LMFDB - Embedded newform 143.2.e.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 2x^{9} + 59x^{8} - 13x^{7} + 175x^{6} - 50x^{5} + 380x^{4} - 64x^{3} + 280x^{2} + 48x + 144 $ x^12 + 9x^10 - 2x^9 + 59x^8 - 13x^7 + 175x^6 - 50x^5 + 380x^4 - 64x^3 + 280x^2 + 48x + 144
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-1.17629 + 2.03740i$ of defining polynomial
Character	$\chi$	$=$	143.100
Dual form			143.2.e.c.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26732 + 2.19506i) q^{2} +(1.49512 - 2.58962i) q^{3} +(-2.21221 - 3.83165i) q^{4} -3.35258 q^{5} +(3.78959 + 6.56377i) q^{6} +(-0.959205 - 1.66139i) q^{7} +6.14501 q^{8} +(-2.97076 - 5.14551i) q^{9} +O(q^{10})$	\(q+(-1.26732 + 2.19506i) q^{2} +(1.49512 - 2.58962i) q^{3} +(-2.21221 - 3.83165i) q^{4} -3.35258 q^{5} +(3.78959 + 6.56377i) q^{6} +(-0.959205 - 1.66139i) q^{7} +6.14501 q^{8} +(-2.97076 - 5.14551i) q^{9} +(4.24880 - 7.35913i) q^{10} +(0.500000 - 0.866025i) q^{11} -13.2300 q^{12} +(0.775195 - 3.52123i) q^{13} +4.86248 q^{14} +(-5.01251 + 8.68192i) q^{15} +(-3.36329 + 5.82540i) q^{16} +(0.986357 + 1.70842i) q^{17} +15.0596 q^{18} +(1.41063 + 2.44328i) q^{19} +(7.41660 + 12.8459i) q^{20} -5.73650 q^{21} +(1.26732 + 2.19506i) q^{22} +(0.219925 - 0.380921i) q^{23} +(9.18753 - 15.9133i) q^{24} +6.23981 q^{25} +(6.74691 + 6.16413i) q^{26} -8.79587 q^{27} +(-4.24392 + 7.35068i) q^{28} +(-1.24922 + 2.16372i) q^{29} +(-12.7049 - 22.0056i) q^{30} -4.63180 q^{31} +(-2.37973 - 4.12182i) q^{32} +(-1.49512 - 2.58962i) q^{33} -5.00013 q^{34} +(3.21581 + 5.56995i) q^{35} +(-13.1439 + 22.7659i) q^{36} +(3.89503 - 6.74640i) q^{37} -7.15087 q^{38} +(-7.95965 - 7.27212i) q^{39} -20.6017 q^{40} +(4.85542 - 8.40984i) q^{41} +(7.26999 - 12.5920i) q^{42} +(3.29747 + 5.71138i) q^{43} -4.42441 q^{44} +(9.95973 + 17.2508i) q^{45} +(0.557431 + 0.965498i) q^{46} -0.104554 q^{47} +(10.0571 + 17.4193i) q^{48} +(1.65985 - 2.87495i) q^{49} +(-7.90784 + 13.6968i) q^{50} +5.89889 q^{51} +(-15.2070 + 4.81941i) q^{52} +0.381991 q^{53} +(11.1472 - 19.3075i) q^{54} +(-1.67629 + 2.90342i) q^{55} +(-5.89433 - 10.2093i) q^{56} +8.43623 q^{57} +(-3.16633 - 5.48425i) q^{58} +(0.516271 + 0.894208i) q^{59} +44.3548 q^{60} +(2.86818 + 4.96782i) q^{61} +(5.86997 - 10.1671i) q^{62} +(-5.69914 + 9.87121i) q^{63} -1.38963 q^{64} +(-2.59890 + 11.8052i) q^{65} +7.57919 q^{66} +(3.62596 - 6.28035i) q^{67} +(4.36405 - 7.55876i) q^{68} +(-0.657628 - 1.13904i) q^{69} -16.3019 q^{70} +(-5.63361 - 9.75770i) q^{71} +(-18.2554 - 31.6193i) q^{72} +0.808179 q^{73} +(9.87252 + 17.0997i) q^{74} +(9.32926 - 16.1587i) q^{75} +(6.24120 - 10.8101i) q^{76} -1.91841 q^{77} +(26.0502 - 8.25584i) q^{78} -7.04501 q^{79} +(11.2757 - 19.5301i) q^{80} +(-4.23859 + 7.34145i) q^{81} +(12.3068 + 21.3159i) q^{82} +8.70830 q^{83} +(12.6903 + 21.9803i) q^{84} +(-3.30684 - 5.72762i) q^{85} -16.7158 q^{86} +(3.73548 + 6.47003i) q^{87} +(3.07251 - 5.32174i) q^{88} +(-5.16604 + 8.94785i) q^{89} -50.4887 q^{90} +(-6.59372 + 2.08968i) q^{91} -1.94608 q^{92} +(-6.92509 + 11.9946i) q^{93} +(0.132503 - 0.229502i) q^{94} +(-4.72925 - 8.19129i) q^{95} -14.2319 q^{96} +(9.69232 + 16.7876i) q^{97} +(4.20713 + 7.28696i) q^{98} -5.94153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.26732	+	2.19506i	−0.896131	+	1.55214i	−0.0637331	+	0.997967i	$0.520301\pi$
$2$	−1.26732	+	2.19506i	−0.896131	+	1.55214i	−0.832398	+	0.554178i	$0.813033\pi$
$3$	1.49512	−	2.58962i	0.863208	−	1.49512i	−0.00560834	−	0.999984i	$-0.501785\pi$
$3$	1.49512	−	2.58962i	0.863208	−	1.49512i	0.868816	−	0.495135i	$-0.164881\pi$
$4$	−2.21221	−	3.83165i	−1.10610	−	1.91583i
$5$	−3.35258			−1.49932			−0.749660	−	0.661823i	$-0.769783\pi$
$5$	−3.35258			−1.49932			−0.749660	+	0.661823i	$0.769783\pi$
$6$	3.78959	+	6.56377i	1.54709	+	2.67965i
$7$	−0.959205	−	1.66139i	−0.362545	−	0.627947i	0.625834	−	0.779957i	$-0.284759\pi$
$7$	−0.959205	−	1.66139i	−0.362545	−	0.627947i	−0.988379	+	0.152009i	$0.951426\pi$
$8$	6.14501			2.17259
$9$	−2.97076	−	5.14551i	−0.990255	−	1.71517i
$10$	4.24880	−	7.35913i	1.34359	−	2.32716i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−13.2300			−3.81919
$13$	0.775195	−	3.52123i	0.215000	−	0.976614i
$13$	0.775195	−	3.52123i	0.215000	−	0.976614i
$14$	4.86248			1.29955
$15$	−5.01251	+	8.68192i	−1.29422	+	2.24166i
$16$	−3.36329	+	5.82540i	−0.840824	+	1.45635i
$17$	0.986357	+	1.70842i	0.239227	+	0.414353i	0.960493	−	0.278305i	$-0.0897727\pi$
$17$	0.986357	+	1.70842i	0.239227	+	0.414353i	−0.721266	+	0.692658i	$0.756439\pi$
$18$	15.0596			3.54959
$19$	1.41063	+	2.44328i	0.323620	+	0.560527i	0.981232	−	0.192830i	$-0.0617666\pi$
$19$	1.41063	+	2.44328i	0.323620	+	0.560527i	−0.657612	+	0.753357i	$0.728433\pi$
$20$	7.41660	+	12.8459i	1.65840	+	2.87244i
$21$	−5.73650			−1.25181
$22$	1.26732	+	2.19506i	0.270194	+	0.467989i
$23$	0.219925	−	0.380921i	0.0458575	−	0.0794275i	−0.842186	−	0.539188i	$-0.818731\pi$
$23$	0.219925	−	0.380921i	0.0458575	−	0.0794275i	0.888043	+	0.459760i	$0.152065\pi$
$24$	9.18753	−	15.9133i	1.87540	−	3.24828i
$25$	6.23981			1.24796
$26$	6.74691	+	6.16413i	1.32318	+	1.20889i
$27$	−8.79587			−1.69277
$28$	−4.24392	+	7.35068i	−0.802025	+	1.38915i
$29$	−1.24922	+	2.16372i	−0.231975	+	0.401792i	−0.958389	−	0.285465i	$-0.907852\pi$
$29$	−1.24922	+	2.16372i	−0.231975	+	0.401792i	0.726414	+	0.687257i	$0.241185\pi$
$30$	−12.7049	−	22.0056i	−2.31959	−	4.01765i
$31$	−4.63180			−0.831895			−0.415948	−	0.909389i	$-0.636550\pi$
$31$	−4.63180			−0.831895			−0.415948	+	0.909389i	$0.636550\pi$
$32$	−2.37973	−	4.12182i	−0.420682	−	0.728642i
$33$	−1.49512	−	2.58962i	−0.260267	−	0.450795i
$34$	−5.00013			−0.857514
$35$	3.21581	+	5.56995i	0.543572	+	0.941494i
$36$	−13.1439	+	22.7659i	−2.19065	+	3.79431i
$37$	3.89503	−	6.74640i	0.640340	−	1.10910i	−0.345017	−	0.938596i	$-0.612127\pi$
$37$	3.89503	−	6.74640i	0.640340	−	1.10910i	0.985357	−	0.170505i	$-0.0545398\pi$
$38$	−7.15087			−1.16002
$39$	−7.95965	−	7.27212i	−1.27456	−	1.16447i
$40$	−20.6017			−3.25741
$41$	4.85542	−	8.40984i	0.758289	−	1.31340i	−0.185433	−	0.982657i	$-0.559369\pi$
$41$	4.85542	−	8.40984i	0.758289	−	1.31340i	0.943722	−	0.330739i	$-0.107298\pi$
$42$	7.26999	−	12.5920i	1.12178	−	1.94299i
$43$	3.29747	+	5.71138i	0.502859	+	0.870977i	0.999995	+	0.00330432i	$0.00105180\pi$
$43$	3.29747	+	5.71138i	0.502859	+	0.870977i	−0.497136	+	0.867673i	$0.665615\pi$
$44$	−4.42441			−0.667005
$45$	9.95973	+	17.2508i	1.48471	+	2.57159i
$46$	0.557431	+	0.965498i	0.0821887	+	0.142355i
$47$	−0.104554			−0.0152507			−0.00762536	−	0.999971i	$-0.502427\pi$
$47$	−0.104554			−0.0152507			−0.00762536	+	0.999971i	$0.502427\pi$
$48$	10.0571	+	17.4193i	1.45161	+	2.51426i
$49$	1.65985	−	2.87495i	0.237122	−	0.410707i
$50$	−7.90784	+	13.6968i	−1.11834	+	1.93702i
$51$	5.89889			0.826010
$52$	−15.2070	+	4.81941i	−2.10883	+	0.668332i
$53$	0.381991			0.0524705			0.0262352	−	0.999656i	$-0.491648\pi$
$53$	0.381991			0.0524705			0.0262352	+	0.999656i	$0.491648\pi$
$54$	11.1472	−	19.3075i	1.51694	−	2.62742i
$55$	−1.67629	+	2.90342i	−0.226031	+	0.391497i
$56$	−5.89433	−	10.2093i	−0.787663	−	1.36427i
$57$	8.43623			1.11741
$58$	−3.16633	−	5.48425i	−0.415760	−	0.720117i
$59$	0.516271	+	0.894208i	0.0672128	+	0.116416i	0.897673	−	0.440661i	$-0.145256\pi$
$59$	0.516271	+	0.894208i	0.0672128	+	0.116416i	−0.830461	+	0.557077i	$0.811923\pi$
$60$	44.3548			5.72618
$61$	2.86818	+	4.96782i	0.367232	+	0.636065i	0.989132	−	0.147032i	$-0.0469721\pi$
$61$	2.86818	+	4.96782i	0.367232	+	0.636065i	−0.621900	+	0.783097i	$0.713639\pi$
$62$	5.86997	−	10.1671i	0.745487	−	1.29122i
$63$	−5.69914	+	9.87121i	−0.718025	+	1.24366i
$64$	−1.38963			−0.173704
$65$	−2.59890	+	11.8052i	−0.322354	+	1.46426i
$66$	7.57919			0.932933
$67$	3.62596	−	6.28035i	0.442982	−	0.767267i	−0.554927	−	0.831899i	$-0.687254\pi$
$67$	3.62596	−	6.28035i	0.442982	−	0.767267i	0.997909	+	0.0646315i	$0.0205872\pi$
$68$	4.36405	−	7.55876i	0.529219	−	0.916634i
$69$	−0.657628	−	1.13904i	−0.0791691	−	0.137125i
$70$	−16.3019			−1.94845
$71$	−5.63361	−	9.75770i	−0.668586	−	1.15803i	−0.978300	−	0.207195i	$-0.933566\pi$
$71$	−5.63361	−	9.75770i	−0.668586	−	1.15803i	0.309713	−	0.950830i	$-0.399767\pi$
$72$	−18.2554	−	31.6193i	−2.15142	−	3.72637i
$73$	0.808179			0.0945902			0.0472951	−	0.998881i	$-0.484940\pi$
$73$	0.808179			0.0945902			0.0472951	+	0.998881i	$0.484940\pi$
$74$	9.87252	+	17.0997i	1.14766	+	1.98780i
$75$	9.32926	−	16.1587i	1.07725	−	1.86585i
$76$	6.24120	−	10.8101i	0.715914	−	1.24000i
$77$	−1.91841			−0.218623
$78$	26.0502	−	8.25584i	2.94961	−	0.934789i
$79$	−7.04501			−0.792625			−0.396313	−	0.918116i	$-0.629710\pi$
$79$	−7.04501			−0.792625			−0.396313	+	0.918116i	$0.629710\pi$
$80$	11.2757	−	19.5301i	1.26066	−	2.18353i
$81$	−4.23859	+	7.34145i	−0.470954	+	0.815717i
$82$	12.3068	+	21.3159i	1.35905	+	2.35395i
$83$	8.70830			0.955860			0.477930	−	0.878398i	$-0.341387\pi$
$83$	8.70830			0.955860			0.477930	+	0.878398i	$0.341387\pi$
$84$	12.6903	+	21.9803i	1.38463	+	2.39825i
$85$	−3.30684	−	5.72762i	−0.358678	−	0.621248i
$86$	−16.7158			−1.80251
$87$	3.73548	+	6.47003i	0.400485	+	0.693660i
$88$	3.07251	−	5.32174i	0.327530	−	0.567299i
$89$	−5.16604	+	8.94785i	−0.547599	+	0.948470i	0.450839	+	0.892605i	$0.351125\pi$
$89$	−5.16604	+	8.94785i	−0.547599	+	0.948470i	−0.998438	+	0.0558646i	$0.982208\pi$
$90$	−50.4887			−5.32198
$91$	−6.59372	+	2.08968i	−0.691209	+	0.219058i
$92$	−1.94608			−0.202892
$93$	−6.92509	+	11.9946i	−0.718098	+	1.24378i
$94$	0.132503	−	0.229502i	0.0136666	−	0.0236713i
$95$	−4.72925	−	8.19129i	−0.485210	−	0.840409i
$96$	−14.2319			−1.45254
$97$	9.69232	+	16.7876i	0.984106	+	1.70452i	0.645844	+	0.763469i	$0.276506\pi$
$97$	9.69232	+	16.7876i	0.984106	+	1.70452i	0.338262	+	0.941052i	$0.390161\pi$
$98$	4.20713	+	7.28696i	0.424984	+	0.736094i
$99$	−5.94153			−0.597146
$100$	−13.8037	−	23.9088i	−1.38037	−	2.39088i
$101$	−1.67327	+	2.89819i	−0.166497	+	0.288380i	−0.937186	−	0.348831i	$-0.886579\pi$
$101$	−1.67327	+	2.89819i	−0.166497	+	0.288380i	0.770689	+	0.637211i	$0.219912\pi$
$102$	−7.47578	+	12.9484i	−0.740213	+	1.28209i
$103$	18.4647			1.81939			0.909693	−	0.415282i	$-0.136317\pi$
$103$	18.4647			1.81939			0.909693	+	0.415282i	$0.136317\pi$
$104$	4.76358	−	21.6380i	0.467108	−	2.12178i
$105$	19.2321			1.87686
$106$	−0.484105	+	0.838495i	−0.0470204	+	0.0814418i
$107$	6.19747	−	10.7343i	0.599132	−	1.03773i	−0.393817	−	0.919189i	$-0.628846\pi$
$107$	6.19747	−	10.7343i	0.599132	−	1.03773i	0.992949	−	0.118539i	$-0.0378210\pi$
$108$	19.4583	+	33.7027i	1.87237	+	3.24305i
$109$	−3.51113			−0.336305			−0.168153	−	0.985761i	$-0.553780\pi$
$109$	−3.51113			−0.336305			−0.168153	+	0.985761i	$0.553780\pi$
$110$	−4.24880	−	7.35913i	−0.405107	−	0.701666i
$111$	−11.6471	−	20.1733i	−1.10549	−	1.91477i
$112$	12.9044			1.21935
$113$	−8.51508	−	14.7485i	−0.801031	−	1.38743i	−0.918938	−	0.394402i	$-0.870952\pi$
$113$	−8.51508	−	14.7485i	−0.801031	−	1.38743i	0.117907	−	0.993025i	$-0.462382\pi$
$114$	−10.6914	+	18.5181i	−1.00134	+	1.73438i
$115$	−0.737316	+	1.27707i	−0.0687551	+	0.119087i
$116$	11.0542			1.02635
$117$	−20.4215	+	6.47197i	−1.88797	+	0.598334i
$118$	−2.61712			−0.240926
$119$	1.89224	−	3.27745i	0.173461	−	0.300444i
$120$	−30.8019	+	53.3505i	−2.81182	+	4.87022i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−14.5396			−1.31635
$123$	−14.5189	−	25.1474i	−1.30912	−	2.26747i
$124$	10.2465	+	17.7474i	0.920162	+	1.59377i
$125$	−4.15655			−0.371773
$126$	−14.4453	−	25.0200i	−1.28689	−	2.22896i
$127$	−1.28036	+	2.21765i	−0.113614	+	0.196785i	−0.917225	−	0.398370i	$-0.869576\pi$
$127$	−1.28036	+	2.21765i	−0.113614	+	0.196785i	0.803611	+	0.595155i	$0.202909\pi$
$128$	6.52057	−	11.2940i	0.576343	−	0.998255i
$129$	19.7204			1.73629
$130$	−22.6196	−	20.6658i	−1.98387	−	1.81251i
$131$	−12.1666			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$131$	−12.1666			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$132$	−6.61502	+	11.4576i	−0.575764	+	0.997252i
$133$	2.70616	−	4.68721i	0.234654	−	0.406433i
$134$	9.19052	+	15.9185i	0.793940	+	1.37514i
$135$	29.4889			2.53800
$136$	6.06118	+	10.4983i	0.519742	+	0.900219i
$137$	−5.46972	−	9.47384i	−0.467310	−	0.809405i	0.531992	−	0.846749i	$-0.321443\pi$
$137$	−5.46972	−	9.47384i	−0.467310	−	0.809405i	−0.999302	+	0.0373444i	$0.988110\pi$
$138$	3.33370			0.283784
$139$	3.00390	+	5.20291i	0.254788	+	0.441305i	0.964838	−	0.262846i	$-0.0846611\pi$
$139$	3.00390	+	5.20291i	0.254788	+	0.441305i	−0.710050	+	0.704151i	$0.751328\pi$
$140$	14.2281	−	24.6438i	1.20249	−	2.08278i
$141$	−0.156320	+	0.270755i	−0.0131645	+	0.0228016i
$142$	28.5584			2.39656
$143$	−2.66188	−	2.43195i	−0.222597	−	0.203370i
$144$	39.9662			3.33052
$145$	4.18812	−	7.25404i	0.347805	−	0.602415i
$146$	−1.02422	+	1.77400i	−0.0847652	+	0.146818i
$147$	−4.96335	−	8.59678i	−0.409370	−	0.709050i
$148$	−34.4665			−2.83313
$149$	6.71908	+	11.6378i	0.550448	+	0.953405i	0.998242	+	0.0592678i	$0.0188766\pi$
$149$	6.71908	+	11.6378i	0.550448	+	0.953405i	−0.447794	+	0.894137i	$0.647790\pi$
$150$	23.6463	+	40.9566i	1.93071	+	3.34410i
$151$	−7.46127			−0.607190			−0.303595	−	0.952801i	$-0.598187\pi$
$151$	−7.46127			−0.607190			−0.303595	+	0.952801i	$0.598187\pi$
$152$	8.66833	+	15.0140i	0.703094	+	1.21779i
$153$	5.86047	−	10.1506i	0.473791	−	0.820630i
$154$	2.43124	−	4.21103i	0.195915	−	0.339335i
$155$	15.5285			1.24728
$156$	−10.2559	+	46.5861i	−0.821126	+	3.72987i
$157$	13.7742			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$157$	13.7742			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$158$	8.92828	−	15.4642i	0.710296	−	1.23027i
$159$	0.571122	−	0.989212i	0.0452929	−	0.0784496i
$160$	7.97825	+	13.8187i	0.630736	+	1.09247i
$161$	−0.843812			−0.0665017
$162$	−10.7433	−	18.6079i	−0.844074	−	1.46198i
$163$	7.91932	+	13.7167i	0.620289	+	1.07437i	0.989432	+	0.144999i	$0.0463179\pi$
$163$	7.91932	+	13.7167i	0.620289	+	1.07437i	−0.369143	+	0.929373i	$0.620349\pi$
$164$	−42.9648			−3.35498
$165$	5.01251	+	8.68192i	0.390223	+	0.675887i
$166$	−11.0362	+	19.1153i	−0.856576	+	1.48363i
$167$	−9.64729	+	16.7096i	−0.746530	+	1.29303i	0.202947	+	0.979190i	$0.434948\pi$
$167$	−9.64729	+	16.7096i	−0.746530	+	1.29303i	−0.949477	+	0.313838i	$0.898385\pi$
$168$	−35.2509			−2.71967
$169$	−11.7981	−	5.45928i	−0.907550	−	0.419945i
$170$	16.7633			1.28569
$171$	8.38129	−	14.5168i	0.640933	−	1.11013i
$172$	14.5893	−	25.2695i	1.11243	−	1.92678i
$173$	8.01257	+	13.8782i	0.609185	+	1.05514i	0.991375	+	0.131055i	$0.0418365\pi$
$173$	8.01257	+	13.8782i	0.609185	+	1.05514i	−0.382190	+	0.924084i	$0.624830\pi$
$174$	−18.9362			−1.43555
$175$	−5.98525	−	10.3668i	−0.452443	−	0.783654i
$176$	3.36329	+	5.82540i	0.253518	+	0.439106i
$177$	3.08755			0.232074
$178$	−13.0941	−	22.6796i	−0.981442	−	1.69991i
$179$	−5.03280	+	8.71707i	−0.376169	+	0.651545i	−0.990501	−	0.137503i	$-0.956092\pi$
$179$	−5.03280	+	8.71707i	−0.376169	+	0.651545i	0.614332	+	0.789048i	$0.289426\pi$
$180$	44.0659	−	76.3244i	3.28448	−	5.68889i
$181$	−9.77673			−0.726698			−0.363349	−	0.931653i	$-0.618367\pi$
$181$	−9.77673			−0.726698			−0.363349	+	0.931653i	$0.618367\pi$
$182$	3.76937	−	17.1219i	0.279404	−	1.26916i
$183$	17.1531			1.26799
$184$	1.35144	−	2.34076i	0.0996295	−	0.172563i
$185$	−13.0584	+	22.6179i	−0.960074	+	1.66290i
$186$	−17.5526	−	30.4020i	−1.28702	−	2.22919i
$187$	1.97271			0.144259
$188$	0.231294	+	0.400613i	0.0168689	+	0.0292177i
$189$	8.43705	+	14.6134i	0.613705	+	1.06297i
$190$	23.9739			1.73925
$191$	0.512923	+	0.888408i	0.0371138	+	0.0642830i	0.883986	−	0.467514i	$-0.154850\pi$
$191$	0.512923	+	0.888408i	0.0371138	+	0.0642830i	−0.846872	+	0.531797i	$0.821517\pi$
$192$	−2.07766	+	3.59861i	−0.149942	+	0.259708i
$193$	10.4131	−	18.0361i	0.749554	−	1.29826i	−0.198483	−	0.980104i	$-0.563602\pi$
$193$	10.4131	−	18.0361i	0.749554	−	1.29826i	0.948037	−	0.318161i	$-0.103065\pi$
$194$	−49.1331			−3.52755
$195$	26.6854	+	24.3804i	1.91098	+	1.74592i
$196$	−14.6877			−1.04912
$197$	−4.02751	+	6.97585i	−0.286948	+	0.497009i	−0.973080	−	0.230469i	$-0.925974\pi$
$197$	−4.02751	+	6.97585i	−0.286948	+	0.497009i	0.686132	+	0.727477i	$0.259307\pi$
$198$	7.52982	−	13.0420i	0.535121	−	0.926857i
$199$	−9.51451	−	16.4796i	−0.674466	−	1.16821i	−0.976625	−	0.214952i	$-0.931041\pi$
$199$	−9.51451	−	16.4796i	−0.674466	−	1.16821i	0.302159	−	0.953258i	$-0.402293\pi$
$200$	38.3437			2.71131
$201$	−10.8425	−	18.7798i	−0.764771	−	1.32462i
$202$	−4.24114	−	7.34587i	−0.298406	−	0.516853i
$203$	4.79305			0.336406
$204$	−13.0496	−	22.6025i	−0.913651	−	1.58249i
$205$	−16.2782	+	28.1947i	−1.13692	+	1.96920i
$206$	−23.4008	+	40.5313i	−1.63041	+	2.82395i
$207$	−2.61338			−0.181642
$208$	17.9054	+	16.3588i	1.24151	+	1.13428i
$209$	2.82126			0.195150
$210$	−24.3732	+	42.2157i	−1.68191	+	2.91316i
$211$	−9.28069	+	16.0746i	−0.638909	+	1.10662i	0.346763	+	0.937953i	$0.387281\pi$
$211$	−9.28069	+	16.0746i	−0.638909	+	1.10662i	−0.985672	+	0.168670i	$0.946053\pi$
$212$	−0.845042	−	1.46366i	−0.0580377	−	0.100524i
$213$	−33.6917			−2.30852
$214$	15.7084	+	27.2077i	1.07380	+	1.85988i
$215$	−11.0550	−	19.1479i	−0.753947	−	1.30587i
$216$	−54.0508			−3.67769
$217$	4.44284	+	7.69523i	0.301600	+	0.522386i
$218$	4.44973	−	7.70716i	0.301374	−	0.521995i
$219$	1.20832	−	2.09288i	0.0816510	−	0.141424i
$220$	14.8332			1.00005
$221$	6.78037	−	2.14883i	0.456097	−	0.144546i
$222$	59.0424			3.96267
$223$	−1.27819	+	2.21389i	−0.0855938	+	0.148253i	−0.905644	−	0.424039i	$-0.860612\pi$
$223$	−1.27819	+	2.21389i	−0.0855938	+	0.148253i	0.820050	+	0.572291i	$0.193945\pi$
$224$	−4.56531	+	7.90734i	−0.305032	+	0.528332i
$225$	−18.5370	−	32.1070i	−1.23580	−	2.14047i
$226$	43.1654			2.87132
$227$	−5.08827	−	8.81314i	−0.337720	−	0.584949i	0.646283	−	0.763098i	$-0.276322\pi$
$227$	−5.08827	−	8.81314i	−0.337720	−	0.584949i	−0.984004	+	0.178149i	$0.942989\pi$
$228$	−18.6627	−	32.3247i	−1.23597	−	2.14076i
$229$	23.7436			1.56902			0.784510	−	0.620117i	$-0.212915\pi$
$229$	23.7436			1.56902			0.784510	+	0.620117i	$0.212915\pi$
$230$	−1.86883	−	3.23691i	−0.123227	−	0.213436i
$231$	−2.86825	+	4.96796i	−0.188717	+	0.326868i
$232$	−7.67649	+	13.2961i	−0.503987	+	0.872930i
$233$	12.7702			0.836607			0.418303	−	0.908307i	$-0.362625\pi$
$233$	12.7702			0.836607			0.418303	+	0.908307i	$0.362625\pi$
$234$	11.6742	−	53.0285i	0.763164	−	3.46658i
$235$	0.350525			0.0228657
$236$	2.28420	−	3.95634i	0.148688	−	0.257536i
$237$	−10.5331	+	18.2439i	−0.684200	+	1.18507i
$238$	4.79615	+	8.30717i	0.310888	+	0.538474i
$239$	−28.0301			−1.81312			−0.906558	−	0.422081i	$-0.861300\pi$
$239$	−28.0301			−1.81312			−0.906558	+	0.422081i	$0.861300\pi$
$240$	−33.7171	−	58.3997i	−2.17643	−	3.76969i
$241$	3.03335	+	5.25391i	0.195395	+	0.338434i	0.947030	−	0.321145i	$-0.104068\pi$
$241$	3.03335	+	5.25391i	0.195395	+	0.338434i	−0.751635	+	0.659579i	$0.770734\pi$
$242$	2.53464			0.162933
$243$	−0.519419	−	0.899660i	−0.0333207	−	0.0577132i
$244$	12.6900	−	21.9797i	0.812393	−	1.40711i
$245$	−5.56479	+	9.63849i	−0.355521	+	0.615781i
$246$	73.6003			4.69258
$247$	9.69686	−	3.07313i	0.616997	−	0.195539i
$248$	−28.4625			−1.80737
$249$	13.0199	−	22.5512i	0.825105	−	1.42912i
$250$	5.26769	−	9.12390i	0.333158	−	0.577046i
$251$	−8.15708	−	14.1285i	−0.514870	−	0.891781i	−0.999851	−	0.0172564i	$-0.994507\pi$
$251$	−8.15708	−	14.1285i	−0.514870	−	0.891781i	0.484981	−	0.874525i	$-0.338826\pi$
$252$	50.4307			3.17684
$253$	−0.219925	−	0.380921i	−0.0138266	−	0.0239483i
$254$	−3.24526	−	5.62096i	−0.203626	−	0.352690i
$255$	−19.7765			−1.23845
$256$	15.1377	+	26.2193i	0.946106	+	1.63870i
$257$	−6.26792	+	10.8564i	−0.390982	+	0.677201i	−0.992579	−	0.121599i	$-0.961198\pi$
$257$	−6.26792	+	10.8564i	−0.390982	+	0.677201i	0.601597	+	0.798800i	$0.294531\pi$
$258$	−24.9921	+	43.2876i	−1.55594	+	2.69497i
$259$	−14.9445			−0.928609
$260$	50.9828	−	16.1575i	3.16182	−	1.00204i
$261$	14.8446			0.918857
$262$	15.4189	−	26.7064i	0.952585	−	1.64993i
$263$	6.75611	−	11.7019i	0.416599	−	0.721571i	−0.578996	−	0.815331i	$-0.696555\pi$
$263$	6.75611	−	11.7019i	0.416599	−	0.721571i	0.995595	+	0.0937595i	$0.0298885\pi$
$264$	−9.18753	−	15.9133i	−0.565453	−	0.979394i
$265$	−1.28066			−0.0786701
$266$	6.85915	+	11.8804i	0.420562	+	0.728434i
$267$	15.4477	+	26.7562i	0.945384	+	1.63745i
$268$	−32.0855			−1.95993
$269$	5.96942	+	10.3393i	0.363962	+	0.630400i	0.988609	−	0.150507i	$-0.0480905\pi$
$269$	5.96942	+	10.3393i	0.363962	+	0.630400i	−0.624647	+	0.780907i	$0.714757\pi$
$270$	−37.3719	+	64.7300i	−2.27438	+	3.93934i
$271$	−0.399397	+	0.691775i	−0.0242616	+	0.0420223i	−0.877901	−	0.478842i	$-0.841057\pi$
$271$	−0.399397	+	0.691775i	−0.0242616	+	0.0420223i	0.853640	+	0.520864i	$0.174390\pi$
$272$	−13.2696			−0.804590
$273$	−4.44691	+	20.1996i	−0.269139	+	1.22253i
$274$	27.7276			1.67508
$275$	3.11990	−	5.40383i	0.188137	−	0.325863i
$276$	−2.90961	+	5.03960i	−0.175138	+	0.303348i
$277$	−7.24946	−	12.5564i	−0.435578	−	0.754443i	0.561765	−	0.827297i	$-0.310123\pi$
$277$	−7.24946	−	12.5564i	−0.435578	−	0.754443i	−0.997343	+	0.0728543i	$0.976789\pi$
$278$	−15.2276			−0.913292
$279$	13.7600	+	23.8330i	0.823788	+	1.42684i
$280$	19.7612	+	34.2274i	1.18096	+	2.04548i
$281$	12.0278			0.717520			0.358760	−	0.933430i	$-0.383200\pi$
$281$	12.0278			0.717520			0.358760	+	0.933430i	$0.383200\pi$
$282$	−0.396216	−	0.686266i	−0.0235943	−	0.0408665i
$283$	−6.50783	+	11.2719i	−0.386850	+	0.670044i	−0.992024	−	0.126049i	$-0.959770\pi$
$283$	−6.50783	+	11.2719i	−0.386850	+	0.670044i	0.605174	+	0.796093i	$0.293104\pi$
$284$	−24.9254	+	43.1721i	−1.47905	+	2.56179i
$285$	−28.2832			−1.67535
$286$	8.71175	−	2.76093i	0.515137	−	0.163257i
$287$	−18.6294			−1.09966
$288$	−14.1393	+	24.4899i	−0.833164	+	1.44308i
$289$	6.55420	−	11.3522i	0.385541	−	0.667777i
$290$	10.6154	+	18.3864i	0.623357	+	1.07969i
$291$	57.9647			3.39795
$292$	−1.78786	−	3.09666i	−0.104626	−	0.181218i
$293$	4.67858	+	8.10354i	0.273326	+	0.473414i	0.969711	−	0.244254i	$-0.0785430\pi$
$293$	4.67858	+	8.10354i	0.273326	+	0.473414i	−0.696386	+	0.717668i	$0.745210\pi$
$294$	25.1606			1.46740
$295$	−1.73084	−	2.99790i	−0.100773	−	0.174545i
$296$	23.9350	−	41.4567i	1.39120	−	2.40962i
$297$	−4.39794	+	7.61745i	−0.255194	+	0.442009i
$298$	−34.0609			−1.97310
$299$	−1.17083	−	1.06969i	−0.0677106	−	0.0618620i
$300$	−82.5529			−4.76619
$301$	6.32589	−	10.9568i	0.364618	−	0.631538i
$302$	9.45583	−	16.3780i	0.544122	−	0.942447i
$303$	5.00348	+	8.66627i	0.287442	+	0.497864i
$304$	−18.9774			−1.08843
$305$	−9.61579	−	16.6550i	−0.550599	−	0.953665i
$306$	14.8542	+	25.7282i	0.849158	+	1.47078i
$307$	−14.3957			−0.821604			−0.410802	−	0.911725i	$-0.634751\pi$
$307$	−14.3957			−0.821604			−0.410802	+	0.911725i	$0.634751\pi$
$308$	4.24392	+	7.35068i	0.241820	+	0.418844i
$309$	27.6070	−	47.8167i	1.57051	−	2.72020i
$310$	−19.6796	+	34.0860i	−1.11772	+	1.93596i
$311$	18.9376			1.07385			0.536926	−	0.843629i	$-0.319585\pi$
$311$	18.9376			1.07385			0.536926	+	0.843629i	$0.319585\pi$
$312$	−48.9122	−	44.6873i	−2.76911	−	2.52992i
$313$	−15.9761			−0.903024			−0.451512	−	0.892265i	$-0.649115\pi$
$313$	−15.9761			−0.903024			−0.451512	+	0.892265i	$0.649115\pi$
$314$	−17.4563	+	30.2352i	−0.985117	+	1.70627i
$315$	19.1068	−	33.0940i	1.07655	−	1.86464i
$316$	15.5850	+	26.9940i	0.876725	+	1.51853i
$317$	12.0125			0.674691			0.337346	−	0.941381i	$-0.390471\pi$
$317$	12.0125			0.674691			0.337346	+	0.941381i	$0.390471\pi$
$318$	1.44759	+	2.50730i	0.0811768	+	0.140602i
$319$	1.24922	+	2.16372i	0.0699431	+	0.121145i
$320$	4.65884			0.260437
$321$	−18.5319	−	32.0982i	−1.03435	−	1.79155i
$322$	1.06938	−	1.85222i	0.0595943	−	0.103220i
$323$	−2.78277	+	4.81989i	−0.154837	+	0.268186i
$324$	37.5065			2.08369
$325$	4.83706	−	21.9718i	0.268312	−	1.21878i
$326$	−40.1453			−2.22344
$327$	−5.24956	+	9.09251i	−0.290301	+	0.502817i
$328$	29.8366	−	51.6786i	1.64745	−	2.85347i
$329$	0.100288	+	0.173705i	0.00552908	+	0.00957665i
$330$	−25.4098			−1.39877
$331$	10.5750	+	18.3165i	0.581256	+	1.00676i	0.995331	+	0.0965216i	$0.0307717\pi$
$331$	10.5750	+	18.3165i	0.581256	+	1.00676i	−0.414075	+	0.910243i	$0.635895\pi$
$332$	−19.2645	−	33.3672i	−1.05728	−	1.83126i
$333$	−46.2849			−2.53640
$334$	−24.4524	−	42.3528i	−1.33798	−	2.31744i
$335$	−12.1563	+	21.0554i	−0.664172	+	1.15038i
$336$	19.2936	−	33.4174i	1.05255	−	1.82307i
$337$	6.26056			0.341034			0.170517	−	0.985355i	$-0.445456\pi$
$337$	6.26056			0.341034			0.170517	+	0.985355i	$0.445456\pi$
$338$	26.9355	−	18.9790i	1.46510	−	1.03232i
$339$	−50.9242			−2.76582
$340$	−14.6308	+	25.3413i	−0.793468	+	1.37433i
$341$	−2.31590	+	4.01125i	−0.125413	+	0.217222i
$342$	21.2436	+	36.7949i	1.14872	+	1.98964i
$343$	−19.7974			−1.06896
$344$	20.2630	+	35.0965i	1.09251	+	1.89228i
$345$	2.20475	+	3.81874i	0.118700	+	0.205594i
$346$	−40.6180			−2.18364
$347$	5.20496	+	9.01526i	0.279417	+	0.483964i	0.971240	−	0.238103i	$-0.0765255\pi$
$347$	5.20496	+	9.01526i	0.279417	+	0.483964i	−0.691823	+	0.722067i	$0.743192\pi$
$348$	16.5273	−	28.6261i	0.885955	−	1.53452i
$349$	13.7757	−	23.8602i	0.737394	−	1.27720i	−0.216270	−	0.976333i	$-0.569389\pi$
$349$	13.7757	−	23.8602i	0.737394	−	1.27720i	0.953665	−	0.300871i	$-0.0972774\pi$
$350$	30.3410			1.62179
$351$	−6.81851	+	30.9723i	−0.363945	+	1.65318i
$352$	−4.75947			−0.253681
$353$	2.64314	−	4.57805i	0.140680	−	0.243665i	−0.787073	−	0.616860i	$-0.788404\pi$
$353$	2.64314	−	4.57805i	0.140680	−	0.243665i	0.927753	+	0.373195i	$0.121738\pi$
$354$	−3.91291	+	6.77737i	−0.207969	+	0.360213i
$355$	18.8871	+	32.7135i	1.00243	+	1.73625i
$356$	45.7134			2.42280
$357$	−5.65824	−	9.80036i	−0.299466	−	0.518690i
$358$	−12.7564	−	22.0947i	−0.674194	−	1.16774i
$359$	23.0174			1.21481			0.607407	−	0.794391i	$-0.292210\pi$
$359$	23.0174			1.21481			0.607407	+	0.794391i	$0.292210\pi$
$360$	61.2027	+	106.006i	3.22566	+	5.58701i
$361$	5.52026	−	9.56137i	0.290540	−	0.503230i
$362$	12.3903	−	21.4605i	0.651217	−	1.12794i
$363$	−2.99024			−0.156947
$364$	22.5936	+	20.6420i	1.18423	+	1.08194i
$365$	−2.70949			−0.141821
$366$	−21.7384	+	37.6521i	−1.13629	+	1.96811i
$367$	−9.31691	+	16.1374i	−0.486339	+	0.842363i	−0.999877	−	0.0157037i	$-0.995001\pi$
$367$	−9.31691	+	16.1374i	−0.486339	+	0.842363i	0.513538	+	0.858067i	$0.328334\pi$
$368$	1.47934	+	2.56230i	0.0771161	+	0.133569i
$369$	−57.6972			−3.00360
$370$	−33.0984	−	57.3282i	−1.72071	−	2.98035i
$371$	−0.366408	−	0.634637i	−0.0190229	−	0.0329487i
$372$	61.2789			3.17716
$373$	−0.217128	−	0.376076i	−0.0112424	−	0.0194725i	0.860349	−	0.509705i	$-0.170245\pi$
$373$	−0.217128	−	0.376076i	−0.0112424	−	0.0194725i	−0.871592	+	0.490232i	$0.836912\pi$
$374$	−2.50006	+	4.33024i	−0.129275	+	0.223911i
$375$	−6.21454	+	10.7639i	−0.320918	+	0.555845i
$376$	−0.642484			−0.0331336
$377$	6.65056	+	6.07611i	0.342521	+	0.312935i
$378$	−42.7698			−2.19984
$379$	−9.59993	+	16.6276i	−0.493115	+	0.854101i	−0.999969	−	0.00793148i	$-0.997475\pi$
$379$	−9.59993	+	16.6276i	−0.493115	+	0.854101i	0.506853	+	0.862032i	$0.330809\pi$
$380$	−20.9241	+	36.2417i	−1.07339	+	1.85916i
$381$	3.82859	+	6.63131i	0.196145	+	0.339733i
$382$	−2.60015			−0.133035
$383$	−2.89647	−	5.01684i	−0.148003	−	0.256348i	0.782486	−	0.622668i	$-0.213951\pi$
$383$	−2.89647	−	5.01684i	−0.148003	−	0.256348i	−0.930489	+	0.366319i	$0.880618\pi$
$384$	−19.4981	−	33.7717i	−0.995007	−	1.72340i
$385$	6.43163			0.327786
$386$	26.3936	+	45.7150i	1.34340	+	2.32683i
$387$	19.5920	−	33.9343i	0.995917	−	1.72498i
$388$	42.8828	−	74.2752i	2.17704	−	3.77075i
$389$	22.3481			1.13309			0.566546	−	0.824030i	$-0.308279\pi$
$389$	22.3481			1.13309			0.566546	+	0.824030i	$0.308279\pi$
$390$	−87.3355	+	27.6784i	−4.42240	+	1.40155i
$391$	0.867698			0.0438814
$392$	10.1998	−	17.6666i	0.515168	−	0.892297i
$393$	−18.1905	+	31.5068i	−0.917588	+	1.58931i
$394$	−10.2083	−	17.6813i	−0.514286	−	0.890770i
$395$	23.6190			1.18840
$396$	13.1439	+	22.7659i	0.660505	+	1.14403i
$397$	16.3642	+	28.3436i	0.821294	+	1.42252i	0.904719	+	0.426008i	$0.140081\pi$
$397$	16.3642	+	28.3436i	0.821294	+	1.42252i	−0.0834255	+	0.996514i	$0.526586\pi$
$398$	48.2318			2.41764
$399$	−8.09207	−	14.0159i	−0.405110	−	0.701672i
$400$	−20.9863	+	36.3493i	−1.04932	+	1.81747i
$401$	9.10938	−	15.7779i	0.454901	−	0.787911i	−0.543782	−	0.839227i	$-0.683008\pi$
$401$	9.10938	−	15.7779i	0.454901	−	0.787911i	0.998682	+	0.0513156i	$0.0163414\pi$
$402$	54.9637			2.74134
$403$	−3.59054	+	16.3096i	−0.178858	+	0.812440i
$404$	14.8065			0.736649
$405$	14.2102	−	24.6128i	0.706111	−	1.22302i
$406$	−6.07433	+	10.5210i	−0.301464	+	0.522151i
$407$	−3.89503	−	6.74640i	−0.193070	−	0.334407i
$408$	36.2487			1.79458
$409$	19.6485	+	34.0323i	0.971558	+	1.68279i	0.690856	+	0.722993i	$0.257234\pi$
$409$	19.6485	+	34.0323i	0.971558	+	1.68279i	0.280702	+	0.959795i	$0.409433\pi$
$410$	−41.2594	−	71.4634i	−2.03766	−	3.52932i
$411$	−32.7116			−1.61354
$412$	−40.8478	−	70.7505i	−2.01243	−	3.48563i
$413$	0.990420	−	1.71546i	0.0487354	−	0.0844121i
$414$	3.31199	−	5.73654i	0.162775	−	0.281935i
$415$	−29.1953			−1.43314
$416$	−16.3586	+	5.18438i	−0.802048	+	0.254185i
$417$	17.9648			0.879738
$418$	−3.57544	+	6.19284i	−0.174880	+	0.302902i
$419$	0.788473	−	1.36567i	0.0385194	−	0.0667176i	−0.846123	−	0.532988i	$-0.821069\pi$
$419$	0.788473	−	1.36567i	0.0385194	−	0.0667176i	0.884642	+	0.466270i	$0.154403\pi$
$420$	−42.5454	−	73.6907i	−2.07600	−	3.59574i
$421$	−10.0373			−0.489189			−0.244595	−	0.969625i	$-0.578655\pi$
$421$	−10.0373			−0.489189			−0.244595	+	0.969625i	$0.578655\pi$
$422$	−23.5232	−	40.7434i	−1.14509	−	1.98336i
$423$	0.310604	+	0.537982i	0.0151021	+	0.0261576i
$424$	2.34734			0.113997
$425$	6.15468	+	10.6602i	0.298546	+	0.517096i
$426$	42.6982	−	73.9554i	2.06873	−	3.58315i
$427$	5.50234	−	9.53033i	0.266277	−	0.461205i
$428$	−54.8403			−2.65081
$429$	−10.2777	+	3.25720i	−0.496211	+	0.157259i
$430$	56.0411			2.70254
$431$	0.502219	−	0.869870i	0.0241911	−	0.0419001i	−0.853676	−	0.520804i	$-0.825632\pi$
$431$	0.502219	−	0.869870i	0.0241911	−	0.0419001i	0.877867	+	0.478904i	$0.158966\pi$
$432$	29.5831	−	51.2395i	1.42332	−	2.46526i
$433$	2.05636	+	3.56172i	0.0988225	+	0.171166i	0.911198	−	0.411970i	$-0.135159\pi$
$433$	2.05636	+	3.56172i	0.0988225	+	0.171166i	−0.812375	+	0.583135i	$0.801826\pi$
$434$	−22.5220			−1.08109
$435$	−12.5235	−	21.6913i	−0.600455	−	1.04002i
$436$	7.76734	+	13.4534i	0.371988	+	0.644303i
$437$	1.24093			0.0593616
$438$	3.06267	+	5.30470i	0.146340	+	0.253468i
$439$	−2.07158	+	3.58809i	−0.0988713	+	0.171250i	−0.911218	−	0.411925i	$-0.864857\pi$
$439$	−2.07158	+	3.58809i	−0.0988713	+	0.171250i	0.812346	+	0.583175i	$0.198190\pi$
$440$	−10.3008	+	17.8416i	−0.491073	+	0.850563i
$441$	−19.7241			−0.939243
$442$	−3.87607	+	17.6066i	−0.184366	+	0.837461i
$443$	−10.3516			−0.491821			−0.245911	−	0.969293i	$-0.579087\pi$
$443$	−10.3516			−0.491821			−0.245911	+	0.969293i	$0.579087\pi$
$444$	−51.5315	+	89.2552i	−2.44558	+	4.23586i
$445$	17.3196	−	29.9984i	0.821027	−	1.42206i
$446$	−3.23975	−	5.61141i	−0.153407	−	0.265708i
$447$	40.1833			1.90061
$448$	1.33294	+	2.30872i	0.0629754	+	0.109077i
$449$	−4.56897	−	7.91369i	−0.215623	−	0.373470i	0.737842	−	0.674973i	$-0.235845\pi$
$449$	−4.56897	−	7.91369i	−0.215623	−	0.373470i	−0.953465	+	0.301503i	$0.902512\pi$
$450$	93.9693			4.42975
$451$	−4.85542	−	8.40984i	−0.228633	−	0.396004i
$452$	−37.6742	+	65.2536i	−1.77205	+	3.06927i
$453$	−11.1555	+	19.3219i	−0.524131	+	0.907821i
$454$	25.7939			1.21057
$455$	22.1060	−	7.00583i	1.03634	−	0.328438i
$456$	51.8407			2.42767
$457$	0.719663	−	1.24649i	0.0336644	−	0.0583084i	−0.848702	−	0.528871i	$-0.822616\pi$
$457$	0.719663	−	1.24649i	0.0336644	−	0.0583084i	0.882367	+	0.470562i	$0.155949\pi$
$458$	−30.0907	+	52.1187i	−1.40605	+	2.43535i
$459$	−8.67587	−	15.0271i	−0.404955	−	0.701403i
$460$	6.52438			0.304201
$461$	12.5964	+	21.8175i	0.586671	+	1.01614i	0.994665	+	0.103159i	$0.0328952\pi$
$461$	12.5964	+	21.8175i	0.586671	+	1.01614i	−0.407994	+	0.912985i	$0.633772\pi$
$462$	−7.26999	−	12.5920i	−0.338231	−	0.585833i
$463$	14.1428			0.657271			0.328635	−	0.944457i	$-0.393411\pi$
$463$	14.1428			0.657271			0.328635	+	0.944457i	$0.393411\pi$
$464$	−8.40301	−	14.5544i	−0.390100	−	0.675673i
$465$	23.2169	−	40.2129i	1.07666	−	1.86483i
$466$	−16.1840	+	28.0315i	−0.749710	+	1.29854i
$467$	18.4384			0.853228			0.426614	−	0.904434i	$-0.359706\pi$
$467$	18.4384			0.853228			0.426614	+	0.904434i	$0.359706\pi$
$468$	69.9748	+	63.9306i	3.23459	+	2.95519i
$469$	−13.9122			−0.642405
$470$	−0.444227	+	0.769424i	−0.0204907	+	0.0354909i
$471$	20.5940	−	35.6699i	0.948924	−	1.64358i
$472$	3.17249	+	5.49492i	0.146026	+	0.252924i
$473$	6.59493			0.303235
$474$	−26.6977	−	46.2418i	−1.22627	−	2.12396i
$475$	8.80205	+	15.2456i	0.403866	+	0.699516i
$476$	−16.7441			−0.767463
$477$	−1.13480	−	1.96554i	−0.0519592	−	0.0899959i
$478$	35.5231	−	61.5279i	1.62479	−	2.81422i
$479$	14.1110	−	24.4410i	0.644750	−	1.11674i	−0.339609	−	0.940567i	$-0.610295\pi$
$479$	14.1110	−	24.4410i	0.644750	−	1.11674i	0.984359	−	0.176173i	$-0.0563718\pi$
$480$	47.7138			2.17783
$481$	−20.7362	−	18.9451i	−0.945490	−	0.863822i
$482$	−15.3769			−0.700399
$483$	−1.26160	+	2.18515i	−0.0574048	+	0.0994280i
$484$	−2.21221	+	3.83165i	−0.100555	+	0.174166i
$485$	−32.4943	−	56.2818i	−1.47549	−	2.55562i
$486$	2.63308			0.119439
$487$	−6.08769	−	10.5442i	−0.275860	−	0.477803i	0.694492	−	0.719501i	$-0.255629\pi$
$487$	−6.08769	−	10.5442i	−0.275860	−	0.477803i	−0.970352	+	0.241697i	$0.922296\pi$
$488$	17.6250	+	30.5274i	0.797845	+	1.38191i
$489$	47.3613			2.14175
$490$	−14.1047	−	24.4301i	−0.637187	−	1.10364i
$491$	−17.5154	+	30.3375i	−0.790458	+	1.36911i	0.135225	+	0.990815i	$0.456824\pi$
$491$	−17.5154	+	30.3375i	−0.790458	+	1.36911i	−0.925683	+	0.378299i	$0.876509\pi$
$492$	−64.2374	+	111.263i	−2.89605	+	5.01610i
$493$	−4.92872			−0.221978
$494$	−5.54332	+	25.1799i	−0.249406	+	1.13290i
$495$	19.9195			0.895313
$496$	15.5781	−	26.9821i	0.699477	−	1.21153i
$497$	−10.8076	+	18.7193i	−0.484786	+	0.839674i
$498$	33.0009	+	57.1592i	1.47881	+	2.56137i
$499$	−7.22186			−0.323295			−0.161648	−	0.986849i	$-0.551681\pi$
$499$	−7.22186			−0.323295			−0.161648	+	0.986849i	$0.551681\pi$
$500$	9.19515	+	15.9265i	0.411219	+	0.712253i
$501$	28.8477	+	49.9657i	1.28882	+	2.23230i
$502$	41.3505			1.84556
$503$	−7.73149	−	13.3913i	−0.344730	−	0.597090i	0.640574	−	0.767896i	$-0.278696\pi$
$503$	−7.73149	−	13.3913i	−0.344730	−	0.597090i	−0.985305	+	0.170806i	$0.945363\pi$
$504$	−35.0213	+	60.6587i	−1.55997	+	2.70195i
$505$	5.60977	−	9.71641i	0.249632	−	0.432375i
$506$	1.11486			0.0495616
$507$	−31.7771	+	22.3905i	−1.41127	+	0.994396i
$508$	11.3297			0.502674
$509$	16.6021	−	28.7557i	0.735876	−	1.27457i	−0.218463	−	0.975845i	$-0.570104\pi$
$509$	16.6021	−	28.7557i	0.735876	−	1.27457i	0.954338	−	0.298728i	$-0.0965625\pi$
$510$	25.0632	−	43.4107i	1.10982	−	1.92226i
$511$	−0.775209	−	1.34270i	−0.0342932	−	0.0593976i
$512$	−50.6550			−2.23865
$513$	−12.4077	−	21.4908i	−0.547814	−	0.948841i
$514$	−15.8869	−	27.5170i	−0.700743	−	1.21372i
$515$	−61.9046			−2.72784
$516$	−43.6256	−	75.5618i	−1.92051	−	3.32642i
$517$	−0.0522768	+	0.0905461i	−0.00229913	+	0.00398221i
$518$	18.9395	−	32.8042i	0.832156	−	1.44134i
$519$	47.9190			2.10341
$520$	−15.9703	+	72.5432i	−0.700344	+	3.18123i
$521$	−22.0340			−0.965325			−0.482663	−	0.875806i	$-0.660330\pi$
$521$	−22.0340			−0.965325			−0.482663	+	0.875806i	$0.660330\pi$
$522$	−18.8129	+	32.5848i	−0.823417	+	1.42620i
$523$	−14.4226	+	24.9807i	−0.630658	+	1.09233i	0.356760	+	0.934196i	$0.383881\pi$
$523$	−14.4226	+	24.9807i	−0.630658	+	1.09233i	−0.987418	+	0.158135i	$0.949452\pi$
$524$	26.9149	+	46.6180i	1.17578	+	2.03652i
$525$	−35.7947			−1.56221
$526$	17.1243	+	29.6602i	0.746655	+	1.29325i
$527$	−4.56861	−	7.91306i	−0.199012	−	0.344698i
$528$	20.1141			0.875354
$529$	11.4033	+	19.7510i	0.495794	+	0.858741i
$530$	1.62300	−	2.81112i	0.0704987	−	0.122107i
$531$	3.06744	−	5.31296i	0.133116	−	0.230563i
$532$	−23.9464			−1.03821
$533$	−25.8491	−	23.6163i	−1.11965	−	1.02294i
$534$	−78.3088			−3.38875
$535$	−20.7775	+	35.9877i	−0.898291	+	1.55589i
$536$	22.2816	−	38.5929i	0.962419	−	1.66696i
$537$	15.0493	+	26.0661i	0.649425	+	1.12484i
$538$	−30.2607			−1.30463
$539$	−1.65985	−	2.87495i	−0.0714949	−	0.123833i
$540$	−65.2355	−	112.991i	−2.80729	−	4.86237i
$541$	−19.3752			−0.833007			−0.416503	−	0.909134i	$-0.636745\pi$
$541$	−19.3752			−0.833007			−0.416503	+	0.909134i	$0.636745\pi$
$542$	−1.01233	−	1.75340i	−0.0434832	−	0.0753151i
$543$	−14.6174	+	25.3180i	−0.627292	+	1.08650i
$544$	4.69454	−	8.13118i	0.201277	−	0.348621i
$545$	11.7714			0.504230
$546$	−38.7037	−	35.3606i	−1.65636	−	1.51329i
$547$	31.4512			1.34475			0.672377	−	0.740209i	$-0.265273\pi$
$547$	31.4512			1.34475			0.672377	+	0.740209i	$0.265273\pi$
$548$	−24.2003	+	41.9162i	−1.03379	+	1.79057i
$549$	17.0413	−	29.5165i	0.727307	−	1.25973i
$550$	7.90784	+	13.6968i	0.337191	+	0.584033i
$551$	−7.04876			−0.300287
$552$	−4.04113	−	6.99944i	−0.172002	−	0.297916i
$553$	6.75761	+	11.7045i	0.287363	+	0.497727i
$554$	36.7496			1.56134
$555$	39.0478	+	67.6328i	1.65749	+	2.87085i
$556$	13.2905	−	23.0198i	0.563642	−	0.976257i
$557$	12.0633	−	20.8942i	0.511138	−	0.885316i	−0.488779	−	0.872408i	$-0.662558\pi$
$557$	12.0633	−	20.8942i	0.511138	−	0.885316i	0.999917	−	0.0129087i	$-0.00410909\pi$
$558$	−69.7532			−2.95289
$559$	22.6673	−	7.18371i	0.958723	−	0.303839i
$560$	−43.2629			−1.82819
$561$	2.94944	−	5.10859i	0.124526	−	0.215685i
$562$	−15.2431	+	26.4019i	−0.642992	+	1.11370i
$563$	3.87188	+	6.70629i	0.163180	+	0.282636i	0.936008	−	0.351980i	$-0.114491\pi$
$563$	3.87188	+	6.70629i	0.163180	+	0.282636i	−0.772827	+	0.634616i	$0.781158\pi$
$564$	1.38325			0.0582453
$565$	28.5475	+	49.4457i	1.20100	+	2.08020i
$566$	−16.4950	−	28.5702i	−0.693337	−	1.20090i
$567$	16.2627			0.682969
$568$	−34.6186	−	59.9612i	−1.45256	−	2.51592i
$569$	9.19760	−	15.9307i	0.385583	−	0.667850i	−0.606267	−	0.795262i	$-0.707334\pi$
$569$	9.19760	−	15.9307i	0.385583	−	0.667850i	0.991850	+	0.127411i	$0.0406669\pi$
$570$	35.8438	−	62.0833i	1.50133	−	2.60038i
$571$	−9.57839			−0.400843			−0.200422	−	0.979710i	$-0.564231\pi$
$571$	−9.57839			−0.400843			−0.200422	+	0.979710i	$0.564231\pi$
$572$	−3.42978	+	15.5794i	−0.143406	+	0.651406i
$573$	3.06752			0.128148
$574$	23.6094	−	40.8927i	0.985437	−	1.70683i
$575$	1.37229	−	2.37687i	0.0572284	−	0.0991224i
$576$	4.12826	+	7.15035i	0.172011	+	0.297931i
$577$	12.1259			0.504808			0.252404	−	0.967622i	$-0.418779\pi$
$577$	12.1259			0.504808			0.252404	+	0.967622i	$0.418779\pi$
$578$	16.6125	+	28.7738i	0.690991	+	1.19683i
$579$	−31.1378	−	53.9322i	−1.29404	−	2.24134i
$580$	−37.0600			−1.53883
$581$	−8.35304	−	14.4679i	−0.346543	−	0.600229i
$582$	−73.4599	+	127.236i	−3.04501	+	5.27411i
$583$	0.190995	−	0.330814i	0.00791022	−	0.0137009i
$584$	4.96627			0.205506
$585$	68.4647	−	21.6978i	2.83067	−	0.897095i
$586$	−23.7171			−0.979742
$587$	12.6513	−	21.9127i	0.522175	−	0.904434i	−0.477492	−	0.878636i	$-0.658454\pi$
$587$	12.6513	−	21.9127i	0.522175	−	0.904434i	0.999667	−	0.0257979i	$-0.00821263\pi$
$588$	−21.9599	+	38.0357i	−0.905611	+	1.56856i
$589$	−6.53374	−	11.3168i	−0.269218	−	0.466299i
$590$	8.77413			0.361225
$591$	12.0432	+	20.8594i	0.495391	+	0.858043i
$592$	26.2003	+	45.3802i	1.07683	+	1.86512i
$593$	−2.55502			−0.104922			−0.0524610	−	0.998623i	$-0.516707\pi$
$593$	−2.55502			−0.104922			−0.0524610	+	0.998623i	$0.516707\pi$
$594$	−11.1472	−	19.3075i	−0.457375	−	0.792197i
$595$	−6.34388	+	10.9879i	−0.260074	+	0.450461i
$596$	29.7280	−	51.4904i	1.21771	−	2.10913i
$597$	−56.9013			−2.32882
$598$	3.83186	−	1.21439i	0.156696	−	0.0496602i
$599$	43.3849			1.77266			0.886329	−	0.463055i	$-0.153247\pi$
$599$	43.3849			1.77266			0.886329	+	0.463055i	$0.153247\pi$
$600$	57.3284	−	99.2957i	2.34042	−	4.05373i
$601$	−4.77568	+	8.27172i	−0.194804	+	0.337410i	−0.946836	−	0.321716i	$-0.895740\pi$
$601$	−4.77568	+	8.27172i	−0.194804	+	0.337410i	0.752032	+	0.659126i	$0.229074\pi$
$602$	16.0339	+	27.7715i	0.653492	+	1.13188i
$603$	−43.0875			−1.75466
$604$	16.5059	+	28.5890i	0.671614	+	1.16327i
$605$	1.67629	+	2.90342i	0.0681509	+	0.118041i
$606$	−25.3640			−1.03034
$607$	−1.88511	−	3.26511i	−0.0765142	−	0.132527i	0.825230	−	0.564798i	$-0.191046\pi$
$607$	−1.88511	−	3.26511i	−0.0765142	−	0.132527i	−0.901744	+	0.432271i	$0.857712\pi$
$608$	6.71384	−	11.6287i	0.272282	−	0.471606i
$609$	7.16618	−	12.4122i	0.290388	−	0.502967i
$610$	48.7452			1.97363
$611$	−0.0810494	+	0.368158i	−0.00327891	+	0.0148941i
$612$	−51.8583			−2.09625
$613$	−19.6881	+	34.1009i	−0.795197	+	1.37732i	0.127518	+	0.991836i	$0.459299\pi$
$613$	−19.6881	+	34.1009i	−0.795197	+	1.37732i	−0.922714	+	0.385485i	$0.874034\pi$
$614$	18.2439	−	31.5994i	0.736265	−	1.27525i
$615$	48.6757	+	84.3088i	1.96279	+	3.39966i
$616$	−11.7887			−0.474979
$617$	13.4916	+	23.3682i	0.543152	+	0.940766i	0.998721	+	0.0505659i	$0.0161025\pi$
$617$	13.4916	+	23.3682i	0.543152	+	0.940766i	−0.455569	+	0.890200i	$0.650564\pi$
$618$	69.9739	+	121.198i	2.81476	+	4.87531i
$619$	−19.3050			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$619$	−19.3050			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$620$	−34.3522	−	59.4997i	−1.37962	−	2.38957i
$621$	−1.93443	+	3.35053i	−0.0776260	+	0.134452i
$622$	−24.0000	+	41.5693i	−0.962313	+	1.66678i
$623$	19.8212			0.794119
$624$	69.1337	−	21.9098i	2.76756	−	0.877096i
$625$	−17.2638			−0.690554
$626$	20.2469	−	35.0686i	0.809228	−	1.40162i
$627$	4.21811	−	7.30599i	0.168455	−	0.291773i
$628$	−30.4713	−	52.7779i	−1.21594	−	2.10607i
$629$	15.3676			0.612746
$630$	48.4290	+	83.8815i	1.92946	+	3.34192i
$631$	−7.65694	−	13.2622i	−0.304818	−	0.527960i	0.672403	−	0.740185i	$-0.265262\pi$
$631$	−7.65694	−	13.2622i	−0.304818	−	0.527960i	−0.977221	+	0.212225i	$0.931929\pi$
$632$	−43.2917			−1.72205
$633$	27.7515	+	48.0670i	1.10302	+	1.91049i
$634$	−15.2237	+	26.3683i	−0.604612	+	1.04722i
$635$	4.29252	−	7.43487i	0.170344	−	0.295044i
$636$	−5.05376			−0.200395
$637$	−8.83665	−	8.07336i	−0.350121	−	0.319878i
$638$	−6.33267			−0.250713
$639$	−33.4722	+	57.9756i	−1.32414	+	2.29348i
$640$	−21.8608	+	37.8639i	−0.864122	+	1.49670i
$641$	−14.6945	−	25.4517i	−0.580400	−	1.00528i	−0.995432	−	0.0954749i	$-0.969563\pi$
$641$	−14.6945	−	25.4517i	−0.580400	−	1.00528i	0.415032	−	0.909807i	$-0.363770\pi$
$642$	93.9436			3.70766
$643$	−22.3647	−	38.7367i	−0.881976	−	1.52763i	−0.849141	−	0.528166i	$-0.822880\pi$
$643$	−22.3647	−	38.7367i	−0.881976	−	1.52763i	−0.0328349	−	0.999461i	$-0.510454\pi$
$644$	1.86669	+	3.23319i	0.0735577	+	0.127406i
$645$	−66.1143			−2.60325
$646$	−7.05332	−	12.2167i	−0.277509	−	0.480660i
$647$	−8.05631	+	13.9539i	−0.316726	+	0.548586i	−0.979803	−	0.199966i	$-0.935917\pi$
$647$	−8.05631	+	13.9539i	−0.316726	+	0.548586i	0.663077	+	0.748551i	$0.269250\pi$
$648$	−26.0462	+	45.1133i	−1.02319	+	1.77222i
$649$	1.03254			0.0405308
$650$	42.0994	+	38.4630i	1.65127	+	1.50864i
$651$	26.5703			1.04137
$652$	35.0383	−	60.6881i	1.37221	−	2.37673i
$653$	19.2907	−	33.4125i	0.754905	−	1.30753i	−0.190517	−	0.981684i	$-0.561016\pi$
$653$	19.2907	−	33.4125i	0.754905	−	1.30753i	0.945422	−	0.325849i	$-0.105650\pi$
$654$	−13.3058	−	23.0463i	−0.520296	−	0.901180i
$655$	40.7894			1.59377
$656$	32.6604	+	56.5695i	1.27518	+	2.20867i
$657$	−2.40091	−	4.15850i	−0.0936684	−	0.162238i
$658$	−0.508390			−0.0198191
$659$	9.28580	+	16.0835i	0.361723	+	0.626523i	0.988245	−	0.152881i	$-0.0488551\pi$
$659$	9.28580	+	16.0835i	0.361723	+	0.626523i	−0.626521	+	0.779404i	$0.715522\pi$
$660$	22.1774	−	38.4124i	0.863254	−	1.49520i
$661$	6.01244	−	10.4139i	0.233857	−	0.405052i	−0.725083	−	0.688662i	$-0.758199\pi$
$661$	6.01244	−	10.4139i	0.233857	−	0.405052i	0.958940	+	0.283609i	$0.0915319\pi$
$662$	−53.6078			−2.08353
$663$	4.57279	−	20.7714i	0.177592	−	0.806692i
$664$	53.5126			2.07669
$665$	−9.07263	+	15.7143i	−0.351822	+	0.609373i
$666$	58.6579	−	101.598i	2.27295	−	3.93686i
$667$	0.549470	+	0.951711i	0.0212756	+	0.0368504i
$668$	85.3671			3.30295
$669$	3.82209	+	6.62005i	0.147770	+	0.255946i
$670$	−30.8120	−	53.3679i	−1.19037	−	2.06178i
$671$	5.73635			0.221449
$672$	13.6514	+	23.6448i	0.526613	+	0.912120i
$673$	19.9774	−	34.6018i	0.770071	−	1.33380i	−0.167452	−	0.985880i	$-0.553554\pi$
$673$	19.9774	−	34.6018i	0.770071	−	1.33380i	0.937523	−	0.347922i	$-0.113113\pi$
$674$	−7.93414	+	13.7423i	−0.305612	+	0.529335i
$675$	−54.8845			−2.11251
$676$	5.18186	+	57.2834i	0.199302	+	2.20321i
$677$	−1.34058			−0.0515226			−0.0257613	−	0.999668i	$-0.508201\pi$
$677$	−1.34058			−0.0515226			−0.0257613	+	0.999668i	$0.508201\pi$
$678$	64.5374	−	111.782i	2.47854	−	4.29296i
$679$	18.5938	−	32.2055i	0.713566	−	1.23593i
$680$	−20.3206	−	35.1963i	−0.779259	−	1.34972i
$681$	−30.4303			−1.16609
$682$	−5.86997	−	10.1671i	−0.224773	−	0.389318i
$683$	−8.83459	−	15.3020i	−0.338046	−	0.585513i	0.646019	−	0.763321i	$-0.276433\pi$
$683$	−8.83459	−	15.3020i	−0.338046	−	0.585513i	−0.984065	+	0.177808i	$0.943099\pi$
$684$	−74.1645			−2.83575
$685$	18.3377	+	31.7618i	0.700647	+	1.21356i
$686$	25.0897	−	43.4566i	0.957929	−	1.65918i
$687$	35.4995	−	61.4869i	1.35439	−	2.34587i
$688$	−44.3614			−1.69126
$689$	0.296117	−	1.34508i	0.0112812	−	0.0512434i
$690$	−11.1765			−0.425482
$691$	−10.7108	+	18.5516i	−0.407458	+	0.705737i	−0.994604	−	0.103743i	$-0.966918\pi$
$691$	−10.7108	+	18.5516i	−0.407458	+	0.705737i	0.587147	+	0.809481i	$0.300251\pi$
$692$	35.4509	−	61.4028i	1.34764	−	2.33418i
$693$	5.69914	+	9.87121i	0.216493	+	0.374976i
$694$	−26.3854			−1.00158
$695$	−10.0708	−	17.4432i	−0.382008	−	0.661657i
$696$	22.9546	+	39.7584i	0.870090	+	1.50704i
$697$	19.1567			0.725612
$698$	34.9164	+	60.4769i	1.32160	+	2.28909i
$699$	19.0930	−	33.0701i	0.722165	−	1.25083i
$700$	−26.4812	+	45.8668i	−1.00090	+	1.73360i
$701$	7.83629			0.295972			0.147986	−	0.988989i	$-0.452721\pi$
$701$	7.83629			0.295972			0.147986	+	0.988989i	$0.452721\pi$
$702$	−59.3450	−	54.2189i	−2.23983	−	2.04636i
$703$	21.9778			0.828908
$704$	−0.694814	+	1.20345i	−0.0261868	+	0.0453569i
$705$	0.524076	−	0.907727i	0.0197379	−	0.0341870i
$706$	6.69941	+	11.6037i	0.252136	+	0.436712i
$707$	6.42003			0.241450
$708$	−6.83029	−	11.8304i	−0.256698	−	0.444614i
$709$	−2.54895	−	4.41491i	−0.0957279	−	0.165806i	0.814184	−	0.580607i	$-0.197185\pi$
$709$	−2.54895	−	4.41491i	−0.0957279	−	0.165806i	−0.909912	+	0.414801i	$0.863851\pi$
$710$	−95.7443			−3.59322
$711$	20.9291	+	36.2502i	0.784901	+	1.35949i
$712$	−31.7454	+	54.9846i	−1.18971	+	2.06064i
$713$	−1.01865	+	1.76435i	−0.0381486	+	0.0660754i
$714$	28.6832			1.07344
$715$	8.92417	+	8.15333i	0.333745	+	0.304917i
$716$	44.5344			1.66433
$717$	−41.9083	+	72.5874i	−1.56510	+	2.71082i
$718$	−29.1705	+	50.5248i	−1.08863	+	1.88557i
$719$	9.50330	+	16.4602i	0.354413	+	0.613862i	0.987017	−	0.160614i	$-0.0513473\pi$
$719$	9.50330	+	16.4602i	0.354413	+	0.613862i	−0.632604	+	0.774475i	$0.718014\pi$
$720$	−133.990			−4.99351
$721$	−17.7115	−	30.6772i	−0.659610	−	1.14248i
$722$	13.9919	+	24.2346i	0.520724	+	0.901920i
$723$	18.1409			0.674666
$724$	21.6281	+	37.4610i	0.803803	+	1.39223i
$725$	−7.79491	+	13.5012i	−0.289496	+	0.501421i
$726$	3.78959	−	6.56377i	0.140645	−	0.243604i
$727$	4.60308			0.170719			0.0853595	−	0.996350i	$-0.472796\pi$
$727$	4.60308			0.170719			0.0853595	+	0.996350i	$0.472796\pi$
$728$	−40.5185	+	12.8411i	−1.50171	+	0.475924i
$729$	−28.5379			−1.05696
$730$	3.43379	−	5.94750i	0.127090	−	0.220127i
$731$	−6.50496	+	11.2669i	−0.240595	+	0.416722i
$732$	−37.9461	−	65.7245i	−1.40253	−	2.42925i
$733$	22.9104			0.846213			0.423107	−	0.906080i	$-0.360940\pi$
$733$	22.9104			0.846213			0.423107	+	0.906080i	$0.360940\pi$
$734$	−23.6150	−	40.9024i	−0.871646	−	1.50974i
$735$	16.6400	+	28.8214i	0.613777	+	1.06309i
$736$	−2.09345			−0.0771656
$737$	−3.62596	−	6.28035i	−0.133564	−	0.231340i
$738$	73.1209	−	126.649i	2.69162	−	4.66202i
$739$	−1.31682	+	2.28079i	−0.0484398	+	0.0839003i	−0.889229	−	0.457463i	$-0.848758\pi$
$739$	−1.31682	+	2.28079i	−0.0484398	+	0.0839003i	0.840789	+	0.541363i	$0.182092\pi$
$740$	115.552			4.24776
$741$	6.53972	−	29.7059i	0.240243	−	1.09127i
$742$	1.85742			0.0681882
$743$	−3.02923	+	5.24678i	−0.111132	+	0.192486i	−0.916227	−	0.400660i	$-0.868781\pi$
$743$	−3.02923	+	5.24678i	−0.111132	+	0.192486i	0.805095	+	0.593146i	$0.202114\pi$
$744$	−42.5548	+	73.7070i	−1.56013	+	2.70223i
$745$	−22.5263	−	39.0166i	−0.825299	−	1.42946i
$746$	1.10068			0.0402988
$747$	−25.8703	−	44.8087i	−0.946545	−	1.63946i
$748$	−4.36405	−	7.55876i	−0.159565	−	0.276375i
$749$	−23.7786			−0.868851
$750$	−15.7516	−	27.2826i	−0.575169	−	0.996221i
$751$	6.38871	−	11.0656i	0.233127	−	0.403788i	−0.725599	−	0.688117i	$-0.758437\pi$
$751$	6.38871	−	11.0656i	0.233127	−	0.403788i	0.958727	+	0.284329i	$0.0917708\pi$
$752$	0.351645	−	0.609067i	0.0128232	−	0.0222104i
$753$	−48.7832			−1.77776
$754$	−21.7658	+	6.89803i	−0.792665	+	0.251212i
$755$	25.0145			0.910372
$756$	37.3290	−	64.6557i	1.35764	−	2.35150i
$757$	−19.3914	+	33.5868i	−0.704791	+	1.22073i	0.261975	+	0.965075i	$0.415626\pi$
$757$	−19.3914	+	33.5868i	−0.704791	+	1.22073i	−0.966767	+	0.255660i	$0.917707\pi$
$758$	−24.3324	−	42.1449i	−0.883792	−	1.53077i
$759$	−1.31526			−0.0477407
$760$	−29.0613	−	50.3356i	−1.05416	−	1.82586i
$761$	−20.2776	−	35.1218i	−0.735061	−	1.27316i	−0.954697	−	0.297581i	$-0.903820\pi$
$761$	−20.2776	−	35.1218i	−0.735061	−	1.27316i	0.219636	−	0.975582i	$-0.429513\pi$
$762$	−19.4082			−0.703086
$763$	3.36790	+	5.83337i	0.121926	+	0.211182i
$764$	2.26938	−	3.93068i	0.0821033	−	0.142207i
$765$	−19.6477	+	34.0308i	−0.710364	+	1.23039i
$766$	14.6830			0.530520
$767$	3.54892	−	1.12473i	0.128144	−	0.0406115i
$768$	90.5306			3.26674
$769$	−13.2402	+	22.9328i	−0.477455	+	0.826976i	−0.999666	−	0.0258399i	$-0.991774\pi$
$769$	−13.2402	+	22.9328i	−0.477455	+	0.826976i	0.522211	+	0.852816i	$0.325107\pi$
$770$	−8.15094	+	14.1178i	−0.293739	+	0.508772i
$771$	18.7426	+	32.4631i	0.674997	+	1.16913i
$772$	−92.1439			−3.31633
$773$	7.12490	+	12.3407i	0.256265	+	0.443864i	0.965238	−	0.261371i	$-0.0841747\pi$
$773$	7.12490	+	12.3407i	0.256265	+	0.443864i	−0.708973	+	0.705235i	$0.750841\pi$
$774$	49.6587	+	86.0114i	1.78494	+	3.09161i
$775$	−28.9015			−1.03817
$776$	59.5594	+	103.160i	2.13806	+	3.70323i
$777$	−22.3439	+	38.7007i	−0.801582	+	1.38838i
$778$	−28.3222	+	49.0555i	−1.01540	+	1.75872i
$779$	27.3968			0.981591
$780$	34.3836	−	156.184i	1.23113	−	5.59227i
$781$	−11.2672			−0.403173
$782$	−1.09965	+	1.90465i	−0.0393235	+	0.0681102i
$783$	10.9880	−	19.0318i	0.392679	−	0.680141i
$784$	11.1651	+	19.3386i	0.398755	+	0.690664i
$785$	−46.1791			−1.64820
$786$	−46.1063	−	79.8585i	−1.64456	−	2.84846i
$787$	−27.0697	−	46.8861i	−0.964931	−	1.67131i	−0.709800	−	0.704403i	$-0.751215\pi$
$787$	−27.0697	−	46.8861i	−0.964931	−	1.67131i	−0.255131	−	0.966906i	$-0.582119\pi$
$788$	35.6387			1.26958
$789$	−20.2024	−	34.9915i	−0.719223	−	1.24573i
$790$	−29.9328	+	51.8451i	−1.06496	+	1.84457i
$791$	−16.3354	+	28.2938i	−0.580820	+	1.00601i
$792$	−36.5108			−1.29735
$793$	19.7163	−	6.24848i	0.700145	−	0.221890i
$794$	−82.9546			−2.94395
$795$	−1.91473	+	3.31642i	−0.0679086	+	0.117621i
$796$	−42.0961	+	72.9126i	−1.49206	+	2.58432i
$797$	9.88872	+	17.1278i	0.350276	+	0.606696i	0.986298	−	0.164975i	$-0.0527544\pi$
$797$	9.88872	+	17.1278i	0.350276	+	0.606696i	−0.636021	+	0.771671i	$0.719421\pi$
$798$	41.0210			1.45213
$799$	−0.103127	−	0.178622i	−0.00364838	−	0.00631918i
$800$	−14.8491	−	25.7194i	−0.524994	−	0.909317i
$801$	61.3884			2.16905
$802$	23.0890	+	39.9913i	0.815301	+	1.41214i
$803$	0.404089	−	0.699903i	0.0142600	−	0.0246991i
$804$	−47.9717	+	83.0894i	−1.69183	+	2.93034i
$805$	2.82895			0.0997073
$806$	−31.2503	−	28.5510i	−1.10075	−	1.00567i
$807$	35.7000			1.25670
$808$	−10.2823	+	17.8094i	−0.361729	+	0.626533i
$809$	−3.78806	+	6.56111i	−0.133181	+	0.230676i	−0.924901	−	0.380208i	$-0.875852\pi$
$809$	−3.78806	+	6.56111i	−0.133181	+	0.230676i	0.791720	+	0.610884i	$0.209186\pi$
$810$	36.0178	+	62.3847i	1.26554	+	2.19197i
$811$	−36.2578			−1.27318			−0.636592	−	0.771201i	$-0.719657\pi$
$811$	−36.2578			−1.27318			−0.636592	+	0.771201i	$0.719657\pi$
$812$	−10.6032	−	18.3653i	−0.372099	−	0.644495i
$813$	1.19429	+	2.06857i	0.0418856	+	0.0725480i
$814$	19.7450			0.692063
$815$	−26.5502	−	45.9862i	−0.930011	−	1.61083i
$816$	−19.8397	+	34.3634i	−0.694528	+	1.20296i
$817$	−9.30300	+	16.1133i	−0.325471	+	0.563732i
$818$	−99.6040			−3.48257
$819$	30.3409	+	27.7201i	1.06020	+	0.968619i
$820$	144.043			5.03019
$821$	−14.3136	+	24.7918i	−0.499547	+	0.865240i	−1.00000		0.000523406i	$-0.999833\pi$
$821$	−14.3136	+	24.7918i	−0.499547	+	0.865240i	0.500453	+	0.865764i	$0.333167\pi$
$822$	41.4560	−	71.8040i	1.44595	−	2.50445i
$823$	9.76000	+	16.9048i	0.340212	+	0.589265i	0.984472	−	0.175542i	$-0.0561678\pi$
$823$	9.76000	+	16.9048i	0.340212	+	0.589265i	−0.644260	+	0.764807i	$0.722834\pi$
$824$	113.466			3.95278
$825$	−9.32926	−	16.1587i	−0.324803	−	0.562575i
$826$	2.51036	+	4.34807i	0.0873466	+	0.151289i
$827$	4.68925			0.163061			0.0815306	−	0.996671i	$-0.474019\pi$
$827$	4.68925			0.163061			0.0815306	+	0.996671i	$0.474019\pi$
$828$	5.78133	+	10.0136i	0.200915	+	0.347995i
$829$	10.4527	−	18.1045i	0.363036	−	0.628796i	−0.625423	−	0.780286i	$-0.715074\pi$
$829$	10.4527	−	18.1045i	0.363036	−	0.628796i	0.988459	+	0.151489i	$0.0484070\pi$
$830$	36.9998	−	64.0855i	1.28428	−	2.22444i
$831$	−43.3552			−1.50398
$832$	−1.07723	+	4.89320i	−0.0373463	+	0.169641i
$833$	6.54883			0.226903
$834$	−22.7671	+	39.4338i	−0.788361	+	1.36548i
$835$	32.3433	−	56.0203i	1.11929	−	1.93866i
$836$	−6.24120	−	10.8101i	−0.215856	−	0.373874i
$837$	40.7407			1.40820
$838$	1.99850	+	3.46150i	0.0690369	+	0.119575i
$839$	23.5089	+	40.7187i	0.811618	+	1.40576i	0.911731	+	0.410788i	$0.134746\pi$
$839$	23.5089	+	40.7187i	0.811618	+	1.40576i	−0.100113	+	0.994976i	$0.531920\pi$
$840$	118.182			4.07765
$841$	11.3789	+	19.7088i	0.392375	+	0.679614i
$842$	12.7205	−	22.0326i	0.438378	−	0.759293i
$843$	17.9830	−	31.1476i	0.619369	−	1.07278i
$844$	82.1232			2.82680
$845$	39.5543	+	18.3027i	1.36071	+	0.629631i
$846$	−1.57454			−0.0541338
$847$	−0.959205	+	1.66139i	−0.0329587	+	0.0570861i
$848$	−1.28475	+	2.22525i	−0.0441184	+	0.0764154i
$849$	19.4600	+	33.7056i	0.667864	+	1.15677i
$850$	−31.1998			−1.07014
$851$	−1.71323	−	2.96740i	−0.0587288	−	0.101721i
$852$	74.5329	+	129.095i	2.55345	+	4.42271i
$853$	−48.7942			−1.67068			−0.835340	−	0.549733i	$-0.814729\pi$
$853$	−48.7942			−1.67068			−0.835340	+	0.549733i	$0.814729\pi$
$854$	13.9465	+	24.1560i	0.477238	+	0.826600i
$855$	−28.0989	+	48.6688i	−0.960964	+	1.66444i
$856$	38.0836	−	65.9626i	1.30167	−	2.25456i
$857$	−48.2335			−1.64762			−0.823812	−	0.566863i	$-0.808157\pi$
$857$	−48.2335			−1.64762			−0.823812	+	0.566863i	$0.808157\pi$
$858$	5.87534	−	26.6881i	0.200581	−	0.911116i
$859$	26.2337			0.895082			0.447541	−	0.894263i	$-0.352300\pi$
$859$	26.2337			0.895082			0.447541	+	0.894263i	$0.352300\pi$
$860$	−48.9120	+	84.7180i	−1.66788	+	2.88886i
$861$	−27.8531	+	48.2431i	−0.949233	+	1.64412i
$862$	1.27295	+	2.20481i	0.0433567	+	0.0750961i
$863$	−28.5207			−0.970857			−0.485428	−	0.874276i	$-0.661336\pi$
$863$	−28.5207			−0.970857			−0.485428	+	0.874276i	$0.661336\pi$
$864$	20.9318	+	36.2550i	0.712116	+	1.23342i
$865$	−26.8628	−	46.5278i	−0.913363	−	1.58199i
$866$	−10.4243			−0.354232
$867$	−19.5986	−	33.9458i	−0.665604	−	1.15286i
$868$	19.6570	−	34.0469i	0.667201	−	1.15563i
$869$	−3.52250	+	6.10115i	−0.119493	+	0.206967i
$870$	63.4851			2.15235
$871$	−19.3038	−	17.6364i	−0.654083	−	0.597585i
$872$	−21.5760			−0.730654
$873$	57.5872	−	99.7439i	1.94903	−	3.37582i
$874$	−1.57265	+	2.72392i	−0.0531958	+	0.0921379i
$875$	3.98699	+	6.90566i	0.134785	+	0.233454i
$876$	−10.6922			−0.361257
$877$	−0.182859	−	0.316722i	−0.00617472	−	0.0106949i	0.862922	−	0.505338i	$-0.168632\pi$
$877$	−0.182859	−	0.316722i	−0.00617472	−	0.0106949i	−0.869096	+	0.494643i	$0.835299\pi$
$878$	−5.25072	−	9.09452i	−0.177203	−	0.306925i
$879$	27.9801			0.943747
$880$	−11.2757	−	19.5301i	−0.380104	−	0.658360i
$881$	−4.24450	+	7.35170i	−0.143001	+	0.247685i	−0.928625	−	0.371019i	$-0.879009\pi$
$881$	−4.24450	+	7.35170i	−0.143001	+	0.247685i	0.785624	+	0.618704i	$0.212342\pi$
$882$	24.9968	−	43.2957i	0.841685	−	1.45784i
$883$	−12.2202			−0.411244			−0.205622	−	0.978632i	$-0.565922\pi$
$883$	−12.2202			−0.411244			−0.205622	+	0.978632i	$0.565922\pi$
$884$	−23.2331	−	21.2263i	−0.781415	−	0.713919i
$885$	−10.3513			−0.347954
$886$	13.1188	−	22.7225i	0.440736	−	0.763378i
$887$	8.59893	−	14.8938i	0.288724	−	0.500084i	−0.684782	−	0.728748i	$-0.740102\pi$
$887$	8.59893	−	14.8938i	0.288724	−	0.500084i	0.973505	+	0.228664i	$0.0734358\pi$
$888$	−71.5715	−	123.965i	−2.40178	−	4.16001i
$889$	4.91252			0.164761
$890$	43.8989	+	76.0352i	1.47150	+	2.54871i
$891$	4.23859	+	7.34145i	0.141998	+	0.245948i
$892$	11.3105			0.378702
$893$	−0.147486	−	0.255454i	−0.00493544	−	0.00854844i
$894$	−50.9252	+	88.2050i	−1.70319	+	2.95001i
$895$	16.8729	−	29.2247i	0.563998	−	0.976874i
$896$	−25.0183			−0.835802
$897$	−4.52063	+	1.43268i	−0.150939	+	0.0478357i
$898$	23.1614			0.772906
$899$	5.78615	−	10.0219i	0.192979	−	0.334249i
$900$	−82.0153	+	142.055i	−2.73384	+	4.73515i
$901$	0.376780	+	0.652601i	0.0125523	+	0.0217413i
$902$	24.6135			0.819540
$903$	−18.9159	−	32.7634i	−0.629483	−	1.09030i
$904$	−52.3253	−	90.6300i	−1.74031	−	3.01431i
$905$	32.7773			1.08955
$906$	−28.2752	−	48.9741i	−0.939380	−	1.62705i
$907$	2.34901	−	4.06861i	0.0779976	−	0.135096i	−0.824388	−	0.566025i	$-0.808481\pi$
$907$	2.34901	−	4.06861i	0.0779976	−	0.135096i	0.902386	+	0.430929i	$0.141814\pi$
$908$	−22.5126	+	38.9929i	−0.747107	+	1.29403i
$909$	19.8836			0.659496
$910$	−12.6371	+	57.4027i	−0.418917	+	1.90288i
$911$	−30.8968			−1.02366			−0.511828	−	0.859088i	$-0.671032\pi$
$911$	−30.8968			−1.02366			−0.511828	+	0.859088i	$0.671032\pi$
$912$	−28.3735	+	49.1444i	−0.939541	+	1.62733i
$913$	4.35415	−	7.54161i	0.144101	−	0.249591i
$914$	1.82409	+	3.15941i	0.0603354	+	0.104504i
$915$	−57.5070			−1.90112
$916$	−52.5257	−	90.9771i	−1.73550	−	3.00597i
$917$	11.6702	+	20.2134i	0.385385	+	0.667506i
$918$	43.9805			1.45157
$919$	−26.3098	−	45.5699i	−0.867880	−	1.50321i	−0.864158	−	0.503220i	$-0.832149\pi$
$919$	−26.3098	−	45.5699i	−0.867880	−	1.50321i	−0.00372214	−	0.999993i	$-0.501185\pi$
$920$	−4.53082	+	7.84760i	−0.149377	+	0.258728i
$921$	−21.5232	+	37.2794i	−0.709215	+	1.22840i
$922$	−63.8545			−2.10294
$923$	−38.7263	+	12.2731i	−1.27469	+	0.403975i
$924$	25.3807			0.834962
$925$	24.3043	−	42.0962i	0.799119	−	1.38412i
$926$	−17.9234	+	31.0443i	−0.589001	+	1.02018i
$927$	−54.8544	−	95.0106i	−1.80166	−	3.12056i
$928$	11.8913			0.390350
$929$	6.19529	+	10.7306i	0.203261	+	0.352058i	0.949577	−	0.313533i	$-0.101513\pi$
$929$	6.19529	+	10.7306i	0.203261	+	0.352058i	−0.746316	+	0.665592i	$0.768179\pi$
$930$	58.8466	+	101.925i	1.92966	+	3.34226i
$931$	9.36573			0.306949
$932$	−28.2504	−	48.9311i	−0.925373	−	1.60279i
$933$	28.3140	−	49.0412i	0.926958	−	1.60554i
$934$	−23.3674	+	40.4735i	−0.764604	+	1.32433i
$935$	−6.61369			−0.216291
$936$	−125.490	+	39.7704i	−4.10178	+	1.29994i
$937$	18.5056			0.604551			0.302275	−	0.953221i	$-0.402254\pi$
$937$	18.5056			0.604551			0.302275	+	0.953221i	$0.402254\pi$
$938$	17.6312	−	30.5381i	0.575679	−	0.997105i
$939$	−23.8862	+	41.3722i	−0.779498	+	1.35013i
$940$	−0.775433	−	1.34309i	−0.0252918	−	0.0438067i
$941$	40.0842			1.30671			0.653353	−	0.757053i	$-0.273362\pi$
$941$	40.0842			1.30671			0.653353	+	0.757053i	$0.273362\pi$
$942$	52.1985	+	90.4105i	1.70072	+	2.94573i
$943$	−2.13565	−	3.69906i	−0.0695465	−	0.120458i
$944$	−6.94549			−0.226056
$945$	−28.2859	−	48.9926i	−0.920140	−	1.59373i
$946$	−8.35790	+	14.4763i	−0.271739	+	0.470665i
$947$	14.3206	−	24.8041i	0.465358	−	0.806024i	−0.533860	−	0.845573i	$-0.679259\pi$
$947$	14.3206	−	24.8041i	0.465358	−	0.806024i	0.999218	+	0.0395493i	$0.0125922\pi$
$948$	93.2058			3.02718
$949$	0.626496	−	2.84578i	0.0203369	−	0.0923781i
$950$	−44.6201			−1.44767
$951$	17.9602	−	31.1079i	0.582399	−	1.00874i
$952$	11.6278	−	20.1400i	0.376860	−	0.652741i
$953$	−9.33695	−	16.1721i	−0.302453	−	0.523865i	0.674238	−	0.738514i	$-0.264472\pi$
$953$	−9.33695	−	16.1721i	−0.302453	−	0.523865i	−0.976691	+	0.214650i	$0.931139\pi$
$954$	5.75265			0.186249
$955$	−1.71962	−	2.97846i	−0.0556455	−	0.0963808i
$956$	62.0083	+	107.402i	2.00549	+	3.47361i
$957$	7.47095			0.241502
$958$	35.7664	+	61.9493i	1.15556	+	2.00149i
$959$	−10.4932	+	18.1747i	−0.338842	+	0.586892i
$960$	6.96553	−	12.0646i	0.224811	−	0.389385i
$961$	−9.54646			−0.307950
$962$	67.8652	−	21.5078i	2.18806	−	0.693440i
$963$	−73.6449			−2.37317
$964$	13.4208	−	23.2455i	0.432254	−	0.748686i
$965$	−34.9109	+	60.4674i	−1.12382	+	1.94651i
$966$	−3.19770	−	5.53858i	−0.102884	−	0.178201i
$967$	−0.163454			−0.00525631			−0.00262816	−	0.999997i	$-0.500837\pi$
$967$	−0.163454			−0.00525631			−0.00262816	+	0.999997i	$0.500837\pi$
$968$	−3.07251	−	5.32174i	−0.0987541	−	0.171047i
$969$	8.32114	+	14.4126i	0.267313	+	0.463000i
$970$	164.723			5.28893
$971$	12.2231	+	21.1710i	0.392257	+	0.679409i	0.992747	−	0.120223i	$-0.0383610\pi$
$971$	12.2231	+	21.1710i	0.392257	+	0.679409i	−0.600490	+	0.799632i	$0.705028\pi$
$972$	−2.29812	+	3.98046i	−0.0737123	+	0.127673i
$973$	5.76271	−	9.98131i	0.184744	−	0.319986i
$974$	30.8603			0.988826
$975$	−49.6667	−	45.3766i	−1.59061	−	1.45322i
$976$	−38.5861			−1.23511
$977$	5.82961	−	10.0972i	0.186506	−	0.323038i	−0.757577	−	0.652746i	$-0.773617\pi$
$977$	5.82961	−	10.0972i	0.186506	−	0.323038i	0.944083	+	0.329708i	$0.106950\pi$
$978$	−60.0220	+	103.961i	−1.91929	+	3.32431i
$979$	5.16604	+	8.94785i	0.165107	+	0.285974i
$980$	49.2418			1.57297
$981$	10.4307	+	18.0666i	0.333028	+	0.576822i
$982$	−44.3952	−	76.8948i	−1.41671	−	2.45381i
$983$	32.6779			1.04226			0.521132	−	0.853476i	$-0.325510\pi$
$983$	32.6779			1.04226			0.521132	+	0.853476i	$0.325510\pi$
$984$	−89.2186	−	154.531i	−2.84419	−	4.92628i
$985$	13.5025	−	23.3871i	0.430227	−	0.745175i
$986$	6.24627	−	10.8189i	0.198922	−	0.344543i
$987$	0.599773			0.0190910
$988$	−33.2266	−	30.3566i	−1.05708	−	0.965772i
$989$	2.90078			0.0922394
$990$	−25.2444	+	43.7245i	−0.802318	+	1.38966i
$991$	−21.3848	+	37.0396i	−0.679312	+	1.17660i	0.295876	+	0.955226i	$0.404388\pi$
$991$	−21.3848	+	37.0396i	−0.679312	+	1.17660i	−0.975188	+	0.221377i	$0.928945\pi$
$992$	11.0224	+	19.0914i	0.349963	+	0.606154i
$993$	63.2437			2.00698
$994$	−27.3933	−	47.4466i	−0.868864	−	1.50492i
$995$	31.8982	+	55.2493i	1.01124	+	1.75152i
$996$	−115.211			−3.65061
$997$	−15.4786	−	26.8097i	−0.490211	−	0.849071i	0.509725	−	0.860337i	$-0.329747\pi$
$997$	−15.4786	−	26.8097i	−0.490211	−	0.849071i	−0.999937	+	0.0112665i	$0.996414\pi$
$998$	9.15242	−	15.8525i	0.289715	−	0.501801i
$999$	−34.2602	+	59.3405i	−1.08395	+	1.87745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.c.100.1	✓	12
13.3	even	3	inner	143.2.e.c.133.1	yes	12
13.4	even	6		1859.2.a.l.1.1		6
13.9	even	3		1859.2.a.k.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.1	✓	12	1.1	even	1	trivial
143.2.e.c.133.1	yes	12	13.3	even	3	inner
1859.2.a.k.1.6		6	13.9	even	3
1859.2.a.l.1.1		6	13.4	even	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26732 + 2.19506i) q^{2} +(1.49512 - 2.58962i) q^{3} +(-2.21221 - 3.83165i) q^{4} -3.35258 q^{5} +(3.78959 + 6.56377i) q^{6} +(-0.959205 - 1.66139i) q^{7} +6.14501 q^{8} +(-2.97076 - 5.14551i) q^{9} +O(q^{10})\)	\(q+(-1.26732 + 2.19506i) q^{2} +(1.49512 - 2.58962i) q^{3} +(-2.21221 - 3.83165i) q^{4} -3.35258 q^{5} +(3.78959 + 6.56377i) q^{6} +(-0.959205 - 1.66139i) q^{7} +6.14501 q^{8} +(-2.97076 - 5.14551i) q^{9} +(4.24880 - 7.35913i) q^{10} +(0.500000 - 0.866025i) q^{11} -13.2300 q^{12} +(0.775195 - 3.52123i) q^{13} +4.86248 q^{14} +(-5.01251 + 8.68192i) q^{15} +(-3.36329 + 5.82540i) q^{16} +(0.986357 + 1.70842i) q^{17} +15.0596 q^{18} +(1.41063 + 2.44328i) q^{19} +(7.41660 + 12.8459i) q^{20} -5.73650 q^{21} +(1.26732 + 2.19506i) q^{22} +(0.219925 - 0.380921i) q^{23} +(9.18753 - 15.9133i) q^{24} +6.23981 q^{25} +(6.74691 + 6.16413i) q^{26} -8.79587 q^{27} +(-4.24392 + 7.35068i) q^{28} +(-1.24922 + 2.16372i) q^{29} +(-12.7049 - 22.0056i) q^{30} -4.63180 q^{31} +(-2.37973 - 4.12182i) q^{32} +(-1.49512 - 2.58962i) q^{33} -5.00013 q^{34} +(3.21581 + 5.56995i) q^{35} +(-13.1439 + 22.7659i) q^{36} +(3.89503 - 6.74640i) q^{37} -7.15087 q^{38} +(-7.95965 - 7.27212i) q^{39} -20.6017 q^{40} +(4.85542 - 8.40984i) q^{41} +(7.26999 - 12.5920i) q^{42} +(3.29747 + 5.71138i) q^{43} -4.42441 q^{44} +(9.95973 + 17.2508i) q^{45} +(0.557431 + 0.965498i) q^{46} -0.104554 q^{47} +(10.0571 + 17.4193i) q^{48} +(1.65985 - 2.87495i) q^{49} +(-7.90784 + 13.6968i) q^{50} +5.89889 q^{51} +(-15.2070 + 4.81941i) q^{52} +0.381991 q^{53} +(11.1472 - 19.3075i) q^{54} +(-1.67629 + 2.90342i) q^{55} +(-5.89433 - 10.2093i) q^{56} +8.43623 q^{57} +(-3.16633 - 5.48425i) q^{58} +(0.516271 + 0.894208i) q^{59} +44.3548 q^{60} +(2.86818 + 4.96782i) q^{61} +(5.86997 - 10.1671i) q^{62} +(-5.69914 + 9.87121i) q^{63} -1.38963 q^{64} +(-2.59890 + 11.8052i) q^{65} +7.57919 q^{66} +(3.62596 - 6.28035i) q^{67} +(4.36405 - 7.55876i) q^{68} +(-0.657628 - 1.13904i) q^{69} -16.3019 q^{70} +(-5.63361 - 9.75770i) q^{71} +(-18.2554 - 31.6193i) q^{72} +0.808179 q^{73} +(9.87252 + 17.0997i) q^{74} +(9.32926 - 16.1587i) q^{75} +(6.24120 - 10.8101i) q^{76} -1.91841 q^{77} +(26.0502 - 8.25584i) q^{78} -7.04501 q^{79} +(11.2757 - 19.5301i) q^{80} +(-4.23859 + 7.34145i) q^{81} +(12.3068 + 21.3159i) q^{82} +8.70830 q^{83} +(12.6903 + 21.9803i) q^{84} +(-3.30684 - 5.72762i) q^{85} -16.7158 q^{86} +(3.73548 + 6.47003i) q^{87} +(3.07251 - 5.32174i) q^{88} +(-5.16604 + 8.94785i) q^{89} -50.4887 q^{90} +(-6.59372 + 2.08968i) q^{91} -1.94608 q^{92} +(-6.92509 + 11.9946i) q^{93} +(0.132503 - 0.229502i) q^{94} +(-4.72925 - 8.19129i) q^{95} -14.2319 q^{96} +(9.69232 + 16.7876i) q^{97} +(4.20713 + 7.28696i) q^{98} -5.94153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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