LMFDB - Embedded newform 624.2.bn.a.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(187,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("624.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bn (of order $4$, degree $2$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Character	$\chi$	$=$	624.307
Dual form			624.2.bn.a.187.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33764 + 0.459045i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.57856 - 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 - 1.27045i) q^{6} +(0.312171 - 0.312171i) q^{7} +(-1.54780 + 2.36735i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.33764 + 0.459045i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.57856 - 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 - 1.27045i) q^{6} +(0.312171 - 0.312171i) q^{7} +(-1.54780 + 2.36735i) q^{8} -1.00000i q^{9} +(3.47756 - 1.19341i) q^{10} +3.08083 q^{11} +(-0.247828 + 1.98459i) q^{12} +(3.18261 - 1.69440i) q^{13} +(-0.274271 + 0.560872i) q^{14} +(1.83832 - 1.83832i) q^{15} +(0.983672 - 3.87716i) q^{16} +6.87394i q^{17} +(0.459045 + 1.33764i) q^{18} -5.01779 q^{19} +(-4.10389 + 3.19271i) q^{20} +0.441476i q^{21} +(-4.12103 + 1.41424i) q^{22} +1.76637i q^{23} +(-0.579510 - 2.76842i) q^{24} +1.75882 q^{25} +(-3.47937 + 3.72746i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.109410 - 0.876147i) q^{28} +(-5.32160 - 5.32160i) q^{29} +(-1.61513 + 3.30288i) q^{30} +(-1.73409 + 1.73409i) q^{31} +(0.463995 + 5.63779i) q^{32} +(-2.17847 + 2.17847i) q^{33} +(-3.15545 - 9.19485i) q^{34} +(-0.811573 + 0.811573i) q^{35} +(-1.22807 - 1.57856i) q^{36} +6.43566i q^{37} +(6.71199 - 2.30339i) q^{38} +(-1.05232 + 3.44857i) q^{39} +(4.02392 - 6.15457i) q^{40} +(-7.29029 + 7.29029i) q^{41} +(-0.202657 - 0.590536i) q^{42} +(1.90101 - 1.90101i) q^{43} +(4.86325 - 3.78348i) q^{44} +2.59977i q^{45} +(-0.810845 - 2.36277i) q^{46} +(1.14377 + 1.14377i) q^{47} +(2.04601 + 3.43713i) q^{48} +6.80510i q^{49} +(-2.35267 + 0.807380i) q^{50} +(-4.86061 - 4.86061i) q^{51} +(2.94307 - 6.58318i) q^{52} +(4.08570 - 4.08570i) q^{53} +(-1.27045 - 0.621260i) q^{54} -8.00945 q^{55} +(0.255840 + 1.22219i) q^{56} +(3.54811 - 3.54811i) q^{57} +(9.56123 + 4.67552i) q^{58} -13.7329 q^{59} +(0.644297 - 5.15947i) q^{60} +(5.28947 + 5.28947i) q^{61} +(1.52356 - 3.11562i) q^{62} +(-0.312171 - 0.312171i) q^{63} +(-3.20866 - 7.32834i) q^{64} +(-8.27406 + 4.40506i) q^{65} +(1.91399 - 3.91403i) q^{66} -15.7618 q^{67} +(8.44170 + 10.8509i) q^{68} +(-1.24901 - 1.24901i) q^{69} +(0.713043 - 1.45814i) q^{70} +(-11.1059 - 11.1059i) q^{71} +(2.36735 + 1.54780i) q^{72} +(0.621805 + 0.621805i) q^{73} +(-2.95426 - 8.60858i) q^{74} +(-1.24368 + 1.24368i) q^{75} +(-7.92085 + 6.16221i) q^{76} +(0.961744 - 0.961744i) q^{77} +(-0.175424 - 5.09600i) q^{78} +16.7040i q^{79} +(-2.55733 + 10.0797i) q^{80} -1.00000 q^{81} +(6.40520 - 13.0983i) q^{82} -7.48177 q^{83} +(0.542165 + 0.696894i) q^{84} -17.8707i q^{85} +(-1.67021 + 3.41551i) q^{86} +7.52588 q^{87} +(-4.76849 + 7.29338i) q^{88} +(11.0906 + 11.0906i) q^{89} +(-1.19341 - 3.47756i) q^{90} +(0.464574 - 1.52246i) q^{91} +(2.16924 + 2.78832i) q^{92} -2.45238i q^{93} +(-2.05499 - 1.00491i) q^{94} +13.0451 q^{95} +(-4.31462 - 3.65843i) q^{96} +(7.33233 + 7.33233i) q^{97} +(-3.12385 - 9.10276i) q^{98} -3.08083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) $ 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.33764	+	0.459045i	−0.945853	+	0.324594i
$2$	−1.33764	+	0.459045i	−0.945853	+	0.324594i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.57856	−	1.22807i	0.789278	−	0.614037i
$5$	−2.59977			−1.16265			−0.581327	−	0.813670i	$-0.697466\pi$
$5$	−2.59977			−1.16265			−0.581327	+	0.813670i	$0.697466\pi$
$6$	0.621260	−	1.27045i	0.253628	−	0.518658i
$7$	0.312171	−	0.312171i	0.117989	−	0.117989i	−0.645647	−	0.763636i	$-0.723412\pi$
$7$	0.312171	−	0.312171i	0.117989	−	0.117989i	0.763636	+	0.645647i	$0.223412\pi$
$8$	−1.54780	+	2.36735i	−0.547228	+	0.836983i
$9$		−	1.00000i		−	0.333333i
$10$	3.47756	−	1.19341i	1.09970	−	0.377391i
$11$	3.08083			0.928904			0.464452	−	0.885598i	$-0.346251\pi$
$11$	3.08083			0.928904			0.464452	+	0.885598i	$0.346251\pi$
$12$	−0.247828	+	1.98459i	−0.0715418	+	0.572901i
$13$	3.18261	−	1.69440i	0.882697	−	0.469943i
$13$	3.18261	−	1.69440i	0.882697	−	0.469943i
$14$	−0.274271	+	0.560872i	−0.0733021	+	0.149899i
$15$	1.83832	−	1.83832i	0.474652	−	0.474652i
$16$	0.983672	−	3.87716i	0.245918	−	0.969291i
$17$			6.87394i			1.66718i	0.552387	+	0.833588i	$0.313717\pi$
$17$			6.87394i			1.66718i	−0.552387	+	0.833588i	$0.686283\pi$
$18$	0.459045	+	1.33764i	0.108198	+	0.315284i
$19$	−5.01779			−1.15116			−0.575580	−	0.817746i	$-0.695224\pi$
$19$	−5.01779			−1.15116			−0.575580	+	0.817746i	$0.695224\pi$
$20$	−4.10389	+	3.19271i	−0.917657	+	0.713912i
$21$			0.441476i			0.0963380i
$22$	−4.12103	+	1.41424i	−0.878607	+	0.301517i
$23$			1.76637i			0.368314i	0.982897	+	0.184157i	$0.0589555\pi$
$23$			1.76637i			0.368314i	−0.982897	+	0.184157i	$0.941044\pi$
$24$	−0.579510	−	2.76842i	−0.118292	−	0.565102i
$25$	1.75882			0.351765
$26$	−3.47937	+	3.72746i	−0.682361	+	0.731015i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.109410	−	0.876147i	0.0206766	−	0.165576i
$29$	−5.32160	−	5.32160i	−0.988196	−	0.988196i	0.0117353	−	0.999931i	$-0.496264\pi$
$29$	−5.32160	−	5.32160i	−0.988196	−	0.988196i	−0.999931	+	0.0117353i	$0.996264\pi$
$30$	−1.61513	+	3.30288i	−0.294882	+	0.603020i
$31$	−1.73409	+	1.73409i	−0.311453	+	0.311453i	−0.845472	−	0.534020i	$-0.820681\pi$
$31$	−1.73409	+	1.73409i	−0.311453	+	0.311453i	0.534020	+	0.845472i	$0.320681\pi$
$32$	0.463995	+	5.63779i	0.0820234	+	0.996630i
$33$	−2.17847	+	2.17847i	−0.379224	+	0.379224i
$34$	−3.15545	−	9.19485i	−0.541155	−	1.57690i
$35$	−0.811573	+	0.811573i	−0.137181	+	0.137181i
$36$	−1.22807	−	1.57856i	−0.204679	−	0.263093i
$37$			6.43566i			1.05802i	0.848617	+	0.529008i	$0.177436\pi$
$37$			6.43566i			1.05802i	−0.848617	+	0.529008i	$0.822564\pi$
$38$	6.71199	−	2.30339i	1.08883	−	0.373659i
$39$	−1.05232	+	3.44857i	−0.168506	+	0.552213i
$40$	4.02392	−	6.15457i	0.636237	−	0.973122i
$41$	−7.29029	+	7.29029i	−1.13855	+	1.13855i	−0.149842	+	0.988710i	$0.547876\pi$
$41$	−7.29029	+	7.29029i	−1.13855	+	1.13855i	−0.988710	+	0.149842i	$0.952124\pi$
$42$	−0.202657	−	0.590536i	−0.0312707	−	0.0911216i
$43$	1.90101	−	1.90101i	0.289901	−	0.289901i	−0.547140	−	0.837041i	$-0.684284\pi$
$43$	1.90101	−	1.90101i	0.289901	−	0.289901i	0.837041	+	0.547140i	$0.184284\pi$
$44$	4.86325	−	3.78348i	0.733163	−	0.570381i
$45$			2.59977i			0.387551i
$46$	−0.810845	−	2.36277i	−0.119553	−	0.348371i
$47$	1.14377	+	1.14377i	0.166836	+	0.166836i	0.785587	−	0.618751i	$-0.212361\pi$
$47$	1.14377	+	1.14377i	0.166836	+	0.166836i	−0.618751	+	0.785587i	$0.712361\pi$
$48$	2.04601	+	3.43713i	0.295316	+	0.496107i
$49$			6.80510i			0.972157i
$50$	−2.35267	+	0.807380i	−0.332718	+	0.114181i
$51$	−4.86061	−	4.86061i	−0.680622	−	0.680622i
$52$	2.94307	−	6.58318i	0.408131	−	0.912923i
$53$	4.08570	−	4.08570i	0.561214	−	0.561214i	−0.368438	−	0.929652i	$-0.620107\pi$
$53$	4.08570	−	4.08570i	0.561214	−	0.561214i	0.929652	+	0.368438i	$0.120107\pi$
$54$	−1.27045	−	0.621260i	−0.172886	−	0.0845427i
$55$	−8.00945			−1.07999
$56$	0.255840	+	1.22219i	0.0341880	+	0.163322i
$57$	3.54811	−	3.54811i	0.469959	−	0.469959i
$58$	9.56123	+	4.67552i	1.25545	+	0.613926i
$59$	−13.7329			−1.78788			−0.893938	−	0.448192i	$-0.852068\pi$
$59$	−13.7329			−1.78788			−0.893938	+	0.448192i	$0.852068\pi$
$60$	0.644297	−	5.15947i	0.0831784	−	0.666085i
$61$	5.28947	+	5.28947i	0.677248	+	0.677248i	0.959377	−	0.282129i	$-0.0910406\pi$
$61$	5.28947	+	5.28947i	0.677248	+	0.677248i	−0.282129	+	0.959377i	$0.591041\pi$
$62$	1.52356	−	3.11562i	0.193493	−	0.395684i
$63$	−0.312171	−	0.312171i	−0.0393298	−	0.0393298i
$64$	−3.20866	−	7.32834i	−0.401082	−	0.916042i
$65$	−8.27406	+	4.40506i	−1.02627	+	0.546381i
$66$	1.91399	−	3.91403i	0.235596	−	0.481784i
$67$	−15.7618			−1.92561			−0.962804	−	0.270200i	$-0.912910\pi$
$67$	−15.7618			−1.92561			−0.962804	+	0.270200i	$0.912910\pi$
$68$	8.44170	+	10.8509i	1.02371	+	1.31586i
$69$	−1.24901	−	1.24901i	−0.150364	−	0.150364i
$70$	0.713043	−	1.45814i	0.0852250	−	0.174281i
$71$	−11.1059	−	11.1059i	−1.31802	−	1.31802i	−0.915339	−	0.402684i	$-0.868077\pi$
$71$	−11.1059	−	11.1059i	−1.31802	−	1.31802i	−0.402684	−	0.915339i	$-0.631923\pi$
$72$	2.36735	+	1.54780i	0.278994	+	0.182409i
$73$	0.621805	+	0.621805i	0.0727768	+	0.0727768i	0.742558	−	0.669781i	$-0.233612\pi$
$73$	0.621805	+	0.621805i	0.0727768	+	0.0727768i	−0.669781	+	0.742558i	$0.733612\pi$
$74$	−2.95426	−	8.60858i	−0.343425	−	1.00073i
$75$	−1.24368	+	1.24368i	−0.143607	+	0.143607i
$76$	−7.92085	+	6.16221i	−0.908584	+	0.706854i
$77$	0.961744	−	0.961744i	0.109601	−	0.109601i
$78$	−0.175424	−	5.09600i	−0.0198628	−	0.577008i
$79$			16.7040i			1.87935i	0.342066	+	0.939676i	$0.388873\pi$
$79$			16.7040i			1.87935i	−0.342066	+	0.939676i	$0.611127\pi$
$80$	−2.55733	+	10.0797i	−0.285918	+	1.12695i
$81$	−1.00000			−0.111111
$82$	6.40520	−	13.0983i	0.707336	−	1.44647i
$83$	−7.48177			−0.821231			−0.410615	−	0.911809i	$-0.634686\pi$
$83$	−7.48177			−0.821231			−0.410615	+	0.911809i	$0.634686\pi$
$84$	0.542165	+	0.696894i	0.0591551	+	0.0760374i
$85$		−	17.8707i		−	1.93835i
$86$	−1.67021	+	3.41551i	−0.180104	+	0.368304i
$87$	7.52588			0.806859
$88$	−4.76849	+	7.29338i	−0.508323	+	0.777477i
$89$	11.0906	+	11.0906i	1.17560	+	1.17560i	0.980854	+	0.194745i	$0.0623881\pi$
$89$	11.0906	+	11.0906i	1.17560	+	1.17560i	0.194745	+	0.980854i	$0.437612\pi$
$90$	−1.19341	−	3.47756i	−0.125797	−	0.366567i
$91$	0.464574	−	1.52246i	0.0487006	−	0.159597i
$92$	2.16924	+	2.78832i	0.226158	+	0.290702i
$93$		−	2.45238i		−	0.254300i
$94$	−2.05499	−	1.00491i	−0.211956	−	0.103648i
$95$	13.0451			1.33840
$96$	−4.31462	−	3.65843i	−0.440359	−	0.373387i
$97$	7.33233	+	7.33233i	0.744486	+	0.744486i	0.973438	−	0.228952i	$-0.0735299\pi$
$97$	7.33233	+	7.33233i	0.744486	+	0.744486i	−0.228952	+	0.973438i	$0.573530\pi$
$98$	−3.12385	−	9.10276i	−0.315556	−	0.919518i
$99$		−	3.08083i		−	0.309635i
$100$	2.77640	−	2.15997i	0.277640	−	0.215997i
$101$	4.68560	+	4.68560i	0.466234	+	0.466234i	0.900692	−	0.434458i	$-0.143060\pi$
$101$	4.68560	+	4.68560i	0.466234	+	0.466234i	−0.434458	+	0.900692i	$0.643060\pi$
$102$	8.73298	+	4.27050i	0.864694	+	0.422843i
$103$		−	0.250872i		−	0.0247192i	−0.999924	−	0.0123596i	$-0.996066\pi$
$103$		−	0.250872i		−	0.0247192i	0.999924	−	0.0123596i	$-0.00393428\pi$
$104$	−0.914789	+	10.1569i	−0.0897024	+	0.995969i
$105$		−	1.14774i		−	0.112008i
$106$	−3.58967	+	7.34072i	−0.348660	+	0.712993i
$107$	1.84416	+	1.84416i	0.178282	+	0.178282i	0.790606	−	0.612325i	$-0.209766\pi$
$107$	1.84416	+	1.84416i	0.178282	+	0.178282i	−0.612325	+	0.790606i	$0.709766\pi$
$108$	1.98459	+	0.247828i	0.190967	+	0.0238473i
$109$		−	0.584695i		−	0.0560036i	−0.999608	−	0.0280018i	$-0.991086\pi$
$109$		−	0.584695i		−	0.0560036i	0.999608	−	0.0280018i	$-0.00891442\pi$
$110$	10.7138	−	3.67670i	1.02152	−	0.350560i
$111$	−4.55070	−	4.55070i	−0.431933	−	0.431933i
$112$	−0.903263	−	1.51741i	−0.0853503	−	0.143382i
$113$	9.43859			0.887908			0.443954	−	0.896050i	$-0.353575\pi$
$113$	9.43859			0.887908			0.443954	+	0.896050i	$0.353575\pi$
$114$	−3.11735	+	6.37483i	−0.291966	+	0.597058i
$115$		−	4.59217i		−	0.428222i
$116$	−14.9357	−	1.86512i	−1.38675	−	0.173172i
$117$	−1.69440	−	3.18261i	−0.156648	−	0.294232i
$118$	18.3697	−	6.30403i	1.69107	−	0.580333i
$119$	2.14584	+	2.14584i	0.196709	+	0.196709i
$120$	1.50660	+	7.19727i	0.137533	+	0.657018i
$121$	−1.50851			−0.137137
$122$	−9.50351	−	4.64730i	−0.860408	−	0.420747i
$123$		−	10.3100i		−	0.929624i
$124$	−0.607769	+	4.86696i	−0.0545792	+	0.437066i
$125$	8.42632			0.753673
$126$	0.560872	+	0.274271i	0.0499665	+	0.0244340i
$127$	−5.82313			−0.516719			−0.258360	−	0.966049i	$-0.583182\pi$
$127$	−5.82313			−0.516719			−0.258360	+	0.966049i	$0.583182\pi$
$128$	7.65606	+	8.32975i	0.676707	+	0.736253i
$129$			2.68843i			0.236703i
$130$	9.04559	−	9.69055i	0.793350	−	0.849918i
$131$	6.85011	−	6.85011i	0.598497	−	0.598497i	−0.341415	−	0.939912i	$-0.610906\pi$
$131$	6.85011	−	6.85011i	0.598497	−	0.598497i	0.939912	+	0.341415i	$0.110906\pi$
$132$	−0.763515	+	6.11417i	−0.0664555	+	0.532170i
$133$	−1.56641	+	1.56641i	−0.135825	+	0.135825i
$134$	21.0836	−	7.23537i	1.82134	−	0.625041i
$135$	−1.83832	−	1.83832i	−0.158217	−	0.158217i
$136$	−16.2730	−	10.6395i	−1.39540	−	0.912326i
$137$	−0.237416	−	0.237416i	−0.0202838	−	0.0202838i	0.696892	−	0.717176i	$-0.254566\pi$
$137$	−0.237416	−	0.237416i	−0.0202838	−	0.0202838i	−0.717176	+	0.696892i	$0.754566\pi$
$138$	2.24408	+	1.09738i	0.191029	+	0.0934148i
$139$	2.78720	+	2.78720i	0.236407	+	0.236407i	0.815361	−	0.578953i	$-0.196539\pi$
$139$	2.78720	+	2.78720i	0.236407	+	0.236407i	−0.578953	+	0.815361i	$0.696539\pi$
$140$	−0.284442	+	2.27778i	−0.0240397	+	0.192508i
$141$	−1.61753			−0.136221
$142$	19.9537	+	9.75754i	1.67448	+	0.818834i
$143$	9.80507	−	5.22016i	0.819941	−	0.436532i
$144$	−3.87716	−	0.983672i	−0.323097	−	0.0819727i
$145$	13.8350	+	13.8350i	1.14893	+	1.14893i
$146$	−1.11719	−	0.546314i	−0.0924591	−	0.0452133i
$147$	−4.81193	−	4.81193i	−0.396881	−	0.396881i
$148$	7.90346	+	10.1590i	0.649660	+	0.835068i
$149$	−15.1865			−1.24413			−0.622064	−	0.782966i	$-0.713706\pi$
$149$	−15.1865			−1.24413			−0.622064	+	0.782966i	$0.713706\pi$
$150$	1.09269	−	2.23449i	0.0892175	−	0.182446i
$151$	12.1513	−	12.1513i	0.988862	−	0.988862i	−0.0110764	−	0.999939i	$-0.503526\pi$
$151$	12.1513	−	12.1513i	0.988862	−	0.988862i	0.999939	+	0.0110764i	$0.00352578\pi$
$152$	7.76651	−	11.8788i	0.629947	−	0.963501i
$153$	6.87394			0.555725
$154$	−0.844982	+	1.72795i	−0.0680906	+	0.139242i
$155$	4.50825	−	4.50825i	0.362112	−	0.362112i
$156$	2.57395	+	6.73608i	0.206081	+	0.539318i
$157$	4.75195	+	4.75195i	0.379247	+	0.379247i	0.870831	−	0.491583i	$-0.163582\pi$
$157$	4.75195	+	4.75195i	0.379247	+	0.379247i	−0.491583	+	0.870831i	$0.663582\pi$
$158$	−7.66791	−	22.3440i	−0.610026	−	1.77759i
$159$			5.77806i			0.458230i
$160$	−1.20628	−	14.6570i	−0.0953649	−	1.15874i
$161$	0.551410	+	0.551410i	0.0434572	+	0.0434572i
$162$	1.33764	−	0.459045i	0.105095	−	0.0360660i
$163$			7.87339i			0.616692i	0.951274	+	0.308346i	$0.0997754\pi$
$163$			7.87339i			0.616692i	−0.951274	+	0.308346i	$0.900225\pi$
$164$	−2.55511	+	20.4611i	−0.199521	+	1.59775i
$165$	5.66354	−	5.66354i	0.440906	−	0.440906i
$166$	10.0079	−	3.43447i	0.776764	−	0.266567i
$167$	−1.90835	+	1.90835i	−0.147672	+	0.147672i	−0.777077	−	0.629405i	$-0.783299\pi$
$167$	−1.90835	+	1.90835i	−0.147672	+	0.147672i	0.629405	+	0.777077i	$0.283299\pi$
$168$	−1.04513	−	0.683315i	−0.0806333	−	0.0527189i
$169$	7.25800	−	10.7852i	0.558308	−	0.829634i
$170$	8.20345	+	23.9045i	0.629176	+	1.83339i
$171$			5.01779i			0.383720i
$172$	0.666268	−	5.33542i	0.0508025	−	0.406822i
$173$	−0.0223126	+	0.0223126i	−0.00169639	+	0.00169639i	−0.707954	−	0.706258i	$-0.750382\pi$
$173$	−0.0223126	+	0.0223126i	−0.00169639	+	0.00169639i	0.706258	+	0.707954i	$0.250382\pi$
$174$	−10.0669	+	3.45472i	−0.763170	+	0.261901i
$175$	0.549054	−	0.549054i	0.0415045	−	0.0415045i
$176$	3.03052	−	11.9449i	0.228434	−	0.900378i
$177$	9.71065	−	9.71065i	0.729897	−	0.729897i
$178$	−19.9263	−	9.74411i	−1.49354	−	0.730352i
$179$	3.42532	+	3.42532i	0.256021	+	0.256021i	0.823434	−	0.567413i	$-0.192056\pi$
$179$	3.42532	+	3.42532i	0.256021	+	0.256021i	−0.567413	+	0.823434i	$0.692056\pi$
$180$	3.19271	+	4.10389i	0.237971	+	0.305886i
$181$	−4.71779	−	4.71779i	−0.350671	−	0.350671i	0.509688	−	0.860359i	$-0.329761\pi$
$181$	−4.71779	−	4.71779i	−0.350671	−	0.350671i	−0.860359	+	0.509688i	$0.829761\pi$
$182$	0.0774453	+	2.24976i	0.00574063	+	0.166764i
$183$	−7.48044			−0.552970
$184$	−4.18162	−	2.73398i	−0.308273	−	0.201552i
$185$		−	16.7312i		−	1.23011i
$186$	1.12575	+	3.28040i	0.0825442	+	0.240530i
$187$			21.1774i			1.54865i
$188$	3.21014	+	0.400870i	0.234123	+	0.0292365i
$189$	0.441476			0.0321127
$190$	−17.4496	+	5.98830i	−1.26593	+	0.434437i
$191$		−	2.24769i		−	0.162637i	−0.996688	−	0.0813185i	$-0.974087\pi$
$191$		−	2.24769i		−	0.162637i	0.996688	−	0.0813185i	$-0.0259131\pi$
$192$	7.45078	+	2.91305i	0.537714	+	0.210231i
$193$	−6.35227	+	6.35227i	−0.457246	+	0.457246i	−0.897751	−	0.440504i	$-0.854800\pi$
$193$	−6.35227	+	6.35227i	−0.457246	+	0.457246i	0.440504	+	0.897751i	$0.354800\pi$
$194$	−13.1739	−	6.44214i	−0.945830	−	0.462519i
$195$	2.73580	−	8.96550i	0.195914	−	0.642033i
$196$	8.35716	+	10.7422i	0.596940	+	0.767302i
$197$	5.77122			0.411182			0.205591	−	0.978638i	$-0.434088\pi$
$197$	5.77122			0.411182			0.205591	+	0.978638i	$0.434088\pi$
$198$	1.41424	+	4.12103i	0.100506	+	0.292869i
$199$		−	11.5493i		−	0.818709i	−0.912375	−	0.409355i	$-0.865754\pi$
$199$		−	11.5493i		−	0.818709i	0.912375	−	0.409355i	$-0.134246\pi$
$200$	−2.72230	+	4.16375i	−0.192496	+	0.294421i
$201$	11.1453	−	11.1453i	0.786126	−	0.786126i
$202$	−8.41854	−	4.11674i	−0.592326	−	0.289653i
$203$	−3.32249			−0.233193
$204$	−13.6419	−	1.70356i	−0.955126	−	0.119273i
$205$	18.9531	−	18.9531i	1.32374	−	1.32374i
$206$	0.115162	+	0.335576i	0.00802369	+	0.0233807i
$207$	1.76637			0.122771
$208$	−3.43883	−	14.0062i	−0.238440	−	0.971157i
$209$	−15.4589			−1.06932
$210$	0.526864	+	1.53526i	0.0363570	+	0.105943i
$211$	1.67957	−	1.67957i	0.115627	−	0.115627i	−0.646926	−	0.762553i	$-0.723946\pi$
$211$	1.67957	−	1.67957i	0.115627	−	0.115627i	0.762553	+	0.646926i	$0.223946\pi$
$212$	1.43196	−	11.4670i	0.0983477	−	0.787560i
$213$	15.7061			1.07616
$214$	−3.31337	−	1.62027i	−0.226497	−	0.110759i
$215$	−4.94219	+	4.94219i	−0.337054	+	0.337054i
$216$	−2.76842	+	0.579510i	−0.188367	+	0.0394307i
$217$			1.08267i			0.0734962i
$218$	0.268402	+	0.782111i	0.0181784	+	0.0529712i
$219$	−0.879366			−0.0594220
$220$	−12.6434	+	9.83620i	−0.852415	+	0.663156i
$221$	11.6472	+	21.8771i	0.783477	+	1.47161i
$222$	8.17616	+	3.99821i	0.548748	+	0.268342i
$223$	3.12370	−	3.12370i	0.209179	−	0.209179i	−0.594740	−	0.803918i	$-0.702745\pi$
$223$	3.12370	−	3.12370i	0.209179	−	0.209179i	0.803918	+	0.594740i	$0.202745\pi$
$224$	1.90480	+	1.61511i	0.127270	+	0.107914i
$225$		−	1.75882i		−	0.117255i
$226$	−12.6254	+	4.33274i	−0.839831	+	0.288210i
$227$	16.0224			1.06344			0.531721	−	0.846919i	$-0.321545\pi$
$227$	16.0224			1.06344			0.531721	+	0.846919i	$0.321545\pi$
$228$	1.24355	−	9.95823i	0.0823560	−	0.659500i
$229$			6.51126i			0.430276i	0.976584	+	0.215138i	$0.0690202\pi$
$229$			6.51126i			0.430276i	−0.976584	+	0.215138i	$0.930980\pi$
$230$	2.10801	+	6.14266i	0.138998	+	0.405035i
$231$			1.36011i			0.0894888i
$232$	20.8348	−	4.36132i	1.36787	−	0.286335i
$233$	−13.2251			−0.866405			−0.433202	−	0.901297i	$-0.642617\pi$
$233$	−13.2251			−0.866405			−0.433202	+	0.901297i	$0.642617\pi$
$234$	3.72746	+	3.47937i	0.243672	+	0.227454i
$235$	−2.97354	−	2.97354i	−0.193973	−	0.193973i
$236$	−21.6782	+	16.8650i	−1.41113	+	1.09782i
$237$	−11.8115	−	11.8115i	−0.767242	−	0.767242i
$238$	−3.85540	−	1.88532i	−0.249909	−	0.122207i
$239$	1.81466	−	1.81466i	0.117381	−	0.117381i	−0.645977	−	0.763357i	$-0.723550\pi$
$239$	1.81466	−	1.81466i	0.117381	−	0.117381i	0.763357	+	0.645977i	$0.223550\pi$
$240$	−5.31915	−	8.93576i	−0.343350	−	0.576801i
$241$	−12.3236	+	12.3236i	−0.793834	+	0.793834i	−0.982115	−	0.188281i	$-0.939708\pi$
$241$	−12.3236	+	12.3236i	−0.793834	+	0.793834i	0.188281	+	0.982115i	$0.439708\pi$
$242$	2.01784	−	0.692472i	0.129711	−	0.0445138i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	14.8456	+	1.85386i	0.950391	+	0.118681i
$245$		−	17.6917i		−	1.13028i
$246$	4.73277	+	13.7911i	0.301750	+	0.879288i
$247$	−15.9697	+	8.50215i	−1.01612	+	0.540979i
$248$	−1.42118	−	6.78923i	−0.0902450	−	0.431116i
$249$	5.29041	−	5.29041i	0.335266	−	0.335266i
$250$	−11.2714	+	3.86806i	−0.712865	+	0.244638i
$251$	−8.97239	+	8.97239i	−0.566332	+	0.566332i	−0.931099	−	0.364767i	$-0.881149\pi$
$251$	−8.97239	+	8.97239i	−0.566332	+	0.566332i	0.364767	+	0.931099i	$0.381149\pi$
$252$	−0.876147	−	0.109410i	−0.0551921	−	0.00689219i
$253$			5.44189i			0.342129i
$254$	7.78925	−	2.67308i	0.488741	−	0.167724i
$255$	12.6365	+	12.6365i	0.791328	+	0.791328i
$256$	−14.0648	−	7.62771i	−0.879049	−	0.476732i
$257$			1.97467i			0.123176i	0.998102	+	0.0615881i	$0.0196165\pi$
$257$			1.97467i			0.123176i	−0.998102	+	0.0615881i	$0.980383\pi$
$258$	−1.23411	−	3.59615i	−0.0768324	−	0.223886i
$259$	2.00902	+	2.00902i	0.124835	+	0.124835i
$260$	−7.65132	+	17.1148i	−0.474515	+	1.06141i
$261$	−5.32160	+	5.32160i	−0.329399	+	0.329399i
$262$	−6.01846	+	12.3075i	−0.371822	+	0.760359i
$263$	20.1922			1.24510			0.622551	−	0.782579i	$-0.286096\pi$
$263$	20.1922			1.24510			0.622551	+	0.782579i	$0.286096\pi$
$264$	−1.78537	−	8.52903i	−0.109882	−	0.524926i
$265$	−10.6219	+	10.6219i	−0.652498	+	0.652498i
$266$	1.37623	−	2.81434i	0.0843824	−	0.172558i
$267$	−15.6845			−0.959873
$268$	−24.8808	+	19.3566i	−1.51984	+	1.18239i
$269$	−18.9916	−	18.9916i	−1.15794	−	1.15794i	−0.984918	−	0.173020i	$-0.944647\pi$
$269$	−18.9916	−	18.9916i	−1.15794	−	1.15794i	−0.173020	−	0.984918i	$-0.555353\pi$
$270$	3.30288	+	1.61513i	0.201007	+	0.0982939i
$271$	−5.60706	−	5.60706i	−0.340605	−	0.340605i	0.515990	−	0.856595i	$-0.327424\pi$
$271$	−5.60706	−	5.60706i	−0.340605	−	0.340605i	−0.856595	+	0.515990i	$0.827424\pi$
$272$	26.6514	+	6.76170i	1.61598	+	0.409989i
$273$	0.748038	+	1.40505i	0.0452733	+	0.0850372i
$274$	0.426562	+	0.208592i	0.0257696	+	0.0126015i
$275$	5.41863			0.326756
$276$	−3.50552	−	0.437757i	−0.211007	−	0.0263499i
$277$	7.97084	+	7.97084i	0.478922	+	0.478922i	0.904787	−	0.425865i	$-0.140030\pi$
$277$	7.97084	+	7.97084i	0.478922	+	0.478922i	−0.425865	+	0.904787i	$0.640030\pi$
$278$	−5.00772	−	2.44882i	−0.300343	−	0.146870i
$279$	1.73409	+	1.73409i	0.103818	+	0.103818i
$280$	−0.665126	−	3.17742i	−0.0397489	−	0.189887i
$281$	−8.08671	−	8.08671i	−0.482413	−	0.482413i	0.423489	−	0.905901i	$-0.360805\pi$
$281$	−8.08671	−	8.08671i	−0.482413	−	0.482413i	−0.905901	+	0.423489i	$0.860805\pi$
$282$	2.16368	−	0.742521i	0.128845	−	0.0442165i
$283$	−22.7352	+	22.7352i	−1.35147	+	1.35147i	−0.467445	+	0.884022i	$0.654826\pi$
$283$	−22.7352	+	22.7352i	−1.35147	+	1.35147i	−0.884022	+	0.467445i	$0.845174\pi$
$284$	−31.1700	−	3.89240i	−1.84960	−	0.230972i
$285$	−9.22429	+	9.22429i	−0.546400	+	0.546400i
$286$	−10.7193	+	11.4837i	−0.633848	+	0.679043i
$287$			4.55163i			0.268674i
$288$	5.63779	−	0.463995i	0.332210	−	0.0273411i
$289$	−30.2511			−1.77947
$290$	−24.8570	−	12.1553i	−1.45966	−	0.713784i
$291$	−10.3695			−0.607870
$292$	1.74518	+	0.217932i	0.102129	+	0.0127535i
$293$		−	7.84277i		−	0.458180i	−0.973405	−	0.229090i	$-0.926425\pi$
$293$		−	7.84277i		−	0.458180i	0.973405	−	0.229090i	$-0.0735750\pi$
$294$	8.64552	+	4.22773i	0.504217	+	0.246566i
$295$	35.7025			2.07868
$296$	−15.2354	−	9.96108i	−0.885541	−	0.578976i
$297$	2.17847	+	2.17847i	0.126408	+	0.126408i
$298$	20.3141	−	6.97130i	1.17676	−	0.403837i
$299$	2.99295	+	5.62167i	0.173087	+	0.325110i
$300$	−0.435886	+	3.49054i	−0.0251659	+	0.201526i
$301$		−	1.18688i		−	0.0684105i
$302$	−10.6761	+	21.8321i	−0.614340	+	1.25630i
$303$	−6.62644			−0.380679
$304$	−4.93586	+	19.4548i	−0.283091	+	1.11581i
$305$	−13.7514	−	13.7514i	−0.787405	−	0.787405i
$306$	−9.19485	+	3.15545i	−0.525635	+	0.180385i
$307$		−	19.3002i		−	1.10152i	−0.834664	−	0.550760i	$-0.814338\pi$
$307$		−	19.3002i		−	1.10152i	0.834664	−	0.550760i	$-0.185662\pi$
$308$	0.337074	−	2.69926i	0.0192066	−	0.153805i
$309$	0.177393	+	0.177393i	0.0100916	+	0.0100916i
$310$	−3.96092	+	8.09991i	−0.224965	+	0.460044i
$311$		−	25.4700i		−	1.44427i	−0.691750	−	0.722137i	$-0.743160\pi$
$311$		−	25.4700i		−	1.44427i	0.691750	−	0.722137i	$-0.256840\pi$
$312$	−6.53518	−	7.82889i	−0.369982	−	0.443223i
$313$		−	0.779174i		−	0.0440415i	−0.999758	−	0.0220208i	$-0.992990\pi$
$313$		−	0.779174i		−	0.0440415i	0.999758	−	0.0220208i	$-0.00700999\pi$
$314$	−8.53776	−	4.17504i	−0.481814	−	0.235611i
$315$	0.811573	+	0.811573i	0.0457270	+	0.0457270i
$316$	20.5138	+	26.3683i	1.15399	+	1.48333i
$317$			7.53592i			0.423259i	0.977350	+	0.211630i	$0.0678771\pi$
$317$			7.53592i			0.423259i	−0.977350	+	0.211630i	$0.932123\pi$
$318$	−2.65239	−	7.72895i	−0.148739	−	0.433418i
$319$	−16.3949	−	16.3949i	−0.917939	−	0.917939i
$320$	8.34179	+	19.0520i	0.466320	+	1.06504i
$321$	−2.60803			−0.145566
$322$	−0.990709	−	0.484465i	−0.0552101	−	0.0269982i
$323$		−	34.4920i		−	1.91918i
$324$	−1.57856	+	1.22807i	−0.0876975	+	0.0682263i
$325$	5.59765	−	2.98016i	0.310502	−	0.165309i
$326$	−3.61424	−	10.5318i	−0.200174	−	0.583300i
$327$	0.413442	+	0.413442i	0.0228634	+	0.0228634i
$328$	−5.97476	−	28.5425i	−0.329901	−	1.57600i
$329$	0.714103			0.0393698
$330$	−4.97595	+	10.1756i	−0.273917	+	0.560148i
$331$		−	13.2622i		−	0.728959i	−0.931211	−	0.364480i	$-0.881247\pi$
$331$		−	13.2622i		−	0.728959i	0.931211	−	0.364480i	$-0.118753\pi$
$332$	−11.8104	+	9.18816i	−0.648179	+	0.504266i
$333$	6.43566			0.352672
$334$	1.67666	−	3.42869i	0.0917428	−	0.187610i
$335$	40.9771			2.23882
$336$	1.71167	+	0.434268i	0.0933795	+	0.0236912i
$337$			3.21855i			0.175326i	0.996150	+	0.0876629i	$0.0279398\pi$
$337$			3.21855i			0.175326i	−0.996150	+	0.0876629i	$0.972060\pi$
$338$	−4.75767	+	17.7585i	−0.258783	+	0.965935i
$339$	−6.67409	+	6.67409i	−0.362487	+	0.362487i
$340$	−21.9465	−	28.2099i	−1.19022	−	1.52990i
$341$	−5.34244	+	5.34244i	−0.289310	+	0.289310i
$342$	−2.30339	−	6.71199i	−0.124553	−	0.362943i
$343$	4.30955	+	4.30955i	0.232694	+	0.232694i
$344$	1.55797	+	7.44271i	0.0840002	+	0.401284i
$345$	3.24715	+	3.24715i	0.174821	+	0.174821i
$346$	0.0196037	−	0.0400887i	0.00105390	−	0.00215518i
$347$	−6.19697	−	6.19697i	−0.332671	−	0.332671i	0.520929	−	0.853600i	$-0.325586\pi$
$347$	−6.19697	−	6.19697i	−0.332671	−	0.332671i	−0.853600	+	0.520929i	$0.825586\pi$
$348$	11.8800	−	9.24233i	0.636835	−	0.495441i
$349$	25.9541			1.38929			0.694646	−	0.719351i	$-0.255561\pi$
$349$	25.9541			1.38929			0.694646	+	0.719351i	$0.255561\pi$
$350$	−0.482395	+	0.986476i	−0.0257851	+	0.0527293i
$351$	3.44857	+	1.05232i	0.184071	+	0.0561687i
$352$	1.42949	+	17.3691i	0.0761919	+	0.925774i
$353$	23.8028	+	23.8028i	1.26689	+	1.26689i	0.947685	+	0.319208i	$0.103417\pi$
$353$	23.8028	+	23.8028i	1.26689	+	1.26689i	0.319208	+	0.947685i	$0.396583\pi$
$354$	−8.53171	+	17.4470i	−0.453455	+	0.927296i
$355$	28.8727	+	28.8727i	1.53241	+	1.53241i
$356$	31.1271	+	3.88705i	1.64974	+	0.206013i
$357$	−3.03468			−0.160612
$358$	−6.15422	−	3.00947i	−0.325261	−	0.159055i
$359$	−20.6184	+	20.6184i	−1.08820	+	1.08820i	−0.0924811	+	0.995714i	$0.529480\pi$
$359$	−20.6184	+	20.6184i	−1.08820	+	1.08820i	−0.995714	+	0.0924811i	$0.970520\pi$
$360$	−6.15457	−	4.02392i	−0.324374	−	0.212079i
$361$	6.17818			0.325168
$362$	8.47638	+	4.14502i	0.445509	+	0.217858i
$363$	1.06667	−	1.06667i	0.0559859	−	0.0559859i
$364$	−1.13634	−	2.97382i	−0.0595602	−	0.155870i
$365$	−1.61655	−	1.61655i	−0.0846143	−	0.0846143i
$366$	10.0061	−	3.43386i	0.523029	−	0.179491i
$367$			30.9160i			1.61380i	0.590687	+	0.806901i	$0.298857\pi$
$367$			30.9160i			1.61380i	−0.590687	+	0.806901i	$0.701143\pi$
$368$	6.84851	+	1.73753i	0.357003	+	0.0905751i
$369$	7.29029	+	7.29029i	0.379517	+	0.379517i
$370$	7.68040	+	22.3804i	0.399285	+	1.16350i
$371$		−	2.55087i		−	0.132435i
$372$	−3.01170	−	3.87122i	−0.156149	−	0.200713i
$373$	7.25450	−	7.25450i	0.375624	−	0.375624i	−0.493897	−	0.869521i	$-0.664428\pi$
$373$	7.25450	−	7.25450i	0.375624	−	0.375624i	0.869521	+	0.493897i	$0.164428\pi$
$374$	−9.72139	−	28.3277i	−0.502681	−	1.46479i
$375$	−5.95831	+	5.95831i	−0.307686	+	0.307686i
$376$	−4.47802	+	0.937378i	−0.230936	+	0.0483416i
$377$	−25.9535	−	7.91963i	−1.33667	−	0.407882i
$378$	−0.590536	+	0.202657i	−0.0303739	+	0.0104236i
$379$			4.56879i			0.234683i	0.993092	+	0.117341i	$0.0374372\pi$
$379$			4.56879i			0.234683i	−0.993092	+	0.117341i	$0.962563\pi$
$380$	20.5924	−	16.0204i	1.05637	−	0.821827i
$381$	4.11758	−	4.11758i	0.210950	−	0.210950i
$382$	1.03179	+	3.00660i	0.0527910	+	0.153831i
$383$	25.0640	−	25.0640i	1.28071	−	1.28071i	0.340451	−	0.940262i	$-0.389420\pi$
$383$	25.0640	−	25.0640i	1.28071	−	1.28071i	0.940262	−	0.340451i	$-0.110580\pi$
$384$	−11.3037	−	0.476366i	−0.576838	−	0.0243095i
$385$	−2.50032	+	2.50032i	−0.127428	+	0.127428i
$386$	5.58107	−	11.4130i	0.284069	−	0.580908i
$387$	−1.90101	−	1.90101i	−0.0966336	−	0.0966336i
$388$	20.5791	+	2.56985i	1.04475	+	0.130464i
$389$	−9.29703	−	9.29703i	−0.471378	−	0.471378i	0.430982	−	0.902360i	$-0.358167\pi$
$389$	−9.29703	−	9.29703i	−0.471378	−	0.471378i	−0.902360	+	0.430982i	$0.858167\pi$
$390$	0.456061	+	13.2485i	0.0230936	+	0.670861i
$391$	−12.1419			−0.614044
$392$	−16.1100	−	10.5329i	−0.813679	−	0.531992i
$393$			9.68752i			0.488671i
$394$	−7.71981	+	2.64925i	−0.388918	+	0.133467i
$395$		−	43.4267i		−	2.18504i
$396$	−3.78348	−	4.86325i	−0.190127	−	0.244388i
$397$	−9.42160			−0.472856			−0.236428	−	0.971649i	$-0.575977\pi$
$397$	−9.42160			−0.472856			−0.236428	+	0.971649i	$0.575977\pi$
$398$	5.30166	+	15.4488i	0.265748	+	0.774379i
$399$		−	2.21523i		−	0.110900i
$400$	1.73011	−	6.81925i	0.0865053	−	0.340962i
$401$	22.1391	−	22.1391i	1.10557	−	1.10557i	0.111849	−	0.993725i	$-0.464323\pi$
$401$	22.1391	−	22.1391i	1.10557	−	1.10557i	0.993725	−	0.111849i	$-0.0356772\pi$
$402$	−9.79216	+	20.0245i	−0.488388	+	0.998732i
$403$	−2.58069	+	8.45720i	−0.128553	+	0.421283i
$404$	13.1507	+	1.64222i	0.654273	+	0.0817034i
$405$	2.59977			0.129184
$406$	4.44430	−	1.52517i	0.220567	−	0.0756932i
$407$			19.8271i			0.982795i
$408$	19.0300	−	3.98352i	0.942124	−	0.197214i
$409$	6.68243	−	6.68243i	0.330425	−	0.330425i	−0.522323	−	0.852748i	$-0.674934\pi$
$409$	6.68243	−	6.68243i	0.330425	−	0.330425i	0.852748	+	0.522323i	$0.174934\pi$
$410$	−16.6521	+	34.0527i	−0.822387	+	1.68174i
$411$	0.335757			0.0165617
$412$	−0.308089	−	0.396016i	−0.0151785	−	0.0195103i
$413$	−4.28702	+	4.28702i	−0.210950	+	0.210950i
$414$	−2.36277	+	0.810845i	−0.116124	+	0.0398509i
$415$	19.4509			0.954808
$416$	11.0294	+	17.1567i	0.540761	+	0.841176i
$417$	−3.94170			−0.193026
$418$	20.6785	−	7.09635i	1.01142	−	0.347094i
$419$	8.15845	−	8.15845i	0.398567	−	0.398567i	−0.479161	−	0.877727i	$-0.659059\pi$
$419$	8.15845	−	8.15845i	0.398567	−	0.398567i	0.877727	+	0.479161i	$0.159059\pi$
$420$	−1.40951	−	1.81177i	−0.0687769	−	0.0884052i
$421$	−24.2088			−1.17987			−0.589933	−	0.807452i	$-0.700846\pi$
$421$	−24.2088			−1.17987			−0.589933	+	0.807452i	$0.700846\pi$
$422$	−1.47566	+	3.01766i	−0.0718341	+	0.146898i
$423$	1.14377	−	1.14377i	0.0556120	−	0.0556120i
$424$	3.34844	+	15.9961i	0.162615	+	0.776839i
$425$			12.0901i			0.586454i
$426$	−21.0090	+	7.20979i	−1.01789	+	0.349316i
$427$	3.30244			0.159816
$428$	5.17587	+	0.646344i	0.250185	+	0.0312422i
$429$	−3.24202	+	10.6244i	−0.156526	+	0.512953i
$430$	4.34217	−	8.87955i	0.209398	−	0.428210i
$431$	−0.871986	+	0.871986i	−0.0420021	+	0.0420021i	−0.727796	−	0.685794i	$-0.759455\pi$
$431$	−0.871986	+	0.871986i	−0.0420021	+	0.0420021i	0.685794	+	0.727796i	$0.259455\pi$
$432$	3.43713	−	2.04601i	0.165369	−	0.0984385i
$433$		−	6.16927i		−	0.296476i	−0.988952	−	0.148238i	$-0.952640\pi$
$433$		−	6.16927i		−	0.296476i	0.988952	−	0.148238i	$-0.0473602\pi$
$434$	−0.496993	−	1.44822i	−0.0238564	−	0.0695167i
$435$	−19.5656			−0.938098
$436$	−0.718049	−	0.922974i	−0.0343883	−	0.0442024i
$437$		−	8.86328i		−	0.423988i
$438$	1.17627	−	0.403669i	0.0562045	−	0.0192880i
$439$		−	13.5607i		−	0.647217i	−0.946191	−	0.323608i	$-0.895104\pi$
$439$		−	13.5607i		−	0.647217i	0.946191	−	0.323608i	$-0.104896\pi$
$440$	12.3970	−	18.9612i	0.591004	−	0.903937i
$441$	6.80510			0.324052
$442$	−25.6223	−	23.9170i	−1.21873	−	1.13762i
$443$	7.44734	+	7.44734i	0.353834	+	0.353834i	0.861534	−	0.507700i	$-0.169504\pi$
$443$	7.44734	+	7.44734i	0.353834	+	0.353834i	−0.507700	+	0.861534i	$0.669504\pi$
$444$	−12.7721	−	1.59494i	−0.606138	−	0.0756923i
$445$	−28.8330	−	28.8330i	−1.36682	−	1.36682i
$446$	−2.74447	+	5.61231i	−0.129954	+	0.265751i
$447$	10.7385	−	10.7385i	0.507913	−	0.507913i
$448$	−3.28934	−	1.28604i	−0.155407	−	0.0607598i
$449$	15.0382	−	15.0382i	0.709697	−	0.709697i	−0.256775	−	0.966471i	$-0.582660\pi$
$449$	15.0382	−	15.0382i	0.709697	−	0.709697i	0.966471	+	0.256775i	$0.0826598\pi$
$450$	0.807380	+	2.35267i	0.0380602	+	0.110906i
$451$	−22.4601	+	22.4601i	−1.05761	+	1.05761i
$452$	14.8993	−	11.5913i	0.700806	−	0.545208i
$453$			17.1846i			0.807403i
$454$	−21.4322	+	7.35500i	−1.00586	+	0.345187i
$455$	−1.20779	+	3.95805i	−0.0566220	+	0.185556i
$456$	2.90786	+	13.8914i	0.136173	+	0.650522i
$457$	−28.0523	+	28.0523i	−1.31223	+	1.31223i	−0.392460	+	0.919769i	$0.628376\pi$
$457$	−28.0523	+	28.0523i	−1.31223	+	1.31223i	−0.919769	+	0.392460i	$0.871624\pi$
$458$	−2.98896	−	8.70972i	−0.139665	−	0.406978i
$459$	−4.86061	+	4.86061i	−0.226874	+	0.226874i
$460$	−5.63952	−	7.24899i	−0.262944	−	0.337986i
$461$		−	17.7812i		−	0.828155i	−0.910242	−	0.414078i	$-0.864104\pi$
$461$		−	17.7812i		−	0.828155i	0.910242	−	0.414078i	$-0.135896\pi$
$462$	−0.624353	−	1.81934i	−0.0290475	−	0.0846433i
$463$	−5.04088	−	5.04088i	−0.234270	−	0.234270i	0.580203	−	0.814472i	$-0.302973\pi$
$463$	−5.04088	−	5.04088i	−0.234270	−	0.234270i	−0.814472	+	0.580203i	$0.802973\pi$
$464$	−25.8674	+	15.3980i	−1.20086	+	0.714834i
$465$			6.37563i			0.295663i
$466$	17.6904	−	6.07092i	0.819492	−	0.281230i
$467$	−23.4380	−	23.4380i	−1.08458	−	1.08458i	−0.996076	−	0.0885031i	$-0.971792\pi$
$467$	−23.4380	−	23.4380i	−1.08458	−	1.08458i	−0.0885031	−	0.996076i	$-0.528208\pi$
$468$	−6.58318	−	2.94307i	−0.304308	−	0.136044i
$469$	−4.92037	+	4.92037i	−0.227201	+	0.227201i
$470$	5.34252	+	2.61254i	0.246432	+	0.120507i
$471$	−6.72028			−0.309654
$472$	21.2558	−	32.5106i	0.978376	−	1.49642i
$473$	5.85667	−	5.85667i	0.269290	−	0.269290i
$474$	21.2216	+	10.3775i	0.974741	+	0.476656i
$475$	−8.82541			−0.404937
$476$	6.02258	+	0.752079i	0.276045	+	0.0344715i
$477$	−4.08570	−	4.08570i	−0.187071	−	0.187071i
$478$	−1.59435	+	3.26037i	−0.0729239	+	0.149126i
$479$	2.83070	+	2.83070i	0.129338	+	0.129338i	0.768812	−	0.639474i	$-0.220848\pi$
$479$	2.83070	+	2.83070i	0.129338	+	0.129338i	−0.639474	+	0.768812i	$0.720848\pi$
$480$	11.2170	+	9.51109i	0.511985	+	0.434120i
$481$	10.9046	+	20.4822i	0.497207	+	0.933907i
$482$	10.8275	−	22.1417i	0.493177	−	1.00852i
$483$	−0.779811			−0.0354826
$484$	−2.38126	+	1.85256i	−0.108239	+	0.0842071i
$485$	−19.0624	−	19.0624i	−0.865579	−	0.865579i
$486$	−0.621260	+	1.27045i	−0.0281809	+	0.0576287i
$487$	−15.2061	−	15.2061i	−0.689053	−	0.689053i	0.272970	−	0.962023i	$-0.411994\pi$
$487$	−15.2061	−	15.2061i	−0.689053	−	0.689053i	−0.962023	+	0.272970i	$0.911994\pi$
$488$	−20.7090	+	4.33499i	−0.937454	+	0.196236i
$489$	−5.56733	−	5.56733i	−0.251763	−	0.251763i
$490$	8.12130	+	23.6651i	0.366883	+	1.06908i
$491$	−21.3579	+	21.3579i	−0.963868	+	0.963868i	−0.999370	−	0.0355015i	$-0.988697\pi$
$491$	−21.3579	+	21.3579i	−0.963868	+	0.963868i	0.0355015	+	0.999370i	$0.488697\pi$
$492$	−12.6615	−	16.2749i	−0.570823	−	0.733731i
$493$	36.5803	−	36.5803i	1.64750	−	1.64750i
$494$	17.4588	−	18.7036i	0.785507	−	0.841515i
$495$			8.00945i			0.359998i
$496$	5.01759	+	8.42915i	0.225296	+	0.378480i
$497$	−6.93385			−0.311026
$498$	−4.64812	+	9.50519i	−0.208287	+	0.425938i
$499$	26.9120			1.20475			0.602374	−	0.798214i	$-0.294222\pi$
$499$	26.9120			1.20475			0.602374	+	0.798214i	$0.294222\pi$
$500$	13.3014	−	10.3481i	0.594857	−	0.462783i
$501$		−	2.69881i		−	0.120574i
$502$	7.88308	−	16.1205i	0.351839	−	0.719495i
$503$	15.6841			0.699319			0.349660	−	0.936877i	$-0.386297\pi$
$503$	15.6841			0.699319			0.349660	+	0.936877i	$0.386297\pi$
$504$	1.22219	−	0.255840i	0.0544408	−	0.0113960i
$505$	−12.1815	−	12.1815i	−0.542070	−	0.542070i
$506$	−2.49807	−	7.27928i	−0.111053	−	0.323604i
$507$	2.49414	+	12.7585i	0.110769	+	0.566625i
$508$	−9.19213	+	7.15123i	−0.407835	+	0.317285i
$509$			34.3940i			1.52449i	0.647290	+	0.762244i	$0.275902\pi$
$509$			34.3940i			1.52449i	−0.647290	+	0.762244i	$0.724098\pi$
$510$	−22.7038	−	11.1023i	−1.00534	−	0.491620i
$511$	0.388219			0.0171738
$512$	22.3151	+	3.74676i	0.986196	+	0.165585i
$513$	−3.54811	−	3.54811i	−0.156653	−	0.156653i
$514$	−0.906460	−	2.64139i	−0.0399823	−	0.116507i
$515$			0.652211i			0.0287398i
$516$	3.30159	+	4.24383i	0.145344	+	0.186824i
$517$	3.52376	+	3.52376i	0.154975	+	0.154975i
$518$	−3.60958	−	1.76512i	−0.158596	−	0.0775547i
$519$		−	0.0315548i		−	0.00138510i
$520$	2.37824	−	26.4057i	0.104293	−	1.15797i
$521$			45.0314i			1.97286i	0.164183	+	0.986430i	$0.447501\pi$
$521$			45.0314i			1.97286i	−0.164183	+	0.986430i	$0.552499\pi$
$522$	4.67552	−	9.56123i	0.204642	−	0.418484i
$523$	2.59835	+	2.59835i	0.113618	+	0.113618i	0.761630	−	0.648012i	$-0.224399\pi$
$523$	2.59835	+	2.59835i	0.113618	+	0.113618i	−0.648012	+	0.761630i	$0.724399\pi$
$524$	2.40084	−	19.2257i	0.104881	−	0.839879i
$525$			0.776479i			0.0338883i
$526$	−27.0098	+	9.26912i	−1.17768	+	0.404153i
$527$	−11.9201	−	11.9201i	−0.519246	−	0.519246i
$528$	6.30339	+	10.5892i	0.274320	+	0.460836i
$529$	19.8799			0.864345
$530$	9.33234	−	19.0842i	0.405371	−	0.828965i
$531$			13.7329i			0.595958i
$532$	−0.548997	+	4.39632i	−0.0238020	+	0.190605i
$533$	−10.8495	+	35.5548i	−0.469942	+	1.54005i
$534$	20.9801	−	7.19987i	0.907899	−	0.311569i
$535$	−4.79439	−	4.79439i	−0.207280	−	0.207280i
$536$	24.3960	−	37.3136i	1.05375	−	1.61170i
$537$	−4.84414			−0.209040
$538$	34.1219	+	16.6859i	1.47110	+	0.719380i
$539$			20.9653i			0.903041i
$540$	−5.15947	−	0.644297i	−0.222028	−	0.0277261i
$541$	27.3236			1.17474			0.587368	−	0.809320i	$-0.300164\pi$
$541$	27.3236			1.17474			0.587368	+	0.809320i	$0.300164\pi$
$542$	10.0741	+	4.92633i	0.432720	+	0.211604i
$543$	6.67197			0.286322
$544$	−38.7539	+	3.18947i	−1.66156	+	0.136747i
$545$			1.52008i			0.0651129i
$546$	−1.64558	−	1.53606i	−0.0704245	−	0.0657373i
$547$	−4.06928	+	4.06928i	−0.173990	+	0.173990i	−0.788730	−	0.614740i	$-0.789261\pi$
$547$	−4.06928	+	4.06928i	−0.173990	+	0.173990i	0.614740	+	0.788730i	$0.289261\pi$
$548$	−0.666339	−	0.0832101i	−0.0284646	−	0.00355456i
$549$	5.28947	−	5.28947i	0.225749	−	0.225749i
$550$	−7.24817	+	2.48740i	−0.309063	+	0.106063i
$551$	26.7026	+	26.7026i	1.13757	+	1.13757i
$552$	4.89007	−	1.02363i	0.208135	−	0.0435686i
$553$	5.21451	+	5.21451i	0.221744	+	0.221744i
$554$	−14.3211	−	7.00313i	−0.608445	−	0.297535i
$555$	11.8308	+	11.8308i	0.502189	+	0.502189i
$556$	7.82264	+	0.976863i	0.331754	+	0.0414282i
$557$	−25.7141			−1.08954			−0.544771	−	0.838585i	$-0.683383\pi$
$557$	−25.7141			−1.08954			−0.544771	+	0.838585i	$0.683383\pi$
$558$	−3.11562	−	1.52356i	−0.131895	−	0.0644976i
$559$	2.82909	−	9.27123i	0.119658	−	0.392131i
$560$	2.34828	+	3.94492i	0.0992329	+	0.166703i
$561$	−14.9747	−	14.9747i	−0.632232	−	0.632232i
$562$	14.5293	+	7.10494i	0.612880	+	0.299704i
$563$	16.1382	+	16.1382i	0.680143	+	0.680143i	0.960032	−	0.279889i	$-0.0902977\pi$
$563$	16.1382	+	16.1382i	0.680143	+	0.680143i	−0.279889	+	0.960032i	$0.590298\pi$
$564$	−2.55337	+	1.98645i	−0.107516	+	0.0836447i
$565$	−24.5382			−1.03233
$566$	19.9750	−	40.8480i	0.839612	−	1.71697i
$567$	−0.312171	+	0.312171i	−0.0131099	+	0.0131099i
$568$	43.4810	−	9.10182i	1.82442	−	0.381904i
$569$	37.7402			1.58215			0.791075	−	0.611719i	$-0.209522\pi$
$569$	37.7402			1.58215			0.791075	+	0.611719i	$0.209522\pi$
$570$	8.10440	−	16.5731i	0.339456	−	0.694172i
$571$	30.6444	−	30.6444i	1.28243	−	1.28243i	0.343147	−	0.939282i	$-0.388507\pi$
$571$	30.6444	−	30.6444i	1.28243	−	1.28243i	0.939282	−	0.343147i	$-0.111493\pi$
$572$	9.06710	−	20.2817i	0.379114	−	0.848019i
$573$	1.58936	+	1.58936i	0.0663963	+	0.0663963i
$574$	−2.08940	−	6.08844i	−0.0872100	−	0.254126i
$575$			3.10674i			0.129560i
$576$	−7.32834	+	3.20866i	−0.305347	+	0.133694i
$577$	−1.65091	−	1.65091i	−0.0687281	−	0.0687281i	0.671907	−	0.740635i	$-0.265475\pi$
$577$	−1.65091	−	1.65091i	−0.0687281	−	0.0687281i	−0.740635	+	0.671907i	$0.765475\pi$
$578$	40.4650	−	13.8866i	1.68312	−	0.577607i
$579$		−	8.98347i		−	0.373340i
$580$	38.8296	+	4.84890i	1.61231	+	0.201340i
$581$	−2.33559	+	2.33559i	−0.0968966	+	0.0968966i
$582$	13.8706	−	4.76006i	0.574956	−	0.197311i
$583$	12.5873	−	12.5873i	0.521314	−	0.521314i
$584$	−2.43446	+	0.509601i	−0.100739	+	0.0210875i
$585$	4.40506	+	8.27406i	0.182127	+	0.342090i
$586$	3.60019	+	10.4908i	0.148722	+	0.433371i
$587$		−	12.5683i		−	0.518747i	−0.965777	−	0.259374i	$-0.916484\pi$
$587$		−	12.5683i		−	0.518747i	0.965777	−	0.259374i	$-0.0835161\pi$
$588$	−13.5053	−	1.68649i	−0.556949	−	0.0695499i
$589$	8.70132	−	8.70132i	0.358532	−	0.358532i
$590$	−47.7571	+	16.3891i	−1.96613	+	0.674727i
$591$	−4.08087	+	4.08087i	−0.167865	+	0.167865i
$592$	24.9521	+	6.33058i	1.02552	+	0.260185i
$593$	−16.6876	+	16.6876i	−0.685276	+	0.685276i	−0.961184	−	0.275908i	$-0.911021\pi$
$593$	−16.6876	+	16.6876i	−0.685276	+	0.685276i	0.275908	+	0.961184i	$0.411021\pi$
$594$	−3.91403	−	1.91399i	−0.160595	−	0.0785321i
$595$	−5.57871	−	5.57871i	−0.228705	−	0.228705i
$596$	−23.9728	+	18.6502i	−0.981963	+	0.763940i
$597$	8.16660	+	8.16660i	0.334237	+	0.334237i
$598$	−6.58408	−	6.14587i	−0.269243	−	0.251323i
$599$	5.17898			0.211607			0.105804	−	0.994387i	$-0.466258\pi$
$599$	5.17898			0.211607			0.105804	+	0.994387i	$0.466258\pi$
$600$	−1.01926	−	4.86917i	−0.0416110	−	0.198783i
$601$		−	12.7711i		−	0.520946i	−0.965481	−	0.260473i	$-0.916122\pi$
$601$		−	12.7711i		−	0.520946i	0.965481	−	0.260473i	$-0.0838784\pi$
$602$	0.544830	+	1.58761i	0.0222056	+	0.0647063i
$603$			15.7618i			0.641869i
$604$	4.25882	−	34.1043i	0.173289	−	1.38768i
$605$	3.92177			0.159443
$606$	8.86378	−	3.04183i	0.360066	−	0.123566i
$607$		−	5.73009i		−	0.232577i	−0.993215	−	0.116289i	$-0.962900\pi$
$607$		−	5.73009i		−	0.232577i	0.993215	−	0.116289i	$-0.0370997\pi$
$608$	−2.32823	−	28.2892i	−0.0944220	−	1.14728i
$609$	2.34936	−	2.34936i	0.0952008	−	0.0952008i
$610$	24.7070	+	12.0819i	1.00036	+	0.489183i
$611$	5.57818	+	1.70217i	0.225669	+	0.0688622i
$612$	10.8509	−	8.44170i	0.438621	−	0.341236i
$613$	38.1340			1.54022			0.770109	−	0.637912i	$-0.220202\pi$
$613$	38.1340			1.54022			0.770109	+	0.637912i	$0.220202\pi$
$614$	8.85966	+	25.8167i	0.357547	+	1.04188i
$615$			26.8037i			1.08083i
$616$	0.788198	+	3.76536i	0.0317574	+	0.151711i
$617$	−14.6535	+	14.6535i	−0.589927	+	0.589927i	−0.937611	−	0.347685i	$-0.886968\pi$
$617$	−14.6535	+	14.6535i	−0.589927	+	0.589927i	0.347685	+	0.937611i	$0.386968\pi$
$618$	−0.318720	−	0.155857i	−0.0128208	−	0.00626948i
$619$	−12.1900			−0.489959			−0.244980	−	0.969528i	$-0.578781\pi$
$619$	−12.1900			−0.489959			−0.244980	+	0.969528i	$0.578781\pi$
$620$	1.58006	−	12.6530i	0.0634568	−	0.508156i
$621$	−1.24901	+	1.24901i	−0.0501212	+	0.0501212i
$622$	11.6919	+	34.0697i	0.468803	+	1.36607i
$623$	6.92431			0.277417
$624$	12.3355	+	7.47228i	0.493816	+	0.299131i
$625$	−30.7007			−1.22803
$626$	0.357676	+	1.04225i	0.0142956	+	0.0416568i
$627$	10.9311	−	10.9311i	0.436547	−	0.436547i
$628$	13.3370	+	1.66547i	0.532203	+	0.0664596i
$629$	−44.2383			−1.76390
$630$	−1.45814	−	0.713043i	−0.0580937	−	0.0284083i
$631$	18.8694	−	18.8694i	0.751179	−	0.751179i	−0.223520	−	0.974699i	$-0.571755\pi$
$631$	18.8694	−	18.8694i	0.751179	−	0.751179i	0.974699	+	0.223520i	$0.0717548\pi$
$632$	−39.5443	−	25.8544i	−1.57299	−	1.02843i
$633$			2.37528i			0.0944087i
$634$	−3.45933	−	10.0803i	−0.137387	−	0.400341i
$635$	15.1388			0.600766
$636$	7.09588	+	9.12098i	0.281370	+	0.361670i
$637$	11.5306	+	21.6580i	0.456858	+	0.858120i
$638$	29.4565	+	14.4045i	1.16619	+	0.570279i
$639$	−11.1059	+	11.1059i	−0.439341	+	0.439341i
$640$	−19.9040	−	21.6555i	−0.786776	−	0.856007i
$641$		−	43.6031i		−	1.72222i	−0.508419	−	0.861110i	$-0.669770\pi$
$641$		−	43.6031i		−	1.72222i	0.508419	−	0.861110i	$-0.330230\pi$
$642$	3.48861	−	1.19721i	0.137684	−	0.0472499i
$643$	5.43518			0.214342			0.107171	−	0.994241i	$-0.465821\pi$
$643$	5.43518			0.214342			0.107171	+	0.994241i	$0.465821\pi$
$644$	1.54760	+	0.193259i	0.0609841	+	0.00761548i
$645$		−	6.98931i		−	0.275204i
$646$	15.8334	+	46.1378i	0.622956	+	1.81527i
$647$			20.5427i			0.807618i	0.914843	+	0.403809i	$0.132314\pi$
$647$			20.5427i			0.807618i	−0.914843	+	0.403809i	$0.867686\pi$
$648$	1.54780	−	2.36735i	0.0608031	−	0.0929982i
$649$	−42.3088			−1.66076
$650$	−6.11961	+	6.55595i	−0.240031	+	0.257145i
$651$	−0.765561	−	0.765561i	−0.0300047	−	0.0300047i
$652$	9.66910	+	12.4286i	0.378671	+	0.486741i
$653$	22.8348	+	22.8348i	0.893594	+	0.893594i	0.994859	−	0.101265i	$-0.0322891\pi$
$653$	22.8348	+	22.8348i	0.893594	+	0.893594i	−0.101265	+	0.994859i	$0.532289\pi$
$654$	−0.742825	−	0.363247i	−0.0290467	−	0.0142041i
$655$	−17.8087	+	17.8087i	−0.695845	+	0.695845i
$656$	21.0944	+	35.4369i	0.823597	+	1.38358i
$657$	0.621805	−	0.621805i	0.0242589	−	0.0242589i
$658$	−0.955212	+	0.327805i	−0.0372380	+	0.0127792i
$659$	−22.3109	+	22.3109i	−0.869111	+	0.869111i	−0.992374	−	0.123263i	$-0.960664\pi$
$659$	−22.3109	+	22.3109i	−0.869111	+	0.869111i	0.123263	+	0.992374i	$0.460664\pi$
$660$	1.98497	−	15.8954i	0.0772647	−	0.618729i
$661$		−	3.35317i		−	0.130423i	−0.997871	−	0.0652115i	$-0.979228\pi$
$661$		−	3.35317i		−	0.130423i	0.997871	−	0.0652115i	$-0.0207722\pi$
$662$	6.08797	+	17.7401i	0.236616	+	0.689488i
$663$	−23.7053	−	7.23359i	−0.920636	−	0.280929i
$664$	11.5802	−	17.7119i	0.449401	−	0.687357i
$665$	4.07230	−	4.07230i	0.157917	−	0.157917i
$666$	−8.60858	+	2.95426i	−0.333576	+	0.114475i
$667$	9.39993	−	9.39993i	0.363967	−	0.363967i
$668$	−0.668841	+	5.35602i	−0.0258782	+	0.207231i
$669$			4.41759i			0.170794i
$670$	−54.8125	+	18.8103i	−2.11759	+	0.726706i
$671$	16.2960	+	16.2960i	0.629098	+	0.629098i
$672$	−2.48895	+	0.204843i	−0.0960134	+	0.00790197i
$673$		−	28.8339i		−	1.11147i	−0.831361	−	0.555733i	$-0.812438\pi$
$673$		−	28.8339i		−	1.11147i	0.831361	−	0.555733i	$-0.187562\pi$
$674$	−1.47746	−	4.30526i	−0.0569097	−	0.165832i
$675$	1.24368	+	1.24368i	0.0478691	+	0.0478691i
$676$	−1.78792	−	25.9385i	−0.0687660	−	0.997633i
$677$	2.94170	−	2.94170i	0.113059	−	0.113059i	−0.648314	−	0.761373i	$-0.724526\pi$
$677$	2.94170	−	2.94170i	0.113059	−	0.113059i	0.761373	+	0.648314i	$0.224526\pi$
$678$	5.86381	−	11.9912i	0.225198	−	0.460520i
$679$	4.57788			0.175683
$680$	42.3061	+	27.6602i	1.62237	+	1.06072i
$681$	−11.3295	+	11.3295i	−0.434149	+	0.434149i
$682$	4.69384	−	9.59869i	0.179736	−	0.367553i
$683$	7.51526			0.287563			0.143782	−	0.989609i	$-0.454074\pi$
$683$	7.51526			0.287563			0.143782	+	0.989609i	$0.454074\pi$
$684$	6.16221	+	7.92085i	0.235618	+	0.302861i
$685$	0.617229	+	0.617229i	0.0235831	+	0.0235831i
$686$	−7.74290	−	3.78634i	−0.295625	−	0.144563i
$687$	−4.60416	−	4.60416i	−0.175660	−	0.175660i
$688$	−5.50054	−	9.24048i	−0.209706	−	0.352290i
$689$	6.08037	−	19.9260i	0.231644	−	0.759121i
$690$	−5.83411	−	2.85293i	−0.222101	−	0.108609i
$691$	49.5404			1.88461			0.942303	−	0.334761i	$-0.108656\pi$
$691$	49.5404			1.88461			0.942303	+	0.334761i	$0.108656\pi$
$692$	−0.00782015	+	0.0626231i	−0.000297278	+	0.00238057i
$693$	−0.961744	−	0.961744i	−0.0365336	−	0.0365336i
$694$	11.1340	+	5.44462i	0.422641	+	0.206675i
$695$	−7.24609	−	7.24609i	−0.274860	−	0.274860i
$696$	−11.6485	+	17.8164i	−0.441536	+	0.675327i
$697$	−50.1130	−	50.1130i	−1.89817	−	1.89817i
$698$	−34.7172	+	11.9141i	−1.31407	+	0.450956i
$699$	9.35156	−	9.35156i	0.353708	−	0.353708i
$700$	0.192433	−	1.54099i	0.00727329	−	0.0582439i
$701$	−0.00498862	+	0.00498862i	−0.000188418	+	0.000188418i	−0.707201	−	0.707013i	$-0.750042\pi$
$701$	−0.00498862	+	0.00498862i	−0.000188418	+	0.000188418i	0.707013	+	0.707201i	$0.250042\pi$
$702$	−5.09600	+	0.175424i	−0.192336	+	0.00662093i
$703$		−	32.2927i		−	1.21794i
$704$	−9.88532	−	22.5773i	−0.372567	−	0.850915i
$705$	4.20522			0.158378
$706$	−42.7660	−	20.9129i	−1.60952	−	0.787069i
$707$	2.92541			0.110022
$708$	3.40341	−	27.2542i	0.127908	−	1.02427i
$709$		−	9.34496i		−	0.350957i	−0.984483	−	0.175479i	$-0.943853\pi$
$709$		−	9.34496i		−	0.350957i	0.984483	−	0.175479i	$-0.0561473\pi$
$710$	−51.8752	−	25.3674i	−1.94684	−	0.952021i
$711$	16.7040			0.626451
$712$	−43.4212	+	9.08930i	−1.62728	+	0.340636i
$713$	−3.06306	−	3.06306i	−0.114712	−	0.114712i
$714$	4.05931	−	1.39306i	0.151916	−	0.0521338i
$715$	−25.4910	+	13.5712i	−0.953308	+	0.507536i
$716$	9.61361	+	1.20051i	0.359278	+	0.0448653i
$717$			2.56632i			0.0958410i
$718$	18.1152	−	37.0447i	0.676052	−	1.38250i
$719$	−4.52247			−0.168660			−0.0843299	−	0.996438i	$-0.526875\pi$
$719$	−4.52247			−0.168660			−0.0843299	+	0.996438i	$0.526875\pi$
$720$	10.0797	+	2.55733i	0.375650	+	0.0953059i
$721$	−0.0783150	−	0.0783150i	−0.00291660	−	0.00291660i
$722$	−8.26418	+	2.83607i	−0.307561	+	0.105547i
$723$		−	17.4282i		−	0.648163i
$724$	−13.2411	−	1.65350i	−0.492101	−	0.0614519i
$725$	−9.35976	−	9.35976i	−0.347613	−	0.347613i
$726$	−0.937174	+	1.91648i	−0.0347818	+	0.0711271i
$727$			33.8528i			1.25553i	0.778403	+	0.627765i	$0.216030\pi$
$727$			33.8528i			1.25553i	−0.778403	+	0.627765i	$0.783970\pi$
$728$	2.88513	+	3.45627i	0.106930	+	0.128098i
$729$			1.00000i			0.0370370i
$730$	2.90444	+	1.42029i	0.107498	+	0.0525674i
$731$	13.0674	+	13.0674i	0.483315	+	0.483315i
$732$	−11.8083	+	9.18653i	−0.436447	+	0.339544i
$733$		−	33.7659i		−	1.24717i	−0.781755	−	0.623585i	$-0.785675\pi$
$733$		−	33.7659i		−	1.24717i	0.781755	−	0.623585i	$-0.214325\pi$
$734$	−14.1918	−	41.3544i	−0.523830	−	1.52642i
$735$	12.5099	+	12.5099i	0.461436	+	0.461436i
$736$	−9.95844	+	0.819587i	−0.367073	+	0.0302104i
$737$	−48.5593			−1.78871
$738$	−13.0983	−	6.40520i	−0.482157	−	0.235779i
$739$			16.0669i			0.591032i	0.955338	+	0.295516i	$0.0954916\pi$
$739$			16.0669i			0.591032i	−0.955338	+	0.295516i	$0.904508\pi$
$740$	−20.5472	−	26.4112i	−0.755330	−	0.970895i
$741$	5.28032	−	17.3042i	0.193977	−	0.635685i
$742$	1.17097	+	3.41215i	0.0429875	+	0.125264i
$743$	30.5825	+	30.5825i	1.12196	+	1.12196i	0.991446	+	0.130519i	$0.0416642\pi$
$743$	30.5825	+	30.5825i	1.12196	+	1.12196i	0.130519	+	0.991446i	$0.458336\pi$
$744$	5.80563	+	3.79578i	0.212845	+	0.139160i
$745$	39.4815			1.44649
$746$	−6.37376	+	13.0340i	−0.233360	+	0.477210i
$747$			7.48177i			0.273744i
$748$	26.0074	+	33.4297i	0.950926	+	1.22231i
$749$	1.15138			0.0420707
$750$	5.23493	−	10.7052i	0.191153	−	0.390899i
$751$	−49.0740			−1.79074			−0.895368	−	0.445327i	$-0.853087\pi$
$751$	−49.0740			−1.79074			−0.895368	+	0.445327i	$0.853087\pi$
$752$	5.55968	−	3.30949i	0.202740	−	0.120685i
$753$		−	12.6889i		−	0.462408i
$754$	38.3519	−	1.32022i	1.39669	−	0.0480794i
$755$	−31.5907	+	31.5907i	−1.14970	+	1.14970i
$756$	0.696894	−	0.542165i	0.0253458	−	0.0197184i
$757$	−19.2872	+	19.2872i	−0.701004	+	0.701004i	−0.964626	−	0.263622i	$-0.915083\pi$
$757$	−19.2872	+	19.2872i	−0.701004	+	0.701004i	0.263622	+	0.964626i	$0.415083\pi$
$758$	−2.09728	−	6.11139i	−0.0761766	−	0.221976i
$759$	−3.84800	−	3.84800i	−0.139673	−	0.139673i
$760$	−20.1912	+	30.8823i	−0.732410	+	1.12022i
$761$	13.4163	+	13.4163i	0.486341	+	0.486341i	0.907150	−	0.420808i	$-0.138253\pi$
$761$	13.4163	+	13.4163i	0.486341	+	0.486341i	−0.420808	+	0.907150i	$0.638253\pi$
$762$	−3.61768	+	7.39798i	−0.131055	+	0.268001i
$763$	−0.182525	−	0.182525i	−0.00660784	−	0.00660784i
$764$	−2.76033	−	3.54810i	−0.0998651	−	0.128366i
$765$	−17.8707			−0.646116
$766$	−22.0211	+	45.0322i	−0.795655	+	1.62708i
$767$	−43.7065	+	23.2691i	−1.57815	+	0.840199i
$768$	15.3389	−	4.55169i	0.553495	−	0.164245i
$769$	37.1538	+	37.1538i	1.33980	+	1.33980i	0.896250	+	0.443550i	$0.146281\pi$
$769$	37.1538	+	37.1538i	1.33980	+	1.33980i	0.443550	+	0.896250i	$0.353719\pi$
$770$	2.19676	−	4.49228i	0.0791658	−	0.161891i
$771$	−1.39630	−	1.39630i	−0.0502865	−	0.0502865i
$772$	−2.22636	+	17.8285i	−0.0801283	+	0.641660i
$773$	−19.0516			−0.685238			−0.342619	−	0.939474i	$-0.611314\pi$
$773$	−19.0516			−0.685238			−0.342619	+	0.939474i	$0.611314\pi$
$774$	3.41551	+	1.67021i	0.122768	+	0.0600345i
$775$	−3.04997	+	3.04997i	−0.109558	+	0.109558i
$776$	−28.7071	+	6.00922i	−1.03053	+	0.215719i
$777$	−2.84119			−0.101927
$778$	16.7038	+	8.16831i	0.598861	+	0.292848i
$779$	36.5811	−	36.5811i	1.31065	−	1.31065i
$780$	−6.69168	−	17.5123i	−0.239601	−	0.627041i
$781$	−34.2152	−	34.2152i	−1.22432	−	1.22432i
$782$	16.2415	−	5.57370i	0.580796	−	0.199315i
$783$		−	7.52588i		−	0.268953i
$784$	26.3845	+	6.69399i	0.942303	+	0.239071i
$785$	−12.3540	−	12.3540i	−0.440933	−	0.440933i
$786$	−4.44701	−	12.9584i	−0.158620	−	0.462211i
$787$			30.5115i			1.08762i	0.839209	+	0.543809i	$0.183018\pi$
$787$			30.5115i			1.08762i	−0.839209	+	0.543809i	$0.816982\pi$
$788$	9.11019	−	7.08748i	0.324537	−	0.252481i
$789$	−14.2780	+	14.2780i	−0.508311	+	0.508311i
$790$	19.9348	+	58.0893i	0.709250	+	2.06672i
$791$	2.94645	−	2.94645i	0.104764	−	0.104764i
$792$	7.29338	+	4.76849i	0.259159	+	0.169441i
$793$	25.7968	+	7.87183i	0.916072	+	0.279537i
$794$	12.6027	−	4.32494i	0.447253	−	0.153486i
$795$		−	15.0216i		−	0.532763i
$796$	−14.1834	−	18.2312i	−0.502718	−	0.646189i
$797$	−26.4617	+	26.4617i	−0.937323	+	0.937323i	−0.998148	−	0.0608252i	$-0.980627\pi$
$797$	−26.4617	+	26.4617i	−0.937323	+	0.937323i	0.0608252	+	0.998148i	$0.480627\pi$
$798$	1.01689	+	2.96318i	0.0359976	+	0.104895i
$799$	−7.86220	+	7.86220i	−0.278145	+	0.278145i
$800$	0.816085	+	9.91589i	0.0288530	+	0.350580i
$801$	11.0906	−	11.0906i	0.391866	−	0.391866i
$802$	−19.4513	+	39.7770i	−0.686848	+	1.40457i
$803$	1.91567	+	1.91567i	0.0676027	+	0.0676027i
$804$	3.90621	−	31.2806i	0.137761	−	1.10318i
$805$	−1.43354	−	1.43354i	−0.0505257	−	0.0505257i
$806$	−0.430205	−	12.4973i	−0.0151533	−	0.440200i
$807$	26.8582			0.945453
$808$	−18.3448	+	3.84009i	−0.645367	+	0.135094i
$809$		−	19.7169i		−	0.693211i	−0.938011	−	0.346606i	$-0.887334\pi$
$809$		−	19.7169i		−	0.693211i	0.938011	−	0.346606i	$-0.112666\pi$
$810$	−3.47756	+	1.19341i	−0.122189	+	0.0419323i
$811$			34.0528i			1.19576i	0.801587	+	0.597878i	$0.203989\pi$
$811$			34.0528i			1.19576i	−0.801587	+	0.597878i	$0.796011\pi$
$812$	−5.24474	+	4.08027i	−0.184054	+	0.143189i
$813$	7.92958			0.278102
$814$	−9.10155	−	26.5216i	−0.319009	−	0.929580i
$815$		−	20.4690i		−	0.716999i
$816$	−23.6266	+	14.0641i	−0.827097	+	0.492343i
$817$	−9.53884	+	9.53884i	−0.333722	+	0.333722i
$818$	−5.87114	+	12.0062i	−0.205280	+	0.419787i
$819$	−1.52246	−	0.464574i	−0.0531991	−	0.0162335i
$820$	6.64272	−	53.1943i	0.231974	−	1.85763i
$821$	20.9843			0.732357			0.366179	−	0.930545i	$-0.380666\pi$
$821$	20.9843			0.732357			0.366179	+	0.930545i	$0.380666\pi$
$822$	−0.449122	+	0.154128i	−0.0156649	+	0.00537582i
$823$		−	31.0687i		−	1.08299i	−0.840705	−	0.541494i	$-0.817859\pi$
$823$		−	31.0687i		−	1.08299i	0.840705	−	0.541494i	$-0.182141\pi$
$824$	0.593901	+	0.388299i	0.0206895	+	0.0135270i
$825$	−3.83155	+	3.83155i	−0.133398	+	0.133398i
$826$	3.76655	−	7.70242i	0.131055	−	0.268001i
$827$	22.0032			0.765127			0.382563	−	0.923929i	$-0.375041\pi$
$827$	22.0032			0.765127			0.382563	+	0.923929i	$0.375041\pi$
$828$	2.78832	−	2.16924i	0.0969007	−	0.0753861i
$829$	−26.4165	+	26.4165i	−0.917483	+	0.917483i	−0.996846	−	0.0793628i	$-0.974711\pi$
$829$	−26.4165	+	26.4165i	−0.917483	+	0.917483i	0.0793628	+	0.996846i	$0.474711\pi$
$830$	−26.0183	+	8.92885i	−0.903108	+	0.309925i
$831$	−11.2725			−0.391038
$832$	−22.6291	−	17.8865i	−0.784521	−	0.620102i
$833$	−46.7778			−1.62076
$834$	5.27257	−	1.80942i	0.182574	−	0.0626550i
$835$	4.96127	−	4.96127i	0.171692	−	0.171692i
$836$	−24.4028	+	18.9847i	−0.843988	+	0.656600i
$837$	−2.45238			−0.0847667
$838$	−7.16797	+	14.6582i	−0.247613	+	0.506358i
$839$	−19.9383	+	19.9383i	−0.688346	+	0.688346i	−0.961866	−	0.273520i	$-0.911812\pi$
$839$	−19.9383	+	19.9383i	−0.688346	+	0.688346i	0.273520	+	0.961866i	$0.411812\pi$
$840$	2.71709	+	1.77646i	0.0937486	+	0.0612938i
$841$			27.6388i			0.953062i
$842$	32.3827	−	11.1129i	1.11598	−	0.382977i
$843$	11.4363			0.393888
$844$	0.588660	−	4.71394i	0.0202625	−	0.162260i
$845$	−18.8692	+	28.0392i	−0.649119	+	0.964578i
$846$	−1.00491	+	2.05499i	−0.0345495	+	0.0706521i
$847$	−0.470911	+	0.470911i	−0.0161807	+	0.0161807i
$848$	−11.8219	−	19.8599i	−0.405967	−	0.681993i
$849$		−	32.1524i		−	1.10347i
$850$	−5.54988	−	16.1721i	−0.190359	−	0.554699i
$851$	−11.3678			−0.389682
$852$	24.7929	−	19.2882i	0.849390	−	0.660803i
$853$		−	36.3083i		−	1.24317i	−0.783346	−	0.621586i	$-0.786489\pi$
$853$		−	36.3083i		−	1.24317i	0.783346	−	0.621586i	$-0.213511\pi$
$854$	−4.41747	+	1.51597i	−0.151163	+	0.0518754i
$855$		−	13.0451i		−	0.446133i
$856$	−7.22014	+	1.51138i	−0.246779	+	0.0516580i
$857$	18.0709			0.617289			0.308644	−	0.951178i	$-0.400125\pi$
$857$	18.0709			0.617289			0.308644	+	0.951178i	$0.400125\pi$
$858$	−0.540449	−	15.6999i	−0.0184506	−	0.535986i
$859$	−2.21247	−	2.21247i	−0.0754885	−	0.0754885i	0.668354	−	0.743843i	$-0.266999\pi$
$859$	−2.21247	−	2.21247i	−0.0754885	−	0.0754885i	−0.743843	+	0.668354i	$0.766999\pi$
$860$	−1.73215	+	13.8709i	−0.0590657	+	0.472993i
$861$	−3.21849	−	3.21849i	−0.109686	−	0.109686i
$862$	0.766122	−	1.56668i	0.0260942	−	0.0533615i
$863$	−8.59919	+	8.59919i	−0.292720	+	0.292720i	−0.838154	−	0.545434i	$-0.816365\pi$
$863$	−8.59919	+	8.59919i	−0.292720	+	0.292720i	0.545434	+	0.838154i	$0.316365\pi$
$864$	−3.65843	+	4.31462i	−0.124462	+	0.146786i
$865$	0.0580077	−	0.0580077i	0.00197232	−	0.00197232i
$866$	2.83197	+	8.25226i	0.0962344	+	0.280423i
$867$	21.3907	−	21.3907i	0.726467	−	0.726467i
$868$	1.32959	+	1.70905i	0.0451294	+	0.0580089i
$869$			51.4623i			1.74574i
$870$	26.1717	−	8.98148i	0.887303	−	0.304501i
$871$	−50.1636	+	26.7068i	−1.69973	+	0.904926i
$872$	1.38418	+	0.904989i	0.0468741	+	0.0306468i
$873$	7.33233	−	7.33233i	0.248162	−	0.248162i
$874$	4.06865	+	11.8559i	0.137624	+	0.401031i
$875$	2.63045	−	2.63045i	0.0889255	−	0.0889255i
$876$	−1.38813	+	1.07993i	−0.0469005	+	0.0364873i
$877$		−	24.8875i		−	0.840391i	−0.907434	−	0.420195i	$-0.861962\pi$
$877$		−	24.8875i		−	0.840391i	0.907434	−	0.420195i	$-0.138038\pi$
$878$	6.22497	+	18.1393i	0.210083	+	0.612172i
$879$	5.54568	+	5.54568i	0.187051	+	0.187051i
$880$	−7.87868	+	31.0540i	−0.265590	+	1.04683i
$881$		−	39.7663i		−	1.33976i	−0.742469	−	0.669880i	$-0.766345\pi$
$881$		−	39.7663i		−	1.33976i	0.742469	−	0.669880i	$-0.233655\pi$
$882$	−9.10276	+	3.12385i	−0.306506	+	0.105185i
$883$	−0.270023	−	0.270023i	−0.00908699	−	0.00908699i	0.702549	−	0.711636i	$-0.252045\pi$
$883$	−0.270023	−	0.270023i	−0.00908699	−	0.00908699i	−0.711636	+	0.702549i	$0.752045\pi$
$884$	45.2524	+	20.2305i	1.52200	+	0.680426i
$885$	−25.2455	+	25.2455i	−0.848618	+	0.848618i
$886$	−13.3805	−	6.54319i	−0.449527	−	0.219823i
$887$	28.6599			0.962304			0.481152	−	0.876637i	$-0.340218\pi$
$887$	28.6599			0.962304			0.481152	+	0.876637i	$0.340218\pi$
$888$	17.8166	−	3.72953i	0.597887	−	0.125155i
$889$	−1.81781	+	1.81781i	−0.0609674	+	0.0609674i
$890$	51.8038	+	25.3325i	1.73647	+	0.849147i
$891$	−3.08083			−0.103212
$892$	1.09480	−	8.76708i	0.0366567	−	0.293543i
$893$	−5.73919	−	5.73919i	−0.192055	−	0.192055i
$894$	−9.43477	+	19.2937i	−0.315546	+	0.645277i
$895$	−8.90507	−	8.90507i	−0.297664	−	0.297664i
$896$	4.99030	+	0.210304i	0.166714	+	0.00702577i
$897$	−6.09146	−	1.85879i	−0.203388	−	0.0620632i
$898$	−13.2125	+	27.0189i	−0.440906	+	0.901632i
$899$	18.4563			0.615552
$900$	−2.15997	−	2.77640i	−0.0719988	−	0.0925467i
$901$	28.0849	+	28.0849i	0.935643	+	0.935643i
$902$	19.7333	−	40.3537i	0.657047	−	1.34363i
$903$	0.839249	+	0.839249i	0.0279285	+	0.0279285i
$904$	−14.6090	+	22.3444i	−0.485888	+	0.743164i
$905$	12.2652	+	12.2652i	0.407709	+	0.407709i
$906$	−7.88851	−	22.9868i	−0.262078	−	0.763685i
$907$	7.92876	−	7.92876i	0.263270	−	0.263270i	−0.563111	−	0.826381i	$-0.690396\pi$
$907$	7.92876	−	7.92876i	0.263270	−	0.263270i	0.826381	+	0.563111i	$0.190396\pi$
$908$	25.2922	−	19.6767i	0.839351	−	0.652993i
$909$	4.68560	−	4.68560i	0.155411	−	0.155411i
$910$	−0.201340	−	5.84887i	−0.00667436	−	0.193888i
$911$			0.271475i			0.00899435i	0.999990	+	0.00449718i	$0.00143150\pi$
$911$			0.271475i			0.00899435i	−0.999990	+	0.00449718i	$0.998568\pi$
$912$	−10.2664	−	17.2468i	−0.339955	−	0.571098i
$913$	−23.0500			−0.762845
$914$	24.6465	−	50.4010i	0.815235	−	1.66712i
$915$	19.4475			0.642913
$916$	7.99631	+	10.2784i	0.264205	+	0.339607i
$917$		−	4.27681i		−	0.141233i
$918$	4.27050	−	8.73298i	0.140948	−	0.288231i
$919$	−30.8639			−1.01811			−0.509054	−	0.860735i	$-0.670005\pi$
$919$	−30.8639			−1.01811			−0.509054	+	0.860735i	$0.670005\pi$
$920$	10.8713	+	7.10774i	0.358415	+	0.234335i
$921$	13.6473	+	13.6473i	0.449694	+	0.449694i
$922$	8.16239	+	23.7849i	0.268814	+	0.783313i
$923$	−54.1634	−	16.5278i	−1.78281	−	0.544020i
$924$	1.67032	+	2.14701i	0.0549494	+	0.0706315i
$925$			11.3192i			0.372173i
$926$	9.05687	+	4.42889i	0.297627	+	0.145542i
$927$	−0.250872			−0.00823972
$928$	27.5329	−	32.4713i	0.903811	−	1.06592i
$929$	24.5772	+	24.5772i	0.806351	+	0.806351i	0.984080	−	0.177728i	$-0.0568748\pi$
$929$	24.5772	+	24.5772i	0.806351	+	0.806351i	−0.177728	+	0.984080i	$0.556875\pi$
$930$	−2.92670	−	8.52829i	−0.0959704	−	0.279654i
$931$		−	34.1465i		−	1.11911i
$932$	−20.8765	+	16.2414i	−0.683834	+	0.532004i
$933$	18.0100	+	18.0100i	0.589622	+	0.589622i
$934$	42.1106	+	20.5924i	1.37790	+	0.673805i
$935$		−	55.0565i		−	1.80054i
$936$	10.1569	+	0.914789i	0.331990	+	0.0299008i
$937$		−	38.5662i		−	1.25990i	−0.776634	−	0.629952i	$-0.783075\pi$
$937$		−	38.5662i		−	1.25990i	0.776634	−	0.629952i	$-0.216925\pi$
$938$	4.32300	−	8.84035i	0.141151	−	0.288648i
$939$	0.550959	+	0.550959i	0.0179799	+	0.0179799i
$940$	−8.34563	−	1.04217i	−0.272204	−	0.0339919i
$941$		−	17.9469i		−	0.585052i	−0.956258	−	0.292526i	$-0.905504\pi$
$941$		−	17.9469i		−	0.585052i	0.956258	−	0.292526i	$-0.0944958\pi$
$942$	8.98930	−	3.08491i	0.292887	−	0.100512i
$943$	−12.8774	−	12.8774i	−0.419345	−	0.419345i
$944$	−13.5087	+	53.2448i	−0.439671	+	1.73297i
$945$	−1.14774			−0.0373359
$946$	−5.14563	+	10.5226i	−0.167299	+	0.342119i
$947$			16.7657i			0.544812i	0.962182	+	0.272406i	$0.0878193\pi$
$947$			16.7657i			0.544812i	−0.962182	+	0.272406i	$0.912181\pi$
$948$	−33.1506	−	4.13973i	−1.07668	−	0.134452i
$949$	3.03255	+	0.925375i	0.0984408	+	0.0300389i
$950$	11.8052	−	4.05126i	0.383011	−	0.131440i
$951$	−5.32870	−	5.32870i	−0.172795	−	0.172795i
$952$	−8.40128	+	1.75863i	−0.272287	+	0.0569975i
$953$	44.7508			1.44962			0.724810	−	0.688949i	$-0.241927\pi$
$953$	44.7508			1.44962			0.724810	+	0.688949i	$0.241927\pi$
$954$	7.34072	+	3.58967i	0.237664	+	0.116220i
$955$			5.84348i			0.189091i
$956$	0.636006	−	5.09308i	0.0205699	−	0.164722i
$957$	23.1859			0.749494
$958$	−5.08587	−	2.48703i	−0.164317	−	0.0803523i
$959$	−0.148229			−0.00478656
$960$	−19.3703	−	7.57328i	−0.625175	−	0.244426i
$961$			24.9858i			0.805995i
$962$	−23.9886	−	22.3920i	−0.773425	−	0.721949i
$963$	1.84416	−	1.84416i	0.0594272	−	0.0594272i
$964$	−4.31921	+	34.5878i	−0.139112	+	1.11400i
$965$	16.5145	−	16.5145i	0.531620	−	0.531620i
$966$	1.04311	−	0.357969i	0.0335614	−	0.0115175i
$967$	−25.6036	−	25.6036i	−0.823355	−	0.823355i	0.163233	−	0.986588i	$-0.447808\pi$
$967$	−25.6036	−	25.6036i	−0.823355	−	0.823355i	−0.986588	+	0.163233i	$0.947808\pi$
$968$	2.33486	−	3.57116i	0.0750452	−	0.114781i
$969$	24.3895	+	24.3895i	0.783504	+	0.783504i
$970$	34.2491	+	16.7481i	1.09967	+	0.537749i
$971$	6.12175	+	6.12175i	0.196456	+	0.196456i	0.798479	−	0.602023i	$-0.205638\pi$
$971$	6.12175	+	6.12175i	0.196456	+	0.196456i	−0.602023	+	0.798479i	$0.705638\pi$
$972$	0.247828	−	1.98459i	0.00794909	−	0.0636556i
$973$	1.74017			0.0557871
$974$	27.3205	+	13.3600i	0.875406	+	0.428081i
$975$	−1.85085	+	6.06543i	−0.0592745	+	0.194249i
$976$	25.7113	−	15.3050i	0.822997	−	0.489902i
$977$	22.5001	+	22.5001i	0.719842	+	0.719842i	0.968573	−	0.248730i	$-0.0800133\pi$
$977$	22.5001	+	22.5001i	0.719842	+	0.719842i	−0.248730	+	0.968573i	$0.580013\pi$
$978$	10.0027	+	4.89142i	0.319852	+	0.156410i
$979$	34.1682	+	34.1682i	1.09202	+	1.09202i
$980$	−21.7267	−	27.9274i	−0.694035	−	0.892107i
$981$	−0.584695			−0.0186679
$982$	18.7649	−	38.3734i	0.598812	−	1.22454i
$983$	−38.2746	+	38.2746i	−1.22077	+	1.22077i	−0.253411	+	0.967359i	$0.581553\pi$
$983$	−38.2746	+	38.2746i	−1.22077	+	1.22077i	−0.967359	+	0.253411i	$0.918447\pi$
$984$	24.4074	+	15.9578i	0.778079	+	0.508716i
$985$	−15.0039			−0.478063
$986$	−32.1393	+	65.7233i	−1.02352	+	2.09306i
$987$	−0.504947	+	0.504947i	−0.0160726	+	0.0160726i
$988$	−14.7677	+	33.0330i	−0.469823	+	1.05092i
$989$	3.35789	+	3.35789i	0.106775	+	0.106775i
$990$	−3.67670	−	10.7138i	−0.116853	−	0.340506i
$991$		−	21.6332i		−	0.687200i	−0.939116	−	0.343600i	$-0.888354\pi$
$991$		−	21.6332i		−	0.687200i	0.939116	−	0.343600i	$-0.111646\pi$
$992$	−10.5811	−	8.97186i	−0.335950	−	0.284857i
$993$	9.37783	+	9.37783i	0.297596	+	0.297596i
$994$	9.27499	−	3.18295i	0.294185	−	0.100957i
$995$			30.0256i			0.951876i
$996$	1.85419	−	14.8482i	0.0587523	−	0.470484i
$997$	14.0786	−	14.0786i	0.445873	−	0.445873i	−0.448107	−	0.893980i	$-0.647902\pi$
$997$	14.0786	−	14.0786i	0.445873	−	0.445873i	0.893980	+	0.448107i	$0.147902\pi$
$998$	−35.9986	+	12.3538i	−1.13951	+	0.391054i
$999$	−4.55070	+	4.55070i	−0.143978	+	0.143978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bn.a.307.5	yes	112
13.5	odd	4		624.2.r.a.499.33	✓	112
16.11	odd	4		624.2.r.a.619.33	yes	112
208.187	even	4	inner	624.2.bn.a.187.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.r.a.499.33	✓	112	13.5	odd	4
624.2.r.a.619.33	yes	112	16.11	odd	4
624.2.bn.a.187.5	yes	112	208.187	even	4	inner
624.2.bn.a.307.5	yes	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33764 + 0.459045i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.57856 - 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 - 1.27045i) q^{6} +(0.312171 - 0.312171i) q^{7} +(-1.54780 + 2.36735i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.33764 + 0.459045i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.57856 - 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 - 1.27045i) q^{6} +(0.312171 - 0.312171i) q^{7} +(-1.54780 + 2.36735i) q^{8} -1.00000i q^{9} +(3.47756 - 1.19341i) q^{10} +3.08083 q^{11} +(-0.247828 + 1.98459i) q^{12} +(3.18261 - 1.69440i) q^{13} +(-0.274271 + 0.560872i) q^{14} +(1.83832 - 1.83832i) q^{15} +(0.983672 - 3.87716i) q^{16} +6.87394i q^{17} +(0.459045 + 1.33764i) q^{18} -5.01779 q^{19} +(-4.10389 + 3.19271i) q^{20} +0.441476i q^{21} +(-4.12103 + 1.41424i) q^{22} +1.76637i q^{23} +(-0.579510 - 2.76842i) q^{24} +1.75882 q^{25} +(-3.47937 + 3.72746i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.109410 - 0.876147i) q^{28} +(-5.32160 - 5.32160i) q^{29} +(-1.61513 + 3.30288i) q^{30} +(-1.73409 + 1.73409i) q^{31} +(0.463995 + 5.63779i) q^{32} +(-2.17847 + 2.17847i) q^{33} +(-3.15545 - 9.19485i) q^{34} +(-0.811573 + 0.811573i) q^{35} +(-1.22807 - 1.57856i) q^{36} +6.43566i q^{37} +(6.71199 - 2.30339i) q^{38} +(-1.05232 + 3.44857i) q^{39} +(4.02392 - 6.15457i) q^{40} +(-7.29029 + 7.29029i) q^{41} +(-0.202657 - 0.590536i) q^{42} +(1.90101 - 1.90101i) q^{43} +(4.86325 - 3.78348i) q^{44} +2.59977i q^{45} +(-0.810845 - 2.36277i) q^{46} +(1.14377 + 1.14377i) q^{47} +(2.04601 + 3.43713i) q^{48} +6.80510i q^{49} +(-2.35267 + 0.807380i) q^{50} +(-4.86061 - 4.86061i) q^{51} +(2.94307 - 6.58318i) q^{52} +(4.08570 - 4.08570i) q^{53} +(-1.27045 - 0.621260i) q^{54} -8.00945 q^{55} +(0.255840 + 1.22219i) q^{56} +(3.54811 - 3.54811i) q^{57} +(9.56123 + 4.67552i) q^{58} -13.7329 q^{59} +(0.644297 - 5.15947i) q^{60} +(5.28947 + 5.28947i) q^{61} +(1.52356 - 3.11562i) q^{62} +(-0.312171 - 0.312171i) q^{63} +(-3.20866 - 7.32834i) q^{64} +(-8.27406 + 4.40506i) q^{65} +(1.91399 - 3.91403i) q^{66} -15.7618 q^{67} +(8.44170 + 10.8509i) q^{68} +(-1.24901 - 1.24901i) q^{69} +(0.713043 - 1.45814i) q^{70} +(-11.1059 - 11.1059i) q^{71} +(2.36735 + 1.54780i) q^{72} +(0.621805 + 0.621805i) q^{73} +(-2.95426 - 8.60858i) q^{74} +(-1.24368 + 1.24368i) q^{75} +(-7.92085 + 6.16221i) q^{76} +(0.961744 - 0.961744i) q^{77} +(-0.175424 - 5.09600i) q^{78} +16.7040i q^{79} +(-2.55733 + 10.0797i) q^{80} -1.00000 q^{81} +(6.40520 - 13.0983i) q^{82} -7.48177 q^{83} +(0.542165 + 0.696894i) q^{84} -17.8707i q^{85} +(-1.67021 + 3.41551i) q^{86} +7.52588 q^{87} +(-4.76849 + 7.29338i) q^{88} +(11.0906 + 11.0906i) q^{89} +(-1.19341 - 3.47756i) q^{90} +(0.464574 - 1.52246i) q^{91} +(2.16924 + 2.78832i) q^{92} -2.45238i q^{93} +(-2.05499 - 1.00491i) q^{94} +13.0451 q^{95} +(-4.31462 - 3.65843i) q^{96} +(7.33233 + 7.33233i) q^{97} +(-3.12385 - 9.10276i) q^{98} -3.08083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) \) 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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