LMFDB - Embedded newform 950.2.n.b.39.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.3
Character	$\chi$	$=$	950.39
Dual form			950.2.n.b.609.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-2.09906 - 0.682024i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.131723 + 2.23218i) q^{5} +(0.682024 + 2.09906i) q^{6} +4.35569i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.51382 + 1.09986i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.09906 - 0.682024i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.131723 + 2.23218i) q^{5} +(0.682024 + 2.09906i) q^{6} +4.35569i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.51382 + 1.09986i) q^{9} +(1.88330 - 1.20548i) q^{10} +(-5.01376 + 3.64271i) q^{11} +(1.29729 - 1.78556i) q^{12} +(-3.59544 + 4.94870i) q^{13} +(3.52383 - 2.56021i) q^{14} +(1.79890 - 4.59564i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.75069 - 1.21867i) q^{17} -1.87119i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.08223 - 0.815059i) q^{20} +(2.97069 - 9.14284i) q^{21} +(5.89402 + 1.91508i) q^{22} +(-1.46213 - 2.01245i) q^{23} -2.20708 q^{24} +(-4.96530 - 0.588058i) q^{25} +6.11693 q^{26} +(1.46439 + 2.01556i) q^{27} +(-4.14251 - 1.34598i) q^{28} +(1.41644 - 4.35936i) q^{29} +(-4.77532 + 1.24591i) q^{30} +(-2.77358 - 8.53620i) q^{31} +1.00000i q^{32} +(13.0086 - 4.22674i) q^{33} +(-3.19053 - 2.31805i) q^{34} +(-9.72271 - 0.573743i) q^{35} +(-1.51382 + 1.09986i) q^{36} +(2.61577 - 3.60030i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(10.9222 - 7.93542i) q^{39} +(0.564507 + 2.16364i) q^{40} +(0.446222 + 0.324200i) q^{41} +(-9.14284 + 2.97069i) q^{42} +3.90354i q^{43} +(-1.91508 - 5.89402i) q^{44} +(-2.65449 + 3.23426i) q^{45} +(-0.768687 + 2.36577i) q^{46} +(4.71731 + 1.53275i) q^{47} +(1.29729 + 1.78556i) q^{48} -11.9721 q^{49} +(2.44278 + 4.36266i) q^{50} -8.70407 q^{51} +(-3.59544 - 4.94870i) q^{52} +(12.2399 + 3.97698i) q^{53} +(0.769876 - 2.36943i) q^{54} +(-7.47077 - 11.6715i) q^{55} +(1.34598 + 4.14251i) q^{56} +2.20708i q^{57} +(-4.35936 + 1.41644i) q^{58} +(0.986725 + 0.716898i) q^{59} +(3.81482 + 3.13098i) q^{60} +(-2.41552 + 1.75498i) q^{61} +(-5.27566 + 7.26133i) q^{62} +(-4.79064 + 6.59376i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-10.5728 - 8.67755i) q^{65} +(-11.0657 - 8.03973i) q^{66} +(-10.7562 + 3.49489i) q^{67} +3.94371i q^{68} +(1.69655 + 5.22145i) q^{69} +(5.25070 + 8.20308i) q^{70} +(-0.772370 + 2.37711i) q^{71} +(1.77961 + 0.578230i) q^{72} +(-0.281694 - 0.387719i) q^{73} -4.45022 q^{74} +(10.0214 + 4.62082i) q^{75} +1.00000 q^{76} +(-15.8665 - 21.8384i) q^{77} +(-12.8398 - 4.17190i) q^{78} +(-1.29486 + 3.98516i) q^{79} +(1.41861 - 1.72845i) q^{80} +(-3.43386 - 10.5683i) q^{81} -0.551561i q^{82} +(-5.15367 + 1.67453i) q^{83} +(7.77737 + 5.65059i) q^{84} +(2.22625 + 8.53276i) q^{85} +(3.15803 - 2.29444i) q^{86} +(-5.94638 + 8.18449i) q^{87} +(-3.64271 + 5.01376i) q^{88} +(8.30602 - 6.03468i) q^{89} +(4.17684 + 0.246478i) q^{90} +(-21.5550 - 15.6606i) q^{91} +(2.36577 - 0.768687i) q^{92} +19.8096i q^{93} +(-1.53275 - 4.71731i) q^{94} +(2.16364 - 0.564507i) q^{95} +(0.682024 - 2.09906i) q^{96} +(7.83106 + 2.54447i) q^{97} +(7.03700 + 9.68560i) q^{98} -11.5964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−2.09906	−	0.682024i	−1.21189	−	0.393767i	−0.367768	−	0.929918i	$-0.619878\pi$
$3$	−2.09906	−	0.682024i	−1.21189	−	0.393767i	−0.844122	+	0.536151i	$0.819878\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.131723	+	2.23218i	−0.0589081	+	0.998263i
$5$	−0.131723	+	2.23218i	−0.0589081	+	0.998263i
$6$	0.682024	+	2.09906i	0.278435	+	0.856936i
$7$			4.35569i			1.64630i	0.567826	+	0.823149i	$0.307785\pi$
$7$			4.35569i			1.64630i	−0.567826	+	0.823149i	$0.692215\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	1.51382	+	1.09986i	0.504608	+	0.366619i
$10$	1.88330	−	1.20548i	0.595552	−	0.381206i
$11$	−5.01376	+	3.64271i	−1.51170	+	1.09832i	−0.546290	+	0.837596i	$0.683960\pi$
$11$	−5.01376	+	3.64271i	−1.51170	+	1.09832i	−0.965414	+	0.260721i	$0.916040\pi$
$12$	1.29729	−	1.78556i	0.374495	−	0.515448i
$13$	−3.59544	+	4.94870i	−0.997196	+	1.37252i	−0.0701668	+	0.997535i	$0.522353\pi$
$13$	−3.59544	+	4.94870i	−0.997196	+	1.37252i	−0.927030	+	0.374988i	$0.877647\pi$
$14$	3.52383	−	2.56021i	0.941783	−	0.684246i
$15$	1.79890	−	4.59564i	0.464473	−	1.18659i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.75069	−	1.21867i	0.909676	−	0.295572i	0.183451	−	0.983029i	$-0.441273\pi$
$17$	3.75069	−	1.21867i	0.909676	−	0.295572i	0.726225	+	0.687457i	$0.241273\pi$
$18$		−	1.87119i		−	0.441044i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−2.08223	−	0.815059i	−0.465601	−	0.182253i
$21$	2.97069	−	9.14284i	0.648258	−	1.99513i
$22$	5.89402	+	1.91508i	1.25661	+	0.408297i
$23$	−1.46213	−	2.01245i	−0.304875	−	0.419624i	0.628899	−	0.777487i	$-0.283506\pi$
$23$	−1.46213	−	2.01245i	−0.304875	−	0.419624i	−0.933774	+	0.357862i	$0.883506\pi$
$24$	−2.20708			−0.450518
$25$	−4.96530	−	0.588058i	−0.993060	−	0.117612i
$26$	6.11693			1.19963
$27$	1.46439	+	2.01556i	0.281822	+	0.387895i
$28$	−4.14251	−	1.34598i	−0.782861	−	0.254367i
$29$	1.41644	−	4.35936i	0.263027	−	0.809513i	−0.729115	−	0.684391i	$-0.760068\pi$
$29$	1.41644	−	4.35936i	0.263027	−	0.809513i	0.992141	−	0.125121i	$-0.0399320\pi$
$30$	−4.77532	+	1.24591i	−0.871850	+	0.227471i
$31$	−2.77358	−	8.53620i	−0.498150	−	1.53315i	−0.811990	−	0.583671i	$-0.801616\pi$
$31$	−2.77358	−	8.53620i	−0.498150	−	1.53315i	0.313840	−	0.949476i	$-0.398384\pi$
$32$			1.00000i			0.176777i
$33$	13.0086	−	4.22674i	2.26450	−	0.735781i
$34$	−3.19053	−	2.31805i	−0.547171	−	0.397543i
$35$	−9.72271	−	0.573743i	−1.64344	−	0.0969803i
$36$	−1.51382	+	1.09986i	−0.252304	+	0.183310i
$37$	2.61577	−	3.60030i	0.430030	−	0.591886i	−0.537930	−	0.842990i	$-0.680794\pi$
$37$	2.61577	−	3.60030i	0.430030	−	0.591886i	0.967960	+	0.251104i	$0.0807935\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	10.9222	−	7.93542i	1.74895	−	1.27068i
$40$	0.564507	+	2.16364i	0.0892565	+	0.342101i
$41$	0.446222	+	0.324200i	0.0696882	+	0.0506315i	0.622084	−	0.782951i	$-0.286286\pi$
$41$	0.446222	+	0.324200i	0.0696882	+	0.0506315i	−0.552396	+	0.833582i	$0.686286\pi$
$42$	−9.14284	+	2.97069i	−1.41077	+	0.458387i
$43$			3.90354i			0.595284i	0.954678	+	0.297642i	$0.0962001\pi$
$43$			3.90354i			0.595284i	−0.954678	+	0.297642i	$0.903800\pi$
$44$	−1.91508	−	5.89402i	−0.288710	−	0.888557i
$45$	−2.65449	+	3.23426i	−0.395708	+	0.482135i
$46$	−0.768687	+	2.36577i	−0.113337	+	0.348814i
$47$	4.71731	+	1.53275i	0.688090	+	0.223574i	0.632134	−	0.774859i	$-0.282179\pi$
$47$	4.71731	+	1.53275i	0.688090	+	0.223574i	0.0559564	+	0.998433i	$0.482179\pi$
$48$	1.29729	+	1.78556i	0.187247	+	0.257724i
$49$	−11.9721			−1.71030
$50$	2.44278	+	4.36266i	0.345461	+	0.616974i
$51$	−8.70407			−1.21881
$52$	−3.59544	−	4.94870i	−0.498598	−	0.686262i
$53$	12.2399	+	3.97698i	1.68128	+	0.546280i	0.985158	−	0.171648i	$-0.0549093\pi$
$53$	12.2399	+	3.97698i	1.68128	+	0.546280i	0.696117	+	0.717928i	$0.254909\pi$
$54$	0.769876	−	2.36943i	0.104767	−	0.322439i
$55$	−7.47077	−	11.6715i	−1.00736	−	1.57378i
$56$	1.34598	+	4.14251i	0.179865	+	0.553566i
$57$			2.20708i			0.292335i
$58$	−4.35936	+	1.41644i	−0.572412	+	0.185988i
$59$	0.986725	+	0.716898i	0.128461	+	0.0933321i	0.650160	−	0.759797i	$-0.274702\pi$
$59$	0.986725	+	0.716898i	0.128461	+	0.0933321i	−0.521700	+	0.853129i	$0.674702\pi$
$60$	3.81482	+	3.13098i	0.492492	+	0.404208i
$61$	−2.41552	+	1.75498i	−0.309275	+	0.224702i	−0.731585	−	0.681750i	$-0.761219\pi$
$61$	−2.41552	+	1.75498i	−0.309275	+	0.224702i	0.422310	+	0.906451i	$0.361219\pi$
$62$	−5.27566	+	7.26133i	−0.670010	+	0.922189i
$63$	−4.79064	+	6.59376i	−0.603564	+	0.830735i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−10.5728	−	8.67755i	−1.31140	−	1.07632i
$66$	−11.0657	−	8.03973i	−1.36210	−	0.989623i
$67$	−10.7562	+	3.49489i	−1.31408	+	0.426969i	−0.880457	−	0.474127i	$-0.842764\pi$
$67$	−10.7562	+	3.49489i	−1.31408	+	0.426969i	−0.433620	+	0.901096i	$0.642764\pi$
$68$			3.94371i			0.478245i
$69$	1.69655	+	5.22145i	0.204241	+	0.628588i
$70$	5.25070	+	8.20308i	0.627579	+	0.980455i
$71$	−0.772370	+	2.37711i	−0.0916634	+	0.282111i	−0.986370	−	0.164544i	$-0.947385\pi$
$71$	−0.772370	+	2.37711i	−0.0916634	+	0.282111i	0.894706	+	0.446655i	$0.147385\pi$
$72$	1.77961	+	0.578230i	0.209729	+	0.0681450i
$73$	−0.281694	−	0.387719i	−0.0329698	−	0.0453791i	0.792214	−	0.610244i	$-0.208928\pi$
$73$	−0.281694	−	0.387719i	−0.0329698	−	0.0453791i	−0.825184	+	0.564865i	$0.808928\pi$
$74$	−4.45022			−0.517327
$75$	10.0214	+	4.62082i	1.15717	+	0.533566i
$76$	1.00000			0.114708
$77$	−15.8665	−	21.8384i	−1.80816	−	2.48871i
$78$	−12.8398	−	4.17190i	−1.45382	−	0.472374i
$79$	−1.29486	+	3.98516i	−0.145683	+	0.448365i	−0.997098	−	0.0761265i	$-0.975745\pi$
$79$	−1.29486	+	3.98516i	−0.145683	+	0.448365i	0.851415	+	0.524492i	$0.175745\pi$
$80$	1.41861	−	1.72845i	0.158606	−	0.193247i
$81$	−3.43386	−	10.5683i	−0.381540	−	1.17426i
$82$		−	0.551561i		−	0.0609098i
$83$	−5.15367	+	1.67453i	−0.565689	+	0.183804i	−0.577879	−	0.816122i	$-0.696120\pi$
$83$	−5.15367	+	1.67453i	−0.565689	+	0.183804i	0.0121903	+	0.999926i	$0.496120\pi$
$84$	7.77737	+	5.65059i	0.848580	+	0.616530i
$85$	2.22625	+	8.53276i	0.241471	+	0.925508i
$86$	3.15803	−	2.29444i	0.340539	−	0.247416i
$87$	−5.94638	+	8.18449i	−0.637519	+	0.877469i
$88$	−3.64271	+	5.01376i	−0.388314	+	0.534468i
$89$	8.30602	−	6.03468i	0.880436	−	0.639675i	−0.0529304	−	0.998598i	$-0.516856\pi$
$89$	8.30602	−	6.03468i	0.880436	−	0.639675i	0.933367	+	0.358924i	$0.116856\pi$
$90$	4.17684	+	0.246478i	0.440278	+	0.0259811i
$91$	−21.5550	−	15.6606i	−2.25958	−	1.64168i
$92$	2.36577	−	0.768687i	0.246649	−	0.0801411i
$93$			19.8096i			2.05416i
$94$	−1.53275	−	4.71731i	−0.158091	−	0.486553i
$95$	2.16364	−	0.564507i	0.221985	−	0.0579172i
$96$	0.682024	−	2.09906i	0.0696088	−	0.214234i
$97$	7.83106	+	2.54447i	0.795124	+	0.258351i	0.678285	−	0.734799i	$-0.262724\pi$
$97$	7.83106	+	2.54447i	0.795124	+	0.258351i	0.116839	+	0.993151i	$0.462724\pi$
$98$	7.03700	+	9.68560i	0.710845	+	0.978394i
$99$	−11.5964			−1.16548
$100$	2.09364	−	4.54056i	0.209364	−	0.454056i
$101$	−10.5846			−1.05321			−0.526603	−	0.850112i	$-0.676534\pi$
$101$	−10.5846			−1.05321			−0.526603	+	0.850112i	$0.676534\pi$
$102$	5.11613	+	7.04174i	0.506572	+	0.697237i
$103$	6.81806	+	2.21532i	0.671803	+	0.218282i	0.625003	−	0.780622i	$-0.285098\pi$
$103$	6.81806	+	2.21532i	0.671803	+	0.218282i	0.0468001	+	0.998904i	$0.485098\pi$
$104$	−1.89024	+	5.81755i	−0.185353	+	0.570458i
$105$	20.0172	+	7.83545i	1.95348	+	0.764661i
$106$	−3.97698	−	12.2399i	−0.386278	−	1.18884i
$107$			9.77227i			0.944721i	0.881406	+	0.472360i	$0.156598\pi$
$107$			9.77227i			0.944721i	−0.881406	+	0.472360i	$0.843402\pi$
$108$	−2.36943	+	0.769876i	−0.227999	+	0.0740813i
$109$	12.7870	+	9.29033i	1.22478	+	0.889852i	0.996488	−	0.0837410i	$-0.0266868\pi$
$109$	12.7870	+	9.29033i	1.22478	+	0.889852i	0.228289	+	0.973593i	$0.426687\pi$
$110$	−5.05120	+	12.9043i	−0.481613	+	1.23038i
$111$	−7.94614	+	5.77321i	−0.754215	+	0.547969i
$112$	2.56021	−	3.52383i	0.241917	−	0.332971i
$113$	−6.36196	+	8.75649i	−0.598483	+	0.823741i	−0.995568	−	0.0940405i	$-0.970022\pi$
$113$	−6.36196	+	8.75649i	−0.598483	+	0.823741i	0.397085	+	0.917782i	$0.370022\pi$
$114$	1.78556	−	1.29729i	0.167233	−	0.121502i
$115$	4.68475	−	2.99866i	0.436855	−	0.279626i
$116$	3.70829	+	2.69423i	0.344306	+	0.250153i
$117$	−10.8857	+	3.53699i	−1.00639	+	0.326995i
$118$		−	1.21966i		−	0.112279i
$119$	5.30817	+	16.3369i	0.486599	+	1.49760i
$120$	0.290722	−	4.92660i	0.0265391	−	0.449735i
$121$	8.46925	−	26.0657i	0.769931	−	2.36961i
$122$	2.83961	+	0.922645i	0.257086	+	0.0835324i
$123$	−0.715534	−	0.984847i	−0.0645175	−	0.0888007i
$124$	8.97549			0.806023
$125$	1.96670	−	11.0060i	0.175907	−	0.984407i
$126$	8.15033			0.726089
$127$	−12.6320	−	17.3864i	−1.12091	−	1.54279i	−0.804286	−	0.594242i	$-0.797452\pi$
$127$	−12.6320	−	17.3864i	−1.12091	−	1.54279i	−0.316620	−	0.948553i	$-0.602548\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	2.66231	−	8.19374i	0.234403	−	0.721418i
$130$	−0.805738	+	13.6541i	−0.0706679	+	1.19755i
$131$	2.25999	+	6.95554i	0.197456	+	0.607708i	0.999939	+	0.0110329i	$0.00351195\pi$
$131$	2.25999	+	6.95554i	0.197456	+	0.607708i	−0.802483	+	0.596675i	$0.796488\pi$
$132$			13.6780i			1.19052i
$133$	4.14251	−	1.34598i	0.359201	−	0.116712i
$134$	9.14975	+	6.64768i	0.790418	+	0.574272i
$135$	−4.69200	+	3.00330i	−0.403823	+	0.258483i
$136$	3.19053	−	2.31805i	0.273586	−	0.198772i
$137$	−2.47941	+	3.41261i	−0.211830	+	0.291559i	−0.901689	−	0.432384i	$-0.857672\pi$
$137$	−2.47941	+	3.41261i	−0.211830	+	0.291559i	0.689859	+	0.723943i	$0.257672\pi$
$138$	3.22703	−	4.44163i	0.274703	−	0.378096i
$139$	−0.799274	+	0.580707i	−0.0677936	+	0.0492549i	−0.621166	−	0.783679i	$-0.713341\pi$
$139$	−0.799274	+	0.580707i	−0.0677936	+	0.0492549i	0.553372	+	0.832934i	$0.313341\pi$
$140$	3.55015	−	9.06955i	0.300042	−	0.766517i
$141$	−8.85652	−	6.43464i	−0.745854	−	0.541895i
$142$	2.37711	−	0.772370i	0.199483	−	0.0648158i
$143$		−	37.9087i		−	3.17009i
$144$	−0.578230	−	1.77961i	−0.0481858	−	0.148301i
$145$	9.54432	+	3.73599i	0.792613	+	0.310257i
$146$	−0.148095	+	0.455791i	−0.0122565	+	0.0377215i
$147$	25.1300	+	8.16524i	2.07269	+	0.673458i
$148$	2.61577	+	3.60030i	0.215015	+	0.295943i
$149$	21.8426			1.78941			0.894706	−	0.446656i	$-0.147385\pi$
$149$	21.8426			1.78941			0.894706	+	0.446656i	$0.147385\pi$
$150$	−2.15209	−	10.8235i	−0.175717	−	0.883736i
$151$	−11.6363			−0.946949			−0.473475	−	0.880808i	$-0.657000\pi$
$151$	−11.6363			−0.946949			−0.473475	+	0.880808i	$0.657000\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	7.01826	+	2.28037i	0.567392	+	0.184357i
$154$	−8.34152	+	25.6726i	−0.672179	+	2.06875i
$155$	19.4197	−	5.06673i	1.55983	−	0.406970i
$156$	4.17190	+	12.8398i	0.334019	+	1.02801i
$157$			6.73627i			0.537613i	0.963194	+	0.268806i	$0.0866292\pi$
$157$			6.73627i			0.537613i	−0.963194	+	0.268806i	$0.913371\pi$
$158$	3.98516	−	1.29486i	0.317042	−	0.103013i
$159$	−22.9798	−	16.6958i	−1.82241	−	1.32406i
$160$	−2.23218	−	0.131723i	−0.176470	−	0.0104136i
$161$	8.76560	−	6.36858i	0.690826	−	0.501915i
$162$	−6.53160	+	8.98997i	−0.513171	+	0.706319i
$163$	4.94985	−	6.81288i	0.387702	−	0.533626i	−0.569903	−	0.821712i	$-0.693019\pi$
$163$	4.94985	−	6.81288i	0.387702	−	0.533626i	0.957604	+	0.288087i	$0.0930191\pi$
$164$	−0.446222	+	0.324200i	−0.0348441	+	0.0253157i
$165$	7.72134	+	29.5943i	0.601106	+	2.30391i
$166$	4.38398	+	3.18515i	0.340263	+	0.247215i
$167$	2.06370	−	0.670538i	0.159694	−	0.0518878i	−0.228079	−	0.973643i	$-0.573244\pi$
$167$	2.06370	−	0.670538i	0.159694	−	0.0518878i	0.387773	+	0.921755i	$0.373244\pi$
$168$		−	9.61335i		−	0.741686i
$169$	−7.54523	−	23.2218i	−0.580402	−	1.78629i
$170$	5.59459	−	6.81651i	0.429086	−	0.522802i
$171$	0.578230	−	1.77961i	0.0442183	−	0.136090i
$172$	−3.71248	−	1.20626i	−0.283074	−	0.0919764i
$173$	−4.84593	−	6.66985i	−0.368429	−	0.507099i	0.584044	−	0.811722i	$-0.301470\pi$
$173$	−4.84593	−	6.66985i	−0.368429	−	0.507099i	−0.952473	+	0.304623i	$0.901470\pi$
$174$	10.1166			0.766936
$175$	2.56140	−	21.6273i	0.193624	−	1.63487i
$176$	6.19734			0.467142
$177$	−1.58225	−	2.17778i	−0.118929	−	0.163692i
$178$	−9.76431	−	3.17262i	−0.731866	−	0.237798i
$179$	2.76059	−	8.49621i	0.206336	−	0.635037i	−0.793320	−	0.608805i	$-0.791649\pi$
$179$	2.76059	−	8.49621i	0.206336	−	0.635037i	0.999656	−	0.0262317i	$-0.00835078\pi$
$180$	−2.25568	−	3.52401i	−0.168129	−	0.262664i
$181$	−6.55961	−	20.1884i	−0.487572	−	1.50059i	−0.828221	−	0.560402i	$-0.810647\pi$
$181$	−6.55961	−	20.1884i	−0.487572	−	1.50059i	0.340649	−	0.940191i	$-0.389353\pi$
$182$			26.6435i			1.97495i
$183$	6.26724	−	2.03635i	0.463288	−	0.150531i
$184$	−2.01245	−	1.46213i	−0.148360	−	0.107790i
$185$	7.69198	+	6.31313i	0.565526	+	0.464150i
$186$	16.0263	−	11.6438i	1.17511	−	0.853765i
$187$	−14.3658	+	19.7728i	−1.05053	+	1.44593i
$188$	−2.91546	+	4.01278i	−0.212632	+	0.292662i
$189$	−8.77917	+	6.37844i	−0.638590	+	0.463963i
$190$	−1.72845	−	1.41861i	−0.125395	−	0.102917i
$191$	2.69466	+	1.95779i	0.194979	+	0.141660i	0.680991	−	0.732291i	$-0.261549\pi$
$191$	2.69466	+	1.95779i	0.194979	+	0.141660i	−0.486013	+	0.873952i	$0.661549\pi$
$192$	−2.09906	+	0.682024i	−0.151486	+	0.0492209i
$193$			15.1019i			1.08706i	0.839390	+	0.543530i	$0.182913\pi$
$193$			15.1019i			1.08706i	−0.839390	+	0.543530i	$0.817087\pi$
$194$	−2.54447	−	7.83106i	−0.182682	−	0.562238i
$195$	16.2746	+	25.4256i	1.16545	+	1.82076i
$196$	3.69957	−	11.3861i	0.264255	−	0.813294i
$197$	−16.3881	−	5.32483i	−1.16761	−	0.379378i	−0.339857	−	0.940477i	$-0.610379\pi$
$197$	−16.3881	−	5.32483i	−1.16761	−	0.379378i	−0.827749	+	0.561099i	$0.810379\pi$
$198$	6.81620	+	9.38169i	0.484406	+	0.666728i
$199$	−10.9174			−0.773914			−0.386957	−	0.922098i	$-0.626474\pi$
$199$	−10.9174			−0.773914			−0.386957	+	0.922098i	$0.626474\pi$
$200$	−4.90400	+	0.975085i	−0.346765	+	0.0689489i
$201$	24.9614			1.76064
$202$	6.22146	+	8.56311i	0.437740	+	0.602498i
$203$	18.9880	+	6.16959i	1.33270	+	0.433020i
$204$	2.68971	−	8.27807i	0.188317	−	0.579581i
$205$	−0.782451	+	0.953347i	−0.0546487	+	0.0665846i
$206$	−2.21532	−	6.81806i	−0.154349	−	0.475037i
$207$		−	4.65463i		−	0.323519i
$208$	5.81755	−	1.89024i	0.403374	−	0.131064i
$209$	5.01376	+	3.64271i	0.346809	+	0.251971i
$210$	−5.42681	−	20.7998i	−0.374485	−	1.43532i
$211$	−16.7184	+	12.1466i	−1.15094	+	0.836210i	−0.988606	−	0.150525i	$-0.951903\pi$
$211$	−16.7184	+	12.1466i	−1.15094	+	0.836210i	−0.162338	+	0.986735i	$0.551903\pi$
$212$	−7.56466	+	10.4119i	−0.519543	+	0.715089i
$213$	3.24249	−	4.46291i	0.222172	−	0.305794i
$214$	7.90593	−	5.74399i	0.540438	−	0.392651i
$215$	−8.71341	−	0.514184i	−0.594250	−	0.0350670i
$216$	2.01556	+	1.46439i	0.137142	+	0.0996392i
$217$	37.1811	−	12.0809i	2.52402	−	0.820103i
$218$		−	15.8057i		−	1.07049i
$219$	0.326858	+	1.00597i	0.0220870	+	0.0679769i
$220$	13.4088	−	3.49845i	0.904022	−	0.235865i
$221$	−7.45454	+	22.9427i	−0.501447	+	1.54329i
$222$	9.34125	+	3.03516i	0.626944	+	0.203706i
$223$	−2.29364	−	3.15692i	−0.153593	−	0.211403i	0.725285	−	0.688448i	$-0.241708\pi$
$223$	−2.29364	−	3.15692i	−0.153593	−	0.211403i	−0.878879	+	0.477045i	$0.841708\pi$
$224$	−4.35569			−0.291027
$225$	−6.86981	−	6.35134i	−0.457987	−	0.423423i
$226$	10.8236			0.719976
$227$	−0.518028	−	0.713004i	−0.0343827	−	0.0473237i	0.791480	−	0.611196i	$-0.209311\pi$
$227$	−0.518028	−	0.713004i	−0.0343827	−	0.0473237i	−0.825862	+	0.563872i	$0.809311\pi$
$228$	−2.09906	−	0.682024i	−0.139013	−	0.0451682i
$229$	−1.07206	+	3.29946i	−0.0708438	+	0.218035i	−0.980210	−	0.197963i	$-0.936567\pi$
$229$	−1.07206	+	3.29946i	−0.0708438	+	0.218035i	0.909366	+	0.415997i	$0.136567\pi$
$230$	−5.17959	−	2.02748i	−0.341532	−	0.133688i
$231$	18.4104	+	56.6613i	1.21131	+	3.72804i
$232$		−	4.58370i		−	0.300935i
$233$	1.51489	−	0.492218i	0.0992439	−	0.0322463i	−0.258974	−	0.965884i	$-0.583384\pi$
$233$	1.51489	−	0.492218i	0.0992439	−	0.0322463i	0.358218	+	0.933638i	$0.383384\pi$
$234$	9.25996	+	6.72776i	0.605343	+	0.439807i
$235$	−4.04275	+	10.3280i	−0.263720	+	0.673725i
$236$	−0.986725	+	0.716898i	−0.0642303	+	0.0466661i
$237$	5.43595	−	7.48195i	0.353103	−	0.486005i
$238$	10.0967	−	13.8970i	0.654474	−	0.900806i
$239$	−15.9642	+	11.5987i	−1.03264	+	0.750257i	−0.968836	−	0.247705i	$-0.920324\pi$
$239$	−15.9642	+	11.5987i	−1.03264	+	0.750257i	−0.0638052	+	0.997962i	$0.520324\pi$
$240$	−4.15659	+	2.66059i	−0.268307	+	0.171740i
$241$	−13.6960	−	9.95070i	−0.882234	−	0.640981i	0.0516074	−	0.998667i	$-0.483566\pi$
$241$	−13.6960	−	9.95070i	−0.882234	−	0.640981i	−0.933842	+	0.357687i	$0.883566\pi$
$242$	−26.0657	+	8.46925i	−1.67556	+	0.544424i
$243$			17.0514i			1.09385i
$244$	−0.922645	−	2.83961i	−0.0590663	−	0.181787i
$245$	1.57699	−	26.7239i	0.100750	−	1.70732i
$246$	−0.376178	+	1.15776i	−0.0239842	+	0.0738159i
$247$	5.81755	+	1.89024i	0.370162	+	0.120273i
$248$	−5.27566	−	7.26133i	−0.335005	−	0.461095i
$249$	11.9599			0.757929
$250$	−10.0600	+	4.87808i	−0.636253	+	0.308517i
$251$	24.5239			1.54794			0.773968	−	0.633225i	$-0.218269\pi$
$251$	24.5239			1.54794			0.773968	+	0.633225i	$0.218269\pi$
$252$	−4.79064	−	6.59376i	−0.301782	−	0.415368i
$253$	14.6615	+	4.76381i	0.921761	+	0.299498i
$254$	−6.64102	+	20.4390i	−0.416695	+	1.28245i
$255$	1.14652	−	19.4291i	0.0717980	−	1.21670i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	18.1200i		−	1.13029i	−0.824990	−	0.565147i	$-0.808820\pi$
$257$		−	18.1200i		−	1.13029i	0.824990	−	0.565147i	$-0.191180\pi$
$258$	−8.19374	+	2.66231i	−0.510120	+	0.165748i
$259$	15.6818	+	11.3935i	0.974420	+	0.707958i
$260$	11.5200	−	7.37384i	0.714441	−	0.457306i
$261$	6.93892	−	5.04142i	0.429508	−	0.312056i
$262$	4.29876	−	5.91673i	0.265578	−	0.365537i
$263$	−7.16158	+	9.85707i	−0.441602	+	0.607813i	−0.970567	−	0.240831i	$-0.922580\pi$
$263$	−7.16158	+	9.85707i	−0.441602	+	0.607813i	0.528965	+	0.848643i	$0.322580\pi$
$264$	11.0657	−	8.03973i	0.681050	−	0.494811i
$265$	−10.4896	+	26.7978i	−0.644372	+	1.64618i
$266$	−3.52383	−	2.56021i	−0.216060	−	0.156977i
$267$	−21.5506	+	7.00221i	−1.31887	+	0.428528i
$268$		−	11.3097i		−	0.690851i
$269$	3.75927	+	11.5698i	0.229207	+	0.705425i	0.997837	+	0.0657325i	$0.0209384\pi$
$269$	3.75927	+	11.5698i	0.229207	+	0.705425i	−0.768631	+	0.639693i	$0.779062\pi$
$270$	5.18761	+	2.03061i	0.315708	+	0.123579i
$271$	2.35490	−	7.24763i	0.143050	−	0.440262i	−0.853705	−	0.520757i	$-0.825650\pi$
$271$	2.35490	−	7.24763i	0.143050	−	0.440262i	0.996755	+	0.0804943i	$0.0256499\pi$
$272$	−3.75069	−	1.21867i	−0.227419	−	0.0738929i
$273$	34.5643	+	47.5736i	2.09192	+	2.87929i
$274$	4.21822			0.254832
$275$	27.0369	−	15.1387i	1.63039	−	0.912901i
$276$	−5.49015			−0.330468
$277$	−0.729271	−	1.00376i	−0.0438177	−	0.0603099i	0.786546	−	0.617532i	$-0.211867\pi$
$277$	−0.729271	−	1.00376i	−0.0438177	−	0.0603099i	−0.830364	+	0.557222i	$0.811867\pi$
$278$	0.939603	+	0.305296i	0.0563537	+	0.0183104i
$279$	5.18990	−	15.9729i	0.310711	−	0.956270i
$280$	−9.42415	+	2.45882i	−0.563200	+	0.146943i
$281$	−1.69014	−	5.20172i	−0.100825	−	0.310309i	0.887903	−	0.460032i	$-0.152162\pi$
$281$	−1.69014	−	5.20172i	−0.100825	−	0.310309i	−0.988728	+	0.149723i	$0.952162\pi$
$282$			10.9473i			0.651900i
$283$	−27.8317	+	9.04306i	−1.65442	+	0.537554i	−0.979692	−	0.200510i	$-0.935740\pi$
$283$	−27.8317	+	9.04306i	−1.65442	+	0.537554i	−0.674730	+	0.738064i	$0.735740\pi$
$284$	−2.02209	−	1.46913i	−0.119989	−	0.0871771i
$285$	−4.92660	−	0.290722i	−0.291827	−	0.0172209i
$286$	−30.6688	+	22.2822i	−1.81348	+	1.31757i
$287$	−1.41211	+	1.94361i	−0.0833545	+	0.114728i
$288$	−1.09986	+	1.51382i	−0.0648098	+	0.0892030i
$289$	−1.17077	+	0.850612i	−0.0688686	+	0.0500360i
$290$	−2.58753	−	9.91747i	−0.151945	−	0.582374i
$291$	−14.7024	−	10.6820i	−0.861873	−	0.626187i
$292$	0.455791	−	0.148095i	0.0266731	−	0.00866663i
$293$		−	14.1961i		−	0.829344i	−0.909971	−	0.414672i	$-0.863896\pi$
$293$		−	14.1961i		−	0.829344i	0.909971	−	0.414672i	$-0.136104\pi$
$294$	−8.16524	−	25.1300i	−0.476207	−	1.46561i
$295$	−1.73022	+	2.10812i	−0.100737	+	0.122740i
$296$	1.37519	−	4.23241i	0.0799315	−	0.246004i
$297$	−14.6842	−	4.77118i	−0.852063	−	0.276852i
$298$	−12.8387	−	17.6710i	−0.743728	−	1.02365i
$299$	15.2160			0.879964
$300$	−7.49143	+	8.10297i	−0.432518	+	0.467825i
$301$	−17.0026			−0.980014
$302$	6.83965	+	9.41397i	0.393578	+	0.541713i
$303$	22.2176	+	7.21894i	1.27637	+	0.414717i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	−3.59925	−	5.62305i	−0.206093	−	0.321975i
$306$	−2.28037	−	7.01826i	−0.130360	−	0.401207i
$307$		−	21.0416i		−	1.20091i	−0.799660	−	0.600453i	$-0.794987\pi$
$307$		−	21.0416i		−	1.20091i	0.799660	−	0.600453i	$-0.205013\pi$
$308$	25.6726	−	8.34152i	1.46283	−	0.475302i
$309$	−12.8006	−	9.30017i	−0.728200	−	0.529068i
$310$	−15.5137	−	12.7327i	−0.881119	−	0.723171i
$311$	−3.60626	+	2.62010i	−0.204492	+	0.148572i	−0.685318	−	0.728244i	$-0.740337\pi$
$311$	−3.60626	+	2.62010i	−0.204492	+	0.148572i	0.480826	+	0.876816i	$0.340337\pi$
$312$	7.93542	−	10.9222i	0.449255	−	0.618346i
$313$	−16.7264	+	23.0219i	−0.945430	+	1.30127i	0.00809745	+	0.999967i	$0.497422\pi$
$313$	−16.7264	+	23.0219i	−0.945430	+	1.30127i	−0.953528	+	0.301306i	$0.902578\pi$
$314$	5.44976	−	3.95948i	0.307548	−	0.223446i
$315$	−14.0874	−	11.5621i	−0.793738	−	0.651453i
$316$	−3.38998	−	2.46296i	−0.190701	−	0.138553i
$317$	−0.649629	+	0.211077i	−0.0364868	+	0.0118553i	−0.327204	−	0.944954i	$-0.606106\pi$
$317$	−0.649629	+	0.211077i	−0.0364868	+	0.0118553i	0.290717	+	0.956809i	$0.406106\pi$
$318$			28.4046i			1.59285i
$319$	8.77818	+	27.0164i	0.491483	+	1.51263i
$320$	1.20548	+	1.88330i	0.0673884	+	0.105280i
$321$	6.66492	−	20.5125i	0.372000	−	1.14490i
$322$	−10.3046	−	3.34816i	−0.574252	−	0.186586i
$323$	−2.31805	−	3.19053i	−0.128980	−	0.177526i
$324$	11.1122			0.617345
$325$	20.7626	−	22.4575i	1.15170	−	1.24572i
$326$	−8.42118			−0.466406
$327$	−20.5045	−	28.2220i	−1.13390	−	1.56068i
$328$	0.524566	+	0.170442i	0.0289643	+	0.00941107i
$329$	−6.67618	+	20.5472i	−0.368070	+	1.13280i
$330$	19.4038	−	23.6418i	1.06814	−	1.30144i
$331$	−4.30022	−	13.2347i	−0.236362	−	0.727446i	−0.996938	−	0.0781976i	$-0.975084\pi$
$331$	−4.30022	−	13.2347i	−0.236362	−	0.727446i	0.760576	−	0.649249i	$-0.224916\pi$
$332$		−	5.41889i		−	0.297400i
$333$	7.91964	−	2.57325i	0.433994	−	0.141013i
$334$	−1.75549	−	1.27544i	−0.0960562	−	0.0697889i
$335$	−6.38442	−	24.4701i	−0.348818	−	1.33695i
$336$	−7.77737	+	5.65059i	−0.424290	+	0.308265i
$337$	1.78396	−	2.45541i	0.0971786	−	0.133755i	−0.757659	−	0.652651i	$-0.773657\pi$
$337$	1.78396	−	2.45541i	0.0971786	−	0.133755i	0.854837	+	0.518896i	$0.173657\pi$
$338$	−14.3519	+	19.7537i	−0.780639	+	1.07446i
$339$	19.3262	−	14.0413i	1.04966	−	0.762621i
$340$	−8.80309	−	0.519475i	−0.477415	−	0.0281725i
$341$	45.0009	+	32.6951i	2.43694	+	1.77054i
$342$	−1.77961	+	0.578230i	−0.0962302	+	0.0312671i
$343$		−	21.6568i		−	1.16936i
$344$	1.20626	+	3.71248i	0.0650371	+	0.200164i
$345$	−11.8787	+	3.09923i	−0.639528	+	0.166857i
$346$	−2.54766	+	7.84088i	−0.136963	+	0.421528i
$347$	1.23698	+	0.401919i	0.0664046	+	0.0215762i	0.342031	−	0.939689i	$-0.388885\pi$
$347$	1.23698	+	0.401919i	0.0664046	+	0.0215762i	−0.275626	+	0.961265i	$0.588885\pi$
$348$	−5.94638	−	8.18449i	−0.318759	−	0.438735i
$349$	−28.6766			−1.53502			−0.767511	−	0.641036i	$-0.778505\pi$
$349$	−28.6766			−1.53502			−0.767511	+	0.641036i	$0.778505\pi$
$350$	−19.0024	+	10.6400i	−1.01572	+	0.568732i
$351$	−15.2395			−0.813427
$352$	−3.64271	−	5.01376i	−0.194157	−	0.267234i
$353$	19.4103	+	6.30680i	1.03311	+	0.335677i	0.776018	−	0.630711i	$-0.217237\pi$
$353$	19.4103	+	6.30680i	1.03311	+	0.335677i	0.257089	+	0.966388i	$0.417237\pi$
$354$	−0.831837	+	2.56013i	−0.0442117	+	0.136069i
$355$	−5.20441	−	2.03719i	−0.276221	−	0.108123i
$356$	3.17262	+	9.76431i	0.168148	+	0.517508i
$357$		−	37.9123i		−	2.00653i
$358$	−8.49621	+	2.76059i	−0.449039	+	0.145902i
$359$	1.61650	+	1.17446i	0.0853158	+	0.0619856i	0.629625	−	0.776899i	$-0.283208\pi$
$359$	1.61650	+	1.17446i	0.0853158	+	0.0619856i	−0.544310	+	0.838884i	$0.683208\pi$
$360$	−1.52513	+	3.89625i	−0.0803814	+	0.205350i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−12.4771	+	17.1733i	−0.655783	+	0.902608i
$363$	−35.5548	+	48.9370i	−1.86614	+	2.56853i
$364$	21.5550	−	15.6606i	1.12979	−	0.820841i
$365$	0.902566	−	0.577722i	0.0472424	−	0.0302394i
$366$	−5.33123	−	3.87337i	−0.278668	−	0.202464i
$367$	4.53632	−	1.47394i	0.236794	−	0.0769390i	−0.188216	−	0.982128i	$-0.560271\pi$
$367$	4.53632	−	1.47394i	0.236794	−	0.0769390i	0.425010	+	0.905189i	$0.360271\pi$
$368$			2.48752i			0.129671i
$369$	0.318929	+	0.981563i	0.0166028	+	0.0510981i
$370$	0.586194	−	9.93371i	0.0304748	−	0.516429i
$371$	−17.3225	+	53.3131i	−0.899339	+	2.76788i
$372$	−18.8401	−	6.12151i	−0.976811	−	0.317385i
$373$	−9.60622	−	13.2218i	−0.497391	−	0.684600i	0.484339	−	0.874881i	$-0.339060\pi$
$373$	−9.60622	−	13.2218i	−0.497391	−	0.684600i	−0.981730	+	0.190280i	$0.939060\pi$
$374$	24.4405			1.26379
$375$	−11.6346	+	21.7609i	−0.600806	+	1.12373i
$376$	4.96007			0.255796
$377$	16.4804	+	22.6834i	0.848786	+	1.16825i
$378$	10.3205	+	3.35334i	0.530831	+	0.172477i
$379$	−6.30968	+	19.4192i	−0.324106	+	0.997497i	0.647736	+	0.761865i	$0.275716\pi$
$379$	−6.30968	+	19.4192i	−0.324106	+	0.997497i	−0.971842	+	0.235632i	$0.924284\pi$
$380$	−0.131723	+	2.23218i	−0.00675722	+	0.114509i
$381$	14.6572	+	45.1103i	0.750913	+	2.31107i
$382$		−	3.33078i		−	0.170418i
$383$	−21.5671	+	7.00759i	−1.10203	+	0.358071i	−0.802883	−	0.596136i	$-0.796702\pi$
$383$	−21.5671	+	7.00759i	−1.10203	+	0.358071i	−0.299146	+	0.954207i	$0.596702\pi$
$384$	1.78556	+	1.29729i	0.0911191	+	0.0662019i
$385$	50.8373	−	32.5404i	2.59091	−	1.65841i
$386$	12.2177	−	8.87669i	0.621865	−	0.451812i
$387$	−4.29334	+	5.90927i	−0.218243	+	0.300385i
$388$	−4.83986	+	6.66150i	−0.245707	+	0.338186i
$389$	−2.66386	+	1.93541i	−0.135063	+	0.0981290i	−0.653265	−	0.757129i	$-0.726601\pi$
$389$	−2.66386	+	1.93541i	−0.135063	+	0.0981290i	0.518202	+	0.855258i	$0.326601\pi$
$390$	11.0037	−	28.1112i	0.557196	−	1.42347i
$391$	−7.93651	−	5.76621i	−0.401367	−	0.291610i
$392$	−11.3861	+	3.69957i	−0.575085	+	0.186857i
$393$		−	16.1414i		−	0.814227i
$394$	5.32483	+	16.3881i	0.268261	+	0.825622i
$395$	−8.72505	−	3.41529i	−0.439005	−	0.171842i
$396$	3.58349	−	11.0288i	0.180077	−	0.554220i
$397$	−18.2209	−	5.92035i	−0.914483	−	0.297134i	−0.186281	−	0.982496i	$-0.559644\pi$
$397$	−18.2209	−	5.92035i	−0.914483	−	0.297134i	−0.728202	+	0.685363i	$0.759644\pi$
$398$	6.41709	+	8.83236i	0.321660	+	0.442726i
$399$	−9.61335			−0.481270
$400$	3.67136	+	3.39428i	0.183568	+	0.169714i
$401$	35.2397			1.75979			0.879893	−	0.475171i	$-0.157614\pi$
$401$	35.2397			1.75979			0.879893	+	0.475171i	$0.157614\pi$
$402$	−14.6720	−	20.1942i	−0.731770	−	1.00720i
$403$	52.2154	+	16.9658i	2.60103	+	0.845127i
$404$	3.27082	−	10.0665i	0.162729	−	0.500829i
$405$	24.0428	−	6.27293i	1.19470	−	0.311704i
$406$	−6.16959	−	18.9880i	−0.306191	−	0.942360i
$407$			27.5795i			1.36707i
$408$	−8.27807	+	2.68971i	−0.409825	+	0.133160i
$409$	−7.59662	−	5.51927i	−0.375629	−	0.272910i	0.383912	−	0.923370i	$-0.374576\pi$
$409$	−7.59662	−	5.51927i	−0.375629	−	0.272910i	−0.759541	+	0.650459i	$0.774576\pi$
$410$	1.23119	+	0.0726530i	0.0608040	+	0.00358808i
$411$	7.53190	−	5.47225i	0.371521	−	0.269926i
$412$	−4.21379	+	5.79979i	−0.207599	+	0.285735i
$413$	−3.12259	+	4.29787i	−0.153652	+	0.211484i
$414$	−3.76567	+	2.73592i	−0.185073	+	0.134463i
$415$	−3.05901	−	11.7245i	−0.150161	−	0.575534i
$416$	−4.94870	−	3.59544i	−0.242630	−	0.176281i
$417$	2.07378	−	0.673811i	0.101553	−	0.0329967i
$418$		−	6.19734i		−	0.303122i
$419$	−2.39344	−	7.36624i	−0.116927	−	0.359865i	0.875417	−	0.483368i	$-0.160587\pi$
$419$	−2.39344	−	7.36624i	−0.116927	−	0.359865i	−0.992344	+	0.123504i	$0.960587\pi$
$420$	−13.6376	+	16.6162i	−0.665447	+	0.810788i
$421$	−11.1603	+	34.3479i	−0.543920	+	1.67401i	0.179625	+	0.983735i	$0.442512\pi$
$421$	−11.1603	+	34.3479i	−0.543920	+	1.67401i	−0.723545	+	0.690277i	$0.757488\pi$
$422$	19.6537	+	6.38587i	0.956727	+	0.310859i
$423$	5.45538	+	7.50868i	0.265249	+	0.365085i
$424$	12.8698			0.625011
$425$	−19.3400	+	3.84545i	−0.938126	+	0.186532i
$426$	−5.51646			−0.267273
$427$	−7.64413	−	10.5212i	−0.369926	−	0.509159i
$428$	−9.29398	−	3.01980i	−0.449241	−	0.145967i
$429$	−25.8547	+	79.5725i	−1.24828	+	3.84180i
$430$	4.70563	+	7.35153i	0.226926	+	0.354522i
$431$	−4.30050	−	13.2356i	−0.207148	−	0.637535i	−0.999618	−	0.0276248i	$-0.991206\pi$
$431$	−4.30050	−	13.2356i	−0.207148	−	0.637535i	0.792471	−	0.609910i	$-0.208794\pi$
$432$		−	2.49137i		−	0.119866i
$433$	−19.9492	+	6.48189i	−0.958698	+	0.311500i	−0.746245	−	0.665671i	$-0.768145\pi$
$433$	−19.9492	+	6.48189i	−0.958698	+	0.311500i	−0.212453	+	0.977171i	$0.568145\pi$
$434$	−31.6281	−	22.9792i	−1.51820	−	1.10304i
$435$	−17.4860	−	14.3515i	−0.838391	−	0.688102i
$436$	−12.7870	+	9.29033i	−0.612388	+	0.444926i
$437$	−1.46213	+	2.01245i	−0.0699431	+	0.0962684i
$438$	0.621721	−	0.855725i	0.0297070	−	0.0408881i
$439$	16.1936	−	11.7653i	0.772876	−	0.561527i	−0.129956	−	0.991520i	$-0.541484\pi$
$439$	16.1936	−	11.7653i	0.772876	−	0.561527i	0.902833	+	0.429992i	$0.141484\pi$
$440$	−10.7118	−	8.79162i	−0.510665	−	0.419124i
$441$	−18.1236	−	13.1676i	−0.863029	−	0.627027i
$442$	22.9427	−	7.45454i	1.09127	−	0.354577i
$443$		−	0.631230i		−	0.0299907i	−0.999888	−	0.0149953i	$-0.995227\pi$
$443$		−	0.631230i		−	0.0299907i	0.999888	−	0.0149953i	$-0.00477334\pi$
$444$	−3.03516	−	9.34125i	−0.144042	−	0.443316i
$445$	12.3764	+	19.3355i	0.586699	+	0.916590i
$446$	−1.20584	+	3.71119i	−0.0570981	+	0.175730i
$447$	−45.8487	−	14.8972i	−2.16857	−	0.704611i
$448$	2.56021	+	3.52383i	0.120959	+	0.166485i
$449$	17.2518			0.814164			0.407082	−	0.913392i	$-0.366546\pi$
$449$	17.2518			0.814164			0.407082	+	0.913392i	$0.366546\pi$
$450$	−1.10037	+	9.29102i	−0.0518719	+	0.437983i
$451$	−3.41821			−0.160957
$452$	−6.36196	−	8.75649i	−0.299242	−	0.411871i
$453$	24.4252	+	7.93624i	1.14760	+	0.372877i
$454$	−0.272343	+	0.838186i	−0.0127817	+	0.0393380i
$455$	37.7967	−	46.0520i	1.77194	−	2.15895i
$456$	0.682024	+	2.09906i	0.0319387	+	0.0982973i
$457$			18.6252i			0.871248i	0.900129	+	0.435624i	$0.143472\pi$
$457$			18.6252i			0.871248i	−0.900129	+	0.435624i	$0.856528\pi$
$458$	3.29946	−	1.07206i	0.154174	−	0.0500941i
$459$	7.94879	+	5.77513i	0.371018	+	0.269560i
$460$	1.40422	+	5.38210i	0.0654723	+	0.250942i
$461$	−17.2148	+	12.5073i	−0.801774	+	0.582523i	−0.911434	−	0.411446i	$-0.865024\pi$
$461$	−17.2148	+	12.5073i	−0.801774	+	0.582523i	0.109660	+	0.993969i	$0.465024\pi$
$462$	35.0186	−	48.1990i	1.62921	−	2.24242i
$463$	22.4593	−	30.9126i	1.04377	−	1.43663i	0.149689	−	0.988733i	$-0.452173\pi$
$463$	22.4593	−	30.9126i	1.04377	−	1.43663i	0.894085	−	0.447898i	$-0.147827\pi$
$464$	−3.70829	+	2.69423i	−0.172153	+	0.125077i
$465$	−44.2187	−	2.60937i	−2.05059	−	0.121007i
$466$	−1.28864	−	0.936255i	−0.0596953	−	0.0433712i
$467$	12.9377	−	4.20372i	0.598686	−	0.194525i	0.00603177	−	0.999982i	$-0.498080\pi$
$467$	12.9377	−	4.20372i	0.598686	−	0.194525i	0.592654	+	0.805457i	$0.298080\pi$
$468$		−	11.4459i		−	0.529089i
$469$	−15.2227	−	46.8506i	−0.702918	−	2.16336i
$470$	10.7318	−	2.80000i	0.495021	−	0.129154i
$471$	4.59430	−	14.1398i	0.211694	−	0.651528i
$472$	1.15996	+	0.376895i	0.0533917	+	0.0173480i
$473$	−14.2194	−	19.5714i	−0.653810	−	0.899893i
$474$	−9.24819			−0.424784
$475$	0.975085	+	4.90400i	0.0447400	+	0.225011i
$476$	−17.1776			−0.787334
$477$	14.1549	+	19.4826i	0.648109	+	0.892045i
$478$	18.7671	+	6.09780i	0.858387	+	0.278907i
$479$	2.69557	−	8.29611i	0.123164	−	0.379059i	−0.870398	−	0.492348i	$-0.836139\pi$
$479$	2.69557	−	8.29611i	0.123164	−	0.379059i	0.993562	+	0.113289i	$0.0361387\pi$
$480$	4.59564	+	1.79890i	0.209761	+	0.0821081i
$481$	8.41196	+	25.8894i	0.383552	+	1.18045i
$482$			16.9291i			0.771101i
$483$	−22.7430	+	7.38965i	−1.03484	+	0.336241i
$484$	22.1728	+	16.1095i	1.00785	+	0.732248i
$485$	−6.71125	+	17.1452i	−0.304742	+	0.778524i
$486$	13.7949	−	10.0226i	0.625749	−	0.454633i
$487$	7.54964	−	10.3912i	0.342107	−	0.470870i	−0.602948	−	0.797780i	$-0.706008\pi$
$487$	7.54964	−	10.3912i	0.342107	−	0.470870i	0.945055	+	0.326910i	$0.106008\pi$
$488$	−1.75498	+	2.41552i	−0.0794440	+	0.109345i
$489$	−15.0365	+	10.9247i	−0.679976	+	0.494032i
$490$	−22.5470	+	14.4321i	−1.01857	+	0.651975i
$491$	−18.7186	−	13.5999i	−0.844760	−	0.613754i	0.0789361	−	0.996880i	$-0.474848\pi$
$491$	−18.7186	−	13.5999i	−0.844760	−	0.613754i	−0.923696	+	0.383125i	$0.874848\pi$
$492$	1.15776	−	0.376178i	0.0521957	−	0.0169594i
$493$		−	18.0768i		−	0.814138i
$494$	−1.89024	−	5.81755i	−0.0850458	−	0.261744i
$495$	1.52751	−	25.8853i	0.0686564	−	1.16346i
$496$	−2.77358	+	8.53620i	−0.124537	+	0.383287i
$497$	−10.3540	−	3.36421i	−0.464439	−	0.150905i
$498$	−7.02986	−	9.67578i	−0.315016	−	0.433582i
$499$	35.4492			1.58693			0.793463	−	0.608619i	$-0.208276\pi$
$499$	35.4492			1.58693			0.793463	+	0.608619i	$0.208276\pi$
$500$	9.85959	+	5.27148i	0.440934	+	0.235748i
$501$	−4.78915			−0.213963
$502$	−14.4148	−	19.8403i	−0.643364	−	0.885514i
$503$	−13.1755	−	4.28097i	−0.587465	−	0.190879i	0.000177256	−	1.00000i	$-0.499944\pi$
$503$	−13.1755	−	4.28097i	−0.587465	−	0.190879i	−0.587642	+	0.809121i	$0.699944\pi$
$504$	−2.51859	+	7.75143i	−0.112187	+	0.345276i
$505$	1.39423	−	23.6267i	0.0620423	−	1.05138i
$506$	−4.76381	−	14.6615i	−0.211777	−	0.651784i
$507$			53.8899i			2.39334i
$508$	20.4390	−	6.64102i	0.906832	−	0.294648i
$509$	−6.15859	−	4.47448i	−0.272975	−	0.198328i	0.442873	−	0.896585i	$-0.353959\pi$
$509$	−6.15859	−	4.47448i	−0.272975	−	0.198328i	−0.715847	+	0.698257i	$0.753959\pi$
$510$	−16.3924	+	10.4926i	−0.725867	+	0.464619i
$511$	1.68878	−	1.22697i	0.0747074	−	0.0542781i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	1.46439	−	2.01556i	0.0646544	−	0.0889892i
$514$	−14.6594	+	10.6507i	−0.646597	+	0.469780i
$515$	−5.84310	+	14.9274i	−0.257478	+	0.657778i
$516$	6.97001	+	5.06401i	0.306838	+	0.222931i
$517$	−29.2348	+	9.49896i	−1.28574	+	0.417764i
$518$		−	19.3838i		−	0.851674i
$519$	5.62287	+	17.3054i	0.246817	+	0.759624i
$520$	−12.7369	−	4.98566i	−0.558548	−	0.218636i
$521$	−7.79289	+	23.9840i	−0.341413	+	1.05076i	0.622064	+	0.782967i	$0.286294\pi$
$521$	−7.79289	+	23.9840i	−0.341413	+	1.05076i	−0.963476	+	0.267793i	$0.913706\pi$
$522$	−8.15719	−	2.65043i	−0.357031	−	0.116006i
$523$	−19.7006	−	27.1156i	−0.861448	−	1.18568i	−0.981222	−	0.192881i	$-0.938217\pi$
$523$	−19.7006	−	27.1156i	−0.861448	−	1.18568i	0.119774	−	0.992801i	$-0.461783\pi$
$524$	−7.31349			−0.319491
$525$	−20.1269	+	43.6500i	−0.878409	+	1.90504i
$526$	12.1840			0.531248
$527$	−20.8057	−	28.6366i	−0.906310	−	1.24743i
$528$	−13.0086	−	4.22674i	−0.566125	−	0.183945i
$529$	5.19527	−	15.9894i	0.225881	−	0.695191i
$530$	27.8455	−	7.26508i	1.20953	−	0.315575i
$531$	0.705243	+	2.17051i	0.0306049	+	0.0941923i
$532$			4.35569i			0.188843i
$533$	−3.20873	+	1.04258i	−0.138986	+	0.0451592i
$534$	18.3320	+	13.3190i	0.793305	+	0.576369i
$535$	−21.8135	−	1.28723i	−0.943080	−	0.0556517i
$536$	−9.14975	+	6.64768i	−0.395209	+	0.287136i
$537$	−11.5892	+	15.9512i	−0.500113	+	0.688346i
$538$	7.15055	−	9.84189i	0.308282	−	0.424314i
$539$	60.0250	−	43.6107i	2.58546	−	1.87845i
$540$	−1.40640	−	5.39043i	−0.0605217	−	0.231967i
$541$	4.15637	+	3.01978i	0.178696	+	0.129831i	0.673538	−	0.739153i	$-0.264774\pi$
$541$	4.15637	+	3.01978i	0.178696	+	0.129831i	−0.494841	+	0.868983i	$0.664774\pi$
$542$	−7.24763	+	2.35490i	−0.311312	+	0.101152i
$543$			46.8504i			2.01054i
$544$	1.21867	+	3.75069i	0.0522502	+	0.160810i
$545$	−22.4221	+	27.3193i	−0.960456	+	1.17023i
$546$	18.1715	−	55.9261i	0.777669	−	2.39342i
$547$	18.9459	+	6.15590i	0.810069	+	0.263207i	0.684627	−	0.728894i	$-0.259965\pi$
$547$	18.9459	+	6.15590i	0.810069	+	0.263207i	0.125442	+	0.992101i	$0.459965\pi$
$548$	−2.47941	−	3.41261i	−0.105915	−	0.145780i
$549$	−5.58689			−0.238443
$550$	−28.1394	−	12.9750i	−1.19987	−	0.553256i
$551$	−4.58370			−0.195272
$552$	3.22703	+	4.44163i	0.137352	+	0.189048i
$553$	−17.3581	−	5.64000i	−0.738143	−	0.239837i
$554$	−0.383401	+	1.17999i	−0.0162891	+	0.0501328i
$555$	−11.8402	−	18.4977i	−0.502588	−	0.785185i
$556$	−0.305296	−	0.939603i	−0.0129474	−	0.0398481i
$557$			37.8024i			1.60174i	0.598838	+	0.800871i	$0.295630\pi$
$557$			37.8024i			1.60174i	−0.598838	+	0.800871i	$0.704370\pi$
$558$	−15.9729	+	5.18990i	−0.676185	+	0.219706i
$559$	−19.3174	−	14.0349i	−0.817041	−	0.593615i
$560$	7.52860	+	6.17904i	0.318142	+	0.261112i
$561$	43.6401	−	31.7064i	1.84249	−	1.33864i
$562$	−3.21484	+	4.42485i	−0.135610	+	0.186651i
$563$	20.9951	−	28.8973i	0.884839	−	1.21788i	−0.0902185	−	0.995922i	$-0.528757\pi$
$563$	20.9951	−	28.8973i	0.884839	−	1.21788i	0.975057	−	0.221954i	$-0.0712434\pi$
$564$	8.85652	−	6.43464i	0.372927	−	0.270947i
$565$	−18.7081	−	15.3545i	−0.787055	−	0.645969i
$566$	23.6750	+	17.2009i	0.995137	+	0.723009i
$567$	46.0325	−	14.9569i	1.93318	−	0.628129i
$568$			2.49944i			0.104874i
$569$	6.34270	+	19.5208i	0.265900	+	0.818356i	0.991485	+	0.130223i	$0.0415693\pi$
$569$	6.34270	+	19.5208i	0.265900	+	0.818356i	−0.725585	+	0.688133i	$0.758431\pi$
$570$	2.66059	+	4.15659i	0.111440	+	0.174100i
$571$	8.95961	−	27.5748i	0.374948	−	1.15397i	−0.568566	−	0.822638i	$-0.692502\pi$
$571$	8.95961	−	27.5748i	0.374948	−	1.15397i	0.943514	−	0.331333i	$-0.107498\pi$
$572$	36.0533	+	11.7144i	1.50747	+	0.489805i
$573$	−4.32098	−	5.94732i	−0.180512	−	0.248453i
$574$	2.40243			0.100276
$575$	6.07647	+	10.8522i	0.253406	+	0.452569i
$576$	1.87119			0.0779663
$577$	16.8860	+	23.2415i	0.702972	+	0.967558i	0.999920	+	0.0126640i	$0.00403117\pi$
$577$	16.8860	+	23.2415i	0.702972	+	0.967558i	−0.296948	+	0.954894i	$0.595969\pi$
$578$	1.37632	+	0.447193i	0.0572473	+	0.0186008i
$579$	10.2999	−	31.6998i	0.428048	−	1.31740i
$580$	−6.50249	+	7.92270i	−0.270001	+	0.328972i
$581$	−7.29374	−	22.4478i	−0.302595	−	0.931293i
$582$			18.1732i			0.753304i
$583$	−75.8547	+	24.6467i	−3.14158	+	1.02076i
$584$	−0.387719	−	0.281694i	−0.0160439	−	0.0116566i
$585$	−6.46132	−	24.7649i	−0.267143	−	1.02390i
$586$	−11.4849	+	8.34425i	−0.474436	+	0.344698i
$587$	4.71297	−	6.48684i	0.194525	−	0.267741i	−0.700602	−	0.713553i	$-0.747085\pi$
$587$	4.71297	−	6.48684i	0.194525	−	0.267741i	0.895127	+	0.445812i	$0.147085\pi$
$588$	−15.5312	+	21.3769i	−0.640496	+	0.881568i
$589$	−7.26133	+	5.27566i	−0.299198	+	0.217380i
$590$	2.72250	+	0.160657i	0.112084	+	0.00661413i
$591$	30.7679	+	22.3542i	1.26562	+	0.919529i
$592$	−4.23241	+	1.37519i	−0.173951	+	0.0565201i
$593$		−	16.2987i		−	0.669309i	−0.942341	−	0.334655i	$-0.891380\pi$
$593$		−	16.2987i		−	0.669309i	0.942341	−	0.334655i	$-0.108620\pi$
$594$	4.77118	+	14.6842i	0.195764	+	0.602500i
$595$	−37.1661	+	9.69688i	−1.52366	+	0.397533i
$596$	−6.74972	+	20.7735i	−0.276479	+	0.850916i
$597$	22.9162	+	7.44593i	0.937899	+	0.304742i
$598$	−8.94374	−	12.3100i	−0.365737	−	0.503394i
$599$	−22.3957			−0.915065			−0.457533	−	0.889193i	$-0.651267\pi$
$599$	−22.3957			−0.915065			−0.457533	+	0.889193i	$0.651267\pi$
$600$	10.9588	+	1.29789i	0.447391	+	0.0529861i
$601$	−44.5158			−1.81584			−0.907919	−	0.419146i	$-0.862330\pi$
$601$	−44.5158			−1.81584			−0.907919	+	0.419146i	$0.862330\pi$
$602$	9.99388	+	13.7554i	0.407320	+	0.560628i
$603$	−20.1269	−	6.53961i	−0.819629	−	0.266314i
$604$	3.59582	−	11.0668i	0.146312	−	0.450301i
$605$	57.0678	+	22.3384i	2.32014	+	0.908183i
$606$	−7.21894	−	22.2176i	−0.293249	−	0.902529i
$607$			25.8752i			1.05024i	0.851027	+	0.525122i	$0.175980\pi$
$607$			25.8752i			1.05024i	−0.851027	+	0.525122i	$0.824020\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	−35.6491	−	25.9006i	−1.44458	−	1.04955i
$610$	−2.43355	+	6.21700i	−0.0985318	+	0.251719i
$611$	−24.5459	+	17.8337i	−0.993022	+	0.721473i
$612$	−4.33752	+	5.97009i	−0.175334	+	0.241326i
$613$	7.50863	−	10.3347i	0.303271	−	0.417416i	−0.629997	−	0.776597i	$-0.716944\pi$
$613$	7.50863	−	10.3347i	0.303271	−	0.417416i	0.933268	+	0.359181i	$0.116944\pi$
$614$	−17.0230	+	12.3679i	−0.686992	+	0.499129i
$615$	2.29261	−	1.46748i	0.0924471	−	0.0591744i
$616$	−21.8384	−	15.8665i	−0.879893	−	0.639280i
$617$	19.1557	−	6.22407i	0.771180	−	0.250572i	0.103110	−	0.994670i	$-0.467121\pi$
$617$	19.1557	−	6.22407i	0.771180	−	0.250572i	0.668070	+	0.744098i	$0.267121\pi$
$618$			15.8224i			0.636470i
$619$	−3.33150	−	10.2533i	−0.133904	−	0.412115i	0.861514	−	0.507734i	$-0.169517\pi$
$619$	−3.33150	−	10.2533i	−0.133904	−	0.412115i	−0.995418	+	0.0956193i	$0.969517\pi$
$620$	−1.18227	+	20.0350i	−0.0474813	+	0.804623i
$621$	1.91508	−	5.89402i	0.0768496	−	0.236519i
$622$	4.23941	+	1.37747i	0.169985	+	0.0552314i
$623$	26.2852	+	36.1785i	1.05309	+	1.44946i
$624$	−13.5005			−0.540454
$625$	24.3084	+	5.83977i	0.972335	+	0.233591i
$626$	28.4566			1.13735
$627$	−8.03973	−	11.0657i	−0.321076	−	0.441923i
$628$	−6.40657	−	2.08162i	−0.255650	−	0.0830658i
$629$	5.42336	−	16.6914i	0.216244	−	0.665529i
$630$	−1.07358	+	18.1930i	−0.0427725	+	0.724828i
$631$	6.04521	+	18.6052i	0.240656	+	0.740663i	0.996321	+	0.0857044i	$0.0273141\pi$
$631$	6.04521	+	18.6052i	0.240656	+	0.740663i	−0.755665	+	0.654959i	$0.772686\pi$
$632$			4.19024i			0.166679i
$633$	43.3772	−	14.0941i	1.72409	−	0.560191i
$634$	0.552608	+	0.401493i	0.0219469	+	0.0159453i
$635$	40.4736	−	25.9067i	1.60615	−	1.02808i
$636$	22.9798	−	16.6958i	0.911207	−	0.662031i
$637$	43.0449	−	59.2462i	1.70550	−	2.34742i
$638$	16.6971	−	22.9816i	0.661044	−	0.909849i
$639$	−3.78372	+	2.74903i	−0.149681	+	0.108750i
$640$	0.815059	−	2.08223i	0.0322180	−	0.0823073i
$641$	−16.5862	−	12.0506i	−0.655117	−	0.475970i	0.209894	−	0.977724i	$-0.432688\pi$
$641$	−16.5862	−	12.0506i	−0.655117	−	0.475970i	−0.865010	+	0.501754i	$0.832688\pi$
$642$	−20.5125	+	6.66492i	−0.809565	+	0.263044i
$643$		−	12.6111i		−	0.497335i	−0.968589	−	0.248667i	$-0.920007\pi$
$643$		−	12.6111i		−	0.497335i	0.968589	−	0.248667i	$-0.0799926\pi$
$644$	3.34816	+	10.3046i	0.131936	+	0.406058i
$645$	17.9393	+	7.02206i	0.706357	+	0.276493i
$646$	−1.21867	+	3.75069i	−0.0479481	+	0.147569i
$647$	−28.3049	−	9.19683i	−1.11278	−	0.361565i	−0.305773	−	0.952104i	$-0.598915\pi$
$647$	−28.3049	−	9.19683i	−1.11278	−	0.361565i	−0.807008	+	0.590540i	$0.798915\pi$
$648$	−6.53160	−	8.98997i	−0.256585	−	0.353159i
$649$	−7.55865			−0.296703
$650$	−30.3724	−	3.59711i	−1.19130	−	0.141090i
$651$	−86.2846			−3.38176
$652$	4.94985	+	6.81288i	0.193851	+	0.266813i
$653$	−3.00540	−	0.976515i	−0.117611	−	0.0382140i	0.249620	−	0.968344i	$-0.419694\pi$
$653$	−3.00540	−	0.976515i	−0.117611	−	0.0382140i	−0.367231	+	0.930130i	$0.619694\pi$
$654$	−10.7798	+	33.1769i	−0.421525	+	1.29732i
$655$	−15.8237	+	4.12852i	−0.618285	+	0.161315i
$656$	−0.170442	−	0.524566i	−0.00665463	−	0.0204809i
$657$		−	0.896762i		−	0.0349860i
$658$	20.5472	−	6.67618i	0.801012	−	0.260264i
$659$	1.06987	+	0.777305i	0.0416762	+	0.0302795i	0.608428	−	0.793609i	$-0.291800\pi$
$659$	1.06987	+	0.777305i	0.0416762	+	0.0302795i	−0.566752	+	0.823888i	$0.691800\pi$
$660$	−30.5319	−	1.80170i	−1.18845	−	0.0701312i
$661$	16.1185	−	11.7108i	0.626937	−	0.455497i	−0.228401	−	0.973567i	$-0.573350\pi$
$661$	16.1185	−	11.7108i	0.626937	−	0.455497i	0.855338	+	0.518071i	$0.173350\pi$
$662$	−8.17951	+	11.2581i	−0.317906	+	0.437560i
$663$	31.2950	−	43.0739i	1.21540	−	1.67285i
$664$	−4.38398	+	3.18515i	−0.170131	+	0.123608i
$665$	2.45882	+	9.42415i	0.0953490	+	0.365453i
$666$	−6.73685	−	4.89461i	−0.261048	−	0.189662i
$667$	−10.8440	+	3.52343i	−0.419881	+	0.136428i
$668$			2.16991i			0.0839562i
$669$	2.66138	+	8.19088i	0.102895	+	0.316678i
$670$	−16.0441	+	19.5483i	−0.619837	+	0.755216i
$671$	5.71795	−	17.5980i	0.220739	−	0.679365i
$672$	9.14284	+	2.97069i	0.352693	+	0.114597i
$673$	1.10936	+	1.52691i	0.0427628	+	0.0588580i	0.829863	−	0.557967i	$-0.188419\pi$
$673$	1.10936	+	1.52691i	0.0427628	+	0.0588580i	−0.787100	+	0.616825i	$0.788419\pi$
$674$	−3.03506			−0.116906
$675$	−6.08587	−	10.8690i	−0.234245	−	0.418348i
$676$	24.4169			0.939110
$677$	1.55204	+	2.13620i	0.0596496	+	0.0821006i	0.837800	−	0.545978i	$-0.183842\pi$
$677$	1.55204	+	2.13620i	0.0596496	+	0.0821006i	−0.778150	+	0.628078i	$0.783842\pi$
$678$	−22.7194	−	7.38197i	−0.872532	−	0.283503i
$679$	−11.0829	+	34.1097i	−0.425323	+	1.30901i
$680$	4.75406	+	7.42719i	0.182310	+	0.284820i
$681$	0.601083	+	1.84994i	0.0230335	+	0.0708899i
$682$		−	55.6242i		−	2.12996i
$683$	22.4686	−	7.30050i	0.859738	−	0.279346i	0.154219	−	0.988037i	$-0.450714\pi$
$683$	22.4686	−	7.30050i	0.859738	−	0.279346i	0.705519	+	0.708691i	$0.250714\pi$
$684$	1.51382	+	1.09986i	0.0578825	+	0.0420541i
$685$	−7.29099	−	5.98402i	−0.278574	−	0.228637i
$686$	−17.5207	+	12.7295i	−0.668944	+	0.486016i
$687$	4.50063	−	6.19459i	0.171710	−	0.236338i
$688$	2.29444	−	3.15803i	0.0874747	−	0.120399i
$689$	−63.6886	+	46.2725i	−2.42634	+	1.76284i
$690$	9.48946	+	7.78839i	0.361258	+	0.296499i
$691$	18.1146	+	13.1610i	0.689111	+	0.500669i	0.876368	−	0.481642i	$-0.159960\pi$
$691$	18.1146	+	13.1610i	0.689111	+	0.500669i	−0.187256	+	0.982311i	$0.559960\pi$
$692$	7.84088	−	2.54766i	0.298065	−	0.0968473i
$693$		−	50.5104i		−	1.91873i
$694$	−0.401919	−	1.23698i	−0.0152566	−	0.0469551i
$695$	−1.19096	−	1.86062i	−0.0451758	−	0.0705774i
$696$	−3.12620	+	9.62144i	−0.118498	+	0.364700i
$697$	2.06874	+	0.672173i	0.0783590	+	0.0254604i
$698$	16.8557	+	23.1998i	0.637996	+	0.878127i
$699$	−3.51555			−0.132970
$700$	19.7773	+	9.11925i	0.747511	+	0.344675i
$701$	−7.58194			−0.286366			−0.143183	−	0.989696i	$-0.545734\pi$
$701$	−7.58194			−0.286366			−0.143183	+	0.989696i	$0.545734\pi$
$702$	8.95758	+	12.3291i	0.338082	+	0.465330i
$703$	−4.23241	−	1.37519i	−0.159628	−	0.0518664i
$704$	−1.91508	+	5.89402i	−0.0721775	+	0.222139i
$705$	15.5299	−	18.9218i	0.584890	−	0.712637i
$706$	−6.30680	−	19.4103i	−0.237359	−	0.730517i
$707$		−	46.1032i		−	1.73389i
$708$	2.56013	−	0.831837i	0.0962157	−	0.0312624i
$709$	1.53556	+	1.11565i	0.0576694	+	0.0418992i	0.616246	−	0.787553i	$-0.288653\pi$
$709$	1.53556	+	1.11565i	0.0576694	+	0.0418992i	−0.558577	+	0.829453i	$0.688653\pi$
$710$	1.41095	+	5.40789i	0.0529521	+	0.202954i
$711$	−6.34329	+	4.60867i	−0.237892	+	0.172839i
$712$	6.03468	−	8.30602i	0.226159	−	0.311281i
$713$	−13.1233	+	18.0627i	−0.491472	+	0.676454i
$714$	−30.6717	+	22.2843i	−1.14786	+	0.833968i
$715$	84.6193	+	4.99343i	3.16458	+	0.186744i
$716$	7.22731	+	5.25095i	0.270097	+	0.196237i
$717$	41.4204	−	13.4583i	1.54687	−	0.502610i
$718$		−	1.99811i		−	0.0745688i
$719$	8.45853	+	26.0327i	0.315450	+	0.970855i	0.975569	+	0.219694i	$0.0705060\pi$
$719$	8.45853	+	26.0327i	0.315450	+	0.970855i	−0.660119	+	0.751161i	$0.729494\pi$
$720$	4.04858	−	1.05630i	0.150882	−	0.0393660i
$721$	−9.64926	+	29.6974i	−0.359357	+	1.10599i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	21.9620	+	30.2280i	0.816774	+	1.12419i
$724$	21.2274			0.788908
$725$	−9.59661	+	20.8126i	−0.356409	+	0.772960i
$726$	60.4895			2.24498
$727$	1.91823	+	2.64021i	0.0711431	+	0.0979201i	0.843106	−	0.537748i	$-0.180725\pi$
$727$	1.91823	+	2.64021i	0.0711431	+	0.0979201i	−0.771963	+	0.635668i	$0.780725\pi$
$728$	−25.3395	−	8.23329i	−0.939143	−	0.305146i
$729$	1.32789	−	4.08681i	0.0491810	−	0.151363i
$730$	−0.997902	−	0.390614i	−0.0369340	−	0.0144573i
$731$	4.75714	+	14.6410i	0.175949	+	0.541516i
$732$			6.58976i			0.243565i
$733$	−31.4691	+	10.2249i	−1.16234	+	0.377667i	−0.825778	−	0.563995i	$-0.809264\pi$
$733$	−31.4691	+	10.2249i	−1.16234	+	0.377667i	−0.336561	+	0.941662i	$0.609264\pi$
$734$	−3.85882	−	2.80360i	−0.142432	−	0.103483i
$735$	−21.5365	+	55.0193i	−0.794386	+	2.02942i
$736$	2.01245	−	1.46213i	0.0741798	−	0.0538948i
$737$	41.1980	−	56.7041i	1.51755	−	2.08872i
$738$	0.606639	−	0.834967i	0.0223307	−	0.0307356i
$739$	−3.96657	+	2.88188i	−0.145913	+	0.106012i	−0.658347	−	0.752715i	$-0.728744\pi$
$739$	−3.96657	+	2.88188i	−0.145913	+	0.106012i	0.512434	+	0.858727i	$0.328744\pi$
$740$	−8.38109	+	5.36465i	−0.308095	+	0.197208i
$741$	−10.9222	−	7.93542i	−0.401236	−	0.291515i
$742$	53.3131	−	17.3225i	1.95719	−	0.635928i
$743$			14.1266i			0.518256i	0.965843	+	0.259128i	$0.0834351\pi$
$743$			14.1266i			0.518256i	−0.965843	+	0.259128i	$0.916565\pi$
$744$	6.12151	+	18.8401i	0.224425	+	0.690710i
$745$	−2.87716	+	48.7566i	−0.105411	+	1.78630i
$746$	−5.05029	+	15.5432i	−0.184904	+	0.569077i
$747$	−9.64350	−	3.13336i	−0.352837	−	0.114644i
$748$	−14.3658	−	19.7728i	−0.525265	−	0.722965i
$749$	−42.5650			−1.55529
$750$	24.4435	−	3.37816i	0.892552	−	0.123353i
$751$	20.2966			0.740632			0.370316	−	0.928906i	$-0.379249\pi$
$751$	20.2966			0.740632			0.370316	+	0.928906i	$0.379249\pi$
$752$	−2.91546	−	4.01278i	−0.106316	−	0.146331i
$753$	−51.4771	−	16.7259i	−1.87593	−	0.609526i
$754$	8.66428	−	26.6659i	0.315534	−	0.971115i
$755$	1.53276	−	25.9744i	0.0557830	−	0.945305i
$756$	−3.35334	−	10.3205i	−0.121960	−	0.375354i
$757$			49.4359i			1.79678i	0.439200	+	0.898389i	$0.355262\pi$
$757$			49.4359i			1.79678i	−0.439200	+	0.898389i	$0.644738\pi$
$758$	19.4192	−	6.30968i	0.705337	−	0.229178i
$759$	−27.5263	−	19.9990i	−0.999141	−	0.725918i
$760$	1.88330	−	1.20548i	0.0683145	−	0.0437273i
$761$	34.9761	−	25.4116i	1.26788	−	0.921171i	0.268767	−	0.963205i	$-0.413384\pi$
$761$	34.9761	−	25.4116i	1.26788	−	0.921171i	0.999116	+	0.0420337i	$0.0133837\pi$
$762$	27.8797	−	38.3732i	1.00998	−	1.39011i
$763$	−40.4658	+	55.6964i	−1.46496	+	2.01635i
$764$	−2.69466	+	1.95779i	−0.0974894	+	0.0708302i
$765$	−6.01467	+	15.3657i	−0.217461	+	0.555547i
$766$	18.3461	+	13.3292i	0.662872	+	0.481604i
$767$	−7.09543	+	2.30544i	−0.256201	+	0.0832448i
$768$		−	2.20708i		−	0.0796410i
$769$	−16.7412	−	51.5241i	−0.603703	−	1.85801i	−0.505469	−	0.862845i	$-0.668680\pi$
$769$	−16.7412	−	51.5241i	−0.603703	−	1.85801i	−0.0982347	−	0.995163i	$-0.531320\pi$
$770$	−56.2071	−	22.0015i	−2.02556	−	0.792878i
$771$	−12.3583	+	38.0348i	−0.445072	+	1.36979i
$772$	−14.3628	−	4.66675i	−0.516928	−	0.167960i
$773$	−3.90647	−	5.37680i	−0.140506	−	0.193390i	0.732965	−	0.680267i	$-0.238136\pi$
$773$	−3.90647	−	5.37680i	−0.140506	−	0.193390i	−0.873471	+	0.486877i	$0.838136\pi$
$774$	7.30426			0.262546
$775$	8.75187	+	44.0158i	0.314376	+	1.58109i
$776$	8.23407			0.295586
$777$	−25.1463	−	34.6110i	−0.902120	−	1.24166i
$778$	3.13155	+	1.01750i	0.112272	+	0.0364793i
$779$	0.170442	−	0.524566i	0.00610671	−	0.0187945i
$780$	−29.2103	+	7.62116i	−1.04590	+	0.272881i
$781$	−4.78664	−	14.7318i	−0.171279	−	0.527144i
$782$			9.81007i			0.350807i
$783$	10.8608	−	3.52888i	0.388133	−	0.126112i
$784$	9.68560	+	7.03700i	0.345914	+	0.251322i
$785$	−15.0366	−	0.887318i	−0.536679	−	0.0316698i
$786$	−13.0587	+	9.48769i	−0.465788	+	0.338415i
$787$	−11.2768	+	15.5212i	−0.401976	+	0.553273i	−0.961239	−	0.275718i	$-0.911084\pi$
$787$	−11.2768	+	15.5212i	−0.401976	+	0.553273i	0.559262	+	0.828991i	$0.311084\pi$
$788$	10.1284	−	13.9406i	0.360810	−	0.496613i
$789$	21.7553	−	15.8062i	0.774510	−	0.562714i
$790$	2.36542	+	9.06617i	0.0841580	+	0.322560i
$791$	−38.1406	−	27.7108i	−1.35612	−	0.985281i
$792$	−11.0288	+	3.58349i	−0.391893	+	0.127334i
$793$		−	18.2636i		−	0.648559i
$794$	5.92035	+	18.2209i	0.210105	+	0.646637i
$795$	40.2950	−	49.0959i	1.42912	−	1.74125i
$796$	3.37366	−	10.3831i	0.119576	−	0.368018i
$797$	−30.1059	−	9.78199i	−1.06640	−	0.346496i	−0.277318	−	0.960778i	$-0.589446\pi$
$797$	−30.1059	−	9.78199i	−1.06640	−	0.346496i	−0.789086	+	0.614282i	$0.789446\pi$
$798$	5.65059	+	7.77737i	0.200029	+	0.275316i
$799$	19.5611			0.692022
$800$	0.588058	−	4.96530i	0.0207910	−	0.175550i
$801$	19.2111			0.678793
$802$	−20.7134	−	28.5095i	−0.731415	−	1.00671i
$803$	2.82469	+	0.917798i	0.0996812	+	0.0323884i
$804$	−7.71350	+	23.7397i	−0.272034	+	0.837235i
$805$	13.0612	+	20.4053i	0.460348	+	0.719194i
$806$	−16.9658	−	52.2154i	−0.597595	−	1.83921i
$807$		−	26.8496i		−	0.945152i
$808$	−10.0665	+	3.27082i	−0.354139	+	0.115067i
$809$	−31.2677	−	22.7173i	−1.09931	−	0.798698i	−0.118365	−	0.992970i	$-0.537765\pi$
$809$	−31.2677	−	22.7173i	−1.09931	−	0.798698i	−0.980948	+	0.194273i	$0.937765\pi$
$810$	−19.2069	−	15.7639i	−0.674862	−	0.553888i
$811$	−0.768386	+	0.558265i	−0.0269817	+	0.0196033i	−0.601194	−	0.799103i	$-0.705308\pi$
$811$	−0.768386	+	0.558265i	−0.0269817	+	0.0196033i	0.574213	+	0.818706i	$0.305308\pi$
$812$	−11.7353	+	16.1522i	−0.411827	+	0.566831i
$813$	−9.88612	+	13.6071i	−0.346721	+	0.477221i
$814$	22.3123	−	16.2108i	0.782046	−	0.568189i
$815$	14.5556	+	11.9464i	0.509860	+	0.418463i
$816$	7.04174	+	5.11613i	0.246510	+	0.179100i
$817$	3.71248	−	1.20626i	0.129883	−	0.0422017i
$818$			9.38994i			0.328312i
$819$	−15.4061	−	47.4149i	−0.538331	−	1.65681i
$820$	−0.664896	−	1.03876i	−0.0232192	−	0.0362749i
$821$	3.44618	−	10.6062i	0.120272	−	0.370161i	−0.872738	−	0.488189i	$-0.837658\pi$
$821$	3.44618	−	10.6062i	0.120272	−	0.370161i	0.993010	+	0.118029i	$0.0376575\pi$
$822$	−8.85428	−	2.87693i	−0.308828	−	0.100344i
$823$	30.1508	+	41.4991i	1.05099	+	1.44657i	0.887946	+	0.459949i	$0.152132\pi$
$823$	30.1508	+	41.4991i	1.05099	+	1.44657i	0.163047	+	0.986618i	$0.447868\pi$
$824$	7.16893			0.249742
$825$	−67.0770	+	13.3372i	−2.33532	+	0.464343i
$826$	5.31246			0.184844
$827$	28.5054	+	39.2343i	0.991231	+	1.36431i	0.930554	+	0.366154i	$0.119326\pi$
$827$	28.5054	+	39.2343i	0.991231	+	1.36431i	0.0606763	+	0.998157i	$0.480674\pi$
$828$	4.42681	+	1.43836i	0.153842	+	0.0499864i
$829$	3.01385	−	9.27566i	0.104675	−	0.322157i	−0.884979	−	0.465631i	$-0.845827\pi$
$829$	3.01385	−	9.27566i	0.104675	−	0.322157i	0.989654	+	0.143474i	$0.0458274\pi$
$830$	−7.68730	+	9.36629i	−0.266830	+	0.325109i
$831$	0.846195	+	2.60432i	0.0293542	+	0.0903429i
$832$			6.11693i			0.212066i
$833$	−44.9035	+	14.5900i	−1.55581	+	0.505515i
$834$	−1.76406	−	1.28166i	−0.0610844	−	0.0443804i
$835$	1.22493	+	4.69489i	0.0423904	+	0.162473i
$836$	−5.01376	+	3.64271i	−0.173404	+	0.125986i
$837$	13.1436	−	18.0907i	0.454310	−	0.625305i
$838$	−4.55259	+	6.26610i	−0.157267	+	0.216459i
$839$	42.0214	−	30.5303i	1.45074	−	1.05402i	0.465082	−	0.885268i	$-0.346025\pi$
$839$	42.0214	−	30.5303i	1.45074	−	1.05402i	0.985658	−	0.168756i	$-0.0539751\pi$
$840$	21.4588	+	1.26629i	0.740398	+	0.0436913i
$841$	6.46378	+	4.69621i	0.222889	+	0.161938i
$842$	34.3479	−	11.1603i	1.18371	−	0.384609i
$843$			12.0714i			0.415762i
$844$	−6.38587	−	19.6537i	−0.219811	−	0.676508i
$845$	52.8293	−	13.7835i	1.81738	−	0.474167i
$846$	2.86806	−	8.82698i	0.0986060	−	0.303478i
$847$	113.534	+	36.8894i	3.90108	+	1.26754i
$848$	−7.56466	−	10.4119i	−0.259771	−	0.357545i
$849$	64.5878			2.21665
$850$	14.4788	+	13.3861i	0.496618	+	0.459138i
$851$	−11.0700			−0.379475
$852$	3.24249	+	4.46291i	0.111086	+	0.152897i
$853$	−21.3539	−	6.93829i	−0.731143	−	0.237563i	−0.0802952	−	0.996771i	$-0.525586\pi$
$853$	−21.3539	−	6.93829i	−0.731143	−	0.237563i	−0.650848	+	0.759208i	$0.725586\pi$
$854$	−4.01876	+	12.3685i	−0.137519	+	0.423240i
$855$	3.89625	+	1.52513i	0.133249	+	0.0521583i
$856$	3.01980	+	9.29398i	0.103215	+	0.317662i
$857$			21.3166i			0.728161i	0.931368	+	0.364080i	$0.118617\pi$
$857$			21.3166i			0.728161i	−0.931368	+	0.364080i	$0.881383\pi$
$858$	79.5725	−	25.8547i	2.71656	−	0.882664i
$859$	12.5643	+	9.12846i	0.428687	+	0.311459i	0.781124	−	0.624376i	$-0.214647\pi$
$859$	12.5643	+	9.12846i	0.428687	+	0.311459i	−0.352437	+	0.935836i	$0.614647\pi$
$860$	3.18161	−	8.12806i	0.108492	−	0.277164i
$861$	4.28969	−	3.11664i	0.146192	−	0.106215i
$862$	−8.18003	+	11.2588i	−0.278613	+	0.383478i
$863$	19.8307	−	27.2946i	0.675043	−	0.929118i	−0.324818	−	0.945777i	$-0.605303\pi$
$863$	19.8307	−	27.2946i	0.675043	−	0.929118i	0.999861	+	0.0166590i	$0.00530297\pi$
$864$	−2.01556	+	1.46439i	−0.0685708	+	0.0498196i
$865$	15.5267	−	9.93844i	0.527922	−	0.337917i
$866$	16.9698	+	12.3293i	0.576658	+	0.418966i
$867$	3.03764	−	0.986990i	0.103164	−	0.0335199i
$868$			39.0945i			1.32695i
$869$	−8.02467	−	24.6974i	−0.272218	−	0.837802i
$870$	−1.33258	+	22.5821i	−0.0451788	+	0.765604i
$871$	21.3780	−	65.7948i	0.724367	−	2.22937i
$872$	15.0321	+	4.88422i	0.509050	+	0.165400i
$873$	9.05630	+	12.4649i	0.306509	+	0.421874i
$874$	2.48752			0.0841417
$875$	47.9388	+	8.56632i	1.62063	+	0.289595i
$876$	−1.05773			−0.0357375
$877$	5.04874	+	6.94900i	0.170484	+	0.234651i	0.885706	−	0.464246i	$-0.153675\pi$
$877$	5.04874	+	6.94900i	0.170484	+	0.234651i	−0.715222	+	0.698897i	$0.753675\pi$
$878$	−19.0367	−	6.18539i	−0.642456	−	0.208747i
$879$	−9.68207	+	29.7984i	−0.326568	+	1.00507i
$880$	−0.816330	+	13.8336i	−0.0275185	+	0.466331i
$881$	14.7206	+	45.3052i	0.495948	+	1.52637i	0.815474	+	0.578794i	$0.196476\pi$
$881$	14.7206	+	45.3052i	0.495948	+	1.52637i	−0.319526	+	0.947577i	$0.603524\pi$
$882$			22.4020i			0.754315i
$883$	−32.0295	+	10.4070i	−1.07788	+	0.350224i	−0.793551	−	0.608504i	$-0.791770\pi$
$883$	−32.0295	+	10.4070i	−1.07788	+	0.350224i	−0.284327	+	0.958727i	$0.591770\pi$
$884$	−19.5163	−	14.1794i	−0.656403	−	0.476904i
$885$	5.06962	−	3.24501i	0.170413	−	0.109080i
$886$	−0.510676	+	0.371028i	−0.0171565	+	0.0124649i
$887$	2.67621	−	3.68348i	0.0898583	−	0.123679i	−0.761721	−	0.647905i	$-0.775645\pi$
$887$	2.67621	−	3.68348i	0.0898583	−	0.123679i	0.851579	+	0.524226i	$0.175645\pi$
$888$	−5.77321	+	7.94614i	−0.193736	+	0.266655i
$889$	75.7299	−	55.0210i	2.53990	−	1.84534i
$890$	8.36805	−	21.3778i	0.280498	−	0.716587i
$891$	55.7139	+	40.4785i	1.86649	+	1.35608i
$892$	3.71119	−	1.20584i	0.124260	−	0.0403744i
$893$		−	4.96007i		−	0.165983i
$894$	14.8972	+	45.8487i	0.498235	+	1.53341i
$895$	18.6015	+	7.28128i	0.621779	+	0.243386i
$896$	1.34598	−	4.14251i	0.0449661	−	0.138392i
$897$	−31.9392	−	10.3777i	−1.06642	−	0.346501i
$898$	−10.1404	−	13.9570i	−0.338388	−	0.465752i
$899$	−41.1410			−1.37213
$900$	8.16337	−	4.57091i	0.272112	−	0.152364i
$901$	50.7546			1.69088
$902$	2.00918	+	2.76539i	0.0668982	+	0.0920775i
$903$	35.6894	+	11.5962i	1.18767	+	0.385897i
$904$	−3.34468	+	10.2939i	−0.111242	+	0.342369i
$905$	45.9283	−	11.9830i	1.52671	−	0.398328i
$906$	−7.93624	−	24.4252i	−0.263664	−	0.811474i
$907$			19.1387i			0.635491i	0.948176	+	0.317746i	$0.102926\pi$
$907$			19.1387i			0.635491i	−0.948176	+	0.317746i	$0.897074\pi$
$908$	0.838186	−	0.272343i	0.0278162	−	0.00903803i
$909$	−16.0232	−	11.6415i	−0.531456	−	0.386125i
$910$	−59.4732	−	3.50955i	−1.97152	−	0.116340i
$911$	15.1001	−	10.9708i	0.500287	−	0.363480i	−0.308840	−	0.951114i	$-0.599941\pi$
$911$	15.1001	−	10.9708i	0.500287	−	0.363480i	0.809127	+	0.587634i	$0.199941\pi$
$912$	1.29729	−	1.78556i	0.0429575	−	0.0591259i
$913$	19.7394	−	27.1690i	0.653280	−	0.899163i
$914$	15.0681	−	10.9476i	0.498407	−	0.362114i
$915$	3.71997	+	14.2579i	0.122978	+	0.471350i
$916$	−2.80669	−	2.03918i	−0.0927357	−	0.0673764i
$917$	−30.2962	+	9.84383i	−1.00047	+	0.325072i
$918$		−	9.82524i		−	0.324281i
$919$	8.33542	+	25.6538i	0.274960	+	0.846240i	0.989230	+	0.146370i	$0.0467590\pi$
$919$	8.33542	+	25.6538i	0.274960	+	0.846240i	−0.714270	+	0.699870i	$0.753241\pi$
$920$	3.52883	−	4.29956i	0.116342	−	0.141752i
$921$	−14.3509	+	44.1674i	−0.472877	+	1.45537i
$922$	20.2372	+	6.57548i	0.666478	+	0.216552i
$923$	−8.98660	−	12.3690i	−0.295797	−	0.407130i
$924$	−59.5772			−1.95995
$925$	−15.1053	+	16.3383i	−0.496658	+	0.537201i
$926$	−38.2101			−1.25566
$927$	7.88481	+	10.8525i	0.258971	+	0.356443i
$928$	4.35936	+	1.41644i	0.143103	+	0.0464970i
$929$	7.17004	−	22.0671i	0.235241	−	0.723999i	−0.761848	−	0.647756i	$-0.775708\pi$
$929$	7.17004	−	22.0671i	0.235241	−	0.723999i	0.997089	−	0.0762426i	$-0.0242923\pi$
$930$	23.8801	+	37.3074i	0.783059	+	1.22336i
$931$	3.69957	+	11.3861i	0.121249	+	0.373165i
$932$			1.59285i			0.0521756i
$933$	9.35670	−	3.04018i	0.306325	−	0.0995309i
$934$	−11.0055	−	7.99595i	−0.360110	−	0.261635i
$935$	−42.2442	−	34.6716i	−1.38153	−	1.13388i
$936$	−9.25996	+	6.72776i	−0.302671	+	0.219904i
$937$	−35.2719	+	48.5477i	−1.15228	+	1.58598i	−0.415915	+	0.909403i	$0.636539\pi$
$937$	−35.2719	+	48.5477i	−1.15228	+	1.58598i	−0.736369	+	0.676580i	$0.763461\pi$
$938$	−28.9553	+	39.8535i	−0.945423	+	1.30126i
$939$	50.8110	−	36.9164i	1.65816	−	1.20472i
$940$	−8.57324	−	7.03642i	−0.279628	−	0.229503i
$941$	−33.8149	−	24.5680i	−1.10233	−	0.800893i	−0.120895	−	0.992665i	$-0.538576\pi$
$941$	−33.8149	−	24.5680i	−1.10233	−	0.800893i	−0.981439	+	0.191772i	$0.938576\pi$
$942$	−14.1398	+	4.59430i	−0.460700	+	0.149690i
$943$		−	1.37202i		−	0.0446791i
$944$	−0.376895	−	1.15996i	−0.0122669	−	0.0377536i
$945$	−13.0814	−	20.4369i	−0.425539	−	0.664813i
$946$	−7.47560	+	23.0075i	−0.243053	+	0.748039i
$947$	5.17014	+	1.67988i	0.168007	+	0.0545887i	0.391813	−	0.920045i	$-0.371848\pi$
$947$	5.17014	+	1.67988i	0.168007	+	0.0545887i	−0.223806	+	0.974634i	$0.571848\pi$
$948$	5.43595	+	7.48195i	0.176551	+	0.243002i
$949$	2.93152			0.0951612
$950$	3.39428	−	3.67136i	0.110125	−	0.119115i
$951$	1.50757			0.0488862
$952$	10.0967	+	13.8970i	0.327237	+	0.450403i
$953$	−29.0900	−	9.45193i	−0.942319	−	0.306178i	−0.202728	−	0.979235i	$-0.564981\pi$
$953$	−29.0900	−	9.45193i	−0.942319	−	0.306178i	−0.739590	+	0.673057i	$0.764981\pi$
$954$	7.44168	−	22.9031i	0.240933	−	0.741516i
$955$	−4.72509	+	5.75710i	−0.152900	+	0.186295i
$956$	−6.09780	−	18.7671i	−0.197217	−	0.606971i
$957$		−	62.6959i		−	2.02667i
$958$	−8.29611	+	2.69557i	−0.268035	+	0.0870899i
$959$	−14.8643	−	10.7995i	−0.479993	−	0.348735i
$960$	−1.24591	−	4.77532i	−0.0402116	−	0.154123i
$961$	−40.0945	+	29.1303i	−1.29337	+	0.939688i
$962$	16.0005	−	22.0228i	0.515877	−	0.710044i
$963$	−10.7481	+	14.7935i	−0.346353	+	0.476714i
$964$	13.6960	−	9.95070i	0.441117	−	0.320490i
$965$	−33.7103	−	1.98926i	−1.08517	−	0.0640367i
$966$	19.3464	+	14.0560i	0.622459	+	0.452243i
$967$	14.9403	−	4.85440i	0.480448	−	0.156107i	−0.0587732	−	0.998271i	$-0.518719\pi$
$967$	14.9403	−	4.85440i	0.480448	−	0.156107i	0.539221	+	0.842164i	$0.318719\pi$
$968$		−	27.4071i		−	0.880896i
$969$	2.68971	+	8.27807i	0.0864058	+	0.265930i
$970$	17.8155	−	4.64819i	0.572023	−	0.149244i
$971$	7.01357	−	21.5855i	0.225076	−	0.692713i	−0.773208	−	0.634153i	$-0.781349\pi$
$971$	7.01357	−	21.5855i	0.225076	−	0.692713i	0.998284	−	0.0585602i	$-0.0186510\pi$
$972$	−16.2169	−	5.26918i	−0.520156	−	0.169009i
$973$	−2.52938	−	3.48139i	−0.0810882	−	0.111608i
$974$	−12.8442			−0.411555
$975$	−58.8983	+	32.9789i	−1.88626	+	1.05617i
$976$	2.98574			0.0955713
$977$	2.83282	+	3.89905i	0.0906300	+	0.124742i	0.851924	−	0.523665i	$-0.175436\pi$
$977$	2.83282	+	3.89905i	0.0906300	+	0.124742i	−0.761294	+	0.648407i	$0.775436\pi$
$978$	17.6765	+	5.74345i	0.565233	+	0.183655i
$979$	−19.6618	+	60.5128i	−0.628394	+	1.93400i
$980$	24.9286	+	9.75794i	0.796315	+	0.311706i
$981$	9.13930	+	28.1279i	0.291795	+	0.898054i
$982$			23.1375i			0.738348i
$983$	13.0802	−	4.25003i	0.417195	−	0.135555i	−0.0928951	−	0.995676i	$-0.529612\pi$
$983$	13.0802	−	4.25003i	0.417195	−	0.135555i	0.510090	+	0.860121i	$0.329612\pi$
$984$	−0.984847	−	0.715534i	−0.0313958	−	0.0228104i
$985$	14.0447	−	35.8799i	0.447501	−	1.14323i
$986$	−14.6244	+	10.6253i	−0.465737	+	0.338378i
$987$	28.0273	−	38.5763i	0.892120	−	1.22790i
$988$	−3.59544	+	4.94870i	−0.114386	+	0.157439i
$989$	7.85566	−	5.70747i	0.249796	−	0.181487i
$990$	−21.8395	+	13.9792i	−0.694105	+	0.444289i
$991$	28.3228	+	20.5777i	0.899703	+	0.653673i	0.938390	−	0.345579i	$-0.112317\pi$
$991$	28.3228	+	20.5777i	0.899703	+	0.653673i	−0.0386864	+	0.999251i	$0.512317\pi$
$992$	8.53620	−	2.77358i	0.271025	−	0.0880613i
$993$			30.7133i			0.974656i
$994$	3.36421	+	10.3540i	0.106706	+	0.328408i
$995$	1.43807	−	24.3697i	0.0455898	−	0.772570i
$996$	−3.69582	+	11.3746i	−0.117106	+	0.360417i
$997$	−4.15820	−	1.35108i	−0.131691	−	0.0427891i	0.242430	−	0.970169i	$-0.422056\pi$
$997$	−4.15820	−	1.35108i	−0.131691	−	0.0427891i	−0.374121	+	0.927380i	$0.622056\pi$
$998$	−20.8365	−	28.6790i	−0.659569	−	0.907819i
$999$	11.0871			0.350782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.b.39.3	✓	96
25.9	even	10	inner	950.2.n.b.609.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.b.39.3	✓	96	1.1	even	1	trivial
950.2.n.b.609.3	yes	96	25.9	even	10	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.09906 - 0.682024i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.131723 + 2.23218i) q^{5} +(0.682024 + 2.09906i) q^{6} +4.35569i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.51382 + 1.09986i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.09906 - 0.682024i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.131723 + 2.23218i) q^{5} +(0.682024 + 2.09906i) q^{6} +4.35569i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.51382 + 1.09986i) q^{9} +(1.88330 - 1.20548i) q^{10} +(-5.01376 + 3.64271i) q^{11} +(1.29729 - 1.78556i) q^{12} +(-3.59544 + 4.94870i) q^{13} +(3.52383 - 2.56021i) q^{14} +(1.79890 - 4.59564i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.75069 - 1.21867i) q^{17} -1.87119i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.08223 - 0.815059i) q^{20} +(2.97069 - 9.14284i) q^{21} +(5.89402 + 1.91508i) q^{22} +(-1.46213 - 2.01245i) q^{23} -2.20708 q^{24} +(-4.96530 - 0.588058i) q^{25} +6.11693 q^{26} +(1.46439 + 2.01556i) q^{27} +(-4.14251 - 1.34598i) q^{28} +(1.41644 - 4.35936i) q^{29} +(-4.77532 + 1.24591i) q^{30} +(-2.77358 - 8.53620i) q^{31} +1.00000i q^{32} +(13.0086 - 4.22674i) q^{33} +(-3.19053 - 2.31805i) q^{34} +(-9.72271 - 0.573743i) q^{35} +(-1.51382 + 1.09986i) q^{36} +(2.61577 - 3.60030i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(10.9222 - 7.93542i) q^{39} +(0.564507 + 2.16364i) q^{40} +(0.446222 + 0.324200i) q^{41} +(-9.14284 + 2.97069i) q^{42} +3.90354i q^{43} +(-1.91508 - 5.89402i) q^{44} +(-2.65449 + 3.23426i) q^{45} +(-0.768687 + 2.36577i) q^{46} +(4.71731 + 1.53275i) q^{47} +(1.29729 + 1.78556i) q^{48} -11.9721 q^{49} +(2.44278 + 4.36266i) q^{50} -8.70407 q^{51} +(-3.59544 - 4.94870i) q^{52} +(12.2399 + 3.97698i) q^{53} +(0.769876 - 2.36943i) q^{54} +(-7.47077 - 11.6715i) q^{55} +(1.34598 + 4.14251i) q^{56} +2.20708i q^{57} +(-4.35936 + 1.41644i) q^{58} +(0.986725 + 0.716898i) q^{59} +(3.81482 + 3.13098i) q^{60} +(-2.41552 + 1.75498i) q^{61} +(-5.27566 + 7.26133i) q^{62} +(-4.79064 + 6.59376i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-10.5728 - 8.67755i) q^{65} +(-11.0657 - 8.03973i) q^{66} +(-10.7562 + 3.49489i) q^{67} +3.94371i q^{68} +(1.69655 + 5.22145i) q^{69} +(5.25070 + 8.20308i) q^{70} +(-0.772370 + 2.37711i) q^{71} +(1.77961 + 0.578230i) q^{72} +(-0.281694 - 0.387719i) q^{73} -4.45022 q^{74} +(10.0214 + 4.62082i) q^{75} +1.00000 q^{76} +(-15.8665 - 21.8384i) q^{77} +(-12.8398 - 4.17190i) q^{78} +(-1.29486 + 3.98516i) q^{79} +(1.41861 - 1.72845i) q^{80} +(-3.43386 - 10.5683i) q^{81} -0.551561i q^{82} +(-5.15367 + 1.67453i) q^{83} +(7.77737 + 5.65059i) q^{84} +(2.22625 + 8.53276i) q^{85} +(3.15803 - 2.29444i) q^{86} +(-5.94638 + 8.18449i) q^{87} +(-3.64271 + 5.01376i) q^{88} +(8.30602 - 6.03468i) q^{89} +(4.17684 + 0.246478i) q^{90} +(-21.5550 - 15.6606i) q^{91} +(2.36577 - 0.768687i) q^{92} +19.8096i q^{93} +(-1.53275 - 4.71731i) q^{94} +(2.16364 - 0.564507i) q^{95} +(0.682024 - 2.09906i) q^{96} +(7.83106 + 2.54447i) q^{97} +(7.03700 + 9.68560i) q^{98} -11.5964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

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