999473	−	0.0324640i	$-0.989665\pi$
$107$		−	0.671621i		−	0.0649281i	0.999473	−	0.0324640i	$-0.0103354\pi$
$108$	−2.49903	−	1.38521i	−0.240469	−	0.133292i
$109$	4.32136	−	13.2998i	0.413911	−	1.27389i	−0.499310	−	0.866423i	$-0.666413\pi$
$109$	4.32136	−	13.2998i	0.413911	−	1.27389i	0.913221	−	0.407464i	$-0.133587\pi$
$110$	2.34126	+	2.97637i	0.223231	+	0.283785i
$111$	−1.52443	−	0.544819i	−0.144692	−	0.0517119i
$112$	−1.44753	−	6.81012i	−0.136779	−	0.643495i
$113$	−0.769916	−	3.62217i	−0.0724276	−	0.340745i	0.926982	−	0.375106i	$-0.122394\pi$
$113$	−0.769916	−	3.62217i	−0.0724276	−	0.340745i	−0.999409	+	0.0343611i	$0.989060\pi$
$114$	−11.9371	+	10.1354i	−1.11801	+	0.949264i
$115$	12.3804	−	4.55246i	1.15448	−	0.424519i
$116$	−1.03544	+	3.18677i	−0.0961386	+	0.295884i
$117$	−0.0735151	−	0.482285i	−0.00679647	−	0.0445873i
$118$		−	7.15756i		−	0.658907i
$119$	0.472890	−	0.210544i	0.0433497	−	0.0193005i
$120$	−4.93595	−	10.8196i	−0.450589	−	0.987691i
$121$	−8.24218	−	3.66966i	−0.749289	−	0.333605i
$122$	−6.90883	+	15.5175i	−0.625496	+	1.40489i
$123$	9.63673	−	1.75711i	0.868915	−	0.158433i
$124$	0.165484	−	0.286627i	0.0148609	−	0.0257399i
$125$	11.1070	−	1.27876i	0.993438	−	0.114376i
$126$	6.88575	−	6.80615i	0.613431	−	0.606340i
$127$	13.6104	−	4.42230i	1.20773	−	0.392416i	0.365132	−	0.930956i	$-0.381024\pi$
$127$	13.6104	−	4.42230i	1.20773	−	0.392416i	0.842600	+	0.538540i	$0.181024\pi$
$128$	−4.57486	+	0.480838i	−0.404365	+	0.0425004i
$129$	−10.0754	−	6.21458i	−0.887091	−	0.547163i
$130$	0.204295	−	0.387304i	0.0179179	−	0.0339688i
$131$	−1.22397	+	11.6453i	−0.106938	+	1.01745i	0.801090	+	0.598543i	$0.204254\pi$
$131$	−1.22397	+	11.6453i	−0.106938	+	1.01745i	−0.908029	+	0.418908i	$0.862413\pi$
$132$	−1.06027	−	0.818482i	−0.0922847	−	0.0712397i
$133$	8.18392	+	18.3814i	0.709636	+	1.59387i
$134$	−2.40364	+	7.39763i	−0.207643	+	0.639058i
$135$	6.29585	−	9.76536i	0.541861	−	0.840468i
$136$	−0.183274	−	0.564059i	−0.0157156	−	0.0483677i
$137$	−15.2933	+	13.7702i	−1.30660	+	1.17647i	−0.334366	+	0.942443i	$0.608522\pi$
$137$	−15.2933	+	13.7702i	−1.30660	+	1.17647i	−0.972231	+	0.234022i	$0.924811\pi$
$138$	10.1604	−	6.93964i	0.864909	−	0.590742i
$139$	−0.609700	+	0.677140i	−0.0517141	+	0.0574343i	−0.768447	−	0.639914i	$-0.778970\pi$
$139$	−0.609700	+	0.677140i	−0.0517141	+	0.0574343i	0.716733	+	0.697348i	$0.245637\pi$
$140$	−3.26164	+	0.469382i	−0.275659	+	0.0396701i
$141$	0.378034	−	0.0286465i	0.0318362	−	0.00241247i
$142$	−1.75851	−	3.94967i	−0.147571	−	0.331449i
$143$		−	0.228698i		−	0.0191247i
$144$	−4.86938	−	6.08518i	−0.405782	−	0.507098i
$145$	−12.6504	−	5.06254i	−1.05055	−	0.420421i
$146$	1.46450	+	13.9338i	0.121203	+	1.15317i
$147$	−0.149894	−	0.277995i	−0.0123631	−	0.0229286i
$148$	0.381936	+	0.343897i	0.0313949	+	0.0282681i
$149$	10.6085	+	18.3745i	0.869083	+	1.50530i	0.862935	+	0.505315i	$0.168624\pi$
$149$	10.6085	+	18.3745i	0.869083	+	1.50530i	0.00614869	+	0.999981i	$0.498043\pi$
$150$	9.75475	−	3.68832i	0.796472	−	0.301150i
$151$	−2.66528	+	4.61641i	−0.216898	+	0.375678i	−0.953858	−	0.300258i	$-0.902927\pi$
$151$	−2.66528	+	4.61641i	−0.216898	+	0.375678i	0.736960	+	0.675936i	$0.236260\pi$
$152$	21.9252	−	7.12392i	1.77837	−	0.577826i
$153$	0.367273	−	0.448192i	0.0296923	−	0.0362342i
$154$	3.67185	−	2.66775i	0.295886	−	0.214974i
$155$	1.11826	+	0.748912i	0.0898204	+	0.0601540i
$156$	−0.0365940	+	0.150497i	−0.00292986	+	0.0120494i
$157$	10.4979	−	6.06096i	0.837823	−	0.483717i	−0.0187007	−	0.999825i	$-0.505953\pi$
$157$	10.4979	−	6.06096i	0.837823	−	0.483717i	0.856524	+	0.516108i	$0.172620\pi$
$158$	−16.2884	−	1.71198i	−1.29584	−	0.136198i
$159$	12.7081	+	18.6060i	1.00782	+	1.47555i
$160$	0.257344	+	6.73192i	0.0203448	+	0.532205i
$161$	−4.88545	−	15.0359i	−0.385027	−	1.18499i
$162$	3.46870	−	10.2678i	0.272527	−	0.806715i
$163$	−0.508454	−	0.165207i	−0.0398252	−	0.0129400i	0.289037	−	0.957318i	$-0.406665\pi$
$163$	−0.508454	−	0.165207i	−0.0398252	−	0.0129400i	−0.328862	+	0.944378i	$0.606665\pi$
$164$	−3.04190	−	0.646575i	−0.237532	−	0.0504890i
$165$	3.60751	−	4.08080i	0.280844	−	0.317690i
$166$	17.2600	−	3.66872i	1.33963	−	0.284748i
$167$	10.8420	+	1.13954i	0.838979	+	0.0881803i	0.514264	−	0.857632i	$-0.328065\pi$
$167$	10.8420	+	1.13954i	0.838979	+	0.0881803i	0.324715	+	0.945812i	$0.394732\pi$
$168$	−13.1841	+	5.41620i	−1.01718	+	0.417869i
$169$	11.8519	−	5.27682i	0.911687	−	0.405909i
$170$	0.504228	−	0.127488i	0.0386726	−	0.00977791i
$171$	17.4214	+	14.2760i	1.33225	+	1.09172i
$172$	2.20903	+	3.04046i	0.168437	+	0.231833i
$173$	2.18261	−	10.2684i	0.165941	−	0.780689i	−0.813915	−	0.580983i	$-0.802668\pi$
$173$	2.18261	−	10.2684i	0.165941	−	0.780689i	0.979856	−	0.199706i	$-0.0639986\pi$
$174$	−12.5962	−	1.69558i	−0.954912	−	0.128541i
$175$	−1.02300	−	13.3608i	−0.0773313	−	1.00998i
$176$	−1.82675	−	3.16402i	−0.137696	−	0.238497i
$177$	−10.1280	+	1.84667i	−0.761264	+	0.138804i
$178$	−13.1196	+	1.37892i	−0.983352	+	0.103355i
$179$	−11.1491	+	8.10027i	−0.833321	+	0.605443i	−0.920497	−	0.390750i	$-0.872216\pi$
$179$	−11.1491	+	8.10027i	−0.833321	+	0.605443i	0.0871761	+	0.996193i	$0.472216\pi$
$180$	−3.02692	+	2.10817i	−0.225614	+	0.157134i
$181$	−5.95243	−	4.32469i	−0.442441	−	0.321452i	0.344163	−	0.938910i	$-0.388163\pi$
$181$	−5.95243	−	4.32469i	−0.442441	−	0.321452i	−0.786604	+	0.617458i	$0.788163\pi$
$182$	−0.454502	−	0.262407i	−0.0336899	−	0.0194509i
$183$	23.7398	+	5.77245i	1.75490	+	0.426712i
$184$	−17.7180	+	3.76608i	−1.30619	+	0.277639i
$185$	−1.49857	+	1.45675i	−0.110177	+	0.107102i
$186$	1.18216	+	0.422497i	0.0866805	+	0.0309790i
$187$	0.201865	−	0.181760i	0.0147619	−	0.0132916i
$188$	−0.114469	−	0.0371933i	−0.00834852	−	0.00271260i
$189$	−11.4073	−	7.98734i	−0.829757	−	0.580993i
$190$	4.95552	+	19.5995i	0.359511	+	1.42190i
$191$	0.746068	+	0.828592i	0.0539836	+	0.0599548i	0.769532	−	0.638609i	$-0.220490\pi$
$191$	0.746068	+	0.828592i	0.0539836	+	0.0599548i	−0.715548	+	0.698563i	$0.753823\pi$
$192$	4.29806	+	14.6664i	0.310186	+	1.05846i
$193$	−21.9469	+	12.6711i	−1.57977	+	0.912083i	−0.584884	+	0.811117i	$0.698860\pi$
$193$	−21.9469	+	12.6711i	−1.57977	+	0.912083i	−0.994890	+	0.100966i	$0.967807\pi$
$194$	0.390039	−	3.71097i	0.0280031	−	0.266432i
$195$	−0.600744	−	0.189153i	−0.0430202	−	0.0135455i
$196$	0.0104809	+	0.0997191i	0.000748636	+	0.00712279i
$197$	9.37839	+	12.9082i	0.668182	+	0.919674i	0.999717	−	0.0237688i	$-0.00756657\pi$
$197$	9.37839	+	12.9082i	0.668182	+	0.919674i	−0.331535	+	0.943443i	$0.607567\pi$
$198$	2.33282	−	4.51336i	0.165786	−	0.320751i
$199$	−19.2943			−1.36774			−0.683868	−	0.729606i	$-0.739704\pi$
$199$	−19.2943			−1.36774			−0.683868	+	0.729606i	$0.739704\pi$
$200$	−15.3468	−	0.434461i	−1.08518	−	0.0307210i
$201$	11.0878	+	1.49254i	0.782074	+	0.105276i
$202$	−7.19245	−	6.47611i	−0.506059	−	0.455658i
$203$	−6.64235	+	14.9190i	−0.466201	+	1.04711i
$204$	−0.161923	+	0.0873084i	−0.0113369	+	0.00611281i
$205$	3.44557	−	12.1676i	0.240649	−	0.849825i
$206$	−0.525887	−	0.382080i	−0.0366403	−	0.0266207i
$207$	−12.4410	−	12.5865i	−0.864711	−	0.874823i
$208$	−0.248317	+	0.341779i	−0.0172177	+	0.0236981i
$209$	7.06509	+	7.84658i	0.488703	+	0.542759i
$210$	−3.97073	−	11.8517i	−0.274006	−	0.817843i
$211$	2.02834	−	2.25270i	0.139637	−	0.155082i	−0.669270	−	0.743019i	$-0.733393\pi$
$211$	2.02834	−	2.25270i	0.139637	−	0.155082i	0.808907	+	0.587937i	$0.200060\pi$
$212$	−1.48724	−	6.99692i	−0.102144	−	0.480550i
$213$	−5.13510	+	3.50732i	−0.351851	+	0.240318i
$214$	−0.791098	−	0.168153i	−0.0540784	−	0.0114947i
$215$	−12.9336	+	8.14131i	−0.882063	+	0.555233i
$216$	−10.4675	+	12.0417i	−0.712223	+	0.819331i
$217$	0.948134	−	1.30499i	0.0643635	−	0.0885888i
$218$	−14.5838	−	8.41995i	−0.987738	−	0.570271i
$219$	19.3385	−	5.66723i	1.30677	−	0.382956i
$220$	−1.55169	+	0.763161i	−0.104615	+	0.0514523i
$221$	−0.0286944	−	0.0127756i	−0.00193019	−	0.000859378i
$222$	−1.02341	+	1.65921i	−0.0686866	+	0.111359i
$223$	−3.78775	+	17.8200i	−0.253647	+	1.19331i	0.648273	+	0.761408i	$0.275492\pi$
$223$	−3.78775	+	17.8200i	−0.253647	+	1.19331i	−0.901919	+	0.431905i	$0.857842\pi$
$224$	8.07429			0.539486
$225$	−7.73574	−	12.8514i	−0.515716	−	0.856759i
$226$	−4.45929			−0.296628
$227$	−1.75915	+	8.27617i	−0.116759	+	0.549309i	0.880416	+	0.474202i	$0.157263\pi$
$227$	−1.75915	+	8.27617i	−0.116759	+	0.549309i	−0.997175	+	0.0751071i	$0.976070\pi$
$228$	−3.39371	−	6.29399i	−0.224754	−	0.416830i
$229$	−8.93614	−	3.97862i	−0.590517	−	0.262915i	0.0896491	−	0.995973i	$-0.471425\pi$
$229$	−8.93614	−	3.97862i	−0.590517	−	0.262915i	−0.680166	+	0.733059i	$0.738092\pi$
$230$	−2.26264	−	15.7226i	−0.149194	−	1.03672i
$231$	−4.72222	−	4.50738i	−0.310699	−	0.296564i
$232$	16.2042	+	9.35550i	1.06386	+	0.614218i
$233$	−1.49631	+	2.05949i	−0.0980263	+	0.134922i	−0.855213	−	0.518277i	$-0.826573\pi$
$233$	−1.49631	+	2.05949i	−0.0980263	+	0.134922i	0.757186	+	0.653199i	$0.226573\pi$
$234$	−0.586487	−	0.0341563i	−0.0383398	−	0.00223287i
$235$	0.181847	−	0.454403i	0.0118624	−	0.0296420i
$236$	3.19696	+	0.679534i	0.208104	+	0.0442339i
$237$	1.78001	+	23.4898i	0.115624	+	1.52583i
$238$	−0.129602	−	0.609728i	−0.00840082	−	0.0395228i
$239$	7.06013	−	7.84107i	0.456682	−	0.507197i	−0.470195	−	0.882563i	$-0.655816\pi$
$239$	7.06013	−	7.84107i	0.456682	−	0.507197i	0.926877	+	0.375366i	$0.122483\pi$
$240$	−9.82214	+	2.18159i	−0.634016	+	0.140821i
$241$	−2.05683	−	2.28434i	−0.132492	−	0.147147i	0.673248	−	0.739417i	$-0.264899\pi$
$241$	−2.05683	−	2.28434i	−0.132492	−	0.147147i	−0.805740	+	0.592270i	$0.798232\pi$
$242$	−6.38605	+	8.78965i	−0.410511	+	0.565020i
$243$	−15.4239	−	2.25909i	−0.989443	−	0.144921i
$244$	−6.27504	−	4.55908i	−0.401718	−	0.291865i
$245$	−0.407439	+	0.0155754i	−0.0260303	+	0.000995074i
$246$	0.343056	−	11.7910i	0.0218724	−	0.751765i
$247$	0.496591	−	1.11536i	0.0315973	−	0.0709687i
$248$	−1.37345	−	1.23666i	−0.0872142	−	0.0785280i
$249$	−9.64436	−	23.4763i	−0.611187	−	1.48775i
$250$	1.27460	−	13.4030i	0.0806127	−	0.847680i
$251$	−23.8819			−1.50741			−0.753707	−	0.657211i	$-0.771736\pi$
$251$	−23.8819			−1.50741			−0.753707	+	0.657211i	$0.771736\pi$
$252$	2.38627	+	3.72172i	0.150321	+	0.234447i
$253$	−4.87640	−	6.71180i	−0.306577	−	0.421967i
$254$	−1.80137	−	17.1389i	−0.113028	−	1.07539i
$255$	−0.310489	−	0.680592i	−0.0194436	−	0.0426203i
$256$	1.26564	−	12.0418i	0.0791027	−	0.752612i
$257$	−4.15137	+	2.39680i	−0.258955	+	0.149508i	−0.623858	−	0.781538i	$-0.714436\pi$
$257$	−4.15137	+	2.39680i	−0.258955	+	0.149508i	0.364903	+	0.931046i	$0.381102\pi$
$258$	−9.84269	+	10.3118i	−0.612779	+	0.641987i
$259$	1.67607	+	1.86146i	0.104146	+	0.115666i
$260$	0.153595	+	0.128020i	0.00952557	+	0.00793945i
$261$	0.850605	+	18.2610i	0.0526511	+	1.13033i
$262$	13.4104	+	4.35732i	0.828500	+	0.269196i
$263$	17.2869	−	15.5652i	1.06595	−	0.959790i	0.0666763	−	0.997775i	$-0.478761\pi$
$263$	17.2869	−	15.5652i	1.06595	−	0.959790i	0.999278	+	0.0379848i	$0.0120939\pi$
$264$	−5.70157	+	4.84101i	−0.350908	+	0.297944i
$265$	28.7917	−	4.14341i	1.76866	−	0.254528i
$266$	23.7003	−	5.03766i	1.45316	−	0.308879i
$267$	5.33606	+	18.2084i	0.326562	+	1.11434i
$268$	−3.07599	−	1.77592i	−0.187896	−	0.108482i
$269$	6.79619	+	4.93772i	0.414371	+	0.301058i	0.775369	−	0.631508i	$-0.217564\pi$
$269$	6.79619	+	4.93772i	0.414371	+	0.301058i	−0.360998	+	0.932567i	$0.617564\pi$
$270$	−9.92627	−	9.86079i	−0.604093	−	0.600109i
$271$	16.4715	−	11.9673i	1.00058	−	0.726960i	0.0383636	−	0.999264i	$-0.487785\pi$
$271$	16.4715	−	11.9673i	1.00058	−	0.726960i	0.962211	+	0.272304i	$0.0877855\pi$
$272$	−0.499031	+	0.0524503i	−0.0302582	+	0.00318027i
$273$	−0.254043	+	0.710823i	−0.0153754	+	0.0430210i
$274$	12.3908	+	21.4615i	0.748557	+	1.29654i
$275$	−2.67713	−	6.50216i	−0.161437	−	0.392095i
$276$	2.13500	+	5.19703i	0.128512	+	0.312824i
$277$	−2.12195	+	9.98301i	−0.127496	+	0.599821i	0.867287	+	0.497808i	$0.165862\pi$
$277$	−2.12195	+	9.98301i	−0.127496	+	0.599821i	−0.994783	+	0.102013i	$0.967472\pi$
$278$	0.644950	+	0.887697i	0.0386815	+	0.0532405i
$279$	0.292832	−	1.78177i	0.0175314	−	0.106672i
$280$	−1.22296	+	18.3602i	−0.0730859	+	1.09723i
$281$	21.4178	−	9.53583i	1.27768	−	0.568860i	0.348093	−	0.937460i	$-0.386829\pi$
$281$	21.4178	−	9.53583i	1.27768	−	0.568860i	0.929588	+	0.368600i	$0.120163\pi$
$282$	0.0609054	−	0.452456i	0.00362686	−	0.0269433i
$283$	−16.1357	−	1.69593i	−0.959166	−	0.100812i	−0.388011	−	0.921655i	$-0.626838\pi$
$283$	−16.1357	−	1.69593i	−0.959166	−	0.100812i	−0.571155	+	0.820842i	$0.693505\pi$
$284$	1.93109	−	0.410466i	0.114589	−	0.0243567i
$285$	26.4548	−	12.0688i	1.56705	−	0.714895i
$286$	−0.269382	−	0.0572589i	−0.0159289	−	0.00338579i
$287$	−14.4149	−	4.68367i	−0.850882	−	0.276468i
$288$	8.07700	−	4.05647i	0.475942	−	0.239030i
$289$	5.24176	+	16.1325i	0.308339	+	0.948969i
$290$	−9.13040	+	13.6333i	−0.536155	+	0.800573i
$291$	−5.35166	+	0.405537i	−0.313720	+	0.0237730i
$292$	−6.36263	−	0.668739i	−0.372344	−	0.0391350i
$293$	−2.77885	+	1.60437i	−0.162342	+	0.0937283i	−0.578970	−	0.815349i	$-0.696545\pi$
$293$	−2.77885	+	1.60437i	−0.162342	+	0.0937283i	0.416628	+	0.909077i	$0.363212\pi$
$294$	−0.364978	+	0.106958i	−0.0212859	+	0.00623794i
$295$	−3.62121	+	12.7879i	−0.210835	+	0.744539i
$296$	2.32181	−	1.68690i	0.134953	−	0.0980489i
$297$	−6.98829	−	2.13648i	−0.405502	−	0.123971i
$298$	24.2992	−	7.89530i	1.40762	−	0.457363i
$299$	−0.479656	+	0.830788i	−0.0277392	+	0.0480457i
$300$	0.721297	+	4.70717i	0.0416441	+	0.271769i
$301$	9.15833	+	15.8627i	0.527877	+	0.914310i
$302$	4.77033	+	4.29523i	0.274502	+	0.247162i
$303$	−7.30804	+	11.8482i	−0.419836	+	0.680661i
$304$	−2.03876	−	19.3975i	−0.116931	−	1.11252i
$305$	20.1942	−	24.2286i	1.15632	−	1.38732i
$306$	−0.435968	−	0.544822i	−0.0249227	−	0.0311454i
$307$		−	16.5271i		−	0.943250i	−0.881799	−	0.471625i	$-0.843668\pi$
$307$		−	16.5271i		−	0.943250i	0.881799	−	0.471625i	$-0.156332\pi$
$308$	0.842961	+	1.89332i	0.0480322	+	0.107882i
$309$	−0.404963	+	0.842709i	−0.0230375	+	0.0479401i
$310$	1.16212	−	1.12968i	0.0660037	−	0.0641616i
$311$	12.5827	−	13.9745i	0.713499	−	0.792421i	−0.271965	−	0.962307i	$-0.587673\pi$
$311$	12.5827	−	13.9745i	0.713499	−	0.792421i	0.985464	+	0.169886i	$0.0543400\pi$
$312$	0.779537	+	0.374605i	0.0441326	+	0.0212078i
$313$	2.34979	−	2.11576i	0.132818	−	0.119590i	−0.600045	−	0.799967i	$-0.704851\pi$
$313$	2.34979	−	2.11576i	0.132818	−	0.119590i	0.732862	+	0.680377i	$0.238184\pi$
$314$	−4.51082	−	13.8829i	−0.254560	−	0.783456i
$315$	−15.7457	+	8.67636i	−0.887168	+	0.488857i
$316$	2.31108	−	7.11276i	0.130008	−	0.400124i
$317$	−0.163144	−	0.366428i	−0.00916309	−	0.0205806i	0.908906	−	0.417001i	$-0.136919\pi$
$317$	−0.163144	−	0.366428i	−0.00916309	−	0.0205806i	−0.918069	+	0.396421i	$0.870252\pi$
$318$	25.0976	−	10.3104i	1.40740	−	0.578178i
$319$	−0.895781	+	8.52278i	−0.0501541	+	0.477184i
$320$	19.4420	+	3.36199i	1.08684	+	0.187941i
$321$	−0.0338311	+	1.16279i	−0.00188827	+	0.0649006i
$322$	−18.9338	+	1.99003i	−1.05514	+	0.110900i
$323$	1.37917	−	0.448120i	0.0767391	−	0.0249340i
$324$	4.25684	+	2.52413i	0.236491	+	0.140229i
$325$	−0.560947	+	0.588608i	−0.0311157	+	0.0326501i
$326$	−0.321897	+	0.557543i	−0.0178282	+	0.0308794i
$327$	−8.15158	+	22.8085i	−0.450784	+	1.26131i
$328$	−7.06327	+	15.8644i	−0.390004	+	0.875963i
$329$	−0.535891	−	0.238594i	−0.0295446	−	0.0131541i
$330$	−3.90354	−	5.27097i	−0.214883	−	0.290158i
$331$	22.0829	−	9.83194i	1.21379	−	0.540412i	0.302881	−	0.953028i	$-0.402052\pi$
$331$	22.0829	−	9.83194i	1.21379	−	0.540412i	0.910905	+	0.412616i	$0.135385\pi$
$332$			8.05754i			0.442215i
$333$	2.61182	+	1.02004i	0.143127	+	0.0558981i
$334$	4.05676	−	12.4854i	0.221976	−	0.683172i
$335$	8.03707	−	12.0007i	0.439112	−	0.655670i
$336$	2.16310	+	11.8634i	0.118007	+	0.647201i
$337$	6.94302	+	32.6643i	0.378210	+	1.77934i	0.595628	+	0.803260i	$0.296903\pi$
$337$	6.94302	+	32.6643i	0.378210	+	1.77934i	−0.217418	+	0.976079i	$0.569763\pi$
$338$	−3.24818	−	15.2815i	−0.176678	−	0.831202i
$339$	1.15051	+	6.30991i	0.0624872	+	0.342707i
$340$	0.00907213	+	0.237320i	0.000492005	+	0.0128705i
$341$	0.261573	−	0.805038i	0.0141649	−	0.0435952i
$342$	21.1774	−	16.9462i	1.14514	−	0.916348i
$343$		−	18.2712i		−	0.986554i
$344$	19.1719	−	8.53587i	1.03368	−	0.460223i
$345$	−21.6638	+	7.25812i	−1.16634	+	0.390764i
$346$	−11.5486	−	5.14176i	−0.620856	−	0.276423i
$347$	1.52284	−	3.42036i	0.0817505	−	0.183615i	−0.868045	−	0.496485i	$-0.834624\pi$
$347$	1.52284	−	3.42036i	0.0817505	−	0.183615i	0.949796	+	0.312870i	$0.101290\pi$
$348$	1.95321	−	5.46515i	0.104703	−	0.292963i
$349$	−8.67752	+	15.0299i	−0.464497	+	0.804532i	−0.999179	−	0.0405213i	$-0.987098\pi$
$349$	−8.67752	+	15.0299i	−0.464497	+	0.804532i	0.534682	+	0.845053i	$0.320431\pi$
$350$	−15.9938	−	2.14016i	−0.854904	−	0.114396i
$351$	0.102984	+	0.838692i	0.00549689	+	0.0447661i
$352$	4.02967	−	1.30932i	0.214782	−	0.0697869i
$353$	5.49417	−	0.577460i	0.292425	−	0.0307351i	0.0428198	−	0.999083i	$-0.486366\pi$
$353$	5.49417	−	0.577460i	0.292425	−	0.0307351i	0.249605	+	0.968348i	$0.419699\pi$
$354$	−0.360543	+	12.3920i	−0.0191626	+	0.658628i
$355$	1.14355	+	7.94627i	0.0606932	+	0.421744i
$356$	0.629661	−	5.99082i	0.0333720	−	0.317513i
$357$	−0.829328	+	0.340698i	−0.0438927	+	0.0180317i
$358$	6.74988	+	15.1605i	0.356742	+	0.801256i
$359$	−4.30244	+	13.2416i	−0.227074	+	0.698863i	0.771000	+	0.636835i	$0.219757\pi$
$359$	−4.30244	+	13.2416i	−0.227074	+	0.698863i	−0.998074	+	0.0620276i	$0.980243\pi$
$360$	8.00070	+	18.9808i	0.421674	+	1.00038i
$361$	11.5473	+	35.5388i	0.607750	+	1.87046i
$362$	−6.58434	+	5.92856i	−0.346065	+	0.311598i
$363$	14.0850	+	6.76852i	0.739270	+	0.355255i
$364$	0.160355	−	0.178093i	0.00840490	−	0.00933459i
$365$	4.43297	−	25.6354i	0.232032	−	1.34182i
$366$	12.7430	−	26.5177i	0.666089	−	1.38610i
$367$	−14.9221	−	33.5157i	−0.778930	−	1.74950i	−0.652853	−	0.757484i	$-0.726428\pi$
$367$	−14.9221	−	33.5157i	−0.778930	−	1.74950i	−0.126077	−	0.992021i	$-0.540239\pi$
$368$			15.3252i			0.798881i
$369$	−16.7728	+	2.55668i	−0.873155	+	0.133096i
$370$	1.34070	+	2.12988i	0.0696996	+	0.110727i
$371$	−3.64419	−	34.6721i	−0.189197	−	1.80009i
$372$	−0.300944	+	0.487907i	−0.0156032	+	0.0252968i
$373$	−13.9005	−	12.5161i	−0.719740	−	0.648057i	0.225571	−	0.974227i	$-0.427575\pi$
$373$	−13.9005	−	12.5161i	−0.719740	−	0.648057i	−0.945311	+	0.326170i	$0.894242\pi$
$374$	−0.163554	−	0.283283i	−0.00845716	−	0.0146482i
$375$	−19.2941	+	1.65446i	−0.996344	+	0.0854358i
$376$	−0.336051	+	0.582057i	−0.0173305	+	0.0300173i
$377$	0.942436	−	0.306216i	0.0485379	−	0.0157709i
$378$	−12.2643	+	11.4368i	−0.630806	+	0.588244i
$379$	1.54812	−	1.12477i	0.0795216	−	0.0577758i	−0.547314	−	0.836927i	$-0.684350\pi$
$379$	1.54812	−	1.12477i	0.0795216	−	0.0577758i	0.626836	+	0.779151i	$0.284350\pi$
$380$	−9.22470	+	0.352637i	−0.473217	+	0.0180899i
$381$	−23.7868	+	6.97082i	−1.21863	+	0.357126i
$382$	1.16279	−	0.671335i	0.0594933	−	0.0343485i
$383$	9.60659	+	1.00969i	0.490874	+	0.0515929i	0.346732	−	0.937964i	$-0.387291\pi$
$383$	9.60659	+	1.00969i	0.490874	+	0.0515929i	0.144142	+	0.989557i	$0.453958\pi$
$384$	7.94477	−	0.602036i	0.405430	−	0.0307225i
$385$	−7.90990	+	2.90859i	−0.403126	+	0.148235i
$386$	9.43034	+	29.0236i	0.479991	+	1.47726i
$387$	17.1307	+	11.2669i	0.870803	+	0.572731i
$388$	1.62049	+	0.526529i	0.0822680	+	0.0267305i
$389$	−22.3540	−	4.75150i	−1.13339	−	0.240910i	−0.397234	−	0.917717i	$-0.630030\pi$
$389$	−22.3540	−	4.75150i	−1.13339	−	0.240910i	−0.736161	+	0.676807i	$0.763363\pi$
$390$	−0.373209	+	0.660255i	−0.0188982	+	0.0334333i
$391$	−1.11453	+	0.236900i	−0.0563640	+	0.0119805i
$392$	0.556841	+	0.0585263i	0.0281247	+	0.00295603i
$393$	2.70567	−	20.1000i	0.136483	−	1.01391i
$394$	17.5526	−	7.81492i	0.884287	−	0.393710i
$395$	28.2352	+	11.2994i	1.42066	+	0.568536i
$396$	1.79444	+	1.47046i	0.0901739	+	0.0738934i
$397$	5.64077	+	7.76385i	0.283102	+	0.389657i	0.926758	−	0.375658i	$-0.122583\pi$
$397$	5.64077	+	7.76385i	0.283102	+	0.389657i	−0.643656	+	0.765315i	$0.722583\pi$
$398$	−4.83069	+	22.7266i	−0.242141	+	1.13918i
$399$	−13.2431	−	32.2363i	−0.662982	−	1.61383i
$400$	−3.05910	+	12.6240i	−0.152955	+	0.631199i
$401$	−3.09035	−	5.35264i	−0.154325	−	0.267298i	0.778488	−	0.627659i	$-0.215987\pi$
$401$	−3.09035	−	5.35264i	−0.154325	−	0.267298i	−0.932813	+	0.360361i	$0.882653\pi$
$402$	4.53410	−	12.6866i	0.226140	−	0.632749i
$403$	−0.0973425	+	0.0102311i	−0.00484898	+	0.000509648i
$404$	3.57543	−	2.59770i	0.177884	−	0.129241i
$405$	−11.3920	+	16.5898i	−0.566075	+	0.824354i
$406$	15.9099	+	11.5592i	0.789595	+	0.573675i
$407$	1.13834	+	0.657219i	0.0564252	+	0.0325771i
$408$	0.288893	+	0.985798i	0.0143023	+	0.0488043i
$409$	2.87866	−	0.611877i	0.142340	−	0.0302554i	−0.136190	−	0.990683i	$-0.543486\pi$
$409$	2.87866	−	0.611877i	0.142340	−	0.0302554i	0.278531	+	0.960427i	$0.410153\pi$
$410$	−13.4695	−	7.10492i	−0.665212	−	0.350887i
$411$	27.1713	−	23.0702i	1.34026	−	1.13797i
$412$	0.220585	−	0.198616i	0.0108674	−	0.00978509i
$413$	15.1497	+	4.92242i	0.745466	+	0.242216i
$414$	−17.9404	+	11.5029i	−0.881724	+	0.565338i
$415$	−32.6932	−	2.17766i	−1.60484	−	0.106897i
$416$	−0.327833	−	0.364095i	−0.0160733	−	0.0178512i
$417$	1.08969	−	1.14163i	0.0533625	−	0.0559060i
$418$	11.0113	−	6.35739i	0.538581	−	0.310950i
$419$	−0.638257	+	6.07261i	−0.0311809	+	0.296666i	0.967807	+	0.251692i	$0.0809871\pi$
$419$	−0.638257	+	6.07261i	−0.0311809	+	0.296666i	−0.998988	+	0.0449739i	$0.985680\pi$
$420$	5.67058	−	0.648354i	0.276696	−	0.0316364i
$421$	−0.139754	−	1.32967i	−0.00681119	−	0.0648041i	0.990588	−	0.136875i	$-0.0437059\pi$
$421$	−0.139754	−	1.32967i	−0.00681119	−	0.0648041i	−0.997400	+	0.0720709i	$0.977039\pi$
$422$	−2.14561	−	2.95318i	−0.104447	−	0.143759i
$423$	−0.655940	+	0.0305538i	−0.0318929	+	0.00148558i
$424$	−39.9443			−1.93987
$425$	−0.965367	−	0.0273291i	−0.0468272	−	0.00132566i
$426$	2.84558	+	6.92672i	0.137869	+	0.335601i
$427$	−28.0929	−	25.2949i	−1.35951	−	1.22411i
$428$	0.150213	−	0.337383i	0.00726081	−	0.0163080i
$429$	−0.0115200	+	0.395949i	−0.000556193	+	0.0191166i
$430$	6.35143	+	17.2727i	0.306293	+	0.832965i
$431$	−26.8953	−	19.5406i	−1.29550	−	0.941237i	−0.295600	−	0.955312i	$-0.595520\pi$
$431$	−26.8953	−	19.5406i	−1.29550	−	0.941237i	−0.999901	+	0.0140751i	$0.995520\pi$
$432$	8.12392	+	10.7807i	0.390862	+	0.518685i
$433$	−6.84957	+	9.42763i	−0.329169	+	0.453063i	−0.941239	−	0.337741i	$-0.890337\pi$
$433$	−6.84957	+	9.42763i	−0.329169	+	0.453063i	0.612070	+	0.790804i	$0.290337\pi$
$434$	−1.29976	−	1.44353i	−0.0623905	−	0.0692917i
$435$	21.6468	+	9.40210i	1.03788	+	0.450796i
$436$	5.14538	−	5.71453i	0.246419	−	0.273676i
$437$	−9.20838	−	43.3220i	−0.440496	−	2.07237i
$438$	−1.83364	−	24.1976i	−0.0876146	−	1.15621i
$439$	21.7048	+	4.61349i	1.03591	+	0.220190i	0.694326	−	0.719661i	$-0.255703\pi$
$439$	21.7048	+	4.61349i	1.03591	+	0.220190i	0.341586	+	0.939851i	$0.389036\pi$
$440$	2.36693	+	9.36144i	0.112839	+	0.446289i
$441$	0.245512	+	0.488848i	0.0116910	+	0.0232785i
$442$	−0.0222324	+	0.0306003i	−0.00105749	+	0.00145551i
$443$	6.90522	+	3.98673i	0.328077	+	0.189415i	0.654987	−	0.755640i	$-0.272674\pi$
$443$	6.90522	+	3.98673i	0.328077	+	0.189415i	−0.326910	+	0.945055i	$0.606007\pi$
$444$	−0.643930	−	0.614634i	−0.0305596	−	0.0291692i
$445$	24.1374	+	4.17393i	1.14422	+	0.197863i
$446$	20.0417	+	8.92314i	0.949002	+	0.422523i
$447$	−17.4411	−	32.3465i	−0.824938	−	1.52993i
$448$	4.91662	−	23.1309i	0.232289	−	1.09283i
$449$	19.4821			0.919419			0.459710	−	0.888069i	$-0.347953\pi$
$449$	19.4821			0.919419			0.459710	+	0.888069i	$0.347953\pi$
$450$	−17.0744	+	5.89429i	−0.804893	+	0.277860i
$451$	−7.95358			−0.374520
$452$	0.423362	−	1.99176i	0.0199133	−	0.0936847i
$453$	4.84699	−	7.85821i	0.227732	−	0.369211i
$454$	9.30801	+	4.14419i	0.436847	+	0.194497i
$455$	0.679266	+	0.698768i	0.0318445	+	0.0327587i
$456$	−38.3183	+	11.2294i	−1.79442	+	0.525863i
$457$	15.0307	+	8.67800i	0.703108	+	0.405940i	0.808504	−	0.588491i	$-0.200278\pi$
$457$	15.0307	+	8.67800i	0.703108	+	0.405940i	−0.105396	+	0.994430i	$0.533611\pi$
$458$	−6.92373	+	9.52970i	−0.323525	+	0.445293i
$459$	−0.658443	+	0.757462i	−0.0307335	+	0.0353553i
$460$	7.23739	+	0.482076i	0.337445	+	0.0224769i
$461$	−29.1923	−	6.20502i	−1.35962	−	0.288997i	−0.530320	−	0.847798i	$-0.677928\pi$
$461$	−29.1923	−	6.20502i	−1.35962	−	0.288997i	−0.829302	+	0.558801i	$0.811262\pi$
$462$	−6.49152	+	4.43377i	−0.302013	+	0.206278i
$463$	2.42807	+	11.4232i	0.112842	+	0.530879i	0.997864	+	0.0653297i	$0.0208099\pi$
$463$	2.42807	+	11.4232i	0.112842	+	0.530879i	−0.885022	+	0.465549i	$0.845857\pi$
$464$	10.5926	−	11.7643i	0.491750	−	0.546143i
$465$	−1.89833	−	1.35293i	−0.0880330	−	0.0627408i
$466$	2.05123	+	2.27812i	0.0950214	+	0.105532i
$467$	−8.44207	+	11.6195i	−0.390652	+	0.537687i	−0.958367	−	0.285538i	$-0.907828\pi$
$467$	−8.44207	+	11.6195i	−0.390652	+	0.537687i	0.567715	+	0.823225i	$0.307828\pi$
$468$	0.0709367	−	0.258714i	0.00327905	−	0.0119591i
$469$	−14.0048	−	10.1751i	−0.646680	−	0.469840i
$470$	−0.489709	−	0.327965i	−0.0225886	−	0.0151279i
$471$	−18.4805	+	9.96465i	−0.851536	+	0.459147i
$472$	7.42332	−	16.6731i	0.341686	−	0.767439i
$473$	7.14296	+	6.43155i	0.328434	+	0.295723i
$474$	28.1142	+	3.78447i	1.29133	+	0.173826i
$475$	1.06229	−	37.5242i	0.0487414	−	1.72173i
$476$	0.284642			0.0130465
$477$	−21.0645	−	32.8530i	−0.964476	−	1.50424i
$478$	−7.46831	−	10.2792i	−0.341592	−	0.470162i
$479$	−0.537542	−	5.11437i	−0.0245609	−	0.233682i	−0.999915	−	0.0130363i	$-0.995850\pi$
$479$	−0.537542	−	5.11437i	−0.0245609	−	0.233682i	0.975354	−	0.220645i	$-0.0708164\pi$
$480$	−0.106443	−	11.6681i	−0.00485841	−	0.532571i
$481$	0.0158874	−	0.151159i	0.000724403	−	0.00689224i
$482$	−3.20568	+	1.85080i	−0.146015	+	0.0843016i
$483$	7.70088	+	26.2780i	0.350402	+	1.19569i
$484$	−3.31965	−	3.68684i	−0.150893	−	0.167584i
$485$	−2.57433	+	6.43278i	−0.116895	+	0.292098i
$486$	−6.52263	+	17.6021i	−0.295873	+	0.798448i
$487$	38.7356	+	12.5860i	1.75528	+	0.570324i	0.996694	−	0.0812511i	$-0.0258916\pi$
$487$	38.7356	+	12.5860i	1.75528	+	0.570324i	0.758584	+	0.651575i	$0.225892\pi$
$488$	−32.1873	+	28.9816i	−1.45705	+	1.31194i
$489$	0.871975	+	0.311638i	0.0394321	+	0.0140927i
$490$	−0.0836640	+	0.483820i	−0.00377956	+	0.0218568i
$491$	−39.2083	+	8.33398i	−1.76945	+	0.376107i	−0.973397	−	0.229125i	$-0.926414\pi$
$491$	−39.2083	+	8.33398i	−1.76945	+	0.376107i	−0.796049	+	0.605232i	$0.793080\pi$
$492$	5.23392	+	1.27265i	0.235963	+	0.0573757i
$493$	1.01930	+	0.588493i	0.0459070	+	0.0265044i
$494$	−1.18945	−	0.864183i	−0.0535157	−	0.0388814i
$495$	−6.45131	+	6.88345i	−0.289965	+	0.309388i
$496$	−1.26501	+	0.919080i	−0.0568004	+	0.0412679i
$497$	9.56923	−	1.00577i	0.429239	−	0.0451148i
$498$	−30.0673	+	5.48229i	−1.34735	+	0.245667i
$499$	14.6136	+	25.3114i	0.654193	+	1.13310i	0.982096	+	0.188384i	$0.0603249\pi$
$499$	14.6136	+	25.3114i	0.654193	+	1.13310i	−0.327903	+	0.944712i	$0.606342\pi$
$500$	5.86550	+	1.84178i	0.262313	+	0.0823667i
$501$	−18.7136	−	2.51904i	−0.836060	−	0.112543i
$502$	−5.97930	+	28.1304i	−0.266869	+	1.25552i
$503$	4.96862	+	6.83872i	0.221540	+	0.304923i	0.905291	−	0.424792i	$-0.139653\pi$
$503$	4.96862	+	6.83872i	0.221540	+	0.304923i	−0.683751	+	0.729715i	$0.739653\pi$
$504$	23.0988	−	8.71306i	1.02890	−	0.388110i
$505$	9.57377	+	15.2092i	0.426027	+	0.676803i
$506$	−9.12668	+	4.06346i	−0.405731	+	0.180643i
$507$	−20.7853	+	8.53885i	−0.923106	+	0.379223i
$508$	7.82617	+	0.822564i	0.347230	+	0.0364954i
$509$	−12.2912	+	2.61257i	−0.544797	+	0.115800i	−0.472085	−	0.881553i	$-0.656499\pi$
$509$	−12.2912	+	2.61257i	−0.544797	+	0.115800i	−0.0727116	+	0.997353i	$0.523165\pi$
$510$	−0.879402	+	0.195324i	−0.0389406	+	0.00864908i
$511$	−30.4993	−	6.48283i	−1.34921	−	0.286784i
$512$	−22.6169	−	7.34868i	−0.999536	−	0.324769i
$513$	−29.4428	−	25.5939i	−1.29993	−	1.13000i
$514$	1.78380	+	5.48996i	0.0786799	+	0.242152i
$515$	0.746259	+	0.948694i	0.0328841	+	0.0418045i
$516$	−3.67137	−	5.37528i	−0.161623	−	0.236634i
$517$	−0.306140	−	0.0321766i	−0.0134640	−	0.00141512i
$518$	2.61224	−	1.50818i	0.114775	−	0.0662656i
$519$	−4.29603	+	17.6679i	−0.188575	+	0.775533i
$520$	0.877576	−	0.690317i	0.0384843	−	0.0302724i
$521$	15.5846	−	11.3229i	0.682773	−	0.496063i	−0.191504	−	0.981492i	$-0.561336\pi$
$521$	15.5846	−	11.3229i	0.682773	−	0.496063i	0.874276	+	0.485429i	$0.161336\pi$
$522$	21.7225	+	3.57008i	0.950770	+	0.156258i
$523$	24.3250	−	7.90367i	1.06366	−	0.345604i	0.275644	−	0.961260i	$-0.411109\pi$
$523$	24.3250	−	7.90367i	1.06366	−	0.345604i	0.788015	+	0.615656i	$0.211109\pi$
$524$	−3.21939	+	5.57615i	−0.140640	+	0.243595i
$525$	1.09812	+	23.1834i	0.0479258	+	1.01181i
$526$	−14.0060	−	24.2591i	−0.610692	−	1.05775i
$527$	−0.0863949	−	0.0777903i	−0.00376342	−	0.00338860i
$528$	3.00331	+	5.56995i	0.130702	+	0.242401i
$529$	1.23343	+	11.7353i	0.0536273	+	0.510230i
$530$	2.32805	−	34.9509i	0.101124	−	1.51817i
$531$	17.6277	−	2.68701i	0.764979	−	0.116606i
$532$			11.0641i			0.479691i
$533$	0.374071	+	0.840178i	0.0162028	+	0.0363922i
$534$	22.7836	−	1.72649i	0.985942	−	0.0747125i
$535$	1.32832	+	0.700665i	0.0574284	+	0.0302924i
$536$	−13.2714	+	14.7394i	−0.573238	+	0.636645i
$537$	19.7106	−	13.4625i	0.850576	−	0.580952i
$538$	7.51767	−	6.76894i	0.324110	−	0.291830i
$539$	0.0792445	+	0.243890i	0.00341330	+	0.0105051i
$540$	5.34676	−	3.49744i	0.230088	−	0.150506i
$541$	−11.8581	+	36.4956i	−0.509821	+	1.56907i	0.282690	+	0.959211i	$0.408773\pi$
$541$	−11.8581	+	36.4956i	−0.509821	+	1.56907i	−0.792511	+	0.609858i	$0.791227\pi$
$542$	−9.97222	−	22.3980i	−0.428343	−	0.962075i
$543$	10.0877	+	7.78726i	0.432905	+	0.334183i
$544$	0.0608278	−	0.578738i	0.00260797	−	0.0248132i
$545$	21.7959	+	22.4216i	0.933633	+	0.960437i
$546$	0.773670	+	0.477204i	0.0331100	+	0.0204225i
$547$	−31.0946	+	3.26818i	−1.32951	+	0.139737i	−0.742502	−	0.669844i	$-0.766361\pi$
$547$	−31.0946	+	3.26818i	−1.32951	+	0.139737i	−0.587008	+	0.809581i	$0.699694\pi$
$548$	−10.7623	+	3.49687i	−0.459741	+	0.149379i
$549$	−40.8104	−	11.1898i	−1.74174	−	0.477568i
$550$	−8.32913	+	1.52544i	−0.355155	+	0.0650449i
$551$	−22.8750	+	39.6206i	−0.974506	+	1.68789i
$552$	30.8652	−	5.62779i	1.31371	−	0.239535i
$553$	14.8255	−	33.2986i	0.630444	−	1.41600i
$554$	11.2277	+	4.99887i	0.477017	+	0.212382i
$555$	2.66788	−	2.44661i	0.113245	−	0.103853i
$556$	−0.457725	+	0.203792i	−0.0194119	+	0.00864272i
$557$			24.3166i			1.03033i	0.857091	+	0.515165i	$0.172269\pi$
$557$			24.3166i			1.03033i	−0.857091	+	0.515165i	$0.827731\pi$
$558$	−2.02542	−	0.791025i	−0.0857429	−	0.0334868i
$559$	0.343452	−	1.05704i	0.0145265	−	0.0447078i
$560$	14.9791	+	4.24170i	0.632982	+	0.179245i
$561$	−0.358649	+	0.304517i	−0.0151422	+	0.0128567i
$562$	−5.86984	−	27.6154i	−0.247604	−	1.16489i
$563$	3.38628	+	15.9312i	0.142715	+	0.671419i	0.990091	+	0.140427i	$0.0448475\pi$
$563$	3.38628	+	15.9312i	0.142715	+	0.671419i	−0.847376	+	0.530993i	$0.821819\pi$
$564$	0.196309	+	0.0701595i	0.00826610	+	0.00295425i
$565$	7.96709	+	2.25608i	0.335178	+	0.0949140i
$566$	−6.03750	+	18.5815i	−0.253775	+	0.781039i
$567$	19.3473	+	14.4032i	0.812509	+	0.604879i
$568$		−	11.0243i		−	0.462569i
$569$	−17.4967	+	7.79004i	−0.733500	+	0.326575i	−0.739271	−	0.673408i	$-0.764830\pi$
$569$	−17.4967	+	7.79004i	−0.733500	+	0.326575i	0.00577081	+	0.999983i	$0.498163\pi$
$570$	−7.59230	−	34.1827i	−0.318007	−	1.43175i
$571$	4.20374	+	1.87163i	0.175921	+	0.0783251i	0.492807	−	0.870138i	$-0.335971\pi$
$571$	4.20374	+	1.87163i	0.175921	+	0.0783251i	−0.316886	+	0.948464i	$0.602637\pi$
$572$	0.0511499	−	0.114885i	0.00213868	−	0.00480356i
$573$	−1.24994	−	1.47214i	−0.0522171	−	0.0614995i
$574$	−9.12590	+	15.8065i	−0.380908	+	0.659752i
$575$	−3.91201	+	29.2352i	−0.163142	+	1.21919i
$576$	−6.70253	−	25.6087i	−0.279272	−	1.06703i
$577$	−36.5521	+	11.8765i	−1.52168	+	0.494425i	−0.946253	−	0.323427i	$-0.895165\pi$
$577$	−36.5521	+	11.8765i	−1.52168	+	0.494425i	−0.575429	+	0.817852i	$0.695165\pi$
$578$	20.3147	−	2.13516i	0.844981	−	0.0888111i
$579$	38.6354	−	20.8321i	1.60563	−	0.865753i
$580$	−5.22253	−	5.37247i	−0.216854	−	0.223080i
$581$	−4.10489	+	39.0554i	−0.170299	+	1.62029i
$582$	−0.862211	+	6.40522i	−0.0357398	+	0.265505i
$583$	−7.44112	−	16.7130i	−0.308180	−	0.692183i
$584$	−11.0397	+	33.9767i	−0.456826	+	1.40597i
$585$	1.03055	+	0.357744i	0.0426081	+	0.0147909i
$586$	1.19404	+	3.67487i	0.0493253	+	0.151808i
$587$	19.3123	−	17.3889i	0.797103	−	0.717715i	−0.166211	−	0.986090i	$-0.553153\pi$
$587$	19.3123	−	17.3889i	0.797103	−	0.717715i	0.963314	+	0.268375i	$0.0864868\pi$
$588$	−0.0131227	−	0.173173i	−0.000541171	−	0.00714155i
$589$	3.02374	−	3.35820i	0.124591	−	0.138372i
$590$	14.1561	+	7.46709i	0.582798	+	0.307415i
$591$	−15.5868	−	22.8207i	−0.641153	−	0.938717i
$592$	−0.987594	−	2.21817i	−0.0405898	−	0.0911663i
$593$		−	32.5216i		−	1.33550i	−0.744385	−	0.667750i	$-0.767257\pi$
$593$		−	32.5216i		−	1.33550i	0.744385	−	0.667750i	$-0.232743\pi$
$594$	−4.26620	+	7.69656i	−0.175044	+	0.315794i
$595$	−0.0769285	+	1.15492i	−0.00315376	+	0.0473473i
$596$	1.21952	+	11.6029i	0.0499534	+	0.475275i
$597$	33.4045	+	0.971898i	1.36716	+	0.0397771i
$598$	0.858489	+	0.772987i	0.0351062	+	0.0316098i
$599$	5.00962	+	8.67692i	0.204688	+	0.354529i	0.950033	−	0.312149i	$-0.101049\pi$
$599$	5.00962	+	8.67692i	0.204688	+	0.354529i	−0.745346	+	0.666678i	$0.767715\pi$
$600$	26.5483	+	1.52524i	1.08383	+	0.0622678i
$601$	6.09862	−	10.5631i	0.248768	−	0.430878i	−0.714416	−	0.699721i	$-0.753308\pi$
$601$	6.09862	−	10.5631i	0.248768	−	0.430878i	0.963184	+	0.268842i	$0.0866411\pi$
$602$	20.9775	−	6.81601i	0.854980	−	0.277800i
$603$	−19.1214	−	3.14258i	−0.778682	−	0.127976i
$604$	−2.37137	+	1.72290i	−0.0964899	+	0.0701040i
$605$	15.8564	−	12.4729i	0.644655	−	0.507097i
$606$	12.1262	+	11.5745i	0.492593	+	0.470182i
$607$	18.1063	−	10.4537i	0.734910	−	0.424301i	−0.0853054	−	0.996355i	$-0.527187\pi$
$607$	18.1063	−	10.4537i	0.734910	−	0.424301i	0.820216	+	0.572054i	$0.193853\pi$
$608$	22.4957	+	2.36440i	0.912323	+	0.0958890i
$609$	12.2515	−	25.4949i	0.496457	−	1.03310i
$610$	−23.4827	−	29.8527i	−0.950786	−	1.20870i
$611$	0.0109993	+	0.0338524i	0.000444985	+	0.00136952i
$612$	0.284738	−	0.143002i	0.0115098	−	0.00578052i
$613$	−3.43863	−	1.11728i	−0.138885	−	0.0451265i	0.238750	−	0.971081i	$-0.423262\pi$
$613$	−3.43863	−	1.11728i	−0.138885	−	0.0451265i	−0.377635	+	0.925955i	$0.623262\pi$
$614$	−19.4671	−	4.13787i	−0.785630	−	0.166991i
$615$	−6.57829	+	20.8925i	−0.265262	+	0.842466i
$616$	11.3201	−	2.40617i	0.456101	−	0.0969472i
$617$	5.85144	+	0.615011i	0.235570	+	0.0247594i	0.221578	−	0.975143i	$-0.428879\pi$
$617$	5.85144	+	0.615011i	0.235570	+	0.0247594i	0.0139922	+	0.999902i	$0.495546\pi$
$618$	0.891232	+	0.687991i	0.0358506	+	0.0276751i
$619$	−25.2160	+	11.2269i	−1.01352	+	0.451247i	−0.845180	−	0.534482i	$-0.820507\pi$
$619$	−25.2160	+	11.2269i	−1.01352	+	0.451247i	−0.168338	+	0.985729i	$0.553840\pi$
$620$	0.394247	+	0.626315i	0.0158333	+	0.0251534i
$621$	20.9054	+	22.4179i	0.838903	+	0.899601i
$622$	−13.3102	−	18.3199i	−0.533689	−	0.734559i
$623$	6.10401	−	28.7171i	0.244552	−	1.15053i
$624$	0.447131	−	0.579219i	0.0178996	−	0.0231873i
$625$	−9.05817	+	23.3013i	−0.362327	+	0.932051i
$626$	−1.90382	−	3.29752i	−0.0760921	−	0.131795i
$627$	−11.8367	−	13.9408i	−0.472711	−	0.556743i
$628$	6.62910	−	0.696747i	0.264530	−	0.0278032i
$629$	0.146050	−	0.106112i	0.00582340	−	0.00423095i
$630$	6.27760	+	20.7190i	0.250106	+	0.825466i
$631$	−5.50355	−	3.99857i	−0.219093	−	0.159180i	0.472825	−	0.881156i	$-0.343234\pi$
$631$	−5.50355	−	3.99857i	−0.219093	−	0.159180i	−0.691918	+	0.721976i	$0.743234\pi$
$632$	−36.1672	−	20.8811i	−1.43865	−	0.830607i
$633$	−3.62518	+	3.79797i	−0.144088	+	0.150956i
$634$	−0.472460	+	0.100424i	−0.0187638	+	0.00398836i
$635$	−5.45266	+	31.5321i	−0.216382	+	1.25131i
$636$	2.22244	+	12.1888i	0.0881253	+	0.483318i
$637$	0.0220363	−	0.0198416i	0.000873110	−	0.000786152i
$638$	9.81466	+	3.18898i	0.388566	+	0.126253i
$639$	9.06716	−	5.81362i	0.358691	−	0.229983i
$640$	3.82171	−	9.54974i	0.151066	−	0.377486i
$641$	1.26962	+	1.41006i	0.0501471	+	0.0556940i	0.767696	−	0.640814i	$-0.221403\pi$
$641$	1.26962	+	1.41006i	0.0501471	+	0.0556940i	−0.717549	+	0.696508i	$0.754736\pi$
$642$	1.36117	+	0.330976i	0.0537212	+	0.0130626i
$643$	−13.7142	+	7.91791i	−0.540836	+	0.312252i	−0.745418	−	0.666598i	$-0.767750\pi$
$643$	−13.7142	+	7.91791i	−0.540836	+	0.312252i	0.204581	+	0.978850i	$0.434417\pi$
$644$	0.908711	−	8.64581i	0.0358082	−	0.340693i
$645$	22.8022	−	13.4437i	0.897838	−	0.529345i
$646$	−0.182536	−	1.73671i	−0.00718177	−	0.0683300i
$647$	−1.30998	−	1.80303i	−0.0515007	−	0.0708846i	0.782490	−	0.622663i	$-0.213949\pi$
$647$	−1.30998	−	1.80303i	−0.0515007	−	0.0708846i	−0.833991	+	0.551779i	$0.813949\pi$
$648$	18.7291	−	20.3207i	0.735750	−	0.798271i
$649$	8.35902			0.328120
$650$	0.552874	+	0.808105i	0.0216855	+	0.0316965i
$651$	−1.70726	+	2.21160i	−0.0669127	+	0.0866795i
$652$	−0.218468	−	0.196710i	−0.00855588	−	0.00770375i
$653$	0.410721	−	0.922493i	0.0160727	−	0.0361000i	−0.905331	−	0.424707i	$-0.860377\pi$
$653$	0.410721	−	0.922493i	0.0160727	−	0.0361000i	0.921403	+	0.388607i	$0.127044\pi$
$654$	24.8250	+	15.3122i	0.970736	+	0.598756i
$655$	−21.7549	−	14.5696i	−0.850036	−	0.569282i
$656$	11.8863	+	8.63588i	0.464081	+	0.337174i
$657$	−33.7665	+	8.83766i	−1.31736	+	0.344790i
$658$	−0.415209	+	0.571486i	−0.0161865	+	0.0222788i
$659$	9.81851	+	10.9046i	0.382475	+	0.424782i	0.903385	−	0.428830i	$-0.141074\pi$
$659$	9.81851	+	10.9046i	0.382475	+	0.424782i	−0.520910	+	0.853611i	$0.674407\pi$
$660$	2.72490	−	1.24311i	0.106067	−	0.0483881i
$661$	21.1903	−	23.5343i	0.824209	−	0.915377i	−0.173374	−	0.984856i	$-0.555467\pi$
$661$	21.1903	−	23.5343i	0.824209	−	0.915377i	0.997583	+	0.0694791i	$0.0221337\pi$
$662$	−6.05211	−	28.4729i	−0.235222	−	1.10663i
$663$	0.0490356	+	0.0235640i	0.00190438	+	0.000915149i
$664$	44.0108	+	9.35479i	1.70795	+	0.363036i
$665$	−44.8923	−	2.99024i	−1.74085	−	0.115956i
$666$	1.85542	−	2.82106i	0.0718962	−	0.109314i
$667$	21.1292	−	29.0818i	0.818126	−	1.12605i
$668$	5.19152	+	2.99733i	0.200866	+	0.115970i
$669$	7.45544	−	30.6612i	0.288244	−	1.18543i
$670$	−12.1234	−	12.4714i	−0.468366	−	0.481813i
$671$	−18.1222	−	8.06854i	−0.699601	−	0.311483i
$672$	−13.9792	−	0.406720i	−0.539258	−	0.0156896i
$673$	−8.41881	+	39.6074i	−0.324521	+	1.52675i	0.449318	+	0.893372i	$0.351667\pi$
$673$	−8.41881	+	39.6074i	−0.324521	+	1.52675i	−0.773840	+	0.633382i	$0.781666\pi$
$674$	40.2134			1.54896
$675$	12.7457	+	22.6395i	0.490581	+	0.871395i
$676$	7.13392			0.274381
$677$	0.524831	−	2.46914i	0.0201709	−	0.0948967i	−0.966911	−	0.255115i	$-0.917887\pi$
$677$	0.524831	−	2.46914i	0.0201709	−	0.0948967i	0.987082	+	0.160219i	$0.0512199\pi$
$678$	7.72046	+	0.224625i	0.296502	+	0.00862667i
$679$	7.58638	+	3.37767i	0.291138	+	0.129623i
$680$	1.30679	+	0.225975i	0.0501130	+	0.00866575i
$681$	3.46254	−	14.2401i	0.132685	−	0.545681i
$682$	−0.882759	−	0.509661i	−0.0338026	−	0.0195159i
$683$	12.8169	−	17.6409i	0.490425	−	0.675012i	−0.490042	−	0.871699i	$-0.663018\pi$
$683$	12.8169	−	17.6409i	0.490425	−	0.675012i	0.980466	+	0.196687i	$0.0630184\pi$
$684$	5.55855	+	11.0679i	0.212536	+	0.423190i
$685$	−11.2798	−	44.6126i	−0.430978	−	1.70456i
$686$	−21.5216	−	4.57455i	−0.821698	−	0.174657i
$687$	15.2709	+	7.33840i	0.582621	+	0.279977i
$688$	−3.69155	−	17.3674i	−0.140739	−	0.662125i
$689$	−1.41551	+	1.57209i	−0.0539268	+	0.0598918i
$690$	3.12537	+	27.3348i	0.118981	+	1.04062i
$691$	8.57457	+	9.52302i	0.326192	+	0.362273i	0.883827	−	0.467813i	$-0.154958\pi$
$691$	8.57457	+	9.52302i	0.326192	+	0.362273i	−0.557635	+	0.830086i	$0.688291\pi$
$692$	3.39301	−	4.67007i	0.128983	−	0.177529i
$693$	7.94862	+	8.04158i	0.301943	+	0.305474i
$694$	−3.64755	−	2.65010i	−0.138459	−	0.100596i
$695$	−0.703173	−	1.91228i	−0.0266729	−	0.0725369i
$696$	−27.5834	−	17.0136i	−1.04554	−	0.644898i
$697$	−0.444305	+	0.997924i	−0.0168292	+	0.0377991i
$698$	15.5310	+	13.9842i	0.587859	+	0.529310i
$699$	2.69432	−	3.49026i	0.101909	−	0.132014i
$700$	2.47435	−	6.94051i	0.0935217	−	0.262327i
$701$	48.5879			1.83514			0.917569	−	0.397577i	$-0.130149\pi$
$701$	48.5879			1.83514			0.917569	+	0.397577i	$0.130149\pi$
$702$	1.01367	+	0.0886781i	0.0382587	+	0.00334694i
$703$	4.12460	+	5.67702i	0.155562	+	0.214113i
$704$	−1.29712	−	12.3413i	−0.0488872	−	0.465130i
$705$	−0.337725	+	0.777555i	−0.0127195	+	0.0292844i
$706$	0.695382	−	6.61612i	0.0261711	−	0.249001i
$707$	18.6537	−	10.7697i	0.701545	−	0.405037i
$708$	−5.50072	−	1.33753i	−0.206730	−	0.0502674i
$709$	−5.03486	−	5.59178i	−0.189088	−	0.210004i	0.641145	−	0.767420i	$-0.278460\pi$
$709$	−5.03486	−	5.59178i	−0.189088	−	0.210004i	−0.830233	+	0.557416i	$0.811793\pi$
$710$	9.64617	+	0.642523i	0.362014	+	0.0241135i
$711$	−1.89852	−	40.7580i	−0.0712001	−	1.52855i
$712$	−31.9912	−	10.3946i	−1.19892	−	0.389554i
$713$	−2.63864	+	2.37584i	−0.0988179	+	0.0889761i
$714$	0.193668	+	1.06216i	0.00724785	+	0.0397504i
$715$	0.452316	+	0.238588i	0.0169157	+	0.00892268i
$716$	−7.41233	+	1.57554i	−0.277012	+	0.0588806i
$717$	−12.6183	+	13.2197i	−0.471239	+	0.493701i
$718$	14.5199	+	8.38310i	0.541880	+	0.312854i
$719$	−35.5528	−	25.8307i	−1.32590	−	0.963321i	−0.999839	−	0.0179714i	$-0.994279\pi$
$719$	−35.5528	−	25.8307i	−1.32590	−	0.963321i	−0.326059	−	0.945349i	$-0.605721\pi$
$720$	17.1151	−	3.28227i	0.637843	−	0.122323i
$721$	1.17037	−	0.850325i	0.0435869	−	0.0316678i
$722$	44.7520	−	4.70362i	1.66550	−	0.175051i
$723$	3.44596	+	4.05853i	0.128157	+	0.150938i
$724$	−2.02291	−	3.50378i	−0.0751807	−	0.130217i
$725$	23.2100	−	19.7382i	0.862000	−	0.733059i
$726$	11.4990	−	14.8960i	0.426770	−	0.552842i
$727$	−7.73183	+	36.3754i	−0.286758	+	1.34909i	0.564973	+	0.825109i	$0.308886\pi$
$727$	−7.73183	+	36.3754i	−0.286758	+	1.34909i	−0.851731	+	0.523979i	$0.824447\pi$
$728$	−0.786582	−	1.08264i	−0.0291527	−	0.0401252i
$729$	26.5899	+	4.68814i	0.984810	+	0.173635i
$730$	−29.0859	−	11.6399i	−1.07652	−	0.430811i
$731$	1.20598	−	0.536936i	0.0446047	−	0.0198593i
$732$	10.6344	+	8.20931i	0.393060	+	0.303425i
$733$	−5.49330	−	0.577369i	−0.202900	−	0.0213256i	0.00253335	−	0.999997i	$-0.499194\pi$
$733$	−5.49330	−	0.577369i	−0.202900	−	0.0213256i	−0.205433	+	0.978671i	$0.565860\pi$
$734$	−43.2140	+	9.18541i	−1.59506	+	0.339040i
$735$	0.706192	−	0.00644228i	0.0260483	−	0.000237627i
$736$	−17.3846	−	3.69521i	−0.640804	−	0.136207i
$737$	−8.63939	−	2.80711i	−0.318236	−	0.103401i
$738$	−1.18788	+	20.3966i	−0.0437263	+	0.750811i
$739$	13.0729	+	40.2342i	0.480894	+	1.48004i	0.837840	+	0.545915i	$0.183818\pi$
$739$	13.0729	+	40.2342i	0.480894	+	1.48004i	−0.356946	+	0.934125i	$0.616182\pi$
$740$	−1.07861	+	0.396619i	−0.0396504	+	0.0145800i
$741$	−0.915940	+	1.90603i	−0.0336479	+	0.0700198i
$742$	−41.7525	−	4.38836i	−1.53278	−	0.161102i
$743$	16.0074	−	9.24189i	0.587256	−	0.339052i	−0.176756	−	0.984255i	$-0.556560\pi$
$743$	16.0074	−	9.24189i	0.587256	−	0.339052i	0.764012	+	0.645203i	$0.223227\pi$
$744$	2.31559	+	2.21024i	0.0848935	+	0.0810312i
$745$	−47.4081	+	1.81229i	−1.73690	+	0.0663972i
$746$	−18.2228	+	13.2397i	−0.667186	+	0.484739i
$747$	15.5149	+	41.1308i	0.567661	+	1.50490i
$748$	0.142057	−	0.0461573i	0.00519413	−	0.00168768i
$749$	0.899969	−	1.55879i	0.0328841	−	0.0569570i
$750$	−2.88187	+	23.1406i	−0.105231	+	0.844977i
$751$	12.6388	+	21.8911i	0.461197	+	0.798816i	0.999021	−	0.0442409i	$-0.0140869\pi$
$751$	12.6388	+	21.8911i	0.461197	+	0.798816i	−0.537824	+	0.843057i	$0.680754\pi$
$752$	0.422575	+	0.380488i	0.0154097	+	0.0138750i
$753$	41.3472	+	1.20299i	1.50678	+	0.0438393i
$754$	−0.124733	−	1.18676i	−0.00454251	−	0.0432191i
$755$	−6.34972	−	10.0874i	−0.231090	−	0.367118i
$756$	−3.94392	−	6.56369i	−0.143439	−	0.238719i
$757$		−	14.6646i		−	0.532993i	−0.963836	−	0.266497i	$-0.914134\pi$
$757$		−	14.6646i		−	0.532993i	0.963836	−	0.266497i	$-0.0858661\pi$
$758$	−0.937264	−	2.10513i	−0.0340430	−	0.0764617i
$759$	8.10452	+	11.8659i	0.294175	+	0.430705i
$760$	−8.78373	+	50.7953i	−0.318619	+	1.84254i
$761$	6.68308	−	7.42231i	0.242261	−	0.269059i	−0.609736	−	0.792605i	$-0.708725\pi$
$761$	6.68308	−	7.42231i	0.242261	−	0.269059i	0.851997	+	0.523546i	$0.175391\pi$
$762$	2.25542	+	29.7636i	0.0817051	+	1.07822i
$763$	27.8512	−	25.0774i	1.00828	−	0.907861i
$764$	0.189461	+	0.583100i	0.00685444	+	0.0210958i
$765$	0.503272	+	1.19396i	0.0181958	+	0.0431678i
$766$	3.59450	−	11.0627i	0.129875	−	0.399713i
$767$	−0.393140	−	0.883006i	−0.0141954	−	0.0318835i
$768$	−2.79780	+	20.7844i	−0.100957	+	0.749993i
$769$	1.93245	−	18.3860i	0.0696860	−	0.663018i	−0.902801	−	0.430059i	$-0.858493\pi$
$769$	1.93245	−	18.3860i	0.0696860	−	0.663018i	0.972487	−	0.232958i	$-0.0748406\pi$
$770$	1.44561	+	10.0452i	0.0520962	+	0.362006i
$771$	7.30808	−	3.94050i	0.263194	−	0.141914i
$772$	−13.8588	+	1.45662i	−0.498790	+	0.0524250i
$773$	3.41227	−	1.10871i	0.122731	−	0.0398777i	−0.247008	−	0.969014i	$-0.579447\pi$
$773$	3.41227	−	1.10871i	0.122731	−	0.0398777i	0.369739	+	0.929136i	$0.379447\pi$
$774$	17.5603	−	17.3573i	0.631191	−	0.623894i
$775$	−2.64780	+	1.43037i	−0.0951119	+	0.0513805i
$776$	4.75733	−	8.23993i	0.170778	−	0.295796i
$777$	−2.80804	−	3.30721i	−0.100738	−	0.118646i
$778$	−11.1935	+	25.1411i	−0.401307	+	0.901350i
$779$	−38.7897	−	17.2703i	−1.38978	−	0.618772i
$780$	−0.259474	−	0.229380i	−0.00929064	−	0.00821312i
$781$	4.61266	−	2.05369i	0.165054	−	0.0734868i
$782$			1.37211i			0.0490664i
$783$	−0.552816	−	31.6585i	−0.0197560	−	1.13138i
$784$	0.146384	−	0.450524i	0.00522801	−	0.0160902i
$785$	1.03542	+	27.0857i	0.0369556	+	0.966728i
$786$	−22.9982	−	8.21941i	−0.820320	−	0.293177i
$787$	3.36327	+	15.8229i	0.119888	+	0.564026i	0.996555	+	0.0829303i	$0.0264279\pi$
$787$	3.36327	+	15.8229i	0.119888	+	0.564026i	−0.876668	+	0.481096i	$0.840239\pi$
$788$	1.82414	+	8.58189i	0.0649822	+	0.305717i
$789$	−30.7131	+	26.0775i	−1.09342	+	0.928383i
$790$	20.3787	−	30.4290i	0.725043	−	1.08261i
$791$	3.06676	−	9.43852i	0.109041	−	0.335595i
$792$	10.1151	−	8.09413i	0.359424	−	0.287613i
$793$			2.29382i			0.0814561i
$794$	10.5573	−	4.70040i	0.374664	−	0.166811i
$795$	−50.0563	+	5.72326i	−1.77531	+	0.202983i
$796$	−9.69232	−	4.31530i	−0.343535	−	0.152952i
$797$	−7.73579	+	17.3749i	−0.274016	+	0.615450i	−0.997165	−	0.0752419i	$-0.976027\pi$
$797$	−7.73579	+	17.3749i	−0.274016	+	0.615450i	0.723149	+	0.690692i	$0.242694\pi$
$798$	−41.2866	+	7.52795i	−1.46153	+	0.266487i
$799$	−0.0211388	+	0.0366134i	−0.000747836	+	0.00129529i
$800$	−13.5828	−	6.51407i	−0.480224	−	0.230307i
$801$	−8.32122	−	31.7934i	−0.294016	−	1.12336i
$802$	−7.07857	+	2.29997i	−0.249953	+	0.0812146i
$803$	−16.2727	+	1.71033i	−0.574251	+	0.0603562i
$804$	5.23606	+	3.22963i	0.184661	+	0.113900i
$805$	34.8345	+	6.02372i	1.22775	+	0.212308i
$806$	−0.0123204	+	0.117221i	−0.000433967	+	0.00412892i
$807$	−11.5176	−	8.89111i	−0.405440	−	0.312982i
$808$	−10.0378	−	22.5452i	−0.353127	−	0.793137i
$809$	3.06508	−	9.43335i	0.107763	−	0.331659i	−0.882606	−	0.470113i	$-0.844213\pi$
$809$	3.06508	−	9.43335i	0.107763	−	0.331659i	0.990369	+	0.138454i	$0.0442133\pi$
$810$	16.6888	+	17.5722i	0.586385	+	0.617423i
$811$	8.46694	+	26.0585i	0.297314	+	0.915039i	0.982434	+	0.186609i	$0.0597498\pi$
$811$	8.46694	+	26.0585i	0.297314	+	0.915039i	−0.685120	+	0.728430i	$0.740250\pi$
$812$	−6.67346	+	6.00881i	−0.234192	+	0.210868i
$813$	−29.1203	+	19.8895i	−1.02129	+	0.697554i
$814$	1.05914	−	1.17629i	0.0371228	−	0.0412290i
$815$	0.857186	−	0.833263i	0.0300259	−	0.0291879i
$816$	0.866624	−	0.0656708i	0.0303379	−	0.00229894i
$817$	20.8709	+	46.8768i	0.730181	+	1.64001i
$818$		−	3.54395i		−	0.123911i
$819$	0.475636	−	1.21786i	0.0166201	−	0.0425556i
$820$	4.45223	−	5.34169i	0.155479	−	0.186540i
$821$	1.00345	+	9.54718i	0.0350206	+	0.333199i	0.997979	+	0.0635480i	$0.0202416\pi$
$821$	1.00345	+	9.54718i	0.0350206	+	0.333199i	−0.962958	+	0.269651i	$0.913092\pi$
$822$	−20.3714	−	37.7809i	−0.710534	−	1.31776i
$823$	−25.5845	−	23.0364i	−0.891819	−	0.802998i	0.0893794	−	0.995998i	$-0.471512\pi$
$823$	−25.5845	−	23.0364i	−0.891819	−	0.802998i	−0.981199	+	0.193000i	$0.938178\pi$
$824$	−0.828753	−	1.43544i	−0.0288710	−	0.0500060i
$825$	4.30744	+	11.3922i	0.149966	+	0.396624i
$826$	9.59109	−	16.6123i	0.333717	−	0.578014i
$827$	25.3249	−	8.22855i	0.880632	−	0.286135i	0.166412	−	0.986056i	$-0.446782\pi$
$827$	25.3249	−	8.22855i	0.880632	−	0.286135i	0.714220	+	0.699922i	$0.246782\pi$
$828$	−3.43458	−	9.10525i	−0.119360	−	0.316429i
$829$	28.0528	−	20.3815i	0.974314	−	0.707880i	0.0178831	−	0.999840i	$-0.494307\pi$
$829$	28.0528	−	20.3815i	0.974314	−	0.707880i	0.956431	+	0.291960i	$0.0943073\pi$
$830$	−10.7504	+	37.9639i	−0.373152	+	1.31775i
$831$	4.17665	−	17.1769i	0.144886	−	0.595859i
$832$	−1.24267	+	0.717456i	−0.0430818	+	0.0248733i
$833$	0.0350272	+	0.00368151i	0.00121362	+	0.000127557i
$834$	−1.07190	−	1.56937i	−0.0371168	−	0.0543430i
$835$	−13.5646	+	20.2543i	−0.469423	+	0.700931i
$836$	1.79415	+	5.52182i	0.0620519	+	0.190976i
$837$	−0.596738	+	3.07006i	−0.0206263	+	0.106117i
$838$	6.99309	+	2.27219i	0.241572	+	0.0784916i
$839$	−4.59725	−	0.977175i	−0.158715	−	0.0337358i	0.127869	−	0.991791i	$-0.459186\pi$
$839$	−4.59725	−	0.977175i	−0.158715	−	0.0337358i	−0.286584	+	0.958055i	$0.592520\pi$
$840$	3.04218	−	31.7258i	0.104965	−	1.09465i
$841$	−7.95445	+	1.69077i	−0.274291	+	0.0583024i
$842$	−1.60120	−	0.168293i	−0.0551810	−	0.00579975i
$843$	−37.5614	+	15.4307i	−1.29368	+	0.531461i
$844$	1.52275	−	0.677974i	0.0524154	−	0.0233368i
$845$	−1.92804	+	28.9456i	−0.0663267	+	0.995759i
$846$	−0.128238	+	0.780277i	−0.00440891	+	0.0268265i
$847$	−14.2123	−	19.5615i	−0.488340	−	0.672142i
$848$	−7.02634	+	33.0563i	−0.241285	+	1.13516i
$849$	27.8506	+	3.74898i	0.955829	+	0.128665i
$850$	−0.273889	+	1.13026i	−0.00939431	+	0.0387675i
$851$	−2.75681	−	4.77494i	−0.0945023	−	0.163683i
$852$	−3.36401	+	0.613374i	−0.115249	+	0.0210138i
$853$	18.6763	−	1.96296i	0.639465	−	0.0672105i	0.220753	−	0.975330i	$-0.429148\pi$
$853$	18.6763	−	1.96296i	0.639465	−	0.0672105i	0.418712	+	0.908119i	$0.362482\pi$
$854$	−36.8283	+	26.7574i	−1.26024	+	0.915618i
$855$	−46.4097	+	19.5624i	−1.58718	+	0.669019i
$856$	−1.66841	−	1.21217i	−0.0570252	−	0.0414312i
$857$	28.3893	+	16.3906i	0.969759	+	0.559891i	0.899163	−	0.437614i	$-0.144176\pi$
$857$	28.3893	+	16.3906i	0.969759	+	0.559891i	0.0705962	+	0.997505i	$0.477510\pi$
$858$	0.463502	+	0.112703i	0.0158237	+	0.00384761i
$859$	−9.26946	+	1.97028i	−0.316270	+	0.0672252i	−0.363312	−	0.931668i	$-0.618354\pi$
$859$	−9.26946	+	1.97028i	−0.316270	+	0.0672252i	0.0470417	+	0.998893i	$0.485021\pi$
$860$	−8.31794	+	1.19703i	−0.283639	+	0.0408185i
$861$	24.7208	+	8.83504i	0.842482	+	0.301097i
$862$	−29.7505	+	26.7875i	−1.01331	+	0.912384i
$863$	−32.4083	−	10.5301i	−1.10319	−	0.358449i	−0.299862	−	0.953983i	$-0.596941\pi$
$863$	−32.4083	−	10.5301i	−1.10319	−	0.358449i	−0.803330	+	0.595534i	$0.796941\pi$
$864$	−14.1882	+	6.61618i	−0.482692	+	0.225087i
$865$	18.0316	+	15.0291i	0.613094	+	0.511006i
$866$	9.38982	+	10.4285i	0.319079	+	0.354373i
$867$	−8.26252	−	28.1945i	−0.280610	−	0.957535i
$868$	0.768158	−	0.443496i	0.0260730	−	0.0150532i
$869$	1.99935	−	19.0226i	0.0678233	−	0.645296i
$870$	16.4944	−	23.1436i	0.559211	−	0.784642i
$871$	0.109797	+	1.04465i	0.00372032	+	0.0353965i
$872$	−25.2394	−	34.7390i	−0.854712	−	1.17641i
$873$	9.28585	−	0.432538i	0.314279	−	0.0146392i
$874$	−53.3342			−1.80406
$875$	27.4921	+	11.9154i	0.929404	+	0.402813i
$876$	10.9820	+	1.47830i	0.371049	+	0.0499471i
$877$	20.0817	+	18.0816i	0.678109	+	0.610572i	0.934484	−	0.356005i	$-0.115861\pi$
$877$	20.0817	+	18.0816i	0.678109	+	0.610572i	−0.256375	+	0.966577i	$0.582528\pi$
$878$	10.8684	−	24.4108i	0.366791	−	0.823826i
$879$	4.89189	−	2.63770i	0.164999	−	0.0889673i
$880$	8.16351	−	0.312070i	0.275192	−	0.0105199i
$881$	44.5745	+	32.3853i	1.50175	+	1.09109i	0.969676	+	0.244393i	$0.0785886\pi$
$881$	44.5745	+	32.3853i	1.50175	+	1.09109i	0.532078	+	0.846695i	$0.321411\pi$
$882$	0.637280	−	0.166794i	0.0214583	−	0.00561625i
$883$	23.9914	−	33.0214i	0.807376	−	1.11126i	−0.184347	−	0.982861i	$-0.559017\pi$
$883$	23.9914	−	33.0214i	0.807376	−	1.11126i	0.991723	−	0.128396i	$-0.0409829\pi$
$884$	−0.0115570	−	0.0128354i	−0.000388706	−	0.000431701i
$885$	6.91362	−	21.9575i	0.232399	−	0.738093i
$886$	6.42480	−	7.13546i	0.215845	−	0.239721i
$887$	6.07787	+	28.5941i	0.204075	+	0.960096i	0.954285	+	0.298897i	$0.0966188\pi$
$887$	6.07787	+	28.5941i	0.204075	+	0.960096i	−0.750211	+	0.661199i	$0.770048\pi$
$888$	−4.10477	+	2.80360i	−0.137747	+	0.0940826i
$889$	37.5149	+	7.97403i	1.25821	+	0.267440i
$890$	10.9597	−	27.3862i	0.367370	−	0.917989i
$891$	11.9913	+	4.05095i	0.401725	+	0.135712i
$892$	−5.88831	+	8.10456i	−0.197155	+	0.271361i
$893$	−1.42318	−	0.821672i	−0.0476248	−	0.0274962i
$894$	−42.4674	+	12.4453i	−1.42032	+	0.416232i
$895$	−4.38940	−	30.5011i	−0.146722	−	1.01954i
$896$	−11.2623	−	5.01430i	−0.376247	−	0.167516i
$897$	0.872285	−	1.41420i	0.0291247	−	0.0472186i
$898$	4.87773	−	22.9479i	0.162772	−	0.765781i
$899$	3.66769			0.122324
$900$	−1.01168	−	8.18594i	−0.0337228	−	0.272865i
$901$	−2.51264			−0.0837081
$902$	−1.99133	+	9.36848i	−0.0663041	+	0.311936i
$903$	−15.0569	−	27.9247i	−0.501063	−	0.929275i
$904$	−10.3876	−	4.62487i	−0.345487	−	0.153821i
$905$	14.7632	−	7.26093i	0.490744	−	0.241361i
$906$	−8.04260	−	7.67670i	−0.267198	−	0.255041i
$907$	26.5281	+	15.3160i	0.880851	+	0.508560i	0.870939	−	0.491391i	$-0.163511\pi$
$907$	26.5281	+	15.3160i	0.880851	+	0.508560i	0.00991216	+	0.999951i	$0.496845\pi$
$908$	−2.73472	+	3.76402i	−0.0907548	+	0.124913i
$909$	13.2494	−	20.1449i	0.439453	−	0.668163i
$910$	0.993142	−	0.625153i	0.0329223	−	0.0207236i
$911$	9.96400	+	2.11791i	0.330122	+	0.0701696i	0.369991	−	0.929035i	$-0.379361\pi$
$911$	9.96400	+	2.11791i	0.330122	+	0.0701696i	−0.0398691	+	0.999205i	$0.512694\pi$
$912$	2.55265	+	33.6860i	0.0845266	+	1.11545i
$913$	4.28454	+	20.1572i	0.141798	+	0.667105i
$914$	13.9850	−	15.5319i	0.462583	−	0.513750i
$915$	−36.1831	+	40.9302i	−1.19618	+	1.35311i
$916$	−3.59915	−	3.99726i	−0.118919	−	0.132073i
$917$	−18.4453	+	25.3878i	−0.609119	+	0.838380i
$918$	0.727356	+	0.965221i	0.0240063	+	0.0318570i
$919$	21.8946	+	15.9074i	0.722236	+	0.524735i	0.887098	−	0.461581i	$-0.152718\pi$
$919$	21.8946	+	15.9074i	0.722236	+	0.524735i	−0.164862	+	0.986317i	$0.552718\pi$
$920$	11.0357	−	38.9714i	0.363837	−	1.28485i
$921$	−0.832507	+	28.6136i	−0.0274320	+	0.942851i
$922$	−14.6177	+	32.8319i	−0.481409	+	1.08126i
$923$	−0.433884	−	0.390670i	−0.0142814	−	0.0128591i
$924$	−1.36406	−	3.32040i	−0.0448744	−	0.109233i
$925$	−1.31776	−	4.48360i	−0.0433277	−	0.147420i
$926$	14.0632			0.462145
$927$	0.743568	−	1.43860i	0.0244220	−	0.0472498i
$928$	10.7911	+	14.8526i	0.354234	+	0.487562i
$929$	2.13333	+	20.2972i	0.0699922	+	0.665931i	0.972123	+	0.234470i	$0.0753353\pi$
$929$	2.13333	+	20.2972i	0.0699922	+	0.665931i	−0.902131	+	0.431462i	$0.857998\pi$
$930$	−2.06890	+	1.89730i	−0.0678418	+	0.0622149i
$931$	−0.143102	+	1.36152i	−0.00468997	+	0.0446221i
$932$	−1.21228	+	0.699908i	−0.0397094	+	0.0229262i
$933$	−22.4886	+	23.5605i	−0.736243	+	0.771336i
$934$	11.5729	+	12.8530i	0.378677	+	0.420564i
$935$	0.148888	+	0.588867i	0.00486917	+	0.0192580i
$936$	−1.33076	−	0.687828i	−0.0434971	−	0.0224824i
$937$	19.4195	+	6.30978i	0.634408	+	0.206132i	0.608527	−	0.793533i	$-0.291761\pi$
$937$	19.4195	+	6.30978i	0.634408	+	0.206132i	0.0258811	+	0.999665i	$0.491761\pi$
$938$	−15.4915	+	13.9486i	−0.505815	+	0.455438i
$939$	−4.17480	+	3.54469i	−0.136240	+	0.115676i
$940$	0.192980	−	0.187594i	0.00629431	−	0.00611864i
$941$	0.576816	−	0.122606i	0.0188037	−	0.00399684i	−0.198500	−	0.980101i	$-0.563607\pi$
$941$	0.576816	−	0.122606i	0.0188037	−	0.00399684i	0.217304	+	0.976104i	$0.430274\pi$
$942$	7.11035	+	24.2629i	0.231668	+	0.790528i
$943$	28.8929	+	16.6813i	0.940881	+	0.543218i
$944$	−12.4922	−	9.07609i	−0.406585	−	0.295402i
$945$	27.6978	−	14.2284i	0.901010	−	0.462850i
$946$	9.36406	−	6.80339i	0.304452	−	0.221197i
$947$	26.8317	−	2.82012i	0.871913	−	0.0916417i	0.342006	−	0.939698i	$-0.388894\pi$
$947$	26.8317	−	2.82012i	0.871913	−	0.0916417i	0.529907	+	0.848056i	$0.322227\pi$
$948$	−4.35949	+	12.1980i	−0.141590	+	0.396174i
$949$	0.946005	+	1.63853i	0.0307086	+	0.0531889i
$950$	−43.9335	−	10.6462i	−1.42539	−	0.345407i
$951$	0.263997	+	0.642621i	0.00856068	+	0.0208384i
$952$	0.330469	−	1.55473i	0.0107106	−	0.0503892i
$953$	−10.0812	−	13.8756i	−0.326563	−	0.449475i	0.613894	−	0.789388i	$-0.289602\pi$
$953$	−10.0812	−	13.8756i	−0.326563	−	0.449475i	−0.940457	+	0.339913i	$0.889602\pi$
$954$	−43.9712	+	16.5863i	−1.42362	+	0.537003i
$955$	−2.41711	+	0.611139i	−0.0782159	+	0.0197760i
$956$	5.30031	−	2.35985i	0.171424	−	0.0763230i
$957$	1.98019	−	14.7105i	0.0640106	−	0.475524i
$958$	−6.15877	−	0.647313i	−0.198981	−	0.0209137i
$959$	−53.9469	+	11.4668i	−1.74203	+	0.370281i
$960$	−33.4910	−	6.80002i	−1.08092	−	0.219470i
$961$	29.9682	+	6.36994i	0.966717	+	0.205482i
$962$	−0.174071	−	0.0565591i	−0.00561227	−	0.00182354i
$963$	0.117145	−	2.01146i	0.00377494	−	0.0648182i
$964$	−0.522323	−	1.60755i	−0.0168229	−	0.0517756i
$965$	−2.16464	−	56.6254i	−0.0696824	−	1.82283i
$966$	32.8807	−	2.49163i	1.05792	−	0.0801668i
$967$	−13.3682	−	1.40505i	−0.429892	−	0.0451835i	−0.112888	−	0.993608i	$-0.536010\pi$
$967$	−13.3682	−	1.40505i	−0.429892	−	0.0451835i	−0.317004	+	0.948424i	$0.602677\pi$
$968$	−23.9919	+	13.8517i	−0.771129	+	0.445211i
$969$	−2.41036	+	0.706366i	−0.0774318	+	0.0226917i
$970$	6.93260	+	4.64286i	0.222592	+	0.149073i
$971$	−17.9377	+	13.0325i	−0.575648	+	0.418232i	−0.837152	−	0.546970i	$-0.815781\pi$
$971$	−17.9377	+	13.0325i	−0.575648	+	0.418232i	0.261505	+	0.965202i	$0.415781\pi$
$972$	−7.24280	−	4.58450i	−0.232313	−	0.147048i
$973$	−2.32244	+	0.754607i	−0.0744541	+	0.0241916i
$974$	24.5231	−	42.4753i	0.785771	−	1.36100i
$975$	1.00083	−	0.990811i	0.0320521	−	0.0317314i
$976$	18.3222	+	31.7349i	0.586478	+	1.01581i
$977$	−15.5249	−	13.9787i	−0.496687	−	0.447219i	0.382318	−	0.924031i	$-0.375126\pi$
$977$	−15.5249	−	13.9787i	−0.496687	−	0.447219i	−0.879006	+	0.476812i	$0.841792\pi$
$978$	0.585392	−	0.949069i	0.0187188	−	0.0303479i
$979$	−1.61038	−	15.3218i	−0.0514681	−	0.489686i
$980$	−0.208157	−	0.0833025i	−0.00664934	−	0.00266100i
$981$	15.2619	−	39.0781i	0.487275	−	1.24767i
$982$			48.2698i			1.54035i
$983$	−11.1398	−	25.0205i	−0.355306	−	0.798030i	−0.999451	−	0.0331270i	$-0.989453\pi$
$983$	−11.1398	−	25.0205i	−0.355306	−	0.798030i	0.644145	−	0.764903i	$-0.277213\pi$
$984$	13.0279	−	27.1105i	0.415314	−	0.864250i
$985$	−35.3137	+	5.08199i	−1.12519	+	0.161926i
$986$	0.948384	−	1.05329i	0.0302027	−	0.0335435i
$987$	0.915779	+	0.440076i	0.0291496	+	0.0140078i
$988$	0.498917	−	0.449227i	0.0158727	−	0.0142918i
$989$	−12.4590	−	38.3450i	−0.396174	−	1.21930i
$990$	6.49277	+	9.32236i	0.206354	+	0.296284i
$991$	−4.58088	+	14.0985i	−0.145516	+	0.447854i	−0.997077	−	0.0764026i	$-0.975657\pi$
$991$	−4.58088	+	14.0985i	−0.145516	+	0.447854i	0.851561	+	0.524256i	$0.175657\pi$
$992$	−0.737568	−	1.65660i	−0.0234178	−	0.0525973i
$993$	−38.7278	+	15.9098i	−1.22899	+	0.504884i
$994$	1.21115	−	11.5233i	0.0384154	−	0.365498i
$995$	20.1287	−	38.1600i	0.638122	−	1.20975i
$996$	0.405877	−	13.9502i	0.0128607	−	0.442028i
$997$	−2.06076	+	0.216595i	−0.0652651	+	0.00685964i	−0.137105	−	0.990557i	$-0.543780\pi$
$997$	−2.06076	+	0.216595i	−0.0652651	+	0.00685964i	0.0718396	+	0.997416i	$0.477113\pi$
$998$	33.4730	−	10.8760i	1.05957	−	0.344275i
$999$	−4.47051	−	1.89758i	−0.141441	−	0.0600369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.u.a.169.20	yes	224
3.2	odd	2		675.2.y.a.19.9		224
9.4	even	3	inner	225.2.u.a.94.20	yes	224
9.5	odd	6		675.2.y.a.469.9		224
25.4	even	10	inner	225.2.u.a.79.20	yes	224
75.29	odd	10		675.2.y.a.154.9		224
225.4	even	30	inner	225.2.u.a.4.20	✓	224
225.104	odd	30		675.2.y.a.604.9		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.20	✓	224	225.4	even	30	inner
225.2.u.a.79.20	yes	224	25.4	even	10	inner
225.2.u.a.94.20	yes	224	9.4	even	3	inner
225.2.u.a.169.20	yes	224	1.1	even	1	trivial
675.2.y.a.19.9		224	3.2	odd	2
675.2.y.a.154.9		224	75.29	odd	10
675.2.y.a.469.9		224	9.5	odd	6
675.2.y.a.604.9		224	225.104	odd	30

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.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.250369 - 1.17789i) q^{2} +(-1.73132 - 0.0503723i) q^{3} +(0.502342 + 0.223657i) q^{4} +(-1.04324 + 1.97779i) q^{5} +(-0.492802 + 2.02670i) q^{6} +(2.32094 + 1.33999i) q^{7} +(1.80485 - 2.48416i) q^{8} +(2.99493 + 0.174421i) q^{9} +O(q^{10})\)	\(q+(0.250369 - 1.17789i) q^{2} +(-1.73132 - 0.0503723i) q^{3} +(0.502342 + 0.223657i) q^{4} +(-1.04324 + 1.97779i) q^{5} +(-0.492802 + 2.02670i) q^{6} +(2.32094 + 1.33999i) q^{7} +(1.80485 - 2.48416i) q^{8} +(2.99493 + 0.174421i) q^{9} +(2.06843 + 1.72401i) q^{10} +(1.37561 + 0.292396i) q^{11} +(-0.858447 - 0.412525i) q^{12} +(-0.0338103 - 0.159065i) q^{13} +(2.15946 - 2.39833i) q^{14} +(1.90581 - 3.37163i) q^{15} +(-1.73831 - 1.93059i) q^{16} +(0.113531 - 0.156262i) q^{17} +(0.955286 - 3.48403i) q^{18} +(6.07397 + 4.41300i) q^{19} +(-0.966411 + 0.760196i) q^{20} +(-3.95079 - 2.43687i) q^{21} +(0.688822 - 1.54712i) q^{22} +(-4.38392 - 3.94730i) q^{23} +(-3.24990 + 4.20996i) q^{24} +(-2.82328 - 4.12663i) q^{25} -0.195827 q^{26} +(-5.17638 - 0.452840i) q^{27} +(0.866205 + 1.19223i) q^{28} +(0.636956 + 6.06023i) q^{29} +(-3.49426 - 3.08900i) q^{30} +(0.0629147 - 0.598594i) q^{31} +(2.60917 - 1.50640i) q^{32} +(-2.36690 - 0.575523i) q^{33} +(-0.155636 - 0.172851i) q^{34} +(-5.07153 + 3.19238i) q^{35} +(1.46547 + 0.757455i) q^{36} +(0.888903 + 0.288822i) q^{37} +(6.71878 - 6.04962i) q^{38} +(0.0505239 + 0.277095i) q^{39} +(3.03024 + 6.16119i) q^{40} +(-5.53191 + 1.17584i) q^{41} +(-3.85953 + 4.04349i) q^{42} +(5.91893 + 3.41730i) q^{43} +(0.625632 + 0.454548i) q^{44} +(-3.46941 + 5.74136i) q^{45} +(-5.74710 + 4.17551i) q^{46} +(-0.217685 + 0.0228796i) q^{47} +(2.91232 + 3.43003i) q^{48} +(0.0911727 + 0.157916i) q^{49} +(-5.56760 + 2.29234i) q^{50} +(-0.204430 + 0.264821i) q^{51} +(0.0185917 - 0.0874669i) q^{52} +(-7.64631 - 10.5242i) q^{53} +(-1.82940 + 5.98385i) q^{54} +(-2.01340 + 2.41563i) q^{55} +(7.51770 - 3.34710i) q^{56} +(-10.2937 - 7.94626i) q^{57} +(7.29779 + 0.767028i) q^{58} +(5.81390 - 1.23578i) q^{59} +(1.71146 - 1.26746i) q^{60} +(-13.7973 - 2.93271i) q^{61} +(-0.689328 - 0.223976i) q^{62} +(6.71732 + 4.41801i) q^{63} +(-2.72670 - 8.39191i) q^{64} +(0.349869 + 0.0990742i) q^{65} +(-1.27050 + 2.64386i) q^{66} +(-6.42391 - 0.675180i) q^{67} +(0.0919806 - 0.0531050i) q^{68} +(7.39113 + 7.05486i) q^{69} +(2.49053 + 6.77300i) q^{70} +(2.90460 - 2.11032i) q^{71} +(5.83867 - 7.12507i) q^{72} +(-11.0652 + 3.59530i) q^{73} +(0.562756 - 0.974721i) q^{74} +(4.68013 + 7.28673i) q^{75} +(2.06421 + 3.57532i) q^{76} +(2.80091 + 2.52195i) q^{77} +(0.339038 + 0.00986425i) q^{78} +(-1.42166 - 13.5262i) q^{79} +(5.63178 - 1.42393i) q^{80} +(8.93915 + 1.04476i) q^{81} +6.81040i q^{82} +(5.96001 + 13.3864i) q^{83} +(-1.43962 - 2.10776i) q^{84} +(0.190613 + 0.387560i) q^{85} +(5.50713 - 6.11629i) q^{86} +(-0.797506 - 10.5243i) q^{87} +(3.20913 - 2.88951i) q^{88} +(-3.38521 - 10.4186i) q^{89} +(5.89408 + 5.52405i) q^{90} +(0.134675 - 0.414486i) q^{91} +(-1.31938 - 2.96339i) q^{92} +(-0.139078 + 1.03319i) q^{93} +(-0.0275518 + 0.262138i) q^{94} +(-15.0646 + 7.40918i) q^{95} +(-4.59318 + 2.47663i) q^{96} +(3.08167 - 0.323896i) q^{97} +(0.208835 - 0.0678546i) q^{98} +(4.06886 + 1.11564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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