LMFDB - Embedded newform 201.2.e.c.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, 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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3665654523963.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} + 21x^{6} - 5x^{5} + 26x^{4} + 4x^{3} + 13x^{2} - 3x + 1 $ x^10 - 2x^9 + 8x^8 + 21x^6 - 5x^5 + 26x^4 + 4x^3 + 13x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.5
Root			$-0.393795 + 0.682072i$ of defining polynomial
Character	$\chi$	$=$	201.37
Dual form			201.2.e.c.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31682 + 2.28079i) q^{2} +1.00000 q^{3} +(-2.46802 + 4.27473i) q^{4} -0.846046 q^{5} +(1.31682 + 2.28079i) q^{6} +(0.241054 - 0.417518i) q^{7} -7.73244 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.31682 + 2.28079i) q^{2} +1.00000 q^{3} +(-2.46802 + 4.27473i) q^{4} -0.846046 q^{5} +(1.31682 + 2.28079i) q^{6} +(0.241054 - 0.417518i) q^{7} -7.73244 q^{8} +1.00000 q^{9} +(-1.11409 - 1.92966i) q^{10} +(2.25619 - 3.90784i) q^{11} +(-2.46802 + 4.27473i) q^{12} +(-0.355142 - 0.615125i) q^{13} +1.26970 q^{14} -0.846046 q^{15} +(-5.24618 - 9.08665i) q^{16} +(3.30681 + 5.72756i) q^{17} +(1.31682 + 2.28079i) q^{18} +(-2.96109 - 5.12876i) q^{19} +(2.08806 - 3.61662i) q^{20} +(0.241054 - 0.417518i) q^{21} +11.8840 q^{22} +(2.61574 + 4.53060i) q^{23} -7.73244 q^{24} -4.28421 q^{25} +(0.935316 - 1.62001i) q^{26} +1.00000 q^{27} +(1.18985 + 2.06088i) q^{28} +(1.47935 - 2.56232i) q^{29} +(-1.11409 - 1.92966i) q^{30} +(1.64714 - 2.85293i) q^{31} +(6.08409 - 10.5379i) q^{32} +(2.25619 - 3.90784i) q^{33} +(-8.70893 + 15.0843i) q^{34} +(-0.203943 + 0.353240i) q^{35} +(-2.46802 + 4.27473i) q^{36} +(-3.31119 - 5.73516i) q^{37} +(7.79843 - 13.5073i) q^{38} +(-0.355142 - 0.615125i) q^{39} +6.54200 q^{40} +(3.93032 - 6.80752i) q^{41} +1.26970 q^{42} -7.36851 q^{43} +(11.1366 + 19.2892i) q^{44} -0.846046 q^{45} +(-6.88891 + 11.9319i) q^{46} +(-4.62484 + 8.01046i) q^{47} +(-5.24618 - 9.08665i) q^{48} +(3.38379 + 5.86089i) q^{49} +(-5.64152 - 9.77140i) q^{50} +(3.30681 + 5.72756i) q^{51} +3.50599 q^{52} -11.0606 q^{53} +(1.31682 + 2.28079i) q^{54} +(-1.90884 + 3.30621i) q^{55} +(-1.86394 + 3.22843i) q^{56} +(-2.96109 - 5.12876i) q^{57} +7.79216 q^{58} +7.46158 q^{59} +(2.08806 - 3.61662i) q^{60} +(1.40952 + 2.44135i) q^{61} +8.67594 q^{62} +(0.241054 - 0.417518i) q^{63} +11.0618 q^{64} +(0.300467 + 0.520424i) q^{65} +11.8840 q^{66} +(-0.565427 - 8.16580i) q^{67} -32.6450 q^{68} +(2.61574 + 4.53060i) q^{69} -1.07422 q^{70} +(1.71241 - 2.96598i) q^{71} -7.73244 q^{72} +(1.75048 + 3.03192i) q^{73} +(8.72048 - 15.1043i) q^{74} -4.28421 q^{75} +29.2321 q^{76} +(-1.08773 - 1.88400i) q^{77} +(0.935316 - 1.62001i) q^{78} +(1.09426 - 1.89532i) q^{79} +(4.43851 + 7.68773i) q^{80} +1.00000 q^{81} +20.7021 q^{82} +(0.629225 + 1.08985i) q^{83} +(1.18985 + 2.06088i) q^{84} +(-2.79771 - 4.84578i) q^{85} +(-9.70298 - 16.8060i) q^{86} +(1.47935 - 2.56232i) q^{87} +(-17.4459 + 30.2171i) q^{88} -12.9609 q^{89} +(-1.11409 - 1.92966i) q^{90} -0.342434 q^{91} -25.8228 q^{92} +(1.64714 - 2.85293i) q^{93} -24.3603 q^{94} +(2.50522 + 4.33917i) q^{95} +(6.08409 - 10.5379i) q^{96} +(-1.87469 - 3.24706i) q^{97} +(-8.91166 + 15.4354i) q^{98} +(2.25619 - 3.90784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.31682	+	2.28079i	0.931131	+	1.61277i	0.781392	+	0.624040i	$0.214510\pi$
$2$	1.31682	+	2.28079i	0.931131	+	1.61277i	0.149738	+	0.988726i	$0.452157\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.46802	+	4.27473i	−1.23401	+	2.13737i
$5$	−0.846046			−0.378363			−0.189182	−	0.981942i	$-0.560583\pi$
$5$	−0.846046			−0.378363			−0.189182	+	0.981942i	$0.560583\pi$
$6$	1.31682	+	2.28079i	0.537589	+	0.931131i
$7$	0.241054	−	0.417518i	0.0911099	−	0.157807i	−0.816869	−	0.576824i	$-0.804292\pi$
$7$	0.241054	−	0.417518i	0.0911099	−	0.157807i	0.907978	+	0.419017i	$0.137625\pi$
$8$	−7.73244			−2.73383
$9$	1.00000			0.333333
$10$	−1.11409	−	1.92966i	−0.352306	−	0.610211i
$11$	2.25619	−	3.90784i	0.680267	−	1.17826i	−0.294632	−	0.955611i	$-0.595197\pi$
$11$	2.25619	−	3.90784i	0.680267	−	1.17826i	0.974899	−	0.222647i	$-0.0714696\pi$
$12$	−2.46802	+	4.27473i	−0.712455	+	1.23401i
$13$	−0.355142	−	0.615125i	−0.0984988	−	0.170605i	0.812565	−	0.582871i	$-0.198071\pi$
$13$	−0.355142	−	0.615125i	−0.0984988	−	0.170605i	−0.911063	+	0.412266i	$0.864737\pi$
$14$	1.26970			0.339341
$15$	−0.846046			−0.218448
$16$	−5.24618	−	9.08665i	−1.31155	−	2.27166i
$17$	3.30681	+	5.72756i	0.802019	+	1.38914i	0.918285	+	0.395919i	$0.129574\pi$
$17$	3.30681	+	5.72756i	0.802019	+	1.38914i	−0.116266	+	0.993218i	$0.537093\pi$
$18$	1.31682	+	2.28079i	0.310377	+	0.537589i
$19$	−2.96109	−	5.12876i	−0.679321	−	1.17662i	−0.975186	−	0.221388i	$-0.928941\pi$
$19$	−2.96109	−	5.12876i	−0.679321	−	1.17662i	0.295865	−	0.955230i	$-0.404392\pi$
$20$	2.08806	−	3.61662i	0.466904	−	0.808701i
$21$	0.241054	−	0.417518i	0.0526023	−	0.0911099i
$22$	11.8840			2.53367
$23$	2.61574	+	4.53060i	0.545420	+	0.944696i	0.998580	+	0.0532664i	$0.0169633\pi$
$23$	2.61574	+	4.53060i	0.545420	+	0.944696i	−0.453160	+	0.891429i	$0.649703\pi$
$24$	−7.73244			−1.57838
$25$	−4.28421			−0.856841
$26$	0.935316	−	1.62001i	0.183430	−	0.317711i
$27$	1.00000			0.192450
$28$	1.18985	+	2.06088i	0.224861	+	0.389470i
$29$	1.47935	−	2.56232i	0.274709	−	0.475810i	−0.695353	−	0.718669i	$-0.744752\pi$
$29$	1.47935	−	2.56232i	0.274709	−	0.475810i	0.970062	+	0.242859i	$0.0780851\pi$
$30$	−1.11409	−	1.92966i	−0.203404	−	0.352306i
$31$	1.64714	−	2.85293i	0.295835	−	0.512402i	−0.679344	−	0.733820i	$-0.737735\pi$
$31$	1.64714	−	2.85293i	0.295835	−	0.512402i	0.975179	+	0.221419i	$0.0710687\pi$
$32$	6.08409	−	10.5379i	1.07552	−	1.86286i
$33$	2.25619	−	3.90784i	0.392752	−	0.680267i
$34$	−8.70893	+	15.0843i	−1.49357	+	2.58694i
$35$	−0.203943	+	0.353240i	−0.0344726	+	0.0597084i
$36$	−2.46802	+	4.27473i	−0.411336	+	0.712455i
$37$	−3.31119	−	5.73516i	−0.544357	−	0.942854i	−0.998647	−	0.0520001i	$-0.983440\pi$
$37$	−3.31119	−	5.73516i	−0.544357	−	0.942854i	0.454290	−	0.890854i	$-0.349893\pi$
$38$	7.79843	−	13.5073i	1.26507	−	2.19117i
$39$	−0.355142	−	0.615125i	−0.0568683	−	0.0984988i
$40$	6.54200			1.03438
$41$	3.93032	−	6.80752i	0.613813	−	1.06316i	−0.376779	−	0.926303i	$-0.622968\pi$
$41$	3.93032	−	6.80752i	0.613813	−	1.06316i	0.990592	−	0.136852i	$-0.0436984\pi$
$42$	1.26970			0.195919
$43$	−7.36851			−1.12369			−0.561843	−	0.827244i	$-0.689908\pi$
$43$	−7.36851			−1.12369			−0.561843	+	0.827244i	$0.689908\pi$
$44$	11.1366	+	19.2892i	1.67891	+	2.90796i
$45$	−0.846046			−0.126121
$46$	−6.88891	+	11.9319i	−1.01571	+	1.75927i
$47$	−4.62484	+	8.01046i	−0.674602	+	1.16845i	0.301983	+	0.953313i	$0.402351\pi$
$47$	−4.62484	+	8.01046i	−0.674602	+	1.16845i	−0.976585	+	0.215132i	$0.930982\pi$
$48$	−5.24618	−	9.08665i	−0.757221	−	1.31155i
$49$	3.38379	+	5.86089i	0.483398	+	0.837270i
$50$	−5.64152	−	9.77140i	−0.797831	−	1.38188i
$51$	3.30681	+	5.72756i	0.463046	+	0.802019i
$52$	3.50599			0.486193
$53$	−11.0606			−1.51929			−0.759645	−	0.650338i	$-0.774627\pi$
$53$	−11.0606			−1.51929			−0.759645	+	0.650338i	$0.774627\pi$
$54$	1.31682	+	2.28079i	0.179196	+	0.310377i
$55$	−1.90884	+	3.30621i	−0.257388	+	0.445809i
$56$	−1.86394	+	3.22843i	−0.249079	+	0.431418i
$57$	−2.96109	−	5.12876i	−0.392206	−	0.679321i
$58$	7.79216			1.02316
$59$	7.46158			0.971414			0.485707	−	0.874122i	$-0.338562\pi$
$59$	7.46158			0.971414			0.485707	+	0.874122i	$0.338562\pi$
$60$	2.08806	−	3.61662i	0.269567	−	0.466904i
$61$	1.40952	+	2.44135i	0.180470	+	0.312583i	0.942041	−	0.335499i	$-0.108905\pi$
$61$	1.40952	+	2.44135i	0.180470	+	0.312583i	−0.761571	+	0.648082i	$0.775571\pi$
$62$	8.67594			1.10185
$63$	0.241054	−	0.417518i	0.0303700	−	0.0526023i
$64$	11.0618			1.38273
$65$	0.300467	+	0.520424i	0.0372683	+	0.0645506i
$66$	11.8840			1.46282
$67$	−0.565427	−	8.16580i	−0.0690779	−	0.997611i
$67$	−0.565427	−	8.16580i	−0.0690779	−	0.997611i
$68$	−32.6450			−3.95879
$69$	2.61574	+	4.53060i	0.314899	+	0.545420i
$70$	−1.07422			−0.128394
$71$	1.71241	−	2.96598i	0.203226	−	0.351997i	−0.746340	−	0.665565i	$-0.768191\pi$
$71$	1.71241	−	2.96598i	0.203226	−	0.351997i	0.949566	+	0.313567i	$0.101524\pi$
$72$	−7.73244			−0.911277
$73$	1.75048	+	3.03192i	0.204878	+	0.354859i	0.950094	−	0.311964i	$-0.100987\pi$
$73$	1.75048	+	3.03192i	0.204878	+	0.354859i	−0.745216	+	0.666823i	$0.767654\pi$
$74$	8.72048	−	15.1043i	1.01373	−	1.75584i
$75$	−4.28421			−0.494698
$76$	29.2321			3.35315
$77$	−1.08773	−	1.88400i	−0.123958	−	0.214702i
$78$	0.935316	−	1.62001i	0.105904	−	0.183430i
$79$	1.09426	−	1.89532i	0.123114	−	0.213240i	−0.797880	−	0.602816i	$-0.794045\pi$
$79$	1.09426	−	1.89532i	0.123114	−	0.213240i	0.920994	+	0.389576i	$0.127378\pi$
$80$	4.43851	+	7.68773i	0.496241	+	0.859514i
$81$	1.00000			0.111111
$82$	20.7021			2.28616
$83$	0.629225	+	1.08985i	0.0690665	+	0.119627i	0.898491	−	0.438993i	$-0.144665\pi$
$83$	0.629225	+	1.08985i	0.0690665	+	0.119627i	−0.829424	+	0.558619i	$0.811331\pi$
$84$	1.18985	+	2.06088i	0.129823	+	0.224861i
$85$	−2.79771	−	4.84578i	−0.303455	−	0.525599i
$86$	−9.70298	−	16.8060i	−1.04630	−	1.81224i
$87$	1.47935	−	2.56232i	0.158603	−	0.274709i
$88$	−17.4459	+	30.2171i	−1.85974	+	3.22116i
$89$	−12.9609			−1.37385			−0.686926	−	0.726728i	$-0.741040\pi$
$89$	−12.9609			−1.37385			−0.686926	+	0.726728i	$0.741040\pi$
$90$	−1.11409	−	1.92966i	−0.117435	−	0.203404i
$91$	−0.342434			−0.0358969
$92$	−25.8228			−2.69221
$93$	1.64714	−	2.85293i	0.170801	−	0.295835i
$94$	−24.3603			−2.51257
$95$	2.50522	+	4.33917i	0.257030	+	0.445189i
$96$	6.08409	−	10.5379i	0.620955	−	1.07552i
$97$	−1.87469	−	3.24706i	−0.190346	−	0.329689i	0.755019	−	0.655703i	$-0.227628\pi$
$97$	−1.87469	−	3.24706i	−0.190346	−	0.329689i	−0.945365	+	0.326014i	$0.894294\pi$
$98$	−8.91166	+	15.4354i	−0.900213	+	1.55922i
$99$	2.25619	−	3.90784i	0.226756	−	0.392752i
$100$	10.5735	−	18.3138i	1.05735	−	1.83138i
$101$	−9.83253	+	17.0304i	−0.978373	+	1.69459i	−0.310052	+	0.950720i	$0.600346\pi$
$101$	−9.83253	+	17.0304i	−0.978373	+	1.69459i	−0.668321	+	0.743873i	$0.732987\pi$
$102$	−8.70893	+	15.0843i	−0.862312	+	1.49357i
$103$	−7.18376	+	12.4426i	−0.707837	+	1.22601i	0.257821	+	0.966193i	$0.416995\pi$
$103$	−7.18376	+	12.4426i	−0.707837	+	1.22601i	−0.965658	+	0.259816i	$0.916338\pi$
$104$	2.74612	+	4.75642i	0.269279	+	0.466405i
$105$	−0.203943	+	0.353240i	−0.0199028	+	0.0344726i
$106$	−14.5648	−	25.2270i	−1.41466	−	2.45026i
$107$	16.3310			1.57878			0.789388	−	0.613895i	$-0.210398\pi$
$107$	16.3310			1.57878			0.789388	+	0.613895i	$0.210398\pi$
$108$	−2.46802	+	4.27473i	−0.237485	+	0.411336i
$109$	−18.7830			−1.79908			−0.899541	−	0.436837i	$-0.856099\pi$
$109$	−18.7830			−1.79908			−0.899541	+	0.436837i	$0.856099\pi$
$110$	−10.0544			−0.958648
$111$	−3.31119	−	5.73516i	−0.314285	−	0.544357i
$112$	−5.05846			−0.477979
$113$	5.76468	−	9.98472i	0.542296	−	0.939284i	−0.456476	−	0.889736i	$-0.650889\pi$
$113$	5.76468	−	9.98472i	0.542296	−	0.939284i	0.998772	−	0.0495481i	$-0.0157781\pi$
$114$	7.79843	−	13.5073i	0.730390	−	1.26507i
$115$	−2.21304	−	3.83310i	−0.206367	−	0.357438i
$116$	7.30214	+	12.6477i	0.677987	+	1.17431i
$117$	−0.355142	−	0.615125i	−0.0328329	−	0.0568683i
$118$	9.82553	+	17.0183i	0.904514	+	1.56666i
$119$	3.18848			0.292288
$120$	6.54200			0.597200
$121$	−4.68080	−	8.10738i	−0.425527	−	0.737035i
$122$	−3.71215	+	6.42964i	−0.336083	+	0.582112i
$123$	3.93032	−	6.80752i	0.354385	−	0.613813i
$124$	8.13035	+	14.0822i	0.730127	+	1.26462i
$125$	7.85487			0.702561
$126$	1.26970			0.113114
$127$	1.43438	−	2.48442i	0.127281	−	0.220456i	−0.795342	−	0.606162i	$-0.792708\pi$
$127$	1.43438	−	2.48442i	0.127281	−	0.220456i	0.922622	+	0.385705i	$0.126042\pi$
$128$	2.39820	+	4.15381i	0.211973	+	0.367149i
$129$	−7.36851			−0.648761
$130$	−0.791320	+	1.37061i	−0.0694034	+	0.120210i
$131$	12.8012			1.11844			0.559221	−	0.829019i	$-0.311100\pi$
$131$	12.8012			1.11844			0.559221	+	0.829019i	$0.311100\pi$
$132$	11.1366	+	19.2892i	0.969320	+	1.67891i
$133$	−2.85513			−0.247571
$134$	17.8800	−	12.0425i	1.54459	−	1.04031i
$135$	−0.846046			−0.0728160
$136$	−25.5697	−	44.2880i	−2.19258	−	3.79767i
$137$	−12.9209			−1.10391			−0.551954	−	0.833874i	$-0.686118\pi$
$137$	−12.9209			−1.10391			−0.551954	+	0.833874i	$0.686118\pi$
$138$	−6.88891	+	11.9319i	−0.586423	+	1.01571i
$139$	7.10906			0.602983			0.301491	−	0.953469i	$-0.402516\pi$
$139$	7.10906			0.602983			0.301491	+	0.953469i	$0.402516\pi$
$140$	−1.00667	−	1.74360i	−0.0850791	−	0.147361i
$141$	−4.62484	+	8.01046i	−0.389482	+	0.674602i
$142$	9.01973			0.756919
$143$	−3.20508			−0.268022
$144$	−5.24618	−	9.08665i	−0.437182	−	0.757221i
$145$	−1.25160	+	2.16784i	−0.103940	+	0.180029i
$146$	−4.61012	+	7.98496i	−0.381536	+	0.660840i
$147$	3.38379	+	5.86089i	0.279090	+	0.483398i
$148$	32.6883			2.68696
$149$	4.87115			0.399060			0.199530	−	0.979892i	$-0.436058\pi$
$149$	4.87115			0.399060			0.199530	+	0.979892i	$0.436058\pi$
$150$	−5.64152	−	9.77140i	−0.460628	−	0.797831i
$151$	3.76006	+	6.51261i	0.305989	+	0.529989i	0.977481	−	0.211023i	$-0.0676795\pi$
$151$	3.76006	+	6.51261i	0.305989	+	0.529989i	−0.671492	+	0.741012i	$0.734346\pi$
$152$	22.8965	+	39.6578i	1.85715	+	3.21667i
$153$	3.30681	+	5.72756i	0.267340	+	0.463046i
$154$	2.86468	−	4.96177i	0.230843	−	0.399831i
$155$	−1.39356	+	2.41371i	−0.111933	+	0.193874i
$156$	3.50599			0.280704
$157$	8.71894	+	15.1016i	0.695847	+	1.20524i	0.969894	+	0.243526i	$0.0783041\pi$
$157$	8.71894	+	15.1016i	0.695847	+	1.20524i	−0.274047	+	0.961716i	$0.588363\pi$
$158$	5.76379			0.458542
$159$	−11.0606			−0.877162
$160$	−5.14742	+	8.91559i	−0.406939	+	0.704839i
$161$	2.52214			0.198773
$162$	1.31682	+	2.28079i	0.103459	+	0.179196i
$163$	−5.44665	+	9.43388i	−0.426615	+	0.738918i	−0.996570	−	0.0827575i	$-0.973627\pi$
$163$	−5.44665	+	9.43388i	−0.426615	+	0.738918i	0.569955	+	0.821676i	$0.306961\pi$
$164$	19.4002	+	33.6021i	1.51490	+	2.62389i
$165$	−1.90884	+	3.30621i	−0.148603	+	0.257388i
$166$	−1.65715	+	2.87027i	−0.128620	+	0.222776i
$167$	−4.21257	+	7.29638i	−0.325978	+	0.564611i	−0.981710	−	0.190383i	$-0.939027\pi$
$167$	−4.21257	+	7.29638i	−0.325978	+	0.564611i	0.655732	+	0.754994i	$0.272360\pi$
$168$	−1.86394	+	3.22843i	−0.143806	+	0.249079i
$169$	6.24775	−	10.8214i	0.480596	−	0.832417i
$170$	7.36815	−	12.7620i	0.565112	−	0.978802i
$171$	−2.96109	−	5.12876i	−0.226440	−	0.392206i
$172$	18.1856	−	31.4984i	1.38664	−	2.40173i
$173$	3.75652	+	6.50648i	0.285603	+	0.494679i	0.972755	−	0.231835i	$-0.0744729\pi$
$173$	3.75652	+	6.50648i	0.285603	+	0.494679i	−0.687152	+	0.726513i	$0.741140\pi$
$174$	7.79216			0.590722
$175$	−1.03273	+	1.78873i	−0.0780667	+	0.135216i
$176$	−47.3456			−3.56881
$177$	7.46158			0.560846
$178$	−17.0671	−	29.5611i	−1.27923	−	2.21570i
$179$	6.92450			0.517561			0.258781	−	0.965936i	$-0.416679\pi$
$179$	6.92450			0.517561			0.258781	+	0.965936i	$0.416679\pi$
$180$	2.08806	−	3.61662i	0.155635	−	0.269567i
$181$	11.6147	−	20.1173i	0.863314	−	1.49530i	−0.00539686	−	0.999985i	$-0.501718\pi$
$181$	11.6147	−	20.1173i	0.863314	−	1.49530i	0.868711	−	0.495319i	$-0.164949\pi$
$182$	−0.450923	−	0.781022i	−0.0334247	−	0.0578932i
$183$	1.40952	+	2.44135i	0.104194	+	0.180470i
$184$	−20.2261	−	35.0326i	−1.49109	−	2.58264i
$185$	2.80142	+	4.85221i	0.205965	+	0.356741i
$186$	8.67594			0.636151
$187$	29.8432			2.18235
$188$	−22.8284	−	39.5399i	−1.66493	−	2.88374i
$189$	0.241054	−	0.417518i	0.0175341	−	0.0303700i
$190$	−6.59783	+	11.4278i	−0.478657	+	0.829058i
$191$	2.99136	+	5.18120i	0.216448	+	0.374898i	0.953719	−	0.300698i	$-0.0972196\pi$
$191$	2.99136	+	5.18120i	0.216448	+	0.374898i	−0.737272	+	0.675596i	$0.763886\pi$
$192$	11.0618			0.798317
$193$	11.6862			0.841195			0.420597	−	0.907247i	$-0.361821\pi$
$193$	11.6862			0.841195			0.420597	+	0.907247i	$0.361821\pi$
$194$	4.93725	−	8.55156i	0.354474	−	0.613967i
$195$	0.300467	+	0.520424i	0.0215169	+	0.0372683i
$196$	−33.4050			−2.38607
$197$	−4.19926	+	7.27333i	−0.299185	+	0.518203i	−0.975950	−	0.217996i	$-0.930048\pi$
$197$	−4.19926	+	7.27333i	−0.299185	+	0.518203i	0.676765	+	0.736199i	$0.263381\pi$
$198$	11.8840			0.844557
$199$	1.49055	+	2.58171i	0.105662	+	0.183013i	0.914009	−	0.405695i	$-0.132970\pi$
$199$	1.49055	+	2.58171i	0.105662	+	0.183013i	−0.808346	+	0.588707i	$0.799637\pi$
$200$	33.1274			2.34246
$201$	−0.565427	−	8.16580i	−0.0398822	−	0.575971i
$202$	−51.7906			−3.64397
$203$	−0.713209	−	1.23531i	−0.0500574	−	0.0867020i
$204$	−32.6450			−2.28561
$205$	−3.32523	+	5.75947i	−0.232244	+	0.402259i
$206$	−37.8388			−2.63635
$207$	2.61574	+	4.53060i	0.181807	+	0.314899i
$208$	−3.72628	+	6.45411i	−0.258371	+	0.447512i
$209$	−26.7231			−1.84848
$210$	−1.07422			−0.0741284
$211$	5.12374	+	8.87458i	0.352733	+	0.610951i	0.986727	−	0.162386i	$-0.0519191\pi$
$211$	5.12374	+	8.87458i	0.352733	+	0.610951i	−0.633994	+	0.773338i	$0.718586\pi$
$212$	27.2977	−	47.2811i	1.87482	−	3.24728i
$213$	1.71241	−	2.96598i	0.117332	−	0.203226i
$214$	21.5049	+	37.2476i	1.47005	+	2.54620i
$215$	6.23409			0.425162
$216$	−7.73244			−0.526126
$217$	−0.794101	−	1.37542i	−0.0539071	−	0.0933698i
$218$	−24.7337	−	42.8401i	−1.67518	−	2.90150i
$219$	1.75048	+	3.03192i	0.118286	+	0.204878i
$220$	−9.42211	−	16.3196i	−0.635238	−	1.10027i
$221$	2.34878	−	4.06820i	0.157996	−	0.273657i
$222$	8.72048	−	15.1043i	0.585280	−	1.01373i
$223$	15.9623			1.06891			0.534456	−	0.845196i	$-0.320516\pi$
$223$	15.9623			1.06891			0.534456	+	0.845196i	$0.320516\pi$
$224$	−2.93319	−	5.08043i	−0.195982	−	0.339451i
$225$	−4.28421			−0.285614
$226$	30.3641			2.01979
$227$	4.76678	−	8.25630i	0.316382	−	0.547990i	−0.663348	−	0.748311i	$-0.730865\pi$
$227$	4.76678	−	8.25630i	0.316382	−	0.547990i	0.979730	+	0.200321i	$0.0641985\pi$
$228$	29.2321			1.93594
$229$	3.12337	+	5.40983i	0.206398	+	0.357492i	0.950577	−	0.310488i	$-0.100493\pi$
$229$	3.12337	+	5.40983i	0.206398	+	0.357492i	−0.744179	+	0.667980i	$0.767159\pi$
$230$	5.82834	−	10.0950i	0.384309	−	0.665643i
$231$	−1.08773	−	1.88400i	−0.0715673	−	0.123958i
$232$	−11.4390	+	19.8130i	−0.751008	+	1.30078i
$233$	−9.68408	+	16.7733i	−0.634425	+	1.09886i	0.352211	+	0.935921i	$0.385430\pi$
$233$	−9.68408	+	16.7733i	−0.634425	+	1.09886i	−0.986637	+	0.162937i	$0.947903\pi$
$234$	0.935316	−	1.62001i	0.0611435	−	0.105904i
$235$	3.91283	−	6.77722i	0.255245	−	0.442097i
$236$	−18.4153	+	31.8962i	−1.19873	+	2.07627i
$237$	1.09426	−	1.89532i	0.0710801	−	0.123114i
$238$	4.19865	+	7.27227i	0.272158	+	0.471391i
$239$	3.02197	−	5.23421i	0.195475	−	0.338573i	−0.751581	−	0.659641i	$-0.770708\pi$
$239$	3.02197	−	5.23421i	0.195475	−	0.338573i	0.947056	+	0.321068i	$0.104042\pi$
$240$	4.43851	+	7.68773i	0.286505	+	0.496241i
$241$	−11.3737			−0.732643			−0.366322	−	0.930488i	$-0.619383\pi$
$241$	−11.3737			−0.732643			−0.366322	+	0.930488i	$0.619383\pi$
$242$	12.3275	−	21.3519i	0.792443	−	1.37255i
$243$	1.00000			0.0641500
$244$	−13.9148			−0.890807
$245$	−2.86284	−	4.95858i	−0.182900	−	0.316792i
$246$	20.7021			1.31992
$247$	−2.10322	+	3.64288i	−0.133825	+	0.231791i
$248$	−12.7364	+	22.0601i	−0.808764	+	1.40082i
$249$	0.629225	+	1.08985i	0.0398755	+	0.0690665i
$250$	10.3434	+	17.9153i	0.654176	+	1.13307i
$251$	6.33220	+	10.9677i	0.399685	+	0.692275i	0.993687	−	0.112189i	$-0.0357861\pi$
$251$	6.33220	+	10.9677i	0.399685	+	0.692275i	−0.594002	+	0.804464i	$0.702453\pi$
$252$	1.18985	+	2.06088i	0.0749536	+	0.129823i
$253$	23.6065			1.48413
$254$	7.55526			0.474059
$255$	−2.79771	−	4.84578i	−0.175200	−	0.303455i
$256$	4.74581	−	8.21998i	0.296613	−	0.513749i
$257$	−4.48897	+	7.77513i	−0.280014	+	0.484999i	−0.971388	−	0.237498i	$-0.923673\pi$
$257$	−4.48897	+	7.77513i	−0.280014	+	0.484999i	0.691374	+	0.722497i	$0.257006\pi$
$258$	−9.70298	−	16.8060i	−0.604081	−	1.04630i
$259$	−3.19271			−0.198385
$260$	−2.96623			−0.183958
$261$	1.47935	−	2.56232i	0.0915697	−	0.158603i
$262$	16.8568	+	29.1968i	1.04142	+	1.80379i
$263$	29.6560			1.82866			0.914332	−	0.404965i	$-0.132716\pi$
$263$	29.6560			1.82866			0.914332	+	0.404965i	$0.132716\pi$
$264$	−17.4459	+	30.2171i	−1.07372	+	1.85974i
$265$	9.35777			0.574843
$266$	−3.75969	−	6.51197i	−0.230521	−	0.399275i
$267$	−12.9609			−0.793193
$268$	36.3021	+	17.7363i	2.21750	+	1.08342i
$269$	−9.03605			−0.550938			−0.275469	−	0.961310i	$-0.588833\pi$
$269$	−9.03605			−0.550938			−0.275469	+	0.961310i	$0.588833\pi$
$270$	−1.11409	−	1.92966i	−0.0678013	−	0.117435i
$271$	10.3095			0.626257			0.313128	−	0.949711i	$-0.398623\pi$
$271$	10.3095			0.626257			0.313128	+	0.949711i	$0.398623\pi$
$272$	34.6962	−	60.0957i	2.10377	−	3.64383i
$273$	−0.342434			−0.0207251
$274$	−17.0145	−	29.4700i	−1.02788	−	1.78035i
$275$	−9.66599	+	16.7420i	−0.582881	+	1.00958i
$276$	−25.8228			−1.55435
$277$	−16.3506			−0.982414			−0.491207	−	0.871043i	$-0.663444\pi$
$277$	−16.3506			−0.982414			−0.491207	+	0.871043i	$0.663444\pi$
$278$	9.36134	+	16.2143i	0.561456	+	0.972470i
$279$	1.64714	−	2.85293i	0.0986118	−	0.170801i
$280$	1.57698	−	2.73140i	0.0942424	−	0.163233i
$281$	−12.1654	−	21.0711i	−0.725727	−	1.25700i	−0.958674	−	0.284506i	$-0.908170\pi$
$281$	−12.1654	−	21.0711i	−0.725727	−	1.25700i	0.232948	−	0.972489i	$-0.425163\pi$
$282$	−24.3603			−1.45063
$283$	−9.92073			−0.589726			−0.294863	−	0.955540i	$-0.595274\pi$
$283$	−9.92073			−0.589726			−0.294863	+	0.955540i	$0.595274\pi$
$284$	8.45252	+	14.6402i	0.501565	+	0.868736i
$285$	2.50522	+	4.33917i	0.148396	+	0.257030i
$286$	−4.22050	−	7.31012i	−0.249564	−	0.432257i
$287$	−1.89484	−	3.28196i	−0.111849	−	0.193728i
$288$	6.08409	−	10.5379i	0.358508	−	0.620955i
$289$	−13.3700	+	23.1575i	−0.786469	+	1.36220i
$290$	−6.59252			−0.387126
$291$	−1.87469	−	3.24706i	−0.109896	−	0.190346i
$292$	−17.2808			−1.01128
$293$	−6.48252			−0.378713			−0.189356	−	0.981908i	$-0.560640\pi$
$293$	−6.48252			−0.378713			−0.189356	+	0.981908i	$0.560640\pi$
$294$	−8.91166	+	15.4354i	−0.519738	+	0.900213i
$295$	−6.31284			−0.367548
$296$	25.6036	+	44.3468i	1.48818	+	2.57760i
$297$	2.25619	−	3.90784i	0.130917	−	0.226756i
$298$	6.41441	+	11.1101i	0.371577	+	0.643590i
$299$	1.85792	−	3.21802i	0.107446	−	0.186103i
$300$	10.5735	−	18.3138i	0.610461	−	1.05735i
$301$	−1.77621	+	3.07648i	−0.102379	+	0.177326i
$302$	−9.90262	+	17.1518i	−0.569832	+	0.986978i
$303$	−9.83253	+	17.0304i	−0.564864	+	0.978373i
$304$	−31.0688	+	53.8128i	−1.78192	+	3.08638i
$305$	−1.19252	−	2.06550i	−0.0682833	−	0.118270i
$306$	−8.70893	+	15.0843i	−0.497856	+	0.862312i
$307$	3.02197	+	5.23421i	0.172473	+	0.298732i	0.939284	−	0.343141i	$-0.111491\pi$
$307$	3.02197	+	5.23421i	0.172473	+	0.298732i	−0.766811	+	0.641873i	$0.778158\pi$
$308$	10.7381			0.611862
$309$	−7.18376	+	12.4426i	−0.408670	+	0.707837i
$310$	−7.34024			−0.416898
$311$	−2.86610			−0.162522			−0.0812609	−	0.996693i	$-0.525895\pi$
$311$	−2.86610			−0.162522			−0.0812609	+	0.996693i	$0.525895\pi$
$312$	2.74612	+	4.75642i	0.155468	+	0.269279i
$313$	30.2498			1.70982			0.854909	−	0.518779i	$-0.173613\pi$
$313$	30.2498			1.70982			0.854909	+	0.518779i	$0.173613\pi$
$314$	−22.9625	+	39.7722i	−1.29585	+	2.24448i
$315$	−0.203943	+	0.353240i	−0.0114909	+	0.0199028i
$316$	5.40133	+	9.35537i	0.303848	+	0.526281i
$317$	−10.0831	−	17.4645i	−0.566325	−	0.980904i	−0.996925	−	0.0783609i	$-0.975031\pi$
$317$	−10.0831	−	17.4645i	−0.566325	−	0.980904i	0.430600	−	0.902543i	$-0.358302\pi$
$318$	−14.5648	−	25.2270i	−0.816753	−	1.41466i
$319$	−6.67541	−	11.5622i	−0.373751	−	0.647356i
$320$	−9.35880			−0.523173
$321$	16.3310			0.911507
$322$	3.32120	+	5.75249i	0.185083	+	0.320574i
$323$	19.5835	−	33.9196i	1.08966	−	1.88734i
$324$	−2.46802	+	4.27473i	−0.137112	+	0.237485i
$325$	1.52150	+	2.63532i	0.0843978	+	0.146181i
$326$	−28.6890			−1.58894
$327$	−18.7830			−1.03870
$328$	−30.3910	+	52.6387i	−1.67806	+	2.90649i
$329$	2.22967	+	3.86191i	0.122926	+	0.212914i
$330$	−10.0544			−0.553476
$331$	6.31322	−	10.9348i	0.347006	−	0.601032i	−0.638710	−	0.769447i	$-0.720532\pi$
$331$	6.31322	−	10.9348i	0.347006	−	0.601032i	0.985716	+	0.168415i	$0.0538650\pi$
$332$	−6.21176			−0.340914
$333$	−3.31119	−	5.73516i	−0.181452	−	0.314285i
$334$	−22.1887			−1.21411
$335$	0.478377	+	6.90864i	0.0261366	+	0.377459i
$336$	−5.05846			−0.275961
$337$	−11.4905	−	19.9021i	−0.625928	−	1.08414i	−0.988361	−	0.152129i	$-0.951387\pi$
$337$	−11.4905	−	19.9021i	−0.625928	−	1.08414i	0.362433	−	0.932010i	$-0.381946\pi$
$338$	32.9086			1.78999
$339$	5.76468	−	9.98472i	0.313095	−	0.542296i
$340$	27.6192			1.49786
$341$	−7.43253	−	12.8735i	−0.402494	−	0.697140i
$342$	7.79843	−	13.5073i	0.421691	−	0.730390i
$343$	6.63746			0.358389
$344$	56.9765			3.07197
$345$	−2.21304	−	3.83310i	−0.119146	−	0.206367i
$346$	−9.89330	+	17.1357i	−0.531867	+	0.921221i
$347$	−0.827974	+	1.43409i	−0.0444480	+	0.0769862i	−0.887394	−	0.461013i	$-0.847486\pi$
$347$	−0.827974	+	1.43409i	−0.0444480	+	0.0769862i	0.842946	+	0.537999i	$0.180820\pi$
$348$	7.30214	+	12.6477i	0.391436	+	0.677987i
$349$	−13.2755			−0.710619			−0.355309	−	0.934749i	$-0.615625\pi$
$349$	−13.2755			−0.710619			−0.355309	+	0.934749i	$0.615625\pi$
$350$	−5.43965			−0.290761
$351$	−0.355142	−	0.615125i	−0.0189561	−	0.0328329i
$352$	−27.4537	−	47.5513i	−1.46329	−	2.53449i
$353$	−0.464607	−	0.804722i	−0.0247285	−	0.0428310i	0.853396	−	0.521263i	$-0.174539\pi$
$353$	−0.464607	−	0.804722i	−0.0247285	−	0.0428310i	−0.878125	+	0.478432i	$0.841205\pi$
$354$	9.82553	+	17.0183i	0.522221	+	0.904514i
$355$	−1.44878	+	2.50936i	−0.0768932	+	0.133183i
$356$	31.9877	−	55.4043i	1.69534	−	2.93642i
$357$	3.18848			0.168752
$358$	9.11830	+	15.7934i	0.481917	+	0.834705i
$359$	−34.5105			−1.82139			−0.910697	−	0.413074i	$-0.864455\pi$
$359$	−34.5105			−1.82139			−0.910697	+	0.413074i	$0.864455\pi$
$360$	6.54200			0.344794
$361$	−8.03611	+	13.9189i	−0.422953	+	0.732576i
$362$	61.1778			3.21543
$363$	−4.68080	−	8.10738i	−0.245678	−	0.425527i
$364$	0.845134	−	1.46381i	0.0442970	−	0.0767247i
$365$	−1.48098	−	2.56514i	−0.0775183	−	0.134266i
$366$	−3.71215	+	6.42964i	−0.194037	+	0.336083i
$367$	−1.32570	+	2.29618i	−0.0692011	+	0.119860i	−0.898550	−	0.438871i	$-0.855378\pi$
$367$	−1.32570	+	2.29618i	−0.0692011	+	0.119860i	0.829349	+	0.558731i	$0.188712\pi$
$368$	27.4453	−	47.5367i	1.43069	−	2.47802i
$369$	3.93032	−	6.80752i	0.204604	−	0.354385i
$370$	−7.37793	+	12.7789i	−0.383560	+	0.664346i
$371$	−2.66620	+	4.61800i	−0.138422	+	0.239755i
$372$	8.13035	+	14.0822i	0.421539	+	0.730127i
$373$	4.78407	−	8.28626i	0.247710	−	0.429046i	−0.715180	−	0.698940i	$-0.753655\pi$
$373$	4.78407	−	8.28626i	0.247710	−	0.429046i	0.962890	+	0.269894i	$0.0869887\pi$
$374$	39.2980	+	68.0662i	2.03205	+	3.51962i
$375$	7.85487			0.405624
$376$	35.7613	−	61.9404i	1.84425	−	3.19433i
$377$	−2.10153			−0.108234
$378$	1.26970			0.0653062
$379$	−16.7264	−	28.9710i	−0.859177	−	1.48814i	−0.872715	−	0.488230i	$-0.837643\pi$
$379$	−16.7264	−	28.9710i	−0.859177	−	1.48814i	0.0135378	−	0.999908i	$-0.495691\pi$
$380$	−24.7317			−1.26871
$381$	1.43438	−	2.48442i	0.0734855	−	0.127281i
$382$	−7.87816	+	13.6454i	−0.403082	+	0.698158i
$383$	5.48422	+	9.49896i	0.280231	+	0.485374i	0.971441	−	0.237279i	$-0.0762557\pi$
$383$	5.48422	+	9.49896i	0.280231	+	0.485374i	−0.691211	+	0.722653i	$0.742922\pi$
$384$	2.39820	+	4.15381i	0.122383	+	0.211973i
$385$	0.920269	+	1.59395i	0.0469012	+	0.0812353i
$386$	15.3887	+	26.6539i	0.783262	+	1.35665i
$387$	−7.36851			−0.374562
$388$	18.5071			0.939554
$389$	−8.61770	−	14.9263i	−0.436935	−	0.756793i	0.560517	−	0.828143i	$-0.310603\pi$
$389$	−8.61770	−	14.9263i	−0.436935	−	0.756793i	−0.997451	+	0.0713499i	$0.977269\pi$
$390$	−0.791320	+	1.37061i	−0.0400700	+	0.0694034i
$391$	−17.2995	+	29.9637i	−0.874875	+	1.51533i
$392$	−26.1649	−	45.3190i	−1.32153	−	2.28895i
$393$	12.8012			0.645733
$394$	−22.1186			−1.11432
$395$	−0.925798	+	1.60353i	−0.0465820	+	0.0806823i
$396$	11.1366	+	19.2892i	0.559637	+	0.969320i
$397$	−3.55653			−0.178497			−0.0892485	−	0.996009i	$-0.528447\pi$
$397$	−3.55653			−0.178497			−0.0892485	+	0.996009i	$0.528447\pi$
$398$	−3.92557	+	6.79929i	−0.196771	+	0.340817i
$399$	−2.85513			−0.142935
$400$	22.4757	+	38.9291i	1.12379	+	1.94646i
$401$	36.9107			1.84323			0.921616	−	0.388103i	$-0.126870\pi$
$401$	36.9107			1.84323			0.921616	+	0.388103i	$0.126870\pi$
$402$	17.8800	−	12.0425i	0.891771	−	0.600625i
$403$	−2.33988			−0.116558
$404$	−48.5337	−	84.0628i	−2.41464	−	4.18228i
$405$	−0.846046			−0.0420404
$406$	1.87833	−	3.25337i	0.0932200	−	0.161462i
$407$	−29.8828			−1.48123
$408$	−25.5697	−	44.2880i	−1.26589	−	2.19258i
$409$	8.73421	−	15.1281i	0.431879	−	0.748036i	−0.565156	−	0.824984i	$-0.691184\pi$
$409$	8.73421	−	15.1281i	0.431879	−	0.748036i	0.997035	+	0.0769479i	$0.0245175\pi$
$410$	−17.5149			−0.864999
$411$	−12.9209			−0.637342
$412$	−35.4593	−	61.4173i	−1.74695	−	3.02581i
$413$	1.79864	−	3.11534i	0.0885055	−	0.153296i
$414$	−6.88891	+	11.9319i	−0.338572	+	0.586423i
$415$	−0.532354	−	0.922064i	−0.0261322	−	0.0452623i
$416$	−8.64287			−0.423752
$417$	7.10906			0.348132
$418$	−35.1895	−	60.9500i	−1.72117	−	2.98116i
$419$	−7.42612	−	12.8624i	−0.362790	−	0.628370i	0.625629	−	0.780121i	$-0.284842\pi$
$419$	−7.42612	−	12.8624i	−0.362790	−	0.628370i	−0.988419	+	0.151750i	$0.951509\pi$
$420$	−1.00667	−	1.74360i	−0.0491204	−	0.0850791i
$421$	12.9893	+	22.4981i	0.633058	+	1.09649i	0.986923	+	0.161192i	$0.0515338\pi$
$421$	12.9893	+	22.4981i	0.633058	+	1.09649i	−0.353865	+	0.935296i	$0.615133\pi$
$422$	−13.4941	+	23.3724i	−0.656881	+	1.13775i
$423$	−4.62484	+	8.01046i	−0.224867	+	0.389482i
$424$	85.5254			4.15348
$425$	−14.1671	−	24.5381i	−0.687203	−	1.19027i
$426$	9.01973			0.437007
$427$	1.35908			0.0657705
$428$	−40.3052	+	69.8106i	−1.94822	+	3.37442i
$429$	−3.20508			−0.154743
$430$	8.20917	+	14.2187i	0.395881	+	0.685686i
$431$	−7.25757	+	12.5705i	−0.349585	+	0.605499i	−0.986176	−	0.165703i	$-0.947011\pi$
$431$	−7.25757	+	12.5705i	−0.349585	+	0.605499i	0.636591	+	0.771202i	$0.280344\pi$
$432$	−5.24618	−	9.08665i	−0.252407	−	0.437182i
$433$	0.202120	−	0.350082i	0.00971327	−	0.0168239i	−0.861128	−	0.508388i	$-0.830241\pi$
$433$	0.202120	−	0.350082i	0.00971327	−	0.0168239i	0.870841	+	0.491564i	$0.163575\pi$
$434$	2.09137	−	3.62236i	0.100389	−	0.173879i
$435$	−1.25160	+	2.16784i	−0.0600097	+	0.103940i
$436$	46.3567	−	80.2921i	2.22008	−	3.84529i
$437$	15.4909	−	26.8310i	0.741030	−	1.28350i
$438$	−4.61012	+	7.98496i	−0.220280	+	0.381536i
$439$	−18.5063	−	32.0538i	−0.883256	−	1.52984i	−0.847700	−	0.530477i	$-0.822013\pi$
$439$	−18.5063	−	32.0538i	−0.883256	−	1.52984i	−0.0355565	−	0.999368i	$-0.511320\pi$
$440$	14.7600	−	25.5651i	0.703656	−	1.21877i
$441$	3.38379	+	5.86089i	0.161133	+	0.279090i
$442$	12.3716			0.588459
$443$	0.497593	−	0.861857i	0.0236414	−	0.0409481i	−0.853963	−	0.520334i	$-0.825807\pi$
$443$	0.497593	−	0.861857i	0.0236414	−	0.0409481i	0.877604	+	0.479386i	$0.159141\pi$
$444$	32.6883			1.55132
$445$	10.9655			0.519815
$446$	21.0194	+	36.4067i	0.995297	+	1.72390i
$447$	4.87115			0.230397
$448$	2.66649	−	4.61850i	0.125980	−	0.218204i
$449$	−6.86146	+	11.8844i	−0.323812	+	0.560860i	−0.981271	−	0.192631i	$-0.938298\pi$
$449$	−6.86146	+	11.8844i	−0.323812	+	0.560860i	0.657459	+	0.753490i	$0.271631\pi$
$450$	−5.64152	−	9.77140i	−0.265944	−	0.460628i
$451$	−17.7351	−	30.7181i	−0.835114	−	1.44646i
$452$	28.4547	+	49.2849i	1.33840	+	2.31817i
$453$	3.76006	+	6.51261i	0.176663	+	0.305989i
$454$	25.1079			1.17837
$455$	0.289715			0.0135821
$456$	22.8965	+	39.6578i	1.07222	+	1.85715i
$457$	−5.34978	+	9.26609i	−0.250252	+	0.433449i	−0.963595	−	0.267366i	$-0.913847\pi$
$457$	−5.34978	+	9.26609i	−0.250252	+	0.433449i	0.713343	+	0.700815i	$0.247180\pi$
$458$	−8.22581	+	14.2475i	−0.384367	+	0.665743i
$459$	3.30681	+	5.72756i	0.154349	+	0.267340i
$460$	21.8473			1.01863
$461$	−2.65482			−0.123647			−0.0618236	−	0.998087i	$-0.519692\pi$
$461$	−2.65482			−0.123647			−0.0618236	+	0.998087i	$0.519692\pi$
$462$	2.86468	−	4.96177i	0.133277	−	0.230843i
$463$	3.15965	+	5.47267i	0.146841	+	0.254336i	0.930058	−	0.367412i	$-0.119756\pi$
$463$	3.15965	+	5.47267i	0.146841	+	0.254336i	−0.783217	+	0.621748i	$0.786423\pi$
$464$	−31.0438			−1.44117
$465$	−1.39356	+	2.41371i	−0.0646247	+	0.111933i
$466$	−51.0087			−2.36293
$467$	−13.1233	−	22.7302i	−0.607273	−	1.05183i	−0.991688	−	0.128667i	$-0.958930\pi$
$467$	−13.1233	−	22.7302i	−0.607273	−	1.05183i	0.384415	−	0.923160i	$-0.374403\pi$
$468$	3.50599			0.162064
$469$	−3.54567	−	1.73232i	−0.163724	−	0.0799913i
$470$	20.6099			0.950665
$471$	8.71894	+	15.1016i	0.401747	+	0.695847i
$472$	−57.6962			−2.65568
$473$	−16.6248	+	28.7949i	−0.764407	+	1.32399i
$474$	5.76379			0.264739
$475$	12.6859	+	21.9727i	0.582070	+	1.00817i
$476$	−7.86922	+	13.6299i	−0.360685	+	0.624725i
$477$	−11.0606			−0.506430
$478$	15.9176			0.728052
$479$	7.72866	+	13.3864i	0.353132	+	0.611642i	0.986796	−	0.161966i	$-0.0517835\pi$
$479$	7.72866	+	13.3864i	0.353132	+	0.611642i	−0.633665	+	0.773608i	$0.718450\pi$
$480$	−5.14742	+	8.91559i	−0.234946	+	0.406939i
$481$	−2.35189	+	4.07359i	−0.107237	+	0.185740i
$482$	−14.9771	−	25.9410i	−0.682186	−	1.18158i
$483$	2.52214			0.114762
$484$	46.2092			2.10042
$485$	1.58607	+	2.74716i	0.0720199	+	0.124742i
$486$	1.31682	+	2.28079i	0.0597321	+	0.103459i
$487$	−5.85739	−	10.1453i	−0.265424	−	0.459727i	0.702251	−	0.711930i	$-0.252179\pi$
$487$	−5.85739	−	10.1453i	−0.265424	−	0.459727i	−0.967675	+	0.252202i	$0.918845\pi$
$488$	−10.8990	−	18.8776i	−0.493375	−	0.854550i
$489$	−5.44665	+	9.43388i	−0.246306	+	0.426615i
$490$	7.53967	−	13.0591i	0.340608	−	0.589950i
$491$	0.890423			0.0401842			0.0200921	−	0.999798i	$-0.493604\pi$
$491$	0.890423			0.0401842			0.0200921	+	0.999798i	$0.493604\pi$
$492$	19.4002	+	33.6021i	0.874628	+	1.51490i
$493$	19.5678			0.881288
$494$	−11.0782			−0.498432
$495$	−1.90884	+	3.30621i	−0.0857961	+	0.148603i
$496$	−34.5648			−1.55201
$497$	−0.825568	−	1.42992i	−0.0370318	−	0.0641409i
$498$	−1.65715	+	2.87027i	−0.0742587	+	0.128620i
$499$	−5.60459	−	9.70744i	−0.250896	−	0.434565i	0.712877	−	0.701289i	$-0.247392\pi$
$499$	−5.60459	−	9.70744i	−0.250896	−	0.434565i	−0.963773	+	0.266725i	$0.914059\pi$
$500$	−19.3859	+	33.5774i	−0.866966	+	1.50163i
$501$	−4.21257	+	7.29638i	−0.188204	+	0.325978i
$502$	−16.6767	+	28.8849i	−0.744318	+	1.28920i
$503$	1.83789	−	3.18332i	0.0819474	−	0.141937i	−0.822139	−	0.569287i	$-0.807219\pi$
$503$	1.83789	−	3.18332i	0.0819474	−	0.141937i	0.904086	+	0.427350i	$0.140553\pi$
$504$	−1.86394	+	3.22843i	−0.0830264	+	0.143806i
$505$	8.31877	−	14.4085i	0.370181	−	0.641171i
$506$	31.0854	+	53.8415i	1.38192	+	2.39355i
$507$	6.24775	−	10.8214i	0.277472	−	0.480596i
$508$	7.08014	+	12.2632i	0.314131	+	0.544090i
$509$	−5.59342			−0.247924			−0.123962	−	0.992287i	$-0.539560\pi$
$509$	−5.59342			−0.247924			−0.123962	+	0.992287i	$0.539560\pi$
$510$	7.36815	−	12.7620i	0.326267	−	0.565112i
$511$	1.68784			0.0746656
$512$	34.5903			1.52869
$513$	−2.96109	−	5.12876i	−0.130735	−	0.226440i
$514$	−23.6446			−1.04292
$515$	6.07779	−	10.5270i	0.267819	−	0.463877i
$516$	18.1856	−	31.4984i	0.800576	−	1.38664i
$517$	20.8690	+	36.1463i	0.917820	+	1.58971i
$518$	−4.20422	−	7.28191i	−0.184723	−	0.319949i
$519$	3.75652	+	6.50648i	0.164893	+	0.285603i
$520$	−2.32334	−	4.02415i	−0.101885	−	0.176471i
$521$	−12.5959			−0.551837			−0.275918	−	0.961181i	$-0.588982\pi$
$521$	−12.5959			−0.551837			−0.275918	+	0.961181i	$0.588982\pi$
$522$	7.79216			0.341053
$523$	−8.30658	−	14.3874i	−0.363221	−	0.629118i	0.625268	−	0.780410i	$-0.284990\pi$
$523$	−8.30658	−	14.3874i	−0.363221	−	0.629118i	−0.988489	+	0.151293i	$0.951656\pi$
$524$	−31.5935	+	54.7215i	−1.38017	+	2.39052i
$525$	−1.03273	+	1.78873i	−0.0450718	+	0.0780667i
$526$	39.0515	+	67.6391i	1.70273	+	2.94921i
$527$	21.7871			0.949062
$528$	−47.3456			−2.06045
$529$	−2.18423	+	3.78319i	−0.0949664	+	0.164487i
$530$	12.3225	+	21.3432i	0.535254	+	0.927088i
$531$	7.46158			0.323805
$532$	7.04652	−	12.2049i	0.305505	−	0.529151i
$533$	−5.58329			−0.241839
$534$	−17.0671	−	29.5611i	−0.738567	−	1.27923i
$535$	−13.8168			−0.597351
$536$	4.37213	+	63.1416i	0.188847	+	2.72730i
$537$	6.92450			0.298814
$538$	−11.8988	−	20.6094i	−0.512995	−	0.888533i
$539$	30.5379			1.31536
$540$	2.08806	−	3.61662i	0.0898556	−	0.155635i
$541$	−9.10027			−0.391251			−0.195626	−	0.980679i	$-0.562674\pi$
$541$	−9.10027			−0.391251			−0.195626	+	0.980679i	$0.562674\pi$
$542$	13.5757	+	23.5138i	0.583127	+	1.01001i
$543$	11.6147	−	20.1173i	0.498435	−	0.863314i
$544$	80.4757			3.45037
$545$	15.8913			0.680706
$546$	−0.450923	−	0.781022i	−0.0192977	−	0.0334247i
$547$	7.61175	−	13.1839i	0.325455	−	0.563704i	−0.656149	−	0.754631i	$-0.727816\pi$
$547$	7.61175	−	13.1839i	0.325455	−	0.563704i	0.981604	+	0.190927i	$0.0611493\pi$
$548$	31.8891	−	55.2335i	1.36223	−	2.35946i
$549$	1.40952	+	2.44135i	0.0601567	+	0.104194i
$550$	−50.9134			−2.17095
$551$	−17.5220			−0.746462
$552$	−20.2261	−	35.0326i	−0.860879	−	1.49109i
$553$	−0.527554	−	0.913750i	−0.0224339	−	0.0388566i
$554$	−21.5308	−	37.2924i	−0.914756	−	1.58440i
$555$	2.80142	+	4.85221i	0.118914	+	0.205965i
$556$	−17.5453	+	30.3893i	−0.744086	+	1.28879i
$557$	11.7950	−	20.4295i	0.499768	−	0.865624i	−0.500232	−	0.865892i	$-0.666752\pi$
$557$	11.7950	−	20.4295i	0.499768	−	0.865624i	1.00000		0.000267404i	$8.51172e-5\pi$
$558$	8.67594			0.367282
$559$	2.61687	+	4.53255i	0.110682	+	0.191706i
$560$	4.27969			0.180850
$561$	29.8432			1.25998
$562$	32.0392	−	55.4935i	1.35149	−	2.34085i
$563$	37.0524			1.56157			0.780785	−	0.624799i	$-0.214819\pi$
$563$	37.0524			1.56157			0.780785	+	0.624799i	$0.214819\pi$
$564$	−22.8284	−	39.5399i	−0.961248	−	1.66493i
$565$	−4.87719	+	8.44754i	−0.205185	+	0.355391i
$566$	−13.0638	−	22.6271i	−0.549112	−	0.951090i
$567$	0.241054	−	0.417518i	0.0101233	−	0.0175341i
$568$	−13.2411	+	22.9343i	−0.555585	+	0.962301i
$569$	0.357739	−	0.619622i	0.0149972	−	0.0259759i	−0.858429	−	0.512932i	$-0.828559\pi$
$569$	0.357739	−	0.619622i	0.0149972	−	0.0259759i	0.873427	+	0.486956i	$0.161893\pi$
$570$	−6.59783	+	11.4278i	−0.276353	+	0.478657i
$571$	−6.80839	+	11.7925i	−0.284922	+	0.493500i	−0.972590	−	0.232525i	$-0.925301\pi$
$571$	−6.80839	+	11.7925i	−0.284922	+	0.493500i	0.687668	+	0.726025i	$0.258634\pi$
$572$	7.91019	−	13.7008i	0.330741	−	0.572861i
$573$	2.99136	+	5.18120i	0.124966	+	0.216448i
$574$	4.99032	−	8.64349i	0.208292	−	0.360772i
$575$	−11.2064	−	19.4100i	−0.467339	−	0.809454i
$576$	11.0618			0.460909
$577$	7.02095	−	12.1606i	0.292286	−	0.506254i	−0.682064	−	0.731292i	$-0.738917\pi$
$577$	7.02095	−	12.1606i	0.292286	−	0.506254i	0.974350	+	0.225039i	$0.0722508\pi$
$578$	−70.4232			−2.92922
$579$	11.6862			0.485664
$580$	−6.17795	−	10.7005i	−0.256525	−	0.444315i
$581$	0.606710			0.0251706
$582$	4.93725	−	8.55156i	0.204656	−	0.354474i
$583$	−24.9548	+	43.2230i	−1.03352	+	1.79011i
$584$	−13.5355	−	23.4441i	−0.560102	−	0.970125i
$585$	0.300467	+	0.520424i	0.0124228	+	0.0215169i
$586$	−8.53629	−	14.7853i	−0.352631	−	0.610775i
$587$	−0.174263	−	0.301832i	−0.00719260	−	0.0124579i	0.862407	−	0.506216i	$-0.168956\pi$
$587$	−0.174263	−	0.301832i	−0.00719260	−	0.0124579i	−0.869599	+	0.493758i	$0.835623\pi$
$588$	−33.4050			−1.37760
$589$	−19.5093			−0.803868
$590$	−8.31285	−	14.3983i	−0.342235	−	0.592768i
$591$	−4.19926	+	7.27333i	−0.172734	+	0.299185i
$592$	−34.7423	+	60.1754i	−1.42790	+	2.47319i
$593$	14.4647	+	25.0536i	0.593995	+	1.02883i	0.993688	+	0.112180i	$0.0357834\pi$
$593$	14.4647	+	25.0536i	0.593995	+	1.02883i	−0.399693	+	0.916649i	$0.630883\pi$
$594$	11.8840			0.487605
$595$	−2.69760			−0.110591
$596$	−12.0221	+	20.8228i	−0.492443	+	0.852937i
$597$	1.49055	+	2.58171i	0.0610042	+	0.105662i
$598$	9.78618			0.400187
$599$	16.8349	−	29.1589i	0.687856	−	1.19140i	−0.284673	−	0.958625i	$-0.591885\pi$
$599$	16.8349	−	29.1589i	0.687856	−	1.19140i	0.972530	−	0.232778i	$-0.0747815\pi$
$600$	33.1274			1.35242
$601$	−16.3703	−	28.3541i	−0.667757	−	1.15659i	−0.978530	−	0.206105i	$-0.933921\pi$
$601$	−16.3703	−	28.3541i	−0.667757	−	1.15659i	0.310773	−	0.950484i	$-0.399412\pi$
$602$	−9.35577			−0.381313
$603$	−0.565427	−	8.16580i	−0.0230260	−	0.332537i
$604$	−37.1196			−1.51037
$605$	3.96017	+	6.85922i	0.161004	+	0.278867i
$606$	−51.7906			−2.10385
$607$	−20.7001	+	35.8536i	−0.840191	+	1.45525i	0.0495420	+	0.998772i	$0.484224\pi$
$607$	−20.7001	+	35.8536i	−0.840191	+	1.45525i	−0.889733	+	0.456481i	$0.849110\pi$
$608$	−72.0621			−2.92251
$609$	−0.713209	−	1.23531i	−0.0289007	−	0.0500574i
$610$	3.14065	−	5.43977i	0.127161	−	0.220250i
$611$	6.56991			0.265790
$612$	−32.6450			−1.31960
$613$	9.99378	+	17.3097i	0.403645	+	0.699134i	0.994163	−	0.107891i	$-0.0344097\pi$
$613$	9.99378	+	17.3097i	0.403645	+	0.699134i	−0.590518	+	0.807025i	$0.701076\pi$
$614$	−7.95878	+	13.7850i	−0.321190	+	0.556318i
$615$	−3.32523	+	5.75947i	−0.134086	+	0.232244i
$616$	8.41080	+	14.5679i	0.338881	+	0.586959i
$617$	11.3438			0.456684			0.228342	−	0.973581i	$-0.426670\pi$
$617$	11.3438			0.456684			0.228342	+	0.973581i	$0.426670\pi$
$618$	−37.8388			−1.52210
$619$	21.2221	+	36.7577i	0.852986	+	1.47742i	0.878501	+	0.477741i	$0.158544\pi$
$619$	21.2221	+	36.7577i	0.852986	+	1.47742i	−0.0255143	+	0.999674i	$0.508122\pi$
$620$	−6.87865	−	11.9142i	−0.276253	−	0.478484i
$621$	2.61574	+	4.53060i	0.104966	+	0.181807i
$622$	−3.77413	−	6.53699i	−0.151329	−	0.262109i
$623$	−3.12428	+	5.41140i	−0.125171	+	0.216803i
$624$	−3.72628	+	6.45411i	−0.149171	+	0.258371i
$625$	14.7755			0.591018
$626$	39.8334	+	68.9935i	1.59206	+	2.75753i
$627$	−26.7231			−1.06722
$628$	−86.0739			−3.43472
$629$	21.8990	−	37.9301i	0.873169	−	1.51237i
$630$	−1.07422			−0.0427980
$631$	−13.5864	−	23.5323i	−0.540866	−	0.936807i	−0.998855	−	0.0478489i	$-0.984763\pi$
$631$	−13.5864	−	23.5323i	−0.540866	−	0.936807i	0.457989	−	0.888958i	$-0.348570\pi$
$632$	−8.46134	+	14.6555i	−0.336574	+	0.582963i
$633$	5.12374	+	8.87458i	0.203650	+	0.352733i
$634$	26.5553	−	45.9951i	1.05465	−	1.82670i
$635$	−1.21355	+	2.10193i	−0.0481583	+	0.0834126i
$636$	27.2977	−	47.2811i	1.08243	−	1.87482i
$637$	2.40345	−	4.16290i	0.0952282	−	0.164940i
$638$	17.5806	−	30.4505i	0.696022	−	1.20555i
$639$	1.71241	−	2.96598i	0.0677419	−	0.117332i
$640$	−2.02899	−	3.51432i	−0.0802029	−	0.138916i
$641$	−1.07824	+	1.86757i	−0.0425881	+	0.0737648i	−0.886534	−	0.462664i	$-0.846894\pi$
$641$	−1.07824	+	1.86757i	−0.0425881	+	0.0737648i	0.843946	+	0.536429i	$0.180227\pi$
$642$	21.5049	+	37.2476i	0.848732	+	1.47005i
$643$	−23.6552			−0.932868			−0.466434	−	0.884556i	$-0.654462\pi$
$643$	−23.6552			−0.932868			−0.466434	+	0.884556i	$0.654462\pi$
$644$	−6.22469	+	10.7815i	−0.245287	+	0.424850i
$645$	6.23409			0.245467
$646$	103.152			4.05845
$647$	−12.8260	−	22.2154i	−0.504244	−	0.873376i	−0.999988	−	0.00490724i	$-0.998438\pi$
$647$	−12.8260	−	22.2154i	−0.504244	−	0.873376i	0.495744	−	0.868469i	$-0.334895\pi$
$648$	−7.73244			−0.303759
$649$	16.8347	−	29.1586i	0.660821	−	1.14458i
$650$	−4.00708	+	6.94047i	−0.157171	+	0.272228i
$651$	−0.794101	−	1.37542i	−0.0311233	−	0.0539071i
$652$	−26.8849	−	46.5659i	−1.05289	−	1.82366i
$653$	13.5607	+	23.4879i	0.530673	+	0.919152i	0.999359	+	0.0357878i	$0.0113940\pi$
$653$	13.5607	+	23.4879i	0.530673	+	0.919152i	−0.468687	+	0.883365i	$0.655273\pi$
$654$	−24.7337	−	42.8401i	−0.967166	−	1.67518i
$655$	−10.8304			−0.423177
$656$	−82.4767			−3.22017
$657$	1.75048	+	3.03192i	0.0682926	+	0.118286i
$658$	−5.87215	+	10.1709i	−0.228920	+	0.396501i
$659$	−17.6230	+	30.5240i	−0.686496	+	1.18905i	0.286468	+	0.958090i	$0.407519\pi$
$659$	−17.6230	+	30.5240i	−0.686496	+	1.18905i	−0.972964	+	0.230956i	$0.925814\pi$
$660$	−9.42211	−	16.3196i	−0.366755	−	0.635238i
$661$	18.2537			0.709988			0.354994	−	0.934869i	$-0.384483\pi$
$661$	18.2537			0.709988			0.354994	+	0.934869i	$0.384483\pi$
$662$	33.2534			1.29243
$663$	2.34878	−	4.06820i	0.0912189	−	0.157996i
$664$	−4.86545	−	8.42721i	−0.188816	−	0.327039i
$665$	2.41557			0.0936719
$666$	8.72048	−	15.1043i	0.337912	−	0.585280i
$667$	15.4784			0.599328
$668$	−20.7934	−	36.0152i	−0.804520	−	1.39347i
$669$	15.9623			0.617137
$670$	−15.1273	+	10.1885i	−0.584417	+	0.393616i
$671$	12.7206			0.491072
$672$	−2.93319	−	5.08043i	−0.113150	−	0.195982i
$673$	−8.85575			−0.341364			−0.170682	−	0.985326i	$-0.554597\pi$
$673$	−8.85575			−0.341364			−0.170682	+	0.985326i	$0.554597\pi$
$674$	30.2618	−	52.4150i	1.16564	−	2.01895i
$675$	−4.28421			−0.164899
$676$	30.8391	+	53.4149i	1.18612	+	2.05442i
$677$	−7.44684	+	12.8983i	−0.286205	+	0.495722i	−0.972901	−	0.231223i	$-0.925727\pi$
$677$	−7.44684	+	12.8983i	−0.286205	+	0.495722i	0.686695	+	0.726945i	$0.259061\pi$
$678$	30.3641			1.16613
$679$	−1.80761			−0.0693696
$680$	21.6332	+	37.4697i	0.829593	+	1.43690i
$681$	4.76678	−	8.25630i	0.182663	−	0.316382i
$682$	19.5746	−	33.9042i	0.749549	−	1.29826i
$683$	9.81224	+	16.9953i	0.375455	+	0.650307i	0.990395	−	0.138267i	$-0.0441532\pi$
$683$	9.81224	+	16.9953i	0.375455	+	0.650307i	−0.614940	+	0.788574i	$0.710820\pi$
$684$	29.2321			1.11772
$685$	10.9317			0.417679
$686$	8.74033	+	15.1387i	0.333707	+	0.577998i
$687$	3.12337	+	5.40983i	0.119164	+	0.206398i
$688$	38.6565	+	66.9551i	1.47377	+	2.55264i
$689$	3.92809	+	6.80365i	0.149648	+	0.259198i
$690$	5.82834	−	10.0950i	0.221881	−	0.384309i
$691$	8.15287	−	14.1212i	0.310150	−	0.537195i	−0.668245	−	0.743941i	$-0.732954\pi$
$691$	8.15287	−	14.1212i	0.310150	−	0.537195i	0.978395	+	0.206746i	$0.0662874\pi$
$692$	−37.0846			−1.40975
$693$	−1.08773	−	1.88400i	−0.0413194	−	0.0715673i
$694$	−4.36116			−0.165548
$695$	−6.01460			−0.228147
$696$	−11.4390	+	19.8130i	−0.433595	+	0.751008i
$697$	51.9873			1.96916
$698$	−17.4814	−	30.2786i	−0.661679	−	1.14606i
$699$	−9.68408	+	16.7733i	−0.366286	+	0.634425i
$700$	−5.09757	−	8.82925i	−0.192670	−	0.333714i
$701$	−4.13242	+	7.15756i	−0.156079	+	0.270337i	−0.933451	−	0.358704i	$-0.883219\pi$
$701$	−4.13242	+	7.15756i	−0.156079	+	0.270337i	0.777372	+	0.629041i	$0.216552\pi$
$702$	0.935316	−	1.62001i	0.0353012	−	0.0611435i
$703$	−19.6095	+	33.9646i	−0.739586	+	1.28100i
$704$	24.9576	−	43.2277i	0.940623	−	1.62921i
$705$	3.91283	−	6.77722i	0.147366	−	0.255245i
$706$	1.22360	−	2.11934i	0.0460510	−	0.0797626i
$707$	4.74034	+	8.21052i	0.178279	+	0.308788i
$708$	−18.4153	+	31.8962i	−0.692089	+	1.19873i
$709$	−11.7189	−	20.2978i	−0.440114	−	0.762300i	0.557584	−	0.830121i	$-0.311729\pi$
$709$	−11.7189	−	20.2978i	−0.440114	−	0.762300i	−0.997697	+	0.0678212i	$0.978395\pi$
$710$	−7.63111			−0.286390
$711$	1.09426	−	1.89532i	0.0410381	−	0.0710801i
$712$	100.219			3.75588
$713$	17.2340			0.645418
$714$	4.19865	+	7.27227i	0.157130	+	0.272158i
$715$	2.71164			0.101410
$716$	−17.0898	+	29.6004i	−0.638675	+	1.10622i
$717$	3.02197	−	5.23421i	0.112858	−	0.195475i
$718$	−45.4440	−	78.7114i	−1.69596	−	2.93748i
$719$	19.6931	+	34.1095i	0.734430	+	1.27207i	0.954973	+	0.296693i	$0.0958837\pi$
$719$	19.6931	+	34.1095i	0.734430	+	1.27207i	−0.220543	+	0.975377i	$0.570783\pi$
$720$	4.43851	+	7.68773i	0.165414	+	0.286505i
$721$	3.46335	+	5.99870i	0.128982	+	0.223403i
$722$	−42.3284			−1.57530
$723$	−11.3737			−0.422992
$724$	57.3306	+	99.2995i	2.13067	+	3.69044i
$725$	−6.33786	+	10.9775i	−0.235382	+	0.407694i
$726$	12.3275	−	21.3519i	0.457517	−	0.792443i
$727$	−15.0967	−	26.1482i	−0.559904	−	0.969782i	−0.997504	−	0.0706122i	$-0.977505\pi$
$727$	−15.0967	−	26.1482i	−0.559904	−	0.969782i	0.437600	−	0.899170i	$-0.355829\pi$
$728$	2.64785			0.0981360
$729$	1.00000			0.0370370
$730$	3.90037	−	6.75565i	0.144359	−	0.250038i
$731$	−24.3662	−	42.2036i	−0.901218	−	1.56096i
$732$	−13.9148			−0.514308
$733$	−20.6025	+	35.6846i	−0.760971	+	1.31804i	0.181380	+	0.983413i	$0.441944\pi$
$733$	−20.6025	+	35.6846i	−0.760971	+	1.31804i	−0.942351	+	0.334627i	$0.891390\pi$
$734$	−6.98284			−0.257741
$735$	−2.86284	−	4.95858i	−0.105597	−	0.182900i
$736$	63.6577			2.34645
$737$	−33.1863	−	16.2140i	−1.22243	−	0.597251i
$738$	20.7021			0.762053
$739$	15.0914	+	26.1391i	0.555146	+	0.961541i	0.997892	+	0.0648943i	$0.0206710\pi$
$739$	15.0914	+	26.1391i	0.555146	+	0.961541i	−0.442746	+	0.896647i	$0.645996\pi$
$740$	−27.6558			−1.01665
$741$	−2.10322	+	3.64288i	−0.0772636	+	0.133825i
$742$	−14.0436			−0.515557
$743$	12.0292	+	20.8351i	0.441308	+	0.764367i	0.997787	−	0.0664942i	$-0.0211814\pi$
$743$	12.0292	+	20.8351i	0.441308	+	0.764367i	−0.556479	+	0.830862i	$0.687848\pi$
$744$	−12.7364	+	22.0601i	−0.466940	+	0.808764i
$745$	−4.12121			−0.150990
$746$	25.1990			0.922601
$747$	0.629225	+	1.08985i	0.0230222	+	0.0398755i
$748$	−73.6535	+	127.572i	−2.69304	+	4.66448i
$749$	3.93665	−	6.81848i	0.143842	−	0.249142i
$750$	10.3434	+	17.9153i	0.377688	+	0.654176i
$751$	40.1769			1.46607			0.733037	−	0.680189i	$-0.238102\pi$
$751$	40.1769			1.46607			0.733037	+	0.680189i	$0.238102\pi$
$752$	97.0510			3.53909
$753$	6.33220	+	10.9677i	0.230758	+	0.399685i
$754$	−2.76733	−	4.79315i	−0.100780	−	0.174556i
$755$	−3.18118	−	5.50997i	−0.115775	−	0.200528i
$756$	1.18985	+	2.06088i	0.0432745	+	0.0749536i
$757$	6.32764	−	10.9598i	0.229982	−	0.398340i	−0.727821	−	0.685768i	$-0.759467\pi$
$757$	6.32764	−	10.9598i	0.229982	−	0.398340i	0.957802	+	0.287427i	$0.0928000\pi$
$758$	44.0512	−	76.2990i	1.60001	−	2.77130i
$759$	23.6065			0.856861
$760$	−19.3715	−	33.5523i	−0.702677	−	1.21707i
$761$	21.1146			0.765404			0.382702	−	0.923872i	$-0.374994\pi$
$761$	21.1146			0.765404			0.382702	+	0.923872i	$0.374994\pi$
$762$	7.55526			0.273698
$763$	−4.52771	+	7.84223i	−0.163914	+	0.283908i
$764$	−29.5310			−1.06839
$765$	−2.79771	−	4.84578i	−0.101152	−	0.175200i
$766$	−14.4434	+	25.0168i	−0.521863	+	0.903893i
$767$	−2.64992	−	4.58980i	−0.0956831	−	0.165728i
$768$	4.74581	−	8.21998i	0.171250	−	0.296613i
$769$	−20.0517	+	34.7306i	−0.723084	+	1.25242i	0.236673	+	0.971589i	$0.423943\pi$
$769$	−20.0517	+	34.7306i	−0.723084	+	1.25242i	−0.959758	+	0.280830i	$0.909390\pi$
$770$	−2.42365	+	4.19789i	−0.0873423	+	0.151281i
$771$	−4.48897	+	7.77513i	−0.161666	+	0.280014i
$772$	−28.8419	+	49.9556i	−1.03804	+	1.79794i
$773$	14.2972	−	24.7635i	0.514236	−	0.890682i	−0.485628	−	0.874166i	$-0.661409\pi$
$773$	14.2972	−	24.7635i	0.514236	−	0.890682i	0.999864	−	0.0165168i	$-0.00525769\pi$
$774$	−9.70298	−	16.8060i	−0.348766	−	0.604081i
$775$	−7.05669	+	12.2226i	−0.253484	+	0.439047i
$776$	14.4959	+	25.1077i	0.520373	+	0.901313i
$777$	−3.19271			−0.114538
$778$	22.6959	−	39.3104i	0.813687	−	1.40935i
$779$	−46.5521			−1.66790
$780$	−2.96623			−0.106208
$781$	−7.72705	−	13.3836i	−0.276496	−	0.478905i
$782$	−91.1213			−3.25849
$783$	1.47935	−	2.56232i	0.0528678	−	0.0915697i
$784$	35.5039	−	61.4946i	1.26800	−	2.19624i
$785$	−7.37662	−	12.7767i	−0.263283	−	0.456019i
$786$	16.8568	+	29.1968i	0.601262	+	1.04142i
$787$	−15.2517	−	26.4167i	−0.543663	−	0.941652i	−0.998690	−	0.0511742i	$-0.983704\pi$
$787$	−15.2517	−	26.4167i	−0.543663	−	0.941652i	0.455027	−	0.890478i	$-0.349630\pi$
$788$	−20.7277	−	35.9014i	−0.738393	−	1.27893i
$789$	29.6560			1.05578
$790$	−4.87643			−0.173496
$791$	−2.77920	−	4.81372i	−0.0988171	−	0.171156i
$792$	−17.4459	+	30.2171i	−0.619912	+	1.07372i
$793$	1.00116	−	1.73406i	0.0355522	−	0.0615782i
$794$	−4.68330	−	8.11171i	−0.166204	−	0.287874i
$795$	9.35777			0.331886
$796$	−14.7148			−0.521553
$797$	3.63531	−	6.29655i	0.128769	−	0.223035i	−0.794431	−	0.607355i	$-0.792231\pi$
$797$	3.63531	−	6.29655i	0.128769	−	0.223035i	0.923200	+	0.384320i	$0.125564\pi$
$798$	−3.75969	−	6.51197i	−0.133092	−	0.230521i
$799$	−61.1738			−2.16418
$800$	−26.0655	+	45.1467i	−0.921554	+	1.59618i
$801$	−12.9609			−0.457950
$802$	48.6046	+	84.1857i	1.71629	+	2.97270i
$803$	15.7977			0.557487
$804$	36.3021	+	17.7363i	1.28028	+	0.625511i
$805$	−2.13385			−0.0752083
$806$	−3.08119	−	5.33678i	−0.108530	−	0.187980i
$807$	−9.03605			−0.318084
$808$	76.0295	−	131.687i	2.67471	−	4.63273i
$809$	−36.0750			−1.26833			−0.634164	−	0.773198i	$-0.718656\pi$
$809$	−36.0750			−1.26833			−0.634164	+	0.773198i	$0.718656\pi$
$810$	−1.11409	−	1.92966i	−0.0391451	−	0.0678013i
$811$	−7.44857	+	12.9013i	−0.261555	+	0.453026i	−0.966655	−	0.256081i	$-0.917569\pi$
$811$	−7.44857	+	12.9013i	−0.261555	+	0.453026i	0.705100	+	0.709107i	$0.250902\pi$
$812$	7.04085			0.247085
$813$	10.3095			0.361569
$814$	−39.3501	−	68.1564i	−1.37922	−	2.38888i
$815$	4.60812	−	7.98150i	0.161415	−	0.279580i
$816$	34.6962	−	60.0957i	1.21461	−	2.10377i
$817$	21.8188	+	37.7913i	0.763343	+	1.32215i
$818$	46.0054			1.60854
$819$	−0.342434			−0.0119656
$820$	−16.4135	−	28.4289i	−0.573183	−	0.992782i
$821$	19.0301	+	32.9612i	0.664156	+	1.15035i	0.979513	+	0.201379i	$0.0645424\pi$
$821$	19.0301	+	32.9612i	0.664156	+	1.15035i	−0.315357	+	0.948973i	$0.602124\pi$
$822$	−17.0145	−	29.4700i	−0.593449	−	1.02788i
$823$	−20.5130	−	35.5296i	−0.715039	−	1.23848i	−0.962944	−	0.269700i	$-0.913076\pi$
$823$	−20.5130	−	35.5296i	−0.715039	−	1.23848i	0.247905	−	0.968784i	$-0.420258\pi$
$824$	55.5480	−	96.2119i	1.93511	−	3.35170i
$825$	−9.66599	+	16.7420i	−0.336527	+	0.582881i
$826$	9.47394			0.329641
$827$	10.8713	+	18.8297i	0.378033	+	0.654773i	0.990776	−	0.135510i	$-0.0432672\pi$
$827$	10.8713	+	18.8297i	0.378033	+	0.654773i	−0.612743	+	0.790282i	$0.709934\pi$
$828$	−25.8228			−0.897404
$829$	−31.2915			−1.08680			−0.543399	−	0.839475i	$-0.682863\pi$
$829$	−31.2915			−1.08680			−0.543399	+	0.839475i	$0.682863\pi$
$830$	1.40203	−	2.42838i	0.0486650	−	0.0842903i
$831$	−16.3506			−0.567197
$832$	−3.92852	−	6.80439i	−0.136197	−	0.235900i
$833$	−22.3791	+	38.7617i	−0.775389	+	1.34301i
$834$	9.36134	+	16.2143i	0.324157	+	0.561456i
$835$	3.56403	−	6.17308i	0.123338	−	0.213628i
$836$	65.9532	−	114.234i	2.28104	−	3.95087i
$837$	1.64714	−	2.85293i	0.0569335	−	0.0986118i
$838$	19.5577	−	33.8749i	0.675609	−	1.17019i
$839$	−0.308244	+	0.533894i	−0.0106418	+	0.0184321i	−0.871297	−	0.490756i	$-0.836721\pi$
$839$	−0.308244	+	0.533894i	−0.0106418	+	0.0184321i	0.860655	+	0.509188i	$0.170054\pi$
$840$	1.57698	−	2.73140i	0.0544109	−	0.0942424i
$841$	10.1230	+	17.5336i	0.349070	+	0.604607i
$842$	−34.2090	+	59.2517i	−1.17892	+	2.04195i
$843$	−12.1654	−	21.0711i	−0.418998	−	0.725727i
$844$	−50.5819			−1.74110
$845$	−5.28588	+	9.15542i	−0.181840	+	0.314956i
$846$	−24.3603			−0.837524
$847$	−4.51330			−0.155079
$848$	58.0259	+	100.504i	1.99262	+	3.45132i
$849$	−9.92073			−0.340478
$850$	37.3108	−	64.6243i	1.27975	−	2.21659i
$851$	17.3225	−	30.0034i	0.593807	−	1.02850i
$852$	8.45252	+	14.6402i	0.289579	+	0.501565i
$853$	−17.5639	−	30.4215i	−0.601375	−	1.04161i	−0.992613	−	0.121323i	$-0.961286\pi$
$853$	−17.5639	−	30.4215i	−0.601375	−	1.04161i	0.391238	−	0.920290i	$-0.372047\pi$
$854$	1.78966	+	3.09978i	0.0612409	+	0.106072i
$855$	2.50522	+	4.33917i	0.0856767	+	0.148396i
$856$	−126.278			−4.31611
$857$	−34.5987			−1.18187			−0.590934	−	0.806720i	$-0.701241\pi$
$857$	−34.5987			−1.18187			−0.590934	+	0.806720i	$0.701241\pi$
$858$	−4.22050	−	7.31012i	−0.144086	−	0.249564i
$859$	6.04772	−	10.4750i	0.206346	−	0.357401i	−0.744215	−	0.667940i	$-0.767176\pi$
$859$	6.04772	−	10.4750i	0.206346	−	0.357401i	0.950561	+	0.310539i	$0.100510\pi$
$860$	−15.3859	+	26.6491i	−0.524653	+	0.908726i
$861$	−1.89484	−	3.28196i	−0.0645760	−	0.111849i
$862$	−38.2276			−1.30204
$863$	−55.3000			−1.88243			−0.941217	−	0.337803i	$-0.890316\pi$
$863$	−55.3000			−1.88243			−0.941217	+	0.337803i	$0.890316\pi$
$864$	6.08409	−	10.5379i	0.206985	−	0.358508i
$865$	−3.17819	−	5.50478i	−0.108062	−	0.187168i
$866$	1.06462			0.0361773
$867$	−13.3700	+	23.1575i	−0.454068	+	0.786469i
$868$	7.83942			0.266087
$869$	−4.93774	−	8.55242i	−0.167501	−	0.290121i
$870$	−6.59252			−0.223507
$871$	−4.82218	+	3.24783i	−0.163393	+	0.110049i
$872$	145.238			4.91839
$873$	−1.87469	−	3.24706i	−0.0634486	−	0.109896i
$874$	81.5948			2.75998
$875$	1.89345	−	3.27955i	0.0640102	−	0.110869i
$876$	−17.2808			−0.583865
$877$	11.2247	+	19.4417i	0.379030	+	0.656499i	0.990921	−	0.134443i	$-0.0429244\pi$
$877$	11.2247	+	19.4417i	0.379030	+	0.656499i	−0.611891	+	0.790942i	$0.709591\pi$
$878$	48.7388	−	84.4180i	1.64485	−	2.84897i
$879$	−6.48252			−0.218650
$880$	40.0565			1.35031
$881$	16.9406	+	29.3420i	0.570743	+	0.988557i	0.996490	+	0.0837141i	$0.0266782\pi$
$881$	16.9406	+	29.3420i	0.570743	+	0.988557i	−0.425746	+	0.904843i	$0.639988\pi$
$882$	−8.91166	+	15.4354i	−0.300071	+	0.519738i
$883$	26.2192	−	45.4130i	0.882346	−	1.52827i	0.0336203	−	0.999435i	$-0.489296\pi$
$883$	26.2192	−	45.4130i	0.882346	−	1.52827i	0.848726	−	0.528833i	$-0.177370\pi$
$884$	11.5936	+	20.0808i	0.389936	+	0.675389i
$885$	−6.31284			−0.212204
$886$	2.62096			0.0880528
$887$	5.98447	+	10.3654i	0.200939	+	0.348037i	0.948831	−	0.315784i	$-0.102267\pi$
$887$	5.98447	+	10.3654i	0.200939	+	0.348037i	−0.747892	+	0.663820i	$0.768934\pi$
$888$	25.6036	+	44.3468i	0.859201	+	1.48818i
$889$	−0.691526	−	1.19776i	−0.0231930	−	0.0401715i
$890$	14.4396	+	25.0101i	0.484016	+	0.838339i
$891$	2.25619	−	3.90784i	0.0755853	−	0.130917i
$892$	−39.3951	+	68.2344i	−1.31905	+	2.28466i
$893$	54.7783			1.83308
$894$	6.41441	+	11.1101i	0.214530	+	0.371577i
$895$	−5.85845			−0.195826
$896$	2.31239			0.0772515
$897$	1.85792	−	3.21802i	0.0620342	−	0.107446i
$898$	−36.1412			−1.20605
$899$	−4.87341	−	8.44099i	−0.162537	−	0.281523i
$900$	10.5735	−	18.3138i	0.352450	−	0.610461i
$901$	−36.5753	−	63.3502i	−1.21850	−	2.11050i
$902$	46.7078	−	80.9003i	1.55520	−	2.69369i
$903$	−1.77621	+	3.07648i	−0.0591085	+	0.102379i
$904$	−44.5751	+	77.2063i	−1.48255	+	2.56784i
$905$	−9.82658	+	17.0201i	−0.326646	+	0.565768i
$906$	−9.90262	+	17.1518i	−0.328993	+	0.569832i
$907$	7.92616	−	13.7285i	0.263184	−	0.455848i	−0.703902	−	0.710297i	$-0.748561\pi$
$907$	7.92616	−	13.7285i	0.263184	−	0.455848i	0.967086	+	0.254449i	$0.0818940\pi$
$908$	23.5290	+	40.7534i	0.780836	+	1.35245i
$909$	−9.83253	+	17.0304i	−0.326124	+	0.564864i
$910$	0.381502	+	0.660781i	0.0126467	+	0.0219047i
$911$	5.64628			0.187070			0.0935349	−	0.995616i	$-0.470183\pi$
$911$	5.64628			0.187070			0.0935349	+	0.995616i	$0.470183\pi$
$912$	−31.0688	+	53.8128i	−1.02879	+	1.78192i
$913$	5.67861			0.187935
$914$	−28.1787			−0.932069
$915$	−1.19252	−	2.06550i	−0.0394234	−	0.0682833i
$916$	−30.8341			−1.01879
$917$	3.08577	−	5.34471i	0.101901	−	0.176498i
$918$	−8.70893	+	15.0843i	−0.287437	+	0.497856i
$919$	5.38546	+	9.32788i	0.177650	+	0.307698i	0.941075	−	0.338198i	$-0.109817\pi$
$919$	5.38546	+	9.32788i	0.177650	+	0.307698i	−0.763425	+	0.645896i	$0.776484\pi$
$920$	17.1122	+	29.6392i	0.564173	+	0.977175i
$921$	3.02197	+	5.23421i	0.0995774	+	0.172473i
$922$	−3.49591	−	6.05510i	−0.115132	−	0.199414i
$923$	−2.43260			−0.0800700
$924$	10.7381			0.353259
$925$	14.1858	+	24.5706i	0.466428	+	0.807876i
$926$	−8.32136	+	14.4130i	−0.273457	+	0.473641i
$927$	−7.18376	+	12.4426i	−0.235946	+	0.408670i
$928$	−18.0010	−	31.1787i	−0.590913	−	1.02349i
$929$	17.4495			0.572501			0.286250	−	0.958155i	$-0.407591\pi$
$929$	17.4495			0.572501			0.286250	+	0.958155i	$0.407591\pi$
$930$	−7.34024			−0.240696
$931$	20.0394	−	34.7092i	0.656764	−	1.13755i
$932$	−47.8010	−	82.7937i	−1.56577	−	2.71200i
$933$	−2.86610			−0.0938320
$934$	34.5619	−	59.8630i	1.13090	−	1.95878i
$935$	−25.2487			−0.825721
$936$	2.74612	+	4.75642i	0.0897597	+	0.155468i
$937$	11.9549			0.390548			0.195274	−	0.980749i	$-0.437440\pi$
$937$	11.9549			0.390548			0.195274	+	0.980749i	$0.437440\pi$
$938$	−0.717922	−	10.3681i	−0.0234410	−	0.338530i
$939$	30.2498			0.987163
$940$	19.3138	+	33.4526i	0.629948	+	1.09110i
$941$	−17.5600			−0.572439			−0.286219	−	0.958164i	$-0.592399\pi$
$941$	−17.5600			−0.572439			−0.286219	+	0.958164i	$0.592399\pi$
$942$	−22.9625	+	39.7722i	−0.748159	+	1.29585i
$943$	41.1228			1.33914
$944$	−39.1448	−	67.8008i	−1.27405	−	2.20673i
$945$	−0.203943	+	0.353240i	−0.00663426	+	0.0114909i
$946$	−87.5671			−2.84705
$947$	−42.6592			−1.38624			−0.693119	−	0.720823i	$-0.743764\pi$
$947$	−42.6592			−1.38624			−0.693119	+	0.720823i	$0.743764\pi$
$948$	5.40133	+	9.35537i	0.175427	+	0.303848i
$949$	1.24334	−	2.15352i	0.0403605	−	0.0699064i
$950$	−33.4101	+	57.8680i	−1.08397	+	1.87748i
$951$	−10.0831	−	17.4645i	−0.326968	−	0.566325i
$952$	−24.6547			−0.799065
$953$	−21.6979			−0.702863			−0.351432	−	0.936214i	$-0.614305\pi$
$953$	−21.6979			−0.702863			−0.351432	+	0.936214i	$0.614305\pi$
$954$	−14.5648	−	25.2270i	−0.471552	−	0.816753i
$955$	−2.53083	−	4.38353i	−0.0818958	−	0.141848i
$956$	14.9166	+	25.8363i	0.482436	+	0.835604i
$957$	−6.67541	−	11.5622i	−0.215785	−	0.373751i
$958$	−20.3545	+	35.2550i	−0.657623	+	1.13904i
$959$	−3.11464	+	5.39472i	−0.100577	+	0.174205i
$960$	−9.35880			−0.302054
$961$	10.0739	+	17.4484i	0.324963	+	0.562852i
$962$	−12.3880			−0.399407
$963$	16.3310			0.526259
$964$	28.0704	−	48.6194i	0.904088	−	1.56593i
$965$	−9.88710			−0.318277
$966$	3.32120	+	5.75249i	0.106858	+	0.185083i
$967$	20.9715	−	36.3236i	0.674397	−	1.16809i	−0.302248	−	0.953229i	$-0.597737\pi$
$967$	20.9715	−	36.3236i	0.674397	−	1.16809i	0.976645	−	0.214860i	$-0.0689296\pi$
$968$	36.1940	+	62.6899i	1.16332	+	2.01493i
$969$	19.5835	−	33.9196i	0.629113	−	1.08966i
$970$	−4.17714	+	7.23502i	−0.134120	+	0.232302i
$971$	−3.29456	+	5.70635i	−0.105728	+	0.183125i	−0.914035	−	0.405635i	$-0.867050\pi$
$971$	−3.29456	+	5.70635i	−0.105728	+	0.183125i	0.808308	+	0.588760i	$0.200384\pi$
$972$	−2.46802	+	4.27473i	−0.0791617	+	0.137112i
$973$	1.71367	−	2.96816i	0.0549377	−	0.0951549i
$974$	15.4262	−	26.7190i	0.494288	−	0.856133i
$975$	1.52150	+	2.63532i	0.0487271	+	0.0843978i
$976$	14.7892	−	25.6156i	0.473390	−	0.819935i
$977$	5.63508	+	9.76024i	0.180282	+	0.312258i	0.941977	−	0.335679i	$-0.108966\pi$
$977$	5.63508	+	9.76024i	0.180282	+	0.312258i	−0.761695	+	0.647936i	$0.775632\pi$
$978$	−28.6890			−0.917373
$979$	−29.2422	+	50.6490i	−0.934586	+	1.61875i
$980$	28.2621			0.902801
$981$	−18.7830			−0.599694
$982$	1.17252	+	2.03087i	0.0374168	+	0.0648077i
$983$	39.3949			1.25650			0.628251	−	0.778010i	$-0.283771\pi$
$983$	39.3949			1.25650			0.628251	+	0.778010i	$0.283771\pi$
$984$	−30.3910	+	52.6387i	−0.968829	+	1.67806i
$985$	3.55276	−	6.15357i	0.113200	−	0.196069i
$986$	25.7672	+	44.6301i	0.820594	+	1.42131i
$987$	2.22967	+	3.86191i	0.0709713	+	0.122926i
$988$	−10.3816	−	17.9814i	−0.330281	−	0.572064i
$989$	−19.2741	−	33.3838i	−0.612881	−	1.06154i
$990$	−10.0544			−0.319549
$991$	−53.5959			−1.70253			−0.851265	−	0.524736i	$-0.824164\pi$
$991$	−53.5959			−1.70253			−0.851265	+	0.524736i	$0.824164\pi$
$992$	−20.0427	−	34.7150i	−0.636357	−	1.10220i
$993$	6.31322	−	10.9348i	0.200344	−	0.347006i
$994$	2.17424	−	3.76590i	0.0689628	−	0.119447i
$995$	−1.26108	−	2.18425i	−0.0399788	−	0.0692453i
$996$	−6.21176			−0.196827
$997$	57.5089			1.82133			0.910663	−	0.413150i	$-0.135571\pi$
$997$	57.5089			1.82133			0.910663	+	0.413150i	$0.135571\pi$
$998$	14.7605	−	25.5659i	0.467234	−	0.809273i
$999$	−3.31119	−	5.73516i	−0.104762	−	0.181452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.e.c.37.5	✓	10
3.2	odd	2		603.2.g.f.37.1		10
67.29	even	3	inner	201.2.e.c.163.5	yes	10
201.29	odd	6		603.2.g.f.163.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.c.37.5	✓	10	1.1	even	1	trivial
201.2.e.c.163.5	yes	10	67.29	even	3	inner
603.2.g.f.37.1		10	3.2	odd	2
603.2.g.f.163.1		10	201.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31682 + 2.28079i) q^{2} +1.00000 q^{3} +(-2.46802 + 4.27473i) q^{4} -0.846046 q^{5} +(1.31682 + 2.28079i) q^{6} +(0.241054 - 0.417518i) q^{7} -7.73244 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.31682 + 2.28079i) q^{2} +1.00000 q^{3} +(-2.46802 + 4.27473i) q^{4} -0.846046 q^{5} +(1.31682 + 2.28079i) q^{6} +(0.241054 - 0.417518i) q^{7} -7.73244 q^{8} +1.00000 q^{9} +(-1.11409 - 1.92966i) q^{10} +(2.25619 - 3.90784i) q^{11} +(-2.46802 + 4.27473i) q^{12} +(-0.355142 - 0.615125i) q^{13} +1.26970 q^{14} -0.846046 q^{15} +(-5.24618 - 9.08665i) q^{16} +(3.30681 + 5.72756i) q^{17} +(1.31682 + 2.28079i) q^{18} +(-2.96109 - 5.12876i) q^{19} +(2.08806 - 3.61662i) q^{20} +(0.241054 - 0.417518i) q^{21} +11.8840 q^{22} +(2.61574 + 4.53060i) q^{23} -7.73244 q^{24} -4.28421 q^{25} +(0.935316 - 1.62001i) q^{26} +1.00000 q^{27} +(1.18985 + 2.06088i) q^{28} +(1.47935 - 2.56232i) q^{29} +(-1.11409 - 1.92966i) q^{30} +(1.64714 - 2.85293i) q^{31} +(6.08409 - 10.5379i) q^{32} +(2.25619 - 3.90784i) q^{33} +(-8.70893 + 15.0843i) q^{34} +(-0.203943 + 0.353240i) q^{35} +(-2.46802 + 4.27473i) q^{36} +(-3.31119 - 5.73516i) q^{37} +(7.79843 - 13.5073i) q^{38} +(-0.355142 - 0.615125i) q^{39} +6.54200 q^{40} +(3.93032 - 6.80752i) q^{41} +1.26970 q^{42} -7.36851 q^{43} +(11.1366 + 19.2892i) q^{44} -0.846046 q^{45} +(-6.88891 + 11.9319i) q^{46} +(-4.62484 + 8.01046i) q^{47} +(-5.24618 - 9.08665i) q^{48} +(3.38379 + 5.86089i) q^{49} +(-5.64152 - 9.77140i) q^{50} +(3.30681 + 5.72756i) q^{51} +3.50599 q^{52} -11.0606 q^{53} +(1.31682 + 2.28079i) q^{54} +(-1.90884 + 3.30621i) q^{55} +(-1.86394 + 3.22843i) q^{56} +(-2.96109 - 5.12876i) q^{57} +7.79216 q^{58} +7.46158 q^{59} +(2.08806 - 3.61662i) q^{60} +(1.40952 + 2.44135i) q^{61} +8.67594 q^{62} +(0.241054 - 0.417518i) q^{63} +11.0618 q^{64} +(0.300467 + 0.520424i) q^{65} +11.8840 q^{66} +(-0.565427 - 8.16580i) q^{67} -32.6450 q^{68} +(2.61574 + 4.53060i) q^{69} -1.07422 q^{70} +(1.71241 - 2.96598i) q^{71} -7.73244 q^{72} +(1.75048 + 3.03192i) q^{73} +(8.72048 - 15.1043i) q^{74} -4.28421 q^{75} +29.2321 q^{76} +(-1.08773 - 1.88400i) q^{77} +(0.935316 - 1.62001i) q^{78} +(1.09426 - 1.89532i) q^{79} +(4.43851 + 7.68773i) q^{80} +1.00000 q^{81} +20.7021 q^{82} +(0.629225 + 1.08985i) q^{83} +(1.18985 + 2.06088i) q^{84} +(-2.79771 - 4.84578i) q^{85} +(-9.70298 - 16.8060i) q^{86} +(1.47935 - 2.56232i) q^{87} +(-17.4459 + 30.2171i) q^{88} -12.9609 q^{89} +(-1.11409 - 1.92966i) q^{90} -0.342434 q^{91} -25.8228 q^{92} +(1.64714 - 2.85293i) q^{93} -24.3603 q^{94} +(2.50522 + 4.33917i) q^{95} +(6.08409 - 10.5379i) q^{96} +(-1.87469 - 3.24706i) q^{97} +(-8.91166 + 15.4354i) q^{98} +(2.25619 - 3.90784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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