LMFDB - Embedded newform 349.2.e.a.227.20

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			227.20
Character	$\chi$	$=$	349.227
Dual form			349.2.e.a.123.20

$q$-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 $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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	0.764421	−	0.644717i	$-0.223025\pi$
$2$	0.831968	+	0.480337i	0.588290	+	0.339650i	−0.176131	+	0.984367i	$0.556358\pi$
$3$	−1.62465	−	2.81397i	−0.937992	−	1.62465i	−0.769210	−	0.638996i	$-0.779350\pi$
$3$	−1.62465	−	2.81397i	−0.937992	−	1.62465i	−0.168781	−	0.985654i	$-0.553983\pi$
$4$	−0.538552	−	0.932800i	−0.269276	−	0.466400i
$5$	−1.69786	−	2.94079i	−0.759308	−	1.31516i	−0.943204	−	0.332215i	$-0.892204\pi$
$5$	−1.69786	−	2.94079i	−0.759308	−	1.31516i	0.183896	−	0.982946i	$-0.441129\pi$
$6$		−	3.12152i		−	1.27435i
$7$	3.20576	+	1.85085i	1.21166	+	0.699555i	0.963122	−	0.269066i	$-0.0867150\pi$
$7$	3.20576	+	1.85085i	1.21166	+	0.699555i	0.248543	+	0.968621i	$0.420048\pi$
$8$		−	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	$0.148508\pi$
$11$			2.98370i			0.899621i	−0.893124	+	0.449810i	$0.851492\pi$
$12$	−1.74992	+	3.03095i	−0.505158	+	0.874959i
$13$	−3.77890	−	2.18175i	−1.04808	−	0.605108i	−0.125968	−	0.992034i	$-0.540204\pi$
$13$	−3.77890	−	2.18175i	−1.04808	−	0.605108i	−0.922111	+	0.386926i	$0.873537\pi$
$14$	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	0.728963	−	0.684553i	$-0.240003\pi$
$19$	−0.995395	−	1.72407i	−0.228359	−	0.395530i	−0.957322	+	0.289024i	$0.906669\pi$
$20$	−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	−0.697622	−	0.716466i	$-0.745758\pi$
$23$	1.30287	−	2.25663i	0.271667	−	0.470541i	0.969289	+	0.245925i	$0.0790918\pi$
$24$	−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	−0.956359	−	0.292194i	$-0.905615\pi$
$29$	−3.93778	−	6.82043i	−0.731227	−	1.26652i	0.225132	−	0.974328i	$-0.427719\pi$
$30$	−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	−0.406064	−	0.913845i	$-0.633099\pi$
$43$	1.19553	−	0.690240i	0.182317	−	0.105261i	0.588381	+	0.808584i	$0.299766\pi$
$44$	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	$-0.799818\pi$
$47$		−	8.06563i		−	1.17649i	0.808681	−	0.588247i	$-0.200182\pi$
$48$	−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	$0.105571\pi$
$53$			4.74099i			0.651225i	−0.945503	+	0.325613i	$0.894429\pi$
$54$	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	0.00855397	−	0.999963i	$-0.497277\pi$
$59$	6.75038	−	3.89733i	0.878825	−	0.507390i	0.870271	+	0.492574i	$0.163944\pi$
$60$	11.8845			1.53428
$61$			11.6094i			1.48643i	0.669053	+	0.743215i	$0.266700\pi$
$61$			11.6094i			1.48643i	−0.669053	+	0.743215i	$0.733300\pi$
$62$	−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	0.157026	−	0.987594i	$-0.449809\pi$
$71$	−5.22205	−	3.01495i	−0.619743	−	0.357809i	−0.776769	+	0.629786i	$0.783143\pi$
$72$	19.3487	+	11.1710i	2.28027	+	1.31651i
$73$	0.280564	+	0.485951i	0.0328376	+	0.0568763i	0.881977	−	0.471292i	$-0.156212\pi$
$73$	0.280564	+	0.485951i	0.0328376	+	0.0568763i	−0.849140	+	0.528169i	$0.822879\pi$
$74$	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	$-0.810153\pi$
$79$		−	9.98474i		−	1.12337i	0.827351	−	0.561685i	$-0.189847\pi$
$80$	−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	0.157741	−	0.987481i	$-0.449579\pi$
$83$	8.50963	−	14.7391i	0.934054	−	1.61783i	0.776313	−	0.630348i	$-0.217088\pi$
$84$	−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	0.491384	−	0.870943i	$-0.336491\pi$
$89$	14.0692	−	8.12287i	1.49134	−	0.861023i	0.999951	+	0.00992010i	$0.00315772\pi$
$90$	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	0.409817	−	0.912168i	$-0.365592\pi$
$97$	−1.72586	−	0.996423i	−0.175234	−	0.101171i	−0.585052	+	0.810996i	$0.698926\pi$
$98$			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	$0.112967\pi$
$101$			6.98452i			0.694986i	−0.937683	+	0.347493i	$0.887033\pi$
$102$		−	19.8203i		−	1.96250i
$103$			6.03173i			0.594324i	0.954827	+	0.297162i	$0.0960402\pi$
$103$			6.03173i			0.594324i	−0.954827	+	0.297162i	$0.903960\pi$
$104$	−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	0.960206	−	0.279292i	$-0.0900997\pi$
$107$	12.3967	+	7.15725i	1.19844	+	0.691917i	0.238229	+	0.971209i	$0.423433\pi$
$108$	−7.97602	−	13.8149i	−0.767493	−	1.32934i
$109$	−1.77911	−	3.08150i	−0.170407	−	0.295154i	0.768155	−	0.640264i	$-0.221175\pi$
$109$	−1.77911	−	3.08150i	−0.170407	−	0.295154i	−0.938562	+	0.345110i	$0.887842\pi$
$110$	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	0.637640	−	0.770334i	$-0.279911\pi$
$113$	3.07564	+	1.77572i	0.289332	+	0.167046i	−0.348309	+	0.937380i	$0.613244\pi$
$114$	−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	$0.136965\pi$
$127$			9.40171i			0.834267i	−0.908845	+	0.417133i	$0.863035\pi$
$128$	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	$-0.927461\pi$
$131$		−	5.17156i		−	0.451842i	0.974146	−	0.225921i	$-0.0725391\pi$
$132$	−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	−0.269833	−	0.962907i	$-0.586968\pi$
$137$	5.02311	−	2.90009i	0.429153	−	0.247772i	0.698986	+	0.715136i	$0.253635\pi$
$138$	−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	0.958670	−	0.284519i	$-0.0918340\pi$
$149$	14.5454	+	8.39778i	1.19160	+	0.687973i	0.232934	+	0.972493i	$0.425167\pi$
$150$	17.6553	+	10.1933i	1.44155	+	0.832278i
$151$	−2.57957	−	4.46794i	−0.209922	−	0.363596i	0.741768	−	0.670657i	$-0.233988\pi$
$151$	−2.57957	−	4.46794i	−0.209922	−	0.363596i	−0.951690	+	0.307061i	$0.900654\pi$
$152$	−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	0.774651	−	0.632389i	$-0.217926\pi$
$157$	−2.00905	−	3.47977i	−0.160339	−	0.277716i	−0.934990	+	0.354673i	$0.884592\pi$
$158$	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	$-0.961763\pi$
$163$		−	3.05996i		−	0.239674i	0.992794	−	0.119837i	$-0.0382372\pi$
$164$	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	$-0.758430\pi$
$167$		−	17.7853i		−	1.37627i	0.725582	−	0.688135i	$-0.241570\pi$
$168$	−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	0.595688	−	0.803216i	$-0.296879\pi$
$173$	2.60333	+	1.50303i	0.197927	+	0.114273i	−0.397761	+	0.917489i	$0.630213\pi$
$174$	−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	$0.0154987\pi$
$179$			1.30236i			0.0973426i	−0.998815	+	0.0486713i	$0.984501\pi$
$180$	−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	−0.469392	−	0.882990i	$-0.655527\pi$
$191$	7.32468	−	12.6867i	0.529995	−	0.917979i	0.999388	−	0.0349890i	$-0.0111396\pi$
$192$	10.4273	+	18.0606i	0.752526	+	1.30341i
$193$	0.826017	−	0.476901i	0.0594580	−	0.0343281i	−0.469976	−	0.882679i	$-0.655738\pi$
$193$	0.826017	−	0.476901i	0.0594580	−	0.0343281i	0.529434	+	0.848351i	$0.322404\pi$
$194$	−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	−0.920703	−	0.390265i	$-0.872383\pi$
$197$	−14.6402	+	8.45255i	−1.04307	+	0.602219i	−0.122372	+	0.992484i	$0.539050\pi$
$198$	−10.8319	−	18.7614i	−0.769791	−	1.33332i
$199$	7.82396	+	4.51717i	0.554626	+	0.320213i	0.750986	−	0.660318i	$-0.229579\pi$
$199$	7.82396	+	4.51717i	0.554626	+	0.320213i	−0.196360	+	0.980532i	$0.562912\pi$
$200$	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	0.490698	−	0.871330i	$-0.336742\pi$
$211$	−0.269404	−	0.155540i	−0.0185465	−	0.0107078i	−0.509245	+	0.860622i	$0.670075\pi$
$212$	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	−0.740202	−	0.672384i	$-0.765270\pi$
$227$	3.19713	−	5.53759i	0.212201	−	0.367543i	0.952403	+	0.304842i	$0.0986035\pi$
$228$	6.96743			0.461430
$229$	−11.4865	−	6.63171i	−0.759047	−	0.438236i	0.0699067	−	0.997554i	$-0.477730\pi$
$229$	−11.4865	−	6.63171i	−0.759047	−	0.438236i	−0.828953	+	0.559318i	$0.811063\pi$
$230$	−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	0.198291	+	0.980143i	$0.436461\pi$
$233$	−11.4434	+	19.8206i	−0.749684	+	1.29849i	−0.947974	+	0.318347i	$0.896872\pi$
$234$	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	0.989559	−	0.144128i	$-0.0460376\pi$
$241$	5.74335	+	9.94777i	0.369961	+	0.640792i	−0.619598	+	0.784920i	$0.712704\pi$
$242$	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	$0.0385393\pi$
$251$			3.82701i			0.241559i	−0.992679	+	0.120779i	$0.961461\pi$
$252$	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	−0.912274	−	0.409581i	$-0.865675\pi$
$271$	−1.66974	+	2.89207i	−0.101429	+	0.175681i	0.810844	+	0.585262i	$0.199008\pi$
$272$	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	0.983304	+	0.181971i	$0.0582477\pi$
$277$	27.1710	+	15.6872i	1.63255	+	0.942552i	0.649243	+	0.760581i	$0.275086\pi$
$278$	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	0.999921	−	0.0126016i	$-0.00401133\pi$
$281$	8.19792	+	14.1992i	0.489047	+	0.847054i	−0.510874	+	0.859656i	$0.670678\pi$
$282$	−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	−0.650931	−	0.759137i	$-0.725621\pi$
$293$	5.68234	−	9.84210i	0.331966	−	0.574982i	0.982897	+	0.184155i	$0.0589548\pi$
$294$	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	0.322633	+	0.946524i	$0.395432\pi$
$307$	−11.5361	+	19.9810i	−0.658397	+	1.14038i	−0.981031	+	0.193853i	$0.937901\pi$
$308$	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	$-0.947502\pi$
$311$		−	5.79075i		−	0.328363i	0.986430	−	0.164182i	$-0.0524983\pi$
$312$	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	0.327978	−	0.944685i	$-0.393633\pi$
$317$	23.3255	−	13.4670i	1.31009	−	0.756380i	0.982111	+	0.188305i	$0.0602993\pi$
$318$	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	−0.228699	−	0.973497i	$-0.573447\pi$
$331$	9.09716	−	5.25225i	0.500025	−	0.288690i	0.728724	+	0.684807i	$0.240114\pi$
$332$	−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	−0.971809	−	0.235769i	$-0.924239\pi$
$337$	−5.17173	+	8.95770i	−0.281722	+	0.487957i	0.690087	+	0.723727i	$0.257572\pi$
$338$			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	0.539582	−	0.841933i	$-0.318582\pi$
$347$	1.49467	+	0.862948i	0.0802381	+	0.0463255i	−0.459344	+	0.888258i	$0.651916\pi$
$348$	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	0.963873	+	0.266364i	$0.0858223\pi$
$353$	13.3888	+	23.1901i	0.712614	+	1.23428i	−0.251258	+	0.967920i	$0.580844\pi$
$354$	−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	$0.294759\pi$
$359$			30.2865i			1.59846i	−0.601026	+	0.799229i	$0.705241\pi$
$360$		−	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	−0.0305324	−	0.999534i	$-0.509720\pi$
$367$	15.7055	−	9.06760i	0.819823	−	0.473325i	0.850355	+	0.526209i	$0.176387\pi$
$368$	−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	−0.749379	−	0.662142i	$-0.769648\pi$
$373$	−10.6345	+	6.13986i	−0.550636	+	0.317910i	0.198742	+	0.980052i	$0.436314\pi$
$374$	−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	0.520209	−	0.854039i	$-0.325854\pi$
$379$	29.5899	−	17.0838i	1.51993	−	0.877534i	0.999724	−	0.0234946i	$-0.00747925\pi$
$380$	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	0.758200	−	0.652023i	$-0.226079\pi$
$383$	11.2066	+	6.47014i	0.572631	+	0.330609i	−0.185568	+	0.982631i	$0.559413\pi$
$384$		−	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	−0.504544	+	0.863386i	$0.668339\pi$
$389$	−29.6740	+	17.1323i	−1.50453	+	0.868641i	−0.999986	+	0.00525450i	$0.998327\pi$
$390$	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	$-0.549202\pi$
$401$		−	39.5725i		−	1.97615i	0.153958	−	0.988077i	$-0.450798\pi$
$402$			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	−0.636305	−	0.771438i	$-0.719538\pi$
$419$	7.16294	−	12.4066i	0.349932	−	0.606100i	0.986237	+	0.165337i	$0.0528713\pi$
$420$	38.0989	+	21.9964i	1.85903	+	1.07331i
$421$	8.46539	+	4.88749i	0.412578	+	0.238202i	0.691897	−	0.721997i	$-0.256775\pi$
$421$	8.46539	+	4.88749i	0.412578	+	0.238202i	−0.279319	+	0.960198i	$0.590109\pi$
$422$	−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	0.236870	−	0.971541i	$-0.423878\pi$
$431$	−10.0912	−	5.82613i	−0.486074	−	0.280635i	−0.722944	+	0.690906i	$0.757212\pi$
$432$	5.07717	−	8.79391i	0.244275	−	0.423097i
$433$	−30.4483	+	17.5793i	−1.46325	+	0.844809i	−0.999160	−	0.0409780i	$-0.986953\pi$
$433$	−30.4483	+	17.5793i	−1.46325	+	0.844809i	−0.464092	+	0.885787i	$0.653619\pi$
$434$	−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	−0.204792	−	0.978805i	$-0.565652\pi$
$439$	−24.1970	−	13.9701i	−1.15486	−	0.666758i	−0.950067	+	0.312047i	$0.898985\pi$
$440$	−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	−0.869372	−	0.494158i	$-0.835476\pi$
$443$	−0.141711	+	0.245450i	−0.00673288	+	0.0116617i	0.862639	+	0.505820i	$0.168810\pi$
$444$	−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	0.874896	+	0.484310i	$0.160929\pi$
$457$	18.3179	+	31.7275i	0.856873	+	1.48415i	−0.0180234	+	0.999838i	$0.505737\pi$
$458$	−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	−0.900372	−	0.435120i	$-0.856706\pi$
$461$	−20.9069	+	12.0706i	−0.973733	+	0.562185i	−0.0733611	+	0.997305i	$0.523373\pi$
$462$	29.8575	+	17.2382i	1.38909	+	0.801994i
$463$	−8.71155	+	5.02961i	−0.404860	+	0.233746i	−0.688579	−	0.725161i	$-0.741765\pi$
$463$	−8.71155	+	5.02961i	−0.404860	+	0.233746i	0.283719	+	0.958908i	$0.408432\pi$
$464$	−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	−0.467132	−	0.884188i	$-0.654713\pi$
$479$	11.6470	−	20.1731i	0.532163	−	0.921733i	0.999295	−	0.0375455i	$-0.0119539\pi$
$480$		−	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	0.628782	−	0.777582i	$-0.283554\pi$
$487$	5.95323	+	3.43710i	0.269767	+	0.155750i	−0.359015	+	0.933332i	$0.616887\pi$
$488$	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	0.996148	+	0.0876877i	$0.0279477\pi$
$491$	12.7193	+	22.0305i	0.574014	+	0.994221i	−0.422134	+	0.906533i	$0.638719\pi$
$492$	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	0.509672	−	0.860369i	$-0.329767\pi$
$499$	0.433526	+	0.250296i	0.0194073	+	0.0112048i	−0.490265	+	0.871573i	$0.663100\pi$
$500$	−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	−0.916671	−	0.399643i	$-0.869134\pi$
$503$	−23.0760	+	13.3229i	−1.02891	+	0.594039i	−0.112235	+	0.993682i	$0.535801\pi$
$504$	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	0.357380	−	0.933959i	$-0.383670\pi$
$509$	−6.15381	−	3.55291i	−0.272763	−	0.157480i	−0.630143	+	0.776479i	$0.717004\pi$
$510$	−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	0.794464	−	0.607311i	$-0.207752\pi$
$521$	15.1960	+	8.77343i	0.665750	+	0.384371i	−0.128714	+	0.991682i	$0.541085\pi$
$522$	49.5212	+	28.5911i	2.16748	+	1.25140i
$523$	−22.7497	+	13.1345i	−0.994774	+	0.574333i	−0.906698	−	0.421780i	$-0.861405\pi$
$523$	−22.7497	+	13.1345i	−0.994774	+	0.574333i	−0.0880764	+	0.996114i	$0.528072\pi$
$524$	−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	0.950211	+	0.311607i	$0.100867\pi$
$541$	17.3275	+	30.0120i	0.744965	+	1.29032i	−0.205246	+	0.978710i	$0.565799\pi$
$542$	−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	0.856540	−	0.516081i	$-0.172610\pi$
$547$	−0.436650	−	0.756300i	−0.0186698	−	0.0323370i	−0.875209	+	0.483744i	$0.839276\pi$
$548$	−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	−0.132814	−	0.991141i	$-0.542401\pi$
$557$	15.5561	−	8.98130i	0.659132	−	0.380550i	0.791946	+	0.610591i	$0.209068\pi$
$558$	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	−0.999720	−	0.0236722i	$-0.992464\pi$
$563$	−12.3469	−	21.3855i	−0.520361	−	0.901291i	0.479359	−	0.877619i	$-0.340869\pi$
$564$	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	−0.999801	−	0.0199500i	$-0.993649\pi$
$569$	−36.1856	−	20.8918i	−1.51698	−	0.875828i	−0.517178	−	0.855878i	$-0.673017\pi$
$570$	18.2749	+	10.5510i	0.765451	+	0.441933i
$571$		−	2.67483i		−	0.111938i	−0.998432	−	0.0559692i	$-0.982175\pi$
$571$		−	2.67483i		−	0.111938i	0.998432	−	0.0559692i	$-0.0178249\pi$
$572$	−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	0.977205	+	0.212298i	$0.0680946\pi$
$587$	16.2924	+	28.2192i	0.672458	+	1.16473i	−0.304747	+	0.952433i	$0.598572\pi$
$588$	−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	−0.912539	−	0.408991i	$-0.865881\pi$
$593$	−24.7074	+	14.2648i	−1.01461	+	0.585786i	−0.102073	+	0.994777i	$0.532548\pi$
$594$	−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	0.112592	−	0.993641i	$-0.464085\pi$
$599$	−16.9273	−	9.77299i	−0.691631	−	0.399314i	−0.804223	+	0.594328i	$0.797418\pi$
$600$		−	62.7316i		−	2.56101i
$601$	−7.76060	−	4.48058i	−0.316561	−	0.182767i	0.333298	−	0.942822i	$-0.391839\pi$
$601$	−7.76060	−	4.48058i	−0.316561	−	0.182767i	−0.649859	+	0.760055i	$0.725172\pi$
$602$	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	0.875527	+	0.483169i	$0.160514\pi$
$607$	21.0945	+	36.5368i	0.856200	+	1.48298i	−0.0193267	+	0.999813i	$0.506152\pi$
$608$	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	0.993624	−	0.112742i	$-0.0359634\pi$
$613$	9.88310	+	17.1180i	0.399175	+	0.691391i	−0.594450	+	0.804133i	$0.702630\pi$
$614$	−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	−0.974697	−	0.223529i	$-0.928242\pi$
$617$	−16.9140	−	29.2958i	−0.680930	−	1.17941i	0.293767	−	0.955877i	$-0.405091\pi$
$618$	18.8282			0.757379
$619$		−	36.0964i		−	1.45084i	−0.688309	−	0.725418i	$-0.741647\pi$
$619$		−	36.0964i		−	1.45084i	0.688309	−	0.725418i	$-0.258353\pi$
$620$	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	−0.694831	−	0.719173i	$-0.744521\pi$
$641$	6.97274	−	12.0771i	0.275407	−	0.477018i	0.970238	+	0.242155i	$0.0778541\pi$
$642$	22.3415	−	38.6966i	0.881747	−	1.52723i
$643$	11.7058	−	6.75834i	0.461631	−	0.266523i	−0.251099	−	0.967961i	$-0.580792\pi$
$643$	11.7058	−	6.75834i	0.461631	−	0.266523i	0.712730	+	0.701439i	$0.247459\pi$
$644$	−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	−0.998441	−	0.0558096i	$-0.982226\pi$
$647$	−13.9277	−	24.1234i	−0.547553	−	0.948390i	0.450888	−	0.892580i	$-0.351107\pi$
$648$	−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	$-0.850802\pi$
$659$		−	23.1935i		−	0.903490i	0.892147	−	0.451745i	$-0.149198\pi$
$660$			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	−0.964637	−	0.263582i	$-0.915096\pi$
$673$	−6.59063	+	11.4153i	−0.254050	+	0.440028i	0.710587	+	0.703609i	$0.248430\pi$
$674$	−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	$-0.932757\pi$
$677$		−	10.9116i		−	0.419365i	0.977769	−	0.209683i	$-0.0672431\pi$
$678$	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	−0.0424761	+	0.999097i	$0.513525\pi$
$683$	−23.1676	+	40.1274i	−0.886482	+	1.53543i	−0.844006	+	0.536334i	$0.819809\pi$
$684$	−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	0.997491	−	0.0708002i	$-0.0225553\pi$
$691$	37.7196	+	21.7774i	1.43492	+	0.828452i	0.437430	+	0.899252i	$0.355889\pi$
$692$		−	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	0.676667	−	0.736289i	$-0.263424\pi$
$701$	−7.92471	−	13.7260i	−0.299312	−	0.518424i	−0.975979	+	0.217866i	$0.930090\pi$
$702$	−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	$-0.955837\pi$
$709$		−	7.36494i		−	0.276596i	0.990391	−	0.138298i	$-0.0441632\pi$
$710$	−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	$0.0945803\pi$
$719$			15.7013i			0.585559i	−0.956180	+	0.292780i	$0.905420\pi$
$720$	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	−0.781898	−	0.623406i	$-0.785748\pi$
$727$	−25.0980	−	43.4711i	−0.930835	−	1.61225i	−0.148937	−	0.988847i	$-0.547585\pi$
$728$	−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	$0.252147\pi$
$733$			38.5458i			1.42372i	−0.702321	+	0.711861i	$0.747853\pi$
$734$	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	$-0.922911\pi$
$751$		−	13.1443i		−	0.479641i	0.970817	−	0.239821i	$-0.0770886\pi$
$752$	−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	−0.899875	−	0.436148i	$-0.856342\pi$
$757$	−26.7459	+	15.4418i	−0.972097	+	0.561240i	−0.0722219	+	0.997389i	$0.523009\pi$
$758$	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	−0.154315	−	0.988022i	$-0.549317\pi$
$761$	17.2188	−	9.94126i	0.624180	−	0.360370i	0.778494	+	0.627651i	$0.215984\pi$
$762$	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	0.983328	+	0.181839i	$0.0582049\pi$
$769$	45.2698	+	26.1365i	1.63247	+	0.942507i	0.649141	+	0.760668i	$0.275128\pi$
$770$	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	−0.678281	−	0.734802i	$-0.737275\pi$
$787$	−10.6902	+	6.17199i	−0.381065	+	0.220008i	0.297217	+	0.954810i	$0.403942\pi$
$788$	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	0.0456801	−	0.998956i	$-0.485455\pi$
$797$	−22.4890	−	12.9840i	−0.796601	−	0.459918i	−0.842281	+	0.539038i	$0.818788\pi$
$798$	−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	0.757308	−	0.653058i	$-0.226514\pi$
$809$	−5.31628	−	9.20806i	−0.186910	−	0.323738i	−0.944219	+	0.329319i	$0.893181\pi$
$810$	−71.8959	+	41.5091i	−2.52617	+	1.45848i
$811$	−44.3326	−	25.5954i	−1.55673	−	0.898777i	−0.997567	−	0.0697176i	$-0.977790\pi$
$811$	−44.3326	−	25.5954i	−1.55673	−	0.898777i	−0.559161	−	0.829059i	$-0.688876\pi$
$812$	−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	0.924988	−	0.379997i	$-0.124075\pi$
$821$	3.82251	+	6.62078i	0.133406	+	0.231067i	−0.791581	+	0.611064i	$0.790742\pi$
$822$	−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	0.814581	−	0.580050i	$-0.196967\pi$
$827$	20.6921	+	11.9466i	0.719534	+	0.415423i	−0.0950473	+	0.995473i	$0.530300\pi$
$828$	10.6062	−	18.3706i	0.368593	−	0.638421i
$829$			25.3349i			0.879917i	0.898018	+	0.439958i	$0.145007\pi$
$829$			25.3349i			0.879917i	−0.898018	+	0.439958i	$0.854993\pi$
$830$	−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	−0.0689310	−	0.997621i	$-0.521959\pi$
$839$	22.0303	−	12.7192i	0.760569	−	0.439115i	0.829500	+	0.558507i	$0.188626\pi$
$840$	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	−0.989812	−	0.142380i	$-0.954524\pi$
$853$	−18.0556	−	31.2732i	−0.618211	−	1.07077i	0.371601	−	0.928393i	$-0.378809\pi$
$854$	−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	−0.122609	−	0.992455i	$-0.539126\pi$
$857$	19.7772	−	11.4184i	0.675578	−	0.390045i	0.798187	+	0.602410i	$0.205793\pi$
$858$	−35.1955	−	20.3201i	−1.20155	−	0.693718i
$859$	30.0702	−	17.3610i	1.02598	−	0.592350i	0.110150	−	0.993915i	$-0.464867\pi$
$859$	30.0702	−	17.3610i	1.02598	−	0.592350i	0.915831	+	0.401565i	$0.131533\pi$
$860$			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	0.996872	+	0.0790375i	$0.0251847\pi$
$863$	45.9382	+	26.5225i	1.56376	+	0.902835i	0.566884	+	0.823797i	$0.308149\pi$
$864$	−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	$0.116706\pi$
$877$			21.2324i			0.716967i	−0.933536	+	0.358484i	$0.883294\pi$
$878$	−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	−0.546223	−	0.837640i	$-0.683935\pi$
$881$	−2.78760	+	1.60942i	−0.0939166	+	0.0542228i	0.452306	+	0.891863i	$0.350601\pi$
$882$	−42.1454	−	24.3327i	−1.41911	−	0.819324i
$883$	8.27826	+	14.3384i	0.278586	+	0.482525i	0.971034	−	0.238943i	$-0.0768010\pi$
$883$	8.27826	+	14.3384i	0.278586	+	0.482525i	−0.692448	+	0.721468i	$0.743468\pi$
$884$			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	0.366734	−	0.930326i	$-0.380476\pi$
$887$	−7.61197	−	4.39477i	−0.255585	−	0.147562i	−0.622319	+	0.782764i	$0.713809\pi$
$888$	−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	−0.256759	−	0.966476i	$-0.582655\pi$
$907$	13.6082	−	7.85672i	0.451854	−	0.260878i	0.708613	+	0.705597i	$0.249321\pi$
$908$	−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	$0.164791\pi$
$911$			29.8741i			0.989775i	−0.868957	+	0.494887i	$0.835209\pi$
$912$	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	−0.111134	−	0.993805i	$-0.535448\pi$
$919$	−31.1445	−	17.9813i	−1.02736	−	0.593148i	−0.916228	+	0.400658i	$0.868782\pi$
$920$			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	0.183095	+	0.983095i	$0.441388\pi$
$941$	−23.3086	+	40.3716i	−0.759838	+	1.31608i	−0.942933	+	0.332982i	$0.891945\pi$
$942$	−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	−0.763333	−	0.646006i	$-0.776438\pi$
$953$	5.48853	−	9.50641i	0.177791	−	0.307943i	0.941124	+	0.338063i	$0.109772\pi$
$954$	−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	−0.985429	−	0.170088i	$-0.945595\pi$
$971$	−10.7634	+	18.6427i	−0.345413	+	0.598274i	0.640015	+	0.768362i	$0.278928\pi$
$972$	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	0.450329	+	0.892862i	$0.351307\pi$
$977$	−17.1312	+	29.6722i	−0.548077	+	0.949297i	−0.998406	+	0.0564345i	$0.982027\pi$
$978$	−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	−0.745603	−	0.666390i	$-0.767839\pi$
$991$	6.43167	−	11.1400i	0.204309	−	0.353873i	0.949912	+	0.312517i	$0.101172\pi$
$992$	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	−0.418171	−	0.908368i	$-0.637329\pi$
$997$	5.03353	−	2.90611i	0.159414	−	0.0920374i	0.577585	+	0.816331i	$0.303995\pi$
$998$	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.227.20	yes	58
349.123	even	6	inner	349.2.e.a.123.20	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.20	✓	58	349.123	even	6	inner
349.2.e.a.227.20	yes	58	1.1	even	1	trivial

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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