LMFDB - Embedded newform 671.2.h.b.70.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(70,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("671.70");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$59$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			70.19
Character	$\chi$	$=$	671.70
Dual form			671.2.h.b.278.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.418710 - 1.28866i) q^{2} +(-1.45739 + 1.05885i) q^{3} +(0.132718 - 0.0964256i) q^{4} +(2.39305 + 1.73865i) q^{5} +(1.97472 + 1.43472i) q^{6} +(3.32854 + 2.41832i) q^{7} +(-2.37222 - 1.72352i) q^{8} +(0.0757533 - 0.233145i) q^{9} +O(q^{10})$	\(q+(-0.418710 - 1.28866i) q^{2} +(-1.45739 + 1.05885i) q^{3} +(0.132718 - 0.0964256i) q^{4} +(2.39305 + 1.73865i) q^{5} +(1.97472 + 1.43472i) q^{6} +(3.32854 + 2.41832i) q^{7} +(-2.37222 - 1.72352i) q^{8} +(0.0757533 - 0.233145i) q^{9} +(1.23853 - 3.81180i) q^{10} +(2.49631 - 2.18368i) q^{11} +(-0.0913215 + 0.281059i) q^{12} +(-1.23233 - 0.895339i) q^{13} +(1.72269 - 5.30191i) q^{14} -5.32856 q^{15} +(-1.12636 + 3.46659i) q^{16} +(2.65034 + 1.92559i) q^{17} -0.332162 q^{18} +(-6.43075 + 4.67222i) q^{19} +0.485252 q^{20} -7.41161 q^{21} +(-3.85924 - 2.30255i) q^{22} +(1.40791 + 4.33310i) q^{23} +5.28220 q^{24} +(1.15868 + 3.56605i) q^{25} +(-0.637796 + 1.96293i) q^{26} +(-1.53355 - 4.71979i) q^{27} +0.674946 q^{28} +(1.74291 + 5.36411i) q^{29} +(2.23112 + 6.86668i) q^{30} +3.48616 q^{31} -0.925593 q^{32} +(-1.32589 + 5.82568i) q^{33} +(1.37169 - 4.22164i) q^{34} +(3.76072 + 11.5743i) q^{35} +(-0.0124273 - 0.0382471i) q^{36} +(-4.02695 - 2.92575i) q^{37} +(8.71349 + 6.33072i) q^{38} +2.74401 q^{39} +(-2.68024 - 8.24892i) q^{40} +(-1.03360 - 3.18109i) q^{41} +(3.10331 + 9.55101i) q^{42} +(3.84140 - 11.8226i) q^{43} +(0.120744 - 0.530522i) q^{44} +(0.586638 - 0.426217i) q^{45} +(4.99437 - 3.62862i) q^{46} +(-3.03947 + 9.35454i) q^{47} +(-2.02906 - 6.24481i) q^{48} +(3.06774 + 9.44154i) q^{49} +(4.11026 - 2.98628i) q^{50} -5.90149 q^{51} -0.249886 q^{52} +(10.6544 - 7.74088i) q^{53} +(-5.44007 + 3.95244i) q^{54} +(9.77043 - 0.885438i) q^{55} +(-3.72800 - 11.4736i) q^{56} +(4.42490 - 13.6184i) q^{57} +(6.18272 - 4.49201i) q^{58} +(-2.39108 + 7.35899i) q^{59} +(-0.707199 + 0.513810i) q^{60} +(5.05090 - 5.95721i) q^{61} +(-1.45969 - 4.49246i) q^{62} +(0.815966 - 0.592834i) q^{63} +(2.64028 + 8.12595i) q^{64} +(-1.39234 - 4.28517i) q^{65} +(8.06246 - 0.730655i) q^{66} +(-0.609463 - 1.87573i) q^{67} +0.537425 q^{68} +(-6.63998 - 4.82423i) q^{69} +(13.3406 - 9.69255i) q^{70} +(3.68170 + 11.3311i) q^{71} +(-0.581533 + 0.422508i) q^{72} +3.17491 q^{73} +(-2.08416 + 6.41439i) q^{74} +(-5.46456 - 3.97024i) q^{75} +(-0.402958 + 1.24018i) q^{76} +(13.5899 - 1.23157i) q^{77} +(-1.14894 - 3.53608i) q^{78} +(-0.430106 + 0.312490i) q^{79} +(-8.72263 + 6.33736i) q^{80} +(7.82751 + 5.68702i) q^{81} +(-3.66655 + 2.66391i) q^{82} +2.48891 q^{83} +(-0.983657 + 0.714669i) q^{84} +(2.99447 + 9.21603i) q^{85} -16.8437 q^{86} +(-8.21989 - 5.97210i) q^{87} +(-9.68541 + 0.877733i) q^{88} +(7.77459 + 5.64857i) q^{89} +(-0.794878 - 0.577513i) q^{90} +(-1.93663 - 5.96033i) q^{91} +(0.604677 + 0.439324i) q^{92} +(-5.08068 + 3.69133i) q^{93} +13.3274 q^{94} -23.5124 q^{95} +(1.34895 - 0.980067i) q^{96} +5.61830 q^{97} +(10.8824 - 7.90653i) q^{98} +(-0.320009 - 0.747421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 2 q^{2} - 2 q^{3} - 62 q^{4} - 6 q^{5} + 9 q^{6} + q^{7} + 12 q^{8} - 59 q^{9}+O(q^{10}) $ 236 * q + 2 * q^2 - 2 * q^3 - 62 * q^4 - 6 * q^5 + 9 * q^6 + q^7 + 12 * q^8 - 59 * q^9	\( 236 q + 2 q^{2} - 2 q^{3} - 62 q^{4} - 6 q^{5} + 9 q^{6} + q^{7} + 12 q^{8} - 59 q^{9} + 16 q^{10} - 15 q^{11} - 17 q^{12} - 8 q^{13} - 16 q^{14} - 20 q^{15} - 60 q^{16} - q^{17} - 12 q^{18} + 7 q^{19} + 26 q^{20} + 11 q^{22} - 10 q^{23} - 18 q^{24} - 43 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 31 q^{29} + 9 q^{30} + 28 q^{31} - 64 q^{32} + 18 q^{33} + 11 q^{34} + 27 q^{35} + 3 q^{36} + 10 q^{37} + 34 q^{38} - 20 q^{39} - 29 q^{40} - q^{41} - 20 q^{42} + 28 q^{43} + 52 q^{44} + 66 q^{45} + 28 q^{46} - 8 q^{47} + 30 q^{48} - 44 q^{49} + 18 q^{50} - 56 q^{51} - 40 q^{52} - 9 q^{53} - 56 q^{54} + 11 q^{55} - 25 q^{56} + 24 q^{57} + 77 q^{58} + 3 q^{59} + 16 q^{60} + 5 q^{61} + 54 q^{62} + 12 q^{63} - 10 q^{64} + 32 q^{65} + 80 q^{66} + 29 q^{67} + 80 q^{68} + 42 q^{69} - 75 q^{70} - 54 q^{71} - 198 q^{72} + 12 q^{73} + 18 q^{74} + 39 q^{75} + 19 q^{76} - 33 q^{77} + 15 q^{78} - 20 q^{79} + 112 q^{80} - 39 q^{81} - 64 q^{82} - 98 q^{83} - 124 q^{84} - 26 q^{85} - 142 q^{86} + 59 q^{87} - 186 q^{88} - 64 q^{89} - 179 q^{90} - 41 q^{91} + 36 q^{92} + 31 q^{93} - 4 q^{94} - 196 q^{95} - 79 q^{96} + 28 q^{97} - 7 q^{98} + 37 q^{99}+O(q^{100}) \) 236 * q + 2 * q^2 - 2 * q^3 - 62 * q^4 - 6 * q^5 + 9 * q^6 + q^7 + 12 * q^8 - 59 * q^9 + 16 * q^10 - 15 * q^11 - 17 * q^12 - 8 * q^13 - 16 * q^14 - 20 * q^15 - 60 * q^16 - q^17 - 12 * q^18 + 7 * q^19 + 26 * q^20 + 11 * q^22 - 10 * q^23 - 18 * q^24 - 43 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 31 * q^29 + 9 * q^30 + 28 * q^31 - 64 * q^32 + 18 * q^33 + 11 * q^34 + 27 * q^35 + 3 * q^36 + 10 * q^37 + 34 * q^38 - 20 * q^39 - 29 * q^40 - q^41 - 20 * q^42 + 28 * q^43 + 52 * q^44 + 66 * q^45 + 28 * q^46 - 8 * q^47 + 30 * q^48 - 44 * q^49 + 18 * q^50 - 56 * q^51 - 40 * q^52 - 9 * q^53 - 56 * q^54 + 11 * q^55 - 25 * q^56 + 24 * q^57 + 77 * q^58 + 3 * q^59 + 16 * q^60 + 5 * q^61 + 54 * q^62 + 12 * q^63 - 10 * q^64 + 32 * q^65 + 80 * q^66 + 29 * q^67 + 80 * q^68 + 42 * q^69 - 75 * q^70 - 54 * q^71 - 198 * q^72 + 12 * q^73 + 18 * q^74 + 39 * q^75 + 19 * q^76 - 33 * q^77 + 15 * q^78 - 20 * q^79 + 112 * q^80 - 39 * q^81 - 64 * q^82 - 98 * q^83 - 124 * q^84 - 26 * q^85 - 142 * q^86 + 59 * q^87 - 186 * q^88 - 64 * q^89 - 179 * q^90 - 41 * q^91 + 36 * q^92 + 31 * q^93 - 4 * q^94 - 196 * q^95 - 79 * q^96 + 28 * q^97 - 7 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.418710	−	1.28866i	−0.296072	−	0.911217i	−0.982859	−	0.184358i	$-0.940979\pi$
$2$	−0.418710	−	1.28866i	−0.296072	−	0.911217i	0.686787	−	0.726859i	$-0.259021\pi$
$3$	−1.45739	+	1.05885i	−0.841422	+	0.611329i	−0.922768	−	0.385357i	$-0.874078\pi$
$3$	−1.45739	+	1.05885i	−0.841422	+	0.611329i	0.0813455	+	0.996686i	$0.474078\pi$
$4$	0.132718	−	0.0964256i	0.0663592	−	0.0482128i
$5$	2.39305	+	1.73865i	1.07020	+	0.777547i	0.975949	−	0.218001i	$-0.0699535\pi$
$5$	2.39305	+	1.73865i	1.07020	+	0.777547i	0.0942537	+	0.995548i	$0.469954\pi$
$6$	1.97472	+	1.43472i	0.806175	+	0.585721i
$7$	3.32854	+	2.41832i	1.25807	+	0.914040i	0.998661	−	0.0517283i	$-0.0164730\pi$
$7$	3.32854	+	2.41832i	1.25807	+	0.914040i	0.259407	+	0.965768i	$0.416473\pi$
$8$	−2.37222	−	1.72352i	−0.838707	−	0.609356i
$9$	0.0757533	−	0.233145i	0.0252511	−	0.0777149i
$10$	1.23853	−	3.81180i	0.391657	−	1.20540i
$11$	2.49631	−	2.18368i	0.752665	−	0.658404i
$11$	2.49631	−	2.18368i	0.752665	−	0.658404i
$12$	−0.0913215	+	0.281059i	−0.0263622	+	0.0811346i
$13$	−1.23233	−	0.895339i	−0.341786	−	0.248322i	0.403629	−	0.914923i	$-0.367749\pi$
$13$	−1.23233	−	0.895339i	−0.341786	−	0.248322i	−0.745415	+	0.666601i	$0.767749\pi$
$14$	1.72269	−	5.30191i	0.460410	−	1.41700i
$15$	−5.32856			−1.37583
$16$	−1.12636	+	3.46659i	−0.281591	+	0.866648i
$17$	2.65034	+	1.92559i	0.642803	+	0.467024i	0.860812	−	0.508923i	$-0.169956\pi$
$17$	2.65034	+	1.92559i	0.642803	+	0.467024i	−0.218009	+	0.975947i	$0.569956\pi$
$18$	−0.332162			−0.0782913
$19$	−6.43075	+	4.67222i	−1.47532	+	1.07188i	−0.496287	+	0.868159i	$0.665304\pi$
$19$	−6.43075	+	4.67222i	−1.47532	+	1.07188i	−0.979029	+	0.203721i	$0.934696\pi$
$20$	0.485252			0.108506
$21$	−7.41161			−1.61735
$22$	−3.85924	−	2.30255i	−0.822792	−	0.490906i
$23$	1.40791	+	4.33310i	0.293569	+	0.903514i	0.983698	+	0.179827i	$0.0575538\pi$
$23$	1.40791	+	4.33310i	0.293569	+	0.903514i	−0.690129	+	0.723687i	$0.742446\pi$
$24$	5.28220			1.07822
$25$	1.15868	+	3.56605i	0.231736	+	0.713210i
$26$	−0.637796	+	1.96293i	−0.125082	+	0.384963i
$27$	−1.53355	−	4.71979i	−0.295132	−	0.908323i
$28$	0.674946			0.127553
$29$	1.74291	+	5.36411i	0.323650	+	0.996091i	0.972047	+	0.234788i	$0.0754397\pi$
$29$	1.74291	+	5.36411i	0.323650	+	0.996091i	−0.648397	+	0.761302i	$0.724560\pi$
$30$	2.23112	+	6.86668i	0.407345	+	1.25368i
$31$	3.48616			0.626132			0.313066	−	0.949731i	$-0.398644\pi$
$31$	3.48616			0.626132			0.313066	+	0.949731i	$0.398644\pi$
$32$	−0.925593			−0.163623
$33$	−1.32589	+	5.82568i	−0.230808	+	1.01412i
$34$	1.37169	−	4.22164i	0.235244	−	0.724006i
$35$	3.76072	+	11.5743i	0.635678	+	1.95642i
$36$	−0.0124273	−	0.0382471i	−0.00207121	−	0.00637452i
$37$	−4.02695	−	2.92575i	−0.662026	−	0.480990i	0.205321	−	0.978695i	$-0.434176\pi$
$37$	−4.02695	−	2.92575i	−0.662026	−	0.480990i	−0.867347	+	0.497705i	$0.834176\pi$
$38$	8.71349	+	6.33072i	1.41352	+	1.02698i
$39$	2.74401			0.439393
$40$	−2.68024	−	8.24892i	−0.423783	−	1.30427i
$41$	−1.03360	−	3.18109i	−0.161421	−	0.496803i	0.837334	−	0.546692i	$-0.184113\pi$
$41$	−1.03360	−	3.18109i	−0.161421	−	0.496803i	−0.998755	+	0.0498892i	$0.984113\pi$
$42$	3.10331	+	9.55101i	0.478851	+	1.47375i
$43$	3.84140	−	11.8226i	0.585807	−	1.80293i	−0.0101963	−	0.999948i	$-0.503246\pi$
$43$	3.84140	−	11.8226i	0.585807	−	1.80293i	0.596004	−	0.802982i	$-0.296754\pi$
$44$	0.120744	−	0.530522i	0.0182028	−	0.0799793i
$45$	0.586638	−	0.426217i	0.0874508	−	0.0635367i
$46$	4.99437	−	3.62862i	0.736379	−	0.535011i
$47$	−3.03947	+	9.35454i	−0.443353	+	1.36450i	0.440927	+	0.897543i	$0.354650\pi$
$47$	−3.03947	+	9.35454i	−0.443353	+	1.36450i	−0.884280	+	0.466957i	$0.845350\pi$
$48$	−2.02906	−	6.24481i	−0.292870	−	0.901361i
$49$	3.06774	+	9.44154i	0.438249	+	1.34879i
$50$	4.11026	−	2.98628i	0.581278	−	0.422323i
$51$	−5.90149			−0.826373
$52$	−0.249886			−0.0346530
$53$	10.6544	−	7.74088i	1.46350	−	1.06329i	0.481061	−	0.876687i	$-0.340252\pi$
$53$	10.6544	−	7.74088i	1.46350	−	1.06329i	0.982435	−	0.186605i	$-0.0597483\pi$
$54$	−5.44007	+	3.95244i	−0.740299	+	0.537859i
$55$	9.77043	−	0.885438i	1.31744	−	0.119392i
$56$	−3.72800	−	11.4736i	−0.498174	−	1.53322i
$57$	4.42490	−	13.6184i	0.586092	−	1.80381i
$58$	6.18272	−	4.49201i	0.811831	−	0.589830i
$59$	−2.39108	+	7.35899i	−0.311292	+	0.958059i	0.665961	+	0.745986i	$0.268022\pi$
$59$	−2.39108	+	7.35899i	−0.311292	+	0.958059i	−0.977254	+	0.212073i	$0.931978\pi$
$60$	−0.707199	+	0.513810i	−0.0912990	+	0.0663326i
$61$	5.05090	−	5.95721i	0.646702	−	0.762743i
$61$	5.05090	−	5.95721i	0.646702	−	0.762743i
$62$	−1.45969	−	4.49246i	−0.185380	−	0.570542i
$63$	0.815966	−	0.592834i	0.102802	−	0.0746901i
$64$	2.64028	+	8.12595i	0.330035	+	1.01574i
$65$	−1.39234	−	4.28517i	−0.172698	−	0.531510i
$66$	8.06246	−	0.730655i	0.992420	−	0.0899374i
$67$	−0.609463	−	1.87573i	−0.0744578	−	0.229157i	0.906900	−	0.421345i	$-0.138442\pi$
$67$	−0.609463	−	1.87573i	−0.0744578	−	0.229157i	−0.981358	+	0.192187i	$0.938442\pi$
$68$	0.537425			0.0651724
$69$	−6.63998	−	4.82423i	−0.799360	−	0.580769i
$70$	13.3406	−	9.69255i	1.59451	−	1.15848i
$71$	3.68170	+	11.3311i	0.436938	+	1.34476i	0.891088	+	0.453831i	$0.149943\pi$
$71$	3.68170	+	11.3311i	0.436938	+	1.34476i	−0.454150	+	0.890925i	$0.650057\pi$
$72$	−0.581533	+	0.422508i	−0.0685343	+	0.0497931i
$73$	3.17491			0.371595			0.185798	−	0.982588i	$-0.440513\pi$
$73$	3.17491			0.371595			0.185798	+	0.982588i	$0.440513\pi$
$74$	−2.08416	+	6.41439i	−0.242279	+	0.745657i
$75$	−5.46456	−	3.97024i	−0.630993	−	0.458444i
$76$	−0.402958	+	1.24018i	−0.0462225	+	0.142258i
$77$	13.5899	−	1.23157i	1.54871	−	0.140351i
$78$	−1.14894	−	3.53608i	−0.130092	−	0.400383i
$79$	−0.430106	+	0.312490i	−0.0483907	+	0.0351579i	−0.611718	−	0.791076i	$-0.709521\pi$
$79$	−0.430106	+	0.312490i	−0.0483907	+	0.0351579i	0.563327	+	0.826234i	$0.309521\pi$
$80$	−8.72263	+	6.33736i	−0.975219	+	0.708538i
$81$	7.82751	+	5.68702i	0.869723	+	0.631891i
$82$	−3.66655	+	2.66391i	−0.404903	+	0.294179i
$83$	2.48891			0.273194			0.136597	−	0.990627i	$-0.456383\pi$
$83$	2.48891			0.273194			0.136597	+	0.990627i	$0.456383\pi$
$84$	−0.983657	+	0.714669i	−0.107326	+	0.0779768i
$85$	2.99447	+	9.21603i	0.324796	+	0.999619i
$86$	−16.8437			−1.81630
$87$	−8.21989	−	5.97210i	−0.881265	−	0.640277i
$88$	−9.68541	+	0.877733i	−1.03247	+	0.0935666i
$89$	7.77459	+	5.64857i	0.824105	+	0.598747i	0.917885	−	0.396845i	$-0.129895\pi$
$89$	7.77459	+	5.64857i	0.824105	+	0.598747i	−0.0937802	+	0.995593i	$0.529895\pi$
$90$	−0.794878	−	0.577513i	−0.0837875	−	0.0608752i
$91$	−1.93663	−	5.96033i	−0.203014	−	0.624813i
$92$	0.604677	+	0.439324i	0.0630420	+	0.0458027i
$93$	−5.08068	+	3.69133i	−0.526842	+	0.382773i
$94$	13.3274			1.37462
$95$	−23.5124			−2.41232
$96$	1.34895	−	0.980067i	0.137676	−	0.100028i
$97$	5.61830			0.570452			0.285226	−	0.958460i	$-0.407931\pi$
$97$	5.61830			0.570452			0.285226	+	0.958460i	$0.407931\pi$
$98$	10.8824	−	7.90653i	1.09929	−	0.798680i
$99$	−0.320009	−	0.747421i	−0.0321621	−	0.0751187i
$100$	0.497637	+	0.361554i	0.0497637	+	0.0361554i
$101$	−10.1618	−	7.38301i	−1.01114	−	0.734637i	−0.0466928	−	0.998909i	$-0.514868\pi$
$101$	−10.1618	−	7.38301i	−1.01114	−	0.734637i	−0.964448	+	0.264272i	$0.914868\pi$
$102$	2.47101	+	7.60498i	0.244666	+	0.753006i
$103$	−0.0268537	+	0.0826473i	−0.00264598	+	0.00814348i	−0.952371	−	0.304942i	$-0.901363\pi$
$103$	−0.0268537	+	0.0826473i	−0.00264598	+	0.00814348i	0.949725	+	0.313086i	$0.101363\pi$
$104$	1.38022	+	4.24788i	0.135342	+	0.416539i
$105$	−17.7363	−	12.8862i	−1.73089	−	1.25756i
$106$	−14.4364	−	10.4887i	−1.40219	−	1.01875i
$107$	−12.3401	−	8.96563i	−1.19296	−	0.866740i	−0.199390	−	0.979920i	$-0.563896\pi$
$107$	−12.3401	−	8.96563i	−1.19296	−	0.866740i	−0.993574	+	0.113180i	$0.963896\pi$
$108$	−0.658639	−	0.478529i	−0.0633776	−	0.0460465i
$109$	11.2887			1.08126			0.540631	−	0.841260i	$-0.318185\pi$
$109$	11.2887			1.08126			0.540631	+	0.841260i	$0.318185\pi$
$110$	−5.23200	−	12.2200i	−0.498851	−	1.16513i
$111$	8.96675			0.851086
$112$	−12.1325	+	8.81476i	−1.14641	+	0.832917i
$113$	−13.8183			−1.29991			−0.649957	−	0.759971i	$-0.725213\pi$
$113$	−13.8183			−1.29991			−0.649957	+	0.759971i	$0.725213\pi$
$114$	−19.4022			−1.81719
$115$	−4.16455	+	12.8172i	−0.388346	+	1.19521i
$116$	0.748554	+	0.543856i	0.0695015	+	0.0504958i
$117$	−0.302096	+	0.219486i	−0.0279288	+	0.0202915i
$118$	10.4844			0.965165
$119$	4.16507	+	12.8188i	0.381811	+	1.17509i
$120$	12.6405	+	9.18389i	1.15392	+	0.838370i
$121$	1.46310	−	10.9023i	0.133009	−	0.991115i
$122$	−9.79166	−	4.01453i	−0.886495	−	0.363459i
$123$	4.87466	+	3.54165i	0.439533	+	0.319340i
$124$	0.462677	−	0.336155i	0.0415497	−	0.0301876i
$125$	1.14297	−	3.51771i	0.102231	−	0.314634i
$126$	−1.10561	−	0.803274i	−0.0984957	−	0.0715613i
$127$	−14.3314	−	10.4124i	−1.27170	−	0.923947i	−0.272435	−	0.962174i	$-0.587829\pi$
$127$	−14.3314	−	10.4124i	−1.27170	−	0.923947i	−0.999269	+	0.0382270i	$0.987829\pi$
$128$	7.86840	−	5.71673i	0.695475	−	0.505292i
$129$	6.92000	+	21.2976i	0.609272	+	1.87515i
$130$	−4.93913	+	3.58848i	−0.433190	+	0.314731i
$131$	0.0306861	+	0.0944420i	0.00268106	+	0.00825144i	0.952388	−	0.304888i	$-0.0986192\pi$
$131$	0.0306861	+	0.0944420i	0.00268106	+	0.00825144i	−0.949707	+	0.313140i	$0.898619\pi$
$132$	0.385775	+	0.901025i	0.0335774	+	0.0784242i
$133$	−32.7039			−2.83579
$134$	−2.16199	+	1.57078i	−0.186767	+	0.135694i
$135$	4.53619	−	13.9610i	0.390413	−	1.20157i
$136$	−2.96841	−	9.13584i	−0.254539	−	0.783392i
$137$	−0.467206	−	1.43791i	−0.0399161	−	0.122849i	0.929113	−	0.369796i	$-0.120573\pi$
$137$	−0.467206	−	1.43791i	−0.0399161	−	0.122849i	−0.969029	+	0.246947i	$0.920573\pi$
$138$	−3.43655	+	10.5766i	−0.292538	+	0.900340i
$139$	−3.14900	+	2.28788i	−0.267095	+	0.194056i	−0.713269	−	0.700890i	$-0.752786\pi$
$139$	−3.14900	+	2.28788i	−0.267095	+	0.194056i	0.446174	+	0.894946i	$0.352786\pi$
$140$	1.61518	+	1.17349i	0.136507	+	0.0991784i
$141$	−5.47539	−	16.8515i	−0.461111	−	1.41915i
$142$	13.0603	−	9.48890i	1.09600	−	0.796291i
$143$	−5.03140	+	0.455967i	−0.420747	+	0.0381299i
$144$	0.722891	+	0.525211i	0.0602409	+	0.0437676i
$145$	−5.15546	+	15.8669i	−0.428137	+	1.31767i
$146$	−1.32937	−	4.09137i	−0.110019	−	0.338604i
$147$	−14.4681	−	10.5117i	−1.19331	−	0.866989i
$148$	−0.816567			−0.0671214
$149$	1.58555	+	4.87983i	0.129894	+	0.399771i	0.994761	−	0.102229i	$-0.0325976\pi$
$149$	1.58555	+	4.87983i	0.129894	+	0.399771i	−0.864867	+	0.502000i	$0.832598\pi$
$150$	−2.82820	+	8.70432i	−0.230922	+	0.710705i
$151$	3.09491	−	9.52516i	0.251860	−	0.775146i	−0.742572	−	0.669767i	$-0.766394\pi$
$151$	3.09491	−	9.52516i	0.251860	−	0.775146i	0.994432	−	0.105380i	$-0.0336059\pi$
$152$	23.3078			1.89051
$153$	0.649712	−	0.472044i	0.0525261	−	0.0381625i
$154$	−7.27729	−	16.9970i	−0.586421	−	1.36966i
$155$	8.34253	+	6.06120i	0.670088	+	0.486848i
$156$	0.364181	−	0.264593i	0.0291578	−	0.0211844i
$157$	7.33922	−	5.33225i	0.585733	−	0.425560i	−0.255053	−	0.966927i	$-0.582093\pi$
$157$	7.33922	−	5.33225i	0.585733	−	0.425560i	0.840786	+	0.541367i	$0.182093\pi$
$158$	0.582782	+	0.423416i	0.0463636	+	0.0336852i
$159$	−7.33113	+	22.5629i	−0.581397	+	1.78935i
$160$	−2.21499	−	1.60928i	−0.175110	−	0.127225i
$161$	−5.79255	+	17.8277i	−0.456517	+	1.40502i
$162$	4.05115	−	12.4682i	0.318289	−	0.979592i
$163$	−20.0483			−1.57030			−0.785150	−	0.619305i	$-0.787414\pi$
$163$	−20.0483			−1.57030			−0.785150	+	0.619305i	$0.787414\pi$
$164$	−0.443916	−	0.322524i	−0.0346640	−	0.0251849i
$165$	−13.3017	+	11.6359i	−1.03554	+	0.905851i
$166$	−1.04213	−	3.20735i	−0.0808851	−	0.248939i
$167$	−4.15907			−0.321838			−0.160919	−	0.986968i	$-0.551446\pi$
$167$	−4.15907			−0.321838			−0.160919	+	0.986968i	$0.551446\pi$
$168$	17.5820	+	12.7741i	1.35648	+	0.985540i
$169$	−3.30022	−	10.1570i	−0.253863	−	0.781310i
$170$	10.6225	−	7.71768i	0.814707	−	0.591919i
$171$	0.602151	+	1.85323i	0.0460476	+	0.141720i
$172$	−0.630177	−	1.93949i	−0.0480506	−	0.147884i
$173$	6.60656	+	4.79995i	0.502287	+	0.364933i	0.809890	−	0.586582i	$-0.199527\pi$
$173$	6.60656	+	4.79995i	0.502287	+	0.364933i	−0.307603	+	0.951515i	$0.599527\pi$
$174$	−4.25423	+	13.0932i	−0.322513	+	0.992592i
$175$	−4.76715	+	14.6718i	−0.360363	+	1.10908i
$176$	4.75817	+	11.1133i	0.358660	+	0.837696i
$177$	−4.30736	−	13.2567i	−0.323761	−	0.996434i
$178$	4.02377	−	12.3839i	0.301594	−	0.928211i
$179$	17.6356			1.31815			0.659075	−	0.752077i	$-0.270948\pi$
$179$	17.6356			1.31815			0.659075	+	0.752077i	$0.270948\pi$
$180$	0.0367594	−	0.113134i	0.00273988	−	0.00843249i
$181$	7.77564			0.577959			0.288979	−	0.957335i	$-0.406684\pi$
$181$	7.77564			0.577959			0.288979	+	0.957335i	$0.406684\pi$
$182$	−6.86993	+	4.99130i	−0.509233	+	0.369979i
$183$	−1.05330	+	14.0301i	−0.0778623	+	1.03714i
$184$	4.12831	−	12.7056i	0.304343	−	0.936672i
$185$	−4.54982	−	14.0029i	−0.334509	−	1.02951i
$186$	6.88418	+	5.00165i	0.504772	+	0.366739i
$187$	10.8209	−	0.980639i	0.791305	−	0.0717114i
$188$	0.498623	+	1.53460i	0.0363658	+	0.111922i
$189$	6.30948	−	19.4186i	0.458947	−	1.41249i
$190$	9.84488	+	30.2994i	0.714222	+	2.19815i
$191$	2.28966			0.165674			0.0828371	−	0.996563i	$-0.473602\pi$
$191$	2.28966			0.165674			0.0828371	+	0.996563i	$0.473602\pi$
$192$	−12.4521	−	9.04698i	−0.898653	−	0.652909i
$193$	−7.00110	−	21.5472i	−0.503951	−	1.55100i	−0.802528	−	0.596615i	$-0.796512\pi$
$193$	−7.00110	−	21.5472i	−0.503951	−	1.55100i	0.298577	−	0.954385i	$-0.403488\pi$
$194$	−2.35244	−	7.24006i	−0.168895	−	0.519806i
$195$	6.56654	+	4.77087i	0.470240	+	0.341649i
$196$	1.31755	+	0.957258i	0.0941109	+	0.0683756i
$197$	24.3522			1.73502			0.867511	−	0.497418i	$-0.165718\pi$
$197$	24.3522			1.73502			0.867511	+	0.497418i	$0.165718\pi$
$198$	−0.829178	+	0.725334i	−0.0589271	+	0.0515473i
$199$	−4.46923	+	3.24708i	−0.316815	+	0.230180i	−0.734815	−	0.678267i	$-0.762731\pi$
$199$	−4.46923	+	3.24708i	−0.316815	+	0.230180i	0.418000	+	0.908447i	$0.362731\pi$
$200$	3.39751	−	10.4565i	0.240240	−	0.739384i
$201$	2.87435	+	2.08834i	0.202741	+	0.147300i
$202$	−5.25930	+	16.1864i	−0.370043	+	1.13887i
$203$	−7.17083	+	22.0695i	−0.503294	+	1.54898i
$204$	−0.783236	+	0.569054i	−0.0548375	+	0.0398418i
$205$	3.05735	−	9.40956i	0.213535	−	0.657192i
$206$	0.117748			0.00820388
$207$	1.11689			0.0776294
$208$	4.49182	−	3.26350i	0.311452	−	0.226283i
$209$	−5.85052	+	25.7060i	−0.404689	+	1.77812i
$210$	−9.17949	+	28.2516i	−0.633445	+	1.94954i
$211$	−2.39573	−	7.37331i	−0.164929	−	0.507599i	0.834102	−	0.551610i	$-0.185986\pi$
$211$	−2.39573	−	7.37331i	−0.164929	−	0.507599i	−0.999031	+	0.0440108i	$0.985986\pi$
$212$	0.667618	−	2.05472i	0.0458522	−	0.141118i
$213$	−17.3637	−	12.6154i	−1.18974	−	0.864395i
$214$	−6.38667	+	19.6562i	−0.436584	+	1.34367i
$215$	29.7480	−	21.6132i	2.02880	−	1.47401i
$216$	−4.49672	+	13.8395i	−0.305963	+	0.941658i
$217$	11.6038	+	8.43065i	0.787717	+	0.572310i
$218$	−4.72669	−	14.5473i	−0.320132	−	0.985265i
$219$	−4.62707	+	3.36177i	−0.312669	+	0.227167i
$220$	1.21134	−	1.05963i	0.0816683	−	0.0714405i
$221$	−1.54204	−	4.74591i	−0.103729	−	0.319244i
$222$	−3.75446	−	11.5551i	−0.251983	−	0.775524i
$223$	−6.71675	+	20.6720i	−0.449787	+	1.38430i	0.427361	+	0.904081i	$0.359443\pi$
$223$	−6.71675	+	20.6720i	−0.449787	+	1.38430i	−0.877148	+	0.480220i	$0.840557\pi$
$224$	−3.08087	−	2.23838i	−0.205849	−	0.149558i
$225$	0.919179			0.0612786
$226$	5.78584	+	17.8070i	0.384869	+	1.18450i
$227$	1.05324	−	0.765222i	0.0699058	−	0.0507895i	−0.552284	−	0.833656i	$-0.686243\pi$
$227$	1.05324	−	0.765222i	0.0699058	−	0.0507895i	0.622189	+	0.782867i	$0.286243\pi$
$228$	−0.725901	−	2.23409i	−0.0480739	−	0.147956i
$229$	−5.93765	+	4.31395i	−0.392371	+	0.285074i	−0.766426	−	0.642332i	$-0.777967\pi$
$229$	−5.93765	+	4.31395i	−0.392371	+	0.285074i	0.374056	+	0.927406i	$0.377967\pi$
$230$	18.2606			1.20407
$231$	−18.5016	+	16.1846i	−1.21732	+	1.06487i
$232$	5.11060	−	15.7288i	0.335527	−	1.03265i
$233$	−11.7778	−	8.55708i	−0.771590	−	0.560593i	0.130853	−	0.991402i	$-0.458228\pi$
$233$	−11.7778	−	8.55708i	−0.771590	−	0.560593i	−0.902443	+	0.430809i	$0.858228\pi$
$234$	0.409332	+	0.297397i	0.0267589	+	0.0194415i
$235$	−23.5379	+	17.1013i	−1.53544	+	1.11556i
$236$	0.392255	+	1.20724i	0.0255336	+	0.0785844i
$237$	0.295949	−	0.910838i	0.0192240	−	0.0591653i
$238$	14.7750	−	10.7347i	0.957723	−	0.695826i
$239$	−24.8922			−1.61014			−0.805072	−	0.593177i	$-0.797874\pi$
$239$	−24.8922			−1.61014			−0.805072	+	0.593177i	$0.797874\pi$
$240$	6.00190	−	18.4720i	0.387421	−	1.19236i
$241$	−8.33310	−	6.05435i	−0.536782	−	0.389995i	0.286106	−	0.958198i	$-0.407639\pi$
$241$	−8.33310	−	6.05435i	−0.536782	−	0.389995i	−0.822889	+	0.568203i	$0.807639\pi$
$242$	−14.6619	+	2.67945i	−0.942501	+	0.172242i
$243$	−2.54138			−0.163030
$244$	0.0959201	−	1.27767i	0.00614065	−	0.0817943i
$245$	−9.07428	+	27.9278i	−0.579735	+	1.78424i
$246$	2.52290	−	7.76468i	0.160854	−	0.495058i
$247$	12.1080			0.770414
$248$	−8.26994	−	6.00846i	−0.525142	−	0.381538i
$249$	−3.62731	+	2.63539i	−0.229871	+	0.167011i
$250$	−5.01170			−0.316968
$251$	−2.01408			−0.127128			−0.0635640	−	0.997978i	$-0.520247\pi$
$251$	−2.01408			−0.127128			−0.0635640	+	0.997978i	$0.520247\pi$
$252$	0.0511294	−	0.157360i	0.00322085	−	0.00991275i
$253$	12.9767	+	7.74233i	0.815836	+	0.486756i
$254$	−7.41725	+	22.8280i	−0.465400	+	1.43235i
$255$	−14.1225	−	10.2606i	−0.884387	−	0.642545i
$256$	3.16323	+	2.29822i	0.197702	+	0.143639i
$257$	−6.44163	−	19.8253i	−0.401818	−	1.23667i	−0.923523	−	0.383542i	$-0.874704\pi$
$257$	−6.44163	−	19.8253i	−0.401818	−	1.23667i	0.521706	−	0.853125i	$-0.325296\pi$
$258$	24.5478	−	17.8350i	1.52828	−	1.11036i
$259$	−6.32843	−	19.4769i	−0.393230	−	1.21024i
$260$	−0.597989	−	0.434464i	−0.0370857	−	0.0269443i
$261$	1.38264			0.0855836
$262$	0.108855	−	0.0790876i	0.00672507	−	0.00488605i
$263$	−9.48726	−	6.89290i	−0.585009	−	0.425034i	0.255517	−	0.966804i	$-0.417754\pi$
$263$	−9.48726	−	6.89290i	−0.585009	−	0.425034i	−0.840527	+	0.541770i	$0.817754\pi$
$264$	13.1860	−	11.5346i	0.811541	−	0.709907i
$265$	38.9552			2.39300
$266$	13.6934	+	42.1441i	0.839599	+	2.58402i
$267$	−17.3116			−1.05945
$268$	−0.261756	−	0.190177i	−0.0159893	−	0.0116169i
$269$	3.69671	−	11.3773i	0.225393	−	0.693687i	−0.772859	−	0.634578i	$-0.781174\pi$
$269$	3.69671	−	11.3773i	0.225393	−	0.693687i	0.998252	−	0.0591093i	$-0.0188260\pi$
$270$	−19.8902			−1.21048
$271$	5.70734			0.346696			0.173348	−	0.984861i	$-0.444541\pi$
$271$	5.70734			0.346696			0.173348	+	0.984861i	$0.444541\pi$
$272$	−9.66048	+	7.01875i	−0.585752	+	0.425574i
$273$	9.13353	+	6.63590i	0.552786	+	0.401623i
$274$	−1.65735	+	1.20413i	−0.100124	+	0.0727444i
$275$	10.6795	+	6.37177i	0.643999	+	0.384232i
$276$	−1.34643			−0.0810454
$277$	3.50882	+	10.7990i	0.210825	+	0.648852i	0.999424	+	0.0339440i	$0.0108068\pi$
$277$	3.50882	+	10.7990i	0.210825	+	0.648852i	−0.788599	+	0.614908i	$0.789193\pi$
$278$	4.26681	+	3.10002i	0.255906	+	0.185927i
$279$	0.264088	−	0.812779i	0.0158105	−	0.0486598i
$280$	11.0273	−	33.9385i	0.659007	−	2.02821i
$281$	2.56776	−	7.90274i	0.153179	−	0.471438i	−0.844792	−	0.535094i	$-0.820276\pi$
$281$	2.56776	−	7.90274i	0.153179	−	0.471438i	0.997972	+	0.0636563i	$0.0202761\pi$
$282$	−19.4232	+	14.1118i	−1.15664	+	0.840345i
$283$	15.9412	−	11.5820i	0.947606	−	0.688476i	−0.00263350	−	0.999997i	$-0.500838\pi$
$283$	15.9412	−	11.5820i	0.947606	−	0.688476i	0.950239	+	0.311521i	$0.100838\pi$
$284$	1.58124	+	1.14884i	0.0938293	+	0.0681710i
$285$	34.2667	−	24.8962i	2.02978	−	1.47472i
$286$	2.69428	+	6.29282i	0.159316	+	0.372103i
$287$	4.25253	−	13.0879i	0.251019	−	0.772557i
$288$	−0.0701167	+	0.215797i	−0.00413167	+	0.0127160i
$289$	−1.93685	−	5.96103i	−0.113933	−	0.350649i
$290$	22.6056			1.32744
$291$	−8.18804	+	5.94896i	−0.479991	+	0.348734i
$292$	0.421370	−	0.306143i	0.0246588	−	0.0179157i
$293$	33.1707			1.93785			0.968926	−	0.247351i	$-0.0795602\pi$
$293$	33.1707			1.93785			0.968926	+	0.247351i	$0.0795602\pi$
$294$	−7.48801	+	23.0457i	−0.436710	+	1.34405i
$295$	−18.5167	+	13.4532i	−1.07808	+	0.783273i
$296$	4.51023	+	13.8810i	0.262152	+	0.806819i
$297$	−14.1347	−	8.43325i	−0.820179	−	0.489347i
$298$	5.62453	−	4.08646i	0.325820	−	0.236722i
$299$	2.14459	−	6.60035i	0.124025	−	0.381708i
$300$	−1.10808			−0.0639751
$301$	41.3771	−	30.0622i	2.38494	−	1.73276i
$302$	−13.5705			−0.780896
$303$	22.6272			1.29990
$304$	−8.95329	−	27.5554i	−0.513507	−	1.58041i
$305$	22.4445	−	5.47413i	1.28517	−	0.313448i
$306$	−0.880343	−	0.639606i	−0.0503258	−	0.0365639i
$307$	−19.3283	−	14.0428i	−1.10313	−	0.801467i	−0.121558	−	0.992584i	$-0.538789\pi$
$307$	−19.3283	−	14.0428i	−1.10313	−	0.801467i	−0.981567	+	0.191117i	$0.938789\pi$
$308$	1.68487	−	1.47387i	0.0960046	−	0.0839813i
$309$	−0.0483751	−	0.148883i	−0.00275196	−	0.00846967i
$310$	4.31771	−	13.2885i	0.245229	−	0.754738i
$311$	3.63532			0.206140			0.103070	−	0.994674i	$-0.467133\pi$
$311$	3.63532			0.206140			0.103070	+	0.994674i	$0.467133\pi$
$312$	−6.50940	−	4.72935i	−0.368522	−	0.267747i
$313$	−5.93152	−	18.2554i	−0.335270	−	1.03185i	−0.966589	−	0.256331i	$-0.917486\pi$
$313$	−5.93152	−	18.2554i	−0.335270	−	1.03185i	0.631320	−	0.775523i	$-0.282514\pi$
$314$	−9.94444	−	7.22506i	−0.561197	−	0.407734i
$315$	2.98337			0.168094
$316$	−0.0269509	+	0.0829465i	−0.00151611	+	0.00466610i
$317$	−17.2190	+	12.5103i	−0.967115	+	0.702650i	−0.954792	−	0.297274i	$-0.903922\pi$
$317$	−17.2190	+	12.5103i	−0.967115	+	0.702650i	−0.0123225	+	0.999924i	$0.503922\pi$
$318$	32.1454			1.80263
$319$	16.0643	+	9.58453i	0.899430	+	0.536631i
$320$	−7.80987	+	24.0363i	−0.436585	+	1.34367i
$321$	27.4776			1.53365
$322$	25.3991			1.41544
$323$	−26.0405			−1.44893
$324$	1.58723			0.0881794
$325$	1.76495	−	5.43195i	0.0979017	−	0.301310i
$326$	8.39440	+	25.8353i	0.464923	+	1.43088i
$327$	−16.4520	+	11.9531i	−0.909798	+	0.661007i
$328$	−3.03075	+	9.32768i	−0.167345	+	0.515035i
$329$	−32.7393	+	23.7865i	−1.80498	+	1.31139i
$330$	20.5642	+	12.2693i	1.13202	+	0.675403i
$331$	−8.59508	−	6.24469i	−0.472428	−	0.343239i	0.325959	−	0.945384i	$-0.394313\pi$
$331$	−8.59508	−	6.24469i	−0.472428	−	0.343239i	−0.798387	+	0.602145i	$0.794313\pi$
$332$	0.330325	−	0.239995i	0.0181289	−	0.0131714i
$333$	−0.987177	+	0.717226i	−0.0540969	+	0.0393037i
$334$	1.74144	+	5.35960i	0.0952874	+	0.293264i
$335$	1.80277	−	5.54836i	0.0984959	−	0.303139i
$336$	8.34817	−	25.6930i	0.455430	−	1.40167i
$337$	−8.74253	−	26.9068i	−0.476236	−	1.46570i	−0.844283	−	0.535897i	$-0.819973\pi$
$337$	−8.74253	−	26.9068i	−0.476236	−	1.46570i	0.368047	−	0.929807i	$-0.380027\pi$
$338$	−11.7071	+	8.50569i	−0.636781	+	0.462649i
$339$	20.1386	−	14.6315i	1.09378	−	0.794675i
$340$	1.28608	+	0.934394i	0.0697477	+	0.0506746i
$341$	8.70252	−	7.61265i	0.471268	−	0.412248i
$342$	2.13605	−	1.55193i	0.115504	−	0.0839188i
$343$	−3.72189	+	11.4548i	−0.200963	+	0.618502i
$344$	−29.4891	+	21.4251i	−1.58995	+	1.15516i
$345$	−7.50213	−	23.0892i	−0.403901	−	1.24308i
$346$	3.41925	−	10.5234i	0.183820	−	0.565739i
$347$	−0.912091			−0.0489636			−0.0244818	−	0.999700i	$-0.507794\pi$
$347$	−0.912091			−0.0489636			−0.0244818	+	0.999700i	$0.507794\pi$
$348$	−1.66680			−0.0893496
$349$	−18.3013			−0.979647			−0.489824	−	0.871821i	$-0.662939\pi$
$349$	−18.3013			−0.979647			−0.489824	+	0.871821i	$0.662939\pi$
$350$	20.9029			1.11731
$351$	−2.33597	+	7.18937i	−0.124685	+	0.383740i
$352$	−2.31056	+	2.02120i	−0.123154	+	0.107730i
$353$	−3.42531			−0.182311			−0.0911554	−	0.995837i	$-0.529056\pi$
$353$	−3.42531			−0.182311			−0.0911554	+	0.995837i	$0.529056\pi$
$354$	−15.2798	+	11.1014i	−0.812111	+	0.590033i
$355$	−10.8904	+	33.5171i	−0.578000	+	1.77890i
$356$	1.57650			0.0835543
$357$	−19.6433	−	14.2717i	−1.03963	−	0.755338i
$358$	−7.38421	−	22.7263i	−0.390268	−	1.20112i
$359$	13.1375	+	9.54496i	0.693371	+	0.503764i	0.877767	−	0.479089i	$-0.159033\pi$
$359$	13.1375	+	9.54496i	0.693371	+	0.503764i	−0.184395	+	0.982852i	$0.559033\pi$
$360$	−2.12623			−0.112062
$361$	13.6537	−	42.0216i	0.718614	−	2.21167i
$362$	−3.25573	−	10.0201i	−0.171118	−	0.526646i
$363$	9.41159	+	17.4380i	0.493980	+	0.915258i
$364$	−0.831755	−	0.604305i	−0.0435958	−	0.0316742i
$365$	7.59771	+	5.52006i	0.397682	+	0.288933i
$366$	18.5210	−	4.51720i	0.968109	−	0.236118i
$367$	7.69612	+	23.6862i	0.401734	+	1.23641i	0.923591	+	0.383378i	$0.125239\pi$
$367$	7.69612	+	23.6862i	0.401734	+	1.23641i	−0.521857	+	0.853033i	$0.674761\pi$
$368$	−16.6069			−0.865695
$369$	−0.819953			−0.0426850
$370$	−16.1399	+	11.7263i	−0.839071	+	0.609621i
$371$	54.1835			2.81307
$372$	−0.318361	+	0.979815i	−0.0165063	+	0.0508010i
$373$	−7.69256	+	5.58897i	−0.398306	+	0.289386i	−0.768850	−	0.639429i	$-0.779171\pi$
$373$	−7.69256	+	5.58897i	−0.398306	+	0.289386i	0.370545	+	0.928815i	$0.379171\pi$
$374$	−5.79454	−	13.5339i	−0.299628	−	0.699819i
$375$	2.05899	+	6.33691i	0.106326	+	0.327237i
$376$	23.3330	−	16.9524i	1.20331	−	0.874256i
$377$	2.65487	−	8.17084i	0.136733	−	0.420820i
$378$	−27.6657			−1.42297
$379$	−15.3099	+	11.1233i	−0.786418	+	0.571366i	−0.906898	−	0.421350i	$-0.861556\pi$
$379$	−15.3099	+	11.1233i	−0.786418	+	0.571366i	0.120480	+	0.992716i	$0.461556\pi$
$380$	−3.12053	+	2.26720i	−0.160080	+	0.116305i
$381$	31.9115			1.63488
$382$	−0.958704	−	2.95059i	−0.0490515	−	0.150965i
$383$	4.87380	−	15.0000i	0.249039	−	0.766464i	−0.745906	−	0.666051i	$-0.767983\pi$
$383$	4.87380	−	15.0000i	0.249039	−	0.766464i	0.994946	−	0.100414i	$-0.0320166\pi$
$384$	−5.41412	+	16.6630i	−0.276288	+	0.850328i
$385$	34.6625	+	20.6808i	1.76656	+	1.05399i
$386$	−24.8355	+	18.0440i	−1.26409	+	0.918417i
$387$	−2.46538	−	1.79120i	−0.125322	−	0.0910519i
$388$	0.745653	−	0.541748i	0.0378548	−	0.0275031i
$389$	0.152290	−	0.110645i	0.00772139	−	0.00560992i	−0.583918	−	0.811813i	$-0.698481\pi$
$389$	0.152290	−	0.110645i	0.00772139	−	0.00560992i	0.591639	+	0.806203i	$0.298481\pi$
$390$	3.39853	−	10.4596i	0.172091	−	0.529643i
$391$	−4.61232	+	14.1953i	−0.233255	+	0.717885i
$392$	8.99532	−	27.6848i	0.454332	−	1.39829i
$393$	−0.144722	−	0.105146i	−0.00730024	−	0.00530394i
$394$	−10.1965	−	31.3816i	−0.513692	−	1.58098i
$395$	−1.57257			−0.0791248
$396$	−0.114542	−	0.0683395i	−0.00575594	−	0.00343419i
$397$	4.83373	−	3.51191i	0.242598	−	0.176258i	−0.459842	−	0.888001i	$-0.652094\pi$
$397$	4.83373	−	3.51191i	0.242598	−	0.176258i	0.702440	+	0.711743i	$0.252094\pi$
$398$	6.05568	+	4.39971i	0.303544	+	0.220538i
$399$	47.6622	−	34.6286i	2.38609	−	1.73360i
$400$	−13.6671			−0.683356
$401$	−16.4506			−0.821503			−0.410752	−	0.911747i	$-0.634734\pi$
$401$	−16.4506			−0.821503			−0.410752	+	0.911747i	$0.634734\pi$
$402$	1.48763	−	4.57845i	0.0741962	−	0.228353i
$403$	−4.29609	−	3.12129i	−0.214003	−	0.155483i
$404$	−2.06058			−0.102517
$405$	8.84385	+	27.2186i	0.439455	+	1.35250i
$406$	31.4425			1.56047
$407$	−16.4414	+	1.48999i	−0.814969	+	0.0738560i
$408$	13.9996	+	10.1713i	0.693085	+	0.503556i
$409$	19.2795	−	14.0074i	0.953309	−	0.692620i	0.00172184	−	0.999999i	$-0.499452\pi$
$409$	19.2795	−	14.0074i	0.953309	−	0.692620i	0.951587	+	0.307379i	$0.0994519\pi$
$410$	−13.4058			−0.662066
$411$	2.20344	+	1.60089i	0.108687	+	0.0789661i
$412$	0.00440533	+	0.0135582i	0.000217035	+	0.000667965i
$413$	−25.7552	+	18.7123i	−1.26733	+	0.920770i
$414$	−0.467654	−	1.43929i	−0.0229839	−	0.0707372i
$415$	5.95608	+	4.32735i	0.292373	+	0.212421i
$416$	1.14063	+	0.828719i	0.0559242	+	0.0406313i
$417$	2.16678	−	6.66866i	0.106108	−	0.326566i
$418$	35.5758	−	3.22403i	1.74007	−	0.157693i
$419$	0.136475	−	0.420027i	0.00666724	−	0.0205197i	−0.947668	−	0.319259i	$-0.896566\pi$
$419$	0.136475	−	0.420027i	0.00666724	−	0.0205197i	0.954335	+	0.298739i	$0.0965661\pi$
$420$	−3.59649			−0.175491
$421$	17.6910			0.862205			0.431102	−	0.902303i	$-0.358125\pi$
$421$	17.6910			0.862205			0.431102	+	0.902303i	$0.358125\pi$
$422$	−8.49854	+	6.17455i	−0.413702	+	0.300572i
$423$	1.95071	+	1.41727i	0.0948468	+	0.0689102i
$424$	−38.6162			−1.87537
$425$	−3.79584	+	11.6824i	−0.184125	+	0.566679i
$426$	−8.98662	+	27.6580i	−0.435403	+	1.34003i
$427$	31.2186	−	7.61408i	1.51077	−	0.368471i
$428$	−2.50228			−0.120952
$429$	6.84989	−	5.99203i	0.330716	−	0.289298i
$430$	−40.3077	−	29.2853i	−1.94381	−	1.41226i
$431$	−6.25927	+	19.2641i	−0.301498	+	0.927917i	0.679462	+	0.733710i	$0.262213\pi$
$431$	−6.25927	+	19.2641i	−0.301498	+	0.927917i	−0.980961	+	0.194206i	$0.937787\pi$
$432$	18.0889			0.870303
$433$	−6.80705	+	4.94561i	−0.327126	+	0.237671i	−0.739210	−	0.673475i	$-0.764801\pi$
$433$	−6.80705	+	4.94561i	−0.327126	+	0.237671i	0.412084	+	0.911146i	$0.364801\pi$
$434$	6.00559	−	18.4833i	0.288277	−	0.887226i
$435$	−9.28719	−	28.5830i	−0.445286	−	1.37045i
$436$	1.49822	−	1.08852i	0.0717518	−	0.0521307i
$437$	−29.2991	−	21.2870i	−1.40157	−	1.01830i
$438$	6.26956	+	4.55510i	0.299571	+	0.217651i
$439$	−5.78225	+	17.7959i	−0.275972	+	0.849353i	0.712989	+	0.701175i	$0.247341\pi$
$439$	−5.78225	+	17.7959i	−0.275972	+	0.849353i	−0.988961	+	0.148178i	$0.952659\pi$
$440$	−24.7037	−	14.7391i	−1.17770	−	0.702658i
$441$	2.43364			0.115887
$442$	−5.47018	+	3.97432i	−0.260190	+	0.189039i
$443$	−4.19891	−	12.9229i	−0.199496	−	0.613987i	−0.999895	−	0.0145182i	$-0.995379\pi$
$443$	−4.19891	−	12.9229i	−0.199496	−	0.613987i	0.800398	−	0.599469i	$-0.204621\pi$
$444$	1.19005	−	0.864625i	0.0564774	−	0.0410333i
$445$	8.78407	+	27.0346i	0.416405	+	1.28156i
$446$	29.4515			1.39457
$447$	−7.47778	−	5.43293i	−0.353687	−	0.256969i
$448$	−10.8629	+	33.4326i	−0.513224	+	1.57954i
$449$	10.5885	+	32.5879i	0.499701	+	1.53792i	0.809501	+	0.587119i	$0.199738\pi$
$449$	10.5885	+	32.5879i	0.499701	+	1.53792i	−0.309800	+	0.950802i	$0.600262\pi$
$450$	−0.384869	−	1.18450i	−0.0181429	−	0.0558381i
$451$	−9.52666	−	5.68393i	−0.448593	−	0.267646i
$452$	−1.83394	+	1.33244i	−0.0862613	+	0.0626725i
$453$	5.57526	+	17.1589i	0.261949	+	0.806195i
$454$	−1.42711	−	1.03685i	−0.0669775	−	0.0486620i
$455$	5.72848	−	17.6305i	0.268555	−	0.826529i
$456$	−33.9685	+	24.6796i	−1.59072	+	1.15573i
$457$	−4.74514	+	14.6040i	−0.221968	+	0.683148i	0.776617	+	0.629973i	$0.216934\pi$
$457$	−4.74514	+	14.6040i	−0.221968	+	0.683148i	−0.998585	+	0.0531746i	$0.983066\pi$
$458$	8.04535	+	5.84529i	0.375934	+	0.273132i
$459$	5.02392	−	15.4620i	0.234497	−	0.721706i
$460$	0.683190	+	2.10264i	0.0318539	+	0.0980362i
$461$	−5.92538	+	18.2364i	−0.275972	+	0.849355i	0.712988	+	0.701176i	$0.247341\pi$
$461$	−5.92538	+	18.2364i	−0.275972	+	0.849355i	−0.988961	+	0.148179i	$0.952659\pi$
$462$	28.6031	+	17.0656i	1.33074	+	0.793965i
$463$	−7.79491	+	5.66333i	−0.362260	+	0.263197i	−0.753994	−	0.656881i	$-0.771875\pi$
$463$	−7.79491	+	5.66333i	−0.362260	+	0.263197i	0.391734	+	0.920079i	$0.371875\pi$
$464$	−20.5583			−0.954397
$465$	−18.5762			−0.861451
$466$	−6.09564	+	18.7605i	−0.282375	+	0.869062i
$467$	−7.67650	+	5.57730i	−0.355226	+	0.258087i	−0.751058	−	0.660236i	$-0.770456\pi$
$467$	−7.67650	+	5.57730i	−0.355226	+	0.258087i	0.395832	+	0.918323i	$0.370456\pi$
$468$	−0.0189297	+	0.0582596i	−0.000875026	+	0.00269305i
$469$	2.50751	−	7.71733i	0.115786	−	0.356353i
$470$	31.8932	+	23.1717i	1.47112	+	1.06883i
$471$	−5.05000	+	15.5423i	−0.232692	+	0.716151i
$472$	18.3555	−	13.3361i	0.844883	−	0.613843i
$473$	−16.2274	−	37.9012i	−0.746139	−	1.74270i
$474$	−1.29767			−0.0596041
$475$	−24.1125	−	17.5188i	−1.10636	−	0.803817i
$476$	1.78884	+	1.29967i	0.0819913	+	0.0595702i
$477$	−0.997638	−	3.07041i	−0.0456787	−	0.140585i
$478$	10.4226	+	32.0775i	0.476719	+	1.46719i
$479$	16.0366	+	11.6513i	0.732730	+	0.532359i	0.890426	−	0.455128i	$-0.150407\pi$
$479$	16.0366	+	11.6513i	0.732730	+	0.532359i	−0.157696	+	0.987488i	$0.550407\pi$
$480$	4.93208			0.225118
$481$	2.34298	+	7.21096i	0.106831	+	0.328792i
$482$	−4.31283	+	13.2735i	−0.196444	+	0.604592i
$483$	−10.4349	−	32.1152i	−0.474803	−	1.46129i
$484$	−0.857077	−	1.58801i	−0.0389580	−	0.0721824i
$485$	13.4449	+	9.76826i	0.610499	+	0.443554i
$486$	1.06410	+	3.27497i	0.0482687	+	0.148556i
$487$	0.829847	−	2.55401i	0.0376039	−	0.115733i	−0.930492	−	0.366311i	$-0.880621\pi$
$487$	0.829847	−	2.55401i	0.0376039	−	0.115733i	0.968096	+	0.250578i	$0.0806206\pi$
$488$	−22.2492	+	5.42650i	−1.00718	+	0.245646i
$489$	29.2180	−	21.2281i	1.32129	−	0.959970i
$490$	39.7888			1.79747
$491$	9.66340	−	29.7409i	0.436103	−	1.34219i	−0.455849	−	0.890057i	$-0.650664\pi$
$491$	9.66340	−	29.7409i	0.436103	−	1.34219i	0.891952	−	0.452130i	$-0.149336\pi$
$492$	0.988463			0.0445633
$493$	−5.70977	+	17.5729i	−0.257155	+	0.791442i
$494$	−5.06974	−	15.6031i	−0.228098	−	0.702015i
$495$	0.533707	−	2.34500i	0.0239883	−	0.105400i
$496$	−3.92668	+	12.0851i	−0.176313	+	0.542636i
$497$	−15.1476	+	46.6196i	−0.679464	+	2.09117i
$498$	4.91490	+	3.57089i	0.220242	+	0.160015i
$499$	2.62275	+	8.07201i	0.117411	+	0.361353i	0.992442	−	0.122713i	$-0.0391595\pi$
$499$	2.62275	+	8.07201i	0.117411	+	0.361353i	−0.875032	+	0.484066i	$0.839160\pi$
$500$	−0.187504	−	0.577078i	−0.00838543	−	0.0258077i
$501$	6.06136	−	4.40384i	0.270802	−	0.196749i
$502$	0.843317	+	2.59546i	0.0376391	+	0.115841i
$503$	29.8664	+	21.6992i	1.33168	+	0.967520i	0.999706	+	0.0242297i	$0.00771329\pi$
$503$	29.8664	+	21.6992i	1.33168	+	0.967520i	0.331970	+	0.943290i	$0.392287\pi$
$504$	−2.95741			−0.131734
$505$	−11.4813	−	35.3357i	−0.510910	−	1.57242i
$506$	4.54374	−	19.9642i	0.201994	−	0.887519i
$507$	15.5645	+	11.3083i	0.691244	+	0.502218i
$508$	−2.90606			−0.128935
$509$	1.85830	−	5.71927i	0.0823678	−	0.253502i	−0.901388	−	0.433011i	$-0.857451\pi$
$509$	1.85830	−	5.71927i	0.0823678	−	0.253502i	0.983756	+	0.179509i	$0.0574510\pi$
$510$	−7.30916	+	22.4953i	−0.323655	+	0.996108i
$511$	10.5678	+	7.67796i	0.467492	+	0.339653i
$512$	7.64806	−	23.5383i	0.338000	−	1.04026i
$513$	31.9137	+	23.1867i	1.40903	+	1.02372i
$514$	−22.8508	+	16.6021i	−1.00791	+	0.732286i
$515$	−0.207957	+	0.151089i	−0.00916367	+	0.00665780i
$516$	2.97204	+	2.15931i	0.130837	+	0.0950585i
$517$	12.8398	+	29.9890i	0.564696	+	1.31892i
$518$	−22.4493	+	16.3103i	−0.986364	+	0.716635i
$519$	−14.7107			−0.645730
$520$	−4.08265	+	12.5651i	−0.179036	+	0.551016i
$521$	−3.01537	+	9.28036i	−0.132106	+	0.406580i	−0.995129	−	0.0985850i	$-0.968568\pi$
$521$	−3.01537	+	9.28036i	−0.132106	+	0.406580i	0.863023	+	0.505165i	$0.168568\pi$
$522$	−0.578927	−	1.78175i	−0.0253389	−	0.0779852i
$523$	−3.52199			−0.154006			−0.0770030	−	0.997031i	$-0.524535\pi$
$523$	−3.52199			−0.154006			−0.0770030	+	0.997031i	$0.524535\pi$
$524$	0.0131792	+	0.00957528i	0.000575738	+	0.000418298i
$525$	−8.58768	−	26.4302i	−0.374797	−	1.15351i
$526$	−4.91016	+	15.1119i	−0.214093	+	0.658911i
$527$	9.23951	+	6.71290i	0.402480	+	0.292419i
$528$	−18.7018	−	11.1582i	−0.813893	−	0.485596i
$529$	1.81385	−	1.31784i	0.0788630	−	0.0572974i
$530$	−16.3109	−	50.1998i	−0.708500	−	2.18054i
$531$	1.53458	+	1.11494i	0.0665950	+	0.0483841i
$532$	−4.34041	+	3.15349i	−0.188181	+	0.136721i
$533$	−1.57442	+	4.84557i	−0.0681957	+	0.209885i
$534$	7.24853	+	22.3087i	0.313674	+	0.965391i
$535$	−13.9424	−	42.9103i	−0.602782	−	1.85517i
$536$	−1.78708	+	5.50008i	−0.0771903	+	0.237567i
$537$	−25.7019	+	18.6735i	−1.10912	+	0.805823i
$538$	−16.2093			−0.698832
$539$	28.2753	+	16.8700i	1.21790	+	0.726644i
$540$	−0.744158	−	2.29028i	−0.0320235	−	0.0985581i
$541$	−8.71040	+	6.32848i	−0.374489	+	0.272083i	−0.759070	−	0.651009i	$-0.774346\pi$
$541$	−8.71040	+	6.32848i	−0.374489	+	0.272083i	0.384581	+	0.923091i	$0.374346\pi$
$542$	−2.38972	−	7.35480i	−0.102647	−	0.315916i
$543$	−11.3321	+	8.23325i	−0.486307	+	0.353323i
$544$	−2.45314	−	1.78231i	−0.105177	−	0.0764159i
$545$	27.0144	+	19.6271i	1.15717	+	0.840733i
$546$	4.72709	−	14.5485i	0.202301	−	0.622618i
$547$	−0.588095	+	0.427276i	−0.0251451	+	0.0182690i	−0.600287	−	0.799785i	$-0.704947\pi$
$547$	−0.588095	+	0.427276i	−0.0251451	+	0.0182690i	0.575142	+	0.818054i	$0.304947\pi$
$548$	−0.200658	−	0.145787i	−0.00857170	−	0.00622770i
$549$	−1.00627	−	1.62887i	−0.0429465	−	0.0695184i
$550$	3.73940	−	16.4301i	0.159449	−	0.700584i
$551$	−36.2705	−	26.3521i	−1.54517	−	1.12264i
$552$	7.43685	+	22.8883i	0.316533	+	0.974190i
$553$	−2.18733			−0.0930145
$554$	12.4471	−	9.04333i	0.528825	−	0.384214i
$555$	21.4578	+	15.5900i	0.910835	+	0.661760i
$556$	−0.197320	+	0.607289i	−0.00836824	+	0.0257548i
$557$	1.79391			0.0760106			0.0380053	−	0.999278i	$-0.487900\pi$
$557$	1.79391			0.0760106			0.0380053	+	0.999278i	$0.487900\pi$
$558$	−1.15797			−0.0490207
$559$	−15.3191	+	11.1300i	−0.647928	+	0.470748i
$560$	−44.3593			−1.87452
$561$	−14.7319	+	12.8869i	−0.621982	+	0.544087i
$562$	−11.2591			−0.474934
$563$	10.2780	+	7.46741i	0.433166	+	0.314714i	0.782914	−	0.622130i	$-0.213733\pi$
$563$	10.2780	+	7.46741i	0.433166	+	0.314714i	−0.349747	+	0.936844i	$0.613733\pi$
$564$	−2.35161	−	1.70854i	−0.0990204	−	0.0719426i
$565$	−33.0677	−	24.0251i	−1.39117	−	1.01074i
$566$	−21.5999	−	15.6932i	−0.907911	−	0.659636i
$567$	12.3011	+	37.8589i	0.516597	+	1.58992i
$568$	10.7956	−	33.2254i	0.452973	−	1.39411i
$569$	−10.1598	−	31.2685i	−0.425919	−	1.31084i	−0.902112	−	0.431503i	$-0.857983\pi$
$569$	−10.1598	−	31.2685i	−0.425919	−	1.31084i	0.476193	−	0.879341i	$-0.342017\pi$
$570$	−46.4304	−	33.7337i	−1.94476	−	1.41295i
$571$	20.2830	+	14.7364i	0.848816	+	0.616701i	0.924819	−	0.380407i	$-0.124216\pi$
$571$	20.2830	+	14.7364i	0.848816	+	0.616701i	−0.0760035	+	0.997108i	$0.524216\pi$
$572$	−0.623793	+	0.545671i	−0.0260821	+	0.0228157i
$573$	−3.33692	+	2.42442i	−0.139402	+	0.101281i
$574$	−18.6464			−0.778287
$575$	−13.8207	+	10.0413i	−0.576364	+	0.418753i
$576$	2.09453			0.0872722
$577$	−11.1414			−0.463824			−0.231912	−	0.972737i	$-0.574498\pi$
$577$	−11.1414			−0.463824			−0.231912	+	0.972737i	$0.574498\pi$
$578$	−6.87073	+	4.99188i	−0.285785	+	0.207635i
$579$	33.0186	+	23.9894i	1.37221	+	0.996966i
$580$	0.845748	+	2.60294i	0.0351178	+	0.108081i
$581$	8.28444	+	6.01900i	0.343696	+	0.249710i
$582$	11.0946	+	8.06067i	0.459885	+	0.334126i
$583$	9.69309	−	42.5894i	0.401447	−	1.76387i
$584$	−7.53160	−	5.47203i	−0.311660	−	0.226434i
$585$	−1.10454			−0.0456670
$586$	−13.8889	−	42.7456i	−0.573744	−	1.76580i
$587$	34.3051	−	24.9241i	1.41592	−	1.02873i	0.423497	−	0.905898i	$-0.360803\pi$
$587$	34.3051	−	24.9241i	1.41592	−	1.02873i	0.992428	−	0.122831i	$-0.0391974\pi$
$588$	−2.93378			−0.120987
$589$	−22.4186	+	16.2881i	−0.923743	+	0.671139i
$590$	25.0896	+	18.2287i	1.03292	+	0.750462i
$591$	−35.4905	+	25.7854i	−1.45989	+	1.06067i
$592$	14.6782	−	10.6643i	0.603269	−	0.438301i
$593$	−1.11791	−	3.44057i	−0.0459071	−	0.141287i	0.925476	−	0.378807i	$-0.123666\pi$
$593$	−1.11791	−	3.44057i	−0.0459071	−	0.141287i	−0.971383	+	0.237520i	$0.923666\pi$
$594$	−4.94922	+	21.7459i	−0.203069	+	0.892243i
$595$	−12.3201	+	37.9175i	−0.505076	+	1.55447i
$596$	0.680973	+	0.494756i	0.0278937	+	0.0202660i
$597$	3.07520	−	9.46451i	0.125860	−	0.387356i
$598$	−9.40354			−0.384539
$599$	20.7141	−	15.0497i	0.846355	−	0.614913i	−0.0777836	−	0.996970i	$-0.524784\pi$
$599$	20.7141	−	15.0497i	0.846355	−	0.614913i	0.924139	+	0.382057i	$0.124784\pi$
$600$	6.12037	+	18.8366i	0.249863	+	0.769000i
$601$	−27.8950	+	20.2669i	−1.13786	+	0.826703i	−0.986820	−	0.161825i	$-0.948262\pi$
$601$	−27.8950	+	20.2669i	−1.13786	+	0.826703i	−0.151040	+	0.988528i	$0.548262\pi$
$602$	−56.0648	−	40.7335i	−2.28503	−	1.66017i
$603$	−0.483486			−0.0196891
$604$	−0.507717	−	1.56259i	−0.0206587	−	0.0635810i
$605$	22.4565	−	23.5458i	0.912986	−	0.957272i
$606$	−9.47424	−	29.1587i	−0.384865	−	1.18449i
$607$	−9.77787	−	30.0932i	−0.396872	−	1.22145i	−0.927494	−	0.373837i	$-0.878042\pi$
$607$	−9.77787	−	30.0932i	−0.396872	−	1.22145i	0.530623	−	0.847608i	$-0.321958\pi$
$608$	5.95226	−	4.32457i	0.241396	−	0.175384i
$609$	−12.9177	−	39.7567i	−0.523453	−	1.61102i
$610$	−16.4520	−	26.6312i	−0.666123	−	1.07827i
$611$	12.1211	−	8.80650i	0.490368	−	0.356273i
$612$	0.0407117	−	0.125298i	0.00164567	−	0.00506486i
$613$	15.3561	−	11.1568i	0.620225	−	0.450620i	−0.232775	−	0.972531i	$-0.574781\pi$
$613$	15.3561	−	11.1568i	0.620225	−	0.450620i	0.853000	+	0.521911i	$0.174781\pi$
$614$	−10.0034	+	30.7874i	−0.403706	+	1.24248i
$615$	5.50760	+	16.9506i	0.222088	+	0.683516i
$616$	−34.3609	−	20.5009i	−1.38444	−	0.826004i
$617$	1.00219	−	0.728133i	0.0403466	−	0.0293135i	−0.567429	−	0.823422i	$-0.692062\pi$
$617$	1.00219	−	0.728133i	0.0403466	−	0.0293135i	0.607776	+	0.794109i	$0.292062\pi$
$618$	−0.171604	+	0.124678i	−0.00690293	+	0.00501527i
$619$	−3.37761			−0.135757			−0.0678787	−	0.997694i	$-0.521623\pi$
$619$	−3.37761			−0.135757			−0.0678787	+	0.997694i	$0.521623\pi$
$620$	1.69166			0.0679388
$621$	18.2922	−	13.2901i	0.734041	−	0.533312i
$622$	−1.52214	−	4.68468i	−0.0610324	−	0.187839i
$623$	12.2179	+	37.6029i	0.489501	+	1.50653i
$624$	−3.09075	+	9.51236i	−0.123729	+	0.380799i
$625$	24.0186	−	17.4505i	0.960743	−	0.698021i
$626$	−21.0413	+	15.2874i	−0.840979	+	0.611007i
$627$	−18.6924	−	43.6584i	−0.746502	−	1.74355i
$628$	0.459884	−	1.41538i	0.0183514	−	0.0564797i
$629$	−5.03901	−	15.5085i	−0.200918	−	0.618363i
$630$	−1.24917	−	3.84454i	−0.0497680	−	0.153170i
$631$	6.40697	+	19.7186i	0.255058	+	0.784986i	0.993818	+	0.111019i	$0.0354113\pi$
$631$	6.40697	+	19.7186i	0.255058	+	0.784986i	−0.738761	+	0.673968i	$0.764589\pi$
$632$	1.55889			0.0620093
$633$	11.2988	+	8.20903i	0.449085	+	0.326279i
$634$	23.3313	+	16.9512i	0.926603	+	0.673216i
$635$	−16.1922	−	49.8345i	−0.642568	−	1.97762i
$636$	1.20267	+	3.70142i	0.0476888	+	0.146771i
$637$	4.67291	−	14.3817i	0.185148	−	0.569826i
$638$	5.62487	−	24.7145i	0.222691	−	0.978457i
$639$	2.92069			0.115541
$640$	28.7688			1.13719
$641$	−0.147933	−	0.455292i	−0.00584301	−	0.0179830i	0.948093	−	0.317995i	$-0.103009\pi$
$641$	−0.147933	−	0.455292i	−0.00584301	−	0.0179830i	−0.953936	+	0.300012i	$0.903009\pi$
$642$	−11.5051	−	35.4092i	−0.454071	−	1.39749i
$643$	−8.79116			−0.346690			−0.173345	−	0.984861i	$-0.555458\pi$
$643$	−8.79116			−0.346690			−0.173345	+	0.984861i	$0.555458\pi$
$644$	0.950263	+	2.92461i	0.0374456	+	0.115246i
$645$	−20.4691	+	62.9975i	−0.805971	+	2.48052i
$646$	10.9034	+	33.5572i	0.428988	+	1.32029i
$647$	20.3136			0.798610			0.399305	−	0.916818i	$-0.369251\pi$
$647$	20.3136			0.798610			0.399305	+	0.916818i	$0.369251\pi$
$648$	−8.76690	−	26.9817i	−0.344396	−	1.05994i
$649$	10.1008	+	23.5917i	0.396491	+	0.926054i
$650$	−7.73892			−0.303545
$651$	−25.8380			−1.01267
$652$	−2.66077	+	1.93317i	−0.104204	+	0.0757086i
$653$	−12.7448			−0.498741			−0.249371	−	0.968408i	$-0.580224\pi$
$653$	−12.7448			−0.498741			−0.249371	+	0.968408i	$0.580224\pi$
$654$	22.2920	+	16.1961i	0.871687	+	0.633318i
$655$	−0.0907684	+	0.279356i	−0.00354661	+	0.0109154i
$656$	12.1917			0.476008
$657$	0.240510	−	0.740214i	0.00938319	−	0.0288785i
$658$	44.3608	+	32.2300i	1.72937	+	1.25646i
$659$	−8.49078	+	26.1319i	−0.330754	+	1.01796i	0.638022	+	0.770018i	$0.279753\pi$
$659$	−8.49078	+	26.1319i	−0.330754	+	1.01796i	−0.968776	+	0.247938i	$0.920247\pi$
$660$	−0.643390	+	2.82692i	−0.0250439	+	0.110038i
$661$	−8.81711	+	27.1363i	−0.342946	+	1.05548i	0.619728	+	0.784816i	$0.287243\pi$
$661$	−8.81711	+	27.1363i	−0.342946	+	1.05548i	−0.962674	+	0.270663i	$0.912757\pi$
$662$	−4.44841	+	13.6908i	−0.172893	+	0.532109i
$663$	7.27257	+	5.28383i	0.282443	+	0.205207i
$664$	−5.90426	−	4.28969i	−0.229130	−	0.166472i
$665$	−78.2619	−	56.8606i	−3.03487	−	2.20496i
$666$	1.33760	+	0.971821i	0.0518308	+	0.0376573i
$667$	−20.7894	+	15.1044i	−0.804968	+	0.584844i
$668$	−0.551985	+	0.401040i	−0.0213569	+	0.0155167i
$669$	−12.0997	−	37.2392i	−0.467803	−	1.43975i
$670$	−7.90476			−0.305388
$671$	−0.400031	−	25.9006i	−0.0154430	−	0.999881i
$672$	6.86013			0.264635
$673$	3.56798	+	10.9811i	0.137536	+	0.423291i	0.995976	−	0.0896226i	$-0.0285661\pi$
$673$	3.56798	+	10.9811i	0.137536	+	0.423291i	−0.858440	+	0.512914i	$0.828566\pi$
$674$	−31.0130	+	22.5322i	−1.19457	+	0.867909i
$675$	15.0541	−	10.9374i	0.579432	−	0.420982i
$676$	−1.41740	−	1.02980i	−0.0545153	−	0.0396077i
$677$	22.2941	+	16.1976i	0.856834	+	0.622526i	0.927022	−	0.375008i	$-0.122360\pi$
$677$	22.2941	+	16.1976i	0.856834	+	0.622526i	−0.0701882	+	0.997534i	$0.522360\pi$
$678$	−27.2872	−	19.8253i	−1.04796	−	0.761386i
$679$	18.7007	+	13.5869i	0.717668	+	0.521416i
$680$	8.78047	−	27.0235i	0.336716	−	1.03630i
$681$	−0.724716	+	2.23045i	−0.0277712	+	0.0854709i
$682$	−13.4539	−	8.02706i	−0.515177	−	0.307372i
$683$	0.873015	−	2.68686i	0.0334050	−	0.102810i	−0.932964	−	0.359970i	$-0.882787\pi$
$683$	0.873015	−	2.68686i	0.0334050	−	0.102810i	0.966369	+	0.257160i	$0.0827868\pi$
$684$	0.258615	+	0.187895i	0.00988841	+	0.00718435i
$685$	1.38198	−	4.25329i	0.0528027	−	0.162510i
$686$	16.3197			0.623089
$687$	4.08560	−	12.5742i	0.155875	−	0.479735i
$688$	36.6573	+	26.6331i	1.39755	+	1.01538i
$689$	−20.0604			−0.764242
$690$	−26.6128	+	19.3353i	−1.01313	+	0.736084i
$691$	−42.1392			−1.60305			−0.801525	−	0.597961i	$-0.795978\pi$
$691$	−42.1392			−1.60305			−0.801525	+	0.597961i	$0.795978\pi$
$692$	1.33965			0.0509259
$693$	0.742343	−	3.26170i	0.0281993	−	0.123902i
$694$	0.381901	+	1.17537i	0.0144968	+	0.0446165i
$695$	−11.5135			−0.436733
$696$	9.20637	+	28.3343i	0.348967	+	1.07401i
$697$	3.38608	−	10.4213i	0.128257	−	0.394734i
$698$	7.66294	+	23.5841i	0.290047	+	0.892672i
$699$	26.2255			0.991939
$700$	0.782046	+	2.40689i	0.0295586	+	0.0909719i
$701$	9.80580	+	30.1792i	0.370360	+	1.13985i	0.946556	+	0.322539i	$0.104536\pi$
$701$	9.80580	+	30.1792i	0.370360	+	1.13985i	−0.576196	+	0.817312i	$0.695464\pi$
$702$	10.2427			0.386586
$703$	39.5660			1.49226
$704$	24.3354	+	14.5194i	0.917176	+	0.547219i
$705$	16.1960	−	49.8463i	0.609978	−	1.87732i
$706$	1.43421	+	4.41405i	0.0539772	+	0.166125i
$707$	−15.9695	−	49.1492i	−0.600597	−	1.84845i
$708$	−1.84995	−	1.34407i	−0.0695254	−	0.0505132i
$709$	14.9489	+	10.8610i	0.561419	+	0.407895i	0.831978	−	0.554809i	$-0.187208\pi$
$709$	14.9489	+	10.8610i	0.561419	+	0.407895i	−0.270559	+	0.962703i	$0.587208\pi$
$710$	47.7519			1.79210
$711$	0.0402735	+	0.123949i	0.00151037	+	0.00464845i
$712$	−8.70763	−	26.7993i	−0.326332	−	1.00435i
$713$	4.90819	+	15.1059i	0.183813	+	0.565719i
$714$	−10.1665	+	31.2892i	−0.380470	+	1.17097i
$715$	−12.8331	−	7.65669i	−0.479932	−	0.286344i
$716$	2.34057	−	1.70053i	0.0874714	−	0.0635517i
$717$	36.2776	−	26.3572i	1.35481	−	0.984328i
$718$	6.79936	−	20.9263i	0.253750	−	0.780962i
$719$	−12.8391	−	39.5147i	−0.478818	−	1.47365i	−0.840739	−	0.541441i	$-0.817879\pi$
$719$	−12.8391	−	39.5147i	−0.478818	−	1.47365i	0.361921	−	0.932209i	$-0.382121\pi$
$720$	0.816753	+	2.51371i	0.0304386	+	0.0936804i
$721$	−0.289251	+	0.210153i	−0.0107723	+	0.00782652i
$722$	−59.8683			−2.22807
$723$	18.5552			0.690076
$724$	1.03197	−	0.749771i	0.0383529	−	0.0278650i
$725$	−17.1092	+	12.4306i	−0.635420	+	0.461660i
$726$	18.5309	−	19.4298i	0.687745	−	0.721106i
$727$	8.66769	+	26.6764i	0.321467	+	0.989374i	0.973010	+	0.230762i	$0.0741219\pi$
$727$	8.66769	+	26.6764i	0.321467	+	0.989374i	−0.651543	+	0.758612i	$0.725878\pi$
$728$	−5.67864	+	17.4770i	−0.210464	+	0.647743i
$729$	−19.7787	+	14.3701i	−0.732546	+	0.532226i
$730$	3.93222	−	12.1021i	0.145538	−	0.447920i
$731$	32.9465	−	23.9370i	1.21857	−	0.885342i
$732$	1.21307	+	1.96362i	0.0448364	+	0.0725775i
$733$	3.86252	+	11.8876i	0.142666	+	0.439079i	0.996703	−	0.0811314i	$-0.0258534\pi$
$733$	3.86252	+	11.8876i	0.142666	+	0.439079i	−0.854038	+	0.520211i	$0.825853\pi$
$734$	27.3010	−	19.8353i	1.00770	−	0.732135i
$735$	−16.3467	−	50.3099i	−0.602956	−	1.85571i
$736$	−1.30315	−	4.01069i	−0.0480348	−	0.147836i
$737$	−5.61741	−	3.35154i	−0.206920	−	0.123456i
$738$	0.343322	+	1.05664i	0.0126379	+	0.0388953i
$739$	−13.6523			−0.502208			−0.251104	−	0.967960i	$-0.580794\pi$
$739$	−13.6523			−0.502208			−0.251104	+	0.967960i	$0.580794\pi$
$740$	−1.95408	−	1.41972i	−0.0718335	−	0.0521901i
$741$	−17.6460	+	12.8206i	−0.648244	+	0.470977i
$742$	−22.6872	−	69.8239i	−0.832872	−	2.56332i
$743$	−12.9405	+	9.40179i	−0.474739	+	0.344918i	−0.799285	−	0.600952i	$-0.794788\pi$
$743$	−12.9405	+	9.40179i	−0.474739	+	0.344918i	0.324546	+	0.945870i	$0.394788\pi$
$744$	18.4146			0.675111
$745$	−4.69001	+	14.4344i	−0.171829	+	0.528834i
$746$	10.4232	+	7.57290i	0.381621	+	0.277264i
$747$	0.188543	−	0.580277i	0.00689844	−	0.0212312i
$748$	1.34158	−	1.17356i	0.0490530	−	0.0429098i
$749$	−19.3928	−	59.6848i	−0.708596	−	2.18083i
$750$	7.30398	−	5.30665i	0.266703	−	0.193771i
$751$	29.2075	−	21.2205i	1.06580	−	0.774346i	0.0906434	−	0.995883i	$-0.471108\pi$
$751$	29.2075	−	21.2205i	1.06580	−	0.774346i	0.975152	+	0.221538i	$0.0711076\pi$
$752$	−29.0048	−	21.0732i	−1.05770	−	0.768462i
$753$	2.93530	−	2.13262i	0.106968	−	0.0777170i
$754$	−11.6410			−0.423941
$755$	23.9672	−	17.4132i	0.872255	−	0.633730i
$756$	−1.03506	−	3.18560i	−0.0376449	−	0.115859i
$757$	−19.2446			−0.699458			−0.349729	−	0.936851i	$-0.613726\pi$
$757$	−19.2446			−0.699458			−0.349729	+	0.936851i	$0.613726\pi$
$758$	20.7445	+	15.0718i	0.753475	+	0.547432i
$759$	−27.1100	+	2.45682i	−0.984031	+	0.0891770i
$760$	55.7767	+	40.5241i	2.02323	+	1.46996i
$761$	12.0095	+	8.72542i	0.435344	+	0.316296i	0.783782	−	0.621036i	$-0.213288\pi$
$761$	12.0095	+	8.72542i	0.435344	+	0.316296i	−0.348438	+	0.937332i	$0.613288\pi$
$762$	−13.3617	−	41.1229i	−0.484042	−	1.48973i
$763$	37.5749	+	27.2997i	1.36030	+	0.988317i
$764$	0.303880	−	0.220782i	0.0109940	−	0.00798762i
$765$	2.37551			0.0858867
$766$	−21.3705			−0.772149
$767$	9.53539	−	6.92786i	0.344303	−	0.250151i
$768$	−7.04352			−0.254161
$769$	−2.40207	+	1.74520i	−0.0866207	+	0.0629336i	−0.630253	−	0.776390i	$-0.717049\pi$
$769$	−2.40207	+	1.74520i	−0.0866207	+	0.0629336i	0.543632	+	0.839324i	$0.317049\pi$
$770$	12.1370	−	53.3273i	0.437385	−	1.92178i
$771$	30.3800	+	22.0724i	1.09411	+	0.794916i
$772$	−3.00688	−	2.18462i	−0.108220	−	0.0786263i
$773$	−11.9409	−	36.7503i	−0.429484	−	1.32182i	−0.898635	−	0.438697i	$-0.855440\pi$
$773$	−11.9409	−	36.7503i	−0.429484	−	1.32182i	0.469151	−	0.883118i	$-0.344560\pi$
$774$	−1.27596	+	3.92701i	−0.0458636	+	0.141154i
$775$	4.03934	+	12.4318i	0.145097	+	0.446564i
$776$	−13.3279	−	9.68326i	−0.478442	−	0.347609i
$777$	29.8461	+	21.6845i	1.07072	+	0.777927i
$778$	−0.206348	−	0.149921i	−0.00739794	−	0.00537492i
$779$	21.5096	+	15.6276i	0.770660	+	0.559917i
$780$	1.33153			0.0476766
$781$	33.9342	+	20.2463i	1.21426	+	0.724470i
$782$	20.2240			0.723209
$783$	22.6446	−	16.4523i	0.809253	−	0.587957i
$784$	−36.1854			−1.29233
$785$	26.8340			0.957746
$786$	−0.0749012	+	0.230522i	−0.00267164	+	0.00822246i
$787$	−29.5423	−	21.4637i	−1.05307	−	0.765099i	−0.0802746	−	0.996773i	$-0.525580\pi$
$787$	−29.5423	−	21.4637i	−1.05307	−	0.765099i	−0.972793	+	0.231674i	$0.925580\pi$
$788$	3.23199	−	2.34818i	0.115135	−	0.0836503i
$789$	21.1252			0.752075
$790$	0.658452	+	2.02651i	0.0234267	+	0.0720999i
$791$	−45.9946	−	33.4170i	−1.63538	−	1.18817i
$792$	−0.529063	+	2.32459i	−0.0187994	+	0.0826008i
$793$	−11.5581	+	2.81897i	−0.410440	+	0.100105i
$794$	−6.54957	−	4.75854i	−0.232436	−	0.168874i
$795$	−56.7727	+	41.2478i	−2.01352	+	1.46291i
$796$	−0.280047	+	0.861896i	−0.00992600	+	0.0305491i
$797$	27.7399	+	20.1542i	0.982596	+	0.713898i	0.958287	−	0.285807i	$-0.0922615\pi$
$797$	27.7399	+	20.1542i	0.982596	+	0.713898i	0.0243087	+	0.999704i	$0.492262\pi$
$798$	−64.5810	−	46.9208i	−2.28614	−	1.66098i
$799$	−26.0686	+	18.9400i	−0.922242	+	0.670048i
$800$	−1.07247	−	3.30071i	−0.0379174	−	0.116698i
$801$	1.90588	−	1.38471i	0.0673411	−	0.0489262i
$802$	6.88802	+	21.1991i	0.243224	+	0.748568i
$803$	7.92556	−	6.93299i	0.279687	−	0.244660i
$804$	0.582849			0.0205555
$805$	−44.8579	+	32.5912i	−1.58103	+	1.14869i
$806$	−2.22346	+	6.84309i	−0.0783179	+	0.241038i
$807$	6.65936	+	20.4954i	0.234421	+	0.721473i
$808$	11.3814	+	35.0283i	0.400395	+	1.23229i
$809$	−12.9186	+	39.7593i	−0.454193	+	1.39786i	0.417887	+	0.908499i	$0.362771\pi$
$809$	−12.9186	+	39.7593i	−0.454193	+	1.39786i	−0.872080	+	0.489364i	$0.837229\pi$
$810$	31.3724	−	22.7934i	1.10231	−	0.800877i
$811$	−17.8459	−	12.9658i	−0.626656	−	0.455292i	0.228584	−	0.973524i	$-0.426590\pi$
$811$	−17.8459	−	12.9658i	−0.626656	−	0.455292i	−0.855240	+	0.518232i	$0.826590\pi$
$812$	1.17637	+	3.62049i	0.0412824	+	0.127054i
$813$	−8.31780	+	6.04323i	−0.291718	+	0.211945i
$814$	8.80425	+	20.5634i	0.308589	+	0.720747i
$815$	−47.9764	−	34.8569i	−1.68054	−	1.22098i
$816$	6.64722	−	20.4580i	0.232699	−	0.716175i
$817$	30.5347	+	93.9760i	1.06827	+	3.28781i
$818$	−26.1232	−	18.9796i	−0.913375	−	0.663606i
$819$	−1.53633			−0.0536835
$820$	−0.501556	−	1.54363i	−0.0175151	−	0.0539059i
$821$	5.30389	−	16.3237i	0.185107	−	0.569701i	−0.814843	−	0.579681i	$-0.803177\pi$
$821$	5.30389	−	16.3237i	0.185107	−	0.569701i	0.999950	+	0.00998070i	$0.00317701\pi$
$822$	1.14040	−	3.50978i	0.0397759	−	0.122418i
$823$	−52.0255			−1.81350			−0.906748	−	0.421673i	$-0.861443\pi$
$823$	−52.0255			−1.81350			−0.906748	+	0.421673i	$0.861443\pi$
$824$	0.206147	−	0.149775i	0.00718148	−	0.00521765i
$825$	−22.3110	+	2.02191i	−0.776768	+	0.0703940i
$826$	34.8976	+	25.3546i	1.21424	+	0.882199i
$827$	16.1948	−	11.7662i	0.563149	−	0.409152i	−0.269461	−	0.963011i	$-0.586846\pi$
$827$	16.1948	−	11.7662i	0.563149	−	0.409152i	0.832610	+	0.553859i	$0.186846\pi$
$828$	0.148232	−	0.107697i	0.00515143	−	0.00374273i
$829$	29.3861	+	21.3502i	1.02062	+	0.741524i	0.966410	−	0.257006i	$-0.0827359\pi$
$829$	29.3861	+	21.3502i	1.02062	+	0.741524i	0.0542101	+	0.998530i	$0.482736\pi$
$830$	3.08259	−	9.48724i	0.106998	−	0.329307i
$831$	−16.5483	−	12.0230i	−0.574054	−	0.417075i
$832$	4.02179	−	12.3778i	0.139430	−	0.429123i
$833$	−10.0499	+	30.9305i	−0.348210	+	1.07168i
$834$	−9.50086			−0.328988
$835$	−9.95283	−	7.23115i	−0.344432	−	0.250244i
$836$	1.70224	+	3.97580i	0.0588733	+	0.137506i
$837$	−5.34620	−	16.4539i	−0.184792	−	0.568731i
$838$	−0.598414			−0.0206719
$839$	28.6319	+	20.8023i	0.988483	+	0.718175i	0.959588	−	0.281408i	$-0.0908014\pi$
$839$	28.6319	+	20.8023i	0.988483	+	0.718175i	0.0288944	+	0.999582i	$0.490801\pi$
$840$	19.8649	+	61.1378i	0.685403	+	2.10945i
$841$	−2.27450	+	1.65252i	−0.0784309	+	0.0569834i
$842$	−7.40738	−	22.7976i	−0.255275	−	0.785656i
$843$	4.62563	+	14.2362i	0.159315	+	0.490321i
$844$	−1.02893	−	0.747564i	−0.0354174	−	0.0257322i
$845$	9.76194	−	30.0442i	0.335821	−	1.03355i
$846$	1.00960	−	3.10722i	0.0347107	−	0.106828i
$847$	31.2352	−	32.7503i	1.07325	−	1.12531i
$848$	14.8337	+	45.6535i	0.509392	+	1.56775i
$849$	−10.9689	+	33.7588i	−0.376451	+	1.15860i
$850$	16.6439			0.570882
$851$	7.00798	−	21.5683i	0.240230	−	0.739353i
$852$	−3.52093			−0.120625
$853$	−14.1247	+	10.2622i	−0.483621	+	0.351371i	−0.802726	−	0.596348i	$-0.796618\pi$
$853$	−14.1247	+	10.2622i	−0.483621	+	0.351371i	0.319105	+	0.947719i	$0.396618\pi$
$854$	−22.8834	−	37.0419i	−0.783055	−	1.26755i
$855$	−1.78114	+	5.48179i	−0.0609138	+	0.187473i
$856$	13.8211	+	42.5369i	0.472395	+	1.45388i
$857$	−6.68725	−	4.85857i	−0.228432	−	0.165966i	0.467682	−	0.883897i	$-0.345089\pi$
$857$	−6.68725	−	4.85857i	−0.228432	−	0.165966i	−0.696114	+	0.717931i	$0.745089\pi$
$858$	−10.5898	−	6.31823i	−0.361529	−	0.215701i
$859$	−2.84859	−	8.76706i	−0.0971927	−	0.299128i	0.890626	−	0.454736i	$-0.150266\pi$
$859$	−2.84859	−	8.76706i	−0.0971927	−	0.299128i	−0.987819	+	0.155608i	$0.950266\pi$
$860$	1.86404	−	5.73694i	0.0635634	−	0.195628i
$861$	7.66063	+	23.5770i	0.261074	+	0.803502i
$862$	27.4455			0.934799
$863$	13.6410	+	9.91075i	0.464344	+	0.337366i	0.795233	−	0.606304i	$-0.207348\pi$
$863$	13.6410	+	9.91075i	0.464344	+	0.337366i	−0.330889	+	0.943670i	$0.607348\pi$
$864$	1.41944	+	4.36860i	0.0482905	+	0.148623i
$865$	7.46437	+	22.9730i	0.253796	+	0.781105i
$866$	9.22337	+	6.70117i	0.313423	+	0.227715i
$867$	9.13459	+	6.63667i	0.310227	+	0.225393i
$868$	2.35297			0.0798650
$869$	−0.391299	+	1.71929i	−0.0132739	+	0.0583228i
$870$	−32.9450	+	23.9360i	−1.11694	+	0.811505i
$871$	−0.928359	+	2.85720i	−0.0314563	+	0.0968124i
$872$	−26.7793	−	19.4563i	−0.906862	−	0.658874i
$873$	0.425605	−	1.30988i	0.0144045	−	0.0443326i
$874$	−15.1638	+	46.6695i	−0.512925	+	1.57862i
$875$	12.3114	−	8.94475i	0.416201	−	0.302388i
$876$	−0.289938	+	0.892337i	−0.00979609	+	0.0301493i
$877$	−8.60722			−0.290645			−0.145323	−	0.989384i	$-0.546422\pi$
$877$	−8.60722			−0.290645			−0.145323	+	0.989384i	$0.546422\pi$
$878$	25.3539			0.855653
$879$	−48.3425	+	35.1229i	−1.63055	+	1.18466i
$880$	−7.93560	+	34.8674i	−0.267509	+	1.17538i
$881$	−12.8905	+	39.6729i	−0.434292	+	1.33661i	0.459519	+	0.888168i	$0.348022\pi$
$881$	−12.8905	+	39.6729i	−0.434292	+	1.33661i	−0.893811	+	0.448445i	$0.851978\pi$
$882$	−1.01899	−	3.13612i	−0.0343111	−	0.105599i
$883$	16.7716	−	51.6178i	0.564411	−	1.73708i	−0.105285	−	0.994442i	$-0.533575\pi$
$883$	16.7716	−	51.6178i	0.564411	−	1.73708i	0.669696	−	0.742636i	$-0.266425\pi$
$884$	−0.662284	−	0.481178i	−0.0222750	−	0.0161838i
$885$	12.7410	−	39.2129i	0.428285	−	1.31813i
$886$	−14.8951	+	10.8219i	−0.500410	+	0.363569i
$887$	−15.3182	+	47.1445i	−0.514334	+	1.58296i	0.270157	+	0.962816i	$0.412924\pi$
$887$	−15.3182	+	47.1445i	−0.514334	+	1.58296i	−0.784491	+	0.620140i	$0.787076\pi$
$888$	−21.2711	−	15.4544i	−0.713812	−	0.518615i
$889$	−22.5221	−	69.3158i	−0.755366	−	2.32478i
$890$	31.1603	−	22.6393i	1.04450	−	0.758870i
$891$	31.9585	−	2.89621i	1.07065	−	0.0970268i
$892$	1.10188	+	3.39123i	0.0368935	+	0.113547i
$893$	−24.1603	−	74.3578i	−0.808494	−	2.48829i
$894$	−3.87015	+	11.9111i	−0.129437	+	0.398367i
$895$	42.2029	+	30.6622i	1.41069	+	1.02492i
$896$	40.0151			1.33681
$897$	3.86332	+	11.8901i	0.128992	+	0.396998i
$898$	37.5612	−	27.2898i	1.25343	−	0.910672i
$899$	6.07604	+	18.7001i	0.202647	+	0.623685i
$900$	0.121992	−	0.0886324i	0.00406640	−	0.00295441i
$901$	43.1436			1.43732
$902$	−3.33573	+	14.6565i	−0.111068	+	0.488008i
$903$	−28.4709	+	87.6245i	−0.947453	+	2.91596i
$904$	32.7800	+	23.8161i	1.09025	+	0.792111i
$905$	18.6074	+	13.5191i	0.618533	+	0.449390i
$906$	19.7775	−	14.3692i	0.657063	−	0.477384i
$907$	5.31264	+	16.3506i	0.176403	+	0.542914i	0.999695	−	0.0247051i	$-0.00786467\pi$
$907$	5.31264	+	16.3506i	0.176403	+	0.542914i	−0.823291	+	0.567619i	$0.807865\pi$
$908$	0.0659971	−	0.203118i	0.00219019	−	0.00674071i
$909$	−2.49110	+	1.80989i	−0.0826246	+	0.0600303i
$910$	−25.1182			−0.832659
$911$	−12.6392	+	38.8996i	−0.418757	+	1.28880i	0.490091	+	0.871671i	$0.336964\pi$
$911$	−12.6392	+	38.8996i	−0.418757	+	1.28880i	−0.908847	+	0.417129i	$0.863036\pi$
$912$	42.2255	+	30.6786i	1.39823	+	1.01587i
$913$	6.21309	−	5.43499i	0.205623	−	0.179872i
$914$	20.8064			0.688214
$915$	−26.9141	+	31.7434i	−0.889751	+	1.04940i
$916$	−0.372060	+	1.14508i	−0.0122932	+	0.0378346i
$917$	−0.126252	+	0.388562i	−0.00416920	+	0.0128315i
$918$	−22.0288			−0.727059
$919$	−9.64552	−	7.00788i	−0.318176	−	0.231169i	0.417221	−	0.908805i	$-0.363004\pi$
$919$	−9.64552	−	7.00788i	−0.318176	−	0.231169i	−0.735397	+	0.677637i	$0.763004\pi$
$920$	31.9699	−	23.2275i	1.05402	−	0.765787i
$921$	43.0381			1.41815
$922$	25.9815			0.855655
$923$	5.60812	−	17.2600i	0.184594	−	0.568121i
$924$	−0.894904	+	3.93202i	−0.0294402	+	0.129354i
$925$	5.76742	−	17.7503i	0.189632	−	0.583626i
$926$	10.5619	+	7.67366i	0.347085	+	0.252172i
$927$	0.0172345	+	0.0125216i	0.000566056	+	0.000411263i
$928$	−1.61322	−	4.96499i	−0.0529566	−	0.162984i
$929$	2.40781	−	1.74938i	0.0789977	−	0.0573952i	−0.547585	−	0.836750i	$-0.684453\pi$
$929$	2.40781	−	1.74938i	0.0789977	−	0.0573952i	0.626583	+	0.779355i	$0.284453\pi$
$930$	7.77804	+	23.9383i	0.255052	+	0.784969i
$931$	−63.8408	−	46.3831i	−2.09230	−	1.52014i
$932$	−2.38825			−0.0782298
$933$	−5.29807	+	3.84927i	−0.173451	+	0.126020i
$934$	10.4014	+	7.55709i	0.340346	+	0.247276i
$935$	27.6000	+	16.4671i	0.902616	+	0.538532i
$936$	1.09493			0.0357888
$937$	5.71051	+	17.5751i	0.186554	+	0.574154i	0.999972	−	0.00752571i	$-0.00239553\pi$
$937$	5.71051	+	17.5751i	0.186554	+	0.574154i	−0.813418	+	0.581680i	$0.802396\pi$
$938$	−10.9949			−0.358996
$939$	27.9743	+	20.3245i	0.912905	+	0.663264i
$940$	−1.47491	+	4.53931i	−0.0481063	+	0.148056i
$941$	−29.2785			−0.954451			−0.477226	−	0.878781i	$-0.658358\pi$
$941$	−29.2785			−0.954451			−0.477226	+	0.878781i	$0.658358\pi$
$942$	22.1432			0.721463
$943$	12.3288	−	8.95737i	0.401480	−	0.291692i
$944$	−22.8174	−	16.5778i	−0.742643	−	0.539562i
$945$	48.8610	−	35.4996i	1.58945	−	1.15480i
$946$	−42.0470	+	36.7812i	−1.36707	+	1.19586i
$947$	−18.9720			−0.616508			−0.308254	−	0.951304i	$-0.599745\pi$
$947$	−18.9720			−0.616508			−0.308254	+	0.951304i	$0.599745\pi$
$948$	−0.0485502	−	0.149422i	−0.00157684	−	0.00485300i
$949$	−3.91253	−	2.84262i	−0.127006	−	0.0922754i
$950$	−12.4795	+	38.4080i	−0.404889	+	1.24612i
$951$	11.8481	−	36.4647i	0.384201	−	1.18245i
$952$	12.2129	−	37.5875i	0.395823	−	1.21822i
$953$	−37.7894	+	27.4556i	−1.22412	+	0.889375i	−0.996435	−	0.0843597i	$-0.973116\pi$
$953$	−37.7894	+	27.4556i	−1.22412	+	0.889375i	−0.227685	+	0.973735i	$0.573116\pi$
$954$	−3.53899	+	2.57122i	−0.114579	+	0.0832465i
$955$	5.47927	+	3.98092i	0.177305	+	0.128820i
$956$	−3.30366	+	2.40025i	−0.106848	+	0.0776296i
$957$	−33.5605	+	3.04140i	−1.08486	+	0.0983144i
$958$	8.29979	−	25.5441i	0.268154	−	0.825293i
$959$	1.92222	−	5.91599i	0.0620718	−	0.191037i
$960$	−14.0689	−	43.2997i	−0.454072	−	1.39749i
$961$	−18.8467			−0.607958
$962$	8.31142	−	6.03860i	0.267971	−	0.194692i
$963$	−3.02509	+	2.19786i	−0.0974822	+	0.0708250i
$964$	−1.68975			−0.0544232
$965$	20.7090	−	63.7358i	0.666647	−	2.05173i
$966$	−37.0163	+	26.8939i	−1.19098	+	0.865297i
$967$	−13.3321	−	41.0320i	−0.428732	−	1.31950i	−0.899376	−	0.437177i	$-0.855978\pi$
$967$	−13.3321	−	41.0320i	−0.428732	−	1.31950i	0.470644	−	0.882323i	$-0.344022\pi$
$968$	−22.2611	+	23.3409i	−0.715498	+	0.750205i
$969$	37.9510	−	27.5730i	1.21916	−	0.885773i
$970$	6.95843	−	21.4159i	0.223422	−	0.687622i
$971$	−10.2953			−0.330392			−0.165196	−	0.986261i	$-0.552826\pi$
$971$	−10.2953			−0.330392			−0.165196	+	0.986261i	$0.552826\pi$
$972$	−0.337289	+	0.245055i	−0.0108185	+	0.00786013i
$973$	−16.0144			−0.513398
$974$	−3.63870			−0.116591
$975$	3.17943	+	9.78527i	0.101823	+	0.313379i
$976$	14.9621	+	24.2194i	0.478924	+	0.775244i
$977$	34.0416	+	24.7327i	1.08909	+	0.791268i	0.979245	−	0.202681i	$-0.0649654\pi$
$977$	34.0416	+	24.7327i	1.08909	+	0.791268i	0.109843	+	0.993949i	$0.464965\pi$
$978$	−39.5896	−	28.7636i	−1.26594	−	0.919757i
$979$	31.7424	−	2.87663i	1.01449	−	0.0919376i
$980$	1.48863	+	4.58152i	0.0475525	+	0.146351i
$981$	0.855157	−	2.63190i	0.0273031	−	0.0840302i
$982$	−42.3719			−1.35214
$983$	−12.3295	−	8.95791i	−0.393250	−	0.285713i	0.373536	−	0.927616i	$-0.378145\pi$
$983$	−12.3295	−	8.95791i	−0.393250	−	0.285713i	−0.766786	+	0.641903i	$0.778145\pi$
$984$	−5.45967	−	16.8031i	−0.174048	−	0.535665i
$985$	58.2759	+	42.3399i	1.85682	+	1.34906i
$986$	25.0361			0.797312
$987$	22.5274	−	69.3322i	0.717055	−	2.20687i
$988$	1.60696	−	1.16752i	0.0511241	−	0.0371438i
$989$	56.6368			1.80095
$990$	−3.24536	+	0.294108i	−0.103144	+	0.00934738i
$991$	−5.96404	+	18.3554i	−0.189454	+	0.583080i	−0.999997	−	0.00260012i	$-0.999172\pi$
$991$	−5.96404	+	18.3554i	−0.189454	+	0.583080i	0.810543	+	0.585680i	$0.199172\pi$
$992$	−3.22676			−0.102450
$993$	19.1386			0.607344
$994$	66.4190			2.10668
$995$	−16.3406			−0.518032
$996$	−0.227291	+	0.699531i	−0.00720200	+	0.0221655i
$997$	−8.98377	−	27.6492i	−0.284519	−	0.875659i	−0.986542	−	0.163505i	$-0.947720\pi$
$997$	−8.98377	−	27.6492i	−0.284519	−	0.875659i	0.702024	−	0.712154i	$-0.252280\pi$
$998$	9.30387	−	6.75965i	0.294509	−	0.213973i
$999$	−7.63338	+	23.4931i	−0.241509	+	0.743289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.h.b.70.19	✓	236
11.3	even	5		671.2.m.b.619.19	yes	236
61.34	even	5		671.2.m.b.400.19	yes	236
671.278	even	5	inner	671.2.h.b.278.19	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.h.b.70.19	✓	236	1.1	even	1	trivial
671.2.h.b.278.19	yes	236	671.278	even	5	inner
671.2.m.b.400.19	yes	236	61.34	even	5
671.2.m.b.619.19	yes	236	11.3	even	5

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.418710 - 1.28866i) q^{2} +(-1.45739 + 1.05885i) q^{3} +(0.132718 - 0.0964256i) q^{4} +(2.39305 + 1.73865i) q^{5} +(1.97472 + 1.43472i) q^{6} +(3.32854 + 2.41832i) q^{7} +(-2.37222 - 1.72352i) q^{8} +(0.0757533 - 0.233145i) q^{9} +O(q^{10})\)	\(q+(-0.418710 - 1.28866i) q^{2} +(-1.45739 + 1.05885i) q^{3} +(0.132718 - 0.0964256i) q^{4} +(2.39305 + 1.73865i) q^{5} +(1.97472 + 1.43472i) q^{6} +(3.32854 + 2.41832i) q^{7} +(-2.37222 - 1.72352i) q^{8} +(0.0757533 - 0.233145i) q^{9} +(1.23853 - 3.81180i) q^{10} +(2.49631 - 2.18368i) q^{11} +(-0.0913215 + 0.281059i) q^{12} +(-1.23233 - 0.895339i) q^{13} +(1.72269 - 5.30191i) q^{14} -5.32856 q^{15} +(-1.12636 + 3.46659i) q^{16} +(2.65034 + 1.92559i) q^{17} -0.332162 q^{18} +(-6.43075 + 4.67222i) q^{19} +0.485252 q^{20} -7.41161 q^{21} +(-3.85924 - 2.30255i) q^{22} +(1.40791 + 4.33310i) q^{23} +5.28220 q^{24} +(1.15868 + 3.56605i) q^{25} +(-0.637796 + 1.96293i) q^{26} +(-1.53355 - 4.71979i) q^{27} +0.674946 q^{28} +(1.74291 + 5.36411i) q^{29} +(2.23112 + 6.86668i) q^{30} +3.48616 q^{31} -0.925593 q^{32} +(-1.32589 + 5.82568i) q^{33} +(1.37169 - 4.22164i) q^{34} +(3.76072 + 11.5743i) q^{35} +(-0.0124273 - 0.0382471i) q^{36} +(-4.02695 - 2.92575i) q^{37} +(8.71349 + 6.33072i) q^{38} +2.74401 q^{39} +(-2.68024 - 8.24892i) q^{40} +(-1.03360 - 3.18109i) q^{41} +(3.10331 + 9.55101i) q^{42} +(3.84140 - 11.8226i) q^{43} +(0.120744 - 0.530522i) q^{44} +(0.586638 - 0.426217i) q^{45} +(4.99437 - 3.62862i) q^{46} +(-3.03947 + 9.35454i) q^{47} +(-2.02906 - 6.24481i) q^{48} +(3.06774 + 9.44154i) q^{49} +(4.11026 - 2.98628i) q^{50} -5.90149 q^{51} -0.249886 q^{52} +(10.6544 - 7.74088i) q^{53} +(-5.44007 + 3.95244i) q^{54} +(9.77043 - 0.885438i) q^{55} +(-3.72800 - 11.4736i) q^{56} +(4.42490 - 13.6184i) q^{57} +(6.18272 - 4.49201i) q^{58} +(-2.39108 + 7.35899i) q^{59} +(-0.707199 + 0.513810i) q^{60} +(5.05090 - 5.95721i) q^{61} +(-1.45969 - 4.49246i) q^{62} +(0.815966 - 0.592834i) q^{63} +(2.64028 + 8.12595i) q^{64} +(-1.39234 - 4.28517i) q^{65} +(8.06246 - 0.730655i) q^{66} +(-0.609463 - 1.87573i) q^{67} +0.537425 q^{68} +(-6.63998 - 4.82423i) q^{69} +(13.3406 - 9.69255i) q^{70} +(3.68170 + 11.3311i) q^{71} +(-0.581533 + 0.422508i) q^{72} +3.17491 q^{73} +(-2.08416 + 6.41439i) q^{74} +(-5.46456 - 3.97024i) q^{75} +(-0.402958 + 1.24018i) q^{76} +(13.5899 - 1.23157i) q^{77} +(-1.14894 - 3.53608i) q^{78} +(-0.430106 + 0.312490i) q^{79} +(-8.72263 + 6.33736i) q^{80} +(7.82751 + 5.68702i) q^{81} +(-3.66655 + 2.66391i) q^{82} +2.48891 q^{83} +(-0.983657 + 0.714669i) q^{84} +(2.99447 + 9.21603i) q^{85} -16.8437 q^{86} +(-8.21989 - 5.97210i) q^{87} +(-9.68541 + 0.877733i) q^{88} +(7.77459 + 5.64857i) q^{89} +(-0.794878 - 0.577513i) q^{90} +(-1.93663 - 5.96033i) q^{91} +(0.604677 + 0.439324i) q^{92} +(-5.08068 + 3.69133i) q^{93} +13.3274 q^{94} -23.5124 q^{95} +(1.34895 - 0.980067i) q^{96} +5.61830 q^{97} +(10.8824 - 7.90653i) q^{98} +(-0.320009 - 0.747421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 2 q^{2} - 2 q^{3} - 62 q^{4} - 6 q^{5} + 9 q^{6} + q^{7} + 12 q^{8} - 59 q^{9}+O(q^{10}) \) 236 * q + 2 * q^2 - 2 * q^3 - 62 * q^4 - 6 * q^5 + 9 * q^6 + q^7 + 12 * q^8 - 59 * q^9	\( 236 q + 2 q^{2} - 2 q^{3} - 62 q^{4} - 6 q^{5} + 9 q^{6} + q^{7} + 12 q^{8} - 59 q^{9} + 16 q^{10} - 15 q^{11} - 17 q^{12} - 8 q^{13} - 16 q^{14} - 20 q^{15} - 60 q^{16} - q^{17} - 12 q^{18} + 7 q^{19} + 26 q^{20} + 11 q^{22} - 10 q^{23} - 18 q^{24} - 43 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 31 q^{29} + 9 q^{30} + 28 q^{31} - 64 q^{32} + 18 q^{33} + 11 q^{34} + 27 q^{35} + 3 q^{36} + 10 q^{37} + 34 q^{38} - 20 q^{39} - 29 q^{40} - q^{41} - 20 q^{42} + 28 q^{43} + 52 q^{44} + 66 q^{45} + 28 q^{46} - 8 q^{47} + 30 q^{48} - 44 q^{49} + 18 q^{50} - 56 q^{51} - 40 q^{52} - 9 q^{53} - 56 q^{54} + 11 q^{55} - 25 q^{56} + 24 q^{57} + 77 q^{58} + 3 q^{59} + 16 q^{60} + 5 q^{61} + 54 q^{62} + 12 q^{63} - 10 q^{64} + 32 q^{65} + 80 q^{66} + 29 q^{67} + 80 q^{68} + 42 q^{69} - 75 q^{70} - 54 q^{71} - 198 q^{72} + 12 q^{73} + 18 q^{74} + 39 q^{75} + 19 q^{76} - 33 q^{77} + 15 q^{78} - 20 q^{79} + 112 q^{80} - 39 q^{81} - 64 q^{82} - 98 q^{83} - 124 q^{84} - 26 q^{85} - 142 q^{86} + 59 q^{87} - 186 q^{88} - 64 q^{89} - 179 q^{90} - 41 q^{91} + 36 q^{92} + 31 q^{93} - 4 q^{94} - 196 q^{95} - 79 q^{96} + 28 q^{97} - 7 q^{98} + 37 q^{99}+O(q^{100}) \) 236 * q + 2 * q^2 - 2 * q^3 - 62 * q^4 - 6 * q^5 + 9 * q^6 + q^7 + 12 * q^8 - 59 * q^9 + 16 * q^10 - 15 * q^11 - 17 * q^12 - 8 * q^13 - 16 * q^14 - 20 * q^15 - 60 * q^16 - q^17 - 12 * q^18 + 7 * q^19 + 26 * q^20 + 11 * q^22 - 10 * q^23 - 18 * q^24 - 43 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 31 * q^29 + 9 * q^30 + 28 * q^31 - 64 * q^32 + 18 * q^33 + 11 * q^34 + 27 * q^35 + 3 * q^36 + 10 * q^37 + 34 * q^38 - 20 * q^39 - 29 * q^40 - q^41 - 20 * q^42 + 28 * q^43 + 52 * q^44 + 66 * q^45 + 28 * q^46 - 8 * q^47 + 30 * q^48 - 44 * q^49 + 18 * q^50 - 56 * q^51 - 40 * q^52 - 9 * q^53 - 56 * q^54 + 11 * q^55 - 25 * q^56 + 24 * q^57 + 77 * q^58 + 3 * q^59 + 16 * q^60 + 5 * q^61 + 54 * q^62 + 12 * q^63 - 10 * q^64 + 32 * q^65 + 80 * q^66 + 29 * q^67 + 80 * q^68 + 42 * q^69 - 75 * q^70 - 54 * q^71 - 198 * q^72 + 12 * q^73 + 18 * q^74 + 39 * q^75 + 19 * q^76 - 33 * q^77 + 15 * q^78 - 20 * q^79 + 112 * q^80 - 39 * q^81 - 64 * q^82 - 98 * q^83 - 124 * q^84 - 26 * q^85 - 142 * q^86 + 59 * q^87 - 186 * q^88 - 64 * q^89 - 179 * q^90 - 41 * q^91 + 36 * q^92 + 31 * q^93 - 4 * q^94 - 196 * q^95 - 79 * q^96 + 28 * q^97 - 7 * q^98 + 37 * q^99

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