LMFDB - Embedded newform 350.2.m.a.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	350.169
Dual form			350.2.m.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-0.974986 - 1.34195i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.09432 - 0.783465i) q^{5} +(-1.34195 - 0.974986i) q^{6} +1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.0768108 - 0.236399i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.974986 - 1.34195i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.09432 - 0.783465i) q^{5} +(-1.34195 - 0.974986i) q^{6} +1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.0768108 - 0.236399i) q^{9} +(1.74971 - 1.39230i) q^{10} +(-0.424326 - 1.30594i) q^{11} +(-1.57756 - 0.512580i) q^{12} +(1.59998 + 0.519866i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-3.09331 - 2.04661i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.21943 + 3.05479i) q^{17} -0.248565i q^{18} +(-4.29579 - 3.12108i) q^{19} +(1.23383 - 1.86485i) q^{20} +(1.34195 - 0.974986i) q^{21} +(-0.807117 - 1.11090i) q^{22} +(6.79881 - 2.20907i) q^{23} -1.65875 q^{24} +(3.77237 - 3.28165i) q^{25} +1.68232 q^{26} +(-5.12481 + 1.66515i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-6.02244 + 4.37556i) q^{29} +(-3.57435 - 0.990561i) q^{30} +(-1.77167 - 1.28720i) q^{31} -1.00000i q^{32} +(-1.33880 + 1.84270i) q^{33} +(-1.16683 + 3.59112i) q^{34} +(0.783465 + 2.09432i) q^{35} +(-0.0768108 - 0.236399i) q^{36} +(10.9349 + 3.55295i) q^{37} +(-5.05001 - 1.64085i) q^{38} +(-0.862325 - 2.65396i) q^{39} +(0.597175 - 2.15485i) q^{40} +(-0.244857 + 0.753592i) q^{41} +(0.974986 - 1.34195i) q^{42} +3.88458i q^{43} +(-1.11090 - 0.807117i) q^{44} +(-0.0243440 - 0.555275i) q^{45} +(5.78342 - 4.20190i) q^{46} +(0.159731 + 0.219851i) q^{47} +(-1.57756 + 0.512580i) q^{48} -1.00000 q^{49} +(2.57365 - 4.28676i) q^{50} +6.26330 q^{51} +(1.59998 - 0.519866i) q^{52} +(6.32915 + 8.71132i) q^{53} +(-4.35942 + 3.16730i) q^{54} +(-1.91184 - 2.40262i) q^{55} +(0.809017 + 0.587785i) q^{56} +8.80776i q^{57} +(-4.37556 + 6.02244i) q^{58} +(-2.86101 + 8.80527i) q^{59} +(-3.70551 + 0.162454i) q^{60} +(1.63872 + 5.04346i) q^{61} +(-2.08273 - 0.676720i) q^{62} +(0.236399 + 0.0768108i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.75818 - 0.164763i) q^{65} +(-0.703849 + 2.16623i) q^{66} +(-3.00510 + 4.13616i) q^{67} +3.77593i q^{68} +(-9.59321 - 6.96988i) q^{69} +(1.39230 + 1.74971i) q^{70} +(3.93892 - 2.86179i) q^{71} +(-0.146103 - 0.201093i) q^{72} +(9.18633 - 2.98482i) q^{73} +11.4976 q^{74} +(-8.08183 - 1.86277i) q^{75} -5.30989 q^{76} +(1.30594 - 0.424326i) q^{77} +(-1.64024 - 2.25760i) q^{78} +(-9.27884 + 6.74147i) q^{79} +(-0.0979381 - 2.23392i) q^{80} +(6.62789 + 4.81544i) q^{81} +0.792373i q^{82} +(-6.68744 + 9.20446i) q^{83} +(0.512580 - 1.57756i) q^{84} +(-2.25489 + 8.13656i) q^{85} +(1.20040 + 3.69445i) q^{86} +(11.7436 + 3.81572i) q^{87} +(-1.30594 - 0.424326i) q^{88} +(-2.68961 - 8.27777i) q^{89} +(-0.194742 - 0.520575i) q^{90} +(-0.519866 + 1.59998i) q^{91} +(4.20190 - 5.78342i) q^{92} +3.63250i q^{93} +(0.219851 + 0.159731i) q^{94} +(-11.4420 - 3.17094i) q^{95} +(-1.34195 + 0.974986i) q^{96} +(2.25765 + 3.10739i) q^{97} +(-0.951057 + 0.309017i) q^{98} -0.341317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	−0.974986	−	1.34195i	−0.562908	−	0.774777i	0.428784	−	0.903407i	$-0.358942\pi$
$3$	−0.974986	−	1.34195i	−0.562908	−	0.774777i	−0.991693	+	0.128630i	$0.958942\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	2.09432	−	0.783465i	0.936609	−	0.350376i
$5$	2.09432	−	0.783465i	0.936609	−	0.350376i
$6$	−1.34195	−	0.974986i	−0.547850	−	0.398036i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.0768108	−	0.236399i	0.0256036	−	0.0787998i
$10$	1.74971	−	1.39230i	0.553308	−	0.440284i
$11$	−0.424326	−	1.30594i	−0.127939	−	0.393756i	0.866486	−	0.499202i	$-0.166373\pi$
$11$	−0.424326	−	1.30594i	−0.127939	−	0.393756i	−0.994425	+	0.105445i	$0.966373\pi$
$12$	−1.57756	−	0.512580i	−0.455402	−	0.147969i
$13$	1.59998	+	0.519866i	0.443756	+	0.144185i	0.522368	−	0.852720i	$-0.325049\pi$
$13$	1.59998	+	0.519866i	0.443756	+	0.144185i	−0.0786121	+	0.996905i	$0.525049\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−3.09331	−	2.04661i	−0.798688	−	0.528434i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.21943	+	3.05479i	−0.538292	+	0.740895i	−0.988366	−	0.152096i	$-0.951398\pi$
$17$	−2.21943	+	3.05479i	−0.538292	+	0.740895i	0.450074	+	0.892991i	$0.351398\pi$
$18$		−	0.248565i		−	0.0585873i
$19$	−4.29579	−	3.12108i	−0.985522	−	0.716024i	−0.0265865	−	0.999647i	$-0.508464\pi$
$19$	−4.29579	−	3.12108i	−0.985522	−	0.716024i	−0.958936	+	0.283623i	$0.908464\pi$
$20$	1.23383	−	1.86485i	0.275893	−	0.416993i
$21$	1.34195	−	0.974986i	0.292838	−	0.212759i
$22$	−0.807117	−	1.11090i	−0.172078	−	0.236845i
$23$	6.79881	−	2.20907i	1.41765	−	0.460623i	0.502796	−	0.864405i	$-0.332305\pi$
$23$	6.79881	−	2.20907i	1.41765	−	0.460623i	0.914855	+	0.403783i	$0.132305\pi$
$24$	−1.65875			−0.338590
$25$	3.77237	−	3.28165i	0.754473	−	0.656331i
$26$	1.68232			0.329930
$27$	−5.12481	+	1.66515i	−0.986270	+	0.320458i
$28$	0.587785	+	0.809017i	0.111081	+	0.152890i
$29$	−6.02244	+	4.37556i	−1.11834	+	0.812521i	−0.983957	−	0.178408i	$-0.942905\pi$
$29$	−6.02244	+	4.37556i	−1.11834	+	0.812521i	−0.134383	+	0.990929i	$0.542905\pi$
$30$	−3.57435	−	0.990561i	−0.652584	−	0.180851i
$31$	−1.77167	−	1.28720i	−0.318202	−	0.231187i	0.417206	−	0.908812i	$-0.363009\pi$
$31$	−1.77167	−	1.28720i	−0.318202	−	0.231187i	−0.735408	+	0.677625i	$0.763009\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.33880	+	1.84270i	−0.233055	+	0.320773i
$34$	−1.16683	+	3.59112i	−0.200109	+	0.615872i
$35$	0.783465	+	2.09432i	0.132430	+	0.354005i
$36$	−0.0768108	−	0.236399i	−0.0128018	−	0.0393999i
$37$	10.9349	+	3.55295i	1.79768	+	0.584101i	0.999824	−	0.0187494i	$-0.00596847\pi$
$37$	10.9349	+	3.55295i	1.79768	+	0.584101i	0.797854	+	0.602851i	$0.205968\pi$
$38$	−5.05001	−	1.64085i	−0.819219	−	0.266181i
$39$	−0.862325	−	2.65396i	−0.138083	−	0.424974i
$40$	0.597175	−	2.15485i	0.0944217	−	0.340712i
$41$	−0.244857	+	0.753592i	−0.0382402	+	0.117691i	−0.968354	−	0.249579i	$-0.919708\pi$
$41$	−0.244857	+	0.753592i	−0.0382402	+	0.117691i	0.930114	+	0.367271i	$0.119708\pi$
$42$	0.974986	−	1.34195i	0.150444	−	0.207068i
$43$			3.88458i			0.592392i	0.955127	+	0.296196i	$0.0957182\pi$
$43$			3.88458i			0.592392i	−0.955127	+	0.296196i	$0.904282\pi$
$44$	−1.11090	−	0.807117i	−0.167475	−	0.121677i
$45$	−0.0243440	−	0.555275i	−0.00362899	−	0.0827755i
$46$	5.78342	−	4.20190i	0.852718	−	0.619536i
$47$	0.159731	+	0.219851i	0.0232992	+	0.0320686i	0.820508	−	0.571635i	$-0.193691\pi$
$47$	0.159731	+	0.219851i	0.0232992	+	0.0320686i	−0.797208	+	0.603704i	$0.793691\pi$
$48$	−1.57756	+	0.512580i	−0.227701	+	0.0739846i
$49$	−1.00000			−0.142857
$50$	2.57365	−	4.28676i	0.363969	−	0.606240i
$51$	6.26330			0.877037
$52$	1.59998	−	0.519866i	0.221878	−	0.0720925i
$53$	6.32915	+	8.71132i	0.869375	+	1.19659i	0.979252	+	0.202647i	$0.0649544\pi$
$53$	6.32915	+	8.71132i	0.869375	+	1.19659i	−0.109877	+	0.993945i	$0.535046\pi$
$54$	−4.35942	+	3.16730i	−0.593242	+	0.431016i
$55$	−1.91184	−	2.40262i	−0.257792	−	0.323969i
$56$	0.809017	+	0.587785i	0.108109	+	0.0785461i
$57$			8.80776i			1.16662i
$58$	−4.37556	+	6.02244i	−0.574539	+	0.790786i
$59$	−2.86101	+	8.80527i	−0.372471	+	1.14635i	0.572698	+	0.819767i	$0.305897\pi$
$59$	−2.86101	+	8.80527i	−0.372471	+	1.14635i	−0.945169	+	0.326582i	$0.894103\pi$
$60$	−3.70551	+	0.162454i	−0.478379	+	0.0209728i
$61$	1.63872	+	5.04346i	0.209816	+	0.645748i	0.999481	+	0.0322098i	$0.0102545\pi$
$61$	1.63872	+	5.04346i	0.209816	+	0.645748i	−0.789665	+	0.613539i	$0.789746\pi$
$62$	−2.08273	−	0.676720i	−0.264507	−	0.0859435i
$63$	0.236399	+	0.0768108i	0.0297835	+	0.00967725i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	3.75818	−	0.164763i	0.466144	−	0.0204364i
$66$	−0.703849	+	2.16623i	−0.0866379	+	0.266644i
$67$	−3.00510	+	4.13616i	−0.367131	+	0.505313i	−0.952118	−	0.305730i	$-0.901100\pi$
$67$	−3.00510	+	4.13616i	−0.367131	+	0.505313i	0.584987	+	0.811043i	$0.301100\pi$
$68$			3.77593i			0.457898i
$69$	−9.59321	−	6.96988i	−1.15489	−	0.839075i
$70$	1.39230	+	1.74971i	0.166412	+	0.209131i
$71$	3.93892	−	2.86179i	0.467464	−	0.339632i	−0.328988	−	0.944334i	$-0.606708\pi$
$71$	3.93892	−	2.86179i	0.467464	−	0.339632i	0.796452	+	0.604702i	$0.206708\pi$
$72$	−0.146103	−	0.201093i	−0.0172184	−	0.0236991i
$73$	9.18633	−	2.98482i	1.07518	−	0.349347i	0.282676	−	0.959215i	$-0.408778\pi$
$73$	9.18633	−	2.98482i	1.07518	−	0.349347i	0.792502	+	0.609869i	$0.208778\pi$
$74$	11.4976			1.33657
$75$	−8.08183	−	1.86277i	−0.933209	−	0.215094i
$76$	−5.30989			−0.609086
$77$	1.30594	−	0.424326i	0.148826	−	0.0483565i
$78$	−1.64024	−	2.25760i	−0.185721	−	0.255623i
$79$	−9.27884	+	6.74147i	−1.04395	+	0.758474i	−0.971053	−	0.238865i	$-0.923225\pi$
$79$	−9.27884	+	6.74147i	−1.04395	+	0.758474i	−0.0728977	+	0.997339i	$0.523225\pi$
$80$	−0.0979381	−	2.23392i	−0.0109498	−	0.249760i
$81$	6.62789	+	4.81544i	0.736432	+	0.535049i
$82$			0.792373i			0.0875030i
$83$	−6.68744	+	9.20446i	−0.734041	+	1.01032i	0.264898	+	0.964276i	$0.414662\pi$
$83$	−6.68744	+	9.20446i	−0.734041	+	1.01032i	−0.998939	+	0.0460448i	$0.985338\pi$
$84$	0.512580	−	1.57756i	0.0559271	−	0.172126i
$85$	−2.25489	+	8.13656i	−0.244577	+	0.882534i
$86$	1.20040	+	3.69445i	0.129442	+	0.398383i
$87$	11.7436	+	3.81572i	1.25905	+	0.409089i
$88$	−1.30594	−	0.424326i	−0.139214	−	0.0452334i
$89$	−2.68961	−	8.27777i	−0.285098	−	0.877442i	−0.986369	−	0.164547i	$-0.947384\pi$
$89$	−2.68961	−	8.27777i	−0.285098	−	0.877442i	0.701271	−	0.712895i	$-0.252616\pi$
$90$	−0.194742	−	0.520575i	−0.0205276	−	0.0548734i
$91$	−0.519866	+	1.59998i	−0.0544968	+	0.167724i
$92$	4.20190	−	5.78342i	0.438078	−	0.602963i
$93$			3.63250i			0.376673i
$94$	0.219851	+	0.159731i	0.0226759	+	0.0164750i
$95$	−11.4420	−	3.17094i	−1.17393	−	0.325331i
$96$	−1.34195	+	0.974986i	−0.136962	+	0.0995091i
$97$	2.25765	+	3.10739i	0.229230	+	0.315508i	0.908102	−	0.418748i	$-0.137531\pi$
$97$	2.25765	+	3.10739i	0.229230	+	0.315508i	−0.678872	+	0.734256i	$0.737531\pi$
$98$	−0.951057	+	0.309017i	−0.0960712	+	0.0312154i
$99$	−0.341317			−0.0343036
$100$	1.12300	−	4.87226i	0.112300	−	0.487226i
$101$	4.04999			0.402989			0.201494	−	0.979490i	$-0.435420\pi$
$101$	4.04999			0.402989			0.201494	+	0.979490i	$0.435420\pi$
$102$	5.95675	−	1.93547i	0.589806	−	0.191640i
$103$	−4.59902	−	6.33001i	−0.453155	−	0.623714i	0.519917	−	0.854217i	$-0.325963\pi$
$103$	−4.59902	−	6.33001i	−0.453155	−	0.623714i	−0.973072	+	0.230503i	$0.925963\pi$
$104$	1.36103	−	0.988844i	0.133460	−	0.0969641i
$105$	2.04661	−	3.09331i	0.199729	−	0.301876i
$106$	8.71132	+	6.32915i	0.846118	+	0.614741i
$107$		−	11.4354i		−	1.10551i	−0.833345	−	0.552753i	$-0.813577\pi$
$107$		−	11.4354i		−	1.10551i	0.833345	−	0.552753i	$-0.186423\pi$
$108$	−3.16730	+	4.35942i	−0.304774	+	0.419485i
$109$	2.51395	−	7.73716i	0.240793	−	0.741085i	−0.755507	−	0.655141i	$-0.772609\pi$
$109$	2.51395	−	7.73716i	0.240793	−	0.741085i	0.996300	−	0.0859444i	$-0.0273907\pi$
$110$	−2.56071	−	1.69424i	−0.244154	−	0.161539i
$111$	−5.89344	−	18.1381i	−0.559380	−	1.72160i
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	−14.5679	−	4.73340i	−1.37043	−	0.445280i	−0.470920	−	0.882176i	$-0.656078\pi$
$113$	−14.5679	−	4.73340i	−1.37043	−	0.445280i	−0.899512	+	0.436896i	$0.856078\pi$
$114$	2.72175	+	8.37667i	0.254915	+	0.784547i
$115$	12.5082	−	9.95313i	1.16639	−	0.928134i
$116$	−2.30037	+	7.07981i	−0.213584	+	0.657344i
$117$	0.245792	−	0.338304i	0.0227235	−	0.0312762i
$118$			9.25841i			0.852306i
$119$	−3.05479	−	2.21943i	−0.280032	−	0.203455i
$120$	−3.47395	+	1.29957i	−0.317126	+	0.118634i
$121$	7.37375	−	5.35735i	0.670341	−	0.487031i
$122$	3.11703	+	4.29022i	0.282202	+	0.388418i
$123$	1.25002	−	0.406155i	0.112710	−	0.0366218i
$124$	−2.18991			−0.196660
$125$	5.32949	−	9.82835i	0.476684	−	0.879075i
$126$	0.248565			0.0221439
$127$	−1.33759	+	0.434608i	−0.118692	+	0.0385653i	−0.367761	−	0.929920i	$-0.619875\pi$
$127$	−1.33759	+	0.434608i	−0.118692	+	0.0385653i	0.249069	+	0.968486i	$0.419875\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	5.21292	−	3.78741i	0.458972	−	0.333463i
$130$	3.52332	−	1.31804i	0.309016	−	0.115600i
$131$	−9.40915	−	6.83615i	−0.822081	−	0.597277i	0.0952269	−	0.995456i	$-0.469642\pi$
$131$	−9.40915	−	6.83615i	−0.822081	−	0.597277i	−0.917308	+	0.398179i	$0.869642\pi$
$132$			2.27770i			0.198249i
$133$	3.12108	−	4.29579i	0.270632	−	0.372492i
$134$	−1.57987	+	4.86235i	−0.136480	+	0.420043i
$135$	−9.42841	+	7.50247i	−0.811468	+	0.645709i
$136$	1.16683	+	3.59112i	0.100054	+	0.307936i
$137$	−17.8975	−	5.81525i	−1.52909	−	0.496831i	−0.580747	−	0.814084i	$-0.697239\pi$
$137$	−17.8975	−	5.81525i	−1.52909	−	0.496831i	−0.948341	+	0.317254i	$0.897239\pi$
$138$	−11.2775	−	3.66428i	−0.960004	−	0.311924i
$139$	3.65967	+	11.2633i	0.310409	+	0.955341i	0.977603	+	0.210457i	$0.0674951\pi$
$139$	3.65967	+	11.2633i	0.310409	+	0.955341i	−0.667194	+	0.744884i	$0.732505\pi$
$140$	1.86485	+	1.23383i	0.157608	+	0.104278i
$141$	0.139294	−	0.428704i	0.0117307	−	0.0361034i
$142$	2.86179	−	3.93892i	0.240156	−	0.330547i
$143$		−	2.31008i		−	0.193179i
$144$	−0.201093	−	0.146103i	−0.0167578	−	0.0121752i
$145$	−9.18484	+	13.8822i	−0.762759	+	1.15285i
$146$	7.81436	−	5.67746i	0.646721	−	0.469870i
$147$	0.974986	+	1.34195i	0.0804155	+	0.110682i
$148$	10.9349	−	3.55295i	0.898839	−	0.292051i
$149$	3.80792			0.311957			0.155979	−	0.987760i	$-0.450147\pi$
$149$	3.80792			0.311957			0.155979	+	0.987760i	$0.450147\pi$
$150$	−8.26190	+	0.725821i	−0.674582	+	0.0592630i
$151$	14.8112			1.20532			0.602661	−	0.797997i	$-0.294107\pi$
$151$	14.8112			1.20532			0.602661	+	0.797997i	$0.294107\pi$
$152$	−5.05001	+	1.64085i	−0.409610	+	0.133090i
$153$	0.551673	+	0.759313i	0.0446002	+	0.0613868i
$154$	1.11090	−	0.807117i	0.0895190	−	0.0650393i
$155$	−4.71893	−	1.30776i	−0.379034	−	0.105042i
$156$	−2.25760	−	1.64024i	−0.180752	−	0.131324i
$157$			7.44512i			0.594185i	0.954849	+	0.297093i	$0.0960170\pi$
$157$			7.44512i			0.594185i	−0.954849	+	0.297093i	$0.903983\pi$
$158$	−6.74147	+	9.27884i	−0.536322	+	0.738184i
$159$	5.51936	−	16.9868i	0.437713	−	1.34714i
$160$	−0.783465	−	2.09432i	−0.0619383	−	0.165571i
$161$	2.20907	+	6.79881i	0.174099	+	0.535822i
$162$	7.79155	+	2.53163i	0.612162	+	0.198903i
$163$	10.2358	+	3.32582i	0.801733	+	0.260499i	0.681092	−	0.732198i	$-0.261505\pi$
$163$	10.2358	+	3.32582i	0.801733	+	0.260499i	0.120640	+	0.992696i	$0.461505\pi$
$164$	0.244857	+	0.753592i	0.0191201	+	0.0588456i
$165$	−1.36019	+	4.90811i	−0.105891	+	0.382096i
$166$	−3.51579	+	10.8205i	−0.272878	+	0.839833i
$167$	−0.483326	+	0.665240i	−0.0374009	+	0.0514779i	−0.827308	−	0.561749i	$-0.810129\pi$
$167$	−0.483326	+	0.665240i	−0.0374009	+	0.0514779i	0.789907	+	0.613227i	$0.210129\pi$
$168$		−	1.65875i		−	0.127975i
$169$	−8.22754	−	5.97765i	−0.632887	−	0.459820i
$170$	0.369807	+	8.43513i	0.0283629	+	0.646945i
$171$	−1.06778	+	0.775790i	−0.0816554	+	0.0593261i
$172$	2.28330	+	3.14269i	0.174100	+	0.239628i
$173$	−17.7179	+	5.75688i	−1.34706	+	0.437688i	−0.891704	−	0.452620i	$-0.850489\pi$
$173$	−17.7179	+	5.75688i	−1.34706	+	0.437688i	−0.455360	+	0.890307i	$0.650489\pi$
$174$	12.3479			0.936095
$175$	3.28165	+	3.77237i	0.248070	+	0.285164i
$176$	−1.37315			−0.103505
$177$	14.6057	−	4.74568i	1.09783	−	0.356707i
$178$	−5.11594	−	7.04149i	−0.383456	−	0.527782i
$179$	4.01791	−	2.91918i	0.300313	−	0.218190i	−0.427416	−	0.904055i	$-0.640576\pi$
$179$	4.01791	−	2.91918i	0.300313	−	0.218190i	0.727729	+	0.685865i	$0.240576\pi$
$180$	−0.346077	−	0.434918i	−0.0257951	−	0.0324168i
$181$	−18.1678	−	13.1996i	−1.35040	−	0.981122i	−0.998992	−	0.0448994i	$-0.985703\pi$
$181$	−18.1678	−	13.1996i	−1.35040	−	0.981122i	−0.351407	−	0.936223i	$-0.614297\pi$
$182$			1.68232i			0.124702i
$183$	5.17035	−	7.11638i	0.382204	−	0.526058i
$184$	2.20907	−	6.79881i	0.162855	−	0.501215i
$185$	25.6847	−	1.12605i	1.88838	−	0.0827890i
$186$	1.12251	+	3.45472i	0.0823061	+	0.253312i
$187$	4.93114	+	1.60223i	0.360601	+	0.117166i
$188$	0.258451	+	0.0839757i	0.0188495	+	0.00612456i
$189$	−1.66515	−	5.12481i	−0.121122	−	0.372775i
$190$	−11.8619	+	0.520041i	−0.860552	+	0.0377277i
$191$	0.257649	−	0.792962i	0.0186428	−	0.0573767i	−0.941302	−	0.337565i	$-0.890397\pi$
$191$	0.257649	−	0.792962i	0.0186428	−	0.0573767i	0.959945	+	0.280188i	$0.0903968\pi$
$192$	−0.974986	+	1.34195i	−0.0703635	+	0.0968471i
$193$			23.8618i			1.71761i	0.512306	+	0.858803i	$0.328792\pi$
$193$			23.8618i			1.71761i	−0.512306	+	0.858803i	$0.671208\pi$
$194$	3.10739	+	2.25765i	0.223098	+	0.162090i
$195$	−3.88527	−	4.88265i	−0.278230	−	0.349654i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−8.43384	−	11.6082i	−0.600886	−	0.827049i	0.394903	−	0.918723i	$-0.370778\pi$
$197$	−8.43384	−	11.6082i	−0.600886	−	0.827049i	−0.995789	+	0.0916741i	$0.970778\pi$
$198$	−0.324612	+	0.105473i	−0.0230691	+	0.00749562i
$199$	15.4996			1.09874			0.549370	−	0.835579i	$-0.314868\pi$
$199$	15.4996			1.09874			0.549370	+	0.835579i	$0.314868\pi$
$200$	−0.437572	−	4.98082i	−0.0309410	−	0.352197i
$201$	8.48047			0.598166
$202$	3.85177	−	1.25152i	0.271009	−	0.0880563i
$203$	−4.37556	−	6.02244i	−0.307104	−	0.422693i
$204$	5.06712	−	3.68148i	0.354769	−	0.257755i
$205$	0.0776036	+	1.77010i	0.00542007	+	0.123629i
$206$	−6.33001	−	4.59902i	−0.441032	−	0.320429i
$207$		−	1.77692i		−	0.123504i
$208$	0.988844	−	1.36103i	0.0685640	−	0.0943702i
$209$	−2.25313	+	6.93441i	−0.155852	+	0.479663i
$210$	0.990561	−	3.57435i	0.0683552	−	0.246653i
$211$	−6.81736	−	20.9817i	−0.469326	−	1.44444i	−0.853459	−	0.521160i	$-0.825499\pi$
$211$	−6.81736	−	20.9817i	−0.469326	−	1.44444i	0.384132	−	0.923278i	$-0.374501\pi$
$212$	10.2408	+	3.32743i	0.703339	+	0.228529i
$213$	−7.68078	−	2.49564i	−0.526279	−	0.170998i
$214$	−3.53375	−	10.8758i	−0.241562	−	0.743452i
$215$	3.04343	+	8.13555i	0.207560	+	0.554840i
$216$	−1.66515	+	5.12481i	−0.113299	+	0.348699i
$217$	1.28720	−	1.77167i	0.0873806	−	0.120269i
$218$		−	8.13533i		−	0.550994i
$219$	−12.9620	−	9.41746i	−0.875893	−	0.636373i
$220$	−2.95893	−	0.820011i	−0.199491	−	0.0552851i
$221$	−5.13914	+	3.73380i	−0.345696	+	0.251163i
$222$	−11.2100	−	15.4292i	−0.752365	−	1.03554i
$223$	27.5366	−	8.94717i	1.84399	−	0.599147i	0.846183	−	0.532893i	$-0.178895\pi$
$223$	27.5366	−	8.94717i	1.84399	−	0.599147i	0.997803	−	0.0662540i	$-0.0211047\pi$
$224$	1.00000			0.0668153
$225$	−0.486022	−	1.14385i	−0.0324015	−	0.0762567i
$226$	−15.3176			−1.01891
$227$	−22.2960	+	7.24442i	−1.47984	+	0.480829i	−0.934065	−	0.357102i	$-0.883765\pi$
$227$	−22.2960	+	7.24442i	−1.47984	+	0.480829i	−0.545775	+	0.837932i	$0.683765\pi$
$228$	5.17707	+	7.12562i	0.342860	+	0.471906i
$229$	−4.56889	+	3.31949i	−0.301921	+	0.219358i	−0.728422	−	0.685129i	$-0.759746\pi$
$229$	−4.56889	+	3.31949i	−0.301921	+	0.219358i	0.426501	+	0.904487i	$0.359746\pi$
$230$	8.82030	−	13.3312i	0.581593	−	0.879035i
$231$	−1.84270	−	1.33880i	−0.121241	−	0.0880866i
$232$			7.44415i			0.488732i
$233$	1.95440	−	2.69000i	0.128037	−	0.176227i	−0.740186	−	0.672402i	$-0.765263\pi$
$233$	1.95440	−	2.69000i	0.128037	−	0.176227i	0.868223	+	0.496175i	$0.165263\pi$
$234$	0.129220	−	0.397700i	0.00844741	−	0.0259984i
$235$	0.506774	+	0.335295i	0.0330583	+	0.0218723i
$236$	2.86101	+	8.80527i	0.186236	+	0.573174i
$237$	18.0935	+	5.87892i	1.17530	+	0.381877i
$238$	−3.59112	−	1.16683i	−0.232778	−	0.0756341i
$239$	2.17081	+	6.68105i	0.140418	+	0.432161i	0.996393	−	0.0848548i	$-0.0270427\pi$
$239$	2.17081	+	6.68105i	0.140418	+	0.432161i	−0.855976	+	0.517016i	$0.827043\pi$
$240$	−2.90233	+	2.30947i	−0.187345	+	0.149076i
$241$	3.29261	−	10.1336i	0.212096	−	0.652763i	−0.787251	−	0.616632i	$-0.788497\pi$
$241$	3.29261	−	10.1336i	0.212096	−	0.652763i	0.999347	−	0.0361310i	$-0.0115034\pi$
$242$	5.35735	−	7.37375i	0.344383	−	0.474003i
$243$			2.57632i			0.165271i
$244$	4.29022	+	3.11703i	0.274653	+	0.199547i
$245$	−2.09432	+	0.783465i	−0.133801	+	0.0500537i
$246$	1.06333	−	0.772553i	0.0677953	−	0.0492562i
$247$	−5.25065	−	7.22691i	−0.334091	−	0.459837i
$248$	−2.08273	+	0.676720i	−0.132253	+	0.0429717i
$249$	18.8721			1.19597
$250$	2.03152	−	10.9942i	0.128484	−	0.695336i
$251$	−5.13772			−0.324290			−0.162145	−	0.986767i	$-0.551841\pi$
$251$	−5.13772			−0.324290			−0.162145	+	0.986767i	$0.551841\pi$
$252$	0.236399	−	0.0768108i	0.0148918	−	0.00483862i
$253$	−5.76983	−	7.94149i	−0.362746	−	0.499277i
$254$	−1.13782	+	0.826674i	−0.0713932	+	0.0518702i
$255$	13.1174	−	4.90707i	0.821441	−	0.307293i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	9.79456i		−	0.610968i	−0.952197	−	0.305484i	$-0.901182\pi$
$257$		−	9.79456i		−	0.610968i	0.952197	−	0.305484i	$-0.0988183\pi$
$258$	3.78741	−	5.21292i	0.235794	−	0.324542i
$259$	−3.55295	+	10.9349i	−0.220769	+	0.679459i
$260$	2.94358	−	2.34230i	0.182553	−	0.145263i
$261$	0.571791	+	1.75979i	0.0353930	+	0.108928i
$262$	−11.0611	−	3.59397i	−0.683358	−	0.222036i
$263$	−14.8479	−	4.82438i	−0.915562	−	0.297484i	−0.186917	−	0.982376i	$-0.559850\pi$
$263$	−14.8479	−	4.82438i	−0.915562	−	0.297484i	−0.728645	+	0.684892i	$0.759850\pi$
$264$	0.703849	+	2.16623i	0.0433189	+	0.133322i
$265$	20.0803	+	13.2856i	1.23352	+	0.816131i
$266$	1.64085	−	5.05001i	0.100607	−	0.309636i
$267$	−8.48604	+	11.6800i	−0.519337	+	0.714807i
$268$			5.11258i			0.312301i
$269$	−14.5739	−	10.5886i	−0.888586	−	0.645596i	0.0469227	−	0.998899i	$-0.485059\pi$
$269$	−14.5739	−	10.5886i	−0.888586	−	0.645596i	−0.935509	+	0.353303i	$0.885059\pi$
$270$	−6.64856	+	10.0488i	−0.404618	+	0.611551i
$271$	2.83307	−	2.05835i	0.172097	−	0.125036i	−0.498403	−	0.866946i	$-0.666080\pi$
$271$	2.83307	−	2.05835i	0.172097	−	0.125036i	0.670500	+	0.741910i	$0.266080\pi$
$272$	2.21943	+	3.05479i	0.134573	+	0.185224i
$273$	2.65396	−	0.862325i	0.160625	−	0.0521903i
$274$	−18.8186			−1.13687
$275$	−5.88637	−	3.53400i	−0.354961	−	0.213108i
$276$	−11.8579			−0.713760
$277$	−18.2788	+	5.93914i	−1.09827	+	0.356848i	−0.801435	−	0.598082i	$-0.795930\pi$
$277$	−18.2788	+	5.93914i	−1.09827	+	0.356848i	−0.296831	+	0.954930i	$0.595930\pi$
$278$	6.96110	+	9.58114i	0.417499	+	0.574638i
$279$	−0.440376	+	0.319952i	−0.0263646	+	0.0191550i
$280$	2.15485	+	0.597175i	0.128777	+	0.0356880i
$281$	−9.78761	−	7.11112i	−0.583880	−	0.424214i	0.256241	−	0.966613i	$-0.417516\pi$
$281$	−9.78761	−	7.11112i	−0.583880	−	0.424214i	−0.840121	+	0.542399i	$0.817516\pi$
$282$		−	0.450766i		−	0.0268427i
$283$	9.16263	−	12.6113i	0.544662	−	0.749662i	−0.444614	−	0.895722i	$-0.646659\pi$
$283$	9.16263	−	12.6113i	0.544662	−	0.749662i	0.989276	+	0.146060i	$0.0466592\pi$
$284$	1.50453	−	4.63048i	0.0892776	−	0.274768i
$285$	6.90057	+	18.4463i	0.408754	+	1.09266i
$286$	−0.713854	−	2.19702i	−0.0422111	−	0.129912i
$287$	−0.753592	−	0.244857i	−0.0444831	−	0.0144534i
$288$	−0.236399	−	0.0768108i	−0.0139300	−	0.00452612i
$289$	0.847441	+	2.60816i	0.0498495	+	0.153421i
$290$	−4.44546	+	16.0410i	−0.261046	+	0.941962i
$291$	1.96880	−	6.05933i	0.115413	−	0.355204i
$292$	5.67746	−	7.81436i	0.332248	−	0.457301i
$293$			10.1112i			0.590704i	0.955388	+	0.295352i	$0.0954370\pi$
$293$			10.1112i			0.590704i	−0.955388	+	0.295352i	$0.904563\pi$
$294$	1.34195	+	0.974986i	0.0782643	+	0.0568623i
$295$	0.906751	+	20.6826i	0.0527931	+	1.20419i
$296$	9.30174	−	6.75811i	0.540653	−	0.392807i
$297$	4.34918	+	5.98614i	0.252365	+	0.347351i
$298$	3.62155	−	1.17671i	0.209791	−	0.0681651i
$299$	12.0264			0.695505
$300$	−7.63325	+	3.24337i	−0.440706	+	0.187256i
$301$	−3.88458			−0.223903
$302$	14.0863	−	4.57692i	0.810577	−	0.263372i
$303$	−3.94868	−	5.43489i	−0.226846	−	0.312226i
$304$	−4.29579	+	3.12108i	−0.246381	+	0.179006i
$305$	7.38337	+	9.27874i	0.422771	+	0.531299i
$306$	0.759313	+	0.551673i	0.0434071	+	0.0315371i
$307$			19.9922i			1.14101i	0.821293	+	0.570507i	$0.193253\pi$
$307$			19.9922i			1.14101i	−0.821293	+	0.570507i	$0.806747\pi$
$308$	0.807117	−	1.11090i	0.0459898	−	0.0632995i
$309$	−4.01059	+	12.3433i	−0.228155	+	0.702188i
$310$	−4.89209	+	0.214476i	−0.277852	+	0.0121814i
$311$	−0.538803	−	1.65826i	−0.0305527	−	0.0940315i	0.934617	−	0.355655i	$-0.115742\pi$
$311$	−0.538803	−	1.65826i	−0.0305527	−	0.0940315i	−0.965170	+	0.261623i	$0.915742\pi$
$312$	−2.65396	−	0.862325i	−0.150251	−	0.0488196i
$313$	10.0328	+	3.25987i	0.567090	+	0.184259i	0.578509	−	0.815676i	$-0.303635\pi$
$313$	10.0328	+	3.25987i	0.567090	+	0.184259i	−0.0114189	+	0.999935i	$0.503635\pi$
$314$	2.30067	+	7.08073i	0.129834	+	0.399589i
$315$	0.555275	−	0.0243440i	0.0312862	−	0.00137163i
$316$	−3.54420	+	10.9079i	−0.199377	+	0.613619i
$317$	−6.41001	+	8.82263i	−0.360022	+	0.495528i	−0.950155	−	0.311778i	$-0.899075\pi$
$317$	−6.41001	+	8.82263i	−0.360022	+	0.495528i	0.590133	+	0.807306i	$0.299075\pi$
$318$		−	17.8610i		−	1.00160i
$319$	8.26971	+	6.00830i	0.463015	+	0.336400i
$320$	−1.39230	−	1.74971i	−0.0778319	−	0.0978120i
$321$	−15.3458	+	11.1494i	−0.856521	+	0.622299i
$322$	4.20190	+	5.78342i	0.234163	+	0.322297i
$323$	19.0685	−	6.19572i	1.06100	−	0.344739i
$324$	8.19252			0.455140
$325$	7.74174	−	3.28947i	0.429435	−	0.182467i
$326$	10.7626			0.596085
$327$	−12.8340	+	4.17001i	−0.709720	+	0.230602i
$328$	0.465745	+	0.641044i	0.0257165	+	0.0353957i
$329$	−0.219851	+	0.159731i	−0.0121208	+	0.00880627i
$330$	0.223074	+	5.08821i	0.0122798	+	0.280097i
$331$	10.6084	+	7.70745i	0.583090	+	0.423640i	0.839837	−	0.542839i	$-0.182651\pi$
$331$	10.6084	+	7.70745i	0.583090	+	0.423640i	−0.256747	+	0.966479i	$0.582651\pi$
$332$			11.3773i			0.624413i
$333$	1.67983	−	2.31209i	0.0920541	−	0.126702i
$334$	−0.254099	+	0.782037i	−0.0139037	+	0.0427912i
$335$	−3.05311	+	11.0168i	−0.166809	+	0.601915i
$336$	−0.512580	−	1.57756i	−0.0279636	−	0.0860630i
$337$	13.0044	+	4.22539i	0.708395	+	0.230172i	0.640985	−	0.767554i	$-0.278526\pi$
$337$	13.0044	+	4.22539i	0.708395	+	0.230172i	0.0674108	+	0.997725i	$0.478526\pi$
$338$	−9.67205	−	3.14264i	−0.526090	−	0.170937i
$339$	7.85150	+	24.1644i	0.426435	+	1.31243i
$340$	2.95830	+	7.90801i	0.160437	+	0.428872i
$341$	−0.929237	+	2.85990i	−0.0503210	+	0.154872i
$342$	−0.775790	+	1.06778i	−0.0419499	+	0.0577391i
$343$		−	1.00000i		−	0.0539949i
$344$	3.14269	+	2.28330i	0.169442	+	0.123107i
$345$	−25.5519	−	7.08122i	−1.37567	−	0.381240i
$346$	−15.0717	+	10.9502i	−0.810260	+	0.588688i
$347$	−16.5091	−	22.7228i	−0.886256	−	1.21983i	−0.974649	−	0.223741i	$-0.928173\pi$
$347$	−16.5091	−	22.7228i	−0.886256	−	1.21983i	0.0883930	−	0.996086i	$-0.471827\pi$
$348$	11.7436	−	3.81572i	0.629523	−	0.204544i
$349$	−11.0676			−0.592437			−0.296219	−	0.955120i	$-0.595726\pi$
$349$	−11.0676			−0.592437			−0.296219	+	0.955120i	$0.595726\pi$
$350$	4.28676	+	2.57365i	0.229137	+	0.137567i
$351$	−9.06526			−0.483868
$352$	−1.30594	+	0.424326i	−0.0696070	+	0.0226167i
$353$	6.21783	+	8.55811i	0.330942	+	0.455502i	0.941768	−	0.336262i	$-0.109163\pi$
$353$	6.21783	+	8.55811i	0.330942	+	0.455502i	−0.610827	+	0.791764i	$0.709163\pi$
$354$	12.4243	−	9.02682i	0.660347	−	0.479770i
$355$	6.00725	−	9.07952i	0.318832	−	0.481891i
$356$	−7.04149	−	5.11594i	−0.373198	−	0.271144i
$357$			6.26330i			0.331489i
$358$	2.91918	−	4.01791i	0.154284	−	0.212353i
$359$	−5.02053	+	15.4516i	−0.264973	+	0.815504i	0.726726	+	0.686927i	$0.241041\pi$
$359$	−5.02053	+	15.4516i	−0.264973	+	0.815504i	−0.991700	+	0.128577i	$0.958959\pi$
$360$	−0.463536	−	0.306688i	−0.0244305	−	0.0161639i
$361$	2.84140	+	8.74492i	0.149547	+	0.460259i
$362$	−21.3575	−	6.93947i	−1.12252	−	0.364730i
$363$	−14.3786	−	4.67189i	−0.754681	−	0.245211i
$364$	0.519866	+	1.59998i	0.0272484	+	0.0838619i
$365$	16.9006	−	13.4483i	0.884619	−	0.703918i
$366$	2.71822	−	8.36581i	0.142083	−	0.437288i
$367$	4.96742	−	6.83707i	0.259297	−	0.356892i	−0.659443	−	0.751755i	$-0.729208\pi$
$367$	4.96742	−	6.83707i	0.259297	−	0.356892i	0.918740	+	0.394862i	$0.129208\pi$
$368$		−	7.14870i		−	0.372652i
$369$	0.159341	+	0.115768i	0.00829496	+	0.00602664i
$370$	24.0796	−	9.00795i	1.25184	−	0.468301i
$371$	−8.71132	+	6.32915i	−0.452269	+	0.328593i
$372$	2.13513	+	2.93876i	0.110701	+	0.152367i
$373$	6.00688	−	1.95175i	0.311024	−	0.101058i	−0.149346	−	0.988785i	$-0.547717\pi$
$373$	6.00688	−	1.95175i	0.311024	−	0.101058i	0.460370	+	0.887727i	$0.347717\pi$
$374$	5.18491			0.268105
$375$	−18.3854	+	2.43058i	−0.949416	+	0.125515i
$376$	0.271751			0.0140145
$377$	−11.9105	+	3.86996i	−0.613423	+	0.199313i
$378$	−3.16730	−	4.35942i	−0.162909	−	0.224224i
$379$	−12.0974	+	8.78929i	−0.621403	+	0.451476i	−0.853411	−	0.521238i	$-0.825470\pi$
$379$	−12.0974	+	8.78929i	−0.621403	+	0.451476i	0.232008	+	0.972714i	$0.425470\pi$
$380$	−11.1206	+	4.16011i	−0.570476	+	0.213409i
$381$	1.88735	+	1.37124i	0.0966920	+	0.0702509i
$382$		−	0.833769i		−	0.0426594i
$383$	11.3371	−	15.6042i	0.579300	−	0.797338i	−0.414318	−	0.910132i	$-0.635980\pi$
$383$	11.3371	−	15.6042i	0.579300	−	0.797338i	0.993618	+	0.112794i	$0.0359800\pi$
$384$	−0.512580	+	1.57756i	−0.0261575	+	0.0805045i
$385$	2.40262	−	1.91184i	0.122449	−	0.0974362i
$386$	7.37369	+	22.6939i	0.375311	+	1.15509i
$387$	0.918311	+	0.298377i	0.0466804	+	0.0151674i
$388$	3.65296	+	1.18692i	0.185451	+	0.0602567i
$389$	1.42624	+	4.38952i	0.0723132	+	0.222557i	0.980681	−	0.195616i	$-0.0626706\pi$
$389$	1.42624	+	4.38952i	0.0723132	+	0.222557i	−0.908367	+	0.418173i	$0.862671\pi$
$390$	−5.20394	−	3.44306i	−0.263512	−	0.174346i
$391$	−8.34128	+	25.6718i	−0.421837	+	1.29828i
$392$	−0.587785	+	0.809017i	−0.0296876	+	0.0408615i
$393$			19.2918i			0.973141i
$394$	−11.6082	−	8.43384i	−0.584812	−	0.424891i
$395$	−14.1512	+	21.3884i	−0.712022	+	1.07617i
$396$	−0.276131	+	0.200621i	−0.0138761	+	0.0100816i
$397$	10.0635	+	13.8512i	0.505072	+	0.695172i	0.983079	−	0.183185i	$-0.0586406\pi$
$397$	10.0635	+	13.8512i	0.505072	+	0.695172i	−0.478007	+	0.878356i	$0.658641\pi$
$398$	14.7410	−	4.78965i	0.738901	−	0.240083i
$399$	−8.80776			−0.440939
$400$	−1.95531	−	4.60182i	−0.0977656	−	0.230091i
$401$	−17.1311			−0.855484			−0.427742	−	0.903901i	$-0.640691\pi$
$401$	−17.1311			−0.855484			−0.427742	+	0.903901i	$0.640691\pi$
$402$	8.06540	−	2.62061i	0.402266	−	0.130704i
$403$	−2.16548	−	2.98053i	−0.107870	−	0.148471i
$404$	3.27651	−	2.38052i	0.163012	−	0.118435i
$405$	17.6537	+	4.89237i	0.877217	+	0.243104i
$406$	−6.02244	−	4.37556i	−0.298889	−	0.217155i
$407$		−	15.7879i		−	0.782577i
$408$	3.68148	−	5.06712i	0.182260	−	0.250860i
$409$	7.33286	−	22.5682i	0.362587	−	1.11593i	−0.588892	−	0.808212i	$-0.700436\pi$
$409$	7.33286	−	22.5682i	0.362587	−	1.11593i	0.951479	−	0.307715i	$-0.0995644\pi$
$410$	0.620796	+	1.65948i	0.0306590	+	0.0819561i
$411$	9.64602	+	29.6874i	0.475803	+	1.46437i
$412$	−7.44137	−	2.41785i	−0.366610	−	0.119119i
$413$	−8.80527	−	2.86101i	−0.433279	−	0.140781i
$414$	−0.549097	−	1.68995i	−0.0269866	−	0.0830563i
$415$	−6.79427	+	24.5165i	−0.333518	+	1.20347i
$416$	0.519866	−	1.59998i	0.0254885	−	0.0784456i
$417$	11.5467	−	15.8927i	0.565444	−	0.778267i
$418$			7.29127i			0.356628i
$419$	29.6804	+	21.5641i	1.44998	+	1.05347i	0.985835	+	0.167716i	$0.0536390\pi$
$419$	29.6804	+	21.5641i	1.44998	+	1.05347i	0.464147	+	0.885758i	$0.346361\pi$
$420$	−0.162454	−	3.70551i	−0.00792696	−	0.180810i
$421$	−27.3915	+	19.9011i	−1.33498	+	0.969919i	−0.335366	+	0.942088i	$0.608860\pi$
$421$	−27.3915	+	19.9011i	−1.33498	+	0.969919i	−0.999613	+	0.0278305i	$0.991140\pi$
$422$	−12.9674	−	17.8481i	−0.631243	−	0.868831i
$423$	0.0642418	−	0.0208734i	0.00312354	−	0.00101490i
$424$	10.7678			0.522930
$425$	1.65224	+	18.8072i	0.0801454	+	0.912283i
$426$	−8.07605			−0.391286
$427$	−5.04346	+	1.63872i	−0.244070	+	0.0793031i
$428$	−6.72159	−	9.25147i	−0.324900	−	0.447187i
$429$	−3.10002	+	2.25229i	−0.149670	+	0.108742i
$430$	5.40850	+	6.79690i	0.260821	+	0.327776i
$431$	28.8235	+	20.9415i	1.38838	+	1.00872i	0.996041	+	0.0888935i	$0.0283331\pi$
$431$	28.8235	+	20.9415i	1.38838	+	1.00872i	0.392336	+	0.919822i	$0.371667\pi$
$432$			5.38854i			0.259256i
$433$	16.9374	−	23.3124i	0.813960	−	1.12032i	−0.176740	−	0.984258i	$-0.556555\pi$
$433$	16.9374	−	23.3124i	0.813960	−	1.12032i	0.990700	−	0.136063i	$-0.0434448\pi$
$434$	0.676720	−	2.08273i	0.0324836	−	0.0999742i
$435$	27.5843	−	1.20933i	1.32257	−	0.0579831i
$436$	−2.51395	−	7.73716i	−0.120397	−	0.370543i
$437$	−36.1010	−	11.7299i	−1.72694	−	0.561118i
$438$	−15.2378	−	4.95105i	−0.728089	−	0.236571i
$439$	−1.73641	−	5.34412i	−0.0828743	−	0.255061i	0.901030	−	0.433757i	$-0.142812\pi$
$439$	−1.73641	−	5.34412i	−0.0828743	−	0.255061i	−0.983904	+	0.178696i	$0.942812\pi$
$440$	−3.06751	+	0.134484i	−0.146238	+	0.00641126i
$441$	−0.0768108	+	0.236399i	−0.00365766	+	0.0112571i
$442$	−3.73380	+	5.13914i	−0.177599	+	0.244444i
$443$			21.6535i			1.02879i	0.857553	+	0.514395i	$0.171983\pi$
$443$			21.6535i			1.02879i	−0.857553	+	0.514395i	$0.828017\pi$
$444$	−15.4292	−	11.2100i	−0.732238	−	0.532002i
$445$	−12.1182	−	15.2291i	−0.574460	−	0.721928i
$446$	23.4240	−	17.0185i	1.10916	−	0.805851i
$447$	−3.71267	−	5.11005i	−0.175603	−	0.241697i
$448$	0.951057	−	0.309017i	0.0449332	−	0.0145997i
$449$	24.5454			1.15837			0.579184	−	0.815197i	$-0.303371\pi$
$449$	24.5454			1.15837			0.579184	+	0.815197i	$0.303371\pi$
$450$	−0.815704	−	0.937678i	−0.0384527	−	0.0442026i
$451$	1.08805			0.0512341
$452$	−14.5679	+	4.73340i	−0.685216	+	0.222640i
$453$	−14.4407	−	19.8760i	−0.678486	−	0.933855i
$454$	−18.9661	+	13.7797i	−0.890125	+	0.646714i
$455$	0.164763	+	3.75818i	0.00772423	+	0.176186i
$456$	7.12562	+	5.17707i	0.333688	+	0.242438i
$457$		−	38.1950i		−	1.78669i	−0.449375	−	0.893343i	$-0.648353\pi$
$457$		−	38.1950i		−	1.78669i	0.449375	−	0.893343i	$-0.351647\pi$
$458$	−3.31949	+	4.56889i	−0.155110	+	0.213490i
$459$	6.28749	−	19.3509i	0.293475	−	0.903222i
$460$	4.26902	−	15.4044i	0.199044	−	0.718233i
$461$	−8.14501	−	25.0678i	−0.379351	−	1.16752i	−0.940496	−	0.339804i	$-0.889639\pi$
$461$	−8.14501	−	25.0678i	−0.379351	−	1.16752i	0.561145	−	0.827717i	$-0.310361\pi$
$462$	−2.16623	−	0.703849i	−0.100782	−	0.0327460i
$463$	−7.68049	−	2.49554i	−0.356943	−	0.115978i	0.125056	−	0.992150i	$-0.460089\pi$
$463$	−7.68049	−	2.49554i	−0.356943	−	0.115978i	−0.481999	+	0.876172i	$0.660089\pi$
$464$	2.30037	+	7.07981i	0.106792	+	0.328672i
$465$	2.84594	+	7.60763i	0.131977	+	0.352795i
$466$	1.02749	−	3.16228i	0.0475974	−	0.146490i
$467$	22.4464	−	30.8948i	1.03869	−	1.42964i	0.140480	−	0.990084i	$-0.455136\pi$
$467$	22.4464	−	30.8948i	1.03869	−	1.42964i	0.898215	−	0.439557i	$-0.144864\pi$
$468$		−	0.418166i		−	0.0193297i
$469$	−4.13616	−	3.00510i	−0.190990	−	0.138763i
$470$	0.585583	+	0.162283i	0.0270109	+	0.00748556i
$471$	9.99100	−	7.25888i	0.460361	−	0.334472i
$472$	5.44196	+	7.49021i	0.250486	+	0.344765i
$473$	5.07303	−	1.64833i	0.233258	−	0.0757902i
$474$	19.0246			0.873829
$475$	−26.4476	+	2.32346i	−1.21350	+	0.106608i
$476$	−3.77593			−0.173069
$477$	2.54550	−	0.827082i	0.116550	−	0.0378695i
$478$	4.12912	+	5.68324i	0.188861	+	0.259946i
$479$	−20.4437	+	14.8532i	−0.934098	+	0.678662i	−0.946993	−	0.321255i	$-0.895895\pi$
$479$	−20.4437	+	14.8532i	−0.934098	+	0.678662i	0.0128946	+	0.999917i	$0.495895\pi$
$480$	−2.04661	+	3.09331i	−0.0934147	+	0.141189i
$481$	15.6485	+	11.3693i	0.713511	+	0.518396i
$482$		−	10.6551i		−	0.485327i
$483$	6.96988	−	9.59321i	0.317140	−	0.436506i
$484$	2.81652	−	8.66837i	0.128024	−	0.394017i
$485$	7.16279	+	4.73909i	0.325245	+	0.215191i
$486$	0.796127	+	2.45023i	0.0361130	+	0.111144i
$487$	−35.9130	−	11.6688i	−1.62737	−	0.528765i	−0.653707	−	0.756748i	$-0.726787\pi$
$487$	−35.9130	−	11.6688i	−1.62737	−	0.528765i	−0.973665	+	0.227982i	$0.926787\pi$
$488$	5.04346	+	1.63872i	0.228307	+	0.0741813i
$489$	−5.51670	−	16.9786i	−0.249474	−	0.767801i
$490$	−1.74971	+	1.39230i	−0.0790440	+	0.0628977i
$491$	11.5525	−	35.5550i	0.521358	−	1.60458i	−0.250049	−	0.968233i	$-0.580447\pi$
$491$	11.5525	−	35.5550i	0.521358	−	1.60458i	0.771407	−	0.636342i	$-0.219553\pi$
$492$	0.772553	−	1.06333i	0.0348294	−	0.0479385i
$493$		−	28.1086i		−	1.26595i
$494$	−7.22691	−	5.25065i	−0.325154	−	0.236238i
$495$	−0.714827	+	0.267410i	−0.0321291	+	0.0120192i
$496$	−1.77167	+	1.28720i	−0.0795505	+	0.0577969i
$497$	2.86179	+	3.93892i	0.128369	+	0.176685i
$498$	17.9484	−	5.83180i	0.804289	−	0.261329i
$499$	17.3256			0.775602			0.387801	−	0.921743i	$-0.373235\pi$
$499$	17.3256			0.775602			0.387801	+	0.921743i	$0.373235\pi$
$500$	−1.46531	−	11.0839i	−0.0655308	−	0.495687i
$501$	1.36396			0.0609371
$502$	−4.88626	+	1.58764i	−0.218085	+	0.0708600i
$503$	−19.2637	−	26.5141i	−0.858924	−	1.18221i	−0.981825	−	0.189788i	$-0.939220\pi$
$503$	−19.2637	−	26.5141i	−0.858924	−	1.18221i	0.122901	−	0.992419i	$-0.460780\pi$
$504$	0.201093	−	0.146103i	0.00895741	−	0.00650794i
$505$	8.48198	−	3.17302i	0.377443	−	0.141198i
$506$	−7.94149	−	5.76983i	−0.353042	−	0.256500i
$507$			16.8691i			0.749183i
$508$	−0.826674	+	1.13782i	−0.0366777	+	0.0504826i
$509$	10.8504	−	33.3940i	0.480934	−	1.48016i	−0.356851	−	0.934161i	$-0.616150\pi$
$509$	10.8504	−	33.3940i	0.480934	−	1.48016i	0.837785	−	0.546001i	$-0.183850\pi$
$510$	10.9590	−	8.72039i	0.485272	−	0.386145i
$511$	2.98482	+	9.18633i	0.132041	+	0.406379i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	27.2122	+	8.84177i	1.20145	+	0.390374i
$514$	−3.02669	−	9.31518i	−0.133501	−	0.410875i
$515$	−14.5912	−	9.65390i	−0.642963	−	0.425402i
$516$	1.99116	−	6.12815i	0.0876558	−	0.269777i
$517$	0.219335	−	0.301889i	0.00964634	−	0.0132770i
$518$			11.4976i			0.505175i
$519$	25.0001	+	18.1637i	1.09738	+	0.797296i
$520$	2.07570	−	3.13727i	0.0910256	−	0.137579i
$521$	−27.1539	+	19.7285i	−1.18964	+	0.864321i	−0.993226	−	0.116201i	$-0.962928\pi$
$521$	−27.1539	+	19.7285i	−1.18964	+	0.864321i	−0.196410	+	0.980522i	$0.562928\pi$
$522$	1.08761	+	1.49697i	0.0476034	+	0.0655205i
$523$	11.1955	−	3.63763i	0.489544	−	0.159063i	−0.0538351	−	0.998550i	$-0.517145\pi$
$523$	11.1955	−	3.63763i	0.489544	−	0.159063i	0.543379	+	0.839487i	$0.317145\pi$
$524$	−11.6303			−0.508074
$525$	1.86277	−	8.08183i	0.0812980	−	0.352720i
$526$	−15.6120			−0.680717
$527$	7.86423	−	2.55524i	0.342571	−	0.111308i
$528$	1.33880	+	1.84270i	0.0582638	+	0.0801933i
$529$	22.7365	−	16.5190i	0.988543	−	0.718219i
$530$	23.2030	+	6.43026i	1.00787	+	0.279312i
$531$	1.86180	+	1.35268i	0.0807954	+	0.0587013i
$532$		−	5.30989i		−	0.230213i
$533$	−0.783534	+	1.07844i	−0.0339386	+	0.0467125i
$534$	−4.46138	+	13.7307i	−0.193063	+	0.594186i
$535$	−8.95927	−	23.9495i	−0.387343	−	1.03543i
$536$	1.57987	+	4.86235i	0.0682402	+	0.210022i
$537$	−7.83481	−	2.54568i	−0.338097	−	0.109854i
$538$	−17.1326	−	5.56673i	−0.738641	−	0.239999i
$539$	0.424326	+	1.30594i	0.0182770	+	0.0562509i
$540$	−3.21790	+	11.6115i	−0.138477	+	0.499679i
$541$	−4.55152	+	14.0081i	−0.195685	+	0.602257i	0.804283	+	0.594247i	$0.202550\pi$
$541$	−4.55152	+	14.0081i	−0.195685	+	0.602257i	−0.999968	+	0.00801024i	$0.997450\pi$
$542$	2.05835	−	2.83307i	0.0884136	−	0.121691i
$543$			37.2497i			1.59854i
$544$	3.05479	+	2.21943i	0.130973	+	0.0951574i
$545$	−0.796759	−	18.1737i	−0.0341294	−	0.778475i
$546$	2.25760	−	1.64024i	0.0966162	−	0.0701958i
$547$	13.5970	+	18.7147i	0.581366	+	0.800181i	0.993844	−	0.110786i	$-0.0353368\pi$
$547$	13.5970	+	18.7147i	0.581366	+	0.800181i	−0.412479	+	0.910967i	$0.635337\pi$
$548$	−17.8975	+	5.81525i	−0.764544	+	0.248415i
$549$	1.31814			0.0562569
$550$	−6.69033	−	1.54205i	−0.285277	−	0.0657531i
$551$	39.5276			1.68393
$552$	−11.2775	+	3.66428i	−0.480002	+	0.155962i
$553$	−6.74147	−	9.27884i	−0.286676	−	0.394576i
$554$	−15.5489	+	11.2969i	−0.660608	+	0.479960i
$555$	−26.5533	−	33.3698i	−1.12713	−	1.41647i
$556$	9.58114	+	6.96110i	0.406331	+	0.295217i
$557$		−	45.6238i		−	1.93314i	−0.256396	−	0.966572i	$-0.582535\pi$
$557$		−	45.6238i		−	1.93314i	0.256396	−	0.966572i	$-0.417465\pi$
$558$	−0.319952	+	0.440376i	−0.0135446	+	0.0186426i
$559$	−2.01946	+	6.21526i	−0.0854140	+	0.262877i
$560$	2.23392	−	0.0979381i	0.0944004	−	0.00413864i
$561$	−2.65768	−	8.17951i	−0.112207	−	0.345339i
$562$	−11.5060	−	3.73854i	−0.485353	−	0.157701i
$563$	12.2634	+	3.98463i	0.516842	+	0.167932i	0.555812	−	0.831308i	$-0.312408\pi$
$563$	12.2634	+	3.98463i	0.516842	+	0.167932i	−0.0389695	+	0.999240i	$0.512408\pi$
$564$	−0.139294	−	0.428704i	−0.00586535	−	0.0180517i
$565$	−34.2183	+	1.50018i	−1.43957	+	0.0631129i
$566$	4.81708	−	14.8254i	0.202477	−	0.623160i
$567$	−4.81544	+	6.62789i	−0.202230	+	0.278345i
$568$		−	4.86877i		−	0.204289i
$569$	0.372050	+	0.270310i	0.0155972	+	0.0113320i	0.595557	−	0.803313i	$-0.296932\pi$
$569$	0.372050	+	0.270310i	0.0155972	+	0.0113320i	−0.579959	+	0.814645i	$0.696932\pi$
$570$	12.2630	+	15.4111i	0.513642	+	0.645498i
$571$	−23.1138	+	16.7931i	−0.967281	+	0.702771i	−0.954830	−	0.297151i	$-0.903963\pi$
$571$	−23.1138	+	16.7931i	−0.967281	+	0.702771i	−0.0124510	+	0.999922i	$0.503963\pi$
$572$	−1.35783	−	1.86889i	−0.0567737	−	0.0781424i
$573$	−1.31532	+	0.427374i	−0.0549483	+	0.0178538i
$574$	−0.792373			−0.0330730
$575$	18.3982	−	30.6448i	0.767259	−	1.27798i
$576$	−0.248565			−0.0103569
$577$	24.7623	−	8.04575i	1.03087	−	0.334949i	0.255734	−	0.966747i	$-0.417683\pi$
$577$	24.7623	−	8.04575i	1.03087	−	0.334949i	0.775133	+	0.631798i	$0.217683\pi$
$578$	1.61193	+	2.21863i	0.0670474	+	0.0922828i
$579$	32.0213	−	23.2649i	1.33076	−	0.966855i
$580$	0.729066	+	16.6296i	0.0302728	+	0.690509i
$581$	−9.20446	−	6.68744i	−0.381866	−	0.277442i
$582$		−	6.37116i		−	0.264093i
$583$	8.69086	−	11.9619i	0.359939	−	0.495413i
$584$	2.98482	−	9.18633i	0.123513	−	0.380133i
$585$	0.249719	−	0.901086i	0.0103246	−	0.0372553i
$586$	3.12454	+	9.61635i	0.129074	+	0.397248i
$587$	43.5804	+	14.1601i	1.79876	+	0.584452i	0.999855	−	0.0170094i	$-0.00541454\pi$
$587$	43.5804	+	14.1601i	1.79876	+	0.584452i	0.798902	+	0.601461i	$0.205415\pi$
$588$	1.57756	+	0.512580i	0.0650575	+	0.0211385i
$589$	3.59331	+	11.0591i	0.148060	+	0.455681i
$590$	7.25364	+	19.3901i	0.298627	+	0.798277i
$591$	−7.35476	+	22.6356i	−0.302534	+	0.931105i
$592$	6.75811	−	9.30174i	0.277757	−	0.382299i
$593$			47.2064i			1.93853i	0.246010	+	0.969267i	$0.420880\pi$
$593$			47.2064i			1.93853i	−0.246010	+	0.969267i	$0.579120\pi$
$594$	5.98614	+	4.34918i	0.245614	+	0.178449i
$595$	−8.13656	−	2.25489i	−0.333566	−	0.0924415i
$596$	3.08067	−	2.23824i	0.126189	−	0.0916819i
$597$	−15.1119	−	20.7998i	−0.618490	−	0.851278i
$598$	11.4378	−	3.71636i	0.467726	−	0.151973i
$599$	−21.5830			−0.881856			−0.440928	−	0.897543i	$-0.645351\pi$
$599$	−21.5830			−0.881856			−0.440928	+	0.897543i	$0.645351\pi$
$600$	−6.25739	+	5.44343i	−0.255457	+	0.222227i
$601$	29.7945			1.21534			0.607672	−	0.794188i	$-0.292104\pi$
$601$	29.7945			1.21534			0.607672	+	0.794188i	$0.292104\pi$
$602$	−3.69445	+	1.20040i	−0.150575	+	0.0489247i
$603$	0.746962	+	1.02811i	0.0304187	+	0.0418677i
$604$	11.9825	−	8.70583i	0.487563	−	0.354235i
$605$	11.2457	−	16.9971i	0.457204	−	0.691030i
$606$	−5.43489	−	3.94868i	−0.220777	−	0.160404i
$607$			24.1653i			0.980839i	0.871486	+	0.490420i	$0.163156\pi$
$607$			24.1653i			0.980839i	−0.871486	+	0.490420i	$0.836844\pi$
$608$	−3.12108	+	4.29579i	−0.126576	+	0.174217i
$609$	−3.81572	+	11.7436i	−0.154621	+	0.475874i
$610$	9.88929	+	6.54302i	0.400406	+	0.264919i
$611$	0.141274	+	0.434797i	0.00571534	+	0.0175900i
$612$	0.892626	+	0.290032i	0.0360823	+	0.0117238i
$613$	−0.508945	−	0.165366i	−0.0205561	−	0.00667908i	0.298721	−	0.954341i	$-0.403440\pi$
$613$	−0.508945	−	0.165366i	−0.0205561	−	0.00667908i	−0.319277	+	0.947661i	$0.603440\pi$
$614$	6.17792	+	19.0137i	0.249321	+	0.767330i
$615$	2.29973	−	1.82996i	0.0927340	−	0.0737912i
$616$	0.424326	−	1.30594i	0.0170966	−	0.0526179i
$617$	3.04232	−	4.18740i	0.122479	−	0.168578i	−0.743374	−	0.668875i	$-0.766776\pi$
$617$	3.04232	−	4.18740i	0.122479	−	0.168578i	0.865854	+	0.500297i	$0.166776\pi$
$618$			12.9785i			0.522074i
$619$	−4.13986	−	3.00778i	−0.166395	−	0.120893i	0.501471	−	0.865174i	$-0.332792\pi$
$619$	−4.13986	−	3.00778i	−0.166395	−	0.120893i	−0.667866	+	0.744281i	$0.732792\pi$
$620$	−4.58638	+	1.71572i	−0.184193	+	0.0689049i
$621$	−31.1642	+	22.6421i	−1.25058	+	0.908596i
$622$	−1.02486	−	1.41060i	−0.0410933	−	0.0565600i
$623$	8.27777	−	2.68961i	0.331642	−	0.107757i
$624$	−2.79054			−0.111711
$625$	3.46150	−	24.7592i	0.138460	−	0.990368i
$626$	10.5492			0.421629
$627$	11.5024	−	3.73736i	0.459363	−	0.149256i
$628$	4.37613	+	6.02323i	0.174627	+	0.240353i
$629$	−35.1227	+	25.5181i	−1.40043	+	1.01747i
$630$	0.520575	−	0.194742i	0.0207402	−	0.00775870i
$631$	7.23416	+	5.25593i	0.287988	+	0.209235i	0.722394	−	0.691482i	$-0.243042\pi$
$631$	7.23416	+	5.25593i	0.287988	+	0.209235i	−0.434406	+	0.900717i	$0.643042\pi$
$632$			11.4693i			0.456223i
$633$	−21.5096	+	29.6054i	−0.854930	+	1.17671i
$634$	−3.36994	+	10.3716i	−0.133838	+	0.411910i
$635$	−2.46084	+	1.95816i	−0.0976554	+	0.0777073i
$636$	−5.51936	−	16.9868i	−0.218857	−	0.673572i
$637$	−1.59998	−	0.519866i	−0.0633936	−	0.0205978i
$638$	9.72163	+	3.15875i	0.384883	+	0.125056i
$639$	−0.373974	−	1.15097i	−0.0147942	−	0.0455318i
$640$	−1.86485	−	1.23383i	−0.0737146	−	0.0487715i
$641$	−1.86472	+	5.73901i	−0.0736519	+	0.226677i	−0.981105	−	0.193476i	$-0.938024\pi$
$641$	−1.86472	+	5.73901i	−0.0736519	+	0.226677i	0.907453	+	0.420153i	$0.138024\pi$
$642$	−11.1494	+	15.3458i	−0.440032	+	0.605652i
$643$		−	24.2025i		−	0.954453i	−0.878780	−	0.477227i	$-0.841642\pi$
$643$		−	24.2025i		−	0.954453i	0.878780	−	0.477227i	$-0.158358\pi$
$644$	5.78342	+	4.20190i	0.227899	+	0.165578i
$645$	7.95023	−	12.0162i	0.313040	−	0.473137i
$646$	16.2206	−	11.7850i	0.638191	−	0.463673i
$647$	3.67705	+	5.06103i	0.144560	+	0.198969i	0.875157	−	0.483839i	$-0.160758\pi$
$647$	3.67705	+	5.06103i	0.144560	+	0.198969i	−0.730597	+	0.682809i	$0.760758\pi$
$648$	7.79155	−	2.53163i	0.306081	−	0.0994517i
$649$	12.7132			0.499036
$650$	6.34633	−	5.52080i	0.248924	−	0.216544i
$651$	−3.63250			−0.142369
$652$	10.2358	−	3.32582i	0.400866	−	0.130249i
$653$	−2.31259	−	3.18301i	−0.0904986	−	0.124561i	0.761367	−	0.648321i	$-0.224529\pi$
$653$	−2.31259	−	3.18301i	−0.0904986	−	0.124561i	−0.851865	+	0.523761i	$0.824529\pi$
$654$	−10.9172	+	7.93183i	−0.426897	+	0.310159i
$655$	−25.0617	−	6.94535i	−0.979240	−	0.271377i
$656$	0.641044	+	0.465745i	0.0250285	+	0.0181843i
$657$		−	2.40091i		−	0.0936683i
$658$	−0.159731	+	0.219851i	−0.00622697	+	0.00857070i
$659$	1.03159	−	3.17490i	0.0401849	−	0.123676i	−0.928952	−	0.370201i	$-0.879289\pi$
$659$	1.03159	−	3.17490i	0.0401849	−	0.123676i	0.969136	+	0.246525i	$0.0792887\pi$
$660$	1.78450	+	4.77025i	0.0694616	+	0.185682i
$661$	−14.8054	−	45.5663i	−0.575863	−	1.77232i	−0.633221	−	0.773971i	$-0.718268\pi$
$661$	−14.8054	−	45.5663i	−0.575863	−	1.77232i	0.0573579	−	0.998354i	$-0.481732\pi$
$662$	12.4709	+	4.05205i	0.484696	+	0.157487i
$663$	10.0212	+	3.25608i	0.389190	+	0.126456i
$664$	3.51579	+	10.8205i	0.136439	+	0.419917i
$665$	3.17094	−	11.4420i	0.122964	−	0.443703i
$666$	0.883138	−	2.71802i	0.0342209	−	0.105321i
$667$	−31.2796	+	43.0526i	−1.21115	+	1.66700i
$668$			0.822282i			0.0318151i
$669$	−38.8545	−	28.2294i	−1.50220	−	1.09141i
$670$	0.500716	+	11.4211i	0.0193444	+	0.441236i
$671$	5.89111	−	4.28014i	0.227424	−	0.165233i
$672$	−0.974986	−	1.34195i	−0.0376109	−	0.0517670i
$673$	−39.0166	+	12.6772i	−1.50398	+	0.488672i	−0.941175	−	0.337919i	$-0.890277\pi$
$673$	−39.0166	+	12.6772i	−1.50398	+	0.488672i	−0.562803	+	0.826591i	$0.690277\pi$
$674$	13.6736			0.526689
$675$	−13.8682	+	23.0994i	−0.533787	+	0.889096i
$676$	−10.1698			−0.391146
$677$	15.1794	−	4.93208i	0.583391	−	0.189555i	−0.00242790	−	0.999997i	$-0.500773\pi$
$677$	15.1794	−	4.93208i	0.583391	−	0.189555i	0.585819	+	0.810442i	$0.300773\pi$
$678$	14.9344	+	20.5555i	0.573553	+	0.789429i
$679$	−3.10739	+	2.25765i	−0.119251	+	0.0866408i
$680$	5.25722	+	6.60679i	0.201605	+	0.253359i
$681$	31.4600	+	22.8570i	1.20555	+	0.875883i
$682$			3.00707i			0.115147i
$683$	−26.3817	+	36.3113i	−1.00947	+	1.38941i	−0.0901351	+	0.995930i	$0.528730\pi$
$683$	−26.3817	+	36.3113i	−1.00947	+	1.38941i	−0.919332	+	0.393483i	$0.871270\pi$
$684$	−0.407857	+	1.25525i	−0.0155948	+	0.0479959i
$685$	−42.0392	+	1.84305i	−1.60623	+	0.0704195i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	8.90920	+	2.89477i	0.339907	+	0.110443i
$688$	3.69445	+	1.20040i	0.140850	+	0.0457648i
$689$	5.59781	+	17.2283i	0.213259	+	0.656345i
$690$	−26.4895	+	1.16134i	−1.00844	+	0.0442113i
$691$	14.9886	−	46.1302i	0.570194	−	1.75488i	−0.0817953	−	0.996649i	$-0.526065\pi$
$691$	14.9886	−	46.1302i	0.570194	−	1.75488i	0.651989	−	0.758228i	$-0.273935\pi$
$692$	−10.9502	+	15.0717i	−0.416266	+	0.572940i
$693$		−	0.341317i		−	0.0129656i
$694$	−22.7228	−	16.5091i	−0.862547	−	0.626677i
$695$	16.4889	+	20.7218i	0.625460	+	0.786021i
$696$	9.98970	−	7.25794i	0.378659	−	0.275112i
$697$	−1.75862	−	2.42053i	−0.0666125	−	0.0916842i
$698$	−10.5260	+	3.42009i	−0.398413	+	0.129452i
$699$	−5.51536			−0.208610
$700$	4.87226	+	1.12300i	0.184154	+	0.0424454i
$701$	−16.9663			−0.640809			−0.320405	−	0.947281i	$-0.603819\pi$
$701$	−16.9663			−0.640809			−0.320405	+	0.947281i	$0.603819\pi$
$702$	−8.62158	+	2.80132i	−0.325400	+	0.105729i
$703$	−35.8848	−	49.3912i	−1.35342	−	1.86283i
$704$	−1.11090	+	0.807117i	−0.0418687	+	0.0304194i
$705$	−0.0441472	−	1.00698i	−0.00166268	−	0.0379249i
$706$	8.55811	+	6.21783i	0.322089	+	0.234011i
$707$			4.04999i			0.152315i
$708$	9.02682	−	12.4243i	0.339249	−	0.466936i
$709$	11.0915	−	34.1360i	0.416548	−	1.28200i	−0.494310	−	0.869285i	$-0.664579\pi$
$709$	11.0915	−	34.1360i	0.416548	−	1.28200i	0.910859	−	0.412718i	$-0.135421\pi$
$710$	2.90751	−	10.4915i	0.109117	−	0.393738i
$711$	0.880964	+	2.71133i	0.0330387	+	0.101683i
$712$	−8.27777	−	2.68961i	−0.310222	−	0.100797i
$713$	−14.8888	−	4.83766i	−0.557590	−	0.181172i
$714$	1.93547	+	5.95675i	0.0724330	+	0.222926i
$715$	−1.80987	−	4.83805i	−0.0676851	−	0.180933i
$716$	1.53470	−	4.72333i	0.0573546	−	0.176519i
$717$	6.84915	−	9.42705i	0.255786	−	0.352060i
$718$			16.2468i			0.606324i
$719$	18.9743	+	13.7857i	0.707623	+	0.514118i	0.882406	−	0.470489i	$-0.155922\pi$
$719$	18.9743	+	13.7857i	0.707623	+	0.514118i	−0.174783	+	0.984607i	$0.555922\pi$
$720$	−0.535620	−	0.148437i	−0.0199614	−	0.00553191i
$721$	6.33001	−	4.59902i	0.235742	−	0.171276i
$722$	5.40466	+	7.43887i	0.201141	+	0.276846i
$723$	−16.8091	+	5.46160i	−0.625136	+	0.203119i
$724$	−22.4566			−0.834592
$725$	−8.35979	+	36.2698i	−0.310475	+	1.34703i
$726$	−15.1186			−0.561103
$727$	43.7843	−	14.2264i	1.62387	−	0.527628i	0.651020	−	0.759060i	$-0.274341\pi$
$727$	43.7843	−	14.2264i	1.62387	−	0.527628i	0.972851	+	0.231432i	$0.0743412\pi$
$728$	0.988844	+	1.36103i	0.0366490	+	0.0504430i
$729$	23.3410	−	16.9582i	0.864480	−	0.628082i
$730$	11.9177	−	18.0127i	0.441093	−	0.666680i
$731$	−11.8666	−	8.62156i	−0.438901	−	0.318880i
$732$		−	8.79633i		−	0.325122i
$733$	−12.1505	+	16.7237i	−0.448788	+	0.617703i	−0.972137	−	0.234415i	$-0.924682\pi$
$733$	−12.1505	+	16.7237i	−0.448788	+	0.617703i	0.523349	+	0.852119i	$0.324682\pi$
$734$	2.61153	−	8.03746i	0.0963933	−	0.296668i
$735$	3.09331	+	2.04661i	0.114098	+	0.0754905i
$736$	−2.20907	−	6.79881i	−0.0814273	−	0.250608i
$737$	6.67674	+	2.16940i	0.245941	+	0.0799110i
$738$	0.187317	+	0.0608628i	0.00689522	+	0.00224039i
$739$	5.21350	+	16.0455i	0.191782	+	0.590243i	0.999999	+	0.00135917i	$0.000432639\pi$
$739$	5.21350	+	16.0455i	0.191782	+	0.590243i	−0.808217	+	0.588884i	$0.799567\pi$
$740$	20.1175	−	16.0081i	0.739533	−	0.588469i
$741$	−4.57885	+	14.0923i	−0.168208	+	0.517692i
$742$	−6.32915	+	8.71132i	−0.232350	+	0.319803i
$743$			33.4789i			1.22822i	0.789219	+	0.614111i	$0.210485\pi$
$743$			33.4789i			1.22822i	−0.789219	+	0.614111i	$0.789515\pi$
$744$	2.93876	+	2.13513i	0.107740	+	0.0782777i
$745$	7.97501	−	2.98337i	0.292182	−	0.109302i
$746$	5.10976	−	3.71246i	0.187081	−	0.135923i
$747$	1.66226	+	2.28791i	0.0608190	+	0.0837101i
$748$	4.93114	−	1.60223i	0.180300	−	0.0585832i
$749$	11.4354			0.417842
$750$	−16.7344	+	7.99301i	−0.611055	+	0.291864i
$751$	−37.3123			−1.36154			−0.680772	−	0.732496i	$-0.738355\pi$
$751$	−37.3123			−1.36154			−0.680772	+	0.732496i	$0.738355\pi$
$752$	0.258451	−	0.0839757i	0.00942473	−	0.00306228i
$753$	5.00920	+	6.89458i	0.182546	+	0.251252i
$754$	−10.1317	+	7.36110i	−0.368974	+	0.268076i
$755$	31.0195	−	11.6041i	1.12892	−	0.422316i
$756$	−4.35942	−	3.16730i	−0.158551	−	0.115194i
$757$			15.4894i			0.562971i	0.959565	+	0.281485i	$0.0908271\pi$
$757$			15.4894i			0.562971i	−0.959565	+	0.281485i	$0.909173\pi$
$758$	−8.78929	+	12.0974i	−0.319242	+	0.439398i
$759$	−5.03161	+	15.4857i	−0.182636	+	0.562095i
$760$	−9.29079	+	7.39296i	−0.337013	+	0.268171i
$761$	1.13892	+	3.50524i	0.0412858	+	0.127065i	0.969575	−	0.244794i	$-0.0787205\pi$
$761$	1.13892	+	3.50524i	0.0412858	+	0.127065i	−0.928289	+	0.371859i	$0.878720\pi$
$762$	2.21872	+	0.720905i	0.0803756	+	0.0261156i
$763$	7.73716	+	2.51395i	0.280104	+	0.0910113i
$764$	−0.257649	−	0.792962i	−0.00932141	−	0.0286884i
$765$	1.75028	+	1.15803i	0.0632814	+	0.0418687i
$766$	5.96028	−	18.3439i	0.215354	−	0.662790i
$767$	−9.15512	+	12.6009i	−0.330572	+	0.454994i
$768$			1.65875i			0.0598548i
$769$	−41.3209	−	30.0214i	−1.49007	−	1.08260i	−0.974134	−	0.225971i	$-0.927445\pi$
$769$	−41.3209	−	30.0214i	−1.49007	−	1.08260i	−0.515935	−	0.856628i	$-0.672555\pi$
$770$	1.69424	−	2.56071i	0.0610561	−	0.0922817i
$771$	−13.1438	+	9.54956i	−0.473364	+	0.343919i
$772$	14.0256	+	19.3046i	0.504792	+	0.694786i
$773$	−1.20566	+	0.391743i	−0.0433646	+	0.0140900i	−0.330619	−	0.943764i	$-0.607257\pi$
$773$	−1.20566	+	0.391743i	−0.0433646	+	0.0140900i	0.287254	+	0.957854i	$0.407257\pi$
$774$	0.965569			0.0347067
$775$	−10.9075	+	0.958244i	−0.391810	+	0.0344211i
$776$	3.84095			0.137882
$777$	18.1381	−	5.89344i	0.650702	−	0.211426i
$778$	2.71287	+	3.73394i	0.0972611	+	0.133868i
$779$	3.40387	−	2.47306i	0.121956	−	0.0886065i
$780$	−6.01320	−	1.66644i	−0.215307	−	0.0596682i
$781$	−5.40872	−	3.92967i	−0.193539	−	0.140615i
$782$			26.9930i			0.965266i
$783$	23.5779	−	32.4522i	0.842605	−	1.15975i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	5.83299	+	15.5925i	0.208188	+	0.556519i
$786$	5.96149	+	18.3476i	0.212639	+	0.654436i
$787$	−13.8636	−	4.50457i	−0.494186	−	0.160571i	0.0513126	−	0.998683i	$-0.483660\pi$
$787$	−13.8636	−	4.50457i	−0.494186	−	0.160571i	−0.545498	+	0.838112i	$0.683660\pi$
$788$	−13.6462	−	4.43393i	−0.486127	−	0.157952i
$789$	8.00242	+	24.6289i	0.284894	+	0.876813i
$790$	−6.84916	+	24.7146i	−0.243682	+	0.879305i
$791$	4.73340	−	14.5679i	0.168300	−	0.517975i
$792$	−0.200621	+	0.276131i	−0.00712875	+	0.00981189i
$793$			8.92136i			0.316807i
$794$	13.8512	+	10.0635i	0.491561	+	0.357140i
$795$	−1.74927	−	39.9001i	−0.0620403	−	1.41511i
$796$	12.5395	−	9.11046i	0.444450	−	0.322912i
$797$	28.5974	+	39.3609i	1.01297	+	1.39424i	0.917016	+	0.398850i	$0.130590\pi$
$797$	28.5974	+	39.3609i	1.01297	+	1.39424i	0.0959549	+	0.995386i	$0.469410\pi$
$798$	−8.37667	+	2.72175i	−0.296531	+	0.0963488i
$799$	−1.02611			−0.0363012
$800$	−3.28165	−	3.77237i	−0.116024	−	0.133373i
$801$	−2.16345			−0.0764417
$802$	−16.2926	+	5.29379i	−0.575312	+	0.186930i
$803$	−7.79601	−	10.7303i	−0.275115	−	0.378663i
$804$	6.86084	−	4.98469i	0.241963	−	0.175797i
$805$	9.95313	+	12.5082i	0.350802	+	0.440855i
$806$	−2.98053	−	2.16548i	−0.104985	−	0.0762758i
$807$			29.8812i			1.05187i
$808$	2.38052	−	3.27651i	0.0837465	−	0.115267i
$809$	0.854742	−	2.63063i	0.0300511	−	0.0924879i	−0.934906	−	0.354895i	$-0.884516\pi$
$809$	0.854742	−	2.63063i	0.0300511	−	0.0924879i	0.964957	+	0.262408i	$0.0845165\pi$
$810$	18.3015	−	0.802360i	0.643048	−	0.0281921i
$811$	3.20382	+	9.86033i	0.112501	+	0.346243i	0.991418	−	0.130733i	$-0.0417330\pi$
$811$	3.20382	+	9.86033i	0.112501	+	0.346243i	−0.878916	+	0.476976i	$0.841733\pi$
$812$	−7.07981	−	2.30037i	−0.248453	−	0.0807271i
$813$	−5.52441	−	1.79499i	−0.193750	−	0.0629531i
$814$	−4.87873	−	15.0152i	−0.170999	−	0.526282i
$815$	24.0428	−	1.05407i	0.842183	−	0.0369224i
$816$	1.93547	−	5.95675i	0.0677549	−	0.208528i
$817$	12.1241	−	16.6873i	0.424167	−	0.583816i
$818$		−	23.7296i		−	0.829687i
$819$	0.338304	+	0.245792i	0.0118213	+	0.00858867i
$820$	1.10322	+	1.38643i	0.0385262	+	0.0484161i
$821$	−6.14075	+	4.46152i	−0.214314	+	0.155708i	−0.689763	−	0.724035i	$-0.742285\pi$
$821$	−6.14075	+	4.46152i	−0.214314	+	0.155708i	0.475450	+	0.879743i	$0.342285\pi$
$822$	18.3478	+	25.2536i	0.639954	+	0.880821i
$823$	−18.4099	+	5.98174i	−0.641729	+	0.208511i	−0.611764	−	0.791040i	$-0.709540\pi$
$823$	−18.4099	+	5.98174i	−0.641729	+	0.208511i	−0.0299655	+	0.999551i	$0.509540\pi$
$824$	−7.82432			−0.272573
$825$	0.996660	+	11.3448i	0.0346993	+	0.394976i
$826$	−9.25841			−0.322141
$827$	−34.1200	+	11.0863i	−1.18647	+	0.385507i	−0.834766	−	0.550605i	$-0.814397\pi$
$827$	−34.1200	+	11.0863i	−1.18647	+	0.385507i	−0.351702	+	0.936112i	$0.614397\pi$
$828$	−1.04444	−	1.43755i	−0.0362970	−	0.0499585i
$829$	−35.0740	+	25.4828i	−1.21817	+	0.885054i	−0.995947	−	0.0899417i	$-0.971332\pi$
$829$	−35.0740	+	25.4828i	−1.21817	+	0.885054i	−0.222225	+	0.974995i	$0.571332\pi$
$830$	1.11428	+	25.4161i	0.0386771	+	0.882206i
$831$	25.7916	+	18.7387i	0.894701	+	0.650038i
$832$		−	1.68232i		−	0.0583240i
$833$	2.21943	−	3.05479i	0.0768988	−	0.105842i
$834$	6.07046	−	18.6829i	0.210203	−	0.646937i
$835$	−0.491047	+	1.77190i	−0.0169934	+	0.0613190i
$836$	2.25313	+	6.93441i	0.0779260	+	0.239832i
$837$	11.2229	+	3.64653i	0.387919	+	0.126043i
$838$	34.8914	+	11.3369i	1.20530	+	0.391627i
$839$	−3.76548	−	11.5890i	−0.129999	−	0.400096i	0.864780	−	0.502151i	$-0.167458\pi$
$839$	−3.76548	−	11.5890i	−0.129999	−	0.400096i	−0.994779	+	0.102056i	$0.967458\pi$
$840$	−1.29957	−	3.47395i	−0.0448394	−	0.119863i
$841$	8.16279	−	25.1225i	0.281476	−	0.866293i
$842$	−19.9011	+	27.3915i	−0.685836	+	0.943972i
$843$			20.0678i			0.691170i
$844$	−17.8481	−	12.9674i	−0.614356	−	0.446356i
$845$	−21.9144	−	6.07315i	−0.753878	−	0.208923i
$846$	0.0546473	−	0.0397036i	0.00187881	−	0.00136504i
$847$	5.35735	+	7.37375i	0.184081	+	0.253365i
$848$	10.2408	−	3.32743i	0.351670	−	0.114264i
$849$	−25.8572			−0.887416
$850$	7.38312	+	17.3761i	0.253239	+	0.595997i
$851$	82.1927			2.81753
$852$	−7.68078	+	2.49564i	−0.263139	+	0.0854991i
$853$	1.50553	+	2.07219i	0.0515484	+	0.0709503i	0.834013	−	0.551745i	$-0.186038\pi$
$853$	1.50553	+	2.07219i	0.0515484	+	0.0709503i	−0.782465	+	0.622695i	$0.786038\pi$
$854$	−4.29022	+	3.11703i	−0.146808	+	0.106662i
$855$	−1.62848	+	2.46132i	−0.0556928	+	0.0841755i
$856$	−9.25147	−	6.72159i	−0.316209	−	0.229739i
$857$		−	3.77767i		−	0.129043i	−0.997916	−	0.0645214i	$-0.979448\pi$
$857$		−	3.77767i		−	0.129043i	0.997916	−	0.0645214i	$-0.0205521\pi$
$858$	−2.25229	+	3.10002i	−0.0768921	+	0.105833i
$859$	7.05605	−	21.7163i	0.240749	−	0.740950i	−0.755557	−	0.655083i	$-0.772634\pi$
$859$	7.05605	−	21.7163i	0.240749	−	0.740950i	0.996307	−	0.0858676i	$-0.0273662\pi$
$860$	7.24414	+	4.79292i	0.247023	+	0.163437i
$861$	0.406155	+	1.25002i	0.0138417	+	0.0426005i
$862$	33.8840	+	11.0096i	1.15409	+	0.374988i
$863$	−14.0175	−	4.55458i	−0.477163	−	0.155040i	0.0605544	−	0.998165i	$-0.480713\pi$
$863$	−14.0175	−	4.55458i	−0.477163	−	0.155040i	−0.537717	+	0.843125i	$0.680713\pi$
$864$	1.66515	+	5.12481i	0.0566496	+	0.174349i
$865$	−32.5966	+	25.9381i	−1.10832	+	0.881921i
$866$	8.90453	−	27.4053i	0.302588	−	0.931271i
$867$	2.67378	−	3.68014i	0.0908063	−	0.124984i
$868$		−	2.18991i		−	0.0743304i
$869$	12.7412	+	9.25704i	0.432216	+	0.314024i
$870$	25.8606	−	9.67418i	0.876755	−	0.327985i
$871$	−6.95836	+	5.05554i	−0.235775	+	0.171301i
$872$	−4.78183	−	6.58162i	−0.161933	−	0.222882i
$873$	0.907998	−	0.295026i	0.0307311	−	0.00998513i
$874$	−37.9588			−1.28398
$875$	9.82835	+	5.32949i	0.332259	+	0.180170i
$876$	−16.0219			−0.541331
$877$	15.8165	−	5.13910i	0.534086	−	0.173535i	−0.0295422	−	0.999564i	$-0.509405\pi$
$877$	15.8165	−	5.13910i	0.534086	−	0.173535i	0.563629	+	0.826028i	$0.309405\pi$
$878$	−3.30285	−	4.54598i	−0.111466	−	0.153419i
$879$	13.5688	−	9.85831i	0.457664	−	0.332512i
$880$	−2.87582	+	1.07581i	−0.0969437	+	0.0362657i
$881$	9.59721	+	6.97278i	0.323338	+	0.234919i	0.737599	−	0.675239i	$-0.235960\pi$
$881$	9.59721	+	6.97278i	0.323338	+	0.234919i	−0.414260	+	0.910158i	$0.635960\pi$
$882$			0.248565i			0.00836962i
$883$	−0.576346	+	0.793272i	−0.0193956	+	0.0266957i	−0.818605	−	0.574357i	$-0.805252\pi$
$883$	−0.576346	+	0.793272i	−0.0193956	+	0.0266957i	0.799209	+	0.601053i	$0.205252\pi$
$884$	−1.96298	+	6.04142i	−0.0660220	+	0.203195i
$885$	26.8710	−	21.3820i	0.903257	−	0.718749i
$886$	6.69131	+	20.5937i	0.224799	+	0.691860i
$887$	15.6058	+	5.07062i	0.523991	+	0.170255i	0.559056	−	0.829130i	$-0.311164\pi$
$887$	15.6058	+	5.07062i	0.523991	+	0.170255i	−0.0350651	+	0.999385i	$0.511164\pi$
$888$	−18.1381	−	5.89344i	−0.608676	−	0.197771i
$889$	−0.434608	−	1.33759i	−0.0145763	−	0.0448612i
$890$	−16.2312	−	10.7390i	−0.544071	−	0.359972i
$891$	3.47630	−	10.6990i	0.116461	−	0.358429i
$892$	17.0185	−	23.4240i	0.569823	−	0.784294i
$893$		−	1.44297i		−	0.0482871i
$894$	−5.11005	−	3.71267i	−0.170906	−	0.124170i
$895$	6.12772	−	9.26159i	0.204827	−	0.309581i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−11.7256	−	16.1389i	−0.391506	−	0.538861i
$898$	23.3440	−	7.58494i	0.779001	−	0.253113i
$899$	16.3020			0.543703
$900$	−1.06554	−	0.639718i	−0.0355180	−	0.0213239i
$901$	−40.6584			−1.35453
$902$	1.03479	−	0.336225i	0.0344549	−	0.0111951i
$903$	3.78741	+	5.21292i	0.126037	+	0.173475i
$904$	−12.3922	+	9.00345i	−0.412158	+	0.299450i
$905$	−48.3906	−	13.4105i	−1.60856	−	0.445781i
$906$	−19.8760	−	14.4407i	−0.660335	−	0.479762i
$907$			38.3055i			1.27191i	0.771725	+	0.635957i	$0.219394\pi$
$907$			38.3055i			1.27191i	−0.771725	+	0.635957i	$0.780606\pi$
$908$	−13.7797	+	18.9661i	−0.457296	+	0.629414i
$909$	0.311083	−	0.957414i	0.0103180	−	0.0317554i
$910$	1.31804	+	3.52332i	0.0436926	+	0.116797i
$911$	−2.52932	−	7.78443i	−0.0838000	−	0.257910i	0.900373	−	0.435118i	$-0.143293\pi$
$911$	−2.52932	−	7.78443i	−0.0838000	−	0.257910i	−0.984173	+	0.177208i	$0.943293\pi$
$912$	8.37667	+	2.72175i	0.277379	+	0.0901260i
$913$	14.8582	+	4.82771i	0.491733	+	0.159774i
$914$	−11.8029	−	36.3256i	−0.390405	−	1.20154i
$915$	5.25295	−	18.9548i	0.173657	−	0.626626i
$916$	−1.74516	+	5.37105i	−0.0576617	+	0.177464i
$917$	6.83615	−	9.40915i	0.225749	−	0.310717i
$918$		−	20.3467i		−	0.671542i
$919$	6.43656	+	4.67643i	0.212322	+	0.154261i	0.688864	−	0.724891i	$-0.258110\pi$
$919$	6.43656	+	4.67643i	0.212322	+	0.154261i	−0.476541	+	0.879152i	$0.658110\pi$
$920$	−0.700130	−	15.9696i	−0.0230826	−	0.526503i
$921$	26.8286	−	19.4921i	0.884031	−	0.642286i
$922$	−15.4927	−	21.3239i	−0.510226	−	0.702265i
$923$	7.78995	−	2.53111i	0.256409	−	0.0833125i
$924$	−2.27770			−0.0749310
$925$	52.9098	−	22.4814i	1.73966	−	0.739183i
$926$	−8.07574			−0.265385
$927$	−1.84966	+	0.600992i	−0.0607509	+	0.0197392i
$928$	4.37556	+	6.02244i	0.143635	+	0.197696i
$929$	−31.7183	+	23.0447i	−1.04064	+	0.756071i	−0.970411	−	0.241460i	$-0.922374\pi$
$929$	−31.7183	+	23.0447i	−1.04064	+	0.756071i	−0.0702318	+	0.997531i	$0.522374\pi$
$930$	5.05753	+	6.35584i	0.165843	+	0.208416i
$931$	4.29579	+	3.12108i	0.140789	+	0.102289i
$932$		−	3.32502i		−	0.108915i
$933$	−1.69999	+	2.33983i	−0.0556551	+	0.0766026i
$934$	11.8008	−	36.3190i	0.386133	−	1.18839i
$935$	11.5827	−	0.507800i	0.378794	−	0.0166068i
$936$	−0.129220	−	0.397700i	−0.00422370	−	0.0129992i
$937$	−8.28849	−	2.69309i	−0.270773	−	0.0879796i	0.170483	−	0.985361i	$-0.445467\pi$
$937$	−8.28849	−	2.69309i	−0.270773	−	0.0879796i	−0.441257	+	0.897381i	$0.645467\pi$
$938$	−4.86235	−	1.57987i	−0.158761	−	0.0515847i
$939$	−5.40729	−	16.6419i	−0.176460	−	0.543089i
$940$	0.607071	−	0.0266148i	0.0198005	−	0.000868079i
$941$	7.02888	−	21.6327i	0.229135	−	0.705204i	−0.768711	−	0.639597i	$-0.779101\pi$
$941$	7.02888	−	21.6327i	0.229135	−	0.705204i	0.997845	−	0.0656077i	$-0.0208986\pi$
$942$	7.25888	−	9.99100i	0.236507	−	0.325524i
$943$			5.66444i			0.184459i
$944$	7.49021	+	5.44196i	0.243786	+	0.177121i
$945$	−7.50247	−	9.42841i	−0.244055	−	0.306706i
$946$	4.31538	−	3.13531i	0.140305	−	0.101938i
$947$	3.72557	+	5.12781i	0.121065	+	0.166631i	0.865248	−	0.501344i	$-0.167161\pi$
$947$	3.72557	+	5.12781i	0.121065	+	0.166631i	−0.744183	+	0.667976i	$0.767161\pi$
$948$	18.0935	−	5.87892i	0.587648	−	0.190939i
$949$	16.2497			0.527487
$950$	−24.4352	+	10.3825i	−0.792782	+	0.336853i
$951$	18.0892			0.586583
$952$	−3.59112	+	1.16683i	−0.116389	+	0.0378170i
$953$	24.3017	+	33.4484i	0.787209	+	1.08350i	0.994450	+	0.105210i	$0.0335516\pi$
$953$	24.3017	+	33.4484i	0.787209	+	1.08350i	−0.207241	+	0.978290i	$0.566448\pi$
$954$	2.16533	−	1.57320i	0.0701051	−	0.0509344i
$955$	−0.0816578	−	1.86258i	−0.00264238	−	0.0602715i
$956$	5.68324	+	4.12912i	0.183809	+	0.133545i
$957$		−	16.9556i		−	0.548096i
$958$	−14.8532	+	20.4437i	−0.479887	+	0.660507i
$959$	5.81525	−	17.8975i	0.187784	−	0.577941i
$960$	−0.990561	+	3.57435i	−0.0319702	+	0.115362i
$961$	−8.09757	−	24.9218i	−0.261212	−	0.803928i
$962$	18.3959	+	5.97720i	0.593109	+	0.192713i
$963$	−2.70333	−	0.878366i	−0.0871137	−	0.0283049i
$964$	−3.29261	−	10.1336i	−0.106048	−	0.326382i
$965$	18.6948	+	49.9742i	0.601808	+	1.60873i
$966$	3.66428	−	11.2775i	0.117896	−	0.362848i
$967$	−5.42963	+	7.47325i	−0.174605	+	0.240324i	−0.887346	−	0.461104i	$-0.847454\pi$
$967$	−5.42963	+	7.47325i	−0.174605	+	0.240324i	0.712741	+	0.701427i	$0.247454\pi$
$968$		−	9.11446i		−	0.292950i
$969$	−26.9058	−	19.5482i	−0.864340	−	0.627980i
$970$	8.27667	+	2.29372i	0.265748	+	0.0736469i
$971$	27.7480	−	20.1601i	0.890477	−	0.646970i	−0.0455252	−	0.998963i	$-0.514496\pi$
$971$	27.7480	−	20.1601i	0.890477	−	0.646970i	0.936002	+	0.351994i	$0.114496\pi$
$972$	1.51432	+	2.08429i	0.0485719	+	0.0668535i
$973$	−11.2633	+	3.65967i	−0.361085	+	0.117324i
$974$	−37.7611			−1.20995
$975$	−11.9624	−	7.18187i	−0.383103	−	0.230004i
$976$	5.30300			0.169745
$977$	43.0379	−	13.9839i	1.37691	−	0.447384i	0.475255	−	0.879848i	$-0.342356\pi$
$977$	43.0379	−	13.9839i	1.37691	−	0.447384i	0.901651	+	0.432464i	$0.142356\pi$
$978$	−10.4934	−	14.4429i	−0.335541	−	0.461833i
$979$	−9.66902	+	7.02495i	−0.309023	+	0.224518i
$980$	−1.23383	+	1.86485i	−0.0394133	+	0.0595704i
$981$	−1.63596	−	1.18859i	−0.0522322	−	0.0379489i
$982$		−	37.3848i		−	1.19300i
$983$	−24.7296	+	34.0374i	−0.788752	+	1.08562i	0.205510	+	0.978655i	$0.434115\pi$
$983$	−24.7296	+	34.0374i	−0.788752	+	1.08562i	−0.994262	+	0.106969i	$0.965885\pi$
$984$	0.406155	−	1.25002i	0.0129478	−	0.0398491i
$985$	−26.7578	−	17.7037i	−0.852573	−	0.564085i
$986$	−8.68602	−	26.7328i	−0.276619	−	0.851347i
$987$	0.428704	+	0.139294i	0.0136458	+	0.00443379i
$988$	−8.49574	−	2.76043i	−0.270285	−	0.0878211i
$989$	8.58130	+	26.4105i	0.272869	+	0.839805i
$990$	−0.597207	+	0.475215i	−0.0189805	+	0.0151033i
$991$	−9.29253	+	28.5995i	−0.295187	+	0.908492i	0.687972	+	0.725738i	$0.258501\pi$
$991$	−9.29253	+	28.5995i	−0.295187	+	0.908492i	−0.983159	+	0.182754i	$0.941499\pi$
$992$	−1.28720	+	1.77167i	−0.0408685	+	0.0562507i
$993$		−	21.7506i		−	0.690235i
$994$	3.93892	+	2.86179i	0.124935	+	0.0907706i
$995$	32.4612	−	12.1434i	1.02909	−	0.384972i
$996$	15.2679	−	11.0927i	0.483781	−	0.351487i
$997$	28.8274	+	39.6775i	0.912973	+	1.25660i	0.966141	+	0.258014i	$0.0830680\pi$
$997$	28.8274	+	39.6775i	0.912973	+	1.25660i	−0.0531683	+	0.998586i	$0.516932\pi$
$998$	16.4777	−	5.35392i	0.521591	−	0.169475i
$999$	−61.9552			−1.96018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.169.4	yes	24
25.2	odd	20		8750.2.a.bb.1.10		12
25.4	even	10	inner	350.2.m.a.29.4	✓	24
25.23	odd	20		8750.2.a.z.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.29.4	✓	24	25.4	even	10	inner
350.2.m.a.169.4	yes	24	1.1	even	1	trivial
8750.2.a.z.1.3		12	25.23	odd	20
8750.2.a.bb.1.10		12	25.2	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.974986 - 1.34195i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.09432 - 0.783465i) q^{5} +(-1.34195 - 0.974986i) q^{6} +1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.0768108 - 0.236399i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.974986 - 1.34195i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.09432 - 0.783465i) q^{5} +(-1.34195 - 0.974986i) q^{6} +1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.0768108 - 0.236399i) q^{9} +(1.74971 - 1.39230i) q^{10} +(-0.424326 - 1.30594i) q^{11} +(-1.57756 - 0.512580i) q^{12} +(1.59998 + 0.519866i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-3.09331 - 2.04661i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.21943 + 3.05479i) q^{17} -0.248565i q^{18} +(-4.29579 - 3.12108i) q^{19} +(1.23383 - 1.86485i) q^{20} +(1.34195 - 0.974986i) q^{21} +(-0.807117 - 1.11090i) q^{22} +(6.79881 - 2.20907i) q^{23} -1.65875 q^{24} +(3.77237 - 3.28165i) q^{25} +1.68232 q^{26} +(-5.12481 + 1.66515i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-6.02244 + 4.37556i) q^{29} +(-3.57435 - 0.990561i) q^{30} +(-1.77167 - 1.28720i) q^{31} -1.00000i q^{32} +(-1.33880 + 1.84270i) q^{33} +(-1.16683 + 3.59112i) q^{34} +(0.783465 + 2.09432i) q^{35} +(-0.0768108 - 0.236399i) q^{36} +(10.9349 + 3.55295i) q^{37} +(-5.05001 - 1.64085i) q^{38} +(-0.862325 - 2.65396i) q^{39} +(0.597175 - 2.15485i) q^{40} +(-0.244857 + 0.753592i) q^{41} +(0.974986 - 1.34195i) q^{42} +3.88458i q^{43} +(-1.11090 - 0.807117i) q^{44} +(-0.0243440 - 0.555275i) q^{45} +(5.78342 - 4.20190i) q^{46} +(0.159731 + 0.219851i) q^{47} +(-1.57756 + 0.512580i) q^{48} -1.00000 q^{49} +(2.57365 - 4.28676i) q^{50} +6.26330 q^{51} +(1.59998 - 0.519866i) q^{52} +(6.32915 + 8.71132i) q^{53} +(-4.35942 + 3.16730i) q^{54} +(-1.91184 - 2.40262i) q^{55} +(0.809017 + 0.587785i) q^{56} +8.80776i q^{57} +(-4.37556 + 6.02244i) q^{58} +(-2.86101 + 8.80527i) q^{59} +(-3.70551 + 0.162454i) q^{60} +(1.63872 + 5.04346i) q^{61} +(-2.08273 - 0.676720i) q^{62} +(0.236399 + 0.0768108i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.75818 - 0.164763i) q^{65} +(-0.703849 + 2.16623i) q^{66} +(-3.00510 + 4.13616i) q^{67} +3.77593i q^{68} +(-9.59321 - 6.96988i) q^{69} +(1.39230 + 1.74971i) q^{70} +(3.93892 - 2.86179i) q^{71} +(-0.146103 - 0.201093i) q^{72} +(9.18633 - 2.98482i) q^{73} +11.4976 q^{74} +(-8.08183 - 1.86277i) q^{75} -5.30989 q^{76} +(1.30594 - 0.424326i) q^{77} +(-1.64024 - 2.25760i) q^{78} +(-9.27884 + 6.74147i) q^{79} +(-0.0979381 - 2.23392i) q^{80} +(6.62789 + 4.81544i) q^{81} +0.792373i q^{82} +(-6.68744 + 9.20446i) q^{83} +(0.512580 - 1.57756i) q^{84} +(-2.25489 + 8.13656i) q^{85} +(1.20040 + 3.69445i) q^{86} +(11.7436 + 3.81572i) q^{87} +(-1.30594 - 0.424326i) q^{88} +(-2.68961 - 8.27777i) q^{89} +(-0.194742 - 0.520575i) q^{90} +(-0.519866 + 1.59998i) q^{91} +(4.20190 - 5.78342i) q^{92} +3.63250i q^{93} +(0.219851 + 0.159731i) q^{94} +(-11.4420 - 3.17094i) q^{95} +(-1.34195 + 0.974986i) q^{96} +(2.25765 + 3.10739i) q^{97} +(-0.951057 + 0.309017i) q^{98} -0.341317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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