LMFDB - Embedded newform 225.2.u.a.79.20

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			79.20
Character	$\chi$	$=$	225.79
Dual form			225.2.u.a.94.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.894901 - 0.805773i) q^{2} +(0.487100 + 1.66215i) q^{3} +(-0.0574783 + 0.546869i) q^{4} +(2.23444 + 0.0854168i) q^{5} +(1.77522 + 1.09497i) q^{6} +(-2.32094 - 1.33999i) q^{7} +(1.80485 + 2.48416i) q^{8} +(-2.52547 + 1.61926i) q^{9} +O(q^{10})$	\(q+(0.894901 - 0.805773i) q^{2} +(0.487100 + 1.66215i) q^{3} +(-0.0574783 + 0.546869i) q^{4} +(2.23444 + 0.0854168i) q^{5} +(1.77522 + 1.09497i) q^{6} +(-2.32094 - 1.33999i) q^{7} +(1.80485 + 2.48416i) q^{8} +(-2.52547 + 1.61926i) q^{9} +(2.06843 - 1.72401i) q^{10} +(-0.941029 - 1.04512i) q^{11} +(-0.936975 + 0.170843i) q^{12} +(-0.120849 - 0.108813i) q^{13} +(-3.15674 + 0.670987i) q^{14} +(0.946418 + 3.75557i) q^{15} +(2.54110 + 0.540127i) q^{16} +(0.113531 + 0.156262i) q^{17} +(-0.955286 + 3.48403i) q^{18} +(6.07397 - 4.41300i) q^{19} +(-0.175143 + 1.21703i) q^{20} +(1.09674 - 4.51045i) q^{21} +(-1.68426 - 0.177022i) q^{22} +(-1.22650 - 5.77024i) q^{23} +(-3.24990 + 4.20996i) q^{24} +(4.98541 + 0.381717i) q^{25} -0.195827 q^{26} +(-3.92161 - 3.40896i) q^{27} +(0.866205 - 1.19223i) q^{28} +(-5.56680 + 2.47850i) q^{29} +(3.87309 + 2.59827i) q^{30} +(-0.549855 - 0.244811i) q^{31} +(-2.60917 + 1.50640i) q^{32} +(1.27877 - 2.07321i) q^{33} +(0.227511 + 0.0483590i) q^{34} +(-5.07153 - 3.19238i) q^{35} +(-0.740366 - 1.47417i) q^{36} +(0.888903 - 0.288822i) q^{37} +(1.87973 - 8.84344i) q^{38} +(0.121998 - 0.253872i) q^{39} +(3.82063 + 5.70486i) q^{40} +(3.78427 - 4.20285i) q^{41} +(-2.65293 - 4.92014i) q^{42} +(-5.91893 - 3.41730i) q^{43} +(0.625632 - 0.454548i) q^{44} +(-5.78131 + 3.40242i) q^{45} +(-5.74710 - 4.17551i) q^{46} +(0.0890280 + 0.199960i) q^{47} +(0.339998 + 4.48677i) q^{48} +(0.0911727 + 0.157916i) q^{49} +(4.76903 - 3.67551i) q^{50} +(-0.204430 + 0.264821i) q^{51} +(0.0664527 - 0.0598343i) q^{52} +(-7.64631 + 10.5242i) q^{53} +(-6.25630 + 0.109246i) q^{54} +(-2.01340 - 2.41563i) q^{55} +(-0.860180 - 8.18407i) q^{56} +(10.2937 + 7.94626i) q^{57} +(-2.98463 + 6.70358i) q^{58} +(-3.97717 + 4.41709i) q^{59} +(-2.10820 + 0.301703i) q^{60} +(9.43845 + 10.4825i) q^{61} +(-0.689328 + 0.223976i) q^{62} +(8.03126 - 0.374098i) q^{63} +(-2.72670 + 8.39191i) q^{64} +(-0.260735 - 0.253458i) q^{65} +(-0.526163 - 2.88571i) q^{66} +(2.62723 - 5.90086i) q^{67} +(-0.0919806 + 0.0531050i) q^{68} +(8.99355 - 4.84931i) q^{69} +(-7.11085 + 1.22964i) q^{70} +(2.90460 + 2.11032i) q^{71} +(-8.58059 - 3.35114i) q^{72} +(-11.0652 - 3.59530i) q^{73} +(0.562756 - 0.974721i) q^{74} +(1.79392 + 8.47242i) q^{75} +(2.06421 + 3.57532i) q^{76} +(0.783617 + 3.68663i) q^{77} +(-0.0953872 - 0.325493i) q^{78} +(12.4249 - 5.53192i) q^{79} +(5.63178 + 1.42393i) q^{80} +(3.75597 - 8.17879i) q^{81} -6.81040i q^{82} +(-14.5730 + 1.53168i) q^{83} +(2.40359 + 0.859026i) q^{84} +(0.240331 + 0.358856i) q^{85} +(-8.05043 + 1.71117i) q^{86} +(-6.83121 - 8.04556i) q^{87} +(0.897827 - 4.22394i) q^{88} +(-3.38521 + 10.4186i) q^{89} +(-2.43212 + 7.70325i) q^{90} +(0.134675 + 0.414486i) q^{91} +(3.22606 - 0.339073i) q^{92} +(0.139078 - 1.03319i) q^{93} +(0.240794 + 0.107208i) q^{94} +(13.9488 - 9.34174i) q^{95} +(-3.77479 - 3.60305i) q^{96} +(-1.26033 - 2.83075i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.894901	−	0.805773i	0.632791	−	0.569767i	−0.289061	−	0.957311i	$-0.593343\pi$
$2$	0.894901	−	0.805773i	0.632791	−	0.569767i	0.921851	+	0.387543i	$0.126676\pi$
$3$	0.487100	+	1.66215i	0.281227	+	0.959641i
$3$	0.487100	+	1.66215i	0.281227	+	0.959641i
$4$	−0.0574783	+	0.546869i	−0.0287391	+	0.273435i
$5$	2.23444	+	0.0854168i	0.999270	+	0.0381996i
$5$	2.23444	+	0.0854168i	0.999270	+	0.0381996i
$6$	1.77522	+	1.09497i	0.724730	+	0.447018i
$7$	−2.32094	−	1.33999i	−0.877233	−	0.506470i	−0.00748764	−	0.999972i	$-0.502383\pi$
$7$	−2.32094	−	1.33999i	−0.877233	−	0.506470i	−0.869745	+	0.493501i	$0.835717\pi$
$8$	1.80485	+	2.48416i	0.638110	+	0.878283i
$9$	−2.52547	+	1.61926i	−0.841823	+	0.539754i
$10$	2.06843	−	1.72401i	0.654094	−	0.545179i
$11$	−0.941029	−	1.04512i	−0.283731	−	0.315115i	0.584385	−	0.811476i	$-0.301336\pi$
$11$	−0.941029	−	1.04512i	−0.283731	−	0.315115i	−0.868116	+	0.496361i	$0.834669\pi$
$12$	−0.936975	+	0.170843i	−0.270481	+	0.0493180i
$13$	−0.120849	−	0.108813i	−0.0335175	−	0.0301793i	0.652202	−	0.758045i	$-0.273846\pi$
$13$	−0.120849	−	0.108813i	−0.0335175	−	0.0301793i	−0.685719	+	0.727866i	$0.740512\pi$
$14$	−3.15674	+	0.670987i	−0.843675	+	0.179329i
$15$	0.946418	+	3.75557i	0.244364	+	0.969684i
$16$	2.54110	+	0.540127i	0.635274	+	0.135032i
$17$	0.113531	+	0.156262i	0.0275354	+	0.0378992i	0.822563	−	0.568674i	$-0.192544\pi$
$17$	0.113531	+	0.156262i	0.0275354	+	0.0378992i	−0.795027	+	0.606574i	$0.792544\pi$
$18$	−0.955286	+	3.48403i	−0.225163	+	0.821195i
$19$	6.07397	−	4.41300i	1.39346	−	1.01241i	0.397989	−	0.917390i	$-0.369708\pi$
$19$	6.07397	−	4.41300i	1.39346	−	1.01241i	0.995475	−	0.0950213i	$-0.0302919\pi$
$20$	−0.175143	+	1.21703i	−0.0391632	+	0.272137i
$21$	1.09674	−	4.51045i	0.239328	−	0.984262i
$22$	−1.68426	−	0.177022i	−0.359085	−	0.0377413i
$23$	−1.22650	−	5.77024i	−0.255743	−	1.20318i	−0.899146	−	0.437649i	$-0.855811\pi$
$23$	−1.22650	−	5.77024i	−0.255743	−	1.20318i	0.643403	−	0.765528i	$-0.277522\pi$
$24$	−3.24990	+	4.20996i	−0.663383	+	0.859354i
$25$	4.98541	+	0.381717i	0.997082	+	0.0763434i
$26$	−0.195827			−0.0384048
$27$	−3.92161	−	3.40896i	−0.754714	−	0.656054i
$28$	0.866205	−	1.19223i	0.163697	−	0.225310i
$29$	−5.56680	+	2.47850i	−1.03373	+	0.460245i	−0.852242	−	0.523148i	$-0.824757\pi$
$29$	−5.56680	+	2.47850i	−1.03373	+	0.460245i	−0.181486	+	0.983393i	$0.558091\pi$
$30$	3.87309	+	2.59827i	0.707125	+	0.474376i
$31$	−0.549855	−	0.244811i	−0.0987568	−	0.0439694i	0.356764	−	0.934195i	$-0.383880\pi$
$31$	−0.549855	−	0.244811i	−0.0987568	−	0.0439694i	−0.455520	+	0.890225i	$0.650547\pi$
$32$	−2.60917	+	1.50640i	−0.461240	+	0.266297i
$33$	1.27877	−	2.07321i	0.222605	−	0.360899i
$34$	0.227511	+	0.0483590i	0.0390178	+	0.00829350i
$35$	−5.07153	−	3.19238i	−0.857245	−	0.539611i
$36$	−0.740366	−	1.47417i	−0.123394	−	0.245695i
$37$	0.888903	−	0.288822i	0.146135	−	0.0474821i	−0.235036	−	0.971987i	$-0.575521\pi$
$37$	0.888903	−	0.288822i	0.146135	−	0.0474821i	0.381171	+	0.924505i	$0.375521\pi$
$38$	1.87973	−	8.84344i	0.304933	−	1.43460i
$39$	0.121998	−	0.253872i	0.0195353	−	0.0406521i
$40$	3.82063	+	5.70486i	0.604094	+	0.902017i
$41$	3.78427	−	4.20285i	0.591003	−	0.656376i	−0.371249	−	0.928533i	$-0.621071\pi$
$41$	3.78427	−	4.20285i	0.591003	−	0.656376i	0.962253	+	0.272158i	$0.0877372\pi$
$42$	−2.65293	−	4.92014i	−0.409356	−	0.759193i
$43$	−5.91893	−	3.41730i	−0.902629	−	0.521133i	−0.0245768	−	0.999698i	$-0.507824\pi$
$43$	−5.91893	−	3.41730i	−0.902629	−	0.521133i	−0.878052	+	0.478565i	$0.841157\pi$
$44$	0.625632	−	0.454548i	0.0943175	−	0.0685257i
$45$	−5.78131	+	3.40242i	−0.861826	+	0.507203i
$46$	−5.74710	−	4.17551i	−0.847363	−	0.615645i
$47$	0.0890280	+	0.199960i	0.0129861	+	0.0291672i	0.919922	−	0.392101i	$-0.128252\pi$
$47$	0.0890280	+	0.199960i	0.0129861	+	0.0291672i	−0.906936	+	0.421268i	$0.861585\pi$
$48$	0.339998	+	4.48677i	0.0490744	+	0.647610i
$49$	0.0911727	+	0.157916i	0.0130247	+	0.0225594i
$50$	4.76903	−	3.67551i	0.674442	−	0.519795i
$51$	−0.204430	+	0.264821i	−0.0286259	+	0.0370823i
$52$	0.0664527	−	0.0598343i	0.00921534	−	0.00829753i
$53$	−7.64631	+	10.5242i	−1.05030	+	1.44562i	−0.161754	+	0.986831i	$0.551715\pi$
$53$	−7.64631	+	10.5242i	−1.05030	+	1.44562i	−0.888547	+	0.458785i	$0.848285\pi$
$54$	−6.25630	+	0.109246i	−0.851374	+	0.0148666i
$55$	−2.01340	−	2.41563i	−0.271486	−	0.325723i
$56$	−0.860180	−	8.18407i	−0.114946	−	1.09364i
$57$	10.2937	+	7.94626i	1.36343	+	1.05251i
$58$	−2.98463	+	6.70358i	−0.391901	+	0.880224i
$59$	−3.97717	+	4.41709i	−0.517783	+	0.575057i	−0.944159	−	0.329489i	$-0.893123\pi$
$59$	−3.97717	+	4.41709i	−0.517783	+	0.575057i	0.426376	+	0.904546i	$0.359790\pi$
$60$	−2.10820	+	0.301703i	−0.272168	+	0.0389497i
$61$	9.43845	+	10.4825i	1.20847	+	1.34214i	0.923497	+	0.383606i	$0.125318\pi$
$61$	9.43845	+	10.4825i	1.20847	+	1.34214i	0.284972	+	0.958536i	$0.408016\pi$
$62$	−0.689328	+	0.223976i	−0.0875447	+	0.0284450i
$63$	8.03126	−	0.374098i	1.01184	−	0.0471320i
$64$	−2.72670	+	8.39191i	−0.340837	+	1.04899i
$65$	−0.260735	−	0.253458i	−0.0323402	−	0.0314377i
$66$	−0.526163	−	2.88571i	−0.0647662	−	0.355206i
$67$	2.62723	−	5.90086i	0.320967	−	0.720904i	−0.678945	−	0.734190i	$-0.737562\pi$
$67$	2.62723	−	5.90086i	0.320967	−	0.720904i	0.999912	+	0.0132854i	$0.00422899\pi$
$68$	−0.0919806	+	0.0531050i	−0.0111543	+	0.00643993i
$69$	8.99355	−	4.84931i	1.08270	−	0.583788i
$70$	−7.11085	+	1.22964i	−0.849910	+	0.146970i
$71$	2.90460	+	2.11032i	0.344713	+	0.250449i	0.746648	−	0.665220i	$-0.231662\pi$
$71$	2.90460	+	2.11032i	0.344713	+	0.250449i	−0.401935	+	0.915668i	$0.631662\pi$
$72$	−8.58059	−	3.35114i	−1.01123	−	0.394936i
$73$	−11.0652	−	3.59530i	−1.29508	−	0.420798i	−0.421215	−	0.906961i	$-0.638396\pi$
$73$	−11.0652	−	3.59530i	−1.29508	−	0.420798i	−0.873868	+	0.486163i	$0.838396\pi$
$74$	0.562756	−	0.974721i	0.0654190	−	0.113309i
$75$	1.79392	+	8.47242i	0.207144	+	0.978310i
$76$	2.06421	+	3.57532i	0.236781	+	0.410117i
$77$	0.783617	+	3.68663i	0.0893015	+	0.420130i
$78$	−0.0953872	−	0.325493i	−0.0108005	−	0.0368548i
$79$	12.4249	−	5.53192i	1.39791	−	0.622390i	0.437053	−	0.899436i	$-0.356022\pi$
$79$	12.4249	−	5.53192i	1.39791	−	0.622390i	0.960857	+	0.277046i	$0.0893554\pi$
$80$	5.63178	+	1.42393i	0.629653	+	0.159200i
$81$	3.75597	−	8.17879i	0.417330	−	0.908755i
$82$		−	6.81040i		−	0.752083i
$83$	−14.5730	+	1.53168i	−1.59959	+	0.168124i	−0.861922	−	0.507040i	$-0.830740\pi$
$83$	−14.5730	+	1.53168i	−1.59959	+	0.168124i	−0.737668	+	0.675164i	$0.764073\pi$
$84$	2.40359	+	0.859026i	0.262253	+	0.0937275i
$85$	0.240331	+	0.358856i	0.0260675	+	0.0389234i
$86$	−8.05043	+	1.71117i	−0.868100	+	0.184520i
$87$	−6.83121	−	8.04556i	−0.732383	−	0.862574i
$88$	0.897827	−	4.22394i	0.0957087	−	0.450274i
$89$	−3.38521	+	10.4186i	−0.358831	+	1.10437i	0.594923	+	0.803783i	$0.297183\pi$
$89$	−3.38521	+	10.4186i	−0.358831	+	1.10437i	−0.953754	+	0.300587i	$0.902817\pi$
$90$	−2.43212	+	7.70325i	−0.256368	+	0.811994i
$91$	0.134675	+	0.414486i	0.0141177	+	0.0434499i
$92$	3.22606	−	0.339073i	0.336340	−	0.0353508i
$93$	0.139078	−	1.03319i	0.0144217	−	0.107137i
$94$	0.240794	+	0.107208i	0.0248360	+	0.0110577i
$95$	13.9488	−	9.34174i	1.43112	−	0.958443i
$96$	−3.77479	−	3.60305i	−0.385263	−	0.367735i
$97$	−1.26033	−	2.83075i	−0.127967	−	0.287419i	0.838188	−	0.545382i	$-0.183615\pi$
$97$	−1.26033	−	2.83075i	−0.127967	−	0.287419i	−0.966155	+	0.257963i	$0.916949\pi$
$98$	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	$0.0357244\pi$
$102$	0.0304409	+	0.401713i	0.00301410	+	0.0397755i
$103$	−0.536843	−	0.0564245i	−0.0528968	−	0.00555967i	0.0780431	−	0.996950i	$-0.475133\pi$
$103$	−0.536843	−	0.0564245i	−0.0528968	−	0.00555967i	−0.130940	+	0.991390i	$0.541799\pi$
$104$	0.0521947	−	0.496600i	0.00511811	−	0.0486956i
$105$	2.83586	−	9.98464i	0.276752	−	0.974401i
$106$	1.63746	+	15.5794i	0.159044	+	1.51320i
$107$			0.671621i			0.0649281i	0.999473	+	0.0324640i	$0.0103354\pi$
$107$			0.671621i			0.0649281i	−0.999473	+	0.0324640i	$0.989665\pi$
$108$	2.08966	−	1.94867i	0.201078	−	0.187510i
$109$	4.32136	+	13.2998i	0.413911	+	1.27389i	0.913221	+	0.407464i	$0.133587\pi$
$109$	4.32136	+	13.2998i	0.413911	+	1.27389i	−0.499310	+	0.866423i	$0.666413\pi$
$110$	−3.74824	−	0.539409i	−0.357381	−	0.0514306i
$111$	0.913049	+	1.33680i	0.0866628	+	0.126884i
$112$	−5.17397	−	4.65866i	−0.488894	−	0.440202i
$113$	−2.75193	−	2.47785i	−0.258880	−	0.233097i	0.529462	−	0.848333i	$-0.322394\pi$
$113$	−2.75193	−	2.47785i	−0.258880	−	0.233097i	−0.788342	+	0.615237i	$0.789060\pi$
$114$	15.6147	−	1.18325i	1.46245	−	0.110821i
$115$	−2.24766	−	12.9980i	−0.209596	−	1.21207i
$116$	−1.03544	−	3.18677i	−0.0961386	−	0.295884i
$117$	0.481398	+	0.0791173i	0.0445052	+	0.00731440i
$118$			7.15756i			0.658907i
$119$	−0.0541083	−	0.514807i	−0.00496010	−	0.0471922i
$120$	−7.62129	+	9.12928i	−0.695725	+	0.833385i
$121$	0.943076	−	8.97277i	0.0857342	−	0.815706i
$122$	16.8930	+	1.77552i	1.52942	+	0.160748i
$123$	8.82908	+	4.24280i	0.796091	+	0.382560i
$124$	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	0.842600	−	0.538540i	$-0.181024\pi$
$127$	13.6104	+	4.42230i	1.20773	+	0.392416i	0.365132	+	0.930956i	$0.381024\pi$
$128$	1.87101	+	4.20237i	0.165376	+	0.371440i
$129$	2.79694	−	11.5027i	0.246257	−	1.01276i
$130$	−0.437562	−	0.0167269i	−0.0383768	−	0.00146705i
$131$	10.6971	+	4.76265i	0.934608	+	0.416114i	0.816799	−	0.576922i	$-0.195746\pi$
$131$	10.6971	+	4.76265i	0.934608	+	0.416114i	0.117809	+	0.993036i	$0.462413\pi$
$132$	1.06027	+	0.818482i	0.0922847	+	0.0712397i
$133$	−20.0107	+	2.10321i	−1.73515	+	0.182372i
$134$	−2.40364	−	7.39763i	−0.207643	−	0.639058i
$135$	−8.47140	−	7.95207i	−0.729102	−	0.684405i
$136$	−0.183274	+	0.564059i	−0.0157156	+	0.0483677i
$137$	−4.27866	+	20.1295i	−0.365550	+	1.71978i	0.283447	+	0.958988i	$0.408522\pi$
$137$	−4.27866	+	20.1295i	−0.365550	+	1.71978i	−0.648997	+	0.760791i	$0.724811\pi$
$138$	4.14090	−	11.5864i	0.352497	−	0.986301i
$139$	0.891271	−	0.189445i	0.0755966	−	0.0160686i	−0.169958	−	0.985451i	$-0.554363\pi$
$139$	0.891271	−	0.189445i	0.0755966	−	0.0160686i	0.245555	+	0.969383i	$0.421030\pi$
$140$	2.03732	−	2.58997i	0.172185	−	0.218893i
$141$	−0.288998	+	0.245378i	−0.0243380	+	0.0206646i
$142$	4.29977	−	0.451924i	0.360829	−	0.0379246i
$143$			0.228698i			0.0191247i
$144$	−7.29207	+	2.75063i	−0.607672	+	0.229219i
$145$	−12.6504	+	5.06254i	−1.05055	+	0.420421i
$146$	−12.7993	+	5.69860i	−1.05927	+	0.471619i
$147$	−0.218069	+	0.228463i	−0.0179860	+	0.0188433i
$148$	0.106855	+	0.502715i	0.00878345	+	0.0413229i
$149$	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	$0.498043\pi$
$150$	8.43223	+	6.13648i	0.688488	+	0.501042i
$151$	−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
$153$	−0.539749	−	0.210798i	−0.0436361	−	0.0170420i
$154$	3.67185	+	2.66775i	0.295886	+	0.214974i
$155$	−1.20770	−	0.593982i	−0.0970051	−	0.0477098i
$156$	0.131823	+	0.0813090i	0.0105543	+	0.00650993i
$157$	−10.4979	+	6.06096i	−0.837823	+	0.483717i	−0.856524	−	0.516108i	$-0.827380\pi$
$157$	−10.4979	+	6.06096i	−0.837823	+	0.483717i	0.0187007	+	0.999825i	$0.494047\pi$
$158$	6.66159	−	14.9622i	0.529967	−	1.19033i
$159$	−21.2174	−	7.58294i	−1.68265	−	0.601366i
$160$	−5.95868	+	3.14309i	−0.471075	+	0.248483i
$161$	−4.88545	+	15.0359i	−0.385027	+	1.18499i
$162$	−3.22903	−	10.3457i	−0.253696	−	0.812833i
$163$	−0.508454	+	0.165207i	−0.0398252	+	0.0129400i	−0.328862	−	0.944378i	$-0.606665\pi$
$163$	−0.508454	+	0.165207i	−0.0398252	+	0.0129400i	0.289037	+	0.957318i	$0.406665\pi$
$164$	2.08090	+	2.31107i	0.162491	+	0.180464i
$165$	3.03441	−	4.52322i	0.236228	−	0.352132i
$166$	−11.8072	+	13.1132i	−0.916415	+	1.01778i
$167$	−4.43413	+	9.95922i	−0.343123	+	0.770668i	0.656740	+	0.754117i	$0.271935\pi$
$167$	−4.43413	+	9.95922i	−0.343123	+	0.770668i	−0.999863	+	0.0165503i	$0.994732\pi$
$168$	13.1841	−	5.41620i	1.01718	−	0.417869i
$169$	−1.35611	−	12.9025i	−0.104316	−	0.992499i
$170$	0.504228	+	0.127488i	0.0386726	+	0.00977791i
$171$	−8.19381	+	20.9802i	−0.626596	+	1.60440i
$172$	2.20903	−	3.04046i	0.168437	−	0.231833i
$173$	7.80136	−	7.02437i	0.593126	−	0.534053i	−0.316978	−	0.948433i	$-0.602668\pi$
$173$	7.80136	−	7.02437i	0.593126	−	0.534053i	0.910104	+	0.414380i	$0.136001\pi$
$174$	−12.5962	−	1.69558i	−0.954912	−	0.128541i
$175$	−11.0593	−	7.56636i	−0.836007	−	0.571963i
$176$	−1.82675	−	3.16402i	−0.137696	−	0.238497i
$177$	−9.27914	−	4.45908i	−0.697463	−	0.335165i
$178$	5.36560	+	12.0513i	0.402169	+	0.903285i
$179$	−11.1491	−	8.10027i	−0.833321	−	0.605443i	0.0871761	−	0.996193i	$-0.472216\pi$
$179$	−11.1491	−	8.10027i	−0.833321	−	0.605443i	−0.920497	+	0.390750i	$0.872216\pi$
$180$	−1.52838	−	3.35718i	−0.113919	−	0.250230i
$181$	−5.95243	+	4.32469i	−0.442441	+	0.321452i	−0.786604	−	0.617458i	$-0.788163\pi$
$181$	−5.95243	+	4.32469i	−0.442441	+	0.321452i	0.344163	+	0.938910i	$0.388163\pi$
$182$	0.454502	+	0.262407i	0.0336899	+	0.0194509i
$183$	−12.8259	+	20.7941i	−0.948120	+	1.53714i
$184$	12.1205	−	13.4612i	0.893538	−	0.992374i
$185$	2.01087	−	0.569427i	0.147842	−	0.0418651i
$186$	−0.708053	−	1.03667i	−0.0519170	−	0.0760120i
$187$	0.0564765	−	0.265701i	0.00412997	−	0.0194300i
$188$	−0.114469	+	0.0371933i	−0.00834852	+	0.00271260i
$189$	4.53383	+	13.1669i	0.329788	+	0.957752i
$190$	4.95552	−	19.5995i	0.359511	−	1.42190i
$191$	−1.09062	−	0.231818i	−0.0789142	−	0.0167737i	0.168285	−	0.985738i	$-0.446177\pi$
$191$	−1.09062	−	0.231818i	−0.0789142	−	0.0167737i	−0.247200	+	0.968965i	$0.579510\pi$
$192$	−15.2768	−	0.444474i	−1.10251	−	0.0320772i
$193$	21.9469	−	12.6711i	1.57977	−	0.912083i	0.584884	−	0.811117i	$-0.301140\pi$
$193$	21.9469	−	12.6711i	1.57977	−	0.912083i	0.994890	−	0.100966i	$-0.0321934\pi$
$194$	−3.40881	−	1.51770i	−0.244738	−	0.108965i
$195$	0.294281	−	0.556840i	0.0210739	−	0.0398761i
$196$	−0.0915997	+	0.0407828i	−0.00654284	+	0.00291306i
$197$	9.37839	−	12.9082i	0.668182	−	0.919674i	−0.331535	−	0.943443i	$-0.607567\pi$
$197$	9.37839	−	12.9082i	0.668182	−	0.919674i	0.999717	+	0.0237688i	$0.00756657\pi$
$198$	4.54018	−	2.28019i	0.322656	−	0.162046i
$199$	−19.2943			−1.36774			−0.683868	−	0.729606i	$-0.739704\pi$
$199$	−19.2943			−1.36774			−0.683868	+	0.729606i	$0.739704\pi$
$200$	8.04965	+	13.0735i	0.569196	+	0.924435i
$201$	11.0878	+	1.49254i	0.782074	+	0.105276i
$202$	−2.01225	−	9.46690i	−0.141582	−	0.666089i
$203$	16.2414	+	1.70704i	1.13992	+	0.119810i
$204$	−0.133072	−	0.127018i	−0.00931691	−	0.00889303i
$205$	8.81470	−	9.06777i	0.615645	−	0.633320i
$206$	−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
$209$	−10.3279	−	2.19526i	−0.714395	−	0.151849i
$210$	−5.50753	−	11.2203i	−0.380056	−	0.774276i
$211$	−2.96507	+	0.630245i	−0.204124	+	0.0433879i	−0.308839	−	0.951114i	$-0.599940\pi$
$211$	−2.96507	+	0.630245i	−0.204124	+	0.0433879i	0.104715	+	0.994502i	$0.466607\pi$
$212$	−5.31589	−	4.78645i	−0.365097	−	0.328735i
$213$	−2.09283	+	5.85582i	−0.143398	+	0.401234i
$214$	0.541174	+	0.601035i	0.0369939	+	0.0410859i
$215$	−12.9336	−	8.14131i	−0.882063	−	0.555233i
$216$	1.39048	−	15.8945i	0.0946105	−	1.08149i
$217$	0.948134	+	1.30499i	0.0643635	+	0.0885888i
$218$	14.5838	+	8.41995i	0.987738	+	0.570271i
$219$	0.586064	−	20.1433i	0.0396025	−	1.36116i
$220$	1.43676	−	0.962219i	0.0968663	−	0.0648728i
$221$	0.00328323	−	0.0312379i	0.000220854	−	0.00210129i
$222$	1.89425	+	0.460596i	0.127134	+	0.0309132i
$223$	−13.5387	+	12.1903i	−0.906616	+	0.816321i	−0.983535	−	0.180716i	$-0.942158\pi$
$223$	−13.5387	+	12.1903i	−0.906616	+	0.816321i	0.0769189	+	0.997037i	$0.475492\pi$
$224$	8.07429			0.539486
$225$	−13.2086	+	7.10867i	−0.880572	+	0.473912i
$226$	−4.45929			−0.296628
$227$	−6.28780	+	5.66156i	−0.417336	+	0.375771i	−0.850879	−	0.525362i	$-0.823930\pi$
$227$	−6.28780	+	5.66156i	−0.417336	+	0.375771i	0.433543	+	0.901133i	$0.357263\pi$
$228$	−4.93723	+	5.17256i	−0.326976	+	0.342561i
$229$	1.02248	−	9.72823i	0.0675673	−	0.642860i	−0.907363	−	0.420348i	$-0.861908\pi$
$229$	1.02248	−	9.72823i	0.0675673	−	0.642860i	0.974930	−	0.222511i	$-0.0714255\pi$
$230$	−12.4849	−	9.82081i	−0.823227	−	0.647565i
$231$	−5.74602	+	3.09824i	−0.378060	+	0.203849i
$232$	−16.2042	−	9.35550i	−1.06386	−	0.614218i
$233$	−1.49631	−	2.05949i	−0.0980263	−	0.134922i	0.757186	−	0.653199i	$-0.226573\pi$
$233$	−1.49631	−	2.05949i	−0.0980263	−	0.134922i	−0.855213	+	0.518277i	$0.826573\pi$
$234$	0.494554	−	0.317095i	0.0323300	−	0.0207292i
$235$	0.181847	+	0.454403i	0.0118624	+	0.0296420i
$236$	−2.18697	−	2.42888i	−0.142360	−	0.158107i
$237$	15.2470	+	17.9574i	0.990401	+	1.16646i
$238$	−0.463239	−	0.417102i	−0.0300273	−	0.0270367i
$239$	−10.3206	+	2.19372i	−0.667586	+	0.141900i	−0.529224	−	0.848482i	$-0.677517\pi$
$239$	−10.3206	+	2.19372i	−0.667586	+	0.141900i	−0.138362	+	0.990382i	$0.544184\pi$
$240$	0.376457	+	10.0545i	0.0243002	+	0.649012i
$241$	3.00671	+	0.639097i	0.193680	+	0.0411679i	0.303730	−	0.952758i	$-0.401768\pi$
$241$	3.00671	+	0.639097i	0.193680	+	0.0411679i	−0.110050	+	0.993926i	$0.535101\pi$
$242$	−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
$245$	0.190231	+	0.360640i	0.0121534	+	0.0230405i
$246$	11.3199	−	3.31735i	0.721730	−	0.211506i
$247$	−1.21423	−	0.127620i	−0.0772594	−	0.00812029i
$248$	−0.384254	−	1.80777i	−0.0244002	−	0.114794i
$249$	−9.64436	−	23.4763i	−0.611187	−	1.48775i
$250$	10.9700	−	7.80533i	0.693806	−	0.493652i
$251$	−23.8819			−1.50741			−0.753707	−	0.657211i	$-0.771736\pi$
$251$	−23.8819			−1.50741			−0.753707	+	0.657211i	$0.771736\pi$
$252$	−0.257040	+	4.41355i	−0.0161920	+	0.278028i
$253$	−4.87640	+	6.71180i	−0.306577	+	0.421967i
$254$	15.7434	−	7.00940i	0.987827	−	0.439809i
$255$	−0.479406	+	0.574264i	−0.0300216	+	0.0359618i
$256$	−11.0613	−	4.92482i	−0.691333	−	0.307801i
$257$	4.15137	−	2.39680i	0.258955	−	0.149508i	−0.364903	−	0.931046i	$-0.618898\pi$
$257$	4.15137	−	2.39680i	0.258955	−	0.149508i	0.623858	+	0.781538i	$0.285564\pi$
$258$	−6.76558	−	12.5475i	−0.421207	−	0.781173i
$259$	−2.45011	−	0.520787i	−0.152242	−	0.0323601i
$260$	0.153595	−	0.128020i	0.00952557	−	0.00793945i
$261$	10.0454	−	15.2735i	0.621796	−	0.945404i
$262$	13.4104	−	4.35732i	0.828500	−	0.269196i
$263$	4.83640	−	22.7535i	0.298225	−	1.40304i	−0.532535	−	0.846408i	$-0.678761\pi$
$263$	4.83640	−	22.7535i	0.298225	−	1.40304i	0.830760	−	0.556631i	$-0.187906\pi$
$264$	7.45815	−	0.565162i	0.459017	−	0.0347833i
$265$	−17.9841	+	22.8626i	−1.10476	+	1.40444i
$266$	−16.2129	+	18.0063i	−0.994077	+	1.10403i
$267$	−18.9662	−	0.551817i	−1.16071	−	0.0337706i
$268$	3.07599	+	1.77592i	0.187896	+	0.108482i
$269$	6.79619	−	4.93772i	0.414371	−	0.301058i	−0.360998	−	0.932567i	$-0.617564\pi$
$269$	6.79619	−	4.93772i	0.414371	−	0.301058i	0.775369	+	0.631508i	$0.217564\pi$
$270$	−13.9886	−	0.290289i	−0.851321	−	0.0176664i
$271$	16.4715	+	11.9673i	1.00058	+	0.726960i	0.962211	−	0.272304i	$-0.0877855\pi$
$271$	16.4715	+	11.9673i	1.00058	+	0.726960i	0.0383636	+	0.999264i	$0.487785\pi$
$272$	0.204092	+	0.458399i	0.0123749	+	0.0277945i
$273$	−0.623337	+	0.425745i	−0.0377261	+	0.0257673i
$274$	12.3908	+	21.4615i	0.748557	+	1.29654i
$275$	−4.29247	−	5.56955i	−0.258846	−	0.335856i
$276$	2.13500	+	5.19703i	0.128512	+	0.312824i
$277$	−7.58456	+	6.82917i	−0.455712	+	0.410325i	−0.864758	−	0.502189i	$-0.832528\pi$
$277$	−7.58456	+	6.82917i	−0.455712	+	0.410325i	0.409046	+	0.912514i	$0.365862\pi$
$278$	0.644950	−	0.887697i	0.0386815	−	0.0532405i
$279$	1.78505	−	0.272097i	0.106868	−	0.0162900i
$280$	−1.22296	−	18.3602i	−0.0730859	−	1.09723i
$281$	−2.45064	−	23.3163i	−0.146193	−	1.39093i	−0.784011	−	0.620747i	$-0.786829\pi$
$281$	−2.45064	−	23.3163i	−0.146193	−	1.39093i	0.637818	−	0.770187i	$-0.279837\pi$
$282$	−0.0609054	+	0.452456i	−0.00362686	+	0.0269433i
$283$	6.59912	−	14.8219i	0.392277	−	0.881069i	−0.604171	−	0.796855i	$-0.706495\pi$
$283$	6.59912	−	14.8219i	0.392277	−	0.881069i	0.996448	−	0.0842137i	$-0.0268378\pi$
$284$	−1.32102	+	1.46714i	−0.0783881	+	0.0870588i
$285$	22.3218	+	18.6347i	1.32223	+	1.10382i
$286$	0.184279	+	0.204662i	0.0108966	+	0.0121019i
$287$	−14.4149	+	4.68367i	−0.850882	+	0.276468i
$288$	4.15010	−	8.02930i	0.244547	−	0.473131i
$289$	5.24176	−	16.1325i	0.308339	−	0.948969i
$290$	−7.24156	+	14.7238i	−0.425239	+	0.864611i
$291$	4.09122	−	3.47371i	0.239831	−	0.203633i
$292$	2.60217	−	5.84456i	0.152280	−	0.342027i
$293$	2.77885	−	1.60437i	0.162342	−	0.0937283i	−0.416628	−	0.909077i	$-0.636788\pi$
$293$	2.77885	−	1.60437i	0.162342	−	0.0937283i	0.578970	+	0.815349i	$0.303455\pi$
$294$	−0.0110609	+	0.380166i	−0.000645082	+	0.0221717i
$295$	−9.26402	+	9.53000i	−0.539372	+	0.554858i
$296$	2.32181	+	1.68690i	0.134953	+	0.0980489i
$297$	0.127584	+	7.30647i	0.00740320	+	0.423964i
$298$	24.2992	+	7.89530i	1.40762	+	0.457363i
$299$	−0.479656	+	0.830788i	−0.0277392	+	0.0480457i
$300$	−4.73642	+	0.494061i	−0.273457	+	0.0285246i
$301$	9.15833	+	15.8627i	0.527877	+	0.914310i
$302$	1.33461	+	6.27884i	0.0767981	+	0.361307i
$303$	13.5266	+	3.28906i	0.777083	+	0.188952i
$304$	17.8181	−	7.93314i	1.02194	−	0.454997i
$305$	20.1942	+	24.2286i	1.15632	+	1.38732i
$306$	−0.652878	+	0.246271i	−0.0373226	+	0.0140784i
$307$			16.5271i			0.943250i	0.881799	+	0.471625i	$0.156332\pi$
$307$			16.5271i			0.943250i	−0.881799	+	0.471625i	$0.843668\pi$
$308$	−2.06115	+	0.216635i	−0.117445	+	0.0123439i
$309$	−0.167710	−	0.919797i	−0.00954072	−	0.0523254i
$310$	−1.55939	+	0.441580i	−0.0885674	+	0.0250801i
$311$	−18.3936	+	3.90968i	−1.04301	+	0.221698i	−0.697400	−	0.716682i	$-0.745660\pi$
$311$	−18.3936	+	3.90968i	−1.04301	+	0.221698i	−0.345606	+	0.938380i	$0.612327\pi$
$312$	0.850846	−	0.155138i	0.0481697	−	0.00878298i
$313$	0.657406	−	3.09285i	0.0371588	−	0.174818i	−0.955655	−	0.294489i	$-0.904851\pi$
$313$	0.657406	−	3.09285i	0.0371588	−	0.174818i	0.992814	+	0.119671i	$0.0381839\pi$
$314$	−4.51082	+	13.8829i	−0.254560	+	0.783456i
$315$	17.9773	−	0.149894i	1.01291	−	0.00844555i
$316$	2.31108	+	7.11276i	0.130008	+	0.400124i
$317$	0.398908	−	0.0419269i	0.0224049	−	0.00235485i	−0.0933194	−	0.995636i	$-0.529748\pi$
$317$	0.398908	−	0.0419269i	0.0224049	−	0.00235485i	0.115724	+	0.993281i	$0.463081\pi$
$318$	−25.0976	+	10.3104i	−1.40740	+	0.578178i
$319$	7.82884	+	3.48562i	0.438331	+	0.195157i
$320$	−6.80944	+	18.5183i	−0.380659	+	1.03520i
$321$	−1.11633	+	0.327147i	−0.0623076	+	0.0182595i
$322$	7.74350	+	17.3922i	0.431528	+	0.969229i
$323$	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
$327$	−20.0012	+	13.6610i	−1.10607	+	0.755458i
$328$	17.2706	+	1.81521i	0.953608	+	0.100228i
$329$	0.0613170	−	0.583392i	0.00338052	−	0.0321635i
$330$	−0.929190	−	6.49287i	−0.0511502	−	0.357421i
$331$	−2.52674	−	24.0403i	−0.138882	−	1.32138i	−0.812789	−	0.582559i	$-0.802052\pi$
$331$	−2.52674	−	24.0403i	−0.138882	−	1.32138i	0.673906	−	0.738817i	$-0.264615\pi$
$332$		−	8.05754i		−	0.442215i
$333$	−1.77722	+	2.16878i	−0.0973909	+	0.118848i
$334$	4.05676	+	12.4854i	0.221976	+	0.683172i
$335$	6.37441	−	12.9607i	0.348271	−	0.708117i
$336$	5.22314	−	10.8691i	0.284946	−	0.592959i
$337$	24.8166	+	22.3450i	1.35185	+	1.21721i	0.954018	+	0.299750i	$0.0969032\pi$
$337$	24.8166	+	22.3450i	1.35185	+	1.21721i	0.397830	+	0.917459i	$0.369763\pi$
$338$	−11.6101	−	10.4537i	−0.631504	−	0.568608i
$339$	2.77809	−	5.78108i	0.150885	−	0.313985i
$340$	−0.210061	+	0.110803i	−0.0113921	+	0.00600914i
$341$	0.261573	+	0.805038i	0.0141649	+	0.0435952i
$342$	9.57266	+	25.3776i	0.517630	+	1.37226i
$343$			18.2712i			0.986554i
$344$	−2.19366	−	20.8713i	−0.118274	−	1.12530i
$345$	20.5097	−	10.0673i	1.10421	−	0.542003i
$346$	1.32140	−	12.5722i	0.0710387	−	0.675888i
$347$	−3.72354	−	0.391360i	−0.199890	−	0.0210093i	0.00405417	−	0.999992i	$-0.498710\pi$
$347$	−3.72354	−	0.391360i	−0.199890	−	0.0210093i	−0.203944	+	0.978982i	$0.565376\pi$
$348$	4.79251	−	3.27333i	0.256906	−	0.175469i
$349$	−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
$353$	−2.24699	−	5.04682i	−0.119595	−	0.268615i	0.843821	−	0.536624i	$-0.180301\pi$
$353$	−2.24699	−	5.04682i	−0.119595	−	0.268615i	−0.963416	+	0.268009i	$0.913634\pi$
$354$	−11.8969	+	3.48645i	−0.632314	+	0.185302i
$355$	6.30990	+	4.96347i	0.334895	+	0.263434i
$356$	−5.50304	−	2.45011i	−0.291660	−	0.129856i
$357$	0.829328	−	0.340698i	0.0438927	−	0.0180317i
$358$	−16.5043	+	1.73467i	−0.872279	+	0.0916803i
$359$	−4.30244	−	13.2416i	−0.227074	−	0.698863i	−0.998074	−	0.0620276i	$-0.980243\pi$
$359$	−4.30244	−	13.2416i	−0.227074	−	0.698863i	0.771000	−	0.636835i	$-0.219757\pi$
$360$	−18.8865	−	8.22083i	−0.995408	−	0.433276i
$361$	11.5473	−	35.5388i	0.607750	−	1.87046i
$362$	−1.84212	+	8.66648i	−0.0968196	+	0.455500i
$363$	15.3734	−	2.80310i	0.806896	−	0.147125i
$364$	−0.234410	+	0.0498255i	−0.0122864	+	0.00261156i
$365$	−24.4174	−	8.97862i	−1.27806	−	0.469963i
$366$	5.27738	+	28.9434i	0.275853	+	1.51290i
$367$	36.4865	−	3.83489i	1.90458	−	0.200179i	0.922153	−	0.386825i	$-0.126428\pi$
$367$	36.4865	−	3.83489i	1.90458	−	0.200179i	0.982427	+	0.186645i	$0.0597615\pi$
$368$		−	15.3252i		−	0.798881i
$369$	−2.75152	+	16.7419i	−0.143238	+	0.871548i
$370$	1.34070	−	2.12988i	0.0696996	−	0.110727i
$371$	31.8491	−	14.1801i	1.65352	−	0.736195i
$372$	0.557024	+	0.135443i	0.0288804	+	0.00702241i
$373$	−3.88898	−	18.2962i	−0.201364	−	0.947342i	−0.956491	−	0.291763i	$-0.905758\pi$
$373$	−3.88898	−	18.2962i	−0.201364	−	0.947342i	0.755127	−	0.655579i	$-0.227575\pi$
$374$	−0.163554	−	0.283283i	−0.00845716	−	0.0146482i
$375$	3.28472	+	19.0843i	0.169622	+	0.985509i
$376$	−0.336051	+	0.582057i	−0.0173305	+	0.0300173i
$377$	0.942436	+	0.306216i	0.0485379	+	0.0157709i
$378$	14.6669	+	8.12985i	0.754383	+	0.418155i
$379$	1.54812	+	1.12477i	0.0795216	+	0.0577758i	0.626836	−	0.779151i	$-0.284350\pi$
$379$	1.54812	+	1.12477i	0.0795216	+	0.0577758i	−0.547314	+	0.836927i	$0.684350\pi$
$380$	4.30696	+	8.16514i	0.220942	+	0.418863i
$381$	−0.720871	+	24.7767i	−0.0369314	+	1.26935i
$382$	−1.16279	+	0.671335i	−0.0594933	+	0.0343485i
$383$	−3.92887	+	8.82440i	−0.200756	+	0.450906i	−0.985667	−	0.168703i	$-0.946042\pi$
$383$	−3.92887	+	8.82440i	−0.200756	+	0.450906i	0.784911	+	0.619609i	$0.212709\pi$
$384$	−6.07358	+	5.15687i	−0.309941	+	0.263161i
$385$	1.43604	+	8.30447i	0.0731875	+	0.423235i
$386$	9.43034	−	29.0236i	0.479991	−	1.47726i
$387$	20.4816	−	0.954038i	1.04114	−	0.0484965i
$388$	1.62049	−	0.526529i	0.0822680	−	0.0267305i
$389$	15.2919	+	16.9834i	0.775332	+	0.861093i	0.993384	−	0.114844i	$-0.0366368\pi$
$389$	15.2919	+	16.9834i	0.775332	+	0.861093i	−0.218052	+	0.975937i	$0.569970\pi$
$390$	−0.185334	−	0.735441i	−0.00938475	−	0.0372405i
$391$	0.762424	−	0.846758i	0.0385574	−	0.0428224i
$392$	−0.227735	+	0.511501i	−0.0115024	+	0.0258347i
$393$	−2.70567	+	20.1000i	−0.136483	+	1.01391i
$394$	−2.00838	−	19.1085i	−0.101181	−	0.962670i
$395$	28.2352	−	11.2994i	1.42066	−	0.568536i
$396$	−0.843979	+	2.16101i	−0.0424116	+	0.108595i
$397$	5.64077	−	7.76385i	0.283102	−	0.389657i	−0.643656	−	0.765315i	$-0.722583\pi$
$397$	5.64077	−	7.76385i	0.283102	−	0.389657i	0.926758	+	0.375658i	$0.122583\pi$
$398$	−17.2665	+	15.5468i	−0.865491	+	0.779291i
$399$	−13.2431	−	32.2363i	−0.662982	−	1.61383i
$400$	12.4622	+	3.66273i	0.623112	+	0.183137i
$401$	−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	$0.882653\pi$
$402$	11.1251	−	7.59859i	0.554872	−	0.378983i
$403$	0.0398109	+	0.0894166i	0.00198312	+	0.00445416i
$404$	3.57543	+	2.59770i	0.177884	+	0.129241i
$405$	9.09109	−	17.9542i	0.451740	−	0.892150i
$406$	15.9099	−	11.5592i	0.789595	−	0.573675i
$407$	−1.13834	−	0.657219i	−0.0564252	−	0.0325771i
$408$	−1.02682	−	0.0298752i	−0.0508353	−	0.00147904i
$409$	−1.96923	+	2.18705i	−0.0973722	+	0.108143i	−0.789861	−	0.613286i	$-0.789847\pi$
$409$	−1.96923	+	2.18705i	−0.0973722	+	0.108143i	0.692489	+	0.721428i	$0.256514\pi$
$410$	0.581723	−	15.2174i	0.0287292	−	0.751534i
$411$	−35.5423	+	2.69332i	−1.75317	+	0.132852i
$412$	0.0617137	−	0.290340i	0.00304041	−	0.0143040i
$413$	15.1497	−	4.92242i	0.745466	−	0.242216i
$414$	21.2754	+	1.23905i	1.04563	+	0.0608961i
$415$	−32.6932	+	2.17766i	−1.60484	+	0.106897i
$416$	0.479232	+	0.101864i	0.0234963	+	0.00499429i
$417$	0.749024	+	1.38914i	0.0366799	+	0.0680267i
$418$	−11.0113	+	6.35739i	−0.538581	+	0.310950i
$419$	5.57816	+	2.48356i	0.272511	+	0.121330i	0.538443	−	0.842662i	$-0.319013\pi$
$419$	5.57816	+	2.48356i	0.272511	+	0.121330i	−0.265932	+	0.963992i	$0.585680\pi$
$420$	5.29729	+	2.12475i	0.258481	+	0.103677i
$421$	1.22140	−	0.543804i	0.0595276	−	0.0265034i	−0.376757	−	0.926312i	$-0.622961\pi$
$421$	1.22140	−	0.543804i	0.0595276	−	0.0265034i	0.436285	+	0.899809i	$0.356294\pi$
$422$	−2.14561	+	2.95318i	−0.104447	+	0.143759i
$423$	−0.548625	−	0.360833i	−0.0266751	−	0.0175443i
$424$	−39.9443			−1.93987
$425$	0.506351	+	0.822368i	0.0245617	+	0.0398907i
$426$	2.84558	+	6.92672i	0.137869	+	0.335601i
$427$	−7.85962	−	36.9766i	−0.380354	−	1.78942i
$428$	−0.367289	−	0.0386036i	−0.0177536	−	0.00186598i
$429$	−0.380130	+	0.111399i	−0.0183528	+	0.00537838i
$430$	−18.1343	+	3.13586i	−0.874515	+	0.151225i
$431$	−26.8953	+	19.5406i	−1.29550	+	0.941237i	−0.999901	−	0.0140751i	$-0.995520\pi$
$431$	−26.8953	+	19.5406i	−1.29550	+	0.941237i	−0.295600	+	0.955312i	$0.595520\pi$
$432$	−8.12392	−	10.7807i	−0.390862	−	0.518685i
$433$	−6.84957	−	9.42763i	−0.329169	−	0.453063i	0.612070	−	0.790804i	$-0.290337\pi$
$433$	−6.84957	−	9.42763i	−0.329169	−	0.453063i	−0.941239	+	0.337741i	$0.890337\pi$
$434$	1.90002	+	0.403861i	0.0912037	+	0.0193859i
$435$	−14.5767	−	18.5608i	−0.698898	−	0.889922i
$436$	−7.52162	+	1.59877i	−0.360220	+	0.0765672i
$437$	−32.9138	−	29.6357i	−1.57448	−	1.41767i
$438$	−15.7064	−	18.4985i	−0.750482	−	0.883891i
$439$	−14.8478	−	16.4901i	−0.708646	−	0.787031i	0.276081	−	0.961134i	$-0.410964\pi$
$439$	−14.8478	−	16.4901i	−0.708646	−	0.787031i	−0.984727	+	0.174103i	$0.944297\pi$
$440$	2.36693	−	9.36144i	0.112839	−	0.446289i
$441$	−0.485961	−	0.251179i	−0.0231410	−	0.0119609i
$442$	−0.0222324	−	0.0306003i	−0.00105749	−	0.00145551i
$443$	−6.90522	−	3.98673i	−0.328077	−	0.189415i	0.326910	−	0.945055i	$-0.393993\pi$
$443$	−6.90522	−	3.98673i	−0.328077	−	0.189415i	−0.654987	+	0.755640i	$0.727326\pi$
$444$	−0.783537	+	0.422481i	−0.0371850	+	0.0200501i
$445$	−8.45396	+	22.9905i	−0.400756	+	1.08986i
$446$	−2.29318	+	21.8182i	−0.108585	+	1.03312i
$447$	−25.3737	+	26.5831i	−1.20013	+	1.25734i
$448$	17.5736	−	15.8234i	0.830276	−	0.747583i
$449$	19.4821			0.919419			0.459710	−	0.888069i	$-0.347953\pi$
$449$	19.4821			0.919419			0.459710	+	0.888069i	$0.347953\pi$
$450$	−6.09241	+	17.0047i	−0.287199	+	0.801608i
$451$	−7.95358			−0.374520
$452$	1.51324	−	1.36252i	0.0711767	−	0.0640878i
$453$	−8.97141	−	2.18144i	−0.421513	−	0.102493i
$454$	−1.06503	+	10.1331i	−0.0499843	+	0.475569i
$455$	0.265518	+	0.937646i	0.0124477	+	0.0439575i
$456$	−1.16126	+	39.9129i	−0.0543809	+	1.86909i
$457$	−15.0307	−	8.67800i	−0.703108	−	0.405940i	0.105396	−	0.994430i	$-0.466389\pi$
$457$	−15.0307	−	8.67800i	−0.703108	−	0.405940i	−0.808504	+	0.588491i	$0.799722\pi$
$458$	−6.92373	−	9.52970i	−0.323525	−	0.445293i
$459$	0.0874663	−	0.999823i	0.00408258	−	0.0466677i
$460$	7.23739	−	0.482076i	0.337445	−	0.0224769i
$461$	19.9699	+	22.1788i	0.930089	+	1.03297i	0.999374	+	0.0353718i	$0.0112616\pi$
$461$	19.9699	+	22.1788i	0.930089	+	1.03297i	−0.0692850	+	0.997597i	$0.522072\pi$
$462$	−2.64564	+	7.40261i	−0.123086	+	0.344401i
$463$	8.67871	+	7.81435i	0.403334	+	0.363163i	0.845689	−	0.533677i	$-0.179190\pi$
$463$	8.67871	+	7.81435i	0.403334	+	0.363163i	−0.442355	+	0.896840i	$0.645857\pi$
$464$	−15.4845	+	3.29133i	−0.718849	+	0.152796i
$465$	0.399012	−	2.29671i	0.0185038	−	0.106507i
$466$	−2.99853	−	0.637357i	−0.138904	−	0.0295250i
$467$	−8.44207	−	11.6195i	−0.390652	−	0.537687i	0.567715	−	0.823225i	$-0.307828\pi$
$467$	−8.44207	−	11.6195i	−0.390652	−	0.537687i	−0.958367	+	0.285538i	$0.907828\pi$
$468$	−0.0709367	+	0.258714i	−0.00327905	+	0.0119591i
$469$	−14.0048	+	10.1751i	−0.646680	+	0.469840i
$470$	0.528881	+	0.260118i	0.0243954	+	0.0119983i
$471$	−15.1877	−	14.4967i	−0.699814	−	0.667975i
$472$	−18.1509	−	1.90774i	−0.835465	−	0.0878109i
$473$	1.99841	+	9.40176i	0.0918868	+	0.432293i
$474$	28.1142	+	3.78447i	1.29133	+	0.173826i
$475$	31.9657	−	19.6821i	1.46669	−	0.903075i
$476$	0.284642			0.0130465
$477$	2.26899	−	38.9600i	0.103890	−	1.78386i
$478$	−7.46831	+	10.2792i	−0.341592	+	0.470162i
$479$	4.69795	−	2.09166i	0.214655	−	0.0955705i	−0.296592	−	0.955004i	$-0.595850\pi$
$479$	4.69795	−	2.09166i	0.214655	−	0.0955705i	0.511247	+	0.859434i	$0.329184\pi$
$480$	−8.12676	−	8.37321i	−0.370934	−	0.382183i
$481$	−0.138851	−	0.0618204i	−0.00633105	−	0.00281877i
$482$	3.20568	−	1.85080i	0.146015	−	0.0843016i
$483$	−27.3715	−	0.796369i	−1.24545	−	0.0362360i
$484$	4.85272	+	1.03148i	0.220578	+	0.0468854i
$485$	−2.57433	−	6.43278i	−0.116895	−	0.292098i
$486$	15.6232	−	10.4065i	0.708682	−	0.472048i
$487$	38.7356	−	12.5860i	1.75528	−	0.570324i	0.758584	−	0.651575i	$-0.225892\pi$
$487$	38.7356	−	12.5860i	1.75528	−	0.570324i	0.996694	+	0.0812511i	$0.0258916\pi$
$488$	−9.00514	+	42.3658i	−0.407643	+	1.91781i
$489$	−0.522266	−	0.764654i	−0.0236177	−	0.0345788i
$490$	0.460832	+	0.169455i	0.0208183	+	0.00765518i
$491$	26.8216	−	29.7884i	1.21044	−	1.34433i	0.288271	−	0.957549i	$-0.406920\pi$
$491$	26.8216	−	29.7884i	1.21044	−	1.34433i	0.922171	−	0.386783i	$-0.126414\pi$
$492$	−2.82774	+	4.58448i	−0.127484	+	0.206684i
$493$	−1.01930	−	0.588493i	−0.0459070	−	0.0265044i
$494$	−1.18945	+	0.864183i	−0.0535157	+	0.0388814i
$495$	8.99631	+	2.84037i	0.404354	+	0.127665i
$496$	−1.26501	−	0.919080i	−0.0568004	−	0.0412679i
$497$	−3.91359	−	8.79008i	−0.175549	−	0.394289i
$498$	−27.5473	−	13.2378i	−1.23443	−	0.593201i
$499$	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	$0.606342\pi$
$500$	−1.33772	+	6.00056i	−0.0598248	+	0.268353i
$501$	−18.7136	−	2.51904i	−0.836060	−	0.112543i
$502$	−21.3720	+	19.2434i	−0.953878	+	0.858875i
$503$	4.96862	−	6.83872i	0.221540	−	0.304923i	−0.683751	−	0.729715i	$-0.739653\pi$
$503$	4.96862	−	6.83872i	0.221540	−	0.304923i	0.905291	+	0.424792i	$0.139653\pi$
$504$	15.4245	+	19.2757i	0.687063	+	0.858610i
$505$	9.57377	−	15.2092i	0.426027	−	0.676803i
$506$	1.04428	+	9.93567i	0.0464240	+	0.441694i
$507$	20.7853	−	8.53885i	0.923106	−	0.379223i
$508$	−3.20072	+	7.18895i	−0.142009	+	0.318958i
$509$	8.40814	−	9.33819i	0.372684	−	0.413908i	−0.527404	−	0.849614i	$-0.676835\pi$
$509$	8.40814	−	9.33819i	0.372684	−	0.413908i	0.900089	+	0.435706i	$0.143501\pi$
$510$	0.0337052	+	0.900202i	0.00149249	+	0.0398616i
$511$	20.8640	+	23.1718i	0.922968	+	1.02506i
$512$	−22.6169	+	7.34868i	−0.999536	+	0.324769i
$513$	−38.8635	−	3.39985i	−1.71586	−	0.150107i
$514$	1.78380	−	5.48996i	0.0786799	−	0.242152i
$515$	−1.19472	−	0.171932i	−0.0526458	−	0.00757625i
$516$	6.12971	+	2.19072i	0.269846	+	0.0964409i
$517$	0.125204	−	0.281213i	0.00550647	−	0.0123677i
$518$	−2.61224	+	1.50818i	−0.114775	+	0.0662656i
$519$	15.4756	+	9.54544i	0.679303	+	0.418998i
$520$	0.159044	−	1.10516i	0.00697453	−	0.0484646i
$521$	15.5846	+	11.3229i	0.682773	+	0.496063i	0.874276	−	0.485429i	$-0.161336\pi$
$521$	15.5846	+	11.3229i	0.682773	+	0.496063i	−0.191504	+	0.981492i	$0.561336\pi$
$522$	−3.31729	−	21.7626i	−0.145194	−	0.952522i
$523$	24.3250	+	7.90367i	1.06366	+	0.345604i	0.788015	−	0.615656i	$-0.211109\pi$
$523$	24.3250	+	7.90367i	1.06366	+	0.345604i	0.275644	+	0.961260i	$0.411109\pi$
$524$	−3.21939	+	5.57615i	−0.140640	+	0.243595i
$525$	7.18941	−	22.0678i	0.313772	−	0.963118i
$526$	−14.0060	−	24.2591i	−0.610692	−	1.05775i
$527$	−0.0241709	−	0.113715i	−0.00105290	−	0.00495352i
$528$	4.36926	−	4.57752i	0.190148	−	0.199211i
$529$	−10.7798	+	4.79946i	−0.468685	+	0.208672i
$530$	2.32805	+	34.9509i	0.101124	+	1.51817i
$531$	2.89177	−	17.5953i	0.125492	−	0.763571i
$532$		−	11.0641i		−	0.479691i
$533$	−0.914651	+	0.0961337i	−0.0396179	+	0.00416401i
$534$	−17.4175	+	14.7886i	−0.753729	+	0.639966i
$535$	−0.0573678	+	1.50069i	−0.00248022	+	0.0648807i
$536$	19.4004	−	4.12368i	0.837970	−	0.178116i
$537$	8.03314	−	22.4770i	0.346656	−	0.969956i
$538$	2.10324	−	9.89496i	0.0906771	−	0.426602i
$539$	0.0792445	−	0.243890i	0.00341330	−	0.0105051i
$540$	4.83566	−	4.17568i	0.208094	−	0.179693i
$541$	−11.8581	−	36.4956i	−0.509821	−	1.56907i	−0.792511	−	0.609858i	$-0.791227\pi$
$541$	−11.8581	−	36.4956i	−0.509821	−	1.56907i	0.282690	−	0.959211i	$-0.408773\pi$
$542$	24.3833	−	2.56279i	1.04735	−	0.110081i
$543$	−10.0877	−	7.78726i	−0.432905	−	0.334183i
$544$	−0.531616	−	0.236690i	−0.0227928	−	0.0101480i
$545$	8.51977	+	30.0866i	0.364947	+	1.28877i
$546$	−0.214771	+	0.883268i	−0.00919135	+	0.0378004i
$547$	12.7170	+	28.5628i	0.543739	+	1.22126i	0.951353	+	0.308104i	$0.0996944\pi$
$547$	12.7170	+	28.5628i	0.543739	+	1.22126i	−0.407613	+	0.913155i	$0.633639\pi$
$548$	−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
$552$	28.2784	+	13.5892i	1.20361	+	0.578393i
$553$	−36.2502	−	3.81005i	−1.54151	−	0.162020i
$554$	−1.28468	+	12.2229i	−0.0545806	+	0.519300i
$555$	1.92596	+	3.06499i	0.0817526	+	0.130102i
$556$	0.0523732	+	0.498298i	0.00222112	+	0.0211325i
$557$		−	24.3166i		−	1.03033i	−0.857091	−	0.515165i	$-0.827731\pi$
$557$		−	24.3166i		−	1.03033i	0.857091	−	0.515165i	$-0.172269\pi$
$558$	1.37820	−	1.68185i	0.0583438	−	0.0711983i
$559$	0.343452	+	1.05704i	0.0145265	+	0.0447078i
$560$	−11.1630	−	10.8514i	−0.471721	−	0.458556i
$561$	0.469144	−	0.0355506i	0.0198073	−	0.00150095i
$562$	−20.9807	−	18.8911i	−0.885019	−	0.796874i
$563$	12.1037	+	10.8982i	0.510109	+	0.459304i	0.883541	−	0.468353i	$-0.155153\pi$
$563$	12.1037	+	10.8982i	0.510109	+	0.459304i	−0.373432	+	0.927657i	$0.621819\pi$
$564$	−0.117579	−	0.172148i	−0.00495095	−	0.00724873i
$565$	−5.93737	−	5.77166i	−0.249787	−	0.242816i
$566$	−6.03750	−	18.5815i	−0.253775	−	0.781039i
$567$	−19.6769	+	13.9495i	−0.826353	+	0.585824i
$568$			11.0243i			0.462569i
$569$	2.00198	+	19.0476i	0.0839276	+	0.798517i	0.952824	+	0.303523i	$0.0981631\pi$
$569$	2.00198	+	19.0476i	0.0839276	+	0.798517i	−0.868896	+	0.494994i	$0.835170\pi$
$570$	34.9912	−	1.31013i	1.46562	−	0.0548754i
$571$	−0.480995	+	4.57636i	−0.0201290	+	0.191515i	−0.999966	−	0.00828549i	$-0.997363\pi$
$571$	−0.480995	+	4.57636i	−0.0201290	+	0.191515i	0.979837	+	0.199800i	$0.0640293\pi$
$572$	−0.125068	−	0.0131452i	−0.00522935	−	0.000549627i
$573$	−0.145924	−	1.92568i	−0.00609606	−	0.0804466i
$574$	−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	−0.575429	−	0.817852i	$-0.695165\pi$
$577$	−36.5521	−	11.8765i	−1.52168	−	0.494425i	−0.946253	+	0.323427i	$0.895165\pi$
$578$	−8.30826	−	18.6606i	−0.345578	−	0.776181i
$579$	31.7515	+	30.3069i	1.31955	+	1.25951i
$580$	−2.04143	−	7.20907i	−0.0847657	−	0.299341i
$581$	35.8754	+	15.9728i	1.48836	+	0.662662i
$582$	0.862211	−	6.40522i	0.0357398	−	0.265505i
$583$	18.1945	−	1.91232i	0.753538	−	0.0792001i
$584$	−11.0397	−	33.9767i	−0.456826	−	1.40597i
$585$	1.06889	+	0.217902i	0.0441934	+	0.00900914i
$586$	1.19404	−	3.67487i	0.0493253	−	0.151808i
$587$	5.40305	−	25.4193i	0.223008	−	1.04917i	−0.714077	−	0.700067i	$-0.753153\pi$
$587$	5.40305	−	25.4193i	0.223008	−	1.04917i	0.937085	−	0.349102i	$-0.113513\pi$
$588$	−0.112405	−	0.132387i	−0.00463552	−	0.00545955i
$589$	−4.42015	+	0.939533i	−0.182129	+	0.0387128i
$590$	−0.611376	+	15.9931i	−0.0251700	+	0.658426i
$591$	26.0236	+	9.30066i	1.07047	+	0.382578i
$592$	2.41479	−	0.253805i	0.0992472	−	0.0104313i
$593$			32.5216i			1.33550i	0.744385	+	0.667750i	$0.232743\pi$
$593$			32.5216i			1.33550i	−0.744385	+	0.667750i	$0.767257\pi$
$594$	6.00153	+	6.43577i	0.246246	+	0.264063i
$595$	−0.0769285	−	1.15492i	−0.00315376	−	0.0473473i
$596$	−10.6582	+	4.74534i	−0.436577	+	0.194377i
$597$	−9.39824	−	32.0699i	−0.384644	−	1.31254i
$598$	0.240182	+	1.12997i	0.00982176	+	0.0462078i
$599$	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	$0.767715\pi$
$600$	−17.8091	+	19.7478i	−0.727052	+	0.806201i
$601$	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
$603$	2.92005	+	19.1566i	0.118914	+	0.780117i
$604$	−2.37137	−	1.72290i	−0.0964899	−	0.0701040i
$605$	2.87367	−	19.9685i	0.116831	−	0.811836i
$606$	14.7552	−	7.95599i	0.599390	−	0.323190i
$607$	−18.1063	+	10.4537i	−0.734910	+	0.424301i	−0.820216	−	0.572054i	$-0.806147\pi$
$607$	−18.1063	+	10.4537i	−0.734910	+	0.424301i	0.0853054	+	0.996355i	$0.472813\pi$
$608$	−9.20024	+	20.6641i	−0.373119	+	0.838039i
$609$	5.07382	+	27.8270i	0.205602	+	1.12761i
$610$	37.5946	+	5.41023i	1.52216	+	0.219054i
$611$	0.0109993	−	0.0338524i	0.000444985	−	0.00136952i
$612$	0.146303	−	0.283056i	0.00591395	−	0.0114419i
$613$	−3.43863	+	1.11728i	−0.138885	+	0.0451265i	−0.377635	−	0.925955i	$-0.623262\pi$
$613$	−3.43863	+	1.11728i	−0.138885	+	0.0451265i	0.238750	+	0.971081i	$0.423262\pi$
$614$	13.3171	+	14.7901i	0.537433	+	0.596880i
$615$	19.3656	+	10.2344i	0.780897	+	0.412692i
$616$	−7.74386	+	8.60043i	−0.312009	+	0.346521i
$617$	−2.39310	+	5.37500i	−0.0963427	+	0.216389i	−0.955287	−	0.295679i	$-0.904454\pi$
$617$	−2.39310	+	5.37500i	−0.0963427	+	0.216389i	0.858945	+	0.512069i	$0.171121\pi$
$618$	−0.891232	−	0.687991i	−0.0358506	−	0.0276751i
$619$	2.88523	+	27.4512i	0.115967	+	1.10336i	0.885465	+	0.464706i	$0.153840\pi$
$619$	2.88523	+	27.4512i	0.115967	+	1.10336i	−0.769498	+	0.638649i	$0.779493\pi$
$620$	0.394247	−	0.626315i	0.0158333	−	0.0251534i
$621$	−14.8606	+	26.8097i	−0.596336	+	1.07584i
$622$	−13.3102	+	18.3199i	−0.533689	+	0.734559i
$623$	21.8177	−	19.6448i	0.874109	−	0.787051i
$624$	0.447131	−	0.579219i	0.0178996	−	0.0231873i
$625$	24.7086	+	3.80603i	0.988343	+	0.152241i
$626$	−1.90382	−	3.29752i	−0.0760921	−	0.131795i
$627$	−1.38187	−	18.2358i	−0.0551864	−	0.728267i
$628$	−2.71115	−	6.08935i	−0.108187	−	0.242991i
$629$	0.146050	+	0.106112i	0.00582340	+	0.00423095i
$630$	15.9671	−	14.6198i	0.636146	−	0.582465i
$631$	−5.50355	+	3.99857i	−0.219093	+	0.159180i	−0.691918	−	0.721976i	$-0.743234\pi$
$631$	−5.50355	+	3.99857i	−0.219093	+	0.159180i	0.472825	+	0.881156i	$0.343234\pi$
$632$	36.1672	+	20.8811i	1.43865	+	0.830607i
$633$	−2.49185	−	4.62139i	−0.0990420	−	0.183684i
$634$	0.323200	−	0.358950i	0.0128359	−	0.0142557i
$635$	30.0339	+	11.0439i	1.19186	+	0.438264i
$636$	5.36641	−	11.1673i	0.212792	−	0.442811i
$637$	0.00616516	−	0.0290048i	0.000244272	−	0.00114921i
$638$	9.81466	−	3.18898i	0.388566	−	0.126253i
$639$	−10.7526	−	0.626222i	−0.425368	−	0.0247729i
$640$	3.82171	+	9.54974i	0.151066	+	0.377486i
$641$	−1.85596	−	0.394497i	−0.0733060	−	0.0155817i	0.171113	−	0.985251i	$-0.445264\pi$
$641$	−1.85596	−	0.394497i	−0.0733060	−	0.0155817i	−0.244419	+	0.969670i	$0.578597\pi$
$642$	−0.735402	+	1.19227i	−0.0290240	+	0.0470553i
$643$	13.7142	−	7.91791i	0.540836	−	0.312252i	−0.204581	−	0.978850i	$-0.565583\pi$
$643$	13.7142	−	7.91791i	0.540836	−	0.312252i	0.745418	+	0.666598i	$0.232250\pi$
$644$	−7.94185	−	3.53594i	−0.312953	−	0.139335i
$645$	7.23211	−	25.4632i	0.284764	−	1.00261i
$646$	1.59530	−	0.710275i	0.0627664	−	0.0279454i
$647$	−1.30998	+	1.80303i	−0.0515007	+	0.0708846i	−0.833991	−	0.551779i	$-0.813949\pi$
$647$	−1.30998	+	1.80303i	−0.0515007	+	0.0708846i	0.782490	+	0.622663i	$0.213949\pi$
$648$	27.0964	−	5.43104i	1.06445	−	0.213351i
$649$	8.35902			0.328120
$650$	−0.976276	−	0.0747504i	−0.0382927	−	0.00293195i
$651$	−1.70726	+	2.21160i	−0.0669127	+	0.0866795i
$652$	−0.0611215	−	0.287554i	−0.00239370	−	0.0112615i
$653$	−1.00426	−	0.105552i	−0.0392999	−	0.00413058i	0.0848581	−	0.996393i	$-0.472956\pi$
$653$	−1.00426	−	0.105552i	−0.0392999	−	0.00413058i	−0.124158	+	0.992262i	$0.539623\pi$
$654$	−6.89144	+	28.3418i	−0.269477	+	1.10825i
$655$	23.4951	+	11.5555i	0.918030	+	0.451512i
$656$	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
$659$	−14.3529	−	3.05080i	−0.559109	−	0.118842i	−0.0803150	−	0.996770i	$-0.525593\pi$
$659$	−14.3529	−	3.05080i	−0.559109	−	0.118842i	−0.478794	+	0.877927i	$0.658926\pi$
$660$	2.29920	+	1.91941i	0.0894960	+	0.0747129i
$661$	−30.9764	+	6.58425i	−1.20484	+	0.256098i	−0.766223	−	0.642575i	$-0.777866\pi$
$661$	−30.9764	+	6.58425i	−1.20484	+	0.256098i	−0.438621	+	0.898672i	$0.644533\pi$
$662$	−21.6322	−	19.4777i	−0.840760	−	0.757024i
$663$	0.0535212	−	0.00975874i	0.00207859	−	0.000378998i
$664$	−30.1069	−	33.4371i	−1.16837	−	1.29761i
$665$	−44.8923	+	2.99024i	−1.74085	+	0.115956i
$666$	0.157109	+	3.37288i	0.00608787	+	0.130696i
$667$	21.1292	+	29.0818i	0.818126	+	1.12605i
$668$	−5.19152	−	2.99733i	−0.200866	−	0.115970i
$669$	−26.8567	−	16.5654i	−1.03834	−	0.640455i
$670$	−4.73889	−	16.7349i	−0.183079	−	0.646524i
$671$	2.07356	−	19.7286i	0.0800488	−	0.761614i
$672$	3.93298	+	13.4207i	0.151718	+	0.517713i
$673$	−30.0916	+	27.0946i	−1.15995	+	1.04442i	−0.161605	+	0.986856i	$0.551667\pi$
$673$	−30.0916	+	27.0946i	−1.15995	+	1.04442i	−0.998342	+	0.0575650i	$0.981666\pi$
$674$	40.2134			1.54896
$675$	−18.2496	−	18.4920i	−0.702426	−	0.711757i
$676$	7.13392			0.274381
$677$	1.87592	−	1.68909i	0.0720975	−	0.0649169i	−0.632294	−	0.774728i	$-0.717887\pi$
$677$	1.87592	−	1.68909i	0.0720975	−	0.0649169i	0.704392	+	0.709812i	$0.251220\pi$
$678$	−2.17212	−	7.41200i	−0.0834198	−	0.284656i
$679$	−0.868038	+	8.25883i	−0.0333123	+	0.316945i
$680$	−0.457694	+	1.24470i	−0.0175518	+	0.0477320i
$681$	−12.4731	−	7.69350i	−0.477971	−	0.294816i
$682$	0.882759	+	0.509661i	0.0338026	+	0.0195159i
$683$	12.8169	+	17.6409i	0.490425	+	0.675012i	0.980466	−	0.196687i	$-0.0630184\pi$
$683$	12.8169	+	17.6409i	0.490425	+	0.675012i	−0.490042	+	0.871699i	$0.663018\pi$
$684$	−11.0025	−	5.68685i	−0.420690	−	0.217442i
$685$	−11.2798	+	44.6126i	−0.430978	+	1.70456i
$686$	14.7225	+	16.3510i	0.562107	+	0.624283i
$687$	16.6678	−	3.03911i	0.635916	−	0.115949i
$688$	−13.1948	−	11.8807i	−0.503048	−	0.452946i
$689$	2.06923	−	0.439828i	0.0788312	−	0.0167561i
$690$	10.2423	−	25.5354i	0.389916	−	0.972116i
$691$	−12.5345	−	2.66428i	−0.476833	−	0.101354i	−0.0367757	−	0.999324i	$-0.511709\pi$
$691$	−12.5345	−	2.66428i	−0.476833	−	0.101354i	−0.440058	+	0.897969i	$0.645042\pi$
$692$	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
$695$	2.00767	−	0.347174i	0.0761552	−	0.0131691i
$696$	7.65715	−	31.4908i	0.290244	−	1.19366i
$697$	1.08638	+	0.114183i	0.0411496	+	0.00432500i
$698$	4.34516	+	20.4424i	0.164467	+	0.773756i
$699$	2.69432	−	3.49026i	0.101909	−	0.132014i
$700$	4.77348	−	5.61311i	0.180421	−	0.212155i
$701$	48.5879			1.83514			0.917569	−	0.397577i	$-0.130149\pi$
$701$	48.5879			1.83514			0.917569	+	0.397577i	$0.130149\pi$
$702$	0.767956	+	0.667565i	0.0289846	+	0.0251956i
$703$	4.12460	−	5.67702i	0.155562	−	0.214113i
$704$	11.3364	−	5.04731i	0.427258	−	0.190228i
$705$	−0.666706	+	0.523596i	−0.0251096	+	0.0197198i
$706$	−6.07742	−	2.70584i	−0.228727	−	0.101836i
$707$	−18.6537	+	10.7697i	−0.701545	+	0.405037i
$708$	2.97188	−	4.81818i	0.111690	−	0.181078i
$709$	7.36006	+	1.56443i	0.276413	+	0.0587533i	0.344032	−	0.938958i	$-0.388207\pi$
$709$	7.36006	+	1.56443i	0.276413	+	0.0587533i	−0.0676195	+	0.997711i	$0.521540\pi$
$710$	9.64617	−	0.642523i	0.362014	−	0.0241135i
$711$	−22.4210	+	34.0899i	−0.840855	+	1.27847i
$712$	−31.9912	+	10.3946i	−1.19892	+	0.389554i
$713$	−0.738220	+	3.47305i	−0.0276466	+	0.130067i
$714$	0.467642	−	0.973141i	0.0175010	−	0.0364189i
$715$	−0.0195347	+	0.511011i	−0.000730555	+	0.0191107i
$716$	5.07062	−	5.63149i	0.189498	−	0.210459i
$717$	−8.67346	−	16.0858i	−0.323916	−	0.600737i
$718$	−14.5199	−	8.38310i	−0.541880	−	0.312854i
$719$	−35.5528	+	25.8307i	−1.32590	+	0.963321i	−0.326059	+	0.945349i	$0.605721\pi$
$719$	−35.5528	+	25.8307i	−1.32590	+	0.963321i	−0.999839	+	0.0179714i	$0.994279\pi$
$720$	−16.5286	+	5.52325i	−0.615985	+	0.205839i
$721$	1.17037	+	0.850325i	0.0435869	+	0.0316678i
$722$	−18.3025	−	41.1082i	−0.681150	−	1.52989i
$723$	0.402297	+	5.30891i	0.0149616	+	0.197440i
$724$	−2.02291	−	3.50378i	−0.0751807	−	0.130217i
$725$	−28.6988	+	10.2314i	−1.06585	+	0.379984i
$726$	11.4990	−	14.8960i	0.426770	−	0.552842i
$727$	−27.6361	+	24.8837i	−1.02497	+	0.922884i	−0.997052	−	0.0767266i	$-0.975553\pi$
$727$	−27.6361	+	24.8837i	−1.02497	+	0.922884i	−0.0279140	+	0.999610i	$0.508886\pi$
$728$	−0.786582	+	1.08264i	−0.0291527	+	0.0401252i
$729$	3.75804	+	26.7372i	0.139186	+	0.990266i
$730$	−29.0859	+	11.6399i	−1.07652	+	0.430811i
$731$	−0.137989	−	1.31288i	−0.00510370	−	0.0485585i
$732$	−10.6344	−	8.20931i	−0.393060	−	0.303425i
$733$	2.24663	−	5.04602i	0.0829813	−	0.186379i	−0.867289	−	0.497804i	$-0.834140\pi$
$733$	2.24663	−	5.04602i	0.0829813	−	0.186379i	0.950271	+	0.311425i	$0.100806\pi$
$734$	29.5618	−	32.8317i	1.09115	−	1.21184i
$735$	−0.506776	+	0.491860i	−0.0186927	+	0.0181425i
$736$	11.8924	+	13.2079i	0.438361	+	0.486849i
$737$	−8.63939	+	2.80711i	−0.318236	+	0.103401i
$738$	11.0278	+	17.1994i	0.405940	+	0.633120i
$739$	13.0729	−	40.2342i	0.480894	−	1.48004i	−0.356946	−	0.934125i	$-0.616182\pi$
$739$	13.0729	−	40.2342i	0.480894	−	1.48004i	0.837840	−	0.545915i	$-0.183818\pi$
$740$	0.195821	+	1.13241i	0.00719852	+	0.0416282i
$741$	−0.379326	−	2.08039i	−0.0139349	−	0.0764249i
$742$	17.0758	−	38.3529i	0.626873	−	1.40798i
$743$	−16.0074	+	9.24189i	−0.587256	+	0.339052i	−0.764012	−	0.645203i	$-0.776773\pi$
$743$	−16.0074	+	9.24189i	−0.587256	+	0.339052i	0.176756	+	0.984255i	$0.443440\pi$
$744$	2.81762	−	1.51925i	0.103299	−	0.0556985i
$745$	22.1346	+	41.9628i	0.810947	+	1.53740i
$746$	−18.2228	−	13.2397i	−0.667186	−	0.484739i
$747$	34.3233	−	27.4657i	1.25583	−	1.00492i
$748$	0.142057	+	0.0461573i	0.00519413	+	0.00168768i
$749$	0.899969	−	1.55879i	0.0328841	−	0.0569570i
$750$	18.3171	+	14.4318i	0.668846	+	0.526976i
$751$	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	$0.680754\pi$
$752$	0.118225	+	0.556205i	0.00431122	+	0.0202827i
$753$	−11.6329	−	39.6953i	−0.423926	−	1.44658i
$754$	1.09013	−	0.485356i	0.0397001	−	0.0176756i
$755$	−6.34972	+	10.0874i	−0.231090	+	0.367118i
$756$	−7.46118	+	1.72260i	−0.271360	+	0.0626504i
$757$			14.6646i			0.532993i	0.963836	+	0.266497i	$0.0858661\pi$
$757$			14.6646i			0.532993i	−0.963836	+	0.266497i	$0.914134\pi$
$758$	2.29173	−	0.240870i	0.0832393	−	0.00874880i
$759$	−13.5313	−	4.83599i	−0.491155	−	0.175535i
$760$	48.3819	+	17.7907i	1.75500	+	0.645338i
$761$	−9.76945	+	2.07656i	−0.354142	+	0.0752752i	−0.381548	−	0.924349i	$-0.624609\pi$
$761$	−9.76945	+	2.07656i	−0.354142	+	0.0752752i	0.0274055	+	0.999624i	$0.491275\pi$
$762$	19.3193	+	22.7535i	0.699863	+	0.824273i
$763$	7.79202	−	36.6586i	0.282090	−	1.32713i
$764$	0.189461	−	0.583100i	0.00685444	−	0.0210958i
$765$	−1.18803	−	0.517119i	−0.0429533	−	0.0186965i
$766$	3.59450	+	11.0627i	0.129875	+	0.399713i
$767$	0.961275	−	0.101034i	0.0347096	−	0.00364813i
$768$	2.79780	−	20.7844i	0.100957	−	0.749993i
$769$	−16.8890	−	7.51947i	−0.609033	−	0.271159i	0.0789582	−	0.996878i	$-0.474841\pi$
$769$	−16.8890	−	7.51947i	−0.609033	−	0.271159i	−0.687991	+	0.725719i	$0.741507\pi$
$770$	7.97663	+	6.27456i	0.287458	+	0.226119i
$771$	6.00596	+	5.73271i	0.216299	+	0.206459i
$772$	5.66794	+	12.7304i	0.203994	+	0.458177i
$773$	3.41227	+	1.10871i	0.122731	+	0.0398777i	0.369739	−	0.929136i	$-0.379447\pi$
$773$	3.41227	+	1.10871i	0.122731	+	0.0398777i	−0.247008	+	0.969014i	$0.579447\pi$
$774$	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
$777$	−0.327823	−	4.32612i	−0.0117606	−	0.155199i
$778$	27.3695	+	2.87666i	0.981246	+	0.103133i
$779$	4.43834	−	42.2280i	0.159020	−	1.51297i
$780$	0.287604	+	0.192940i	0.0102979	+	0.00690834i
$781$	−0.527784	−	5.02153i	−0.0188856	−	0.179684i
$782$		−	1.37211i		−	0.0490664i
$783$	30.2799	+	9.25727i	1.08211	+	0.330828i
$784$	0.146384	+	0.450524i	0.00522801	+	0.0160902i
$785$	−23.9746	+	12.6461i	−0.855689	+	0.451360i
$786$	13.7747	+	20.1677i	0.491328	+	0.719357i
$787$	12.0214	+	10.8241i	0.428517	+	0.385839i	0.854975	−	0.518669i	$-0.173572\pi$
$787$	12.0214	+	10.8241i	0.428517	+	0.385839i	−0.426458	+	0.904507i	$0.640239\pi$
$788$	6.52007	+	5.87069i	0.232268	+	0.209135i
$789$	40.1754	−	3.04440i	1.43028	−	0.108384i
$790$	16.1629	−	32.8630i	0.575050	−	1.16921i
$791$	3.06676	+	9.43852i	0.109041	+	0.335595i
$792$	4.57224	+	12.1213i	0.162468	+	0.430710i
$793$		−	2.29382i		−	0.0814561i
$794$	−1.20797	−	11.4931i	−0.0428692	−	0.407874i
$795$	−46.7611	−	18.7559i	−1.65845	−	0.665203i
$796$	1.10900	−	10.5514i	0.0393075	−	0.373986i
$797$	18.9150	+	1.98804i	0.670003	+	0.0704202i	0.433421	−	0.901191i	$-0.357306\pi$
$797$	18.9150	+	1.98804i	0.670003	+	0.0704202i	0.236582	+	0.971612i	$0.423973\pi$
$798$	−37.8264	−	18.1774i	−1.33904	−	0.643473i
$799$	−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
$803$	6.65515	+	14.9477i	0.234855	+	0.527494i
$804$	−1.45353	+	5.97780i	−0.0512621	+	0.210821i
$805$	−12.2005	+	33.1794i	−0.430013	+	1.16942i
$806$	0.107676	+	0.0479406i	0.00379274	+	0.00168863i
$807$	11.5176	+	8.89111i	0.405440	+	0.312982i
$808$	24.5436	−	2.57963i	0.863440	−	0.0907512i
$809$	3.06508	+	9.43335i	0.107763	+	0.331659i	0.990369	−	0.138454i	$-0.0442133\pi$
$809$	3.06508	+	9.43335i	0.107763	+	0.331659i	−0.882606	+	0.470113i	$0.844213\pi$
$810$	−6.33136	−	23.3926i	−0.222461	−	0.821931i
$811$	8.46694	−	26.0585i	0.297314	−	0.915039i	−0.685120	−	0.728430i	$-0.740250\pi$
$811$	8.46694	−	26.0585i	0.297314	−	0.915039i	0.982434	−	0.186609i	$-0.0597498\pi$
$812$	−1.86705	+	8.78379i	−0.0655207	+	0.308250i
$813$	−11.8681	+	33.2074i	−0.416232	+	1.16463i
$814$	−1.54827	+	0.329094i	−0.0542668	+	0.0115348i
$815$	−1.15022	+	0.325714i	−0.0402905	+	0.0114092i
$816$	−0.662513	+	0.562518i	−0.0231926	+	0.0196921i
$817$	−51.0320	+	5.36368i	−1.78538	+	0.187651i
$818$			3.54395i			0.123911i
$819$	−1.01128	−	0.828697i	−0.0353369	−	0.0289570i
$820$	4.45223	+	5.34169i	0.155479	+	0.186540i
$821$	−8.76982	+	3.90458i	−0.306069	+	0.136271i	−0.554024	−	0.832501i	$-0.686908\pi$
$821$	−8.76982	+	3.90458i	−0.306069	+	0.136271i	0.247955	+	0.968772i	$0.420242\pi$
$822$	−29.6367	+	31.0493i	−1.03370	+	1.08297i
$823$	−7.15784	−	33.6750i	−0.249507	−	1.17384i	−0.907249	−	0.420594i	$-0.861822\pi$
$823$	−7.15784	−	33.6750i	−0.249507	−	1.17384i	0.657742	−	0.753243i	$-0.271512\pi$
$824$	−0.828753	−	1.43544i	−0.0288710	−	0.0500060i
$825$	7.16655	−	9.84765i	0.249507	−	0.342851i
$826$	9.59109	−	16.6123i	0.333717	−	0.578014i
$827$	25.3249	+	8.22855i	0.880632	+	0.286135i	0.714220	−	0.699922i	$-0.246782\pi$
$827$	25.3249	+	8.22855i	0.880632	+	0.286135i	0.166412	+	0.986056i	$0.446782\pi$
$828$	−7.59826	+	6.08016i	−0.264058	+	0.211300i
$829$	28.0528	+	20.3815i	0.974314	+	0.707880i	0.956431	−	0.291960i	$-0.0943073\pi$
$829$	28.0528	+	20.3815i	0.974314	+	0.707880i	0.0178831	+	0.999840i	$0.494307\pi$
$830$	−27.5025	+	28.2921i	−0.954625	+	0.982032i
$831$	−15.0455	−	9.28017i	−0.521924	−	0.321926i
$832$	1.24267	−	0.717456i	0.0430818	−	0.0248733i
$833$	−0.0143253	+	0.0321752i	−0.000496344	+	0.00111481i
$834$	1.78964	+	0.639604i	0.0619701	+	0.0221477i
$835$	−10.7585	+	21.8745i	−0.372312	+	0.756998i
$836$	1.79415	−	5.52182i	0.0620519	−	0.190976i
$837$	1.32177	+	2.83448i	0.0456869	+	0.0979741i
$838$	6.99309	−	2.27219i	0.241572	−	0.0784916i
$839$	3.14488	+	3.49274i	0.108573	+	0.120583i	0.794982	−	0.606633i	$-0.207480\pi$
$839$	3.14488	+	3.49274i	0.108573	+	0.120583i	−0.686408	+	0.727216i	$0.740814\pi$
$840$	29.9217	−	10.9760i	1.03240	−	0.378708i
$841$	5.44148	−	6.04337i	0.187637	−	0.208392i
$842$	0.654854	−	1.47083i	0.0225677	−	0.0506880i
$843$	37.5614	−	15.4307i	1.29368	−	0.531461i
$844$	−0.174235	−	1.65773i	−0.00599740	−	0.0570614i
$845$	−1.92804	−	28.9456i	−0.0663267	−	0.995759i
$846$	−0.781715	+	0.119157i	−0.0268759	+	0.00409672i
$847$	−14.2123	+	19.5615i	−0.488340	+	0.672142i
$848$	−25.1144	+	22.6132i	−0.862434	+	0.776539i
$849$	27.8506	+	3.74898i	0.955829	+	0.128665i
$850$	1.11578	+	0.327934i	0.0382708	+	0.0112480i
$851$	−2.75681	−	4.77494i	−0.0945023	−	0.163683i
$852$	−3.08207	−	1.48109i	−0.105590	−	0.0507412i
$853$	−7.63819	−	17.1556i	−0.261527	−	0.587398i	0.734284	−	0.678843i	$-0.237518\pi$
$853$	−7.63819	−	17.1556i	−0.261527	−	0.587398i	−0.995810	+	0.0914446i	$0.970852\pi$
$854$	−36.8283	−	26.7574i	−1.26024	−	0.915618i
$855$	−20.1006	+	46.1791i	−0.687426	+	1.57929i
$856$	−1.66841	+	1.21217i	−0.0570252	+	0.0414312i
$857$	−28.3893	−	16.3906i	−0.969759	−	0.559891i	−0.0705962	−	0.997505i	$-0.522490\pi$
$857$	−28.3893	−	16.3906i	−0.969759	−	0.559891i	−0.899163	+	0.437614i	$0.855824\pi$
$858$	−0.250417	+	0.405989i	−0.00854908	+	0.0138602i
$859$	6.34105	−	7.04245i	0.216354	−	0.240285i	−0.625192	−	0.780471i	$-0.714979\pi$
$859$	6.34105	−	7.04245i	0.216354	−	0.240285i	0.841546	+	0.540186i	$0.181646\pi$
$860$	5.19563	−	6.60503i	0.177170	−	0.225230i
$861$	−14.8064	−	21.6782i	−0.504602	−	0.738791i
$862$	−8.32337	+	39.1584i	−0.283495	+	1.33374i
$863$	−32.4083	+	10.5301i	−1.10319	+	0.358449i	−0.803330	−	0.595534i	$-0.796941\pi$
$863$	−32.4083	+	10.5301i	−1.10319	+	0.358449i	−0.299862	+	0.953983i	$0.596941\pi$
$864$	15.3674	+	2.98701i	0.522809	+	0.101620i
$865$	18.0316	−	15.0291i	0.613094	−	0.511006i
$866$	−13.7262	−	2.91760i	−0.466436	−	0.0991440i
$867$	29.3678	+	0.854450i	0.997383	+	0.0290186i
$868$	−0.768158	+	0.443496i	−0.0260730	+	0.0150532i
$869$	−17.4737	−	7.77979i	−0.592754	−	0.263911i
$870$	−28.0005	−	4.86458i	−0.949305	−	0.164925i
$871$	−0.959589	+	0.427237i	−0.0325144	+	0.0144764i
$872$	−25.2394	+	34.7390i	−0.854712	+	1.17641i
$873$	7.76665	+	5.10816i	0.262861	+	0.172885i
$874$	−53.3342			−1.80406
$875$	−24.0651	−	17.8512i	−0.813548	−	0.603481i
$876$	10.9820	+	1.47830i	0.371049	+	0.0499471i
$877$	5.61830	+	26.4320i	0.189716	+	0.892546i	0.965268	+	0.261262i	$0.0841385\pi$
$877$	5.61830	+	26.4320i	0.189716	+	0.892546i	−0.775552	+	0.631284i	$0.782528\pi$
$878$	−26.5746	−	2.79310i	−0.896849	−	0.0942627i
$879$	4.02028	+	3.83737i	0.135601	+	0.129431i
$880$	−3.81149	−	7.22584i	−0.128485	−	0.243583i
$881$	44.5745	−	32.3853i	1.50175	−	1.09109i	0.532078	−	0.846695i	$-0.321411\pi$
$881$	44.5745	−	32.3853i	1.50175	−	1.09109i	0.969676	−	0.244393i	$-0.0785886\pi$
$882$	−0.637280	+	0.166794i	−0.0214583	+	0.00561625i
$883$	23.9914	+	33.0214i	0.807376	+	1.11126i	0.991723	+	0.128396i	$0.0409829\pi$
$883$	23.9914	+	33.0214i	0.807376	+	1.11126i	−0.184347	+	0.982861i	$0.559017\pi$
$884$	0.0168943	+	0.00359100i	0.000568217	+	0.000120778i
$885$	−20.3528	−	10.7561i	−0.684151	−	0.361563i
$886$	−9.39189	+	1.99631i	−0.315527	+	0.0670673i
$887$	21.7243	+	19.5606i	0.729430	+	0.656782i	0.947720	−	0.319102i	$-0.103381\pi$
$887$	21.7243	+	19.5606i	0.729430	+	0.656782i	−0.218290	+	0.975884i	$0.570048\pi$
$888$	−1.67292	+	4.68088i	−0.0561394	+	0.157080i
$889$	−25.6632	−	28.5018i	−0.860714	−	0.955920i
$890$	10.9597	+	27.3862i	0.367370	+	0.917989i
$891$	−12.0823	+	3.77104i	−0.404772	+	0.126335i
$892$	−5.88831	−	8.10456i	−0.197155	−	0.271361i
$893$	1.42318	+	0.821672i	0.0476248	+	0.0274962i
$894$	−1.28700	+	44.2347i	−0.0430437	+	1.47943i
$895$	−24.2200	−	19.0519i	−0.809585	−	0.636834i
$896$	1.28864	−	12.2606i	0.0430504	−	0.409598i
$897$	−1.61453	−	0.392582i	−0.0539076	−	0.0131079i
$898$	17.4346	−	15.6982i	0.581800	−	0.523855i
$899$	3.66769			0.122324
$900$	−3.12831	−	7.63196i	−0.104277	−	0.254399i
$901$	−2.51264			−0.0837081
$902$	−7.11767	+	6.40878i	−0.236993	+	0.213389i
$903$	−21.9051	+	22.9492i	−0.728956	+	0.763701i
$904$	1.18856	−	11.3084i	0.0395309	−	0.376111i
$905$	−13.6697	+	9.15482i	−0.454397	+	0.304316i
$906$	−9.78627	+	5.27674i	−0.325127	+	0.175308i
$907$	−26.5281	−	15.3160i	−0.880851	−	0.508560i	−0.00991216	−	0.999951i	$-0.503155\pi$
$907$	−26.5281	−	15.3160i	−0.880851	−	0.508560i	−0.870939	+	0.491391i	$0.836489\pi$
$908$	−2.73472	−	3.76402i	−0.0907548	−	0.124913i
$909$	1.12190	+	24.0853i	0.0372111	+	0.798859i
$910$	0.993142	+	0.625153i	0.0329223	+	0.0207236i
$911$	−6.81616	−	7.57012i	−0.225830	−	0.250809i	0.619573	−	0.784939i	$-0.287306\pi$
$911$	−6.81616	−	7.57012i	−0.225830	−	0.250809i	−0.845402	+	0.534130i	$0.820639\pi$
$912$	21.8653	+	25.7521i	0.724031	+	0.852738i
$913$	15.3144	+	13.7891i	0.506831	+	0.456353i
$914$	−20.4435	+	4.34541i	−0.676212	+	0.143733i
$915$	−30.4349	+	45.3675i	−1.00615	+	1.49980i
$916$	5.26130	+	1.11832i	0.173838	+	0.0369505i
$917$	−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	−0.164862	−	0.986317i	$-0.552718\pi$
$919$	21.8946	−	15.9074i	0.722236	−	0.524735i	0.887098	+	0.461581i	$0.152718\pi$
$920$	28.2324	−	29.0429i	0.930794	−	0.957517i
$921$	−27.4704	+	8.05034i	−0.905182	+	0.265268i
$922$	35.7421	+	3.75665i	1.17710	+	0.123719i
$923$	−0.121389	−	0.571089i	−0.00399556	−	0.0187976i
$924$	−1.36406	−	3.32040i	−0.0448744	−	0.109233i
$925$	4.54179	−	1.10059i	0.149333	−	0.0361871i
$926$	14.0632			0.462145
$927$	1.44715	−	0.726793i	0.0475305	−	0.0238710i
$928$	10.7911	−	14.8526i	0.354234	−	0.487562i
$929$	−18.6446	+	8.30111i	−0.611709	+	0.272351i	−0.689118	−	0.724649i	$-0.742002\pi$
$929$	−18.6446	+	8.30111i	−0.611709	+	0.272351i	0.0774089	+	0.996999i	$0.475335\pi$
$930$	−1.49355	−	2.37684i	−0.0489755	−	0.0779398i
$931$	1.25066	+	0.556831i	0.0409888	+	0.0182494i
$932$	1.21228	−	0.699908i	0.0397094	−	0.0229262i
$933$	−15.4580	−	28.6685i	−0.506072	−	0.938564i
$934$	−16.9175	−	3.59593i	−0.553558	−	0.117662i
$935$	0.148888	−	0.588867i	0.00486917	−	0.0192580i
$936$	0.672310	+	1.33866i	0.0219751	+	0.0437556i
$937$	19.4195	−	6.30978i	0.634408	−	0.206132i	0.0258811	−	0.999665i	$-0.491761\pi$
$937$	19.4195	−	6.30978i	0.634408	−	0.206132i	0.608527	+	0.793533i	$0.291761\pi$
$938$	−4.33410	+	20.3903i	−0.141513	+	0.665768i
$939$	5.46100	−	0.413822i	0.178213	−	0.0135046i
$940$	−0.258951	+	0.0733284i	−0.00844605	+	0.00239171i
$941$	−0.394588	+	0.438234i	−0.0128632	+	0.0142860i	−0.749542	−	0.661957i	$-0.769726\pi$
$941$	−0.394588	+	0.438234i	−0.0128632	+	0.0142860i	0.736679	+	0.676243i	$0.236393\pi$
$942$	−25.2726	−	0.735301i	−0.823426	−	0.0239574i
$943$	−28.8929	−	16.6813i	−0.940881	−	0.543218i
$944$	−12.4922	+	9.07609i	−0.406585	+	0.295402i
$945$	9.00588	+	29.8079i	0.292961	+	0.969651i
$946$	9.36406	+	6.80339i	0.304452	+	0.221197i
$947$	−10.9735	−	24.6470i	−0.356592	−	0.800919i	−0.999391	−	0.0348845i	$-0.988894\pi$
$947$	−10.9735	−	24.6470i	−0.356592	−	0.800919i	0.642799	−	0.766035i	$-0.277773\pi$
$948$	−10.6967	+	7.30597i	−0.347414	+	0.237287i
$949$	0.946005	+	1.63853i	0.0307086	+	0.0531889i
$950$	12.7469	−	43.3706i	0.413565	−	1.40713i
$951$	0.263997	+	0.642621i	0.00856068	+	0.0208384i
$952$	1.18120	−	1.06356i	0.0382830	−	0.0344702i
$953$	−10.0812	+	13.8756i	−0.326563	+	0.449475i	−0.940457	−	0.339913i	$-0.889602\pi$
$953$	−10.0812	+	13.8756i	−0.326563	+	0.449475i	0.613894	+	0.789388i	$0.289602\pi$
$954$	−29.3624	−	36.6937i	−0.950643	−	1.18800i
$955$	−2.41711	−	0.611139i	−0.0782159	−	0.0197760i
$956$	−0.606465	−	5.77012i	−0.0196145	−	0.186619i
$957$	−1.98019	+	14.7105i	−0.0640106	+	0.475524i
$958$	2.51880	−	5.65731i	0.0813786	−	0.182779i
$959$	36.9039	−	40.9860i	1.19169	−	1.32351i
$960$	−34.0970	−	2.29804i	−1.10048	−	0.0741690i
$961$	−20.5006	−	22.7683i	−0.661311	−	0.734460i
$962$	−0.174071	+	0.0565591i	−0.00561227	+	0.00182354i
$963$	−1.08753	−	1.69616i	−0.0350452	−	0.0546579i
$964$	−0.522323	+	1.60755i	−0.0168229	+	0.0517756i
$965$	50.1213	−	26.4380i	1.61346	−	0.851071i
$966$	−25.1365	+	21.3426i	−0.808754	+	0.686686i
$967$	5.46728	−	12.2797i	0.175816	−	0.394889i	−0.804045	−	0.594568i	$-0.797323\pi$
$967$	5.46728	−	12.2797i	0.175816	−	0.394889i	0.979861	+	0.199679i	$0.0639898\pi$
$968$	23.9919	−	13.8517i	0.771129	−	0.445211i
$969$	−0.0730472	+	2.51066i	−0.00234661	+	0.0806541i
$970$	−7.48714	−	3.68238i	−0.240397	−	0.118234i
$971$	−17.9377	−	13.0325i	−0.575648	−	0.418232i	0.261505	−	0.965202i	$-0.415781\pi$
$971$	−17.9377	−	13.0325i	−0.575648	−	0.418232i	−0.837152	+	0.546970i	$0.815781\pi$
$972$	−2.12197	+	8.30500i	−0.0680621	+	0.266383i
$973$	−2.32244	−	0.754607i	−0.0744541	−	0.0241916i
$974$	24.5231	−	42.4753i	0.785771	−	1.36100i
$975$	0.705116	−	1.21909i	0.0225818	−	0.0390420i
$976$	18.3222	+	31.7349i	0.586478	+	1.01581i
$977$	−4.34346	−	20.4344i	−0.138960	−	0.653753i	−0.991393	−	0.130918i	$-0.958208\pi$
$977$	−4.34346	−	20.4344i	−0.138960	−	0.653753i	0.852434	−	0.522835i	$-0.175126\pi$
$978$	−1.08351	−	0.263462i	−0.0346470	−	0.00842458i
$979$	14.0742	−	6.26626i	0.449815	−	0.200271i
$980$	−0.208157	+	0.0833025i	−0.00664934	+	0.00266100i
$981$	−32.4493	−	26.5907i	−1.03603	−	0.848976i
$982$		−	48.2698i		−	1.54035i
$983$	27.2383	−	2.86286i	0.868767	−	0.0913111i	0.340353	−	0.940298i	$-0.389453\pi$
$983$	27.2383	−	2.86286i	0.868767	−	0.0913111i	0.528414	+	0.848987i	$0.322787\pi$
$984$	5.39535	+	29.5904i	0.171997	+	0.943309i
$985$	22.0580	−	28.0416i	0.702826	−	0.893479i
$986$	−1.38637	+	0.294681i	−0.0441509	+	0.00938456i
$987$	0.999551	−	0.182252i	0.0318161	−	0.00580116i
$988$	0.139583	−	0.656688i	0.00444074	−	0.0208920i
$989$	−12.4590	+	38.3450i	−0.396174	+	1.21930i
$990$	10.3395	−	4.70713i	0.328611	−	0.149602i
$991$	−4.58088	−	14.0985i	−0.145516	−	0.447854i	0.851561	−	0.524256i	$-0.175657\pi$
$991$	−4.58088	−	14.0985i	−0.145516	−	0.447854i	−0.997077	+	0.0764026i	$0.975657\pi$
$992$	1.80345	−	0.189550i	0.0572595	−	0.00601821i
$993$	38.7278	−	15.9098i	1.22899	−	0.504884i
$994$	−10.5851	−	4.71278i	−0.335739	−	0.149480i
$995$	−43.1118	−	1.64806i	−1.36674	−	0.0522469i
$996$	13.3928	−	3.92483i	0.424368	−	0.124363i
$997$	0.842806	+	1.89297i	0.0266919	+	0.0599510i	0.926400	−	0.376542i	$-0.122887\pi$
$997$	0.842806	+	1.89297i	0.0266919	+	0.0599510i	−0.899708	+	0.436493i	$0.856220\pi$
$998$	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.79.20	yes	224
3.2	odd	2		675.2.y.a.154.9		224
9.4	even	3	inner	225.2.u.a.4.20	✓	224
9.5	odd	6		675.2.y.a.604.9		224
25.19	even	10	inner	225.2.u.a.169.20	yes	224
75.44	odd	10		675.2.y.a.19.9		224
225.94	even	30	inner	225.2.u.a.94.20	yes	224
225.194	odd	30		675.2.y.a.469.9		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.20	✓	224	9.4	even	3	inner
225.2.u.a.79.20	yes	224	1.1	even	1	trivial
225.2.u.a.94.20	yes	224	225.94	even	30	inner
225.2.u.a.169.20	yes	224	25.19	even	10	inner
675.2.y.a.19.9		224	75.44	odd	10
675.2.y.a.154.9		224	3.2	odd	2
675.2.y.a.469.9		224	225.194	odd	30
675.2.y.a.604.9		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.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.894901 - 0.805773i) q^{2} +(0.487100 + 1.66215i) q^{3} +(-0.0574783 + 0.546869i) q^{4} +(2.23444 + 0.0854168i) q^{5} +(1.77522 + 1.09497i) q^{6} +(-2.32094 - 1.33999i) q^{7} +(1.80485 + 2.48416i) q^{8} +(-2.52547 + 1.61926i) q^{9} +O(q^{10})\)	\(q+(0.894901 - 0.805773i) q^{2} +(0.487100 + 1.66215i) q^{3} +(-0.0574783 + 0.546869i) q^{4} +(2.23444 + 0.0854168i) q^{5} +(1.77522 + 1.09497i) q^{6} +(-2.32094 - 1.33999i) q^{7} +(1.80485 + 2.48416i) q^{8} +(-2.52547 + 1.61926i) q^{9} +(2.06843 - 1.72401i) q^{10} +(-0.941029 - 1.04512i) q^{11} +(-0.936975 + 0.170843i) q^{12} +(-0.120849 - 0.108813i) q^{13} +(-3.15674 + 0.670987i) q^{14} +(0.946418 + 3.75557i) q^{15} +(2.54110 + 0.540127i) q^{16} +(0.113531 + 0.156262i) q^{17} +(-0.955286 + 3.48403i) q^{18} +(6.07397 - 4.41300i) q^{19} +(-0.175143 + 1.21703i) q^{20} +(1.09674 - 4.51045i) q^{21} +(-1.68426 - 0.177022i) q^{22} +(-1.22650 - 5.77024i) q^{23} +(-3.24990 + 4.20996i) q^{24} +(4.98541 + 0.381717i) q^{25} -0.195827 q^{26} +(-3.92161 - 3.40896i) q^{27} +(0.866205 - 1.19223i) q^{28} +(-5.56680 + 2.47850i) q^{29} +(3.87309 + 2.59827i) q^{30} +(-0.549855 - 0.244811i) q^{31} +(-2.60917 + 1.50640i) q^{32} +(1.27877 - 2.07321i) q^{33} +(0.227511 + 0.0483590i) q^{34} +(-5.07153 - 3.19238i) q^{35} +(-0.740366 - 1.47417i) q^{36} +(0.888903 - 0.288822i) q^{37} +(1.87973 - 8.84344i) q^{38} +(0.121998 - 0.253872i) q^{39} +(3.82063 + 5.70486i) q^{40} +(3.78427 - 4.20285i) q^{41} +(-2.65293 - 4.92014i) q^{42} +(-5.91893 - 3.41730i) q^{43} +(0.625632 - 0.454548i) q^{44} +(-5.78131 + 3.40242i) q^{45} +(-5.74710 - 4.17551i) q^{46} +(0.0890280 + 0.199960i) q^{47} +(0.339998 + 4.48677i) q^{48} +(0.0911727 + 0.157916i) q^{49} +(4.76903 - 3.67551i) q^{50} +(-0.204430 + 0.264821i) q^{51} +(0.0664527 - 0.0598343i) q^{52} +(-7.64631 + 10.5242i) q^{53} +(-6.25630 + 0.109246i) q^{54} +(-2.01340 - 2.41563i) q^{55} +(-0.860180 - 8.18407i) q^{56} +(10.2937 + 7.94626i) q^{57} +(-2.98463 + 6.70358i) q^{58} +(-3.97717 + 4.41709i) q^{59} +(-2.10820 + 0.301703i) q^{60} +(9.43845 + 10.4825i) q^{61} +(-0.689328 + 0.223976i) q^{62} +(8.03126 - 0.374098i) q^{63} +(-2.72670 + 8.39191i) q^{64} +(-0.260735 - 0.253458i) q^{65} +(-0.526163 - 2.88571i) q^{66} +(2.62723 - 5.90086i) q^{67} +(-0.0919806 + 0.0531050i) q^{68} +(8.99355 - 4.84931i) q^{69} +(-7.11085 + 1.22964i) q^{70} +(2.90460 + 2.11032i) q^{71} +(-8.58059 - 3.35114i) q^{72} +(-11.0652 - 3.59530i) q^{73} +(0.562756 - 0.974721i) q^{74} +(1.79392 + 8.47242i) q^{75} +(2.06421 + 3.57532i) q^{76} +(0.783617 + 3.68663i) q^{77} +(-0.0953872 - 0.325493i) q^{78} +(12.4249 - 5.53192i) q^{79} +(5.63178 + 1.42393i) q^{80} +(3.75597 - 8.17879i) q^{81} -6.81040i q^{82} +(-14.5730 + 1.53168i) q^{83} +(2.40359 + 0.859026i) q^{84} +(0.240331 + 0.358856i) q^{85} +(-8.05043 + 1.71117i) q^{86} +(-6.83121 - 8.04556i) q^{87} +(0.897827 - 4.22394i) q^{88} +(-3.38521 + 10.4186i) q^{89} +(-2.43212 + 7.70325i) q^{90} +(0.134675 + 0.414486i) q^{91} +(3.22606 - 0.339073i) q^{92} +(0.139078 - 1.03319i) q^{93} +(0.240794 + 0.107208i) q^{94} +(13.9488 - 9.34174i) q^{95} +(-3.77479 - 3.60305i) q^{96} +(-1.26033 - 2.83075i) 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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