LMFDB - Embedded newform 77.2.f.b.64.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(15,77)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("77.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.4
Root			$-0.788594 + 2.42704i$ of defining polynomial
Character	$\chi$	$=$	77.64
Dual form			77.2.f.b.71.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.788594 - 2.42704i) q^{2} +(0.332181 - 0.241344i) q^{3} +(-3.65062 - 2.65233i) q^{4} +(1.05961 + 3.26115i) q^{5} +(-0.323795 - 0.996539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-5.18703 + 3.76860i) q^{8} +(-0.874954 + 2.69283i) q^{9} +8.75055 q^{10} +(-0.0297703 - 3.31649i) q^{11} -1.85279 q^{12} +(-0.672122 + 2.06858i) q^{13} +(-2.06456 + 1.49999i) q^{14} +(1.13904 + 0.827562i) q^{15} +(2.26726 + 6.97792i) q^{16} +(-1.39588 - 4.29606i) q^{17} +(5.84563 + 4.24710i) q^{18} +(1.96090 - 1.42468i) q^{19} +(4.78140 - 14.7156i) q^{20} -0.410598 q^{21} +(-8.07274 - 2.54311i) q^{22} +0.648403 q^{23} +(-0.813506 + 2.50371i) q^{24} +(-5.46724 + 3.97218i) q^{25} +(4.49050 + 3.26254i) q^{26} +(0.739900 + 2.27718i) q^{27} +(1.39441 + 4.29156i) q^{28} +(1.01366 + 0.736466i) q^{29} +(2.90677 - 2.11189i) q^{30} +(-2.48433 + 7.64599i) q^{31} +5.90061 q^{32} +(-0.810303 - 1.09449i) q^{33} -11.5275 q^{34} +(1.05961 - 3.26115i) q^{35} +(10.3364 - 7.50983i) q^{36} +(-4.05584 - 2.94674i) q^{37} +(-1.91140 - 5.88269i) q^{38} +(0.275972 + 0.849355i) q^{39} +(-17.7862 - 12.9224i) q^{40} +(2.12100 - 1.54100i) q^{41} +(-0.323795 + 0.996539i) q^{42} -1.46138 q^{43} +(-8.68774 + 12.1862i) q^{44} -9.70884 q^{45} +(0.511326 - 1.57370i) q^{46} +(4.07776 - 2.96267i) q^{47} +(2.43722 + 1.77074i) q^{48} +(0.309017 + 0.951057i) q^{49} +(5.32922 + 16.4017i) q^{50} +(-1.50051 - 1.09019i) q^{51} +(7.94021 - 5.76890i) q^{52} +(4.14022 - 12.7423i) q^{53} +6.11028 q^{54} +(10.7840 - 3.61128i) q^{55} +6.41153 q^{56} +(0.307538 - 0.946503i) q^{57} +(2.58680 - 1.87942i) q^{58} +(-6.20498 - 4.50818i) q^{59} +(-1.96324 - 6.04222i) q^{60} +(4.42970 + 13.6332i) q^{61} +(16.5980 + 12.0591i) q^{62} +(2.29066 - 1.66426i) q^{63} +(0.118654 - 0.365178i) q^{64} -7.45814 q^{65} +(-3.29537 + 1.10353i) q^{66} +6.22696 q^{67} +(-6.29876 + 19.3856i) q^{68} +(0.215387 - 0.156488i) q^{69} +(-7.07934 - 5.14344i) q^{70} +(1.30713 + 4.02294i) q^{71} +(-5.60979 - 17.2651i) q^{72} +(4.79356 + 3.48273i) q^{73} +(-10.3503 + 7.51991i) q^{74} +(-0.857452 + 2.63897i) q^{75} -10.9372 q^{76} +(-1.92530 + 2.70060i) q^{77} +2.27905 q^{78} +(3.01699 - 9.28534i) q^{79} +(-20.3536 + 14.7878i) q^{80} +(-6.07661 - 4.41492i) q^{81} +(-2.06746 - 6.36299i) q^{82} +(-2.58881 - 7.96754i) q^{83} +(1.49894 + 1.08904i) q^{84} +(12.5310 - 9.10432i) q^{85} +(-1.15243 + 3.54683i) q^{86} +0.514460 q^{87} +(12.6529 + 17.0906i) q^{88} +4.76249 q^{89} +(-7.65633 + 23.5637i) q^{90} +(1.75964 - 1.27845i) q^{91} +(-2.36707 - 1.71978i) q^{92} +(1.02006 + 3.13943i) q^{93} +(-3.97482 - 12.2332i) q^{94} +(6.72389 + 4.88520i) q^{95} +(1.96007 - 1.42407i) q^{96} +(-2.69021 + 8.27962i) q^{97} +2.55194 q^{98} +(8.95679 + 2.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19}+ \cdots + 16 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.788594	−	2.42704i	0.557620	−	1.71618i	−0.131303	−	0.991342i	$-0.541916\pi$
$2$	0.788594	−	2.42704i	0.557620	−	1.71618i	0.688922	−	0.724835i	$-0.258084\pi$
$3$	0.332181	−	0.241344i	0.191785	−	0.139340i	−0.487749	−	0.872984i	$-0.662182\pi$
$3$	0.332181	−	0.241344i	0.191785	−	0.139340i	0.679534	+	0.733644i	$0.262182\pi$
$4$	−3.65062	−	2.65233i	−1.82531	−	1.32616i
$5$	1.05961	+	3.26115i	0.473873	+	1.45843i	0.847472	+	0.530841i	$0.178124\pi$
$5$	1.05961	+	3.26115i	0.473873	+	1.45843i	−0.373599	+	0.927590i	$0.621876\pi$
$6$	−0.323795	−	0.996539i	−0.132189	−	0.406835i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−5.18703	+	3.76860i	−1.83389	+	1.33240i
$9$	−0.874954	+	2.69283i	−0.291651	+	0.897610i
$10$	8.75055			2.76717
$11$	−0.0297703	−	3.31649i	−0.00897607	−	0.999960i
$11$	−0.0297703	−	3.31649i	−0.00897607	−	0.999960i
$12$	−1.85279			−0.534854
$13$	−0.672122	+	2.06858i	−0.186413	+	0.573720i	−0.999970	−	0.00776501i	$-0.997528\pi$
$13$	−0.672122	+	2.06858i	−0.186413	+	0.573720i	0.813557	+	0.581486i	$0.197528\pi$
$14$	−2.06456	+	1.49999i	−0.551778	+	0.400890i
$15$	1.13904	+	0.827562i	0.294099	+	0.213675i
$16$	2.26726	+	6.97792i	0.566816	+	1.74448i
$17$	−1.39588	−	4.29606i	−0.338550	−	1.04195i	−0.964947	−	0.262445i	$-0.915471\pi$
$17$	−1.39588	−	4.29606i	−0.338550	−	1.04195i	0.626397	−	0.779504i	$-0.284529\pi$
$18$	5.84563	+	4.24710i	1.37783	+	1.00105i
$19$	1.96090	−	1.42468i	0.449862	−	0.326844i	−0.339679	−	0.940541i	$-0.610318\pi$
$19$	1.96090	−	1.42468i	0.449862	−	0.326844i	0.789541	+	0.613697i	$0.210318\pi$
$20$	4.78140	−	14.7156i	1.06915	−	3.29052i
$21$	−0.410598			−0.0895999
$22$	−8.07274	−	2.54311i	−1.72111	−	0.542193i
$23$	0.648403			0.135201			0.0676006	−	0.997712i	$-0.478466\pi$
$23$	0.648403			0.135201			0.0676006	+	0.997712i	$0.478466\pi$
$24$	−0.813506	+	2.50371i	−0.166056	+	0.511069i
$25$	−5.46724	+	3.97218i	−1.09345	+	0.794437i
$26$	4.49050	+	3.26254i	0.880659	+	0.639836i
$27$	0.739900	+	2.27718i	0.142394	+	0.438243i
$28$	1.39441	+	4.29156i	0.263519	+	0.811028i
$29$	1.01366	+	0.736466i	0.188232	+	0.136758i	0.677910	−	0.735145i	$-0.262886\pi$
$29$	1.01366	+	0.736466i	0.188232	+	0.136758i	−0.489678	+	0.871903i	$0.662886\pi$
$30$	2.90677	−	2.11189i	0.530700	−	0.385576i
$31$	−2.48433	+	7.64599i	−0.446199	+	1.37326i	0.434964	+	0.900448i	$0.356761\pi$
$31$	−2.48433	+	7.64599i	−0.446199	+	1.37326i	−0.881163	+	0.472812i	$0.843239\pi$
$32$	5.90061			1.04309
$33$	−0.810303	−	1.09449i	−0.141056	−	0.190526i
$34$	−11.5275			−1.97695
$35$	1.05961	−	3.26115i	0.179107	−	0.551235i
$36$	10.3364	−	7.50983i	1.72273	−	1.25164i
$37$	−4.05584	−	2.94674i	−0.666776	−	0.484441i	0.202169	−	0.979351i	$-0.435201\pi$
$37$	−4.05584	−	2.94674i	−0.666776	−	0.484441i	−0.868944	+	0.494910i	$0.835201\pi$
$38$	−1.91140	−	5.88269i	−0.310070	−	0.954298i
$39$	0.275972	+	0.849355i	0.0441909	+	0.136006i
$40$	−17.7862	−	12.9224i	−2.81225	−	2.04322i
$41$	2.12100	−	1.54100i	0.331245	−	0.240664i	−0.409714	−	0.912214i	$-0.634371\pi$
$41$	2.12100	−	1.54100i	0.331245	−	0.240664i	0.740959	+	0.671551i	$0.234371\pi$
$42$	−0.323795	+	0.996539i	−0.0499627	+	0.153769i
$43$	−1.46138			−0.222858			−0.111429	−	0.993772i	$-0.535543\pi$
$43$	−1.46138			−0.222858			−0.111429	+	0.993772i	$0.535543\pi$
$44$	−8.68774	+	12.1862i	−1.30973	+	1.83714i
$45$	−9.70884			−1.44731
$46$	0.511326	−	1.57370i	0.0753909	−	0.232029i
$47$	4.07776	−	2.96267i	0.594802	−	0.432149i	−0.249228	−	0.968445i	$-0.580177\pi$
$47$	4.07776	−	2.96267i	0.594802	−	0.432149i	0.844030	+	0.536296i	$0.180177\pi$
$48$	2.43722	+	1.77074i	0.351782	+	0.255585i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	5.32922	+	16.4017i	0.753666	+	2.31954i
$51$	−1.50051	−	1.09019i	−0.210114	−	0.152656i
$52$	7.94021	−	5.76890i	1.10111	−	0.800002i
$53$	4.14022	−	12.7423i	0.568703	−	1.75029i	−0.0879820	−	0.996122i	$-0.528042\pi$
$53$	4.14022	−	12.7423i	0.568703	−	1.75029i	0.656685	−	0.754165i	$-0.271958\pi$
$54$	6.11028			0.831504
$55$	10.7840	−	3.61128i	1.45412	−	0.486945i
$56$	6.41153			0.856776
$57$	0.307538	−	0.946503i	0.0407343	−	0.125367i
$58$	2.58680	−	1.87942i	0.339663	−	0.246780i
$59$	−6.20498	−	4.50818i	−0.807820	−	0.586916i	0.105378	−	0.994432i	$-0.466395\pi$
$59$	−6.20498	−	4.50818i	−0.807820	−	0.586916i	−0.913198	+	0.407517i	$0.866395\pi$
$60$	−1.96324	−	6.04222i	−0.253453	−	0.780047i
$61$	4.42970	+	13.6332i	0.567166	+	1.74556i	0.661428	+	0.750009i	$0.269951\pi$
$61$	4.42970	+	13.6332i	0.567166	+	1.74556i	−0.0942623	+	0.995547i	$0.530049\pi$
$62$	16.5980	+	12.0591i	2.10795	+	1.53151i
$63$	2.29066	−	1.66426i	0.288596	−	0.209677i
$64$	0.118654	−	0.365178i	0.0148317	−	0.0456473i
$65$	−7.45814			−0.925068
$66$	−3.29537	+	1.10353i	−0.405632	+	0.135835i
$67$	6.22696			0.760744			0.380372	−	0.924834i	$-0.375796\pi$
$67$	6.22696			0.760744			0.380372	+	0.924834i	$0.375796\pi$
$68$	−6.29876	+	19.3856i	−0.763837	+	2.35085i
$69$	0.215387	−	0.156488i	0.0259295	−	0.0188389i
$70$	−7.07934	−	5.14344i	−0.846144	−	0.614759i
$71$	1.30713	+	4.02294i	0.155128	+	0.477435i	0.998174	−	0.0604069i	$-0.0192398\pi$
$71$	1.30713	+	4.02294i	0.155128	+	0.477435i	−0.843046	+	0.537842i	$0.819240\pi$
$72$	−5.60979	−	17.2651i	−0.661120	−	2.03472i
$73$	4.79356	+	3.48273i	0.561044	+	0.407622i	0.831841	−	0.555014i	$-0.187287\pi$
$73$	4.79356	+	3.48273i	0.561044	+	0.407622i	−0.270797	+	0.962637i	$0.587287\pi$
$74$	−10.3503	+	7.51991i	−1.20319	+	0.874172i
$75$	−0.857452	+	2.63897i	−0.0990101	+	0.304722i
$76$	−10.9372			−1.25459
$77$	−1.92530	+	2.70060i	−0.219408	+	0.307762i
$78$	2.27905			0.258051
$79$	3.01699	−	9.28534i	0.339438	−	1.04468i	−0.625057	−	0.780579i	$-0.714924\pi$
$79$	3.01699	−	9.28534i	0.339438	−	1.04468i	0.964495	−	0.264103i	$-0.0850758\pi$
$80$	−20.3536	+	14.7878i	−2.27561	+	1.65332i
$81$	−6.07661	−	4.41492i	−0.675179	−	0.490546i
$82$	−2.06746	−	6.36299i	−0.228313	−	0.702674i
$83$	−2.58881	−	7.96754i	−0.284159	−	0.874551i	−0.986650	−	0.162858i	$-0.947929\pi$
$83$	−2.58881	−	7.96754i	−0.284159	−	0.874551i	0.702491	−	0.711693i	$-0.252071\pi$
$84$	1.49894	+	1.08904i	0.163547	+	0.118824i
$85$	12.5310	−	9.10432i	1.35918	−	0.987503i
$86$	−1.15243	+	3.54683i	−0.124270	+	0.382465i
$87$	0.514460			0.0551559
$88$	12.6529	+	17.0906i	1.34881	+	1.82186i
$89$	4.76249			0.504823			0.252412	−	0.967620i	$-0.418776\pi$
$89$	4.76249			0.504823			0.252412	+	0.967620i	$0.418776\pi$
$90$	−7.65633	+	23.5637i	−0.807048	+	2.48384i
$91$	1.75964	−	1.27845i	0.184460	−	0.134018i
$92$	−2.36707	−	1.71978i	−0.246784	−	0.179299i
$93$	1.02006	+	3.13943i	0.105776	+	0.325544i
$94$	−3.97482	−	12.2332i	−0.409971	−	1.26176i
$95$	6.72389	+	4.88520i	0.689857	+	0.501210i
$96$	1.96007	−	1.42407i	0.200049	−	0.145344i
$97$	−2.69021	+	8.27962i	−0.273150	+	0.840668i	0.716554	+	0.697532i	$0.245719\pi$
$97$	−2.69021	+	8.27962i	−0.273150	+	0.840668i	−0.989703	+	0.143136i	$0.954281\pi$
$98$	2.55194			0.257785
$99$	8.95679	+	2.82161i	0.900192	+	0.283582i
$100$	30.4943			3.04943
$101$	−1.78446	+	5.49199i	−0.177560	+	0.546474i	−0.999741	−	0.0227524i	$-0.992757\pi$
$101$	−1.78446	+	5.49199i	−0.177560	+	0.546474i	0.822181	+	0.569226i	$0.192757\pi$
$102$	−3.82922	+	2.78209i	−0.379149	+	0.275468i
$103$	3.75463	+	2.72790i	0.369955	+	0.268788i	0.757192	−	0.653192i	$-0.226571\pi$
$103$	3.75463	+	2.72790i	0.369955	+	0.268788i	−0.387237	+	0.921980i	$0.626571\pi$
$104$	−4.30933	−	13.2627i	−0.422564	−	1.30052i
$105$	−0.435075	−	1.33902i	−0.0424590	−	0.130675i
$106$	−27.6611	−	20.0970i	−2.68668	−	1.95199i
$107$	3.25388	−	2.36409i	0.314565	−	0.228545i	−0.419288	−	0.907853i	$-0.637720\pi$
$107$	3.25388	−	2.36409i	0.314565	−	0.228545i	0.733853	+	0.679309i	$0.237720\pi$
$108$	3.33873	−	10.2756i	0.321270	−	0.988766i
$109$	−6.14762			−0.588835			−0.294418	−	0.955677i	$-0.595126\pi$
$109$	−6.14762			−0.588835			−0.294418	+	0.955677i	$0.595126\pi$
$110$	−0.260506	−	29.0211i	−0.0248383	−	2.76706i
$111$	−2.05845			−0.195379
$112$	2.26726	−	6.97792i	0.214236	−	0.659352i
$113$	2.00504	−	1.45675i	0.188618	−	0.137039i	−0.489469	−	0.872021i	$-0.662809\pi$
$113$	2.00504	−	1.45675i	0.188618	−	0.137039i	0.678087	+	0.734982i	$0.262809\pi$
$114$	−2.05468	−	1.49281i	−0.192438	−	0.139815i
$115$	0.687055	+	2.11454i	0.0640682	+	0.197182i
$116$	−1.74713	−	5.37711i	−0.162217	−	0.499252i
$117$	−4.98226	−	3.61982i	−0.460610	−	0.334653i
$118$	−15.8348	+	11.5046i	−1.45771	+	1.05909i
$119$	−1.39588	+	4.29606i	−0.127960	+	0.393820i
$120$	−9.02699			−0.824048
$121$	−10.9982	+	0.197466i	−0.999839	+	0.0179514i
$122$	36.5817			3.31195
$123$	0.332647	−	1.02378i	0.0299937	−	0.0923112i
$124$	29.3490	−	21.3233i	2.63562	−	1.91489i
$125$	−4.87654	−	3.54301i	−0.436171	−	0.316897i
$126$	−2.23283	−	6.87195i	−0.198916	−	0.612202i
$127$	−2.14890	−	6.61362i	−0.190684	−	0.586864i	0.809316	−	0.587373i	$-0.199838\pi$
$127$	−2.14890	−	6.61362i	−0.190684	−	0.586864i	−1.00000		0.000509338i	$0.999838\pi$
$128$	8.75466	+	6.36063i	0.773810	+	0.562206i
$129$	−0.485443	+	0.352695i	−0.0427408	+	0.0310530i
$130$	−5.88144	+	18.1012i	−0.515836	+	1.58758i
$131$	−20.9388			−1.82943			−0.914715	−	0.404101i	$-0.867585\pi$
$131$	−20.9388			−1.82943			−0.914715	+	0.404101i	$0.867585\pi$
$132$	0.0551580	+	6.14475i	0.00480089	+	0.534832i
$133$	−2.42381			−0.210171
$134$	4.91054	−	15.1131i	0.424206	−	1.30557i
$135$	−6.64221	+	4.82585i	−0.571671	+	0.415343i
$136$	23.4306	+	17.0233i	2.00916	+	1.45974i
$137$	2.82332	+	8.68927i	0.241212	+	0.742375i	0.996236	+	0.0866778i	$0.0276251\pi$
$137$	2.82332	+	8.68927i	0.241212	+	0.742375i	−0.755024	+	0.655697i	$0.772375\pi$
$138$	−0.209950	−	0.646158i	−0.0178721	−	0.0550047i
$139$	−8.69844	−	6.31979i	−0.737792	−	0.536037i	0.154227	−	0.988035i	$-0.450711\pi$
$139$	−8.69844	−	6.31979i	−0.737792	−	0.536037i	−0.892019	+	0.451998i	$0.850711\pi$
$140$	−12.5179	+	9.09477i	−1.05795	+	0.768648i
$141$	0.639534	−	1.96828i	0.0538585	−	0.165759i
$142$	10.7946			0.905865
$143$	6.88043	+	2.16750i	0.575371	+	0.181256i
$144$	−20.7741			−1.73118
$145$	−1.32764	+	4.08606i	−0.110255	+	0.339329i
$146$	12.2329	−	8.88772i	1.01240	−	0.735553i
$147$	0.332181	+	0.241344i	0.0273978	+	0.0199057i
$148$	6.99059	+	21.5148i	0.574623	+	1.76851i
$149$	3.32361	+	10.2290i	0.272281	+	0.837993i	0.989926	+	0.141585i	$0.0452198\pi$
$149$	3.32361	+	10.2290i	0.272281	+	0.837993i	−0.717646	+	0.696409i	$0.754780\pi$
$150$	5.72870	+	4.16214i	0.467746	+	0.339838i
$151$	6.20049	−	4.50492i	0.504588	−	0.366605i	−0.306178	−	0.951974i	$-0.599050\pi$
$151$	6.20049	−	4.50492i	0.504588	−	0.366605i	0.810767	+	0.585369i	$0.199050\pi$
$152$	−4.80222	+	14.7797i	−0.389512	+	1.19879i
$153$	12.7899			1.03400
$154$	5.03618	+	6.80246i	0.405827	+	0.548157i
$155$	−27.5671			−2.21425
$156$	1.24530	−	3.83264i	0.0997037	−	0.306857i
$157$	−14.8447	+	10.7853i	−1.18473	+	0.860760i	−0.992698	−	0.120628i	$-0.961509\pi$
$157$	−14.8447	+	10.7853i	−1.18473	+	0.860760i	−0.192036	+	0.981388i	$0.561509\pi$
$158$	−20.1567	−	14.6447i	−1.60358	−	1.16507i
$159$	−1.69997	−	5.23196i	−0.134816	−	0.414921i
$160$	6.25236	+	19.2428i	0.494292	+	1.52128i
$161$	−0.524569	−	0.381121i	−0.0413418	−	0.0300366i
$162$	−15.5072	+	11.2666i	−1.21836	+	0.885189i
$163$	0.116680	−	0.359105i	0.00913909	−	0.0281272i	−0.946383	−	0.323047i	$-0.895293\pi$
$163$	0.116680	−	0.359105i	0.00913909	−	0.0281272i	0.955522	+	0.294920i	$0.0952929\pi$
$164$	−11.8302			−0.923784
$165$	2.71069	−	3.80226i	0.211027	−	0.296005i
$166$	−21.3791			−1.65934
$167$	−0.0352708	+	0.108552i	−0.00272934	+	0.00840003i	−0.952412	−	0.304814i	$-0.901406\pi$
$167$	−0.0352708	+	0.108552i	−0.00272934	+	0.00840003i	0.949683	+	0.313214i	$0.101406\pi$
$168$	2.12979	−	1.54738i	0.164317	−	0.119383i
$169$	6.68995	+	4.86053i	0.514612	+	0.373887i
$170$	−12.2147	−	37.5929i	−0.936823	−	2.88325i
$171$	2.12072	+	6.52691i	0.162176	+	0.499125i
$172$	5.33494	+	3.87606i	0.406785	+	0.295547i
$173$	10.7608	−	7.81814i	0.818125	−	0.594403i	−0.0980499	−	0.995181i	$-0.531260\pi$
$173$	10.7608	−	7.81814i	0.818125	−	0.594403i	0.916175	+	0.400779i	$0.131260\pi$
$174$	0.405700	−	1.24861i	0.0307560	−	0.0946572i
$175$	6.75788			0.510848
$176$	23.0747	−	7.72710i	1.73932	−	0.582452i
$177$	−3.14920			−0.236708
$178$	3.75567	−	11.5588i	0.281500	−	0.866366i
$179$	−9.17505	+	6.66606i	−0.685775	+	0.498245i	−0.875269	−	0.483637i	$-0.839315\pi$
$179$	−9.17505	+	6.66606i	−0.685775	+	0.498245i	0.189493	+	0.981882i	$0.439315\pi$
$180$	35.4432	+	25.7510i	2.64178	+	1.91937i
$181$	3.63307	+	11.1814i	0.270044	+	0.831109i	0.990488	+	0.137597i	$0.0439378\pi$
$181$	3.63307	+	11.1814i	0.270044	+	0.831109i	−0.720445	+	0.693512i	$0.756062\pi$
$182$	−1.71522	−	5.27889i	−0.127140	−	0.391298i
$183$	4.76176	+	3.45962i	0.351999	+	0.255742i
$184$	−3.36329	+	2.44357i	−0.247945	+	0.180142i
$185$	5.31215	−	16.3491i	0.390557	−	1.20201i
$186$	8.42394			0.617673
$187$	−14.2063	+	4.75731i	−1.03887	+	0.347889i
$188$	−22.7443			−1.65880
$189$	0.739900	−	2.27718i	0.0538198	−	0.165640i
$190$	17.1590	−	12.4667i	1.24484	−	0.904432i
$191$	18.2307	+	13.2454i	1.31913	+	0.958402i	0.999943	+	0.0107095i	$0.00340899\pi$
$191$	18.2307	+	13.2454i	1.31913	+	0.958402i	0.319185	+	0.947693i	$0.396591\pi$
$192$	−0.0487190	−	0.149942i	−0.00351599	−	0.0108211i
$193$	1.06402	+	3.27471i	0.0765896	+	0.235718i	0.982020	−	0.188776i	$-0.0604519\pi$
$193$	1.06402	+	3.27471i	0.0765896	+	0.235718i	−0.905431	+	0.424494i	$0.860452\pi$
$194$	17.9735	+	13.0585i	1.29042	+	0.937546i
$195$	−2.47745	+	1.79997i	−0.177414	+	0.128899i
$196$	1.39441	−	4.29156i	0.0996008	−	0.306540i
$197$	−2.18213			−0.155470			−0.0777352	−	0.996974i	$-0.524769\pi$
$197$	−2.18213			−0.155470			−0.0777352	+	0.996974i	$0.524769\pi$
$198$	13.9114	−	19.5134i	0.988643	−	1.38676i
$199$	2.33434			0.165477			0.0827386	−	0.996571i	$-0.473633\pi$
$199$	2.33434			0.165477			0.0827386	+	0.996571i	$0.473633\pi$
$200$	13.3892	−	41.2077i	0.946759	−	2.91382i
$201$	2.06848	−	1.50284i	0.145899	−	0.106002i
$202$	11.9221	+	8.66190i	0.838835	+	0.609449i
$203$	−0.387183	−	1.19163i	−0.0271749	−	0.0836359i
$204$	2.58626	+	7.95969i	0.181075	+	0.557290i
$205$	7.27287	+	5.28405i	0.507959	+	0.369054i
$206$	9.58160	−	6.96144i	0.667582	−	0.485027i
$207$	−0.567322	+	1.74604i	−0.0394316	+	0.121358i
$208$	−15.9583			−1.10651
$209$	−4.78332	−	6.46091i	−0.330869	−	0.446910i
$210$	−3.59296			−0.247938
$211$	−4.22360	+	12.9989i	−0.290765	+	0.894882i	0.693846	+	0.720123i	$0.255915\pi$
$211$	−4.22360	+	12.9989i	−0.290765	+	0.894882i	−0.984611	+	0.174759i	$0.944085\pi$
$212$	−48.9111	+	35.5360i	−3.35923	+	2.44062i
$213$	1.40511	+	1.02088i	0.0962768	+	0.0699492i
$214$	−3.17174	−	9.76162i	−0.216816	−	0.667290i
$215$	−1.54850	−	4.76578i	−0.105607	−	0.325024i
$216$	−12.4197	−	9.02341i	−0.845051	−	0.613965i
$217$	6.50406	−	4.72548i	0.441525	−	0.320786i
$218$	−4.84798	+	14.9205i	−0.328346	+	1.01055i
$219$	2.43286			0.164398
$220$	−48.9467	−	15.4194i	−3.29998	−	1.03958i
$221$	9.82495			0.660897
$222$	−1.62328	+	4.99594i	−0.108947	+	0.335306i
$223$	4.34333	−	3.15561i	0.290851	−	0.211315i	−0.432786	−	0.901497i	$-0.642469\pi$
$223$	4.34333	−	3.15561i	0.290851	−	0.211315i	0.723636	+	0.690181i	$0.242469\pi$
$224$	−4.77369	−	3.46829i	−0.318956	−	0.231735i
$225$	−5.91283	−	18.1978i	−0.394189	−	1.21319i
$226$	−1.95442	−	6.01510i	−0.130006	−	0.400119i
$227$	−8.58608	−	6.23815i	−0.569878	−	0.414041i	0.265183	−	0.964198i	$-0.414568\pi$
$227$	−8.58608	−	6.23815i	−0.569878	−	0.414041i	−0.835061	+	0.550158i	$0.814568\pi$
$228$	−3.63314	+	2.63963i	−0.240610	+	0.174814i
$229$	6.99644	−	21.5328i	0.462338	−	1.42293i	−0.399962	−	0.916532i	$-0.630977\pi$
$229$	6.99644	−	21.5328i	0.462338	−	1.42293i	0.862300	−	0.506398i	$-0.169023\pi$
$230$	5.67388			0.374125
$231$	0.0122236	+	1.36175i	0.000804255	+	0.0895963i
$232$	−8.03333			−0.527414
$233$	4.58075	−	14.0981i	0.300095	−	0.923598i	−0.681367	−	0.731942i	$-0.738614\pi$
$233$	4.58075	−	14.0981i	0.300095	−	0.923598i	0.981462	−	0.191656i	$-0.0613857\pi$
$234$	−12.7144	+	9.23757i	−0.831168	+	0.603879i
$235$	13.9825	+	10.1589i	0.912121	+	0.662694i
$236$	10.6948	+	32.9153i	0.696174	+	2.14260i
$237$	−1.23877	−	3.81254i	−0.0804668	−	0.247651i
$238$	9.32595	+	6.77570i	0.604511	+	0.439203i
$239$	−1.58511	+	1.15165i	−0.102532	+	0.0744938i	−0.637870	−	0.770144i	$-0.720184\pi$
$239$	−1.58511	+	1.15165i	−0.102532	+	0.0744938i	0.535338	+	0.844638i	$0.320184\pi$
$240$	−3.19215	+	9.82444i	−0.206053	+	0.634165i
$241$	0.790252			0.0509046			0.0254523	−	0.999676i	$-0.491897\pi$
$241$	0.790252			0.0509046			0.0254523	+	0.999676i	$0.491897\pi$
$242$	−8.19387	+	26.8489i	−0.526722	+	1.72591i
$243$	−10.2671			−0.658638
$244$	19.9886	−	61.5187i	1.27964	−	3.93833i
$245$	−2.77410	+	2.01550i	−0.177231	+	0.128766i
$246$	−2.22244	−	1.61469i	−0.141697	−	0.102949i
$247$	1.62910	+	5.01384i	0.103657	+	0.319023i
$248$	−15.9284	−	49.0224i	−1.01145	−	3.11293i
$249$	−2.78287	−	2.02187i	−0.176357	−	0.128131i
$250$	−12.4446	+	9.04157i	−0.787069	+	0.571839i
$251$	−6.37051	+	19.6064i	−0.402103	+	1.23755i	0.521187	+	0.853442i	$0.325489\pi$
$251$	−6.37051	+	19.6064i	−0.402103	+	1.23755i	−0.923290	+	0.384103i	$0.874511\pi$
$252$	−12.7765			−0.804842
$253$	−0.0193031	−	2.15042i	−0.00121358	−	0.135196i
$254$	−17.7461			−1.11349
$255$	1.96530	−	6.04857i	0.123072	−	0.378776i
$256$	22.9627	−	16.6833i	1.43517	−	1.04271i
$257$	−4.19039	−	3.04450i	−0.261389	−	0.189911i	0.449370	−	0.893346i	$-0.351649\pi$
$257$	−4.19039	−	3.04450i	−0.261389	−	0.189911i	−0.710759	+	0.703435i	$0.751649\pi$
$258$	0.473188	+	1.45632i	0.0294594	+	0.0906667i
$259$	1.54919	+	4.76792i	0.0962621	+	0.296264i
$260$	27.2268	+	19.7814i	1.68853	+	1.22679i
$261$	−2.87008	+	2.08524i	−0.177654	+	0.129073i
$262$	−16.5122	+	50.8193i	−1.02013	+	3.13962i
$263$	23.1920			1.43008			0.715041	−	0.699083i	$-0.246408\pi$
$263$	23.1920			1.43008			0.715041	+	0.699083i	$0.246408\pi$
$264$	8.32776	+	2.62345i	0.512538	+	0.161462i
$265$	45.9415			2.82217
$266$	−1.91140	+	5.88269i	−0.117196	+	0.360691i
$267$	1.58201	−	1.14940i	0.0968174	−	0.0703420i
$268$	−22.7322	−	16.5159i	−1.38859	−	1.00887i
$269$	5.76625	+	17.7467i	0.351575	+	1.08204i	0.957969	+	0.286871i	$0.0926152\pi$
$269$	5.76625	+	17.7467i	0.351575	+	1.08204i	−0.606395	+	0.795164i	$0.707385\pi$
$270$	6.47453	+	19.9266i	0.394027	+	1.21269i
$271$	−24.4556	−	17.7680i	−1.48557	−	1.07933i	−0.975708	−	0.219074i	$-0.929696\pi$
$271$	−24.4556	−	17.7680i	−1.48557	−	1.07933i	−0.509862	−	0.860256i	$-0.670304\pi$
$272$	26.8128	−	19.4806i	1.62576	−	1.18119i
$273$	0.275972	−	0.849355i	0.0167026	−	0.0514053i
$274$	23.3157			1.40855
$275$	13.3365	+	18.0138i	0.804219	+	1.08627i
$276$	−1.20135			−0.0723129
$277$	4.16928	−	12.8317i	0.250508	−	0.770983i	−0.744174	−	0.667986i	$-0.767157\pi$
$277$	4.16928	−	12.8317i	0.250508	−	0.770983i	0.994682	−	0.102997i	$-0.0328434\pi$
$278$	−22.1979	+	16.1277i	−1.33134	+	0.967277i
$279$	−18.4157	−	13.3798i	−1.10252	−	0.801025i
$280$	6.79373	+	20.9090i	0.406003	+	1.24955i
$281$	2.50388	+	7.70614i	0.149369	+	0.459710i	0.997547	−	0.0700014i	$-0.0223004\pi$
$281$	2.50388	+	7.70614i	0.149369	+	0.459710i	−0.848178	+	0.529711i	$0.822300\pi$
$282$	−4.27277	−	3.10435i	−0.254440	−	0.184861i
$283$	−8.08303	+	5.87266i	−0.480486	+	0.349094i	−0.801514	−	0.597976i	$-0.795972\pi$
$283$	−8.08303	+	5.87266i	−0.480486	+	0.349094i	0.321028	+	0.947070i	$0.395972\pi$
$284$	5.89831	−	18.1531i	0.350000	−	1.07719i
$285$	3.41256			0.202143
$286$	10.6865	−	14.9898i	0.631905	−	0.886366i
$287$	−2.62170			−0.154754
$288$	−5.16276	+	15.8893i	−0.304219	+	0.936288i
$289$	−2.75441	+	2.00120i	−0.162024	+	0.117717i
$290$	8.87007	+	6.44449i	0.520869	+	0.378433i
$291$	1.10460	+	3.39960i	0.0647526	+	0.199288i
$292$	−8.26212	−	25.4282i	−0.483504	−	1.48807i
$293$	−24.8608	−	18.0624i	−1.45238	−	1.05522i	−0.985267	−	0.171022i	$-0.945293\pi$
$293$	−24.8608	−	18.0624i	−1.45238	−	1.05522i	−0.467116	−	0.884196i	$-0.654707\pi$
$294$	0.847707	−	0.615895i	0.0494393	−	0.0359197i
$295$	8.12699	−	25.0123i	0.473172	−	1.45627i
$296$	32.1429			1.86827
$297$	7.53021	−	2.52166i	0.436947	−	0.146322i
$298$	27.4472			1.58997
$299$	−0.435806	+	1.34127i	−0.0252033	+	0.0775678i
$300$	10.1296	−	7.35961i	0.584835	−	0.424907i
$301$	1.18228	+	0.858978i	0.0681456	+	0.0495107i
$302$	−6.04396	−	18.6014i	−0.347791	−	1.07039i
$303$	0.732695	+	2.25500i	0.0420922	+	0.129546i
$304$	14.3872	+	10.4529i	0.825163	+	0.599516i
$305$	−39.7662	+	28.8919i	−2.27701	+	1.65434i
$306$	10.0860	−	31.0416i	0.576580	−	1.77453i
$307$	−20.0677			−1.14532			−0.572661	−	0.819792i	$-0.694089\pi$
$307$	−20.0677			−1.14532			−0.572661	+	0.819792i	$0.694089\pi$
$308$	14.1914	−	4.75231i	0.808630	−	0.270788i
$309$	1.90558			0.108405
$310$	−21.7393	+	66.9066i	−1.23471	+	3.80004i
$311$	18.9846	−	13.7931i	1.07652	−	0.782135i	0.0994439	−	0.995043i	$-0.468294\pi$
$311$	18.9846	−	13.7931i	1.07652	−	0.782135i	0.977072	+	0.212908i	$0.0682936\pi$
$312$	−4.63235	−	3.36560i	−0.262255	−	0.190540i
$313$	−4.53420	−	13.9548i	−0.256288	−	0.788774i	−0.993573	−	0.113192i	$-0.963892\pi$
$313$	−4.53420	−	13.9548i	−0.256288	−	0.788774i	0.737285	−	0.675582i	$-0.236108\pi$
$314$	14.4699	+	44.5338i	0.816585	+	2.51319i
$315$	7.85461	+	5.70671i	0.442557	+	0.321537i
$316$	−35.6416	+	25.8952i	−2.00500	+	1.45672i
$317$	5.57804	−	17.1675i	0.313294	−	0.964220i	−0.663157	−	0.748481i	$-0.730784\pi$
$317$	5.57804	−	17.1675i	0.313294	−	0.964220i	0.976451	−	0.215740i	$-0.0692163\pi$
$318$	−14.0388			−0.787255
$319$	2.41231	−	3.38372i	0.135063	−	0.189452i
$320$	1.31663			0.0736018
$321$	0.510322	−	1.57061i	0.0284834	−	0.0876628i
$322$	−1.33867	+	0.972600i	−0.0746011	+	0.0542009i
$323$	−8.85770	−	6.43549i	−0.492855	−	0.358080i
$324$	10.4736	+	32.2343i	0.581865	+	1.79080i
$325$	−4.54212	−	13.9792i	−0.251952	−	0.775427i
$326$	−0.779548	−	0.566375i	−0.0431752	−	0.0313686i
$327$	−2.04212	+	1.48369i	−0.112930	+	0.0820482i
$328$	−5.19431	+	15.9864i	−0.286808	+	0.882703i
$329$	−5.04039			−0.277886
$330$	−7.09060	−	9.57739i	−0.390325	−	0.527218i
$331$	−19.8300			−1.08996			−0.544979	−	0.838450i	$-0.683462\pi$
$331$	−19.8300			−1.08996			−0.544979	+	0.838450i	$0.683462\pi$
$332$	−11.6818	+	35.9528i	−0.641120	+	1.97317i
$333$	11.4837	−	8.34343i	0.629305	−	0.457217i
$334$	0.235647	+	0.171207i	0.0128940	+	0.00936805i
$335$	6.59816	+	20.3071i	0.360496	+	1.10949i
$336$	−0.930935	−	2.86512i	−0.0507867	−	0.156305i
$337$	15.7826	+	11.4667i	0.859734	+	0.624633i	0.927812	−	0.373047i	$-0.121687\pi$
$337$	15.7826	+	11.4667i	0.859734	+	0.624633i	−0.0680789	+	0.997680i	$0.521687\pi$
$338$	17.0724	−	12.4038i	0.928615	−	0.674678i
$339$	0.314460	−	0.967808i	0.0170791	−	0.0525641i
$340$	−69.8936			−3.79051
$341$	25.4318	+	8.01164i	1.37721	+	0.433855i
$342$	17.5135			0.947020
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	7.58023	−	5.50736i	0.408698	−	0.296937i
$345$	0.738557	+	0.536593i	0.0397626	+	0.0288892i
$346$	−10.4891	−	32.2821i	−0.563898	−	1.73550i
$347$	−8.79003	−	27.0529i	−0.471873	−	1.45228i	−0.850128	−	0.526575i	$-0.823476\pi$
$347$	−8.79003	−	27.0529i	−0.471873	−	1.45228i	0.378255	−	0.925701i	$-0.376524\pi$
$348$	−1.87809	−	1.36452i	−0.100676	−	0.0731457i
$349$	−16.2506	+	11.8067i	−0.869873	+	0.632000i	−0.930553	−	0.366158i	$-0.880673\pi$
$349$	−16.2506	+	11.8067i	−0.869873	+	0.632000i	0.0606798	+	0.998157i	$0.480673\pi$
$350$	5.32922	−	16.4017i	0.284859	−	0.876705i
$351$	−5.20782			−0.277973
$352$	−0.175663	−	19.5693i	−0.00936286	−	1.04305i
$353$	8.99700			0.478862			0.239431	−	0.970913i	$-0.423039\pi$
$353$	8.99700			0.478862			0.239431	+	0.970913i	$0.423039\pi$
$354$	−2.48344	+	7.64324i	−0.131993	+	0.406233i
$355$	−11.7344	+	8.52550i	−0.622795	+	0.452487i
$356$	−17.3860	−	12.6317i	−0.921458	−	0.669479i
$357$	0.573144	+	1.76396i	0.0303340	+	0.0933585i
$358$	8.94342	+	27.5250i	0.472675	+	1.45474i
$359$	−7.65816	−	5.56398i	−0.404182	−	0.293656i	0.367060	−	0.930197i	$-0.380364\pi$
$359$	−7.65816	−	5.56398i	−0.404182	−	0.293656i	−0.771242	+	0.636542i	$0.780364\pi$
$360$	50.3601	−	36.5887i	2.65421	−	1.92839i
$361$	−4.05589	+	12.4828i	−0.213468	+	0.656987i
$362$	30.0028			1.57691
$363$	−3.60574	+	2.71995i	−0.189253	+	0.142760i
$364$	−9.81464			−0.514427
$365$	−6.27838	+	19.3229i	−0.328625	+	1.01141i
$366$	12.1517	−	8.82875i	0.635181	−	0.461486i
$367$	−1.11251	−	0.808283i	−0.0580723	−	0.0421920i	0.558370	−	0.829592i	$-0.311427\pi$
$367$	−1.11251	−	0.808283i	−0.0580723	−	0.0421920i	−0.616443	+	0.787400i	$0.711427\pi$
$368$	1.47010	+	4.52450i	0.0766343	+	0.235856i
$369$	2.29387	+	7.05981i	0.119414	+	0.367519i
$370$	−35.4908	−	25.7856i	−1.84508	−	1.34053i
$371$	−10.8392	+	7.87516i	−0.562745	+	0.408858i
$372$	4.60294	−	14.1664i	0.238651	−	0.734493i
$373$	5.07180			0.262608			0.131304	−	0.991342i	$-0.458084\pi$
$373$	5.07180			0.262608			0.131304	+	0.991342i	$0.458084\pi$
$374$	0.343177	+	38.2309i	0.0177453	+	1.97687i
$375$	−2.47498			−0.127807
$376$	−9.98637	+	30.7349i	−0.515008	+	1.58503i
$377$	−2.20474	+	1.60184i	−0.113550	+	0.0824989i
$378$	−4.94332	−	3.59154i	−0.254257	−	0.184729i
$379$	−8.64698	−	26.6127i	−0.444166	−	1.36700i	−0.883396	−	0.468627i	$-0.844749\pi$
$379$	−8.64698	−	26.6127i	−0.444166	−	1.36700i	0.439231	−	0.898374i	$-0.355251\pi$
$380$	−11.5892	−	35.6679i	−0.594514	−	1.82973i
$381$	−2.30998	−	1.67830i	−0.118344	−	0.0859817i
$382$	46.5237	−	33.8014i	2.38036	−	1.72943i
$383$	−9.66622	+	29.7496i	−0.493921	+	1.52013i	0.324711	+	0.945813i	$0.394733\pi$
$383$	−9.66622	+	29.7496i	−0.493921	+	1.52013i	−0.818632	+	0.574318i	$0.805267\pi$
$384$	4.44323			0.226742
$385$	−10.8471	−	3.41711i	−0.552821	−	0.174152i
$386$	8.78692			0.447243
$387$	1.27864	−	3.93525i	0.0649969	−	0.200040i
$388$	31.7812	−	23.0904i	1.61345	−	1.17224i
$389$	−8.61893	−	6.26202i	−0.436997	−	0.317497i	0.347444	−	0.937701i	$-0.387050\pi$
$389$	−8.61893	−	6.26202i	−0.436997	−	0.317497i	−0.784441	+	0.620204i	$0.787050\pi$
$390$	2.41491	+	7.43232i	0.122284	+	0.376350i
$391$	−0.905090	−	2.78558i	−0.0457723	−	0.140873i
$392$	−5.18703	−	3.76860i	−0.261985	−	0.190343i
$393$	−6.95546	+	5.05344i	−0.350857	+	0.254912i
$394$	−1.72082	+	5.29613i	−0.0866934	+	0.266815i
$395$	33.4777			1.68445
$396$	−25.2140	−	34.0570i	−1.26705	−	1.71143i
$397$	21.1755			1.06277			0.531385	−	0.847131i	$-0.321672\pi$
$397$	21.1755			1.06277			0.531385	+	0.847131i	$0.321672\pi$
$398$	1.84085	−	5.66554i	0.0922733	−	0.283988i
$399$	−0.805144	+	0.584971i	−0.0403076	+	0.0292852i
$400$	−40.1133	−	29.1440i	−2.00566	−	1.45720i
$401$	−10.4173	−	32.0610i	−0.520213	−	1.60105i	−0.773592	−	0.633684i	$-0.781542\pi$
$401$	−10.4173	−	32.0610i	−0.520213	−	1.60105i	0.253379	−	0.967367i	$-0.418458\pi$
$402$	−2.01626	−	6.20541i	−0.100562	−	0.309498i
$403$	−14.1465	−	10.2781i	−0.704690	−	0.511987i
$404$	21.0809	−	15.3162i	1.04882	−	0.762009i
$405$	7.95886	−	24.4948i	0.395479	−	1.21716i
$406$	−3.19746			−0.158687
$407$	−9.65209	+	13.5389i	−0.478436	+	0.671097i
$408$	11.8917			0.588725
$409$	−0.817053	+	2.51463i	−0.0404006	+	0.124340i	−0.969223	−	0.246186i	$-0.920823\pi$
$409$	−0.817053	+	2.51463i	−0.0404006	+	0.124340i	0.928822	+	0.370526i	$0.120823\pi$
$410$	18.5600	−	13.4846i	0.916611	−	0.665957i
$411$	3.03495	+	2.20502i	0.149703	+	0.108766i
$412$	−6.47144	−	19.9170i	−0.318825	−	0.981242i
$413$	2.37009	+	7.29440i	0.116625	+	0.358934i
$414$	3.79032	+	2.75383i	0.186284	+	0.135343i
$415$	23.2402	−	16.8850i	1.14082	−	0.828852i
$416$	−3.96593	+	12.2059i	−0.194446	+	0.598442i
$417$	−4.41470			−0.216189
$418$	−19.4530	+	6.51428i	−0.951477	+	0.318624i
$419$	33.0757			1.61585			0.807926	−	0.589284i	$-0.200590\pi$
$419$	33.0757			1.61585			0.807926	+	0.589284i	$0.200590\pi$
$420$	−1.96324	+	6.04222i	−0.0957961	+	0.294830i
$421$	−27.2492	+	19.7977i	−1.32804	+	0.964881i	−0.328251	+	0.944591i	$0.606459\pi$
$421$	−27.2492	+	19.7977i	−1.32804	+	0.964881i	−0.999794	+	0.0202902i	$0.993541\pi$
$422$	28.2182	+	20.5017i	1.37364	+	0.998008i
$423$	4.41011	+	13.5729i	0.214427	+	0.659937i
$424$	26.5451	+	81.6975i	1.28914	+	3.96758i
$425$	24.6963	+	17.9429i	1.19795	+	0.870361i
$426$	3.58577	−	2.60521i	0.173731	−	0.126223i
$427$	4.42970	−	13.6332i	0.214368	−	0.659758i
$428$	−18.1490			−0.877266
$429$	2.80866	−	0.940545i	0.135603	−	0.0454099i
$430$	−12.7879			−0.616686
$431$	−9.19405	+	28.2964i	−0.442862	+	1.36299i	0.441950	+	0.897040i	$0.354287\pi$
$431$	−9.19405	+	28.2964i	−0.442862	+	1.36299i	−0.884812	+	0.465949i	$0.845713\pi$
$432$	−14.2124	+	10.3259i	−0.683796	+	0.496807i
$433$	18.7295	+	13.6078i	0.900083	+	0.653949i	0.938487	−	0.345314i	$-0.112227\pi$
$433$	18.7295	+	13.6078i	0.900083	+	0.653949i	−0.0384041	+	0.999262i	$0.512227\pi$
$434$	−6.33987	−	19.5121i	−0.304324	−	0.936611i
$435$	0.545128	+	1.67773i	0.0261369	+	0.0804410i
$436$	22.4426	+	16.3055i	1.07481	+	0.780892i
$437$	1.27146	−	0.923766i	0.0608220	−	0.0441897i
$438$	1.91854	−	5.90466i	0.0916714	−	0.282136i
$439$	15.8166			0.754884			0.377442	−	0.926033i	$-0.376804\pi$
$439$	15.8166			0.754884			0.377442	+	0.926033i	$0.376804\pi$
$440$	−42.3277	+	59.3725i	−2.01789	+	2.83047i
$441$	−2.83141			−0.134829
$442$	7.74789	−	23.8456i	0.368530	−	1.13422i
$443$	8.11174	−	5.89352i	0.385400	−	0.280010i	−0.378168	−	0.925737i	$-0.623446\pi$
$443$	8.11174	−	5.89352i	0.385400	−	0.280010i	0.763568	+	0.645727i	$0.223446\pi$
$444$	7.51461	+	5.45968i	0.356628	+	0.259105i
$445$	5.04640	+	15.5312i	0.239222	+	0.736250i
$446$	−4.23368	−	13.0299i	−0.200471	−	0.616985i
$447$	3.57275	+	2.59575i	0.168985	+	0.122775i
$448$	−0.310639	+	0.225693i	−0.0146763	+	0.0106630i
$449$	0.496363	−	1.52765i	0.0234248	−	0.0720942i	−0.938661	−	0.344842i	$-0.887932\pi$
$449$	0.496363	−	1.52765i	0.0234248	−	0.0720942i	0.962086	+	0.272748i	$0.0879325\pi$
$450$	−48.8297			−2.30185
$451$	−5.17385	−	6.98841i	−0.243627	−	0.329072i
$452$	−11.1834			−0.526023
$453$	0.972451	−	2.99290i	0.0456897	−	0.140618i
$454$	−21.9112	+	15.9194i	−1.02834	+	0.747134i
$455$	6.03376	+	4.38378i	0.282867	+	0.205515i
$456$	1.97178	+	6.06853i	0.0923373	+	0.284185i
$457$	1.16096	+	3.57308i	0.0543075	+	0.167141i	0.974531	−	0.224251i	$-0.0719935\pi$
$457$	1.16096	+	3.57308i	0.0543075	+	0.167141i	−0.920224	+	0.391392i	$0.871994\pi$
$458$	−46.7437	−	33.9613i	−2.18419	−	1.58691i
$459$	8.75009	−	6.35732i	0.408419	−	0.296734i
$460$	3.10027	−	9.54166i	0.144551	−	0.444882i
$461$	−14.1849			−0.660657			−0.330329	−	0.943866i	$-0.607160\pi$
$461$	−14.1849			−0.660657			−0.330329	+	0.943866i	$0.607160\pi$
$462$	3.31465	+	1.04420i	0.154212	+	0.0485804i
$463$	−5.34265			−0.248294			−0.124147	−	0.992264i	$-0.539619\pi$
$463$	−5.34265			−0.248294			−0.124147	+	0.992264i	$0.539619\pi$
$464$	−2.84077	+	8.74300i	−0.131880	+	0.405884i
$465$	−9.15728	+	6.65315i	−0.424659	+	0.308533i
$466$	−30.6043	−	22.2354i	−1.41772	−	1.03003i
$467$	−7.37610	−	22.7013i	−0.341325	−	1.05049i	−0.963522	−	0.267630i	$-0.913760\pi$
$467$	−7.37610	−	22.7013i	−0.341325	−	1.05049i	0.622197	−	0.782861i	$-0.286240\pi$
$468$	8.58735	+	26.4292i	0.396950	+	1.22169i
$469$	−5.03772	−	3.66012i	−0.232620	−	0.169008i
$470$	35.6826	−	25.9250i	1.64592	−	1.19583i
$471$	−2.32816	+	7.16533i	−0.107276	+	0.330161i
$472$	49.1750			2.26346
$473$	0.0435057	+	4.84665i	0.00200039	+	0.222849i
$474$	−10.2301			−0.469883
$475$	−5.06164	+	15.5781i	−0.232244	+	0.714774i
$476$	16.4904	−	11.9810i	0.755835	−	0.549146i
$477$	30.6903	+	22.2978i	1.40521	+	1.02095i
$478$	1.54509	+	4.75530i	0.0706707	+	0.217502i
$479$	−0.134891	−	0.415152i	−0.00616333	−	0.0189688i	0.947928	−	0.318486i	$-0.103174\pi$
$479$	−0.134891	−	0.415152i	−0.00616333	−	0.0189688i	−0.954091	+	0.299517i	$0.903174\pi$
$480$	6.72104	+	4.88312i	0.306772	+	0.222883i
$481$	8.82158	−	6.40925i	0.402229	−	0.292237i
$482$	0.623188	−	1.91798i	0.0283854	−	0.0873614i
$483$	−0.266233			−0.0121140
$484$	40.6741	+	28.4500i	1.84882	+	1.29318i
$485$	−29.8517			−1.35549
$486$	−8.09660	+	24.9188i	−0.367269	+	1.13034i
$487$	−0.593559	+	0.431246i	−0.0268967	+	0.0195416i	−0.601152	−	0.799134i	$-0.705292\pi$
$487$	−0.593559	+	0.431246i	−0.0268967	+	0.0195416i	0.574256	+	0.818676i	$0.305292\pi$
$488$	−74.3552	−	54.0222i	−3.36590	−	2.44547i
$489$	−0.0479087	−	0.147448i	−0.00216650	−	0.00666782i
$490$	2.70407	+	8.32227i	0.122157	+	0.375962i
$491$	−2.10952	−	1.53266i	−0.0952013	−	0.0691678i	0.539166	−	0.842199i	$-0.318739\pi$
$491$	−2.10952	−	1.53266i	−0.0952013	−	0.0691678i	−0.634368	+	0.773032i	$0.718739\pi$
$492$	−3.92977	+	2.85514i	−0.177168	+	0.128720i
$493$	1.74896	−	5.38276i	0.0787694	−	0.242427i
$494$	13.4535			0.605302
$495$	0.289035	+	32.1993i	0.0129911	+	1.44725i
$496$	−58.9857			−2.64854
$497$	1.30713	−	4.02294i	0.0586329	−	0.180453i
$498$	−7.10172	+	5.15970i	−0.318236	+	0.231212i
$499$	6.68087	+	4.85393i	0.299077	+	0.217292i	0.727195	−	0.686431i	$-0.240823\pi$
$499$	6.68087	+	4.85393i	0.299077	+	0.217292i	−0.428119	+	0.903723i	$0.640823\pi$
$500$	8.40514	+	25.8684i	0.375889	+	1.15687i
$501$	0.0144821	+	0.0445714i	0.000647014	+	0.00199130i
$502$	42.5618	+	30.9230i	1.89963	+	1.38016i
$503$	−27.4351	+	19.9328i	−1.22327	+	0.888759i	−0.996367	−	0.0851577i	$-0.972861\pi$
$503$	−27.4351	+	19.9328i	−1.22327	+	0.888759i	−0.226905	+	0.973917i	$0.572861\pi$
$504$	−5.60979	+	17.2651i	−0.249880	+	0.769051i
$505$	−19.8010			−0.881135
$506$	−5.23438	−	1.64896i	−0.232697	−	0.0733052i
$507$	3.39533			0.150792
$508$	−9.69670	+	29.8434i	−0.430221	+	1.32408i
$509$	23.6586	−	17.1890i	1.04865	−	0.761889i	0.0766953	−	0.997055i	$-0.475563\pi$
$509$	23.6586	−	17.1890i	1.04865	−	0.761889i	0.971955	+	0.235165i	$0.0755631\pi$
$510$	−13.1303	−	9.53972i	−0.581419	−	0.422426i
$511$	−1.83098	−	5.63517i	−0.0809977	−	0.249285i
$512$	−15.6950	−	48.3043i	−0.693628	−	2.13477i
$513$	4.69512	+	3.41121i	0.207295	+	0.150608i
$514$	−10.6936	+	7.76938i	−0.471676	+	0.342693i
$515$	−4.91764	+	15.1349i	−0.216697	+	0.666925i
$516$	2.70763			0.119197
$517$	−9.94705	−	13.4357i	−0.437471	−	0.590899i
$518$	12.7936			0.562120
$519$	1.68766	−	5.19408i	0.0740800	−	0.227995i
$520$	38.6856	−	28.1067i	1.69648	−	1.23256i
$521$	7.86001	+	5.71063i	0.344353	+	0.250187i	0.746496	−	0.665390i	$-0.231735\pi$
$521$	7.86001	+	5.71063i	0.344353	+	0.250187i	−0.402143	+	0.915577i	$0.631735\pi$
$522$	2.79763	+	8.61022i	0.122449	+	0.376859i
$523$	−3.96337	−	12.1980i	−0.173306	−	0.533382i	0.826246	−	0.563310i	$-0.190472\pi$
$523$	−3.96337	−	12.1980i	−0.173306	−	0.533382i	−0.999552	+	0.0299279i	$0.990472\pi$
$524$	76.4394	+	55.5365i	3.33927	+	2.42612i
$525$	2.24484	−	1.63097i	0.0979728	−	0.0711814i
$526$	18.2891	−	56.2880i	0.797442	−	2.45427i
$527$	36.3155			1.58193
$528$	5.80010	−	8.13573i	0.252417	−	0.354062i
$529$	−22.5796			−0.981721
$530$	36.2292	−	111.502i	1.57370	−	4.84334i
$531$	17.5688	−	12.7645i	0.762423	−	0.553933i
$532$	8.84840	+	6.42874i	0.383627	+	0.278721i
$533$	1.76211	+	5.42320i	0.0763253	+	0.234905i
$534$	−1.54207	−	4.74601i	−0.0667320	−	0.205380i
$535$	11.1575	+	8.10639i	0.482381	+	0.350470i
$536$	−32.2994	+	23.4669i	−1.39512	+	1.01362i
$537$	−1.43896	+	4.42868i	−0.0620959	+	0.191112i
$538$	47.6192			2.05301
$539$	3.14497	−	1.05317i	0.135463	−	0.0453630i
$540$	37.0479			1.59429
$541$	−2.13261	+	6.56348i	−0.0916879	+	0.282186i	−0.986376	−	0.164504i	$-0.947398\pi$
$541$	−2.13261	+	6.56348i	−0.0916879	+	0.282186i	0.894688	+	0.446691i	$0.147398\pi$
$542$	−62.4092	+	45.3430i	−2.68071	+	1.94765i
$543$	3.90540	+	2.83744i	0.167597	+	0.121766i
$544$	−8.23652	−	25.3494i	−0.353138	−	1.08685i
$545$	−6.51410	−	20.0483i	−0.279033	−	0.858776i
$546$	−1.84379	−	1.33959i	−0.0789069	−	0.0573292i
$547$	14.3372	−	10.4166i	0.613016	−	0.445382i	−0.237459	−	0.971398i	$-0.576315\pi$
$547$	14.3372	−	10.4166i	0.613016	−	0.445382i	0.850475	+	0.526015i	$0.176315\pi$
$548$	12.7400	−	39.2096i	0.544224	−	1.67495i
$549$	−40.5878			−1.73224
$550$	54.2373	−	18.1626i	2.31269	−	0.774456i
$551$	3.03692			0.129377
$552$	−0.527479	+	1.62341i	−0.0224510	+	0.0690971i
$553$	−7.89858	+	5.73865i	−0.335882	+	0.244032i
$554$	−27.8552	−	20.2380i	−1.18346	−	0.859831i
$555$	−2.18116	−	6.71291i	−0.0925850	−	0.284947i
$556$	14.9925	+	46.1422i	0.635824	+	1.95687i
$557$	−35.1334	−	25.5259i	−1.48865	−	1.08157i	−0.974639	−	0.223785i	$-0.928159\pi$
$557$	−35.1334	−	25.5259i	−1.48865	−	1.08157i	−0.514012	−	0.857783i	$-0.671841\pi$
$558$	−46.9957	+	34.1444i	−1.98949	+	1.44545i
$559$	0.982226	−	3.02298i	0.0415437	−	0.127858i
$560$	25.1585			1.06314
$561$	−3.57092	+	5.00889i	−0.150764	+	0.211475i
$562$	20.6777			0.872234
$563$	6.89532	−	21.2216i	0.290603	−	0.894385i	−0.694060	−	0.719918i	$-0.744180\pi$
$563$	6.89532	−	21.2216i	0.290603	−	0.894385i	0.984663	−	0.174467i	$-0.0558204\pi$
$564$	−7.55522	+	5.48919i	−0.318132	+	0.231137i
$565$	6.87524	+	4.99515i	0.289244	+	0.210148i
$566$	7.87898	+	24.2490i	0.331178	+	1.01926i
$567$	2.32106	+	7.14349i	0.0974753	+	0.299998i
$568$	−21.9410	−	15.9411i	−0.920623	−	0.668872i
$569$	−18.3397	+	13.3245i	−0.768839	+	0.558594i	−0.901609	−	0.432553i	$-0.857613\pi$
$569$	−18.3397	+	13.3245i	−0.768839	+	0.558594i	0.132770	+	0.991147i	$0.457613\pi$
$570$	2.69112	−	8.28243i	0.112719	−	0.346913i
$571$	35.0994			1.46886			0.734432	−	0.678683i	$-0.237449\pi$
$571$	35.0994			1.46886			0.734432	+	0.678683i	$0.237449\pi$
$572$	−19.3689	−	26.1619i	−0.809854	−	1.09388i
$573$	9.25258			0.386532
$574$	−2.06746	+	6.36299i	−0.0862941	+	0.265586i
$575$	−3.54497	+	2.57557i	−0.147836	+	0.107409i
$576$	0.879547	+	0.639028i	0.0366478	+	0.0266262i
$577$	−10.0850	−	31.0385i	−0.419844	−	1.29215i	−0.907846	−	0.419305i	$-0.862274\pi$
$577$	−10.0850	−	31.0385i	−0.419844	−	1.29215i	0.488001	−	0.872843i	$-0.337726\pi$
$578$	2.68488	+	8.26320i	0.111676	+	0.343704i
$579$	1.14378	+	0.831001i	0.0475337	+	0.0345352i
$580$	15.6843	−	11.3953i	0.651255	−	0.473164i
$581$	−2.58881	+	7.96754i	−0.107402	+	0.330549i
$582$	9.12204			0.378121
$583$	−42.3829	−	13.3517i	−1.75532	−	0.552969i
$584$	−37.9894			−1.57201
$585$	6.52552	−	20.0835i	0.269797	−	0.830350i
$586$	−63.4433	+	46.0943i	−2.62082	+	1.90414i
$587$	−29.9477	−	21.7583i	−1.23607	−	0.898061i	−0.238744	−	0.971082i	$-0.576736\pi$
$587$	−29.9477	−	21.7583i	−1.23607	−	0.898061i	−0.997330	+	0.0730216i	$0.976736\pi$
$588$	−0.572543	−	1.76211i	−0.0236113	−	0.0726680i
$589$	6.02155	+	18.5324i	0.248114	+	0.763615i
$590$	−54.2970	−	39.4491i	−2.23537	−	1.62409i
$591$	−0.724863	+	0.526644i	−0.0298169	+	0.0216632i
$592$	11.3665	−	34.9824i	0.467159	−	1.43777i
$593$	−16.2161			−0.665915			−0.332958	−	0.942942i	$-0.608047\pi$
$593$	−16.2161			−0.665915			−0.332958	+	0.942942i	$0.608047\pi$
$594$	−0.181905	−	20.2647i	−0.00746364	−	0.831471i
$595$	−15.4892			−0.634995
$596$	14.9975	−	46.1575i	0.614321	−	1.89068i
$597$	0.775424	−	0.563378i	0.0317360	−	0.0230575i
$598$	2.91165	+	2.11544i	0.119066	+	0.0865066i
$599$	3.25937	+	10.0313i	0.133174	+	0.409868i	0.995302	−	0.0968238i	$-0.0308683\pi$
$599$	3.25937	+	10.0313i	0.133174	+	0.409868i	−0.862127	+	0.506691i	$0.830868\pi$
$600$	−5.49758	−	16.9198i	−0.224438	−	0.690748i
$601$	29.5220	+	21.4490i	1.20423	+	0.874921i	0.994694	−	0.102880i	$-0.0328059\pi$
$601$	29.5220	+	21.4490i	1.20423	+	0.874921i	0.209532	+	0.977802i	$0.432806\pi$
$602$	3.01711	−	2.19206i	0.122968	−	0.0893418i
$603$	−5.44830	+	16.7681i	−0.221872	+	0.682852i
$604$	−34.5841			−1.40721
$605$	−12.2978	−	35.6576i	−0.499977	−	1.44969i
$606$	6.05078			0.245796
$607$	−10.4174	+	32.0615i	−0.422829	+	1.30133i	0.482229	+	0.876045i	$0.339827\pi$
$607$	−10.4174	+	32.0615i	−0.422829	+	1.30133i	−0.905058	+	0.425289i	$0.860173\pi$
$608$	11.5705	−	8.40648i	0.469247	−	0.340928i
$609$	−0.416207	−	0.302392i	−0.0168655	−	0.0122535i
$610$	38.7624	+	119.298i	1.56944	+	4.83025i
$611$	3.38776	+	10.4264i	0.137054	+	0.421809i
$612$	−46.6910	−	33.9230i	−1.88737	−	1.37126i
$613$	−19.5836	+	14.2283i	−0.790974	+	0.574676i	−0.908252	−	0.418423i	$-0.862583\pi$
$613$	−19.5836	+	14.2283i	−0.790974	+	0.574676i	0.117278	+	0.993099i	$0.462583\pi$
$614$	−15.8252	+	48.7051i	−0.638655	+	1.96558i
$615$	3.69118			0.148843
$616$	−0.190873	−	21.2638i	−0.00769048	−	0.856742i
$617$	17.6040			0.708710			0.354355	−	0.935111i	$-0.384700\pi$
$617$	17.6040			0.708710			0.354355	+	0.935111i	$0.384700\pi$
$618$	1.50273	−	4.62492i	0.0604485	−	0.186041i
$619$	19.6734	−	14.2935i	0.790739	−	0.574505i	−0.117444	−	0.993080i	$-0.537470\pi$
$619$	19.6734	−	14.2935i	0.790739	−	0.574505i	0.908183	+	0.418574i	$0.137470\pi$
$620$	100.637	+	73.1171i	4.04168	+	2.93645i
$621$	0.479753	+	1.47653i	0.0192518	+	0.0592510i
$622$	−18.5053	−	56.9535i	−0.741995	−	2.28363i
$623$	−3.85294	−	2.79932i	−0.154365	−	0.112153i
$624$	−5.30103	+	3.85142i	−0.212211	+	0.154180i
$625$	−4.05444	+	12.4783i	−0.162178	+	0.499131i
$626$	−37.4446			−1.49659
$627$	−3.14823	−	0.991768i	−0.125728	−	0.0396074i
$628$	82.7983			3.30401
$629$	−6.99793	+	21.5374i	−0.279026	+	0.858754i
$630$	20.0445	−	14.5632i	0.798593	−	0.580212i
$631$	−3.26881	−	2.37493i	−0.130129	−	0.0945443i	0.520817	−	0.853669i	$-0.325628\pi$
$631$	−3.26881	−	2.37493i	−0.130129	−	0.0945443i	−0.650946	+	0.759124i	$0.725628\pi$
$632$	19.3435	+	59.5332i	0.769443	+	2.36810i
$633$	1.73420	+	5.33733i	0.0689284	+	0.212140i
$634$	−37.2673	−	27.0763i	−1.48007	−	1.07534i
$635$	19.2910	−	14.0157i	0.765540	−	0.556198i
$636$	−7.67095	+	23.6087i	−0.304173	+	0.936148i
$637$	−2.17503			−0.0861779
$638$	−6.31009	−	8.52315i	−0.249819	−	0.337435i
$639$	−11.9768			−0.473793
$640$	−11.4664	+	35.2900i	−0.453251	+	1.39496i
$641$	17.2873	−	12.5599i	0.682805	−	0.496087i	−0.191482	−	0.981496i	$-0.561329\pi$
$641$	17.2873	−	12.5599i	0.682805	−	0.496087i	0.874287	+	0.485409i	$0.161329\pi$
$642$	−3.40950	−	2.47714i	−0.134562	−	0.0977650i
$643$	6.97607	+	21.4701i	0.275109	+	0.846700i	0.989190	+	0.146637i	$0.0468448\pi$
$643$	6.97607	+	21.4701i	0.275109	+	0.846700i	−0.714081	+	0.700063i	$0.753155\pi$
$644$	0.904140	+	2.78266i	0.0356281	+	0.109652i
$645$	−1.66457	−	1.20938i	−0.0655424	−	0.0476194i
$646$	−22.6043	+	16.4230i	−0.889356	+	0.646155i
$647$	5.28947	−	16.2793i	0.207951	−	0.640006i	−0.791629	−	0.611003i	$-0.790767\pi$
$647$	5.28947	−	16.2793i	0.207951	−	0.640006i	0.999579	−	0.0290038i	$-0.00923348\pi$
$648$	48.1576			1.89181
$649$	−14.7666	+	20.7130i	−0.579641	+	0.813056i
$650$	−37.5100			−1.47126
$651$	1.02006	−	3.13943i	0.0399794	−	0.123044i
$652$	−1.37842	+	1.00148i	−0.0539830	+	0.0392209i
$653$	10.7123	+	7.78293i	0.419204	+	0.304570i	0.777317	−	0.629109i	$-0.216580\pi$
$653$	10.7123	+	7.78293i	0.419204	+	0.304570i	−0.358113	+	0.933678i	$0.616580\pi$
$654$	1.99057	+	6.12635i	0.0778375	+	0.239559i
$655$	−22.1870	−	68.2845i	−0.866917	−	2.66810i
$656$	15.5619	+	11.3063i	0.607588	+	0.441439i
$657$	−13.5725	+	9.86103i	−0.529515	+	0.384715i
$658$	−3.97482	+	12.2332i	−0.154955	+	0.476901i
$659$	28.3747			1.10532			0.552660	−	0.833407i	$-0.313613\pi$
$659$	28.3747			1.10532			0.552660	+	0.833407i	$0.313613\pi$
$660$	−19.9805	+	6.69093i	−0.777741	+	0.260444i
$661$	18.9657			0.737679			0.368840	−	0.929493i	$-0.379755\pi$
$661$	18.9657			0.737679			0.368840	+	0.929493i	$0.379755\pi$
$662$	−15.6378	+	48.1283i	−0.607782	+	1.87056i
$663$	3.26366	−	2.37119i	0.126750	−	0.0920893i
$664$	43.4547	+	31.5717i	1.68637	+	1.22522i
$665$	−2.56830	−	7.90441i	−0.0995944	−	0.306520i
$666$	−11.1938	−	34.4511i	−0.433752	−	1.33495i
$667$	0.657259	+	0.477527i	0.0254492	+	0.0184899i
$668$	0.416677	−	0.302733i	0.0161217	−	0.0117131i
$669$	0.681184	−	2.09647i	0.0263361	−	0.0810542i
$670$	54.4893			2.10511
$671$	45.0826	−	15.0969i	1.74039	−	0.582811i
$672$	−2.42278			−0.0934608
$673$	14.3830	−	44.2662i	0.554423	−	1.70634i	−0.143039	−	0.989717i	$-0.545688\pi$
$673$	14.3830	−	44.2662i	0.554423	−	1.70634i	0.697462	−	0.716621i	$-0.254312\pi$
$674$	40.2763	−	29.2625i	1.55139	−	1.12715i
$675$	−13.0906	−	9.51086i	−0.503857	−	0.366073i
$676$	−11.5307	−	35.4879i	−0.443489	−	1.36492i
$677$	8.82845	+	27.1712i	0.339305	+	1.04427i	0.964562	+	0.263855i	$0.0849939\pi$
$677$	8.82845	+	27.1712i	0.339305	+	1.04427i	−0.625258	+	0.780418i	$0.715006\pi$
$678$	−2.10093	−	1.52641i	−0.0806857	−	0.0586216i
$679$	7.04306	−	5.11708i	0.270288	−	0.196376i
$680$	−30.6883	+	94.4489i	−1.17684	+	3.62195i
$681$	−4.35767			−0.166986
$682$	39.4999	−	55.4061i	1.51253	−	2.12161i
$683$	−21.9450			−0.839704			−0.419852	−	0.907593i	$-0.637918\pi$
$683$	−21.9450			−0.839704			−0.419852	+	0.907593i	$0.637918\pi$
$684$	9.56957	−	29.4521i	0.365902	−	1.12613i
$685$	−25.3454	+	18.4145i	−0.968398	+	0.703582i
$686$	−2.06456	−	1.49999i	−0.0788254	−	0.0572700i
$687$	−2.87273	−	8.84135i	−0.109601	−	0.337318i
$688$	−3.31334	−	10.1974i	−0.126320	−	0.388772i
$689$	23.5757	+	17.1287i	0.898162	+	0.652553i
$690$	1.88475	−	1.36935i	0.0717514	−	0.0521304i
$691$	3.43923	−	10.5849i	0.130835	−	0.402668i	−0.864084	−	0.503347i	$-0.832102\pi$
$691$	3.43923	−	10.5849i	0.130835	−	0.402668i	0.994919	+	0.100680i	$0.0321017\pi$
$692$	−60.0197			−2.28161
$693$	−5.58770	−	7.54740i	−0.212259	−	0.286702i
$694$	−72.5903			−2.75549
$695$	11.3928	−	35.0634i	0.432154	−	1.33003i
$696$	−2.66852	+	1.93879i	−0.101150	+	0.0734897i
$697$	−9.58089	−	6.96092i	−0.362902	−	0.263664i
$698$	15.8403	+	48.7515i	0.599565	+	1.84527i
$699$	−1.88085	−	5.78866i	−0.0711402	−	0.218947i
$700$	−24.6704	−	17.9241i	−0.932455	−	0.677468i
$701$	31.0633	−	22.5688i	1.17324	−	0.852411i	0.181849	−	0.983326i	$-0.441792\pi$
$701$	31.0633	−	22.5688i	1.17324	−	0.852411i	0.991394	+	0.130915i	$0.0417917\pi$
$702$	−4.10686	+	12.6396i	−0.155003	+	0.477051i
$703$	−12.1513			−0.458294
$704$	−1.21464	−	0.382642i	−0.0457786	−	0.0144214i
$705$	7.09652			0.267271
$706$	7.09498	−	21.8361i	0.267023	−	0.821812i
$707$	4.67177	−	3.39424i	0.175700	−	0.127653i
$708$	11.4965	+	8.35271i	0.432066	+	0.313914i
$709$	−0.148483	−	0.456985i	−0.00557641	−	0.0171624i	0.948230	−	0.317586i	$-0.102872\pi$
$709$	−0.148483	−	0.456985i	−0.00557641	−	0.0171624i	−0.953806	+	0.300423i	$0.902872\pi$
$710$	11.4381	+	35.2029i	0.429265	+	1.32114i
$711$	22.3641	+	16.2485i	0.838720	+	0.609366i
$712$	−24.7032	+	17.9479i	−0.925792	+	0.672627i
$713$	−1.61085	+	4.95768i	−0.0603267	+	0.185666i
$714$	4.73317			0.177135
$715$	0.222031	+	24.7348i	0.00830348	+	0.925031i
$716$	51.1752			1.91251
$717$	−0.248599	+	0.765110i	−0.00928411	+	0.0285736i
$718$	−19.5432	+	14.1990i	−0.729345	+	0.529900i
$719$	−29.5046	−	21.4364i	−1.10034	−	0.799442i	−0.119223	−	0.992868i	$-0.538040\pi$
$719$	−29.5046	−	21.4364i	−1.10034	−	0.799442i	−0.981115	+	0.193426i	$0.938040\pi$
$720$	−22.0125	−	67.7475i	−0.820358	−	2.52480i
$721$	−1.43414	−	4.41383i	−0.0534102	−	0.164380i
$722$	27.0977	+	19.6876i	1.00847	+	0.732698i
$723$	0.262507	−	0.190722i	0.00976273	−	0.00709304i
$724$	16.3939	−	50.4552i	0.609274	−	1.87515i
$725$	−8.46730			−0.314467
$726$	3.75795	+	10.8962i	0.139471	+	0.404397i
$727$	−33.6867			−1.24937			−0.624686	−	0.780876i	$-0.714773\pi$
$727$	−33.6867			−1.24937			−0.624686	+	0.780876i	$0.714773\pi$
$728$	−4.30933	+	13.2627i	−0.159714	+	0.491550i
$729$	14.8193	−	10.7668i	0.548862	−	0.398772i
$730$	41.9463	+	30.4758i	1.55250	+	1.12796i
$731$	2.03991	+	6.27818i	0.0754486	+	0.232207i
$732$	−8.20730	−	25.2595i	−0.303351	−	0.933617i
$733$	21.8950	+	15.9076i	0.808709	+	0.587562i	0.913456	−	0.406937i	$-0.133403\pi$
$733$	21.8950	+	15.9076i	0.808709	+	0.587562i	−0.104747	+	0.994499i	$0.533403\pi$
$734$	−2.83905	+	2.06269i	−0.104791	+	0.0761353i
$735$	−0.435075	+	1.33902i	−0.0160480	+	0.0493906i
$736$	3.82597			0.141027
$737$	−0.185378	−	20.6517i	−0.00682850	−	0.760714i
$738$	18.9434			0.697315
$739$	−3.21768	+	9.90300i	−0.118364	+	0.364288i	−0.992634	−	0.121153i	$-0.961341\pi$
$739$	−3.21768	+	9.90300i	−0.118364	+	0.364288i	0.874270	+	0.485441i	$0.161341\pi$
$740$	−62.7558	+	45.5948i	−2.30695	+	1.67610i
$741$	1.75121	+	1.27233i	0.0643324	+	0.0467403i
$742$	10.5656	+	32.5176i	0.387875	+	1.19376i
$743$	14.6944	+	45.2248i	0.539086	+	1.65914i	0.734651	+	0.678446i	$0.237346\pi$
$743$	14.6944	+	45.2248i	0.539086	+	1.65914i	−0.195565	+	0.980691i	$0.562654\pi$
$744$	−17.1223	−	12.4401i	−0.627736	−	0.456077i
$745$	−29.8366	+	21.6776i	−1.09313	+	0.794205i
$746$	3.99959	−	12.3095i	0.146435	−	0.450681i
$747$	23.7203			0.867881
$748$	64.4797	+	20.3127i	2.35761	+	0.742705i
$749$	−4.02202			−0.146961
$750$	−1.95175	+	6.00687i	−0.0712679	+	0.219340i
$751$	24.0074	−	17.4424i	0.876043	−	0.636483i	−0.0561585	−	0.998422i	$-0.517885\pi$
$751$	24.0074	−	17.4424i	0.876043	−	0.636483i	0.932202	+	0.361939i	$0.117885\pi$
$752$	29.9186	+	21.7372i	1.09102	+	0.792672i
$753$	2.61572	+	8.05036i	0.0953221	+	0.293371i
$754$	2.14908	+	6.61420i	0.0782650	+	0.240875i
$755$	21.2613	+	15.4473i	0.773779	+	0.562183i
$756$	−8.74091	+	6.35064i	−0.317904	+	0.230971i
$757$	−9.57305	+	29.4628i	−0.347938	+	1.07084i	0.612053	+	0.790816i	$0.290344\pi$
$757$	−9.57305	+	29.4628i	−0.347938	+	1.07084i	−0.959992	+	0.280028i	$0.909656\pi$
$758$	−71.4090			−2.59369
$759$	−0.525403	−	0.709670i	−0.0190709	−	0.0257594i
$760$	−53.2874			−1.93294
$761$	3.63629	−	11.1913i	0.131815	−	0.405686i	−0.863266	−	0.504750i	$-0.831585\pi$
$761$	3.63629	−	11.1913i	0.131815	−	0.405686i	0.995081	+	0.0990637i	$0.0315848\pi$
$762$	−5.89493	+	4.28292i	−0.213551	+	0.155154i
$763$	4.97353	+	3.61348i	0.180054	+	0.130817i
$764$	−31.4222	−	96.7076i	−1.13682	−	3.49876i
$765$	13.5523	+	41.7098i	0.489986	+	1.50802i
$766$	64.5807	+	46.9206i	2.33340	+	1.69531i
$767$	13.4960	−	9.80545i	0.487314	−	0.354054i
$768$	3.60134	−	11.0838i	0.129952	−	0.399951i
$769$	4.17897			0.150697			0.0753487	−	0.997157i	$-0.475993\pi$
$769$	4.17897			0.150697			0.0753487	+	0.997157i	$0.475993\pi$
$770$	−16.8474	+	23.6317i	−0.607139	+	0.851628i
$771$	−2.12674			−0.0765926
$772$	4.80128	−	14.7768i	0.172802	−	0.531829i
$773$	−0.0677907	+	0.0492529i	−0.00243826	+	0.00177150i	−0.589004	−	0.808130i	$-0.700480\pi$
$773$	−0.0677907	+	0.0492529i	−0.00243826	+	0.00177150i	0.586565	+	0.809902i	$0.300480\pi$
$774$	−8.54268	−	6.20662i	−0.307060	−	0.223092i
$775$	−16.7888	−	51.6707i	−0.603072	−	1.85606i
$776$	−17.2484	−	53.0850i	−0.619180	−	1.90564i
$777$	1.66532	+	1.20993i	0.0597430	+	0.0434059i
$778$	−21.9950	+	15.9803i	−0.788559	+	0.572922i
$779$	1.96365	−	6.04350i	0.0703552	−	0.216531i
$780$	13.8183			0.494776
$781$	13.3031	−	4.45485i	0.476023	−	0.159407i
$782$	−7.47446			−0.267286
$783$	−0.927059	+	2.85319i	−0.0331304	+	0.101965i
$784$	−5.93578	+	4.31259i	−0.211992	+	0.154021i
$785$	−50.9020	−	36.9825i	−1.81677	−	1.31996i
$786$	6.77987	+	20.8663i	0.241830	+	0.744276i
$787$	4.15302	+	12.7817i	0.148039	+	0.455618i	0.997389	−	0.0722119i	$-0.0230058\pi$
$787$	4.15302	+	12.7817i	0.148039	+	0.455618i	−0.849350	+	0.527830i	$0.823006\pi$
$788$	7.96613	+	5.78773i	0.283782	+	0.206179i
$789$	7.70395	−	5.59725i	0.274268	−	0.199267i
$790$	26.4003	−	81.2518i	0.939281	−	2.89081i
$791$	−2.47837			−0.0881206
$792$	−57.0927	+	19.1188i	−2.02870	+	0.679357i
$793$	−31.1787			−1.10719
$794$	16.6989	−	51.3939i	0.592621	−	1.82390i
$795$	15.2609	−	11.0877i	0.541248	−	0.393240i
$796$	−8.52179	−	6.19144i	−0.302047	−	0.219450i
$797$	−4.20197	−	12.9323i	−0.148842	−	0.458087i	0.848643	−	0.528965i	$-0.177420\pi$
$797$	−4.20197	−	12.9323i	−0.148842	−	0.458087i	−0.997485	+	0.0708782i	$0.977420\pi$
$798$	0.784818	+	2.41542i	0.0277823	+	0.0855050i
$799$	−18.4199	−	13.3828i	−0.651648	−	0.473450i
$800$	−32.2601	+	23.4383i	−1.14057	+	0.828669i
$801$	−4.16696	+	12.8246i	−0.147232	+	0.453134i
$802$	−86.0284			−3.03777
$803$	11.4077	−	16.0015i	0.402570	−	0.564680i
$804$	−11.5372			−0.406887
$805$	0.687055	−	2.11454i	0.0242155	−	0.0745277i
$806$	−36.1012	+	26.2290i	−1.27161	+	0.923879i
$807$	6.19849	+	4.50347i	0.218197	+	0.158530i
$808$	−11.4411	−	35.2120i	−0.402496	−	1.23876i
$809$	13.7513	+	42.3220i	0.483469	+	1.48796i	0.834186	+	0.551482i	$0.185938\pi$
$809$	13.7513	+	42.3220i	0.483469	+	1.48796i	−0.350718	+	0.936481i	$0.614062\pi$
$810$	−53.1737	−	38.6330i	−1.86833	−	1.35742i
$811$	19.5819	−	14.2271i	0.687612	−	0.499579i	−0.188262	−	0.982119i	$-0.560285\pi$
$811$	19.5819	−	14.2271i	0.687612	−	0.499579i	0.875874	+	0.482539i	$0.160285\pi$
$812$	−1.74713	+	5.37711i	−0.0613122	+	0.188700i
$813$	−12.4119			−0.435303
$814$	25.2478	+	34.1027i	0.884936	+	1.19530i
$815$	1.29473			0.0453524
$816$	4.20517	−	12.9422i	0.147210	−	0.453067i
$817$	−2.86563	+	2.08200i	−0.100256	+	0.0728399i
$818$	5.45879	+	3.96604i	0.190862	+	0.138669i
$819$	1.90305	+	5.85699i	0.0664980	+	0.204660i
$820$	−12.5354	−	38.5801i	−0.437756	−	1.34728i
$821$	7.50797	+	5.45486i	0.262030	+	0.190376i	0.711042	−	0.703150i	$-0.248224\pi$
$821$	7.50797	+	5.45486i	0.262030	+	0.190376i	−0.449011	+	0.893526i	$0.648224\pi$
$822$	7.74502	−	5.62709i	0.270139	−	0.196267i
$823$	−7.25674	+	22.3339i	−0.252954	+	0.778512i	0.741272	+	0.671205i	$0.234223\pi$
$823$	−7.25674	+	22.3339i	−0.252954	+	0.778512i	−0.994226	+	0.107307i	$0.965777\pi$
$824$	−29.7558			−1.03659
$825$	8.77764	+	2.76517i	0.305598	+	0.0962709i
$826$	19.5728			0.681026
$827$	−6.09962	+	18.7727i	−0.212105	+	0.652791i	0.787242	+	0.616644i	$0.211508\pi$
$827$	−6.09962	+	18.7727i	−0.212105	+	0.652791i	−0.999346	+	0.0361466i	$0.988492\pi$
$828$	6.70214	−	4.86939i	0.232916	−	0.169223i
$829$	32.3557	+	23.5078i	1.12376	+	0.816459i	0.984775	−	0.173836i	$-0.0556163\pi$
$829$	32.3557	+	23.5078i	1.12376	+	0.816459i	0.138984	+	0.990295i	$0.455616\pi$
$830$	−22.6535	−	69.7203i	−0.786315	−	2.42003i
$831$	−1.71190	−	5.26868i	−0.0593851	−	0.182769i
$832$	0.675650	+	0.490889i	0.0234240	+	0.0170185i
$833$	3.65445	−	2.65511i	0.126619	−	0.0919942i
$834$	−3.48140	+	10.7146i	−0.120551	+	0.371018i
$835$	−0.391379			−0.0135442
$836$	0.325604	+	36.2732i	0.0112613	+	1.25454i
$837$	−19.2494			−0.665357
$838$	26.0833	−	80.2760i	0.901031	−	2.77309i
$839$	6.34929	−	4.61303i	0.219202	−	0.159259i	−0.472766	−	0.881188i	$-0.656744\pi$
$839$	6.34929	−	4.61303i	0.219202	−	0.159259i	0.691967	+	0.721929i	$0.256744\pi$
$840$	7.30299	+	5.30593i	0.251977	+	0.183072i
$841$	−8.47637	−	26.0876i	−0.292289	−	0.899572i
$842$	26.5613	+	81.7473i	0.915363	+	2.81720i
$843$	2.69157	+	1.95554i	0.0927025	+	0.0673523i
$844$	49.8962	−	36.2517i	1.71750	−	1.24783i
$845$	−8.76218	+	26.9672i	−0.301428	+	0.927701i
$846$	36.4198			1.25214
$847$	9.01382	+	6.30484i	0.309719	+	0.216637i
$848$	98.3017			3.37569
$849$	−1.26770	+	3.90157i	−0.0435073	+	0.133902i
$850$	63.0236	−	45.7894i	2.16169	−	1.57056i
$851$	−2.62982	−	1.91067i	−0.0901490	−	0.0654970i
$852$	−2.42184	−	7.45365i	−0.0829708	−	0.255358i
$853$	−12.6694	−	38.9924i	−0.433792	−	1.33507i	−0.894320	−	0.447428i	$-0.852340\pi$
$853$	−12.6694	−	38.9924i	−0.433792	−	1.33507i	0.460528	−	0.887645i	$-0.347660\pi$
$854$	−29.5952	−	21.5022i	−1.01273	−	0.735789i
$855$	−19.0381	+	13.8320i	−0.651089	+	0.473044i
$856$	−7.96871	+	24.5252i	−0.272365	+	0.838253i
$857$	31.1892			1.06540			0.532702	−	0.846303i	$-0.321177\pi$
$857$	31.1892			1.06540			0.532702	+	0.846303i	$0.321177\pi$
$858$	−0.0678479	−	7.55845i	−0.00231629	−	0.258041i
$859$	7.95825			0.271532			0.135766	−	0.990741i	$-0.456650\pi$
$859$	7.95825			0.271532			0.135766	+	0.990741i	$0.456650\pi$
$860$	−6.98745	+	21.5052i	−0.238270	+	0.733320i
$861$	−0.870880	+	0.632732i	−0.0296795	+	0.0215634i
$862$	61.4261	+	44.6287i	2.09218	+	1.52006i
$863$	9.61174	+	29.5819i	0.327187	+	1.00698i	0.970444	+	0.241328i	$0.0775830\pi$
$863$	9.61174	+	29.5819i	0.327187	+	1.00698i	−0.643256	+	0.765651i	$0.722417\pi$
$864$	4.36586	+	13.4367i	0.148530	+	0.457127i
$865$	36.8984	+	26.8082i	1.25458	+	0.911507i
$866$	47.7967	−	34.7263i	1.62420	−	1.18005i
$867$	−0.431987	+	1.32952i	−0.0146710	+	0.0451528i
$868$	−36.2774			−1.23133
$869$	−30.8846	−	9.72939i	−1.04769	−	0.330047i
$870$	4.50180			0.152625
$871$	−4.18528	+	12.8810i	−0.141813	+	0.436455i
$872$	31.8879	−	23.1679i	1.07986	−	0.784565i
$873$	−19.9418	−	14.4886i	−0.674927	−	0.490363i
$874$	−1.23936	−	3.81435i	−0.0419219	−	0.129022i
$875$	1.86267	+	5.73272i	0.0629698	+	0.193801i
$876$	−8.88145	−	6.45275i	−0.300077	−	0.218018i
$877$	41.9857	−	30.5044i	1.41776	−	1.03006i	0.425618	−	0.904903i	$-0.360057\pi$
$877$	41.9857	−	30.5044i	1.41776	−	1.03006i	0.992137	−	0.125157i	$-0.0399434\pi$
$878$	12.4729	−	38.3875i	0.420938	−	1.29552i
$879$	−12.6175			−0.425579
$880$	49.6495	+	67.0624i	1.67368	+	2.26067i
$881$	42.1448			1.41989			0.709947	−	0.704256i	$-0.248719\pi$
$881$	42.1448			1.41989			0.709947	+	0.704256i	$0.248719\pi$
$882$	−2.23283	+	6.87195i	−0.0751833	+	0.231390i
$883$	14.2855	−	10.3790i	0.480744	−	0.349281i	−0.320870	−	0.947123i	$-0.603975\pi$
$883$	14.2855	−	10.3790i	0.480744	−	0.349281i	0.801614	+	0.597842i	$0.203975\pi$
$884$	−35.8671	−	26.0590i	−1.20634	−	0.876458i
$885$	−3.33693	−	10.2700i	−0.112170	−	0.345223i
$886$	−7.90696	−	24.3351i	−0.265640	−	0.817554i
$887$	8.61844	+	6.26166i	0.289379	+	0.210246i	0.722998	−	0.690850i	$-0.242764\pi$
$887$	8.61844	+	6.26166i	0.289379	+	0.210246i	−0.433619	+	0.901096i	$0.642764\pi$
$888$	10.6772	−	7.75747i	0.358305	−	0.260324i
$889$	−2.14890	+	6.61362i	−0.0720716	+	0.221814i
$890$	41.6744			1.39693
$891$	−14.4611	+	20.2845i	−0.484466	+	0.679555i
$892$	−24.2255			−0.811131
$893$	3.77524	−	11.6190i	0.126334	−	0.388815i
$894$	9.11744	−	6.62421i	0.304933	−	0.221547i
$895$	−31.4610	−	22.8578i	−1.05163	−	0.764051i
$896$	−3.34398	−	10.2917i	−0.111715	−	0.343822i
$897$	0.178941	+	0.550724i	0.00597467	+	0.0183881i
$898$	−3.31624	−	2.40939i	−0.110664	−	0.0804024i
$899$	−8.14928	+	5.92079i	−0.271794	+	0.197470i
$900$	−26.6811	+	82.1160i	−0.889371	+	2.73720i
$901$	−60.5209			−2.01624
$902$	−21.0412	+	7.04614i	−0.700597	+	0.234611i
$903$	0.600040			0.0199681
$904$	−4.91032	+	15.1124i	−0.163315	+	0.502631i
$905$	−32.6147	+	23.6960i	−1.08415	+	0.787680i
$906$	−6.49701	−	4.72036i	−0.215849	−	0.156823i
$907$	15.5437	+	47.8386i	0.516120	+	1.58845i	0.781235	+	0.624237i	$0.214590\pi$
$907$	15.5437	+	47.8386i	0.516120	+	1.58845i	−0.265115	+	0.964217i	$0.585410\pi$
$908$	14.7989	+	45.5462i	0.491117	+	1.51150i
$909$	−13.2277	−	9.61047i	−0.438735	−	0.318759i
$910$	15.3978	−	11.1872i	0.510432	−	0.370851i
$911$	−7.11891	+	21.9097i	−0.235860	+	0.725902i	0.761146	+	0.648580i	$0.224637\pi$
$911$	−7.11891	+	21.9097i	−0.235860	+	0.725902i	−0.997006	+	0.0773220i	$0.975363\pi$
$912$	7.30190			0.241790
$913$	−26.3472	+	8.82296i	−0.871965	+	0.291997i
$914$	9.58753			0.317127
$915$	−6.23672	+	19.1947i	−0.206180	+	0.634556i
$916$	−82.6535	+	60.0513i	−2.73095	+	1.98415i
$917$	16.9398	+	12.3075i	0.559402	+	0.406430i
$918$	−8.52920	−	26.2502i	−0.281506	−	0.866385i
$919$	−11.7629	−	36.2024i	−0.388022	−	1.19421i	−0.934264	−	0.356581i	$-0.883942\pi$
$919$	−11.7629	−	36.2024i	−0.388022	−	1.19421i	0.546243	−	0.837627i	$-0.316058\pi$
$920$	−11.5326	−	8.37894i	−0.380219	−	0.276246i
$921$	−6.66610	+	4.84320i	−0.219655	+	0.159589i
$922$	−11.1861	+	34.4274i	−0.368396	+	1.13381i
$923$	−9.20031			−0.302832
$924$	3.56717	−	5.00363i	0.117351	−	0.164607i
$925$	33.8792			1.11394
$926$	−4.21318	+	12.9668i	−0.138454	+	0.426117i
$927$	−10.6309	+	7.72380i	−0.349165	+	0.253683i
$928$	5.98121	+	4.34560i	0.196343	+	0.142651i
$929$	−5.41960	−	16.6798i	−0.177811	−	0.547247i	0.821939	−	0.569575i	$-0.192892\pi$
$929$	−5.41960	−	16.6798i	−0.177811	−	0.547247i	−0.999751	+	0.0223282i	$0.992892\pi$
$930$	8.92610	+	27.4717i	0.292699	+	0.900833i
$931$	1.96090	+	1.42468i	0.0642660	+	0.0466920i
$932$	−54.1154	+	39.3171i	−1.77261	+	1.28788i
$933$	2.97744	−	9.16361i	0.0974769	−	0.300003i
$934$	−60.9137			−1.99316
$935$	−30.5675	−	41.2880i	−0.999663	−	1.35026i
$936$	39.4848			1.29060
$937$	−17.5395	+	53.9810i	−0.572990	+	1.76348i	0.0699341	+	0.997552i	$0.477721\pi$
$937$	−17.5395	+	53.9810i	−0.572990	+	1.76348i	−0.642924	+	0.765930i	$0.722279\pi$
$938$	−12.8560	+	9.34040i	−0.419762	+	0.304975i
$939$	−4.87409	−	3.54123i	−0.159060	−	0.115564i
$940$	−24.1001	−	74.1726i	−0.786060	−	2.41924i
$941$	−6.89063	−	21.2072i	−0.224628	−	0.691335i	−0.998329	−	0.0577836i	$-0.981597\pi$
$941$	−6.89063	−	21.2072i	−0.224628	−	0.691335i	0.773701	−	0.633551i	$-0.218403\pi$
$942$	15.5546	+	11.3011i	0.506796	+	0.368209i
$943$	1.37526	−	0.999188i	0.0447848	−	0.0325380i
$944$	17.3894	−	53.5192i	0.565978	−	1.74190i
$945$	8.21023			0.267079
$946$	11.7973	+	3.71645i	0.383565	+	0.120832i
$947$	44.7782			1.45510			0.727548	−	0.686057i	$-0.240660\pi$
$947$	44.7782			1.45510			0.727548	+	0.686057i	$0.240660\pi$
$948$	−5.58984	+	17.2038i	−0.181550	+	0.558752i
$949$	−10.4262	+	7.57504i	−0.338447	+	0.245896i
$950$	33.8172	+	24.5696i	1.09718	+	0.797144i
$951$	−2.29034	−	7.04893i	−0.0742692	−	0.228577i
$952$	−8.94969	−	27.5443i	−0.290061	−	0.892717i
$953$	−1.49815	−	1.08847i	−0.0485298	−	0.0352590i	0.563256	−	0.826283i	$-0.309549\pi$
$953$	−1.49815	−	1.08847i	−0.0485298	−	0.0352590i	−0.611786	+	0.791024i	$0.709549\pi$
$954$	78.3199	−	56.9027i	2.53570	−	1.84229i
$955$	−23.8777	+	73.4880i	−0.772664	+	2.37802i
$956$	8.84115			0.285943
$957$	−0.0153156	−	1.70620i	−0.000495083	−	0.0551536i
$958$	−1.11396			−0.0359906
$959$	2.82332	−	8.68927i	0.0911696	−	0.280591i
$960$	0.437359	−	0.317760i	0.0141157	−	0.0102557i
$961$	−27.2097	−	19.7690i	−0.877731	−	0.637709i
$962$	−8.59888	−	26.4646i	−0.277239	−	0.853254i
$963$	3.51908	+	10.8306i	0.113401	+	0.349012i
$964$	−2.88491	−	2.09601i	−0.0929166	−	0.0675079i
$965$	−9.55186	+	6.93984i	−0.307485	+	0.223401i
$966$	−0.209950	+	0.646158i	−0.00675502	+	0.0207898i
$967$	−33.5800			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$967$	−33.5800			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$968$	56.3040	−	42.4722i	1.80968	−	1.36511i
$969$	−4.49552			−0.144417
$970$	−23.5408	+	72.4512i	−0.755850	+	2.32627i
$971$	−34.3624	+	24.9658i	−1.10274	+	0.801190i	−0.981506	−	0.191434i	$-0.938686\pi$
$971$	−34.3624	+	24.9658i	−1.10274	+	0.801190i	−0.121237	+	0.992624i	$0.538686\pi$
$972$	37.4814	+	27.2318i	1.20222	+	0.873462i
$973$	3.32251	+	10.2256i	0.106515	+	0.327819i
$974$	0.578575	+	1.78067i	0.0185387	+	0.0570564i
$975$	−4.88260	−	3.54742i	−0.156368	−	0.113608i
$976$	−85.0883	+	61.8203i	−2.72361	+	1.97882i
$977$	14.3176	−	44.0650i	0.458060	−	1.40976i	−0.409445	−	0.912335i	$-0.634278\pi$
$977$	14.3176	−	44.0650i	0.458060	−	1.40976i	0.867505	−	0.497429i	$-0.165722\pi$
$978$	−0.395642			−0.0126512
$979$	−0.141781	−	15.7948i	−0.00453133	−	0.504803i
$980$	15.4729			0.494265
$981$	5.37888	−	16.5545i	0.171735	−	0.528545i
$982$	−5.38338	+	3.91125i	−0.171790	+	0.124813i
$983$	−20.2988	−	14.7479i	−0.647430	−	0.470386i	0.214965	−	0.976622i	$-0.431036\pi$
$983$	−20.2988	−	14.7479i	−0.647430	−	0.470386i	−0.862395	+	0.506236i	$0.831036\pi$
$984$	2.13277	+	6.56400i	0.0679903	+	0.209253i
$985$	−2.31221	−	7.11626i	−0.0736733	−	0.226743i
$986$	−11.6850	−	8.48962i	−0.372125	−	0.270365i
$987$	−1.67432	+	1.21647i	−0.0532942	+	0.0387205i
$988$	7.35115	−	22.6245i	0.233871	−	0.719782i
$989$	−0.947563			−0.0301307
$990$	78.3769	+	24.6906i	2.49098	+	0.784720i
$991$	37.5645			1.19328			0.596638	−	0.802510i	$-0.296503\pi$
$991$	37.5645			1.19328			0.596638	+	0.802510i	$0.296503\pi$
$992$	−14.6591	+	45.1160i	−0.465426	+	1.43243i
$993$	−6.58716	+	4.78585i	−0.209037	+	0.151874i
$994$	−8.73304	−	6.34492i	−0.276995	−	0.201249i
$995$	2.47350	+	7.61264i	0.0784151	+	0.241337i
$996$	4.79651	+	14.7622i	0.151983	+	0.467757i
$997$	−28.9944	−	21.0656i	−0.918261	−	0.667156i	0.0248294	−	0.999692i	$-0.492096\pi$
$997$	−28.9944	−	21.0656i	−0.918261	−	0.667156i	−0.943091	+	0.332536i	$0.892096\pi$
$998$	17.0492	−	12.3870i	0.539683	−	0.392102i
$999$	3.70933	−	11.4162i	0.117358	−	0.361191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.b.64.4	✓	16
3.2	odd	2		693.2.m.i.64.1		16
7.2	even	3		539.2.q.g.361.1		32
7.3	odd	6		539.2.q.f.471.4		32
7.4	even	3		539.2.q.g.471.4		32
7.5	odd	6		539.2.q.f.361.1		32
7.6	odd	2		539.2.f.e.295.4		16
11.2	odd	10		847.2.f.v.729.4		16
11.3	even	5		847.2.f.w.323.1		16
11.4	even	5		847.2.a.p.1.8		8
11.5	even	5	inner	77.2.f.b.71.4	yes	16
11.6	odd	10		847.2.f.x.148.1		16
11.7	odd	10		847.2.a.o.1.1		8
11.8	odd	10		847.2.f.v.323.4		16
11.9	even	5		847.2.f.w.729.1		16
11.10	odd	2		847.2.f.x.372.1		16
33.5	odd	10		693.2.m.i.379.1		16
33.26	odd	10		7623.2.a.ct.1.1		8
33.29	even	10		7623.2.a.cw.1.8		8
77.5	odd	30		539.2.q.f.214.4		32
77.16	even	15		539.2.q.g.214.4		32
77.27	odd	10		539.2.f.e.148.4		16
77.38	odd	30		539.2.q.f.324.1		32
77.48	odd	10		5929.2.a.bt.1.8		8
77.60	even	15		539.2.q.g.324.1		32
77.62	even	10		5929.2.a.bs.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.4	✓	16	1.1	even	1	trivial
77.2.f.b.71.4	yes	16	11.5	even	5	inner
539.2.f.e.148.4		16	77.27	odd	10
539.2.f.e.295.4		16	7.6	odd	2
539.2.q.f.214.4		32	77.5	odd	30
539.2.q.f.324.1		32	77.38	odd	30
539.2.q.f.361.1		32	7.5	odd	6
539.2.q.f.471.4		32	7.3	odd	6
539.2.q.g.214.4		32	77.16	even	15
539.2.q.g.324.1		32	77.60	even	15
539.2.q.g.361.1		32	7.2	even	3
539.2.q.g.471.4		32	7.4	even	3
693.2.m.i.64.1		16	3.2	odd	2
693.2.m.i.379.1		16	33.5	odd	10
847.2.a.o.1.1		8	11.7	odd	10
847.2.a.p.1.8		8	11.4	even	5
847.2.f.v.323.4		16	11.8	odd	10
847.2.f.v.729.4		16	11.2	odd	10
847.2.f.w.323.1		16	11.3	even	5
847.2.f.w.729.1		16	11.9	even	5
847.2.f.x.148.1		16	11.6	odd	10
847.2.f.x.372.1		16	11.10	odd	2
5929.2.a.bs.1.1		8	77.62	even	10
5929.2.a.bt.1.8		8	77.48	odd	10
7623.2.a.ct.1.1		8	33.26	odd	10
7623.2.a.cw.1.8		8	33.29	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.788594 - 2.42704i) q^{2} +(0.332181 - 0.241344i) q^{3} +(-3.65062 - 2.65233i) q^{4} +(1.05961 + 3.26115i) q^{5} +(-0.323795 - 0.996539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-5.18703 + 3.76860i) q^{8} +(-0.874954 + 2.69283i) q^{9} +8.75055 q^{10} +(-0.0297703 - 3.31649i) q^{11} -1.85279 q^{12} +(-0.672122 + 2.06858i) q^{13} +(-2.06456 + 1.49999i) q^{14} +(1.13904 + 0.827562i) q^{15} +(2.26726 + 6.97792i) q^{16} +(-1.39588 - 4.29606i) q^{17} +(5.84563 + 4.24710i) q^{18} +(1.96090 - 1.42468i) q^{19} +(4.78140 - 14.7156i) q^{20} -0.410598 q^{21} +(-8.07274 - 2.54311i) q^{22} +0.648403 q^{23} +(-0.813506 + 2.50371i) q^{24} +(-5.46724 + 3.97218i) q^{25} +(4.49050 + 3.26254i) q^{26} +(0.739900 + 2.27718i) q^{27} +(1.39441 + 4.29156i) q^{28} +(1.01366 + 0.736466i) q^{29} +(2.90677 - 2.11189i) q^{30} +(-2.48433 + 7.64599i) q^{31} +5.90061 q^{32} +(-0.810303 - 1.09449i) q^{33} -11.5275 q^{34} +(1.05961 - 3.26115i) q^{35} +(10.3364 - 7.50983i) q^{36} +(-4.05584 - 2.94674i) q^{37} +(-1.91140 - 5.88269i) q^{38} +(0.275972 + 0.849355i) q^{39} +(-17.7862 - 12.9224i) q^{40} +(2.12100 - 1.54100i) q^{41} +(-0.323795 + 0.996539i) q^{42} -1.46138 q^{43} +(-8.68774 + 12.1862i) q^{44} -9.70884 q^{45} +(0.511326 - 1.57370i) q^{46} +(4.07776 - 2.96267i) q^{47} +(2.43722 + 1.77074i) q^{48} +(0.309017 + 0.951057i) q^{49} +(5.32922 + 16.4017i) q^{50} +(-1.50051 - 1.09019i) q^{51} +(7.94021 - 5.76890i) q^{52} +(4.14022 - 12.7423i) q^{53} +6.11028 q^{54} +(10.7840 - 3.61128i) q^{55} +6.41153 q^{56} +(0.307538 - 0.946503i) q^{57} +(2.58680 - 1.87942i) q^{58} +(-6.20498 - 4.50818i) q^{59} +(-1.96324 - 6.04222i) q^{60} +(4.42970 + 13.6332i) q^{61} +(16.5980 + 12.0591i) q^{62} +(2.29066 - 1.66426i) q^{63} +(0.118654 - 0.365178i) q^{64} -7.45814 q^{65} +(-3.29537 + 1.10353i) q^{66} +6.22696 q^{67} +(-6.29876 + 19.3856i) q^{68} +(0.215387 - 0.156488i) q^{69} +(-7.07934 - 5.14344i) q^{70} +(1.30713 + 4.02294i) q^{71} +(-5.60979 - 17.2651i) q^{72} +(4.79356 + 3.48273i) q^{73} +(-10.3503 + 7.51991i) q^{74} +(-0.857452 + 2.63897i) q^{75} -10.9372 q^{76} +(-1.92530 + 2.70060i) q^{77} +2.27905 q^{78} +(3.01699 - 9.28534i) q^{79} +(-20.3536 + 14.7878i) q^{80} +(-6.07661 - 4.41492i) q^{81} +(-2.06746 - 6.36299i) q^{82} +(-2.58881 - 7.96754i) q^{83} +(1.49894 + 1.08904i) q^{84} +(12.5310 - 9.10432i) q^{85} +(-1.15243 + 3.54683i) q^{86} +0.514460 q^{87} +(12.6529 + 17.0906i) q^{88} +4.76249 q^{89} +(-7.65633 + 23.5637i) q^{90} +(1.75964 - 1.27845i) q^{91} +(-2.36707 - 1.71978i) q^{92} +(1.02006 + 3.13943i) q^{93} +(-3.97482 - 12.2332i) q^{94} +(6.72389 + 4.88520i) q^{95} +(1.96007 - 1.42407i) q^{96} +(-2.69021 + 8.27962i) q^{97} +2.55194 q^{98} +(8.95679 + 2.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19}+ \cdots + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

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