LMFDB - Embedded newform 349.2.e.a.227.17

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			227.17
Character	$\chi$	$=$	349.227
Dual form			349.2.e.a.123.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.499056 + 0.288130i) q^{2} +(-0.844268 - 1.46231i) q^{3} +(-0.833962 - 1.44447i) q^{4} +(0.707762 + 1.22588i) q^{5} -0.973035i q^{6} +(1.68926 + 0.975293i) q^{7} -2.11368i q^{8} +(0.0744233 - 0.128905i) q^{9} +O(q^{10})$	\(q+(0.499056 + 0.288130i) q^{2} +(-0.844268 - 1.46231i) q^{3} +(-0.833962 - 1.44447i) q^{4} +(0.707762 + 1.22588i) q^{5} -0.973035i q^{6} +(1.68926 + 0.975293i) q^{7} -2.11368i q^{8} +(0.0744233 - 0.128905i) q^{9} +0.815710i q^{10} -4.02851i q^{11} +(-1.40818 + 2.43903i) q^{12} +(-2.31456 - 1.33631i) q^{13} +(0.562022 + 0.973451i) q^{14} +(1.19508 - 2.06994i) q^{15} +(-1.05891 + 1.83409i) q^{16} -4.81926 q^{17} +(0.0742827 - 0.0428871i) q^{18} +(-0.128339 - 0.222289i) q^{19} +(1.18049 - 2.04467i) q^{20} -3.29363i q^{21} +(1.16073 - 2.01045i) q^{22} +(4.23068 - 7.32776i) q^{23} +(-3.09086 + 1.78451i) q^{24} +(1.49815 - 2.59486i) q^{25} +(-0.770062 - 1.33379i) q^{26} -5.31694 q^{27} -3.25343i q^{28} +(4.16127 + 7.20752i) q^{29} +(1.19282 - 0.688677i) q^{30} -2.97089 q^{31} +(-4.71791 + 2.72389i) q^{32} +(-5.89095 + 3.40114i) q^{33} +(-2.40508 - 1.38857i) q^{34} +2.76110i q^{35} -0.248265 q^{36} +3.32524 q^{37} -0.147913i q^{38} +4.51281i q^{39} +(2.59111 - 1.49598i) q^{40} +8.59566 q^{41} +(0.948994 - 1.64371i) q^{42} +(5.22416 - 3.01617i) q^{43} +(-5.81904 + 3.35962i) q^{44} +0.210696 q^{45} +(4.22269 - 2.43797i) q^{46} +6.48701i q^{47} +3.57602 q^{48} +(-1.59761 - 2.76714i) q^{49} +(1.49532 - 0.863321i) q^{50} +(4.06874 + 7.04727i) q^{51} +4.45773i q^{52} +13.0872i q^{53} +(-2.65345 - 1.53197i) q^{54} +(4.93847 - 2.85122i) q^{55} +(2.06145 - 3.57054i) q^{56} +(-0.216705 + 0.375344i) q^{57} +4.79594i q^{58} +(1.29504 - 0.747694i) q^{59} -3.98661 q^{60} +5.93283i q^{61} +(-1.48264 - 0.856003i) q^{62} +(0.251440 - 0.145169i) q^{63} +1.09631 q^{64} -3.78316i q^{65} -3.91988 q^{66} +16.0507 q^{67} +(4.01908 + 6.96125i) q^{68} -14.2873 q^{69} +(-0.795556 + 1.37794i) q^{70} +(9.23197 + 5.33008i) q^{71} +(-0.272463 - 0.157307i) q^{72} +(-7.92689 - 13.7298i) q^{73} +(1.65948 + 0.958101i) q^{74} -5.05935 q^{75} +(-0.214060 + 0.370762i) q^{76} +(3.92897 - 6.80518i) q^{77} +(-1.30028 + 2.25215i) q^{78} +12.4810i q^{79} -2.99783 q^{80} +(4.26565 + 7.38833i) q^{81} +(4.28971 + 2.47667i) q^{82} +(2.47290 - 4.28318i) q^{83} +(-4.75754 + 2.74677i) q^{84} +(-3.41089 - 5.90783i) q^{85} +3.47620 q^{86} +(7.02645 - 12.1702i) q^{87} -8.51497 q^{88} +(-8.26544 + 4.77205i) q^{89} +(0.105149 + 0.0607078i) q^{90} +(-2.60659 - 4.51474i) q^{91} -14.1129 q^{92} +(2.50823 + 4.34438i) q^{93} +(-1.86910 + 3.23738i) q^{94} +(0.181667 - 0.314656i) q^{95} +(7.96636 + 4.59938i) q^{96} +(-10.9351 - 6.31338i) q^{97} -1.84127i q^{98} +(-0.519294 - 0.299815i) 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 $

$2$	0.499056	+	0.288130i	0.352886	+	0.203739i	0.665955	−	0.745991i	$-0.268024\pi$
$2$	0.499056	+	0.288130i	0.352886	+	0.203739i	−0.313070	+	0.949730i	$0.601357\pi$
$3$	−0.844268	−	1.46231i	−0.487438	−	0.844268i	0.512457	−	0.858713i	$-0.328735\pi$
$3$	−0.844268	−	1.46231i	−0.487438	−	0.844268i	−0.999896	+	0.0144447i	$0.995402\pi$
$4$	−0.833962	−	1.44447i	−0.416981	−	0.722233i
$5$	0.707762	+	1.22588i	0.316521	+	0.548230i	0.979760	−	0.200178i	$-0.0641520\pi$
$5$	0.707762	+	1.22588i	0.316521	+	0.548230i	−0.663239	+	0.748408i	$0.730819\pi$
$6$		−	0.973035i		−	0.397240i
$7$	1.68926	+	0.975293i	0.638479	+	0.368626i	0.784028	−	0.620725i	$-0.213162\pi$
$7$	1.68926	+	0.975293i	0.638479	+	0.368626i	−0.145549	+	0.989351i	$0.546495\pi$
$8$		−	2.11368i		−	0.747298i
$9$	0.0744233	−	0.128905i	0.0248078	−	0.0429683i
$10$			0.815710i			0.257950i
$11$		−	4.02851i		−	1.21464i	−0.794457	−	0.607320i	$-0.792244\pi$
$11$		−	4.02851i		−	1.21464i	0.794457	−	0.607320i	$-0.207756\pi$
$12$	−1.40818	+	2.43903i	−0.406505	+	0.704088i
$13$	−2.31456	−	1.33631i	−0.641942	−	0.370626i	0.143420	−	0.989662i	$-0.454190\pi$
$13$	−2.31456	−	1.33631i	−0.641942	−	0.370626i	−0.785362	+	0.619036i	$0.787523\pi$
$14$	0.562022	+	0.973451i	0.150207	+	0.260166i
$15$	1.19508	−	2.06994i	0.308569	−	0.534457i
$16$	−1.05891	+	1.83409i	−0.264728	+	0.458522i
$17$	−4.81926			−1.16884			−0.584421	−	0.811451i	$-0.698678\pi$
$17$	−4.81926			−1.16884			−0.584421	+	0.811451i	$0.698678\pi$
$18$	0.0742827	−	0.0428871i	0.0175086	−	0.0101086i
$19$	−0.128339	−	0.222289i	−0.0294430	−	0.0509967i	0.850928	−	0.525282i	$-0.176040\pi$
$19$	−0.128339	−	0.222289i	−0.0294430	−	0.0509967i	−0.880371	+	0.474285i	$0.842707\pi$
$20$	1.18049	−	2.04467i	0.263966	−	0.457203i
$21$		−	3.29363i		−	0.718730i
$22$	1.16073	−	2.01045i	0.247469	−	0.428629i
$23$	4.23068	−	7.32776i	0.882158	−	1.52794i	0.0332215	−	0.999448i	$-0.489423\pi$
$23$	4.23068	−	7.32776i	0.882158	−	1.52794i	0.848937	−	0.528495i	$-0.177243\pi$
$24$	−3.09086	+	1.78451i	−0.630920	+	0.364262i
$25$	1.49815	−	2.59486i	0.299629	−	0.518973i
$26$	−0.770062	−	1.33379i	−0.151022	−	0.261577i
$27$	−5.31694			−1.02325
$28$		−	3.25343i		−	0.614840i
$29$	4.16127	+	7.20752i	0.772728	+	1.33840i	0.936063	+	0.351833i	$0.114442\pi$
$29$	4.16127	+	7.20752i	0.772728	+	1.33840i	−0.163335	+	0.986571i	$0.552225\pi$
$30$	1.19282	−	0.688677i	0.217779	−	0.125735i
$31$	−2.97089			−0.533588			−0.266794	−	0.963754i	$-0.585964\pi$
$31$	−2.97089			−0.533588			−0.266794	+	0.963754i	$0.585964\pi$
$32$	−4.71791	+	2.72389i	−0.834016	+	0.481519i
$33$	−5.89095	+	3.40114i	−1.02548	+	0.592062i
$34$	−2.40508	−	1.38857i	−0.412467	−	0.238138i
$35$			2.76110i			0.466711i
$36$	−0.248265			−0.0413775
$37$	3.32524			0.546666			0.273333	−	0.961919i	$-0.411874\pi$
$37$	3.32524			0.546666			0.273333	+	0.961919i	$0.411874\pi$
$38$		−	0.147913i		−	0.0239947i
$39$			4.51281i			0.722629i
$40$	2.59111	−	1.49598i	0.409691	−	0.236535i
$41$	8.59566			1.34242			0.671208	−	0.741269i	$-0.265776\pi$
$41$	8.59566			1.34242			0.671208	+	0.741269i	$0.265776\pi$
$42$	0.948994	−	1.64371i	0.146433	−	0.253629i
$43$	5.22416	−	3.01617i	0.796677	−	0.459962i	−0.0456307	−	0.998958i	$-0.514530\pi$
$43$	5.22416	−	3.01617i	0.796677	−	0.459962i	0.842308	+	0.538997i	$0.181196\pi$
$44$	−5.81904	+	3.35962i	−0.877253	+	0.506482i
$45$	0.210696			0.0314087
$46$	4.22269	−	2.43797i	0.622602	−	0.359459i
$47$			6.48701i			0.946228i	0.881001	+	0.473114i	$0.156870\pi$
$47$			6.48701i			0.946228i	−0.881001	+	0.473114i	$0.843130\pi$
$48$	3.57602			0.516154
$49$	−1.59761	−	2.76714i	−0.228230	−	0.395305i
$50$	1.49532	−	0.863321i	0.211470	−	0.122092i
$51$	4.06874	+	7.04727i	0.569738	+	0.986816i
$52$			4.45773i			0.618176i
$53$			13.0872i			1.79767i	0.438291	+	0.898833i	$0.355584\pi$
$53$			13.0872i			1.79767i	−0.438291	+	0.898833i	$0.644416\pi$
$54$	−2.65345	−	1.53197i	−0.361089	−	0.208475i
$55$	4.93847	−	2.85122i	0.665903	−	0.384459i
$56$	2.06145	−	3.57054i	0.275473	−	0.477134i
$57$	−0.216705	+	0.375344i	−0.0287032	+	0.0497155i
$58$			4.79594i			0.629738i
$59$	1.29504	−	0.747694i	0.168600	−	0.0973414i	−0.413325	−	0.910583i	$-0.635633\pi$
$59$	1.29504	−	0.747694i	0.168600	−	0.0973414i	0.581926	+	0.813242i	$0.302299\pi$
$60$	−3.98661			−0.514669
$61$			5.93283i			0.759622i	0.925064	+	0.379811i	$0.124011\pi$
$61$			5.93283i			0.759622i	−0.925064	+	0.379811i	$0.875989\pi$
$62$	−1.48264	−	0.856003i	−0.188295	−	0.108712i
$63$	0.251440	−	0.145169i	0.0316785	−	0.0182896i
$64$	1.09631			0.137039
$65$		−	3.78316i		−	0.469243i
$66$	−3.91988			−0.482504
$67$	16.0507			1.96091			0.980454	−	0.196748i	$-0.0630380\pi$
$67$	16.0507			1.96091			0.980454	+	0.196748i	$0.0630380\pi$
$68$	4.01908	+	6.96125i	0.487385	+	0.844175i
$69$	−14.2873			−1.71999
$70$	−0.795556	+	1.37794i	−0.0950871	+	0.164696i
$71$	9.23197	+	5.33008i	1.09563	+	0.632564i	0.935071	−	0.354461i	$-0.115336\pi$
$71$	9.23197	+	5.33008i	1.09563	+	0.632564i	0.160563	+	0.987026i	$0.448669\pi$
$72$	−0.272463	−	0.157307i	−0.0321101	−	0.0185388i
$73$	−7.92689	−	13.7298i	−0.927773	−	1.60695i	−0.787040	−	0.616902i	$-0.788387\pi$
$73$	−7.92689	−	13.7298i	−0.927773	−	1.60695i	−0.140733	−	0.990048i	$-0.544946\pi$
$74$	1.65948	+	0.958101i	0.192911	+	0.111377i
$75$	−5.05935			−0.584203
$76$	−0.214060	+	0.370762i	−0.0245543	+	0.0425293i
$77$	3.92897	−	6.80518i	0.447748	−	0.775523i
$78$	−1.30028	+	2.25215i	−0.147227	+	0.255005i
$79$			12.4810i			1.40422i	0.712068	+	0.702111i	$0.247759\pi$
$79$			12.4810i			1.40422i	−0.712068	+	0.702111i	$0.752241\pi$
$80$	−2.99783			−0.335167
$81$	4.26565	+	7.38833i	0.473961	+	0.820925i
$82$	4.28971	+	2.47667i	0.473720	+	0.273502i
$83$	2.47290	−	4.28318i	0.271436	−	0.470140i	−0.697794	−	0.716298i	$-0.745835\pi$
$83$	2.47290	−	4.28318i	0.271436	−	0.470140i	0.969230	+	0.246158i	$0.0791683\pi$
$84$	−4.75754	+	2.74677i	−0.519090	+	0.299697i
$85$	−3.41089	−	5.90783i	−0.369963	−	0.640794i
$86$	3.47620			0.374848
$87$	7.02645	−	12.1702i	0.753314	−	1.30478i
$88$	−8.51497			−0.907699
$89$	−8.26544	+	4.77205i	−0.876135	+	0.505837i	−0.869382	−	0.494140i	$-0.835483\pi$
$89$	−8.26544	+	4.77205i	−0.876135	+	0.505837i	−0.00675292	+	0.999977i	$0.502150\pi$
$90$	0.105149	+	0.0607078i	0.0110837	+	0.00639916i
$91$	−2.60659	−	4.51474i	−0.273245	−	0.473273i
$92$	−14.1129			−1.47137
$93$	2.50823	+	4.34438i	0.260091	+	0.450491i
$94$	−1.86910	+	3.23738i	−0.192783	+	0.333910i
$95$	0.181667	−	0.314656i	0.0186386	−	0.0322830i
$96$	7.96636	+	4.59938i	0.813063	+	0.469422i
$97$	−10.9351	−	6.31338i	−1.11029	−	0.641027i	−0.171386	−	0.985204i	$-0.554825\pi$
$97$	−10.9351	−	6.31338i	−1.11029	−	0.641027i	−0.938905	+	0.344177i	$0.888158\pi$
$98$		−	1.84127i		−	0.185997i
$99$	−0.519294	−	0.299815i	−0.0521910	−	0.0301325i
$100$	−4.99759			−0.499759
$101$			2.95413i			0.293947i	0.989140	+	0.146974i	$0.0469533\pi$
$101$			2.95413i			0.293947i	−0.989140	+	0.146974i	$0.953047\pi$
$102$			4.68931i			0.464311i
$103$			1.12183i			0.110537i	0.998472	+	0.0552684i	$0.0176014\pi$
$103$			1.12183i			0.110537i	−0.998472	+	0.0552684i	$0.982399\pi$
$104$	−2.82453	+	4.89223i	−0.276968	+	0.479722i
$105$	4.03760	−	2.33111i	0.394029	−	0.227493i
$106$	−3.77082	+	6.53125i	−0.366254	+	0.634371i
$107$	13.8900	+	8.01941i	1.34280	+	0.775265i	0.987217	−	0.159380i	$-0.0509495\pi$
$107$	13.8900	+	8.01941i	1.34280	+	0.775265i	0.355582	+	0.934645i	$0.384283\pi$
$108$	4.43413	+	7.68013i	0.426674	+	0.739021i
$109$	−6.45309	−	11.1771i	−0.618094	−	1.07057i	−0.989833	−	0.142233i	$-0.954572\pi$
$109$	−6.45309	−	11.1771i	−0.618094	−	1.07057i	0.371739	−	0.928337i	$-0.378762\pi$
$110$	3.28609			0.313317
$111$	−2.80739	−	4.86255i	−0.266466	−	0.461533i
$112$	−3.57754	+	2.06550i	−0.338046	+	0.195171i
$113$	−12.6399	−	7.29764i	−1.18906	−	0.686504i	−0.230967	−	0.972962i	$-0.574189\pi$
$113$	−12.6399	−	7.29764i	−1.18906	−	0.686504i	−0.958093	+	0.286458i	$0.907522\pi$
$114$	−0.216295	+	0.124878i	−0.0202579	+	0.0116959i
$115$	11.9773			1.11689
$116$	6.94068	−	12.0216i	0.644426	−	1.11618i
$117$	−0.344514	+	0.198905i	−0.0318503	+	0.0183888i
$118$	0.861732			0.0793288
$119$	−8.14096	−	4.70019i	−0.746281	−	0.430865i
$120$	−4.37519	−	2.52602i	−0.399398	−	0.230593i
$121$	−5.22887			−0.475352
$122$	−1.70943	+	2.96081i	−0.154764	+	0.268060i
$123$	−7.25704	−	12.5696i	−0.654345	−	1.13336i
$124$	2.47761	+	4.29135i	0.222496	+	0.385374i
$125$	11.3189			1.01240
$126$	0.167310			0.0149052
$127$		−	3.59668i		−	0.319153i	−0.987186	−	0.159577i	$-0.948987\pi$
$127$		−	3.59668i		−	0.319153i	0.987186	−	0.159577i	$-0.0510129\pi$
$128$	9.98294	+	5.76365i	0.882375	+	0.509440i
$129$	−8.82119	−	5.09291i	−0.776662	−	0.448406i
$130$	1.09004	−	1.88801i	0.0956029	−	0.165589i
$131$			1.37680i			0.120291i	0.998190	+	0.0601456i	$0.0191565\pi$
$131$			1.37680i			0.120291i	−0.998190	+	0.0601456i	$0.980843\pi$
$132$	9.82566	+	5.67285i	0.855214	+	0.493758i
$133$		−	0.500672i		−	0.0434138i
$134$	8.01021	+	4.62469i	0.691976	+	0.399513i
$135$	−3.76313	−	6.51793i	−0.323879	−	0.560974i
$136$			10.1864i			0.873473i
$137$	−2.07514	+	1.19808i	−0.177291	+	0.102359i	−0.586019	−	0.810297i	$-0.699306\pi$
$137$	−2.07514	+	1.19808i	−0.177291	+	0.102359i	0.408728	+	0.912656i	$0.365972\pi$
$138$	−7.13017	−	4.11660i	−0.606960	−	0.350429i
$139$	2.64865			0.224655			0.112328	−	0.993671i	$-0.464169\pi$
$139$	2.64865			0.224655			0.112328	+	0.993671i	$0.464169\pi$
$140$	3.98831	−	2.30265i	0.337074	−	0.194610i
$141$	9.48605	−	5.47677i	0.798870	−	0.461228i
$142$	3.07151	+	5.32001i	0.257756	+	0.446446i
$143$	−5.38333	+	9.32421i	−0.450177	+	0.779729i
$144$	0.157615	+	0.272998i	0.0131346	+	0.0227498i
$145$	−5.89037	+	10.2024i	−0.489169	+	0.847265i
$146$		−	9.13590i		−	0.756093i
$147$	−2.69762	+	4.67241i	−0.222496	+	0.385374i
$148$	−2.77313	−	4.80319i	−0.227950	−	0.394820i
$149$	11.4168	+	6.59151i	0.935303	+	0.539997i	0.888485	−	0.458906i	$-0.151759\pi$
$149$	11.4168	+	6.59151i	0.935303	+	0.539997i	0.0468180	+	0.998903i	$0.485092\pi$
$150$	−2.52490	−	1.45775i	−0.206157	−	0.119025i
$151$	1.25076	+	2.16638i	0.101785	+	0.176297i	0.912420	−	0.409254i	$-0.134211\pi$
$151$	1.25076	+	2.16638i	0.101785	+	0.176297i	−0.810635	+	0.585552i	$0.800878\pi$
$152$	−0.469848	+	0.271267i	−0.0381097	+	0.0220027i
$153$	−0.358665	+	0.621226i	−0.0289963	+	0.0502231i
$154$	3.92155	−	2.26411i	0.316008	−	0.182447i
$155$	−2.10268	−	3.64195i	−0.168892	−	0.292529i
$156$	6.51860	−	3.76352i	0.521906	−	0.301322i
$157$	2.02878	+	3.51395i	0.161914	+	0.280444i	0.935555	−	0.353180i	$-0.114900\pi$
$157$	2.02878	+	3.51395i	0.161914	+	0.280444i	−0.773641	+	0.633624i	$0.781567\pi$
$158$	−3.59615	+	6.22871i	−0.286094	+	0.495530i
$159$	19.1376	−	11.0491i	1.51771	−	0.876252i
$160$	−6.67831	−	3.85573i	−0.527967	−	0.304822i
$161$	14.2934	−	8.25231i	1.12648	−	0.650373i
$162$			4.91625i			0.386257i
$163$			4.94137i			0.387038i	0.981096	+	0.193519i	$0.0619902\pi$
$163$			4.94137i			0.387038i	−0.981096	+	0.193519i	$0.938010\pi$
$164$	−7.16846	−	12.4161i	−0.559763	−	0.969537i
$165$	−8.33878	−	4.81440i	−0.649173	−	0.374800i
$166$	2.46823	−	1.42503i	0.191571	−	0.110604i
$167$		−	11.8533i		−	0.917236i	−0.888634	−	0.458618i	$-0.848345\pi$
$167$		−	11.8533i		−	0.917236i	0.888634	−	0.458618i	$-0.151655\pi$
$168$	−6.96168			−0.537105
$169$	−2.92855	−	5.07240i	−0.225273	−	0.390185i
$170$		−	3.93111i		−	0.301503i
$171$	−0.0382056			−0.00292165
$172$	−8.71351	−	5.03075i	−0.664399	−	0.383591i
$173$	9.82778	+	5.67407i	0.747192	+	0.431392i	0.824679	−	0.565602i	$-0.191356\pi$
$173$	9.82778	+	5.67407i	0.747192	+	0.431392i	−0.0774862	+	0.996993i	$0.524689\pi$
$174$	7.01318	−	4.04906i	0.531668	−	0.306958i
$175$	5.06151	−	2.92226i	0.382614	−	0.220902i
$176$	7.38864	+	4.26583i	0.556939	+	0.321549i
$177$	−2.18673	−	1.26251i	−0.164364	−	0.0948959i
$178$	−5.49989			−0.412234
$179$			9.79201i			0.731889i	0.930637	+	0.365945i	$0.119254\pi$
$179$			9.79201i			0.731889i	−0.930637	+	0.365945i	$0.880746\pi$
$180$	−0.175712	−	0.304343i	−0.0130968	−	0.0226844i
$181$	7.31572			0.543773			0.271886	−	0.962329i	$-0.412352\pi$
$181$	7.31572			0.543773			0.271886	+	0.962329i	$0.412352\pi$
$182$		−	3.00414i		−	0.222682i
$183$	8.67567	−	5.00890i	0.641324	−	0.370269i
$184$	−15.4885	−	8.94230i	−1.14183	−	0.659235i
$185$	2.35348	+	4.07635i	0.173031	+	0.299699i
$186$			2.89078i			0.211962i
$187$			19.4144i			1.41972i
$188$	9.37026	−	5.40992i	0.683396	−	0.394559i
$189$	−8.98168	−	5.18557i	−0.653321	−	0.377195i
$190$	0.181324	−	0.104687i	0.0131546	−	0.00759481i
$191$	5.34207	−	9.25275i	0.386539	−	0.669505i	−0.605442	−	0.795889i	$-0.707004\pi$
$191$	5.34207	−	9.25275i	0.386539	−	0.669505i	0.991981	+	0.126384i	$0.0403371\pi$
$192$	−0.925581	−	1.60315i	−0.0667981	−	0.115698i
$193$	−11.4598	+	6.61631i	−0.824894	+	0.476253i	−0.852101	−	0.523377i	$-0.824672\pi$
$193$	−11.4598	+	6.61631i	−0.824894	+	0.476253i	0.0272073	+	0.999630i	$0.491339\pi$
$194$	−3.63815	−	6.30146i	−0.261204	−	0.452418i
$195$	−5.53217	+	3.19400i	−0.396167	+	0.228727i
$196$	−2.66469	+	4.61538i	−0.190335	+	0.329670i
$197$	−11.8354	+	6.83315i	−0.843234	+	0.486841i	−0.858362	−	0.513044i	$-0.828518\pi$
$197$	−11.8354	+	6.83315i	−0.843234	+	0.486841i	0.0151281	+	0.999886i	$0.495184\pi$
$198$	−0.172771	−	0.299248i	−0.0122783	−	0.0212667i
$199$	7.35407	+	4.24587i	0.521316	+	0.300982i	0.737473	−	0.675377i	$-0.236019\pi$
$199$	7.35407	+	4.24587i	0.521316	+	0.300982i	−0.216157	+	0.976359i	$0.569352\pi$
$200$	−5.48471	−	3.16660i	−0.387827	−	0.223912i
$201$	−13.5511	−	23.4712i	−0.955822	−	1.65553i
$202$	−0.851174	+	1.47428i	−0.0598884	+	0.103730i
$203$			16.2338i			1.13939i
$204$	6.78636	−	11.7543i	0.475140	−	0.822967i
$205$	6.08368	+	10.5372i	0.424903	+	0.735953i
$206$	−0.323231	+	0.559853i	−0.0225206	+	0.0390068i
$207$	−0.629722	−	1.09071i	−0.0437687	−	0.0758097i
$208$	4.90182	−	2.83007i	0.339880	−	0.196230i
$209$	−0.895495	+	0.517014i	−0.0619427	+	0.0357626i
$210$	2.68665			0.185396
$211$	−16.0097	−	9.24319i	−1.10215	−	0.636327i	−0.165366	−	0.986232i	$-0.552881\pi$
$211$	−16.0097	−	9.24319i	−1.10215	−	0.636327i	−0.936785	+	0.349905i	$0.886214\pi$
$212$	18.9040	−	10.9142i	1.29833	−	0.749593i
$213$		−	18.0001i		−	1.23334i
$214$	4.62126	+	8.00426i	0.315903	+	0.547160i
$215$	7.39493	+	4.26946i	0.504330	+	0.291175i
$216$			11.2383i			0.764669i
$217$	−5.01860	−	2.89749i	−0.340685	−	0.196694i
$218$		−	7.43732i		−	0.503719i
$219$	−13.3848	+	23.1832i	−0.904464	+	1.56658i
$220$	−8.23699	−	4.75563i	−0.555338	−	0.320624i
$221$	11.1544	+	6.44002i	0.750329	+	0.433203i
$222$		−	3.23558i		−	0.217158i
$223$	−20.7005			−1.38621			−0.693103	−	0.720838i	$-0.743757\pi$
$223$	−20.7005			−1.38621			−0.693103	+	0.720838i	$0.743757\pi$
$224$	−10.6263			−0.710002
$225$	−0.222994	−	0.386237i	−0.0148663	−	0.0257491i
$226$	−4.20534	−	7.28385i	−0.279735	−	0.484515i
$227$	10.7133	−	18.5559i	0.711063	−	1.23160i	−0.253395	−	0.967363i	$-0.581547\pi$
$227$	10.7133	−	18.5559i	0.711063	−	1.23160i	0.964458	−	0.264235i	$-0.0851195\pi$
$228$	0.722894			0.0478749
$229$	−1.48595	−	0.857915i	−0.0981945	−	0.0566926i	0.450099	−	0.892979i	$-0.351389\pi$
$229$	−1.48595	−	0.857915i	−0.0981945	−	0.0566926i	−0.548293	+	0.836286i	$0.684722\pi$
$230$	5.97732	+	3.45101i	0.394133	+	0.227553i
$231$	−13.2684			−0.872999
$232$	15.2344	−	8.79558i	1.00019	−	0.577458i
$233$	−4.87292	+	8.44015i	−0.319236	+	0.552932i	−0.980329	−	0.197372i	$-0.936759\pi$
$233$	−4.87292	+	8.44015i	−0.319236	+	0.552932i	0.661093	+	0.750304i	$0.270093\pi$
$234$	−0.229242			−0.0149860
$235$	−7.95229	+	4.59126i	−0.518750	+	0.299501i
$236$	−2.16003	−	1.24710i	−0.140606	−	0.0811791i
$237$	18.2511	−	10.5373i	1.18554	−	0.684472i
$238$	−2.70853	−	4.69131i	−0.175568	−	0.304092i
$239$	11.6262			0.752033			0.376017	−	0.926613i	$-0.377294\pi$
$239$	11.6262			0.752033			0.376017	+	0.926613i	$0.377294\pi$
$240$	2.53097	+	4.38377i	0.163373	+	0.282971i
$241$	6.62998	+	11.4835i	0.427075	+	0.739715i	0.996612	−	0.0822508i	$-0.0262109\pi$
$241$	6.62998	+	11.4835i	0.427075	+	0.739715i	−0.569537	+	0.821966i	$0.692878\pi$
$242$	−2.60950	−	1.50660i	−0.167745	−	0.0968476i
$243$	−0.772703	+	1.33836i	−0.0495689	+	0.0858559i
$244$	8.56977	−	4.94776i	0.548623	−	0.316748i
$245$	2.26145	−	3.91695i	0.144479	−	0.250245i
$246$		−	8.36388i		−	0.533262i
$247$			0.686002i			0.0436493i
$248$			6.27951i			0.398749i
$249$	−8.35115			−0.529232
$250$	5.64878	+	3.26133i	0.357260	+	0.206264i
$251$		−	13.3054i		−	0.839827i	−0.907564	−	0.419913i	$-0.862060\pi$
$251$		−	13.3054i		−	0.839827i	0.907564	−	0.419913i	$-0.137940\pi$
$252$	−0.419383	−	0.242131i	−0.0264186	−	0.0152528i
$253$	−29.5199	−	17.0433i	−1.85590	−	1.07151i
$254$	1.03631	−	1.79494i	0.0650239	−	0.112625i
$255$	−5.75941	+	9.97558i	−0.360668	+	0.624695i
$256$	2.22505	+	3.85390i	0.139066	+	0.240869i
$257$	−20.3861			−1.27165			−0.635824	−	0.771834i	$-0.719340\pi$
$257$	−20.3861			−1.27165			−0.635824	+	0.771834i	$0.719340\pi$
$258$	−2.93484	−	5.08329i	−0.182715	−	0.316472i
$259$	5.61719	+	3.24308i	0.349035	+	0.201515i
$260$	−5.46464	+	3.15501i	−0.338902	+	0.195665i
$261$	1.23878			0.0766786
$262$	−0.396696	+	0.687098i	−0.0245080	+	0.0424491i
$263$	−2.81765			−0.173744			−0.0868718	−	0.996220i	$-0.527687\pi$
$263$	−2.81765			−0.173744			−0.0868718	+	0.996220i	$0.527687\pi$
$264$	7.18891	+	12.4516i	0.442447	+	0.766341i
$265$	−16.0433	+	9.26263i	−0.985535	+	0.568999i
$266$	0.144259	−	0.249863i	0.00884506	−	0.0153201i
$267$	13.9565	+	8.05779i	0.854124	+	0.493128i
$268$	−13.3857	−	23.1847i	−0.817662	−	1.41623i
$269$	27.4597			1.67425			0.837123	−	0.547014i	$-0.184236\pi$
$269$	27.4597			1.67425			0.837123	+	0.547014i	$0.184236\pi$
$270$		−	4.33708i		−	0.263946i
$271$	1.89034	−	3.27416i	0.114830	−	0.198891i	−0.802882	−	0.596138i	$-0.796701\pi$
$271$	1.89034	−	3.27416i	0.114830	−	0.198891i	0.917712	+	0.397247i	$0.130034\pi$
$272$	5.10316	−	8.83894i	0.309425	−	0.535939i
$273$	−4.40132	+	7.62330i	−0.266380	+	0.461383i
$274$	−1.38081			−0.0834180
$275$	−10.4534	−	6.03529i	−0.630366	−	0.363942i
$276$	11.9151	+	20.6375i	0.717204	+	1.24223i
$277$	−14.3536	−	8.28705i	−0.862423	−	0.497920i	0.00239964	−	0.999997i	$-0.499236\pi$
$277$	−14.3536	−	8.28705i	−0.862423	−	0.497920i	−0.864823	+	0.502077i	$0.832570\pi$
$278$	1.32182	+	0.763154i	0.0792776	+	0.0457709i
$279$	−0.221103	+	0.382962i	−0.0132371	+	0.0229274i
$280$	5.83608			0.348772
$281$	12.5280	+	21.6990i	0.747355	+	1.29446i	0.949086	+	0.315016i	$0.102010\pi$
$281$	12.5280	+	21.6990i	0.747355	+	1.29446i	−0.201732	+	0.979441i	$0.564657\pi$
$282$	6.31209			0.375879
$283$	12.3301			0.732947			0.366473	−	0.930428i	$-0.380565\pi$
$283$	12.3301			0.732947			0.366473	+	0.930428i	$0.380565\pi$
$284$		−	17.7803i		−	1.05507i
$285$	−0.613502			−0.0363407
$286$	−5.37317	+	3.10220i	−0.317722	+	0.183437i
$287$	14.5203	+	8.38329i	0.857105	+	0.494850i
$288$			0.810882i			0.0477817i
$289$	6.22524			0.366191
$290$	−5.87925	+	3.39438i	−0.345241	+	0.199325i
$291$			21.3207i			1.24984i
$292$	−13.2215	+	22.9002i	−0.773728	+	1.34014i
$293$	−12.9886	+	22.4970i	−0.758803	+	1.31429i	0.184658	+	0.982803i	$0.440882\pi$
$293$	−12.9886	+	22.4970i	−0.758803	+	1.31429i	−0.943461	+	0.331483i	$0.892451\pi$
$294$	−2.69252	+	1.55453i	−0.157031	+	0.0906620i
$295$	1.83316	+	1.05838i	0.106731	+	0.0616212i
$296$		−	7.02849i		−	0.408523i
$297$			21.4193i			1.24288i
$298$	3.79842	+	6.57906i	0.220037	+	0.381115i
$299$	−19.5843	+	11.3070i	−1.13259	+	0.653901i
$300$	4.21930	+	7.30805i	0.243602	+	0.421930i
$301$	11.7666			0.678216
$302$			1.44153i			0.0829505i
$303$	4.31987	−	2.49408i	0.248170	−	0.143281i
$304$	0.543598			0.0311775
$305$	−7.27294	+	4.19903i	−0.416447	+	0.240436i
$306$	−0.357988	+	0.206684i	−0.0204648	+	0.0118153i
$307$	12.6705	−	21.9459i	0.723142	−	1.25252i	−0.236592	−	0.971609i	$-0.576030\pi$
$307$	12.6705	−	21.9459i	0.723142	−	1.25252i	0.959734	−	0.280910i	$-0.0906362\pi$
$308$	−13.1065			−0.746810
$309$	1.64046	−	0.947121i	0.0933226	−	0.0538798i
$310$		−	2.42338i		−	0.137639i
$311$			9.19891i			0.521622i	0.965390	+	0.260811i	$0.0839900\pi$
$311$			9.19891i			0.521622i	−0.965390	+	0.260811i	$0.916010\pi$
$312$	9.53863			0.540019
$313$	−4.53967			−0.256597			−0.128299	−	0.991736i	$-0.540952\pi$
$313$	−4.53967			−0.256597			−0.128299	+	0.991736i	$0.540952\pi$
$314$			2.33821i			0.131953i
$315$	0.355919	+	0.205490i	0.0200538	+	0.0115781i
$316$	18.0284	−	10.4087i	1.01417	−	0.585534i
$317$	−15.6334	+	9.02593i	−0.878057	+	0.506947i	−0.870017	−	0.493021i	$-0.835893\pi$
$317$	−15.6334	+	9.02593i	−0.878057	+	0.506947i	−0.00803990	+	0.999968i	$0.502559\pi$
$318$	12.7343			0.714105
$319$	29.0356	−	16.7637i	1.62568	−	0.938587i
$320$	0.775928	+	1.34395i	0.0433757	+	0.0751289i
$321$		−	27.0821i		−	1.51158i
$322$	9.51095			0.530024
$323$	0.618498	+	1.07127i	0.0344141	+	0.0596071i
$324$	7.11479	−	12.3232i	0.395266	−	0.684621i
$325$	−6.93509	+	4.00397i	−0.384689	+	0.222101i
$326$	−1.42376	+	2.46602i	−0.0788546	+	0.136580i
$327$	−10.8963	+	18.8729i	−0.602566	+	1.04367i
$328$		−	18.1685i		−	1.00319i
$329$	−6.32673	+	10.9582i	−0.348804	+	0.604146i
$330$	−2.77434	−	4.80530i	−0.152723	−	0.264523i
$331$	8.32482	−	4.80634i	0.457574	−	0.264180i	−0.253450	−	0.967349i	$-0.581565\pi$
$331$	8.32482	−	4.80634i	0.457574	−	0.264180i	0.711023	+	0.703168i	$0.248232\pi$
$332$	−8.24921			−0.452734
$333$	0.247475	−	0.428640i	0.0135616	−	0.0234893i
$334$	3.41529	−	5.91545i	0.186876	−	0.323679i
$335$	11.3601	+	19.6763i	0.620668	+	1.07503i
$336$	6.04081	+	3.48766i	0.329553	+	0.190268i
$337$	5.84682	−	10.1270i	0.318497	−	0.551652i	−0.661678	−	0.749788i	$-0.730155\pi$
$337$	5.84682	−	10.1270i	0.318497	−	0.551652i	0.980175	+	0.198136i	$0.0634888\pi$
$338$		−	3.37521i		−	0.183587i
$339$			24.6446i			1.33851i
$340$	−5.68910	+	9.85382i	−0.308535	+	0.534398i
$341$			11.9683i			0.648117i
$342$	−0.0190667	−	0.0110082i	−0.00103101	−	0.000595254i
$343$		−	19.8866i		−	1.07378i
$344$	−6.37521	−	11.0422i	−0.343729	−	0.595355i
$345$	−10.1120	−	17.5145i	−0.544413	−	0.942951i
$346$	3.26974	+	5.66336i	0.175782	+	0.304464i
$347$	−9.41790	−	5.43743i	−0.505579	−	0.291896i	0.225435	−	0.974258i	$-0.427620\pi$
$347$	−9.41790	−	5.43743i	−0.505579	−	0.291896i	−0.731015	+	0.682362i	$0.760953\pi$
$348$	−23.4392			−1.25647
$349$	−17.8224	+	5.60021i	−0.954011	+	0.299772i
$349$	−17.8224	+	5.60021i	−0.954011	+	0.299772i
$350$	3.36796			0.180025
$351$	12.3064	+	7.10508i	0.656865	+	0.379241i
$352$	10.9732	+	19.0061i	0.584873	+	1.01303i
$353$	4.82782	+	8.36204i	0.256959	+	0.445066i	0.965426	−	0.260678i	$-0.0839461\pi$
$353$	4.82782	+	8.36204i	0.256959	+	0.445066i	−0.708467	+	0.705744i	$0.750613\pi$
$354$	−0.727532	−	1.26012i	−0.0386679	−	0.0669748i
$355$			15.0897i			0.800879i
$356$	13.7861	+	7.95943i	0.730664	+	0.421849i
$357$			15.8729i			0.840081i
$358$	−2.82137	+	4.88676i	−0.149114	+	0.258273i
$359$			9.93353i			0.524272i	0.965031	+	0.262136i	$0.0844268\pi$
$359$			9.93353i			0.524272i	−0.965031	+	0.262136i	$0.915573\pi$
$360$		−	0.445343i		−	0.0234716i
$361$	9.46706	−	16.3974i	0.498266	−	0.863022i
$362$	3.65095	+	2.10788i	0.191890	+	0.110788i
$363$	4.41457	+	7.64626i	0.231705	+	0.401325i
$364$	−4.34759	+	7.53025i	−0.227876	+	0.394692i
$365$	11.2207	−	19.4348i	0.587319	−	1.01727i
$366$	5.77286			0.301752
$367$	−31.9069	+	18.4215i	−1.66553	+	0.961593i	−0.695524	+	0.718503i	$0.744828\pi$
$367$	−31.9069	+	18.4215i	−1.66553	+	0.961593i	−0.970004	+	0.243090i	$0.921839\pi$
$368$	8.95983	+	15.5189i	0.467063	+	0.808978i
$369$	0.639717	−	1.10802i	0.0333024	−	0.0576814i
$370$			2.71243i			0.141013i
$371$	−12.7639	+	22.1077i	−0.662667	+	1.14777i
$372$	4.18354	−	7.24610i	0.216906	−	0.375693i
$373$	15.2388	−	8.79812i	0.789035	−	0.455549i	−0.0505880	−	0.998720i	$-0.516110\pi$
$373$	15.2388	−	8.79812i	0.789035	−	0.455549i	0.839623	+	0.543170i	$0.182776\pi$
$374$	−5.59387	+	9.68887i	−0.289252	+	0.501000i
$375$	−9.55622	−	16.5519i	−0.493481	−	0.854734i
$376$	13.7114			0.707114
$377$		−	22.2430i		−	1.14557i
$378$	−2.98824	−	5.17578i	−0.153698	−	0.266213i
$379$	−5.62025	+	3.24485i	−0.288693	+	0.166677i	−0.637352	−	0.770573i	$-0.719970\pi$
$379$	−5.62025	+	3.24485i	−0.288693	+	0.166677i	0.348659	+	0.937250i	$0.386637\pi$
$380$	−0.606013			−0.0310878
$381$	−5.25947	+	3.03656i	−0.269451	+	0.155568i
$382$	5.33199	−	3.07842i	0.272808	−	0.157506i
$383$	−26.3436	−	15.2095i	−1.34609	−	0.777168i	−0.358401	−	0.933568i	$-0.616678\pi$
$383$	−26.3436	−	15.2095i	−1.34609	−	0.777168i	−0.987694	+	0.156400i	$0.950011\pi$
$384$		−	19.4643i		−	0.993282i
$385$	11.1231			0.566886
$386$	−7.62543			−0.388124
$387$		−	0.897893i		−	0.0456425i
$388$			21.0605i			1.06918i
$389$	7.38536	−	4.26394i	0.374453	−	0.216190i	−0.300949	−	0.953640i	$-0.597303\pi$
$389$	7.38536	−	4.26394i	0.374453	−	0.216190i	0.675402	+	0.737450i	$0.263970\pi$
$390$	−3.68115			−0.186402
$391$	−20.3887	+	35.3143i	−1.03110	+	1.78592i
$392$	−5.84884	+	3.37683i	−0.295411	+	0.170556i
$393$	2.01331	−	1.16238i	0.101558	−	0.0586346i
$394$	−7.87533			−0.396754
$395$	−15.3002	+	8.83357i	−0.769837	+	0.444465i
$396$			1.00014i			0.0502588i
$397$	−3.60957			−0.181159			−0.0905796	−	0.995889i	$-0.528872\pi$
$397$	−3.60957			−0.181159			−0.0905796	+	0.995889i	$0.528872\pi$
$398$	2.44673	+	4.23785i	0.122643	+	0.212424i
$399$	−0.732140	+	0.422701i	−0.0366528	+	0.0211615i
$400$	3.17281	+	5.49546i	0.158640	+	0.274773i
$401$		−	18.3471i		−	0.916209i	−0.888898	−	0.458104i	$-0.848529\pi$
$401$		−	18.3471i		−	0.916209i	0.888898	−	0.458104i	$-0.151471\pi$
$402$		−	15.6179i		−	0.778951i
$403$	6.87629	+	3.97003i	0.342533	+	0.197761i
$404$	4.26714	−	2.46364i	0.212298	−	0.122570i
$405$	−6.03813	+	10.4584i	−0.300037	+	0.519680i
$406$	−4.67745	+	8.10158i	−0.232138	+	0.402074i
$407$		−	13.3958i		−	0.664003i
$408$	14.8957	−	8.60001i	0.737445	−	0.425764i
$409$	10.2445			0.506558			0.253279	−	0.967393i	$-0.418491\pi$
$409$	10.2445			0.506558			0.253279	+	0.967393i	$0.418491\pi$
$410$			7.01156i			0.346276i
$411$	3.50395	+	2.02301i	0.172837	+	0.0997875i
$412$	1.62044	−	0.935560i	0.0798332	−	0.0460917i
$413$	2.91688			0.143530
$414$		−	0.725767i		−	0.0356695i
$415$	7.00089			0.343660
$416$	14.5598			0.713854
$417$	−2.23617	−	3.87315i	−0.109506	−	0.189669i
$418$	−0.595869			−0.0291449
$419$	−4.46258	+	7.72942i	−0.218012	+	0.377607i	−0.954200	−	0.299170i	$-0.903290\pi$
$419$	−4.46258	+	7.72942i	−0.218012	+	0.377607i	0.736188	+	0.676777i	$0.236624\pi$
$420$	−6.73441	−	3.88811i	−0.328606	−	0.189721i
$421$	16.0408	+	9.26119i	0.781783	+	0.451363i	0.837062	−	0.547108i	$-0.184271\pi$
$421$	16.0408	+	9.26119i	0.781783	+	0.451363i	−0.0552788	+	0.998471i	$0.517605\pi$
$422$	−5.32648	−	9.22573i	−0.259289	−	0.449102i
$423$	0.836207	+	0.482785i	0.0406578	+	0.0234738i
$424$	27.6621			1.34339
$425$	−7.21995	+	12.5053i	−0.350219	+	0.606597i
$426$	5.18636	−	8.98304i	0.251280	−	0.435229i
$427$	−5.78625	+	10.0221i	−0.280016	+	0.485002i
$428$		−	26.7515i		−	1.29308i
$429$	18.1799			0.877734
$430$	2.46032	+	4.26140i	0.118647	+	0.205503i
$431$	17.0111	+	9.82134i	0.819394	+	0.473077i	0.850207	−	0.526448i	$-0.176477\pi$
$431$	17.0111	+	9.82134i	0.819394	+	0.473077i	−0.0308137	+	0.999525i	$0.509810\pi$
$432$	5.63017	−	9.75173i	0.270881	−	0.469180i
$433$	30.2573	−	17.4691i	1.45407	−	0.839509i	0.455364	−	0.890305i	$-0.349509\pi$
$433$	30.2573	−	17.4691i	1.45407	−	0.839509i	0.998709	+	0.0507960i	$0.0161758\pi$
$434$	−1.66971	−	2.89202i	−0.0801485	−	0.138821i
$435$	19.8922			0.953758
$436$	−10.7633	+	18.6425i	−0.515467	+	0.892816i
$437$	−2.17184			−0.103893
$438$	−13.3596	+	7.71315i	−0.638345	+	0.368549i
$439$	6.36277	+	3.67355i	0.303679	+	0.175329i	0.644094	−	0.764946i	$-0.277234\pi$
$439$	6.36277	+	3.67355i	0.303679	+	0.175329i	−0.340416	+	0.940275i	$0.610568\pi$
$440$	−6.02657	−	10.4383i	−0.287305	−	0.497628i
$441$	−0.475597			−0.0226475
$442$	3.71113	+	6.42786i	0.176520	+	0.305742i
$443$	9.44486	−	16.3590i	0.448739	−	0.777239i	−0.549565	−	0.835451i	$-0.685207\pi$
$443$	9.44486	−	16.3590i	0.448739	−	0.777239i	0.998304	+	0.0582122i	$0.0185400\pi$
$444$	−4.68252	+	8.11037i	−0.222223	+	0.384901i
$445$	−11.6999	−	6.75496i	−0.554630	−	0.320216i
$446$	−10.3307	−	5.96443i	−0.489172	−	0.282424i
$447$		−	22.2600i		−	1.05286i
$448$	1.85195	+	1.06923i	0.0874965	+	0.0505161i
$449$	−9.26949			−0.437454			−0.218727	−	0.975786i	$-0.570190\pi$
$449$	−9.26949			−0.437454			−0.218727	+	0.975786i	$0.570190\pi$
$450$		−	0.257005i		−	0.0121153i
$451$		−	34.6277i		−	1.63055i
$452$			24.3438i			1.14504i
$453$	2.11195	−	3.65801i	0.0992282	−	0.171868i
$454$	10.6930	−	6.17362i	0.501848	−	0.289742i
$455$	3.68969	−	6.39072i	0.172975	−	0.299602i
$456$	0.793355	+	0.458044i	0.0371523	+	0.0214499i
$457$	−0.445695	−	0.771966i	−0.0208487	−	0.0361111i	0.855413	−	0.517947i	$-0.173304\pi$
$457$	−0.445695	−	0.771966i	−0.0208487	−	0.0361111i	−0.876262	+	0.481836i	$0.839970\pi$
$458$	−0.494382	−	0.856295i	−0.0231010	−	0.0400120i
$459$	25.6237			1.19601
$460$	−9.98859	−	17.3007i	−0.465720	−	0.806651i
$461$	−22.3995	+	12.9323i	−1.04325	+	0.602319i	−0.920751	−	0.390150i	$-0.872423\pi$
$461$	−22.3995	+	12.9323i	−1.04325	+	0.602319i	−0.122496	+	0.992469i	$0.539090\pi$
$462$	−6.62169	−	3.82303i	−0.308069	−	0.177864i
$463$	−21.7375	+	12.5501i	−1.01023	+	0.583254i	−0.911258	−	0.411837i	$-0.864887\pi$
$463$	−21.7375	+	12.5501i	−1.01023	+	0.583254i	−0.0989675	+	0.995091i	$0.531554\pi$
$464$	−17.6256			−0.818250
$465$	−3.55046	+	6.14957i	−0.164648	+	0.285180i
$466$	−4.86372	+	2.80807i	−0.225307	+	0.130081i
$467$	0.452095			0.0209204			0.0104602	−	0.999945i	$-0.496670\pi$
$467$	0.452095			0.0209204			0.0104602	+	0.999945i	$0.496670\pi$
$468$	0.574623	+	0.331759i	0.0265620	+	0.0153356i
$469$	27.1138	+	15.6542i	1.25200	+	0.722842i
$470$	−5.29152			−0.244079
$471$	3.42567	−	5.93343i	0.157847	−	0.273398i
$472$	−1.58038	−	2.73730i	−0.0727430	−	0.125995i
$473$	−12.1507	−	21.0456i	−0.558688	−	0.967677i
$474$	12.1445			0.557813
$475$	−0.769081			−0.0352879
$476$			15.6791i			0.718651i
$477$	1.68701	+	0.973993i	0.0772427	+	0.0445961i
$478$	5.80210	+	3.34984i	0.265382	+	0.153218i
$479$	2.09749	−	3.63296i	0.0958368	−	0.165994i	−0.814121	−	0.580696i	$-0.802781\pi$
$479$	2.09749	−	3.63296i	0.0958368	−	0.165994i	0.909958	+	0.414701i	$0.136114\pi$
$480$			13.0211i			0.594327i
$481$	−7.69646	−	4.44355i	−0.350928	−	0.202609i
$482$			7.64118i			0.348046i
$483$	−24.1349	−	13.9343i	−1.09818	−	0.634033i
$484$	4.36068	+	7.55293i	0.198213	+	0.343315i
$485$		−	17.8735i		−	0.811593i
$486$	−0.771244	+	0.445278i	−0.0349843	+	0.0201982i
$487$	−26.2925	−	15.1800i	−1.19143	−	0.687872i	−0.232798	−	0.972525i	$-0.574788\pi$
$487$	−26.2925	−	15.1800i	−1.19143	−	0.687872i	−0.958631	+	0.284653i	$0.908122\pi$
$488$	12.5401			0.567664
$489$	7.22585	−	4.17184i	0.326764	−	0.188657i
$490$	2.25718	−	1.30318i	0.101969	−	0.0588718i
$491$	−0.349992	−	0.606203i	−0.0157949	−	0.0273576i	0.858020	−	0.513616i	$-0.171695\pi$
$491$	−0.349992	−	0.606203i	−0.0157949	−	0.0273576i	−0.873815	+	0.486259i	$0.838361\pi$
$492$	−12.1042	+	20.9651i	−0.545699	+	0.945179i
$493$	−20.0542	−	34.7349i	−0.903196	−	1.56438i
$494$	−0.197658	+	0.342353i	−0.00889304	+	0.0154032i
$495$		−	0.848790i		−	0.0381503i
$496$	3.14591	−	5.44887i	0.141255	−	0.244662i
$497$	10.3968	+	18.0078i	0.466359	+	0.807758i
$498$	−4.16769	−	2.40622i	−0.186759	−	0.107825i
$499$	−34.1555	−	19.7197i	−1.52901	−	0.882774i	−0.999404	−	0.0345293i	$-0.989007\pi$
$499$	−34.1555	−	19.7197i	−1.52901	−	0.882774i	−0.529605	−	0.848244i	$-0.677660\pi$
$500$	−9.43957	−	16.3498i	−0.422150	−	0.731186i
$501$	−17.3333	+	10.0074i	−0.774393	+	0.447096i
$502$	3.83367	−	6.64012i	0.171105	−	0.296363i
$503$	17.5955	−	10.1587i	0.784542	−	0.452956i	−0.0534953	−	0.998568i	$-0.517036\pi$
$503$	17.5955	−	10.1587i	0.784542	−	0.452956i	0.838038	+	0.545612i	$0.183703\pi$
$504$	−0.306840	−	0.531463i	−0.0136678	−	0.0236733i
$505$	−3.62141	+	2.09082i	−0.161151	+	0.0930404i
$506$	−9.82139	−	17.0111i	−0.436614	−	0.756238i
$507$	−4.94497	+	8.56493i	−0.219614	+	0.380382i
$508$	−5.19527	+	2.99949i	−0.230503	+	0.133081i
$509$	−15.9740	−	9.22261i	−0.708037	−	0.408785i	0.102297	−	0.994754i	$-0.467381\pi$
$509$	−15.9740	−	9.22261i	−0.708037	−	0.408785i	−0.810334	+	0.585969i	$0.800714\pi$
$510$	−5.74853	+	3.31891i	−0.254549	+	0.146964i
$511$		−	30.9242i		−	1.36800i
$512$		−	20.4902i		−	0.905547i
$513$	0.682370	+	1.18190i	0.0301274	+	0.0521821i
$514$	−10.1738	−	5.87384i	−0.448747	−	0.259084i
$515$	−1.37522	+	0.793985i	−0.0605996	+	0.0349872i
$516$			16.9892i			0.747907i
$517$	26.1330			1.14933
$518$	1.86886	+	3.23696i	0.0821129	+	0.142224i
$519$		−	19.1617i		−	0.841107i
$520$	−7.99637			−0.350664
$521$	−12.6823	−	7.32212i	−0.555621	−	0.320788i	0.195765	−	0.980651i	$-0.437281\pi$
$521$	−12.6823	−	7.32212i	−0.555621	−	0.320788i	−0.751386	+	0.659863i	$0.770614\pi$
$522$	0.618220	+	0.356930i	0.0270588	+	0.0156224i
$523$	−24.9662	+	14.4143i	−1.09170	+	0.630292i	−0.934028	−	0.357200i	$-0.883731\pi$
$523$	−24.9662	+	14.4143i	−1.09170	+	0.630292i	−0.157669	+	0.987492i	$0.550398\pi$
$524$	1.98873	−	1.14820i	0.0868783	−	0.0501592i
$525$	−8.54654	−	4.93434i	−0.373001	−	0.215352i
$526$	−1.40616	−	0.811848i	−0.0613116	−	0.0353983i
$527$	14.3175			0.623680
$528$		−	14.4060i		−	0.626941i
$529$	−24.2973	−	42.0842i	−1.05641	−	1.82975i
$530$	−10.6754			−0.463708
$531$		−	0.222583i		−	0.00965929i
$532$	−0.723203	+	0.417541i	−0.0313548	+	0.0181027i
$533$	−19.8951	−	11.4865i	−0.861754	−	0.497534i
$534$	4.64338	+	8.04257i	0.200939	+	0.348036i
$535$			22.7033i			0.981550i
$536$		−	33.9261i		−	1.46538i
$537$	14.3190	−	8.26708i	0.617911	−	0.356751i
$538$	13.7039	+	7.91196i	0.590818	+	0.341109i
$539$	−11.1474	+	6.43598i	−0.480154	+	0.277217i
$540$	−6.27661	+	10.8714i	−0.270102	+	0.467831i
$541$	11.2969	+	19.5668i	0.485692	+	0.841243i	0.999865	−	0.0164433i	$-0.00523431\pi$
$541$	11.2969	+	19.5668i	0.485692	+	0.841243i	−0.514173	+	0.857687i	$0.671901\pi$
$542$	1.88677	−	1.08933i	0.0810436	−	0.0467905i
$543$	−6.17642	−	10.6979i	−0.265056	−	0.459090i
$544$	22.7368	−	13.1271i	0.974833	−	0.562820i
$545$	9.13451	−	15.8214i	0.391279	−	0.677716i
$546$	−4.39300	+	2.53630i	−0.188003	+	0.108544i
$547$	5.38583	+	9.32852i	0.230281	+	0.398859i	0.957891	−	0.287133i	$-0.0927020\pi$
$547$	5.38583	+	9.32852i	0.230281	+	0.398859i	−0.727610	+	0.685991i	$0.759369\pi$
$548$	3.46118	+	1.99831i	0.147854	+	0.0853637i
$549$	0.764771	+	0.441541i	0.0326396	+	0.0188445i
$550$	−3.47790	−	6.02389i	−0.148298	−	0.256860i
$551$	1.06810	−	1.85001i	0.0455028	−	0.0788131i
$552$			30.1988i			1.28535i
$553$	−12.1726	+	21.0836i	−0.517633	+	0.896566i
$554$	−4.77549	−	8.27140i	−0.202891	−	0.351418i
$555$	3.97393	−	6.88306i	0.168684	−	0.292169i
$556$	−2.20887	−	3.82588i	−0.0936770	−	0.162253i
$557$	−2.58753	+	1.49391i	−0.109637	+	0.0632991i	−0.553816	−	0.832639i	$-0.686829\pi$
$557$	−2.58753	+	1.49391i	−0.109637	+	0.0632991i	0.444179	+	0.895938i	$0.353496\pi$
$558$	−0.220686	+	0.127413i	−0.00934238	+	0.00539382i
$559$	−16.1222			−0.681895
$560$	−5.06410	−	2.92376i	−0.213997	−	0.123551i
$561$	28.3900	−	16.3910i	1.19863	−	0.692027i
$562$			14.4387i			0.609060i
$563$	−1.79031	−	3.10092i	−0.0754528	−	0.130688i	0.825830	−	0.563919i	$-0.190707\pi$
$563$	−1.79031	−	3.10092i	−0.0754528	−	0.130688i	−0.901283	+	0.433231i	$0.857374\pi$
$564$	−15.8220	−	9.13485i	−0.666227	−	0.384646i
$565$		−	20.6600i		−	0.869171i
$566$	6.15339	+	3.55266i	0.258646	+	0.149330i
$567$			16.6410i			0.698858i
$568$	11.2661	−	19.5134i	0.472714	−	0.818765i
$569$	24.8794	+	14.3641i	1.04300	+	0.602176i	0.920682	−	0.390315i	$-0.127634\pi$
$569$	24.8794	+	14.3641i	1.04300	+	0.602176i	0.122318	+	0.992491i	$0.460967\pi$
$570$	−0.306171	−	0.176768i	−0.0128241	−	0.00740400i
$571$			1.61544i			0.0676039i	0.999429	+	0.0338019i	$0.0107615\pi$
$571$			1.61544i			0.0676039i	−0.999429	+	0.0338019i	$0.989238\pi$
$572$	17.9580			0.750861
$573$	−18.0406			−0.753656
$574$	4.83095	+	8.36746i	0.201640	+	0.349251i
$575$	−12.6764	−	21.9561i	−0.528641	−	0.915632i
$576$	0.0815911	−	0.141320i	0.00339963	−	0.00588833i
$577$	15.8924			0.661607			0.330804	−	0.943700i	$-0.392680\pi$
$577$	15.8924			0.661607			0.330804	+	0.943700i	$0.392680\pi$
$578$	3.10674	+	1.79368i	0.129224	+	0.0746072i
$579$	19.3503	+	11.1719i	0.804170	+	0.464288i
$580$	19.6494			0.815897
$581$	8.35471	−	4.82360i	0.346612	−	0.200116i
$582$	−6.14314	+	10.6402i	−0.254642	+	0.441052i
$583$	52.7219			2.18352
$584$	−29.0203	+	16.7549i	−1.20087	+	0.693323i
$585$	−0.487667	−	0.281555i	−0.0201626	−	0.0116409i
$586$	−12.9641	+	7.48482i	−0.535542	+	0.309195i
$587$	15.6168	+	27.0492i	0.644576	+	1.11644i	0.984399	+	0.175949i	$0.0562994\pi$
$587$	15.6168	+	27.0492i	0.644576	+	1.11644i	−0.339823	+	0.940489i	$0.610367\pi$
$588$	8.99885			0.371106
$589$	0.381281	+	0.660398i	0.0157104	+	0.0272112i
$590$	0.609901	+	1.05638i	0.0251092	+	0.0434904i
$591$	19.9844	+	11.5380i	0.822049	+	0.474610i
$592$	−3.52113	+	6.09878i	−0.144718	+	0.250658i
$593$	18.0022	−	10.3935i	0.739260	−	0.426812i	−0.0825404	−	0.996588i	$-0.526303\pi$
$593$	18.0022	−	10.3935i	0.739260	−	0.426812i	0.821800	+	0.569776i	$0.192970\pi$
$594$	−6.17155	+	10.6894i	−0.253222	+	0.438593i
$595$		−	13.3065i		−	0.545512i
$596$		−	21.9883i		−	0.900675i
$597$		−	14.3386i		−	0.586841i
$598$	−13.0315			−0.532899
$599$	16.3589	+	9.44480i	0.668405	+	0.385904i	0.795472	−	0.605990i	$-0.207223\pi$
$599$	16.3589	+	9.44480i	0.668405	+	0.385904i	−0.127067	+	0.991894i	$0.540556\pi$
$600$			10.6938i			0.436574i
$601$	37.9558	+	21.9138i	1.54825	+	0.893883i	0.998276	+	0.0587026i	$0.0186964\pi$
$601$	37.9558	+	21.9138i	1.54825	+	0.893883i	0.549976	+	0.835181i	$0.314637\pi$
$602$	5.87219	+	3.39031i	0.239333	+	0.138179i
$603$	1.19455	−	2.06902i	0.0486457	−	0.0842569i
$604$	2.08617	−	3.61336i	0.0848852	−	0.147025i
$605$	−3.70080	−	6.40997i	−0.150459	−	0.260602i
$606$	2.87448			0.116768
$607$	−15.3200	−	26.5350i	−0.621819	−	1.07702i	−0.989147	−	0.146931i	$-0.953060\pi$
$607$	−15.3200	−	26.5350i	−0.621819	−	1.07702i	0.367327	−	0.930092i	$-0.380273\pi$
$608$	1.21098	+	0.699161i	0.0491118	+	0.0283547i
$609$	23.7389	−	13.7057i	0.961951	−	0.555383i
$610$	−4.83947			−0.195944
$611$	8.66865	−	15.0145i	0.350696	−	0.607424i
$612$	1.19645			0.0483637
$613$	7.22720	+	12.5179i	0.291904	+	0.505592i	0.974260	−	0.225428i	$-0.0723780\pi$
$613$	7.22720	+	12.5179i	0.291904	+	0.505592i	−0.682356	+	0.731020i	$0.739045\pi$
$614$	12.6465	−	7.30148i	0.510373	−	0.294664i
$615$	10.2725	−	17.7925i	0.414228	−	0.717464i
$616$	−14.3840	−	8.30459i	−0.579546	−	0.334601i
$617$	14.1661	+	24.5363i	0.570304	+	0.987796i	0.996534	+	0.0831811i	$0.0265080\pi$
$617$	14.1661	+	24.5363i	0.570304	+	0.987796i	−0.426230	+	0.904615i	$0.640159\pi$
$618$	1.09158			0.0439096
$619$			28.5378i			1.14703i	0.819195	+	0.573515i	$0.194421\pi$
$619$			28.5378i			1.14703i	−0.819195	+	0.573515i	$0.805579\pi$
$620$	−3.50712	+	6.07451i	−0.140849	+	0.243958i
$621$	−22.4943	+	38.9612i	−0.902664	+	1.56346i
$622$	−2.65048	+	4.59077i	−0.106275	+	0.184073i
$623$	−18.6166			−0.745858
$624$	−8.27690	−	4.77867i	−0.331341	−	0.191300i
$625$	0.520387	+	0.901337i	0.0208155	+	0.0360535i
$626$	−2.26555	−	1.30802i	−0.0905496	−	0.0522788i
$627$	1.51207	+	0.872997i	0.0603865	+	0.0348641i
$628$	3.38385	−	5.86101i	0.135030	−	0.233880i
$629$	−16.0252			−0.638966
$630$	0.118416	+	0.205102i	0.00471780	+	0.00817146i
$631$	5.72773			0.228017			0.114009	−	0.993480i	$-0.463631\pi$
$631$	5.72773			0.228017			0.114009	+	0.993480i	$0.463631\pi$
$632$	26.3808			1.04937
$633$			31.2149i			1.24068i
$634$	−10.4026			−0.413138
$635$	4.40909	−	2.54559i	0.174970	−	0.101019i
$636$	−31.9201	−	18.4291i	−1.26571	−	0.730761i
$637$			8.53960i			0.338351i
$638$	19.3205			0.764905
$639$	1.37415	−	0.793364i	0.0543604	−	0.0313850i
$640$			16.3172i			0.644993i
$641$	−11.0363	+	19.1154i	−0.435906	+	0.755012i	−0.997369	−	0.0724900i	$-0.976905\pi$
$641$	−11.0363	+	19.1154i	−0.435906	+	0.755012i	0.561463	+	0.827502i	$0.310239\pi$
$642$	7.80317	−	13.5155i	0.307966	−	0.533413i
$643$	9.76633	−	5.63859i	0.385147	−	0.222364i	−0.294909	−	0.955525i	$-0.595289\pi$
$643$	9.76633	−	5.63859i	0.385147	−	0.222364i	0.680055	+	0.733161i	$0.261956\pi$
$644$	−23.8403	−	13.7642i	−0.939441	−	0.542386i
$645$		−	14.4183i		−	0.567719i
$646$			0.712831i			0.0280460i
$647$	−5.67436	−	9.82828i	−0.223082	−	0.386390i	0.732660	−	0.680595i	$-0.238279\pi$
$647$	−5.67436	−	9.82828i	−0.223082	−	0.386390i	−0.955742	+	0.294205i	$0.904945\pi$
$648$	15.6165	−	9.01621i	0.613476	−	0.354190i
$649$	−3.01209	−	5.21709i	−0.118235	−	0.204789i
$650$	−4.61466			−0.181002
$651$			9.78503i			0.383505i
$652$	7.13764	−	4.12092i	0.279532	−	0.161388i
$653$	−30.4809			−1.19281			−0.596405	−	0.802684i	$-0.703405\pi$
$653$	−30.4809			−1.19281			−0.596405	+	0.802684i	$0.703405\pi$
$654$	−10.8757	+	6.27909i	−0.425274	+	0.245532i
$655$	−1.68779	+	0.974444i	−0.0659473	+	0.0380747i
$656$	−9.10204	+	15.7652i	−0.355375	+	0.615528i
$657$	−2.35978			−0.0920639
$658$	−6.31478	+	3.64584i	−0.246176	+	0.142130i
$659$		−	7.44776i		−	0.290124i	−0.989423	−	0.145062i	$-0.953662\pi$
$659$		−	7.44776i		−	0.290124i	0.989423	−	0.145062i	$-0.0463381\pi$
$660$			16.0601i			0.625138i
$661$	27.7912			1.08095			0.540476	−	0.841359i	$-0.318244\pi$
$661$	27.7912			1.08095			0.540476	+	0.841359i	$0.318244\pi$
$662$	5.53940			0.215295
$663$		−	21.7484i		−	0.844638i
$664$	−9.05326	−	5.22690i	−0.351335	−	0.202843i
$665$	0.613763	−	0.354356i	0.0238007	−	0.0137414i
$666$	0.247008	−	0.142610i	0.00957136	−	0.00552603i
$667$	70.4200			2.72667
$668$	−17.1217	+	9.88520i	−0.662457	+	0.382470i
$669$	17.4767	+	30.2706i	0.675690	+	1.17033i
$670$			13.0927i			0.505816i
$671$	23.9005			0.922667
$672$	8.97148	+	15.5391i	0.346082	+	0.599432i
$673$	−19.9410	+	34.5389i	−0.768671	+	1.33138i	0.169613	+	0.985511i	$0.445748\pi$
$673$	−19.9410	+	34.5389i	−0.768671	+	1.33138i	−0.938284	+	0.345866i	$0.887585\pi$
$674$	5.83578	−	3.36929i	0.224786	−	0.129780i
$675$	−7.96555	+	13.7967i	−0.306594	+	0.531037i
$676$	−4.88460	+	8.46038i	−0.187869	+	0.325399i
$677$			5.90438i			0.226924i	0.993542	+	0.113462i	$0.0361940\pi$
$677$			5.90438i			0.226924i	−0.993542	+	0.113462i	$0.963806\pi$
$678$	−7.10086	+	12.2990i	−0.272707	+	0.472342i
$679$	−12.3148	−	21.3298i	−0.472598	−	0.818564i
$680$	−12.4872	+	7.20952i	−0.478864	+	0.276472i
$681$	−36.1794			−1.38640
$682$	−3.44841	+	5.97283i	−0.132047	+	0.228711i
$683$	−13.8194	+	23.9360i	−0.528786	+	0.915884i	0.470650	+	0.882320i	$0.344019\pi$
$683$	−13.8194	+	23.9360i	−0.528786	+	0.915884i	−0.999437	+	0.0335647i	$0.989314\pi$
$684$	0.0318620	+	0.0551866i	0.00121827	+	0.00211011i
$685$	−2.93741	−	1.69592i	−0.112233	−	0.0647976i
$686$	5.72994	−	9.92454i	0.218770	−	0.378921i
$687$			2.89724i			0.110537i
$688$			12.7754i			0.487059i
$689$	17.4886	−	30.2911i	0.666261	−	1.15400i
$690$		−	11.6543i		−	0.443672i
$691$	11.5460	+	6.66610i	0.439231	+	0.253590i	0.703271	−	0.710921i	$-0.251722\pi$
$691$	11.5460	+	6.66610i	0.439231	+	0.253590i	−0.264040	+	0.964512i	$0.585055\pi$
$692$		−	18.9278i		−	0.719529i
$693$	−0.584814	−	1.01293i	−0.0222153	−	0.0384780i
$694$	−3.13337	−	5.42716i	−0.118941	−	0.206012i
$695$	1.87461	+	3.24692i	0.0711080	+	0.123163i
$696$	−25.7238	−	14.8516i	−0.975058	−	0.562950i
$697$	−41.4247			−1.56907
$698$	−10.5080	−	2.34035i	−0.397732	−	0.0885835i
$699$	16.4562			0.622431
$700$	−8.44221	−	4.87411i	−0.319086	−	0.184224i
$701$	−14.2975	−	24.7640i	−0.540010	−	0.935324i	−0.998903	−	0.0468328i	$-0.985087\pi$
$701$	−14.2975	−	24.7640i	−0.540010	−	0.935324i	0.458893	−	0.888492i	$-0.348246\pi$
$702$	4.09437	+	7.09166i	0.154532	+	0.267657i
$703$	−0.426758	−	0.739166i	−0.0160955	−	0.0278782i
$704$		−	4.41650i		−	0.166453i
$705$	13.4277	+	7.75251i	0.505718	+	0.291976i
$706$			5.56416i			0.209410i
$707$	−2.88115	+	4.99029i	−0.108357	+	0.187679i
$708$			4.21153i			0.158279i
$709$		−	22.7417i		−	0.854081i	−0.904233	−	0.427040i	$-0.859556\pi$
$709$		−	22.7417i		−	0.854081i	0.904233	−	0.427040i	$-0.140444\pi$
$710$	−4.34780	+	7.53061i	−0.163170	+	0.282619i
$711$	1.60886	+	0.928877i	0.0603370	+	0.0348356i
$712$	10.0866	+	17.4705i	0.378011	+	0.654734i
$713$	−12.5689	+	21.7700i	−0.470709	+	0.815291i
$714$	−4.57345	+	7.92145i	−0.171157	+	0.296453i
$715$	−15.2405			−0.569962
$716$	14.1442	−	8.16617i	0.528594	−	0.305184i
$717$	−9.81559	−	17.0011i	−0.366570	−	0.634918i
$718$	−2.86215	+	4.95738i	−0.106814	+	0.185008i
$719$		−	7.79895i		−	0.290852i	−0.989369	−	0.145426i	$-0.953545\pi$
$719$		−	7.79895i		−	0.290852i	0.989369	−	0.145426i	$-0.0464552\pi$
$720$	−0.223108	+	0.386435i	−0.00831475	+	0.0144016i
$721$	−1.09411	+	1.89505i	−0.0407467	+	0.0705754i
$722$	9.44918	−	5.45549i	0.351662	−	0.203032i
$723$	11.1950	−	19.3902i	0.416345	−	0.721131i
$724$	−6.10103	−	10.5673i	−0.226743	−	0.392730i
$725$	24.9367			0.926127
$726$			5.08788i			0.188829i
$727$	−17.9180	−	31.0349i	−0.664542	−	1.15102i	−0.979409	−	0.201885i	$-0.935293\pi$
$727$	−17.9180	−	31.0349i	−0.664542	−	1.15102i	0.314868	−	0.949136i	$-0.398040\pi$
$728$	−9.54271	+	5.50948i	−0.353676	+	0.204195i
$729$	28.2034			1.04457
$730$	11.1995	−	6.46604i	0.414513	−	0.239319i
$731$	−25.1766	+	14.5357i	−0.931190	+	0.537623i
$732$	−14.4704	−	8.35447i	−0.534840	−	0.308790i
$733$			45.0455i			1.66379i	0.554930	+	0.831897i	$0.312745\pi$
$733$			45.0455i			1.66379i	−0.554930	+	0.831897i	$0.687255\pi$
$734$	−21.2311			−0.783654
$735$	−7.63709			−0.281698
$736$			46.0956i			1.69911i
$737$		−	64.6605i		−	2.38180i
$738$	0.638509	−	0.368643i	0.0235038	−	0.0135700i
$739$	23.0163			0.846670			0.423335	−	0.905973i	$-0.360859\pi$
$739$	23.0163			0.846670			0.423335	+	0.905973i	$0.360859\pi$
$740$	3.92543	−	6.79904i	0.144302	−	0.249938i
$741$	1.00315	−	0.579169i	0.0368517	−	0.0212763i
$742$	−12.7398	+	7.35530i	−0.467691	+	0.270022i
$743$	−1.71131			−0.0627817			−0.0313909	−	0.999507i	$-0.509994\pi$
$743$	−1.71131			−0.0627817			−0.0313909	+	0.999507i	$0.509994\pi$
$744$	9.18262	−	5.30159i	0.336651	−	0.194366i
$745$			18.6609i			0.683681i
$746$	10.1400			0.371252
$747$	−0.368082	−	0.637537i	−0.0134674	−	0.0233263i
$748$	28.0434	−	16.1909i	1.02537	−	0.591998i
$749$	15.6425	+	27.0937i	0.571566	+	0.989981i
$750$		−	11.0137i		−	0.402165i
$751$			45.4727i			1.65932i	0.558268	+	0.829661i	$0.311466\pi$
$751$			45.4727i			1.65932i	−0.558268	+	0.829661i	$0.688534\pi$
$752$	−11.8977	−	6.86916i	−0.433866	−	0.250493i
$753$	−19.4566	+	11.2333i	−0.709039	+	0.409364i
$754$	6.40886	−	11.1005i	0.233397	−	0.404256i
$755$	−1.77048	+	3.06656i	−0.0644344	+	0.111604i
$756$			17.2983i			0.629133i
$757$	−30.6971	+	17.7230i	−1.11571	+	0.644153i	−0.940301	−	0.340343i	$-0.889457\pi$
$757$	−30.6971	+	17.7230i	−1.11571	+	0.644153i	−0.175405	+	0.984496i	$0.556123\pi$
$758$	−3.73976			−0.135834
$759$			57.5566i			2.08917i
$760$	−0.665081	−	0.383985i	−0.0241250	−	0.0139286i
$761$	−42.7367	+	24.6740i	−1.54920	+	0.894433i	−0.551000	+	0.834505i	$0.685754\pi$
$761$	−42.7367	+	24.6740i	−1.54920	+	0.894433i	−0.998203	+	0.0599279i	$0.980913\pi$
$762$	−3.49969			−0.126781
$763$		−	25.1746i		−	0.911383i
$764$	−17.8204			−0.644718
$765$	−1.01540			−0.0367118
$766$	−8.76461	−	15.1808i	−0.316678	−	0.548503i
$767$	−3.99660			−0.144309
$768$	3.75707	−	6.50744i	0.135572	−	0.234817i
$769$	8.20127	+	4.73501i	0.295746	+	0.170749i	0.640530	−	0.767933i	$-0.278715\pi$
$769$	8.20127	+	4.73501i	0.295746	+	0.170749i	−0.344785	+	0.938682i	$0.612048\pi$
$770$	5.55105	+	3.20490i	0.200046	+	0.115497i
$771$	17.2113	+	29.8109i	0.619850	+	1.07361i
$772$	19.1141	+	11.0355i	0.687930	+	0.397177i
$773$	30.4680			1.09586			0.547929	−	0.836525i	$-0.315417\pi$
$773$	30.4680			1.09586			0.547929	+	0.836525i	$0.315417\pi$
$774$	0.258710	−	0.448099i	0.00929914	−	0.0161066i
$775$	−4.45083	+	7.70906i	−0.159878	+	0.276918i
$776$	−13.3445	+	23.1133i	−0.479038	+	0.829718i
$777$		−	10.9521i		−	0.392905i
$778$	4.91428			0.176185
$779$	−1.10316	−	1.91072i	−0.0395247	−	0.0684588i
$780$	9.22724	+	5.32735i	0.330388	+	0.190750i
$781$	21.4723	−	37.1911i	0.768338	−	1.33080i
$782$	−20.3502	+	11.7492i	−0.727723	+	0.420151i
$783$	−22.1252	−	38.3220i	−0.790690	−	1.36952i
$784$	6.76690			0.241675
$785$	−2.87179	+	4.97408i	−0.102499	+	0.177533i
$786$	1.33967			0.0477845
$787$	35.0419	−	20.2314i	1.24911	−	0.721173i	0.278176	−	0.960530i	$-0.410270\pi$
$787$	35.0419	−	20.2314i	1.24911	−	0.721173i	0.970932	+	0.239357i	$0.0769367\pi$
$788$	19.7405	+	11.3972i	0.703225	+	0.406007i
$789$	2.37885	+	4.12029i	0.0846893	+	0.146686i
$790$	−10.1809			−0.362219
$791$	−14.2347	−	24.6552i	−0.506126	−	0.876637i
$792$	−0.633712	+	1.09762i	−0.0225180	+	0.0390023i
$793$	7.92810	−	13.7319i	0.281535	−	0.487633i
$794$	−1.80138	−	1.04003i	−0.0639285	−	0.0369091i
$795$	27.0898	+	15.6403i	0.960775	+	0.554704i
$796$		−	14.1636i		−	0.502015i
$797$	−12.7473	−	7.35967i	−0.451533	−	0.260693i	0.256944	−	0.966426i	$-0.417284\pi$
$797$	−12.7473	−	7.35967i	−0.451533	−	0.260693i	−0.708477	+	0.705733i	$0.750618\pi$
$798$	−0.487171			−0.0172457
$799$		−	31.2626i		−	1.10599i
$800$			16.3231i			0.577109i
$801$			1.42061i			0.0501947i
$802$	5.28634	−	9.15621i	0.186667	−	0.323317i
$803$	−55.3105	+	31.9336i	−1.95187	+	1.12691i
$804$	−22.6022	+	39.1482i	−0.797119	+	1.38065i
$805$	20.2327	+	11.6813i	0.713108	+	0.411713i
$806$	2.28777	+	3.96253i	0.0805832	+	0.139574i
$807$	−23.1833	−	40.1547i	−0.816092	−	1.41351i
$808$	6.24409			0.219666
$809$	11.7999	+	20.4380i	0.414862	+	0.718562i	0.995414	−	0.0956611i	$-0.0304965\pi$
$809$	11.7999	+	20.4380i	0.414862	+	0.718562i	−0.580552	+	0.814223i	$0.697163\pi$
$810$	−6.02673	+	3.47953i	−0.211758	+	0.122258i
$811$	42.9812	+	24.8152i	1.50927	+	0.871380i	0.999942	+	0.0108109i	$0.00344128\pi$
$811$	42.9812	+	24.8152i	1.50927	+	0.871380i	0.509333	+	0.860569i	$0.329892\pi$
$812$	23.4492	−	13.5384i	0.822905	−	0.475104i
$813$	−6.38380			−0.223890
$814$	3.85972	−	6.68523i	0.135283	−	0.234317i
$815$	−6.05753	+	3.49732i	−0.212186	+	0.122506i
$816$	−17.2338			−0.603302
$817$	−1.34093	−	0.774184i	−0.0469131	−	0.0270853i
$818$	5.11257	+	2.95175i	0.178757	+	0.103205i
$819$	−0.775963			−0.0271143
$820$	10.1471	−	17.5753i	0.354353	−	0.613757i
$821$	5.80878	+	10.0611i	0.202728	+	0.351135i	0.949406	−	0.314050i	$-0.101686\pi$
$821$	5.80878	+	10.0611i	0.202728	+	0.351135i	−0.746679	+	0.665185i	$0.768353\pi$
$822$	1.16578	+	2.01919i	0.0406611	+	0.0704272i
$823$	−15.3282			−0.534308			−0.267154	−	0.963654i	$-0.586083\pi$
$823$	−15.3282			−0.534308			−0.267154	+	0.963654i	$0.586083\pi$
$824$	2.37118			0.0826039
$825$			20.3816i			0.709597i
$826$	1.45569	+	0.840441i	0.0506498	+	0.0292427i
$827$	−20.8194	−	12.0201i	−0.723963	−	0.417980i	0.0922467	−	0.995736i	$-0.470595\pi$
$827$	−20.8194	−	12.0201i	−0.723963	−	0.417980i	−0.816209	+	0.577756i	$0.803928\pi$
$828$	−1.05033	+	1.81922i	−0.0365015	+	0.0632224i
$829$			3.18924i			0.110767i	0.998465	+	0.0553835i	$0.0176381\pi$
$829$			3.18924i			0.110767i	−0.998465	+	0.0553835i	$0.982362\pi$
$830$	3.49383	+	2.01716i	0.121273	+	0.0700168i
$831$			27.9860i			0.970822i
$832$	−2.53748	−	1.46501i	−0.0879711	−	0.0507902i
$833$	7.69928	+	13.3355i	0.266764	+	0.462049i
$834$		−	2.57723i		−	0.0892420i
$835$	14.5307	−	8.38931i	0.502856	−	0.290324i
$836$	1.49362	+	0.862340i	0.0516578	+	0.0298247i
$837$	15.7960			0.545991
$838$	−4.45416	+	2.57161i	−0.153866	+	0.0888347i
$839$	−5.93144	+	3.42452i	−0.204776	+	0.118227i	−0.598881	−	0.800838i	$-0.704388\pi$
$839$	−5.93144	+	3.42452i	−0.204776	+	0.118227i	0.394105	+	0.919065i	$0.371055\pi$
$840$	−4.92721	−	8.53418i	−0.170005	−	0.294457i
$841$	−20.1323	+	34.8701i	−0.694216	+	1.20242i
$842$	5.33685	+	9.24370i	0.183920	+	0.318559i
$843$	21.1539	−	36.6396i	0.728579	−	1.26194i
$844$			30.8339i			1.06135i
$845$	4.14544	−	7.18011i	0.142607	−	0.247003i
$846$	0.278209	+	0.481873i	0.00956503	+	0.0165671i
$847$	−8.83291	−	5.09968i	−0.303502	−	0.175227i
$848$	−24.0031	−	13.8582i	−0.824269	−	0.475892i
$849$	−10.4099	−	18.0305i	−0.357266	−	0.618804i
$850$	−7.20632	+	4.16057i	−0.247175	+	0.142706i
$851$	14.0680	−	24.3666i	0.482246	−	0.835275i
$852$	−26.0005	+	15.0114i	−0.890761	+	0.514281i
$853$	24.6267	+	42.6546i	0.843200	+	1.46047i	0.887175	+	0.461433i	$0.152665\pi$
$853$	24.6267	+	42.6546i	0.843200	+	1.46047i	−0.0439744	+	0.999033i	$0.514002\pi$
$854$	−5.77532	+	3.33438i	−0.197627	+	0.114100i
$855$	−0.0270405	−	0.0468355i	−0.000924764	−	0.00160174i
$856$	16.9504	−	29.3590i	0.579354	−	1.00347i
$857$	46.9455	−	27.1040i	1.60363	−	0.925855i	0.612874	−	0.790181i	$-0.290013\pi$
$857$	46.9455	−	27.1040i	1.60363	−	0.925855i	0.990754	−	0.135674i	$-0.0433200\pi$
$858$	9.07279	+	5.23817i	0.309740	+	0.178828i
$859$	−28.6432	+	16.5372i	−0.977293	+	0.564240i	−0.901452	−	0.432879i	$-0.857498\pi$
$859$	−28.6432	+	16.5372i	−0.977293	+	0.564240i	−0.0758414	+	0.997120i	$0.524164\pi$
$860$		−	14.2423i		−	0.485658i
$861$		−	28.3110i		−	0.964835i
$862$	5.65964	+	9.80279i	0.192768	+	0.333884i
$863$	6.27838	+	3.62483i	0.213719	+	0.123391i	0.603038	−	0.797712i	$-0.293957\pi$
$863$	6.27838	+	3.62483i	0.213719	+	0.123391i	−0.389320	+	0.921103i	$0.627290\pi$
$864$	25.0848	−	14.4827i	0.853403	−	0.492713i
$865$			16.0636i			0.546178i
$866$	20.1334			0.684162
$867$	−5.25577	−	9.10327i	−0.178495	−	0.309163i
$868$			9.66559i			0.328071i
$869$	50.2798			1.70563
$870$	9.92732	+	5.73154i	0.336568	+	0.194317i
$871$	−37.1503	−	21.4487i	−1.25879	−	0.726763i
$872$	−23.6248	+	13.6398i	−0.800035	+	0.461901i
$873$	−1.62765	+	0.939725i	−0.0550877	+	0.0318049i
$874$	−1.08387	−	0.625773i	−0.0366625	−	0.0211671i
$875$	19.1206	+	11.0393i	0.646394	+	0.373196i
$876$	44.6498			1.50858
$877$		−	29.6613i		−	1.00159i	−0.865566	−	0.500795i	$-0.833041\pi$
$877$		−	29.6613i		−	1.00159i	0.865566	−	0.500795i	$-0.166959\pi$
$878$	2.11692	+	3.66661i	0.0714426	+	0.123742i
$879$	43.8635			1.47948
$880$			12.0768i			0.407108i
$881$	−41.6885	+	24.0689i	−1.40452	+	0.810901i	−0.994853	−	0.101333i	$-0.967689\pi$
$881$	−41.6885	+	24.0689i	−1.40452	+	0.810901i	−0.409669	+	0.912234i	$0.634356\pi$
$882$	−0.237349	−	0.137034i	−0.00799197	−	0.00461416i
$883$	19.7309	+	34.1749i	0.663997	+	1.15008i	0.979556	+	0.201171i	$0.0644747\pi$
$883$	19.7309	+	34.1749i	0.663997	+	1.15008i	−0.315559	+	0.948906i	$0.602192\pi$
$884$		−	21.4829i		−	0.722549i
$885$		−	3.57422i		−	0.120146i
$886$	9.42702	−	5.44269i	0.316707	−	0.182851i
$887$	2.34664	+	1.35483i	0.0787925	+	0.0454909i	0.538879	−	0.842383i	$-0.318848\pi$
$887$	2.34664	+	1.35483i	0.0787925	+	0.0454909i	−0.460086	+	0.887874i	$0.652181\pi$
$888$	−10.2779	+	5.93393i	−0.344902	+	0.199130i
$889$	3.50781	−	6.07571i	0.117648	−	0.203773i
$890$	−3.89261	−	6.74220i	−0.130481	−	0.225999i
$891$	29.7639	−	17.1842i	0.997129	−	0.575693i
$892$	17.2634	+	29.9011i	0.578022	+	1.00116i
$893$	1.44199	−	0.832535i	0.0482545	−	0.0278597i
$894$	6.41377	−	11.1090i	0.214509	−	0.371540i
$895$	−12.0038	+	6.93041i	−0.401244	+	0.231658i
$896$	11.2425	+	19.4726i	0.375585	+	0.650533i
$897$	33.0688	+	19.0923i	1.10414	+	0.637473i
$898$	−4.62599	−	2.67082i	−0.154371	−	0.0891263i
$899$	−12.3627	−	21.4128i	−0.412318	−	0.714156i
$900$	−0.371937	+	0.644214i	−0.0123979	+	0.0214738i
$901$		−	63.0706i		−	2.10119i
$902$	9.97727	−	17.2811i	0.332207	−	0.575399i
$903$	−9.93416	−	17.2065i	−0.330588	−	0.572596i
$904$	−15.4249	+	26.7166i	−0.513023	+	0.888582i
$905$	5.17779	+	8.96819i	0.172115	+	0.298113i
$906$	2.10796	−	1.21703i	0.0700324	−	0.0404332i
$907$	−30.2205	+	17.4478i	−1.00345	+	0.579345i	−0.909269	−	0.416210i	$-0.863358\pi$
$907$	−30.2205	+	17.4478i	−1.00345	+	0.579345i	−0.0941861	+	0.995555i	$0.530025\pi$
$908$	−35.7378			−1.18600
$909$	0.380802	+	0.219856i	0.0126304	+	0.00729217i
$910$	3.68272	−	2.12622i	0.122081	−	0.0704834i
$911$		−	29.6399i		−	0.982015i	−0.871155	−	0.491007i	$-0.836629\pi$
$911$		−	29.6399i		−	0.982015i	0.871155	−	0.491007i	$-0.163371\pi$
$912$	−0.458942	−	0.794911i	−0.0151971	−	0.0263221i
$913$	−17.2548	−	9.96208i	−0.571052	−	0.329697i
$914$		−	0.513672i		−	0.0169908i
$915$	12.2806	+	7.09022i	0.405985	+	0.234395i
$916$			2.86188i			0.0945591i
$917$	−1.34278	+	2.32576i	−0.0443425	+	0.0768034i
$918$	12.7877	+	7.38296i	0.422056	+	0.243674i
$919$	−35.8516	−	20.6990i	−1.18264	−	0.682796i	−0.226014	−	0.974124i	$-0.572569\pi$
$919$	−35.8516	−	20.6990i	−1.18264	−	0.682796i	−0.956623	+	0.291329i	$0.905903\pi$
$920$		−	25.3161i		−	0.834646i
$921$	−42.7891			−1.40995
$922$	−14.9048			−0.490863
$923$	−14.2453	−	24.6735i	−0.468889	−	0.812140i
$924$	11.0654	+	19.1658i	0.364024	+	0.630508i
$925$	4.98170	−	8.62855i	0.163797	−	0.283705i
$926$	−14.4643			−0.475325
$927$	0.144609	+	0.0834899i	0.00474958	+	0.00274217i
$928$	−39.2649	−	22.6696i	−1.28893	−	0.744167i
$929$	45.8571			1.50452			0.752262	−	0.658865i	$-0.228963\pi$
$929$	45.8571			1.50452			0.752262	+	0.658865i	$0.228963\pi$
$930$	−3.54375	+	2.04599i	−0.116204	+	0.0670905i
$931$	−0.410070	+	0.710263i	−0.0134395	+	0.0232779i
$932$	16.2553			0.532461
$933$	13.4517	−	7.76634i	0.440389	−	0.254259i
$934$	0.225620	+	0.130262i	0.00738252	+	0.00426230i
$935$	−23.7997	+	13.7408i	−0.778335	+	0.449372i
$936$	0.420421	+	0.728191i	0.0137419	+	0.0238017i
$937$	12.9452			0.422901			0.211451	−	0.977389i	$-0.432181\pi$
$937$	12.9452			0.422901			0.211451	+	0.977389i	$0.432181\pi$
$938$	9.02086	+	15.6246i	0.294542	+	0.510161i
$939$	3.83270	+	6.63843i	0.125075	+	0.216637i
$940$	13.2638	+	7.65787i	0.432618	+	0.249772i
$941$	−22.7077	+	39.3310i	−0.740251	+	1.28215i	0.212130	+	0.977242i	$0.431960\pi$
$941$	−22.7077	+	39.3310i	−0.740251	+	1.28215i	−0.952381	+	0.304911i	$0.901373\pi$
$942$	3.41920	−	1.97408i	0.111404	−	0.0643189i
$943$	36.3655	−	62.9869i	1.18422	−	2.05114i
$944$			3.16696i			0.103076i
$945$		−	14.6806i		−	0.477560i
$946$		−	14.0039i		−	0.455306i
$947$	−18.7224			−0.608395			−0.304198	−	0.952609i	$-0.598388\pi$
$947$	−18.7224			−0.608395			−0.304198	+	0.952609i	$0.598388\pi$
$948$	−30.4415	−	17.5754i	−0.988695	−	0.570823i
$949$			42.3711i			1.37543i
$950$	−0.383814	−	0.221595i	−0.0124526	−	0.00718950i
$951$	26.3975	+	15.2406i	0.855998	+	0.494210i
$952$	−9.93468	+	17.2074i	−0.321985	+	0.557694i
$953$	−22.9124	+	39.6855i	−0.742206	+	1.28554i	0.209282	+	0.977855i	$0.432887\pi$
$953$	−22.9124	+	39.6855i	−0.742206	+	1.28554i	−0.951489	+	0.307684i	$0.900446\pi$
$954$	0.561273	+	0.972154i	0.0181719	+	0.0314746i
$955$	15.1237			0.489390
$956$	−9.69578	−	16.7936i	−0.313584	−	0.543143i
$957$	−49.0276	−	28.3061i	−1.58484	−	0.915006i
$958$	2.09353	−	1.20870i	0.0676389	−	0.0390513i
$959$	−4.67393			−0.150929
$960$	1.31018	−	2.26930i	0.0422859	−	0.0732414i
$961$	−22.1738			−0.715284
$962$	−2.56064	−	4.43516i	−0.0825584	−	0.142995i
$963$	2.06748	−	1.19366i	0.0666237	−	0.0384652i
$964$	11.0583	−	19.1535i	0.356164	−	0.616894i
$965$	−16.2216	−	9.36555i	−0.522192	−	0.301488i
$966$	−8.02979	−	13.9080i	−0.258354	−	0.447483i
$967$	22.8144			0.733662			0.366831	−	0.930288i	$-0.380443\pi$
$967$	22.8144			0.733662			0.366831	+	0.930288i	$0.380443\pi$
$968$			11.0522i			0.355230i
$969$	1.04436	−	1.80888i	0.0335496	−	0.0581095i
$970$	5.14989	−	8.91987i	0.165353	−	0.286400i
$971$	−15.1766	+	26.2866i	−0.487040	+	0.843578i	−0.999889	−	0.0149011i	$-0.995257\pi$
$971$	−15.1766	+	26.2866i	−0.487040	+	0.843578i	0.512849	+	0.858479i	$0.328590\pi$
$972$	2.57762			0.0826773
$973$	4.47424	+	2.58321i	0.143438	+	0.0828138i
$974$	−8.74763	−	15.1513i	−0.280292	−	0.485480i
$975$	11.7101	+	6.76085i	0.375025	+	0.216521i
$976$	−10.8813	−	6.28234i	−0.348303	−	0.201093i
$977$	−2.94949	+	5.10867i	−0.0943626	+	0.163441i	−0.909342	−	0.416048i	$-0.863415\pi$
$977$	−2.94949	+	5.10867i	−0.0943626	+	0.163441i	0.814980	+	0.579489i	$0.196748\pi$
$978$	4.80813			0.153747
$979$	19.2243	+	33.2974i	0.614410	+	1.06419i
$980$	−7.54386			−0.240980
$981$	−1.92104			−0.0613341
$982$		−	0.403372i		−	0.0128721i
$983$	−14.3683			−0.458277			−0.229139	−	0.973394i	$-0.573591\pi$
$983$	−14.3683			−0.458277			−0.229139	+	0.973394i	$0.573591\pi$
$984$	−26.5680	+	15.3390i	−0.846957	+	0.488991i
$985$	−16.7532	−	9.67248i	−0.533802	−	0.308191i
$986$		−	23.1129i		−	0.736064i
$987$	21.3658			0.680082
$988$	0.990906	−	0.572100i	0.0315249	−	0.0182009i
$989$		−	51.0418i		−	1.62304i
$990$	0.244562	−	0.423593i	0.00777268	−	0.0134627i
$991$	4.78739	−	8.29201i	0.152077	−	0.263404i	−0.779914	−	0.625887i	$-0.784737\pi$
$991$	4.78739	−	8.29201i	0.152077	−	0.263404i	0.931991	+	0.362482i	$0.118071\pi$
$992$	14.0164	−	8.09237i	0.445021	−	0.256933i
$993$	−14.0568	−	8.11568i	−0.446078	−	0.257543i
$994$			11.9825i			0.380062i
$995$			12.0203i			0.381068i
$996$	6.96454	+	12.0629i	0.220680	+	0.382229i
$997$	7.19212	−	4.15237i	0.227777	−	0.131507i	−0.381769	−	0.924258i	$-0.624685\pi$
$997$	7.19212	−	4.15237i	0.227777	−	0.131507i	0.609546	+	0.792751i	$0.291352\pi$
$998$	−11.3637	−	19.6824i	−0.359710	−	0.623036i
$999$	−17.6801			−0.559374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.227.17	yes	58
349.123	even	6	inner	349.2.e.a.123.17	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.17	✓	58	349.123	even	6	inner
349.2.e.a.227.17	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)

\(f(q)\)	\(=\)	\(q+(0.499056 + 0.288130i) q^{2} +(-0.844268 - 1.46231i) q^{3} +(-0.833962 - 1.44447i) q^{4} +(0.707762 + 1.22588i) q^{5} -0.973035i q^{6} +(1.68926 + 0.975293i) q^{7} -2.11368i q^{8} +(0.0744233 - 0.128905i) q^{9} +O(q^{10})\)	\(q+(0.499056 + 0.288130i) q^{2} +(-0.844268 - 1.46231i) q^{3} +(-0.833962 - 1.44447i) q^{4} +(0.707762 + 1.22588i) q^{5} -0.973035i q^{6} +(1.68926 + 0.975293i) q^{7} -2.11368i q^{8} +(0.0744233 - 0.128905i) q^{9} +0.815710i q^{10} -4.02851i q^{11} +(-1.40818 + 2.43903i) q^{12} +(-2.31456 - 1.33631i) q^{13} +(0.562022 + 0.973451i) q^{14} +(1.19508 - 2.06994i) q^{15} +(-1.05891 + 1.83409i) q^{16} -4.81926 q^{17} +(0.0742827 - 0.0428871i) q^{18} +(-0.128339 - 0.222289i) q^{19} +(1.18049 - 2.04467i) q^{20} -3.29363i q^{21} +(1.16073 - 2.01045i) q^{22} +(4.23068 - 7.32776i) q^{23} +(-3.09086 + 1.78451i) q^{24} +(1.49815 - 2.59486i) q^{25} +(-0.770062 - 1.33379i) q^{26} -5.31694 q^{27} -3.25343i q^{28} +(4.16127 + 7.20752i) q^{29} +(1.19282 - 0.688677i) q^{30} -2.97089 q^{31} +(-4.71791 + 2.72389i) q^{32} +(-5.89095 + 3.40114i) q^{33} +(-2.40508 - 1.38857i) q^{34} +2.76110i q^{35} -0.248265 q^{36} +3.32524 q^{37} -0.147913i q^{38} +4.51281i q^{39} +(2.59111 - 1.49598i) q^{40} +8.59566 q^{41} +(0.948994 - 1.64371i) q^{42} +(5.22416 - 3.01617i) q^{43} +(-5.81904 + 3.35962i) q^{44} +0.210696 q^{45} +(4.22269 - 2.43797i) q^{46} +6.48701i q^{47} +3.57602 q^{48} +(-1.59761 - 2.76714i) q^{49} +(1.49532 - 0.863321i) q^{50} +(4.06874 + 7.04727i) q^{51} +4.45773i q^{52} +13.0872i q^{53} +(-2.65345 - 1.53197i) q^{54} +(4.93847 - 2.85122i) q^{55} +(2.06145 - 3.57054i) q^{56} +(-0.216705 + 0.375344i) q^{57} +4.79594i q^{58} +(1.29504 - 0.747694i) q^{59} -3.98661 q^{60} +5.93283i q^{61} +(-1.48264 - 0.856003i) q^{62} +(0.251440 - 0.145169i) q^{63} +1.09631 q^{64} -3.78316i q^{65} -3.91988 q^{66} +16.0507 q^{67} +(4.01908 + 6.96125i) q^{68} -14.2873 q^{69} +(-0.795556 + 1.37794i) q^{70} +(9.23197 + 5.33008i) q^{71} +(-0.272463 - 0.157307i) q^{72} +(-7.92689 - 13.7298i) q^{73} +(1.65948 + 0.958101i) q^{74} -5.05935 q^{75} +(-0.214060 + 0.370762i) q^{76} +(3.92897 - 6.80518i) q^{77} +(-1.30028 + 2.25215i) q^{78} +12.4810i q^{79} -2.99783 q^{80} +(4.26565 + 7.38833i) q^{81} +(4.28971 + 2.47667i) q^{82} +(2.47290 - 4.28318i) q^{83} +(-4.75754 + 2.74677i) q^{84} +(-3.41089 - 5.90783i) q^{85} +3.47620 q^{86} +(7.02645 - 12.1702i) q^{87} -8.51497 q^{88} +(-8.26544 + 4.77205i) q^{89} +(0.105149 + 0.0607078i) q^{90} +(-2.60659 - 4.51474i) q^{91} -14.1129 q^{92} +(2.50823 + 4.34438i) q^{93} +(-1.86910 + 3.23738i) q^{94} +(0.181667 - 0.314656i) q^{95} +(7.96636 + 4.59938i) q^{96} +(-10.9351 - 6.31338i) q^{97} -1.84127i q^{98} +(-0.519294 - 0.299815i) 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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