LMFDB - Embedded newform 349.2.e.a.123.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.20
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +O(q^{10})$	\(q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +3.26219i q^{10} -2.98370i q^{11} +(-1.74992 - 3.03095i) q^{12} +(-3.77890 + 2.18175i) q^{13} +(1.77806 - 3.07969i) q^{14} +(-5.51687 - 9.55550i) q^{15} +(0.342818 + 0.593778i) q^{16} +6.34956 q^{17} +(-6.28797 - 3.63036i) q^{18} +(-0.995395 + 1.72407i) q^{19} +(-1.82878 - 3.16754i) q^{20} +12.0279i q^{21} +(-1.43318 - 2.48235i) q^{22} +(1.30287 + 2.25663i) q^{23} +(-8.31838 - 4.80262i) q^{24} +(-3.26549 - 5.65599i) q^{25} +(-2.09595 + 3.63029i) q^{26} +14.8101 q^{27} +3.98711i q^{28} +(-3.93778 + 6.82043i) q^{29} +(-9.17972 - 5.29991i) q^{30} -3.57639 q^{31} +(-4.54968 - 2.62676i) q^{32} +(8.39607 + 4.84747i) q^{33} +(5.28263 - 3.04993i) q^{34} +12.5700i q^{35} +8.14069 q^{36} +1.15990 q^{37} +1.91250i q^{38} -14.1783i q^{39} +(-8.69325 - 5.01905i) q^{40} -1.68052 q^{41} +(5.77745 + 10.0068i) q^{42} +(1.19553 + 0.690240i) q^{43} +(2.78320 + 1.60688i) q^{44} +25.6647 q^{45} +(2.16789 + 1.25163i) q^{46} +8.06563i q^{47} -2.22783 q^{48} +(3.35128 - 5.80458i) q^{49} +(-5.43357 - 3.13707i) q^{50} +(-10.3158 + 17.8675i) q^{51} -4.69995i q^{52} -4.74099i q^{53} +(12.3215 - 7.11384i) q^{54} +(8.77444 + 5.06593i) q^{55} +(5.47128 + 9.47654i) q^{56} +(-3.23433 - 5.60203i) q^{57} +7.56584i q^{58} +(6.75038 + 3.89733i) q^{59} +11.8845 q^{60} -11.6094i q^{61} +(-2.97545 + 1.71787i) q^{62} +(-24.2290 - 13.9886i) q^{63} -6.41819 q^{64} -14.8173i q^{65} +9.31368 q^{66} -8.07146 q^{67} +(-3.41957 + 5.92287i) q^{68} -8.46681 q^{69} +(6.03782 + 10.4578i) q^{70} +(-5.22205 + 3.01495i) q^{71} +(19.3487 - 11.1710i) q^{72} +(0.280564 - 0.485951i) q^{73} +(0.965003 - 0.557145i) q^{74} +21.2211 q^{75} +(-1.07214 - 1.85701i) q^{76} +(-5.52238 - 9.56505i) q^{77} +(-6.81037 - 11.7959i) q^{78} +9.98474i q^{79} -2.32823 q^{80} +(-12.7243 + 22.0392i) q^{81} +(-1.39814 + 0.807217i) q^{82} +(8.50963 + 14.7391i) q^{83} +(-11.2196 - 6.47766i) q^{84} +(-10.7807 + 18.6727i) q^{85} +1.32619 q^{86} +(-12.7950 - 22.1616i) q^{87} +8.82011 q^{88} +(14.0692 + 8.12287i) q^{89} +(21.3522 - 12.3277i) q^{90} +(-8.07617 + 13.9883i) q^{91} -2.80665 q^{92} +(5.81038 - 10.0639i) q^{93} +(3.87422 + 6.71035i) q^{94} +(-3.38009 - 5.85449i) q^{95} +(14.7833 - 8.53512i) q^{96} +(-1.72586 + 0.996423i) q^{97} -6.43897i q^{98} +(-19.5294 + 11.2753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.831968	−	0.480337i	0.588290	−	0.339650i	−0.176131	−	0.984367i	$-0.556358\pi$
$2$	0.831968	−	0.480337i	0.588290	−	0.339650i	0.764421	+	0.644717i	$0.223025\pi$
$3$	−1.62465	+	2.81397i	−0.937992	+	1.62465i	−0.168781	+	0.985654i	$0.553983\pi$
$3$	−1.62465	+	2.81397i	−0.937992	+	1.62465i	−0.769210	+	0.638996i	$0.779350\pi$
$4$	−0.538552	+	0.932800i	−0.269276	+	0.466400i
$5$	−1.69786	+	2.94079i	−0.759308	+	1.31516i	0.183896	+	0.982946i	$0.441129\pi$
$5$	−1.69786	+	2.94079i	−0.759308	+	1.31516i	−0.943204	+	0.332215i	$0.892204\pi$
$6$			3.12152i			1.27435i
$7$	3.20576	−	1.85085i	1.21166	−	0.699555i	0.248543	−	0.968621i	$-0.420048\pi$
$7$	3.20576	−	1.85085i	1.21166	−	0.699555i	0.963122	+	0.269066i	$0.0867150\pi$
$8$			2.95610i			1.04514i
$9$	−3.77897	−	6.54537i	−1.25966	−	2.18179i
$10$			3.26219i			1.03160i
$11$		−	2.98370i		−	0.899621i	−0.893124	−	0.449810i	$-0.851492\pi$
$11$		−	2.98370i		−	0.899621i	0.893124	−	0.449810i	$-0.148508\pi$
$12$	−1.74992	−	3.03095i	−0.505158	−	0.874959i
$13$	−3.77890	+	2.18175i	−1.04808	+	0.605108i	−0.922111	−	0.386926i	$-0.873537\pi$
$13$	−3.77890	+	2.18175i	−1.04808	+	0.605108i	−0.125968	+	0.992034i	$0.540204\pi$
$14$	1.77806	−	3.07969i	0.475207	−	0.823083i
$15$	−5.51687	−	9.55550i	−1.42445	−	2.46722i
$16$	0.342818	+	0.593778i	0.0857044	+	0.148444i
$17$	6.34956			1.53999			0.769997	−	0.638048i	$-0.220258\pi$
$17$	6.34956			1.53999			0.769997	+	0.638048i	$0.220258\pi$
$18$	−6.28797	−	3.63036i	−1.48209	−	0.855684i
$19$	−0.995395	+	1.72407i	−0.228359	+	0.395530i	−0.957322	−	0.289024i	$-0.906669\pi$
$19$	−0.995395	+	1.72407i	−0.228359	+	0.395530i	0.728963	+	0.684553i	$0.240003\pi$
$20$	−1.82878	−	3.16754i	−0.408927	−	0.708283i
$21$			12.0279i			2.62471i
$22$	−1.43318	−	2.48235i	−0.305556	−	0.529238i
$23$	1.30287	+	2.25663i	0.271667	+	0.470541i	0.969289	−	0.245925i	$-0.0790918\pi$
$23$	1.30287	+	2.25663i	0.271667	+	0.470541i	−0.697622	+	0.716466i	$0.745758\pi$
$24$	−8.31838	−	4.80262i	−1.69798	−	0.980330i
$25$	−3.26549	−	5.65599i	−0.653098	−	1.13120i
$26$	−2.09595	+	3.63029i	−0.411050	+	0.711959i
$27$	14.8101			2.85021
$28$			3.98711i			0.753494i
$29$	−3.93778	+	6.82043i	−0.731227	+	1.26652i	0.225132	+	0.974328i	$0.427719\pi$
$29$	−3.93778	+	6.82043i	−0.731227	+	1.26652i	−0.956359	+	0.292194i	$0.905615\pi$
$30$	−9.17972	−	5.29991i	−1.67598	−	0.967628i
$31$	−3.57639			−0.642339			−0.321170	−	0.947022i	$-0.604076\pi$
$31$	−3.57639			−0.642339			−0.321170	+	0.947022i	$0.604076\pi$
$32$	−4.54968	−	2.62676i	−0.804278	−	0.464350i
$33$	8.39607	+	4.84747i	1.46157	+	0.843836i
$34$	5.28263	−	3.04993i	0.905964	−	0.523058i
$35$			12.5700i			2.12471i
$36$	8.14069			1.35678
$37$	1.15990			0.190687			0.0953434	−	0.995444i	$-0.469605\pi$
$37$	1.15990			0.190687			0.0953434	+	0.995444i	$0.469605\pi$
$38$			1.91250i			0.310249i
$39$		−	14.1783i		−	2.27035i
$40$	−8.69325	−	5.01905i	−1.37452	−	0.793582i
$41$	−1.68052			−0.262453			−0.131227	−	0.991352i	$-0.541892\pi$
$41$	−1.68052			−0.262453			−0.131227	+	0.991352i	$0.541892\pi$
$42$	5.77745	+	10.0068i	0.891480	+	1.54409i
$43$	1.19553	+	0.690240i	0.182317	+	0.105261i	0.588381	−	0.808584i	$-0.299766\pi$
$43$	1.19553	+	0.690240i	0.182317	+	0.105261i	−0.406064	+	0.913845i	$0.633099\pi$
$44$	2.78320	+	1.60688i	0.419583	+	0.242246i
$45$	25.6647			3.82587
$46$	2.16789	+	1.25163i	0.319638	+	0.184543i
$47$			8.06563i			1.17649i	0.808681	+	0.588247i	$0.200182\pi$
$47$			8.06563i			1.17649i	−0.808681	+	0.588247i	$0.799818\pi$
$48$	−2.22783			−0.321560
$49$	3.35128	−	5.80458i	0.478754	−	0.829226i
$50$	−5.43357	−	3.13707i	−0.768422	−	0.443649i
$51$	−10.3158	+	17.8675i	−1.44450	+	2.50195i
$52$		−	4.69995i		−	0.651765i
$53$		−	4.74099i		−	0.651225i	−0.945503	−	0.325613i	$-0.894429\pi$
$53$		−	4.74099i		−	0.651225i	0.945503	−	0.325613i	$-0.105571\pi$
$54$	12.3215	−	7.11384i	1.67675	−	0.968071i
$55$	8.77444	+	5.06593i	1.18315	+	0.683089i
$56$	5.47128	+	9.47654i	0.731131	+	1.26636i
$57$	−3.23433	−	5.60203i	−0.428398	−	0.742007i
$58$			7.56584i			0.993444i
$59$	6.75038	+	3.89733i	0.878825	+	0.507390i	0.870271	−	0.492574i	$-0.163944\pi$
$59$	6.75038	+	3.89733i	0.878825	+	0.507390i	0.00855397	+	0.999963i	$0.497277\pi$
$60$	11.8845			1.53428
$61$		−	11.6094i		−	1.48643i	−0.669053	−	0.743215i	$-0.733300\pi$
$61$		−	11.6094i		−	1.48643i	0.669053	−	0.743215i	$-0.266700\pi$
$62$	−2.97545	+	1.71787i	−0.377882	+	0.218170i
$63$	−24.2290	−	13.9886i	−3.05256	−	1.76240i
$64$	−6.41819			−0.802274
$65$		−	14.8173i		−	1.83786i
$66$	9.31368			1.14644
$67$	−8.07146			−0.986086			−0.493043	−	0.870005i	$-0.664115\pi$
$67$	−8.07146			−0.986086			−0.493043	+	0.870005i	$0.664115\pi$
$68$	−3.41957	+	5.92287i	−0.414684	+	0.718253i
$69$	−8.46681			−1.01928
$70$	6.03782	+	10.4578i	0.721657	+	1.24995i
$71$	−5.22205	+	3.01495i	−0.619743	+	0.357809i	−0.776769	−	0.629786i	$-0.783143\pi$
$71$	−5.22205	+	3.01495i	−0.619743	+	0.357809i	0.157026	+	0.987594i	$0.449809\pi$
$72$	19.3487	−	11.1710i	2.28027	−	1.31651i
$73$	0.280564	−	0.485951i	0.0328376	−	0.0568763i	−0.849140	−	0.528169i	$-0.822879\pi$
$73$	0.280564	−	0.485951i	0.0328376	−	0.0568763i	0.881977	+	0.471292i	$0.156212\pi$
$74$	0.965003	−	0.557145i	0.112179	−	0.0647667i
$75$	21.2211			2.45040
$76$	−1.07214	−	1.85701i	−0.122983	−	0.213014i
$77$	−5.52238	−	9.56505i	−0.629334	−	1.09004i
$78$	−6.81037	−	11.7959i	−0.771122	−	1.33562i
$79$			9.98474i			1.12337i	0.827351	+	0.561685i	$0.189847\pi$
$79$			9.98474i			1.12337i	−0.827351	+	0.561685i	$0.810153\pi$
$80$	−2.32823			−0.260304
$81$	−12.7243	+	22.0392i	−1.41381	+	2.44880i
$82$	−1.39814	+	0.807217i	−0.154399	+	0.0891422i
$83$	8.50963	+	14.7391i	0.934054	+	1.61783i	0.776313	+	0.630348i	$0.217088\pi$
$83$	8.50963	+	14.7391i	0.934054	+	1.61783i	0.157741	+	0.987481i	$0.449579\pi$
$84$	−11.2196	−	6.47766i	−1.22416	−	0.706771i
$85$	−10.7807	+	18.6727i	−1.16933	+	2.02534i
$86$	1.32619			0.143007
$87$	−12.7950	−	22.1616i	−1.37177	−	2.37597i
$88$	8.82011			0.940227
$89$	14.0692	+	8.12287i	1.49134	+	0.861023i	0.999951	−	0.00992010i	$-0.00315772\pi$
$89$	14.0692	+	8.12287i	1.49134	+	0.861023i	0.491384	+	0.870943i	$0.336491\pi$
$90$	21.3522	−	12.3277i	2.25072	−	1.29946i
$91$	−8.07617	+	13.9883i	−0.846613	+	1.46638i
$92$	−2.80665			−0.292614
$93$	5.81038	−	10.0639i	0.602509	−	1.04358i
$94$	3.87422	+	6.71035i	0.399596	+	0.692120i
$95$	−3.38009	−	5.85449i	−0.346790	−	0.600658i
$96$	14.7833	−	8.53512i	1.50881	−	0.871113i
$97$	−1.72586	+	0.996423i	−0.175234	+	0.101171i	−0.585052	−	0.810996i	$-0.698926\pi$
$97$	−1.72586	+	0.996423i	−0.175234	+	0.101171i	0.409817	+	0.912168i	$0.365592\pi$
$98$		−	6.43897i		−	0.650434i
$99$	−19.5294	+	11.2753i	−1.96278	+	1.13321i
$100$	7.03455			0.703455
$101$		−	6.98452i		−	0.694986i	−0.937683	−	0.347493i	$-0.887033\pi$
$101$		−	6.98452i		−	0.694986i	0.937683	−	0.347493i	$-0.112967\pi$
$102$			19.8203i			1.96250i
$103$		−	6.03173i		−	0.594324i	−0.954827	−	0.297162i	$-0.903960\pi$
$103$		−	6.03173i		−	0.594324i	0.954827	−	0.297162i	$-0.0960402\pi$
$104$	−6.44946	−	11.1708i	−0.632422	−	1.09539i
$105$	−35.3715	−	20.4218i	−3.45191	−	1.99296i
$106$	−2.27727	−	3.94435i	−0.221188	−	0.383110i
$107$	12.3967	−	7.15725i	1.19844	−	0.691917i	0.238229	−	0.971209i	$-0.423433\pi$
$107$	12.3967	−	7.15725i	1.19844	−	0.691917i	0.960206	+	0.279292i	$0.0900997\pi$
$108$	−7.97602	+	13.8149i	−0.767493	+	1.32934i
$109$	−1.77911	+	3.08150i	−0.170407	+	0.295154i	−0.938562	−	0.345110i	$-0.887842\pi$
$109$	−1.77911	+	3.08150i	−0.170407	+	0.295154i	0.768155	+	0.640264i	$0.221175\pi$
$110$	9.73341			0.928044
$111$	−1.88444	+	3.26394i	−0.178863	+	0.309799i
$112$	2.19798	+	1.26901i	0.207690	+	0.119910i
$113$	3.07564	−	1.77572i	0.289332	−	0.167046i	−0.348309	−	0.937380i	$-0.613244\pi$
$113$	3.07564	−	1.77572i	0.289332	−	0.167046i	0.637640	+	0.770334i	$0.279911\pi$
$114$	−5.38173	−	3.10714i	−0.504045	−	0.291011i
$115$	−8.84837			−0.825115
$116$	−4.24140	−	7.34632i	−0.393804	−	0.682088i
$117$	28.5607	+	16.4895i	2.64044	+	1.52446i
$118$	7.48814			0.689339
$119$	20.3552	−	11.7521i	1.86596	−	1.07731i
$120$	28.2470	−	16.3084i	2.57858	−	1.48875i
$121$	2.09751			0.190683
$122$	−5.57642	−	9.65864i	−0.504865	−	0.874452i
$123$	2.73026	−	4.72894i	0.246179	−	0.426394i
$124$	1.92607	−	3.33606i	0.172967	−	0.299587i
$125$	5.19879			0.464994
$126$	−26.8770			−2.39439
$127$		−	9.40171i		−	0.834267i	−0.908845	−	0.417133i	$-0.863035\pi$
$127$		−	9.40171i		−	0.834267i	0.908845	−	0.417133i	$-0.136965\pi$
$128$	3.75963	−	2.17062i	0.332307	−	0.191858i
$129$	−3.88464	+	2.24280i	−0.342023	+	0.197467i
$130$	−7.11728	−	12.3275i	−0.624227	−	1.08119i
$131$			5.17156i			0.451842i	0.974146	+	0.225921i	$0.0725391\pi$
$131$			5.17156i			0.451842i	−0.974146	+	0.225921i	$0.927461\pi$
$132$	−9.04344	+	5.22124i	−0.787131	+	0.454450i
$133$			7.36930i			0.638999i
$134$	−6.71520	+	3.87702i	−0.580105	+	0.334924i
$135$	−25.1456	+	43.5534i	−2.16418	+	3.74848i
$136$			18.7699i			1.60951i
$137$	5.02311	+	2.90009i	0.429153	+	0.247772i	0.698986	−	0.715136i	$-0.253635\pi$
$137$	5.02311	+	2.90009i	0.429153	+	0.247772i	−0.269833	+	0.962907i	$0.586968\pi$
$138$	−7.04412	+	4.06692i	−0.599635	+	0.346200i
$139$	7.79745			0.661371			0.330686	−	0.943741i	$-0.392720\pi$
$139$	7.79745			0.661371			0.330686	+	0.943741i	$0.392720\pi$
$140$	−11.7253	−	6.76958i	−0.990965	−	0.572134i
$141$	−22.6965	−	13.1038i	−1.91139	−	1.10354i
$142$	−2.89638	+	5.01668i	−0.243059	+	0.420991i
$143$	6.50969	+	11.2751i	0.544368	+	0.942873i
$144$	2.59100	−	4.48774i	0.215916	−	0.373978i
$145$	−13.3716	−	23.1603i	−1.11045	−	1.92336i
$146$		−	0.539062i		−	0.0446131i
$147$	10.8893	+	18.8608i	0.898134	+	1.55561i
$148$	−0.624669	+	1.08196i	−0.0513474	+	0.0889364i
$149$	14.5454	−	8.39778i	1.19160	−	0.687973i	0.232934	−	0.972493i	$-0.425167\pi$
$149$	14.5454	−	8.39778i	1.19160	−	0.687973i	0.958670	+	0.284519i	$0.0918340\pi$
$150$	17.6553	−	10.1933i	1.44155	−	0.832278i
$151$	−2.57957	+	4.46794i	−0.209922	+	0.363596i	−0.951690	−	0.307061i	$-0.900654\pi$
$151$	−2.57957	+	4.46794i	−0.209922	+	0.363596i	0.741768	+	0.670657i	$0.233988\pi$
$152$	−5.09653	−	2.94248i	−0.413383	−	0.238667i
$153$	−23.9948	−	41.5602i	−1.93986	−	3.35994i
$154$	−9.18889	−	5.30521i	−0.740462	−	0.427506i
$155$	6.07223	−	10.5174i	0.487733	−	0.844779i
$156$	13.2255	+	7.63576i	1.05889	+	0.611350i
$157$	−2.00905	+	3.47977i	−0.160339	+	0.277716i	−0.934990	−	0.354673i	$-0.884592\pi$
$157$	−2.00905	+	3.47977i	−0.160339	+	0.277716i	0.774651	+	0.632389i	$0.217926\pi$
$158$	4.79604	+	8.30698i	0.381552	+	0.660868i
$159$	13.3410	+	7.70245i	1.05801	+	0.610844i
$160$	15.4495	−	8.91976i	1.22139	−	0.705169i
$161$	8.35337	+	4.82282i	0.658338	+	0.380092i
$162$			24.4478i			1.92080i
$163$			3.05996i			0.239674i	0.992794	+	0.119837i	$0.0382372\pi$
$163$			3.05996i			0.239674i	−0.992794	+	0.119837i	$0.961763\pi$
$164$	0.905048	−	1.56759i	0.0706724	−	0.122408i
$165$	−28.5108	+	16.4607i	−2.21956	+	1.28146i
$166$	14.1595	+	8.17499i	1.09899	+	0.634502i
$167$			17.7853i			1.37627i	0.725582	+	0.688135i	$0.241570\pi$
$167$			17.7853i			1.37627i	−0.725582	+	0.688135i	$0.758430\pi$
$168$	−35.5557			−2.74318
$169$	3.02006	−	5.23090i	0.232312	−	0.402377i
$170$			20.7135i			1.58865i
$171$	15.0463			1.15062
$172$	−1.28771	+	0.743461i	−0.0981871	+	0.0566884i
$173$	2.60333	−	1.50303i	0.197927	−	0.114273i	−0.397761	−	0.917489i	$-0.630213\pi$
$173$	2.60333	−	1.50303i	0.197927	−	0.114273i	0.595688	+	0.803216i	$0.296879\pi$
$174$	−21.2901	−	12.2918i	−1.61400	−	0.931842i
$175$	−20.9368	−	12.0878i	−1.58267	−	0.913755i
$176$	1.77166	−	1.02287i	0.133544	−	0.0771015i
$177$	−21.9340	+	12.6636i	−1.64866	+	0.951854i
$178$	15.6069			1.16978
$179$		−	1.30236i		−	0.0973426i	−0.998815	−	0.0486713i	$-0.984501\pi$
$179$		−	1.30236i		−	0.0973426i	0.998815	−	0.0486713i	$-0.0154987\pi$
$180$	−13.8218	+	23.9401i	−1.03022	+	1.78439i
$181$	4.32195			0.321248			0.160624	−	0.987016i	$-0.448649\pi$
$181$	4.32195			0.321248			0.160624	+	0.987016i	$0.448649\pi$
$182$			15.5171i			1.15021i
$183$	32.6685	+	18.8612i	2.41493	+	1.39426i
$184$	−6.67082	+	3.85140i	−0.491780	+	0.283929i
$185$	−1.96936	+	3.41103i	−0.144790	+	0.250784i
$186$		−	11.1638i		−	0.818567i
$187$		−	18.9452i		−	1.38541i
$188$	−7.52362	−	4.34377i	−0.548717	−	0.316802i
$189$	47.4777	−	27.4113i	3.45349	−	1.99388i
$190$	−5.62426	−	3.24717i	−0.408027	−	0.235574i
$191$	7.32468	+	12.6867i	0.529995	+	0.917979i	0.999388	+	0.0349890i	$0.0111396\pi$
$191$	7.32468	+	12.6867i	0.529995	+	0.917979i	−0.469392	+	0.882990i	$0.655527\pi$
$192$	10.4273	−	18.0606i	0.752526	−	1.30341i
$193$	0.826017	+	0.476901i	0.0594580	+	0.0343281i	0.529434	−	0.848351i	$-0.322404\pi$
$193$	0.826017	+	0.476901i	0.0594580	+	0.0343281i	−0.469976	+	0.882679i	$0.655738\pi$
$194$	−0.957238	+	1.65799i	−0.0687257	+	0.119036i
$195$	41.6954	+	24.0729i	2.98587	+	1.72389i
$196$	3.60968	+	6.25214i	0.257834	+	0.446581i
$197$	−14.6402	−	8.45255i	−1.04307	−	0.602219i	−0.122372	−	0.992484i	$-0.539050\pi$
$197$	−14.6402	−	8.45255i	−1.04307	−	0.602219i	−0.920703	+	0.390265i	$0.872383\pi$
$198$	−10.8319	+	18.7614i	−0.769791	+	1.33332i
$199$	7.82396	−	4.51717i	0.554626	−	0.320213i	−0.196360	−	0.980532i	$-0.562912\pi$
$199$	7.82396	−	4.51717i	0.554626	−	0.320213i	0.750986	+	0.660318i	$0.229579\pi$
$200$	16.7197	−	9.65310i	1.18226	−	0.682577i
$201$	13.1133	−	22.7129i	0.924940	−	1.60204i
$202$	−3.35493	−	5.81090i	−0.236052	−	0.408854i
$203$			29.1529i			2.04613i
$204$	−11.1112	−	19.2452i	−0.777940	−	1.34743i
$205$	2.85330	−	4.94206i	0.199283	−	0.345168i
$206$	−2.89726	−	5.01821i	−0.201862	−	0.349635i
$207$	9.84700	−	17.0555i	0.684414	−	1.18544i
$208$	−2.59095	−	1.49588i	−0.179650	−	0.103721i
$209$	5.14413	+	2.96996i	0.355827	+	0.205437i
$210$	−39.2373			−2.70763
$211$	−0.269404	+	0.155540i	−0.0185465	+	0.0107078i	−0.509245	−	0.860622i	$-0.670075\pi$
$211$	−0.269404	+	0.155540i	−0.0185465	+	0.0107078i	0.490698	+	0.871330i	$0.336742\pi$
$212$	4.42240	+	2.55327i	0.303732	+	0.175359i
$213$		−	19.5929i		−	1.34249i
$214$	6.87578	−	11.9092i	0.470019	−	0.814097i
$215$	−4.05970	+	2.34387i	−0.276869	+	0.159850i
$216$			43.7801i			2.97886i
$217$	−11.4651	+	6.61936i	−0.778299	+	0.449351i
$218$			3.41828i			0.231515i
$219$	0.911637	+	1.57900i	0.0616027	+	0.106699i
$220$	−9.45099	+	5.45653i	−0.637186	+	0.367879i
$221$	−23.9943	+	13.8531i	−1.61403	+	0.931863i
$222$			3.62066i			0.243003i
$223$	−2.03911			−0.136549			−0.0682745	−	0.997667i	$-0.521749\pi$
$223$	−2.03911			−0.136549			−0.0682745	+	0.997667i	$0.521749\pi$
$224$	−19.4469			−1.29935
$225$	−24.6804	+	42.7477i	−1.64536	+	2.84984i
$226$	1.70589	−	2.95468i	0.113474	−	0.196543i
$227$	3.19713	+	5.53759i	0.212201	+	0.367543i	0.952403	−	0.304842i	$-0.0986035\pi$
$227$	3.19713	+	5.53759i	0.212201	+	0.367543i	−0.740202	+	0.672384i	$0.765270\pi$
$228$	6.96743			0.461430
$229$	−11.4865	+	6.63171i	−0.759047	+	0.438236i	−0.828953	−	0.559318i	$-0.811063\pi$
$229$	−11.4865	+	6.63171i	−0.759047	+	0.438236i	0.0699067	+	0.997554i	$0.477730\pi$
$230$	−7.36157	+	4.25020i	−0.485407	+	0.280250i
$231$	35.8877			2.36124
$232$	−20.1618	−	11.6404i	−1.32369	−	0.764233i
$233$	−11.4434	−	19.8206i	−0.749684	−	1.29849i	−0.947974	−	0.318347i	$-0.896872\pi$
$233$	−11.4434	−	19.8206i	−0.749684	−	1.29849i	0.198291	−	0.980143i	$-0.436461\pi$
$234$	31.6821			2.07113
$235$	−23.7193	−	13.6944i	−1.54728	−	0.893321i
$236$	−7.27087	+	4.19784i	−0.473293	+	0.273256i
$237$	−28.0968	−	16.2217i	−1.82508	−	1.05371i
$238$	11.2899	−	19.5547i	0.731816	−	1.26754i
$239$	−12.5876			−0.814223			−0.407112	−	0.913378i	$-0.633464\pi$
$239$	−12.5876			−0.814223			−0.407112	+	0.913378i	$0.633464\pi$
$240$	3.78256	−	6.55159i	0.244163	−	0.422903i
$241$	5.74335	−	9.94777i	0.369961	−	0.640792i	−0.619598	−	0.784920i	$-0.712704\pi$
$241$	5.74335	−	9.94777i	0.369961	−	0.640792i	0.989559	+	0.144128i	$0.0460376\pi$
$242$	1.74506	−	1.00751i	0.112177	−	0.0647654i
$243$	−19.1299	−	33.1340i	−1.22719	−	2.12555i
$244$	10.8292	+	6.25226i	0.693271	+	0.400260i
$245$	11.3800	+	19.7108i	0.727043	+	1.25928i
$246$		−	5.24577i		−	0.334458i
$247$		−	8.68681i		−	0.552728i
$248$		−	10.5722i		−	0.671333i
$249$	−55.3007			−3.50454
$250$	4.32523	−	2.49717i	0.273551	−	0.157935i
$251$		−	3.82701i		−	0.241559i	−0.992679	−	0.120779i	$-0.961461\pi$
$251$		−	3.82701i		−	0.241559i	0.992679	−	0.120779i	$-0.0385393\pi$
$252$	26.0971	−	15.0672i	1.64396	−	0.949143i
$253$	6.73313	−	3.88737i	0.423308	−	0.244397i
$254$	−4.51599	−	7.82192i	−0.283358	−	0.490791i
$255$	−35.0297	−	60.6732i	−2.19364	−	3.79950i
$256$	8.50345	−	14.7284i	0.531466	−	0.920526i
$257$	−3.10779			−0.193859			−0.0969294	−	0.995291i	$-0.530902\pi$
$257$	−3.10779			−0.193859			−0.0969294	+	0.995291i	$0.530902\pi$
$258$	−2.15460	+	3.73187i	−0.134139	+	0.232336i
$259$	3.71837	−	2.14680i	0.231049	−	0.133396i
$260$	13.8215	+	7.97987i	0.857176	+	0.494891i
$261$	59.5230			3.68438
$262$	2.48409	+	4.30258i	0.153468	+	0.265814i
$263$	10.4265			0.642928			0.321464	−	0.946922i	$-0.395825\pi$
$263$	10.4265			0.642928			0.321464	+	0.946922i	$0.395825\pi$
$264$	−14.3296	+	24.8196i	−0.881925	+	1.52754i
$265$	13.9423	+	8.04956i	0.856466	+	0.494481i
$266$	3.53975	+	6.13102i	0.217036	+	0.375917i
$267$	−45.7151	+	26.3936i	−2.79772	+	1.61526i
$268$	4.34690	−	7.52906i	0.265529	−	0.459910i
$269$	6.35180			0.387276			0.193638	−	0.981073i	$-0.437971\pi$
$269$	6.35180			0.387276			0.193638	+	0.981073i	$0.437971\pi$
$270$			48.3134i			2.94026i
$271$	−1.66974	−	2.89207i	−0.101429	−	0.175681i	0.810844	−	0.585262i	$-0.199008\pi$
$271$	−1.66974	−	2.89207i	−0.101429	−	0.175681i	−0.912274	+	0.409581i	$0.865675\pi$
$272$	2.17674	+	3.77023i	0.131984	+	0.228603i
$273$	−26.2419	−	45.4523i	−1.58823	−	2.75090i
$274$	5.57209			0.336622
$275$	−16.8758	+	9.74325i	−1.01765	+	0.587540i
$276$	4.55982	−	7.89784i	0.274469	−	0.475394i
$277$	27.1710	−	15.6872i	1.63255	−	0.942552i	0.649243	−	0.760581i	$-0.275086\pi$
$277$	27.1710	−	15.6872i	1.63255	−	0.942552i	0.983304	−	0.181971i	$-0.0582477\pi$
$278$	6.48723	−	3.74541i	0.389078	−	0.224635i
$279$	13.5151	+	23.4088i	0.809127	+	1.40145i
$280$	−37.1580			−2.22061
$281$	8.19792	−	14.1992i	0.489047	−	0.847054i	−0.510874	−	0.859656i	$-0.670678\pi$
$281$	8.19792	−	14.1992i	0.489047	−	0.847054i	0.999921	+	0.0126016i	$0.00401133\pi$
$282$	−25.1770			−1.49927
$283$	−11.4878			−0.682882			−0.341441	−	0.939903i	$-0.610915\pi$
$283$	−11.4878			−0.682882			−0.341441	+	0.939903i	$0.610915\pi$
$284$		−	6.49483i		−	0.385397i
$285$	21.9658			1.30114
$286$	10.8317	+	6.25370i	0.640493	+	0.369789i
$287$	−5.38735	+	3.11039i	−0.318005	+	0.183600i
$288$			39.7058i			2.33969i
$289$	23.3169			1.37158
$290$	−22.2495	−	12.8458i	−1.30654	−	0.754330i
$291$		−	6.47535i		−	0.379592i
$292$	0.302197	+	0.523421i	0.0176847	+	0.0306309i
$293$	5.68234	+	9.84210i	0.331966	+	0.574982i	0.982897	−	0.184155i	$-0.0589548\pi$
$293$	5.68234	+	9.84210i	0.331966	+	0.574982i	−0.650931	+	0.759137i	$0.725621\pi$
$294$	18.1191	+	10.4611i	1.05673	+	0.610102i
$295$	−22.9225	+	13.2343i	−1.33460	+	0.770530i
$296$			3.42878i			0.199294i
$297$		−	44.1890i		−	2.56410i
$298$	8.06753	−	13.9734i	0.467340	−	0.809456i
$299$	−9.84682	−	5.68506i	−0.569456	−	0.328776i
$300$	−11.4287	+	19.7950i	−0.659835	+	1.14287i
$301$	5.11012			0.294542
$302$			4.95624i			0.285200i
$303$	19.6543	+	11.3474i	1.12911	+	0.651891i
$304$	−1.36496			−0.0782856
$305$	34.1407	+	19.7112i	1.95489	+	1.12866i
$306$	−39.9258	−	23.0512i	−2.28241	−	1.31775i
$307$	−11.5361	−	19.9810i	−0.658397	−	1.14038i	−0.981031	−	0.193853i	$-0.937901\pi$
$307$	−11.5361	−	19.9810i	−0.658397	−	1.14038i	0.322633	−	0.946524i	$-0.395432\pi$
$308$	11.8964			0.677858
$309$	16.9731	+	9.79945i	0.965568	+	0.557471i
$310$		−	11.6669i		−	0.662634i
$311$			5.79075i			0.328363i	0.986430	+	0.164182i	$0.0524983\pi$
$311$			5.79075i			0.328363i	−0.986430	+	0.164182i	$0.947502\pi$
$312$	41.9124			2.37282
$313$	−20.9591			−1.18468			−0.592338	−	0.805689i	$-0.701795\pi$
$313$	−20.9591			−1.18468			−0.592338	+	0.805689i	$0.701795\pi$
$314$			3.86008i			0.217837i
$315$	82.2750	−	47.5015i	4.63567	−	2.67641i
$316$	−9.31376	−	5.37730i	−0.523940	−	0.302497i
$317$	23.3255	+	13.4670i	1.31009	+	0.756380i	0.982111	−	0.188305i	$-0.0602993\pi$
$317$	23.3255	+	13.4670i	1.31009	+	0.756380i	0.327978	+	0.944685i	$0.393633\pi$
$318$	14.7991			0.829892
$319$	20.3501	+	11.7492i	1.13939	+	0.657827i
$320$	10.8972	−	18.8745i	0.609173	−	1.05512i
$321$			46.5121i			2.59605i
$322$	9.26632			0.516392
$323$	−6.32031	+	10.9471i	−0.351672	+	0.609113i
$324$	−13.7054	−	23.7385i	−0.761412	−	1.31880i
$325$	24.6799	+	14.2490i	1.36900	+	0.790390i
$326$	1.46981	+	2.54579i	0.0814053	+	0.140998i
$327$	−5.78085	−	10.0127i	−0.319682	−	0.553705i
$328$		−	4.96778i		−	0.274300i
$329$	14.9283	+	25.8565i	0.823022	+	1.42552i
$330$	−15.8134	+	27.3896i	−0.870498	+	1.50775i
$331$	9.09716	+	5.25225i	0.500025	+	0.288690i	0.728724	−	0.684807i	$-0.240114\pi$
$331$	9.09716	+	5.25225i	0.500025	+	0.288690i	−0.228699	+	0.973497i	$0.573447\pi$
$332$	−18.3315			−1.00607
$333$	−4.38324	−	7.59199i	−0.240200	−	0.416039i
$334$	8.54296	+	14.7968i	0.467450	+	0.809647i
$335$	13.7042	−	23.7364i	0.748743	−	1.29686i
$336$	−7.14191	+	4.12338i	−0.389623	+	0.224949i
$337$	−5.17173	−	8.95770i	−0.281722	−	0.487957i	0.690087	−	0.723727i	$-0.257572\pi$
$337$	−5.17173	−	8.95770i	−0.281722	−	0.487957i	−0.971809	+	0.235769i	$0.924239\pi$
$338$		−	5.80259i		−	0.315619i
$339$			11.5397i			0.626750i
$340$	−11.6119	−	20.1125i	−0.629745	−	1.09075i
$341$			10.6709i			0.577861i
$342$	12.5180	−	7.22728i	0.676897	−	0.390807i
$343$			1.10106i			0.0594519i
$344$	−2.04042	+	3.53410i	−0.110012	+	0.190546i
$345$	14.3755	−	24.8991i	0.773951	−	1.34052i
$346$	1.44392	−	2.50095i	0.0776258	−	0.134452i
$347$	1.49467	−	0.862948i	0.0802381	−	0.0463255i	−0.459344	−	0.888258i	$-0.651916\pi$
$347$	1.49467	−	0.862948i	0.0802381	−	0.0463255i	0.539582	+	0.841933i	$0.318582\pi$
$348$	27.5631			1.47754
$349$	−10.1115	+	15.7085i	−0.541259	+	0.840856i
$349$	−10.1115	+	15.7085i	−0.541259	+	0.840856i
$350$	−23.2250			−1.24143
$351$	−55.9659	+	32.3119i	−2.98724	+	1.72468i
$352$	−7.83747	+	13.5749i	−0.417739	+	0.723545i
$353$	13.3888	−	23.1901i	0.712614	−	1.23428i	−0.251258	−	0.967920i	$-0.580844\pi$
$353$	13.3888	−	23.1901i	0.712614	−	1.23428i	0.963873	−	0.266364i	$-0.0858223\pi$
$354$	−12.1656	+	21.0714i	−0.646594	+	1.11993i
$355$		−	20.4759i		−	1.08675i
$356$	−15.1540	+	8.74919i	−0.803162	+	0.463706i
$357$			76.3719i			4.04203i
$358$	−0.625570	−	1.08352i	−0.0330624	−	0.0572657i
$359$		−	30.2865i		−	1.59846i	−0.601026	−	0.799229i	$-0.705241\pi$
$359$		−	30.2865i		−	1.59846i	0.601026	−	0.799229i	$-0.294759\pi$
$360$			75.8674i			3.99856i
$361$	7.51838	+	13.0222i	0.395704	+	0.685380i
$362$	3.59572	−	2.07599i	0.188987	−	0.109112i
$363$	−3.40772	+	5.90235i	−0.178859	+	0.309793i
$364$	−8.69888	−	15.0669i	−0.455945	−	0.789721i
$365$	0.952720	+	1.65016i	0.0498676	+	0.0863733i
$366$	36.2389			1.89424
$367$	15.7055	+	9.06760i	0.819823	+	0.473325i	0.850355	−	0.526209i	$-0.176387\pi$
$367$	15.7055	+	9.06760i	0.819823	+	0.473325i	−0.0305324	+	0.999534i	$0.509720\pi$
$368$	−0.893292	+	1.54723i	−0.0465661	+	0.0806548i
$369$	6.35064	+	10.9996i	0.330601	+	0.572618i
$370$			3.78382i			0.196712i
$371$	−8.77485	−	15.1985i	−0.455568	−	0.789066i
$372$	6.25839	+	10.8399i	0.324482	+	0.562020i
$373$	−10.6345	−	6.13986i	−0.550636	−	0.317910i	0.198742	−	0.980052i	$-0.436314\pi$
$373$	−10.6345	−	6.13986i	−0.550636	−	0.317910i	−0.749379	+	0.662142i	$0.769648\pi$
$374$	−9.10008	−	15.7618i	−0.470554	−	0.815023i
$375$	−8.44621	+	14.6293i	−0.436160	+	0.755452i
$376$	−23.8428			−1.22960
$377$		−	34.3650i		−	1.76989i
$378$	26.3333	−	45.6106i	1.35444	−	2.34596i
$379$	29.5899	+	17.0838i	1.51993	+	0.877534i	0.999724	+	0.0234946i	$0.00747925\pi$
$379$	29.5899	+	17.0838i	1.51993	+	0.877534i	0.520209	+	0.854039i	$0.325854\pi$
$380$	7.28142			0.373529
$381$	26.4562	+	15.2745i	1.35539	+	0.782535i
$382$	12.1878	+	7.03663i	0.623582	+	0.360025i
$383$	11.2066	−	6.47014i	0.572631	−	0.330609i	−0.185568	−	0.982631i	$-0.559413\pi$
$383$	11.2066	−	6.47014i	0.572631	−	0.330609i	0.758200	+	0.652023i	$0.226079\pi$
$384$			14.1060i			0.719844i
$385$	37.5050			1.91143
$386$	0.916293			0.0466381
$387$		−	10.4336i		−	0.530369i
$388$		−	2.14650i		−	0.108972i
$389$	−29.6740	−	17.1323i	−1.50453	−	0.868641i	−0.999986	−	0.00525450i	$-0.998327\pi$
$389$	−29.6740	−	17.1323i	−1.50453	−	0.868641i	−0.504544	−	0.863386i	$-0.668339\pi$
$390$	46.2523			2.34208
$391$	8.27263	+	14.3286i	0.418365	+	0.724630i
$392$	17.1589	+	9.90669i	0.866655	+	0.500363i
$393$	−14.5527	−	8.40198i	−0.734084	−	0.423824i
$394$	−16.2403			−0.818174
$395$	−29.3630	−	16.9527i	−1.47741	−	0.852984i
$396$		−	24.2894i		−	1.22059i
$397$	0.348649			0.0174982			0.00874911	−	0.999962i	$-0.497215\pi$
$397$	0.348649			0.0174982			0.00874911	+	0.999962i	$0.497215\pi$
$398$	4.33953	−	7.51628i	0.217521	−	0.376757i
$399$	−20.7370	−	11.9725i	−1.03815	−	0.599376i
$400$	2.23894	−	3.87795i	0.111947	−	0.193897i
$401$			39.5725i			1.97615i	0.153958	+	0.988077i	$0.450798\pi$
$401$			39.5725i			1.97615i	−0.153958	+	0.988077i	$0.549202\pi$
$402$		−	25.1952i		−	1.25662i
$403$	13.5148	−	7.80279i	0.673222	−	0.388685i
$404$	6.51516	+	3.76153i	0.324141	+	0.187143i
$405$	−43.2083	−	74.8390i	−2.14704	−	3.71878i
$406$	14.0032	+	24.2543i	0.694968	+	1.20372i
$407$		−	3.46081i		−	0.171546i
$408$	−52.8180	−	30.4945i	−2.61488	−	1.50970i
$409$	25.1943			1.24578			0.622890	−	0.782309i	$-0.285958\pi$
$409$	25.1943			1.24578			0.622890	+	0.782309i	$0.285958\pi$
$410$		−	5.48218i		−	0.270745i
$411$	−16.3216	+	9.42327i	−0.805084	+	0.464815i
$412$	5.62640	+	3.24840i	0.277193	+	0.160037i
$413$	28.8535			1.41979
$414$		−	18.9195i		−	0.929843i
$415$	−57.7928			−2.83694
$416$	22.9237			1.12393
$417$	−12.6681	+	21.9418i	−0.620361	+	1.07450i
$418$	5.70633			0.279106
$419$	7.16294	+	12.4066i	0.349932	+	0.606100i	0.986237	−	0.165337i	$-0.0528713\pi$
$419$	7.16294	+	12.4066i	0.349932	+	0.606100i	−0.636305	+	0.771438i	$0.719538\pi$
$420$	38.0989	−	21.9964i	1.85903	−	1.07331i
$421$	8.46539	−	4.88749i	0.412578	−	0.238202i	−0.279319	−	0.960198i	$-0.590109\pi$
$421$	8.46539	−	4.88749i	0.412578	−	0.238202i	0.691897	+	0.721997i	$0.256775\pi$
$422$	−0.149424	+	0.258809i	−0.00727383	+	0.0125986i
$423$	52.7925	−	30.4798i	2.56686	−	1.48198i
$424$	14.0148			0.680620
$425$	−20.7344	−	35.9130i	−1.00577	−	1.74204i
$426$	−9.41122	−	16.3007i	−0.455975	−	0.789772i
$427$	−21.4872	−	37.2169i	−1.03984	−	1.80105i
$428$			15.4182i			0.745267i
$429$	−42.3039			−2.04245
$430$	−2.25169	+	3.90005i	−0.108586	+	0.188077i
$431$	−10.0912	+	5.82613i	−0.486074	+	0.280635i	−0.722944	−	0.690906i	$-0.757212\pi$
$431$	−10.0912	+	5.82613i	−0.486074	+	0.280635i	0.236870	+	0.971541i	$0.423878\pi$
$432$	5.07717	+	8.79391i	0.244275	+	0.423097i
$433$	−30.4483	−	17.5793i	−1.46325	−	0.844809i	−0.464092	−	0.885787i	$-0.653619\pi$
$433$	−30.4483	−	17.5793i	−1.46325	−	0.844809i	−0.999160	+	0.0409780i	$0.986953\pi$
$434$	−6.35905	+	11.0142i	−0.305244	+	0.528698i
$435$	86.8968			4.16638
$436$	−1.91628	−	3.31910i	−0.0917734	−	0.158956i
$437$	−5.18747			−0.248150
$438$	1.51691	+	0.875786i	0.0724806	+	0.0418467i
$439$	−24.1970	+	13.9701i	−1.15486	+	0.666758i	−0.950067	−	0.312047i	$-0.898985\pi$
$439$	−24.1970	+	13.9701i	−1.15486	+	0.666758i	−0.204792	+	0.978805i	$0.565652\pi$
$440$	−14.9754	+	25.9381i	−0.713922	+	1.23655i
$441$	−50.6575			−2.41226
$442$	−13.3084	+	23.0507i	−0.633014	+	1.09641i
$443$	−0.141711	−	0.245450i	−0.00673288	−	0.0116617i	0.862639	−	0.505820i	$-0.168810\pi$
$443$	−0.141711	−	0.245450i	−0.00673288	−	0.0116617i	−0.869372	+	0.494158i	$0.835476\pi$
$444$	−2.02973	−	3.51560i	−0.0963269	−	0.166843i
$445$	−47.7753	+	27.5831i	−2.26477	+	1.30756i
$446$	−1.69648	+	0.979461i	−0.0803305	+	0.0463788i
$447$			54.5738i			2.58125i
$448$	−20.5752	+	11.8791i	−0.972087	+	0.561235i
$449$	11.3534			0.535798			0.267899	−	0.963447i	$-0.413671\pi$
$449$	11.3534			0.535798			0.267899	+	0.963447i	$0.413671\pi$
$450$			47.4196i			2.23538i
$451$			5.01418i			0.236108i
$452$			3.82527i			0.179926i
$453$	−8.38178	−	14.5177i	−0.393810	−	0.682099i
$454$	5.31982	+	3.07140i	0.249672	+	0.144148i
$455$	−27.4245	−	47.5006i	−1.28568	−	2.22686i
$456$	16.5601	−	9.56100i	0.775500	−	0.447735i
$457$	18.3179	−	31.7275i	0.856873	−	1.48415i	−0.0180234	−	0.999838i	$-0.505737\pi$
$457$	18.3179	−	31.7275i	0.856873	−	1.48415i	0.874896	−	0.484310i	$-0.160929\pi$
$458$	−6.37091	+	11.0347i	−0.297693	+	0.515620i
$459$	94.0376			4.38930
$460$	4.76531	−	8.25376i	0.222184	−	0.384834i
$461$	−20.9069	−	12.0706i	−0.973733	−	0.562185i	−0.0733611	−	0.997305i	$-0.523373\pi$
$461$	−20.9069	−	12.0706i	−0.973733	−	0.562185i	−0.900372	+	0.435120i	$0.856706\pi$
$462$	29.8575	−	17.2382i	1.38909	−	0.801994i
$463$	−8.71155	−	5.02961i	−0.404860	−	0.233746i	0.283719	−	0.958908i	$-0.408432\pi$
$463$	−8.71155	−	5.02961i	−0.404860	−	0.233746i	−0.688579	+	0.725161i	$0.741765\pi$
$464$	−5.39976			−0.250678
$465$	19.7305	+	34.1742i	0.914979	+	1.58479i
$466$	−19.0411	−	10.9934i	−0.882064	−	0.509260i
$467$	23.7954			1.10112			0.550560	−	0.834796i	$-0.314414\pi$
$467$	23.7954			1.10112			0.550560	+	0.834796i	$0.314414\pi$
$468$	−30.7629	+	17.7610i	−1.42201	+	0.821000i
$469$	−25.8752	+	14.9390i	−1.19480	+	0.689821i
$470$	−26.3116			−1.21367
$471$	−6.52799	−	11.3068i	−0.300794	−	0.520990i
$472$	−11.5209	+	19.9548i	−0.530292	+	0.918493i
$473$	2.05947	−	3.56711i	0.0946946	−	0.164016i
$474$	−31.1675			−1.43157
$475$	13.0018			0.596564
$476$			25.3164i			1.16038i
$477$	−31.0315	+	17.9161i	−1.42084	+	0.820320i
$478$	−10.4725	+	6.04628i	−0.479000	+	0.276551i
$479$	11.6470	+	20.1731i	0.532163	+	0.921733i	0.999295	+	0.0375455i	$0.0119539\pi$
$479$	11.6470	+	20.1731i	0.532163	+	0.921733i	−0.467132	+	0.884188i	$0.654713\pi$
$480$			57.9659i			2.64577i
$481$	−4.38316	+	2.53062i	−0.199855	+	0.115386i
$482$		−	11.0350i		−	0.502629i
$483$	−27.1426	+	15.6708i	−1.23503	+	0.713045i
$484$	−1.12962	+	1.95656i	−0.0513464	+	0.0889345i
$485$		−	6.76717i		−	0.307281i
$486$	−31.8310	−	18.3776i	−1.44388	−	0.833627i
$487$	5.95323	−	3.43710i	0.269767	−	0.155750i	−0.359015	−	0.933332i	$-0.616887\pi$
$487$	5.95323	−	3.43710i	0.269767	−	0.155750i	0.628782	+	0.777582i	$0.283554\pi$
$488$	34.3185			1.55352
$489$	−8.61064	−	4.97136i	−0.389387	−	0.224812i
$490$	18.9356	+	10.9325i	0.855425	+	0.493880i
$491$	12.7193	−	22.0305i	0.574014	−	0.994221i	−0.422134	−	0.906533i	$-0.638719\pi$
$491$	12.7193	−	22.0305i	0.574014	−	0.994221i	0.996148	−	0.0876877i	$-0.0279477\pi$
$492$	2.94077	+	5.09357i	0.132580	+	0.229636i
$493$	−25.0031	+	43.3067i	−1.12608	+	1.95044i
$494$	−4.17260	−	7.22715i	−0.187734	−	0.325165i
$495$		−	76.5759i		−	3.44183i
$496$	−1.22605	−	2.12358i	−0.0550513	−	0.0953517i
$497$	−11.1604	+	19.3304i	−0.500613	+	0.867088i
$498$	−46.0084	+	26.5630i	−2.06169	+	1.19032i
$499$	0.433526	−	0.250296i	0.0194073	−	0.0112048i	−0.490265	−	0.871573i	$-0.663100\pi$
$499$	0.433526	−	0.250296i	0.0194073	−	0.0112048i	0.509672	+	0.860369i	$0.329767\pi$
$500$	−2.79982	+	4.84943i	−0.125212	+	0.216873i
$501$	−50.0475	−	28.8949i	−2.23596	−	1.29093i
$502$	−1.83825	−	3.18395i	−0.0820453	−	0.142107i
$503$	−23.0760	−	13.3229i	−1.02891	−	0.594039i	−0.112235	−	0.993682i	$-0.535801\pi$
$503$	−23.0760	−	13.3229i	−1.02891	−	0.594039i	−0.916671	+	0.399643i	$0.869134\pi$
$504$	41.3516	−	71.6231i	1.84195	−	3.19035i
$505$	20.5400	+	11.8588i	0.914018	+	0.527708i
$506$	3.73450	−	6.46834i	0.166019	−	0.287553i
$507$	9.81308	+	16.9967i	0.435814	+	0.754852i
$508$	8.76992	+	5.06331i	0.389102	+	0.224648i
$509$	−6.15381	+	3.55291i	−0.272763	+	0.157480i	−0.630143	−	0.776479i	$-0.717004\pi$
$509$	−6.15381	+	3.55291i	−0.272763	+	0.157480i	0.357380	+	0.933959i	$0.383670\pi$
$510$	−58.2872	−	33.6521i	−2.58100	−	1.49014i
$511$		−	2.07713i		−	0.0918867i
$512$		−	7.65561i		−	0.338333i
$513$	−14.7419	+	25.5337i	−0.650871	+	1.12734i
$514$	−2.58559	+	1.49279i	−0.114045	+	0.0658441i
$515$	17.7380	+	10.2411i	0.781632	+	0.451275i
$516$		−	4.83145i		−	0.212693i
$517$	24.0655			1.05840
$518$	2.06238	−	3.57215i	0.0906158	−	0.156951i
$519$			9.76760i			0.428750i
$520$	43.8012			1.92081
$521$	15.1960	−	8.77343i	0.665750	−	0.384371i	−0.128714	−	0.991682i	$-0.541085\pi$
$521$	15.1960	−	8.77343i	0.665750	−	0.384371i	0.794464	+	0.607311i	$0.207752\pi$
$522$	49.5212	−	28.5911i	2.16748	−	1.25140i
$523$	−22.7497	−	13.1345i	−0.994774	−	0.574333i	−0.0880764	−	0.996114i	$-0.528072\pi$
$523$	−22.7497	−	13.1345i	−0.994774	−	0.574333i	−0.906698	+	0.421780i	$0.861405\pi$
$524$	−4.82404	−	2.78516i	−0.210739	−	0.121670i
$525$	68.0298	−	39.2770i	2.96906	−	1.71419i
$526$	8.67455	−	5.00825i	0.378228	−	0.218370i
$527$	−22.7085			−0.989198
$528$			6.64720i			0.289282i
$529$	8.10507	−	14.0384i	0.352394	−	0.610365i
$530$	15.4660			0.671801
$531$		−	58.9116i		−	2.55655i
$532$	−6.87408	−	3.96875i	−0.298029	−	0.172067i
$533$	6.35052	−	3.66648i	0.275072	−	0.158813i
$534$	−25.3557	+	43.9173i	−1.09725	+	1.90049i
$535$			48.6081i			2.10151i
$536$		−	23.8600i		−	1.03060i
$537$	3.66480	+	2.11587i	0.158148	+	0.0913066i
$538$	5.28450	−	3.05101i	0.227831	−	0.131538i
$539$	−17.3191	−	9.99921i	−0.745988	−	0.430697i
$540$	−27.0844	−	46.9116i	−1.16553	−	2.01875i
$541$	17.3275	−	30.0120i	0.744965	−	1.29032i	−0.205246	−	0.978710i	$-0.565799\pi$
$541$	17.3275	−	30.0120i	0.744965	−	1.29032i	0.950211	−	0.311607i	$-0.100867\pi$
$542$	−2.77834	−	1.60407i	−0.119340	−	0.0689009i
$543$	−7.02164	+	12.1618i	−0.301328	+	0.521915i
$544$	−28.8885	−	16.6788i	−1.23858	−	0.715096i
$545$	−6.04136	−	10.4639i	−0.258784	−	0.448226i
$546$	−43.6648	−	25.2099i	−1.86868	−	1.07888i
$547$	−0.436650	+	0.756300i	−0.0186698	+	0.0323370i	−0.875209	−	0.483744i	$-0.839276\pi$
$547$	−0.436650	+	0.756300i	−0.0186698	+	0.0323370i	0.856540	+	0.516081i	$0.172610\pi$
$548$	−5.41041	+	3.12370i	−0.231121	+	0.133438i
$549$	−75.9877	+	43.8715i	−3.24308	+	1.87239i
$550$	−9.36009	+	16.2122i	−0.399116	+	0.691289i
$551$	−7.83928	−	13.5780i	−0.333965	−	0.578444i
$552$		−	25.0287i		−	1.06529i
$553$	18.4802	+	32.0087i	0.785859	+	1.36115i
$554$	15.0703	−	26.1025i	0.640275	−	1.10899i
$555$	−6.39903	−	11.0835i	−0.271624	−	0.470466i
$556$	−4.19934	+	7.27346i	−0.178092	+	0.308464i
$557$	15.5561	+	8.98130i	0.659132	+	0.380550i	0.791946	−	0.610591i	$-0.209068\pi$
$557$	15.5561	+	8.98130i	0.659132	+	0.380550i	−0.132814	+	0.991141i	$0.542401\pi$
$558$	22.4882	+	12.9836i	0.952003	+	0.549639i
$559$	−6.02372			−0.254776
$560$	−7.46376	+	4.30920i	−0.315401	+	0.182097i
$561$	53.3113	+	30.7793i	2.25080	+	1.29950i
$562$		−	15.7511i		−	0.664419i
$563$	−12.3469	+	21.3855i	−0.520361	+	0.901291i	0.479359	+	0.877619i	$0.340869\pi$
$563$	−12.3469	+	21.3855i	−0.520361	+	0.901291i	−0.999720	+	0.0236722i	$0.992464\pi$
$564$	24.4465	−	14.1142i	1.02938	−	0.594315i
$565$			12.0597i			0.507356i
$566$	−9.55753	+	5.51804i	−0.401733	+	0.231941i
$567$			94.2031i			3.95616i
$568$	−8.91248	−	15.4369i	−0.373959	−	0.647716i
$569$	−36.1856	+	20.8918i	−1.51698	+	0.875828i	−0.517178	+	0.855878i	$0.673017\pi$
$569$	−36.1856	+	20.8918i	−1.51698	+	0.875828i	−0.999801	+	0.0199500i	$0.993649\pi$
$570$	18.2749	−	10.5510i	0.765451	−	0.441933i
$571$			2.67483i			0.111938i	0.998432	+	0.0559692i	$0.0178249\pi$
$571$			2.67483i			0.111938i	−0.998432	+	0.0559692i	$0.982175\pi$
$572$	−14.0232			−0.586341
$573$	−47.6001			−1.98852
$574$	−2.98807	+	5.17549i	−0.124720	+	0.216021i
$575$	8.50900	−	14.7380i	0.354850	−	0.614618i
$576$	24.2542	+	42.0094i	1.01059	+	1.75039i
$577$	35.0719			1.46006			0.730032	−	0.683413i	$-0.239505\pi$
$577$	35.0719			1.46006			0.730032	+	0.683413i	$0.239505\pi$
$578$	19.3989	−	11.2000i	0.806888	−	0.465857i
$579$	−2.68397	+	1.54959i	−0.111542	+	0.0643989i
$580$	28.8053			1.19607
$581$	54.5597	+	31.5001i	2.26352	+	1.30684i
$582$	−3.11035	−	5.38729i	−0.128928	−	0.223310i
$583$	−14.1457			−0.585856
$584$	1.43652	+	0.829375i	0.0594436	+	0.0343198i
$585$	−96.9844	+	55.9940i	−4.00981	+	2.31507i
$586$	9.45506	+	5.45888i	0.390585	+	0.225504i
$587$	16.2924	−	28.2192i	0.672458	−	1.16473i	−0.304747	−	0.952433i	$-0.598572\pi$
$587$	16.2924	−	28.2192i	0.672458	−	1.16473i	0.977205	−	0.212298i	$-0.0680946\pi$
$588$	−23.4578			−0.967384
$589$	3.55992	−	6.16597i	0.146684	−	0.254064i
$590$	−12.7138	+	22.0210i	−0.523421	+	0.906591i
$591$	47.5705	−	27.4649i	1.95679	−	1.12975i
$592$	0.397635	+	0.688725i	0.0163427	+	0.0283064i
$593$	−24.7074	−	14.2648i	−1.01461	−	0.585786i	−0.102073	−	0.994777i	$-0.532548\pi$
$593$	−24.7074	−	14.2648i	−1.01461	−	0.585786i	−0.912539	+	0.408991i	$0.865881\pi$
$594$	−21.2256	−	36.7638i	−0.870897	−	1.50844i
$595$			79.8137i			3.27204i
$596$			18.0906i			0.741019i
$597$			29.3552i			1.20143i
$598$	−10.9230			−0.446674
$599$	−16.9273	+	9.77299i	−0.691631	+	0.399314i	−0.804223	−	0.594328i	$-0.797418\pi$
$599$	−16.9273	+	9.77299i	−0.691631	+	0.399314i	0.112592	+	0.993641i	$0.464085\pi$
$600$			62.7316i			2.56101i
$601$	−7.76060	+	4.48058i	−0.316561	+	0.182767i	−0.649859	−	0.760055i	$-0.725172\pi$
$601$	−7.76060	+	4.48058i	−0.316561	+	0.182767i	0.333298	+	0.942822i	$0.391839\pi$
$602$	4.25146	−	2.45458i	0.173276	−	0.100041i
$603$	30.5018	+	52.8307i	1.24213	+	2.15143i
$604$	−2.77846	−	4.81244i	−0.113054	−	0.195815i
$605$	−3.56129	+	6.16834i	−0.144787	+	0.250779i
$606$	21.8023			0.885658
$607$	21.0945	−	36.5368i	0.856200	−	1.48298i	−0.0193267	−	0.999813i	$-0.506152\pi$
$607$	21.0945	−	36.5368i	0.856200	−	1.48298i	0.875527	−	0.483169i	$-0.160514\pi$
$608$	9.05746	−	5.22932i	0.367328	−	0.212077i
$609$	−82.0355	−	47.3632i	−3.32425	−	1.91926i
$610$	37.8720			1.53339
$611$	−17.5972	−	30.4792i	−0.711906	−	1.23306i
$612$	51.6898			2.08944
$613$	9.88310	−	17.1180i	0.399175	−	0.691391i	−0.594450	−	0.804133i	$-0.702630\pi$
$613$	9.88310	−	17.1180i	0.399175	−	0.691391i	0.993624	+	0.112742i	$0.0359634\pi$
$614$	−19.1953	−	11.0824i	−0.774658	−	0.447249i
$615$	9.27121	+	16.0582i	0.373851	+	0.647530i
$616$	28.2752	−	16.3247i	1.13924	−	0.657740i
$617$	−16.9140	+	29.2958i	−0.680930	+	1.17941i	0.293767	+	0.955877i	$0.405091\pi$
$617$	−16.9140	+	29.2958i	−0.680930	+	1.17941i	−0.974697	+	0.223529i	$0.928242\pi$
$618$	18.8282			0.757379
$619$			36.0964i			1.45084i	0.688309	+	0.725418i	$0.258353\pi$
$619$			36.0964i			1.45084i	−0.688309	+	0.725418i	$0.741647\pi$
$620$	6.54043	+	11.3284i	0.262670	+	0.454958i
$621$	19.2956	+	33.4210i	0.774306	+	1.34114i
$622$	2.78151	+	4.81772i	0.111528	+	0.193173i
$623$	60.1368			2.40933
$624$	8.41876	−	4.86058i	0.337020	−	0.194579i
$625$	7.50061	−	12.9914i	0.300024	−	0.519657i
$626$	−17.4373	+	10.0674i	−0.696934	+	0.402375i
$627$	−16.7148	+	9.65030i	−0.667525	+	0.385396i
$628$	−2.16395	−	3.74808i	−0.0863512	−	0.149565i
$629$	7.36487			0.293657
$630$	45.6335	−	79.0395i	1.81808	−	3.14901i
$631$	−11.9846			−0.477099			−0.238550	−	0.971130i	$-0.576672\pi$
$631$	−11.9846			−0.477099			−0.238550	+	0.971130i	$0.576672\pi$
$632$	−29.5158			−1.17408
$633$		−	1.01079i		−	0.0401755i
$634$	25.8747			1.02762
$635$	27.6484	+	15.9628i	1.09719	+	0.633466i
$636$	−14.3697	+	8.29634i	−0.569795	+	0.328971i
$637$			29.2466i			1.15879i
$638$	22.5742			0.893722
$639$	39.4679	+	22.7868i	1.56133	+	0.901432i
$640$			14.7417i			0.582717i
$641$	6.97274	+	12.0771i	0.275407	+	0.477018i	0.970238	−	0.242155i	$-0.0778541\pi$
$641$	6.97274	+	12.0771i	0.275407	+	0.477018i	−0.694831	+	0.719173i	$0.744521\pi$
$642$	22.3415	+	38.6966i	0.881747	+	1.52723i
$643$	11.7058	+	6.75834i	0.461631	+	0.266523i	0.712730	−	0.701439i	$-0.247459\pi$
$643$	11.7058	+	6.75834i	0.461631	+	0.266523i	−0.251099	+	0.967961i	$0.580792\pi$
$644$	−8.99746	+	5.19468i	−0.354549	+	0.204699i
$645$		−	15.2319i		−	0.599754i
$646$			12.1435i			0.477781i
$647$	−13.9277	+	24.1234i	−0.547553	+	0.948390i	0.450888	+	0.892580i	$0.351107\pi$
$647$	−13.9277	+	24.1234i	−0.547553	+	0.948390i	−0.998441	+	0.0558096i	$0.982226\pi$
$648$	−65.1499	−	37.6143i	−2.55933	−	1.47763i
$649$	11.6285	−	20.1411i	0.456458	−	0.790609i
$650$	27.3772			1.07382
$651$		−	43.0165i		−	1.68595i
$652$	−2.85433	−	1.64795i	−0.111784	−	0.0645386i
$653$	−23.1161			−0.904603			−0.452301	−	0.891865i	$-0.649397\pi$
$653$	−23.1161			−0.904603			−0.452301	+	0.891865i	$0.649397\pi$
$654$	−9.61896	−	5.55351i	−0.376131	−	0.217159i
$655$	−15.2085	−	8.78062i	−0.594244	−	0.343087i
$656$	−0.576112	−	0.997856i	−0.0224934	−	0.0389597i
$657$	−4.24097			−0.165456
$658$	24.8397	+	14.3412i	0.968352	+	0.559078i
$659$			23.1935i			0.903490i	0.892147	+	0.451745i	$0.149198\pi$
$659$			23.1935i			0.903490i	−0.892147	+	0.451745i	$0.850802\pi$
$660$		−	35.4598i		−	1.38027i
$661$	42.5075			1.65335			0.826676	−	0.562679i	$-0.190229\pi$
$661$	42.5075			1.65335			0.826676	+	0.562679i	$0.190229\pi$
$662$	10.0914			0.392214
$663$		−	90.0260i		−	3.49632i
$664$	−43.5702	+	25.1553i	−1.69085	+	0.976215i
$665$	−21.6715	−	12.5121i	−0.840386	−	0.485197i
$666$	−7.29343	−	4.21086i	−0.282615	−	0.163168i
$667$	−20.5216			−0.794600
$668$	−16.5902	−	9.57834i	−0.641893	−	0.370597i
$669$	3.31284	−	5.73801i	0.128082	−	0.221844i
$670$		−	26.3306i		−	1.01724i
$671$	−34.6390			−1.33722
$672$	31.5944	−	54.7232i	1.21878	−	2.11099i
$673$	−6.59063	−	11.4153i	−0.254050	−	0.440028i	0.710587	−	0.703609i	$-0.248430\pi$
$673$	−6.59063	−	11.4153i	−0.254050	−	0.440028i	−0.964637	+	0.263582i	$0.915096\pi$
$674$	−8.60543	−	4.96835i	−0.331469	−	0.191374i
$675$	−48.3622	−	83.7658i	−1.86146	−	3.22415i
$676$	3.25292	+	5.63423i	0.125112	+	0.216701i
$677$			10.9116i			0.419365i	0.977769	+	0.209683i	$0.0672431\pi$
$677$			10.9116i			0.419365i	−0.977769	+	0.209683i	$0.932757\pi$
$678$	5.54294	+	9.60065i	0.212875	+	0.368711i
$679$	−3.68846	+	6.38859i	−0.141550	+	0.245172i
$680$	−55.1983	−	31.8687i	−2.11676	−	1.22211i
$681$	−20.7769			−0.796171
$682$	5.12563	+	8.87785i	0.196270	+	0.339950i
$683$	−23.1676	−	40.1274i	−0.886482	−	1.53543i	−0.844006	−	0.536334i	$-0.819809\pi$
$683$	−23.1676	−	40.1274i	−0.886482	−	1.53543i	−0.0424761	−	0.999097i	$-0.513525\pi$
$684$	−8.10320	+	14.0352i	−0.309834	+	0.536648i
$685$	−17.0571	+	9.84793i	−0.651719	+	0.376270i
$686$	0.528882	+	0.916051i	0.0201928	+	0.0349750i
$687$		−	43.0968i		−	1.64425i
$688$			0.946506i			0.0360852i
$689$	10.3437	+	17.9157i	0.394062	+	0.682535i
$690$		−	27.6204i		−	1.05149i
$691$	37.7196	−	21.7774i	1.43492	−	0.828452i	0.437430	−	0.899252i	$-0.355889\pi$
$691$	37.7196	−	21.7774i	1.43492	−	0.828452i	0.997491	+	0.0708002i	$0.0225553\pi$
$692$			3.23785i			0.123084i
$693$	−41.7378	+	72.2920i	−1.58549	+	2.74615i
$694$	0.829012	−	1.43589i	0.0314689	−	0.0545057i
$695$	−13.2390	+	22.9307i	−0.502185	+	0.869809i
$696$	65.5118	−	37.8233i	2.48322	−	1.43369i
$697$	−10.6706			−0.404176
$698$	−0.867119	+	17.9259i	−0.0328209	+	0.678506i
$699$	74.3662			2.81279
$700$	22.5511	−	13.0199i	0.852351	−	0.492105i
$701$	−7.92471	+	13.7260i	−0.299312	+	0.518424i	−0.975979	−	0.217866i	$-0.930090\pi$
$701$	−7.92471	+	13.7260i	−0.299312	+	0.518424i	0.676667	+	0.736289i	$0.263424\pi$
$702$	−31.0412	+	53.7650i	−1.17158	+	2.02923i
$703$	−1.15456	+	1.99976i	−0.0435451	+	0.0754223i
$704$			19.1500i			0.721742i
$705$	77.0711	−	44.4970i	2.90267	−	1.67586i
$706$		−	25.7246i		−	0.968157i
$707$	−12.9273	−	22.3907i	−0.486181	−	0.842090i
$708$		−	27.2801i		−	1.02525i
$709$			7.36494i			0.276596i	0.990391	+	0.138298i	$0.0441632\pi$
$709$			7.36494i			0.276596i	−0.990391	+	0.138298i	$0.955837\pi$
$710$	−9.83534	−	17.0353i	−0.369114	−	0.639324i
$711$	65.3538	−	37.7320i	2.45096	−	1.41506i
$712$	−24.0120	+	41.5900i	−0.899887	+	1.55865i
$713$	−4.65957	−	8.07061i	−0.174502	−	0.302247i
$714$	36.6843	+	63.5390i	1.37287	+	2.37789i
$715$	−44.2103			−1.65337
$716$	1.21484	+	0.701387i	0.0454006	+	0.0262121i
$717$	20.4504	−	35.4211i	0.763734	−	1.32283i
$718$	−14.5477	−	25.1974i	−0.542916	−	0.940358i
$719$		−	15.7013i		−	0.585559i	−0.956180	−	0.292780i	$-0.905420\pi$
$719$		−	15.7013i		−	0.585559i	0.956180	−	0.292780i	$-0.0945803\pi$
$720$	8.79832	+	15.2391i	0.327894	+	0.567929i
$721$	−11.1638	−	19.3363i	−0.415762	−	0.720121i
$722$	12.5101	+	7.22271i	0.465578	+	0.268802i
$723$	18.6618	+	32.3233i	0.694041	+	1.20211i
$724$	−2.32759	+	4.03151i	−0.0865044	+	0.149830i
$725$	51.4351			1.91025
$726$			6.54742i			0.242998i
$727$	−25.0980	+	43.4711i	−0.930835	+	1.61225i	−0.148937	+	0.988847i	$0.547585\pi$
$727$	−25.0980	+	43.4711i	−0.930835	+	1.61225i	−0.781898	+	0.623406i	$0.785748\pi$
$728$	−41.3509	−	23.8739i	−1.53257	−	0.884827i
$729$	47.9719			1.77674
$730$	1.58527	+	0.915254i	0.0586733	+	0.0338751i
$731$	7.59109	+	4.38272i	0.280767	+	0.162101i
$732$	−35.1874	+	20.3155i	−1.30056	+	0.750881i
$733$		−	38.5458i		−	1.42372i	−0.702321	−	0.711861i	$-0.747853\pi$
$733$		−	38.5458i		−	1.42372i	0.702321	−	0.711861i	$-0.252147\pi$
$734$	17.4220			0.643059
$735$	−73.9542			−2.72784
$736$		−	13.6893i		−	0.504594i
$737$			24.0828i			0.887103i
$738$	10.5671	+	6.10089i	0.388979	+	0.224577i
$739$	−43.6269			−1.60484			−0.802421	−	0.596759i	$-0.796455\pi$
$739$	−43.6269			−1.60484			−0.802421	+	0.596759i	$0.796455\pi$
$740$	−2.12121	−	3.67404i	−0.0779771	−	0.135060i
$741$	24.4445	+	14.1130i	0.897990	+	0.518455i
$742$	−14.6008	−	8.42978i	−0.536012	−	0.309467i
$743$	−9.29924			−0.341156			−0.170578	−	0.985344i	$-0.554563\pi$
$743$	−9.29924			−0.341156			−0.170578	+	0.985344i	$0.554563\pi$
$744$	29.7498	+	17.1760i	1.09068	+	0.629704i
$745$			57.0332i			2.08953i
$746$	−11.7968			−0.431912
$747$	64.3153	−	111.397i	2.35317	−	4.07582i
$748$	17.6721	+	10.2030i	0.646155	+	0.373058i
$749$	26.4939	−	45.8889i	0.968068	−	1.67674i
$750$			16.2281i			0.592567i
$751$			13.1443i			0.479641i	0.970817	+	0.239821i	$0.0770886\pi$
$751$			13.1443i			0.479641i	−0.970817	+	0.239821i	$0.922911\pi$
$752$	−4.78919	+	2.76504i	−0.174644	+	0.100831i
$753$	10.7691	+	6.21755i	0.392448	+	0.226580i
$754$	−16.5068	−	28.5906i	−0.601141	−	1.04121i
$755$	−8.75951	−	15.1719i	−0.318791	−	0.552162i
$756$			59.0496i			2.14761i
$757$	−26.7459	−	15.4418i	−0.972097	−	0.561240i	−0.0722219	−	0.997389i	$-0.523009\pi$
$757$	−26.7459	−	15.4418i	−0.972097	−	0.561240i	−0.899875	+	0.436148i	$0.856342\pi$
$758$	32.8239			1.19222
$759$			25.2625i			0.916969i
$760$	17.3064	−	9.99187i	0.627770	−	0.362443i
$761$	17.2188	+	9.94126i	0.624180	+	0.360370i	0.778494	−	0.627651i	$-0.215984\pi$
$761$	17.2188	+	9.94126i	0.624180	+	0.360370i	−0.154315	+	0.988022i	$0.549317\pi$
$762$	29.3476			1.06315
$763$			13.1714i			0.476837i
$764$	−15.7789			−0.570860
$765$	162.960			5.89182
$766$	6.21570	−	10.7659i	0.224582	−	0.388988i
$767$	−34.0120			−1.22810
$768$	27.6303	+	47.8570i	0.997021	+	1.72689i
$769$	45.2698	−	26.1365i	1.63247	−	0.942507i	0.649141	−	0.760668i	$-0.275128\pi$
$769$	45.2698	−	26.1365i	1.63247	−	0.942507i	0.983328	−	0.181839i	$-0.0582049\pi$
$770$	31.2030	−	18.0151i	1.12448	−	0.649218i
$771$	5.04907	−	8.74525i	0.181838	−	0.314952i
$772$	−0.889706	+	0.513672i	−0.0320212	+	0.0184875i
$773$	−37.3967			−1.34507			−0.672533	−	0.740067i	$-0.734794\pi$
$773$	−37.3967			−1.34507			−0.672533	+	0.740067i	$0.734794\pi$
$774$	−5.01164	−	8.68041i	−0.180140	−	0.312011i
$775$	11.6787	+	20.2281i	0.419510	+	0.726613i
$776$	−2.94552	−	5.10179i	−0.105738	−	0.183144i
$777$			13.9512i			0.500497i
$778$	−32.9171			−1.18013
$779$	1.67278	−	2.89734i	0.0599336	−	0.103808i
$780$	−44.9103	+	25.9290i	−1.60805	+	0.928407i
$781$	8.99572	+	15.5810i	0.321892	+	0.557533i
$782$	13.7651	+	7.94731i	0.492240	+	0.284195i
$783$	−58.3189	+	101.011i	−2.08415	+	3.60985i
$784$	4.59551			0.164125
$785$	−6.82218	−	11.8164i	−0.243494	−	0.421744i
$786$	−16.1431			−0.575806
$787$	−10.6902	−	6.17199i	−0.381065	−	0.220008i	0.297217	−	0.954810i	$-0.403942\pi$
$787$	−10.6902	−	6.17199i	−0.381065	−	0.220008i	−0.678281	+	0.734802i	$0.737275\pi$
$788$	15.7691	−	9.10428i	0.561750	−	0.324327i
$789$	−16.9395	+	29.3400i	−0.603061	+	1.04453i
$790$	−32.5721			−1.15886
$791$	6.57317	−	11.3851i	0.233715	−	0.404806i
$792$	−33.3309	−	57.7309i	−1.18436	−	2.05138i
$793$	25.3288	+	43.8707i	0.899451	+	1.55789i
$794$	0.290065	−	0.167469i	0.0102940	−	0.00594326i
$795$	−45.3025	+	26.1554i	−1.60672	+	0.927637i
$796$			9.73092i			0.344903i
$797$	−22.4890	+	12.9840i	−0.796601	+	0.459918i	−0.842281	−	0.539038i	$-0.818788\pi$
$797$	−22.4890	+	12.9840i	−0.796601	+	0.459918i	0.0456801	+	0.998956i	$0.485455\pi$
$798$	−23.0034			−0.814311
$799$			51.2132i			1.81179i
$800$			34.3106i			1.21306i
$801$		−	122.784i		−	4.33837i
$802$	19.0081	+	32.9230i	0.671200	+	1.16255i
$803$	−1.44994	−	0.837120i	−0.0511671	−	0.0295413i
$804$	14.1244	+	24.4642i	0.498129	+	0.862784i
$805$	−28.3658	+	16.3770i	−0.999763	+	0.577213i
$806$	7.49594	−	12.9834i	0.264033	−	0.457319i
$807$	−10.3195	+	17.8738i	−0.363262	+	0.629188i
$808$	20.6469			0.726356
$809$	−5.31628	+	9.20806i	−0.186910	+	0.323738i	−0.944219	−	0.329319i	$-0.893181\pi$
$809$	−5.31628	+	9.20806i	−0.186910	+	0.323738i	0.757308	+	0.653058i	$0.226514\pi$
$810$	−71.8959	−	41.5091i	−2.52617	−	1.45848i
$811$	−44.3326	+	25.5954i	−1.55673	+	0.898777i	−0.559161	+	0.829059i	$0.688876\pi$
$811$	−44.3326	+	25.5954i	−1.55673	+	0.898777i	−0.997567	+	0.0697176i	$0.977790\pi$
$812$	−27.1938	−	15.7004i	−0.954316	−	0.550975i
$813$	10.8510			0.380560
$814$	−1.66235	−	2.87928i	−0.0582655	−	0.100919i
$815$	−8.99868	−	5.19539i	−0.315210	−	0.181987i
$816$	−14.1458			−0.495201
$817$	−2.38005	+	1.37412i	−0.0832674	+	0.0480745i
$818$	20.9609	−	12.1018i	0.732880	−	0.423129i
$819$	122.078			4.26577
$820$	3.07330	+	5.32311i	0.107324	+	0.185891i
$821$	3.82251	−	6.62078i	0.133406	−	0.231067i	−0.791581	−	0.611064i	$-0.790742\pi$
$821$	3.82251	−	6.62078i	0.133406	−	0.231067i	0.924988	+	0.379997i	$0.124075\pi$
$822$	−9.05269	+	15.6797i	−0.315749	+	0.546893i
$823$	30.8440			1.07516			0.537578	−	0.843214i	$-0.319339\pi$
$823$	30.8440			1.07516			0.537578	+	0.843214i	$0.319339\pi$
$824$	17.8304			0.621150
$825$		−	63.3175i		−	2.20443i
$826$	24.0052	−	13.8594i	0.835247	−	0.482230i
$827$	20.6921	−	11.9466i	0.719534	−	0.415423i	−0.0950473	−	0.995473i	$-0.530300\pi$
$827$	20.6921	−	11.9466i	0.719534	−	0.415423i	0.814581	+	0.580050i	$0.196967\pi$
$828$	10.6062	+	18.3706i	0.368593	+	0.638421i
$829$		−	25.3349i		−	0.879917i	−0.898018	−	0.439958i	$-0.854993\pi$
$829$		−	25.3349i		−	0.879917i	0.898018	−	0.439958i	$-0.145007\pi$
$830$	−48.0818	+	27.7600i	−1.66894	+	0.963565i
$831$			101.945i			3.53642i
$832$	24.2537	−	14.0029i	0.840846	−	0.485463i
$833$	21.2791	−	36.8565i	0.737278	−	1.27700i
$834$			24.3399i			0.842821i
$835$	−52.3029	−	30.1971i	−1.81002	−	1.04501i
$836$	−5.54076	+	3.19896i	−0.191631	+	0.110638i
$837$	−52.9667			−1.83080
$838$	11.9187	+	6.88125i	0.411724	+	0.237709i
$839$	22.0303	+	12.7192i	0.760569	+	0.439115i	0.829500	−	0.558507i	$-0.188626\pi$
$839$	22.0303	+	12.7192i	0.760569	+	0.439115i	−0.0689310	+	0.997621i	$0.521959\pi$
$840$	60.3687	−	104.562i	2.08292	−	3.60772i
$841$	−16.5122	−	28.5999i	−0.569385	−	0.986204i
$842$	4.69529	−	8.13248i	0.161810	−	0.280264i
$843$	26.6375	+	46.1375i	0.917444	+	1.58906i
$844$		−	0.335067i		−	0.0115335i
$845$	10.2553	+	17.7627i	0.352793	+	0.611056i
$846$	29.2811	−	50.7164i	1.00671	−	1.74367i
$847$	6.72413	−	3.88218i	0.231044	−	0.133393i
$848$	2.81510	−	1.62530i	0.0966708	−	0.0558129i
$849$	18.6637	−	32.3265i	0.640537	−	1.10944i
$850$	−34.5007	−	19.9190i	−1.18337	−	0.683216i
$851$	1.51120	+	2.61748i	0.0518033	+	0.0897259i
$852$	18.2763	+	10.5518i	0.626136	+	0.361500i
$853$	−18.0556	+	31.2732i	−0.618211	+	1.07077i	0.371601	+	0.928393i	$0.378809\pi$
$853$	−18.0556	+	31.2732i	−0.618211	+	1.07077i	−0.989812	+	0.142380i	$0.954524\pi$
$854$	−35.7534	−	20.6422i	−1.22345	−	0.706362i
$855$	−25.5465	+	44.2479i	−0.873673	+	1.51325i
$856$	21.1575	+	36.6459i	0.723149	+	1.25253i
$857$	19.7772	+	11.4184i	0.675578	+	0.390045i	0.798187	−	0.602410i	$-0.205793\pi$
$857$	19.7772	+	11.4184i	0.675578	+	0.390045i	−0.122609	+	0.992455i	$0.539126\pi$
$858$	−35.1955	+	20.3201i	−1.20155	+	0.693718i
$859$	30.0702	+	17.3610i	1.02598	+	0.592350i	0.915831	−	0.401565i	$-0.131533\pi$
$859$	30.0702	+	17.3610i	1.02598	+	0.592350i	0.110150	+	0.993915i	$0.464867\pi$
$860$		−	5.04918i		−	0.172176i
$861$		−	20.2132i		−	0.688863i
$862$	−5.59702	+	9.69432i	−0.190635	+	0.330190i
$863$	45.9382	−	26.5225i	1.56376	−	0.902835i	0.566884	−	0.823797i	$-0.308149\pi$
$863$	45.9382	−	26.5225i	1.56376	−	0.902835i	0.996872	−	0.0790375i	$-0.0251847\pi$
$864$	−67.3812	−	38.9026i	−2.29236	−	1.32349i
$865$			10.2078i			0.347075i
$866$	−33.7760			−1.14776
$867$	−37.8817	+	65.6131i	−1.28653	+	2.22834i
$868$		−	14.2595i		−	0.483998i
$869$	29.7915			1.01061
$870$	72.2954	−	41.7398i	2.45104	−	1.41511i
$871$	30.5012	−	17.6099i	1.03350	−	0.596689i
$872$	−9.10922	−	5.25921i	−0.308477	−	0.178099i
$873$	13.0439	+	7.53091i	0.441470	+	0.254883i
$874$	−4.31581	+	2.49174i	−0.145985	+	0.0842842i
$875$	16.6661	−	9.62216i	0.563416	−	0.325289i
$876$	−1.96386			−0.0663526
$877$		−	21.2324i		−	0.716967i	−0.933536	−	0.358484i	$-0.883294\pi$
$877$		−	21.2324i		−	0.716967i	0.933536	−	0.358484i	$-0.116706\pi$
$878$	−13.4207	+	23.2454i	−0.452928	+	0.784495i
$879$	−36.9272			−1.24552
$880$			6.94676i			0.234175i
$881$	−2.78760	−	1.60942i	−0.0939166	−	0.0542228i	0.452306	−	0.891863i	$-0.350601\pi$
$881$	−2.78760	−	1.60942i	−0.0939166	−	0.0542228i	−0.546223	+	0.837640i	$0.683935\pi$
$882$	−42.1454	+	24.3327i	−1.41911	+	0.819324i
$883$	8.27826	−	14.3384i	0.278586	−	0.482525i	−0.692448	−	0.721468i	$-0.743468\pi$
$883$	8.27826	−	14.3384i	0.278586	−	0.482525i	0.971034	+	0.238943i	$0.0768010\pi$
$884$		−	29.8426i		−	1.00371i
$885$		−	86.0043i		−	2.89100i
$886$	−0.235798	−	0.136138i	−0.00792178	−	0.00457364i
$887$	−7.61197	+	4.39477i	−0.255585	+	0.147562i	−0.622319	−	0.782764i	$-0.713809\pi$
$887$	−7.61197	+	4.39477i	−0.255585	+	0.147562i	0.366734	+	0.930326i	$0.380476\pi$
$888$	−9.64851	−	5.57057i	−0.323783	−	0.186936i
$889$	−17.4011	−	30.1396i	−0.583615	−	1.01085i
$890$	−26.4984	+	45.8965i	−0.888227	+	1.53845i
$891$	65.7583	+	37.9656i	2.20299	+	1.27189i
$892$	1.09817	−	1.90208i	0.0367694	−	0.0636865i
$893$	−13.9058	−	8.02849i	−0.465338	−	0.268663i
$894$	26.2138	+	45.4037i	0.876721	+	1.51853i
$895$	3.82995	+	2.21122i	0.128021	+	0.0739131i
$896$	8.03499	−	13.9170i	0.268430	−	0.464934i
$897$	31.9952	−	18.4725i	1.06829	−	0.616778i
$898$	9.44564	−	5.45344i	0.315205	−	0.181984i
$899$	14.0830	−	24.3925i	0.469696	−	0.813537i
$900$	−26.5833	−	46.0437i	−0.886111	−	1.53479i
$901$		−	30.1032i		−	1.00288i
$902$	2.40849	+	4.17164i	0.0801941	+	0.138900i
$903$	−8.30215	+	14.3797i	−0.276278	+	0.478528i
$904$	5.24920	+	9.09187i	0.174586	+	0.302391i
$905$	−7.33808	+	12.7099i	−0.243926	+	0.422492i
$906$	−13.9467	−	8.05216i	−0.463350	−	0.267515i
$907$	13.6082	+	7.85672i	0.451854	+	0.260878i	0.708613	−	0.705597i	$-0.249321\pi$
$907$	13.6082	+	7.85672i	0.451854	+	0.260878i	−0.256759	+	0.966476i	$0.582655\pi$
$908$	−6.88729			−0.228563
$909$	−45.7163	+	26.3943i	−1.51631	+	0.875444i
$910$	−45.6326	−	26.3460i	−1.51271	−	0.873362i
$911$		−	29.8741i		−	0.989775i	−0.868957	−	0.494887i	$-0.835209\pi$
$911$		−	29.8741i		−	0.989775i	0.868957	−	0.494887i	$-0.164791\pi$
$912$	2.21757	−	3.84095i	0.0734312	−	0.127187i
$913$	43.9772	−	25.3902i	1.45543	−	0.840294i
$914$		−	35.1950i		−	1.16415i
$915$	−110.933	+	64.0475i	−3.66735	+	2.11734i
$916$		−	14.2861i		−	0.472026i
$917$	9.57178	+	16.5788i	0.316088	+	0.547480i
$918$	78.2363	−	45.1698i	2.58218	−	1.49082i
$919$	−31.1445	+	17.9813i	−1.02736	+	0.593148i	−0.916228	−	0.400658i	$-0.868782\pi$
$919$	−31.1445	+	17.9813i	−1.02736	+	0.593148i	−0.111134	+	0.993805i	$0.535448\pi$
$920$		−	26.1566i		−	0.862359i
$921$	74.9681			2.47028
$922$	−23.1919			−0.763784
$923$	13.1557	−	22.7864i	0.433026	−	0.750023i
$924$	−19.3274	+	33.4761i	−0.635826	+	1.10128i
$925$	−3.78765	−	6.56040i	−0.124537	−	0.215705i
$926$	−9.66364			−0.317567
$927$	−39.4799	+	22.7937i	−1.29669	+	0.748644i
$928$	35.8313	−	20.6872i	1.17622	−	0.679090i
$929$	−59.9184			−1.96586			−0.982929	−	0.183985i	$-0.941100\pi$
$929$	−59.9184			−1.96586			−0.982929	+	0.183985i	$0.941100\pi$
$930$	32.8303	+	18.9546i	1.07655	+	0.621545i
$931$	6.67168	+	11.5557i	0.218656	+	0.378723i
$932$	24.6515			0.807488
$933$	−16.2950	−	9.40793i	−0.533475	−	0.308002i
$934$	19.7970	−	11.4298i	0.647778	−	0.373995i
$935$	55.7138	+	32.1664i	1.82204	+	1.05195i
$936$	−48.7446	+	84.4282i	−1.59327	+	2.75962i
$937$	22.7017			0.741631			0.370815	−	0.928707i	$-0.379078\pi$
$937$	22.7017			0.741631			0.370815	+	0.928707i	$0.379078\pi$
$938$	−14.3516	+	24.8576i	−0.468595	+	0.811630i
$939$	34.0511	−	58.9783i	1.11122	−	1.92468i
$940$	25.5482	−	14.7503i	0.833290	−	0.481100i
$941$	−23.3086	−	40.3716i	−0.759838	−	1.31608i	−0.942933	−	0.332982i	$-0.891945\pi$
$941$	−23.3086	−	40.3716i	−0.759838	−	1.31608i	0.183095	−	0.983095i	$-0.441388\pi$
$942$	−10.8622	−	6.27127i	−0.353908	−	0.204329i
$943$	−2.18950	−	3.79232i	−0.0712998	−	0.123495i
$944$			5.34430i			0.173942i
$945$			186.162i			6.05586i
$946$		−	3.95696i		−	0.128652i
$947$	−47.7263			−1.55090			−0.775448	−	0.631411i	$-0.782476\pi$
$947$	−47.7263			−1.55090			−0.775448	+	0.631411i	$0.782476\pi$
$948$	30.2632	−	17.4725i	0.982903	−	0.567479i
$949$			2.44848i			0.0794811i
$950$	10.8171	−	6.24525i	0.350953	−	0.202623i
$951$	−75.7914	+	43.7582i	−2.45771	+	1.41896i
$952$	34.7402	+	60.1718i	1.12594	+	1.95018i
$953$	5.48853	+	9.50641i	0.177791	+	0.307943i	0.941124	−	0.338063i	$-0.109772\pi$
$953$	5.48853	+	9.50641i	0.177791	+	0.307943i	−0.763333	+	0.646006i	$0.776438\pi$
$954$	−17.2115	+	29.8112i	−0.557243	+	0.965173i
$955$	−49.7453			−1.60972
$956$	6.77907	−	11.7417i	0.219251	−	0.379754i
$957$	−66.1237	+	38.1765i	−2.13747	+	1.23407i
$958$	19.3798	+	11.1889i	0.626133	+	0.361498i
$959$	21.4705			0.693319
$960$	35.4083	+	61.3290i	1.14280	+	1.97939i
$961$	−18.2094			−0.587401
$962$	−2.43110	+	4.21079i	−0.0783818	+	0.135761i
$963$	−93.6936	−	54.0940i	−3.01923	−	1.74316i
$964$	6.18619	+	10.7148i	0.199244	+	0.345100i
$965$	−2.80493	+	1.61943i	−0.0902938	+	0.0521312i
$966$	−15.0545	+	26.0752i	−0.484371	+	0.838956i
$967$	51.4761			1.65536			0.827679	−	0.561201i	$-0.189661\pi$
$967$	51.4761			1.65536			0.827679	+	0.561201i	$0.189661\pi$
$968$			6.20045i			0.199290i
$969$	−20.5366	−	35.5704i	−0.659730	−	1.14269i
$970$	−3.25052	−	5.63007i	−0.104368	−	0.180771i
$971$	−10.7634	−	18.6427i	−0.345413	−	0.598274i	0.640015	−	0.768362i	$-0.278928\pi$
$971$	−10.7634	−	18.6427i	−0.345413	−	0.598274i	−0.985429	+	0.170088i	$0.945595\pi$
$972$	41.2099			1.32181
$973$	24.9968	−	14.4319i	0.801360	−	0.462665i
$974$	3.30193	−	5.71912i	0.105801	−	0.183252i
$975$	−80.1924	+	46.2991i	−2.56821	+	1.48276i
$976$	6.89339	−	3.97990i	0.220652	−	0.127394i
$977$	−17.1312	−	29.6722i	−0.548077	−	0.949297i	−0.998406	−	0.0564345i	$-0.982027\pi$
$977$	−17.1312	−	29.6722i	−0.548077	−	0.949297i	0.450329	−	0.892862i	$-0.351307\pi$
$978$	−9.55171			−0.305430
$979$	24.2362	−	41.9784i	0.774594	−	1.34164i
$980$	−24.5150			−0.783102
$981$	26.8928			0.858620
$982$		−	24.4382i		−	0.779854i
$983$	−4.16469			−0.132833			−0.0664164	−	0.997792i	$-0.521157\pi$
$983$	−4.16469			−0.132833			−0.0664164	+	0.997792i	$0.521157\pi$
$984$	13.9792	+	8.07090i	0.445641	+	0.257291i
$985$	49.7143	−	28.7026i	1.58403	−	0.914540i
$986$			48.0397i			1.52990i
$987$	−97.0127			−3.08795
$988$	8.10305	+	4.67830i	0.257793	+	0.148837i
$989$			3.59717i			0.114383i
$990$	−36.7823	−	63.7087i	−1.16902	−	2.02480i
$991$	6.43167	+	11.1400i	0.204309	+	0.353873i	0.949912	−	0.312517i	$-0.101172\pi$
$991$	6.43167	+	11.1400i	0.204309	+	0.353873i	−0.745603	+	0.666390i	$0.767839\pi$
$992$	16.2714	+	9.39432i	0.516619	+	0.298270i
$993$	−29.5594	+	17.0661i	−0.938039	+	0.541577i
$994$			21.4431i			0.680133i
$995$			30.6782i			0.972563i
$996$	29.7823	−	51.5845i	0.943689	−	1.63452i
$997$	5.03353	+	2.90611i	0.159414	+	0.0920374i	0.577585	−	0.816331i	$-0.303995\pi$
$997$	5.03353	+	2.90611i	0.159414	+	0.0920374i	−0.418171	+	0.908368i	$0.637329\pi$
$998$	0.240453	−	0.416477i	0.00761142	−	0.0131834i
$999$	17.1783			0.543497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.20	✓	58
349.227	even	6	inner	349.2.e.a.227.20	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.20	✓	58	1.1	even	1	trivial
349.2.e.a.227.20	yes	58	349.227	even	6	inner

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +O(q^{10})\)	\(q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +3.26219i q^{10} -2.98370i q^{11} +(-1.74992 - 3.03095i) q^{12} +(-3.77890 + 2.18175i) q^{13} +(1.77806 - 3.07969i) q^{14} +(-5.51687 - 9.55550i) q^{15} +(0.342818 + 0.593778i) q^{16} +6.34956 q^{17} +(-6.28797 - 3.63036i) q^{18} +(-0.995395 + 1.72407i) q^{19} +(-1.82878 - 3.16754i) q^{20} +12.0279i q^{21} +(-1.43318 - 2.48235i) q^{22} +(1.30287 + 2.25663i) q^{23} +(-8.31838 - 4.80262i) q^{24} +(-3.26549 - 5.65599i) q^{25} +(-2.09595 + 3.63029i) q^{26} +14.8101 q^{27} +3.98711i q^{28} +(-3.93778 + 6.82043i) q^{29} +(-9.17972 - 5.29991i) q^{30} -3.57639 q^{31} +(-4.54968 - 2.62676i) q^{32} +(8.39607 + 4.84747i) q^{33} +(5.28263 - 3.04993i) q^{34} +12.5700i q^{35} +8.14069 q^{36} +1.15990 q^{37} +1.91250i q^{38} -14.1783i q^{39} +(-8.69325 - 5.01905i) q^{40} -1.68052 q^{41} +(5.77745 + 10.0068i) q^{42} +(1.19553 + 0.690240i) q^{43} +(2.78320 + 1.60688i) q^{44} +25.6647 q^{45} +(2.16789 + 1.25163i) q^{46} +8.06563i q^{47} -2.22783 q^{48} +(3.35128 - 5.80458i) q^{49} +(-5.43357 - 3.13707i) q^{50} +(-10.3158 + 17.8675i) q^{51} -4.69995i q^{52} -4.74099i q^{53} +(12.3215 - 7.11384i) q^{54} +(8.77444 + 5.06593i) q^{55} +(5.47128 + 9.47654i) q^{56} +(-3.23433 - 5.60203i) q^{57} +7.56584i q^{58} +(6.75038 + 3.89733i) q^{59} +11.8845 q^{60} -11.6094i q^{61} +(-2.97545 + 1.71787i) q^{62} +(-24.2290 - 13.9886i) q^{63} -6.41819 q^{64} -14.8173i q^{65} +9.31368 q^{66} -8.07146 q^{67} +(-3.41957 + 5.92287i) q^{68} -8.46681 q^{69} +(6.03782 + 10.4578i) q^{70} +(-5.22205 + 3.01495i) q^{71} +(19.3487 - 11.1710i) q^{72} +(0.280564 - 0.485951i) q^{73} +(0.965003 - 0.557145i) q^{74} +21.2211 q^{75} +(-1.07214 - 1.85701i) q^{76} +(-5.52238 - 9.56505i) q^{77} +(-6.81037 - 11.7959i) q^{78} +9.98474i q^{79} -2.32823 q^{80} +(-12.7243 + 22.0392i) q^{81} +(-1.39814 + 0.807217i) q^{82} +(8.50963 + 14.7391i) q^{83} +(-11.2196 - 6.47766i) q^{84} +(-10.7807 + 18.6727i) q^{85} +1.32619 q^{86} +(-12.7950 - 22.1616i) q^{87} +8.82011 q^{88} +(14.0692 + 8.12287i) q^{89} +(21.3522 - 12.3277i) q^{90} +(-8.07617 + 13.9883i) q^{91} -2.80665 q^{92} +(5.81038 - 10.0639i) q^{93} +(3.87422 + 6.71035i) q^{94} +(-3.38009 - 5.85449i) q^{95} +(14.7833 - 8.53512i) q^{96} +(-1.72586 + 0.996423i) q^{97} -6.43897i q^{98} +(-19.5294 + 11.2753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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