LMFDB - Embedded newform 220.2.r.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	220.151
Dual form			220.2.r.c.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26745 + 0.627351i) q^{2} +(2.42619 - 0.788316i) q^{3} +(1.21286 - 1.59027i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-2.58052 + 2.52122i) q^{6} +(-1.33130 + 4.09732i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(2.83789 - 2.06185i) q^{9} +(-1.39414 - 0.237451i) q^{10} +(2.39183 + 2.29764i) q^{11} +(1.68899 - 4.81442i) q^{12} +(-1.01942 - 1.40312i) q^{13} +(-0.883099 - 6.02834i) q^{14} +(2.42619 + 0.788316i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(3.03242 - 4.17376i) q^{17} +(-2.30338 + 4.39364i) q^{18} +(-2.01930 - 6.21477i) q^{19} +(1.91596 - 0.573655i) q^{20} +10.9903i q^{21} +(-4.47295 - 1.41162i) q^{22} +1.33787i q^{23} +(0.879611 + 7.16163i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.17231 + 1.13884i) q^{26} +(0.761464 - 1.04807i) q^{27} +(4.90117 + 7.08661i) q^{28} +(-0.243271 - 0.0790436i) q^{29} +(-3.56962 + 0.522918i) q^{30} +(-5.24387 - 7.21757i) q^{31} +(3.76092 + 4.22558i) q^{32} +(7.61430 + 3.68897i) q^{33} +(-1.22503 + 7.19243i) q^{34} +(-3.48539 + 2.53228i) q^{35} +(0.163071 - 7.01375i) q^{36} +(-1.11016 + 3.41671i) q^{37} +(6.45820 + 6.61010i) q^{38} +(-3.57941 - 2.60059i) q^{39} +(-2.06851 + 1.92906i) q^{40} +(1.57918 - 0.513105i) q^{41} +(-6.89480 - 13.9297i) q^{42} -9.15066 q^{43} +(6.55483 - 1.01695i) q^{44} +3.50782 q^{45} +(-0.839316 - 1.69569i) q^{46} +(6.69361 - 2.17489i) q^{47} +(-5.60771 - 8.52518i) q^{48} +(-9.35254 - 6.79502i) q^{49} +(-0.988310 - 1.01156i) q^{50} +(4.06697 - 12.5168i) q^{51} +(-3.46776 - 0.0806258i) q^{52} +(-6.18088 + 4.49067i) q^{53} +(-0.307614 + 1.80608i) q^{54} +(0.584518 + 3.26471i) q^{55} +(-10.6578 - 5.90718i) q^{56} +(-9.79840 - 13.4863i) q^{57} +(0.357922 - 0.0524325i) q^{58} +(-2.55261 - 0.829393i) q^{59} +(4.19627 - 2.90218i) q^{60} +(5.66529 - 7.79760i) q^{61} +(11.1743 + 5.85816i) q^{62} +(4.66996 + 14.3727i) q^{63} +(-7.41770 - 2.99629i) q^{64} -1.73435i q^{65} +(-11.9650 + 0.101244i) q^{66} +7.61856i q^{67} +(-2.95952 - 9.88457i) q^{68} +(1.05467 + 3.24593i) q^{69} +(2.82893 - 5.39610i) q^{70} +(-1.31712 + 1.81286i) q^{71} +(4.19340 + 8.99189i) q^{72} +(6.10877 + 1.98486i) q^{73} +(-0.736407 - 5.02697i) q^{74} +(1.49947 + 2.06384i) q^{75} +(-12.3323 - 4.32642i) q^{76} +(-12.5984 + 6.74126i) q^{77} +(6.16821 + 1.05058i) q^{78} +(-2.57147 + 1.86828i) q^{79} +(1.41153 - 3.74267i) q^{80} +(-2.23068 + 6.86534i) q^{81} +(-1.67963 + 1.64103i) q^{82} +(5.87283 + 4.26686i) q^{83} +(17.4776 + 13.3298i) q^{84} +(4.90655 - 1.59424i) q^{85} +(11.5980 - 5.74067i) q^{86} -0.652533 q^{87} +(-7.66994 + 5.40111i) q^{88} +2.42654 q^{89} +(-4.44599 + 2.20064i) q^{90} +(7.10617 - 2.30893i) q^{91} +(2.12758 + 1.62266i) q^{92} +(-18.4123 - 13.3773i) q^{93} +(-7.11941 + 6.95581i) q^{94} +(2.01930 - 6.21477i) q^{95} +(12.4558 + 7.28724i) q^{96} +(4.29974 - 3.12394i) q^{97} +(16.1167 + 2.74503i) q^{98} +(11.5251 + 1.58884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) $ 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$3$	2.42619	−	0.788316i	1.40076	−	0.455134i	0.491323	−	0.870977i	$-0.336513\pi$
$3$	2.42619	−	0.788316i	1.40076	−	0.455134i	0.909436	+	0.415843i	$0.136513\pi$
$4$	1.21286	−	1.59027i	0.606431	−	0.795136i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−2.58052	+	2.52122i	−1.05349	+	1.02928i
$7$	−1.33130	+	4.09732i	−0.503184	+	1.54864i	0.300619	+	0.953744i	$0.402807\pi$
$7$	−1.33130	+	4.09732i	−0.503184	+	1.54864i	−0.803803	+	0.594896i	$0.797193\pi$
$8$	−0.539585	+	2.77648i	−0.190772	+	0.981634i
$9$	2.83789	−	2.06185i	0.945963	−	0.687282i
$10$	−1.39414	−	0.237451i	−0.440865	−	0.0750887i
$11$	2.39183	+	2.29764i	0.721165	+	0.692763i
$11$	2.39183	+	2.29764i	0.721165	+	0.692763i
$12$	1.68899	−	4.81442i	0.487570	−	1.38980i
$13$	−1.01942	−	1.40312i	−0.282737	−	0.389154i	0.643901	−	0.765109i	$-0.277315\pi$
$13$	−1.01942	−	1.40312i	−0.282737	−	0.389154i	−0.926638	+	0.375955i	$0.877315\pi$
$14$	−0.883099	−	6.02834i	−0.236018	−	1.61114i
$15$	2.42619	+	0.788316i	0.626439	+	0.203542i
$16$	−1.05793	−	3.85756i	−0.264483	−	0.964390i
$17$	3.03242	−	4.17376i	0.735469	−	1.01229i	−0.263397	−	0.964687i	$-0.584843\pi$
$17$	3.03242	−	4.17376i	0.735469	−	1.01229i	0.998867	−	0.0475992i	$-0.0151570\pi$
$18$	−2.30338	+	4.39364i	−0.542913	+	1.03559i
$19$	−2.01930	−	6.21477i	−0.463259	−	1.42577i	−0.861158	−	0.508337i	$-0.830261\pi$
$19$	−2.01930	−	6.21477i	−0.463259	−	1.42577i	0.397899	−	0.917429i	$-0.369739\pi$
$20$	1.91596	−	0.573655i	0.428423	−	0.128273i
$21$			10.9903i			2.39829i
$22$	−4.47295	−	1.41162i	−0.953637	−	0.300959i
$23$			1.33787i			0.278966i	0.990224	+	0.139483i	$0.0445441\pi$
$23$			1.33787i			0.278966i	−0.990224	+	0.139483i	$0.955456\pi$
$24$	0.879611	+	7.16163i	0.179550	+	1.46186i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	2.17231	+	1.13884i	0.426026	+	0.223346i
$27$	0.761464	−	1.04807i	0.146544	−	0.201700i
$28$	4.90117	+	7.08661i	0.926234	+	1.33924i
$29$	−0.243271	−	0.0790436i	−0.0451743	−	0.0146780i	0.286343	−	0.958127i	$-0.407560\pi$
$29$	−0.243271	−	0.0790436i	−0.0451743	−	0.0146780i	−0.331517	+	0.943449i	$0.607560\pi$
$30$	−3.56962	+	0.522918i	−0.651721	+	0.0954714i
$31$	−5.24387	−	7.21757i	−0.941827	−	1.29631i	−0.955064	−	0.296401i	$-0.904214\pi$
$31$	−5.24387	−	7.21757i	−0.941827	−	1.29631i	0.0132368	−	0.999912i	$-0.495786\pi$
$32$	3.76092	+	4.22558i	0.664843	+	0.746983i
$33$	7.61430	+	3.68897i	1.32548	+	0.642168i
$34$	−1.22503	+	7.19243i	−0.210090	+	1.23349i
$35$	−3.48539	+	2.53228i	−0.589138	+	0.428034i
$36$	0.163071	−	7.01375i	0.0271784	−	1.16896i
$37$	−1.11016	+	3.41671i	−0.182509	+	0.561704i	−0.999897	−	0.0143840i	$-0.995421\pi$
$37$	−1.11016	+	3.41671i	−0.182509	+	0.561704i	0.817388	+	0.576088i	$0.195421\pi$
$38$	6.45820	+	6.61010i	1.04766	+	1.07230i
$39$	−3.57941	−	2.60059i	−0.573164	−	0.416428i
$40$	−2.06851	+	1.92906i	−0.327060	+	0.305011i
$41$	1.57918	−	0.513105i	0.246626	−	0.0801336i	−0.183096	−	0.983095i	$-0.558612\pi$
$41$	1.57918	−	0.513105i	0.246626	−	0.0801336i	0.429721	+	0.902962i	$0.358612\pi$
$42$	−6.89480	−	13.9297i	−1.06389	−	2.14940i
$43$	−9.15066			−1.39546			−0.697731	−	0.716359i	$-0.745807\pi$
$43$	−9.15066			−1.39546			−0.697731	+	0.716359i	$0.745807\pi$
$44$	6.55483	−	1.01695i	0.988178	−	0.153311i
$45$	3.50782			0.522915
$46$	−0.839316	−	1.69569i	−0.123750	−	0.250016i
$47$	6.69361	−	2.17489i	0.976364	−	0.317240i	0.222982	−	0.974823i	$-0.428421\pi$
$47$	6.69361	−	2.17489i	0.976364	−	0.317240i	0.753382	+	0.657583i	$0.228421\pi$
$48$	−5.60771	−	8.52518i	−0.809404	−	1.23050i
$49$	−9.35254	−	6.79502i	−1.33608	−	0.970716i
$50$	−0.988310	−	1.01156i	−0.139768	−	0.143056i
$51$	4.06697	−	12.5168i	0.569489	−	1.75271i
$52$	−3.46776	−	0.0806258i	−0.480891	−	0.0111808i
$53$	−6.18088	+	4.49067i	−0.849008	+	0.616841i	−0.924872	−	0.380277i	$-0.875829\pi$
$53$	−6.18088	+	4.49067i	−0.849008	+	0.616841i	0.0758640	+	0.997118i	$0.475829\pi$
$54$	−0.307614	+	1.80608i	−0.0418609	+	0.245776i
$55$	0.584518	+	3.26471i	0.0788164	+	0.440214i
$56$	−10.6578	−	5.90718i	−1.42421	−	0.789380i
$57$	−9.79840	−	13.4863i	−1.29783	−	1.78631i
$58$	0.357922	−	0.0524325i	0.0469975	−	0.00688473i
$59$	−2.55261	−	0.829393i	−0.332321	−	0.107978i	0.138104	−	0.990418i	$-0.455899\pi$
$59$	−2.55261	−	0.829393i	−0.332321	−	0.107978i	−0.470425	+	0.882440i	$0.655899\pi$
$60$	4.19627	−	2.90218i	0.541736	−	0.374670i
$61$	5.66529	−	7.79760i	0.725366	−	0.998381i	−0.273962	−	0.961740i	$-0.588334\pi$
$61$	5.66529	−	7.79760i	0.725366	−	0.998381i	0.999329	−	0.0366403i	$-0.0116656\pi$
$62$	11.1743	+	5.85816i	1.41914	+	0.743988i
$63$	4.66996	+	14.3727i	0.588360	+	1.81079i
$64$	−7.41770	−	2.99629i	−0.927212	−	0.374537i
$65$		−	1.73435i		−	0.215119i
$66$	−11.9650	+	0.101244i	−1.47279	+	0.0124623i
$67$			7.61856i			0.930755i	0.885112	+	0.465378i	$0.154081\pi$
$67$			7.61856i			0.930755i	−0.885112	+	0.465378i	$0.845919\pi$
$68$	−2.95952	−	9.88457i	−0.358894	−	1.19868i
$69$	1.05467	+	3.24593i	0.126967	+	0.390764i
$70$	2.82893	−	5.39610i	0.338121	−	0.644958i
$71$	−1.31712	+	1.81286i	−0.156313	+	0.215147i	−0.879990	−	0.474993i	$-0.842451\pi$
$71$	−1.31712	+	1.81286i	−0.156313	+	0.215147i	0.723677	+	0.690139i	$0.242451\pi$
$72$	4.19340	+	8.99189i	0.494197	+	1.05970i
$73$	6.10877	+	1.98486i	0.714977	+	0.232310i	0.643844	−	0.765157i	$-0.277339\pi$
$73$	6.10877	+	1.98486i	0.714977	+	0.232310i	0.0711331	+	0.997467i	$0.477339\pi$
$74$	−0.736407	−	5.02697i	−0.0856056	−	0.584373i
$75$	1.49947	+	2.06384i	0.173143	+	0.238311i
$76$	−12.3323	−	4.32642i	−1.41461	−	0.496274i
$77$	−12.5984	+	6.74126i	−1.43572	+	0.768238i
$78$	6.16821	+	1.05058i	0.698412	+	0.118955i
$79$	−2.57147	+	1.86828i	−0.289313	+	0.210198i	−0.722969	−	0.690880i	$-0.757223\pi$
$79$	−2.57147	+	1.86828i	−0.289313	+	0.210198i	0.433656	+	0.901078i	$0.357223\pi$
$80$	1.41153	−	3.74267i	0.157814	−	0.418443i
$81$	−2.23068	+	6.86534i	−0.247854	+	0.762815i
$82$	−1.67963	+	1.64103i	−0.185484	+	0.181222i
$83$	5.87283	+	4.26686i	0.644627	+	0.468349i	0.861437	−	0.507865i	$-0.169565\pi$
$83$	5.87283	+	4.26686i	0.644627	+	0.468349i	−0.216810	+	0.976214i	$0.569565\pi$
$84$	17.4776	+	13.3298i	1.90697	+	1.45440i
$85$	4.90655	−	1.59424i	0.532191	−	0.172919i
$86$	11.5980	−	5.74067i	1.25065	−	0.619033i
$87$	−0.652533			−0.0699589
$88$	−7.66994	+	5.40111i	−0.817618	+	0.575761i
$89$	2.42654			0.257213			0.128607	−	0.991696i	$-0.458950\pi$
$89$	2.42654			0.257213			0.128607	+	0.991696i	$0.458950\pi$
$90$	−4.44599	+	2.20064i	−0.468649	+	0.231967i
$91$	7.10617	−	2.30893i	0.744929	−	0.242042i
$92$	2.12758	+	1.62266i	0.221816	+	0.169174i
$93$	−18.4123	−	13.3773i	−1.90927	−	1.38717i
$94$	−7.11941	+	6.95581i	−0.734311	+	0.717437i
$95$	2.01930	−	6.21477i	0.207176	−	0.637622i
$96$	12.4558	+	7.28724i	1.27126	+	0.743751i
$97$	4.29974	−	3.12394i	0.436572	−	0.317188i	−0.347699	−	0.937606i	$-0.613037\pi$
$97$	4.29974	−	3.12394i	0.436572	−	0.317188i	0.784271	+	0.620418i	$0.213037\pi$
$98$	16.1167	+	2.74503i	1.62804	+	0.277290i
$99$	11.5251	+	1.58884i	1.15832	+	0.159684i
$100$	1.88723	+	0.662079i	0.188723	+	0.0662079i
$101$	1.39769	+	1.92376i	0.139076	+	0.191421i	0.872873	−	0.487947i	$-0.162254\pi$
$101$	1.39769	+	1.92376i	0.139076	+	0.191421i	−0.733798	+	0.679368i	$0.762254\pi$
$102$	2.69777	+	18.4159i	0.267119	+	1.82344i
$103$	−8.93517	−	2.90321i	−0.880409	−	0.286062i	−0.166282	−	0.986078i	$-0.553176\pi$
$103$	−8.93517	−	2.90321i	−0.880409	−	0.286062i	−0.714127	+	0.700016i	$0.753176\pi$
$104$	4.44579	−	2.07331i	0.435946	−	0.203305i
$105$	−6.45996	+	8.89137i	−0.630428	+	0.867709i
$106$	5.01673	−	9.56928i	0.487268	−	0.929450i
$107$	−4.49037	−	13.8199i	−0.434101	−	1.33602i	−0.894005	−	0.448057i	$-0.852116\pi$
$107$	−4.49037	−	13.8199i	−0.434101	−	1.33602i	0.459904	−	0.887968i	$-0.347884\pi$
$108$	−0.743158	−	2.48209i	−0.0715104	−	0.238840i
$109$			3.73071i			0.357337i	0.983909	+	0.178669i	$0.0571790\pi$
$109$			3.73071i			0.357337i	−0.983909	+	0.178669i	$0.942821\pi$
$110$	−2.78897	−	3.77116i	−0.265917	−	0.359566i
$111$			9.16473i			0.869878i
$112$	17.2141	+	0.800892i	1.62658	+	0.0756772i
$113$	−2.26263	−	6.96365i	−0.212850	−	0.655085i	−0.999299	−	0.0374300i	$-0.988083\pi$
$113$	−2.26263	−	6.96365i	−0.212850	−	0.655085i	0.786449	−	0.617655i	$-0.211917\pi$
$114$	20.8797	+	10.9462i	1.95556	+	1.02521i
$115$	−0.786383	+	1.08236i	−0.0733306	+	0.100931i
$116$	−0.420755	+	0.290998i	−0.0390662	+	0.0270185i
$117$	−5.78602	−	1.87999i	−0.534918	−	0.173805i
$118$	3.75563	−	0.550166i	0.345733	−	0.0506469i
$119$	13.0642	+	17.9813i	1.19759	+	1.64834i
$120$	−3.49788	+	6.31090i	−0.319311	+	0.576104i
$121$	0.441739	+	10.9911i	0.0401581	+	0.999193i
$122$	−2.28864	+	13.4372i	−0.207204	+	1.21655i
$123$	3.42689	−	2.48978i	0.308992	−	0.224496i
$124$	−17.8380	−	0.414736i	−1.60190	−	0.0372444i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−14.9357	−	15.2869i	−1.33057	−	1.36187i
$127$	2.28822	+	1.66249i	0.203047	+	0.147522i	0.684662	−	0.728861i	$-0.259950\pi$
$127$	2.28822	+	1.66249i	0.203047	+	0.147522i	−0.481615	+	0.876383i	$0.659950\pi$
$128$	11.2813	−	0.855842i	0.997135	−	0.0756465i
$129$	−22.2012	+	7.21361i	−1.95471	+	0.635123i
$130$	1.08804	+	2.19820i	0.0954277	+	0.192795i
$131$	−9.35511			−0.817360			−0.408680	−	0.912678i	$-0.634011\pi$
$131$	−9.35511			−0.817360			−0.408680	+	0.912678i	$0.634011\pi$
$132$	15.1016	−	7.63459i	1.31442	−	0.664506i
$133$	28.1522			2.44110
$134$	−4.77951	−	9.65615i	−0.412887	−	0.834164i
$135$	1.23207	−	0.400325i	0.106040	−	0.0344545i
$136$	9.95213	+	10.6716i	0.853388	+	0.915078i
$137$	4.04286	+	2.93731i	0.345405	+	0.250951i	0.746939	−	0.664893i	$-0.231523\pi$
$137$	4.04286	+	2.93731i	0.345405	+	0.250951i	−0.401534	+	0.915844i	$0.631523\pi$
$138$	−3.37308	−	3.45241i	−0.287135	−	0.293889i
$139$	0.900407	−	2.77117i	0.0763715	−	0.235047i	−0.905582	−	0.424172i	$-0.860565\pi$
$139$	0.900407	−	2.77117i	0.0763715	−	0.235047i	0.981953	+	0.189125i	$0.0605651\pi$
$140$	−0.200277	+	8.61402i	−0.0169265	+	0.728018i
$141$	14.5255	−	10.5534i	1.22326	−	0.888754i
$142$	0.532085	−	3.12400i	0.0446515	−	0.262160i
$143$	0.785558	−	5.69828i	0.0656917	−	0.476514i
$144$	−10.9560	−	8.76604i	−0.912999	−	0.730503i
$145$	−0.150350	−	0.206939i	−0.0124859	−	0.0171853i
$146$	−8.98776	+	1.31663i	−0.743833	+	0.108965i
$147$	−28.0476	−	9.11322i	−2.31333	−	0.751646i
$148$	4.08703	+	5.90945i	0.335952	+	0.485754i
$149$	0.222964	−	0.306884i	0.0182659	−	0.0251409i	−0.799786	−	0.600285i	$-0.795054\pi$
$149$	0.222964	−	0.306884i	0.0182659	−	0.0251409i	0.818052	+	0.575144i	$0.195054\pi$
$150$	−3.19525	−	1.67512i	−0.260891	−	0.136773i
$151$	5.75152	+	17.7013i	0.468052	+	1.44052i	0.855104	+	0.518457i	$0.173493\pi$
$151$	5.75152	+	17.7013i	0.468052	+	1.44052i	−0.387052	+	0.922058i	$0.626507\pi$
$152$	18.3448	−	2.25316i	1.48796	−	0.182755i
$153$		−	18.0971i		−	1.46306i
$154$	11.7387	−	16.4478i	0.945932	−	1.32540i
$155$		−	8.92140i		−	0.716584i
$156$	−8.47698	+	2.53807i	−0.678702	+	0.203209i
$157$	−4.88319	−	15.0289i	−0.389721	−	1.19944i	−0.932997	−	0.359883i	$-0.882816\pi$
$157$	−4.88319	−	15.0289i	−0.389721	−	1.19944i	0.543277	−	0.839554i	$-0.317184\pi$
$158$	2.08714	−	3.98117i	0.166044	−	0.316725i
$159$	−11.4559	+	15.7677i	−0.908511	+	1.25046i
$160$	0.558916	+	5.62918i	0.0441862	+	0.445025i
$161$	−5.48170	−	1.78111i	−0.432018	−	0.140371i
$162$	−1.47969	−	10.1009i	−0.116256	−	0.793602i
$163$	−2.02014	−	2.78049i	−0.158230	−	0.217785i	0.722540	−	0.691329i	$-0.242974\pi$
$163$	−2.02014	−	2.78049i	−0.158230	−	0.217785i	−0.880770	+	0.473544i	$0.842974\pi$
$164$	1.09935	−	3.13364i	0.0858445	−	0.244697i
$165$	3.99177	+	7.46001i	0.310759	+	0.580761i
$166$	−10.1203	−	1.72371i	−0.785491	−	0.133786i
$167$	−6.72865	+	4.88865i	−0.520678	+	0.378295i	−0.816859	−	0.576837i	$-0.804287\pi$
$167$	−6.72865	+	4.88865i	−0.520678	+	0.378295i	0.296181	+	0.955132i	$0.404287\pi$
$168$	−30.5145	−	5.93022i	−2.35424	−	0.457526i
$169$	3.08771	−	9.50300i	0.237516	−	0.731000i
$170$	−5.21867	+	5.09875i	−0.400254	+	0.391056i
$171$	−18.5445	−	13.4733i	−1.41813	−	1.03033i
$172$	−11.0985	+	14.5520i	−0.846252	+	1.10958i
$173$	−10.4776	+	3.40437i	−0.796595	+	0.258829i	−0.678910	−	0.734222i	$-0.737547\pi$
$173$	−10.4776	+	3.40437i	−0.796595	+	0.258829i	−0.117685	+	0.993051i	$0.537547\pi$
$174$	0.827053	−	0.409367i	0.0626987	−	0.0310340i
$175$	−4.30817			−0.325667
$176$	6.33288	−	11.6574i	0.477359	−	0.878709i
$177$	−6.84693			−0.514647
$178$	−3.07552	+	1.52229i	−0.230520	+	0.114101i
$179$	−3.32045	+	1.07888i	−0.248182	+	0.0806392i	−0.430466	−	0.902607i	$-0.641651\pi$
$179$	−3.32045	+	1.07888i	−0.248182	+	0.0806392i	0.182284	+	0.983246i	$0.441651\pi$
$180$	4.25451	−	5.57839i	0.317112	−	0.415789i
$181$	11.9677	+	8.69505i	0.889553	+	0.646298i	0.935761	−	0.352634i	$-0.114714\pi$
$181$	11.9677	+	8.69505i	0.889553	+	0.646298i	−0.0462087	+	0.998932i	$0.514714\pi$
$182$	−7.55821	+	7.38452i	−0.560252	+	0.547377i
$183$	7.59808	−	23.3845i	0.561666	−	1.72863i
$184$	−3.71458	−	0.721897i	−0.273843	−	0.0532189i
$185$	−2.90643	+	2.11164i	−0.213685	+	0.155251i
$186$	31.7290	+	5.40413i	2.32648	+	0.396250i
$187$	16.8428	−	3.01556i	1.23167	−	0.220520i
$188$	4.65977	−	13.2825i	0.339849	−	0.968726i
$189$	3.28052	+	4.51525i	0.238623	+	0.328436i
$190$	1.33948	+	9.14372i	0.0971758	+	0.663355i
$191$	22.8345	+	7.41939i	1.65225	+	0.536848i	0.979226	−	0.202773i	$-0.0649953\pi$
$191$	22.8345	+	7.41939i	1.65225	+	0.536848i	0.673023	+	0.739621i	$0.264995\pi$
$192$	−20.3587	−	1.42208i	−1.46927	−	0.102630i
$193$	−15.2026	+	20.9246i	−1.09431	+	1.50619i	−0.251590	+	0.967834i	$0.580953\pi$
$193$	−15.2026	+	20.9246i	−1.09431	+	1.50619i	−0.842719	+	0.538353i	$0.819047\pi$
$194$	−3.48990	+	6.65689i	−0.250560	+	0.477937i
$195$	−1.36721	−	4.20785i	−0.0979082	−	0.301330i
$196$	−22.1493	+	6.63166i	−1.58209	+	0.473690i
$197$		−	3.88832i		−	0.277032i	−0.990360	−	0.138516i	$-0.955767\pi$
$197$		−	3.88832i		−	0.277032i	0.990360	−	0.138516i	$-0.0442332\pi$
$198$	−15.6043	+	5.21652i	−1.10895	+	0.370722i
$199$		−	15.5977i		−	1.10569i	−0.833283	−	0.552846i	$-0.813542\pi$
$199$		−	15.5977i		−	1.10569i	0.833283	−	0.552846i	$-0.186458\pi$
$200$	−2.80733	+	0.344804i	−0.198508	+	0.0243813i
$201$	6.00583	+	18.4841i	0.423619	+	1.30376i
$202$	−2.97838	−	1.56143i	−0.209558	−	0.109862i
$203$	0.647734	−	0.891529i	0.0454620	−	0.0625731i
$204$	−14.9725	−	21.6488i	−1.04828	−	1.51572i
$205$	1.57918	+	0.513105i	0.110294	+	0.0358368i
$206$	13.1462	−	1.92581i	0.915941	−	0.134177i
$207$	2.75849	+	3.79674i	0.191728	+	0.263892i
$208$	−4.33413	+	5.41689i	−0.300518	+	0.375594i
$209$	9.44944	−	19.5043i	0.653632	−	1.34914i
$210$	2.60967	−	15.3220i	0.180085	−	1.05732i
$211$	12.7386	−	9.25514i	0.876962	−	0.637150i	−0.0554843	−	0.998460i	$-0.517670\pi$
$211$	12.7386	−	9.25514i	0.876962	−	0.637150i	0.932446	+	0.361310i	$0.117670\pi$
$212$	−0.355165	+	15.2758i	−0.0243928	+	1.04915i
$213$	−1.76647	+	5.43663i	−0.121036	+	0.372512i
$214$	14.3613	+	14.6991i	0.981717	+	1.00481i
$215$	−7.40304	−	5.37862i	−0.504883	−	0.366819i
$216$	2.49906	+	2.67971i	0.170039	+	0.182331i
$217$	36.5538	−	11.8771i	2.48144	−	0.806267i
$218$	−2.34047	−	4.72849i	−0.158516	−	0.320254i
$219$	16.3857			1.10724
$220$	5.90072	+	3.03010i	0.397826	+	0.204289i
$221$	−8.94759			−0.601880
$222$	−5.74950	−	11.6158i	−0.385881	−	0.779604i
$223$	2.12951	−	0.691921i	0.142603	−	0.0463345i	−0.236846	−	0.971547i	$-0.576114\pi$
$223$	2.12951	−	0.691921i	0.142603	−	0.0463345i	0.379449	+	0.925213i	$0.376114\pi$
$224$	−22.3204	+	9.78417i	−1.49135	+	0.653733i
$225$	2.83789	+	2.06185i	0.189193	+	0.137456i
$226$	7.23642	+	7.40662i	0.481359	+	0.492681i
$227$	4.57796	−	14.0895i	0.303850	−	0.935153i	−0.676254	−	0.736668i	$-0.736398\pi$
$227$	4.57796	−	14.0895i	0.303850	−	0.935153i	0.980104	−	0.198485i	$-0.0636021\pi$
$228$	−33.3311	−	0.774952i	−2.20740	−	0.0513224i
$229$	15.2098	−	11.0505i	1.00509	−	0.730241i	0.0419165	−	0.999121i	$-0.486654\pi$
$229$	15.2098	−	11.0505i	1.00509	−	0.730241i	0.963174	+	0.268880i	$0.0866537\pi$
$230$	0.317680	−	1.86518i	0.0209472	−	0.122986i
$231$	−25.2518	+	26.2871i	−1.66145	+	1.72956i
$232$	0.350729	−	0.632787i	0.0230265	−	0.0415445i
$233$	11.9887	+	16.5011i	0.785407	+	1.08102i	0.994665	+	0.103160i	$0.0328953\pi$
$233$	11.9887	+	16.5011i	0.785407	+	1.08102i	−0.209258	+	0.977861i	$0.567105\pi$
$234$	8.51291	−	1.24707i	0.556506	−	0.0815233i
$235$	6.69361	+	2.17489i	0.436643	+	0.141874i
$236$	−4.41492	+	3.05340i	−0.287387	+	0.198760i
$237$	−4.76607	+	6.55993i	−0.309590	+	0.426113i
$238$	−27.8388	−	14.5946i	−1.80452	−	0.946027i
$239$	5.62371	+	17.3080i	0.363767	+	1.11956i	0.950749	+	0.309961i	$0.100316\pi$
$239$	5.62371	+	17.3080i	0.363767	+	1.11956i	−0.586982	+	0.809600i	$0.699684\pi$
$240$	0.474240	−	10.1931i	0.0306121	−	0.657965i
$241$			27.1662i			1.74993i	0.484189	+	0.874963i	$0.339115\pi$
$241$			27.1662i			1.74993i	−0.484189	+	0.874963i	$0.660885\pi$
$242$	−7.45517	−	13.6536i	−0.479237	−	0.877686i
$243$			22.3015i			1.43064i
$244$	−5.52909	−	18.4668i	−0.353964	−	1.18221i
$245$	−3.57235	−	10.9946i	−0.228229	−	0.702417i
$246$	−2.78144	+	5.30553i	−0.177338	+	0.338268i
$247$	−6.66152	+	9.16879i	−0.423862	+	0.583396i
$248$	22.8690	−	10.6650i	1.45218	−	0.677229i
$249$	17.6122	+	5.72256i	1.11613	+	0.362652i
$250$	−0.204982	−	1.39928i	−0.0129642	−	0.0884982i
$251$	10.1585	+	13.9820i	0.641201	+	0.882538i	0.998679	−	0.0513838i	$-0.0163632\pi$
$251$	10.1585	+	13.9820i	0.641201	+	0.882538i	−0.357478	+	0.933922i	$0.616363\pi$
$252$	28.5205	+	10.0056i	1.79662	+	0.630291i
$253$	−3.07395	+	3.19997i	−0.193257	+	0.201181i
$254$	−3.94317	−	0.671606i	−0.247416	−	0.0421403i
$255$	10.6475	−	7.73583i	0.666770	−	0.484436i
$256$	−13.7616	+	8.16206i	−0.860098	+	0.510129i
$257$	−7.28925	+	22.4340i	−0.454691	+	1.39939i	0.416807	+	0.908995i	$0.363149\pi$
$257$	−7.28925	+	22.4340i	−0.454691	+	1.39939i	−0.871498	+	0.490399i	$0.836851\pi$
$258$	23.6135	−	23.0708i	1.47011	−	1.43633i
$259$	−12.5214	−	9.09733i	−0.778042	−	0.565280i
$260$	−2.75808	−	2.10352i	−0.171049	−	0.130455i
$261$	−0.853353	+	0.277271i	−0.0528212	+	0.0171627i
$262$	11.8571	−	5.86894i	0.732537	−	0.362584i
$263$	0.128504			0.00792390			0.00396195	−	0.999992i	$-0.498739\pi$
$263$	0.128504			0.00792390			0.00396195	+	0.999992i	$0.498739\pi$
$264$	−14.3509	+	19.1504i	−0.883238	+	1.17863i
$265$	−7.63998			−0.469320
$266$	−35.6815	+	17.6613i	−2.18777	+	1.08288i
$267$	5.88725	−	1.91288i	0.360294	−	0.117066i
$268$	12.1156	+	9.24027i	0.740077	+	0.564439i
$269$	12.0703	+	8.76955i	0.735936	+	0.534689i	0.891436	−	0.453147i	$-0.149699\pi$
$269$	12.0703	+	8.76955i	0.735936	+	0.534689i	−0.155500	+	0.987836i	$0.549699\pi$
$270$	−1.31045	+	1.28034i	−0.0797514	+	0.0779187i
$271$	4.61574	−	14.2058i	0.280386	−	0.862941i	−0.707357	−	0.706856i	$-0.750113\pi$
$271$	4.61574	−	14.2058i	0.280386	−	0.862941i	0.987744	−	0.156085i	$-0.0498873\pi$
$272$	−19.3086	−	7.28219i	−1.17076	−	0.441547i
$273$	15.4207	−	11.2038i	0.933305	−	0.678086i
$274$	−6.96684	−	1.18660i	−0.420882	−	0.0716853i
$275$	−1.44606	+	2.98478i	−0.0872010	+	0.179989i
$276$	6.44108	+	2.25966i	0.387708	+	0.136016i
$277$	−6.35827	−	8.75141i	−0.382031	−	0.525821i	0.574090	−	0.818792i	$-0.305356\pi$
$277$	−6.35827	−	8.75141i	−0.382031	−	0.525821i	−0.956121	+	0.292971i	$0.905356\pi$
$278$	0.597272	+	4.07719i	0.0358220	+	0.244533i
$279$	−29.7630	−	9.67060i	−1.78187	−	0.578964i
$280$	−5.15017	−	11.0435i	−0.307782	−	0.659975i
$281$	4.09440	−	5.63545i	0.244251	−	0.336183i	−0.669236	−	0.743050i	$-0.733379\pi$
$281$	4.09440	−	5.63545i	0.244251	−	0.336183i	0.913488	+	0.406867i	$0.133379\pi$
$282$	−11.7896	+	22.4884i	−0.702063	+	1.33917i
$283$	−8.26226	−	25.4286i	−0.491140	−	1.51157i	−0.822886	−	0.568206i	$-0.807638\pi$
$283$	−8.26226	−	25.4286i	−0.491140	−	1.51157i	0.331746	−	0.943369i	$-0.392362\pi$
$284$	1.28545	+	4.29332i	0.0762776	+	0.254762i
$285$		−	16.6700i		−	0.987448i
$286$	2.57917	+	7.71511i	0.152509	+	0.456204i
$287$			7.15348i			0.422257i
$288$	19.3856	+	4.23728i	1.14231	+	0.249684i
$289$	−2.97147	−	9.14523i	−0.174792	−	0.537955i
$290$	0.320384	+	0.167963i	0.0188136	+	0.00986311i
$291$	7.96932	−	10.9688i	0.467170	−	0.643004i
$292$	10.5656	−	7.30724i	0.618303	−	0.427624i
$293$	−17.8955	−	5.81460i	−1.04547	−	0.339692i	−0.264578	−	0.964364i	$-0.585233\pi$
$293$	−17.8955	−	5.81460i	−1.04547	−	0.339692i	−0.780888	+	0.624672i	$0.785233\pi$
$294$	41.2662	−	6.04513i	2.40669	−	0.352559i
$295$	−1.57760	−	2.17138i	−0.0918514	−	0.126423i
$296$	−8.88741	−	4.92593i	−0.516570	−	0.286314i
$297$	4.22937	−	0.757231i	0.245413	−	0.0439390i
$298$	−0.0900723	+	0.528837i	−0.00521775	+	0.0306347i
$299$	1.87719	−	1.36386i	0.108561	−	0.0788741i
$300$	5.10071	+	0.118592i	0.294490	+	0.00684692i
$301$	12.1823	−	37.4932i	0.702174	−	2.16107i
$302$	−18.3947	−	18.8274i	−1.05850	−	1.08339i
$303$	4.90759	+	3.56557i	0.281934	+	0.204837i
$304$	−21.8376	+	14.3644i	−1.25247	+	0.823853i
$305$	9.16663	−	2.97842i	0.524880	−	0.170544i
$306$	11.3532	+	22.9371i	0.649019	+	1.31123i
$307$	10.0682			0.574623			0.287312	−	0.957837i	$-0.407238\pi$
$307$	10.0682			0.574623			0.287312	+	0.957837i	$0.407238\pi$
$308$	−4.55967	+	28.2111i	−0.259811	+	1.60748i
$309$	−23.9670			−1.36344
$310$	5.59685	+	11.3074i	0.317880	+	0.642219i
$311$	−6.73055	+	2.18689i	−0.381654	+	0.124007i	−0.493560	−	0.869712i	$-0.664305\pi$
$311$	−6.73055	+	2.18689i	−0.381654	+	0.124007i	0.111905	+	0.993719i	$0.464305\pi$
$312$	9.15189	−	8.53492i	0.518124	−	0.483195i
$313$	1.68909	+	1.22720i	0.0954732	+	0.0693653i	0.634498	−	0.772925i	$-0.281207\pi$
$313$	1.68909	+	1.22720i	0.0954732	+	0.0693653i	−0.539025	+	0.842290i	$0.681207\pi$
$314$	15.6176	+	15.9849i	0.881352	+	0.902081i
$315$	−4.66996	+	14.3727i	−0.263123	+	0.809808i
$316$	−0.147762	+	6.35531i	−0.00831225	+	0.357514i
$317$	−16.5981	+	12.0592i	−0.932241	+	0.677313i	−0.946541	−	0.322585i	$-0.895448\pi$
$317$	−16.5981	+	12.0592i	−0.932241	+	0.677313i	0.0142993	+	0.999898i	$0.495448\pi$
$318$	4.62791	−	27.1716i	0.259520	−	1.52371i
$319$	−0.400251	−	0.748008i	−0.0224098	−	0.0418804i
$320$	−4.23987	−	6.78407i	−0.237016	−	0.379241i
$321$	−21.7890	−	29.9899i	−1.21614	−	1.67388i
$322$	8.06516	−	1.18148i	0.449454	−	0.0658411i
$323$	−32.0623	−	10.4177i	−1.78400	−	0.579656i
$324$	8.21224	+	11.8741i	0.456236	+	0.659672i
$325$	1.01942	−	1.40312i	0.0565474	−	0.0778309i
$326$	4.30477	+	2.25679i	0.238419	+	0.124992i
$327$	2.94098	+	9.05141i	0.162637	+	0.500544i
$328$	0.572528	+	4.66142i	0.0316126	+	0.257384i
$329$			30.3213i			1.67167i
$330$	−9.73942	−	6.95096i	−0.536137	−	0.382638i
$331$			18.0641i			0.992892i	0.868068	+	0.496446i	$0.165362\pi$
$331$			18.0641i			0.992892i	−0.868068	+	0.496446i	$0.834638\pi$
$332$	13.9084	−	4.16428i	0.763323	−	0.228545i
$333$	3.89423	+	11.9852i	0.213403	+	0.656786i
$334$	5.46133	−	10.4173i	0.298831	−	0.570012i
$335$	−4.47808	+	6.16355i	−0.244664	+	0.336750i
$336$	42.3959	−	11.6270i	2.31289	−	0.634306i
$337$	11.9493	+	3.88256i	0.650919	+	0.211496i	0.615819	−	0.787888i	$-0.288825\pi$
$337$	11.9493	+	3.88256i	0.650919	+	0.211496i	0.0350995	+	0.999384i	$0.488825\pi$
$338$	2.04819	+	13.9817i	0.111407	+	0.760502i
$339$	−10.9791	−	15.1114i	−0.596303	−	0.820741i
$340$	3.41571	−	9.73635i	0.185243	−	0.528027i
$341$	4.04088	−	29.3117i	0.218826	−	1.58732i
$342$	31.9567	+	5.44291i	1.72802	+	0.294319i
$343$	15.8947	−	11.5481i	0.858231	−	0.623541i
$344$	4.93756	−	25.4066i	0.266215	−	1.36983i
$345$	−1.05467	+	3.24593i	−0.0567814	+	0.174755i
$346$	11.1441	−	10.8880i	0.599109	−	0.585341i
$347$	26.2300	+	19.0572i	1.40810	+	1.02305i	0.993595	+	0.112998i	$0.0360455\pi$
$347$	26.2300	+	19.0572i	1.40810	+	1.02305i	0.414506	+	0.910047i	$0.363954\pi$
$348$	−0.791432	+	1.03770i	−0.0424252	+	0.0556268i
$349$	−23.8079	+	7.73566i	−1.27441	+	0.414080i	−0.866607	−	0.498990i	$-0.833704\pi$
$349$	−23.8079	+	7.73566i	−1.27441	+	0.414080i	−0.407801	+	0.913071i	$0.633704\pi$
$350$	5.46040	−	2.70274i	0.291871	−	0.144467i
$351$	−2.24681			−0.119926
$352$	−0.713342	+	18.7481i	−0.0380213	+	0.999277i
$353$	−10.4552			−0.556474			−0.278237	−	0.960512i	$-0.589750\pi$
$353$	−10.4552			−0.556474			−0.278237	+	0.960512i	$0.589750\pi$
$354$	8.67814	−	4.29543i	0.461238	−	0.228299i
$355$	−2.13114	+	0.692450i	−0.113109	+	0.0367514i
$356$	2.94306	−	3.85886i	0.155982	−	0.204519i
$357$	45.8711	+	33.3273i	2.42776	+	1.76387i
$358$	3.53167	−	3.45051i	0.186655	−	0.182365i
$359$	4.82319	−	14.8443i	0.254558	−	0.783450i	−0.739358	−	0.673312i	$-0.764871\pi$
$359$	4.82319	−	14.8443i	0.254558	−	0.783450i	0.993916	−	0.110137i	$-0.0351291\pi$
$360$	−1.89277	+	9.73941i	−0.0997576	+	0.513312i
$361$	−19.1745	+	13.9311i	−1.00918	+	0.733213i
$362$	−20.6233	−	3.51259i	−1.08394	−	0.184618i
$363$	9.73622	+	26.3183i	0.511019	+	1.38135i
$364$	4.94697	−	14.1012i	0.259292	−	0.739102i
$365$	3.77543	+	5.19643i	0.197615	+	0.271993i
$366$	5.04008	+	34.4053i	0.263449	+	1.79840i
$367$	−2.10151	−	0.682821i	−0.109698	−	0.0356430i	0.253654	−	0.967295i	$-0.418368\pi$
$367$	−2.10151	−	0.682821i	−0.109698	−	0.0356430i	−0.363352	+	0.931652i	$0.618368\pi$
$368$	5.16093	−	1.41538i	0.269032	−	0.0737817i
$369$	3.42358	−	4.71215i	0.178224	−	0.245305i
$370$	2.35901	−	4.49975i	0.122639	−	0.233931i
$371$	−10.1711	−	31.3034i	−0.528057	−	1.62519i
$372$	−43.6052	+	13.0557i	−2.26083	+	0.676909i
$373$		−	11.6841i		−	0.604981i	−0.953152	−	0.302490i	$-0.902182\pi$
$373$		−	11.6841i		−	0.604981i	0.953152	−	0.302490i	$-0.0978180\pi$
$374$	−19.4556	+	14.3884i	−1.00603	+	0.744008i
$375$			2.55104i			0.131735i
$376$	2.42676	+	19.7582i	0.125151	+	1.01895i
$377$	0.137089	+	0.421917i	0.00706045	+	0.0217298i
$378$	−6.99054	−	3.66482i	−0.359555	−	0.188498i
$379$	−9.66514	+	13.3029i	−0.496465	+	0.683325i	−0.981564	−	0.191134i	$-0.938784\pi$
$379$	−9.66514	+	13.3029i	−0.496465	+	0.683325i	0.485099	+	0.874459i	$0.338784\pi$
$380$	−7.43404	−	10.7489i	−0.381358	−	0.551407i
$381$	6.86221	+	2.22967i	0.351562	+	0.114229i
$382$	−33.5962	+	4.92155i	−1.71893	+	0.251808i
$383$	4.75275	+	6.54160i	0.242854	+	0.334260i	0.912993	−	0.407976i	$-0.133765\pi$
$383$	4.75275	+	6.54160i	0.242854	+	0.334260i	−0.670138	+	0.742236i	$0.733765\pi$
$384$	26.6958	−	10.9697i	1.36232	−	0.559793i
$385$	−14.1547	−	1.95135i	−0.721392	−	0.0994501i
$386$	6.14150	−	36.0583i	0.312594	−	1.83532i
$387$	−25.9686	+	18.8673i	−1.32006	+	0.959077i
$388$	0.247071	−	10.6267i	0.0125432	−	0.539487i
$389$	3.44719	−	10.6094i	0.174779	−	0.537916i	−0.824844	−	0.565361i	$-0.808737\pi$
$389$	3.44719	−	10.6094i	0.174779	−	0.537916i	0.999623	+	0.0274447i	$0.00873702\pi$
$390$	4.37267	+	4.47552i	0.221419	+	0.226627i
$391$	5.58397	+	4.05699i	0.282394	+	0.205171i
$392$	23.9127	−	22.3007i	1.20777	−	1.12635i
$393$	−22.6973	+	7.37479i	−1.14493	+	0.372009i
$394$	2.43934	+	4.92826i	0.122892	+	0.248282i
$395$	−3.17851			−0.159928
$396$	16.5051	−	16.4011i	0.829412	−	0.824184i
$397$	−28.7325			−1.44204			−0.721022	−	0.692912i	$-0.756327\pi$
$397$	−28.7325			−1.44204			−0.721022	+	0.692912i	$0.756327\pi$
$398$	9.78523	+	19.7693i	0.490489	+	0.990947i
$399$	68.3024	−	22.1928i	3.41940	−	1.11103i
$400$	3.34184	−	2.19820i	0.167092	−	0.109910i
$401$	−20.3649	−	14.7959i	−1.01697	−	0.738874i	−0.0513128	−	0.998683i	$-0.516341\pi$
$401$	−20.3649	−	14.7959i	−1.01697	−	0.738874i	−0.965660	+	0.259809i	$0.916341\pi$
$402$	−19.2081	−	19.6599i	−0.958012	−	0.980545i
$403$	−4.78136	+	14.7155i	−0.238177	+	0.733032i
$404$	4.75451	+	0.110543i	0.236546	+	0.00549972i
$405$	−5.84001	+	4.24301i	−0.290192	+	0.210837i
$406$	−0.261669	+	1.53633i	−0.0129864	+	0.0762465i
$407$	−10.5057	+	5.62147i	−0.520746	+	0.278646i
$408$	32.5583	+	18.0457i	1.61188	+	0.893398i
$409$	18.9000	+	26.0136i	0.934542	+	1.28629i	0.958061	+	0.286564i	$0.0925131\pi$
$409$	18.9000	+	26.0136i	0.934542	+	1.28629i	−0.0235187	+	0.999723i	$0.507487\pi$
$410$	−2.32342	+	0.340361i	−0.114746	+	0.0168092i
$411$	12.1243	+	3.93941i	0.598045	+	0.194317i
$412$	−15.4540	+	10.6882i	−0.761365	+	0.526568i
$413$	6.79657	−	9.35468i	0.334437	−	0.460314i
$414$	−5.87814	−	3.08164i	−0.288895	−	0.151454i
$415$	2.24322	+	6.90393i	0.110115	+	0.338900i
$416$	2.09500	−	9.58466i	0.102716	−	0.469926i
$417$		−	7.43317i		−	0.364004i
$418$	0.259340	+	30.6489i	0.0126847	+	1.49909i
$419$			6.67229i			0.325963i	0.986629	+	0.162981i	$0.0521111\pi$
$419$			6.67229i			0.325963i	−0.986629	+	0.162981i	$0.947889\pi$
$420$	6.30466	+	21.0571i	0.307636	+	1.02748i
$421$	−1.64589	−	5.06554i	−0.0802160	−	0.246879i	0.902904	−	0.429843i	$-0.141431\pi$
$421$	−1.64589	−	5.06554i	−0.0802160	−	0.246879i	−0.983120	+	0.182963i	$0.941431\pi$
$422$	−10.3393	+	19.7220i	−0.503311	+	0.960052i
$423$	14.5114	−	19.9733i	0.705571	−	0.971135i
$424$	−9.13315	−	19.5842i	−0.443545	−	0.951092i
$425$	4.90655	+	1.59424i	0.238003	+	0.0773318i
$426$	−1.17176	−	7.99886i	−0.0567721	−	0.387546i
$427$	24.4071	+	33.5934i	1.18114	+	1.62570i
$428$	−27.4237	−	9.62078i	−1.32557	−	0.465038i
$429$	−2.58614	−	14.4444i	−0.124860	−	0.697381i
$430$	12.7573	+	2.17284i	0.615210	+	0.104784i
$431$	−20.9879	+	15.2486i	−1.01095	+	0.734501i	−0.964409	−	0.264416i	$-0.914821\pi$
$431$	−20.9879	+	15.2486i	−1.01095	+	0.734501i	−0.0465445	+	0.998916i	$0.514821\pi$
$432$	−4.84855	−	1.82861i	−0.233276	−	0.0879793i
$433$	6.74295	−	20.7527i	0.324046	−	0.997310i	−0.647824	−	0.761790i	$-0.724321\pi$
$433$	6.74295	−	20.7527i	0.324046	−	0.997310i	0.971870	−	0.235520i	$-0.0756792\pi$
$434$	−38.8791	+	37.9857i	−1.86626	+	1.82337i
$435$	−0.527910	−	0.383549i	−0.0253114	−	0.0183898i
$436$	5.93285	+	4.52484i	0.284132	+	0.216701i
$437$	8.31458	−	2.70157i	0.397740	−	0.129234i
$438$	−20.7681	+	10.2796i	−0.992337	+	0.491178i
$439$	−27.4201			−1.30869			−0.654346	−	0.756195i	$-0.727056\pi$
$439$	−27.4201			−1.30869			−0.654346	+	0.756195i	$0.727056\pi$
$440$	−9.37981	−	0.138686i	−0.447165	−	0.00661158i
$441$	−40.5517			−1.93104
$442$	11.3406	−	5.61328i	0.539419	−	0.266996i
$443$	−15.4358	+	5.01540i	−0.733377	+	0.238289i	−0.651813	−	0.758379i	$-0.725991\pi$
$443$	−15.4358	+	5.01540i	−0.733377	+	0.238289i	−0.0815638	+	0.996668i	$0.525991\pi$
$444$	14.5744	+	11.1156i	0.691671	+	0.527521i
$445$	1.96311	+	1.42629i	0.0930605	+	0.0676124i
$446$	−2.26498	+	2.21293i	−0.107250	+	0.104785i
$447$	0.299031	−	0.920324i	0.0141437	−	0.0435298i
$448$	22.1519	−	26.4037i	1.04658	−	1.24746i
$449$	−3.87086	+	2.81234i	−0.182677	+	0.132723i	−0.675366	−	0.737483i	$-0.736014\pi$
$449$	−3.87086	+	2.81234i	−0.182677	+	0.132723i	0.492689	+	0.870206i	$0.336014\pi$
$450$	−4.89039	−	0.832938i	−0.230535	−	0.0392651i
$451$	4.95605	+	2.40111i	0.233372	+	0.113064i
$452$	−13.8183	−	4.84775i	−0.649960	−	0.228019i
$453$	27.9085	+	38.4128i	1.31126	+	1.80479i
$454$	3.03673	+	20.7297i	0.142521	+	0.972895i
$455$	7.10617	+	2.30893i	0.333142	+	0.108245i
$456$	42.7316	−	19.9281i	2.00109	−	0.933217i
$457$	4.20348	−	5.78560i	0.196631	−	0.270639i	−0.699304	−	0.714824i	$-0.746507\pi$
$457$	4.20348	−	5.78560i	0.196631	−	0.270639i	0.895935	+	0.444185i	$0.146507\pi$
$458$	−12.3451	+	23.5479i	−0.576847	+	1.10032i
$459$	−2.06530	−	6.35634i	−0.0964000	−	0.296689i
$460$	0.767478	+	2.56332i	0.0357838	+	0.119515i
$461$		−	20.4640i		−	0.953101i	−0.879147	−	0.476551i	$-0.841887\pi$
$461$		−	20.4640i		−	0.953101i	0.879147	−	0.476551i	$-0.158113\pi$
$462$	15.5142	−	49.1593i	0.721786	−	2.28710i
$463$		−	30.2664i		−	1.40660i	−0.710895	−	0.703299i	$-0.751710\pi$
$463$		−	30.2664i		−	1.40660i	0.710895	−	0.703299i	$-0.248290\pi$
$464$	−0.0475516	+	1.02206i	−0.00220753	+	0.0474478i
$465$	−7.03288	−	21.6450i	−0.326142	−	1.00376i
$466$	−25.5471	−	13.3931i	−1.18344	−	0.620426i
$467$	24.8675	−	34.2272i	1.15073	−	1.58385i	0.409943	−	0.912111i	$-0.365549\pi$
$467$	24.8675	−	34.2272i	1.15073	−	1.58385i	0.740790	−	0.671736i	$-0.234451\pi$
$468$	−10.0073	+	6.92118i	−0.462590	+	0.319931i
$469$	−31.2157	−	10.1426i	−1.44141	−	0.468341i
$470$	−9.84824	+	1.44268i	−0.454266	+	0.0665459i
$471$	−23.6950	−	32.6134i	−1.09181	−	1.50275i
$472$	3.68014	−	6.63974i	0.169392	−	0.305619i
$473$	−21.8869	−	21.0249i	−1.00636	−	0.966725i
$474$	1.92538	−	11.3044i	0.0884357	−	0.519228i
$475$	5.28660	−	3.84094i	0.242566	−	0.176234i
$476$	44.4402	+	1.03324i	2.03691	+	0.0473585i
$477$	−8.28157	+	25.4880i	−0.379187	+	1.16702i
$478$	−17.9860	−	18.4090i	−0.822658	−	0.842007i
$479$	−7.82255	−	5.68342i	−0.357422	−	0.259682i	0.394554	−	0.918873i	$-0.370899\pi$
$479$	−7.82255	−	5.68342i	−0.357422	−	0.259682i	−0.751976	+	0.659191i	$0.770899\pi$
$480$	5.79360	+	13.2168i	0.264441	+	0.603263i
$481$	5.92576	−	1.92540i	0.270191	−	0.0877905i
$482$	−17.0427	−	34.4318i	−0.776274	−	1.56832i
$483$	−14.7037			−0.669041
$484$	18.0146	+	12.6282i	0.818848	+	0.574011i
$485$	5.31477			0.241331
$486$	−13.9909	−	28.2661i	−0.634639	−	1.28218i
$487$	6.92209	−	2.24912i	0.313670	−	0.101918i	−0.147951	−	0.988995i	$-0.547268\pi$
$487$	6.92209	−	2.24912i	0.313670	−	0.101918i	0.461621	+	0.887077i	$0.347268\pi$
$488$	18.5930	+	19.9370i	0.841665	+	0.902507i
$489$	−7.09315	−	5.15348i	−0.320763	−	0.233048i
$490$	11.4252	+	11.6940i	0.516139	+	0.528279i
$491$	0.210365	−	0.647438i	0.00949366	−	0.0292185i	−0.946197	−	0.323590i	$-0.895110\pi$
$491$	0.210365	−	0.647438i	0.00949366	−	0.0292185i	0.955691	+	0.294371i	$0.0951102\pi$
$492$	0.196916	−	8.46944i	0.00887764	−	0.381832i
$493$	−1.06761	+	0.775664i	−0.0480827	+	0.0349341i
$494$	2.69110	−	15.8001i	0.121078	−	0.710880i
$495$	8.39013	+	8.05970i	0.377108	+	0.362257i
$496$	−22.2946	+	27.8642i	−1.00106	+	1.25114i
$497$	−5.67437	−	7.81010i	−0.254530	−	0.350331i
$498$	−25.9127	+	3.79598i	−1.16117	+	0.170102i
$499$	14.9177	+	4.84704i	0.667806	+	0.216983i	0.623249	−	0.782023i	$-0.285812\pi$
$499$	14.9177	+	4.84704i	0.667806	+	0.216983i	0.0445573	+	0.999007i	$0.485812\pi$
$500$	1.13764	+	1.64492i	0.0508770	+	0.0735631i
$501$	−12.4712	+	17.1651i	−0.557170	+	0.766879i
$502$	−21.6471	−	11.3486i	−0.966157	−	0.506511i
$503$	−1.75473	−	5.40052i	−0.0782397	−	0.240797i	0.904285	−	0.426929i	$-0.140405\pi$
$503$	−1.75473	−	5.40052i	−0.0782397	−	0.240797i	−0.982525	+	0.186132i	$0.940405\pi$
$504$	−42.4253	+	5.21079i	−1.88977	+	0.232107i
$505$			2.37790i			0.105815i
$506$	1.88857	−	5.98425i	0.0839573	−	0.266032i
$507$		−	25.4901i		−	1.13206i
$508$	5.41910	−	1.62252i	0.240434	−	0.0719878i
$509$	13.6955	+	42.1505i	0.607044	+	1.86829i	0.482082	+	0.876126i	$0.339881\pi$
$509$	13.6955	+	42.1505i	0.607044	+	1.86829i	0.124962	+	0.992162i	$0.460119\pi$
$510$	−8.64205	+	16.4845i	−0.382676	+	0.729945i
$511$	−16.2652	+	22.3871i	−0.719530	+	0.990348i
$512$	12.3216	−	18.9783i	0.544544	−	0.838732i
$513$	−8.05111	−	2.61596i	−0.355465	−	0.115498i
$514$	−4.83522	−	33.0069i	−0.213272	−	1.45587i
$515$	−5.52224	−	7.60071i	−0.243339	−	0.334927i
$516$	−15.4554	+	44.0551i	−0.680386	+	1.93942i
$517$	21.0071	+	10.1775i	0.923892	+	0.447607i
$518$	21.5775	+	3.67511i	0.948059	+	0.161475i
$519$	−22.7368	+	16.5193i	−0.998036	+	0.725115i
$520$	4.81538	+	0.935827i	0.211168	+	0.0410387i
$521$	−8.03350	+	24.7246i	−0.351954	+	1.08320i	0.605800	+	0.795617i	$0.292853\pi$
$521$	−8.03350	+	24.7246i	−0.351954	+	1.08320i	−0.957755	+	0.287587i	$0.907147\pi$
$522$	0.907636	−	0.886779i	0.0397262	−	0.0388133i
$523$	15.9618	+	11.5970i	0.697963	+	0.507100i	0.879268	−	0.476327i	$-0.158032\pi$
$523$	15.9618	+	11.5970i	0.697963	+	0.507100i	−0.181305	+	0.983427i	$0.558032\pi$
$524$	−11.3465	+	14.8772i	−0.495673	+	0.649913i
$525$	−10.4524	+	3.39620i	−0.456182	+	0.148222i
$526$	−0.162873	+	0.0806171i	−0.00710158	+	0.00351507i
$527$	−46.0260			−2.00493
$528$	6.17504	−	33.2753i	0.268734	−	1.44812i
$529$	21.2101			0.922178
$530$	9.68330	−	4.79295i	0.420616	−	0.208192i
$531$	−8.95410	+	2.90936i	−0.388575	+	0.126256i
$532$	34.1447	−	44.7696i	1.48036	−	1.94101i
$533$	−2.32979	−	1.69270i	−0.100915	−	0.0733188i
$534$	−6.26175	+	6.11785i	−0.270972	+	0.264745i
$535$	4.49037	−	13.8199i	0.194136	−	0.597489i
$536$	−21.1528	−	4.11086i	−0.913662	−	0.177562i
$537$	−7.20553	+	5.23512i	−0.310942	+	0.225912i
$538$	−20.8000	−	3.54269i	−0.896753	−	0.152736i
$539$	−6.75724	−	37.7413i	−0.291055	−	1.62563i
$540$	0.857711	−	2.44487i	0.0369100	−	0.105211i
$541$	−6.39305	−	8.79928i	−0.274859	−	0.378310i	0.649164	−	0.760649i	$-0.275119\pi$
$541$	−6.39305	−	8.79928i	−0.274859	−	0.378310i	−0.924022	+	0.382338i	$0.875119\pi$
$542$	3.06179	+	20.9008i	0.131515	+	0.897768i
$543$	35.8903	+	11.6615i	1.54020	+	0.500442i
$544$	29.0412	−	2.88348i	1.24513	−	0.123628i
$545$	−2.19286	+	3.01821i	−0.0939317	+	0.129286i
$546$	−12.5163	+	23.8745i	−0.535648	+	1.02173i
$547$	2.30074	+	7.08096i	0.0983727	+	0.302760i	0.988118	−	0.153697i	$-0.0491181\pi$
$547$	2.30074	+	7.08096i	0.0983727	+	0.302760i	−0.889745	+	0.456457i	$0.849118\pi$
$548$	9.57455	−	2.86669i	0.409004	−	0.122459i
$549$		−	33.8097i		−	1.44296i
$550$	−0.0396873	−	4.69025i	−0.00169227	−	0.199993i
$551$			1.67149i			0.0712078i
$552$	−9.58135	+	1.17681i	−0.407809	+	0.0500883i
$553$	−4.23155	−	13.0234i	−0.179944	−	0.553810i
$554$	13.5490	+	7.10311i	0.575642	+	0.301782i
$555$	−5.38689	+	7.41442i	−0.228661	+	0.314725i
$556$	−3.31484	−	4.79293i	−0.140581	−	0.203266i
$557$	25.7210	+	8.35725i	1.08983	+	0.354108i	0.798182	−	0.602417i	$-0.205795\pi$
$557$	25.7210	+	8.35725i	1.08983	+	0.354108i	0.291651	+	0.956525i	$0.405795\pi$
$558$	43.7900	−	6.41486i	1.85378	−	0.271563i
$559$	9.32840	+	12.8394i	0.394549	+	0.543050i
$560$	13.4557	+	10.7661i	0.568608	+	0.454951i
$561$	38.4866	−	20.5938i	1.62491	−	0.869470i
$562$	−1.65404	+	9.71128i	−0.0697714	+	0.409646i
$563$	−7.89201	+	5.73388i	−0.332609	+	0.241654i	−0.741537	−	0.670912i	$-0.765903\pi$
$563$	−7.89201	+	5.73388i	−0.332609	+	0.241654i	0.408928	+	0.912567i	$0.365903\pi$
$564$	0.834661	−	35.8992i	0.0351456	−	1.51163i
$565$	2.26263	−	6.96365i	0.0951894	−	0.292963i
$566$	26.4247	+	27.0462i	1.11071	+	1.13684i
$567$	−25.1598	−	18.2796i	−1.05661	−	0.767673i
$568$	−4.32267	−	4.63514i	−0.181375	−	0.194486i
$569$	38.4320	−	12.4873i	1.61115	−	0.523495i	0.641322	−	0.767272i	$-0.278386\pi$
$569$	38.4320	−	12.4873i	1.61115	−	0.523495i	0.969831	+	0.243777i	$0.0783864\pi$
$570$	10.4580	+	21.1284i	0.438036	+	0.884973i
$571$	21.6002			0.903941			0.451970	−	0.892033i	$-0.350721\pi$
$571$	21.6002			0.903941			0.451970	+	0.892033i	$0.350721\pi$
$572$	−8.10905	−	8.16048i	−0.339056	−	0.341207i
$573$	61.2497			2.55874
$574$	−4.48774	−	9.06668i	−0.187315	−	0.378436i
$575$	−1.27239	+	0.413426i	−0.0530625	+	0.0172411i
$576$	−27.2285	+	6.79101i	−1.13452	+	0.282959i
$577$	−2.00268	−	1.45503i	−0.0833725	−	0.0605736i	0.545318	−	0.838229i	$-0.316409\pi$
$577$	−2.00268	−	1.45503i	−0.0833725	−	0.0605736i	−0.628691	+	0.777655i	$0.716409\pi$
$578$	9.50346	+	9.72698i	0.395292	+	0.404589i
$579$	−20.3892	+	62.7515i	−0.847346	+	2.60786i
$580$	−0.511443	−	0.0118911i	−0.0212365	−	0.000493752i
$581$	−25.3012	+	18.3824i	−1.04967	+	0.762630i
$582$	−3.21942	+	18.9020i	−0.133449	+	0.783513i
$583$	−25.1015	−	3.46047i	−1.03960	−	0.143318i
$584$	−8.80712	+	15.8899i	−0.364441	+	0.657528i
$585$	−3.57596	−	4.92188i	−0.147848	−	0.203495i
$586$	26.3294	−	3.85703i	1.08766	−	0.159333i
$587$	−22.8279	−	7.41724i	−0.942210	−	0.306142i	−0.202664	−	0.979248i	$-0.564960\pi$
$587$	−22.8279	−	7.41724i	−0.942210	−	0.306142i	−0.739546	+	0.673106i	$0.764960\pi$
$588$	−48.5104	+	33.5503i	−2.00054	+	1.38359i
$589$	−34.2666	+	47.1639i	−1.41193	+	1.94335i
$590$	3.36174	+	1.76241i	0.138401	+	0.0725572i
$591$	−3.06523	−	9.43380i	−0.126087	−	0.388055i
$592$	14.3546	+	0.667855i	0.589972	+	0.0274487i
$593$			25.4191i			1.04384i	0.852995	+	0.521919i	$0.174784\pi$
$593$			25.4191i			1.04384i	−0.852995	+	0.521919i	$0.825216\pi$
$594$	−4.88547	+	3.61305i	−0.200453	+	0.148245i
$595$			22.2261i			0.911182i
$596$	−0.217604	−	0.726782i	−0.00891341	−	0.0297701i
$597$	−12.2959	−	37.8430i	−0.503239	−	1.54881i
$598$	−1.52363	+	2.90628i	−0.0623059	+	0.118847i
$599$	26.8751	−	36.9904i	1.09809	−	1.51139i	0.260189	−	0.965558i	$-0.416215\pi$
$599$	26.8751	−	36.9904i	1.09809	−	1.51139i	0.837897	−	0.545828i	$-0.183785\pi$
$600$	−6.53930	+	3.04962i	−0.266966	+	0.124500i
$601$	−16.3229	−	5.30365i	−0.665827	−	0.216340i	−0.0434471	−	0.999056i	$-0.513834\pi$
$601$	−16.3229	−	5.30365i	−0.665827	−	0.216340i	−0.622380	+	0.782715i	$0.713834\pi$
$602$	8.08094	+	55.1633i	0.329355	+	2.24829i
$603$	15.7083	+	21.6206i	0.639692	+	0.880460i
$604$	35.1258	+	12.3228i	1.42925	+	0.501408i
$605$	−6.10305	+	9.15166i	−0.248124	+	0.372068i
$606$	−8.45700	−	1.44041i	−0.343542	−	0.0585126i
$607$	9.78537	−	7.10949i	0.397176	−	0.288565i	−0.371214	−	0.928547i	$-0.621058\pi$
$607$	9.78537	−	7.10949i	0.397176	−	0.288565i	0.768390	+	0.639982i	$0.221058\pi$
$608$	18.6666	−	31.9059i	0.757029	−	1.29396i
$609$	0.868717	−	2.67363i	0.0352022	−	0.108341i
$610$	−9.74974	+	9.52569i	−0.394755	+	0.385684i
$611$	−9.87525	−	7.17479i	−0.399510	−	0.290261i
$612$	−28.7793	−	21.9492i	−1.16333	−	0.887246i
$613$	7.51934	−	2.44318i	0.303703	−	0.0986792i	−0.153201	−	0.988195i	$-0.548958\pi$
$613$	7.51934	−	2.44318i	0.303703	−	0.0986792i	0.456904	+	0.889516i	$0.348958\pi$
$614$	−12.7610	+	6.31630i	−0.514990	+	0.254905i
$615$	4.23586			0.170807
$616$	−11.9191	−	38.6167i	−0.480234	−	1.55591i
$617$	13.5544			0.545678			0.272839	−	0.962060i	$-0.412037\pi$
$617$	13.5544			0.545678			0.272839	+	0.962060i	$0.412037\pi$
$618$	30.3770	−	15.0357i	1.22194	−	0.604826i
$619$	−10.8446	+	3.52363i	−0.435882	+	0.141627i	−0.518735	−	0.854935i	$-0.673597\pi$
$619$	−10.8446	+	3.52363i	−0.435882	+	0.141627i	0.0828527	+	0.996562i	$0.473597\pi$
$620$	−14.1875	−	10.8204i	−0.569782	−	0.434559i
$621$	1.40218	+	1.01874i	0.0562675	+	0.0408808i
$622$	7.15869	−	6.99419i	0.287037	−	0.280441i
$623$	−3.23045	+	9.94232i	−0.129425	+	0.398331i
$624$	−6.24518	+	16.5590i	−0.250007	+	0.662892i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−2.91073	−	0.495759i	−0.116336	−	0.0198145i
$627$	7.55056	−	54.7702i	0.301540	−	2.18731i
$628$	−29.8227	−	10.4624i	−1.19005	−	0.417495i
$629$	10.8941	+	14.9944i	0.434376	+	0.597867i
$630$	−3.09776	−	21.1464i	−0.123418	−	0.842491i
$631$	−4.58601	−	1.49008i	−0.182566	−	0.0593193i	0.216307	−	0.976325i	$-0.430599\pi$
$631$	−4.58601	−	1.49008i	−0.182566	−	0.0593193i	−0.398873	+	0.917006i	$0.630599\pi$
$632$	−3.79973	−	8.14774i	−0.151145	−	0.324100i
$633$	23.6103	−	32.4967i	0.938423	−	1.29163i
$634$	13.4719	−	25.6973i	0.535037	−	1.02057i
$635$	0.874022	+	2.68996i	0.0346845	+	0.106748i
$636$	11.1805	+	37.3420i	0.443335	+	1.48071i
$637$			20.0497i			0.794398i
$638$	0.976562	+	0.696966i	0.0386625	+	0.0275931i
$639$			7.86038i			0.310952i
$640$	9.62981	+	5.93859i	0.380652	+	0.234743i
$641$	3.15617	+	9.71368i	0.124661	+	0.383667i	0.993839	−	0.110832i	$-0.0353515\pi$
$641$	3.15617	+	9.71368i	0.124661	+	0.383667i	−0.869178	+	0.494499i	$0.835352\pi$
$642$	46.4307	+	24.3414i	1.83247	+	0.960680i
$643$	−25.3327	+	34.8675i	−0.999024	+	1.37504i	−0.0731021	+	0.997324i	$0.523290\pi$
$643$	−25.3327	+	34.8675i	−0.999024	+	1.37504i	−0.925922	+	0.377714i	$0.876710\pi$
$644$	−9.48099	+	6.55715i	−0.373603	+	0.258388i
$645$	−22.2012	−	7.21361i	−0.874172	−	0.284036i
$646$	47.1730	−	6.91043i	1.85600	−	0.271887i
$647$	17.5088	+	24.0988i	0.688342	+	0.947421i	0.999996	−	0.00277453i	$-0.000883162\pi$
$647$	17.5088	+	24.0988i	0.688342	+	0.947421i	−0.311655	+	0.950195i	$0.600883\pi$
$648$	−17.8578	−	9.89788i	−0.701522	−	0.388826i
$649$	−4.19977	−	7.84874i	−0.164856	−	0.308090i
$650$	−0.411823	+	2.41792i	−0.0161530	+	0.0948385i
$651$	79.3235	−	57.6319i	3.10893	−	2.25877i
$652$	−6.87189	−	0.159772i	−0.269124	−	0.00625717i
$653$	2.57906	−	7.93754i	0.100927	−	0.310620i	−0.887826	−	0.460179i	$-0.847785\pi$
$653$	2.57906	−	7.93754i	0.100927	−	0.310620i	0.988753	+	0.149559i	$0.0477853\pi$
$654$	−9.40595	−	9.62718i	−0.367802	−	0.376453i
$655$	−7.56845	−	5.49880i	−0.295724	−	0.214856i
$656$	−3.64999	−	5.54894i	−0.142508	−	0.216650i
$657$	21.4285	−	6.96254i	0.836005	−	0.271634i
$658$	−19.0221	−	38.4307i	−0.741558	−	1.49819i
$659$	−2.55620			−0.0995756			−0.0497878	−	0.998760i	$-0.515855\pi$
$659$	−2.55620			−0.0995756			−0.0497878	+	0.998760i	$0.515855\pi$
$660$	16.7049	+	2.69996i	0.650238	+	0.105096i
$661$	18.1644			0.706514			0.353257	−	0.935526i	$-0.385074\pi$
$661$	18.1644			0.706514			0.353257	+	0.935526i	$0.385074\pi$
$662$	−11.3325	−	22.8953i	−0.440451	−	0.889852i
$663$	−21.7085	+	7.05353i	−0.843090	+	0.273936i
$664$	−15.0158	+	14.0035i	−0.582724	+	0.543440i
$665$	22.7756	+	16.5474i	0.883199	+	0.641682i
$666$	−12.4547	−	12.7476i	−0.482609	−	0.493960i
$667$	0.105750	−	0.325466i	0.00409467	−	0.0126021i
$668$	−0.386641	+	16.6296i	−0.0149596	+	0.643420i
$669$	4.62115	−	3.35746i	0.178664	−	0.129807i
$670$	1.80904	−	10.6213i	0.0698892	−	0.410337i
$671$	31.4665	−	5.63380i	1.21475	−	0.217490i
$672$	−46.4405	+	41.3338i	−1.79148	+	1.59449i
$673$	13.0092	+	17.9057i	0.501469	+	0.690212i	0.982452	−	0.186518i	$-0.0597202\pi$
$673$	13.0092	+	17.9057i	0.501469	+	0.690212i	−0.480983	+	0.876730i	$0.659720\pi$
$674$	−17.5808	+	2.57544i	−0.677189	+	0.0992022i
$675$	1.23207	+	0.400325i	0.0474226	+	0.0154085i
$676$	−11.3674	−	16.4361i	−0.437207	−	0.632159i
$677$	15.8934	−	21.8754i	0.610834	−	0.840741i	−0.385812	−	0.922577i	$-0.626079\pi$
$677$	15.8934	−	21.8754i	0.610834	−	0.840741i	0.996646	+	0.0818368i	$0.0260786\pi$
$678$	23.3957	+	12.2653i	0.898505	+	0.471045i
$679$	7.07555	+	21.7763i	0.271535	+	0.835698i
$680$	1.77886	+	14.4832i	0.0682164	+	0.555405i
$681$		−	37.7927i		−	1.44822i
$682$	13.2671	+	39.6862i	0.508024	+	1.51966i
$683$			15.2834i			0.584802i	0.956296	+	0.292401i	$0.0944542\pi$
$683$			15.2834i			0.584802i	−0.956296	+	0.292401i	$0.905546\pi$
$684$	−43.9181	+	13.1494i	−1.67925	+	0.502781i
$685$	1.54423	+	4.75266i	0.0590021	+	0.181590i
$686$	−12.9010	+	24.6082i	−0.492561	+	0.939546i
$687$	28.1904	−	38.8008i	1.07553	−	1.48034i
$688$	9.68076	+	35.2992i	0.369076	+	1.34577i
$689$	12.6019	+	4.09459i	0.480093	+	0.155992i
$690$	−0.699599	−	4.77571i	−0.0266333	−	0.181808i
$691$	−25.6479	−	35.3013i	−0.975693	−	1.34293i	−0.939118	−	0.343596i	$-0.888355\pi$
$691$	−25.6479	−	35.3013i	−0.975693	−	1.34293i	−0.0365754	−	0.999331i	$-0.511645\pi$
$692$	−7.29397	+	20.7912i	−0.277275	+	0.790363i
$693$	−21.8534	+	45.1069i	−0.830141	+	1.71347i
$694$	−45.2008	−	7.69867i	−1.71580	−	0.292237i
$695$	2.35730	−	1.71268i	0.0894173	−	0.0649655i
$696$	0.352097	−	1.81175i	0.0133462	−	0.0686740i
$697$	2.64714	−	8.14706i	0.100268	−	0.308592i
$698$	25.3224	−	24.7405i	0.958466	−	0.936441i
$699$	42.0949	+	30.5838i	1.59218	+	1.15678i
$700$	−5.22522	+	6.85117i	−0.197495	+	0.258950i
$701$	−0.434206	+	0.141082i	−0.0163997	+	0.00532859i	−0.317205	−	0.948357i	$-0.602744\pi$
$701$	−0.434206	+	0.141082i	−0.0163997	+	0.00532859i	0.300806	+	0.953685i	$0.402744\pi$
$702$	2.84772	−	1.40954i	0.107480	−	0.0531996i
$703$	23.4758			0.885407
$704$	−10.8575	−	24.2098i	−0.409208	−	0.912441i
$705$	17.9545			0.676204
$706$	13.2515	−	6.55908i	0.498725	−	0.246854i
$707$	−9.74300	+	3.16569i	−0.366423	+	0.119058i
$708$	−8.30438	+	10.8885i	−0.312098	+	0.409214i
$709$	−36.4824	−	26.5060i	−1.37013	−	0.995454i	−0.997727	−	0.0673810i	$-0.978536\pi$
$709$	−36.4824	−	26.5060i	−1.37013	−	0.995454i	−0.372398	−	0.928073i	$-0.621464\pi$
$710$	2.26671	−	2.21462i	0.0850680	−	0.0831132i
$711$	−3.44543	+	10.6040i	−0.129214	+	0.397679i
$712$	−1.30933	+	6.73725i	−0.0490691	+	0.252489i
$713$	9.65620	−	7.01564i	0.361627	−	0.262738i
$714$	−79.0473	−	13.4634i	−2.95827	−	0.503857i
$715$	3.98490	−	4.14827i	0.149027	−	0.155136i
$716$	−2.31154	+	6.58895i	−0.0863861	+	0.246241i
$717$	27.2883	+	37.5592i	1.01910	+	1.40267i
$718$	3.19940	+	21.8402i	0.119400	+	0.815069i
$719$	29.9893	+	9.74412i	1.11841	+	0.363394i	0.809162	−	0.587586i	$-0.199922\pi$
$719$	29.9893	+	9.74412i	1.11841	+	0.363394i	0.309251	+	0.950980i	$0.399922\pi$
$720$	−3.71103	−	13.5316i	−0.138302	−	0.504295i
$721$	23.7908	−	32.7452i	0.886015	−	1.21949i
$722$	15.5630	−	29.6860i	0.579195	−	1.10480i
$723$	21.4155	+	65.9102i	0.796452	+	2.45123i
$724$	28.3427	−	8.48601i	1.05335	−	0.315380i
$725$		−	0.255791i		−	0.00949982i
$726$	−28.8510	−	27.2491i	−1.07076	−	1.01131i
$727$		−	20.6716i		−	0.766667i	−0.923610	−	0.383333i	$-0.874776\pi$
$727$		−	20.6716i		−	0.766667i	0.923610	−	0.383333i	$-0.125224\pi$
$728$	2.57633	+	20.9760i	0.0954852	+	0.777423i
$729$	10.8886	+	33.5116i	0.403281	+	1.24117i
$730$	−8.04515	−	4.21770i	−0.297764	−	0.156104i
$731$	−27.7486	+	38.1927i	−1.02632	+	1.41261i
$732$	−27.9723	−	40.4452i	−1.03388	−	1.49490i
$733$	−19.7153	−	6.40590i	−0.728202	−	0.236607i	−0.0786263	−	0.996904i	$-0.525053\pi$
$733$	−19.7153	−	6.40590i	−0.728202	−	0.236607i	−0.649576	+	0.760297i	$0.725053\pi$
$734$	3.09192	−	0.452940i	0.114125	−	0.0167183i
$735$	−17.3344	−	23.8587i	−0.639388	−	0.880042i
$736$	−5.65329	+	5.03164i	−0.208383	+	0.185469i
$737$	−17.5047	+	18.2223i	−0.644793	+	0.671228i
$738$	−1.38305	+	8.12021i	−0.0509106	+	0.298909i
$739$	−2.65639	+	1.92998i	−0.0977167	+	0.0709954i	−0.635571	−	0.772043i	$-0.719235\pi$
$739$	−2.65639	+	1.92998i	−0.0977167	+	0.0709954i	0.537854	+	0.843038i	$0.319235\pi$
$740$	−0.167009	+	7.18314i	−0.00613937	+	0.264058i
$741$	−8.93418	+	27.4966i	−0.328205	+	1.01011i
$742$	32.5296	+	33.2947i	1.19420	+	1.22229i
$743$	−1.10557	−	0.803245i	−0.0405595	−	0.0294682i	0.567321	−	0.823497i	$-0.307980\pi$
$743$	−1.10557	−	0.803245i	−0.0405595	−	0.0294682i	−0.607880	+	0.794029i	$0.707980\pi$
$744$	47.0769	−	43.9033i	1.72592	−	1.60957i
$745$	0.360764	−	0.117219i	0.0132174	−	0.00429458i
$746$	7.33004	+	14.8090i	0.268372	+	0.542197i
$747$	25.4641			0.931681
$748$	15.6325	−	30.4421i	0.571580	−	1.11307i
$749$	62.6028			2.28745
$750$	−1.60040	−	3.23332i	−0.0584383	−	0.118064i
$751$	−20.5244	+	6.66878i	−0.748946	+	0.243347i	−0.658527	−	0.752557i	$-0.728820\pi$
$751$	−20.5244	+	6.66878i	−0.748946	+	0.243347i	−0.0904182	+	0.995904i	$0.528820\pi$
$752$	−15.4711	−	23.5202i	−0.564174	−	0.857692i
$753$	35.6688	+	25.9149i	1.29984	+	0.944391i
$754$	−0.438443	−	0.448756i	−0.0159672	−	0.0163427i
$755$	−5.75152	+	17.7013i	−0.209319	+	0.644218i
$756$	11.1593	+	0.259455i	0.405860	+	0.00943629i
$757$	−41.3119	+	30.0149i	−1.50151	+	1.09091i	−0.531732	+	0.846913i	$0.678459\pi$
$757$	−41.3119	+	30.0149i	−1.50151	+	1.09091i	−0.969776	+	0.243997i	$0.921541\pi$
$758$	3.90449	−	22.9242i	0.141817	−	0.832646i
$759$	−4.93538	+	10.1870i	−0.179143	+	0.369764i
$760$	16.1656	+	8.95995i	0.586388	+	0.325011i
$761$	−6.96503	−	9.58654i	−0.252482	−	0.347512i	0.663897	−	0.747824i	$-0.268902\pi$
$761$	−6.96503	−	9.58654i	−0.252482	−	0.347512i	−0.916379	+	0.400313i	$0.868902\pi$
$762$	−10.0963	+	1.47902i	−0.365750	+	0.0535792i
$763$	−15.2859	−	4.96670i	−0.553387	−	0.179806i
$764$	39.4940	−	27.3144i	1.42884	−	0.988201i
$765$	10.6372	−	14.6408i	0.384588	−	0.529340i
$766$	−10.1278	−	5.30951i	−0.365931	−	0.191840i
$767$	1.43845	+	4.42711i	0.0519396	+	0.159854i
$768$	−26.9538	+	30.6512i	−0.972613	+	1.10603i
$769$			15.0239i			0.541775i	0.962611	+	0.270887i	$0.0873171\pi$
$769$			15.0239i			0.541775i	−0.962611	+	0.270887i	$0.912683\pi$
$770$	19.1646	−	6.40673i	0.690644	−	0.230883i
$771$			60.1753i			2.16716i
$772$	14.8371	+	49.5550i	0.534001	+	1.78352i
$773$	−5.82383	−	17.9239i	−0.209469	−	0.644678i	−0.999500	−	0.0316121i	$-0.989936\pi$
$773$	−5.82383	−	17.9239i	−0.209469	−	0.644678i	0.790032	−	0.613066i	$-0.210064\pi$
$774$	21.0775	−	40.2047i	0.757614	−	1.44513i
$775$	5.24387	−	7.21757i	0.188365	−	0.259263i
$776$	6.35350	+	13.6238i	0.228077	+	0.489065i
$777$	−37.5508	−	12.2010i	−1.34713	−	0.437708i
$778$	2.28665	+	15.6094i	0.0819802	+	0.559625i
$779$	−6.37766	−	8.77810i	−0.228503	−	0.314508i
$780$	−8.34987	−	2.92930i	−0.298973	−	0.104886i
$781$	−7.31561	+	1.30980i	−0.261773	+	0.0468682i
$782$	−9.62257	−	1.63893i	−0.344102	−	0.0586080i
$783$	−0.268085	+	0.194775i	−0.00958058	+	0.00696070i
$784$	−16.3179	+	43.2666i	−0.582781	+	1.54524i
$785$	4.88319	−	15.0289i	0.174288	−	0.536405i
$786$	24.1411	−	23.5863i	0.861084	−	0.841296i
$787$	−9.37966	−	6.81472i	−0.334349	−	0.242919i	0.407925	−	0.913016i	$-0.366253\pi$
$787$	−9.37966	−	6.81472i	−0.334349	−	0.242919i	−0.742274	+	0.670097i	$0.766253\pi$
$788$	−6.18349	−	4.71600i	−0.220278	−	0.168001i
$789$	0.311775	−	0.101302i	0.0110995	−	0.00360644i
$790$	4.02861	−	1.99404i	0.143331	−	0.0709448i
$791$	31.5445			1.12159
$792$	−10.6302	+	31.1420i	−0.377727	+	1.10658i
$793$	−16.7163			−0.593612
$794$	36.4171	−	18.0254i	1.29239	−	0.639696i
$795$	−18.5360	+	6.02272i	−0.657405	+	0.213604i
$796$	−24.8046	−	18.9179i	−0.879176	−	0.670526i
$797$	−39.2753	−	28.5352i	−1.39120	−	1.01077i	−0.995732	−	0.0922881i	$-0.970582\pi$
$797$	−39.2753	−	28.5352i	−1.39120	−	1.01077i	−0.395469	−	0.918479i	$-0.629418\pi$
$798$	−72.6473	+	70.9779i	−2.57169	+	2.51259i
$799$	11.2204	−	34.5327i	0.396948	−	1.22168i
$800$	−2.85657	+	4.88262i	−0.100995	+	0.172627i
$801$	6.88626	−	5.00316i	0.243314	−	0.176778i
$802$	35.0937	+	5.97721i	1.23920	+	0.211063i
$803$	10.0507	+	18.7832i	0.354681	+	0.662844i
$804$	36.6789	+	12.8677i	1.29357	+	0.453809i
$805$	−3.38787	−	4.66301i	−0.119407	−	0.164349i
$806$	−3.17165	−	21.6508i	−0.111717	−	0.762616i
$807$	36.1979	+	11.7614i	1.27423	+	0.414021i
$808$	−6.09545	+	2.84264i	−0.214437	+	0.100004i
$809$	28.6502	−	39.4337i	1.00729	−	1.38641i	0.0865439	−	0.996248i	$-0.472418\pi$
$809$	28.6502	−	39.4337i	1.00729	−	1.38641i	0.920745	−	0.390166i	$-0.127582\pi$
$810$	4.74006	−	9.04154i	0.166549	−	0.317687i
$811$	−14.9845	−	46.1176i	−0.526178	−	1.61941i	−0.761975	−	0.647606i	$-0.775770\pi$
$811$	−14.9845	−	46.1176i	−0.526178	−	1.61941i	0.235797	−	0.971802i	$-0.424230\pi$
$812$	−0.632162	−	2.11137i	−0.0221845	−	0.0740947i
$813$		−	38.1046i		−	1.33639i
$814$	9.78878	−	13.7157i	0.343097	−	0.480734i
$815$		−	3.43687i		−	0.120388i
$816$	−52.5870	−	2.44663i	−1.84091	−	0.0856493i
$817$	18.4779	+	56.8692i	0.646461	+	1.98960i
$818$	−40.2744	−	21.1140i	−1.40816	−	0.738234i
$819$	15.4059	−	21.2043i	0.538324	−	0.740939i
$820$	2.73130	−	1.88899i	0.0953811	−	0.0659665i
$821$	13.7235	+	4.45903i	0.478953	+	0.155621i	0.538537	−	0.842602i	$-0.318977\pi$
$821$	13.7235	+	4.45903i	0.478953	+	0.155621i	−0.0595835	+	0.998223i	$0.518977\pi$
$822$	−17.8383	+	2.61315i	−0.622181	+	0.0911441i
$823$	−22.3072	−	30.7032i	−0.777579	−	1.07025i	−0.995545	−	0.0942897i	$-0.969942\pi$
$823$	−22.3072	−	30.7032i	−0.777579	−	1.07025i	0.217965	−	0.975956i	$-0.430058\pi$
$824$	12.8820	−	23.2418i	0.448766	−	0.809667i
$825$	−1.15547	+	8.38158i	−0.0402285	+	0.291809i
$826$	−2.74566	+	16.1204i	−0.0955336	+	0.560901i
$827$	−40.0241	+	29.0792i	−1.39177	+	1.01118i	−0.396104	+	0.918206i	$0.629638\pi$
$827$	−40.0241	+	29.0792i	−1.39177	+	1.01118i	−0.995668	+	0.0929765i	$0.970362\pi$
$828$	9.38352	+	0.218168i	0.326100	+	0.00758186i
$829$	−1.02397	+	3.15147i	−0.0355641	+	0.109455i	−0.967263	−	0.253777i	$-0.918327\pi$
$829$	−1.02397	+	3.15147i	−0.0355641	+	0.109455i	0.931699	+	0.363232i	$0.118327\pi$
$830$	−7.17436	−	7.34310i	−0.249026	−	0.254883i
$831$	−22.3252	−	16.2202i	−0.774453	−	0.562673i
$832$	3.35763	+	13.4624i	0.116405	+	0.466724i
$833$	−56.7216	+	18.4300i	−1.96529	+	0.638560i
$834$	4.66321	+	9.42118i	0.161474	+	0.326229i
$835$	−8.31707			−0.287824
$836$	−19.5563	−	38.6832i	−0.676368	−	1.33789i
$837$	−11.5575			−0.399486
$838$	−4.18587	−	8.45680i	−0.144598	−	0.292135i
$839$	−49.5575	+	16.1022i	−1.71091	+	0.555910i	−0.990485	−	0.137618i	$-0.956055\pi$
$839$	−49.5575	+	16.1022i	−1.71091	+	0.555910i	−0.720429	+	0.693528i	$0.756055\pi$
$840$	−21.2010	−	22.7336i	−0.731505	−	0.784384i
$841$	−23.4086	−	17.0073i	−0.807192	−	0.586459i
$842$	5.26396	+	5.38777i	0.181408	+	0.185675i
$843$	5.49125	−	16.9003i	0.189129	−	0.582078i
$844$	0.731985	−	31.4830i	0.0251960	−	1.08369i
$845$	8.08373	−	5.87317i	0.278089	−	0.202043i
$846$	−5.86228	+	34.4189i	−0.201549	+	1.18335i
$847$	−45.6222	−	12.8225i	−1.56760	−	0.440588i
$848$	23.8620	+	19.0923i	0.819423	+	0.655632i
$849$	−40.0916	−	55.1813i	−1.37594	−	1.89382i
$850$	−7.21896	+	1.05751i	−0.247608	+	0.0362725i
$851$	−4.57113	−	1.48525i	−0.156696	−	0.0509137i
$852$	6.50324	+	9.40306i	0.222797	+	0.322143i
$853$	−18.5650	+	25.5525i	−0.635654	+	0.874902i	−0.998374	−	0.0569957i	$-0.981848\pi$
$853$	−18.5650	+	25.5525i	−0.635654	+	0.874902i	0.362721	+	0.931898i	$0.381848\pi$
$854$	−52.0096	−	27.2662i	−1.77973	−	0.933031i
$855$	−7.08335	−	21.8003i	−0.242245	−	0.745555i
$856$	40.7938	−	5.01040i	1.39430	−	0.171252i
$857$			10.3018i			0.351903i	0.984399	+	0.175952i	$0.0563002\pi$
$857$			10.3018i			0.351903i	−0.984399	+	0.175952i	$0.943700\pi$
$858$	12.3395	+	16.6851i	0.421263	+	0.569620i
$859$		−	28.0391i		−	0.956682i	−0.878174	−	0.478341i	$-0.841238\pi$
$859$		−	28.0391i		−	0.956682i	0.878174	−	0.478341i	$-0.158762\pi$
$860$	−17.5323	+	5.24932i	−0.597848	+	0.179000i
$861$	5.63920	+	17.3557i	0.192184	+	0.591480i
$862$	17.0349	−	32.4937i	0.580212	−	1.10674i
$863$	33.1212	−	45.5874i	1.12746	−	1.55181i	0.334649	−	0.942343i	$-0.391382\pi$
$863$	33.1212	−	45.5874i	1.12746	−	1.55181i	0.792809	−	0.609470i	$-0.208618\pi$
$864$	7.29248	−	0.724064i	0.248095	−	0.0246332i
$865$	−10.4776	−	3.40437i	−0.356248	−	0.115752i
$866$	4.47284	+	30.5332i	0.151993	+	1.03756i
$867$	−14.4187	−	19.8456i	−0.489684	−	0.673992i
$868$	25.4470	−	72.5358i	0.863728	−	2.46202i
$869$	−10.4432	−	1.43968i	−0.354260	−	0.0488378i
$870$	0.909720	+	0.154945i	0.0308424	+	0.00525312i
$871$	10.6897	−	7.76654i	0.362208	−	0.263159i
$872$	−10.3583	−	2.01304i	−0.350775	−	0.0681700i
$873$	5.76109	−	17.7308i	0.194983	−	0.600097i
$874$	−8.84349	+	8.64026i	−0.299135	+	0.292261i
$875$	−3.48539	−	2.53228i	−0.117828	−	0.0856067i
$876$	19.8736	−	26.0577i	0.671467	−	0.880409i
$877$	19.2329	−	6.24915i	0.649449	−	0.211019i	0.0342780	−	0.999412i	$-0.489087\pi$
$877$	19.2329	−	6.24915i	0.649449	−	0.211019i	0.615171	+	0.788393i	$0.289087\pi$
$878$	34.7537	−	17.2020i	1.17288	−	0.580541i
$879$	−48.0016			−1.61905
$880$	11.9754	−	5.70865i	0.403692	−	0.192439i
$881$	11.7896			0.397200			0.198600	−	0.980081i	$-0.436361\pi$
$881$	11.7896			0.397200			0.198600	+	0.980081i	$0.436361\pi$
$882$	51.3973	−	25.4402i	1.73064	−	0.856615i
$883$	34.8828	−	11.3341i	1.17390	−	0.381423i	0.343802	−	0.939042i	$-0.388285\pi$
$883$	34.8828	−	11.3341i	1.17390	−	0.381423i	0.830097	+	0.557619i	$0.188285\pi$
$884$	−10.8522	+	14.2291i	−0.364999	+	0.478577i
$885$	−5.53928	−	4.02452i	−0.186201	−	0.135283i
$886$	16.4177	−	16.0404i	0.551564	−	0.538889i
$887$	−3.37381	+	10.3835i	−0.113281	+	0.348644i	−0.991585	−	0.129460i	$-0.958676\pi$
$887$	−3.37381	+	10.3835i	−0.113281	+	0.348644i	0.878303	+	0.478104i	$0.158676\pi$
$888$	−25.4457	−	4.94515i	−0.853902	−	0.165948i
$889$	−9.85805	+	7.16229i	−0.330628	+	0.240216i
$890$	−3.38293	−	0.576186i	−0.113396	−	0.0193138i
$891$	−21.1095	+	11.2955i	−0.707194	+	0.378412i
$892$	1.48246	−	4.22571i	0.0496366	−	0.141487i
$893$	−27.0328	−	37.2075i	−0.904620	−	1.24510i
$894$	0.198358	+	1.35406i	0.00663409	+	0.0452866i
$895$	−3.32045	−	1.07888i	−0.110990	−	0.0360630i
$896$	−11.5121	+	47.3624i	−0.384593	+	1.58227i
$897$	3.47927	−	4.78880i	0.116169	−	0.159893i
$898$	3.14180	−	5.99289i	0.104843	−	0.199985i
$899$	0.705180	+	2.17032i	0.0235191	+	0.0723843i
$900$	6.72087	−	2.01228i	0.224029	−	0.0670760i
$901$			39.4151i			1.31311i
$902$	−7.78789	+	0.0658985i	−0.259308	+	0.00219418i
$903$		−	100.569i		−	3.34672i
$904$	20.5553	−	2.52466i	0.683660	−	0.0839690i
$905$	4.57126	+	14.0689i	0.151954	+	0.467665i
$906$	−59.4709	−	31.1779i	−1.97579	−	1.03581i
$907$	−27.0714	+	37.2607i	−0.898893	+	1.23722i	0.0719272	+	0.997410i	$0.477085\pi$
$907$	−27.0714	+	37.2607i	−0.898893	+	1.23722i	−0.970820	+	0.239810i	$0.922915\pi$
$908$	−16.8537	−	24.3688i	−0.559310	−	0.808708i
$909$	7.93299	+	2.57759i	0.263121	+	0.0854931i
$910$	−10.4552	+	1.53160i	−0.346588	+	0.0507720i
$911$	1.71426	+	2.35947i	0.0567959	+	0.0781728i	0.836470	−	0.548012i	$-0.184615\pi$
$911$	1.71426	+	2.35947i	0.0567959	+	0.0781728i	−0.779674	+	0.626185i	$0.784615\pi$
$912$	−41.6584	+	52.0655i	−1.37945	+	1.72406i
$913$	4.24314	+	23.6993i	0.140428	+	0.784331i
$914$	−1.69811	+	9.97001i	−0.0561684	+	0.329779i
$915$	19.8920	−	14.4524i	0.657610	−	0.477782i
$916$	0.873983	−	37.5905i	0.0288772	−	1.24202i
$917$	12.4545	−	38.3309i	0.411282	−	1.26580i
$918$	6.60532	+	6.76068i	0.218008	+	0.223136i
$919$	−4.64650	−	3.37588i	−0.153274	−	0.111360i	0.508505	−	0.861059i	$-0.330198\pi$
$919$	−4.64650	−	3.37588i	−0.153274	−	0.111360i	−0.661779	+	0.749699i	$0.730198\pi$
$920$	−2.58084	−	2.76740i	−0.0850878	−	0.0912386i
$921$	24.4274	−	7.93693i	0.804909	−	0.261531i
$922$	12.8381	+	25.9371i	0.422800	+	0.854191i
$923$	3.88635			0.127921
$924$	11.1766	+	72.0398i	0.367684	+	2.36994i
$925$	−3.59254			−0.118122
$926$	18.9876	+	38.3611i	0.623972	+	1.26062i
$927$	−31.3430	+	10.1840i	−1.02944	+	0.334485i
$928$	−0.580919	−	1.32524i	−0.0190696	−	0.0435031i
$929$	−14.3351	−	10.4150i	−0.470319	−	0.341706i	0.327247	−	0.944939i	$-0.393879\pi$
$929$	−14.3351	−	10.4150i	−0.470319	−	0.341706i	−0.797565	+	0.603232i	$0.793879\pi$
$930$	22.4928	+	23.0219i	0.737569	+	0.754917i
$931$	−23.3439	+	71.8450i	−0.765064	+	2.35463i
$932$	40.7818	+	0.948183i	1.33585	+	0.0310588i
$933$	−14.6056	+	10.6116i	−0.478166	+	0.347408i
$934$	−10.0459	+	58.9820i	−0.328712	+	1.92995i
$935$	15.3986	+	7.46033i	0.503589	+	0.243979i
$936$	8.34181	−	15.0504i	0.272661	−	0.491937i
$937$	−17.9540	−	24.7116i	−0.586533	−	0.807293i	0.407860	−	0.913045i	$-0.366275\pi$
$937$	−17.9540	−	24.7116i	−0.586533	−	0.807293i	−0.994393	+	0.105752i	$0.966275\pi$
$938$	45.9273	−	6.72794i	1.49958	−	0.219675i
$939$	5.06547	+	1.64587i	0.165306	+	0.0537110i
$940$	11.5771	−	8.00683i	0.377603	−	0.261154i
$941$	−15.2197	+	20.9482i	−0.496149	+	0.682890i	−0.981507	−	0.191425i	$-0.938689\pi$
$941$	−15.2197	+	20.9482i	−0.496149	+	0.682890i	0.485358	+	0.874315i	$0.338689\pi$
$942$	50.4924	+	26.4708i	1.64513	+	0.862466i
$943$	0.686470	+	2.11274i	0.0223545	+	0.0688002i
$944$	−0.498952	+	10.7243i	−0.0162395	+	0.349046i
$945$			5.58115i			0.181555i
$946$	40.9305	+	12.9173i	1.33077	+	0.419977i
$947$		−	13.0064i		−	0.422652i	−0.977416	−	0.211326i	$-0.932222\pi$
$947$		−	13.0064i		−	0.422652i	0.977416	−	0.211326i	$-0.0677781\pi$
$948$	4.65149	+	15.5356i	0.151073	+	0.504574i
$949$	−3.44243	−	10.5947i	−0.111746	−	0.343919i
$950$	−4.29089	+	8.18475i	−0.139215	+	0.265548i
$951$	−30.7636	+	42.3424i	−0.997577	+	1.37305i
$952$	−56.9740	+	26.5700i	−1.84654	+	0.861139i
$953$	−24.8235	−	8.06563i	−0.804111	−	0.261271i	−0.122009	−	0.992529i	$-0.538934\pi$
$953$	−24.8235	−	8.06563i	−0.804111	−	0.261271i	−0.682101	+	0.731258i	$0.738934\pi$
$954$	−5.49346	−	37.5003i	−0.177857	−	1.21412i
$955$	14.1125	+	19.4242i	0.456670	+	0.628553i
$956$	34.3452	+	12.0490i	1.11080	+	0.389692i
$957$	−1.56075	−	1.49928i	−0.0504519	−	0.0484649i
$958$	13.4802	+	2.29597i	0.435525	+	0.0741793i
$959$	−17.4173	+	12.6544i	−0.562435	+	0.408633i
$960$	−15.6347	−	13.1171i	−0.504607	−	0.423351i
$961$	−15.0156	+	46.2132i	−0.484374	+	1.49075i
$962$	−6.30271	+	6.15787i	−0.203207	+	0.198538i
$963$	−41.2378	−	29.9610i	−1.32887	−	0.965480i
$964$	43.2016	+	32.9488i	1.39143	+	1.06121i
$965$	−24.5984	+	7.99249i	−0.791850	+	0.257288i
$966$	18.6362	−	9.22437i	0.599610	−	0.296789i
$967$	54.4136			1.74982			0.874912	−	0.484282i	$-0.160919\pi$
$967$	54.4136			1.74982			0.874912	+	0.484282i	$0.160919\pi$
$968$	−30.7550	−	4.70417i	−0.988504	−	0.151198i
$969$	−86.0017			−2.76277
$970$	−6.73621	+	3.33422i	−0.216287	+	0.107055i
$971$	34.0770	−	11.0723i	1.09358	−	0.355327i	0.293953	−	0.955820i	$-0.405029\pi$
$971$	34.0770	−	11.0723i	1.09358	−	0.355327i	0.799630	+	0.600493i	$0.205029\pi$
$972$	35.4655	+	27.0487i	1.13756	+	0.867586i
$973$	10.1556	+	7.37850i	0.325575	+	0.236544i
$974$	−7.36242	+	7.19323i	−0.235907	+	0.230486i
$975$	1.36721	−	4.20785i	0.0437859	−	0.134759i
$976$	−36.0732	−	13.6049i	−1.15468	−	0.435482i
$977$	32.1413	−	23.3520i	1.02829	−	0.747098i	0.0603259	−	0.998179i	$-0.480786\pi$
$977$	32.1413	−	23.3520i	1.02829	−	0.747098i	0.967966	+	0.251081i	$0.0807860\pi$
$978$	12.2233	+	2.08188i	0.390857	+	0.0665713i
$979$	5.80389	+	5.57531i	0.185493	+	0.178188i
$980$	−21.8171	−	7.65388i	−0.696922	−	0.244494i
$981$	7.69216	+	10.5873i	0.245592	+	0.338028i
$982$	0.139543	+	0.952569i	0.00445300	+	0.0303977i
$983$	34.8133	+	11.3115i	1.11037	+	0.360782i	0.806086	−	0.591799i	$-0.201582\pi$
$983$	34.8133	+	11.3115i	1.11037	+	0.360782i	0.304286	+	0.952581i	$0.401582\pi$
$984$	5.06373	+	10.8581i	0.161426	+	0.346145i
$985$	2.28550	−	3.14572i	0.0728221	−	0.100231i
$986$	0.866529	−	1.65288i	0.0275959	−	0.0526385i
$987$	23.9028	+	73.5651i	0.760833	+	2.34160i
$988$	6.50137	+	21.7141i	0.206836	+	0.690818i
$989$		−	12.2424i		−	0.389287i
$990$	−15.6903	−	4.95172i	−0.498672	−	0.157376i
$991$			28.5017i			0.905388i	0.891666	+	0.452694i	$0.149537\pi$
$991$			28.5017i			0.905388i	−0.891666	+	0.452694i	$0.850463\pi$
$992$	10.7766	−	49.3031i	0.342158	−	1.56537i
$993$	14.2402	+	43.8268i	0.451899	+	1.39080i
$994$	12.0917	+	6.33910i	0.383524	+	0.201064i
$995$	9.16810	−	12.6188i	0.290648	−	0.400043i
$996$	30.4616	−	21.0675i	0.965213	−	0.667551i
$997$	11.8947	+	3.86484i	0.376710	+	0.122401i	0.491251	−	0.871018i	$-0.336540\pi$
$997$	11.8947	+	3.86484i	0.376710	+	0.122401i	−0.114541	+	0.993419i	$0.536540\pi$
$998$	−21.9482	+	3.21522i	−0.694758	+	0.101776i
$999$	2.73559	+	3.76522i	0.0865503	+	0.119126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.c.151.2	yes	32
4.3	odd	2	inner	220.2.r.c.151.7	yes	32
11.7	odd	10	inner	220.2.r.c.51.7	yes	32
44.7	even	10	inner	220.2.r.c.51.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.c.51.2	✓	32	44.7	even	10	inner
220.2.r.c.51.7	yes	32	11.7	odd	10	inner
220.2.r.c.151.2	yes	32	1.1	even	1	trivial
220.2.r.c.151.7	yes	32	4.3	odd	2	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26745 + 0.627351i) q^{2} +(2.42619 - 0.788316i) q^{3} +(1.21286 - 1.59027i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-2.58052 + 2.52122i) q^{6} +(-1.33130 + 4.09732i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(2.83789 - 2.06185i) q^{9} +(-1.39414 - 0.237451i) q^{10} +(2.39183 + 2.29764i) q^{11} +(1.68899 - 4.81442i) q^{12} +(-1.01942 - 1.40312i) q^{13} +(-0.883099 - 6.02834i) q^{14} +(2.42619 + 0.788316i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(3.03242 - 4.17376i) q^{17} +(-2.30338 + 4.39364i) q^{18} +(-2.01930 - 6.21477i) q^{19} +(1.91596 - 0.573655i) q^{20} +10.9903i q^{21} +(-4.47295 - 1.41162i) q^{22} +1.33787i q^{23} +(0.879611 + 7.16163i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.17231 + 1.13884i) q^{26} +(0.761464 - 1.04807i) q^{27} +(4.90117 + 7.08661i) q^{28} +(-0.243271 - 0.0790436i) q^{29} +(-3.56962 + 0.522918i) q^{30} +(-5.24387 - 7.21757i) q^{31} +(3.76092 + 4.22558i) q^{32} +(7.61430 + 3.68897i) q^{33} +(-1.22503 + 7.19243i) q^{34} +(-3.48539 + 2.53228i) q^{35} +(0.163071 - 7.01375i) q^{36} +(-1.11016 + 3.41671i) q^{37} +(6.45820 + 6.61010i) q^{38} +(-3.57941 - 2.60059i) q^{39} +(-2.06851 + 1.92906i) q^{40} +(1.57918 - 0.513105i) q^{41} +(-6.89480 - 13.9297i) q^{42} -9.15066 q^{43} +(6.55483 - 1.01695i) q^{44} +3.50782 q^{45} +(-0.839316 - 1.69569i) q^{46} +(6.69361 - 2.17489i) q^{47} +(-5.60771 - 8.52518i) q^{48} +(-9.35254 - 6.79502i) q^{49} +(-0.988310 - 1.01156i) q^{50} +(4.06697 - 12.5168i) q^{51} +(-3.46776 - 0.0806258i) q^{52} +(-6.18088 + 4.49067i) q^{53} +(-0.307614 + 1.80608i) q^{54} +(0.584518 + 3.26471i) q^{55} +(-10.6578 - 5.90718i) q^{56} +(-9.79840 - 13.4863i) q^{57} +(0.357922 - 0.0524325i) q^{58} +(-2.55261 - 0.829393i) q^{59} +(4.19627 - 2.90218i) q^{60} +(5.66529 - 7.79760i) q^{61} +(11.1743 + 5.85816i) q^{62} +(4.66996 + 14.3727i) q^{63} +(-7.41770 - 2.99629i) q^{64} -1.73435i q^{65} +(-11.9650 + 0.101244i) q^{66} +7.61856i q^{67} +(-2.95952 - 9.88457i) q^{68} +(1.05467 + 3.24593i) q^{69} +(2.82893 - 5.39610i) q^{70} +(-1.31712 + 1.81286i) q^{71} +(4.19340 + 8.99189i) q^{72} +(6.10877 + 1.98486i) q^{73} +(-0.736407 - 5.02697i) q^{74} +(1.49947 + 2.06384i) q^{75} +(-12.3323 - 4.32642i) q^{76} +(-12.5984 + 6.74126i) q^{77} +(6.16821 + 1.05058i) q^{78} +(-2.57147 + 1.86828i) q^{79} +(1.41153 - 3.74267i) q^{80} +(-2.23068 + 6.86534i) q^{81} +(-1.67963 + 1.64103i) q^{82} +(5.87283 + 4.26686i) q^{83} +(17.4776 + 13.3298i) q^{84} +(4.90655 - 1.59424i) q^{85} +(11.5980 - 5.74067i) q^{86} -0.652533 q^{87} +(-7.66994 + 5.40111i) q^{88} +2.42654 q^{89} +(-4.44599 + 2.20064i) q^{90} +(7.10617 - 2.30893i) q^{91} +(2.12758 + 1.62266i) q^{92} +(-18.4123 - 13.3773i) q^{93} +(-7.11941 + 6.95581i) q^{94} +(2.01930 - 6.21477i) q^{95} +(12.4558 + 7.28724i) q^{96} +(4.29974 - 3.12394i) q^{97} +(16.1167 + 2.74503i) q^{98} +(11.5251 + 1.58884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) \) 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

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