LMFDB - Embedded newform 209.2.f.c.191.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(20,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("209.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.7
Character	$\chi$	$=$	209.191
Dual form			209.2.f.c.58.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.760694 + 0.552677i) q^{2} +(0.608863 - 1.87389i) q^{3} +(-0.344830 - 1.06128i) q^{4} +(-2.22112 + 1.61374i) q^{5} +(1.49881 - 1.08895i) q^{6} +(-1.54336 - 4.74997i) q^{7} +(0.905352 - 2.78639i) q^{8} +(-0.713688 - 0.518524i) q^{9} -2.58147 q^{10} +(2.51987 + 2.15645i) q^{11} -2.19867 q^{12} +(2.58028 + 1.87469i) q^{13} +(1.45117 - 4.46625i) q^{14} +(1.67161 + 5.14468i) q^{15} +(0.423116 - 0.307412i) q^{16} +(-0.464166 + 0.337237i) q^{17} +(-0.256322 - 0.788877i) q^{18} +(0.309017 - 0.951057i) q^{19} +(2.47853 + 1.80076i) q^{20} -9.84060 q^{21} +(0.725032 + 3.03307i) q^{22} +3.70874 q^{23} +(-4.67014 - 3.39305i) q^{24} +(0.784142 - 2.41334i) q^{25} +(0.926712 + 2.85213i) q^{26} +(3.37588 - 2.45272i) q^{27} +(-4.50883 + 3.27586i) q^{28} +(2.78806 + 8.58077i) q^{29} +(-1.57176 + 4.83739i) q^{30} +(-5.05222 - 3.67065i) q^{31} -5.36780 q^{32} +(5.57519 - 3.40897i) q^{33} -0.539472 q^{34} +(11.0932 + 8.05968i) q^{35} +(-0.304197 + 0.936222i) q^{36} +(-0.109678 - 0.337553i) q^{37} +(0.760694 - 0.552677i) q^{38} +(5.08399 - 3.69373i) q^{39} +(2.48560 + 7.64991i) q^{40} +(1.21389 - 3.73597i) q^{41} +(-7.48569 - 5.43867i) q^{42} +11.4373 q^{43} +(1.41966 - 3.41788i) q^{44} +2.42195 q^{45} +(2.82122 + 2.04973i) q^{46} +(-0.451822 + 1.39057i) q^{47} +(-0.318435 - 0.980043i) q^{48} +(-14.5171 + 10.5473i) q^{49} +(1.93029 - 1.40244i) q^{50} +(0.349330 + 1.07513i) q^{51} +(1.09980 - 3.38484i) q^{52} +(-2.90123 - 2.10787i) q^{53} +3.92357 q^{54} +(-9.07688 - 0.723318i) q^{55} -14.6325 q^{56} +(-1.59402 - 1.15813i) q^{57} +(-2.62153 + 8.06824i) q^{58} +(-1.08360 - 3.33498i) q^{59} +(4.88351 - 3.54807i) q^{60} +(-4.61568 + 3.35349i) q^{61} +(-1.81451 - 5.58449i) q^{62} +(-1.36150 + 4.19026i) q^{63} +(-4.92949 - 3.58148i) q^{64} -8.75638 q^{65} +(6.12508 + 0.488095i) q^{66} -0.524152 q^{67} +(0.517960 + 0.376320i) q^{68} +(2.25811 - 6.94976i) q^{69} +(3.98413 + 12.2619i) q^{70} +(-9.80018 + 7.12025i) q^{71} +(-2.09095 + 1.51916i) q^{72} +(2.36170 + 7.26856i) q^{73} +(0.103127 - 0.317391i) q^{74} +(-4.04489 - 2.93879i) q^{75} -1.11589 q^{76} +(6.35399 - 15.2975i) q^{77} +5.90880 q^{78} +(2.47378 + 1.79730i) q^{79} +(-0.443710 + 1.36560i) q^{80} +(-3.35848 - 10.3363i) q^{81} +(2.98819 - 2.17104i) q^{82} +(1.17866 - 0.856349i) q^{83} +(3.39333 + 10.4436i) q^{84} +(0.486758 - 1.49809i) q^{85} +(8.70029 + 6.32113i) q^{86} +17.7769 q^{87} +(8.29006 - 5.06899i) q^{88} +14.1332 q^{89} +(1.84236 + 1.33856i) q^{90} +(4.92239 - 15.1496i) q^{91} +(-1.27888 - 3.93600i) q^{92} +(-9.95449 + 7.23236i) q^{93} +(-1.11223 + 0.808084i) q^{94} +(0.848393 + 2.61109i) q^{95} +(-3.26825 + 10.0586i) q^{96} +(0.209648 + 0.152319i) q^{97} -16.8723 q^{98} +(-0.680229 - 2.84564i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) $ 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.760694	+	0.552677i	0.537892	+	0.390802i	0.823302	−	0.567604i	$-0.192130\pi$
$2$	0.760694	+	0.552677i	0.537892	+	0.390802i	−0.285409	+	0.958406i	$0.592130\pi$
$3$	0.608863	−	1.87389i	0.351527	−	1.08189i	−0.606469	−	0.795107i	$-0.707415\pi$
$3$	0.608863	−	1.87389i	0.351527	−	1.08189i	0.957996	−	0.286782i	$-0.0925855\pi$
$4$	−0.344830	−	1.06128i	−0.172415	−	0.530638i
$5$	−2.22112	+	1.61374i	−0.993316	+	0.721686i	−0.960645	−	0.277780i	$-0.910401\pi$
$5$	−2.22112	+	1.61374i	−0.993316	+	0.721686i	−0.0326711	+	0.999466i	$0.510401\pi$
$6$	1.49881	−	1.08895i	0.611888	−	0.444562i
$7$	−1.54336	−	4.74997i	−0.583334	−	1.79532i	−0.605858	−	0.795573i	$-0.707170\pi$
$7$	−1.54336	−	4.74997i	−0.583334	−	1.79532i	0.0225238	−	0.999746i	$-0.492830\pi$
$8$	0.905352	−	2.78639i	0.320090	−	0.985136i
$9$	−0.713688	−	0.518524i	−0.237896	−	0.172841i
$10$	−2.58147			−0.816333
$11$	2.51987	+	2.15645i	0.759769	+	0.650193i
$11$	2.51987	+	2.15645i	0.759769	+	0.650193i
$12$	−2.19867			−0.634700
$13$	2.58028	+	1.87469i	0.715642	+	0.519944i	0.884989	−	0.465612i	$-0.154166\pi$
$13$	2.58028	+	1.87469i	0.715642	+	0.519944i	−0.169347	+	0.985556i	$0.554166\pi$
$14$	1.45117	−	4.46625i	0.387842	−	1.19366i
$15$	1.67161	+	5.14468i	0.431607	+	1.32835i
$16$	0.423116	−	0.307412i	0.105779	−	0.0768530i
$17$	−0.464166	+	0.337237i	−0.112577	+	0.0817919i	−0.642649	−	0.766161i	$-0.722165\pi$
$17$	−0.464166	+	0.337237i	−0.112577	+	0.0817919i	0.530072	+	0.847952i	$0.322165\pi$
$18$	−0.256322	−	0.788877i	−0.0604156	−	0.185940i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	2.47853	+	1.80076i	0.554217	+	0.402662i
$21$	−9.84060			−2.14739
$22$	0.725032	+	3.03307i	0.154577	+	0.646653i
$23$	3.70874			0.773325			0.386663	−	0.922221i	$-0.373628\pi$
$23$	3.70874			0.773325			0.386663	+	0.922221i	$0.373628\pi$
$24$	−4.67014	−	3.39305i	−0.953288	−	0.692604i
$25$	0.784142	−	2.41334i	0.156828	−	0.482668i
$26$	0.926712	+	2.85213i	0.181743	+	0.559348i
$27$	3.37588	−	2.45272i	0.649688	−	0.472026i
$28$	−4.50883	+	3.27586i	−0.852089	+	0.619079i
$29$	2.78806	+	8.58077i	0.517730	+	1.59341i	0.778259	+	0.627943i	$0.216103\pi$
$29$	2.78806	+	8.58077i	0.517730	+	1.59341i	−0.260529	+	0.965466i	$0.583897\pi$
$30$	−1.57176	+	4.83739i	−0.286963	+	0.883182i
$31$	−5.05222	−	3.67065i	−0.907405	−	0.659268i	0.0329522	−	0.999457i	$-0.489509\pi$
$31$	−5.05222	−	3.67065i	−0.907405	−	0.659268i	−0.940357	+	0.340189i	$0.889509\pi$
$32$	−5.36780			−0.948902
$33$	5.57519	−	3.40897i	0.970516	−	0.593425i
$34$	−0.539472			−0.0925186
$35$	11.0932	+	8.05968i	1.87509	+	1.36233i
$36$	−0.304197	+	0.936222i	−0.0506995	+	0.156037i
$37$	−0.109678	−	0.337553i	−0.0180309	−	0.0554934i	0.941636	−	0.336632i	$-0.109288\pi$
$37$	−0.109678	−	0.337553i	−0.0180309	−	0.0554934i	−0.959667	+	0.281139i	$0.909288\pi$
$38$	0.760694	−	0.552677i	0.123401	−	0.0896560i
$39$	5.08399	−	3.69373i	0.814090	−	0.591471i
$40$	2.48560	+	7.64991i	0.393009	+	1.20956i
$41$	1.21389	−	3.73597i	0.189578	−	0.583461i	−0.810419	−	0.585850i	$-0.800761\pi$
$41$	1.21389	−	3.73597i	0.189578	−	0.583461i	0.999997	+	0.00238946i	$0.000760588\pi$
$42$	−7.48569	−	5.43867i	−1.15507	−	0.839205i
$43$	11.4373			1.74417			0.872086	−	0.489352i	$-0.162767\pi$
$43$	11.4373			1.74417			0.872086	+	0.489352i	$0.162767\pi$
$44$	1.41966	−	3.41788i	0.214022	−	0.515265i
$45$	2.42195			0.361043
$46$	2.82122	+	2.04973i	0.415966	+	0.302217i
$47$	−0.451822	+	1.39057i	−0.0659050	+	0.202835i	−0.978586	−	0.205838i	$-0.934008\pi$
$47$	−0.451822	+	1.39057i	−0.0659050	+	0.202835i	0.912681	+	0.408672i	$0.134008\pi$
$48$	−0.318435	−	0.980043i	−0.0459622	−	0.141457i
$49$	−14.5171	+	10.5473i	−2.07387	+	1.50676i
$50$	1.93029	−	1.40244i	0.272984	−	0.198335i
$51$	0.349330	+	1.07513i	0.0489159	+	0.150548i
$52$	1.09980	−	3.38484i	0.152515	−	0.469393i
$53$	−2.90123	−	2.10787i	−0.398515	−	0.289538i	0.370421	−	0.928864i	$-0.379213\pi$
$53$	−2.90123	−	2.10787i	−0.398515	−	0.289538i	−0.768936	+	0.639326i	$0.779213\pi$
$54$	3.92357			0.533930
$55$	−9.07688	−	0.723318i	−1.22393	−	0.0975321i
$56$	−14.6325			−1.95535
$57$	−1.59402	−	1.15813i	−0.211134	−	0.153398i
$58$	−2.62153	+	8.06824i	−0.344224	+	1.05941i
$59$	−1.08360	−	3.33498i	−0.141073	−	0.434178i	0.855412	−	0.517948i	$-0.173304\pi$
$59$	−1.08360	−	3.33498i	−0.141073	−	0.434178i	−0.996485	+	0.0837699i	$0.973304\pi$
$60$	4.88351	−	3.54807i	0.630458	−	0.458054i
$61$	−4.61568	+	3.35349i	−0.590978	+	0.429370i	−0.842665	−	0.538438i	$-0.819015\pi$
$61$	−4.61568	+	3.35349i	−0.590978	+	0.429370i	0.251687	+	0.967809i	$0.419015\pi$
$62$	−1.81451	−	5.58449i	−0.230443	−	0.709231i
$63$	−1.36150	+	4.19026i	−0.171533	+	0.527923i
$64$	−4.92949	−	3.58148i	−0.616186	−	0.447685i
$65$	−8.75638			−1.08609
$66$	6.12508	+	0.488095i	0.753945	+	0.0600803i
$67$	−0.524152			−0.0640354			−0.0320177	−	0.999487i	$-0.510193\pi$
$67$	−0.524152			−0.0640354			−0.0320177	+	0.999487i	$0.510193\pi$
$68$	0.517960	+	0.376320i	0.0628118	+	0.0456355i
$69$	2.25811	−	6.94976i	0.271845	−	0.836652i
$70$	3.98413	+	12.2619i	0.476195	+	1.46558i
$71$	−9.80018	+	7.12025i	−1.16307	+	0.845018i	−0.990163	−	0.139921i	$-0.955315\pi$
$71$	−9.80018	+	7.12025i	−1.16307	+	0.845018i	−0.172904	+	0.984939i	$0.555315\pi$
$72$	−2.09095	+	1.51916i	−0.246421	+	0.179035i
$73$	2.36170	+	7.26856i	0.276416	+	0.850720i	0.988841	+	0.148972i	$0.0475966\pi$
$73$	2.36170	+	7.26856i	0.276416	+	0.850720i	−0.712426	+	0.701748i	$0.752403\pi$
$74$	0.103127	−	0.317391i	0.0119882	−	0.0368960i
$75$	−4.04489	−	2.93879i	−0.467064	−	0.339342i
$76$	−1.11589			−0.128002
$77$	6.35399	−	15.2975i	0.724104	−	1.74331i
$78$	5.90880			0.669040
$79$	2.47378	+	1.79730i	0.278321	+	0.202212i	0.718185	−	0.695852i	$-0.244973\pi$
$79$	2.47378	+	1.79730i	0.278321	+	0.202212i	−0.439863	+	0.898065i	$0.644973\pi$
$80$	−0.443710	+	1.36560i	−0.0496083	+	0.152679i
$81$	−3.35848	−	10.3363i	−0.373165	−	1.14848i
$82$	2.98819	−	2.17104i	0.329990	−	0.239752i
$83$	1.17866	−	0.856349i	0.129375	−	0.0939965i	−0.521216	−	0.853425i	$-0.674521\pi$
$83$	1.17866	−	0.856349i	0.129375	−	0.0939965i	0.650591	+	0.759428i	$0.274521\pi$
$84$	3.39333	+	10.4436i	0.370243	+	1.13949i
$85$	0.486758	−	1.49809i	0.0527963	−	0.162490i
$86$	8.70029	+	6.32113i	0.938177	+	0.681625i
$87$	17.7769			1.90589
$88$	8.29006	−	5.06899i	0.883723	−	0.540356i
$89$	14.1332			1.49812			0.749061	−	0.662502i	$-0.230505\pi$
$89$	14.1332			1.49812			0.749061	+	0.662502i	$0.230505\pi$
$90$	1.84236	+	1.33856i	0.194202	+	0.141096i
$91$	4.92239	−	15.1496i	0.516007	−	1.58811i
$92$	−1.27888	−	3.93600i	−0.133333	−	0.410356i
$93$	−9.95449	+	7.23236i	−1.03223	+	0.749961i
$94$	−1.11223	+	0.808084i	−0.114718	+	0.0833475i
$95$	0.848393	+	2.61109i	0.0870433	+	0.267892i
$96$	−3.26825	+	10.0586i	−0.333565	+	1.02661i
$97$	0.209648	+	0.152319i	0.0212866	+	0.0154656i	0.598378	−	0.801214i	$-0.295812\pi$
$97$	0.209648	+	0.152319i	0.0212866	+	0.0154656i	−0.577091	+	0.816680i	$0.695812\pi$
$98$	−16.8723			−1.70436
$99$	−0.680229	−	2.84564i	−0.0683656	−	0.285998i
$100$	−2.83162			−0.283162
$101$	−2.77596	−	2.01685i	−0.276218	−	0.200684i	0.441048	−	0.897484i	$-0.354607\pi$
$101$	−2.77596	−	2.01685i	−0.276218	−	0.200684i	−0.717266	+	0.696799i	$0.754607\pi$
$102$	−0.328464	+	1.01091i	−0.0325228	+	0.100095i
$103$	−3.77052	−	11.6045i	−0.371520	−	1.14342i	−0.945796	−	0.324760i	$-0.894716\pi$
$103$	−3.77052	−	11.6045i	−0.371520	−	1.14342i	0.574276	−	0.818662i	$-0.305284\pi$
$104$	7.55966	−	5.49242i	0.741286	−	0.538576i
$105$	21.8572	−	15.8802i	2.13304	−	1.54974i
$106$	−1.04198	−	3.20689i	−0.101206	−	0.311480i
$107$	−3.36137	+	10.3452i	−0.324956	+	1.00011i	0.646505	+	0.762910i	$0.276230\pi$
$107$	−3.36137	+	10.3452i	−0.324956	+	1.00011i	−0.971461	+	0.237201i	$0.923770\pi$
$108$	−3.76711	−	2.73697i	−0.362491	−	0.263365i
$109$	12.2649			1.17476			0.587382	−	0.809310i	$-0.300159\pi$
$109$	12.2649			1.17476			0.587382	+	0.809310i	$0.300159\pi$
$110$	−6.50497	−	5.56680i	−0.620225	−	0.530774i
$111$	−0.699315			−0.0663760
$112$	−2.11322	−	1.53534i	−0.199680	−	0.145076i
$113$	−1.96635	+	6.05181i	−0.184979	+	0.569306i	−0.999948	−	0.0101980i	$-0.996754\pi$
$113$	−1.96635	+	6.05181i	−0.184979	+	0.569306i	0.814969	+	0.579504i	$0.196754\pi$
$114$	−0.572495	−	1.76196i	−0.0536191	−	0.165023i
$115$	−8.23756	+	5.98494i	−0.768156	+	0.558098i
$116$	8.14517	−	5.91781i	0.756260	−	0.549455i
$117$	−0.869446	−	2.67588i	−0.0803803	−	0.247385i
$118$	1.01888	−	3.13579i	0.0937954	−	0.288673i
$119$	2.31824	+	1.68430i	0.212512	+	0.154399i
$120$	15.8485			1.44676
$121$	1.69948	+	10.8679i	0.154498	+	0.987993i
$122$	−5.36452			−0.485681
$123$	−6.26170	−	4.54939i	−0.564598	−	0.410205i
$124$	−2.15342	+	6.62755i	−0.193383	+	0.595171i
$125$	−2.08914	−	6.42970i	−0.186858	−	0.575090i
$126$	−3.35154	+	2.43504i	−0.298579	+	0.216931i
$127$	−7.91134	+	5.74793i	−0.702018	+	0.510046i	−0.880589	−	0.473881i	$-0.842853\pi$
$127$	−7.91134	+	5.74793i	−0.702018	+	0.510046i	0.178571	+	0.983927i	$0.442853\pi$
$128$	1.54705	+	4.76133i	0.136741	+	0.420846i
$129$	6.96375	−	21.4322i	0.613124	−	1.88700i
$130$	−6.66093	−	4.83945i	−0.584202	−	0.424448i
$131$	−18.1963			−1.58981			−0.794907	−	0.606731i	$-0.792481\pi$
$131$	−18.1963			−1.58981			−0.794907	+	0.606731i	$0.792481\pi$
$132$	−5.54035	−	4.74131i	−0.482226	−	0.412678i
$133$	−4.99441			−0.433070
$134$	−0.398719	−	0.289687i	−0.0344441	−	0.0250251i
$135$	−3.54019	+	10.8956i	−0.304691	+	0.937741i
$136$	0.519438	+	1.59866i	0.0445414	+	0.137084i
$137$	7.46194	−	5.42142i	0.637517	−	0.463183i	−0.221480	−	0.975165i	$-0.571089\pi$
$137$	7.46194	−	5.42142i	0.637517	−	0.463183i	0.858996	+	0.511982i	$0.171089\pi$
$138$	5.55870	−	4.03863i	0.473188	−	0.343791i
$139$	4.43954	+	13.6635i	0.376557	+	1.15892i	0.942422	+	0.334425i	$0.108542\pi$
$139$	4.43954	+	13.6635i	0.376557	+	1.15892i	−0.565866	+	0.824497i	$0.691458\pi$
$140$	4.72828	−	14.5522i	0.399613	−	1.22988i
$141$	2.33067	+	1.69333i	0.196277	+	0.142604i
$142$	−11.3901			−0.955839
$143$	2.45932	+	10.2882i	0.205658	+	0.860343i
$144$	−0.461373			−0.0384478
$145$	−20.0398	−	14.5597i	−1.66421	−	1.20912i
$146$	−2.22063	+	6.83441i	−0.183781	+	0.565619i
$147$	10.9255	+	33.6253i	0.901122	+	2.77337i
$148$	−0.320417	+	0.232797i	−0.0263381	+	0.0191358i
$149$	11.1827	−	8.12470i	0.916122	−	0.665601i	−0.0264340	−	0.999651i	$-0.508415\pi$
$149$	11.1827	−	8.12470i	0.916122	−	0.665601i	0.942556	+	0.334049i	$0.108415\pi$
$150$	−1.45273	−	4.47104i	−0.118615	−	0.365059i
$151$	−0.0778625	+	0.239636i	−0.00633636	+	0.0195013i	−0.954175	−	0.299250i	$-0.903264\pi$
$151$	−0.0778625	+	0.239636i	−0.00633636	+	0.0195013i	0.947838	+	0.318751i	$0.103264\pi$
$152$	−2.37024	−	1.72208i	−0.192252	−	0.139679i
$153$	0.506135			0.0409186
$154$	13.2880	−	8.12499i	1.07078	−	0.654731i
$155$	17.1451			1.37712
$156$	−5.67318	−	4.12181i	−0.454218	−	0.330009i
$157$	−2.54817	+	7.84246i	−0.203366	+	0.625897i	0.796410	+	0.604757i	$0.206730\pi$
$157$	−2.54817	+	7.84246i	−0.203366	+	0.625897i	−0.999777	+	0.0211400i	$0.993270\pi$
$158$	0.888459	+	2.73440i	0.0706820	+	0.217537i
$159$	−5.71636	+	4.15318i	−0.453337	+	0.329368i
$160$	11.9225	−	8.66223i	0.942559	−	0.684809i
$161$	−5.72391	−	17.6164i	−0.451107	−	1.38837i
$162$	3.15788	−	9.71896i	0.248107	−	0.763594i
$163$	−13.2308	−	9.61271i	−1.03631	−	0.752925i	−0.0667505	−	0.997770i	$-0.521263\pi$
$163$	−13.2308	−	9.61271i	−1.03631	−	0.752925i	−0.969562	+	0.244844i	$0.921263\pi$
$164$	−4.38349			−0.342293
$165$	−6.88199	+	16.5686i	−0.535762	+	1.28987i
$166$	1.36989			0.106324
$167$	4.22451	+	3.06929i	0.326902	+	0.237508i	0.739115	−	0.673579i	$-0.235244\pi$
$167$	4.22451	+	3.06929i	0.326902	+	0.237508i	−0.412213	+	0.911088i	$0.635244\pi$
$168$	−8.90920	+	27.4197i	−0.687360	+	2.11548i
$169$	−0.873805	−	2.68929i	−0.0672158	−	0.206869i
$170$	1.19823	−	0.870566i	0.0919002	−	0.0667694i
$171$	−0.713688	+	0.518524i	−0.0545771	+	0.0396525i
$172$	−3.94392	−	12.1381i	−0.300721	−	0.925525i
$173$	−0.648296	+	1.99525i	−0.0492891	+	0.151696i	−0.972672	−	0.232185i	$-0.925413\pi$
$173$	−0.648296	+	1.99525i	−0.0492891	+	0.151696i	0.923383	+	0.383881i	$0.125413\pi$
$174$	13.5228	+	9.82491i	1.02516	+	0.744824i
$175$	−12.6735			−0.958026
$176$	1.72911	+	0.137790i	0.130337	+	0.0103863i
$177$	−6.90915			−0.519323
$178$	10.7511	+	7.81112i	0.805828	+	0.585468i
$179$	2.43314	−	7.48844i	0.181862	−	0.559713i	−0.818019	−	0.575192i	$-0.804927\pi$
$179$	2.43314	−	7.48844i	0.181862	−	0.559713i	0.999880	+	0.0154792i	$0.00492739\pi$
$180$	−0.835160	−	2.57036i	−0.0622492	−	0.191583i
$181$	−5.49288	+	3.99081i	−0.408283	+	0.296635i	−0.772906	−	0.634520i	$-0.781198\pi$
$181$	−5.49288	+	3.99081i	−0.408283	+	0.296635i	0.364623	+	0.931155i	$0.381198\pi$
$182$	12.1173	−	8.80370i	0.898191	−	0.652574i
$183$	3.47374	+	10.6911i	0.256787	+	0.790308i
$184$	3.35771	−	10.3340i	0.247534	−	0.761831i
$185$	0.788330	+	0.572755i	0.0579592	+	0.0421098i
$186$	−11.5695			−0.848316
$187$	−1.89687	−	0.151158i	−0.138713	−	0.0110537i
$188$	1.63158			0.118995
$189$	−16.8605	−	12.2499i	−1.22642	−	0.891048i
$190$	−0.797719	+	2.45513i	−0.0578726	+	0.178114i
$191$	4.90928	+	15.1092i	0.355223	+	1.09326i	0.955880	+	0.293758i	$0.0949059\pi$
$191$	4.90928	+	15.1092i	0.355223	+	1.09326i	−0.600657	+	0.799507i	$0.705094\pi$
$192$	−9.71267	+	7.05667i	−0.700952	+	0.509271i
$193$	2.47305	−	1.79677i	0.178014	−	0.129335i	−0.495210	−	0.868773i	$-0.664909\pi$
$193$	2.47305	−	1.79677i	0.178014	−	0.129335i	0.673224	+	0.739439i	$0.264909\pi$
$194$	0.0752955	+	0.231736i	0.00540590	+	0.0166377i
$195$	−5.33143	+	16.4085i	−0.381792	+	1.17503i
$196$	16.1995	+	11.7697i	1.15711	+	0.840689i
$197$	−13.0646			−0.930813			−0.465406	−	0.885097i	$-0.654092\pi$
$197$	−13.0646			−0.930813			−0.465406	+	0.885097i	$0.654092\pi$
$198$	1.05527	−	2.54061i	0.0749951	−	0.180553i
$199$	−26.6627			−1.89007			−0.945036	−	0.326966i	$-0.893974\pi$
$199$	−26.6627			−1.89007			−0.945036	+	0.326966i	$0.893974\pi$
$200$	−6.01457	−	4.36984i	−0.425295	−	0.308995i
$201$	−0.319137	+	0.982202i	−0.0225102	+	0.0692792i
$202$	−0.996990	−	3.06842i	−0.0701480	−	0.215893i
$203$	36.4554	−	26.4864i	2.55867	−	1.85898i
$204$	1.02055	−	0.741471i	0.0714526	−	0.0519133i
$205$	3.33269	+	10.2570i	0.232765	+	0.716377i
$206$	3.54531	−	10.9113i	0.247013	−	0.760228i
$207$	−2.64688	−	1.92307i	−0.183971	−	0.133663i
$208$	1.66806			0.115659
$209$	2.82958	−	1.73016i	0.195726	−	0.119678i
$210$	25.4032			1.75299
$211$	14.1744	+	10.2983i	0.975807	+	0.708965i	0.956768	−	0.290853i	$-0.0939391\pi$
$211$	14.1744	+	10.2983i	0.975807	+	0.708965i	0.0190396	+	0.999819i	$0.493939\pi$
$212$	−1.23660	+	3.80586i	−0.0849300	+	0.261388i
$213$	7.37557	+	22.6997i	0.505366	+	1.55536i
$214$	−8.27455	+	6.01181i	−0.565636	+	0.410959i
$215$	−25.4036	+	18.4568i	−1.73251	+	1.25875i
$216$	−3.77786	−	11.6271i	−0.257051	−	0.791122i
$217$	−9.63809	+	29.6630i	−0.654276	+	2.01366i
$218$	9.32983	+	6.77852i	0.631896	+	0.459099i
$219$	15.0584			1.01755
$220$	2.36234	+	9.88250i	0.159269	+	0.666278i
$221$	−1.82989			−0.123092
$222$	−0.531965	−	0.386495i	−0.0357031	−	0.0259399i
$223$	−2.85165	+	8.77646i	−0.190960	+	0.587715i	−1.00000		3.86367e-5i	$-0.999988\pi$
$223$	−2.85165	+	8.77646i	−0.190960	+	0.587715i	0.809040	+	0.587754i	$0.199988\pi$
$224$	8.28443	+	25.4969i	0.553527	+	1.70358i
$225$	−1.81101	+	1.31577i	−0.120734	+	0.0877183i
$226$	−4.84049	+	3.51682i	−0.321985	+	0.233935i
$227$	4.02728	+	12.3947i	0.267300	+	0.822664i	0.991155	+	0.132712i	$0.0423685\pi$
$227$	4.02728	+	12.3947i	0.267300	+	0.822664i	−0.723855	+	0.689952i	$0.757632\pi$
$228$	−0.679425	+	2.09106i	−0.0449960	+	0.138484i
$229$	−17.7472	−	12.8941i	−1.17277	−	0.852065i	−0.181429	−	0.983404i	$-0.558072\pi$
$229$	−17.7472	−	12.8941i	−1.17277	−	0.852065i	−0.991337	+	0.131340i	$0.958072\pi$
$230$	−9.57400			−0.631291
$231$	−24.7970	−	21.2207i	−1.63152	−	1.39622i
$232$	26.4335			1.73545
$233$	2.58946	+	1.88135i	0.169641	+	0.123251i	0.669366	−	0.742933i	$-0.266566\pi$
$233$	2.58946	+	1.88135i	0.169641	+	0.123251i	−0.499725	+	0.866184i	$0.666566\pi$
$234$	0.817514	−	2.51605i	0.0534426	−	0.164479i
$235$	−1.24046	−	3.81774i	−0.0809186	−	0.249042i
$236$	−3.16568	+	2.30000i	−0.206068	+	0.149717i
$237$	4.87413	−	3.54126i	0.316609	−	0.230030i
$238$	0.832598	+	2.56247i	0.0539693	+	0.166100i
$239$	1.78193	−	5.48421i	0.115263	−	0.354744i	−0.876739	−	0.480967i	$-0.840286\pi$
$239$	1.78193	−	5.48421i	0.115263	−	0.354744i	0.992002	+	0.126223i	$0.0402856\pi$
$240$	2.28882	+	1.66292i	0.147743	+	0.107341i
$241$	16.7845			1.08118			0.540591	−	0.841285i	$-0.318201\pi$
$241$	16.7845			1.08118			0.540591	+	0.841285i	$0.318201\pi$
$242$	−4.71367	+	9.20643i	−0.303006	+	0.591812i
$243$	−8.89557			−0.570651
$244$	5.15060	+	3.74213i	0.329734	+	0.239566i
$245$	15.2237	−	46.8537i	0.972606	−	2.99337i
$246$	−2.24890	−	6.92139i	−0.143384	−	0.441292i
$247$	2.58028	−	1.87469i	0.164179	−	0.119283i
$248$	−14.8019	+	10.7542i	−0.939921	+	0.682892i
$249$	−0.887057	−	2.73008i	−0.0562150	−	0.173012i
$250$	1.96435	−	6.04566i	0.124237	−	0.382361i
$251$	−11.0684	−	8.04166i	−0.698631	−	0.507585i	0.180855	−	0.983510i	$-0.442113\pi$
$251$	−11.0684	−	8.04166i	−0.698631	−	0.507585i	−0.879486	+	0.475925i	$0.842113\pi$
$252$	4.91651			0.309711
$253$	9.34553	+	7.99769i	0.587549	+	0.502811i
$254$	−9.19486			−0.576937
$255$	−2.51088	−	1.82426i	−0.157237	−	0.114240i
$256$	−5.22044	+	16.0669i	−0.326277	+	1.00418i
$257$	3.88196	+	11.9475i	0.242150	+	0.745262i	0.996092	+	0.0883206i	$0.0281500\pi$
$257$	3.88196	+	11.9475i	0.242150	+	0.745262i	−0.753942	+	0.656941i	$0.771850\pi$
$258$	17.1424	−	12.4547i	1.06724	−	0.775394i
$259$	−1.43409	+	1.04193i	−0.0891103	+	0.0647424i
$260$	3.01946	+	9.29294i	0.187259	+	0.576324i
$261$	2.45953	−	7.56967i	0.152241	−	0.468551i
$262$	−13.8418	−	10.0567i	−0.855149	−	0.621302i
$263$	24.5679			1.51492			0.757461	−	0.652880i	$-0.226440\pi$
$263$	24.5679			1.51492			0.757461	+	0.652880i	$0.226440\pi$
$264$	−4.45120	−	18.6210i	−0.273952	−	1.14604i
$265$	9.84553			0.604806
$266$	−3.79922	−	2.76030i	−0.232945	−	0.169245i
$267$	8.60521	−	26.4841i	0.526630	−	1.62080i
$268$	0.180743	+	0.556270i	0.0110406	+	0.0339796i
$269$	−15.3059	+	11.1204i	−0.933215	+	0.678020i	−0.946778	−	0.321888i	$-0.895683\pi$
$269$	−15.3059	+	11.1204i	−0.933215	+	0.678020i	0.0135629	+	0.999908i	$0.495683\pi$
$270$	−8.71473	+	6.33162i	−0.530362	+	0.385330i
$271$	−5.56769	−	17.1356i	−0.338213	−	1.04091i	−0.965118	−	0.261817i	$-0.915678\pi$
$271$	−5.56769	−	17.1356i	−0.338213	−	1.04091i	0.626905	−	0.779096i	$-0.284322\pi$
$272$	−0.0927257	+	0.285380i	−0.00562232	+	0.0173037i
$273$	−25.3915	−	18.4480i	−1.53676	−	1.11653i
$274$	8.67255			0.523928
$275$	7.18017	−	4.39034i	0.432981	−	0.264748i
$276$	−8.15428			−0.490830
$277$	−14.9588	−	10.8682i	−0.898788	−	0.653007i	0.0393668	−	0.999225i	$-0.487466\pi$
$277$	−14.9588	−	10.8682i	−0.898788	−	0.653007i	−0.938154	+	0.346217i	$0.887466\pi$
$278$	−4.17437	+	12.8474i	−0.250362	+	0.770534i
$279$	1.70238	+	5.23940i	0.101919	+	0.313674i
$280$	32.5006	−	23.6131i	1.94228	−	1.41115i
$281$	−14.9799	+	10.8836i	−0.893628	+	0.649259i	−0.936821	−	0.349808i	$-0.886247\pi$
$281$	−14.9799	+	10.8836i	−0.893628	+	0.649259i	0.0431936	+	0.999067i	$0.486247\pi$
$282$	0.837061	+	2.57621i	0.0498463	+	0.153411i
$283$	4.98138	−	15.3311i	0.296112	−	0.911340i	−0.686733	−	0.726910i	$-0.740956\pi$
$283$	4.98138	−	15.3311i	0.296112	−	0.911340i	0.982846	−	0.184431i	$-0.0590441\pi$
$284$	10.9359	+	7.94543i	0.648929	+	0.471474i
$285$	5.40943			0.320427
$286$	−3.81526	+	9.18539i	−0.225601	+	0.543143i
$287$	−19.6192			−1.15809
$288$	3.83093	+	2.78333i	0.225740	+	0.164010i
$289$	−5.15157	+	15.8549i	−0.303033	+	0.932641i
$290$	−7.19730	−	22.1510i	−0.422640	−	1.30075i
$291$	0.413075	−	0.300116i	0.0242149	−	0.0175931i
$292$	6.89956	−	5.01283i	0.403766	−	0.293354i
$293$	0.697202	+	2.14577i	0.0407310	+	0.125357i	0.969354	−	0.245667i	$-0.0790069\pi$
$293$	0.697202	+	2.14577i	0.0407310	+	0.125357i	−0.928623	+	0.371024i	$0.879007\pi$
$294$	−10.2729	+	31.6169i	−0.599130	+	1.84393i
$295$	7.78861	+	5.65876i	0.453470	+	0.329465i
$296$	−1.03985			−0.0604401
$297$	13.7959	+	1.09937i	0.800521	+	0.0637918i
$298$	12.9969			0.752893
$299$	9.56960	+	6.95272i	0.553424	+	0.402086i
$300$	−1.72407	+	5.30613i	−0.0995390	+	0.306350i
$301$	−17.6519	−	54.3268i	−1.01744	−	3.13135i
$302$	−0.191671	+	0.139257i	−0.0110294	+	0.00801334i
$303$	−5.46954	+	3.97385i	−0.314217	+	0.228292i
$304$	−0.161616	−	0.497403i	−0.00926931	−	0.0285280i
$305$	4.84033	−	14.8970i	0.277157	−	0.853001i
$306$	0.385014	+	0.279729i	0.0220098	+	0.0159911i
$307$	−22.6147			−1.29069			−0.645343	−	0.763893i	$-0.723286\pi$
$307$	−22.6147			−1.29069			−0.645343	+	0.763893i	$0.723286\pi$
$308$	−18.4259	−	1.46832i	−1.04991	−	0.0836653i
$309$	−24.0412			−1.36765
$310$	13.0422	+	9.47568i	0.740745	+	0.538182i
$311$	−7.00059	+	21.5456i	−0.396967	+	1.22174i	0.530452	+	0.847715i	$0.322022\pi$
$311$	−7.00059	+	21.5456i	−0.396967	+	1.22174i	−0.927419	+	0.374024i	$0.877978\pi$
$312$	−5.68937	−	17.5101i	−0.322097	−	0.991313i
$313$	10.1425	−	7.36896i	0.573288	−	0.416518i	−0.263010	−	0.964793i	$-0.584715\pi$
$313$	10.1425	−	7.36896i	0.573288	−	0.416518i	0.836298	+	0.548275i	$0.184715\pi$
$314$	−6.27273	+	4.55740i	−0.353990	+	0.257189i
$315$	−3.73794	−	11.5042i	−0.210609	−	0.648187i
$316$	1.05440	−	3.24512i	0.0593149	−	0.182552i
$317$	5.89796	+	4.28512i	0.331263	+	0.240676i	0.740966	−	0.671542i	$-0.234368\pi$
$317$	5.89796	+	4.28512i	0.331263	+	0.240676i	−0.409704	+	0.912219i	$0.634368\pi$
$318$	−6.64377			−0.372564
$319$	−11.4784	+	27.6347i	−0.642668	+	1.54725i
$320$	16.7286			0.935155
$321$	17.3392	+	12.5977i	0.967779	+	0.703133i
$322$	5.38202	−	16.5642i	0.299928	−	0.923085i
$323$	0.177296	+	0.545660i	0.00986500	+	0.0303613i
$324$	−9.81162	+	7.12856i	−0.545090	+	0.396031i
$325$	6.54756	−	4.75708i	0.363193	−	0.263875i
$326$	−4.75184	−	14.6247i	−0.263180	−	0.809985i
$327$	7.46764	−	22.9830i	0.412961	−	1.27096i
$328$	−9.31087	−	6.76474i	−0.514107	−	0.373520i
$329$	7.30247			0.402598
$330$	−14.3922	+	8.80016i	−0.792264	+	0.484433i
$331$	31.8272			1.74938			0.874691	−	0.484681i	$-0.161064\pi$
$331$	31.8272			1.74938			0.874691	+	0.484681i	$0.161064\pi$
$332$	−1.31526	−	0.955593i	−0.0721843	−	0.0524450i
$333$	−0.0967539	+	0.297778i	−0.00530208	+	0.0163181i
$334$	1.51724	+	4.66958i	0.0830196	+	0.255508i
$335$	1.16421	−	0.845845i	0.0636073	−	0.0462134i
$336$	−4.16371	+	3.02512i	−0.227149	+	0.165034i
$337$	1.90882	+	5.87474i	0.103980	+	0.320017i	0.989490	−	0.144603i	$-0.0461906\pi$
$337$	1.90882	+	5.87474i	0.103980	+	0.320017i	−0.885510	+	0.464621i	$0.846191\pi$
$338$	0.821612	−	2.52866i	0.0446898	−	0.137541i
$339$	10.1432	+	7.36944i	0.550901	+	0.400253i
$340$	−1.75773			−0.0953265
$341$	−4.81536	−	20.1444i	−0.260767	−	1.09088i
$342$	−0.829475			−0.0448528
$343$	44.2205	+	32.1281i	2.38768	+	1.73475i
$344$	10.3548	−	31.8688i	0.558293	−	1.71825i
$345$	6.19955	+	19.0803i	0.333773	+	1.02725i
$346$	−1.59588	+	1.15948i	−0.0857953	+	0.0623339i
$347$	2.13796	−	1.55332i	0.114772	−	0.0833865i	−0.528919	−	0.848672i	$-0.677402\pi$
$347$	2.13796	−	1.55332i	0.114772	−	0.0833865i	0.643691	+	0.765286i	$0.277402\pi$
$348$	−6.13002	−	18.8663i	−0.328603	−	1.01134i
$349$	9.27919	−	28.5584i	0.496703	−	1.52870i	−0.317582	−	0.948231i	$-0.602871\pi$
$349$	9.27919	−	28.5584i	0.496703	−	1.52870i	0.814285	−	0.580465i	$-0.197129\pi$
$350$	−9.64066	−	7.00435i	−0.515315	−	0.374398i
$351$	13.3088			0.710371
$352$	−13.5261	−	11.5754i	−0.720946	−	0.616969i
$353$	1.48192			0.0788746			0.0394373	−	0.999222i	$-0.487443\pi$
$353$	1.48192			0.0788746			0.0394373	+	0.999222i	$0.487443\pi$
$354$	−5.25575	−	3.81853i	−0.279340	−	0.202952i
$355$	10.2772	−	31.6299i	0.545455	−	1.67874i
$356$	−4.87356	−	14.9993i	−0.258298	−	0.794960i
$357$	4.56767	−	3.31861i	0.241747	−	0.175639i
$358$	5.98957	−	4.35168i	0.316559	−	0.229993i
$359$	2.36074	+	7.26562i	0.124595	+	0.383465i	0.993827	−	0.110940i	$-0.0353861\pi$
$359$	2.36074	+	7.26562i	0.124595	+	0.383465i	−0.869232	+	0.494405i	$0.835386\pi$
$360$	2.19272	−	6.74849i	0.115566	−	0.355677i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−6.38404			−0.335537
$363$	21.4000	+	3.43244i	1.12321	+	0.180156i
$364$	−17.7753			−0.931677
$365$	−16.9752	−	12.3332i	−0.888521	−	0.645548i
$366$	−3.26626	+	10.0525i	−0.170730	+	0.525453i
$367$	−8.11281	−	24.9687i	−0.423485	−	1.30335i	−0.904437	−	0.426606i	$-0.859709\pi$
$367$	−8.11281	−	24.9687i	−0.423485	−	1.30335i	0.480952	−	0.876747i	$-0.340291\pi$
$368$	1.56923	−	1.14011i	0.0818016	−	0.0594323i
$369$	−2.80353	+	2.03689i	−0.145946	+	0.106036i
$370$	0.283130	+	0.871383i	0.0147192	+	0.0453011i
$371$	−5.53466	+	17.0339i	−0.287345	+	0.884358i
$372$	11.1081	+	8.07054i	0.575930	+	0.418438i
$373$	27.4114			1.41931			0.709655	−	0.704550i	$-0.248851\pi$
$373$	27.4114			1.41931			0.709655	+	0.704550i	$0.248851\pi$
$374$	−1.35940	−	1.16334i	−0.0702928	−	0.0601550i
$375$	−13.3205			−0.687869
$376$	3.46560	+	2.51790i	0.178724	+	0.129851i
$377$	−8.89226	+	27.3676i	−0.457975	+	1.40950i
$378$	−6.05547	−	18.6368i	−0.311460	−	0.958575i
$379$	8.64122	−	6.27821i	0.443869	−	0.322490i	−0.343301	−	0.939225i	$-0.611545\pi$
$379$	8.64122	−	6.27821i	0.443869	−	0.322490i	0.787171	+	0.616735i	$0.211545\pi$
$380$	2.47853	−	1.80076i	0.127146	−	0.0923770i
$381$	5.95404	+	18.3247i	0.305035	+	0.938801i
$382$	−4.61605	+	14.2067i	−0.236178	+	0.726880i
$383$	12.4481	+	9.04410i	0.636070	+	0.462132i	0.858498	−	0.512817i	$-0.171398\pi$
$383$	12.4481	+	9.04410i	0.636070	+	0.462132i	−0.222428	+	0.974949i	$0.571398\pi$
$384$	9.86414			0.503377
$385$	10.5731	+	44.2312i	0.538857	+	2.25423i
$386$	2.87427			0.146296
$387$	−8.16266	−	5.93052i	−0.414931	−	0.301465i
$388$	0.0893591	−	0.275019i	0.00453652	−	0.0139620i
$389$	2.90022	+	8.92596i	0.147047	+	0.452564i	0.997269	−	0.0738608i	$-0.0235321\pi$
$389$	2.90022	+	8.92596i	0.147047	+	0.452564i	−0.850222	+	0.526425i	$0.823532\pi$
$390$	−13.1242	+	9.53527i	−0.664568	+	0.482837i
$391$	−1.72147	+	1.25072i	−0.0870585	+	0.0632517i
$392$	16.2458	+	49.9993i	0.820535	+	2.52535i
$393$	−11.0790	+	34.0977i	−0.558863	+	1.72000i
$394$	−9.93816	−	7.22049i	−0.500677	−	0.363763i
$395$	−8.39493			−0.422395
$396$	−2.78545	+	1.70317i	−0.139974	+	0.0855877i
$397$	−2.02408			−0.101585			−0.0507927	−	0.998709i	$-0.516175\pi$
$397$	−2.02408			−0.101585			−0.0507927	+	0.998709i	$0.516175\pi$
$398$	−20.2822	−	14.7359i	−1.01665	−	0.738643i
$399$	−3.04091	+	9.35896i	−0.152236	+	0.468534i
$400$	−0.410106	−	1.26218i	−0.0205053	−	0.0631089i
$401$	9.95306	−	7.23132i	0.497032	−	0.361115i	−0.310850	−	0.950459i	$-0.600614\pi$
$401$	9.95306	−	7.23132i	0.497032	−	0.361115i	0.807882	+	0.589344i	$0.200614\pi$
$402$	−0.785606	+	0.570776i	−0.0391824	+	0.0284677i
$403$	−6.15484	−	18.9426i	−0.306594	−	0.943600i
$404$	−1.18321	+	3.64153i	−0.0588667	+	0.181173i
$405$	24.1398	+	17.5386i	1.19952	+	0.871499i
$406$	42.3699			2.10278
$407$	0.451542	−	1.08710i	0.0223821	−	0.0538857i
$408$	3.31198			0.163968
$409$	2.38814	+	1.73508i	0.118086	+	0.0857943i	0.645261	−	0.763962i	$-0.276749\pi$
$409$	2.38814	+	1.73508i	0.118086	+	0.0857943i	−0.527175	+	0.849757i	$0.676749\pi$
$410$	−3.13363	+	9.64431i	−0.154759	+	0.476298i
$411$	−5.61583	−	17.2837i	−0.277008	−	0.852544i
$412$	−11.0154	+	8.00312i	−0.542688	+	0.394286i
$413$	−14.1687	+	10.2941i	−0.697195	+	0.506542i
$414$	−0.950630	−	2.92574i	−0.0467209	−	0.143792i
$415$	−1.23603	+	3.80411i	−0.0606743	+	0.186736i
$416$	−13.8504	−	10.0629i	−0.679074	−	0.493376i
$417$	28.3069			1.38620
$418$	3.10867	+	0.247723i	0.152050	+	0.0121165i
$419$	−29.1134			−1.42228			−0.711142	−	0.703049i	$-0.751822\pi$
$419$	−29.1134			−1.42228			−0.711142	+	0.703049i	$0.751822\pi$
$420$	−24.3902	−	17.7205i	−1.19012	−	0.864674i
$421$	8.06491	−	24.8212i	0.393060	−	1.20971i	−0.537403	−	0.843326i	$-0.680595\pi$
$421$	8.06491	−	24.8212i	0.393060	−	1.20971i	0.930462	−	0.366387i	$-0.119405\pi$
$422$	5.09076	+	15.6677i	0.247814	+	0.762694i
$423$	1.04350	−	0.758149i	0.0507368	−	0.0368625i
$424$	−8.49997	+	6.17559i	−0.412795	+	0.299913i
$425$	0.449894	+	1.38463i	0.0218231	+	0.0671645i
$426$	−6.93503	+	21.3438i	−0.336003	+	1.03411i
$427$	23.0526	+	16.7487i	1.11559	+	0.810527i
$428$	12.1383			0.586725
$429$	20.7763	+	1.65562i	1.00309	+	0.0799342i
$430$	−29.5251			−1.42383
$431$	−22.4422	−	16.3052i	−1.08100	−	0.785394i	−0.103144	−	0.994666i	$-0.532890\pi$
$431$	−22.4422	−	16.3052i	−1.08100	−	0.785394i	−0.977857	+	0.209273i	$0.932890\pi$
$432$	0.674393	−	2.07557i	0.0324468	−	0.0998608i
$433$	1.46117	+	4.49701i	0.0702192	+	0.216112i	0.980008	−	0.198960i	$-0.0637563\pi$
$433$	1.46117	+	4.49701i	0.0702192	+	0.216112i	−0.909788	+	0.415072i	$0.863756\pi$
$434$	−23.7257	+	17.2377i	−1.13887	+	0.827437i
$435$	−39.4848	+	28.6874i	−1.89315	+	1.37545i
$436$	−4.22930	−	13.0164i	−0.202547	−	0.623374i
$437$	1.14606	−	3.52722i	0.0548236	−	0.168730i
$438$	11.4548	+	8.32243i	0.547334	+	0.397661i
$439$	−15.3410			−0.732185			−0.366092	−	0.930578i	$-0.619305\pi$
$439$	−15.3410			−0.732185			−0.366092	+	0.930578i	$0.619305\pi$
$440$	−10.2332	+	24.6368i	−0.487849	+	1.17451i
$441$	15.8297			0.753796
$442$	−1.39199	−	1.01134i	−0.0662102	−	0.0481045i
$443$	3.60469	−	11.0941i	0.171264	−	0.527096i	−0.828179	−	0.560463i	$-0.810623\pi$
$443$	3.60469	−	11.0941i	0.171264	−	0.527096i	0.999443	+	0.0333671i	$0.0106231\pi$
$444$	0.241145	+	0.742166i	0.0114442	+	0.0352217i
$445$	−31.3917	+	22.8074i	−1.48811	+	1.08117i
$446$	−7.01978	+	5.10017i	−0.332396	+	0.241500i
$447$	−8.41605	−	25.9019i	−0.398065	−	1.22512i
$448$	−9.40396	+	28.9424i	−0.444295	+	1.36740i
$449$	−12.9947	−	9.44122i	−0.613259	−	0.445559i	0.237301	−	0.971436i	$-0.423737\pi$
$449$	−12.9947	−	9.44122i	−0.613259	−	0.445559i	−0.850560	+	0.525877i	$0.823737\pi$
$450$	−2.10482			−0.0992222
$451$	11.1153	−	6.79647i	0.523398	−	0.320033i
$452$	7.10070			0.333989
$453$	0.401643	+	0.291811i	0.0188709	+	0.0137105i
$454$	−3.78673	+	11.6544i	−0.177720	+	0.546966i
$455$	13.5142	+	41.5925i	0.633557	+	1.94989i
$456$	−4.67014	+	3.39305i	−0.218699	+	0.158894i
$457$	−11.3552	+	8.25003i	−0.531174	+	0.385920i	−0.820797	−	0.571221i	$-0.806470\pi$
$457$	−11.3552	+	8.25003i	−0.531174	+	0.385920i	0.289623	+	0.957141i	$0.406470\pi$
$458$	−6.37392	−	19.6169i	−0.297834	−	0.916638i
$459$	−0.739822	+	2.27694i	−0.0345319	+	0.106278i
$460$	9.19223	+	6.67854i	0.428590	+	0.311389i
$461$	0.179717			0.00837025			0.00418512	−	0.999991i	$-0.498668\pi$
$461$	0.179717			0.00837025			0.00418512	+	0.999991i	$0.498668\pi$
$462$	−7.13475	−	29.8472i	−0.331939	−	1.38862i
$463$	−18.9180			−0.879192			−0.439596	−	0.898196i	$-0.644878\pi$
$463$	−18.9180			−0.879192			−0.439596	+	0.898196i	$0.644878\pi$
$464$	3.81750	+	2.77358i	0.177223	+	0.128760i
$465$	10.4390	−	32.1279i	0.484097	−	1.48990i
$466$	0.930006	+	2.86226i	0.0430817	+	0.132592i
$467$	8.64885	−	6.28376i	0.400221	−	0.290778i	−0.369410	−	0.929267i	$-0.620440\pi$
$467$	8.64885	−	6.28376i	0.400221	−	0.290778i	0.769631	+	0.638489i	$0.220440\pi$
$468$	−2.54004	+	1.84545i	−0.117413	+	0.0853057i
$469$	0.808954	+	2.48970i	0.0373540	+	0.114964i
$470$	1.16637	−	3.58971i	0.0538005	−	0.165581i
$471$	13.1444	+	9.54997i	0.605662	+	0.440039i
$472$	−10.2736			−0.472881
$473$	28.8205	+	24.6639i	1.32517	+	1.13405i
$474$	5.66490			0.260198
$475$	−2.05291	−	1.49153i	−0.0941940	−	0.0684359i
$476$	0.988109	−	3.04109i	0.0452899	−	0.139388i
$477$	0.977592	+	3.00872i	0.0447608	+	0.137760i
$478$	4.38650	−	3.18698i	0.200634	−	0.145769i
$479$	4.18828	−	3.04297i	0.191368	−	0.139037i	−0.487976	−	0.872857i	$-0.662265\pi$
$479$	4.18828	−	3.04297i	0.191368	−	0.139037i	0.679344	+	0.733820i	$0.262265\pi$
$480$	−8.97285	−	27.6156i	−0.409553	−	1.26047i
$481$	0.349806	−	1.07659i	0.0159498	−	0.0490884i
$482$	12.7678	+	9.27638i	0.581560	+	0.422528i
$483$	−36.4962			−1.66063
$484$	10.9478	−	5.55120i	0.497629	−	0.252327i
$485$	−0.711457			−0.0323056
$486$	−6.76681	−	4.91638i	−0.306949	−	0.223011i
$487$	10.9510	−	33.7037i	0.496238	−	1.52726i	−0.318781	−	0.947828i	$-0.603274\pi$
$487$	10.9510	−	33.7037i	0.496238	−	1.52726i	0.815019	−	0.579434i	$-0.196726\pi$
$488$	5.16530	+	15.8972i	0.233822	+	0.719631i
$489$	−26.0688	+	18.9401i	−1.17887	+	0.856502i
$490$	37.4755	−	27.2276i	1.69297	−	1.23002i
$491$	−8.64181	−	26.5968i	−0.389999	−	1.20029i	−0.932788	−	0.360425i	$-0.882632\pi$
$491$	−8.64181	−	26.5968i	−0.389999	−	1.20029i	0.542789	−	0.839869i	$-0.317368\pi$
$492$	−2.66894	+	8.21416i	−0.120325	+	0.370323i
$493$	−4.18787	−	3.04267i	−0.188612	−	0.137035i
$494$	2.99890			0.134927
$495$	6.10300	+	5.22280i	0.274309	+	0.234748i
$496$	−3.26608			−0.146651
$497$	48.9461	+	35.5614i	2.19553	+	1.59515i
$498$	0.834073	−	2.56701i	0.0373757	−	0.115031i
$499$	−8.77032	−	26.9923i	−0.392614	−	1.20834i	−0.930804	−	0.365517i	$-0.880892\pi$
$499$	−8.77032	−	26.9923i	−0.392614	−	1.20834i	0.538191	−	0.842823i	$-0.319108\pi$
$500$	−6.10330	+	4.43430i	−0.272948	+	0.198308i
$501$	8.32364	−	6.04748i	0.371873	−	0.270181i
$502$	−3.97523	−	12.2345i	−0.177423	−	0.546052i
$503$	2.44375	−	7.52108i	0.108961	−	0.335348i	−0.881678	−	0.471851i	$-0.843586\pi$
$503$	2.44375	−	7.52108i	0.108961	−	0.335348i	0.990640	+	0.136502i	$0.0435861\pi$
$504$	10.4431	+	7.58732i	0.465171	+	0.337966i
$505$	9.42042			0.419203
$506$	2.68896	+	11.2489i	0.119539	+	0.500073i
$507$	−5.57146			−0.247437
$508$	8.82820	+	6.41406i	0.391688	+	0.284578i
$509$	2.69604	−	8.29757i	0.119500	−	0.367783i	−0.873359	−	0.487077i	$-0.838063\pi$
$509$	2.69604	−	8.29757i	0.119500	−	0.367783i	0.992859	+	0.119294i	$0.0380631\pi$
$510$	−0.901784	−	2.77541i	−0.0399317	−	0.122897i
$511$	30.8805	−	22.4360i	1.36607	−	0.992509i
$512$	−4.75048	+	3.45142i	−0.209943	+	0.152533i
$513$	−1.28947	−	3.96858i	−0.0569315	−	0.175217i
$514$	−3.65009	+	11.2338i	−0.160999	+	0.495503i
$515$	27.1014	+	19.6903i	1.19423	+	0.867658i
$516$	−25.1468			−1.10703
$517$	−4.13721	+	2.52971i	−0.181954	+	0.111257i
$518$	−1.66676			−0.0732331
$519$	3.34415	+	2.42967i	0.146792	+	0.106651i
$520$	−7.92760	+	24.3987i	−0.347648	+	1.06995i
$521$	−8.27694	−	25.4738i	−0.362619	−	1.11603i	−0.951459	−	0.307777i	$-0.900415\pi$
$521$	−8.27694	−	25.4738i	−0.362619	−	1.11603i	0.588839	−	0.808250i	$-0.299585\pi$
$522$	6.05454	−	4.39888i	0.265000	−	0.192534i
$523$	35.8585	−	26.0527i	1.56798	−	1.13921i	0.638925	−	0.769269i	$-0.279379\pi$
$523$	35.8585	−	26.0527i	1.56798	−	1.13921i	0.929057	−	0.369937i	$-0.120621\pi$
$524$	6.27461	+	19.3113i	0.274108	+	0.843616i
$525$	−7.71642	+	23.7487i	−0.336772	+	1.03648i
$526$	18.6887	+	13.5781i	0.814865	+	0.592034i
$527$	3.58295			0.156076
$528$	1.31100	−	3.15627i	0.0570537	−	0.137359i
$529$	−9.24526			−0.401968
$530$	7.48944	+	5.44140i	0.325321	+	0.236359i
$531$	−0.955917	+	2.94201i	−0.0414833	+	0.127672i
$532$	1.72222	+	5.30045i	0.0746678	+	0.229804i
$533$	10.1360	−	7.36421i	0.439037	−	0.318979i
$534$	21.1831	−	15.3904i	0.916682	−	0.666008i
$535$	−9.22850	−	28.4024i	−0.398983	−	1.22794i
$536$	−0.474542	+	1.46049i	−0.0204971	+	0.0630836i
$537$	−12.5510	−	9.11887i	−0.541618	−	0.393508i
$538$	−17.7891			−0.766941
$539$	−59.3259	−	4.72756i	−2.55535	−	0.203630i
$540$	12.7840			0.550135
$541$	−11.9063	−	8.65043i	−0.511892	−	0.371911i	0.301649	−	0.953419i	$-0.402463\pi$
$541$	−11.9063	−	8.65043i	−0.511892	−	0.371911i	−0.813541	+	0.581508i	$0.802463\pi$
$542$	5.23513	−	16.1121i	0.224868	−	0.692073i
$543$	4.13392	+	12.7229i	0.177404	+	0.545992i
$544$	2.49155	−	1.81022i	0.106824	−	0.0776125i
$545$	−27.2418	+	19.7923i	−1.16691	+	0.847811i
$546$	−9.11940	−	28.0666i	−0.390274	−	1.20114i
$547$	1.78483	−	5.49314i	0.0763138	−	0.234870i	−0.905621	−	0.424087i	$-0.860595\pi$
$547$	1.78483	−	5.49314i	0.0763138	−	0.234870i	0.981935	+	0.189217i	$0.0605950\pi$
$548$	−8.32672	−	6.04972i	−0.355700	−	0.258431i
$549$	5.03302			0.214804
$550$	7.88836	+	0.628607i	0.336361	+	0.0268039i
$551$	9.02236			0.384365
$552$	−17.3203	−	12.5839i	−0.737202	−	0.535608i
$553$	4.71921	−	14.5242i	0.200681	−	0.617633i
$554$	−5.37247	−	16.5348i	−0.228255	−	0.702495i
$555$	1.55326	−	1.12851i	0.0659324	−	0.0479027i
$556$	12.9699	−	9.42316i	0.550045	−	0.399631i
$557$	6.04390	+	18.6012i	0.256088	+	0.788159i	0.993613	+	0.112839i	$0.0359945\pi$
$557$	6.04390	+	18.6012i	0.256088	+	0.788159i	−0.737525	+	0.675320i	$0.764006\pi$
$558$	−1.60070	+	4.92645i	−0.0677630	+	0.208553i
$559$	29.5115	+	21.4414i	1.24820	+	0.906873i
$560$	7.17135			0.303045
$561$	−1.43819	+	3.46249i	−0.0607203	+	0.146186i
$562$	−17.4102			−0.734407
$563$	31.3301	+	22.7627i	1.32041	+	0.959332i	0.999927	+	0.0120770i	$0.00384431\pi$
$563$	31.3301	+	22.7627i	1.32041	+	0.959332i	0.320480	+	0.947255i	$0.396156\pi$
$564$	0.993406	−	3.05739i	0.0418300	−	0.128739i
$565$	−5.39854	−	16.6150i	−0.227118	−	0.698998i
$566$	12.2625	−	8.90920i	0.515430	−	0.374482i
$567$	−43.9140	+	31.9054i	−1.84421	+	1.33990i
$568$	10.9671	+	33.7534i	0.460171	+	1.41626i
$569$	−4.56806	+	14.0590i	−0.191503	+	0.589385i	0.808497	+	0.588501i	$0.200282\pi$
$569$	−4.56806	+	14.0590i	−0.191503	+	0.589385i	−1.00000		0.000884651i	$0.999718\pi$
$570$	4.11493	+	2.98967i	0.172355	+	0.125223i
$571$	−7.79965			−0.326405			−0.163203	−	0.986593i	$-0.552182\pi$
$571$	−7.79965			−0.326405			−0.163203	+	0.986593i	$0.552182\pi$
$572$	10.0706	−	6.15769i	0.421072	−	0.257466i
$573$	31.3021			1.30766
$574$	−14.9242	−	10.8431i	−0.622925	−	0.452582i
$575$	2.90818	−	8.95045i	0.121279	−	0.373259i
$576$	1.66103	+	5.11212i	0.0692095	+	0.213005i
$577$	−14.8446	+	10.7853i	−0.617990	+	0.448996i	−0.852219	−	0.523185i	$-0.824744\pi$
$577$	−14.8446	+	10.7853i	−0.617990	+	0.448996i	0.234229	+	0.972182i	$0.424744\pi$
$578$	−12.6814	+	9.21358i	−0.527477	+	0.383234i
$579$	−1.86120	−	5.72820i	−0.0773490	−	0.238056i
$580$	−8.54160	+	26.2884i	−0.354671	+	1.09156i
$581$	−5.88673	−	4.27696i	−0.244223	−	0.177438i
$582$	0.480091			0.0199004
$583$	−2.76522	−	11.5679i	−0.114524	−	0.479093i
$584$	22.3912			0.926553
$585$	6.24932	+	4.54039i	0.258377	+	0.187722i
$586$	−0.655558	+	2.01760i	−0.0270809	+	0.0833463i
$587$	4.04042	+	12.4351i	0.166766	+	0.513253i	0.999162	−	0.0409284i	$-0.0130315\pi$
$587$	4.04042	+	12.4351i	0.166766	+	0.513253i	−0.832396	+	0.554181i	$0.813032\pi$
$588$	31.9183	−	23.1900i	1.31629	−	0.956339i
$589$	−5.05222	+	3.67065i	−0.208173	+	0.151247i
$590$	2.79729	+	8.60917i	0.115163	+	0.354434i
$591$	−7.95454	+	24.4816i	−0.327206	+	1.00704i
$592$	−0.150174	−	0.109108i	−0.00617212	−	0.00448431i
$593$	−7.22254			−0.296594			−0.148297	−	0.988943i	$-0.547379\pi$
$593$	−7.22254			−0.296594			−0.148297	+	0.988943i	$0.547379\pi$
$594$	9.88689	+	8.46097i	0.405664	+	0.347158i
$595$	−7.86710			−0.322520
$596$	−12.4787	−	9.06629i	−0.511146	−	0.371370i
$597$	−16.2340	+	49.9630i	−0.664411	+	2.04485i
$598$	3.43693	+	10.5778i	0.140547	+	0.432558i
$599$	16.0190	−	11.6385i	0.654518	−	0.475535i	−0.210290	−	0.977639i	$-0.567441\pi$
$599$	16.0190	−	11.6385i	0.654518	−	0.475535i	0.864807	+	0.502104i	$0.167441\pi$
$600$	−11.8506	+	8.61000i	−0.483801	+	0.351502i
$601$	−10.5979	−	32.6171i	−0.432299	−	1.33048i	−0.895829	−	0.444398i	$-0.853418\pi$
$601$	−10.5979	−	32.6171i	−0.432299	−	1.33048i	0.463530	−	0.886081i	$-0.346582\pi$
$602$	16.5975	−	51.0819i	0.676464	−	2.08194i
$603$	0.374081	+	0.271786i	0.0152337	+	0.0110680i
$604$	0.281169			0.0114406
$605$	−21.3127	−	21.3965i	−0.866486	−	0.869890i
$606$	−6.35690			−0.258231
$607$	−8.87807	−	6.45030i	−0.360350	−	0.261809i	0.392848	−	0.919603i	$-0.371490\pi$
$607$	−8.87807	−	6.45030i	−0.360350	−	0.261809i	−0.753198	+	0.657794i	$0.771490\pi$
$608$	−1.65874	+	5.10508i	−0.0672708	+	0.207038i
$609$	−27.4362	−	84.4399i	−1.11177	−	3.42168i
$610$	11.9153	−	8.65694i	0.482435	−	0.350509i
$611$	−3.77270	+	2.74103i	−0.152627	+	0.110890i
$612$	−0.174530	−	0.537149i	−0.00705497	−	0.0217130i
$613$	−4.67775	+	14.3966i	−0.188932	+	0.581474i	−0.999994	−	0.00348679i	$-0.998890\pi$
$613$	−4.67775	+	14.3966i	−0.188932	+	0.581474i	0.811062	+	0.584961i	$0.198890\pi$
$614$	−17.2028	−	12.4986i	−0.694250	−	0.504402i
$615$	21.2495			0.856864
$616$	−36.8721	−	31.5543i	−1.48562	−	1.27136i
$617$	−24.6690			−0.993135			−0.496567	−	0.867998i	$-0.665406\pi$
$617$	−24.6690			−0.993135			−0.496567	+	0.867998i	$0.665406\pi$
$618$	−18.2880	−	13.2870i	−0.735651	−	0.534482i
$619$	1.05053	−	3.23319i	0.0422243	−	0.129953i	−0.927722	−	0.373271i	$-0.878236\pi$
$619$	1.05053	−	3.23319i	0.0422243	−	0.129953i	0.969946	+	0.243319i	$0.0782360\pi$
$620$	−5.91213	−	18.1957i	−0.237437	−	0.730755i
$621$	12.5202	−	9.09649i	0.502420	−	0.365030i
$622$	−17.2331	+	12.5205i	−0.690983	+	0.502028i
$623$	−21.8127	−	67.1325i	−0.873906	−	2.68961i
$624$	1.01562	−	3.12576i	0.0406573	−	0.125130i
$625$	25.2806	+	18.3675i	1.01123	+	0.734698i
$626$	11.7880			0.471143
$627$	−1.51929	−	6.35575i	−0.0606748	−	0.253824i
$628$	9.20170			0.367188
$629$	0.164744	+	0.119693i	0.00656877	+	0.00477249i
$630$	3.51467	−	10.8170i	0.140028	−	0.430961i
$631$	5.56075	+	17.1142i	0.221370	+	0.681306i	0.998640	+	0.0521391i	$0.0166039\pi$
$631$	5.56075	+	17.1142i	0.221370	+	0.681306i	−0.777270	+	0.629167i	$0.783396\pi$
$632$	7.24762	−	5.26570i	0.288295	−	0.209458i
$633$	27.9282	−	20.2910i	1.11004	−	0.806495i
$634$	2.11826	+	6.51934i	0.0841269	+	0.258916i
$635$	8.29640	−	25.5337i	0.329232	−	1.01327i
$636$	6.37884	+	4.63450i	0.252937	+	0.183770i
$637$	−57.2311			−2.26758
$638$	−24.0047	+	14.6777i	−0.950353	+	0.581097i
$639$	10.6863			0.422743
$640$	−11.1197	−	8.07896i	−0.439546	−	0.319349i
$641$	3.65260	−	11.2416i	0.144269	−	0.444015i	−0.852647	−	0.522487i	$-0.825004\pi$
$641$	3.65260	−	11.2416i	0.144269	−	0.444015i	0.996916	+	0.0784723i	$0.0250042\pi$
$642$	6.22739	+	19.1659i	0.245775	+	0.756419i
$643$	−7.58280	+	5.50923i	−0.299037	+	0.217263i	−0.727178	−	0.686449i	$-0.759169\pi$
$643$	−7.58280	+	5.50923i	−0.299037	+	0.217263i	0.428141	+	0.903712i	$0.359169\pi$
$644$	−16.7221	+	12.1493i	−0.658942	+	0.478750i
$645$	19.1187	+	58.8412i	0.752797	+	2.31687i
$646$	−0.166706	+	0.513068i	−0.00655896	+	0.0201864i
$647$	−17.3649	−	12.6164i	−0.682686	−	0.496000i	0.191562	−	0.981481i	$-0.438645\pi$
$647$	−17.3649	−	12.6164i	−0.682686	−	0.496000i	−0.874248	+	0.485480i	$0.838645\pi$
$648$	−31.8417			−1.25086
$649$	4.46118	−	10.7405i	0.175117	−	0.421600i
$650$	7.60982			0.298482
$651$	49.7168	+	36.1214i	1.94856	+	1.41571i
$652$	−5.63938	+	17.3562i	−0.220855	+	0.679723i
$653$	3.82776	+	11.7806i	0.149792	+	0.461012i	0.997596	−	0.0692974i	$-0.0220757\pi$
$653$	3.82776	+	11.7806i	0.149792	+	0.461012i	−0.847804	+	0.530309i	$0.822076\pi$
$654$	18.3828	−	13.3559i	0.718823	−	0.522256i
$655$	40.4161	−	29.3640i	1.57919	−	1.14735i
$656$	−0.634865	−	1.95391i	−0.0247873	−	0.0762876i
$657$	2.08341	−	6.41208i	0.0812815	−	0.250159i
$658$	5.55495	+	4.03590i	0.216554	+	0.157336i
$659$	−7.33727			−0.285819			−0.142910	−	0.989736i	$-0.545646\pi$
$659$	−7.33727			−0.285819			−0.142910	+	0.989736i	$0.545646\pi$
$660$	19.9570	+	1.59033i	0.776826	+	0.0619037i
$661$	15.4591			0.601291			0.300645	−	0.953736i	$-0.402798\pi$
$661$	15.4591			0.601291			0.300645	+	0.953736i	$0.402798\pi$
$662$	24.2108	+	17.5902i	0.940979	+	0.683661i
$663$	−1.11415	+	3.42901i	−0.0432701	+	0.133172i
$664$	−1.31901	−	4.05951i	−0.0511877	−	0.157539i
$665$	11.0932	−	8.05968i	0.430176	−	0.312541i
$666$	−0.238175	+	0.173044i	−0.00922910	+	0.00670533i
$667$	10.3402	+	31.8238i	0.400374	+	1.23222i
$668$	1.80062	−	5.54175i	0.0696683	−	0.214417i
$669$	14.7098	+	10.6873i	0.568715	+	0.413196i
$670$	1.35308			0.0522742
$671$	−18.8625	−	1.50312i	−0.728180	−	0.0580272i
$672$	52.8223			2.03767
$673$	−2.42075	−	1.75878i	−0.0933132	−	0.0677960i	0.540150	−	0.841569i	$-0.318367\pi$
$673$	−2.42075	−	1.75878i	−0.0933132	−	0.0677960i	−0.633464	+	0.773772i	$0.718367\pi$
$674$	−1.79480	+	5.52384i	−0.0691333	+	0.212770i
$675$	−3.27208	−	10.0704i	−0.125942	−	0.387611i
$676$	−2.55277	+	1.85470i	−0.0981835	+	0.0713345i
$677$	−3.85917	+	2.80385i	−0.148320	+	0.107761i	−0.659471	−	0.751730i	$-0.729219\pi$
$677$	−3.85917	+	2.80385i	−0.148320	+	0.107761i	0.511150	+	0.859491i	$0.329219\pi$
$678$	3.64293	+	11.2118i	0.139906	+	0.430586i
$679$	0.399945	−	1.23091i	0.0153485	−	0.0472378i
$680$	−3.73356	−	2.71259i	−0.143176	−	0.104023i
$681$	25.6783			0.983994
$682$	7.47032	−	17.9851i	0.286053	−	0.688684i
$683$	−26.1249			−0.999641			−0.499821	−	0.866129i	$-0.666601\pi$
$683$	−26.1249			−0.999641			−0.499821	+	0.866129i	$0.666601\pi$
$684$	0.796398	+	0.578617i	0.0304511	+	0.0221240i
$685$	−7.82512	+	24.0833i	−0.298983	+	0.920174i
$686$	15.8818	+	48.8793i	0.606372	+	1.86622i
$687$	−34.9676	+	25.4055i	−1.33410	+	0.969279i
$688$	4.83931	−	3.51596i	0.184497	−	0.134045i
$689$	−3.53441	−	10.8778i	−0.134650	−	0.414411i
$690$	−5.82925	+	17.9406i	−0.221916	+	0.682987i
$691$	41.0320	+	29.8115i	1.56093	+	1.13408i	0.935242	+	0.354008i	$0.115181\pi$
$691$	41.0320	+	29.8115i	1.56093	+	1.13408i	0.625688	+	0.780074i	$0.284819\pi$
$692$	2.34106			0.0889939
$693$	−12.4669	+	7.62291i	−0.473577	+	0.289570i
$694$	2.48482			0.0943224
$695$	−31.9101	−	23.1840i	−1.21042	−	0.879420i
$696$	16.0944	−	49.5334i	0.610056	−	1.87756i
$697$	0.696459	+	2.14348i	0.0263803	+	0.0811901i
$698$	22.8422	−	16.5958i	0.864590	−	0.628161i
$699$	5.10206	−	3.70686i	0.192978	−	0.140206i
$700$	4.37020	+	13.4501i	0.165178	+	0.508365i
$701$	−12.7242	+	39.1612i	−0.480588	+	1.47910i	0.357682	+	0.933843i	$0.383567\pi$
$701$	−12.7242	+	39.1612i	−0.480588	+	1.47910i	−0.838270	+	0.545255i	$0.816433\pi$
$702$	10.1239	+	7.35546i	0.382103	+	0.277614i
$703$	−0.354924			−0.0133862
$704$	−4.69839	−	19.6550i	−0.177077	−	0.740777i
$705$	−7.90928			−0.297881
$706$	1.12729	+	0.819022i	0.0424260	+	0.0308243i
$707$	−5.29569	+	16.2985i	−0.199165	+	0.612966i
$708$	2.38248	+	7.33252i	0.0895391	+	0.275573i
$709$	28.4240	−	20.6512i	1.06749	−	0.775573i	0.0920267	−	0.995757i	$-0.470665\pi$
$709$	28.4240	−	20.6512i	1.06749	−	0.775573i	0.975459	+	0.220183i	$0.0706655\pi$
$710$	25.2989	−	18.3807i	0.949450	−	0.689816i
$711$	−0.833557	−	2.56543i	−0.0312608	−	0.0962110i
$712$	12.7956	−	39.3807i	0.479534	−	1.47585i
$713$	−18.7374	−	13.6135i	−0.701719	−	0.509829i
$714$	5.30872			0.198674
$715$	−22.0649	−	18.8827i	−0.825181	−	0.706171i
$716$	−8.78633			−0.328361
$717$	−9.19184	−	6.67826i	−0.343276	−	0.249404i
$718$	−2.21974	+	6.83165i	−0.0828398	+	0.254955i
$719$	9.92454	+	30.5446i	0.370123	+	1.13912i	0.946711	+	0.322086i	$0.104384\pi$
$719$	9.92454	+	30.5446i	0.370123	+	1.13912i	−0.576588	+	0.817035i	$0.695616\pi$
$720$	1.02477	−	0.744536i	0.0381908	−	0.0277472i
$721$	−49.3016	+	35.8197i	−1.83609	+	1.33399i
$722$	−0.290559	−	0.894250i	−0.0108135	−	0.0332805i
$723$	10.2194	−	31.4522i	0.380065	−	1.16972i
$724$	6.12947	+	4.45332i	0.227800	+	0.165506i
$725$	22.8946			0.850283
$726$	14.3818	+	14.4383i	0.533760	+	0.535857i
$727$	24.3551			0.903282			0.451641	−	0.892200i	$-0.350839\pi$
$727$	24.3551			0.903282			0.451641	+	0.892200i	$0.350839\pi$
$728$	−37.7561	−	27.4314i	−1.39933	−	1.01667i
$729$	4.65927	−	14.3398i	0.172566	−	0.531102i
$730$	−6.09665	−	18.7636i	−0.225647	−	0.694471i
$731$	−5.30881	+	3.85708i	−0.196353	+	0.142659i
$732$	10.1483	−	7.37321i	0.375094	−	0.272522i
$733$	−7.07939	−	21.7881i	−0.261483	−	0.804762i	−0.992483	−	0.122385i	$-0.960946\pi$
$733$	−7.07939	−	21.7881i	−0.261483	−	0.804762i	0.731000	−	0.682378i	$-0.239054\pi$
$734$	7.62823	−	23.4773i	0.281563	−	0.866562i
$735$	−78.5294	−	57.0549i	−2.89660	−	2.10450i
$736$	−19.9078			−0.733810
$737$	−1.32079	−	1.13031i	−0.0486521	−	0.0416353i
$738$	−3.25837			−0.119942
$739$	−9.84782	−	7.15486i	−0.362258	−	0.263196i	0.391735	−	0.920078i	$-0.371875\pi$
$739$	−9.84782	−	7.15486i	−0.362258	−	0.263196i	−0.753993	+	0.656882i	$0.771875\pi$
$740$	0.336012	−	1.03414i	0.0123521	−	0.0380157i
$741$	−1.94191	−	5.97659i	−0.0713379	−	0.219555i
$742$	−13.6245	+	9.89875i	−0.500169	+	0.363394i
$743$	−13.0479	+	9.47984i	−0.478680	+	0.347781i	−0.800814	−	0.598912i	$-0.795600\pi$
$743$	−13.0479	+	9.47984i	−0.478680	+	0.347781i	0.322134	+	0.946694i	$0.395600\pi$
$744$	11.1398	+	34.2849i	0.408406	+	1.25695i
$745$	−11.7270	+	36.0919i	−0.429643	+	1.32230i
$746$	20.8517	+	15.1497i	0.763436	+	0.554668i
$747$	−1.28524			−0.0470243
$748$	0.493677	+	2.06523i	0.0180506	+	0.0755122i
$749$	54.3273			1.98508
$750$	−10.1329	−	7.36195i	−0.370000	−	0.268820i
$751$	−10.5170	+	32.3680i	−0.383771	+	1.18112i	0.553598	+	0.832784i	$0.313255\pi$
$751$	−10.5170	+	32.3680i	−0.383771	+	1.18112i	−0.937368	+	0.348340i	$0.886745\pi$
$752$	0.236303	+	0.727266i	0.00861709	+	0.0265207i
$753$	−21.8083	+	15.8447i	−0.794738	+	0.577411i
$754$	−21.8897	+	15.9038i	−0.797176	+	0.579183i
$755$	−0.213768	−	0.657911i	−0.00777982	−	0.0239438i
$756$	−7.18651	+	22.1178i	−0.261371	+	0.804416i
$757$	−14.8996	−	10.8252i	−0.541534	−	0.393448i	0.283120	−	0.959084i	$-0.408630\pi$
$757$	−14.8996	−	10.8252i	−0.541534	−	0.393448i	−0.824654	+	0.565637i	$0.808630\pi$
$758$	10.0431			0.364784
$759$	20.6769	−	12.6430i	0.750525	−	0.458911i
$760$	8.04359			0.291772
$761$	28.0707	+	20.3945i	1.01756	+	0.739302i	0.965782	−	0.259357i	$-0.0835106\pi$
$761$	28.0707	+	20.3945i	1.01756	+	0.739302i	0.0517800	+	0.998659i	$0.483511\pi$
$762$	−5.59841	+	17.2301i	−0.202809	+	0.624182i
$763$	−18.9291	−	58.2578i	−0.685280	−	2.10908i
$764$	14.3422	−	10.4202i	0.518882	−	0.376990i
$765$	−1.12419	+	0.816770i	−0.0406451	+	0.0295304i
$766$	4.47076	+	13.7596i	0.161535	+	0.497154i
$767$	3.45605	−	10.6366i	0.124791	−	0.384066i
$768$	26.9289	+	19.5650i	0.971715	+	0.705992i
$769$	−23.5242			−0.848305			−0.424153	−	0.905591i	$-0.639428\pi$
$769$	−23.5242			−0.848305			−0.424153	+	0.905591i	$0.639428\pi$
$770$	−16.4026	+	39.4900i	−0.591110	+	1.42312i
$771$	24.7518			0.891413
$772$	−2.75965	−	2.00501i	−0.0993221	−	0.0721617i
$773$	−8.37740	+	25.7830i	−0.301314	+	0.927350i	0.679713	+	0.733478i	$0.262104\pi$
$773$	−8.37740	+	25.7830i	−0.301314	+	0.927350i	−0.981027	+	0.193871i	$0.937896\pi$
$774$	−2.93163	−	9.02263i	−0.105375	−	0.324312i
$775$	−12.8202	+	9.31441i	−0.460515	+	0.334583i
$776$	0.614224	−	0.446260i	0.0220494	−	0.0160198i
$777$	1.07929	+	3.32172i	0.0387194	+	0.119166i
$778$	−2.72699	+	8.39282i	−0.0977674	+	0.300897i
$779$	−3.17801	−	2.30896i	−0.113864	−	0.0827270i
$780$	19.2524			0.689345
$781$	−40.0496	−	3.19147i	−1.43309	−	0.114200i
$782$	−2.00076			−0.0715470
$783$	30.4584	+	22.1293i	1.08849	+	0.790837i
$784$	−2.90006	+	8.92547i	−0.103574	+	0.318767i
$785$	−6.99589	−	21.5311i	−0.249694	−	0.768479i
$786$	−27.2728	+	19.8148i	−0.972788	+	0.706772i
$787$	36.6742	−	26.6453i	1.30729	−	0.949804i	0.307295	−	0.951614i	$-0.400576\pi$
$787$	36.6742	−	26.6453i	1.30729	−	0.949804i	0.999998	+	0.00181036i	$0.000576255\pi$
$788$	4.50506	+	13.8651i	0.160486	+	0.493925i
$789$	14.9585	−	46.0375i	0.532536	−	1.63898i
$790$	−6.38598	−	4.63969i	−0.227203	−	0.165073i
$791$	31.7807			1.12999
$792$	−8.54491	−	0.680926i	−0.303630	−	0.0241957i
$793$	−18.1965			−0.646177
$794$	−1.53970	−	1.11866i	−0.0546420	−	0.0396998i
$795$	5.99458	−	18.4494i	0.212606	−	0.654333i
$796$	9.19411	+	28.2965i	0.325876	+	1.00294i
$797$	6.63263	−	4.81889i	0.234940	−	0.170694i	−0.464086	−	0.885790i	$-0.653617\pi$
$797$	6.63263	−	4.81889i	0.234940	−	0.170694i	0.699026	+	0.715096i	$0.253617\pi$
$798$	−7.48569	+	5.43867i	−0.264990	+	0.192527i
$799$	−0.259229	−	0.797825i	−0.00917086	−	0.0282250i
$800$	−4.20912	+	12.9543i	−0.148815	+	0.458005i
$801$	−10.0867	−	7.32843i	−0.356397	−	0.258937i
$802$	11.5678			0.408474
$803$	−9.72308	+	23.4087i	−0.343120	+	0.826074i
$804$	1.15244			0.0406433
$805$	41.1418	+	29.8912i	1.45006	+	1.05353i
$806$	5.78721	−	17.8112i	0.203846	−	0.627373i
$807$	11.5191	+	35.4522i	0.405493	+	1.24798i
$808$	−8.13296	+	5.90894i	−0.286116	+	0.207876i
$809$	−9.13848	+	6.63950i	−0.321292	+	0.233432i	−0.736727	−	0.676191i	$-0.763630\pi$
$809$	−9.13848	+	6.63950i	−0.321292	+	0.233432i	0.415435	+	0.909623i	$0.363630\pi$
$810$	8.66983	+	26.6830i	0.304627	+	0.937545i
$811$	−0.658163	+	2.02562i	−0.0231112	+	0.0711291i	−0.961947	−	0.273236i	$-0.911906\pi$
$811$	−0.658163	+	2.02562i	−0.0231112	+	0.0711291i	0.938836	+	0.344365i	$0.111906\pi$
$812$	−40.6803	−	29.5560i	−1.42760	−	1.03721i
$813$	−35.5001			−1.24504
$814$	0.944302	−	0.577397i	0.0330978	−	0.0202377i
$815$	44.8995			1.57276
$816$	0.478313	+	0.347515i	0.0167443	+	0.0121655i
$817$	3.53432	−	10.8775i	0.123650	−	0.380556i
$818$	0.857702	+	2.63973i	0.0299888	+	0.0922961i
$819$	−11.3685	+	8.25968i	−0.397247	+	0.288617i
$820$	9.73626	−	7.07380i	0.340005	−	0.247028i
$821$	3.04957	+	9.38561i	0.106431	+	0.327560i	0.990064	−	0.140621i	$-0.0449097\pi$
$821$	3.04957	+	9.38561i	0.106431	+	0.327560i	−0.883633	+	0.468180i	$0.844910\pi$
$822$	5.28039	−	16.2514i	0.184175	−	0.566832i
$823$	−23.1302	−	16.8050i	−0.806267	−	0.585787i	0.106479	−	0.994315i	$-0.466042\pi$
$823$	−23.1302	−	16.8050i	−0.806267	−	0.585787i	−0.912746	+	0.408528i	$0.866042\pi$
$824$	−35.7482			−1.24535
$825$	−3.85526	−	16.1279i	−0.134223	−	0.561503i
$826$	−16.4674			−0.572973
$827$	−9.95596	−	7.23343i	−0.346203	−	0.251531i	0.401072	−	0.916047i	$-0.368638\pi$
$827$	−9.95596	−	7.23343i	−0.346203	−	0.251531i	−0.747274	+	0.664516i	$0.768638\pi$
$828$	−1.12819	+	3.47220i	−0.0392072	+	0.120667i
$829$	13.2659	+	40.8281i	0.460743	+	1.41802i	0.864259	+	0.503047i	$0.167788\pi$
$829$	13.2659	+	40.8281i	0.460743	+	1.41802i	−0.403516	+	0.914973i	$0.632212\pi$
$830$	−3.04269	+	2.21064i	−0.105613	+	0.0767324i
$831$	−29.4737	+	21.4139i	−1.02243	+	0.742839i
$832$	−6.00532	−	18.4825i	−0.208197	−	0.640765i
$833$	3.18142	−	9.79140i	0.110230	−	0.339252i
$834$	21.5329	+	15.6446i	0.745624	+	0.541727i
$835$	−14.3362			−0.496124
$836$	−2.81190	−	2.40636i	−0.0972517	−	0.0832258i
$837$	−26.0587			−0.900722
$838$	−22.1464	−	16.0903i	−0.765035	−	0.555831i
$839$	−11.0446	+	33.9919i	−0.381304	+	1.17353i	0.557823	+	0.829960i	$0.311637\pi$
$839$	−11.0446	+	33.9919i	−0.381304	+	1.17353i	−0.939126	+	0.343572i	$0.888363\pi$
$840$	−24.4598	−	75.2796i	−0.843944	−	2.59739i
$841$	−42.3949	+	30.8017i	−1.46189	+	1.06213i
$842$	19.8531	−	14.4241i	0.684181	−	0.497087i
$843$	11.2738	+	34.6973i	0.388291	+	1.19504i
$844$	6.04160	−	18.5941i	0.207961	−	0.640037i
$845$	6.28065	+	4.56316i	0.216061	+	0.156977i
$846$	1.21280			0.0416968
$847$	48.9994	−	24.8456i	1.68364	−	0.853704i
$848$	−1.87554			−0.0644063
$849$	−25.6958	−	18.6691i	−0.881877	−	0.640721i
$850$	−0.423022	+	1.30193i	−0.0145095	+	0.0446558i
$851$	−0.406766	−	1.25190i	−0.0139437	−	0.0429144i
$852$	21.5473	−	15.6550i	0.738199	−	0.536333i
$853$	5.36452	−	3.89755i	0.183678	−	0.133450i	−0.492147	−	0.870512i	$-0.663788\pi$
$853$	5.36452	−	3.89755i	0.183678	−	0.133450i	0.675825	+	0.737063i	$0.263788\pi$
$854$	8.27938	+	25.4813i	0.283314	+	0.871952i
$855$	0.748424	−	2.30341i	0.0255956	−	0.0787750i
$856$	25.7826	+	18.7322i	0.881231	+	0.640252i
$857$	−23.3711			−0.798342			−0.399171	−	0.916877i	$-0.630702\pi$
$857$	−23.3711			−0.798342			−0.399171	+	0.916877i	$0.630702\pi$
$858$	14.8894	+	12.7420i	0.508316	+	0.435005i
$859$	−34.0447			−1.16159			−0.580795	−	0.814050i	$-0.697258\pi$
$859$	−34.0447			−1.16159			−0.580795	+	0.814050i	$0.697258\pi$
$860$	28.3477	+	20.5958i	0.966650	+	0.702312i
$861$	−11.9454	+	36.7642i	−0.407099	+	1.25292i
$862$	−8.06014	−	24.8065i	−0.274529	−	0.844914i
$863$	13.2647	−	9.63737i	0.451536	−	0.328060i	−0.338666	−	0.940907i	$-0.609976\pi$
$863$	13.2647	−	9.63737i	0.451536	−	0.328060i	0.790202	+	0.612847i	$0.209976\pi$
$864$	−18.1210	+	13.1657i	−0.616490	+	0.447906i
$865$	−1.77987	−	5.47788i	−0.0605174	−	0.186253i
$866$	−1.37389	+	4.22840i	−0.0466867	+	0.143687i
$867$	26.5737	+	19.3069i	0.902489	+	0.655697i
$868$	34.8041			1.18133
$869$	2.35780	+	9.86353i	0.0799830	+	0.334597i
$870$	−45.8907			−1.55584
$871$	−1.35246	−	0.982620i	−0.0458264	−	0.0332948i
$872$	11.1040	−	34.1747i	0.376030	−	1.15730i
$873$	−0.0706426	−	0.217416i	−0.00239089	−	0.00735841i
$874$	2.82122	−	2.04973i	0.0954291	−	0.0693333i
$875$	−27.3166	+	19.8467i	−0.923469	+	0.670940i
$876$	−5.19258	−	15.9811i	−0.175441	−	0.539952i
$877$	−4.33858	+	13.3528i	−0.146504	+	0.450892i	−0.997201	−	0.0747636i	$-0.976180\pi$
$877$	−4.33858	+	13.3528i	−0.146504	+	0.450892i	0.850698	+	0.525655i	$0.176180\pi$
$878$	−11.6698	−	8.47860i	−0.393837	−	0.286139i
$879$	4.44543			0.149941
$880$	−4.06293	+	2.48429i	−0.136961	+	0.0837455i
$881$	−3.87269			−0.130474			−0.0652371	−	0.997870i	$-0.520780\pi$
$881$	−3.87269			−0.130474			−0.0652371	+	0.997870i	$0.520780\pi$
$882$	12.0416	+	8.74872i	0.405461	+	0.294585i
$883$	1.48040	−	4.55622i	0.0498196	−	0.153329i	−0.923052	−	0.384676i	$-0.874313\pi$
$883$	1.48040	−	4.55622i	0.0498196	−	0.153329i	0.972871	+	0.231347i	$0.0743132\pi$
$884$	0.631001	+	1.94202i	0.0212229	+	0.0653173i
$885$	15.3461	−	11.1496i	0.515852	−	0.374789i
$886$	8.87352	−	6.44699i	0.298112	−	0.216591i
$887$	−2.25153	−	6.92951i	−0.0755991	−	0.232670i	0.906115	−	0.423031i	$-0.139034\pi$
$887$	−2.25153	−	6.92951i	−0.0755991	−	0.232670i	−0.981714	+	0.190361i	$0.939034\pi$
$888$	−0.633126	+	1.94856i	−0.0212463	+	0.0653894i
$889$	39.5125	+	28.7075i	1.32521	+	0.962819i
$890$	−36.4846			−1.22297
$891$	13.8268	−	33.2886i	0.463217	−	1.11521i
$892$	10.2976			0.344789
$893$	1.18289	+	0.859417i	0.0395838	+	0.0287593i
$894$	7.91336	−	24.3548i	0.264662	−	0.814546i
$895$	6.68009	+	20.5592i	0.223291	+	0.687218i
$896$	20.2285	−	14.6969i	0.675788	−	0.490988i
$897$	18.8552	−	13.6991i	0.629556	−	0.457399i
$898$	−4.66707	−	14.3638i	−0.155742	−	0.479325i
$899$	17.4111	−	53.5859i	0.580694	−	1.78719i
$900$	2.02089	+	1.46826i	0.0673630	+	0.0489421i
$901$	2.05750			0.0685454
$902$	12.2116	+	0.973116i	0.406601	+	0.0324012i
$903$	−112.550			−3.74543
$904$	15.0824	+	10.9580i	0.501635	+	0.364459i
$905$	5.76023	−	17.7282i	0.191477	−	0.589304i
$906$	0.144251	+	0.443958i	0.00479241	+	0.0147495i
$907$	−34.0784	+	24.7594i	−1.13155	+	0.822122i	−0.985920	−	0.167217i	$-0.946522\pi$
$907$	−34.0784	+	24.7594i	−1.13155	+	0.822122i	−0.145633	+	0.989339i	$0.546522\pi$
$908$	11.7655	−	8.54811i	0.390451	−	0.283679i
$909$	0.935381	+	2.87881i	0.0310246	+	0.0954840i
$910$	−12.7070	+	39.1082i	−0.421234	+	1.29642i
$911$	46.7931	+	33.9971i	1.55032	+	1.12638i	0.943420	+	0.331600i	$0.107588\pi$
$911$	46.7931	+	33.9971i	1.55032	+	1.12638i	0.606903	+	0.794776i	$0.292412\pi$
$912$	−1.03048			−0.0341226
$913$	4.81675	+	0.383837i	0.159411	+	0.0127031i
$914$	−13.1974			−0.436532
$915$	−24.9682	−	18.1405i	−0.825424	−	0.599706i
$916$	−7.56443	+	23.2809i	−0.249936	+	0.769223i
$917$	28.0833	+	86.4316i	0.927394	+	2.85422i
$918$	−1.82119	+	1.32317i	−0.0601082	+	0.0436712i
$919$	−11.1558	+	8.10519i	−0.367997	+	0.267365i	−0.756380	−	0.654133i	$-0.773034\pi$
$919$	−11.1558	+	8.10519i	−0.367997	+	0.267365i	0.388383	+	0.921498i	$0.373034\pi$
$920$	9.21846	+	28.3715i	0.303924	+	0.935381i
$921$	−13.7692	+	42.3773i	−0.453711	+	1.39638i
$922$	0.136710	+	0.0993254i	0.00450229	+	0.00327111i
$923$	−38.6355			−1.27170
$924$	−13.9703	+	33.6340i	−0.459589	+	1.10648i
$925$	−0.900633			−0.0296126
$926$	−14.3908	−	10.4555i	−0.472911	−	0.343590i
$927$	−3.32622	+	10.2371i	−0.109248	+	0.336229i
$928$	−14.9658	−	46.0599i	−0.491275	−	1.51199i
$929$	−26.0374	+	18.9173i	−0.854259	+	0.620656i	−0.926317	−	0.376745i	$-0.877043\pi$
$929$	−26.0374	+	18.9173i	−0.854259	+	0.620656i	0.0720579	+	0.997400i	$0.477043\pi$
$930$	25.6972	−	18.6701i	0.842646	−	0.612218i
$931$	5.54505	+	17.0659i	0.181732	+	0.559312i
$932$	1.10371	−	3.39687i	0.0361533	−	0.111268i
$933$	36.1116	+	26.2366i	1.18224	+	0.858948i
$934$	10.0520			0.328912
$935$	4.45711	−	2.72532i	0.145763	−	0.0891273i
$936$	−8.24319			−0.269437
$937$	−29.7158	−	21.5898i	−0.970771	−	0.705307i	−0.0151440	−	0.999885i	$-0.504821\pi$
$937$	−29.7158	−	21.5898i	−0.970771	−	0.705307i	−0.955627	+	0.294579i	$0.904821\pi$
$938$	−0.760635	+	2.34099i	−0.0248356	+	0.0764362i
$939$	−7.63321	−	23.4926i	−0.249100	−	0.766652i
$940$	−3.62393	+	2.63294i	−0.118200	+	0.0858770i
$941$	18.5500	−	13.4774i	0.604713	−	0.439350i	−0.242836	−	0.970067i	$-0.578078\pi$
$941$	18.5500	−	13.4774i	0.604713	−	0.439350i	0.847549	+	0.530718i	$0.178078\pi$
$942$	4.72083	+	14.5292i	0.153813	+	0.473387i
$943$	4.50200	−	13.8557i	0.146605	−	0.451205i
$944$	−1.48370	−	1.07797i	−0.0482904	−	0.0350850i
$945$	57.2174			1.86128
$946$	8.29242	+	34.6901i	0.269610	+	1.12787i
$947$	58.7224			1.90822			0.954111	−	0.299454i	$-0.0968045\pi$
$947$	58.7224			1.90822			0.954111	+	0.299454i	$0.0968045\pi$
$948$	−5.43901	−	3.95167i	−0.176651	−	0.128344i
$949$	−7.53241	+	23.1824i	−0.244512	+	0.752532i
$950$	−0.737305	−	2.26919i	−0.0239213	−	0.0736223i
$951$	11.6209	−	8.44306i	0.376833	−	0.273785i
$952$	6.79193	−	4.93462i	0.220128	−	0.159932i
$953$	1.25486	+	3.86205i	0.0406488	+	0.125104i	0.969322	−	0.245796i	$-0.0790493\pi$
$953$	1.25486	+	3.86205i	0.0406488	+	0.125104i	−0.928673	+	0.370900i	$0.879049\pi$
$954$	−0.919200	+	2.82901i	−0.0297602	+	0.0915925i
$955$	−35.2865	−	25.6371i	−1.14184	−	0.829598i
$956$	−6.43473			−0.208114
$957$	44.7956	+	38.3350i	1.44804	+	1.23920i
$958$	4.86778			0.157271
$959$	−37.2680	−	27.0768i	−1.20345	−	0.874355i
$960$	10.1854	−	31.3474i	0.328732	−	1.01173i
$961$	2.47170	+	7.60710i	0.0797321	+	0.245390i
$962$	0.861104	−	0.625629i	0.0277631	−	0.0201711i
$963$	7.76322	−	5.64031i	0.250166	−	0.181757i
$964$	−5.78778	−	17.8130i	−0.186412	−	0.573717i
$965$	−2.59341	+	7.98171i	−0.0834849	+	0.256940i
$966$	−27.7624	−	20.1706i	−0.893242	−	0.648978i
$967$	16.6365			0.534994			0.267497	−	0.963559i	$-0.413804\pi$
$967$	16.6365			0.534994			0.267497	+	0.963559i	$0.413804\pi$
$968$	31.8209	+	5.10389i	1.02276	+	0.164045i
$969$	1.13045			0.0363154
$970$	−0.541201	−	0.393206i	−0.0173769	−	0.0126251i
$971$	11.2190	−	34.5285i	0.360035	−	1.10807i	−0.592997	−	0.805204i	$-0.702056\pi$
$971$	11.2190	−	34.5285i	0.360035	−	1.10807i	0.953032	−	0.302869i	$-0.0979445\pi$
$972$	3.06746	+	9.44066i	0.0983887	+	0.302809i
$973$	58.0494	−	42.1753i	1.86098	−	1.35208i
$974$	26.9577	−	19.5859i	0.863779	−	0.627572i
$975$	−4.92767	−	15.1658i	−0.157812	−	0.485694i
$976$	−0.922067	+	2.83783i	−0.0295147	+	0.0908368i
$977$	−47.5851	−	34.5726i	−1.52238	−	1.10608i	−0.960291	−	0.279001i	$-0.909997\pi$
$977$	−47.5851	−	34.5726i	−1.52238	−	1.10608i	−0.562092	−	0.827075i	$-0.690003\pi$
$978$	−30.2982			−0.968829
$979$	35.6139	+	30.4776i	1.13823	+	0.974068i
$980$	−54.9743			−1.75609
$981$	−8.75330	−	6.35964i	−0.279471	−	0.203048i
$982$	8.12563	−	25.0081i	0.259299	−	0.798041i
$983$	2.32084	+	7.14280i	0.0740232	+	0.227820i	0.981222	−	0.192883i	$-0.0617836\pi$
$983$	2.32084	+	7.14280i	0.0740232	+	0.227820i	−0.907199	+	0.420702i	$0.861784\pi$
$984$	−18.3454	+	13.3287i	−0.584830	+	0.424904i
$985$	29.0180	−	21.0828i	0.924591	−	0.671755i
$986$	−1.50408	−	4.62908i	−0.0478997	−	0.147420i
$987$	4.44620	−	13.6840i	0.141524	−	0.435566i
$988$	−2.87932	−	2.09195i	−0.0916033	−	0.0665537i
$989$	42.4180			1.34881
$990$	1.75599	+	7.34594i	0.0558091	+	0.233469i
$991$	−12.2699			−0.389765			−0.194882	−	0.980827i	$-0.562433\pi$
$991$	−12.2699			−0.389765			−0.194882	+	0.980827i	$0.562433\pi$
$992$	27.1193	+	19.7033i	0.861038	+	0.625581i
$993$	19.3784	−	59.6406i	0.614955	−	1.89264i
$994$	17.5791	+	54.1028i	0.557574	+	1.71604i
$995$	59.2212	−	43.0267i	1.87744	−	1.36404i
$996$	−2.59149	+	1.88283i	−0.0821144	+	0.0596596i
$997$	4.98701	+	15.3484i	0.157940	+	0.486089i	0.998447	−	0.0557114i	$-0.0177427\pi$
$997$	4.98701	+	15.3484i	0.157940	+	0.486089i	−0.840507	+	0.541801i	$0.817743\pi$
$998$	8.24647	−	25.3800i	0.261038	−	0.803391i
$999$	−1.19818	−	0.870529i	−0.0379088	−	0.0275423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.c.191.7	yes	40
11.3	even	5	inner	209.2.f.c.58.7	✓	40
11.5	even	5		2299.2.a.x.1.8		20
11.6	odd	10		2299.2.a.y.1.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.c.58.7	✓	40	11.3	even	5	inner
209.2.f.c.191.7	yes	40	1.1	even	1	trivial
2299.2.a.x.1.8		20	11.5	even	5
2299.2.a.y.1.13		20	11.6	odd	10

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.760694 + 0.552677i) q^{2} +(0.608863 - 1.87389i) q^{3} +(-0.344830 - 1.06128i) q^{4} +(-2.22112 + 1.61374i) q^{5} +(1.49881 - 1.08895i) q^{6} +(-1.54336 - 4.74997i) q^{7} +(0.905352 - 2.78639i) q^{8} +(-0.713688 - 0.518524i) q^{9} -2.58147 q^{10} +(2.51987 + 2.15645i) q^{11} -2.19867 q^{12} +(2.58028 + 1.87469i) q^{13} +(1.45117 - 4.46625i) q^{14} +(1.67161 + 5.14468i) q^{15} +(0.423116 - 0.307412i) q^{16} +(-0.464166 + 0.337237i) q^{17} +(-0.256322 - 0.788877i) q^{18} +(0.309017 - 0.951057i) q^{19} +(2.47853 + 1.80076i) q^{20} -9.84060 q^{21} +(0.725032 + 3.03307i) q^{22} +3.70874 q^{23} +(-4.67014 - 3.39305i) q^{24} +(0.784142 - 2.41334i) q^{25} +(0.926712 + 2.85213i) q^{26} +(3.37588 - 2.45272i) q^{27} +(-4.50883 + 3.27586i) q^{28} +(2.78806 + 8.58077i) q^{29} +(-1.57176 + 4.83739i) q^{30} +(-5.05222 - 3.67065i) q^{31} -5.36780 q^{32} +(5.57519 - 3.40897i) q^{33} -0.539472 q^{34} +(11.0932 + 8.05968i) q^{35} +(-0.304197 + 0.936222i) q^{36} +(-0.109678 - 0.337553i) q^{37} +(0.760694 - 0.552677i) q^{38} +(5.08399 - 3.69373i) q^{39} +(2.48560 + 7.64991i) q^{40} +(1.21389 - 3.73597i) q^{41} +(-7.48569 - 5.43867i) q^{42} +11.4373 q^{43} +(1.41966 - 3.41788i) q^{44} +2.42195 q^{45} +(2.82122 + 2.04973i) q^{46} +(-0.451822 + 1.39057i) q^{47} +(-0.318435 - 0.980043i) q^{48} +(-14.5171 + 10.5473i) q^{49} +(1.93029 - 1.40244i) q^{50} +(0.349330 + 1.07513i) q^{51} +(1.09980 - 3.38484i) q^{52} +(-2.90123 - 2.10787i) q^{53} +3.92357 q^{54} +(-9.07688 - 0.723318i) q^{55} -14.6325 q^{56} +(-1.59402 - 1.15813i) q^{57} +(-2.62153 + 8.06824i) q^{58} +(-1.08360 - 3.33498i) q^{59} +(4.88351 - 3.54807i) q^{60} +(-4.61568 + 3.35349i) q^{61} +(-1.81451 - 5.58449i) q^{62} +(-1.36150 + 4.19026i) q^{63} +(-4.92949 - 3.58148i) q^{64} -8.75638 q^{65} +(6.12508 + 0.488095i) q^{66} -0.524152 q^{67} +(0.517960 + 0.376320i) q^{68} +(2.25811 - 6.94976i) q^{69} +(3.98413 + 12.2619i) q^{70} +(-9.80018 + 7.12025i) q^{71} +(-2.09095 + 1.51916i) q^{72} +(2.36170 + 7.26856i) q^{73} +(0.103127 - 0.317391i) q^{74} +(-4.04489 - 2.93879i) q^{75} -1.11589 q^{76} +(6.35399 - 15.2975i) q^{77} +5.90880 q^{78} +(2.47378 + 1.79730i) q^{79} +(-0.443710 + 1.36560i) q^{80} +(-3.35848 - 10.3363i) q^{81} +(2.98819 - 2.17104i) q^{82} +(1.17866 - 0.856349i) q^{83} +(3.39333 + 10.4436i) q^{84} +(0.486758 - 1.49809i) q^{85} +(8.70029 + 6.32113i) q^{86} +17.7769 q^{87} +(8.29006 - 5.06899i) q^{88} +14.1332 q^{89} +(1.84236 + 1.33856i) q^{90} +(4.92239 - 15.1496i) q^{91} +(-1.27888 - 3.93600i) q^{92} +(-9.95449 + 7.23236i) q^{93} +(-1.11223 + 0.808084i) q^{94} +(0.848393 + 2.61109i) q^{95} +(-3.26825 + 10.0586i) q^{96} +(0.209648 + 0.152319i) q^{97} -16.8723 q^{98} +(-0.680229 - 2.84564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) \) 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

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