LMFDB - Embedded newform 603.2.e.b.202.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(202,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("603.202");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			202.12
Character	$\chi$	$=$	603.202
Dual form			603.2.e.b.403.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.343920 - 0.595686i) q^{2} +(1.47268 + 0.911703i) q^{3} +(0.763439 - 1.32231i) q^{4} +(2.04306 - 3.53869i) q^{5} +(0.0366045 - 1.19081i) q^{6} +(-0.487864 - 0.845004i) q^{7} -2.42592 q^{8} +(1.33759 + 2.68530i) q^{9} +O(q^{10})$	\(q+(-0.343920 - 0.595686i) q^{2} +(1.47268 + 0.911703i) q^{3} +(0.763439 - 1.32231i) q^{4} +(2.04306 - 3.53869i) q^{5} +(0.0366045 - 1.19081i) q^{6} +(-0.487864 - 0.845004i) q^{7} -2.42592 q^{8} +(1.33759 + 2.68530i) q^{9} -2.81060 q^{10} +(0.759806 + 1.31602i) q^{11} +(2.32986 - 1.25132i) q^{12} +(0.554102 - 0.959733i) q^{13} +(-0.335572 + 0.581227i) q^{14} +(6.23502 - 3.34870i) q^{15} +(-0.692554 - 1.19954i) q^{16} -3.83614 q^{17} +(1.13957 - 1.72031i) q^{18} +5.87909 q^{19} +(-3.11951 - 5.40314i) q^{20} +(0.0519249 - 1.68921i) q^{21} +(0.522624 - 0.905212i) q^{22} +(-3.35976 + 5.81928i) q^{23} +(-3.57262 - 2.21172i) q^{24} +(-5.84821 - 10.1294i) q^{25} -0.762267 q^{26} +(-0.478346 + 5.17409i) q^{27} -1.48982 q^{28} +(0.607611 + 1.05241i) q^{29} +(-4.13912 - 2.56243i) q^{30} +(-5.08065 + 8.79994i) q^{31} +(-2.90229 + 5.02691i) q^{32} +(-0.0808685 + 2.63080i) q^{33} +(1.31932 + 2.28513i) q^{34} -3.98694 q^{35} +(4.57198 + 0.281343i) q^{36} +3.74762 q^{37} +(-2.02193 - 3.50209i) q^{38} +(1.69101 - 0.908207i) q^{39} +(-4.95632 + 8.58459i) q^{40} +(3.60470 - 6.24352i) q^{41} +(-1.02410 + 0.550022i) q^{42} +(4.25750 + 7.37421i) q^{43} +2.32026 q^{44} +(12.2352 + 0.752912i) q^{45} +4.62196 q^{46} +(-6.24583 - 10.8181i) q^{47} +(0.0737107 - 2.39794i) q^{48} +(3.02398 - 5.23768i) q^{49} +(-4.02263 + 6.96740i) q^{50} +(-5.64941 - 3.49742i) q^{51} +(-0.846046 - 1.46539i) q^{52} -6.52501 q^{53} +(3.24665 - 1.49453i) q^{54} +6.20932 q^{55} +(1.18352 + 2.04992i) q^{56} +(8.65803 + 5.35998i) q^{57} +(0.417938 - 0.723891i) q^{58} +(3.24516 - 5.62077i) q^{59} +(0.332019 - 10.8012i) q^{60} +(4.52351 + 7.83495i) q^{61} +6.98934 q^{62} +(1.61653 - 2.44033i) q^{63} +1.22240 q^{64} +(-2.26413 - 3.92159i) q^{65} +(1.59495 - 0.856612i) q^{66} +(0.500000 - 0.866025i) q^{67} +(-2.92865 + 5.07258i) q^{68} +(-10.2533 + 5.50685i) q^{69} +(1.37119 + 2.37497i) q^{70} +1.69853 q^{71} +(-3.24490 - 6.51434i) q^{72} +15.2771 q^{73} +(-1.28888 - 2.23240i) q^{74} +(0.622444 - 20.2492i) q^{75} +(4.48832 - 7.77400i) q^{76} +(0.741363 - 1.28408i) q^{77} +(-1.12258 - 0.694961i) q^{78} +(0.727525 + 1.26011i) q^{79} -5.65973 q^{80} +(-5.42169 + 7.18368i) q^{81} -4.95890 q^{82} +(9.06855 + 15.7072i) q^{83} +(-2.19403 - 1.35827i) q^{84} +(-7.83747 + 13.5749i) q^{85} +(2.92848 - 5.07227i) q^{86} +(-0.0646699 + 2.10383i) q^{87} +(-1.84323 - 3.19257i) q^{88} -1.41450 q^{89} +(-3.75944 - 7.54730i) q^{90} -1.08131 q^{91} +(5.12995 + 8.88533i) q^{92} +(-15.5051 + 8.32749i) q^{93} +(-4.29613 + 7.44111i) q^{94} +(12.0113 - 20.8043i) q^{95} +(-8.85721 + 4.75703i) q^{96} +(-3.07152 - 5.32002i) q^{97} -4.16002 q^{98} +(-2.51761 + 3.80061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.343920	−	0.595686i	−0.243188	−	0.421214i	0.718433	−	0.695597i	$-0.244860\pi$
$2$	−0.343920	−	0.595686i	−0.243188	−	0.421214i	−0.961621	+	0.274383i	$0.911527\pi$
$3$	1.47268	+	0.911703i	0.850254	+	0.526372i
$3$	1.47268	+	0.911703i	0.850254	+	0.526372i
$4$	0.763439	−	1.32231i	0.381719	−	0.661157i
$5$	2.04306	−	3.53869i	0.913686	−	1.58255i	0.104871	−	0.994486i	$-0.466557\pi$
$5$	2.04306	−	3.53869i	0.913686	−	1.58255i	0.808814	−	0.588064i	$-0.200110\pi$
$6$	0.0366045	−	1.19081i	0.0149437	−	0.486146i
$7$	−0.487864	−	0.845004i	−0.184395	−	0.319382i	0.758977	−	0.651117i	$-0.225699\pi$
$7$	−0.487864	−	0.845004i	−0.184395	−	0.319382i	−0.943373	+	0.331735i	$0.892366\pi$
$8$	−2.42592			−0.857694
$9$	1.33759	+	2.68530i	0.445865	+	0.895100i
$10$	−2.81060			−0.888789
$11$	0.759806	+	1.31602i	0.229090	+	0.396796i	0.957539	−	0.288305i	$-0.0930916\pi$
$11$	0.759806	+	1.31602i	0.229090	+	0.396796i	−0.728449	+	0.685100i	$0.759758\pi$
$12$	2.32986	−	1.25132i	0.672573	−	0.361225i
$13$	0.554102	−	0.959733i	0.153680	−	0.266182i	−0.778897	−	0.627151i	$-0.784221\pi$
$13$	0.554102	−	0.959733i	0.153680	−	0.266182i	0.932578	+	0.360969i	$0.117554\pi$
$14$	−0.335572	+	0.581227i	−0.0896853	+	0.155340i
$15$	6.23502	−	3.34870i	1.60988	−	0.864631i
$16$	−0.692554	−	1.19954i	−0.173138	−	0.299885i
$17$	−3.83614			−0.930400			−0.465200	−	0.885206i	$-0.654018\pi$
$17$	−3.83614			−0.930400			−0.465200	+	0.885206i	$0.654018\pi$
$18$	1.13957	−	1.72031i	0.268600	−	0.405482i
$19$	5.87909			1.34875			0.674377	−	0.738387i	$-0.264412\pi$
$19$	5.87909			1.34875			0.674377	+	0.738387i	$0.264412\pi$
$20$	−3.11951	−	5.40314i	−0.697543	−	1.20818i
$21$	0.0519249	−	1.68921i	0.0113309	−	0.368616i
$22$	0.522624	−	0.905212i	0.111424	−	0.192992i
$23$	−3.35976	+	5.81928i	−0.700559	+	1.21340i	0.267711	+	0.963499i	$0.413733\pi$
$23$	−3.35976	+	5.81928i	−0.700559	+	1.21340i	−0.968270	+	0.249905i	$0.919601\pi$
$24$	−3.57262	−	2.21172i	−0.729258	−	0.451466i
$25$	−5.84821	−	10.1294i	−1.16964	−	2.02588i
$26$	−0.762267			−0.149493
$27$	−0.478346	+	5.17409i	−0.0920578	+	0.995754i
$28$	−1.48982			−0.281549
$29$	0.607611	+	1.05241i	0.112830	+	0.195428i	0.916910	−	0.399093i	$-0.130675\pi$
$29$	0.607611	+	1.05241i	0.112830	+	0.195428i	−0.804080	+	0.594521i	$0.797342\pi$
$30$	−4.13912	−	2.56243i	−0.755697	−	0.467834i
$31$	−5.08065	+	8.79994i	−0.912512	+	1.58052i	−0.102007	+	0.994784i	$0.532527\pi$
$31$	−5.08065	+	8.79994i	−0.912512	+	1.58052i	−0.810504	+	0.585733i	$0.800807\pi$
$32$	−2.90229	+	5.02691i	−0.513057	+	0.888641i
$33$	−0.0808685	+	2.63080i	−0.0140774	+	0.457964i
$34$	1.31932	+	2.28513i	0.226262	+	0.391897i
$35$	−3.98694			−0.673916
$36$	4.57198	+	0.281343i	0.761997	+	0.0468906i
$37$	3.74762			0.616104			0.308052	−	0.951369i	$-0.400323\pi$
$37$	3.74762			0.616104			0.308052	+	0.951369i	$0.400323\pi$
$38$	−2.02193	−	3.50209i	−0.328001	−	0.568114i
$39$	1.69101	−	0.908207i	0.270778	−	0.145429i
$40$	−4.95632	+	8.58459i	−0.783662	+	1.35734i
$41$	3.60470	−	6.24352i	0.562959	−	0.975074i	−0.434277	−	0.900779i	$-0.642996\pi$
$41$	3.60470	−	6.24352i	0.562959	−	0.975074i	0.997236	−	0.0742945i	$-0.0236705\pi$
$42$	−1.02410	+	0.550022i	−0.158022	+	0.0848702i
$43$	4.25750	+	7.37421i	0.649263	+	1.12456i	0.983299	+	0.181996i	$0.0582558\pi$
$43$	4.25750	+	7.37421i	0.649263	+	1.12456i	−0.334036	+	0.942560i	$0.608411\pi$
$44$	2.32026			0.349792
$45$	12.2352	+	0.752912i	1.82392	+	0.112238i
$46$	4.62196			0.681470
$47$	−6.24583	−	10.8181i	−0.911048	−	1.57798i	−0.812587	−	0.582840i	$-0.801941\pi$
$47$	−6.24583	−	10.8181i	−0.911048	−	1.57798i	−0.0984613	−	0.995141i	$-0.531392\pi$
$48$	0.0737107	−	2.39794i	0.0106392	−	0.346113i
$49$	3.02398	−	5.23768i	0.431997	−	0.748241i
$50$	−4.02263	+	6.96740i	−0.568886	+	0.985339i
$51$	−5.64941	−	3.49742i	−0.791076	−	0.489737i
$52$	−0.846046	−	1.46539i	−0.117325	−	0.203214i
$53$	−6.52501			−0.896279			−0.448139	−	0.893964i	$-0.647913\pi$
$53$	−6.52501			−0.896279			−0.448139	+	0.893964i	$0.647913\pi$
$54$	3.24665	−	1.49453i	0.441813	−	0.203379i
$55$	6.20932			0.837265
$56$	1.18352	+	2.04992i	0.158155	+	0.273932i
$57$	8.65803	+	5.35998i	1.14678	+	0.709947i
$58$	0.417938	−	0.723891i	0.0548780	−	0.0950515i
$59$	3.24516	−	5.62077i	0.422483	−	0.731762i	−0.573698	−	0.819067i	$-0.694492\pi$
$59$	3.24516	−	5.62077i	0.422483	−	0.731762i	0.996182	+	0.0873042i	$0.0278252\pi$
$60$	0.332019	−	10.8012i	0.0428635	−	1.39443i
$61$	4.52351	+	7.83495i	0.579176	+	1.00316i	0.995574	+	0.0939797i	$0.0299589\pi$
$61$	4.52351	+	7.83495i	0.579176	+	1.00316i	−0.416398	+	0.909182i	$0.636708\pi$
$62$	6.98934			0.887647
$63$	1.61653	−	2.44033i	0.203663	−	0.307453i
$64$	1.22240			0.152800
$65$	−2.26413	−	3.92159i	−0.280831	−	0.486414i
$66$	1.59495	−	0.856612i	0.196324	−	0.105442i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$68$	−2.92865	+	5.07258i	−0.355151	+	0.615140i
$69$	−10.2533	+	5.50685i	−1.23436	+	0.662947i
$70$	1.37119	+	2.37497i	0.163888	+	0.283863i
$71$	1.69853			0.201578			0.100789	−	0.994908i	$-0.467863\pi$
$71$	1.69853			0.201578			0.100789	+	0.994908i	$0.467863\pi$
$72$	−3.24490	−	6.51434i	−0.382415	−	0.767722i
$73$	15.2771			1.78805			0.894024	−	0.448020i	$-0.147871\pi$
$73$	15.2771			1.78805			0.894024	+	0.448020i	$0.147871\pi$
$74$	−1.28888	−	2.23240i	−0.149829	−	0.259512i
$75$	0.622444	−	20.2492i	0.0718736	−	2.33818i
$76$	4.48832	−	7.77400i	0.514846	−	0.891739i
$77$	0.741363	−	1.28408i	0.0844862	−	0.146334i
$78$	−1.12258	−	0.694961i	−0.127107	−	0.0786889i
$79$	0.727525	+	1.26011i	0.0818529	+	0.141773i	0.904046	−	0.427435i	$-0.140583\pi$
$79$	0.727525	+	1.26011i	0.0818529	+	0.141773i	−0.822193	+	0.569209i	$0.807250\pi$
$80$	−5.65973			−0.632777
$81$	−5.42169	+	7.18368i	−0.602410	+	0.798187i
$82$	−4.95890			−0.547619
$83$	9.06855	+	15.7072i	0.995403	+	1.72409i	0.580648	+	0.814154i	$0.302799\pi$
$83$	9.06855	+	15.7072i	0.995403	+	1.72409i	0.414754	+	0.909934i	$0.363868\pi$
$84$	−2.19403	−	1.35827i	−0.239388	−	0.148199i
$85$	−7.83747	+	13.5749i	−0.850093	+	1.47240i
$86$	2.92848	−	5.07227i	0.315786	−	0.546957i
$87$	−0.0646699	+	2.10383i	−0.00693334	+	0.225554i
$88$	−1.84323	−	3.19257i	−0.196489	−	0.340329i
$89$	−1.41450			−0.149937			−0.0749685	−	0.997186i	$-0.523886\pi$
$89$	−1.41450			−0.149937			−0.0749685	+	0.997186i	$0.523886\pi$
$90$	−3.75944	−	7.54730i	−0.396280	−	0.795556i
$91$	−1.08131			−0.113352
$92$	5.12995	+	8.88533i	0.534834	+	0.926360i
$93$	−15.5051	+	8.32749i	−1.60781	+	0.863520i
$94$	−4.29613	+	7.44111i	−0.443112	+	0.767492i
$95$	12.0113	−	20.8043i	1.23234	−	2.13447i
$96$	−8.85721	+	4.75703i	−0.903985	+	0.485512i
$97$	−3.07152	−	5.32002i	−0.311865	−	0.540167i	0.666901	−	0.745146i	$-0.267620\pi$
$97$	−3.07152	−	5.32002i	−0.311865	−	0.540167i	−0.978766	+	0.204980i	$0.934287\pi$
$98$	−4.16002			−0.420226
$99$	−2.51761	+	3.80061i	−0.253029	+	0.381976i
$100$	−17.8590			−1.78590
$101$	−1.40455	−	2.43275i	−0.139758	−	0.242067i	0.787647	−	0.616127i	$-0.211299\pi$
$101$	−1.40455	−	2.43275i	−0.139758	−	0.242067i	−0.927405	+	0.374059i	$0.877966\pi$
$102$	−0.140420	+	4.56811i	−0.0139036	+	0.452310i
$103$	0.594452	−	1.02962i	0.0585731	−	0.101451i	−0.835252	−	0.549867i	$-0.814678\pi$
$103$	0.594452	−	1.02962i	0.0585731	−	0.101451i	0.893825	+	0.448416i	$0.148012\pi$
$104$	−1.34421	+	2.32824i	−0.131811	+	0.228303i
$105$	−5.87151	−	3.63491i	−0.573000	−	0.354731i
$106$	2.24408	+	3.88686i	0.217964	+	0.377525i
$107$	−5.61948			−0.543256			−0.271628	−	0.962402i	$-0.587562\pi$
$107$	−5.61948			−0.543256			−0.271628	+	0.962402i	$0.587562\pi$
$108$	6.47658	+	4.58262i	0.623209	+	0.440963i
$109$	−1.21036			−0.115932			−0.0579658	−	0.998319i	$-0.518461\pi$
$109$	−1.21036			−0.115932			−0.0579658	+	0.998319i	$0.518461\pi$
$110$	−2.13551	−	3.69881i	−0.203613	−	0.352668i
$111$	5.51905	+	3.41672i	0.523845	+	0.324300i
$112$	−0.675744	+	1.17042i	−0.0638518	+	0.110595i
$113$	−2.69808	+	4.67321i	−0.253814	+	0.439618i	−0.964573	−	0.263817i	$-0.915018\pi$
$113$	−2.69808	+	4.67321i	−0.253814	+	0.439618i	0.710759	+	0.703436i	$0.248352\pi$
$114$	0.215201	−	7.00088i	0.0201554	−	0.655692i
$115$	13.7284	+	23.7783i	1.28018	+	2.21734i
$116$	1.85549			0.172278
$117$	3.31834	+	0.204198i	0.306780	+	0.0188782i
$118$	−4.46429			−0.410971
$119$	1.87151	+	3.24155i	0.171561	+	0.297153i
$120$	−15.1257	+	8.12370i	−1.38078	+	0.741589i
$121$	4.34539	−	7.52644i	0.395035	−	0.684221i
$122$	3.11145	−	5.38918i	0.281697	−	0.487914i
$123$	11.0008	−	5.90831i	0.991910	−	0.532735i
$124$	7.75753	+	13.4364i	0.696647	+	1.20663i
$125$	−27.3624			−2.44737
$126$	−2.00963	−	0.123665i	−0.179032	−	0.0110170i
$127$	−12.0096			−1.06568			−0.532840	−	0.846216i	$-0.678875\pi$
$127$	−12.0096			−1.06568			−0.532840	+	0.846216i	$0.678875\pi$
$128$	5.38417	+	9.32566i	0.475898	+	0.824280i
$129$	−0.453139	+	14.7415i	−0.0398967	+	1.29791i
$130$	−1.55736	+	2.69742i	−0.136589	+	0.236580i
$131$	−5.71772	+	9.90338i	−0.499559	+	0.865262i	−1.00000		0.000508664i	$-0.999838\pi$
$131$	−5.71772	+	9.90338i	−0.499559	+	0.865262i	0.500440	+	0.865771i	$0.333171\pi$
$132$	3.41701	+	2.11539i	0.297412	+	0.184121i
$133$	−2.86819	−	4.96785i	−0.248704	−	0.430768i
$134$	−0.687839			−0.0594203
$135$	17.3322	+	12.2637i	1.49172	+	1.05549i
$136$	9.30618			0.797998
$137$	−5.17295	−	8.95982i	−0.441955	−	0.765489i	0.555879	−	0.831263i	$-0.312382\pi$
$137$	−5.17295	−	8.95982i	−0.441955	−	0.765489i	−0.997835	+	0.0657742i	$0.979048\pi$
$138$	6.80668	+	4.21385i	0.579423	+	0.358707i
$139$	9.75095	−	16.8891i	0.827065	−	1.43252i	−0.0732666	−	0.997312i	$-0.523342\pi$
$139$	9.75095	−	16.8891i	0.827065	−	1.43252i	0.900331	−	0.435205i	$-0.143324\pi$
$140$	−3.04379	+	5.27199i	−0.257247	+	0.445565i
$141$	0.664763	−	21.6260i	0.0559832	−	1.82124i
$142$	−0.584156	−	1.01179i	−0.0490213	−	0.0849074i
$143$	1.68404			0.140827
$144$	2.29477	−	3.46421i	0.191231	−	0.288684i
$145$	4.96555			0.412366
$146$	−5.25409	−	9.10035i	−0.434832	−	0.753150i
$147$	9.22858	−	4.95648i	0.761160	−	0.408804i
$148$	2.86108	−	4.95553i	0.235179	−	0.407342i
$149$	−7.98380	+	13.8284i	−0.654059	+	1.13286i	0.328070	+	0.944653i	$0.393602\pi$
$149$	−7.98380	+	13.8284i	−0.654059	+	1.13286i	−0.982129	+	0.188209i	$0.939732\pi$
$150$	−12.2763	+	6.59333i	−1.00235	+	0.538343i
$151$	−0.870568	−	1.50787i	−0.0708458	−	0.122709i	0.828426	−	0.560098i	$-0.189236\pi$
$151$	−0.870568	−	1.50787i	−0.0708458	−	0.122709i	−0.899272	+	0.437389i	$0.855903\pi$
$152$	−14.2622			−1.15682
$153$	−5.13119	−	10.3012i	−0.414832	−	0.832801i
$154$	−1.01988			−0.0821841
$155$	20.7602	+	35.9577i	1.66750	+	2.88819i
$156$	0.0900474	−	2.92941i	0.00720956	−	0.234540i
$157$	−6.22045	+	10.7741i	−0.496446	+	0.859870i	−0.999992	−	0.00409892i	$-0.998695\pi$
$157$	−6.22045	+	10.7741i	−0.496446	+	0.859870i	0.503546	+	0.863969i	$0.332029\pi$
$158$	0.500420	−	0.866753i	0.0398113	−	0.0689552i
$159$	−9.60927	−	5.94887i	−0.762065	−	0.471776i
$160$	11.8591	+	20.5406i	0.937546	+	1.62388i
$161$	6.55643			0.516719
$162$	6.14385	+	0.759014i	0.482706	+	0.0596338i
$163$	−5.50719			−0.431357			−0.215678	−	0.976464i	$-0.569196\pi$
$163$	−5.50719			−0.431357			−0.215678	+	0.976464i	$0.569196\pi$
$164$	−5.50393	−	9.53309i	−0.429785	−	0.744409i
$165$	9.14437	+	5.66106i	0.711888	+	0.440713i
$166$	6.23770	−	10.8040i	0.484140	−	0.838555i
$167$	2.78549	−	4.82461i	0.215548	−	0.373340i	−0.737894	−	0.674916i	$-0.764180\pi$
$167$	2.78549	−	4.82461i	0.215548	−	0.373340i	0.953442	+	0.301577i	$0.0975130\pi$
$168$	−0.125966	+	4.09790i	−0.00971847	+	0.316160i
$169$	5.88594	+	10.1947i	0.452765	+	0.784211i
$170$	10.7818			0.826929
$171$	7.86383	+	15.7871i	0.601362	+	1.20727i
$172$	13.0014			0.991345
$173$	−3.60210	−	6.23902i	−0.273862	−	0.474344i	0.695985	−	0.718056i	$-0.254968\pi$
$173$	−3.60210	−	6.23902i	−0.273862	−	0.474344i	−0.969847	+	0.243713i	$0.921635\pi$
$174$	1.27546	−	0.685026i	0.0966927	−	0.0519317i
$175$	−5.70626	+	9.88353i	−0.431353	+	0.747125i
$176$	1.05241	−	1.82283i	0.0793286	−	0.137401i
$177$	9.90356	−	5.31900i	0.744398	−	0.399801i
$178$	0.486475	+	0.842600i	0.0364629	+	0.0631555i
$179$	3.42978			0.256354			0.128177	−	0.991751i	$-0.459087\pi$
$179$	3.42978			0.256354			0.128177	+	0.991751i	$0.459087\pi$
$180$	10.3364	−	15.6040i	0.770432	−	1.16306i
$181$	−6.97181			−0.518211			−0.259105	−	0.965849i	$-0.583428\pi$
$181$	−6.97181			−0.518211			−0.259105	+	0.965849i	$0.583428\pi$
$182$	0.371882	+	0.644119i	0.0275657	+	0.0477453i
$183$	−0.481451	+	15.6625i	−0.0355899	+	1.15780i
$184$	8.15054	−	14.1171i	0.600865	−	1.04073i
$185$	7.65662	−	13.2617i	0.562926	−	0.975016i
$186$	10.2931	+	6.37221i	0.754726	+	0.467233i
$187$	−2.91472	−	5.04844i	−0.213145	−	0.369179i
$188$	−19.0732			−1.39106
$189$	4.60549	−	2.12004i	0.335000	−	0.154211i
$190$	−16.5237			−1.19876
$191$	5.82150	+	10.0831i	0.421229	+	0.729590i	0.996060	−	0.0886821i	$-0.0282655\pi$
$191$	5.82150	+	10.0831i	0.421229	+	0.729590i	−0.574831	+	0.818272i	$0.694932\pi$
$192$	1.80021	+	1.11447i	0.129919	+	0.0804299i
$193$	−11.4770	+	19.8788i	−0.826134	+	1.43091i	0.0749147	+	0.997190i	$0.476132\pi$
$193$	−11.4770	+	19.8788i	−0.826134	+	1.43091i	−0.901049	+	0.433717i	$0.857202\pi$
$194$	−2.11271	+	3.65932i	−0.151684	+	0.262724i
$195$	0.240979	−	7.83948i	0.0172568	−	0.561397i
$196$	−4.61724	−	7.99730i	−0.329803	−	0.571236i
$197$	−6.15333			−0.438407			−0.219203	−	0.975679i	$-0.570346\pi$
$197$	−6.15333			−0.438407			−0.219203	+	0.975679i	$0.570346\pi$
$198$	3.12983	+	0.192598i	0.222427	+	0.0136874i
$199$	−18.6665			−1.32323			−0.661616	−	0.749843i	$-0.730129\pi$
$199$	−18.6665			−1.32323			−0.661616	+	0.749843i	$0.730129\pi$
$200$	14.1873	+	24.5732i	1.00320	+	1.73759i
$201$	1.52590	−	0.819530i	0.107629	−	0.0578052i
$202$	−0.966103	+	1.67334i	−0.0679748	+	0.117736i
$203$	0.592862	−	1.02687i	0.0416108	−	0.0720720i
$204$	−8.93767	+	4.80024i	−0.625762	+	0.336084i
$205$	−14.7292	−	25.5118i	−1.02874	−	1.78182i
$206$	−0.817774			−0.0569770
$207$	−20.1205	−	1.23814i	−1.39847	−	0.0860570i
$208$	−1.53498			−0.106432
$209$	4.46696	+	7.73701i	0.308986	+	0.535180i
$210$	−0.145940	+	4.74769i	−0.0100708	+	0.327622i
$211$	−1.24853	+	2.16252i	−0.0859526	+	0.148874i	−0.905797	−	0.423712i	$-0.860727\pi$
$211$	−1.24853	+	2.16252i	−0.0859526	+	0.148874i	0.819844	+	0.572587i	$0.194060\pi$
$212$	−4.98144	+	8.62811i	−0.342127	+	0.592581i
$213$	2.50139	+	1.54855i	0.171392	+	0.106105i
$214$	1.93265	+	3.34745i	0.132113	+	0.228827i
$215$	34.7934			2.37289
$216$	1.16043	−	12.5519i	0.0789574	−	0.854052i
$217$	9.91465			0.673051
$218$	0.416267	+	0.720995i	0.0281932	+	0.0488320i
$219$	22.4983	+	13.9282i	1.52029	+	0.941178i
$220$	4.74044	−	8.21068i	0.319600	−	0.553564i
$221$	−2.12561	+	3.68167i	−0.142984	+	0.247656i
$222$	0.137179	−	4.46270i	0.00920688	−	0.299517i
$223$	−3.21882	−	5.57516i	−0.215548	−	0.373340i	0.737894	−	0.674917i	$-0.235821\pi$
$223$	−3.21882	−	5.57516i	−0.215548	−	0.373340i	−0.953442	+	0.301576i	$0.902487\pi$
$224$	5.66369			0.378421
$225$	19.3780	−	29.2532i	1.29186	−	1.95022i
$226$	3.71169			0.246898
$227$	−3.97320	−	6.88179i	−0.263711	−	0.456761i	0.703514	−	0.710681i	$-0.251613\pi$
$227$	−3.97320	−	6.88179i	−0.263711	−	0.456761i	−0.967225	+	0.253921i	$0.918280\pi$
$228$	13.6975	−	7.35662i	0.907136	−	0.487204i
$229$	2.36249	−	4.09196i	0.156118	−	0.270404i	−0.777348	−	0.629071i	$-0.783435\pi$
$229$	2.36249	−	4.09196i	0.156118	−	0.270404i	0.933466	+	0.358667i	$0.116769\pi$
$230$	9.44295	−	16.3557i	0.622649	−	1.07846i
$231$	2.26249	−	1.21514i	0.148861	−	0.0799502i
$232$	−1.47402	−	2.55307i	−0.0967740	−	0.167617i
$233$	−0.433895			−0.0284254			−0.0142127	−	0.999899i	$-0.504524\pi$
$233$	−0.433895			−0.0284254			−0.0142127	+	0.999899i	$0.504524\pi$
$234$	−1.01960	−	2.04692i	−0.0666535	−	0.133811i
$235$	−51.0425			−3.32965
$236$	−4.95495	−	8.58223i	−0.322540	−	0.558656i
$237$	−0.0774328	+	2.51903i	−0.00502980	+	0.163629i
$238$	1.28730	−	2.22967i	0.0834432	−	0.144528i
$239$	−11.1215	+	19.2631i	−0.719393	+	1.24602i	0.241848	+	0.970314i	$0.422246\pi$
$239$	−11.1215	+	19.2631i	−0.719393	+	1.24602i	−0.961241	+	0.275710i	$0.911087\pi$
$240$	−8.33498	−	5.15999i	−0.538021	−	0.333076i
$241$	3.47387	+	6.01692i	0.223772	+	0.387584i	0.955950	−	0.293529i	$-0.0948297\pi$
$241$	3.47387	+	6.01692i	0.223772	+	0.387584i	−0.732179	+	0.681113i	$0.761496\pi$
$242$	−5.97786			−0.384271
$243$	−14.5338	+	5.63632i	−0.932345	+	0.361570i
$244$	13.8137			0.884330
$245$	−12.3564	−	21.4018i	−0.789419	−	1.36731i
$246$	−7.30290	−	4.52105i	−0.465616	−	0.288252i
$247$	3.25762	−	5.64236i	0.207277	−	0.359014i
$248$	12.3253	−	21.3480i	0.782656	−	1.35560i
$249$	−0.965194	+	31.3995i	−0.0611667	+	1.98987i
$250$	9.41048	+	16.2994i	0.595171	+	1.03087i
$251$	15.1645			0.957176			0.478588	−	0.878039i	$-0.341149\pi$
$251$	15.1645			0.957176			0.478588	+	0.878039i	$0.341149\pi$
$252$	−1.99277	−	4.00060i	−0.125533	−	0.252014i
$253$	−10.2111			−0.641965
$254$	4.13034	+	7.15396i	0.259161	+	0.448879i
$255$	−23.9184	+	12.8461i	−1.49783	+	0.804452i
$256$	4.92585	−	8.53182i	0.307866	−	0.533239i
$257$	3.38448	−	5.86209i	0.211118	−	0.365667i	−0.740947	−	0.671564i	$-0.765623\pi$
$257$	3.38448	−	5.86209i	0.211118	−	0.365667i	0.952065	+	0.305897i	$0.0989562\pi$
$258$	8.93713	−	4.79995i	0.556401	−	0.298832i
$259$	−1.82833	−	3.16675i	−0.113607	−	0.196772i
$260$	−6.91410			−0.428794
$261$	−2.01331	+	3.03932i	−0.124621	+	0.188129i
$262$	7.86574			0.485947
$263$	1.56769	+	2.71531i	0.0966677	+	0.167433i	0.910303	−	0.413942i	$-0.135848\pi$
$263$	1.56769	+	2.71531i	0.0966677	+	0.167433i	−0.813636	+	0.581375i	$0.802515\pi$
$264$	0.196181	−	6.38213i	0.0120741	−	0.392793i
$265$	−13.3310	+	23.0900i	−0.818917	+	1.41841i
$266$	−1.97286	+	3.41709i	−0.120964	+	0.209515i
$267$	−2.08311	−	1.28961i	−0.127485	−	0.0789227i
$268$	−0.763439	−	1.32231i	−0.0466344	−	0.0807732i
$269$	−28.3023			−1.72562			−0.862810	−	0.505528i	$-0.831298\pi$
$269$	−28.3023			−1.72562			−0.862810	+	0.505528i	$0.831298\pi$
$270$	1.34444	−	14.5423i	0.0818200	−	0.885015i
$271$	11.8346			0.718898			0.359449	−	0.933165i	$-0.382965\pi$
$271$	11.8346			0.718898			0.359449	+	0.933165i	$0.382965\pi$
$272$	2.65673	+	4.60159i	0.161088	+	0.279013i
$273$	−1.59242	−	0.985830i	−0.0963777	−	0.0596651i
$274$	−3.55816	+	6.16291i	−0.214956	+	0.372315i
$275$	8.88701	−	15.3928i	0.535907	−	0.928218i
$276$	−0.545997	+	17.7623i	−0.0328651	+	1.06916i
$277$	−1.26755	−	2.19546i	−0.0761598	−	0.131913i	0.825430	−	0.564504i	$-0.190933\pi$
$277$	−1.26755	−	2.19546i	−0.0761598	−	0.131913i	−0.901590	+	0.432592i	$0.857599\pi$
$278$	−13.4142			−0.804528
$279$	−30.4263	−	1.87233i	−1.82158	−	0.112093i
$280$	9.67203			0.578014
$281$	1.77889	+	3.08113i	0.106120	+	0.183805i	0.914195	−	0.405274i	$-0.132824\pi$
$281$	1.77889	+	3.08113i	0.106120	+	0.183805i	−0.808075	+	0.589079i	$0.799491\pi$
$282$	−13.1109	+	7.04161i	−0.780744	+	0.419322i
$283$	1.95746	−	3.39043i	0.116359	−	0.201540i	−0.801963	−	0.597374i	$-0.796211\pi$
$283$	1.95746	−	3.39043i	0.116359	−	0.201540i	0.918322	+	0.395834i	$0.129544\pi$
$284$	1.29672	−	2.24598i	0.0769462	−	0.133275i
$285$	36.6562	−	19.6873i	2.17133	−	1.16618i
$286$	−0.579175	−	1.00316i	−0.0342473	−	0.0593181i
$287$	−7.03440			−0.415228
$288$	−17.3809	−	1.06956i	−1.02418	−	0.0630242i
$289$	−2.28406			−0.134357
$290$	−1.70775	−	2.95791i	−0.100282	−	0.173694i
$291$	0.326911	−	10.6350i	0.0191639	−	0.623436i
$292$	11.6631	−	20.2011i	0.682532	−	1.18218i
$293$	4.77554	−	8.27147i	0.278990	−	0.483225i	−0.692144	−	0.721759i	$-0.743334\pi$
$293$	4.77554	−	8.27147i	0.278990	−	0.483225i	0.971134	+	0.238535i	$0.0766671\pi$
$294$	−6.12640	−	3.79271i	−0.357299	−	0.221195i
$295$	−13.2601	−	22.9672i	−0.772034	−	1.33720i
$296$	−9.09144			−0.528429
$297$	−7.17267	+	3.30179i	−0.416200	+	0.191589i
$298$	10.9831			0.636237
$299$	3.72331	+	6.44896i	0.215324	+	0.372953i
$300$	−26.3007	−	16.2821i	−1.51847	−	0.940048i
$301$	4.15416	−	7.19522i	0.239442	−	0.414725i
$302$	−0.598811	+	1.03717i	−0.0344577	+	0.0596825i
$303$	0.149490	−	4.86320i	0.00858800	−	0.279383i
$304$	−4.07158	−	7.05219i	−0.233521	−	0.404471i
$305$	36.9672			2.11674
$306$	−4.37156	+	6.59936i	−0.249905	+	0.377260i
$307$	5.08306			0.290106			0.145053	−	0.989424i	$-0.453665\pi$
$307$	5.08306			0.290106			0.145053	+	0.989424i	$0.453665\pi$
$308$	−1.13197	−	1.96063i	−0.0645000	−	0.111717i
$309$	1.81415	−	0.974341i	0.103203	−	0.0554283i
$310$	14.2797	−	24.7331i	0.811030	−	1.40475i
$311$	15.2901	−	26.4833i	0.867023	−	1.50173i	0.00199871	−	0.999998i	$-0.499364\pi$
$311$	15.2901	−	26.4833i	0.867023	−	1.50173i	0.865024	−	0.501730i	$-0.167303\pi$
$312$	−4.10226	+	2.20324i	−0.232245	+	0.124734i
$313$	−7.79469	−	13.5008i	−0.440582	−	0.763111i	0.557151	−	0.830412i	$-0.311895\pi$
$313$	−7.79469	−	13.5008i	−0.440582	−	0.763111i	−0.997733	+	0.0673008i	$0.978561\pi$
$314$	8.55734			0.482919
$315$	−5.33291	−	10.7061i	−0.300475	−	0.603223i
$316$	2.22168			0.124979
$317$	−0.107469	−	0.186142i	−0.00603607	−	0.0104548i	0.862992	−	0.505218i	$-0.168588\pi$
$317$	−0.107469	−	0.186142i	−0.00603607	−	0.0104548i	−0.869028	+	0.494764i	$0.835255\pi$
$318$	−0.238844	+	7.77004i	−0.0133937	+	0.435722i
$319$	−0.923332	+	1.59926i	−0.0516967	+	0.0895413i
$320$	2.49745	−	4.32570i	0.139612	−	0.241814i
$321$	−8.27572	−	5.12330i	−0.461905	−	0.285955i
$322$	−2.25488	−	3.90557i	−0.125660	−	0.217649i
$323$	−22.5530			−1.25488
$324$	5.35996	+	12.6535i	0.297776	+	0.702971i
$325$	−12.9620			−0.719004
$326$	1.89403	+	3.28056i	0.104901	+	0.181693i
$327$	−1.78248	−	1.10349i	−0.0985713	−	0.0610231i
$328$	−8.74472	+	15.1463i	−0.482847	+	0.836315i
$329$	−6.09423	+	10.5555i	−0.335986	+	0.581944i
$330$	0.227289	−	7.39413i	0.0125118	−	0.407033i
$331$	−3.44101	−	5.96001i	−0.189135	−	0.327592i	0.755827	−	0.654771i	$-0.227235\pi$
$331$	−3.44101	−	5.96001i	−0.189135	−	0.327592i	−0.944962	+	0.327180i	$0.893902\pi$
$332$	27.6931			1.51986
$333$	5.01279	+	10.0635i	0.274699	+	0.551475i
$334$	−3.83194			−0.209674
$335$	−2.04306	−	3.53869i	−0.111624	−	0.193339i
$336$	−2.06223	+	1.10758i	−0.112504	+	0.0604237i
$337$	12.4919	−	21.6366i	0.680477	−	1.17862i	−0.294358	−	0.955695i	$-0.595106\pi$
$337$	12.4919	−	21.6366i	0.680477	−	1.17862i	0.974835	−	0.222926i	$-0.0715608\pi$
$338$	4.04858	−	7.01235i	0.220214	−	0.381422i
$339$	−8.23399	+	4.42231i	−0.447209	+	0.240187i
$340$	11.9668	+	20.7272i	0.648994	+	1.12409i
$341$	−15.4412			−0.836189
$342$	6.69965	−	10.1139i	0.362275	−	0.546896i
$343$	−12.7312			−0.687423
$344$	−10.3284	−	17.8893i	−0.556869	−	0.964525i
$345$	−1.46116	+	47.5342i	−0.0786662	+	2.55915i
$346$	−2.47766	+	4.29144i	−0.133200	+	0.230709i
$347$	12.3600	−	21.4082i	0.663522	−	1.14925i	−0.316162	−	0.948705i	$-0.602394\pi$
$347$	12.3600	−	21.4082i	0.663522	−	1.14925i	0.979684	−	0.200548i	$-0.0642723\pi$
$348$	2.73255	+	1.69166i	0.146480	+	0.0906825i
$349$	−0.0814865	−	0.141139i	−0.00436187	−	0.00755499i	0.863836	−	0.503773i	$-0.168055\pi$
$349$	−0.0814865	−	0.141139i	−0.00436187	−	0.00755499i	−0.868198	+	0.496218i	$0.834722\pi$
$350$	7.84998			0.419599
$351$	4.70069	+	3.32606i	0.250904	+	0.177532i
$352$	−8.82071			−0.470145
$353$	3.81666	+	6.61065i	0.203140	+	0.351849i	0.949539	−	0.313650i	$-0.101552\pi$
$353$	3.81666	+	6.61065i	0.203140	+	0.351849i	−0.746398	+	0.665500i	$0.768219\pi$
$354$	−6.57449	−	4.07011i	−0.349430	−	0.216324i
$355$	3.47019	−	6.01055i	0.184179	−	0.319007i
$356$	−1.07989	+	1.87042i	−0.0572338	+	0.0991319i
$357$	−0.199191	+	6.48004i	−0.0105423	+	0.342960i
$358$	−1.17957	−	2.04307i	−0.0623421	−	0.107980i
$359$	9.83641			0.519146			0.259573	−	0.965724i	$-0.416418\pi$
$359$	9.83641			0.519146			0.259573	+	0.965724i	$0.416418\pi$
$360$	−29.6818	−	1.82651i	−1.56437	−	0.0962654i
$361$	15.5637			0.819140
$362$	2.39774	+	4.15301i	0.126023	+	0.218277i
$363$	13.2613	−	7.12235i	0.696036	−	0.373827i
$364$	−0.825510	+	1.42983i	−0.0432685	+	0.0749432i
$365$	31.2120	−	54.0608i	1.63371	−	2.82967i
$366$	9.49551	−	5.09985i	0.496338	−	0.266573i
$367$	−4.01840	−	6.96007i	−0.209759	−	0.363312i	0.741880	−	0.670533i	$-0.233934\pi$
$367$	−4.01840	−	6.96007i	−0.209759	−	0.363312i	−0.951638	+	0.307220i	$0.900601\pi$
$368$	9.30727			0.485175
$369$	21.5873	+	1.32841i	1.12379	+	0.0691541i
$370$	−10.5330			−0.547587
$371$	3.18331	+	5.51366i	0.165269	+	0.286255i
$372$	−0.825658	+	26.8602i	−0.0428084	+	1.39264i
$373$	−7.44570	+	12.8963i	−0.385524	+	0.667747i	−0.991842	−	0.127475i	$-0.959313\pi$
$373$	−7.44570	+	12.8963i	−0.385524	+	0.667747i	0.606318	+	0.795222i	$0.292646\pi$
$374$	−2.00486	+	3.47252i	−0.103669	+	0.179560i
$375$	−40.2962	−	24.9464i	−2.08089	−	1.28823i
$376$	15.1519	+	26.2439i	0.781400	+	1.35342i
$377$	1.34671			0.0693593
$378$	−2.84680	−	2.01431i	−0.146424	−	0.103605i
$379$	15.2557			0.783631			0.391815	−	0.920044i	$-0.371847\pi$
$379$	15.2557			0.783631			0.391815	+	0.920044i	$0.371847\pi$
$380$	−18.3398	−	31.7655i	−0.940814	−	1.62954i
$381$	−17.6864	−	10.9492i	−0.906099	−	0.560945i
$382$	4.00426	−	6.93558i	0.204876	−	0.354855i
$383$	13.8950	−	24.0668i	0.710000	−	1.22976i	−0.254856	−	0.966979i	$-0.582028\pi$
$383$	13.8950	−	24.0668i	0.710000	−	1.22976i	0.964856	−	0.262777i	$-0.0846385\pi$
$384$	−0.573054	+	18.6425i	−0.0292436	+	0.951347i
$385$	−3.02930	−	5.24691i	−0.154388	−	0.267407i
$386$	15.7887			0.803624
$387$	−14.1072	+	21.2964i	−0.717108	+	1.08256i
$388$	−9.37966			−0.476180
$389$	14.0144	+	24.2737i	0.710560	+	1.23073i	0.964647	+	0.263545i	$0.0848917\pi$
$389$	14.0144	+	24.2737i	0.710560	+	1.23073i	−0.254087	+	0.967181i	$0.581775\pi$
$390$	−4.75275	+	2.55260i	−0.240665	+	0.129256i
$391$	12.8885	−	22.3236i	0.651800	−	1.12895i
$392$	−7.33594	+	12.7062i	−0.370521	+	0.641761i
$393$	−17.4493	+	9.37168i	−0.880203	+	0.472739i
$394$	2.11625	+	3.66545i	0.106615	+	0.184663i
$395$	5.94552			0.299151
$396$	3.10357	+	6.23060i	0.155960	+	0.313099i
$397$	−24.2751			−1.21833			−0.609167	−	0.793042i	$-0.708496\pi$
$397$	−24.2751			−1.21833			−0.609167	+	0.793042i	$0.708496\pi$
$398$	6.41977	+	11.1194i	0.321794	+	0.557364i
$399$	0.305271	−	9.93102i	0.0152827	−	0.497173i
$400$	−8.10041	+	14.0303i	−0.405020	+	0.701516i
$401$	12.8295	−	22.2213i	0.640672	−	1.10968i	−0.344611	−	0.938746i	$-0.611989\pi$
$401$	12.8295	−	22.2213i	0.640672	−	1.10968i	0.985283	−	0.170931i	$-0.0546776\pi$
$402$	−1.01297	−	0.627105i	−0.0505223	−	0.0312772i
$403$	5.63040	+	9.75214i	0.280470	+	0.485789i
$404$	−4.28914			−0.213393
$405$	14.3440	+	33.8624i	0.712758	+	1.68264i
$406$	−0.815588			−0.0404769
$407$	2.84746	+	4.93195i	0.141143	+	0.244468i
$408$	13.7051	+	8.48447i	0.678501	+	0.420044i
$409$	2.70178	−	4.67963i	0.133595	−	0.231393i	−0.791465	−	0.611214i	$-0.790681\pi$
$409$	2.70178	−	4.67963i	0.133595	−	0.231393i	0.925060	+	0.379822i	$0.124015\pi$
$410$	−10.1314	+	17.5480i	−0.500352	+	0.866635i
$411$	0.550574	−	17.9112i	0.0271578	−	0.883493i
$412$	−0.907654	−	1.57210i	−0.0447169	−	0.0774520i
$413$	−6.33277			−0.311615
$414$	6.18230	+	12.4113i	0.303843	+	0.609984i
$415$	74.1105			3.63794
$416$	3.21633	+	5.57085i	0.157694	+	0.273133i
$417$	29.7579	−	15.9824i	1.45725	−	0.782661i
$418$	3.07255	−	5.32182i	0.150284	−	0.260299i
$419$	−8.71869	+	15.1012i	−0.425936	+	0.737742i	−0.996507	−	0.0835056i	$-0.973388\pi$
$419$	−8.71869	+	15.1012i	−0.425936	+	0.737742i	0.570572	+	0.821248i	$0.306722\pi$
$420$	−9.28903	+	4.98895i	−0.453258	+	0.243436i
$421$	−8.08512	−	14.0038i	−0.394044	−	0.682505i	0.598934	−	0.800798i	$-0.295591\pi$
$421$	−8.08512	−	14.0038i	−0.394044	−	0.682505i	−0.992979	+	0.118293i	$0.962258\pi$
$422$	1.71758			0.0836105
$423$	20.6955	−	31.2422i	1.00625	−	1.51905i
$424$	15.8292			0.768733
$425$	22.4345	+	38.8578i	1.08823	+	1.88488i
$426$	0.0621736	−	2.02262i	0.00301232	−	0.0979963i
$427$	4.41371	−	7.64477i	0.213594	−	0.369956i
$428$	−4.29013	+	7.43072i	−0.207371	+	0.359177i
$429$	2.48006	+	1.53535i	0.119738	+	0.0741272i
$430$	−11.9661	−	20.7259i	−0.577058	−	0.999493i
$431$	−12.8859			−0.620691			−0.310345	−	0.950624i	$-0.600445\pi$
$431$	−12.8859			−0.620691			−0.310345	+	0.950624i	$0.600445\pi$
$432$	6.53780	−	3.00954i	0.314550	−	0.144797i
$433$	−26.7884			−1.28737			−0.643683	−	0.765292i	$-0.722594\pi$
$433$	−26.7884			−1.28737			−0.643683	+	0.765292i	$0.722594\pi$
$434$	−3.40984	−	5.90602i	−0.163678	−	0.283498i
$435$	7.31268	+	4.52711i	0.350616	+	0.217058i
$436$	−0.924036	+	1.60048i	−0.0442533	+	0.0766490i
$437$	−19.7523	+	34.2121i	−0.944883	+	1.63659i
$438$	0.559209	−	18.1921i	0.0267201	−	0.869252i
$439$	6.50831	+	11.2727i	0.310624	+	0.538017i	0.978498	−	0.206258i	$-0.0661285\pi$
$439$	6.50831	+	11.2727i	0.310624	+	0.538017i	−0.667873	+	0.744275i	$0.732795\pi$
$440$	−15.0634			−0.718117
$441$	18.1096	+	1.11440i	0.862363	+	0.0530667i
$442$	2.92416			0.139088
$443$	17.5338	+	30.3695i	0.833058	+	1.44290i	0.895602	+	0.444857i	$0.146746\pi$
$443$	17.5338	+	30.3695i	0.833058	+	1.44290i	−0.0625433	+	0.998042i	$0.519921\pi$
$444$	8.73143	−	4.68947i	0.414375	−	0.222552i
$445$	−2.88992	+	5.00548i	−0.136995	+	0.237283i
$446$	−2.21403	+	3.83482i	−0.104837	+	0.181584i
$447$	−24.3650	+	13.0859i	−1.15242	+	0.618943i
$448$	−0.596366	−	1.03294i	−0.0281756	−	0.0488016i
$449$	−21.7593			−1.02689			−0.513443	−	0.858124i	$-0.671630\pi$
$449$	−21.7593			−1.02689			−0.513443	+	0.858124i	$0.671630\pi$
$450$	−24.0902	−	1.48242i	−1.13562	−	0.0698822i
$451$	10.9555			0.515873
$452$	4.11963	+	7.13541i	0.193771	+	0.335621i
$453$	0.0926573	−	3.01431i	0.00435342	−	0.141625i
$454$	−2.73293	+	4.73357i	−0.128263	+	0.222157i
$455$	−2.20917	+	3.82640i	−0.103568	+	0.179385i
$456$	−21.0037	−	13.0029i	−0.983590	−	0.608917i
$457$	−11.8568	−	20.5365i	−0.554636	−	0.960658i	−0.997932	−	0.0642827i	$-0.979524\pi$
$457$	−11.8568	−	20.5365i	−0.554636	−	0.960658i	0.443295	−	0.896376i	$-0.353809\pi$
$458$	−3.25003			−0.151864
$459$	1.83500	−	19.8485i	0.0856505	−	0.926449i
$460$	41.9232			1.95468
$461$	7.80124	+	13.5121i	0.363340	+	0.629323i	0.988508	−	0.151167i	$-0.0483030\pi$
$461$	7.80124	+	13.5121i	0.363340	+	0.629323i	−0.625168	+	0.780490i	$0.714970\pi$
$462$	−1.50196	−	0.929826i	−0.0698773	−	0.0432594i
$463$	−12.0942	+	20.9477i	−0.562063	+	0.973522i	0.435253	+	0.900308i	$0.356659\pi$
$463$	−12.0942	+	20.9477i	−0.562063	+	0.973522i	−0.997316	+	0.0732137i	$0.976674\pi$
$464$	0.841606	−	1.45770i	0.0390706	−	0.0676722i
$465$	−2.20957	+	71.8814i	−0.102466	+	3.33342i
$466$	0.149225	+	0.258465i	0.00691272	+	0.0119732i
$467$	30.7023			1.42074			0.710368	−	0.703831i	$-0.248529\pi$
$467$	30.7023			1.42074			0.710368	+	0.703831i	$0.248529\pi$
$468$	2.80336	−	4.23199i	0.129585	−	0.195624i
$469$	−0.975727			−0.0450549
$470$	17.5545	+	30.4053i	0.809729	+	1.40249i
$471$	−18.9836	+	10.1957i	−0.874717	+	0.469792i
$472$	−7.87250	+	13.6356i	−0.362361	+	0.627628i
$473$	−6.46975	+	11.2059i	−0.297479	+	0.515249i
$474$	1.52718	−	0.820218i	0.0701458	−	0.0376739i
$475$	−34.3821	−	59.5516i	−1.57756	−	2.73242i
$476$	5.71513			0.261953
$477$	−8.72781	−	17.5216i	−0.399619	−	0.802259i
$478$	15.2997			0.699790
$479$	−7.91974	−	13.7174i	−0.361862	−	0.626764i	0.626405	−	0.779498i	$-0.284526\pi$
$479$	−7.91974	−	13.7174i	−0.361862	−	0.626764i	−0.988267	+	0.152734i	$0.951192\pi$
$480$	−1.26220	+	41.0618i	−0.0576115	+	1.87421i
$481$	2.07656	−	3.59671i	0.0946831	−	0.163996i
$482$	2.38946	−	4.13867i	0.108837	−	0.188511i
$483$	9.65554	+	5.97752i	0.439342	+	0.271986i
$484$	−6.63488	−	11.4919i	−0.301585	−	0.522361i
$485$	−25.1012			−1.13979
$486$	8.35595	+	6.71915i	0.379033	+	0.304787i
$487$	−31.2723			−1.41708			−0.708541	−	0.705670i	$-0.750646\pi$
$487$	−31.2723			−1.41708			−0.708541	+	0.705670i	$0.750646\pi$
$488$	−10.9737	−	19.0070i	−0.496756	−	0.860406i
$489$	−8.11035	−	5.02093i	−0.366763	−	0.227054i
$490$	−8.49919	+	14.7210i	−0.383954	+	0.665028i
$491$	−3.77834	+	6.54428i	−0.170514	+	0.295339i	−0.938600	−	0.345008i	$-0.887876\pi$
$491$	−3.77834	+	6.54428i	−0.170514	+	0.295339i	0.768086	+	0.640347i	$0.221210\pi$
$492$	0.585801	−	19.0572i	0.0264099	−	0.859164i
$493$	−2.33088	−	4.03720i	−0.104977	−	0.181826i
$494$	−4.48143			−0.201629
$495$	8.30555	+	16.6739i	0.373307	+	0.749436i
$496$	14.0745			0.631963
$497$	−0.828649	−	1.43526i	−0.0371700	−	0.0643803i
$498$	19.0362	−	10.2240i	0.853034	−	0.458147i
$499$	6.57203	−	11.3831i	0.294204	−	0.509577i	−0.680595	−	0.732660i	$-0.738279\pi$
$499$	6.57203	−	11.3831i	0.294204	−	0.509577i	0.974800	+	0.223083i	$0.0716120\pi$
$500$	−20.8895	+	36.1817i	−0.934209	+	1.61810i
$501$	8.50076	−	4.56558i	0.379786	−	0.203975i
$502$	−5.21538	−	9.03330i	−0.232774	−	0.403176i
$503$	−24.6747			−1.10019			−0.550094	−	0.835102i	$-0.685408\pi$
$503$	−24.6747			−1.10019			−0.550094	+	0.835102i	$0.685408\pi$
$504$	−3.92158	+	5.92006i	−0.174681	+	0.263701i
$505$	−11.4783			−0.510778
$506$	3.51179	+	6.08260i	0.156118	+	0.270404i
$507$	−0.626459	+	20.3799i	−0.0278220	+	0.905102i
$508$	−9.16860	+	15.8805i	−0.406791	+	0.704582i
$509$	0.879393	−	1.52315i	0.0389784	−	0.0675126i	−0.845878	−	0.533376i	$-0.820923\pi$
$509$	0.879393	−	1.52315i	0.0389784	−	0.0675126i	0.884856	+	0.465864i	$0.154256\pi$
$510$	15.8782	+	9.82984i	0.703100	+	0.435273i
$511$	−7.45313	−	12.9092i	−0.329707	−	0.571070i
$512$	14.7603			0.652320
$513$	−2.81224	+	30.4189i	−0.124163	+	1.34303i
$514$	−4.65596			−0.205365
$515$	−2.42900	−	4.20716i	−0.107035	−	0.185390i
$516$	19.1469	+	11.8534i	0.842895	+	0.521816i
$517$	9.49124	−	16.4393i	0.417424	−	0.723000i
$518$	−1.25759	+	2.17822i	−0.0552555	+	0.0957054i
$519$	0.383383	−	12.4721i	0.0168286	−	0.547466i
$520$	5.49261	+	9.51348i	0.240867	+	0.417194i
$521$	9.39213			0.411477			0.205738	−	0.978607i	$-0.434040\pi$
$521$	9.39213			0.411477			0.205738	+	0.978607i	$0.434040\pi$
$522$	2.50290	+	0.154019i	0.109549	+	0.00674124i
$523$	−30.6577			−1.34057			−0.670284	−	0.742104i	$-0.733828\pi$
$523$	−30.6577			−1.34057			−0.670284	+	0.742104i	$0.733828\pi$
$524$	8.73025	+	15.1212i	0.381383	+	0.660575i
$525$	−17.4144	+	9.35290i	−0.760025	+	0.408194i
$526$	1.07832	−	1.86770i	0.0470168	−	0.0814355i
$527$	19.4901	−	33.7578i	0.849000	−	1.47051i
$528$	3.21175	−	1.72497i	0.139774	−	0.0750696i
$529$	−11.0760	−	19.1843i	−0.481567	−	0.834098i
$530$	18.3392			0.796603
$531$	19.4342	+	1.19591i	0.843371	+	0.0518980i
$532$	−8.75875			−0.379740
$533$	−3.99474	−	6.91910i	−0.173031	−	0.299699i
$534$	−0.0517771	+	1.68440i	−0.00224061	+	0.0728913i
$535$	−11.4810	+	19.8856i	−0.496365	+	0.859729i
$536$	−1.21296	+	2.10091i	−0.0523920	+	0.0907456i
$537$	5.05098	+	3.12694i	0.217966	+	0.134937i
$538$	9.73371	+	16.8593i	0.419650	+	0.726855i
$539$	9.19055			0.395865
$540$	29.4485	−	13.5560i	1.26726	−	0.583358i
$541$	25.4809			1.09551			0.547755	−	0.836639i	$-0.315483\pi$
$541$	25.4809			1.09551			0.547755	+	0.836639i	$0.315483\pi$
$542$	−4.07014	−	7.04968i	−0.174827	−	0.302810i
$543$	−10.2673	−	6.35622i	−0.440611	−	0.272772i
$544$	11.1336	−	19.2839i	0.477348	−	0.826792i
$545$	−2.47284	+	4.28309i	−0.105925	+	0.183467i
$546$	−0.0395806	+	1.28763i	−0.00169389	+	0.0551054i
$547$	10.1531	+	17.5856i	0.434114	+	0.751907i	0.997223	−	0.0744755i	$-0.0237283\pi$
$547$	10.1531	+	17.5856i	0.434114	+	0.751907i	−0.563109	+	0.826383i	$0.690395\pi$
$548$	−15.7969			−0.674811
$549$	−14.9886	+	22.6270i	−0.639697	+	0.965695i
$550$	−12.2257			−0.521304
$551$	3.57220	+	6.18722i	0.152181	+	0.263585i
$552$	24.8738	−	13.3592i	1.05870	−	0.568606i
$553$	0.709866	−	1.22952i	0.0301866	−	0.0522847i
$554$	−0.871872	+	1.51013i	−0.0370423	+	0.0641591i
$555$	23.3665	−	12.5496i	0.991851	−	0.532703i
$556$	−14.8885	−	25.7876i	−0.631413	−	1.09364i
$557$	−29.0696			−1.23172			−0.615859	−	0.787857i	$-0.711191\pi$
$557$	−29.0696			−1.23172			−0.615859	+	0.787857i	$0.711191\pi$
$558$	9.34890	+	18.7685i	0.395770	+	0.794533i
$559$	9.43637			0.399116
$560$	2.76117	+	4.78249i	0.116681	+	0.202097i
$561$	0.310223	−	10.0921i	0.0130976	−	0.426089i
$562$	1.22359	−	2.11932i	0.0516141	−	0.0893983i
$563$	−1.61441	+	2.79624i	−0.0680394	+	0.117848i	−0.898038	−	0.439918i	$-0.855008\pi$
$563$	−1.61441	+	2.79624i	−0.0680394	+	0.117848i	0.829999	+	0.557765i	$0.188341\pi$
$564$	−28.0888	−	17.3891i	−1.18275	−	0.732214i
$565$	11.0247	+	19.0953i	0.463812	+	0.803346i
$566$	−2.69284			−0.113189
$567$	8.71529	+	1.07669i	0.366008	+	0.0452168i
$568$	−4.12049			−0.172892
$569$	−18.5551	−	32.1385i	−0.777872	−	1.34731i	−0.933166	−	0.359446i	$-0.882966\pi$
$569$	−18.5551	−	32.1385i	−0.777872	−	1.34731i	0.155294	−	0.987868i	$-0.450368\pi$
$570$	−24.3343	−	15.0648i	−1.01925	−	0.630993i
$571$	21.0988	−	36.5441i	0.882956	−	1.52932i	0.0349169	−	0.999390i	$-0.488883\pi$
$571$	21.0988	−	36.5441i	0.882956	−	1.52932i	0.848039	−	0.529934i	$-0.177783\pi$
$572$	1.28566	−	2.22683i	0.0537562	−	0.0931085i
$573$	−0.619601	+	20.1568i	−0.0258842	+	0.842060i
$574$	2.41927	+	4.19030i	0.100978	+	0.174900i
$575$	78.5945			3.27762
$576$	1.63508	+	3.28252i	0.0681283	+	0.136772i
$577$	−19.6471			−0.817918			−0.408959	−	0.912553i	$-0.634108\pi$
$577$	−19.6471			−0.817918			−0.408959	+	0.912553i	$0.634108\pi$
$578$	0.785533	+	1.36058i	0.0326739	+	0.0565928i
$579$	−35.0256	+	18.8115i	−1.45561	+	0.781780i
$580$	3.79089	−	6.56601i	0.157408	−	0.272639i
$581$	8.84843	−	15.3259i	0.367095	−	0.635827i
$582$	−6.44757	+	3.46286i	−0.267260	+	0.143540i
$583$	−4.95774	−	8.58705i	−0.205329	−	0.355639i
$584$	−37.0611			−1.53360
$585$	7.50217	−	11.3254i	0.310176	−	0.468246i
$586$	−6.56960			−0.271388
$587$	21.8107	+	37.7772i	0.900224	+	1.55923i	0.827203	+	0.561903i	$0.189931\pi$
$587$	21.8107	+	37.7772i	0.900224	+	1.55923i	0.0730205	+	0.997330i	$0.476736\pi$
$588$	0.491428	−	15.9870i	0.0202661	−	0.659295i
$589$	−29.8696	+	51.7356i	−1.23075	+	2.13173i
$590$	−9.12083	+	15.7977i	−0.375498	+	0.650382i
$591$	−9.06191	−	5.61001i	−0.372757	−	0.230765i
$592$	−2.59543	−	4.49541i	−0.106671	−	0.184760i
$593$	3.70008			0.151944			0.0759721	−	0.997110i	$-0.475794\pi$
$593$	3.70008			0.151944			0.0759721	+	0.997110i	$0.475794\pi$
$594$	4.43365	+	3.13711i	0.181915	+	0.128717i
$595$	15.2945			0.627012
$596$	12.1903	+	21.1142i	0.499333	+	0.864871i
$597$	−27.4898	−	17.0183i	−1.12508	−	0.696512i
$598$	2.56104	−	4.43585i	0.104729	−	0.181395i
$599$	5.94865	−	10.3034i	0.243055	−	0.420984i	−0.718528	−	0.695498i	$-0.755184\pi$
$599$	5.94865	−	10.3034i	0.243055	−	0.420984i	0.961583	+	0.274514i	$0.0885171\pi$
$600$	−1.51000	+	49.1231i	−0.0616456	+	2.00544i
$601$	−13.9489	−	24.1603i	−0.568989	−	0.985518i	−0.996666	−	0.0815864i	$-0.974001\pi$
$601$	−13.9489	−	24.1603i	−0.568989	−	0.985518i	0.427677	−	0.903932i	$-0.359332\pi$
$602$	−5.71479			−0.232917
$603$	2.99434	+	0.184261i	0.121939	+	0.00750367i
$604$	−2.65850			−0.108173
$605$	−17.7558	−	30.7540i	−0.721876	−	1.25033i
$606$	−2.94835	+	1.58350i	−0.119769	+	0.0643253i
$607$	4.69346	−	8.12930i	0.190502	−	0.329958i	−0.754915	−	0.655823i	$-0.772322\pi$
$607$	4.69346	−	8.12930i	0.190502	−	0.329958i	0.945417	+	0.325864i	$0.105655\pi$
$608$	−17.0628	+	29.5537i	−0.691989	+	1.19856i
$609$	1.80930	−	0.971736i	0.0733164	−	0.0393767i
$610$	−12.7138	−	22.0209i	−0.514765	−	0.891599i
$611$	−13.8433			−0.560041
$612$	−17.5387	−	1.07927i	−0.708962	−	0.0436270i
$613$	29.1482			1.17729			0.588643	−	0.808393i	$-0.299662\pi$
$613$	29.1482			1.17729			0.588643	+	0.808393i	$0.299662\pi$
$614$	−1.74817	−	3.02791i	−0.0705502	−	0.122197i
$615$	1.56768	−	50.9995i	0.0632150	−	2.05650i
$616$	−1.79849	+	3.11508i	−0.0724633	+	0.125510i
$617$	−10.5193	+	18.2200i	−0.423492	+	0.733510i	−0.996278	−	0.0861949i	$-0.972529\pi$
$617$	−10.5193	+	18.2200i	−0.423492	+	0.733510i	0.572786	+	0.819705i	$0.305863\pi$
$618$	−1.20432	−	0.745568i	−0.0484450	−	0.0299911i
$619$	−6.81483	−	11.8036i	−0.273911	−	0.474428i	0.695949	−	0.718091i	$-0.254984\pi$
$619$	−6.81483	−	11.8036i	−0.273911	−	0.474428i	−0.969860	+	0.243664i	$0.921651\pi$
$620$	63.3965			2.54606
$621$	−28.5023	−	20.1673i	−1.14376	−	0.809288i
$622$	−21.0343			−0.843398
$623$	0.690084	+	1.19526i	0.0276476	+	0.0478871i
$624$	−2.26054	−	1.39945i	−0.0904942	−	0.0560228i
$625$	−26.6621	+	46.1801i	−1.06648	+	1.84721i
$626$	−5.36150	+	9.28639i	−0.214289	+	0.371159i
$627$	−0.475433	+	15.4667i	−0.0189870	+	0.617681i
$628$	9.49786	+	16.4508i	0.379006	+	0.656458i
$629$	−14.3764			−0.573223
$630$	−4.54341	+	6.85880i	−0.181014	+	0.273261i
$631$	16.6505			0.662847			0.331424	−	0.943482i	$-0.392471\pi$
$631$	16.6505			0.662847			0.331424	+	0.943482i	$0.392471\pi$
$632$	−1.76492	−	3.05693i	−0.0702048	−	0.121598i
$633$	−3.81028	+	2.04642i	−0.151445	+	0.0813379i
$634$	−0.0739215	+	0.128036i	−0.00293580	+	0.00508495i
$635$	−24.5364	+	42.4983i	−0.973697	+	1.68649i
$636$	−15.2024	+	8.16488i	−0.602813	+	0.323758i
$637$	−3.35119	−	5.80443i	−0.132779	−	0.229980i
$638$	1.27021			0.0502880
$639$	2.27194	+	4.56105i	0.0898764	+	0.180432i
$640$	44.0008			1.73928
$641$	−23.8257	−	41.2673i	−0.941058	−	1.62996i	−0.763458	−	0.645858i	$-0.776500\pi$
$641$	−23.8257	−	41.2673i	−0.941058	−	1.62996i	−0.177601	−	0.984103i	$-0.556834\pi$
$642$	−0.205698	+	6.69174i	−0.00811825	+	0.264102i
$643$	1.43814	−	2.49093i	0.0567146	−	0.0982326i	−0.836274	−	0.548312i	$-0.815271\pi$
$643$	1.43814	−	2.49093i	0.0567146	−	0.0982326i	0.892989	+	0.450079i	$0.148604\pi$
$644$	5.00543	−	8.66966i	0.197242	−	0.341632i
$645$	51.2396	+	31.7212i	2.01756	+	1.24902i
$646$	7.75641	+	13.4345i	0.305172	+	0.528573i
$647$	−23.8907			−0.939239			−0.469619	−	0.882869i	$-0.655609\pi$
$647$	−23.8907			−0.939239			−0.469619	+	0.882869i	$0.655609\pi$
$648$	13.1526	−	17.4271i	0.516683	−	0.684600i
$649$	9.86275			0.387147
$650$	4.45790	+	7.72130i	0.174853	+	0.302854i
$651$	14.6011	+	9.03922i	0.572264	+	0.354275i
$652$	−4.20440	+	7.28224i	−0.164657	+	0.285195i
$653$	5.04219	−	8.73334i	0.197316	−	0.341762i	−0.750341	−	0.661051i	$-0.770111\pi$
$653$	5.04219	−	8.73334i	0.197316	−	0.341762i	0.947657	+	0.319289i	$0.103444\pi$
$654$	−0.0443046	+	1.44131i	−0.00173245	+	0.0563597i
$655$	23.3633	+	40.4665i	0.912880	+	1.58116i
$656$	−9.98579			−0.389880
$657$	20.4345	+	41.0236i	0.797227	+	1.60048i
$658$	8.38370			0.326830
$659$	−19.4265	−	33.6477i	−0.756749	−	1.31073i	−0.944500	−	0.328511i	$-0.893453\pi$
$659$	−19.4265	−	33.6477i	−0.756749	−	1.31073i	0.187752	−	0.982217i	$-0.439880\pi$
$660$	14.4669	−	7.76986i	0.563122	−	0.302441i
$661$	4.48048	−	7.76042i	0.174270	−	0.301845i	−0.765638	−	0.643272i	$-0.777577\pi$
$661$	4.48048	−	7.76042i	0.174270	−	0.301845i	0.939909	+	0.341426i	$0.110910\pi$
$662$	−2.36687	+	4.09953i	−0.0919908	+	0.159333i
$663$	−6.48694	+	3.48400i	−0.251932	+	0.135307i
$664$	−21.9996	−	38.1045i	−0.853751	−	1.47874i
$665$	−23.4396			−0.908948
$666$	4.27068	−	6.44708i	0.165486	−	0.249819i
$667$	−8.16571			−0.316178
$668$	−4.25310	−	7.36659i	−0.164557	−	0.285022i
$669$	0.342589	−	11.1451i	0.0132453	−	0.430893i
$670$	−1.40530	+	2.43405i	−0.0542914	+	0.0940355i
$671$	−6.87398	+	11.9061i	−0.265367	+	0.459629i
$672$	8.34082	+	5.16360i	0.321754	+	0.199190i
$673$	14.7663	+	25.5760i	0.569199	+	0.985882i	0.996645	+	0.0818409i	$0.0260799\pi$
$673$	14.7663	+	25.5760i	0.569199	+	0.985882i	−0.427446	+	0.904041i	$0.640587\pi$
$674$	−17.1848			−0.661935
$675$	55.2079	−	25.4138i	2.12495	−	0.978178i
$676$	17.9742			0.691316
$677$	22.8581	+	39.5913i	0.878507	+	1.52162i	0.852979	+	0.521945i	$0.174793\pi$
$677$	22.8581	+	39.5913i	0.878507	+	1.52162i	0.0255277	+	0.999674i	$0.491873\pi$
$678$	5.46614	+	3.38396i	0.209926	+	0.129960i
$679$	−2.99696	+	5.19089i	−0.115013	+	0.199208i
$680$	19.0131	−	32.9317i	0.729119	−	1.26287i
$681$	0.422881	−	13.7571i	0.0162048	−	0.527173i
$682$	5.31054	+	9.19813i	0.203351	+	0.352215i
$683$	−19.3226			−0.739358			−0.369679	−	0.929159i	$-0.620532\pi$
$683$	−19.3226			−0.739358			−0.369679	+	0.929159i	$0.620532\pi$
$684$	26.8791	+	1.65404i	1.02775	+	0.0632439i
$685$	−42.2747			−1.61523
$686$	4.37853	+	7.58383i	0.167173	+	0.289552i
$687$	7.20986	−	3.87227i	0.275073	−	0.147736i
$688$	5.89710	−	10.2141i	0.224825	−	0.389408i
$689$	−3.61552	+	6.26227i	−0.137740	+	0.238573i
$690$	28.8180	−	15.4776i	1.09708	−	0.589220i
$691$	17.4648	+	30.2499i	0.664391	+	1.15076i	0.979450	+	0.201687i	$0.0646423\pi$
$691$	17.4648	+	30.2499i	0.664391	+	1.15076i	−0.315059	+	0.949072i	$0.602024\pi$
$692$	−10.9999			−0.418154
$693$	4.43978	+	0.273208i	0.168653	+	0.0103783i
$694$	−17.0034			−0.645442
$695$	−39.8436	−	69.0111i	−1.51135	−	2.61774i
$696$	0.156884	−	5.10374i	0.00594669	−	0.193457i
$697$	−13.8281	+	23.9510i	−0.523777	+	0.907208i
$698$	−0.0560496	+	0.0970808i	−0.00212151	+	0.00367456i
$699$	−0.638990	−	0.395584i	−0.0241688	−	0.0149623i
$700$	8.71276	+	15.0909i	0.329311	+	0.570384i
$701$	25.3208			0.956352			0.478176	−	0.878264i	$-0.341298\pi$
$701$	25.3208			0.956352			0.478176	+	0.878264i	$0.341298\pi$
$702$	0.364628	−	3.94403i	0.0137620	−	0.148858i
$703$	22.0326			0.830974
$704$	0.928789	+	1.60871i	0.0350051	+	0.0606305i
$705$	−75.1694	−	46.5356i	−2.83104	−	1.75263i
$706$	2.62525	−	4.54706i	0.0988025	−	0.171131i
$707$	−1.37046	+	2.37370i	−0.0515413	+	0.0892721i
$708$	0.527371	−	17.1564i	0.0198198	−	0.644775i
$709$	−2.90272	−	5.02766i	−0.109014	−	0.188818i	0.806357	−	0.591429i	$-0.201436\pi$
$709$	−2.90272	−	5.02766i	−0.109014	−	0.188818i	−0.915371	+	0.402611i	$0.868103\pi$
$710$	−4.77387			−0.179160
$711$	−2.41064	+	3.63914i	−0.0904061	+	0.136478i
$712$	3.43148			0.128600
$713$	−34.1396	−	59.1315i	−1.27854	−	2.21449i
$714$	3.92858	−	2.10996i	0.147023	−	0.0789632i
$715$	3.44060	−	5.95930i	0.128671	−	0.222865i
$716$	2.61843	−	4.53525i	0.0978552	−	0.169490i
$717$	−33.9407	+	18.2289i	−1.26754	+	0.680769i
$718$	−3.38293	−	5.85941i	−0.126250	−	0.218671i
$719$	2.56813			0.0957751			0.0478876	−	0.998853i	$-0.484751\pi$
$719$	2.56813			0.0957751			0.0478876	+	0.998853i	$0.484751\pi$
$720$	−7.57041	−	15.1981i	−0.282133	−	0.566399i
$721$	−1.16004			−0.0432023
$722$	−5.35265	−	9.27106i	−0.199205	−	0.345033i
$723$	−0.369735	+	12.0282i	−0.0137506	+	0.447332i
$724$	−5.32255	+	9.21892i	−0.197811	+	0.342619i
$725$	7.10687	−	12.3095i	0.263943	−	0.457162i
$726$	−8.80350	−	5.45004i	−0.326728	−	0.202270i
$727$	−0.268767	−	0.465518i	−0.00996802	−	0.0172651i	0.860998	−	0.508608i	$-0.169840\pi$
$727$	−0.268767	−	0.465518i	−0.00996802	−	0.0172651i	−0.870966	+	0.491343i	$0.836506\pi$
$728$	2.62317			0.0972210
$729$	−26.5424	−	4.95001i	−0.983051	−	0.183334i
$730$	−42.9377			−1.58920
$731$	−16.3324	−	28.2885i	−0.604074	−	1.04629i
$732$	20.3432	+	12.5940i	0.751906	+	0.465487i
$733$	9.27231	−	16.0601i	0.342481	−	0.593194i	−0.642412	−	0.766359i	$-0.722066\pi$
$733$	9.27231	−	16.0601i	0.342481	−	0.593194i	0.984893	+	0.173166i	$0.0553996\pi$
$734$	−2.76401	+	4.78741i	−0.102021	+	0.176706i
$735$	1.31513	−	42.7835i	0.0485092	−	1.57809i
$736$	−19.5020	−	33.7785i	−0.718854	−	1.24509i
$737$	1.51961			0.0559756
$738$	−6.63300	−	13.3162i	−0.244164	−	0.490174i
$739$	−21.6665			−0.797014			−0.398507	−	0.917165i	$-0.630471\pi$
$739$	−21.6665			−0.797014			−0.398507	+	0.917165i	$0.630471\pi$
$740$	−11.6907	−	20.2489i	−0.429759	−	0.744365i
$741$	9.94159	−	5.33942i	0.365213	−	0.196149i
$742$	2.18961	−	3.79251i	0.0803830	−	0.139227i
$743$	13.3860	−	23.1853i	0.491086	−	0.850586i	−0.508861	−	0.860849i	$-0.669933\pi$
$743$	13.3860	−	23.1853i	0.491086	−	0.850586i	0.999947	+	0.0102625i	$0.00326670\pi$
$744$	37.6143	−	20.2019i	1.37901	−	0.740636i
$745$	32.6228	+	56.5044i	1.19521	+	2.07016i
$746$	10.2429			0.375019
$747$	−30.0485	+	45.3616i	−1.09942	+	1.65969i
$748$	−8.90083			−0.325447
$749$	2.74154	+	4.74849i	0.100174	+	0.173506i
$750$	−1.00159	+	32.5835i	−0.0365728	+	1.18978i
$751$	−19.0441	+	32.9854i	−0.694929	+	1.20365i	0.275275	+	0.961365i	$0.411231\pi$
$751$	−19.0441	+	32.9854i	−0.694929	+	1.20365i	−0.970205	+	0.242287i	$0.922102\pi$
$752$	−8.65115	+	14.9842i	−0.315475	+	0.546419i
$753$	22.3325	+	13.8256i	0.813843	+	0.503831i
$754$	−0.463161	−	0.802219i	−0.0168673	−	0.0292151i
$755$	−7.11450			−0.258923
$756$	0.712648	−	7.70844i	0.0259187	−	0.280353i
$757$	23.0086			0.836260			0.418130	−	0.908387i	$-0.362686\pi$
$757$	23.0086			0.836260			0.418130	+	0.908387i	$0.362686\pi$
$758$	−5.24672	−	9.08759i	−0.190570	−	0.330076i
$759$	−15.0377	−	9.30947i	−0.545833	−	0.337912i
$760$	−29.1386	+	50.4696i	−1.05697	+	1.83072i
$761$	−3.98727	+	6.90616i	−0.144539	+	0.250348i	−0.929201	−	0.369575i	$-0.879503\pi$
$761$	−3.98727	+	6.90616i	−0.144539	+	0.250348i	0.784662	+	0.619924i	$0.212836\pi$
$762$	−0.439605	+	14.3012i	−0.0159252	+	0.518077i
$763$	0.590491	+	1.02276i	0.0213772	+	0.0370264i
$764$	17.7774			0.643165
$765$	−46.9360	−	2.88827i	−1.69698	−	0.104426i
$766$	−19.1150			−0.690654
$767$	−3.59630	−	6.22897i	−0.129855	−	0.224915i
$768$	15.0327	−	8.07376i	0.542446	−	0.291337i
$769$	−20.2734	+	35.1146i	−0.731078	+	1.26626i	0.225345	+	0.974279i	$0.427649\pi$
$769$	−20.2734	+	35.1146i	−0.731078	+	1.26626i	−0.956423	+	0.291985i	$0.905684\pi$
$770$	−2.08367	+	3.60903i	−0.0750904	+	0.130060i
$771$	10.3288	−	5.54736i	0.371981	−	0.199783i
$772$	17.5240	+	30.3525i	0.630703	+	1.09241i
$773$	54.5788			1.96306			0.981531	−	0.191301i	$-0.0612706\pi$
$773$	54.5788			1.96306			0.981531	+	0.191301i	$0.0612706\pi$
$774$	17.5377	+	1.07921i	0.630379	+	0.0387913i
$775$	118.851			4.26925
$776$	7.45127	+	12.9060i	0.267485	+	0.463298i
$777$	0.194594	−	6.33052i	0.00698104	−	0.227106i
$778$	9.63968	−	16.6964i	0.345599	−	0.598596i
$779$	21.1923	−	36.7062i	0.759294	−	1.31514i
$780$	−10.1823	−	6.30361i	−0.364584	−	0.225705i
$781$	1.29055	+	2.23530i	0.0461795	+	0.0799852i
$782$	−17.7305			−0.634040
$783$	−5.73592	+	2.64041i	−0.204985	+	0.0943607i
$784$	−8.37707			−0.299181
$785$	25.4175	+	44.0245i	0.907191	+	1.57130i
$786$	11.5838	+	7.17123i	0.413179	+	0.255789i
$787$	−19.4359	+	33.6640i	−0.692816	+	1.19999i	0.278095	+	0.960553i	$0.410297\pi$
$787$	−19.4359	+	33.6640i	−0.692816	+	1.19999i	−0.970911	+	0.239439i	$0.923036\pi$
$788$	−4.69769	+	8.13663i	−0.167348	+	0.289856i
$789$	−0.166854	+	5.42806i	−0.00594015	+	0.193244i
$790$	−2.04478	−	3.54166i	−0.0727500	−	0.126007i
$791$	5.26517			0.187208
$792$	6.10752	−	9.22000i	0.217021	−	0.327618i
$793$	10.0259			0.356032
$794$	8.34869	+	14.4604i	0.296284	+	0.513179i
$795$	−40.6835	+	21.8503i	−1.44290	+	0.774950i
$796$	−14.2507	+	24.6830i	−0.505103	+	0.874864i
$797$	−1.83052	+	3.17056i	−0.0648404	+	0.112307i	−0.896623	−	0.442794i	$-0.853987\pi$
$797$	−1.83052	+	3.17056i	−0.0648404	+	0.112307i	0.831783	+	0.555101i	$0.187320\pi$
$798$	−6.02076	+	3.23363i	−0.213133	+	0.114469i
$799$	23.9599	+	41.4997i	0.847639	+	1.46815i
$800$	67.8928			2.40037
$801$	−1.89203	−	3.79837i	−0.0668516	−	0.134209i
$802$	−17.6492			−0.623215
$803$	11.6076	+	20.1050i	0.409624	+	0.709489i
$804$	0.0812552	−	2.64338i	0.00286565	−	0.0932248i
$805$	13.3952	−	23.2012i	0.472118	−	0.817733i
$806$	3.87281	−	6.70790i	0.136414	−	0.236276i
$807$	−41.6803	−	25.8033i	−1.46722	−	0.908319i
$808$	3.40733	+	5.90166i	0.119869	+	0.207620i
$809$	32.3549			1.13754			0.568769	−	0.822498i	$-0.307420\pi$
$809$	32.3549			1.13754			0.568769	+	0.822498i	$0.307420\pi$
$810$	15.2382	−	20.1904i	0.535415	−	0.709420i
$811$	−45.0903			−1.58333			−0.791667	−	0.610953i	$-0.790786\pi$
$811$	−45.0903			−1.58333			−0.791667	+	0.610953i	$0.790786\pi$
$812$	−0.905228	−	1.56790i	−0.0317673	−	0.0550225i
$813$	17.4286	+	10.7896i	0.611246	+	0.378408i
$814$	1.95860	−	3.39239i	0.0686487	−	0.118903i
$815$	−11.2515	+	19.4882i	−0.394124	+	0.682643i
$816$	−0.282764	+	9.19884i	−0.00989873	+	0.322024i
$817$	25.0302	+	43.3536i	0.875697	+	1.51675i
$818$	−3.71679			−0.129954
$819$	−1.44635	−	2.90363i	−0.0505395	−	0.101461i
$820$	−44.9795			−1.57075
$821$	10.5954	+	18.3517i	0.369781	+	0.640479i	0.989531	−	0.144320i	$-0.0460994\pi$
$821$	10.5954	+	18.3517i	0.369781	+	0.640479i	−0.619750	+	0.784799i	$0.712766\pi$
$822$	−10.8588	+	5.83203i	−0.378744	+	0.203416i
$823$	12.6137	−	21.8476i	0.439686	−	0.761558i	−0.557979	−	0.829855i	$-0.688423\pi$
$823$	12.6137	−	21.8476i	0.439686	−	0.761558i	0.997665	+	0.0682965i	$0.0217564\pi$
$824$	−1.44209	+	2.49778i	−0.0502377	+	0.0870143i
$825$	27.1214	−	14.5663i	0.944245	−	0.507135i
$826$	2.17796	+	3.77235i	0.0757811	+	0.131257i
$827$	−4.51706			−0.157074			−0.0785368	−	0.996911i	$-0.525025\pi$
$827$	−4.51706			−0.157074			−0.0785368	+	0.996911i	$0.525025\pi$
$828$	−16.9980	+	25.6604i	−0.590721	+	0.891761i
$829$	5.04001			0.175047			0.0875234	−	0.996162i	$-0.472105\pi$
$829$	5.04001			0.175047			0.0875234	+	0.996162i	$0.472105\pi$
$830$	−25.4880	−	44.1466i	−0.884703	−	1.53235i
$831$	0.134909	−	4.38885i	0.00467996	−	0.152248i
$832$	0.677336	−	1.17318i	0.0234824	−	0.0406727i
$833$	−11.6004	+	20.0925i	−0.401930	+	0.696163i
$834$	−19.7548	−	12.2297i	−0.684054	−	0.423481i
$835$	−11.3819	−	19.7140i	−0.393886	−	0.682230i
$836$	13.6410			0.471784
$837$	−43.1014	−	30.4971i	−1.48980	−	1.05414i
$838$	11.9941			0.414330
$839$	−6.59765	−	11.4275i	−0.227776	−	0.394520i	0.729373	−	0.684117i	$-0.239812\pi$
$839$	−6.59765	−	11.4275i	−0.227776	−	0.394520i	−0.957149	+	0.289597i	$0.906479\pi$
$840$	14.2438	+	8.81802i	0.491459	+	0.304251i
$841$	13.7616	−	23.8358i	0.474539	−	0.821925i
$842$	−5.56126	+	9.63239i	−0.191654	+	0.331954i
$843$	−0.189333	+	6.15936i	−0.00652098	+	0.212139i
$844$	1.90636	+	3.30191i	0.0656195	+	0.113656i
$845$	48.1014			1.65474
$846$	−25.7281	−	1.58321i	−0.884550	−	0.0544320i
$847$	−8.47983			−0.291370
$848$	4.51892	+	7.82700i	0.155180	+	0.268780i
$849$	5.97379	−	3.20840i	0.205020	−	0.110112i
$850$	15.4314	−	26.7279i	0.529291	−	0.916759i
$851$	−12.5911	+	21.8084i	−0.431618	+	0.747584i
$852$	3.95733	−	2.12540i	0.135576	−	0.0728150i
$853$	20.7840	+	35.9989i	0.711630	+	1.23258i	0.964245	+	0.265013i	$0.0853761\pi$
$853$	20.7840	+	35.9989i	0.711630	+	1.23258i	−0.252615	+	0.967567i	$0.581291\pi$
$854$	−6.07185			−0.207774
$855$	71.9320	+	4.42644i	2.46002	+	0.151381i
$856$	13.6324			0.465947
$857$	−8.37675	−	14.5090i	−0.286144	−	0.495616i	0.686742	−	0.726901i	$-0.259040\pi$
$857$	−8.37675	−	14.5090i	−0.286144	−	0.495616i	−0.972886	+	0.231285i	$0.925707\pi$
$858$	0.0616434	−	2.00537i	0.00210447	−	0.0684623i
$859$	27.9748	−	48.4538i	0.954488	−	1.65322i	0.218952	−	0.975736i	$-0.429736\pi$
$859$	27.9748	−	48.4538i	0.954488	−	1.65322i	0.735536	−	0.677486i	$-0.236930\pi$
$860$	26.5626	−	46.0078i	0.905777	−	1.56885i
$861$	−10.3594	−	6.41329i	−0.353049	−	0.218564i
$862$	4.43171	+	7.67594i	0.150945	+	0.261444i
$863$	−2.66594			−0.0907496			−0.0453748	−	0.998970i	$-0.514448\pi$
$863$	−2.66594			−0.0907496			−0.0453748	+	0.998970i	$0.514448\pi$
$864$	−24.6214	−	17.4213i	−0.837637	−	0.592685i
$865$	−29.4373			−1.00090
$866$	9.21304	+	15.9575i	0.313072	+	0.542256i
$867$	−3.36370	−	2.08239i	−0.114237	−	0.0707215i
$868$	7.56923	−	13.1103i	0.256916	−	0.444992i
$869$	−1.10556	+	1.91488i	−0.0375034	+	0.0649578i
$870$	0.181761	−	5.91302i	0.00616228	−	0.200470i
$871$	−0.554102	−	0.959733i	−0.0187750	−	0.0325193i
$872$	2.93624			0.0994338
$873$	10.1774	−	15.3640i	0.344454	−	0.519992i
$874$	27.1729			0.919136
$875$	13.3491	+	23.1214i	0.451283	+	0.781645i
$876$	35.5935	−	19.1165i	1.20259	−	0.645888i
$877$	−22.9943	+	39.8272i	−0.776461	+	1.34487i	0.157508	+	0.987518i	$0.449654\pi$
$877$	−22.9943	+	39.8272i	−0.776461	+	1.34487i	−0.933970	+	0.357353i	$0.883679\pi$
$878$	4.47667	−	7.75382i	0.151080	−	0.261679i
$879$	14.5740	−	7.82739i	0.491568	−	0.264011i
$880$	−4.30029	−	7.44832i	−0.144963	−	0.251083i
$881$	−36.4081			−1.22662			−0.613309	−	0.789843i	$-0.710162\pi$
$881$	−36.4081			−1.22662			−0.613309	+	0.789843i	$0.710162\pi$
$882$	−5.56442	−	11.1709i	−0.187364	−	0.376144i
$883$	−52.5568			−1.76868			−0.884338	−	0.466846i	$-0.845390\pi$
$883$	−52.5568			−1.76868			−0.884338	+	0.466846i	$0.845390\pi$
$884$	3.24555	+	5.62145i	0.109160	+	0.189070i
$885$	1.41132	−	45.9127i	0.0474409	−	1.54334i
$886$	12.0605	−	20.8893i	0.405179	−	0.701791i
$887$	11.7882	−	20.4178i	0.395809	−	0.685562i	−0.597395	−	0.801947i	$-0.703797\pi$
$887$	11.7882	−	20.4178i	0.395809	−	0.685562i	0.993204	+	0.116386i	$0.0371308\pi$
$888$	−13.3888	−	8.28869i	−0.449299	−	0.278150i
$889$	5.85905	+	10.1482i	0.196506	+	0.340359i
$890$	3.97560			0.133262
$891$	−13.5733	−	1.67686i	−0.454723	−	0.0561768i
$892$	−9.82949			−0.329116
$893$	−36.7198	−	63.6005i	−1.22878	−	2.12831i
$894$	16.1747	+	10.0134i	0.540963	+	0.334897i
$895$	7.00725	−	12.1369i	0.234227	−	0.405693i
$896$	5.25348	−	9.09930i	0.175507	−	0.303986i
$897$	−0.396283	+	12.8918i	−0.0132315	+	0.430445i
$898$	7.48346	+	12.9617i	0.249726	+	0.432539i
$899$	−12.3482			−0.411836
$900$	−23.8881	−	47.9568i	−0.796270	−	1.59856i
$901$	25.0308			0.833897
$902$	−3.76780	−	6.52603i	−0.125454	−	0.217293i
$903$	12.6777	−	6.80891i	0.421886	−	0.226586i
$904$	6.54533	−	11.3368i	0.217694	−	0.377058i
$905$	−14.2438	+	24.6711i	−0.473481	+	0.820094i
$906$	−1.82745	+	0.981487i	−0.0607130	+	0.0326077i
$907$	−27.9777	−	48.4589i	−0.928986	−	1.60905i	−0.785022	−	0.619468i	$-0.787349\pi$
$907$	−27.9777	−	48.4589i	−0.928986	−	1.60905i	−0.143964	−	0.989583i	$-0.545985\pi$
$908$	−12.1332			−0.402654
$909$	4.65395	−	7.02566i	0.154362	−	0.233026i
$910$	3.03911			0.100746
$911$	2.80213	+	4.85343i	0.0928387	+	0.160801i	0.908705	−	0.417440i	$-0.137073\pi$
$911$	2.80213	+	4.85343i	0.0928387	+	0.160801i	−0.815866	+	0.578241i	$0.803739\pi$
$912$	0.433352	−	14.0977i	0.0143497	−	0.466822i
$913$	−13.7807	+	23.8688i	−0.456074	+	0.789943i
$914$	−8.15555	+	14.1258i	−0.269762	+	0.467241i
$915$	54.4411	+	33.7032i	1.79977	+	1.11419i
$916$	−3.60724	−	6.24792i	−0.119186	−	0.206437i
$917$	11.1579			0.368465
$918$	−12.4546	+	5.73321i	−0.411062	+	0.189224i
$919$	48.5628			1.60194			0.800969	−	0.598705i	$-0.204318\pi$
$919$	48.5628			1.60194			0.800969	+	0.598705i	$0.204318\pi$
$920$	−33.3041	−	57.6844i	−1.09800	−	1.90180i
$921$	7.48574	+	4.63425i	0.246664	+	0.152704i
$922$	5.36600	−	9.29419i	0.176720	−	0.306088i
$923$	0.941157	−	1.63013i	0.0309786	−	0.0536564i
$924$	0.120479	−	3.91941i	0.00396347	−	0.128939i
$925$	−21.9169	−	37.9611i	−0.720622	−	1.24815i
$926$	16.6377			0.546748
$927$	3.55998	+	0.219068i	0.116925	+	0.00719514i
$928$	−7.05385			−0.231554
$929$	−8.30302	−	14.3813i	−0.272413	−	0.471834i	0.697066	−	0.717007i	$-0.254488\pi$
$929$	−8.30302	−	14.3813i	−0.272413	−	0.471834i	−0.969479	+	0.245173i	$0.921155\pi$
$930$	43.5787	−	23.4052i	1.42900	−	0.767487i
$931$	17.7782	−	30.7928i	0.582658	−	1.00919i
$932$	−0.331252	+	0.573746i	−0.0108505	+	0.0187937i
$933$	46.6624	−	25.0614i	1.52766	−	0.820474i
$934$	−10.5591	−	18.2890i	−0.345506	−	0.598433i
$935$	−23.8198			−0.778991
$936$	−8.05004	−	0.495370i	−0.263124	−	0.0161917i
$937$	15.8645			0.518270			0.259135	−	0.965841i	$-0.416563\pi$
$937$	15.8645			0.518270			0.259135	+	0.965841i	$0.416563\pi$
$938$	0.335572	+	0.581227i	0.0109568	+	0.0189777i
$939$	0.829614	−	26.9889i	0.0270734	−	0.880748i
$940$	−38.9678	+	67.4942i	−1.27099	+	2.20142i
$941$	6.07930	−	10.5296i	0.198179	−	0.343257i	−0.749759	−	0.661711i	$-0.769830\pi$
$941$	6.07930	−	10.5296i	0.198179	−	0.343257i	0.947938	+	0.318455i	$0.103164\pi$
$942$	12.6023	+	7.80176i	0.410604	+	0.254195i
$943$	24.2219	+	41.9535i	0.788773	+	1.36619i
$944$	−8.98978			−0.292592
$945$	1.90714	−	20.6288i	0.0620393	−	0.671055i
$946$	8.90030			0.289374
$947$	−15.3955	−	26.6658i	−0.500286	−	0.866521i	−1.00000		0.000330369i	$-0.999895\pi$
$947$	−15.3955	−	26.6658i	−0.500286	−	0.866521i	0.499714	−	0.866191i	$-0.333438\pi$
$948$	3.27183	+	2.02552i	0.106264	+	0.0657857i
$949$	8.46507	−	14.6619i	0.274788	−	0.475946i
$950$	−23.6494	+	40.9619i	−0.767288	+	1.32898i
$951$	0.0114383	−	0.372108i	0.000370912	−	0.0120664i
$952$	−4.54014	−	7.86376i	−0.147147	−	0.254866i
$953$	34.3628			1.11312			0.556560	−	0.830807i	$-0.312121\pi$
$953$	34.3628			1.11312			0.556560	+	0.830807i	$0.312121\pi$
$954$	−7.43572	+	11.2251i	−0.240740	+	0.363425i
$955$	47.5748			1.53948
$956$	16.9812	+	29.4123i	0.549212	+	0.951263i
$957$	−2.81783	+	1.51340i	−0.0910874	+	0.0489212i
$958$	−5.44751	+	9.43536i	−0.176001	+	0.304843i
$959$	−5.04739	+	8.74234i	−0.162989	+	0.282305i
$960$	7.62171	−	4.09346i	0.245990	−	0.132116i
$961$	−36.1260	−	62.5721i	−1.16535	−	2.01845i
$962$	−2.85668			−0.0921032
$963$	−7.51658	−	15.0900i	−0.242218	−	0.486268i
$964$	10.6083			0.341672
$965$	46.8966	+	81.2273i	1.50965	+	2.61480i
$966$	0.239994	−	7.80746i	0.00772169	−	0.251201i
$967$	13.4582	−	23.3103i	0.432787	−	0.749609i	−0.564325	−	0.825553i	$-0.690864\pi$
$967$	13.4582	−	23.3103i	0.432787	−	0.749609i	0.997112	+	0.0759435i	$0.0241969\pi$
$968$	−10.5416	+	18.2586i	−0.338820	+	0.586853i
$969$	−33.2134	−	20.5616i	−1.06697	−	0.660535i
$970$	8.63280	+	14.9524i	0.277182	+	0.480094i
$971$	31.0508			0.996469			0.498234	−	0.867042i	$-0.333982\pi$
$971$	31.0508			0.996469			0.498234	+	0.867042i	$0.333982\pi$
$972$	−3.64269	+	23.5213i	−0.116839	+	0.754445i
$973$	−19.0285			−0.610027
$974$	10.7551	+	18.6285i	0.344617	+	0.596894i
$975$	−19.0890	−	11.8175i	−0.611336	−	0.378464i
$976$	6.26555	−	10.8522i	0.200555	−	0.347372i
$977$	−7.35227	+	12.7345i	−0.235220	+	0.407413i	−0.959337	−	0.282265i	$-0.908914\pi$
$977$	−7.35227	+	12.7345i	−0.235220	+	0.407413i	0.724117	+	0.689677i	$0.242248\pi$
$978$	−0.201588	+	6.55802i	−0.00644607	+	0.209702i
$979$	−1.07475	−	1.86152i	−0.0343491	−	0.0594943i
$980$	−37.7333			−1.20535
$981$	−1.61897	−	3.25018i	−0.0516898	−	0.103770i
$982$	5.19779			0.165868
$983$	2.12706	+	3.68418i	0.0678427	+	0.117507i	0.897951	−	0.440095i	$-0.145055\pi$
$983$	2.12706	+	3.68418i	0.0678427	+	0.117507i	−0.830109	+	0.557601i	$0.811722\pi$
$984$	−26.6872	+	14.3331i	−0.850755	+	0.456923i
$985$	−12.5716	+	21.7747i	−0.400566	+	0.693800i
$986$	−1.60327	+	2.77694i	−0.0510585	+	0.0884359i
$987$	−18.5984	+	9.98880i	−0.591992	+	0.317947i
$988$	−4.97398	−	8.61518i	−0.158243	−	0.274085i
$989$	−57.2168			−1.81939
$990$	7.07598	−	10.6820i	0.224889	−	0.339496i
$991$	−58.7703			−1.86690			−0.933450	−	0.358706i	$-0.883218\pi$
$991$	−58.7703			−1.86690			−0.933450	+	0.358706i	$0.883218\pi$
$992$	−29.4910	−	51.0800i	−0.936341	−	1.62179i
$993$	0.366238	−	11.9144i	0.0116222	−	0.378092i
$994$	−0.569977	+	0.987229i	−0.0180786	+	0.0313130i
$995$	−38.1368	+	66.0549i	−1.20902	+	2.09408i
$996$	40.7832	+	25.2479i	1.29227	+	0.800011i
$997$	−20.3428	−	35.2348i	−0.644263	−	1.11590i	−0.984471	−	0.175546i	$-0.943831\pi$
$997$	−20.3428	−	35.2348i	−0.644263	−	1.11590i	0.340208	−	0.940350i	$-0.389502\pi$
$998$	−9.04100			−0.286188
$999$	−1.79266	+	19.3905i	−0.0567172	+	0.613488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.e.b.202.12	✓	66
9.4	even	3		5427.2.a.n.1.22		33
9.5	odd	6		5427.2.a.q.1.12		33
9.7	even	3	inner	603.2.e.b.403.12	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.e.b.202.12	✓	66	1.1	even	1	trivial
603.2.e.b.403.12	yes	66	9.7	even	3	inner
5427.2.a.n.1.22		33	9.4	even	3
5427.2.a.q.1.12		33	9.5	odd	6

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.343920 - 0.595686i) q^{2} +(1.47268 + 0.911703i) q^{3} +(0.763439 - 1.32231i) q^{4} +(2.04306 - 3.53869i) q^{5} +(0.0366045 - 1.19081i) q^{6} +(-0.487864 - 0.845004i) q^{7} -2.42592 q^{8} +(1.33759 + 2.68530i) q^{9} +O(q^{10})\)	\(q+(-0.343920 - 0.595686i) q^{2} +(1.47268 + 0.911703i) q^{3} +(0.763439 - 1.32231i) q^{4} +(2.04306 - 3.53869i) q^{5} +(0.0366045 - 1.19081i) q^{6} +(-0.487864 - 0.845004i) q^{7} -2.42592 q^{8} +(1.33759 + 2.68530i) q^{9} -2.81060 q^{10} +(0.759806 + 1.31602i) q^{11} +(2.32986 - 1.25132i) q^{12} +(0.554102 - 0.959733i) q^{13} +(-0.335572 + 0.581227i) q^{14} +(6.23502 - 3.34870i) q^{15} +(-0.692554 - 1.19954i) q^{16} -3.83614 q^{17} +(1.13957 - 1.72031i) q^{18} +5.87909 q^{19} +(-3.11951 - 5.40314i) q^{20} +(0.0519249 - 1.68921i) q^{21} +(0.522624 - 0.905212i) q^{22} +(-3.35976 + 5.81928i) q^{23} +(-3.57262 - 2.21172i) q^{24} +(-5.84821 - 10.1294i) q^{25} -0.762267 q^{26} +(-0.478346 + 5.17409i) q^{27} -1.48982 q^{28} +(0.607611 + 1.05241i) q^{29} +(-4.13912 - 2.56243i) q^{30} +(-5.08065 + 8.79994i) q^{31} +(-2.90229 + 5.02691i) q^{32} +(-0.0808685 + 2.63080i) q^{33} +(1.31932 + 2.28513i) q^{34} -3.98694 q^{35} +(4.57198 + 0.281343i) q^{36} +3.74762 q^{37} +(-2.02193 - 3.50209i) q^{38} +(1.69101 - 0.908207i) q^{39} +(-4.95632 + 8.58459i) q^{40} +(3.60470 - 6.24352i) q^{41} +(-1.02410 + 0.550022i) q^{42} +(4.25750 + 7.37421i) q^{43} +2.32026 q^{44} +(12.2352 + 0.752912i) q^{45} +4.62196 q^{46} +(-6.24583 - 10.8181i) q^{47} +(0.0737107 - 2.39794i) q^{48} +(3.02398 - 5.23768i) q^{49} +(-4.02263 + 6.96740i) q^{50} +(-5.64941 - 3.49742i) q^{51} +(-0.846046 - 1.46539i) q^{52} -6.52501 q^{53} +(3.24665 - 1.49453i) q^{54} +6.20932 q^{55} +(1.18352 + 2.04992i) q^{56} +(8.65803 + 5.35998i) q^{57} +(0.417938 - 0.723891i) q^{58} +(3.24516 - 5.62077i) q^{59} +(0.332019 - 10.8012i) q^{60} +(4.52351 + 7.83495i) q^{61} +6.98934 q^{62} +(1.61653 - 2.44033i) q^{63} +1.22240 q^{64} +(-2.26413 - 3.92159i) q^{65} +(1.59495 - 0.856612i) q^{66} +(0.500000 - 0.866025i) q^{67} +(-2.92865 + 5.07258i) q^{68} +(-10.2533 + 5.50685i) q^{69} +(1.37119 + 2.37497i) q^{70} +1.69853 q^{71} +(-3.24490 - 6.51434i) q^{72} +15.2771 q^{73} +(-1.28888 - 2.23240i) q^{74} +(0.622444 - 20.2492i) q^{75} +(4.48832 - 7.77400i) q^{76} +(0.741363 - 1.28408i) q^{77} +(-1.12258 - 0.694961i) q^{78} +(0.727525 + 1.26011i) q^{79} -5.65973 q^{80} +(-5.42169 + 7.18368i) q^{81} -4.95890 q^{82} +(9.06855 + 15.7072i) q^{83} +(-2.19403 - 1.35827i) q^{84} +(-7.83747 + 13.5749i) q^{85} +(2.92848 - 5.07227i) q^{86} +(-0.0646699 + 2.10383i) q^{87} +(-1.84323 - 3.19257i) q^{88} -1.41450 q^{89} +(-3.75944 - 7.54730i) q^{90} -1.08131 q^{91} +(5.12995 + 8.88533i) q^{92} +(-15.5051 + 8.32749i) q^{93} +(-4.29613 + 7.44111i) q^{94} +(12.0113 - 20.8043i) q^{95} +(-8.85721 + 4.75703i) q^{96} +(-3.07152 - 5.32002i) q^{97} -4.16002 q^{98} +(-2.51761 + 3.80061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

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