LMFDB - Embedded newform 310.2.k.a.149.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(129,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("310.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.k (of order $6$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.9
Character	$\chi$	$=$	310.149
Dual form			310.2.k.a.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(1.78669 + 1.34453i) q^{5} +(-1.34467 - 2.32904i) q^{6} +(-2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 - 3.66553i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(1.78669 + 1.34453i) q^{5} +(-1.34467 - 2.32904i) q^{6} +(-2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 - 3.66553i) q^{9} +(-1.34453 + 1.78669i) q^{10} +(-1.25570 + 2.17494i) q^{11} +(2.32904 - 1.34467i) q^{12} +(-0.925785 - 0.534502i) q^{13} +(-1.66997 - 2.89246i) q^{14} +(-5.96922 - 0.728949i) q^{15} +1.00000 q^{16} +(0.979392 - 0.565452i) q^{17} +(3.66553 + 2.11630i) q^{18} +(-3.42647 - 5.93482i) q^{19} +(-1.78669 - 1.34453i) q^{20} +(4.49112 - 7.77885i) q^{21} +(-2.17494 - 1.25570i) q^{22} -4.55942i q^{23} +(1.34467 + 2.32904i) q^{24} +(1.38450 + 4.80449i) q^{25} +(0.534502 - 0.925785i) q^{26} +3.31488i q^{27} +(2.89246 - 1.66997i) q^{28} +2.14564 q^{29} +(0.728949 - 5.96922i) q^{30} +(0.527107 + 5.54276i) q^{31} +1.00000i q^{32} -6.75404i q^{33} +(0.565452 + 0.979392i) q^{34} +(-7.41324 - 0.905290i) q^{35} +(-2.11630 + 3.66553i) q^{36} +(-9.97382 + 5.75839i) q^{37} +(5.93482 - 3.42647i) q^{38} +2.87493 q^{39} +(1.34453 - 1.78669i) q^{40} +(-3.61032 + 6.25326i) q^{41} +(7.77885 + 4.49112i) q^{42} +(-0.400075 + 0.230984i) q^{43} +(1.25570 - 2.17494i) q^{44} +(8.70957 - 3.70374i) q^{45} +4.55942 q^{46} +6.54587i q^{47} +(-2.32904 + 1.34467i) q^{48} +(2.07757 - 3.59845i) q^{49} +(-4.80449 + 1.38450i) q^{50} +(-1.52070 + 2.63393i) q^{51} +(0.925785 + 0.534502i) q^{52} +(-8.42860 - 4.86625i) q^{53} -3.31488 q^{54} +(-5.16781 + 2.19761i) q^{55} +(1.66997 + 2.89246i) q^{56} +(15.9608 + 9.21497i) q^{57} +2.14564i q^{58} +(4.93480 + 8.54733i) q^{59} +(5.96922 + 0.728949i) q^{60} -1.86761 q^{61} +(-5.54276 + 0.527107i) q^{62} +14.1366i q^{63} -1.00000 q^{64} +(-0.935436 - 2.19973i) q^{65} +6.75404 q^{66} +(13.8308 + 7.98521i) q^{67} +(-0.979392 + 0.565452i) q^{68} +(6.13094 + 10.6191i) q^{69} +(0.905290 - 7.41324i) q^{70} +(1.50751 - 2.61109i) q^{71} +(-3.66553 - 2.11630i) q^{72} +(3.62147 + 2.09086i) q^{73} +(-5.75839 - 9.97382i) q^{74} +(-9.68504 - 9.32818i) q^{75} +(3.42647 + 5.93482i) q^{76} -8.38791i q^{77} +2.87493i q^{78} +(2.71853 + 4.70863i) q^{79} +(1.78669 + 1.34453i) q^{80} +(1.89146 + 3.27611i) q^{81} +(-6.25326 - 3.61032i) q^{82} +(-11.7770 - 6.79944i) q^{83} +(-4.49112 + 7.77885i) q^{84} +(2.51013 + 0.306532i) q^{85} +(-0.230984 - 0.400075i) q^{86} +(-4.99729 + 2.88519i) q^{87} +(2.17494 + 1.25570i) q^{88} -13.9990 q^{89} +(3.70374 + 8.70957i) q^{90} +3.57040 q^{91} +4.55942i q^{92} +(-8.68086 - 12.2005i) q^{93} -6.54587 q^{94} +(1.85749 - 15.2106i) q^{95} +(-1.34467 - 2.32904i) q^{96} -10.0509i q^{97} +(3.59845 + 2.07757i) q^{98} +(5.31487 + 9.20563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9	$ 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} + 8 q^{15} + 32 q^{16} - 8 q^{19} + 2 q^{20} + 16 q^{21} - 4 q^{24} + 22 q^{25} + 12 q^{26} - 8 q^{29} + 28 q^{30} + 12 q^{31} - 12 q^{34} - 32 q^{35} - 8 q^{36} - 64 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{44} - 24 q^{45} - 8 q^{46} + 20 q^{49} - 40 q^{51} + 8 q^{54} - 8 q^{55} + 16 q^{59} - 8 q^{60} - 40 q^{61} - 32 q^{64} - 6 q^{65} - 24 q^{66} + 36 q^{69} + 36 q^{70} + 48 q^{71} - 28 q^{74} + 8 q^{75} + 8 q^{76} + 4 q^{79} - 2 q^{80} - 32 q^{81} - 16 q^{84} - 84 q^{85} + 12 q^{86} + 72 q^{89} + 40 q^{90} + 24 q^{91} + 16 q^{94} - 48 q^{95} + 4 q^{96} + 64 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 + 8 * q^15 + 32 * q^16 - 8 * q^19 + 2 * q^20 + 16 * q^21 - 4 * q^24 + 22 * q^25 + 12 * q^26 - 8 * q^29 + 28 * q^30 + 12 * q^31 - 12 * q^34 - 32 * q^35 - 8 * q^36 - 64 * q^39 + 4 * q^40 - 16 * q^41 - 4 * q^44 - 24 * q^45 - 8 * q^46 + 20 * q^49 - 40 * q^51 + 8 * q^54 - 8 * q^55 + 16 * q^59 - 8 * q^60 - 40 * q^61 - 32 * q^64 - 6 * q^65 - 24 * q^66 + 36 * q^69 + 36 * q^70 + 48 * q^71 - 28 * q^74 + 8 * q^75 + 8 * q^76 + 4 * q^79 - 2 * q^80 - 32 * q^81 - 16 * q^84 - 84 * q^85 + 12 * q^86 + 72 * q^89 + 40 * q^90 + 24 * q^91 + 16 * q^94 - 48 * q^95 + 4 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−2.32904	+	1.34467i	−1.34467	+	0.776348i	−0.987489	−	0.157686i	$-0.949597\pi$
$3$	−2.32904	+	1.34467i	−1.34467	+	0.776348i	−0.357185	+	0.934034i	$0.616263\pi$
$4$	−1.00000			−0.500000
$5$	1.78669	+	1.34453i	0.799031	+	0.601290i
$5$	1.78669	+	1.34453i	0.799031	+	0.601290i
$6$	−1.34467	−	2.32904i	−0.548961	−	0.950828i
$7$	−2.89246	+	1.66997i	−1.09325	+	0.631188i	−0.934440	−	0.356122i	$-0.884099\pi$
$7$	−2.89246	+	1.66997i	−1.09325	+	0.631188i	−0.158809	+	0.987309i	$0.550766\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.11630	−	3.66553i	0.705432	−	1.22184i
$10$	−1.34453	+	1.78669i	−0.425177	+	0.565000i
$11$	−1.25570	+	2.17494i	−0.378608	+	0.655769i	−0.990860	−	0.134894i	$-0.956931\pi$
$11$	−1.25570	+	2.17494i	−0.378608	+	0.655769i	0.612252	+	0.790663i	$0.290264\pi$
$12$	2.32904	−	1.34467i	0.672337	−	0.388174i
$13$	−0.925785	−	0.534502i	−0.256767	−	0.148244i	0.366092	−	0.930579i	$-0.380696\pi$
$13$	−0.925785	−	0.534502i	−0.256767	−	0.148244i	−0.622859	+	0.782334i	$0.714029\pi$
$14$	−1.66997	−	2.89246i	−0.446317	−	0.773044i
$15$	−5.96922	−	0.728949i	−1.54125	−	0.188214i
$16$	1.00000			0.250000
$17$	0.979392	−	0.565452i	0.237537	−	0.137142i	−0.376507	−	0.926414i	$-0.622875\pi$
$17$	0.979392	−	0.565452i	0.237537	−	0.137142i	0.614044	+	0.789271i	$0.289542\pi$
$18$	3.66553	+	2.11630i	0.863975	+	0.498816i
$19$	−3.42647	−	5.93482i	−0.786086	−	1.36154i	−0.928348	−	0.371712i	$-0.878771\pi$
$19$	−3.42647	−	5.93482i	−0.786086	−	1.36154i	0.142262	−	0.989829i	$-0.454562\pi$
$20$	−1.78669	−	1.34453i	−0.399515	−	0.300645i
$21$	4.49112	−	7.77885i	0.980042	−	1.69748i
$22$	−2.17494	−	1.25570i	−0.463698	−	0.267716i
$23$		−	4.55942i		−	0.950705i	−0.879795	−	0.475353i	$-0.842321\pi$
$23$		−	4.55942i		−	0.950705i	0.879795	−	0.475353i	$-0.157679\pi$
$24$	1.34467	+	2.32904i	0.274480	+	0.475414i
$25$	1.38450	+	4.80449i	0.276900	+	0.960899i
$26$	0.534502	−	0.925785i	0.104825	−	0.181561i
$27$			3.31488i			0.637948i
$28$	2.89246	−	1.66997i	0.546624	−	0.315594i
$29$	2.14564			0.398436			0.199218	−	0.979955i	$-0.436160\pi$
$29$	2.14564			0.398436			0.199218	+	0.979955i	$0.436160\pi$
$30$	0.728949	−	5.96922i	0.133087	−	1.08983i
$31$	0.527107	+	5.54276i	0.0946712	+	0.995509i
$31$	0.527107	+	5.54276i	0.0946712	+	0.995509i
$32$			1.00000i			0.176777i
$33$		−	6.75404i		−	1.17573i
$34$	0.565452	+	0.979392i	0.0969743	+	0.167964i
$35$	−7.41324	−	0.905290i	−1.25307	−	0.153022i
$36$	−2.11630	+	3.66553i	−0.352716	+	0.610922i
$37$	−9.97382	+	5.75839i	−1.63969	+	0.946673i	−0.658745	+	0.752367i	$0.728912\pi$
$37$	−9.97382	+	5.75839i	−1.63969	+	0.946673i	−0.980941	+	0.194306i	$0.937754\pi$
$38$	5.93482	−	3.42647i	0.962755	−	0.555847i
$39$	2.87493			0.460357
$40$	1.34453	−	1.78669i	0.212588	−	0.282500i
$41$	−3.61032	+	6.25326i	−0.563838	+	0.976595i	0.433319	+	0.901241i	$0.357342\pi$
$41$	−3.61032	+	6.25326i	−0.563838	+	0.976595i	−0.997157	+	0.0753549i	$0.975991\pi$
$42$	7.77885	+	4.49112i	1.20030	+	0.692995i
$43$	−0.400075	+	0.230984i	−0.0610109	+	0.0352247i	−0.530195	−	0.847876i	$-0.677881\pi$
$43$	−0.400075	+	0.230984i	−0.0610109	+	0.0352247i	0.469184	+	0.883100i	$0.344548\pi$
$44$	1.25570	−	2.17494i	0.189304	−	0.327884i
$45$	8.70957	−	3.70374i	1.29835	−	0.552122i
$46$	4.55942			0.672250
$47$			6.54587i			0.954813i	0.878683	+	0.477406i	$0.158423\pi$
$47$			6.54587i			0.954813i	−0.878683	+	0.477406i	$0.841577\pi$
$48$	−2.32904	+	1.34467i	−0.336169	+	0.194087i
$49$	2.07757	−	3.59845i	0.296796	−	0.514065i
$50$	−4.80449	+	1.38450i	−0.679458	+	0.195798i
$51$	−1.52070	+	2.63393i	−0.212940	+	0.368823i
$52$	0.925785	+	0.534502i	0.128383	+	0.0741222i
$53$	−8.42860	−	4.86625i	−1.15776	−	0.668431i	−0.206992	−	0.978343i	$-0.566367\pi$
$53$	−8.42860	−	4.86625i	−1.15776	−	0.668431i	−0.950765	+	0.309911i	$0.899701\pi$
$54$	−3.31488			−0.451098
$55$	−5.16781	+	2.19761i	−0.696827	+	0.296326i
$56$	1.66997	+	2.89246i	0.223159	+	0.386522i
$57$	15.9608	+	9.21497i	2.11406	+	1.22055i
$58$			2.14564i			0.281737i
$59$	4.93480	+	8.54733i	0.642457	+	1.11277i	0.984883	+	0.173223i	$0.0554180\pi$
$59$	4.93480	+	8.54733i	0.642457	+	1.11277i	−0.342426	+	0.939545i	$0.611249\pi$
$60$	5.96922	+	0.728949i	0.770623	+	0.0941070i
$61$	−1.86761			−0.239123			−0.119562	−	0.992827i	$-0.538149\pi$
$61$	−1.86761			−0.239123			−0.119562	+	0.992827i	$0.538149\pi$
$62$	−5.54276	+	0.527107i	−0.703931	+	0.0669426i
$63$			14.1366i			1.78104i
$64$	−1.00000			−0.125000
$65$	−0.935436	−	2.19973i	−0.116027	−	0.272843i
$66$	6.75404			0.831364
$67$	13.8308	+	7.98521i	1.68970	+	0.975549i	0.954742	+	0.297436i	$0.0961314\pi$
$67$	13.8308	+	7.98521i	1.68970	+	0.975549i	0.734958	+	0.678113i	$0.237202\pi$
$68$	−0.979392	+	0.565452i	−0.118769	+	0.0685712i
$69$	6.13094	+	10.6191i	0.738078	+	1.27839i
$70$	0.905290	−	7.41324i	0.108203	−	0.886052i
$71$	1.50751	−	2.61109i	0.178909	−	0.309879i	−0.762598	−	0.646872i	$-0.776077\pi$
$71$	1.50751	−	2.61109i	0.178909	−	0.309879i	0.941507	+	0.336993i	$0.109410\pi$
$72$	−3.66553	−	2.11630i	−0.431987	−	0.249408i
$73$	3.62147	+	2.09086i	0.423861	+	0.244716i	0.696728	−	0.717336i	$-0.254639\pi$
$73$	3.62147	+	2.09086i	0.423861	+	0.244716i	−0.272867	+	0.962052i	$0.587972\pi$
$74$	−5.75839	−	9.97382i	−0.669399	−	1.15943i
$75$	−9.68504	−	9.32818i	−1.11833	−	1.07713i
$76$	3.42647	+	5.93482i	0.393043	+	0.680770i
$77$		−	8.38791i		−	0.955891i
$78$			2.87493i			0.325521i
$79$	2.71853	+	4.70863i	0.305859	+	0.529763i	0.977452	−	0.211157i	$-0.0677232\pi$
$79$	2.71853	+	4.70863i	0.305859	+	0.529763i	−0.671594	+	0.740920i	$0.734390\pi$
$80$	1.78669	+	1.34453i	0.199758	+	0.150323i
$81$	1.89146	+	3.27611i	0.210163	+	0.364012i
$82$	−6.25326	−	3.61032i	−0.690557	−	0.398693i
$83$	−11.7770	−	6.79944i	−1.29269	−	0.746336i	−0.313561	−	0.949568i	$-0.601522\pi$
$83$	−11.7770	−	6.79944i	−1.29269	−	0.746336i	−0.979130	+	0.203233i	$0.934855\pi$
$84$	−4.49112	+	7.77885i	−0.490021	+	0.848742i
$85$	2.51013	+	0.306532i	0.272262	+	0.0332481i
$86$	−0.230984	−	0.400075i	−0.0249076	−	0.0431412i
$87$	−4.99729	+	2.88519i	−0.535766	+	0.309325i
$88$	2.17494	+	1.25570i	0.231849	+	0.133858i
$89$	−13.9990			−1.48389			−0.741947	−	0.670459i	$-0.766097\pi$
$89$	−13.9990			−1.48389			−0.741947	+	0.670459i	$0.766097\pi$
$90$	3.70374	+	8.70957i	0.390409	+	0.918069i
$91$	3.57040			0.374280
$92$			4.55942i			0.475353i
$93$	−8.68086	−	12.2005i	−0.900163	−	1.26514i
$94$	−6.54587			−0.675155
$95$	1.85749	−	15.2106i	0.190575	−	1.56058i
$96$	−1.34467	−	2.32904i	−0.137240	−	0.237707i
$97$		−	10.0509i		−	1.02052i	−0.860021	−	0.510259i	$-0.829550\pi$
$97$		−	10.0509i		−	1.02052i	0.860021	−	0.510259i	$-0.170450\pi$
$98$	3.59845	+	2.07757i	0.363499	+	0.209866i
$99$	5.31487	+	9.20563i	0.534165	+	0.925201i
$100$	−1.38450	−	4.80449i	−0.138450	−	0.480449i
$101$	−14.8784			−1.48045			−0.740227	−	0.672357i	$-0.765282\pi$
$101$	−14.8784			−1.48045			−0.740227	+	0.672357i	$0.765282\pi$
$102$	−2.63393	−	1.52070i	−0.260798	−	0.150572i
$103$	3.70015	+	2.13628i	0.364587	+	0.210494i	0.671091	−	0.741375i	$-0.265826\pi$
$103$	3.70015	+	2.13628i	0.364587	+	0.210494i	−0.306504	+	0.951869i	$0.599159\pi$
$104$	−0.534502	+	0.925785i	−0.0524123	+	0.0907807i
$105$	18.4831	−	7.85993i	1.80376	−	0.767051i
$106$	4.86625	−	8.42860i	0.472652	−	0.818658i
$107$	−8.51540	+	4.91637i	−0.823215	+	0.475283i	−0.851524	−	0.524316i	$-0.824321\pi$
$107$	−8.51540	+	4.91637i	−0.823215	+	0.475283i	0.0283088	+	0.999599i	$0.490988\pi$
$108$		−	3.31488i		−	0.318974i
$109$	12.2368			1.17207			0.586037	−	0.810284i	$-0.300687\pi$
$109$	12.2368			1.17207			0.586037	+	0.810284i	$0.300687\pi$
$110$	−2.19761	−	5.16781i	−0.209534	−	0.492731i
$111$	15.4863	−	26.8231i	1.46990	−	2.54593i
$112$	−2.89246	+	1.66997i	−0.273312	+	0.157797i
$113$	11.9249	+	6.88486i	1.12180	+	0.647673i	0.941860	−	0.336004i	$-0.109076\pi$
$113$	11.9249	+	6.88486i	1.12180	+	0.647673i	0.179942	+	0.983677i	$0.442409\pi$
$114$	−9.21497	+	15.9608i	−0.863061	+	1.49487i
$115$	6.13026	−	8.14626i	0.571650	−	0.759642i
$116$	−2.14564			−0.199218
$117$	−3.91847	+	2.26233i	−0.362263	+	0.209153i
$118$	−8.54733	+	4.93480i	−0.786845	+	0.454285i
$119$	−1.88857	+	3.27110i	−0.173125	+	0.299861i
$120$	−0.728949	+	5.96922i	−0.0665437	+	0.544913i
$121$	2.34643	+	4.06414i	0.213312	+	0.369467i
$122$		−	1.86761i		−	0.169086i
$123$		−	19.4188i		−	1.75094i
$124$	−0.527107	−	5.54276i	−0.0473356	−	0.497754i
$125$	−3.98610	+	10.4456i	−0.356528	+	0.934285i
$126$	−14.1366			−1.25939
$127$	1.09323	−	0.631179i	0.0970088	−	0.0560081i	−0.450711	−	0.892670i	$-0.648829\pi$
$127$	1.09323	−	0.631179i	0.0970088	−	0.0560081i	0.547720	+	0.836662i	$0.315496\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.621195	−	1.07594i	0.0546932	−	0.0947314i
$130$	2.19973	−	0.935436i	0.192929	−	0.0820431i
$131$	−2.00041	−	3.46482i	−0.174777	−	0.302723i	0.765307	−	0.643665i	$-0.222587\pi$
$131$	−2.00041	−	3.46482i	−0.174777	−	0.302723i	−0.940084	+	0.340943i	$0.889254\pi$
$132$			6.75404i			0.587863i
$133$	19.8219	+	11.4442i	1.71878	+	0.992335i
$134$	−7.98521	+	13.8308i	−0.689817	+	1.19480i
$135$	−4.45694	+	5.92265i	−0.383592	+	0.509740i
$136$	−0.565452	−	0.979392i	−0.0484871	−	0.0839822i
$137$	9.42943	+	5.44408i	0.805611	+	0.465119i	0.845429	−	0.534087i	$-0.179345\pi$
$137$	9.42943	+	5.44408i	0.805611	+	0.465119i	−0.0398187	+	0.999207i	$0.512678\pi$
$138$	−10.6191	+	6.13094i	−0.903957	+	0.521900i
$139$	−10.7590			−0.912569			−0.456285	−	0.889834i	$-0.650820\pi$
$139$	−10.7590			−0.912569			−0.456285	+	0.889834i	$0.650820\pi$
$140$	7.41324	+	0.905290i	0.626533	+	0.0765110i
$141$	−8.80206	−	15.2456i	−0.741267	−	1.28391i
$142$	2.61109	+	1.50751i	0.219118	+	0.126508i
$143$	2.32502	−	1.34235i	0.194428	−	0.112253i
$144$	2.11630	−	3.66553i	0.176358	−	0.305461i
$145$	3.83359	+	2.88487i	0.318362	+	0.239576i
$146$	−2.09086	+	3.62147i	−0.173040	+	0.299715i
$147$			11.1746i			0.921666i
$148$	9.97382	−	5.75839i	0.819843	−	0.473336i
$149$	−5.86843	−	10.1644i	−0.480761	−	0.832702i	0.518996	−	0.854777i	$-0.326306\pi$
$149$	−5.86843	−	10.1644i	−0.480761	−	0.832702i	−0.999756	+	0.0220752i	$0.992973\pi$
$150$	9.32818	−	9.68504i	0.761643	−	0.790780i
$151$	5.08955			0.414182			0.207091	−	0.978322i	$-0.433600\pi$
$151$	5.08955			0.414182			0.207091	+	0.978322i	$0.433600\pi$
$152$	−5.93482	+	3.42647i	−0.481377	+	0.277923i
$153$		−	4.78666i		−	0.386979i
$154$	8.38791			0.675917
$155$	−6.51061	+	10.6119i	−0.522945	+	0.852367i
$156$	−2.87493			−0.230178
$157$		−	5.04463i		−	0.402605i	−0.979529	−	0.201303i	$-0.935483\pi$
$157$		−	5.04463i		−	0.402605i	0.979529	−	0.201303i	$-0.0645175\pi$
$158$	−4.70863	+	2.71853i	−0.374599	+	0.216275i
$159$	26.1741			2.07574
$160$	−1.34453	+	1.78669i	−0.106294	+	0.141250i
$161$	7.61408	+	13.1880i	0.600073	+	1.03936i
$162$	−3.27611	+	1.89146i	−0.257395	+	0.148607i
$163$			12.4987i			0.978972i	0.872011	+	0.489486i	$0.162816\pi$
$163$			12.4987i			0.978972i	−0.872011	+	0.489486i	$0.837184\pi$
$164$	3.61032	−	6.25326i	0.281919	−	0.488298i
$165$	9.08098	−	12.0673i	0.706953	−	0.939442i
$166$	6.79944	−	11.7770i	0.527739	−	0.914071i
$167$	15.4460	−	8.91775i	1.19525	−	0.690076i	0.235755	−	0.971812i	$-0.424244\pi$
$167$	15.4460	−	8.91775i	1.19525	−	0.690076i	0.959492	+	0.281736i	$0.0909103\pi$
$168$	−7.77885	−	4.49112i	−0.600151	−	0.346497i
$169$	−5.92861	−	10.2687i	−0.456047	−	0.789897i
$170$	−0.306532	+	2.51013i	−0.0235100	+	0.192518i
$171$	−29.0057			−2.21812
$172$	0.400075	−	0.230984i	0.0305055	−	0.0176123i
$173$	7.01810	+	4.05190i	0.533576	+	0.308060i	0.742472	−	0.669878i	$-0.233653\pi$
$173$	7.01810	+	4.05190i	0.533576	+	0.308060i	−0.208895	+	0.977938i	$0.566987\pi$
$174$	−2.88519	−	4.99729i	−0.218726	−	0.378844i
$175$	−12.0280	−	11.5848i	−0.909228	−	0.875726i
$176$	−1.25570	+	2.17494i	−0.0946520	+	0.163942i
$177$	−22.9867	−	13.2714i	−1.72779	−	0.997540i
$178$		−	13.9990i		−	1.04927i
$179$	−9.47460	−	16.4105i	−0.708165	−	1.22658i	−0.965537	−	0.260265i	$-0.916190\pi$
$179$	−9.47460	−	16.4105i	−0.708165	−	1.22658i	0.257373	−	0.966312i	$-0.417143\pi$
$180$	−8.70957	+	3.70374i	−0.649173	+	0.276061i
$181$	−6.25755	+	10.8384i	−0.465120	+	0.805612i	−0.999207	−	0.0398180i	$-0.987322\pi$
$181$	−6.25755	+	10.8384i	−0.465120	+	0.805612i	0.534087	+	0.845430i	$0.320656\pi$
$182$			3.57040i			0.264656i
$183$	4.34975	−	2.51133i	0.321543	−	0.185643i
$184$	−4.55942			−0.336125
$185$	−25.5624	−	3.12163i	−1.87938	−	0.229507i
$186$	12.2005	−	8.68086i	0.894587	−	0.636511i
$187$			2.84016i			0.207693i
$188$		−	6.54587i		−	0.477406i
$189$	−5.53573	−	9.58817i	−0.402665	−	0.697436i
$190$	15.2106	+	1.85749i	1.10350	+	0.134757i
$191$	−0.719583	+	1.24636i	−0.0520672	+	0.0901831i	−0.890884	−	0.454230i	$-0.849914\pi$
$191$	−0.719583	+	1.24636i	−0.0520672	+	0.0901831i	0.838817	+	0.544413i	$0.183248\pi$
$192$	2.32904	−	1.34467i	0.168084	−	0.0970435i
$193$	15.8380	−	9.14408i	1.14005	−	0.658205i	0.193603	−	0.981080i	$-0.437982\pi$
$193$	15.8380	−	9.14408i	1.14005	−	0.658205i	0.946442	+	0.322874i	$0.104649\pi$
$194$	10.0509			0.721615
$195$	5.13659	+	3.86541i	0.367839	+	0.276808i
$196$	−2.07757	+	3.59845i	−0.148398	+	0.257032i
$197$	2.76140	+	1.59430i	0.196742	+	0.113589i	0.595135	−	0.803626i	$-0.297099\pi$
$197$	2.76140	+	1.59430i	0.196742	+	0.113589i	−0.398393	+	0.917215i	$0.630432\pi$
$198$	−9.20563	+	5.31487i	−0.654216	+	0.377712i
$199$	−7.53070	+	13.0436i	−0.533837	+	0.924633i	0.465381	+	0.885110i	$0.345917\pi$
$199$	−7.53070	+	13.0436i	−0.533837	+	0.924633i	−0.999219	+	0.0395230i	$0.987416\pi$
$200$	4.80449	−	1.38450i	0.339729	−	0.0978988i
$201$	−42.9500			−3.02946
$202$		−	14.8784i		−	1.04684i
$203$	−6.20619	+	3.58315i	−0.435589	+	0.251488i
$204$	1.52070	−	2.63393i	0.106470	−	0.184412i
$205$	−14.8582	+	6.31845i	−1.03774	+	0.441299i
$206$	−2.13628	+	3.70015i	−0.148842	+	0.257802i
$207$	−16.7127	−	9.64909i	−1.16161	−	0.670658i
$208$	−0.925785	−	0.534502i	−0.0641917	−	0.0370611i
$209$	17.2105			1.19047
$210$	7.85993	+	18.4831i	0.542387	+	1.27545i
$211$	9.05661	+	15.6865i	0.623483	+	1.07990i	0.988832	+	0.149033i	$0.0476161\pi$
$211$	9.05661	+	15.6865i	0.623483	+	1.07990i	−0.365350	+	0.930870i	$0.619051\pi$
$212$	8.42860	+	4.86625i	0.578879	+	0.334216i
$213$			8.10845i			0.555582i
$214$	−4.91637	−	8.51540i	−0.336076	−	0.582101i
$215$	−1.02537	−	0.125216i	−0.0699298	−	0.00853969i
$216$	3.31488			0.225549
$217$	−10.7809	−	15.1520i	−0.731852	−	1.02858i
$218$			12.2368i			0.828782i
$219$	−11.2461			−0.759940
$220$	5.16781	−	2.19761i	0.348413	−	0.148163i
$221$	−1.20894			−0.0813223
$222$	26.8231	+	15.4863i	1.80025	+	1.03937i
$223$	−5.50332	+	3.17734i	−0.368529	+	0.212770i	−0.672816	−	0.739810i	$-0.734915\pi$
$223$	−5.50332	+	3.17734i	−0.368529	+	0.212770i	0.304286	+	0.952581i	$0.401582\pi$
$224$	−1.66997	−	2.89246i	−0.111579	−	0.193261i
$225$	20.5411	+	5.09281i	1.36940	+	0.339521i
$226$	−6.88486	+	11.9249i	−0.457974	+	0.793234i
$227$	20.3941	+	11.7745i	1.35360	+	0.781503i	0.988752	−	0.149562i	$-0.0477865\pi$
$227$	20.3941	+	11.7745i	1.35360	+	0.781503i	0.364851	+	0.931066i	$0.381120\pi$
$228$	−15.9608	−	9.21497i	−1.05703	−	0.610276i
$229$	11.2948	+	19.5632i	0.746384	+	1.29278i	0.949545	+	0.313630i	$0.101545\pi$
$229$	11.2948	+	19.5632i	0.746384	+	1.29278i	−0.203161	+	0.979145i	$0.565122\pi$
$230$	8.14626	+	6.13026i	0.537148	+	0.404218i
$231$	11.2790	+	19.5358i	0.742104	+	1.28536i
$232$		−	2.14564i		−	0.140868i
$233$		−	11.4137i		−	0.747735i	−0.927482	−	0.373867i	$-0.878032\pi$
$233$		−	11.4137i		−	0.747735i	0.927482	−	0.373867i	$-0.121968\pi$
$234$	−2.26233	−	3.91847i	−0.147893	−	0.256159i
$235$	−8.80109	+	11.6954i	−0.574120	+	0.762925i
$236$	−4.93480	−	8.54733i	−0.321228	−	0.556384i
$237$	−12.6632	−	7.31108i	−0.822560	−	0.474905i
$238$	−3.27110	−	1.88857i	−0.212034	−	0.122418i
$239$	7.99093	−	13.8407i	0.516890	−	0.895280i	−0.482918	−	0.875666i	$-0.660423\pi$
$239$	7.99093	−	13.8407i	0.516890	−	0.895280i	0.999808	−	0.0196140i	$-0.00624373\pi$
$240$	−5.96922	−	0.728949i	−0.385312	−	0.0470535i
$241$	−3.42853	−	5.93840i	−0.220851	−	0.382526i	0.734215	−	0.678917i	$-0.237550\pi$
$241$	−3.42853	−	5.93840i	−0.220851	−	0.382526i	−0.955067	+	0.296391i	$0.904217\pi$
$242$	−4.06414	+	2.34643i	−0.261253	+	0.150834i
$243$	−17.4229	−	10.0591i	−1.11768	−	0.645293i
$244$	1.86761			0.119562
$245$	8.55018	−	3.63596i	0.546251	−	0.232293i
$246$	19.4188			1.23810
$247$			7.32582i			0.466131i
$248$	5.54276	−	0.527107i	0.351965	−	0.0334713i
$249$	36.5721			2.31766
$250$	−10.4456	−	3.98610i	−0.660639	−	0.252103i
$251$	−0.519274	−	0.899409i	−0.0327763	−	0.0567702i	0.849172	−	0.528116i	$-0.177102\pi$
$251$	−0.519274	−	0.899409i	−0.0327763	−	0.0567702i	−0.881948	+	0.471346i	$0.843768\pi$
$252$		−	14.1366i		−	0.890520i
$253$	9.91646	+	5.72527i	0.623443	+	0.359945i
$254$	0.631179	+	1.09323i	0.0396037	+	0.0685956i
$255$	−6.25839	+	2.66138i	−0.391916	+	0.166662i
$256$	1.00000			0.0625000
$257$	−9.99457	−	5.77037i	−0.623444	−	0.359946i	0.154765	−	0.987951i	$-0.450538\pi$
$257$	−9.99457	−	5.77037i	−0.623444	−	0.359946i	−0.778209	+	0.628006i	$0.783871\pi$
$258$	1.07594	+	0.621195i	0.0669852	+	0.0386739i
$259$	19.2326	−	33.3119i	1.19506	−	2.06990i
$260$	0.935436	+	2.19973i	0.0580133	+	0.136422i
$261$	4.54082	−	7.86492i	0.281069	−	0.486827i
$262$	3.46482	−	2.00041i	0.214057	−	0.123586i
$263$			27.8728i			1.71871i	0.511377	+	0.859356i	$0.329136\pi$
$263$			27.8728i			1.71871i	−0.511377	+	0.859356i	$0.670864\pi$
$264$	−6.75404			−0.415682
$265$	−8.51646	−	20.0269i	−0.523162	−	1.23025i
$266$	−11.4442	+	19.8219i	−0.701687	+	1.21536i
$267$	32.6043	−	18.8241i	1.99535	−	1.15202i
$268$	−13.8308	−	7.98521i	−0.844850	−	0.487774i
$269$	−3.72020	+	6.44358i	−0.226825	+	0.392872i	−0.956865	−	0.290532i	$-0.906168\pi$
$269$	−3.72020	+	6.44358i	−0.226825	+	0.392872i	0.730040	+	0.683404i	$0.239501\pi$
$270$	−5.92265	−	4.45694i	−0.360441	−	0.271241i
$271$	12.3624			0.750962			0.375481	−	0.926830i	$-0.377478\pi$
$271$	12.3624			0.750962			0.375481	+	0.926830i	$0.377478\pi$
$272$	0.979392	−	0.565452i	0.0593844	−	0.0342856i
$273$	−8.31562	+	4.80103i	−0.503284	+	0.290571i
$274$	−5.44408	+	9.42943i	−0.328889	+	0.569653i
$275$	−12.1880	−	3.02181i	−0.734964	−	0.182222i
$276$	−6.13094	−	10.6191i	−0.369039	−	0.639194i
$277$			11.1581i			0.670423i	0.942143	+	0.335211i	$0.108808\pi$
$277$			11.1581i			0.670423i	−0.942143	+	0.335211i	$0.891192\pi$
$278$		−	10.7590i		−	0.645284i
$279$	21.4327	+	9.79800i	1.28314	+	0.586591i
$280$	−0.905290	+	7.41324i	−0.0541014	+	0.443026i
$281$	3.11884			0.186055			0.0930273	−	0.995664i	$-0.470346\pi$
$281$	3.11884			0.186055			0.0930273	+	0.995664i	$0.470346\pi$
$282$	15.2456	−	8.80206i	0.907863	−	0.524155i
$283$			22.2481i			1.32251i	0.750161	+	0.661255i	$0.229976\pi$
$283$			22.2481i			1.32251i	−0.750161	+	0.661255i	$0.770024\pi$
$284$	−1.50751	+	2.61109i	−0.0894544	+	0.154940i
$285$	16.1272	+	37.9240i	0.955291	+	2.24642i
$286$	1.34235	+	2.32502i	0.0793749	+	0.137481i
$287$		−	24.1165i		−	1.42355i
$288$	3.66553	+	2.11630i	0.215994	+	0.124704i
$289$	−7.86053	+	13.6148i	−0.462384	+	0.800873i
$290$	−2.88487	+	3.83359i	−0.169405	+	0.225116i
$291$	13.5152	+	23.4091i	0.792277	+	1.37226i
$292$	−3.62147	−	2.09086i	−0.211930	−	0.122358i
$293$	−26.5745	+	15.3428i	−1.55250	+	0.896335i	−0.554559	+	0.832144i	$0.687113\pi$
$293$	−26.5745	+	15.3428i	−1.55250	+	0.896335i	−0.997938	+	0.0641905i	$0.979553\pi$
$294$	−11.1746			−0.651717
$295$	−2.67516	+	21.9064i	−0.155754	+	1.27544i
$296$	5.75839	+	9.97382i	0.334699	+	0.579716i
$297$	−7.20965	−	4.16249i	−0.418346	−	0.241532i
$298$	10.1644	−	5.86843i	0.588809	−	0.339949i
$299$	−2.43702	+	4.22105i	−0.140937	+	0.244109i
$300$	9.68504	+	9.32818i	0.559166	+	0.538563i
$301$	0.771469	−	1.33622i	0.0444667	−	0.0770187i
$302$			5.08955i			0.292871i
$303$	34.6524	−	20.0066i	1.99073	−	1.14935i
$304$	−3.42647	−	5.93482i	−0.196521	−	0.340385i
$305$	−3.33683	−	2.51105i	−0.191067	−	0.143782i
$306$	4.78666			0.273635
$307$	−11.7719	+	6.79649i	−0.671855	+	0.387896i	−0.796779	−	0.604270i	$-0.793465\pi$
$307$	−11.7719	+	6.79649i	−0.671855	+	0.387896i	0.124924	+	0.992166i	$0.460131\pi$
$308$			8.38791i			0.477945i
$309$	−11.4904			−0.653667
$310$	−10.6119	−	6.51061i	−0.602714	−	0.369778i
$311$	8.28787			0.469962			0.234981	−	0.972000i	$-0.424497\pi$
$311$	8.28787			0.469962			0.234981	+	0.972000i	$0.424497\pi$
$312$		−	2.87493i		−	0.162761i
$313$	8.61486	−	4.97379i	0.486940	−	0.281135i	−0.236364	−	0.971665i	$-0.575956\pi$
$313$	8.61486	−	4.97379i	0.486940	−	0.281135i	0.723304	+	0.690529i	$0.242622\pi$
$314$	5.04463			0.284685
$315$	−19.0070	+	25.2576i	−1.07092	+	1.42311i
$316$	−2.71853	−	4.70863i	−0.152929	−	0.264881i
$317$	−1.94235	+	1.12141i	−0.109093	+	0.0629849i	−0.553554	−	0.832813i	$-0.686729\pi$
$317$	−1.94235	+	1.12141i	−0.109093	+	0.0629849i	0.444461	+	0.895798i	$0.353395\pi$
$318$			26.1741i			1.46777i
$319$	−2.69428	+	4.66664i	−0.150851	+	0.261282i
$320$	−1.78669	−	1.34453i	−0.0998788	−	0.0751613i
$321$	13.2218	−	22.9009i	0.737971	−	1.27820i
$322$	−13.1880	+	7.61408i	−0.734937	+	0.424316i
$323$	−6.71171	−	3.87501i	−0.373450	−	0.215611i
$324$	−1.89146	−	3.27611i	−0.105081	−	0.182006i
$325$	1.28627	−	5.18795i	0.0713492	−	0.287776i
$326$	−12.4987			−0.692238
$327$	−28.5001	+	16.4545i	−1.57606	+	0.909938i
$328$	6.25326	+	3.61032i	0.345279	+	0.199347i
$329$	−10.9314	−	18.9337i	−0.602666	−	1.04385i
$330$	12.0673	+	9.08098i	0.664285	+	0.499891i
$331$	11.7477	−	20.3476i	0.645712	−	1.11841i	−0.338424	−	0.940994i	$-0.609894\pi$
$331$	11.7477	−	20.3476i	0.645712	−	1.11841i	0.984137	−	0.177413i	$-0.0567727\pi$
$332$	11.7770	+	6.79944i	0.646346	+	0.373168i
$333$			48.7458i			2.67126i
$334$	8.91775	+	15.4460i	0.487958	+	0.845167i
$335$	13.9750	+	32.8629i	0.763534	+	1.79549i
$336$	4.49112	−	7.77885i	0.245011	−	0.424371i
$337$		−	5.10345i		−	0.278003i	−0.990292	−	0.139001i	$-0.955611\pi$
$337$		−	5.10345i		−	0.278003i	0.990292	−	0.139001i	$-0.0443893\pi$
$338$	10.2687	−	5.92861i	0.558542	−	0.322474i
$339$	−37.0316			−2.01128
$340$	−2.51013	−	0.306532i	−0.136131	−	0.0166240i
$341$	−12.7170	−	5.81362i	−0.688666	−	0.314825i
$342$		−	29.0057i		−	1.56845i
$343$		−	9.50164i		−	0.513041i
$344$	0.230984	+	0.400075i	0.0124538	+	0.0215706i
$345$	−3.32359	+	27.2162i	−0.178936	+	1.46527i
$346$	−4.05190	+	7.01810i	−0.217832	+	0.377296i
$347$	26.2194	−	15.1378i	1.40753	−	0.812639i	0.412382	−	0.911011i	$-0.364697\pi$
$347$	26.2194	−	15.1378i	1.40753	−	0.812639i	0.995150	+	0.0983723i	$0.0313636\pi$
$348$	4.99729	−	2.88519i	0.267883	−	0.154662i
$349$	11.9756			0.641038			0.320519	−	0.947242i	$-0.396143\pi$
$349$	11.9756			0.641038			0.320519	+	0.947242i	$0.396143\pi$
$350$	11.5848	−	12.0280i	0.619232	−	0.642921i
$351$	1.77181	−	3.06886i	0.0945722	−	0.163804i
$352$	−2.17494	−	1.25570i	−0.115925	−	0.0669291i
$353$	14.7949	−	8.54181i	0.787450	−	0.454635i	−0.0516138	−	0.998667i	$-0.516436\pi$
$353$	14.7949	−	8.54181i	0.787450	−	0.454635i	0.839064	+	0.544032i	$0.183103\pi$
$354$	13.2714	−	22.9867i	0.705367	−	1.22173i
$355$	6.20413	−	2.63831i	0.329281	−	0.140027i
$356$	13.9990			0.741947
$357$		−	10.1581i		−	0.537621i
$358$	16.4105	−	9.47460i	0.867321	−	0.500748i
$359$	14.7258	−	25.5058i	0.777198	−	1.34615i	−0.156352	−	0.987701i	$-0.549974\pi$
$359$	14.7258	−	25.5058i	0.777198	−	1.34615i	0.933551	−	0.358446i	$-0.116693\pi$
$360$	−3.70374	−	8.70957i	−0.195204	−	0.459035i
$361$	−13.9814	+	24.2165i	−0.735862	+	1.27455i
$362$	−10.8384	−	6.25755i	−0.569653	−	0.328890i
$363$	−10.9299	−	6.31037i	−0.573670	−	0.331208i
$364$	−3.57040			−0.187140
$365$	3.65922	+	8.60486i	0.191532	+	0.450399i
$366$	2.51133	+	4.34975i	0.131269	+	0.227365i
$367$	−27.0994	−	15.6459i	−1.41458	−	0.816707i	−0.418763	−	0.908096i	$-0.637536\pi$
$367$	−27.0994	−	15.6459i	−1.41458	−	0.816707i	−0.995815	+	0.0913882i	$0.970870\pi$
$368$		−	4.55942i		−	0.237676i
$369$	15.2810	+	26.4675i	0.795499	+	1.37784i
$370$	3.12163	−	25.5624i	0.162286	−	1.32893i
$371$	32.5059			1.68762
$372$	8.68086	+	12.2005i	0.450082	+	0.632568i
$373$		−	19.9316i		−	1.03202i	−0.856583	−	0.516009i	$-0.827417\pi$
$373$		−	19.9316i		−	1.03202i	0.856583	−	0.516009i	$-0.172583\pi$
$374$	−2.84016			−0.146861
$375$	−4.76214	−	29.6883i	−0.245916	−	1.53310i
$376$	6.54587			0.337577
$377$	−1.98640	−	1.14685i	−0.102305	−	0.0590658i
$378$	9.58817	−	5.53573i	0.493162	−	0.284727i
$379$	7.41755	+	12.8476i	0.381014	+	0.659936i	0.991207	−	0.132317i	$-0.0422416\pi$
$379$	7.41755	+	12.8476i	0.381014	+	0.659936i	−0.610193	+	0.792252i	$0.708908\pi$
$380$	−1.85749	+	15.2106i	−0.0952874	+	0.780289i
$381$	−1.69746	+	2.94009i	−0.0869635	+	0.150625i
$382$	−1.24636	−	0.719583i	−0.0637691	−	0.0368171i
$383$	−4.20151	−	2.42574i	−0.214687	−	0.123950i	0.388801	−	0.921322i	$-0.372889\pi$
$383$	−4.20151	−	2.42574i	−0.214687	−	0.123950i	−0.603488	+	0.797372i	$0.706223\pi$
$384$	1.34467	+	2.32904i	0.0686201	+	0.118854i
$385$	11.2778	−	14.9866i	0.574768	−	0.763786i
$386$	9.14408	+	15.8380i	0.465422	+	0.806134i
$387$			1.95532i			0.0993945i
$388$			10.0509i			0.510259i
$389$	1.13556	+	1.96685i	0.0575752	+	0.0997232i	0.893376	−	0.449309i	$-0.148330\pi$
$389$	1.13556	+	1.96685i	0.0575752	+	0.0997232i	−0.835801	+	0.549032i	$0.814996\pi$
$390$	−3.86541	+	5.13659i	−0.195733	+	0.260101i
$391$	−2.57814	−	4.46546i	−0.130382	−	0.225828i
$392$	−3.59845	−	2.07757i	−0.181749	−	0.104933i
$393$	9.31811	+	5.37981i	0.470036	+	0.271376i
$394$	−1.59430	+	2.76140i	−0.0803194	+	0.139117i
$395$	−1.47372	+	12.0680i	−0.0741508	+	0.607206i
$396$	−5.31487	−	9.20563i	−0.267082	−	0.462600i
$397$	8.18167	−	4.72369i	0.410626	−	0.237075i	−0.280432	−	0.959874i	$-0.590478\pi$
$397$	8.18167	−	4.72369i	0.410626	−	0.237075i	0.691059	+	0.722799i	$0.257145\pi$
$398$	−13.0436	−	7.53070i	−0.653814	−	0.377480i
$399$	−61.5547			−3.08159
$400$	1.38450	+	4.80449i	0.0692249	+	0.240225i
$401$	20.3650			1.01698			0.508490	−	0.861068i	$-0.330204\pi$
$401$	20.3650			1.01698			0.508490	+	0.861068i	$0.330204\pi$
$402$		−	42.9500i		−	2.14215i
$403$	2.47463	−	5.41314i	0.123270	−	0.269648i
$404$	14.8784			0.740227
$405$	−1.02536	+	8.39650i	−0.0509507	+	0.417226i
$406$	−3.58315	−	6.20619i	−0.177829	−	0.308008i
$407$		−	28.9232i		−	1.43367i
$408$	2.63393	+	1.52070i	0.130399	+	0.0752858i
$409$	6.41855	+	11.1173i	0.317377	+	0.549713i	0.979940	−	0.199293i	$-0.0638646\pi$
$409$	6.41855	+	11.1173i	0.317377	+	0.549713i	−0.662563	+	0.749006i	$0.730531\pi$
$410$	−6.31845	−	14.8582i	−0.312046	−	0.733794i
$411$	−29.2821			−1.44438
$412$	−3.70015	−	2.13628i	−0.182293	−	0.105247i
$413$	−28.5475	−	16.4819i	−1.40473	−	0.811021i
$414$	9.64909	−	16.7127i	0.474227	−	0.821385i
$415$	−11.8997	−	27.9829i	−0.584135	−	1.37363i
$416$	0.534502	−	0.925785i	0.0262061	−	0.0453904i
$417$	25.0583	−	14.4674i	1.22711	−	0.708471i
$418$			17.2105i			0.841792i
$419$	−16.9178			−0.826488			−0.413244	−	0.910620i	$-0.635604\pi$
$419$	−16.9178			−0.826488			−0.413244	+	0.910620i	$0.635604\pi$
$420$	−18.4831	+	7.85993i	−0.901882	+	0.383525i
$421$	4.96613	−	8.60160i	0.242035	−	0.419216i	−0.719259	−	0.694742i	$-0.755519\pi$
$421$	4.96613	−	8.60160i	0.242035	−	0.419216i	0.961294	+	0.275526i	$0.0888519\pi$
$422$	−15.6865	+	9.05661i	−0.763607	+	0.440869i
$423$	23.9941	+	13.8530i	1.16663	+	0.673556i
$424$	−4.86625	+	8.42860i	−0.236326	+	0.409329i
$425$	4.07268	+	3.92262i	0.197554	+	0.190275i
$426$	−8.10845			−0.392856
$427$	5.40200	−	3.11885i	0.261421	−	0.150931i
$428$	8.51540	−	4.91637i	0.411608	−	0.237642i
$429$	−3.61005	+	6.25279i	−0.174295	+	0.301887i
$430$	0.125216	−	1.02537i	0.00603847	−	0.0494479i
$431$	0.257626	+	0.446222i	0.0124094	+	0.0214938i	0.872163	−	0.489215i	$-0.162717\pi$
$431$	0.257626	+	0.446222i	0.0124094	+	0.0214938i	−0.859754	+	0.510708i	$0.829383\pi$
$432$			3.31488i			0.159487i
$433$			37.7395i			1.81365i	0.421511	+	0.906823i	$0.361500\pi$
$433$			37.7395i			1.81365i	−0.421511	+	0.906823i	$0.638500\pi$
$434$	15.1520	−	10.7809i	0.727318	−	0.517497i
$435$	−12.8078	−	1.56406i	−0.614088	−	0.0749911i
$436$	−12.2368			−0.586037
$437$	−27.0593	+	15.6227i	−1.29442	+	0.747336i
$438$		−	11.2461i		−	0.537358i
$439$	−7.16777	+	12.4149i	−0.342099	+	0.592533i	−0.984822	−	0.173566i	$-0.944471\pi$
$439$	−7.16777	+	12.4149i	−0.342099	+	0.592533i	0.642723	+	0.766098i	$0.277804\pi$
$440$	2.19761	+	5.16781i	0.104767	+	0.246365i
$441$	−8.79351	−	15.2308i	−0.418738	−	0.725276i
$442$		−	1.20894i		−	0.0575035i
$443$	−23.7485	−	13.7112i	−1.12833	−	0.651440i	−0.184813	−	0.982774i	$-0.559168\pi$
$443$	−23.7485	−	13.7112i	−1.12833	−	0.651440i	−0.943514	+	0.331334i	$0.892501\pi$
$444$	−15.4863	+	26.8231i	−0.734948	+	1.27297i
$445$	−25.0119	−	18.8221i	−1.18568	−	0.892251i
$446$	−3.17734	−	5.50332i	−0.150451	−	0.260590i
$447$	27.3357	+	15.7823i	1.29293	+	0.746475i
$448$	2.89246	−	1.66997i	0.136656	−	0.0788984i
$449$	39.8495			1.88062			0.940308	−	0.340326i	$-0.110537\pi$
$449$	39.8495			1.88062			0.940308	+	0.340326i	$0.110537\pi$
$450$	−5.09281	+	20.5411i	−0.240077	+	0.968314i
$451$	−9.06697	−	15.7045i	−0.426947	−	0.739494i
$452$	−11.9249	−	6.88486i	−0.560901	−	0.323836i
$453$	−11.8538	+	6.84379i	−0.556940	+	0.321549i
$454$	−11.7745	+	20.3941i	−0.552606	+	0.957142i
$455$	6.37919	+	4.80050i	0.299061	+	0.225051i
$456$	9.21497	−	15.9608i	0.431530	−	0.747433i
$457$		−	17.5445i		−	0.820696i	−0.911929	−	0.410348i	$-0.865407\pi$
$457$		−	17.5445i		−	0.820696i	0.911929	−	0.410348i	$-0.134593\pi$
$458$	−19.5632	+	11.2948i	−0.914130	+	0.527773i
$459$	1.87440	+	3.24656i	0.0874897	+	0.151537i
$460$	−6.13026	+	8.14626i	−0.285825	+	0.379821i
$461$	−9.00321			−0.419321			−0.209661	−	0.977774i	$-0.567236\pi$
$461$	−9.00321			−0.419321			−0.209661	+	0.977774i	$0.567236\pi$
$462$	−19.5358	+	11.2790i	−0.908888	+	0.524747i
$463$			23.2104i			1.07868i	0.842088	+	0.539340i	$0.181326\pi$
$463$			23.2104i			1.07868i	−0.842088	+	0.539340i	$0.818674\pi$
$464$	2.14564			0.0996089
$465$	0.893973	−	33.4702i	0.0414570	−	1.55214i
$466$	11.4137			0.528728
$467$		−	6.78086i		−	0.313781i	−0.987616	−	0.156890i	$-0.949853\pi$
$467$		−	6.78086i		−	0.313781i	0.987616	−	0.156890i	$-0.0501470\pi$
$468$	3.91847	−	2.26233i	0.181132	−	0.104576i
$469$	−53.3401			−2.46302
$470$	−11.6954	−	8.80109i	−0.539469	−	0.405964i
$471$	6.78338	+	11.7492i	0.312562	+	0.541373i
$472$	8.54733	−	4.93480i	0.393423	−	0.227143i
$473$		−	1.16019i		−	0.0533454i
$474$	7.31108	−	12.6632i	0.335809	−	0.581638i
$475$	23.7699	−	24.6792i	1.09064	−	1.13236i
$476$	1.88857	−	3.27110i	0.0865625	−	0.149931i
$477$	−35.6748	+	20.5969i	−1.63344	+	0.943066i
$478$	13.8407	+	7.99093i	0.633058	+	0.365496i
$479$	−6.75903	−	11.7070i	−0.308828	−	0.534906i	0.669278	−	0.743012i	$-0.266603\pi$
$479$	−6.75903	−	11.7070i	−0.308828	−	0.534906i	−0.978106	+	0.208106i	$0.933270\pi$
$480$	0.728949	−	5.96922i	0.0332718	−	0.272456i
$481$	12.3115			0.561355
$482$	5.93840	−	3.42853i	0.270487	−	0.156165i
$483$	−35.4670	−	20.4769i	−1.61381	−	0.931731i
$484$	−2.34643	−	4.06414i	−0.106656	−	0.184733i
$485$	13.5138	−	17.9579i	0.613628	−	0.815425i
$486$	10.0591	−	17.4229i	0.456291	−	0.790319i
$487$	13.1954	+	7.61835i	0.597939	+	0.345220i	0.768230	−	0.640173i	$-0.221137\pi$
$487$	13.1954	+	7.61835i	0.597939	+	0.345220i	−0.170291	+	0.985394i	$0.554471\pi$
$488$			1.86761i			0.0845428i
$489$	−16.8066	−	29.1100i	−0.760023	−	1.31640i
$490$	3.63596	+	8.55018i	0.164256	+	0.386258i
$491$	13.4117	−	23.2298i	0.605262	−	1.04834i	−0.386748	−	0.922186i	$-0.626402\pi$
$491$	13.4117	−	23.2298i	0.605262	−	1.04834i	0.992010	−	0.126159i	$-0.0402651\pi$
$492$			19.4188i			0.875468i
$493$	2.10142	−	1.21326i	0.0946434	−	0.0546424i
$494$	−7.32582			−0.329604
$495$	−2.88120	+	23.5936i	−0.129500	+	1.06045i
$496$	0.527107	+	5.54276i	0.0236678	+	0.248877i
$497$			10.0700i			0.451700i
$498$			36.5721i			1.63884i
$499$	−12.6708	−	21.9465i	−0.567224	−	0.982461i	−0.996839	−	0.0794487i	$-0.974684\pi$
$499$	−12.6708	−	21.9465i	−0.567224	−	0.982461i	0.429615	−	0.903012i	$-0.358649\pi$
$500$	3.98610	−	10.4456i	0.178264	−	0.467142i
$501$	−23.9829	+	41.5397i	−1.07148	+	1.85586i
$502$	0.899409	−	0.519274i	0.0401426	−	0.0231763i
$503$	−18.8555	+	10.8862i	−0.840723	+	0.485392i	−0.857510	−	0.514467i	$-0.827990\pi$
$503$	−18.8555	+	10.8862i	−0.840723	+	0.485392i	0.0167866	+	0.999859i	$0.494656\pi$
$504$	14.1366			0.629693
$505$	−26.5830	−	20.0044i	−1.18293	−	0.890183i
$506$	−5.72527	+	9.91646i	−0.254519	+	0.440840i
$507$	27.6160	+	15.9441i	1.22647	+	0.708103i
$508$	−1.09323	+	0.631179i	−0.0485044	+	0.0280040i
$509$	−6.84283	+	11.8521i	−0.303303	+	0.525337i	−0.976882	−	0.213779i	$-0.931423\pi$
$509$	−6.84283	+	11.8521i	−0.303303	+	0.525337i	0.673579	+	0.739115i	$0.264756\pi$
$510$	−2.66138	−	6.25839i	−0.117848	−	0.277126i
$511$	−13.9666			−0.617847
$512$			1.00000i			0.0441942i
$513$	19.6732	−	11.3583i	0.868593	−	0.501482i
$514$	5.77037	−	9.99457i	0.254520	−	0.440842i
$515$	3.73872	+	8.79182i	0.164748	+	0.387414i
$516$	−0.621195	+	1.07594i	−0.0273466	+	0.0473657i
$517$	−14.2369	−	8.21965i	−0.626136	−	0.361500i
$518$	33.3119	+	19.2326i	1.46364	+	0.845032i
$519$	−21.7940			−0.956649
$520$	−2.19973	+	0.935436i	−0.0964646	+	0.0410216i
$521$	9.85190	+	17.0640i	0.431620	+	0.747587i	0.997013	−	0.0772342i	$-0.0246089\pi$
$521$	9.85190	+	17.0640i	0.431620	+	0.747587i	−0.565393	+	0.824821i	$0.691276\pi$
$522$	7.86492	+	4.54082i	0.344238	+	0.198746i
$523$			2.63019i			0.115010i	0.998345	+	0.0575050i	$0.0183145\pi$
$523$			2.63019i			0.115010i	−0.998345	+	0.0575050i	$0.981685\pi$
$524$	2.00041	+	3.46482i	0.0873885	+	0.151361i
$525$	43.5914	+	10.8078i	1.90248	+	0.471689i
$526$	−27.8728			−1.21531
$527$	3.65041	+	5.13048i	0.159014	+	0.223487i
$528$		−	6.75404i		−	0.293932i
$529$	2.21167			0.0961597
$530$	20.0269	−	8.51646i	0.869915	−	0.369931i
$531$	41.7740			1.81284
$532$	−19.8219	−	11.4442i	−0.859388	−	0.496168i
$533$	6.68477	−	3.85945i	0.289549	−	0.167171i
$534$	18.8241	+	32.6043i	0.814600	+	1.41093i
$535$	−21.8245	−	2.66517i	−0.943557	−	0.115225i
$536$	7.98521	−	13.8308i	0.344909	−	0.597399i
$537$	44.1335	+	25.4805i	1.90450	+	1.09956i
$538$	−6.44358	−	3.72020i	−0.277803	−	0.160389i
$539$	5.21761	+	9.03717i	0.224738	+	0.389258i
$540$	4.45694	−	5.92265i	0.191796	−	0.254870i
$541$	−3.36443	−	5.82736i	−0.144648	−	0.250538i	0.784594	−	0.620010i	$-0.212872\pi$
$541$	−3.36443	−	5.82736i	−0.144648	−	0.250538i	−0.929242	+	0.369473i	$0.879538\pi$
$542$			12.3624i			0.531010i
$543$		−	33.6575i		−	1.44438i
$544$	0.565452	+	0.979392i	0.0242436	+	0.0419911i
$545$	21.8634	+	16.4527i	0.936524	+	0.704757i
$546$	−4.80103	−	8.31562i	−0.205465	−	0.355876i
$547$	7.58550	+	4.37949i	0.324333	+	0.187254i	0.653322	−	0.757080i	$-0.273375\pi$
$547$	7.58550	+	4.37949i	0.324333	+	0.187254i	−0.328989	+	0.944334i	$0.606708\pi$
$548$	−9.42943	−	5.44408i	−0.402805	−	0.232560i
$549$	−3.95242	+	6.84579i	−0.168685	+	0.292171i
$550$	3.02181	−	12.1880i	0.128850	−	0.519698i
$551$	−7.35198	−	12.7340i	−0.313205	−	0.542486i
$552$	10.6191	−	6.13094i	0.451979	−	0.260950i
$553$	−15.7265	−	9.07970i	−0.668759	−	0.386108i
$554$	−11.1581			−0.474060
$555$	63.7335	−	27.1027i	2.70534	−	1.15044i
$556$	10.7590			0.456285
$557$			26.2133i			1.11069i	0.831619	+	0.555347i	$0.187414\pi$
$557$			26.2133i			1.11069i	−0.831619	+	0.555347i	$0.812586\pi$
$558$	−9.79800	+	21.4327i	−0.414782	+	0.907318i
$559$	0.493845			0.0208874
$560$	−7.41324	−	0.905290i	−0.313267	−	0.0382555i
$561$	−3.81908	−	6.61485i	−0.161242	−	0.279279i
$562$			3.11884i			0.131560i
$563$	−28.2023	−	16.2826i	−1.18858	−	0.686230i	−0.230600	−	0.973049i	$-0.574069\pi$
$563$	−28.2023	−	16.2826i	−1.18858	−	0.686230i	−0.957985	+	0.286819i	$0.907402\pi$
$564$	8.80206	+	15.2456i	0.370634	+	0.641956i
$565$	12.0492	+	28.3345i	0.506915	+	1.19204i
$566$	−22.2481			−0.935156
$567$	−10.9420	−	6.31735i	−0.459520	−	0.265304i
$568$	−2.61109	−	1.50751i	−0.109559	−	0.0632538i
$569$	−6.76602	+	11.7191i	−0.283646	+	0.491290i	−0.972280	−	0.233820i	$-0.924877\pi$
$569$	−6.76602	+	11.7191i	−0.283646	+	0.491290i	0.688634	+	0.725109i	$0.258211\pi$
$570$	−37.9240	+	16.1272i	−1.58846	+	0.675493i
$571$	5.51144	−	9.54610i	0.230647	−	0.399492i	−0.727352	−	0.686265i	$-0.759249\pi$
$571$	5.51144	−	9.54610i	0.230647	−	0.399492i	0.957999	+	0.286773i	$0.0925825\pi$
$572$	−2.32502	+	1.34235i	−0.0972139	+	0.0561265i
$573$		−	3.87042i		−	0.161689i
$574$	24.1165			1.00660
$575$	21.9057	−	6.31251i	0.913532	−	0.263250i
$576$	−2.11630	+	3.66553i	−0.0881791	+	0.152731i
$577$	31.6666	−	18.2827i	1.31830	−	0.761119i	0.334842	−	0.942274i	$-0.391317\pi$
$577$	31.6666	−	18.2827i	1.31830	−	0.761119i	0.983455	+	0.181155i	$0.0579837\pi$
$578$	−13.6148	−	7.86053i	−0.566302	−	0.326955i
$579$	−24.5916	+	42.5939i	−1.02199	+	1.77014i
$580$	−3.83359	−	2.88487i	−0.159181	−	0.119788i
$581$	45.4193			1.88431
$582$	−23.4091	+	13.5152i	−0.970337	+	0.560225i
$583$	21.1676	−	12.2211i	0.876672	−	0.506147i
$584$	2.09086	−	3.62147i	0.0865202	−	0.149857i
$585$	−10.0429	−	1.22641i	−0.415221	−	0.0507059i
$586$	−15.3428	−	26.5745i	−0.633804	−	1.09778i
$587$			4.97632i			0.205395i	0.994713	+	0.102697i	$0.0327473\pi$
$587$			4.97632i			0.205395i	−0.994713	+	0.102697i	$0.967253\pi$
$588$		−	11.1746i		−	0.460833i
$589$	31.0891	−	22.1204i	1.28101	−	0.911454i
$590$	−21.9064	−	2.67516i	−0.901871	−	0.110135i
$591$	−8.57523			−0.352738
$592$	−9.97382	+	5.75839i	−0.409921	+	0.236668i
$593$			4.23391i			0.173866i	0.996214	+	0.0869330i	$0.0277066\pi$
$593$			4.23391i			0.173866i	−0.996214	+	0.0869330i	$0.972293\pi$
$594$	4.16249	−	7.20965i	0.170789	−	0.295816i
$595$	−7.77237	+	3.30520i	−0.318636	+	0.135500i
$596$	5.86843	+	10.1644i	0.240380	+	0.416351i
$597$		−	40.5054i		−	1.65777i
$598$	−4.22105	−	2.43702i	−0.172611	−	0.0996572i
$599$	−15.3524	+	26.5911i	−0.627282	+	1.08648i	0.360813	+	0.932638i	$0.382499\pi$
$599$	−15.3524	+	26.5911i	−0.627282	+	1.08648i	−0.988095	+	0.153845i	$0.950834\pi$
$600$	−9.32818	+	9.68504i	−0.380821	+	0.395390i
$601$	−9.18723	−	15.9128i	−0.374755	−	0.649095i	0.615535	−	0.788109i	$-0.288940\pi$
$601$	−9.18723	−	15.9128i	−0.374755	−	0.649095i	−0.990290	+	0.139015i	$0.955607\pi$
$602$	1.33622	+	0.771469i	0.0544604	+	0.0314427i
$603$	58.5401	−	33.7982i	2.38394	−	1.37637i
$604$	−5.08955			−0.207091
$605$	−1.27200	+	10.4162i	−0.0517142	+	0.423478i
$606$	20.0066	+	34.6524i	0.812711	+	1.40766i
$607$	32.5339	+	18.7835i	1.32051	+	0.762398i	0.983810	−	0.179214i	$-0.0573555\pi$
$607$	32.5339	+	18.7835i	1.32051	+	0.762398i	0.336701	+	0.941612i	$0.390689\pi$
$608$	5.93482	−	3.42647i	0.240689	−	0.138962i
$609$	9.63633	−	16.6906i	0.390484	−	0.676338i
$610$	2.51105	−	3.33683i	0.101670	−	0.135104i
$611$	3.49878	−	6.06007i	0.141546	−	0.245164i
$612$			4.78666i			0.193489i
$613$	−23.5128	+	13.5751i	−0.949674	+	0.548295i	−0.892980	−	0.450097i	$-0.851389\pi$
$613$	−23.5128	+	13.5751i	−0.949674	+	0.548295i	−0.0566946	+	0.998392i	$0.518056\pi$
$614$	−6.79649	−	11.7719i	−0.274284	−	0.475074i
$615$	26.1091	−	34.6954i	1.05282	−	1.39905i
$616$	−8.38791			−0.337958
$617$	−5.08011	+	2.93300i	−0.204518	+	0.118078i	−0.598761	−	0.800928i	$-0.704340\pi$
$617$	−5.08011	+	2.93300i	−0.204518	+	0.118078i	0.394243	+	0.919006i	$0.371007\pi$
$618$		−	11.4904i		−	0.462213i
$619$	23.8518			0.958683			0.479342	−	0.877628i	$-0.340876\pi$
$619$	23.8518			0.958683			0.479342	+	0.877628i	$0.340876\pi$
$620$	6.51061	−	10.6119i	0.261472	−	0.426183i
$621$	15.1139			0.606501
$622$			8.28787i			0.332313i
$623$	40.4917	−	23.3779i	1.62227	−	0.936615i
$624$	2.87493			0.115089
$625$	−21.1663	+	13.3036i	−0.846653	+	0.532145i
$626$	4.97379	+	8.61486i	0.198793	+	0.344319i
$627$	−40.0840	+	23.1425i	−1.60080	+	0.924222i
$628$			5.04463i			0.201303i
$629$	−6.51219	+	11.2794i	−0.259658	+	0.449741i
$630$	−25.2576	−	19.0070i	−1.00629	−	0.757257i
$631$	−21.9338	+	37.9904i	−0.873170	+	1.51238i	−0.0144711	+	0.999895i	$0.504606\pi$
$631$	−21.9338	+	37.9904i	−0.873170	+	1.51238i	−0.858699	+	0.512480i	$0.828727\pi$
$632$	4.70863	−	2.71853i	0.187299	−	0.108137i
$633$	−42.1865	−	24.3564i	−1.67676	−	0.968079i
$634$	−1.12141	−	1.94235i	−0.0445371	−	0.0771404i
$635$	2.80190	+	0.342163i	0.111190	+	0.0135783i
$636$	−26.1741			−1.03787
$637$	−3.84677	+	2.22093i	−0.152414	+	0.0879965i
$638$	−4.66664	−	2.69428i	−0.184754	−	0.106668i
$639$	−6.38069	−	11.0517i	−0.252416	−	0.437198i
$640$	1.34453	−	1.78669i	0.0531471	−	0.0706250i
$641$	2.13146	−	3.69179i	0.0841874	−	0.145817i	−0.820857	−	0.571133i	$-0.806504\pi$
$641$	2.13146	−	3.69179i	0.0841874	−	0.145817i	0.905045	+	0.425317i	$0.139837\pi$
$642$	22.9009	+	13.2218i	0.903826	+	0.521824i
$643$			22.7470i			0.897055i	0.893769	+	0.448528i	$0.148051\pi$
$643$			22.7470i			0.897055i	−0.893769	+	0.448528i	$0.851949\pi$
$644$	−7.61408	−	13.1880i	−0.300037	−	0.519679i
$645$	2.55651	−	1.08716i	0.100663	−	0.0428068i
$646$	3.87501	−	6.71171i	0.152460	−	0.264069i
$647$		−	21.1723i		−	0.832368i	−0.909280	−	0.416184i	$-0.863367\pi$
$647$		−	21.1723i		−	0.832368i	0.909280	−	0.416184i	$-0.136633\pi$
$648$	3.27611	−	1.89146i	0.128698	−	0.0743037i
$649$	−24.7865			−0.972957
$650$	5.18795	+	1.28627i	0.203488	+	0.0504515i
$651$	45.4836	+	20.7929i	1.78264	+	0.814938i
$652$		−	12.4987i		−	0.489486i
$653$		−	7.50358i		−	0.293638i	−0.989163	−	0.146819i	$-0.953097\pi$
$653$		−	7.50358i		−	0.293638i	0.989163	−	0.146819i	$-0.0469035\pi$
$654$	−16.4545	−	28.5001i	−0.643423	−	1.11444i
$655$	1.08443	−	8.88016i	0.0423721	−	0.346976i
$656$	−3.61032	+	6.25326i	−0.140959	+	0.244149i
$657$	15.3282	−	8.84975i	0.598010	−	0.345261i
$658$	18.9337	−	10.9314i	0.738112	−	0.426149i
$659$	41.7093			1.62476			0.812382	−	0.583126i	$-0.198171\pi$
$659$	41.7093			1.62476			0.812382	+	0.583126i	$0.198171\pi$
$660$	−9.08098	+	12.0673i	−0.353477	+	0.469721i
$661$	−18.3974	+	31.8652i	−0.715576	+	1.23941i	0.247161	+	0.968974i	$0.420502\pi$
$661$	−18.3974	+	31.8652i	−0.715576	+	1.23941i	−0.962737	+	0.270439i	$0.912831\pi$
$662$	20.3476	+	11.7477i	0.790833	+	0.456587i
$663$	2.81568	−	1.62563i	0.109352	−	0.0631344i
$664$	−6.79944	+	11.7770i	−0.263869	+	0.457035i
$665$	20.0285	+	47.0982i	0.776672	+	1.82639i
$666$	−48.7458			−1.88886
$667$		−	9.78289i		−	0.378795i
$668$	−15.4460	+	8.91775i	−0.597624	+	0.345038i
$669$	8.54498	−	14.8003i	0.330368	−	0.572214i
$670$	−32.8629	+	13.9750i	−1.26961	+	0.539900i
$671$	2.34516	−	4.06194i	0.0905339	−	0.156809i
$672$	7.77885	+	4.49112i	0.300075	+	0.173249i
$673$	−4.09110	−	2.36200i	−0.157700	−	0.0910483i	0.419073	−	0.907952i	$-0.362355\pi$
$673$	−4.09110	−	2.36200i	−0.157700	−	0.0910483i	−0.576773	+	0.816904i	$0.695688\pi$
$674$	5.10345			0.196578
$675$	−15.9263	+	4.58944i	−0.613004	+	0.176648i
$676$	5.92861	+	10.2687i	0.228024	+	0.394949i
$677$	9.66900	+	5.58240i	0.371610	+	0.214549i	0.674162	−	0.738584i	$-0.264505\pi$
$677$	9.66900	+	5.58240i	0.371610	+	0.214549i	−0.302552	+	0.953133i	$0.597838\pi$
$678$		−	37.0316i		−	1.42219i
$679$	16.7847	+	29.0720i	0.644138	+	1.11568i
$680$	0.306532	−	2.51013i	0.0117550	−	0.0962592i
$681$	−63.3317			−2.42687
$682$	5.81362	−	12.7170i	0.222615	−	0.486961i
$683$		−	27.2295i		−	1.04191i	−0.853585	−	0.520954i	$-0.825576\pi$
$683$		−	27.2295i		−	1.04191i	0.853585	−	0.520954i	$-0.174424\pi$
$684$	29.0057			1.10906
$685$	9.52772	+	22.4050i	0.364036	+	0.856051i
$686$	9.50164			0.362774
$687$	−52.6124	−	30.3758i	−2.00729	−	1.15891i
$688$	−0.400075	+	0.230984i	−0.0152527	+	0.00880617i
$689$	5.20205	+	9.01021i	0.198182	+	0.343262i
$690$	−27.2162	−	3.32359i	−1.03610	−	0.126527i
$691$	18.4515	−	31.9589i	0.701927	−	1.21577i	−0.265862	−	0.964011i	$-0.585657\pi$
$691$	18.4515	−	31.9589i	0.701927	−	1.21577i	0.967789	−	0.251762i	$-0.0810101\pi$
$692$	−7.01810	−	4.05190i	−0.266788	−	0.154030i
$693$	−30.7462	−	17.7513i	−1.16795	−	0.674317i
$694$	15.1378	+	26.2194i	0.574622	+	0.995275i
$695$	−19.2230	−	14.4658i	−0.729171	−	0.548719i
$696$	2.88519	+	4.99729i	0.109363	+	0.189422i
$697$			8.16586i			0.309304i
$698$			11.9756i			0.453282i
$699$	15.3477	+	26.5829i	0.580502	+	1.00546i
$700$	12.0280	+	11.5848i	0.454614	+	0.437863i
$701$	−15.2412	−	26.3985i	−0.575652	−	0.997058i	−0.995970	−	0.0896816i	$-0.971415\pi$
$701$	−15.2412	−	26.3985i	−0.575652	−	0.997058i	0.420319	−	0.907377i	$-0.361918\pi$
$702$	3.06886	+	1.77181i	0.115827	+	0.0668727i
$703$	68.3500	+	39.4619i	2.57787	+	1.48833i
$704$	1.25570	−	2.17494i	0.0473260	−	0.0819711i
$705$	4.77161	−	39.0737i	0.179709	−	1.47160i
$706$	8.54181	+	14.7949i	0.321475	+	0.556812i
$707$	43.0352	−	24.8464i	1.61850	−	0.934444i
$708$	22.9867	+	13.2714i	0.863895	+	0.498770i
$709$	−30.1272			−1.13145			−0.565726	−	0.824593i	$-0.691404\pi$
$709$	−30.1272			−1.13145			−0.565726	+	0.824593i	$0.691404\pi$
$710$	2.63831	+	6.20413i	0.0990139	+	0.232837i
$711$	23.0129			0.863050
$712$			13.9990i			0.524636i
$713$	25.2718	−	2.40330i	0.946435	−	0.0900044i
$714$	10.1581			0.380156
$715$	5.95891	+	0.727690i	0.222850	+	0.0272141i
$716$	9.47460	+	16.4105i	0.354082	+	0.613289i
$717$			42.9808i			1.60515i
$718$	25.5058	+	14.7258i	0.951870	+	0.549562i
$719$	−14.7187	−	25.4936i	−0.548917	−	0.950752i	−0.998349	−	0.0574372i	$-0.981707\pi$
$719$	−14.7187	−	25.4936i	−0.548917	−	0.950752i	0.449432	−	0.893314i	$-0.351626\pi$
$720$	8.70957	−	3.70374i	0.324586	−	0.138030i
$721$	−14.2701			−0.531446
$722$	−24.2165	−	13.9814i	−0.901244	−	0.520333i
$723$	15.9704	+	9.22052i	0.593946	+	0.342915i
$724$	6.25755	−	10.8384i	0.232560	−	0.402806i
$725$	2.97064	+	10.3087i	0.110327	+	0.382856i
$726$	6.31037	−	10.9299i	0.234200	−	0.405646i
$727$	−9.81546	+	5.66696i	−0.364035	+	0.210176i	−0.670849	−	0.741594i	$-0.734070\pi$
$727$	−9.81546	+	5.66696i	−0.364035	+	0.210176i	0.306814	+	0.951769i	$0.400737\pi$
$728$		−	3.57040i		−	0.132328i
$729$	42.7562			1.58356
$730$	−8.60486	+	3.65922i	−0.318480	+	0.135434i
$731$	−0.261220	+	0.452447i	−0.00966159	+	0.0167344i
$732$	−4.34975	+	2.51133i	−0.160771	+	0.0928213i
$733$	5.22234	+	3.01512i	0.192891	+	0.111366i	0.593335	−	0.804955i	$-0.297811\pi$
$733$	5.22234	+	3.01512i	0.192891	+	0.111366i	−0.400444	+	0.916321i	$0.631144\pi$
$734$	15.6459	−	27.0994i	0.577499	−	1.00026i
$735$	−15.0246	+	19.9655i	−0.554189	+	0.736440i
$736$	4.55942			0.168063
$737$	−34.7347	+	20.0541i	−1.27947	+	0.738701i
$738$	−26.4675	+	15.2810i	−0.974283	+	0.562503i
$739$	4.45863	−	7.72257i	0.164013	−	0.284079i	−0.772291	−	0.635269i	$-0.780889\pi$
$739$	4.45863	−	7.72257i	0.164013	−	0.284079i	0.936304	+	0.351189i	$0.114223\pi$
$740$	25.5624	+	3.12163i	0.939692	+	0.114753i
$741$	−9.85085	−	17.0622i	−0.361880	−	0.626794i
$742$			32.5059i			1.19333i
$743$			33.6977i			1.23625i	0.786081	+	0.618124i	$0.212107\pi$
$743$			33.6977i			1.23625i	−0.786081	+	0.618124i	$0.787893\pi$
$744$	−12.2005	+	8.68086i	−0.447293	+	0.318256i
$745$	3.18128	−	26.0509i	0.116553	−	0.954431i
$746$	19.9316			0.729747
$747$	−49.8472	+	28.7793i	−1.82381	+	1.05298i
$748$		−	2.84016i		−	0.103846i
$749$	16.4203	−	28.4409i	0.599986	−	1.03921i
$750$	29.6883	−	4.76214i	1.08406	−	0.173889i
$751$	15.1183	+	26.1857i	0.551675	+	0.955529i	0.998154	+	0.0607351i	$0.0193445\pi$
$751$	15.1183	+	26.1857i	0.551675	+	0.955529i	−0.446479	+	0.894794i	$0.647322\pi$
$752$			6.54587i			0.238703i
$753$	2.41882	+	1.39651i	0.0881468	+	0.0508916i
$754$	1.14685	−	1.98640i	0.0417658	−	0.0723406i
$755$	9.09344	+	6.84304i	0.330944	+	0.249044i
$756$	5.53573	+	9.58817i	0.201333	+	0.348718i
$757$	17.9791	+	10.3803i	0.653463	+	0.377277i	0.789782	−	0.613388i	$-0.210194\pi$
$757$	17.9791	+	10.3803i	0.653463	+	0.377277i	−0.136319	+	0.990665i	$0.543527\pi$
$758$	−12.8476	+	7.41755i	−0.466645	+	0.269418i
$759$	−30.7945			−1.11777
$760$	−15.2106	−	1.85749i	−0.551748	−	0.0673783i
$761$	−18.2860	−	31.6722i	−0.662866	−	1.14812i	−0.979859	−	0.199690i	$-0.936007\pi$
$761$	−18.2860	−	31.6722i	−0.662866	−	1.14812i	0.316993	−	0.948428i	$-0.397327\pi$
$762$	−2.94009	−	1.69746i	−0.106508	−	0.0614925i
$763$	−35.3946	+	20.4351i	−1.28137	+	0.739799i
$764$	0.719583	−	1.24636i	0.0260336	−	0.0450915i
$765$	6.43579	−	8.55226i	0.232687	−	0.309208i
$766$	2.42574	−	4.20151i	0.0876457	−	0.151807i
$767$		−	10.5507i		−	0.380962i
$768$	−2.32904	+	1.34467i	−0.0840421	+	0.0485218i
$769$	−4.76428	−	8.25198i	−0.171804	−	0.297574i	0.767246	−	0.641353i	$-0.221626\pi$
$769$	−4.76428	−	8.25198i	−0.171804	−	0.297574i	−0.939051	+	0.343779i	$0.888293\pi$
$770$	14.9866	+	11.2778i	0.540078	+	0.406422i
$771$	31.0371			1.11777
$772$	−15.8380	+	9.14408i	−0.570023	+	0.329103i
$773$		−	3.33060i		−	0.119793i	−0.998205	−	0.0598966i	$-0.980923\pi$
$773$		−	3.33060i		−	0.119793i	0.998205	−	0.0598966i	$-0.0190771\pi$
$774$	−1.95532			−0.0702825
$775$	−25.9004	+	10.2064i	−0.930369	+	0.366625i
$776$	−10.0509			−0.360808
$777$			103.446i			3.71112i
$778$	−1.96685	+	1.13556i	−0.0705149	+	0.0407118i
$779$	49.4826			1.77290
$780$	−5.13659	−	3.86541i	−0.183920	−	0.138404i
$781$	3.78597	+	6.55749i	0.135473	+	0.234646i
$782$	4.46546	−	2.57814i	0.159685	−	0.0921939i
$783$			7.11254i			0.254181i
$784$	2.07757	−	3.59845i	0.0741989	−	0.128516i
$785$	6.78264	−	9.01317i	0.242083	−	0.321694i
$786$	−5.37981	+	9.31811i	−0.191892	+	0.332366i
$787$	−23.2991	+	13.4518i	−0.830524	+	0.479503i	−0.854032	−	0.520220i	$-0.825850\pi$
$787$	−23.2991	+	13.4518i	−0.830524	+	0.479503i	0.0235082	+	0.999724i	$0.492516\pi$
$788$	−2.76140	−	1.59430i	−0.0983708	−	0.0567944i
$789$	−37.4799	−	64.9171i	−1.33432	−	2.31111i
$790$	−12.0680	−	1.47372i	−0.429360	−	0.0524325i
$791$	−45.9899			−1.63521
$792$	9.20563	−	5.31487i	0.327108	−	0.188856i
$793$	1.72901	+	0.998242i	0.0613988	+	0.0354486i
$794$	4.72369	+	8.18167i	0.167637	+	0.290357i
$795$	46.7649	+	35.1918i	1.65858	+	1.24812i
$796$	7.53070	−	13.0436i	0.266919	−	0.462317i
$797$	17.0397	+	9.83785i	0.603576	+	0.348474i	0.770447	−	0.637504i	$-0.220033\pi$
$797$	17.0397	+	9.83785i	0.603576	+	0.348474i	−0.166871	+	0.985979i	$0.553366\pi$
$798$		−	61.5547i		−	2.17901i
$799$	3.70138	+	6.41097i	0.130945	+	0.226804i
$800$	−4.80449	+	1.38450i	−0.169865	+	0.0489494i
$801$	−29.6261	+	51.3139i	−1.04679	+	1.81309i
$802$			20.3650i			0.719113i
$803$	−9.09496	+	5.25098i	−0.320954	+	0.185303i
$804$	42.9500			1.51473
$805$	−4.12760	+	33.8001i	−0.145479	+	1.19130i
$806$	5.41314	+	2.47463i	0.190670	+	0.0871651i
$807$		−	20.0099i		−	0.704380i
$808$			14.8784i			0.523419i
$809$	19.5953	+	33.9401i	0.688936	+	1.19327i	0.972183	+	0.234225i	$0.0752551\pi$
$809$	19.5953	+	33.9401i	0.688936	+	1.19327i	−0.283247	+	0.959047i	$0.591412\pi$
$810$	−8.39650	−	1.02536i	−0.295023	−	0.0360276i
$811$	−6.00390	+	10.3991i	−0.210825	+	0.365160i	−0.951973	−	0.306182i	$-0.900948\pi$
$811$	−6.00390	+	10.3991i	−0.210825	+	0.365160i	0.741148	+	0.671342i	$0.234282\pi$
$812$	6.20619	−	3.58315i	0.217795	−	0.125744i
$813$	−28.7926	+	16.6234i	−1.00980	+	0.583008i
$814$	28.9232			1.01376
$815$	−16.8048	+	22.3312i	−0.588646	+	0.782228i
$816$	−1.52070	+	2.63393i	−0.0532351	+	0.0922059i
$817$	2.74169	+	1.58292i	0.0959197	+	0.0553792i
$818$	−11.1173	+	6.41855i	−0.388706	+	0.224419i
$819$	7.55603	−	13.0874i	0.264029	−	0.457312i
$820$	14.8582	−	6.31845i	0.518871	−	0.220650i
$821$	−45.3721			−1.58350			−0.791748	−	0.610848i	$-0.790829\pi$
$821$	−45.3721			−1.58350			−0.791748	+	0.610848i	$0.790829\pi$
$822$		−	29.2821i		−	1.02133i
$823$	−34.4620	+	19.8966i	−1.20127	+	0.693553i	−0.960838	−	0.277112i	$-0.910623\pi$
$823$	−34.4620	+	19.8966i	−1.20127	+	0.693553i	−0.240432	+	0.970666i	$0.577289\pi$
$824$	2.13628	−	3.70015i	0.0744210	−	0.128901i
$825$	32.4497	−	9.35095i	1.12975	−	0.325558i
$826$	16.4819	−	28.5475i	0.573479	−	0.993294i
$827$	−10.8815	−	6.28245i	−0.378387	−	0.218462i	0.298729	−	0.954338i	$-0.403437\pi$
$827$	−10.8815	−	6.28245i	−0.378387	−	0.218462i	−0.677116	+	0.735876i	$0.736771\pi$
$828$	16.7127	+	9.64909i	0.580807	+	0.335329i
$829$	−48.2511			−1.67583			−0.837914	−	0.545802i	$-0.816225\pi$
$829$	−48.2511			−1.67583			−0.837914	+	0.545802i	$0.816225\pi$
$830$	27.9829	−	11.8997i	0.971302	−	0.413046i
$831$	−15.0040	−	25.9876i	−0.520481	−	0.901500i
$832$	0.925785	+	0.534502i	0.0320958	+	0.0185305i
$833$		−	4.69906i		−	0.162813i
$834$	14.4674	+	25.0583i	0.500965	+	0.867696i
$835$	39.5873	+	4.83432i	1.36998	+	0.167299i
$836$	−17.2105			−0.595237
$837$	−18.3736	+	1.74729i	−0.635083	+	0.0603953i
$838$		−	16.9178i		−	0.584415i
$839$	−32.2788			−1.11439			−0.557193	−	0.830383i	$-0.688122\pi$
$839$	−32.2788			−1.11439			−0.557193	+	0.830383i	$0.688122\pi$
$840$	−7.85993	−	18.4831i	−0.271193	−	0.637727i
$841$	−24.3962			−0.841249
$842$	8.60160	+	4.96613i	0.296431	+	0.171144i
$843$	−7.26392	+	4.19383i	−0.250183	+	0.144443i
$844$	−9.05661	−	15.6865i	−0.311741	−	0.539952i
$845$	3.21391	−	26.3181i	0.110562	−	0.905369i
$846$	−13.8530	+	23.9941i	−0.476276	+	0.824934i
$847$	−13.5739	−	7.83691i	−0.466406	−	0.269279i
$848$	−8.42860	−	4.86625i	−0.289439	−	0.167108i
$849$	−29.9164	−	51.8167i	−1.02673	−	1.77834i
$850$	−3.92262	+	4.07268i	−0.134545	+	0.139692i
$851$	26.2549	+	45.4748i	0.900007	+	1.55886i
$852$		−	8.10845i		−	0.277791i
$853$		−	3.23296i		−	0.110694i	−0.998467	−	0.0553472i	$-0.982373\pi$
$853$		−	3.23296i		−	0.110694i	0.998467	−	0.0553472i	$-0.0176266\pi$
$854$	3.11885	+	5.40200i	0.106725	+	0.184853i
$855$	−51.8241	−	38.9989i	−1.77235	−	1.33374i
$856$	4.91637	+	8.51540i	0.168038	+	0.291050i
$857$	−2.10784	−	1.21696i	−0.0720025	−	0.0415707i	0.463567	−	0.886062i	$-0.346570\pi$
$857$	−2.10784	−	1.21696i	−0.0720025	−	0.0415707i	−0.535569	+	0.844491i	$0.679903\pi$
$858$	−6.25279	−	3.61005i	−0.213467	−	0.123245i
$859$	4.93095	−	8.54066i	0.168242	−	0.291403i	−0.769560	−	0.638575i	$-0.779524\pi$
$859$	4.93095	−	8.54066i	0.168242	−	0.291403i	0.937802	+	0.347171i	$0.112858\pi$
$860$	1.02537	+	0.125216i	0.0349649	+	0.00426985i
$861$	32.4288	+	56.1683i	1.10517	+	1.91421i
$862$	−0.446222	+	0.257626i	−0.0151984	+	0.00877479i
$863$	6.80650	+	3.92974i	0.231696	+	0.133770i	0.611354	−	0.791357i	$-0.290625\pi$
$863$	6.80650	+	3.92974i	0.231696	+	0.133770i	−0.379658	+	0.925127i	$0.623958\pi$
$864$	−3.31488			−0.112774
$865$	7.09126	+	16.6755i	0.241110	+	0.566984i
$866$	−37.7395			−1.28244
$867$		−	42.2794i		−	1.43588i
$868$	10.7809	+	15.1520i	0.365926	+	0.514292i
$869$	−13.6546			−0.463202
$870$	1.56406	−	12.8078i	0.0530267	−	0.434225i
$871$	−8.53623	−	14.7852i	−0.289239	−	0.500977i
$872$		−	12.2368i		−	0.414391i
$873$	−36.8421	−	21.2708i	−1.24691	−	0.719907i
$874$	−15.6227	−	27.0593i	−0.528446	−	0.915296i
$875$	−5.91416	−	36.8702i	−0.199935	−	1.24644i
$876$	11.2461			0.379970
$877$	46.5201	+	26.8584i	1.57087	+	0.906943i	0.996062	+	0.0886546i	$0.0282567\pi$
$877$	46.5201	+	26.8584i	1.57087	+	0.906943i	0.574808	+	0.818288i	$0.305077\pi$
$878$	−12.4149	−	7.16777i	−0.418984	−	0.241900i
$879$	41.2621	−	71.4680i	1.39174	−	2.41056i
$880$	−5.16781	+	2.19761i	−0.174207	+	0.0740814i
$881$	15.3470	−	26.5818i	0.517054	−	0.895564i	−0.482750	−	0.875758i	$-0.660362\pi$
$881$	15.3470	−	26.5818i	0.517054	−	0.895564i	0.999804	−	0.0198057i	$-0.00630477\pi$
$882$	15.2308	−	8.79351i	0.512848	−	0.296093i
$883$		−	47.7407i		−	1.60660i	−0.595573	−	0.803301i	$-0.703075\pi$
$883$		−	47.7407i		−	1.60660i	0.595573	−	0.803301i	$-0.296925\pi$
$884$	1.20894			0.0406611
$885$	−23.2264	−	54.6181i	−0.780746	−	1.83597i
$886$	13.7112	−	23.7485i	0.460637	−	0.797847i
$887$	−18.4652	+	10.6609i	−0.620001	+	0.357958i	−0.776869	−	0.629662i	$-0.783193\pi$
$887$	−18.4652	+	10.6609i	−0.620001	+	0.357958i	0.156868	+	0.987620i	$0.449860\pi$
$888$	−26.8231	−	15.4863i	−0.900123	−	0.519686i
$889$	−2.10809	+	3.65132i	−0.0707032	+	0.122461i
$890$	18.8221	−	25.0119i	0.630917	−	0.838400i
$891$	−9.50045			−0.318277
$892$	5.50332	−	3.17734i	0.184265	−	0.106385i
$893$	38.8485	−	22.4292i	1.30002	−	0.750565i
$894$	−15.7823	+	27.3357i	−0.527837	+	0.914241i
$895$	5.13619	−	42.0592i	0.171684	−	1.40589i
$896$	1.66997	+	2.89246i	0.0557896	+	0.0966305i
$897$		−	13.1080i		−	0.437663i
$898$			39.8495i			1.32980i
$899$	1.13098	+	11.8928i	0.0377204	+	0.396646i
$900$	−20.5411	−	5.09281i	−0.684702	−	0.169760i
$901$	−11.0065			−0.366681
$902$	15.7045	−	9.06697i	0.522901	−	0.301897i
$903$			4.14950i			0.138087i
$904$	6.88486	−	11.9249i	0.228987	−	0.396617i
$905$	−25.7528	+	10.9514i	−0.856052	+	0.364036i
$906$	−6.84379	−	11.8538i	−0.227370	−	0.393816i
$907$			3.01352i			0.100062i	0.998748	+	0.0500311i	$0.0159321\pi$
$907$			3.01352i			0.100062i	−0.998748	+	0.0500311i	$0.984068\pi$
$908$	−20.3941	−	11.7745i	−0.676802	−	0.390752i
$909$	−31.4871	+	54.5372i	−1.04436	+	1.80888i
$910$	−4.80050	+	6.37919i	−0.159135	+	0.211468i
$911$	9.27333	+	16.0619i	0.307239	+	0.532154i	0.977757	−	0.209739i	$-0.0672615\pi$
$911$	9.27333	+	16.0619i	0.307239	+	0.532154i	−0.670518	+	0.741893i	$0.733928\pi$
$912$	15.9608	+	9.21497i	0.528515	+	0.305138i
$913$	29.5767	−	17.0761i	0.978847	−	0.565137i
$914$	17.5445			0.580319
$915$	11.1482	+	1.36139i	0.368548	+	0.0450063i
$916$	−11.2948	−	19.5632i	−0.373192	−	0.646388i
$917$	11.5723	+	6.68125i	0.382150	+	0.220634i
$918$	−3.24656	+	1.87440i	−0.107153	+	0.0618646i
$919$	5.30786	−	9.19349i	0.175090	−	0.303265i	−0.765102	−	0.643909i	$-0.777312\pi$
$919$	5.30786	−	9.19349i	0.175090	−	0.303265i	0.940192	+	0.340644i	$0.110645\pi$
$920$	−8.14626	−	6.13026i	−0.268574	−	0.202109i
$921$	18.2781	−	31.6586i	0.602285	−	1.04319i
$922$		−	9.00321i		−	0.296505i
$923$	−2.79127	+	1.61154i	−0.0918757	+	0.0530444i
$924$	−11.2790	−	19.5358i	−0.371052	−	0.642681i
$925$	−41.4749	−	39.9467i	−1.36369	−	1.31344i
$926$	−23.2104			−0.762742
$927$	15.6612	−	9.04202i	0.514383	−	0.296979i
$928$			2.14564i			0.0704341i
$929$	28.8336			0.945999			0.473000	−	0.881063i	$-0.343171\pi$
$929$	28.8336			0.945999			0.473000	+	0.881063i	$0.343171\pi$
$930$	33.4702	+	0.893973i	1.09753	+	0.0293145i
$931$	−28.4749			−0.933227
$932$			11.4137i			0.373867i
$933$	−19.3028	+	11.1445i	−0.631946	+	0.364854i
$934$	6.78086			0.221877
$935$	−3.81866	+	5.07447i	−0.124884	+	0.165953i
$936$	2.26233	+	3.91847i	0.0739466	+	0.128079i
$937$	19.2047	−	11.0878i	0.627390	−	0.362224i	−0.152350	−	0.988327i	$-0.548684\pi$
$937$	19.2047	−	11.0878i	0.627390	−	0.362224i	0.779741	+	0.626103i	$0.215351\pi$
$938$		−	53.3401i		−	1.74162i
$939$	−13.3763	+	23.1683i	−0.436517	+	0.756070i
$940$	8.80109	−	11.6954i	0.287060	−	0.381462i
$941$	5.67462	−	9.82873i	0.184987	−	0.320407i	−0.758585	−	0.651574i	$-0.774109\pi$
$941$	5.67462	−	9.82873i	0.184987	−	0.320407i	0.943572	+	0.331167i	$0.107442\pi$
$942$	−11.7492	+	6.78338i	−0.382808	+	0.221015i
$943$	28.5113	+	16.4610i	0.928454	+	0.536043i
$944$	4.93480	+	8.54733i	0.160614	+	0.278192i
$945$	3.00093	−	24.5740i	0.0976201	−	0.799392i
$946$	1.16019			0.0377209
$947$	−1.41654	+	0.817838i	−0.0460313	+	0.0265762i	−0.522839	−	0.852431i	$-0.675127\pi$
$947$	−1.41654	+	0.817838i	−0.0460313	+	0.0265762i	0.476808	+	0.879008i	$0.341794\pi$
$948$	12.6632	+	7.31108i	0.411280	+	0.237453i
$949$	−2.23514	−	3.87137i	−0.0725556	−	0.125670i
$950$	24.6792	+	23.7699i	0.800699	+	0.771196i
$951$	3.01587	−	5.22365i	0.0977964	−	0.169388i
$952$	3.27110	+	1.88857i	0.106017	+	0.0612090i
$953$			2.67046i			0.0865047i	0.999064	+	0.0432524i	$0.0137719\pi$
$953$			2.67046i			0.0865047i	−0.999064	+	0.0432524i	$0.986228\pi$
$954$	−20.5969	−	35.6748i	−0.666849	−	1.15502i
$955$	−2.96143	+	1.25935i	−0.0958295	+	0.0407515i
$956$	−7.99093	+	13.8407i	−0.258445	+	0.447640i
$957$		−	14.4917i		−	0.468451i
$958$	11.7070	−	6.75903i	0.378235	−	0.218374i
$959$	−36.3657			−1.17431
$960$	5.96922	+	0.728949i	0.192656	+	0.0235267i
$961$	−30.4443	+	5.84325i	−0.982075	+	0.188492i
$962$			12.3115i			0.396938i
$963$			41.6180i			1.34112i
$964$	3.42853	+	5.93840i	0.110426	+	0.191263i
$965$	40.5920	+	4.95702i	1.30670	+	0.159572i
$966$	20.4769	−	35.4670i	0.658834	−	1.14113i
$967$	−52.6039	+	30.3709i	−1.69163	+	0.976662i	−0.738424	+	0.674337i	$0.764430\pi$
$967$	−52.6039	+	30.3709i	−1.69163	+	0.976662i	−0.953205	+	0.302326i	$0.902237\pi$
$968$	4.06414	−	2.34643i	0.130626	−	0.0754171i
$969$	20.8425			0.669558
$970$	17.9579	+	13.5138i	0.576593	+	0.433900i
$971$	23.2342	−	40.2428i	0.745621	−	1.29145i	−0.204283	−	0.978912i	$-0.565486\pi$
$971$	23.2342	−	40.2428i	0.745621	−	1.29145i	0.949904	−	0.312542i	$-0.101180\pi$
$972$	17.4229	+	10.0591i	0.558840	+	0.322646i
$973$	31.1201	−	17.9672i	0.997665	−	0.576002i
$974$	−7.61835	+	13.1954i	−0.244108	+	0.422807i
$975$	3.98033	+	13.8126i	0.127473	+	0.442356i
$976$	−1.86761			−0.0597808
$977$			1.40935i			0.0450891i	0.999746	+	0.0225445i	$0.00717675\pi$
$977$			1.40935i			0.0450891i	−0.999746	+	0.0225445i	$0.992823\pi$
$978$	29.1100	−	16.8066i	0.930834	−	0.537417i
$979$	17.5786	−	30.4470i	0.561814	−	0.973091i
$980$	−8.55018	+	3.63596i	−0.273126	+	0.116147i
$981$	25.8968	−	44.8545i	0.826820	−	1.43209i
$982$	23.2298	+	13.4117i	0.741292	+	0.427985i
$983$	−17.0388	−	9.83737i	−0.543454	−	0.313763i	0.203024	−	0.979174i	$-0.434923\pi$
$983$	−17.0388	−	9.83737i	−0.543454	−	0.313763i	−0.746478	+	0.665410i	$0.768257\pi$
$984$	−19.4188			−0.619050
$985$	2.79019	+	6.56128i	0.0889027	+	0.209060i
$986$	1.21326	+	2.10142i	0.0386380	+	0.0669230i
$987$	50.9193	+	29.3983i	1.62078	+	0.935757i
$988$		−	7.32582i		−	0.233066i
$989$	1.05315	+	1.82411i	0.0334883	+	0.0580034i
$990$	−23.5936	−	2.88120i	−0.749853	−	0.0915705i
$991$	28.9565			0.919834			0.459917	−	0.887962i	$-0.347879\pi$
$991$	28.9565			0.919834			0.459917	+	0.887962i	$0.347879\pi$
$992$	−5.54276	+	0.527107i	−0.175983	+	0.0167357i
$993$			63.1873i			2.00519i
$994$	−10.0700			−0.319400
$995$	−30.9924	+	13.1795i	−0.982525	+	0.417819i
$996$	−36.5721			−1.15883
$997$	−26.1902	−	15.1209i	−0.829451	−	0.478884i	0.0242137	−	0.999707i	$-0.492292\pi$
$997$	−26.1902	−	15.1209i	−0.829451	−	0.478884i	−0.853665	+	0.520823i	$0.825625\pi$
$998$	21.9465	−	12.6708i	0.694705	−	0.401088i
$999$	−19.0883	−	33.0620i	−0.603928	−	1.04603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.k.a.149.9	yes	32
5.2	odd	4		1550.2.e.q.1451.8		16
5.3	odd	4		1550.2.e.r.1451.1		16
5.4	even	2	inner	310.2.k.a.149.8	yes	32
31.5	even	3	inner	310.2.k.a.129.16	yes	32
155.67	odd	12		1550.2.e.q.501.8		16
155.98	odd	12		1550.2.e.r.501.1		16
155.129	even	6	inner	310.2.k.a.129.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.k.a.129.1	✓	32	155.129	even	6	inner
310.2.k.a.129.16	yes	32	31.5	even	3	inner
310.2.k.a.149.8	yes	32	5.4	even	2	inner
310.2.k.a.149.9	yes	32	1.1	even	1	trivial
1550.2.e.q.501.8		16	155.67	odd	12
1550.2.e.q.1451.8		16	5.2	odd	4
1550.2.e.r.501.1		16	155.98	odd	12
1550.2.e.r.1451.1		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(1.78669 + 1.34453i) q^{5} +(-1.34467 - 2.32904i) q^{6} +(-2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 - 3.66553i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(1.78669 + 1.34453i) q^{5} +(-1.34467 - 2.32904i) q^{6} +(-2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 - 3.66553i) q^{9} +(-1.34453 + 1.78669i) q^{10} +(-1.25570 + 2.17494i) q^{11} +(2.32904 - 1.34467i) q^{12} +(-0.925785 - 0.534502i) q^{13} +(-1.66997 - 2.89246i) q^{14} +(-5.96922 - 0.728949i) q^{15} +1.00000 q^{16} +(0.979392 - 0.565452i) q^{17} +(3.66553 + 2.11630i) q^{18} +(-3.42647 - 5.93482i) q^{19} +(-1.78669 - 1.34453i) q^{20} +(4.49112 - 7.77885i) q^{21} +(-2.17494 - 1.25570i) q^{22} -4.55942i q^{23} +(1.34467 + 2.32904i) q^{24} +(1.38450 + 4.80449i) q^{25} +(0.534502 - 0.925785i) q^{26} +3.31488i q^{27} +(2.89246 - 1.66997i) q^{28} +2.14564 q^{29} +(0.728949 - 5.96922i) q^{30} +(0.527107 + 5.54276i) q^{31} +1.00000i q^{32} -6.75404i q^{33} +(0.565452 + 0.979392i) q^{34} +(-7.41324 - 0.905290i) q^{35} +(-2.11630 + 3.66553i) q^{36} +(-9.97382 + 5.75839i) q^{37} +(5.93482 - 3.42647i) q^{38} +2.87493 q^{39} +(1.34453 - 1.78669i) q^{40} +(-3.61032 + 6.25326i) q^{41} +(7.77885 + 4.49112i) q^{42} +(-0.400075 + 0.230984i) q^{43} +(1.25570 - 2.17494i) q^{44} +(8.70957 - 3.70374i) q^{45} +4.55942 q^{46} +6.54587i q^{47} +(-2.32904 + 1.34467i) q^{48} +(2.07757 - 3.59845i) q^{49} +(-4.80449 + 1.38450i) q^{50} +(-1.52070 + 2.63393i) q^{51} +(0.925785 + 0.534502i) q^{52} +(-8.42860 - 4.86625i) q^{53} -3.31488 q^{54} +(-5.16781 + 2.19761i) q^{55} +(1.66997 + 2.89246i) q^{56} +(15.9608 + 9.21497i) q^{57} +2.14564i q^{58} +(4.93480 + 8.54733i) q^{59} +(5.96922 + 0.728949i) q^{60} -1.86761 q^{61} +(-5.54276 + 0.527107i) q^{62} +14.1366i q^{63} -1.00000 q^{64} +(-0.935436 - 2.19973i) q^{65} +6.75404 q^{66} +(13.8308 + 7.98521i) q^{67} +(-0.979392 + 0.565452i) q^{68} +(6.13094 + 10.6191i) q^{69} +(0.905290 - 7.41324i) q^{70} +(1.50751 - 2.61109i) q^{71} +(-3.66553 - 2.11630i) q^{72} +(3.62147 + 2.09086i) q^{73} +(-5.75839 - 9.97382i) q^{74} +(-9.68504 - 9.32818i) q^{75} +(3.42647 + 5.93482i) q^{76} -8.38791i q^{77} +2.87493i q^{78} +(2.71853 + 4.70863i) q^{79} +(1.78669 + 1.34453i) q^{80} +(1.89146 + 3.27611i) q^{81} +(-6.25326 - 3.61032i) q^{82} +(-11.7770 - 6.79944i) q^{83} +(-4.49112 + 7.77885i) q^{84} +(2.51013 + 0.306532i) q^{85} +(-0.230984 - 0.400075i) q^{86} +(-4.99729 + 2.88519i) q^{87} +(2.17494 + 1.25570i) q^{88} -13.9990 q^{89} +(3.70374 + 8.70957i) q^{90} +3.57040 q^{91} +4.55942i q^{92} +(-8.68086 - 12.2005i) q^{93} -6.54587 q^{94} +(1.85749 - 15.2106i) q^{95} +(-1.34467 - 2.32904i) q^{96} -10.0509i q^{97} +(3.59845 + 2.07757i) q^{98} +(5.31487 + 9.20563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9	\( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} + 8 q^{15} + 32 q^{16} - 8 q^{19} + 2 q^{20} + 16 q^{21} - 4 q^{24} + 22 q^{25} + 12 q^{26} - 8 q^{29} + 28 q^{30} + 12 q^{31} - 12 q^{34} - 32 q^{35} - 8 q^{36} - 64 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{44} - 24 q^{45} - 8 q^{46} + 20 q^{49} - 40 q^{51} + 8 q^{54} - 8 q^{55} + 16 q^{59} - 8 q^{60} - 40 q^{61} - 32 q^{64} - 6 q^{65} - 24 q^{66} + 36 q^{69} + 36 q^{70} + 48 q^{71} - 28 q^{74} + 8 q^{75} + 8 q^{76} + 4 q^{79} - 2 q^{80} - 32 q^{81} - 16 q^{84} - 84 q^{85} + 12 q^{86} + 72 q^{89} + 40 q^{90} + 24 q^{91} + 16 q^{94} - 48 q^{95} + 4 q^{96} + 64 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 + 8 * q^15 + 32 * q^16 - 8 * q^19 + 2 * q^20 + 16 * q^21 - 4 * q^24 + 22 * q^25 + 12 * q^26 - 8 * q^29 + 28 * q^30 + 12 * q^31 - 12 * q^34 - 32 * q^35 - 8 * q^36 - 64 * q^39 + 4 * q^40 - 16 * q^41 - 4 * q^44 - 24 * q^45 - 8 * q^46 + 20 * q^49 - 40 * q^51 + 8 * q^54 - 8 * q^55 + 16 * q^59 - 8 * q^60 - 40 * q^61 - 32 * q^64 - 6 * q^65 - 24 * q^66 + 36 * q^69 + 36 * q^70 + 48 * q^71 - 28 * q^74 + 8 * q^75 + 8 * q^76 + 4 * q^79 - 2 * q^80 - 32 * q^81 - 16 * q^84 - 84 * q^85 + 12 * q^86 + 72 * q^89 + 40 * q^90 + 24 * q^91 + 16 * q^94 - 48 * q^95 + 4 * q^96 + 64 * q^99

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