LMFDB - Embedded newform 349.2.c.a.122.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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([4]))

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.14
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0965034 + 0.167149i) q^{2} +(-1.64186 - 2.84379i) q^{3} +(0.981374 + 1.69979i) q^{4} +(0.242663 + 0.420304i) q^{5} +0.633781 q^{6} +(-1.37278 + 2.37772i) q^{7} -0.764837 q^{8} +(-3.89141 + 6.74013i) q^{9} +O(q^{10})$	\(q+(-0.0965034 + 0.167149i) q^{2} +(-1.64186 - 2.84379i) q^{3} +(0.981374 + 1.69979i) q^{4} +(0.242663 + 0.420304i) q^{5} +0.633781 q^{6} +(-1.37278 + 2.37772i) q^{7} -0.764837 q^{8} +(-3.89141 + 6.74013i) q^{9} -0.0936712 q^{10} -6.08805 q^{11} +(3.22256 - 5.58164i) q^{12} +(1.48735 - 2.57617i) q^{13} +(-0.264956 - 0.458916i) q^{14} +(0.796837 - 1.38016i) q^{15} +(-1.88894 + 3.27174i) q^{16} -1.93378 q^{17} +(-0.751069 - 1.30089i) q^{18} +(3.54957 + 6.14803i) q^{19} +(-0.476286 + 0.824952i) q^{20} +9.01564 q^{21} +(0.587517 - 1.01761i) q^{22} +(-3.86683 + 6.69754i) q^{23} +(1.25576 + 2.17503i) q^{24} +(2.38223 - 4.12614i) q^{25} +(0.287069 + 0.497218i) q^{26} +15.7055 q^{27} -5.38884 q^{28} +(0.0514318 + 0.0890825i) q^{29} +(0.153795 + 0.266381i) q^{30} -3.91505 q^{31} +(-1.12942 - 1.95620i) q^{32} +(9.99572 + 17.3131i) q^{33} +(0.186616 - 0.323229i) q^{34} -1.33249 q^{35} -15.2757 q^{36} +1.53923 q^{37} -1.37018 q^{38} -9.76810 q^{39} +(-0.185598 - 0.321464i) q^{40} +0.161876 q^{41} +(-0.870040 + 1.50695i) q^{42} +(-3.26095 - 5.64813i) q^{43} +(-5.97465 - 10.3484i) q^{44} -3.77721 q^{45} +(-0.746324 - 1.29267i) q^{46} +1.74553 q^{47} +12.4055 q^{48} +(-0.269041 - 0.465994i) q^{49} +(0.459786 + 0.796373i) q^{50} +(3.17499 + 5.49925i) q^{51} +5.83860 q^{52} +2.58263 q^{53} +(-1.51563 + 2.62515i) q^{54} +(-1.47734 - 2.55883i) q^{55} +(1.04995 - 1.81857i) q^{56} +(11.6558 - 20.1884i) q^{57} -0.0198534 q^{58} +(-2.96262 - 5.13140i) q^{59} +3.12798 q^{60} -4.23381 q^{61} +(0.377816 - 0.654396i) q^{62} +(-10.6841 - 18.5054i) q^{63} -7.11979 q^{64} +1.44370 q^{65} -3.85848 q^{66} +6.88046 q^{67} +(-1.89776 - 3.28702i) q^{68} +25.3952 q^{69} +(0.128590 - 0.222724i) q^{70} +(-6.17437 + 10.6943i) q^{71} +(2.97630 - 5.15510i) q^{72} +(-0.123270 - 0.213510i) q^{73} +(-0.148541 + 0.257281i) q^{74} -15.6452 q^{75} +(-6.96691 + 12.0670i) q^{76} +(8.35754 - 14.4757i) q^{77} +(0.942655 - 1.63273i) q^{78} -8.96321 q^{79} -1.83350 q^{80} +(-14.1120 - 24.4426i) q^{81} +(-0.0156216 + 0.0270573i) q^{82} +(-6.82682 + 11.8244i) q^{83} +(8.84772 + 15.3247i) q^{84} +(-0.469256 - 0.812775i) q^{85} +1.25877 q^{86} +(0.168888 - 0.292522i) q^{87} +4.65636 q^{88} +(-6.49572 - 11.2509i) q^{89} +(0.364513 - 0.631355i) q^{90} +(4.08361 + 7.07302i) q^{91} -15.1792 q^{92} +(6.42797 + 11.1336i) q^{93} +(-0.168450 + 0.291764i) q^{94} +(-1.72270 + 2.98380i) q^{95} +(-3.70869 + 6.42363i) q^{96} +(-2.57858 + 4.46624i) q^{97} +0.103854 q^{98} +(23.6911 - 41.0342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0965034	+	0.167149i	−0.0682382	+	0.118192i	−0.898126	−	0.439739i	$-0.855071\pi$
$2$	−0.0965034	+	0.167149i	−0.0682382	+	0.118192i	0.829888	+	0.557931i	$0.188404\pi$
$3$	−1.64186	−	2.84379i	−0.947929	−	1.64186i	−0.749778	−	0.661689i	$-0.769840\pi$
$3$	−1.64186	−	2.84379i	−0.947929	−	1.64186i	−0.198150	−	0.980172i	$-0.563493\pi$
$4$	0.981374	+	1.69979i	0.490687	+	0.849895i
$5$	0.242663	+	0.420304i	0.108522	+	0.187966i	0.915172	−	0.403064i	$-0.132055\pi$
$5$	0.242663	+	0.420304i	0.108522	+	0.187966i	−0.806650	+	0.591030i	$0.798721\pi$
$6$	0.633781			0.258740
$7$	−1.37278	+	2.37772i	−0.518861	+	0.898694i	0.480898	+	0.876776i	$0.340311\pi$
$7$	−1.37278	+	2.37772i	−0.518861	+	0.898694i	−0.999760	+	0.0219181i	$0.993023\pi$
$8$	−0.764837			−0.270411
$9$	−3.89141	+	6.74013i	−1.29714	+	2.24671i
$10$	−0.0936712			−0.0296214
$11$	−6.08805			−1.83561			−0.917807	−	0.397026i	$-0.870042\pi$
$11$	−6.08805			−1.83561			−0.917807	+	0.397026i	$0.870042\pi$
$12$	3.22256	−	5.58164i	0.930273	−	1.61128i
$13$	1.48735	−	2.57617i	0.412517	−	0.714501i	−0.582647	−	0.812725i	$-0.697983\pi$
$13$	1.48735	−	2.57617i	0.412517	−	0.714501i	0.995164	+	0.0982245i	$0.0313163\pi$
$14$	−0.264956	−	0.458916i	−0.0708124	−	0.122651i
$15$	0.796837	−	1.38016i	0.205743	−	0.356356i
$16$	−1.88894	+	3.27174i	−0.472235	+	0.817935i
$17$	−1.93378			−0.469010			−0.234505	−	0.972115i	$-0.575347\pi$
$17$	−1.93378			−0.469010			−0.234505	+	0.972115i	$0.575347\pi$
$18$	−0.751069	−	1.30089i	−0.177029	−	0.306623i
$19$	3.54957	+	6.14803i	0.814326	+	1.41045i	0.909811	+	0.415024i	$0.136227\pi$
$19$	3.54957	+	6.14803i	0.814326	+	1.41045i	−0.0954840	+	0.995431i	$0.530440\pi$
$20$	−0.476286	+	0.824952i	−0.106501	+	0.184465i
$21$	9.01564			1.96737
$22$	0.587517	−	1.01761i	0.125259	−	0.216955i
$23$	−3.86683	+	6.69754i	−0.806289	+	1.39653i	0.109129	+	0.994028i	$0.465194\pi$
$23$	−3.86683	+	6.69754i	−0.806289	+	1.39653i	−0.915417	+	0.402506i	$0.868139\pi$
$24$	1.25576	+	2.17503i	0.256330	+	0.443977i
$25$	2.38223	−	4.12614i	0.476446	−	0.825228i
$26$	0.287069	+	0.497218i	0.0562989	+	0.0975125i
$27$	15.7055			3.02252
$28$	−5.38884			−1.01839
$29$	0.0514318	+	0.0890825i	0.00955065	+	0.0165422i	0.870761	−	0.491706i	$-0.163627\pi$
$29$	0.0514318	+	0.0890825i	0.00955065	+	0.0165422i	−0.861211	+	0.508248i	$0.830293\pi$
$30$	0.153795	+	0.266381i	0.0280790	+	0.0486342i
$31$	−3.91505			−0.703164			−0.351582	−	0.936157i	$-0.614356\pi$
$31$	−3.91505			−0.703164			−0.351582	+	0.936157i	$0.614356\pi$
$32$	−1.12942	−	1.95620i	−0.199654	−	0.345811i
$33$	9.99572	+	17.3131i	1.74003	+	3.01382i
$34$	0.186616	−	0.323229i	0.0320044	−	0.0554332i
$35$	−1.33249			−0.225232
$36$	−15.2757			−2.54596
$37$	1.53923			0.253048			0.126524	−	0.991964i	$-0.459618\pi$
$37$	1.53923			0.253048			0.126524	+	0.991964i	$0.459618\pi$
$38$	−1.37018			−0.222273
$39$	−9.76810			−1.56415
$40$	−0.185598	−	0.321464i	−0.0293456	−	0.0508280i
$41$	0.161876			0.0252807			0.0126404	−	0.999920i	$-0.495976\pi$
$41$	0.161876			0.0252807			0.0126404	+	0.999920i	$0.495976\pi$
$42$	−0.870040	+	1.50695i	−0.134250	+	0.232528i
$43$	−3.26095	−	5.64813i	−0.497290	−	0.861332i	0.502705	−	0.864458i	$-0.332338\pi$
$43$	−3.26095	−	5.64813i	−0.497290	−	0.861332i	−0.999995	+	0.00312603i	$0.999005\pi$
$44$	−5.97465	−	10.3484i	−0.900712	−	1.56008i
$45$	−3.77721			−0.563073
$46$	−0.746324	−	1.29267i	−0.110039	−	0.190594i
$47$	1.74553			0.254612			0.127306	−	0.991863i	$-0.459367\pi$
$47$	1.74553			0.254612			0.127306	+	0.991863i	$0.459367\pi$
$48$	12.4055			1.79058
$49$	−0.269041	−	0.465994i	−0.0384345	−	0.0665705i
$50$	0.459786	+	0.796373i	0.0650236	+	0.112624i
$51$	3.17499	+	5.49925i	0.444588	+	0.770049i
$52$	5.83860			0.809667
$53$	2.58263			0.354751			0.177376	−	0.984143i	$-0.443239\pi$
$53$	2.58263			0.354751			0.177376	+	0.984143i	$0.443239\pi$
$54$	−1.51563	+	2.62515i	−0.206251	+	0.357238i
$55$	−1.47734	−	2.55883i	−0.199205	−	0.345033i
$56$	1.04995	−	1.81857i	0.140306	−	0.243017i
$57$	11.6558	−	20.1884i	1.54385	−	2.67402i
$58$	−0.0198534			−0.00260688
$59$	−2.96262	−	5.13140i	−0.385700	−	0.668052i	0.606166	−	0.795338i	$-0.292707\pi$
$59$	−2.96262	−	5.13140i	−0.385700	−	0.668052i	−0.991866	+	0.127286i	$0.959373\pi$
$60$	3.12798			0.403821
$61$	−4.23381			−0.542083			−0.271042	−	0.962568i	$-0.587368\pi$
$61$	−4.23381			−0.542083			−0.271042	+	0.962568i	$0.587368\pi$
$62$	0.377816	−	0.654396i	0.0479826	−	0.0831083i
$63$	−10.6841	−	18.5054i	−1.34607	−	2.33146i
$64$	−7.11979			−0.889973
$65$	1.44370			0.179069
$66$	−3.85848			−0.474947
$67$	6.88046			0.840582			0.420291	−	0.907389i	$-0.361928\pi$
$67$	6.88046			0.840582			0.420291	+	0.907389i	$0.361928\pi$
$68$	−1.89776	−	3.28702i	−0.230137	−	0.398609i
$69$	25.3952			3.05722
$70$	0.128590	−	0.222724i	0.0153694	−	0.0266206i
$71$	−6.17437	+	10.6943i	−0.732763	+	1.26918i	0.222935	+	0.974833i	$0.428436\pi$
$71$	−6.17437	+	10.6943i	−0.732763	+	1.26918i	−0.955698	+	0.294349i	$0.904897\pi$
$72$	2.97630	−	5.15510i	0.350760	−	0.607534i
$73$	−0.123270	−	0.213510i	−0.0144276	−	0.0249894i	0.858721	−	0.512443i	$-0.171259\pi$
$73$	−0.123270	−	0.213510i	−0.0144276	−	0.0249894i	−0.873149	+	0.487453i	$0.837926\pi$
$74$	−0.148541	+	0.257281i	−0.0172675	+	0.0299083i
$75$	−15.6452			−1.80655
$76$	−6.96691	+	12.0670i	−0.799159	+	1.38418i
$77$	8.35754	−	14.4757i	0.952430	−	1.64966i
$78$	0.942655	−	1.63273i	0.106735	−	0.184870i
$79$	−8.96321			−1.00844			−0.504220	−	0.863575i	$-0.668220\pi$
$79$	−8.96321			−1.00844			−0.504220	+	0.863575i	$0.668220\pi$
$80$	−1.83350			−0.204992
$81$	−14.1120	−	24.4426i	−1.56800	−	2.71585i
$82$	−0.0156216	+	0.0270573i	−0.00172511	+	0.00298798i
$83$	−6.82682	+	11.8244i	−0.749340	+	1.29790i	0.198799	+	0.980040i	$0.436296\pi$
$83$	−6.82682	+	11.8244i	−0.749340	+	1.29790i	−0.948139	+	0.317855i	$0.897037\pi$
$84$	8.84772	+	15.3247i	0.965365	+	1.67206i
$85$	−0.469256	−	0.812775i	−0.0508980	−	0.0881579i
$86$	1.25877			0.135737
$87$	0.168888	−	0.292522i	0.0181067	−	0.0313617i
$88$	4.65636			0.496370
$89$	−6.49572	−	11.2509i	−0.688545	−	1.19260i	−0.972309	−	0.233701i	$-0.924916\pi$
$89$	−6.49572	−	11.2509i	−0.688545	−	1.19260i	0.283763	−	0.958894i	$-0.408417\pi$
$90$	0.364513	−	0.631355i	0.0384231	−	0.0665507i
$91$	4.08361	+	7.07302i	0.428079	+	0.741454i
$92$	−15.1792			−1.58254
$93$	6.42797	+	11.1336i	0.666549	+	1.15450i
$94$	−0.168450	+	0.291764i	−0.0173743	+	0.0300931i
$95$	−1.72270	+	2.98380i	−0.176745	+	0.306131i
$96$	−3.70869	+	6.42363i	−0.378516	+	0.655609i
$97$	−2.57858	+	4.46624i	−0.261816	+	0.453478i	−0.966724	−	0.255820i	$-0.917655\pi$
$97$	−2.57858	+	4.46624i	−0.261816	+	0.453478i	0.704909	+	0.709298i	$0.250988\pi$
$98$	0.103854			0.0104908
$99$	23.6911	−	41.0342i	2.38105	−	4.12409i
$100$	9.35143			0.935143
$101$	−4.23633			−0.421531			−0.210765	−	0.977537i	$-0.567596\pi$
$101$	−4.23633			−0.421531			−0.210765	+	0.977537i	$0.567596\pi$
$102$	−1.22559			−0.121352
$103$	8.92513			0.879419			0.439710	−	0.898140i	$-0.355081\pi$
$103$	8.92513			0.879419			0.439710	+	0.898140i	$0.355081\pi$
$104$	−1.13758	+	1.97035i	−0.111549	+	0.193209i
$105$	2.18776	+	3.78932i	0.213504	+	0.369799i
$106$	−0.249232	+	0.431683i	−0.0242076	+	0.0419287i
$107$	8.91961	−	15.4492i	0.862292	−	1.49353i	−0.00741973	−	0.999972i	$-0.502362\pi$
$107$	8.91961	−	15.4492i	0.862292	−	1.49353i	0.869711	−	0.493561i	$-0.164305\pi$
$108$	15.4129	+	26.6960i	1.48311	+	2.56882i
$109$	8.66799	+	15.0134i	0.830243	+	1.43802i	0.897846	+	0.440311i	$0.145132\pi$
$109$	8.66799	+	15.0134i	0.830243	+	1.43802i	−0.0676027	+	0.997712i	$0.521535\pi$
$110$	0.570274			0.0543735
$111$	−2.52720	−	4.37724i	−0.239871	−	0.415469i
$112$	−5.18619	−	8.98274i	−0.490049	−	0.848790i
$113$	−0.244523	+	0.423527i	−0.0230028	+	0.0398420i	−0.877298	−	0.479947i	$-0.840656\pi$
$113$	−0.244523	+	0.423527i	−0.0230028	+	0.0398420i	0.854295	+	0.519789i	$0.173989\pi$
$114$	2.24965	+	3.89650i	0.210699	+	0.364941i
$115$	−3.75334			−0.350001
$116$	−0.100948	+	0.174847i	−0.00937276	+	0.0162341i
$117$	11.5758	+	20.0499i	1.07018	+	1.85361i
$118$	1.14361			0.105278
$119$	2.65465	−	4.59799i	0.243351	−	0.421497i
$120$	−0.609451	+	1.05560i	−0.0556350	+	0.0963626i
$121$	26.0643			2.36948
$122$	0.408577	−	0.707676i	0.0369908	−	0.0640699i
$123$	−0.265777	−	0.460340i	−0.0239643	−	0.0415075i
$124$	−3.84213	−	6.65476i	−0.345033	−	0.597615i
$125$	4.73894			0.423864
$126$	4.12421			0.367414
$127$	−11.9509			−1.06047			−0.530237	−	0.847850i	$-0.677897\pi$
$127$	−11.9509			−1.06047			−0.530237	+	0.847850i	$0.677897\pi$
$128$	2.94591	−	5.10247i	0.260384	−	0.450999i
$129$	−10.7081	+	18.5469i	−0.942792	+	1.63296i
$130$	−0.139322	+	0.241313i	−0.0122193	+	0.0211645i
$131$	4.83555			0.422484			0.211242	−	0.977434i	$-0.432249\pi$
$131$	4.83555			0.422484			0.211242	+	0.977434i	$0.432249\pi$
$132$	−19.6191	+	33.9813i	−1.70762	+	2.95769i
$133$	−19.4911			−1.69009
$134$	−0.663987	+	1.15006i	−0.0573598	+	0.0993500i
$135$	3.81114	+	6.60108i	0.328010	+	0.568130i
$136$	1.47903			0.126825
$137$	−2.65621	−	4.60070i	−0.226936	−	0.393064i	0.729963	−	0.683487i	$-0.239537\pi$
$137$	−2.65621	−	4.60070i	−0.226936	−	0.393064i	−0.956898	+	0.290423i	$0.906204\pi$
$138$	−2.45072	+	4.24477i	−0.208619	+	0.361339i
$139$	12.0247			1.01992			0.509961	−	0.860198i	$-0.329660\pi$
$139$	12.0247			1.01992			0.509961	+	0.860198i	$0.329660\pi$
$140$	−1.30767	−	2.26495i	−0.110518	−	0.191423i
$141$	−2.86592	−	4.96392i	−0.241354	−	0.418038i
$142$	−1.19170	−	2.06408i	−0.100005	−	0.173213i
$143$	−9.05507	+	15.6838i	−0.757223	+	1.31155i
$144$	−14.7013	−	25.4634i	−1.22511	−	2.12195i
$145$	−0.0249612	+	0.0432340i	−0.00207291	+	0.00359039i
$146$	0.0475838			0.00393807
$147$	−0.883457	+	1.53019i	−0.0728663	+	0.126208i
$148$	1.51056	+	2.61637i	0.124167	+	0.215064i
$149$	0.0976068	−	0.169060i	0.00799626	−	0.0138499i	−0.862000	−	0.506909i	$-0.830788\pi$
$149$	0.0976068	−	0.169060i	0.00799626	−	0.0138499i	0.869996	+	0.493059i	$0.164121\pi$
$150$	1.50981	−	2.61507i	0.123276	−	0.213519i
$151$	3.29911	+	5.71422i	0.268477	+	0.465016i	0.968469	−	0.249135i	$-0.0801462\pi$
$151$	3.29911	+	5.71422i	0.268477	+	0.465016i	−0.699991	+	0.714151i	$0.746813\pi$
$152$	−2.71484	−	4.70224i	−0.220203	−	0.381402i
$153$	7.52513	−	13.0339i	0.608371	−	1.05373i
$154$	1.61306	+	2.79390i	0.129984	+	0.225139i
$155$	−0.950037	−	1.64551i	−0.0763088	−	0.132171i
$156$	−9.58616	−	16.6037i	−0.767507	−	1.32936i
$157$	11.5256	+	19.9629i	0.919843	+	1.59321i	0.799652	+	0.600464i	$0.205017\pi$
$157$	11.5256	+	19.9629i	0.919843	+	1.59321i	0.120191	+	0.992751i	$0.461649\pi$
$158$	0.864980	−	1.49819i	0.0688141	−	0.119190i
$159$	−4.24031	−	7.34444i	−0.336279	−	0.582452i
$160$	0.548134	−	0.949397i	0.0433338	−	0.0750564i
$161$	−10.6166	−	18.3885i	−0.836705	−	1.44921i
$162$	5.44741			0.427989
$163$	−14.6382			−1.14655			−0.573275	−	0.819363i	$-0.694327\pi$
$163$	−14.6382			−1.14655			−0.573275	+	0.819363i	$0.694327\pi$
$164$	0.158861	+	0.275155i	0.0124049	+	0.0214860i
$165$	−4.85118	+	8.40249i	−0.377664	+	0.654133i
$166$	−1.31762	−	2.28219i	−0.102267	−	0.177132i
$167$	22.3326			1.72815			0.864073	−	0.503366i	$-0.167905\pi$
$167$	22.3326			1.72815			0.864073	+	0.503366i	$0.167905\pi$
$168$	−6.89550			−0.531999
$169$	2.07557	+	3.59499i	0.159659	+	0.276538i
$170$	0.181139			0.0138927
$171$	−55.2513			−4.22517
$172$	6.40043	−	11.0859i	0.488028	−	0.845289i
$173$	−0.0685029	+	0.118650i	−0.00520818	+	0.00902083i	−0.868618	−	0.495483i	$-0.834991\pi$
$173$	−0.0685029	+	0.118650i	−0.00520818	+	0.00902083i	0.863410	+	0.504504i	$0.168324\pi$
$174$	0.0325965	+	0.0564587i	0.00247113	+	0.00428013i
$175$	6.54055	+	11.3286i	0.494419	+	0.856359i
$176$	11.4999	−	19.9185i	0.866841	−	1.50141i
$177$	−9.72841	+	16.8501i	−0.731232	+	1.26653i
$178$	2.50744			0.187940
$179$	17.9587			1.34229			0.671147	−	0.741324i	$-0.265802\pi$
$179$	17.9587			1.34229			0.671147	+	0.741324i	$0.265802\pi$
$180$	−3.70685	−	6.42046i	−0.276292	−	0.478553i
$181$	−22.5224			−1.67408			−0.837039	−	0.547143i	$-0.815715\pi$
$181$	−22.5224			−1.67408			−0.837039	+	0.547143i	$0.815715\pi$
$182$	−1.57633			−0.116845
$183$	6.95132	+	12.0400i	0.513856	+	0.890025i
$184$	2.95749	−	5.12253i	0.218029	−	0.377638i
$185$	0.373514	+	0.646945i	0.0274613	+	0.0475644i
$186$	−2.48128			−0.181936
$187$	11.7729			0.860922
$188$	1.71302	+	2.96704i	0.124935	+	0.216394i
$189$	−21.5601	+	37.3432i	−1.56827	+	2.71632i
$190$	−0.332492	−	0.575893i	−0.0241215	−	0.0417797i
$191$	−2.30744	+	3.99660i	−0.166961	+	0.289184i	−0.937350	−	0.348390i	$-0.886729\pi$
$191$	−2.30744	+	3.99660i	−0.166961	+	0.289184i	0.770389	+	0.637574i	$0.220062\pi$
$192$	11.6897	+	20.2472i	0.843631	+	1.46121i
$193$	−2.11545	−	3.66406i	−0.152273	−	0.263745i	0.779790	−	0.626042i	$-0.215326\pi$
$193$	−2.11545	−	3.66406i	−0.152273	−	0.263745i	−0.932063	+	0.362297i	$0.881993\pi$
$194$	−0.497684	−	0.862014i	−0.0357316	−	0.0618890i
$195$	−2.37036	−	4.10558i	−0.169745	−	0.294006i
$196$	0.528061	−	0.914628i	0.0377186	−	0.0653306i
$197$	9.05981	+	15.6920i	0.645485	+	1.11801i	0.984189	+	0.177119i	$0.0566778\pi$
$197$	9.05981	+	15.6920i	0.645485	+	1.11801i	−0.338705	+	0.940893i	$0.609989\pi$
$198$	4.57254	+	7.91988i	0.324956	+	0.562841i
$199$	4.74172	−	8.21289i	0.336131	−	0.582196i	−0.647570	−	0.762006i	$-0.724215\pi$
$199$	4.74172	−	8.21289i	0.336131	−	0.582196i	0.983701	+	0.179809i	$0.0575481\pi$
$200$	−1.82202	+	3.15583i	−0.128836	+	0.223151i
$201$	−11.2968	−	19.5665i	−0.796811	−	1.38012i
$202$	0.408820	−	0.708097i	0.0287645	−	0.0498216i
$203$	−0.282418			−0.0198218
$204$	−6.23171	+	10.7936i	−0.436307	+	0.755706i
$205$	0.0392812	+	0.0680371i	0.00274352	+	0.00475192i
$206$	−0.861306	+	1.49182i	−0.0600100	+	0.103940i
$207$	−30.0948	−	52.1258i	−2.09174	−	3.62299i
$208$	5.61903	+	9.73245i	0.389610	+	0.674824i
$209$	−21.6099	−	37.4295i	−1.49479	−	2.58905i
$210$	−0.844506			−0.0582764
$211$	−3.92657	+	6.80102i	−0.270316	+	0.468202i	−0.968943	−	0.247285i	$-0.920462\pi$
$211$	−3.92657	+	6.80102i	−0.270316	+	0.468202i	0.698626	+	0.715487i	$0.253795\pi$
$212$	2.53452	+	4.38992i	0.174072	+	0.301501i
$213$	40.5498			2.77843
$214$	1.72155	+	2.98181i	0.117682	+	0.203832i
$215$	1.58262	−	2.74118i	0.107934	−	0.186947i
$216$	−12.0121			−0.817322
$217$	5.37450	−	9.30890i	0.364845	−	0.631929i
$218$	−3.34596			−0.226617
$219$	−0.404784	+	0.701106i	−0.0273528	+	0.0473764i
$220$	2.89965	−	5.02234i	0.195494	−	0.338606i
$221$	−2.87621	+	4.98174i	−0.193475	+	0.335108i
$222$	0.975534			0.0654736
$223$	−0.694740			−0.0465233			−0.0232616	−	0.999729i	$-0.507405\pi$
$223$	−0.694740			−0.0465233			−0.0232616	+	0.999729i	$0.507405\pi$
$224$	6.20175			0.414372
$225$	18.5405	+	32.1131i	1.23603	+	2.14087i
$226$	−0.0471947	−	0.0817435i	−0.00313934	−	0.00543750i
$227$	−7.25455	+	12.5653i	−0.481502	+	0.833985i	−0.999775	−	0.0212299i	$-0.993242\pi$
$227$	−7.25455	+	12.5653i	−0.481502	+	0.833985i	0.518273	+	0.855215i	$0.326575\pi$
$228$	45.7548			3.03018
$229$	−9.10945	+	15.7780i	−0.601969	+	1.04264i	0.390553	+	0.920580i	$0.372284\pi$
$229$	−9.10945	+	15.7780i	−0.601969	+	1.04264i	−0.992523	+	0.122061i	$0.961050\pi$
$230$	0.362210	−	0.627366i	0.0238834	−	0.0413673i
$231$	−54.8876			−3.61134
$232$	−0.0393370	−	0.0681336i	−0.00258260	−	0.00447319i
$233$	−5.81622	+	10.0740i	−0.381033	+	0.659969i	−0.991210	−	0.132296i	$-0.957765\pi$
$233$	−5.81622	+	10.0740i	−0.381033	+	0.659969i	0.610177	+	0.792265i	$0.291098\pi$
$234$	−4.46842			−0.292110
$235$	0.423576	+	0.733655i	0.0276311	+	0.0478584i
$236$	5.81487	−	10.0717i	0.378516	−	0.655609i
$237$	14.7163	+	25.4895i	0.955929	+	1.65572i
$238$	0.512365	+	0.887442i	0.0332117	+	0.0575244i
$239$	1.26915			0.0820947			0.0410473	−	0.999157i	$-0.486931\pi$
$239$	1.26915			0.0820947			0.0410473	+	0.999157i	$0.486931\pi$
$240$	3.01035	+	5.21409i	0.194318	+	0.336568i
$241$	4.49597	+	7.78726i	0.289611	+	0.501621i	0.973717	−	0.227762i	$-0.0731407\pi$
$241$	4.49597	+	7.78726i	0.289611	+	0.501621i	−0.684106	+	0.729383i	$0.739807\pi$
$242$	−2.51529	+	4.35661i	−0.161689	+	0.280054i
$243$	−22.7815	+	39.4588i	−1.46144	+	2.53128i
$244$	−4.15495	−	7.19658i	−0.265993	−	0.460714i
$245$	0.130573	−	0.226159i	0.00834199	−	0.0144487i
$246$	0.102594			0.00654113
$247$	21.1178			1.34369
$248$	2.99438			0.190143
$249$	44.8347			2.84128
$250$	−0.457324	+	0.792109i	−0.0289237	+	0.0500973i
$251$	17.3565			1.09553			0.547766	−	0.836632i	$-0.315479\pi$
$251$	17.3565			1.09553			0.547766	+	0.836632i	$0.315479\pi$
$252$	20.9702	−	36.3214i	1.32100	−	2.28804i
$253$	23.5414	−	40.7749i	1.48004	−	2.56350i
$254$	1.15331	−	1.99758i	0.0723648	−	0.125340i
$255$	−1.54091	+	2.66893i	−0.0964953	+	0.167135i
$256$	−6.55120	−	11.3470i	−0.409450	−	0.709189i
$257$	−8.08889			−0.504571			−0.252285	−	0.967653i	$-0.581182\pi$
$257$	−8.08889			−0.504571			−0.252285	+	0.967653i	$0.581182\pi$
$258$	−2.06673	−	3.57968i	−0.128669	−	0.222861i
$259$	−2.11302	+	3.65986i	−0.131297	+	0.227413i
$260$	1.41681	+	2.45399i	0.0878668	+	0.152190i
$261$	−0.800570			−0.0495540
$262$	−0.466647	+	0.808256i	−0.0288295	+	0.0499342i
$263$	−10.7702			−0.664120			−0.332060	−	0.943258i	$-0.607744\pi$
$263$	−10.7702			−0.664120			−0.332060	+	0.943258i	$0.607744\pi$
$264$	−7.64510	−	13.2417i	−0.470523	−	0.814971i
$265$	0.626708	+	1.08549i	0.0384983	+	0.0666811i
$266$	1.88095	−	3.25791i	0.115329	−	0.199755i
$267$	−21.3301	+	36.9449i	−1.30538	+	2.26099i
$268$	6.75230	+	11.6953i	0.412463	+	0.714406i
$269$	18.9517			1.15550			0.577752	−	0.816213i	$-0.303930\pi$
$269$	18.9517			1.15550			0.577752	+	0.816213i	$0.303930\pi$
$270$	−1.47115			−0.0895313
$271$	9.42952	−	16.3324i	0.572802	−	0.992123i	−0.423474	−	0.905908i	$-0.639190\pi$
$271$	9.42952	−	16.3324i	0.572802	−	0.992123i	0.996277	−	0.0862146i	$-0.0274771\pi$
$272$	3.65279	−	6.32681i	0.221483	−	0.383619i
$273$	13.4094	−	23.2258i	0.811576	−	1.40569i
$274$	1.02533			0.0619427
$275$	−14.5031	+	25.1201i	−0.874571	+	1.51480i
$276$	24.9222	+	43.1664i	1.50014	+	2.59831i
$277$	0.833616	−	1.44387i	0.0500871	−	0.0867535i	−0.839895	−	0.542749i	$-0.817383\pi$
$277$	0.833616	−	1.44387i	0.0500871	−	0.0867535i	0.889982	+	0.455996i	$0.150717\pi$
$278$	−1.16042	+	2.00991i	−0.0695976	+	0.120547i
$279$	15.2351	−	26.3879i	0.912100	−	1.57980i
$280$	1.01914			0.0609051
$281$	11.4750	+	19.8752i	0.684539	+	1.18566i	0.973581	+	0.228340i	$0.0733297\pi$
$281$	11.4750	+	19.8752i	0.684539	+	1.18566i	−0.289043	+	0.957316i	$0.593337\pi$
$282$	1.10629			0.0658783
$283$	0.772090			0.0458960			0.0229480	−	0.999737i	$-0.492695\pi$
$283$	0.772090			0.0458960			0.0229480	+	0.999737i	$0.492695\pi$
$284$	−24.2375			−1.43823
$285$	11.3137			0.670166
$286$	−1.74769	−	3.02709i	−0.103343	−	0.178995i
$287$	−0.222220	+	0.384895i	−0.0131172	+	0.0227197i
$288$	17.5801			1.03592
$289$	−13.2605			−0.780030
$290$	−0.00481768	−	0.00834446i	−0.000282904	−	0.000490004i
$291$	16.9347			0.992730
$292$	0.241948	−	0.419066i	0.0141589	−	0.0245240i
$293$	−1.48250	+	2.56776i	−0.0866085	+	0.150010i	−0.906075	−	0.423116i	$-0.860936\pi$
$293$	−1.48250	+	2.56776i	−0.0866085	+	0.150010i	0.819467	+	0.573126i	$0.194270\pi$
$294$	−0.170513	−	0.295338i	−0.00994453	−	0.0172244i
$295$	1.43783	−	2.49040i	0.0837139	−	0.144997i
$296$	−1.17726			−0.0684269
$297$	−95.6156			−5.54818
$298$	0.0188388	+	0.0326297i	0.00109130	+	0.00189019i
$299$	11.5027	+	19.9232i	0.665216	+	1.15219i
$300$	−15.3538	−	26.5935i	−0.886449	−	1.53538i
$301$	17.9063			1.03210
$302$	−1.27350			−0.0732817
$303$	6.95546	+	12.0472i	0.399581	+	0.692095i
$304$	−26.8197			−1.53821
$305$	−1.02739	−	1.77949i	−0.0588280	−	0.101893i
$306$	1.45240	+	2.51563i	0.0830282	+	0.143809i
$307$	9.54368	−	16.5301i	0.544686	−	0.943425i	−0.453940	−	0.891032i	$-0.649982\pi$
$307$	9.54368	−	16.5301i	0.544686	−	0.943425i	0.998627	−	0.0523925i	$-0.0166847\pi$
$308$	32.8075			1.86938
$309$	−14.6538	−	25.3812i	−0.833627	−	1.44388i
$310$	0.366727			0.0208287
$311$	8.46981			0.480279			0.240139	−	0.970738i	$-0.422807\pi$
$311$	8.46981			0.480279			0.240139	+	0.970738i	$0.422807\pi$
$312$	7.47101			0.422962
$313$	−5.59585			−0.316296			−0.158148	−	0.987415i	$-0.550552\pi$
$313$	−5.59585			−0.316296			−0.158148	+	0.987415i	$0.550552\pi$
$314$	−4.44904			−0.251074
$315$	5.18527	−	8.98115i	0.292157	−	0.506030i
$316$	−8.79627	−	15.2356i	−0.494829	−	0.857068i
$317$	−7.91809	−	13.7145i	−0.444724	−	0.770285i	0.553309	−	0.832976i	$-0.313365\pi$
$317$	−7.91809	−	13.7145i	−0.444724	−	0.770285i	−0.998033	+	0.0626910i	$0.980032\pi$
$318$	1.63682			0.0917882
$319$	−0.313119	−	0.542338i	−0.0175313	−	0.0303651i
$320$	−1.72771	−	2.99248i	−0.0965818	−	0.167285i
$321$	−58.5791			−3.26956
$322$	4.09815			0.228381
$323$	−6.86407	−	11.8889i	−0.381927	−	0.661517i
$324$	27.6982	−	47.9747i	1.53879	−	2.66526i
$325$	−7.08643	−	12.2741i	−0.393084	−	0.680842i
$326$	1.41263	−	2.44675i	0.0782385	−	0.135513i
$327$	28.4633	−	49.2998i	1.57402	−	2.72629i
$328$	−0.123809			−0.00683619
$329$	−2.39623	+	4.15039i	−0.132108	+	0.228819i
$330$	−0.936311	−	1.62174i	−0.0515422	−	0.0892737i
$331$	−2.19144	−	3.79568i	−0.120452	−	0.208630i	0.799494	−	0.600674i	$-0.205101\pi$
$331$	−2.19144	−	3.79568i	−0.120452	−	0.208630i	−0.919946	+	0.392045i	$0.871768\pi$
$332$	−26.7986			−1.47077
$333$	−5.98978	+	10.3746i	−0.328238	+	0.568525i
$334$	−2.15517	+	3.73286i	−0.117926	+	0.204253i
$335$	1.66963	+	2.89189i	0.0912217	+	0.158001i
$336$	−17.0300	+	29.4968i	−0.929063	+	1.60918i
$337$	10.6850	−	18.5070i	0.582051	−	1.00814i	−0.413185	−	0.910647i	$-0.635584\pi$
$337$	10.6850	−	18.5070i	0.582051	−	1.00814i	0.995236	−	0.0974951i	$-0.0310830\pi$
$338$	−0.801198			−0.0435794
$339$	1.60589			0.0872201
$340$	0.921032	−	1.59527i	0.0499499	−	0.0865158i
$341$	23.8350			1.29074
$342$	5.33194	−	9.23519i	0.288318	−	0.499382i
$343$	−17.7416			−0.957954
$344$	2.49410	+	4.31990i	0.134473	+	0.232914i
$345$	6.16246	+	10.6737i	0.331776	+	0.574653i
$346$	−0.0132215	−	0.0229003i	−0.000710793	−	0.00123113i
$347$	−1.83692	+	3.18164i	−0.0986110	+	0.170799i	−0.911110	−	0.412163i	$-0.864773\pi$
$347$	−1.83692	+	3.18164i	−0.0986110	+	0.170799i	0.812499	+	0.582963i	$0.198107\pi$
$348$	0.662968			0.0355388
$349$	5.92697	+	17.7164i	0.317263	+	0.948338i
$349$	5.92697	+	17.7164i	0.317263	+	0.948338i
$350$	−2.52474			−0.134953
$351$	23.3596	−	40.4600i	1.24684	−	2.15959i
$352$	6.87593	+	11.9095i	0.366488	+	0.634776i
$353$	−1.91385	−	3.31489i	−0.101864	−	0.176434i	0.810589	−	0.585616i	$-0.199147\pi$
$353$	−1.91385	−	3.31489i	−0.101864	−	0.176434i	−0.912453	+	0.409182i	$0.865814\pi$
$354$	−1.87765	−	3.25218i	−0.0997959	−	0.172852i
$355$	−5.99316			−0.318084
$356$	12.7495	−	22.0827i	0.675720	−	1.17038i
$357$	−17.4343			−0.922718
$358$	−1.73307	+	3.00177i	−0.0915958	+	0.158648i
$359$	−15.1664			−0.800453			−0.400226	−	0.916416i	$-0.631068\pi$
$359$	−15.1664			−0.800453			−0.400226	+	0.916416i	$0.631068\pi$
$360$	2.88895			0.152261
$361$	−15.6988	+	27.1912i	−0.826255	+	1.43112i
$362$	2.17349	−	3.76459i	0.114236	−	0.197863i
$363$	−42.7939	−	74.1213i	−2.24610	−	3.89036i
$364$	−8.01510	+	13.8826i	−0.420105	+	0.727644i
$365$	0.0598260	−	0.103622i	0.00313144	−	0.00542381i
$366$	−2.68330			−0.140259
$367$	6.52242	+	11.2972i	0.340468	+	0.589707i	0.984520	−	0.175274i	$-0.0560813\pi$
$367$	6.52242	+	11.2972i	0.340468	+	0.589707i	−0.644052	+	0.764982i	$0.722748\pi$
$368$	−14.6084	−	25.3025i	−0.761515	−	1.31898i
$369$	−0.629925	+	1.09106i	−0.0327926	+	0.0567985i
$370$	−0.144182			−0.00749564
$371$	−3.54537	+	6.14077i	−0.184067	+	0.318813i
$372$	−12.6165	+	21.8524i	−0.654134	+	1.13299i
$373$	−6.50116	−	11.2603i	−0.336617	−	0.583038i	0.647177	−	0.762340i	$-0.275949\pi$
$373$	−6.50116	−	11.2603i	−0.336617	−	0.583038i	−0.983794	+	0.179302i	$0.942616\pi$
$374$	−1.13613	+	1.96783i	−0.0587477	+	0.101754i
$375$	−7.78069	−	13.4765i	−0.401793	−	0.695926i
$376$	−1.33505			−0.0688499
$377$	0.305989			0.0157592
$378$	−4.16125	−	7.20750i	−0.214032	−	0.370714i
$379$	9.49327	+	16.4428i	0.487637	+	0.844611i	0.999899	−	0.0142176i	$-0.00452577\pi$
$379$	9.49327	+	16.4428i	0.487637	+	0.844611i	−0.512262	+	0.858829i	$0.671192\pi$
$380$	−6.76244			−0.346906
$381$	19.6218	+	33.9859i	1.00525	+	1.74115i
$382$	−0.445352	−	0.771372i	−0.0227862	−	0.0394668i
$383$	5.68785	−	9.85165i	0.290636	−	0.503396i	−0.683325	−	0.730115i	$-0.739467\pi$
$383$	5.68785	−	9.85165i	0.290636	−	0.503396i	0.973960	+	0.226719i	$0.0727999\pi$
$384$	−19.3471			−0.987304
$385$	8.11226			0.413439
$386$	0.816592			0.0415634
$387$	50.7588			2.58022
$388$	−10.1222			−0.513878
$389$	6.02017	+	10.4272i	0.305235	+	0.528682i	0.977314	−	0.211797i	$-0.0679317\pi$
$389$	6.02017	+	10.4272i	0.305235	+	0.528682i	−0.672079	+	0.740480i	$0.734598\pi$
$390$	0.914989			0.0463323
$391$	7.47758	−	12.9516i	0.378158	−	0.654988i
$392$	0.205773	+	0.356409i	0.0103931	+	0.0180014i
$393$	−7.93930	−	13.7513i	−0.400485	−	0.693660i
$394$	−3.49721			−0.176187
$395$	−2.17504	−	3.76728i	−0.109438	−	0.189552i
$396$	92.9993			4.67339
$397$	−27.6469			−1.38756			−0.693780	−	0.720187i	$-0.744056\pi$
$397$	−27.6469			−1.38756			−0.693780	+	0.720187i	$0.744056\pi$
$398$	0.915183	+	1.58514i	0.0458740	+	0.0794561i
$399$	32.0016	+	55.4285i	1.60209	+	2.77489i
$400$	8.99977	+	15.5881i	0.449989	+	0.779403i
$401$	−0.389185			−0.0194350			−0.00971749	−	0.999953i	$-0.503093\pi$
$401$	−0.389185			−0.0194350			−0.00971749	+	0.999953i	$0.503093\pi$
$402$	4.36070			0.217492
$403$	−5.82306	+	10.0858i	−0.290067	+	0.502411i
$404$	−4.15743	−	7.20087i	−0.206840	−	0.358257i
$405$	6.84890	−	11.8626i	0.340324	−	0.589459i
$406$	0.0272543	−	0.0472058i	0.00135261	−	0.00234278i
$407$	−9.37091			−0.464499
$408$	−2.42835	−	4.20603i	−0.120221	−	0.208230i
$409$	−10.2292			−0.505804			−0.252902	−	0.967492i	$-0.581385\pi$
$409$	−10.2292			−0.505804			−0.252902	+	0.967492i	$0.581385\pi$
$410$	−0.0151631			−0.000748851
$411$	−8.72226	+	15.1074i	−0.430238	+	0.745193i
$412$	8.75889	+	15.1709i	0.431520	+	0.747414i
$413$	16.2681			0.800499
$414$	11.6170			0.570945
$415$	−6.62646			−0.325280
$416$	−6.71935			−0.329443
$417$	−19.7429	−	34.1957i	−0.966813	−	1.67457i
$418$	8.34172			0.408007
$419$	−8.09991	+	14.0295i	−0.395707	+	0.685384i	−0.993191	−	0.116497i	$-0.962834\pi$
$419$	−8.09991	+	14.0295i	−0.395707	+	0.685384i	0.597485	+	0.801880i	$0.296167\pi$
$420$	−4.29403	+	7.43747i	−0.209527	+	0.362911i
$421$	11.4529	−	19.8371i	0.558182	−	0.966800i	−0.439466	−	0.898259i	$-0.644832\pi$
$421$	11.4529	−	19.8371i	0.558182	−	0.966800i	0.997648	−	0.0685409i	$-0.0218344\pi$
$422$	−0.757855	−	1.31264i	−0.0368918	−	0.0638985i
$423$	−6.79259	+	11.7651i	−0.330267	+	0.572040i
$424$	−1.97529			−0.0959285
$425$	−4.60670	+	7.97904i	−0.223458	+	0.387040i
$426$	−3.91320	+	6.77785i	−0.189595	+	0.328388i
$427$	5.81208	−	10.0668i	0.281266	−	0.487167i
$428$	35.0139			1.69246
$429$	59.4686			2.87117
$430$	0.305457	+	0.529067i	0.0147304	+	0.0255139i
$431$	7.92508	−	13.7266i	0.381738	−	0.661189i	−0.609573	−	0.792730i	$-0.708659\pi$
$431$	7.92508	−	13.7266i	0.381738	−	0.661189i	0.991311	+	0.131541i	$0.0419925\pi$
$432$	−29.6667	+	51.3842i	−1.42734	+	2.47222i
$433$	10.3712	+	17.9635i	0.498410	+	0.863272i	0.999998	−	0.00183495i	$-0.000584083\pi$
$433$	10.3712	+	17.9635i	0.498410	+	0.863272i	−0.501588	+	0.865106i	$0.667251\pi$
$434$	1.03731	+	1.79668i	0.0497927	+	0.0862434i
$435$	0.163931			0.00785990
$436$	−17.0131	+	29.4675i	−0.814779	+	1.41124i
$437$	−54.9022			−2.62633
$438$	−0.0781260	−	0.135318i	−0.00373301	−	0.00646575i
$439$	−6.54454	+	11.3355i	−0.312354	+	0.541013i	−0.978871	−	0.204477i	$-0.934451\pi$
$439$	−6.54454	+	11.3355i	−0.312354	+	0.541013i	0.666518	+	0.745489i	$0.267784\pi$
$440$	1.12993	+	1.95709i	0.0538671	+	0.0933006i
$441$	4.18781			0.199419
$442$	−0.555128	−	0.961509i	−0.0264047	−	0.0457343i
$443$	7.41282	−	12.8394i	0.352194	−	0.610018i	−0.634440	−	0.772972i	$-0.718769\pi$
$443$	7.41282	−	12.8394i	0.352194	−	0.610018i	0.986634	+	0.162955i	$0.0521024\pi$
$444$	4.96026	−	8.59143i	0.235404	−	0.407731i
$445$	3.15254	−	5.46036i	0.149445	−	0.258846i
$446$	0.0670448	−	0.116125i	0.00317466	−	0.00549868i
$447$	−0.641027			−0.0303195
$448$	9.77389	−	16.9289i	0.461773	−	0.799814i
$449$	−20.3128			−0.958622			−0.479311	−	0.877645i	$-0.659113\pi$
$449$	−20.3128			−0.958622			−0.479311	+	0.877645i	$0.659113\pi$
$450$	−7.15688			−0.337378
$451$	−0.985507			−0.0464057
$452$	−0.959875			−0.0451487
$453$	10.8333	−	18.7639i	0.508995	−	0.881605i
$454$	−1.40018	−	2.42518i	−0.0657136	−	0.113819i
$455$	−1.98188	+	3.43272i	−0.0929120	+	0.160928i
$456$	−8.91478	+	15.4409i	−0.417473	+	0.723084i
$457$	15.9448	+	27.6172i	0.745868	+	1.29188i	0.949788	+	0.312893i	$0.101298\pi$
$457$	15.9448	+	27.6172i	0.745868	+	1.29188i	−0.203921	+	0.978987i	$0.565369\pi$
$458$	−1.75819	−	3.04527i	−0.0821546	−	0.142296i
$459$	−30.3709			−1.41759
$460$	−3.68343	−	6.37989i	−0.171741	−	0.297464i
$461$	4.14239	+	7.17482i	0.192930	+	0.334165i	0.946220	−	0.323524i	$-0.104868\pi$
$461$	4.14239	+	7.17482i	0.192930	+	0.334165i	−0.753290	+	0.657689i	$0.771534\pi$
$462$	5.29684	−	9.17440i	0.246431	−	0.426832i
$463$	−3.02745	−	5.24370i	−0.140698	−	0.243696i	0.787062	−	0.616874i	$-0.211601\pi$
$463$	−3.02745	−	5.24370i	−0.140698	−	0.243696i	−0.927760	+	0.373179i	$0.878268\pi$
$464$	−0.388606			−0.0180406
$465$	−3.11966	+	5.40341i	−0.144671	+	0.250577i
$466$	−1.12257	−	1.94435i	−0.0520021	−	0.0900702i
$467$	−14.4589			−0.669078			−0.334539	−	0.942382i	$-0.608581\pi$
$467$	−14.4589			−0.669078			−0.334539	+	0.942382i	$0.608581\pi$
$468$	−22.7204	+	39.3529i	−1.05025	+	1.81909i
$469$	−9.44534	+	16.3598i	−0.436145	+	0.755426i
$470$	−0.163506			−0.00754198
$471$	37.8469	−	65.5527i	1.74389	−	3.02051i
$472$	2.26592	+	3.92469i	0.104297	+	0.180648i
$473$	19.8528	+	34.3861i	0.912833	+	1.58107i
$474$	−5.68071			−0.260924
$475$	33.8235			1.55193
$476$	10.4208			0.477637
$477$	−10.0501	+	17.4072i	−0.460161	+	0.797022i
$478$	−0.122478	+	0.212137i	−0.00560199	+	0.00970294i
$479$	1.57486	−	2.72774i	0.0719571	−	0.124633i	−0.827802	−	0.561021i	$-0.810409\pi$
$479$	1.57486	−	2.72774i	0.0719571	−	0.124633i	0.899759	+	0.436387i	$0.143742\pi$
$480$	−3.59984			−0.164310
$481$	2.28938	−	3.96532i	0.104387	−	0.180803i
$482$	−1.73551			−0.0790502
$483$	−34.8619	+	60.3826i	−1.58627	+	2.74750i
$484$	25.5788	+	44.3038i	1.16267	+	2.01381i
$485$	−2.50291			−0.113651
$486$	−4.39699	−	7.61581i	−0.199452	−	0.345460i
$487$	0.919421	−	1.59248i	0.0416629	−	0.0721623i	−0.844442	−	0.535647i	$-0.820068\pi$
$487$	0.919421	−	1.59248i	0.0416629	−	0.0721623i	0.886105	+	0.463485i	$0.153401\pi$
$488$	3.23817			0.146585
$489$	24.0338	+	41.6278i	1.08685	+	1.88248i
$490$	0.0252014	+	0.0436502i	0.00113848	+	0.00197191i
$491$	2.96126	+	5.12905i	0.133640	+	0.231471i	0.925077	−	0.379780i	$-0.124000\pi$
$491$	2.96126	+	5.12905i	0.133640	+	0.231471i	−0.791437	+	0.611250i	$0.790667\pi$
$492$	0.521654	−	0.903532i	0.0235180	−	0.0407343i
$493$	−0.0994577	−	0.172266i	−0.00447935	−	0.00775846i
$494$	−2.03794	+	3.52982i	−0.0916913	+	0.158814i
$495$	22.9958			1.03358
$496$	7.39529	−	12.8090i	0.332058	−	0.575142i
$497$	−16.9521	−	29.3619i	−0.760405	−	1.31706i
$498$	−4.32670	+	7.49407i	−0.193884	+	0.335817i
$499$	10.3911	−	17.9980i	0.465171	−	0.805699i	−0.534039	−	0.845460i	$-0.679326\pi$
$499$	10.3911	−	17.9980i	0.465171	−	0.805699i	0.999209	+	0.0397609i	$0.0126596\pi$
$500$	4.65068	+	8.05521i	0.207985	+	0.360240i
$501$	−36.6670	−	63.5091i	−1.63816	−	2.83738i
$502$	−1.67496	+	2.90111i	−0.0747571	+	0.129483i
$503$	1.35731	+	2.35093i	0.0605196	+	0.104823i	0.894698	−	0.446672i	$-0.147391\pi$
$503$	1.35731	+	2.35093i	0.0605196	+	0.104823i	−0.834178	+	0.551495i	$0.814058\pi$
$504$	8.17160	+	14.1536i	0.363992	+	0.630452i
$505$	−1.02800	−	1.78055i	−0.0457454	−	0.0792334i
$506$	4.54365	+	7.86984i	0.201990	+	0.349857i
$507$	6.81559	−	11.8049i	0.302691	−	0.524276i
$508$	−11.7283	−	20.3141i	−0.520361	−	0.901291i
$509$	−14.9253	+	25.8514i	−0.661552	+	1.14584i	0.318656	+	0.947871i	$0.396769\pi$
$509$	−14.9253	+	25.8514i	−0.661552	+	1.14584i	−0.980208	+	0.197972i	$0.936565\pi$
$510$	−0.297405	−	0.515121i	−0.0131693	−	0.0228099i
$511$	0.676889			0.0299438
$512$	14.3125			0.632530
$513$	55.7476	+	96.5577i	2.46132	+	4.26313i
$514$	0.780605	−	1.35205i	0.0344310	−	0.0596363i
$515$	2.16580	+	3.75127i	0.0954365	+	0.165301i
$516$	−42.0344			−1.85046
$517$	−10.6269			−0.467370
$518$	−0.407828	−	0.706378i	−0.0179189	−	0.0310365i
$519$	0.449889			0.0197479
$520$	−1.10420			−0.0484222
$521$	−20.4580	+	35.4344i	−0.896283	+	1.55241i	−0.0640751	+	0.997945i	$0.520410\pi$
$521$	−20.4580	+	35.4344i	−0.896283	+	1.55241i	−0.832208	+	0.554463i	$0.812924\pi$
$522$	0.0772577	−	0.133814i	0.00338148	−	0.00585689i
$523$	−20.2393	−	35.0554i	−0.885001	−	1.53287i	−0.845712	−	0.533640i	$-0.820824\pi$
$523$	−20.2393	−	35.0554i	−0.885001	−	1.53287i	−0.0392894	−	0.999228i	$-0.512509\pi$
$524$	4.74548	+	8.21942i	0.207307	+	0.359067i
$525$	21.4773	−	37.1998i	0.937348	−	1.62353i
$526$	1.03936	−	1.80023i	0.0453184	−	0.0784937i
$527$	7.57084			0.329791
$528$	−75.5252			−3.28681
$529$	−18.4047	−	31.8778i	−0.800204	−	1.38599i
$530$	−0.241918			−0.0105082
$531$	46.1151			2.00122
$532$	−19.1280	−	33.1307i	−0.829306	−	1.43640i
$533$	0.240766	−	0.417019i	0.0104287	−	0.0180631i
$534$	−4.11686	−	7.13061i	−0.178154	−	0.308572i
$535$	8.65784			0.374311
$536$	−5.26243			−0.227302
$537$	−29.4856	−	51.0706i	−1.27240	−	2.20386i
$538$	−1.82890	+	3.16775i	−0.0788495	+	0.136571i
$539$	1.63794	+	2.83699i	0.0705509	+	0.122198i
$540$	−7.48030	+	12.9563i	−0.321901	+	0.557549i
$541$	−3.06229	−	5.30404i	−0.131658	−	0.228038i	0.792658	−	0.609667i	$-0.208697\pi$
$541$	−3.06229	−	5.30404i	−0.131658	−	0.228038i	−0.924316	+	0.381628i	$0.875363\pi$
$542$	1.81996	+	3.15226i	0.0781740	+	0.135401i
$543$	36.9787	+	64.0489i	1.58691	+	2.74860i
$544$	2.18404	+	3.78287i	0.0936399	+	0.162189i
$545$	−4.20680	+	7.28639i	−0.180199	+	0.312115i
$546$	2.58811	+	4.48274i	0.110761	+	0.191844i
$547$	−16.5880	−	28.7312i	−0.709251	−	1.22846i	−0.965135	−	0.261751i	$-0.915700\pi$
$547$	−16.5880	−	28.7312i	−0.709251	−	1.22846i	0.255885	−	0.966707i	$-0.417633\pi$
$548$	5.21348	−	9.03001i	0.222709	−	0.385743i
$549$	16.4755	−	28.5364i	0.703157	−	1.21790i
$550$	−2.79920	−	4.84836i	−0.119358	−	0.206735i
$551$	−0.365121	+	0.632409i	−0.0155547	+	0.0269415i
$552$	−19.4232			−0.826705
$553$	12.3045	−	21.3120i	0.523241	−	0.906280i
$554$	0.160894	+	0.278676i	0.00683571	+	0.0118398i
$555$	1.22652	−	2.12439i	0.0520627	−	0.0901753i
$556$	11.8007	+	20.4395i	0.500462	+	0.866826i
$557$	16.8468	+	29.1795i	0.713823	+	1.23638i	0.963412	+	0.268025i	$0.0863710\pi$
$557$	16.8468	+	29.1795i	0.713823	+	1.23638i	−0.249589	+	0.968352i	$0.580296\pi$
$558$	2.94047	+	5.09305i	0.124480	+	0.215606i
$559$	−19.4007			−0.820563
$560$	2.51699	−	4.35956i	0.106362	−	0.184225i
$561$	−19.3295	−	33.4797i	−0.816092	−	1.41351i
$562$	−4.42949			−0.186847
$563$	−0.0564189	−	0.0977205i	−0.00237778	−	0.00411843i	0.864834	−	0.502058i	$-0.167424\pi$
$563$	−0.0564189	−	0.0977205i	−0.00237778	−	0.00411843i	−0.867212	+	0.497939i	$0.834090\pi$
$564$	5.62509	−	9.74293i	0.236859	−	0.410252i
$565$	−0.237347			−0.00998526
$566$	−0.0745093	+	0.129054i	−0.00313186	+	0.00542454i
$567$	77.4904			3.25429
$568$	4.72239	−	8.17942i	0.198147	−	0.343201i
$569$	−13.9195	+	24.1093i	−0.583535	+	1.01071i	0.411521	+	0.911400i	$0.364998\pi$
$569$	−13.9195	+	24.1093i	−0.583535	+	1.01071i	−0.995056	+	0.0993127i	$0.968336\pi$
$570$	−1.09181	+	1.89107i	−0.0457309	+	0.0792083i
$571$	−36.3472			−1.52108			−0.760541	−	0.649290i	$-0.775066\pi$
$571$	−36.3472			−1.52108			−0.760541	+	0.649290i	$0.775066\pi$
$572$	−35.5456			−1.48624
$573$	15.1540			0.633067
$574$	−0.0428899	−	0.0742874i	−0.00179019	−	0.00310070i
$575$	18.4233	+	31.9101i	0.768306	+	1.33075i
$576$	27.7060	−	47.9883i	1.15442	−	1.99951i
$577$	−7.84966			−0.326786			−0.163393	−	0.986561i	$-0.552244\pi$
$577$	−7.84966			−0.326786			−0.163393	+	0.986561i	$0.552244\pi$
$578$	1.27968	−	2.21648i	0.0532278	−	0.0921933i
$579$	−6.94654	+	12.0318i	−0.288688	+	0.500023i
$580$	−0.0979850			−0.00406861
$581$	−18.7434	−	32.4645i	−0.777608	−	1.34686i
$582$	−1.63426	+	2.83062i	−0.0677421	+	0.117333i
$583$	−15.7231			−0.651186
$584$	0.0942814	+	0.163300i	0.00390139	+	0.00675741i
$585$	−5.61804	+	9.73072i	−0.232277	+	0.402316i
$586$	−0.286132	−	0.495596i	−0.0118200	−	0.0204729i
$587$	−15.1292	−	26.2045i	−0.624447	−	1.08157i	−0.988647	−	0.150254i	$-0.951991\pi$
$587$	−15.1292	−	26.2045i	−0.624447	−	1.08157i	0.364200	−	0.931321i	$-0.381342\pi$
$588$	−3.46801			−0.143018
$589$	−13.8967	−	24.0698i	−0.572605	−	0.991781i
$590$	0.277512	+	0.480664i	0.0114250	+	0.0197886i
$591$	29.7499	−	51.5283i	1.22375	−	2.11959i
$592$	−2.90751	+	5.03596i	−0.119498	+	0.206977i
$593$	−4.95747	−	8.58659i	−0.203579	−	0.352609i	0.746100	−	0.665834i	$-0.231924\pi$
$593$	−4.95747	−	8.58659i	−0.203579	−	0.352609i	−0.949679	+	0.313225i	$0.898591\pi$
$594$	9.22723	−	15.9820i	0.378598	−	0.655751i
$595$	2.57674			0.105636
$596$	0.383155			0.0156946
$597$	−31.1409			−1.27451
$598$	−4.44018			−0.181573
$599$	−16.3371	+	28.2967i	−0.667516	+	1.15617i	0.311081	+	0.950383i	$0.399309\pi$
$599$	−16.3371	+	28.2967i	−0.667516	+	1.15617i	−0.978597	+	0.205788i	$0.934024\pi$
$600$	11.9660			0.488510
$601$	2.74441	−	4.75345i	0.111947	−	0.193897i	−0.804608	−	0.593806i	$-0.797625\pi$
$601$	2.74441	−	4.75345i	0.111947	−	0.193897i	0.916555	+	0.399908i	$0.130958\pi$
$602$	−1.72801	+	2.99301i	−0.0704286	+	0.121986i
$603$	−26.7747	+	46.3751i	−1.09035	+	1.88854i
$604$	−6.47531	+	11.2156i	−0.263477	+	0.456355i
$605$	6.32484	+	10.9549i	0.257141	+	0.445382i
$606$	−2.68490			−0.109067
$607$	−9.41369	−	16.3050i	−0.382090	−	0.661799i	0.609271	−	0.792962i	$-0.291462\pi$
$607$	−9.41369	−	16.3050i	−0.382090	−	0.661799i	−0.991361	+	0.131163i	$0.958129\pi$
$608$	8.01787	−	13.8874i	0.325168	−	0.563207i
$609$	0.463691	+	0.803136i	0.0187897	+	0.0325447i
$610$	0.396586			0.0160573
$611$	2.59622	−	4.49679i	0.105032	−	0.181921i
$612$	29.5399			1.19408
$613$	2.00995	+	3.48133i	0.0811810	+	0.140610i	0.903757	−	0.428045i	$-0.140797\pi$
$613$	2.00995	+	3.48133i	0.0811810	+	0.140610i	−0.822576	+	0.568655i	$0.807464\pi$
$614$	1.84199	+	3.19043i	0.0743369	+	0.128755i
$615$	0.128989	−	0.223415i	0.00520132	−	0.00900896i
$616$	−6.39216	+	11.0715i	−0.257547	+	0.446085i
$617$	−6.98657	−	12.1011i	−0.281269	−	0.487171i	0.690429	−	0.723400i	$-0.257422\pi$
$617$	−6.98657	−	12.1011i	−0.281269	−	0.487171i	−0.971697	+	0.236229i	$0.924088\pi$
$618$	5.65658			0.227541
$619$	−20.8565			−0.838293			−0.419146	−	0.907919i	$-0.637671\pi$
$619$	−20.8565			−0.838293			−0.419146	+	0.907919i	$0.637671\pi$
$620$	1.86468	−	3.22973i	0.0748875	−	0.129709i
$621$	−60.7303	+	105.188i	−2.43702	+	4.22105i
$622$	−0.817365	+	1.41572i	−0.0327734	+	0.0567651i
$623$	35.6688			1.42904
$624$	18.4513	−	31.9587i	0.738645	−	1.27937i
$625$	−10.7612	−	18.6389i	−0.430447	−	0.745557i
$626$	0.540018	−	0.935339i	0.0215835	−	0.0373837i
$627$	−70.9610	+	122.908i	−2.83391	+	4.90847i
$628$	−22.6218	+	39.1822i	−0.902710	+	1.56354i
$629$	−2.97653			−0.118682
$630$	1.00079	+	1.73342i	0.0398725	+	0.0690612i
$631$	−42.0709			−1.67482			−0.837408	−	0.546579i	$-0.815930\pi$
$631$	−42.0709			−1.67482			−0.837408	+	0.546579i	$0.815930\pi$
$632$	6.85540			0.272693
$633$	25.7875			1.02496
$634$	3.05649			0.121389
$635$	−2.90005	−	5.02303i	−0.115085	−	0.199333i
$636$	8.32267	−	14.4153i	0.330015	−	0.571603i
$637$	−1.60064			−0.0634196
$638$	0.120868			0.00478522
$639$	−48.0541	−	83.2321i	−1.90099	−	3.29261i
$640$	2.85946			0.113030
$641$	5.14496	−	8.91133i	0.203214	−	0.351976i	−0.746348	−	0.665555i	$-0.768195\pi$
$641$	5.14496	−	8.91133i	0.203214	−	0.351976i	0.949562	+	0.313579i	$0.101528\pi$
$642$	5.65308	−	9.79142i	0.223109	−	0.386436i
$643$	17.2748	+	29.9209i	0.681253	+	1.17997i	0.974599	+	0.223959i	$0.0718981\pi$
$643$	17.2748	+	29.9209i	0.681253	+	1.17997i	−0.293345	+	0.956007i	$0.594769\pi$
$644$	20.8377	−	36.0919i	0.821120	−	1.42222i
$645$	−10.3938			−0.409255
$646$	2.64963			0.104248
$647$	21.8920	+	37.9180i	0.860662	+	1.49071i	0.871291	+	0.490768i	$0.163284\pi$
$647$	21.8920	+	37.9180i	0.860662	+	1.49071i	−0.0106281	+	0.999944i	$0.503383\pi$
$648$	10.7934	+	18.6946i	0.424003	+	0.734395i
$649$	18.0365	+	31.2402i	0.707996	+	1.22629i
$650$	2.73546			0.107293
$651$	−35.2967			−1.38339
$652$	−14.3655	−	24.8818i	−0.562597	−	0.974447i
$653$	−34.9739			−1.36863			−0.684317	−	0.729185i	$-0.739899\pi$
$653$	−34.9739			−1.36863			−0.684317	+	0.729185i	$0.739899\pi$
$654$	5.49360	+	9.51520i	0.214817	+	0.372074i
$655$	1.17341	+	2.03240i	0.0458489	+	0.0794126i
$656$	−0.305773	+	0.529615i	−0.0119384	+	0.0206780i
$657$	1.91878			0.0748586
$658$	−0.462489	−	0.801054i	−0.0180297	−	0.0312283i
$659$	21.4708			0.836384			0.418192	−	0.908359i	$-0.362664\pi$
$659$	21.4708			0.836384			0.418192	+	0.908359i	$0.362664\pi$
$660$	−19.0433			−0.741259
$661$	39.7325			1.54542			0.772708	−	0.634761i	$-0.218901\pi$
$661$	39.7325			1.54542			0.772708	+	0.634761i	$0.218901\pi$
$662$	0.845925			0.0328778
$663$	18.8893			0.733601
$664$	5.22140	−	9.04373i	0.202630	−	0.350965i
$665$	−4.72976	−	8.19219i	−0.183412	−	0.317679i
$666$	−1.15607	−	2.00237i	−0.0447968	−	0.0775903i
$667$	−0.795511			−0.0308023
$668$	21.9166	+	37.9607i	0.847979	+	1.46874i
$669$	1.14067	+	1.97569i	0.0441007	+	0.0763847i
$670$	−0.644500			−0.0248992
$671$	25.7756			0.995056
$672$	−10.1824	−	17.6364i	−0.392795	−	0.680341i
$673$	16.0495	−	27.7985i	0.618662	−	1.07155i	−0.371068	−	0.928606i	$-0.621008\pi$
$673$	16.0495	−	27.7985i	0.618662	−	1.07155i	0.989730	−	0.142948i	$-0.0456582\pi$
$674$	2.06229	+	3.57198i	0.0794363	+	0.137588i
$675$	37.4140	−	64.8030i	1.44007	−	2.49427i
$676$	−4.07382	+	7.05606i	−0.156685	+	0.271387i
$677$	36.5823			1.40597			0.702987	−	0.711203i	$-0.251849\pi$
$677$	36.5823			1.40597			0.702987	+	0.711203i	$0.251849\pi$
$678$	−0.154974	+	0.268423i	−0.00595174	+	0.0103087i
$679$	−7.07965	−	12.2623i	−0.271692	−	0.470584i
$680$	0.358905	+	0.621641i	0.0137634	+	0.0238388i
$681$	47.6439			1.82572
$682$	−2.30016	+	3.98399i	−0.0880776	+	0.152555i
$683$	−1.57553	+	2.72890i	−0.0602860	+	0.104418i	−0.894593	−	0.446881i	$-0.852535\pi$
$683$	−1.57553	+	2.72890i	−0.0602860	+	0.104418i	0.834307	+	0.551300i	$0.185868\pi$
$684$	−54.2222	−	93.9157i	−2.07324	−	3.59095i
$685$	1.28913	−	2.23284i	0.0492551	−	0.0853123i
$686$	1.71212	−	2.96548i	0.0653691	−	0.113223i
$687$	59.8258			2.28250
$688$	24.6389			0.939351
$689$	3.84127	−	6.65328i	0.146341	−	0.253470i
$690$	−2.37879			−0.0905591
$691$	8.05416	−	13.9502i	0.306395	−	0.530691i	−0.671176	−	0.741298i	$-0.734211\pi$
$691$	8.05416	−	13.9502i	0.306395	−	0.530691i	0.977571	+	0.210607i	$0.0675440\pi$
$692$	−0.268908			−0.0102223
$693$	65.0453	+	112.662i	2.47087	+	4.27966i
$694$	−0.354538	−	0.614078i	−0.0134581	−	0.0233101i
$695$	2.91795	+	5.05403i	0.110684	+	0.191710i
$696$	−0.129172	+	0.223732i	−0.00489624	+	0.00848053i
$697$	−0.313032			−0.0118569
$698$	−3.53325	−	0.719008i	−0.133735	−	0.0272149i
$699$	38.1977			1.44477
$700$	−12.8374	+	22.2351i	−0.485210	+	0.840408i
$701$	14.3948	+	24.9326i	0.543685	+	0.941690i	0.998688	+	0.0512004i	$0.0163047\pi$
$701$	14.3948	+	24.9326i	0.543685	+	0.941690i	−0.455003	+	0.890490i	$0.650362\pi$
$702$	4.50855	+	7.80905i	0.170164	+	0.294733i
$703$	5.46360	+	9.46324i	0.206064	+	0.356913i
$704$	43.3456			1.63365
$705$	1.39091	−	2.40912i	0.0523846	−	0.0907327i
$706$	0.738774			0.0278041
$707$	5.81554	−	10.0728i	0.218716	−	0.378827i
$708$	−38.1888			−1.43522
$709$	−37.8517			−1.42155			−0.710776	−	0.703418i	$-0.751656\pi$
$709$	−37.8517			−1.42155			−0.710776	+	0.703418i	$0.751656\pi$
$710$	0.578360	−	1.00175i	0.0217055	−	0.0375950i
$711$	34.8796	−	60.4132i	1.30809	−	2.26567i
$712$	4.96817	+	8.60512i	0.186190	+	0.322491i
$713$	15.1388	−	26.2212i	0.566953	−	0.981991i
$714$	1.68246	−	2.91411i	0.0629646	−	0.109058i
$715$	−8.78931			−0.328702
$716$	17.6242	+	30.5260i	0.658647	+	1.14081i
$717$	−2.08377	−	3.60920i	−0.0778199	−	0.134788i
$718$	1.46361	−	2.53505i	0.0546214	−	0.0946071i
$719$	4.80419			0.179166			0.0895830	−	0.995979i	$-0.471447\pi$
$719$	4.80419			0.179166			0.0895830	+	0.995979i	$0.471447\pi$
$720$	7.13491	−	12.3580i	0.265902	−	0.460557i
$721$	−12.2522	+	21.2215i	−0.456297	+	0.790329i
$722$	−3.02998	−	5.24809i	−0.112764	−	0.195314i
$723$	14.7635	−	25.5712i	0.549062	−	0.951002i
$724$	−22.1029	−	38.2834i	−0.821448	−	1.42279i
$725$	0.490089			0.0182015
$726$	16.5190			0.613079
$727$	19.1306	+	33.1351i	0.709514	+	1.22891i	0.965038	+	0.262112i	$0.0844188\pi$
$727$	19.1306	+	33.1351i	0.709514	+	1.22891i	−0.255524	+	0.966803i	$0.582248\pi$
$728$	−3.12330	−	5.40971i	−0.115757	−	0.200497i
$729$	64.9447			2.40536
$730$	0.0115468	+	0.0199997i	0.000427367	+	0.000740222i
$731$	6.30595	+	10.9222i	0.233234	+	0.403973i
$732$	−13.6437	+	23.6316i	−0.504285	+	0.873448i
$733$	40.0255			1.47838			0.739188	−	0.673499i	$-0.235210\pi$
$733$	40.0255			1.47838			0.739188	+	0.673499i	$0.235210\pi$
$734$	−2.51774			−0.0929316
$735$	−0.857529			−0.0316304
$736$	17.4690			0.643916
$737$	−41.8885			−1.54298
$738$	−0.121580	−	0.210583i	−0.00447542	−	0.00775165i
$739$	20.8926			0.768545			0.384273	−	0.923220i	$-0.374452\pi$
$739$	20.8926			0.768545			0.384273	+	0.923220i	$0.374452\pi$
$740$	−0.733114	+	1.26979i	−0.0269498	+	0.0466784i
$741$	−34.6725	−	60.0546i	−1.27373	−	2.20616i
$742$	−0.684281	−	1.18521i	−0.0251208	−	0.0435104i
$743$	30.7859			1.12943			0.564713	−	0.825287i	$-0.308987\pi$
$743$	30.7859			1.12943			0.564713	+	0.825287i	$0.308987\pi$
$744$	−4.91635	−	8.51536i	−0.180242	−	0.312188i
$745$	0.0947422			0.00347108
$746$	2.50953			0.0918806
$747$	−53.1319	−	92.0272i	−1.94400	−	3.36710i
$748$	11.5536	+	20.0115i	0.422443	+	0.731693i
$749$	24.4893	+	42.4167i	0.894820	+	1.54987i
$750$	3.00345			0.109670
$751$	−4.07977			−0.148873			−0.0744366	−	0.997226i	$-0.523716\pi$
$751$	−4.07977			−0.148873			−0.0744366	+	0.997226i	$0.523716\pi$
$752$	−3.29721	+	5.71093i	−0.120237	+	0.208256i
$753$	−28.4969	−	49.3581i	−1.03849	−	1.79871i
$754$	−0.0295290	+	0.0511456i	−0.00107538	+	0.00186261i
$755$	−1.60114	+	2.77326i	−0.0582715	+	0.100929i
$756$	−84.6342			−3.07812
$757$	−8.43785	−	14.6148i	−0.306679	−	0.531183i	0.670955	−	0.741498i	$-0.265884\pi$
$757$	−8.43785	−	14.6148i	−0.306679	−	0.531183i	−0.977634	+	0.210315i	$0.932551\pi$
$758$	−3.66453			−0.133102
$759$	−154.607			−5.61187
$760$	1.31758	−	2.28212i	0.0477937	−	0.0827812i
$761$	19.1471	+	33.1637i	0.694082	+	1.20218i	0.970489	+	0.241144i	$0.0775227\pi$
$761$	19.1471	+	33.1637i	0.694082	+	1.20218i	−0.276408	+	0.961041i	$0.589144\pi$
$762$	−7.57427			−0.274387
$763$	−47.5969			−1.72312
$764$	−9.05785			−0.327701
$765$	7.30428			0.264087
$766$	1.09779	+	1.90143i	0.0396649	+	0.0687016i
$767$	−17.6258			−0.636431
$768$	−21.5123	+	37.2605i	−0.776259	+	1.34452i
$769$	−16.8691	+	29.2181i	−0.608314	+	1.05363i	0.383204	+	0.923664i	$0.374821\pi$
$769$	−16.8691	+	29.2181i	−0.608314	+	1.05363i	−0.991518	+	0.129967i	$0.958513\pi$
$770$	−0.782860	+	1.35595i	−0.0282123	+	0.0488652i
$771$	13.2808	+	23.0031i	0.478297	+	0.828435i
$772$	4.15209	−	7.19163i	0.149437	−	0.258833i
$773$	−22.8826			−0.823029			−0.411514	−	0.911403i	$-0.635000\pi$
$773$	−22.8826			−0.823029			−0.411514	+	0.911403i	$0.635000\pi$
$774$	−4.89840	+	8.48428i	−0.176069	+	0.304961i
$775$	−9.32655	+	16.1541i	−0.335019	+	0.580271i
$776$	1.97220	−	3.41595i	0.0707978	−	0.122625i
$777$	13.8772			0.497840
$778$	−2.32387			−0.0833147
$779$	0.574589	+	0.995217i	0.0205868	+	0.0356573i
$780$	4.65241	−	8.05821i	0.166583	−	0.288530i
$781$	37.5898	−	65.1075i	1.34507	−	2.32973i
$782$	1.44322	+	2.49974i	0.0516096	+	0.0893904i
$783$	0.807761	+	1.39908i	0.0288670	+	0.0499991i
$784$	2.03281			0.0726004
$785$	−5.59367	+	9.68852i	−0.199647	+	0.345798i
$786$	3.06468			0.109313
$787$	7.40862	+	12.8321i	0.264089	+	0.457415i	0.967324	−	0.253542i	$-0.0815955\pi$
$787$	7.40862	+	12.8321i	0.264089	+	0.457415i	−0.703236	+	0.710957i	$0.748262\pi$
$788$	−17.7821	+	30.7995i	−0.633462	+	1.09719i
$789$	17.6832	+	30.6282i	0.629539	+	1.09039i
$790$	0.839594			0.0298714
$791$	−0.671353	−	1.16282i	−0.0238706	−	0.0413450i
$792$	−18.1198	+	31.3845i	−0.643860	+	1.11520i
$793$	−6.29716	+	10.9070i	−0.223619	+	0.387319i
$794$	2.66802	−	4.62115i	0.0946846	−	0.163998i
$795$	2.05793	−	3.56444i	0.0729874	−	0.126418i
$796$	18.6136			0.659741
$797$	7.07631	−	12.2565i	0.250656	−	0.434148i	−0.713051	−	0.701112i	$-0.752687\pi$
$797$	7.07631	−	12.2565i	0.250656	−	0.434148i	0.963706	+	0.266964i	$0.0860205\pi$
$798$	−12.3531			−0.437294
$799$	−3.37547			−0.119416
$800$	−10.7621			−0.380498
$801$	101.110			3.57255
$802$	0.0375577	−	0.0650518i	0.00132621	−	0.00229706i
$803$	0.750472	+	1.29986i	0.0264836	+	0.0458709i
$804$	22.1727	−	38.4042i	0.781970	−	1.35441i
$805$	5.15250	−	8.92440i	0.181602	−	0.314544i
$806$	−1.12389	−	1.94663i	−0.0395873	−	0.0685672i
$807$	−31.1160	−	53.8945i	−1.09533	−	1.89718i
$808$	3.24010			0.113986
$809$	−11.7365	−	20.3283i	−0.412635	−	0.714704i	0.582542	−	0.812800i	$-0.302058\pi$
$809$	−11.7365	−	20.3283i	−0.412635	−	0.714704i	−0.995177	+	0.0980964i	$0.968725\pi$
$810$	1.32188	+	2.28957i	0.0464463	+	0.0804473i
$811$	−13.3929	+	23.1973i	−0.470290	+	0.814566i	−0.999423	−	0.0339729i	$-0.989184\pi$
$811$	−13.3929	+	23.1973i	−0.470290	+	0.814566i	0.529133	+	0.848539i	$0.322517\pi$
$812$	−0.277158	−	0.480051i	−0.00972633	−	0.0168465i
$813$	−61.9278			−2.17190
$814$	0.904324	−	1.56634i	0.0316965	−	0.0549000i
$815$	−3.55214	−	6.15249i	−0.124426	−	0.215512i
$816$	−23.9895			−0.839800
$817$	23.1499	−	40.0968i	0.809913	−	1.40281i
$818$	0.987157	−	1.70981i	0.0345151	−	0.0597820i
$819$	−63.5641			−2.22111
$820$	−0.0770992	+	0.133540i	−0.00269242	+	0.00466341i
$821$	−8.38429	−	14.5220i	−0.292614	−	0.506822i	0.681813	−	0.731526i	$-0.261192\pi$
$821$	−8.38429	−	14.5220i	−0.292614	−	0.506822i	−0.974427	+	0.224704i	$0.927858\pi$
$822$	−1.68346	−	2.91583i	−0.0587173	−	0.101701i
$823$	−28.8328			−1.00505			−0.502524	−	0.864563i	$-0.667595\pi$
$823$	−28.8328			−1.00505			−0.502524	+	0.864563i	$0.667595\pi$
$824$	−6.82627			−0.237805
$825$	95.2484			3.31612
$826$	−1.56992	+	2.71919i	−0.0546246	+	0.0946126i
$827$	0.263345	−	0.456127i	0.00915740	−	0.0158611i	−0.861410	−	0.507910i	$-0.830418\pi$
$827$	0.263345	−	0.456127i	0.00915740	−	0.0158611i	0.870568	+	0.492048i	$0.163752\pi$
$828$	59.0686	−	102.310i	2.05278	−	3.55551i
$829$	−31.5279			−1.09501			−0.547504	−	0.836803i	$-0.684422\pi$
$829$	−31.5279			−1.09501			−0.547504	+	0.836803i	$0.684422\pi$
$830$	0.639476	−	1.10760i	0.0221965	−	0.0384455i
$831$	−5.47473			−0.189916
$832$	−10.5896	+	18.3418i	−0.367129	+	0.635887i
$833$	0.520266	+	0.901128i	0.0180262	+	0.0312222i
$834$	7.62102			0.263894
$835$	5.41929	+	9.38648i	0.187542	+	0.324833i
$836$	42.4148	−	73.4647i	1.46695	−	2.54083i
$837$	−61.4877			−2.12533
$838$	−1.56334	−	2.70778i	−0.0540046	−	0.0935387i
$839$	13.6399	+	23.6251i	0.470903	+	0.815627i	0.999446	−	0.0332789i	$-0.0105950\pi$
$839$	13.6399	+	23.6251i	0.470903	+	0.815627i	−0.528543	+	0.848906i	$0.677262\pi$
$840$	−1.67328	−	2.89821i	−0.0577337	−	0.0999977i
$841$	14.4947	−	25.1056i	0.499818	−	0.865709i
$842$	2.21050	+	3.82869i	0.0761787	+	0.131945i
$843$	37.6806	−	65.2647i	1.29779	−	2.24783i
$844$	−15.4137			−0.530563
$845$	−1.00733	+	1.74474i	−0.0346531	+	0.0600209i
$846$	−1.31102	−	2.27075i	−0.0450737	−	0.0780699i
$847$	−35.7805	+	61.9736i	−1.22943	+	2.12944i
$848$	−4.87842	+	8.44968i	−0.167526	+	0.290163i
$849$	−1.26766	−	2.19566i	−0.0435061	−	0.0753548i
$850$	−0.889125	−	1.54001i	−0.0304967	−	0.0528219i
$851$	−5.95194	+	10.3091i	−0.204030	+	0.353390i
$852$	39.7946	+	68.9262i	1.36334	+	2.36137i
$853$	10.3131	+	17.8628i	0.353113	+	0.611609i	0.986793	−	0.161986i	$-0.0517899\pi$
$853$	10.3131	+	17.8628i	0.353113	+	0.611609i	−0.633680	+	0.773595i	$0.718457\pi$
$854$	1.12177	+	1.94296i	0.0383862	+	0.0664868i
$855$	−13.4074	−	23.2224i	−0.458525	−	0.794189i
$856$	−6.82205	+	11.8161i	−0.233173	+	0.403867i
$857$	−21.3988	−	37.0638i	−0.730969	−	1.26608i	−0.956470	−	0.291832i	$-0.905735\pi$
$857$	−21.3988	−	37.0638i	−0.730969	−	1.26608i	0.225501	−	0.974243i	$-0.427598\pi$
$858$	−5.73892	+	9.94011i	−0.195924	+	0.339350i
$859$	10.8802	+	18.8451i	0.371228	+	0.642986i	0.989755	−	0.142778i	$-0.0456034\pi$
$859$	10.8802	+	18.8451i	0.371228	+	0.642986i	−0.618526	+	0.785764i	$0.712270\pi$
$860$	6.21258			0.211847
$861$	1.45941			0.0497367
$862$	1.52959	+	2.64933i	0.0520982	+	0.0902367i
$863$	27.4190	−	47.4912i	0.933355	−	1.61662i	0.155814	−	0.987786i	$-0.450200\pi$
$863$	27.4190	−	47.4912i	0.933355	−	1.61662i	0.777541	−	0.628832i	$-0.216467\pi$
$864$	−17.7380	−	30.7231i	−0.603459	−	1.04522i
$865$	−0.0664924			−0.00226081
$866$	−4.00344			−0.136042
$867$	21.7719	+	37.7100i	0.739413	+	1.28070i
$868$	21.0976			0.716098
$869$	54.5684			1.85111
$870$	−0.0158199	+	0.0274009i	−0.000536345	+	0.000928977i
$871$	10.2337	−	17.7252i	0.346754	−	0.600596i
$872$	−6.62960	−	11.4828i	−0.224507	−	0.388857i
$873$	−20.0687	−	34.7600i	−0.679222	−	1.17645i
$874$	5.29825	−	9.17684i	0.179216	−	0.310411i
$875$	−6.50552	+	11.2679i	−0.219927	+	0.380924i
$876$	−1.58898			−0.0536866
$877$	13.0879			0.441948			0.220974	−	0.975280i	$-0.429076\pi$
$877$	13.0879			0.441948			0.220974	+	0.975280i	$0.429076\pi$
$878$	−1.26314	−	2.18782i	−0.0426289	−	0.0738355i
$879$	9.73622			0.328395
$880$	11.1624			0.376286
$881$	13.0457	+	22.5958i	0.439521	+	0.761273i	0.997652	−	0.0684799i	$-0.0218149\pi$
$881$	13.0457	+	22.5958i	0.439521	+	0.761273i	−0.558132	+	0.829752i	$0.688482\pi$
$882$	−0.404138	+	0.699987i	−0.0136080	+	0.0235698i
$883$	−25.9466	−	44.9408i	−0.873172	−	1.51238i	−0.858697	−	0.512484i	$-0.828725\pi$
$883$	−25.9466	−	44.9408i	−0.873172	−	1.51238i	−0.0144756	−	0.999895i	$-0.504608\pi$
$884$	−11.2905			−0.379742
$885$	−9.44289			−0.317419
$886$	1.43073	+	2.47809i	0.0480662	+	0.0832530i
$887$	−8.44489	+	14.6270i	−0.283552	+	0.491126i	−0.972257	−	0.233916i	$-0.924846\pi$
$887$	−8.44489	+	14.6270i	−0.283552	+	0.491126i	0.688705	+	0.725041i	$0.258179\pi$
$888$	1.93290	+	3.34788i	0.0648638	+	0.112347i
$889$	16.4060	−	28.4160i	0.550239	−	0.953042i
$890$	0.608462	+	1.05389i	0.0203957	+	0.0353264i
$891$	85.9142	+	148.808i	2.87824	+	4.98525i
$892$	−0.681800	−	1.18091i	−0.0228284	−	0.0395399i
$893$	6.19589	+	10.7316i	0.207337	+	0.359119i
$894$	0.0618613	−	0.107147i	0.00206895	−	0.00358353i
$895$	4.35790	+	7.54811i	0.145669	+	0.252305i
$896$	8.08818	+	14.0091i	0.270207	+	0.468012i
$897$	37.7715	−	65.4222i	1.26115	−	2.18438i
$898$	1.96026	−	3.39527i	0.0654147	−	0.113302i
$899$	−0.201358	−	0.348762i	−0.00671567	−	0.0116319i
$900$	−36.3903	+	63.0298i	−1.21301	+	2.10099i
$901$	−4.99423			−0.166382
$902$	0.0951047	−	0.164726i	0.00316664	−	0.00548478i
$903$	−29.3996	−	50.9216i	−0.978357	−	1.69456i
$904$	0.187021	−	0.323929i	0.00622021	−	0.0107737i
$905$	−5.46535	−	9.46627i	−0.181674	−	0.314669i
$906$	2.09091	+	3.62156i	0.0694658	+	0.120318i
$907$	8.86545	+	15.3554i	0.294373	+	0.509868i	0.974839	−	0.222911i	$-0.0715560\pi$
$907$	8.86545	+	15.3554i	0.294373	+	0.509868i	−0.680466	+	0.732779i	$0.738223\pi$
$908$	−28.4777			−0.945067
$909$	16.4853	−	28.5534i	0.546783	−	0.947057i
$910$	−0.382516	−	0.662538i	−0.0126803	−	0.0219629i
$911$	−47.4402			−1.57176			−0.785882	−	0.618377i	$-0.787791\pi$
$911$	−47.4402			−1.57176			−0.785882	+	0.618377i	$0.787791\pi$
$912$	44.0341	+	76.2694i	1.45812	+	2.52553i
$913$	41.5620	−	71.9874i	1.37550	−	2.38244i
$914$	−6.15492			−0.203587
$915$	−3.37365	+	5.84334i	−0.111530	+	0.193175i
$916$	−35.7591			−1.18151
$917$	−6.63814	+	11.4976i	−0.219211	+	0.379684i
$918$	2.93089	−	5.07646i	0.0967339	−	0.167548i
$919$	12.4375	−	21.5425i	0.410277	−	0.710620i	−0.584643	−	0.811291i	$-0.698765\pi$
$919$	12.4375	−	21.5425i	0.410277	−	0.710620i	0.994920	+	0.100671i	$0.0320988\pi$
$920$	2.87069			0.0946440
$921$	−62.6776			−2.06530
$922$	−1.59902			−0.0526608
$923$	18.3669	+	31.8124i	0.604555	+	1.04712i
$924$	−53.8653	−	93.2975i	−1.77204	−	3.06926i
$925$	3.66680	−	6.35108i	0.120564	−	0.208822i
$926$	1.16864			0.0384038
$927$	−34.7314	+	60.1565i	−1.14073	+	1.97580i
$928$	0.116176	−	0.201222i	0.00381366	−	0.00660544i
$929$	24.9389			0.818220			0.409110	−	0.912485i	$-0.365839\pi$
$929$	24.9389			0.818220			0.409110	+	0.912485i	$0.365839\pi$
$930$	−0.602115	−	1.04289i	−0.0197441	−	0.0341978i
$931$	1.90996	−	3.30815i	0.0625965	−	0.108420i
$932$	−22.8316			−0.747873
$933$	−13.9062	−	24.0863i	−0.455270	−	0.788551i
$934$	1.39533	−	2.41679i	0.0456567	−	0.0790796i
$935$	2.85685	+	4.94821i	0.0934290	+	0.161824i
$936$	−8.85361	−	15.3349i	−0.289389	−	0.501237i
$937$	−2.05837			−0.0672440			−0.0336220	−	0.999435i	$-0.510704\pi$
$937$	−2.05837			−0.0672440			−0.0336220	+	0.999435i	$0.510704\pi$
$938$	−1.82302	−	3.15756i	−0.0595236	−	0.103098i
$939$	9.18761	+	15.9134i	0.299826	+	0.519314i
$940$	−0.831374	+	1.43998i	−0.0271164	+	0.0469670i
$941$	19.9078	−	34.4813i	0.648975	−	1.12406i	−0.334392	−	0.942434i	$-0.608531\pi$
$941$	19.9078	−	34.4813i	0.648975	−	1.12406i	0.983368	−	0.181625i	$-0.0581356\pi$
$942$	7.30470	+	12.6521i	0.238000	+	0.412228i
$943$	−0.625945	+	1.08417i	−0.0203836	+	0.0353054i
$944$	22.3848			0.728563
$945$	−20.9274			−0.680768
$946$	−7.66346			−0.249160
$947$	21.1926			0.688668			0.344334	−	0.938847i	$-0.388105\pi$
$947$	21.1926			0.688668			0.344334	+	0.938847i	$0.388105\pi$
$948$	−28.8845	+	50.0294i	−0.938124	+	1.62488i
$949$	−0.733382			−0.0238066
$950$	−3.26409	+	5.65356i	−0.105901	+	0.183426i
$951$	−26.0008	+	45.0347i	−0.843134	+	1.46035i
$952$	−2.03037	+	3.51671i	−0.0658048	+	0.113977i
$953$	23.8710	−	41.3459i	0.773259	−	1.33932i	−0.162509	−	0.986707i	$-0.551959\pi$
$953$	23.8710	−	41.3459i	0.773259	−	1.33932i	0.935768	−	0.352617i	$-0.114708\pi$
$954$	−1.93973	−	3.35971i	−0.0628011	−	0.108775i
$955$	−2.23972			−0.0724756
$956$	1.24551	+	2.15729i	0.0402828	+	0.0697719i
$957$	−1.02820	+	1.78089i	−0.0332369	+	0.0575679i
$958$	0.303958	+	0.526472i	0.00982045	+	0.0170095i
$959$	14.5856			0.470993
$960$	−5.67331	+	9.82646i	−0.183105	+	0.317148i
$961$	−15.6724			−0.505561
$962$	0.441865	+	0.765333i	0.0142463	+	0.0246753i
$963$	69.4198	+	120.239i	2.23702	+	3.87464i
$964$	−8.82447	+	15.2844i	−0.284217	+	0.492278i
$965$	1.02668	−	1.77826i	0.0330500	−	0.0572444i
$966$	−6.72859	−	11.6543i	−0.216489	−	0.374970i
$967$	34.6039			1.11279			0.556393	−	0.830920i	$-0.312185\pi$
$967$	34.6039			1.11279			0.556393	+	0.830920i	$0.312185\pi$
$968$	−19.9349			−0.640733
$969$	−22.5397	+	39.0399i	−0.724080	+	1.25414i
$970$	0.241539	−	0.418358i	0.00775535	−	0.0134327i
$971$	5.57433	−	9.65502i	0.178889	−	0.309844i	−0.762611	−	0.646857i	$-0.776083\pi$
$971$	5.57433	−	9.65502i	0.178889	−	0.309844i	0.941500	+	0.337012i	$0.109416\pi$
$972$	−89.4288			−2.86843
$973$	−16.5072	+	28.5914i	−0.529198	+	0.916597i
$974$	0.177454	+	0.307360i	0.00568601	+	0.00984845i
$975$	−23.2699	+	40.3046i	−0.745232	+	1.29078i
$976$	7.99740	−	13.8519i	0.255991	−	0.443389i
$977$	−10.4390	+	18.0808i	−0.333972	+	0.578457i	−0.983287	−	0.182063i	$-0.941723\pi$
$977$	−10.4390	+	18.0808i	−0.333972	+	0.578457i	0.649315	+	0.760520i	$0.275056\pi$
$978$	−9.27739			−0.296658
$979$	39.5462	+	68.4961i	1.26390	+	2.18915i
$980$	0.512563			0.0163732
$981$	−134.923			−4.30776
$982$	−1.14309			−0.0364773
$983$	−33.7099			−1.07518			−0.537589	−	0.843207i	$-0.680665\pi$
$983$	−33.7099			−1.07518			−0.537589	+	0.843207i	$0.680665\pi$
$984$	0.203276	+	0.352085i	0.00648022	+	0.0112241i
$985$	−4.39696	+	7.61575i	−0.140099	+	0.242658i
$986$	0.0383920			0.00122265
$987$	15.7371			0.500918
$988$	20.7245	+	35.8959i	0.659334	+	1.14200i
$989$	50.4381			1.60384
$990$	−2.21917	+	3.84372i	−0.0705299	+	0.122161i
$991$	−22.9483	+	39.7476i	−0.728977	+	1.26262i	0.228339	+	0.973582i	$0.426670\pi$
$991$	−22.9483	+	39.7476i	−0.728977	+	1.26262i	−0.957316	+	0.289043i	$0.906663\pi$
$992$	4.42172	+	7.65864i	0.140390	+	0.243162i
$993$	−7.19607	+	12.4640i	−0.228361	+	0.395532i
$994$	6.54373			0.207555
$995$	4.60255			0.145911
$996$	43.9996	+	76.2096i	1.39418	+	2.41479i
$997$	−15.5006	−	26.8478i	−0.490908	−	0.850278i	0.509037	−	0.860745i	$-0.330002\pi$
$997$	−15.5006	−	26.8478i	−0.490908	−	0.850278i	−0.999945	+	0.0104669i	$0.996668\pi$
$998$	2.00556	+	3.47373i	0.0634848	+	0.109959i
$999$	24.1743			0.764842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.14	✓	56
349.226	even	3	inner	349.2.c.a.226.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.14	✓	56	1.1	even	1	trivial
349.2.c.a.226.14	yes	56	349.226	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0965034 + 0.167149i) q^{2} +(-1.64186 - 2.84379i) q^{3} +(0.981374 + 1.69979i) q^{4} +(0.242663 + 0.420304i) q^{5} +0.633781 q^{6} +(-1.37278 + 2.37772i) q^{7} -0.764837 q^{8} +(-3.89141 + 6.74013i) q^{9} +O(q^{10})\)	\(q+(-0.0965034 + 0.167149i) q^{2} +(-1.64186 - 2.84379i) q^{3} +(0.981374 + 1.69979i) q^{4} +(0.242663 + 0.420304i) q^{5} +0.633781 q^{6} +(-1.37278 + 2.37772i) q^{7} -0.764837 q^{8} +(-3.89141 + 6.74013i) q^{9} -0.0936712 q^{10} -6.08805 q^{11} +(3.22256 - 5.58164i) q^{12} +(1.48735 - 2.57617i) q^{13} +(-0.264956 - 0.458916i) q^{14} +(0.796837 - 1.38016i) q^{15} +(-1.88894 + 3.27174i) q^{16} -1.93378 q^{17} +(-0.751069 - 1.30089i) q^{18} +(3.54957 + 6.14803i) q^{19} +(-0.476286 + 0.824952i) q^{20} +9.01564 q^{21} +(0.587517 - 1.01761i) q^{22} +(-3.86683 + 6.69754i) q^{23} +(1.25576 + 2.17503i) q^{24} +(2.38223 - 4.12614i) q^{25} +(0.287069 + 0.497218i) q^{26} +15.7055 q^{27} -5.38884 q^{28} +(0.0514318 + 0.0890825i) q^{29} +(0.153795 + 0.266381i) q^{30} -3.91505 q^{31} +(-1.12942 - 1.95620i) q^{32} +(9.99572 + 17.3131i) q^{33} +(0.186616 - 0.323229i) q^{34} -1.33249 q^{35} -15.2757 q^{36} +1.53923 q^{37} -1.37018 q^{38} -9.76810 q^{39} +(-0.185598 - 0.321464i) q^{40} +0.161876 q^{41} +(-0.870040 + 1.50695i) q^{42} +(-3.26095 - 5.64813i) q^{43} +(-5.97465 - 10.3484i) q^{44} -3.77721 q^{45} +(-0.746324 - 1.29267i) q^{46} +1.74553 q^{47} +12.4055 q^{48} +(-0.269041 - 0.465994i) q^{49} +(0.459786 + 0.796373i) q^{50} +(3.17499 + 5.49925i) q^{51} +5.83860 q^{52} +2.58263 q^{53} +(-1.51563 + 2.62515i) q^{54} +(-1.47734 - 2.55883i) q^{55} +(1.04995 - 1.81857i) q^{56} +(11.6558 - 20.1884i) q^{57} -0.0198534 q^{58} +(-2.96262 - 5.13140i) q^{59} +3.12798 q^{60} -4.23381 q^{61} +(0.377816 - 0.654396i) q^{62} +(-10.6841 - 18.5054i) q^{63} -7.11979 q^{64} +1.44370 q^{65} -3.85848 q^{66} +6.88046 q^{67} +(-1.89776 - 3.28702i) q^{68} +25.3952 q^{69} +(0.128590 - 0.222724i) q^{70} +(-6.17437 + 10.6943i) q^{71} +(2.97630 - 5.15510i) q^{72} +(-0.123270 - 0.213510i) q^{73} +(-0.148541 + 0.257281i) q^{74} -15.6452 q^{75} +(-6.96691 + 12.0670i) q^{76} +(8.35754 - 14.4757i) q^{77} +(0.942655 - 1.63273i) q^{78} -8.96321 q^{79} -1.83350 q^{80} +(-14.1120 - 24.4426i) q^{81} +(-0.0156216 + 0.0270573i) q^{82} +(-6.82682 + 11.8244i) q^{83} +(8.84772 + 15.3247i) q^{84} +(-0.469256 - 0.812775i) q^{85} +1.25877 q^{86} +(0.168888 - 0.292522i) q^{87} +4.65636 q^{88} +(-6.49572 - 11.2509i) q^{89} +(0.364513 - 0.631355i) q^{90} +(4.08361 + 7.07302i) q^{91} -15.1792 q^{92} +(6.42797 + 11.1336i) q^{93} +(-0.168450 + 0.291764i) q^{94} +(-1.72270 + 2.98380i) q^{95} +(-3.70869 + 6.42363i) q^{96} +(-2.57858 + 4.46624i) q^{97} +0.103854 q^{98} +(23.6911 - 41.0342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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