LMFDB - Embedded newform 354.2.e.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	354.19
Dual form			354.2.e.c.205.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(2.03876 - 0.448764i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-0.284870 + 0.216552i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})$	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(2.03876 - 0.448764i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-0.284870 + 0.216552i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.558482 - 2.01147i) q^{10} +(-1.78668 - 4.48424i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(0.0677744 + 1.25003i) q^{13} +(0.0578912 + 0.353121i) q^{14} +(1.17151 - 1.72785i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(5.16669 + 3.92761i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(2.53928 - 0.855582i) q^{19} +(-1.51556 - 1.43562i) q^{20} +(-0.0578912 + 0.353121i) q^{21} +(-4.79878 - 0.521898i) q^{22} +(-2.75562 + 1.65800i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(-0.582738 + 0.269603i) q^{25} +(1.13616 + 0.525643i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(0.339103 + 0.114257i) q^{28} +(-1.24596 - 2.35013i) q^{29} +(-0.977832 - 1.84439i) q^{30} +(-1.75943 - 0.592822i) q^{31} +(0.647386 + 0.762162i) q^{32} +(-4.38093 - 2.02684i) q^{33} +(5.89021 - 2.72510i) q^{34} +(-0.483599 + 0.569337i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-9.72602 - 1.05777i) q^{37} +(0.433502 - 2.64424i) q^{38} +(0.908845 + 0.860904i) q^{39} +(-1.97829 + 0.666562i) q^{40} +(7.74500 + 4.66001i) q^{41} +(0.284870 + 0.216552i) q^{42} +(-0.156164 + 0.391943i) q^{43} +(-2.70889 + 3.99532i) q^{44} +(-0.337730 - 2.06006i) q^{45} +(0.174109 + 3.21125i) q^{46} +(9.69903 + 2.13492i) q^{47} +(0.370138 + 0.928977i) q^{48} +(-1.83844 + 6.62147i) q^{49} +(-0.0347616 + 0.641140i) q^{50} +(6.45201 - 0.701698i) q^{51} +(0.996598 - 0.757594i) q^{52} +(1.99258 + 7.17661i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(-5.65498 - 8.34047i) q^{55} +(0.259786 - 0.246083i) q^{56} +(1.25512 - 2.36741i) q^{57} -2.65999 q^{58} +(5.90865 + 4.90794i) q^{59} -2.08756 q^{60} +(2.50681 - 4.72835i) q^{61} +(-1.34790 + 1.27680i) q^{62} +(0.200812 + 0.296176i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.699142 + 2.51808i) q^{65} +(-3.84280 + 2.92122i) q^{66} +(-9.01767 + 0.980731i) q^{67} +(0.351364 - 6.48053i) q^{68} +(-0.860362 + 3.09874i) q^{69} +(0.276494 + 0.693947i) q^{70} +(1.30724 + 0.287746i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(1.58671 + 9.67851i) q^{73} +(-5.49030 + 8.09758i) q^{74} +(-0.237659 + 0.596479i) q^{75} +(-2.13316 - 1.62159i) q^{76} +(1.48004 + 0.890513i) q^{77} +(1.18633 - 0.399721i) q^{78} +(-1.00845 - 0.955251i) q^{79} +(-0.337730 + 2.06006i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(7.74500 - 4.66001i) q^{82} +(-5.06181 + 5.95923i) q^{83} +(0.324762 - 0.150251i) q^{84} +(12.2962 + 5.68882i) q^{85} +(0.273137 + 0.321562i) q^{86} +(-2.52075 - 0.849339i) q^{87} +(2.26104 + 4.26478i) q^{88} +(-0.128736 - 0.242821i) q^{89} +(-1.97829 - 0.666562i) q^{90} +(-0.290003 - 0.341417i) q^{91} +(2.91873 + 1.35035i) q^{92} +(-1.68502 + 0.779574i) q^{93} +(6.42933 - 7.56920i) q^{94} +(4.79301 - 2.88386i) q^{95} +(0.994138 + 0.108119i) q^{96} +(1.09015 - 6.64961i) q^{97} +(4.98901 + 4.72584i) q^{98} +(-4.57439 + 1.54129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{19}{29}\right)$	$1$

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 $

$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$4$	−0.561187	−	0.827689i	−0.280594	−	0.413844i
$5$	2.03876	−	0.448764i	0.911760	−	0.200693i	0.265767	−	0.964037i	$-0.414375\pi$
$5$	2.03876	−	0.448764i	0.911760	−	0.200693i	0.645992	+	0.763344i	$0.276444\pi$
$6$	−0.267528	−	0.963550i	−0.109218	−	0.393368i
$7$	−0.284870	+	0.216552i	−0.107671	+	0.0818491i	−0.657624	−	0.753346i	$-0.728438\pi$
$7$	−0.284870	+	0.216552i	−0.107671	+	0.0818491i	0.549954	+	0.835195i	$0.314645\pi$
$8$	−0.994138	+	0.108119i	−0.351481	+	0.0382258i
$9$	0.0541389	−	0.998533i	0.0180463	−	0.332844i
$10$	0.558482	−	2.01147i	0.176608	−	0.636083i
$11$	−1.78668	−	4.48424i	−0.538706	−	1.35205i	−0.906525	−	0.422152i	$-0.861275\pi$
$11$	−1.78668	−	4.48424i	−0.538706	−	1.35205i	0.367820	−	0.929897i	$-0.380104\pi$
$12$	−0.976621	−	0.214970i	−0.281926	−	0.0620566i
$13$	0.0677744	+	1.25003i	0.0187972	+	0.346695i	0.992770	+	0.120030i	$0.0382992\pi$
$13$	0.0677744	+	1.25003i	0.0187972	+	0.346695i	−0.973973	+	0.226664i	$0.927218\pi$
$14$	0.0578912	+	0.353121i	0.0154721	+	0.0943755i
$15$	1.17151	−	1.72785i	0.302483	−	0.446130i
$16$	−0.370138	+	0.928977i	−0.0925345	+	0.232244i
$17$	5.16669	+	3.92761i	1.25311	+	0.952586i	0.999890	−	0.0148242i	$-0.00471887\pi$
$17$	5.16669	+	3.92761i	1.25311	+	0.952586i	0.253215	+	0.967410i	$0.418512\pi$
$18$	−0.856857	−	0.515554i	−0.201963	−	0.121517i
$19$	2.53928	−	0.855582i	0.582550	−	0.196284i	−0.0125698	−	0.999921i	$-0.504001\pi$
$19$	2.53928	−	0.855582i	0.582550	−	0.196284i	0.595120	+	0.803637i	$0.297105\pi$
$20$	−1.51556	−	1.43562i	−0.338890	−	0.321013i
$21$	−0.0578912	+	0.353121i	−0.0126329	+	0.0770572i
$22$	−4.79878	−	0.521898i	−1.02310	−	0.111269i
$23$	−2.75562	+	1.65800i	−0.574587	+	0.345718i	−0.773005	−	0.634400i	$-0.781247\pi$
$23$	−2.75562	+	1.65800i	−0.574587	+	0.345718i	0.198418	+	0.980118i	$0.436420\pi$
$24$	−0.647386	+	0.762162i	−0.132147	+	0.155576i
$25$	−0.582738	+	0.269603i	−0.116548	+	0.0539207i
$26$	1.13616	+	0.525643i	0.222819	+	0.103087i
$27$	−0.647386	−	0.762162i	−0.124590	−	0.146678i
$28$	0.339103	+	0.114257i	0.0640844	+	0.0215926i
$29$	−1.24596	−	2.35013i	−0.231369	−	0.436409i	0.740458	−	0.672103i	$-0.234609\pi$
$29$	−1.24596	−	2.35013i	−0.231369	−	0.436409i	−0.971827	+	0.235694i	$0.924264\pi$
$30$	−0.977832	−	1.84439i	−0.178527	−	0.336737i
$31$	−1.75943	−	0.592822i	−0.316003	−	0.106474i	0.156831	−	0.987626i	$-0.449872\pi$
$31$	−1.75943	−	0.592822i	−0.316003	−	0.106474i	−0.472834	+	0.881152i	$0.656769\pi$
$32$	0.647386	+	0.762162i	0.114443	+	0.134732i
$33$	−4.38093	−	2.02684i	−0.762623	−	0.352827i
$34$	5.89021	−	2.72510i	1.01016	−	0.467351i
$35$	−0.483599	+	0.569337i	−0.0817431	+	0.0962354i
$36$	−0.856857	+	0.515554i	−0.142810	+	0.0859256i
$37$	−9.72602	−	1.05777i	−1.59895	−	0.173896i	−0.735210	−	0.677839i	$-0.762917\pi$
$37$	−9.72602	−	1.05777i	−1.59895	−	0.173896i	−0.863737	+	0.503943i	$0.831882\pi$
$38$	0.433502	−	2.64424i	0.0703232	−	0.428953i
$39$	0.908845	+	0.860904i	0.145532	+	0.137855i
$40$	−1.97829	+	0.666562i	−0.312794	+	0.105393i
$41$	7.74500	+	4.66001i	1.20957	+	0.727771i	0.969999	−	0.243109i	$-0.0781672\pi$
$41$	7.74500	+	4.66001i	1.20957	+	0.727771i	0.239566	+	0.970880i	$0.422995\pi$
$42$	0.284870	+	0.216552i	0.0439563	+	0.0334147i
$43$	−0.156164	+	0.391943i	−0.0238148	+	0.0597707i	−0.940403	−	0.340061i	$-0.889552\pi$
$43$	−0.156164	+	0.391943i	−0.0238148	+	0.0597707i	0.916588	+	0.399832i	$0.130932\pi$
$44$	−2.70889	+	3.99532i	−0.408381	+	0.602316i
$45$	−0.337730	−	2.06006i	−0.0503458	−	0.307096i
$46$	0.174109	+	3.21125i	0.0256710	+	0.473473i
$47$	9.69903	+	2.13492i	1.41475	+	0.311410i	0.855592	−	0.517651i	$-0.173194\pi$
$47$	9.69903	+	2.13492i	1.41475	+	0.311410i	0.559158	+	0.829061i	$0.311125\pi$
$48$	0.370138	+	0.928977i	0.0534248	+	0.134086i
$49$	−1.83844	+	6.62147i	−0.262635	+	0.945925i
$50$	−0.0347616	+	0.641140i	−0.00491604	+	0.0906710i
$51$	6.45201	−	0.701698i	0.903462	−	0.0982574i
$52$	0.996598	−	0.757594i	0.138203	−	0.105059i
$53$	1.99258	+	7.17661i	0.273701	+	0.985783i	0.964792	+	0.263015i	$0.0847167\pi$
$53$	1.99258	+	7.17661i	0.273701	+	0.985783i	−0.691091	+	0.722768i	$0.742869\pi$
$54$	−0.976621	+	0.214970i	−0.132901	+	0.0292538i
$55$	−5.65498	−	8.34047i	−0.762517	−	1.12463i
$56$	0.259786	−	0.246083i	0.0347154	−	0.0328842i
$57$	1.25512	−	2.36741i	0.166245	−	0.313571i
$58$	−2.65999			−0.349274
$59$	5.90865	+	4.90794i	0.769240	+	0.638959i
$59$	5.90865	+	4.90794i	0.769240	+	0.638959i
$60$	−2.08756			−0.269503
$61$	2.50681	−	4.72835i	0.320964	−	0.605403i	−0.669557	−	0.742760i	$-0.733516\pi$
$61$	2.50681	−	4.72835i	0.320964	−	0.605403i	0.990522	+	0.137358i	$0.0438610\pi$
$62$	−1.34790	+	1.27680i	−0.171183	+	0.162153i
$63$	0.200812	+	0.296176i	0.0252999	+	0.0373146i
$64$	0.976621	−	0.214970i	0.122078	−	0.0268713i
$65$	0.699142	+	2.51808i	0.0867179	+	0.312330i
$66$	−3.84280	+	2.92122i	−0.473016	+	0.359577i
$67$	−9.01767	+	0.980731i	−1.10168	+	0.119815i	−0.640846	−	0.767669i	$-0.721416\pi$
$67$	−9.01767	+	0.980731i	−1.10168	+	0.119815i	−0.460838	+	0.887484i	$0.652451\pi$
$68$	0.351364	−	6.48053i	0.0426092	−	0.785880i
$69$	−0.860362	+	3.09874i	−0.103575	+	0.373045i
$70$	0.276494	+	0.693947i	0.0330473	+	0.0829426i
$71$	1.30724	+	0.287746i	0.155141	+	0.0341491i	0.291862	−	0.956460i	$-0.405725\pi$
$71$	1.30724	+	0.287746i	0.155141	+	0.0341491i	−0.136721	+	0.990610i	$0.543656\pi$
$72$	0.0541389	+	0.998533i	0.00638033	+	0.117678i
$73$	1.58671	+	9.67851i	0.185710	+	1.13278i	0.900956	+	0.433910i	$0.142867\pi$
$73$	1.58671	+	9.67851i	0.185710	+	1.13278i	−0.715246	+	0.698873i	$0.753685\pi$
$74$	−5.49030	+	8.09758i	−0.638234	+	0.941325i
$75$	−0.237659	+	0.596479i	−0.0274425	+	0.0688755i
$76$	−2.13316	−	1.62159i	−0.244691	−	0.186009i
$77$	1.48004	+	0.890513i	0.168667	+	0.101483i
$78$	1.18633	−	0.399721i	0.134325	−	0.0452595i
$79$	−1.00845	−	0.955251i	−0.113459	−	0.107474i	0.628867	−	0.777513i	$-0.283519\pi$
$79$	−1.00845	−	0.955251i	−0.113459	−	0.107474i	−0.742326	+	0.670039i	$0.766278\pi$
$80$	−0.337730	+	2.06006i	−0.0377594	+	0.230322i
$81$	−0.994138	−	0.108119i	−0.110460	−	0.0120132i
$82$	7.74500	−	4.66001i	0.855292	−	0.514612i
$83$	−5.06181	+	5.95923i	−0.555606	+	0.654110i	−0.966226	−	0.257697i	$-0.917037\pi$
$83$	−5.06181	+	5.95923i	−0.555606	+	0.654110i	0.410620	+	0.911807i	$0.365312\pi$
$84$	0.324762	−	0.150251i	0.0354344	−	0.0163937i
$85$	12.2962	+	5.68882i	1.33371	+	0.617039i
$86$	0.273137	+	0.321562i	0.0294532	+	0.0346749i
$87$	−2.52075	−	0.849339i	−0.270253	−	0.0910587i
$88$	2.26104	+	4.26478i	0.241028	+	0.454627i
$89$	−0.128736	−	0.242821i	−0.0136459	−	0.0257390i	0.876595	−	0.481228i	$-0.159809\pi$
$89$	−0.128736	−	0.242821i	−0.0136459	−	0.0257390i	−0.890241	+	0.455489i	$0.849464\pi$
$90$	−1.97829	−	0.666562i	−0.208530	−	0.0702618i
$91$	−0.290003	−	0.341417i	−0.0304005	−	0.0357903i
$92$	2.91873	+	1.35035i	0.304299	+	0.140784i
$93$	−1.68502	+	0.779574i	−0.174729	+	0.0808381i
$94$	6.42933	−	7.56920i	0.663135	−	0.780703i
$95$	4.79301	−	2.88386i	0.491753	−	0.295878i
$96$	0.994138	+	0.108119i	0.101464	+	0.0110349i
$97$	1.09015	−	6.64961i	0.110688	−	0.675165i	−0.871945	−	0.489604i	$-0.837141\pi$
$97$	1.09015	−	6.64961i	0.110688	−	0.675165i	0.982633	−	0.185561i	$-0.0594104\pi$
$98$	4.98901	+	4.72584i	0.503966	+	0.477382i
$99$	−4.57439	+	1.54129i	−0.459744	+	0.154906i
$100$	0.550173	+	0.331028i	0.0550173	+	0.0331028i
$101$	−4.25586	−	3.23522i	−0.423474	−	0.321916i	0.371640	−	0.928377i	$-0.378796\pi$
$101$	−4.25586	−	3.23522i	−0.423474	−	0.321916i	−0.795114	+	0.606461i	$0.792589\pi$
$102$	2.40222	−	6.02911i	0.237855	−	0.596971i
$103$	0.211766	−	0.312331i	0.0208659	−	0.0307749i	−0.817113	−	0.576478i	$-0.804427\pi$
$103$	0.211766	−	0.312331i	0.0208659	−	0.0307749i	0.837979	+	0.545703i	$0.183737\pi$
$104$	−0.202529	−	1.23537i	−0.0198596	−	0.121138i
$105$	0.0404419	+	0.745906i	0.00394672	+	0.0727930i
$106$	7.27396	+	1.60112i	0.706509	+	0.155514i
$107$	−3.87162	−	9.71703i	−0.374284	−	0.939381i	−0.988633	−	0.150347i	$-0.951961\pi$
$107$	−3.87162	−	9.71703i	−0.374284	−	0.939381i	0.614350	−	0.789034i	$-0.289418\pi$
$108$	−0.267528	+	0.963550i	−0.0257429	+	0.0927176i
$109$	−0.117551	+	2.16810i	−0.0112594	+	0.207667i	0.987490	+	0.157679i	$0.0504010\pi$
$109$	−0.117551	+	2.16810i	−0.0112594	+	0.207667i	−0.998750	+	0.0499879i	$0.984082\pi$
$110$	−10.0177	+	1.08950i	−0.955155	+	0.103879i
$111$	−7.78847	+	5.92064i	−0.739249	+	0.561962i
$112$	−0.0957309	−	0.344791i	−0.00904572	−	0.0325797i
$113$	19.8795	−	4.37581i	1.87011	−	0.411642i	0.873004	−	0.487713i	$-0.162169\pi$
$113$	19.8795	−	4.37581i	1.87011	−	0.411642i	0.997102	+	0.0760710i	$0.0242376\pi$
$114$	−1.50372	−	2.21783i	−0.140837	−	0.207719i
$115$	−4.87399	+	4.61689i	−0.454502	+	0.430527i
$116$	−1.24596	+	2.35013i	−0.115685	+	0.218204i
$117$	1.25186			0.115735
$118$	7.10389	−	2.92144i	0.653966	−	0.268940i
$119$	−2.32236			−0.212891
$120$	−0.977832	+	1.84439i	−0.0892634	+	0.168369i
$121$	−8.93021	+	8.45914i	−0.811837	+	0.769013i
$122$	−3.00334	−	4.42960i	−0.271910	−	0.401037i
$123$	8.82752	−	1.94308i	0.795951	−	0.175202i
$124$	0.496698	+	1.78895i	0.0446048	+	0.160652i
$125$	−9.37654	+	7.12786i	−0.838664	+	0.637535i
$126$	0.355737	−	0.0386887i	0.0316916	−	0.00344666i
$127$	0.0561869	−	1.03631i	0.00498578	−	0.0919573i	−0.994981	−	0.100060i	$-0.968096\pi$
$127$	0.0561869	−	1.03631i	0.00498578	−	0.0919573i	0.999967	+	0.00810283i	$0.00257924\pi$
$128$	0.267528	−	0.963550i	0.0236464	−	0.0851666i
$129$	0.156164	+	0.391943i	0.0137495	+	0.0345086i
$130$	2.55224	+	0.561790i	0.223846	+	0.0492723i
$131$	−0.610761	−	11.2648i	−0.0533624	−	0.984212i	−0.895532	−	0.444998i	$-0.853204\pi$
$131$	−0.610761	−	11.2648i	−0.0533624	−	0.984212i	0.842169	−	0.539213i	$-0.181278\pi$
$132$	0.780934	+	4.76348i	0.0679715	+	0.414608i
$133$	−0.538084	+	0.793615i	−0.0466578	+	0.0688152i
$134$	−3.35747	+	8.42661i	−0.290041	+	0.727948i
$135$	−1.66189	−	1.26334i	−0.143033	−	0.108731i
$136$	−5.56105	−	3.34597i	−0.476856	−	0.286915i
$137$	−15.5492	+	5.23913i	−1.32846	+	0.447609i	−0.891967	−	0.452100i	$-0.850675\pi$
$137$	−15.5492	+	5.23913i	−1.32846	+	0.447609i	−0.436490	+	0.899709i	$0.643779\pi$
$138$	2.33478	+	2.21162i	0.198749	+	0.188265i
$139$	0.611918	−	3.73253i	0.0519022	−	0.316589i	−0.948097	−	0.317982i	$-0.896995\pi$
$139$	0.611918	−	3.73253i	0.0519022	−	0.316589i	0.999999	+	0.00139244i	$0.000443226\pi$
$140$	0.742623	+	0.0807651i	0.0627631	+	0.00682590i
$141$	8.50964	−	5.12008i	0.716641	−	0.431188i
$142$	0.866550	−	1.02018i	0.0727193	−	0.0856117i
$143$	5.48432	−	2.53732i	0.458622	−	0.212181i
$144$	0.907575	+	0.419889i	0.0756313	+	0.0349908i
$145$	−3.59487	−	4.23221i	−0.298538	−	0.351466i
$146$	9.29431	+	3.13162i	0.769202	+	0.259174i
$147$	3.21888	+	6.07145i	0.265489	+	0.500765i
$148$	4.58261	+	8.64372i	0.376688	+	0.710510i
$149$	−17.0551	−	5.74654i	−1.39721	−	0.470775i	−0.482860	−	0.875698i	$-0.660402\pi$
$149$	−17.0551	−	5.74654i	−1.39721	−	0.470775i	−0.914351	+	0.404923i	$0.867298\pi$
$150$	0.415675	+	0.489371i	0.0339397	+	0.0399569i
$151$	−20.2435	−	9.36563i	−1.64739	−	0.762164i	−1.00000		6.45095e-6i	$-0.999998\pi$
$151$	−20.2435	−	9.36563i	−1.64739	−	0.762164i	−0.647391	−	0.762158i	$-0.724140\pi$
$152$	−2.43189	+	1.12511i	−0.197252	+	0.0912585i
$153$	4.20157	−	4.94647i	0.339677	−	0.399898i
$154$	1.48004	−	0.890513i	0.119265	−	0.0717596i
$155$	−3.85309	−	0.419049i	−0.309488	−	0.0336588i
$156$	0.202529	−	1.23537i	0.0162153	−	0.0989087i
$157$	1.27318	+	1.20602i	0.101611	+	0.0962512i	0.736819	−	0.676090i	$-0.236327\pi$
$157$	1.27318	+	1.20602i	0.101611	+	0.0962512i	−0.635208	+	0.772341i	$0.719086\pi$
$158$	−1.31634	+	0.443527i	−0.104722	+	0.0352851i
$159$	6.38195	+	3.83989i	0.506121	+	0.304523i
$160$	1.66189	+	1.26334i	0.131384	+	0.0998757i
$161$	0.425949	−	1.06905i	0.0335695	−	0.0842530i
$162$	−0.561187	+	0.827689i	−0.0440910	+	0.0650294i
$163$	−0.984770	−	6.00683i	−0.0771331	−	0.470491i	−0.996943	−	0.0781278i	$-0.975106\pi$
$163$	−0.984770	−	6.00683i	−0.0771331	−	0.470491i	0.919810	−	0.392364i	$-0.128342\pi$
$164$	−0.489353	−	9.02559i	−0.0382121	−	0.704780i
$165$	−9.84123	−	2.16622i	−0.766139	−	0.168640i
$166$	2.89405	+	7.26352i	0.224622	+	0.563759i
$167$	−0.925502	+	3.33336i	−0.0716175	+	0.257943i	−0.990688	−	0.136149i	$-0.956527\pi$
$167$	−0.925502	+	3.33336i	−0.0716175	+	0.257943i	0.919071	+	0.394093i	$0.128941\pi$
$168$	0.0193728	−	0.357310i	0.00149464	−	0.0275670i
$169$	11.3658	−	1.23611i	0.874294	−	0.0950852i
$170$	10.7858	−	8.19914i	0.827231	−	0.628845i
$171$	−0.716853	−	2.58187i	−0.0548191	−	0.197441i
$172$	0.412044	−	0.0906977i	0.0314181	−	0.00691564i
$173$	10.9615	+	16.1670i	0.833387	+	1.22915i	0.971098	+	0.238681i	$0.0767151\pi$
$173$	10.9615	+	16.1670i	0.833387	+	1.22915i	−0.137711	+	0.990472i	$0.543975\pi$
$174$	−1.93114	+	1.82927i	−0.146399	+	0.138677i
$175$	0.107621	−	0.202995i	0.00813539	−	0.0153450i
$176$	4.82707			0.363854
$177$	7.66484	−	0.500231i	0.576125	−	0.0375997i
$178$	−0.274836			−0.0205998
$179$	3.15217	−	5.94561i	0.235604	−	0.444396i	−0.737313	−	0.675551i	$-0.763906\pi$
$179$	3.15217	−	5.94561i	0.235604	−	0.444396i	0.972917	+	0.231155i	$0.0742505\pi$
$180$	−1.51556	+	1.43562i	−0.112963	+	0.107004i
$181$	−4.88018	−	7.19772i	−0.362741	−	0.535002i	0.601900	−	0.798572i	$-0.294411\pi$
$181$	−4.88018	−	7.19772i	−0.362741	−	0.535002i	−0.964640	+	0.263569i	$0.915100\pi$
$182$	−0.437486	+	0.0962980i	−0.0324286	+	0.00713808i
$183$	−1.43175	−	5.15669i	−0.105838	−	0.381194i
$184$	2.56021	−	1.94622i	0.188741	−	0.143477i
$185$	−20.3037	+	2.20816i	−1.49276	+	0.162347i
$186$	−0.100515	+	1.85390i	−0.00737014	+	0.135934i
$187$	8.38112	−	30.1861i	0.612888	−	2.20742i
$188$	−3.67592	−	9.22587i	−0.268094	−	0.672866i
$189$	0.349469	+	0.0769238i	0.0254201	+	0.00559539i
$190$	−0.302837	−	5.58551i	−0.0219701	−	0.405215i
$191$	−2.97468	−	18.1448i	−0.215240	−	1.31291i	−0.844434	−	0.535660i	$-0.820063\pi$
$191$	−2.97468	−	18.1448i	−0.215240	−	1.31291i	0.629194	−	0.777249i	$-0.283385\pi$
$192$	0.561187	−	0.827689i	0.0405002	−	0.0597333i
$193$	−0.800104	+	2.00811i	−0.0575928	+	0.144547i	−0.954957	−	0.296743i	$-0.904100\pi$
$193$	−0.800104	+	2.00811i	−0.0575928	+	0.144547i	0.897365	+	0.441290i	$0.145479\pi$
$194$	−5.36437	−	4.07789i	−0.385140	−	0.292776i
$195$	2.23926	+	1.34732i	0.160357	+	0.0964833i
$196$	6.51223	−	2.19423i	0.465159	−	0.156730i
$197$	−18.2518	−	17.2890i	−1.30039	−	1.23179i	−0.956138	−	0.292915i	$-0.905375\pi$
$197$	−18.2518	−	17.2890i	−1.30039	−	1.23179i	−0.344250	−	0.938878i	$-0.611867\pi$
$198$	−0.780934	+	4.76348i	−0.0554985	+	0.338526i
$199$	7.95310	+	0.864951i	0.563780	+	0.0613148i	0.385571	−	0.922678i	$-0.374004\pi$
$199$	7.95310	+	0.864951i	0.563780	+	0.0613148i	0.178209	+	0.983993i	$0.442970\pi$
$200$	0.550173	−	0.331028i	0.0389031	−	0.0234072i
$201$	−5.87234	+	6.91345i	−0.414203	+	0.487638i
$202$	−4.85184	+	2.24470i	−0.341374	+	0.157936i
$203$	0.863863	+	0.399666i	0.0606313	+	0.0280510i
$204$	−4.20157	−	4.94647i	−0.294169	−	0.346322i
$205$	17.8814	+	6.02495i	1.24889	+	0.420801i
$206$	−0.176756	−	0.333396i	−0.0123151	−	0.0232288i
$207$	1.50639	+	2.84134i	0.104701	+	0.197487i
$208$	−1.18633	−	0.399721i	−0.0822572	−	0.0277157i
$209$	−8.37352	−	9.85807i	−0.579208	−	0.681897i
$210$	0.677961	+	0.313658i	0.0467837	+	0.0216445i
$211$	−20.7682	+	9.60839i	−1.42974	+	0.661469i	−0.973563	−	0.228420i	$-0.926644\pi$
$211$	−20.7682	+	9.60839i	−1.42974	+	0.661469i	−0.456178	+	0.889888i	$0.650782\pi$
$212$	4.82179	−	5.67665i	0.331162	−	0.389874i
$213$	1.14693	−	0.690087i	0.0785866	−	0.0472840i
$214$	−10.3986	−	1.13092i	−0.710835	−	0.0773079i
$215$	−0.142491	+	0.869156i	−0.00971780	+	0.0592760i
$216$	0.725995	+	0.687699i	0.0493977	+	0.0467920i
$217$	0.629585	−	0.212132i	0.0427390	−	0.0144005i
$218$	1.86048	+	1.11942i	0.126008	+	0.0758164i
$219$	7.80785	+	5.93537i	0.527606	+	0.401075i
$220$	−3.72981	+	9.36113i	−0.251464	+	0.631127i
$221$	−4.55944	+	6.72468i	−0.306701	+	0.452351i
$222$	1.58277	+	9.65449i	0.106229	+	0.647967i
$223$	−0.473550	−	8.73412i	−0.0317113	−	0.584880i	−0.970606	−	0.240675i	$-0.922631\pi$
$223$	−0.473550	−	8.73412i	−0.0317113	−	0.584880i	0.938894	−	0.344205i	$-0.111852\pi$
$224$	−0.349469	−	0.0769238i	−0.0233499	−	0.00513969i
$225$	0.237659	+	0.596479i	0.0158439	+	0.0397653i
$226$	5.44565	−	19.6134i	0.362239	−	1.30467i
$227$	0.971818	−	17.9241i	0.0645018	−	1.18967i	−0.769773	−	0.638318i	$-0.779631\pi$
$227$	0.971818	−	17.9241i	0.0645018	−	1.18967i	0.834275	−	0.551349i	$-0.185887\pi$
$228$	−2.66383	+	0.289709i	−0.176417	+	0.0191865i
$229$	−18.5063	+	14.0681i	−1.22293	+	0.929647i	−0.998989	−	0.0449555i	$-0.985685\pi$
$229$	−18.5063	+	14.0681i	−1.22293	+	0.929647i	−0.223941	+	0.974603i	$0.571892\pi$
$230$	1.79606	+	6.46882i	0.118429	+	0.426541i
$231$	1.68691	−	0.371317i	0.110991	−	0.0244309i
$232$	1.49275	+	2.20165i	0.0980040	+	0.144545i
$233$	18.3407	−	17.3732i	1.20154	−	1.13816i	0.214662	−	0.976688i	$-0.431135\pi$
$233$	18.3407	−	17.3732i	1.20154	−	1.13816i	0.986878	−	0.161471i	$-0.0516237\pi$
$234$	0.586382	−	1.10603i	0.0383330	−	0.0723037i
$235$	20.7320			1.35241
$236$	0.746392	−	7.64480i	0.0485860	−	0.497634i
$237$	−1.38905			−0.0902287
$238$	−1.08782	+	2.05184i	−0.0705126	+	0.133001i
$239$	−1.82541	+	1.72912i	−0.118076	+	0.111847i	−0.744460	−	0.667667i	$-0.767293\pi$
$239$	−1.82541	+	1.72912i	−0.118076	+	0.111847i	0.626384	+	0.779515i	$0.284534\pi$
$240$	1.17151	+	1.72785i	0.0756208	+	0.111532i
$241$	0.965328	−	0.212485i	0.0621823	−	0.0136874i	−0.183770	−	0.982969i	$-0.558830\pi$
$241$	0.965328	−	0.212485i	0.0621823	−	0.0136874i	0.245953	+	0.969282i	$0.420899\pi$
$242$	3.29077	+	11.8523i	0.211539	+	0.761893i
$243$	−0.796093	+	0.605174i	−0.0510694	+	0.0388219i
$244$	−5.32039	+	0.578627i	−0.340603	+	0.0370428i
$245$	−0.776657	+	14.3246i	−0.0496188	+	0.915165i
$246$	2.41815	−	8.70938i	0.154175	−	0.555290i
$247$	1.24160	+	3.11617i	0.0790009	+	0.198277i
$248$	1.81321	+	0.399118i	0.115139	+	0.0253440i
$249$	0.423304	+	7.80738i	0.0268258	+	0.494772i
$250$	1.90550	+	11.6230i	0.120514	+	0.735106i
$251$	3.10384	−	4.57783i	0.195913	−	0.288950i	−0.717026	−	0.697047i	$-0.754497\pi$
$251$	3.10384	−	4.57783i	0.195913	−	0.288950i	0.912939	+	0.408097i	$0.133807\pi$
$252$	0.132448	−	0.332420i	0.00834345	−	0.0209405i
$253$	12.3583	+	9.39454i	0.776960	+	0.590630i
$254$	−0.889271	−	0.535056i	−0.0557978	−	0.0335724i
$255$	12.8392	−	4.32602i	0.804020	−	0.270906i
$256$	−0.725995	−	0.687699i	−0.0453747	−	0.0429812i
$257$	1.64149	−	10.0126i	0.102393	−	0.624570i	−0.884915	−	0.465753i	$-0.845784\pi$
$257$	1.64149	−	10.0126i	0.102393	−	0.624570i	0.987308	−	0.158817i	$-0.0507681\pi$
$258$	0.419435	+	0.0456163i	0.0261129	+	0.00283994i
$259$	2.99971	−	1.80486i	0.186393	−	0.112149i
$260$	1.69184	−	1.99179i	0.104923	−	0.123525i
$261$	−2.41414	+	1.11690i	−0.149432	+	0.0691344i
$262$	−10.2387	−	4.73692i	−0.632548	−	0.292648i
$263$	2.73039	+	3.21446i	0.168363	+	0.198212i	0.839873	−	0.542784i	$-0.182630\pi$
$263$	2.73039	+	3.21446i	0.168363	+	0.198212i	−0.671510	+	0.740996i	$0.734354\pi$
$264$	4.57439	+	1.54129i	0.281534	+	0.0948600i
$265$	7.28298	+	13.7372i	0.447390	+	0.843867i
$266$	0.449125	+	0.847140i	0.0275376	+	0.0519415i
$267$	−0.260449	−	0.0877556i	−0.0159392	−	0.00537055i
$268$	5.87234	+	6.91345i	0.358710	+	0.422306i
$269$	11.5648	+	5.35046i	0.705120	+	0.326223i	0.739473	−	0.673187i	$-0.235075\pi$
$269$	11.5648	+	5.35046i	0.705120	+	0.326223i	−0.0343530	+	0.999410i	$0.510937\pi$
$270$	−1.89462	+	0.876545i	−0.115303	+	0.0533448i
$271$	−17.3614	+	20.4394i	−1.05463	+	1.24161i	−0.0851688	+	0.996367i	$0.527143\pi$
$271$	−17.3614	+	20.4394i	−1.05463	+	1.24161i	−0.969462	+	0.245241i	$0.921133\pi$
$272$	−5.56105	+	3.34597i	−0.337188	+	0.202879i
$273$	−0.445333	−	0.0484329i	−0.0269528	−	0.00293129i
$274$	−2.65454	+	16.1920i	−0.160366	+	0.978192i
$275$	2.25013	+	2.13144i	0.135688	+	0.128531i
$276$	3.04762	−	1.02686i	0.183445	−	0.0618099i
$277$	−5.21322	−	3.13669i	−0.313232	−	0.188465i	0.350253	−	0.936655i	$-0.386096\pi$
$277$	−5.21322	−	3.13669i	−0.313232	−	0.188465i	−0.663485	+	0.748190i	$0.730923\pi$
$278$	−3.01111	−	2.28899i	−0.180594	−	0.137284i
$279$	−0.687206	+	1.72476i	−0.0411419	+	0.103258i
$280$	0.419208	−	0.618285i	0.0250525	−	0.0369496i
$281$	−3.90947	−	23.8467i	−0.233219	−	1.42258i	−0.800639	−	0.599147i	$-0.795507\pi$
$281$	−3.90947	−	23.8467i	−0.233219	−	1.42258i	0.567420	−	0.823429i	$-0.307942\pi$
$282$	−0.537665	−	9.91665i	−0.0320175	−	0.590528i
$283$	−18.6955	−	4.11519i	−1.11133	−	0.244623i	−0.378884	−	0.925444i	$-0.623692\pi$
$283$	−18.6955	−	4.11519i	−1.11133	−	0.244623i	−0.732449	+	0.680821i	$0.761623\pi$
$284$	−0.495443	−	1.24347i	−0.0293991	−	0.0737863i
$285$	1.49648	−	5.38982i	0.0886436	−	0.319265i
$286$	0.327152	−	6.03396i	0.0193449	−	0.356796i
$287$	−3.21545	+	0.349701i	−0.189802	+	0.0206422i
$288$	0.796093	−	0.605174i	0.0469102	−	0.0356602i
$289$	6.72052	+	24.2051i	0.395325	+	1.42383i
$290$	−5.42307	+	1.19371i	−0.318454	+	0.0700970i
$291$	−3.78149	−	5.57728i	−0.221675	−	0.326946i
$292$	7.12035	−	6.74476i	0.416687	−	0.394707i
$293$	−6.81438	+	12.8533i	−0.398101	+	0.750897i	−0.998820	−	0.0485624i	$-0.984536\pi$
$293$	−6.81438	+	12.8533i	−0.398101	+	0.750897i	0.600720	+	0.799460i	$0.294881\pi$
$294$	6.87195			0.400781
$295$	14.2488	+	7.35451i	0.829597	+	0.428196i
$296$	9.78337			0.568647
$297$	−2.26104	+	4.26478i	−0.131199	+	0.247467i
$298$	−13.0659	+	12.3767i	−0.756888	+	0.716962i
$299$	−2.25931	−	3.33223i	−0.130659	−	0.192708i
$300$	0.627071	−	0.138029i	0.0362039	−	0.00796909i
$301$	−0.0403896	−	0.145470i	−0.00232802	−	0.00838477i
$302$	−17.7569	+	13.4984i	−1.02179	+	0.776747i
$303$	−5.31459	+	0.577997i	−0.305315	+	0.0332051i
$304$	−0.145067	+	2.67561i	−0.00832019	+	0.153457i
$305$	2.98886	−	10.7649i	0.171142	−	0.616397i
$306$	−2.40222	−	6.02911i	−0.137326	−	0.344661i
$307$	19.5808	+	4.31005i	1.11753	+	0.245988i	0.735075	−	0.677985i	$-0.237147\pi$
$307$	19.5808	+	4.31005i	1.11753	+	0.245988i	0.382458	+	0.923973i	$0.375078\pi$
$308$	−0.0935138	−	1.72476i	−0.00532844	−	0.0982773i
$309$	−0.0610490	−	0.372382i	−0.00347296	−	0.0211841i
$310$	−2.17505	+	3.20797i	−0.123535	+	0.182200i
$311$	−5.62426	+	14.1158i	−0.318923	+	0.800435i	0.678884	+	0.734245i	$0.262464\pi$
$311$	−5.62426	+	14.1158i	−0.318923	+	0.800435i	−0.997807	+	0.0661902i	$0.978916\pi$
$312$	−0.996598	−	0.757594i	−0.0564212	−	0.0428903i
$313$	25.6912	+	15.4579i	1.45215	+	0.873732i	0.999836	−	0.0181238i	$-0.00576930\pi$
$313$	25.6912	+	15.4579i	1.45215	+	0.873732i	0.452319	+	0.891856i	$0.350597\pi$
$314$	1.66191	−	0.559962i	0.0937868	−	0.0316005i
$315$	0.542320	+	0.513713i	0.0305563	+	0.0289444i
$316$	−0.224724	+	1.37075i	−0.0126417	+	0.0771110i
$317$	4.79813	+	0.521828i	0.269490	+	0.0293088i	0.241866	−	0.970310i	$-0.422240\pi$
$317$	4.79813	+	0.521828i	0.269490	+	0.0293088i	0.0276237	+	0.999618i	$0.491206\pi$
$318$	6.38195	−	3.83989i	0.357882	−	0.215330i
$319$	−8.31242	+	9.78614i	−0.465406	+	0.547919i
$320$	1.89462	−	0.876545i	0.105913	−	0.0490003i
$321$	−9.49318	−	4.39201i	−0.529857	−	0.245138i
$322$	−0.745002	−	0.877084i	−0.0415173	−	0.0488780i
$323$	16.4800	+	5.55277i	0.916973	+	0.308964i
$324$	0.468408	+	0.883512i	0.0260227	+	0.0490840i
$325$	−0.376506	−	0.710165i	−0.0208848	−	0.0393929i
$326$	−5.76838	−	1.94359i	−0.319481	−	0.107646i
$327$	1.40566	+	1.65487i	0.0777332	+	0.0915146i
$328$	−8.20343	−	3.79531i	−0.452959	−	0.209561i
$329$	−3.22528	+	1.49217i	−0.177815	+	0.0822662i
$330$	−6.52359	+	7.68017i	−0.359112	+	0.422779i
$331$	14.0861	−	8.47531i	0.774241	−	0.465845i	−0.0728176	−	0.997345i	$-0.523199\pi$
$331$	14.0861	−	8.47531i	0.774241	−	0.465845i	0.847058	+	0.531500i	$0.178371\pi$
$332$	7.77301	+	0.845366i	0.426599	+	0.0463955i
$333$	−1.58277	+	9.65449i	−0.0867354	+	0.529063i
$334$	2.51155	+	2.37907i	0.137426	+	0.130177i
$335$	−17.9447	+	6.04628i	−0.980425	+	0.330344i
$336$	−0.306613	−	0.184483i	−0.0167271	−	0.0100644i
$337$	5.37465	+	4.08570i	0.292776	+	0.222562i	0.741243	−	0.671237i	$-0.234237\pi$
$337$	5.37465	+	4.08570i	0.292776	+	0.222562i	−0.448467	+	0.893799i	$0.648030\pi$
$338$	4.23173	−	10.6208i	0.230176	−	0.577698i
$339$	11.4232	−	16.8479i	0.620422	−	0.915055i
$340$	−2.19189	−	13.3699i	−0.118872	−	0.725085i
$341$	0.485195	+	8.94890i	0.0262748	+	0.484610i
$342$	−2.61690	−	0.576022i	−0.141505	−	0.0311477i
$343$	−1.83732	−	4.61131i	−0.0992057	−	0.248988i
$344$	0.112872	−	0.406529i	0.00608567	−	0.0219186i
$345$	−0.363463	+	6.70368i	−0.0195682	+	0.360914i
$346$	19.4182	−	2.11186i	1.04393	−	0.113534i
$347$	6.42834	−	4.88670i	0.345091	−	0.262332i	−0.418243	−	0.908335i	$-0.637354\pi$
$347$	6.42834	−	4.88670i	0.345091	−	0.262332i	0.763334	+	0.646004i	$0.223561\pi$
$348$	0.711623	+	2.56303i	0.0381470	+	0.137393i
$349$	−5.51281	+	1.21346i	−0.295094	+	0.0649551i	−0.360050	−	0.932933i	$-0.617240\pi$
$349$	−5.51281	+	1.21346i	−0.295094	+	0.0649551i	0.0649558	+	0.997888i	$0.479309\pi$
$350$	−0.128938	−	0.190169i	−0.00689202	−	0.0101650i
$351$	0.908845	−	0.860904i	0.0485106	−	0.0459517i
$352$	2.26104	−	4.26478i	0.120514	−	0.227313i
$353$	−11.4939			−0.611760			−0.305880	−	0.952070i	$-0.598951\pi$
$353$	−11.4939			−0.611760			−0.305880	+	0.952070i	$0.598951\pi$
$354$	3.14832	−	7.00629i	0.167331	−	0.372380i
$355$	2.79428			0.148305
$356$	−0.128736	+	0.242821i	−0.00682297	+	0.0128695i
$357$	−1.68603	+	1.59709i	−0.0892340	+	0.0845269i
$358$	−3.77652	−	5.56995i	−0.199595	−	0.294381i
$359$	−31.9516	+	7.03307i	−1.68634	+	0.371191i	−0.951643	−	0.307205i	$-0.900606\pi$
$359$	−31.9516	+	7.03307i	−1.68634	+	0.371191i	−0.734696	+	0.678396i	$0.762675\pi$
$360$	0.558482	+	2.01147i	0.0294346	+	0.106014i
$361$	−9.40987	+	7.15319i	−0.495256	+	0.376484i
$362$	−8.64519	+	0.940221i	−0.454381	+	0.0494169i
$363$	−0.665943	+	12.2826i	−0.0349529	+	0.644669i
$364$	−0.119842	+	0.431631i	−0.00628141	+	0.0226236i
$365$	7.57828	+	19.0201i	0.396666	+	0.995555i
$366$	−5.22664	−	1.15047i	−0.273201	−	0.0601361i
$367$	−0.264316	−	4.87502i	−0.0137972	−	0.254474i	−0.997292	−	0.0735393i	$-0.976571\pi$
$367$	−0.264316	−	4.87502i	−0.0137972	−	0.254474i	0.983495	−	0.180934i	$-0.0579122\pi$
$368$	−0.520285	−	3.17360i	−0.0271217	−	0.165435i
$369$	5.07248	−	7.48135i	0.264063	−	0.389464i
$370$	−7.55948	+	18.9729i	−0.392998	+	0.986352i
$371$	−2.12173	−	1.61290i	−0.110155	−	0.0837376i
$372$	1.59086	+	0.957187i	0.0824821	+	0.0496279i
$373$	1.63405	−	0.550577i	0.0846081	−	0.0285078i	−0.276679	−	0.960962i	$-0.589234\pi$
$373$	1.63405	−	0.550577i	0.0846081	−	0.0285078i	0.361287	+	0.932455i	$0.382337\pi$
$374$	−22.7440	−	21.5442i	−1.17606	−	1.11402i
$375$	−1.90550	+	11.6230i	−0.0983996	+	0.600211i
$376$	−9.87300	−	1.07375i	−0.509161	−	0.0553746i
$377$	2.85328	−	1.71676i	0.146951	−	0.0884178i
$378$	0.231657	−	0.272728i	0.0119152	−	0.0140276i
$379$	10.4485	−	4.83398i	0.536702	−	0.248305i	−0.132763	−	0.991148i	$-0.542385\pi$
$379$	10.4485	−	4.83398i	0.536702	−	0.248305i	0.669466	+	0.742843i	$0.266523\pi$
$380$	−5.07671	−	2.34874i	−0.260430	−	0.120488i
$381$	−0.671876	−	0.790993i	−0.0344212	−	0.0405238i
$382$	−17.4245	−	5.87099i	−0.891514	−	0.300386i
$383$	13.7205	+	25.8797i	0.701087	+	1.32239i	0.936559	+	0.350510i	$0.113992\pi$
$383$	13.7205	+	25.8797i	0.701087	+	1.32239i	−0.235472	+	0.971881i	$0.575664\pi$
$384$	−0.468408	−	0.883512i	−0.0239034	−	0.0450865i
$385$	3.41708	+	1.15135i	0.174150	+	0.0586781i
$386$	1.39941	+	1.64752i	0.0712283	+	0.0838565i
$387$	0.382913	+	0.177155i	0.0194646	+	0.00900527i
$388$	−6.11558	+	2.82937i	−0.310472	+	0.143640i
$389$	20.5293	−	24.1690i	1.04088	−	1.22542i	0.0671413	−	0.997743i	$-0.478612\pi$
$389$	20.5293	−	24.1690i	1.04088	−	1.22542i	0.973737	−	0.227674i	$-0.0731120\pi$
$390$	2.23926	−	1.34732i	0.113389	−	0.0682240i
$391$	−20.7494	−	2.25664i	−1.04934	−	0.114123i
$392$	1.11176	−	6.78143i	0.0561523	−	0.342514i
$393$	−8.19022	−	7.75819i	−0.413142	−	0.391349i
$394$	−23.8244	+	8.02737i	−1.20026	+	0.404413i
$395$	−2.48466	−	1.49497i	−0.125017	−	0.0752201i
$396$	3.84280	+	2.92122i	0.193108	+	0.146797i
$397$	13.1339	−	32.9637i	0.659173	−	1.65440i	−0.0931883	−	0.995649i	$-0.529706\pi$
$397$	13.1339	−	32.9637i	0.659173	−	1.65440i	0.752361	−	0.658751i	$-0.228915\pi$
$398$	4.48949	−	6.62151i	0.225038	−	0.331906i
$399$	0.155122	+	0.946201i	0.00776580	+	0.0473693i
$400$	−0.0347616	−	0.641140i	−0.00173808	−	0.0320570i
$401$	−8.33124	−	1.83384i	−0.416042	−	0.0915778i	0.00201620	−	0.999998i	$-0.499358\pi$
$401$	−8.33124	−	1.83384i	−0.416042	−	0.0915778i	−0.418058	+	0.908420i	$0.637289\pi$
$402$	3.35747	+	8.42661i	0.167455	+	0.420281i
$403$	0.621797	−	2.23951i	0.0309739	−	0.111558i
$404$	−0.289423	+	5.33809i	−0.0143993	+	0.265580i
$405$	−2.07533	+	0.225705i	−0.103124	+	0.0112154i
$406$	0.757750	−	0.576027i	0.0376065	−	0.0285877i
$407$	12.6340	+	45.5037i	0.626246	+	2.25553i
$408$	−6.33832	+	1.39517i	−0.313793	+	0.0690712i
$409$	6.24482	+	9.21043i	0.308787	+	0.455426i	0.950142	−	0.311818i	$-0.100938\pi$
$409$	6.24482	+	9.21043i	0.308787	+	0.455426i	−0.641355	+	0.767244i	$0.721628\pi$
$410$	13.6989	−	12.9763i	0.676541	−	0.640854i
$411$	−7.68569	+	14.4968i	−0.379107	+	0.715072i
$412$	−0.377354			−0.0185909
$413$	−2.74602	−	0.118592i	−0.135123	−	0.00583554i
$414$	3.21597			0.158056
$415$	−7.64552	+	14.4210i	−0.375304	+	0.707898i
$416$	−0.908845	+	0.860904i	−0.0445598	+	0.0422093i
$417$	−2.12261	−	3.13062i	−0.103945	−	0.153307i
$418$	−12.6319	+	2.78050i	−0.617849	+	0.135999i
$419$	2.69327	+	9.70028i	0.131575	+	0.473889i	0.999750	−	0.0223687i	$-0.00712076\pi$
$419$	2.69327	+	9.70028i	0.131575	+	0.473889i	−0.868175	+	0.496258i	$0.834707\pi$
$420$	0.594683	−	0.452066i	0.0290176	−	0.0220586i
$421$	34.0443	−	3.70254i	1.65922	−	0.180451i	0.770034	−	0.638003i	$-0.220239\pi$
$421$	34.0443	−	3.70254i	1.65922	−	0.180451i	0.889182	+	0.457553i	$0.151274\pi$
$422$	−1.23887	+	22.8496i	−0.0603072	+	1.11230i
$423$	2.65688	−	9.56923i	0.129182	−	0.465272i
$424$	−2.75682	−	6.91910i	−0.133883	−	0.336021i
$425$	−4.06972	−	0.895813i	−0.197410	−	0.0434533i
$426$	−0.0724669	−	1.33657i	−0.00351103	−	0.0647572i
$427$	0.309820	+	1.88982i	0.0149932	+	0.0914547i
$428$	−5.86998	+	8.65757i	−0.283736	+	0.418479i
$429$	2.23668	−	5.61364i	0.107988	−	0.271029i
$430$	0.701166	+	0.533013i	0.0338132	+	0.0257042i
$431$	31.9222	+	19.2070i	1.53764	+	0.925168i	0.996443	+	0.0842721i	$0.0268565\pi$
$431$	31.9222	+	19.2070i	1.53764	+	0.925168i	0.541198	+	0.840895i	$0.317971\pi$
$432$	0.947653	−	0.319302i	0.0455940	−	0.0153624i
$433$	11.8211	+	11.1975i	0.568086	+	0.538120i	0.916923	−	0.399064i	$-0.130665\pi$
$433$	11.8211	+	11.1975i	0.568086	+	0.538120i	−0.348837	+	0.937183i	$0.613423\pi$
$434$	0.107482	−	0.655611i	0.00515930	−	0.0314703i
$435$	−5.52035	−	0.600374i	−0.264680	−	0.0287857i
$436$	1.86048	−	1.11942i	0.0891009	−	0.0536103i
$437$	−5.57873	+	6.56779i	−0.266867	+	0.314180i
$438$	8.90123	−	4.11815i	0.425317	−	0.196773i
$439$	−15.9113	−	7.36136i	−0.759406	−	0.351339i	0.00167238	−	0.999999i	$-0.499468\pi$
$439$	−15.9113	−	7.36136i	−0.759406	−	0.351339i	−0.761078	+	0.648660i	$0.775330\pi$
$440$	6.52359	+	7.68017i	0.311000	+	0.366138i
$441$	6.51223	+	2.19423i	0.310106	+	0.104487i
$442$	3.80565	+	7.17822i	0.181016	+	0.341433i
$443$	15.1971	+	28.6648i	0.722036	+	1.36191i	0.923954	+	0.382503i	$0.124938\pi$
$443$	15.1971	+	28.6648i	0.722036	+	1.36191i	−0.201918	+	0.979402i	$0.564717\pi$
$444$	9.27124	+	3.12384i	0.439994	+	0.148251i
$445$	−0.371430	−	0.437281i	−0.0176075	−	0.0207291i
$446$	−7.93852	−	3.67275i	−0.375900	−	0.173910i
$447$	−16.3338	+	7.55684i	−0.772564	+	0.357426i
$448$	−0.231657	+	0.272728i	−0.0109448	+	0.0128852i
$449$	−8.99308	+	5.41096i	−0.424410	+	0.255359i	−0.711698	−	0.702485i	$-0.752074\pi$
$449$	−8.99308	+	5.41096i	−0.424410	+	0.255359i	0.287289	+	0.957844i	$0.407246\pi$
$450$	0.638318	+	0.0694213i	0.0300906	+	0.00327255i
$451$	7.05874	−	43.0564i	0.332383	−	2.02745i
$452$	−14.7779	−	13.9984i	−0.695095	−	0.658429i
$453$	−21.1374	+	7.12202i	−0.993122	+	0.334622i
$454$	−15.3810	−	9.25442i	−0.721865	−	0.434332i
$455$	−0.744461	−	0.565924i	−0.0349009	−	0.0265309i
$456$	−0.991801	+	2.48923i	−0.0464453	+	0.116569i
$457$	−0.345511	+	0.509590i	−0.0161623	+	0.0238376i	−0.835684	−	0.549210i	$-0.814929\pi$
$457$	−0.345511	+	0.509590i	−0.0161623	+	0.0238376i	0.819522	+	0.573048i	$0.194239\pi$
$458$	3.76085	+	22.9402i	0.175733	+	1.07192i
$459$	−0.351364	−	6.48053i	−0.0164003	−	0.302485i
$460$	6.55657	+	1.44321i	0.305702	+	0.0672900i
$461$	−11.6057	−	29.1280i	−0.540529	−	1.35663i	−0.905000	−	0.425411i	$-0.860129\pi$
$461$	−11.6057	−	29.1280i	−0.540529	−	1.35663i	0.364471	−	0.931215i	$-0.381250\pi$
$462$	0.462100	−	1.66433i	0.0214988	−	0.0774318i
$463$	0.476973	−	8.79725i	0.0221668	−	0.408843i	−0.966301	−	0.257414i	$-0.917130\pi$
$463$	0.476973	−	8.79725i	0.0221668	−	0.408843i	0.988468	−	0.151429i	$-0.0483875\pi$
$464$	2.64440	−	0.287596i	0.122763	−	0.0133513i
$465$	−3.08551	+	2.34554i	−0.143087	+	0.108772i
$466$	−6.75853	−	24.3420i	−0.313083	−	1.12762i
$467$	33.5458	−	7.38399i	1.55231	−	0.341690i	0.645680	−	0.763608i	$-0.276574\pi$
$467$	33.5458	−	7.38399i	1.55231	−	0.341690i	0.906634	+	0.421918i	$0.138643\pi$
$468$	−0.702528	−	1.03615i	−0.0324744	−	0.0478961i
$469$	2.35648	−	2.23218i	0.108812	−	0.103072i
$470$	9.71106	−	18.3170i	0.447938	−	0.844901i
$471$	1.75371			0.0808066
$472$	−6.40465	−	4.24033i	−0.294798	−	0.195177i
$473$	2.03658			0.0936421
$474$	−0.650644	+	1.22725i	−0.0298851	+	0.0563692i
$475$	−1.24906	+	1.18318i	−0.0573110	+	0.0542879i
$476$	1.30328	+	1.92220i	0.0597358	+	0.0881037i
$477$	7.27396	−	1.60112i	0.333052	−	0.0733102i
$478$	0.672660	+	2.42270i	0.0307668	+	0.110812i
$479$	−10.7986	+	8.20891i	−0.493402	+	0.375075i	−0.822084	−	0.569366i	$-0.807189\pi$
$479$	−10.7986	+	8.20891i	−0.493402	+	0.375075i	0.328682	+	0.944441i	$0.393396\pi$
$480$	2.07533	−	0.225705i	0.0947252	−	0.0103020i
$481$	0.663062	−	12.2295i	0.0302330	−	0.557615i
$482$	0.264435	−	0.952409i	0.0120447	−	0.0433810i
$483$	−0.425949	−	1.06905i	−0.0193813	−	0.0486435i
$484$	12.0131	+	2.64427i	0.546048	+	0.120194i
$485$	−0.761560	−	14.0462i	−0.0345807	−	0.637803i
$486$	0.161782	+	0.986827i	0.00733858	+	0.0447634i
$487$	−20.5808	+	30.3544i	−0.932606	+	1.37549i	−0.00578688	+	0.999983i	$0.501842\pi$
$487$	−20.5808	+	30.3544i	−0.932606	+	1.37549i	−0.926819	+	0.375508i	$0.877468\pi$
$488$	−1.98089	+	4.97166i	−0.0896708	+	0.225057i
$489$	−4.84583	−	3.68371i	−0.219136	−	0.166583i
$490$	12.2922	+	7.39595i	0.555303	+	0.334115i
$491$	12.3327	−	4.15535i	0.556565	−	0.187529i	−0.0269416	−	0.999637i	$-0.508577\pi$
$491$	12.3327	−	4.15535i	0.556565	−	0.187529i	0.583506	+	0.812108i	$0.301680\pi$
$492$	−6.56216	−	6.21601i	−0.295845	−	0.280239i
$493$	2.79292	−	17.0361i	0.125787	−	0.767265i
$494$	3.33475	+	0.362676i	0.150037	+	0.0163176i
$495$	−8.63439	+	5.19514i	−0.388087	+	0.233504i
$496$	1.20195	−	1.41505i	0.0539692	−	0.0635374i
$497$	−0.434705	+	0.201116i	−0.0194992	+	0.00902129i
$498$	7.09619	+	3.28305i	0.317988	+	0.147117i
$499$	−5.18237	−	6.10115i	−0.231995	−	0.273125i	0.633830	−	0.773472i	$-0.281482\pi$
$499$	−5.18237	−	6.10115i	−0.231995	−	0.273125i	−0.865825	+	0.500347i	$0.833206\pi$
$500$	11.1616	+	3.76080i	0.499164	+	0.168188i
$501$	1.62044	+	3.05647i	0.0723958	+	0.136553i
$502$	−2.59070	−	4.88657i	−0.115628	−	0.218098i
$503$	−39.7827	−	13.4043i	−1.77382	−	0.597670i	−0.774434	−	0.632655i	$-0.781965\pi$
$503$	−39.7827	−	13.4043i	−1.77382	−	0.597670i	−0.999388	+	0.0349853i	$0.988862\pi$
$504$	−0.231657	−	0.272728i	−0.0103188	−	0.0121483i
$505$	−10.1285	−	4.68595i	−0.450713	−	0.208522i
$506$	14.0889	−	6.51823i	0.626329	−	0.289771i
$507$	7.40147	−	8.71368i	0.328711	−	0.386988i
$508$	−0.889271	+	0.535056i	−0.0394550	+	0.0237393i
$509$	−9.09404	−	0.989036i	−0.403086	−	0.0438383i	−0.0956693	−	0.995413i	$-0.530499\pi$
$509$	−9.09404	−	0.989036i	−0.403086	−	0.0438383i	−0.307417	+	0.951575i	$0.599465\pi$
$510$	2.19189	−	13.3699i	0.0970583	−	0.592030i
$511$	−2.54791	−	2.41351i	−0.112713	−	0.106767i
$512$	−0.947653	+	0.319302i	−0.0418807	+	0.0141113i
$513$	−2.29598	−	1.38145i	−0.101370	−	0.0609924i
$514$	−8.07738	−	6.14027i	−0.356278	−	0.270836i
$515$	0.291576	−	0.731801i	0.0128484	−	0.0322470i
$516$	0.236769	−	0.349209i	0.0104232	−	0.0153730i
$517$	−7.75562	−	47.3072i	−0.341092	−	2.08057i
$518$	−0.189531	−	3.49569i	−0.00832751	−	0.153592i
$519$	19.0760	+	4.19895i	0.837345	+	0.184314i
$520$	−0.967296	−	2.42773i	−0.0424187	−	0.106463i
$521$	10.1628	−	36.6032i	0.445242	−	1.60362i	−0.311730	−	0.950171i	$-0.600909\pi$
$521$	10.1628	−	36.6032i	0.445242	−	1.60362i	0.756973	−	0.653447i	$-0.226678\pi$
$522$	−0.144009	+	2.65609i	−0.00630310	+	0.116254i
$523$	4.49778	−	0.489163i	0.196674	−	0.0213896i	−0.00925168	−	0.999957i	$-0.502945\pi$
$523$	4.49778	−	0.489163i	0.196674	−	0.0213896i	0.205926	+	0.978568i	$0.433979\pi$
$524$	−8.98101	+	6.82719i	−0.392337	+	0.298247i
$525$	−0.0614671	−	0.221384i	−0.00268264	−	0.00966201i
$526$	4.11895	−	0.906650i	0.179595	−	0.0395318i
$527$	−6.76206	−	9.97329i	−0.294560	−	0.434443i
$528$	3.50443	−	3.31958i	0.152511	−	0.144466i
$529$	−5.92891	+	11.1831i	−0.257779	+	0.486222i
$530$	15.5484			0.675377
$531$	5.22063	−	5.63427i	0.226556	−	0.244507i
$532$	0.958832			0.0415707
$533$	−5.30022	+	9.99727i	−0.229578	+	0.433030i
$534$	−0.199530	+	0.189005i	−0.00863450	+	0.00817903i
$535$	−12.2539	−	18.0732i	−0.529784	−	0.781373i
$536$	8.85877	−	1.94996i	0.382641	−	0.0842256i
$537$	−1.80034	−	6.48423i	−0.0776903	−	0.279815i
$538$	10.1443	−	7.71146i	0.437350	−	0.332465i
$539$	32.9770	−	3.58646i	1.42042	−	0.154480i
$540$	−0.113018	+	2.08450i	−0.00486354	+	0.0897026i
$541$	9.02684	−	32.5118i	0.388094	−	1.39779i	−0.469259	−	0.883061i	$-0.655479\pi$
$541$	9.02684	−	32.5118i	0.388094	−	1.39779i	0.857353	−	0.514729i	$-0.172107\pi$
$542$	9.92626	+	24.9130i	0.426369	+	1.07011i
$543$	−8.49285	−	1.86942i	−0.364463	−	0.0802244i
$544$	0.351364	+	6.48053i	0.0150646	+	0.277851i
$545$	0.733309	+	4.47299i	0.0314115	+	0.191602i
$546$	−0.251389	+	0.370771i	−0.0107584	+	0.0158675i
$547$	12.0130	−	30.1504i	0.513640	−	1.28914i	−0.412155	−	0.911114i	$-0.635224\pi$
$547$	12.0130	−	30.1504i	0.513640	−	1.28914i	0.925795	−	0.378026i	$-0.123397\pi$
$548$	13.0624	+	9.92976i	0.557997	+	0.424178i
$549$	−4.58570	−	2.75912i	−0.195713	−	0.117756i
$550$	2.93713	−	0.989636i	0.125240	−	0.0421982i
$551$	−5.17457	−	4.90162i	−0.220444	−	0.208816i
$552$	0.520285	−	3.17360i	0.0221448	−	0.135077i
$553$	0.494137	+	0.0537407i	0.0210129	+	0.00228529i
$554$	−5.21322	+	3.13669i	−0.221488	+	0.133265i
$555$	−13.2218	+	15.5659i	−0.561235	+	0.660737i
$556$	−3.43278	+	1.58817i	−0.145582	+	0.0673535i
$557$	23.1365	+	10.7041i	0.980324	+	0.453546i	0.843547	−	0.537056i	$-0.180463\pi$
$557$	23.1365	+	10.7041i	0.980324	+	0.453546i	0.136777	+	0.990602i	$0.456326\pi$
$558$	1.20195	+	1.41505i	0.0508826	+	0.0599036i
$559$	−0.500522	−	0.168645i	−0.0211698	−	0.00713294i
$560$	−0.349902	−	0.659985i	−0.0147861	−	0.0278895i
$561$	−14.6743	−	27.6786i	−0.619549	−	1.16859i
$562$	−22.9001	−	7.71594i	−0.965982	−	0.325477i
$563$	15.7464	+	18.5381i	0.663633	+	0.781289i	0.986253	−	0.165239i	$-0.0528397\pi$
$563$	15.7464	+	18.5381i	0.663633	+	0.781289i	−0.322621	+	0.946528i	$0.604564\pi$
$564$	−9.01333	−	4.17001i	−0.379530	−	0.175589i
$565$	38.5658	−	17.8424i	1.62247	−	0.750636i
$566$	−12.3930	+	14.5901i	−0.520915	+	0.613269i
$567$	0.306613	−	0.184483i	0.0128765	−	0.00774756i
$568$	−1.33069	−	0.144721i	−0.0558345	−	0.00607237i
$569$	3.76479	−	22.9642i	0.157828	−	0.962708i	−0.782553	−	0.622585i	$-0.786083\pi$
$569$	3.76479	−	22.9642i	0.157828	−	0.962708i	0.940381	−	0.340124i	$-0.110469\pi$
$570$	−4.06101	−	3.84679i	−0.170097	−	0.161124i
$571$	−38.4418	+	12.9526i	−1.60874	+	0.542048i	−0.973188	−	0.230010i	$-0.926124\pi$
$571$	−38.4418	+	12.9526i	−1.60874	+	0.542048i	−0.635552	+	0.772058i	$0.719228\pi$
$572$	−5.17784	−	3.11540i	−0.216496	−	0.130261i
$573$	−14.6377	−	11.1273i	−0.611500	−	0.464851i
$574$	−1.19718	+	3.00469i	−0.0499693	+	0.125413i
$575$	1.15880	−	1.70911i	0.0483254	−	0.0712747i
$576$	−0.161782	−	0.986827i	−0.00674092	−	0.0411178i
$577$	−1.33852	−	24.6876i	−0.0557233	−	1.02776i	−0.884015	−	0.467459i	$-0.845170\pi$
$577$	−1.33852	−	24.6876i	−0.0557233	−	1.02776i	0.828291	−	0.560298i	$-0.189313\pi$
$578$	24.5335	+	5.40022i	1.02046	+	0.224620i
$579$	0.800104	+	2.00811i	0.0332512	+	0.0834542i
$580$	−1.48556	+	5.35049i	−0.0616844	+	0.222167i
$581$	0.151473	−	2.79375i	0.00628415	−	0.115904i
$582$	−6.69888	+	0.728547i	−0.277677	+	0.0301992i
$583$	28.6215	−	21.7575i	1.18538	−	0.901104i
$584$	−2.62384	−	9.45022i	−0.108575	−	0.391053i
$585$	2.55224	−	0.561790i	0.105522	−	0.0232272i
$586$	8.16412	+	12.0412i	0.337257	+	0.497417i
$587$	−9.09360	+	8.61391i	−0.375333	+	0.355534i	−0.851993	−	0.523554i	$-0.824606\pi$
$587$	−9.09360	+	8.61391i	−0.375333	+	0.355534i	0.476660	+	0.879088i	$0.341847\pi$
$588$	3.21888	−	6.07145i	0.132744	−	0.250383i
$589$	−4.97489			−0.204987
$590$	13.1721	−	9.14408i	0.542285	−	0.376456i
$591$	−25.1404			−1.03414
$592$	4.58261	−	8.64372i	0.188344	−	0.355255i
$593$	4.69649	−	4.44875i	0.192862	−	0.182688i	−0.585175	−	0.810907i	$-0.698974\pi$
$593$	4.69649	−	4.44875i	0.192862	−	0.182688i	0.778037	+	0.628219i	$0.216216\pi$
$594$	2.70889	+	3.99532i	0.111147	+	0.163930i
$595$	−4.73474	+	1.04219i	−0.194105	+	0.0427258i
$596$	4.81477	+	17.3412i	0.197221	+	0.710324i
$597$	6.36874	−	4.84139i	0.260655	−	0.198145i
$598$	−4.00234	+	0.435281i	−0.163668	+	0.0178000i
$599$	−0.0812100	+	1.49783i	−0.00331815	+	0.0611997i	−0.999724	−	0.0235136i	$-0.992515\pi$
$599$	−0.0812100	+	1.49783i	−0.00331815	+	0.0611997i	0.996405	+	0.0847133i	$0.0269974\pi$
$600$	0.171775	−	0.618678i	0.00701269	−	0.0252574i
$601$	2.15480	+	5.40813i	0.0878960	+	0.220602i	0.966353	−	0.257219i	$-0.0828061\pi$
$601$	2.15480	+	5.40813i	0.0878960	+	0.220602i	−0.878457	+	0.477821i	$0.841427\pi$
$602$	−0.147444	−	0.0324548i	−0.00600935	−	0.00132276i
$603$	0.491086	+	9.05754i	0.0199986	+	0.368852i
$604$	3.60855	+	22.0112i	0.146830	+	0.895622i
$605$	−14.4104	+	21.2537i	−0.585864	+	0.864085i
$606$	−1.97873	+	4.96625i	−0.0803806	+	0.201740i
$607$	29.6975	+	22.5754i	1.20538	+	0.916309i	0.998078	−	0.0619678i	$-0.0197376\pi$
$607$	29.6975	+	22.5754i	1.20538	+	0.916309i	0.207305	+	0.978276i	$0.433531\pi$
$608$	2.29598	+	1.38145i	0.0931145	+	0.0560251i
$609$	0.902011	−	0.303923i	0.0365513	−	0.0123156i
$610$	−8.11092	−	7.68307i	−0.328402	−	0.311079i
$611$	−2.01136	+	12.2687i	−0.0813707	+	0.496340i
$612$	−6.45201	−	0.701698i	−0.260807	−	0.0283645i
$613$	−13.2352	+	7.96333i	−0.534563	+	0.321636i	−0.757111	−	0.653286i	$-0.773390\pi$
$613$	−13.2352	+	7.96333i	−0.534563	+	0.321636i	0.222548	+	0.974922i	$0.428562\pi$
$614$	12.9798	−	15.2810i	0.523821	−	0.616690i
$615$	17.1252	−	7.92295i	0.690554	−	0.319484i
$616$	−1.56765	−	0.725272i	−0.0631624	−	0.0292220i
$617$	−14.3347	−	16.8761i	−0.577094	−	0.679408i	0.393723	−	0.919229i	$-0.371187\pi$
$617$	−14.3347	−	16.8761i	−0.577094	−	0.679408i	−0.970817	+	0.239821i	$0.922911\pi$
$618$	−0.357600	−	0.120490i	−0.0143848	−	0.00484680i
$619$	18.1452	+	34.2255i	0.729317	+	1.37564i	0.919184	+	0.393828i	$0.128849\pi$
$619$	18.1452	+	34.2255i	0.729317	+	1.37564i	−0.189867	+	0.981810i	$0.560806\pi$
$620$	1.81546	+	3.42432i	0.0729107	+	0.137524i
$621$	3.04762	+	1.02686i	0.122297	+	0.0412066i
$622$	9.83705	+	11.5811i	0.394430	+	0.464359i
$623$	0.0892563	+	0.0412943i	0.00357598	+	0.00165442i
$624$	−1.13616	+	0.525643i	−0.0454827	+	0.0210426i
$625$	−13.8394	+	16.2930i	−0.553575	+	0.651719i
$626$	25.6912	−	15.4579i	1.02683	−	0.617822i
$627$	−12.8585	−	1.39845i	−0.513520	−	0.0558487i
$628$	0.283718	−	1.73061i	0.0113216	−	0.0690587i
$629$	−46.0968	−	43.6652i	−1.83800	−	1.74104i
$630$	0.707899	−	0.238519i	0.0282034	−	0.00950282i
$631$	15.7758	+	9.49198i	0.628024	+	0.377870i	0.793699	−	0.608311i	$-0.208153\pi$
$631$	15.7758	+	9.49198i	0.628024	+	0.377870i	−0.165675	+	0.986180i	$0.552980\pi$
$632$	1.10582	+	0.840619i	0.0439870	+	0.0334380i
$633$	−8.46993	+	21.2579i	−0.336649	+	0.844926i
$634$	2.70853	−	3.99478i	0.107569	−	0.158653i
$635$	−0.350506	−	2.13799i	−0.0139094	−	0.0848436i
$636$	−0.403231	−	7.43717i	−0.0159892	−	0.294903i
$637$	−8.40160	−	1.84933i	−0.332884	−	0.0732732i
$638$	4.75256	+	11.9280i	0.188156	+	0.472235i
$639$	0.358096	−	1.28975i	0.0141661	−	0.0510216i
$640$	0.113018	−	2.08450i	0.00446744	−	0.0823971i
$641$	7.20213	−	0.783279i	0.284467	−	0.0309376i	0.0352267	−	0.999379i	$-0.488785\pi$
$641$	7.20213	−	0.783279i	0.284467	−	0.0309376i	0.249240	+	0.968442i	$0.419819\pi$
$642$	−8.32708	+	6.33008i	−0.328644	+	0.249828i
$643$	9.68715	+	34.8900i	0.382024	+	1.37593i	0.865649	+	0.500651i	$0.166906\pi$
$643$	9.68715	+	34.8900i	0.382024	+	1.37593i	−0.483625	+	0.875275i	$0.660680\pi$
$644$	−1.12388	+	0.247384i	−0.0442870	+	0.00974831i
$645$	0.494271	+	0.728995i	0.0194619	+	0.0287041i
$646$	12.6253	−	11.9593i	0.496737	−	0.470534i
$647$	−11.2298	+	21.1816i	−0.441488	+	0.832734i	0.558507	+	0.829500i	$0.311374\pi$
$647$	−11.2298	+	21.1816i	−0.441488	+	0.832734i	−0.999995	+	0.00323455i	$0.998970\pi$
$648$	1.00000			0.0392837
$649$	11.4515	−	35.2647i	0.449510	−	1.38426i
$650$	−0.803798			−0.0315275
$651$	0.311193	−	0.586972i	0.0121966	−	0.0230053i
$652$	−4.41915	+	4.18604i	−0.173067	+	0.163938i
$653$	24.5653	+	36.2311i	0.961315	+	1.41783i	0.907865	+	0.419263i	$0.137711\pi$
$653$	24.5653	+	36.2311i	0.961315	+	1.41783i	0.0534500	+	0.998571i	$0.482978\pi$
$654$	2.12052	−	0.466762i	0.0829190	−	0.0182519i
$655$	−6.30044	−	22.6921i	−0.246179	−	0.886655i
$656$	−7.19576	+	5.47007i	−0.280947	+	0.213571i
$657$	9.75022	−	1.06040i	0.380392	−	0.0413701i
$658$	−0.192395	+	3.54852i	−0.00750035	+	0.138336i
$659$	−10.4754	+	37.7289i	−0.408063	+	1.46971i	0.419199	+	0.907894i	$0.362311\pi$
$659$	−10.4754	+	37.7289i	−0.408063	+	1.46971i	−0.827262	+	0.561816i	$0.810103\pi$
$660$	3.72981	+	9.36113i	0.145183	+	0.364381i
$661$	−45.9008	−	10.1035i	−1.78533	−	0.392981i	−0.805467	−	0.592640i	$-0.798086\pi$
$661$	−45.9008	−	10.1035i	−1.78533	−	0.392981i	−0.979865	+	0.199659i	$0.936017\pi$
$662$	−0.890002	−	16.4151i	−0.0345909	−	0.637992i
$663$	1.31442	+	8.01761i	0.0510479	+	0.311378i
$664$	4.38783	−	6.47157i	0.170281	−	0.251146i
$665$	−0.740877	+	1.85946i	−0.0287300	+	0.0721068i
$666$	7.78847	+	5.92064i	0.301797	+	0.229420i
$667$	7.32993	+	4.41027i	0.283816	+	0.170766i
$668$	3.27836	−	1.10461i	0.126844	−	0.0427386i
$669$	−6.35025	−	6.01527i	−0.245515	−	0.232564i
$670$	−3.06350	+	18.6865i	−0.118353	+	0.721923i
$671$	−25.6819	−	2.79308i	−0.991439	−	0.107826i
$672$	−0.306613	+	0.184483i	−0.0118279	+	0.00711659i
$673$	−26.3897	+	31.0684i	−1.01725	+	1.19760i	−0.0371042	+	0.999311i	$0.511813\pi$
$673$	−26.3897	+	31.0684i	−1.01725	+	1.19760i	−0.980144	+	0.198286i	$0.936463\pi$
$674$	6.12730	−	2.83479i	0.236015	−	0.109192i
$675$	0.582738	+	0.269603i	0.0224296	+	0.0103770i
$676$	−7.40147	−	8.71368i	−0.284672	−	0.335142i
$677$	29.4866	+	9.93518i	1.13326	+	0.381840i	0.822566	−	0.568670i	$-0.192542\pi$
$677$	29.4866	+	9.93518i	1.13326	+	0.381840i	0.310695	+	0.950510i	$0.399438\pi$
$678$	−9.53464	−	17.9842i	−0.366176	−	0.690681i
$679$	1.12944	+	2.13035i	0.0433438	+	0.0817551i
$680$	−12.8392	−	4.32602i	−0.492360	−	0.165895i
$681$	−11.6209	−	13.6812i	−0.445313	−	0.524263i
$682$	8.13373	+	3.76306i	0.311456	+	0.144095i
$683$	8.83414	−	4.08711i	0.338029	−	0.156389i	−0.243529	−	0.969894i	$-0.578305\pi$
$683$	8.83414	−	4.08711i	0.338029	−	0.156389i	0.581558	+	0.813505i	$0.302443\pi$
$684$	−1.73470	+	2.04224i	−0.0663278	+	0.0780872i
$685$	−29.3499	+	17.6592i	−1.12140	+	0.674725i
$686$	−4.93477	−	0.536688i	−0.188410	−	0.0204908i
$687$	−3.76085	+	22.9402i	−0.143485	+	0.875221i
$688$	−0.306303	−	0.290146i	−0.0116777	−	0.0110617i
$689$	−8.83589	+	2.97716i	−0.336621	+	0.113421i
$690$	5.75254	+	3.46119i	0.218995	+	0.131765i
$691$	−17.8188	−	13.5455i	−0.677860	−	0.515296i	0.208659	−	0.977988i	$-0.433090\pi$
$691$	−17.8188	−	13.5455i	−0.677860	−	0.515296i	−0.886519	+	0.462693i	$0.846883\pi$
$692$	7.22979	−	18.1454i	0.274836	−	0.689785i
$693$	0.969335	−	1.42966i	0.0368220	−	0.0543084i
$694$	−1.30637	−	7.96848i	−0.0495890	−	0.302479i
$695$	−0.427476	−	7.88433i	−0.0162151	−	0.299070i
$696$	2.59780	+	0.571819i	0.0984694	+	0.0216748i
$697$	21.7132	+	54.4961i	0.822448	+	2.06419i
$698$	−1.51014	+	5.43903i	−0.0571597	+	0.205870i
$699$	1.36770	−	25.2258i	0.0517313	−	0.954127i
$700$	−0.228412	+	0.0248413i	−0.00863317	+	0.000938914i
$701$	−18.1828	+	13.8222i	−0.686755	+	0.522058i	−0.889363	−	0.457202i	$-0.848852\pi$
$701$	−18.1828	+	13.8222i	−0.686755	+	0.522058i	0.202608	+	0.979260i	$0.435058\pi$
$702$	−0.334908	−	1.20623i	−0.0126403	−	0.0455262i
$703$	−25.6020	+	5.63544i	−0.965599	+	0.212545i
$704$	−2.70889	−	3.99532i	−0.102095	−	0.150579i
$705$	15.0514	−	14.2574i	0.566867	−	0.536965i
$706$	−5.38385	+	10.1550i	−0.202624	+	0.382189i
$707$	1.91296			0.0719442
$708$	−4.71544	−	6.06338i	−0.177217	−	0.227876i
$709$	43.9863			1.65194			0.825970	−	0.563715i	$-0.190628\pi$
$709$	43.9863			1.65194			0.825970	+	0.563715i	$0.190628\pi$
$710$	1.30886	−	2.46878i	0.0491208	−	0.0926516i
$711$	−1.00845	+	0.955251i	−0.0378197	+	0.0358247i
$712$	0.154234	+	0.227479i	0.00578018	+	0.00852513i
$713$	5.83123	−	1.28355i	0.218381	−	0.0480694i
$714$	0.621298	+	2.23771i	0.0232515	+	0.0837444i
$715$	10.0425	−	7.63414i	0.375570	−	0.285501i
$716$	−6.69007	+	0.727589i	−0.250020	+	0.0271913i
$717$	−0.136124	+	2.51066i	−0.00508365	+	0.0937625i
$718$	−8.75258	+	31.5239i	−0.326643	+	1.17646i
$719$	−8.91960	−	22.3865i	−0.332645	−	0.834876i	−0.996228	−	0.0867734i	$-0.972344\pi$
$719$	−8.91960	−	22.3865i	−0.332645	−	0.834876i	0.663583	−	0.748103i	$-0.269035\pi$
$720$	2.03876	+	0.448764i	0.0759800	+	0.0167245i
$721$	0.00731038	+	0.134832i	0.000272253	+	0.00502141i
$722$	1.91227	+	11.6643i	0.0711674	+	0.434102i
$723$	0.554698	−	0.818119i	0.0206295	−	0.0304262i
$724$	−3.21878	+	8.07854i	−0.119625	+	0.300236i
$725$	1.35967	+	1.03360i	0.0504970	+	0.0383868i
$726$	10.5399	+	6.34164i	0.391172	+	0.235360i
$727$	−49.9388	+	16.8263i	−1.85213	+	0.624054i	−0.858294	+	0.513159i	$0.828475\pi$
$727$	−49.9388	+	16.8263i	−1.85213	+	0.624054i	−0.993832	+	0.110895i	$0.964628\pi$
$728$	0.325216	+	0.308061i	0.0120533	+	0.0114175i
$729$	−0.161782	+	0.986827i	−0.00599193	+	0.0365491i
$730$	20.3542	+	2.21365i	0.753342	+	0.0819309i
$731$	−2.34625	+	1.41169i	−0.0867792	+	0.0522133i
$732$	−3.46466	+	4.07891i	−0.128057	+	0.150761i
$733$	25.5958	−	11.8419i	0.945404	−	0.437391i	0.114262	−	0.993451i	$-0.463550\pi$
$733$	25.5958	−	11.8419i	0.945404	−	0.437391i	0.831142	+	0.556060i	$0.187688\pi$
$734$	−4.43094	−	2.04997i	−0.163549	−	0.0756659i
$735$	9.28717	+	10.9337i	0.342562	+	0.403296i
$736$	−3.04762	−	1.02686i	−0.112337	−	0.0378507i
$737$	20.5096	+	38.6851i	0.755479	+	1.42499i
$738$	−4.23387	−	7.98593i	−0.155851	−	0.293966i
$739$	0.994245	+	0.335000i	0.0365739	+	0.0123232i	0.337529	−	0.941315i	$-0.390409\pi$
$739$	0.994245	+	0.335000i	0.0365739	+	0.0123232i	−0.300955	+	0.953638i	$0.597305\pi$
$740$	13.2218	+	15.5659i	0.486044	+	0.572215i
$741$	3.04438	+	1.40848i	0.111838	+	0.0517419i
$742$	−2.41886	+	1.11908i	−0.0887990	+	0.0410828i
$743$	14.7849	−	17.4062i	0.542406	−	0.638570i	−0.420858	−	0.907127i	$-0.638271\pi$
$743$	14.7849	−	17.4062i	0.542406	−	0.638570i	0.963264	+	0.268557i	$0.0865467\pi$
$744$	1.59086	−	0.957187i	0.0583237	−	0.0350922i
$745$	−37.3501	−	4.06207i	−1.36840	−	0.148823i
$746$	0.278963	−	1.70160i	0.0102136	−	0.0623000i
$747$	5.67645	+	5.37702i	0.207690	+	0.196735i
$748$	−29.6880	+	10.0031i	−1.08550	+	0.365748i
$749$	3.20715	+	1.92968i	0.117187	+	0.0705089i
$750$	9.37654	+	7.12786i	0.342383	+	0.260273i
$751$	−13.1747	+	33.0659i	−0.480750	+	1.20659i	0.466047	+	0.884760i	$0.345678\pi$
$751$	−13.1747	+	33.0659i	−0.480750	+	1.20659i	−0.946797	+	0.321832i	$0.895701\pi$
$752$	−5.57327	+	8.21996i	−0.203236	+	0.299751i
$753$	−0.894792	−	5.45799i	−0.0326080	−	0.198900i
$754$	−0.180279	−	3.32505i	−0.00656538	−	0.121091i
$755$	−45.4745	−	10.0097i	−1.65499	−	0.364290i
$756$	−0.132448	−	0.332420i	−0.00481709	−	0.0120900i
$757$	−2.50329	+	9.01603i	−0.0909836	+	0.327693i	−0.995009	−	0.0997855i	$-0.968184\pi$
$757$	−2.50329	+	9.01603i	−0.0909836	+	0.327693i	0.904025	+	0.427479i	$0.140598\pi$
$758$	0.623275	−	11.4956i	0.0226384	−	0.417540i
$759$	15.4327	−	1.67841i	0.560172	−	0.0609223i
$760$	−4.45311	+	3.38517i	−0.161531	+	0.122793i
$761$	5.48976	+	19.7723i	0.199004	+	0.716747i	0.993927	+	0.110037i	$0.0350970\pi$
$761$	5.48976	+	19.7723i	0.199004	+	0.716747i	−0.794924	+	0.606709i	$0.792489\pi$
$762$	−1.01356	+	0.223102i	−0.0367176	+	0.00808215i
$763$	−0.436021	−	0.643082i	−0.0157850	−	0.0232811i
$764$	−13.3489	+	12.6447i	−0.482945	+	0.457470i
$765$	6.34618	−	11.9702i	0.229447	−	0.432782i
$766$	29.2918			1.05836
$767$	−5.73459	+	7.71859i	−0.207064	+	0.278702i
$768$	−1.00000			−0.0360844
$769$	9.03039	−	17.0331i	0.325644	−	0.614230i	−0.665594	−	0.746314i	$-0.731822\pi$
$769$	9.03039	−	17.0331i	0.325644	−	0.614230i	0.991239	+	0.132084i	$0.0421667\pi$
$770$	2.61782	−	2.47973i	0.0943396	−	0.0893633i
$771$	−5.69396	−	8.39796i	−0.205063	−	0.302445i
$772$	2.11110	−	0.464688i	0.0759801	−	0.0167245i
$773$	−5.40991	−	19.4847i	−0.194581	−	0.700817i	−0.994866	−	0.101198i	$-0.967733\pi$
$773$	−5.40991	−	19.4847i	−0.194581	−	0.700817i	0.800285	−	0.599619i	$-0.204681\pi$
$774$	0.335878	−	0.255328i	0.0120729	−	0.00917757i
$775$	1.18511	−	0.128889i	0.0425706	−	0.00462983i
$776$	−0.364808	+	6.72849i	−0.0130959	+	0.241539i
$777$	0.936570	−	3.37322i	0.0335993	−	0.121014i
$778$	−11.7375	−	29.4589i	−0.420809	−	1.05615i
$779$	23.6537	+	5.20657i	0.847482	+	0.186545i
$780$	−0.141483	−	2.60951i	−0.00506591	−	0.0934353i
$781$	−1.04531	−	6.37610i	−0.0374041	−	0.228155i
$782$	−11.7130	+	17.2753i	−0.418855	+	0.617765i
$783$	−0.984564	+	2.47107i	−0.0351854	+	0.0883088i
$784$	−5.47072	−	4.15873i	−0.195383	−	0.148526i
$785$	3.13693	+	1.88743i	0.111962	+	0.0673653i
$786$	−10.6908	+	3.60216i	−0.381329	+	0.128485i
$787$	−33.1078	−	31.3613i	−1.18016	−	1.11791i	−0.990706	−	0.136022i	$-0.956568\pi$
$787$	−33.1078	−	31.3613i	−1.18016	−	1.11791i	−0.189459	−	0.981889i	$-0.560673\pi$
$788$	−4.06727	+	24.8092i	−0.144890	+	0.883792i
$789$	4.19283	+	0.455998i	0.149269	+	0.0162340i
$790$	−2.48466	+	1.49497i	−0.0884002	+	0.0531886i
$791$	−4.71548	+	5.55149i	−0.167663	+	0.197388i
$792$	4.38093	−	2.02684i	0.155670	−	0.0720205i
$793$	6.08045	+	2.81312i	0.215923	+	0.0998967i
$794$	−22.9718	−	27.0444i	−0.815237	−	0.959771i
$795$	14.7344	+	4.96461i	0.522577	+	0.176077i
$796$	−3.74726	−	7.06809i	−0.132818	−	0.250522i
$797$	1.27938	+	2.41317i	0.0453180	+	0.0854787i	0.905137	−	0.425121i	$-0.139768\pi$
$797$	1.27938	+	2.41317i	0.0453180	+	0.0854787i	−0.859819	+	0.510599i	$0.829424\pi$
$798$	0.908641	+	0.306157i	0.0321655	+	0.0108378i
$799$	41.7267	+	49.1245i	1.47618	+	1.73790i
$800$	−0.582738	−	0.269603i	−0.0206029	−	0.00953192i
$801$	−0.249434	+	0.115401i	−0.00881333	+	0.00407748i
$802$	−5.52265	+	6.50176i	−0.195011	+	0.229585i
$803$	40.5658	−	24.4076i	1.43154	−	0.861326i
$804$	9.01767	+	0.980731i	0.318029	+	0.0345877i
$805$	0.388654	−	2.37069i	0.0136983	−	0.0835557i
$806$	−1.68738	−	1.59837i	−0.0594354	−	0.0563002i
$807$	12.0755	−	4.06871i	0.425078	−	0.143226i
$808$	4.58070	+	2.75612i	0.161148	+	0.0969598i
$809$	−19.0406	−	14.4743i	−0.669433	−	0.508890i	0.214368	−	0.976753i	$-0.431231\pi$
$809$	−19.0406	−	14.4743i	−0.669433	−	0.508890i	−0.883801	+	0.467863i	$0.845024\pi$
$810$	−0.772687	+	1.93930i	−0.0271494	+	0.0681400i
$811$	10.1101	−	14.9112i	0.355012	−	0.523604i	−0.607687	−	0.794176i	$-0.707903\pi$
$811$	10.1101	−	14.9112i	0.355012	−	0.523604i	0.962700	+	0.270573i	$0.0872130\pi$
$812$	−0.153990	−	0.939298i	−0.00540399	−	0.0329629i
$813$	1.45188	+	26.7784i	0.0509197	+	0.939159i
$814$	46.1209	+	10.1520i	1.61654	+	0.355827i
$815$	−4.70336	−	11.8045i	−0.164751	−	0.413495i
$816$	−1.73627	+	6.25349i	−0.0607817	+	0.218916i
$817$	−0.0612051	+	1.12886i	−0.00214130	+	0.0394939i
$818$	11.0626	−	1.20314i	0.386796	−	0.0420667i
$819$	−0.356617	+	0.271093i	−0.0124612	+	0.00947277i
$820$	−5.04803	−	18.1814i	−0.176285	−	0.634921i
$821$	−13.7645	+	3.02980i	−0.480385	+	0.105741i	−0.448560	−	0.893753i	$-0.648063\pi$
$821$	−13.7645	+	3.02980i	−0.480385	+	0.105741i	−0.0318251	+	0.999493i	$0.510132\pi$
$822$	9.20802	+	13.5808i	0.321166	+	0.473685i
$823$	−24.2116	+	22.9344i	−0.843962	+	0.799444i	−0.981582	−	0.191042i	$-0.938813\pi$
$823$	−24.2116	+	22.9344i	−0.843962	+	0.799444i	0.137620	+	0.990485i	$0.456055\pi$
$824$	−0.176756	+	0.333396i	−0.00615757	+	0.0116144i
$825$	3.09938			0.107906
$826$	−1.39104	+	2.37059i	−0.0484003	+	0.0824834i
$827$	−35.2688			−1.22642			−0.613208	−	0.789922i	$-0.710121\pi$
$827$	−35.2688			−1.22642			−0.613208	+	0.789922i	$0.710121\pi$
$828$	1.50639	−	2.84134i	0.0523505	−	0.0987435i
$829$	−17.3168	+	16.4034i	−0.601439	+	0.569713i	−0.926648	−	0.375929i	$-0.877324\pi$
$829$	−17.3168	+	16.4034i	−0.601439	+	0.569713i	0.325210	+	0.945642i	$0.394565\pi$
$830$	9.15988	+	13.5098i	0.317944	+	0.468932i
$831$	−5.94187	+	1.30791i	−0.206121	+	0.0453707i
$832$	0.334908	+	1.20623i	0.0116109	+	0.0418185i
$833$	−35.5052	+	26.9904i	−1.23018	+	0.935161i
$834$	−3.76019	+	0.408945i	−0.130205	+	0.0141606i
$835$	−0.390982	+	7.21124i	−0.0135305	+	0.249555i
$836$	−3.46030	+	12.4629i	−0.119677	+	0.431038i
$837$	0.687206	+	1.72476i	0.0237533	+	0.0596163i
$838$	9.83186	+	2.16416i	0.339636	+	0.0747595i
$839$	1.72311	+	31.7808i	0.0594882	+	1.09720i	0.864076	+	0.503361i	$0.167904\pi$
$839$	1.72311	+	31.7808i	0.0594882	+	1.09720i	−0.804588	+	0.593834i	$0.797614\pi$
$840$	−0.120851	−	0.737161i	−0.00416977	−	0.0254345i
$841$	12.3037	−	18.1466i	0.424266	−	0.625746i
$842$	12.6754	−	31.8128i	0.436823	−	1.09634i
$843$	−19.2376	−	14.6241i	−0.662579	−	0.503679i
$844$	19.6076	+	11.7975i	0.674921	+	0.406087i
$845$	22.6174	−	7.62070i	0.778063	−	0.262160i
$846$	−7.21002	−	6.82969i	−0.247886	−	0.234810i
$847$	0.712098	−	4.34361i	0.0244680	−	0.149248i
$848$	−7.40443	−	0.805280i	−0.254269	−	0.0276534i
$849$	−16.4029	+	9.86928i	−0.562945	+	0.338713i
$850$	−2.69775	+	3.17604i	−0.0925322	+	0.108937i
$851$	28.5550	−	13.2110i	0.978853	−	0.452866i
$852$	−1.21482	−	0.562037i	−0.0416191	−	0.0192551i
$853$	−7.47946	−	8.80550i	−0.256092	−	0.301495i	0.619059	−	0.785344i	$-0.287514\pi$
$853$	−7.47946	−	8.80550i	−0.256092	−	0.301495i	−0.875151	+	0.483850i	$0.839238\pi$
$854$	1.81480	+	0.611477i	0.0621011	+	0.0209243i
$855$	−2.62014	−	4.94211i	−0.0896069	−	0.169017i
$856$	4.89952	+	9.24147i	0.167462	+	0.315867i
$857$	6.93983	+	2.33830i	0.237060	+	0.0798749i	0.435324	−	0.900274i	$-0.356634\pi$
$857$	6.93983	+	2.33830i	0.237060	+	0.0798749i	−0.198264	+	0.980149i	$0.563530\pi$
$858$	−3.91204	−	4.60561i	−0.133555	−	0.157233i
$859$	29.1601	+	13.4909i	0.994931	+	0.460304i	0.848659	−	0.528940i	$-0.177410\pi$
$859$	29.1601	+	13.4909i	0.994931	+	0.460304i	0.146272	+	0.989244i	$0.453273\pi$
$860$	0.799355	−	0.369821i	0.0272578	−	0.0126108i
$861$	−2.09391	+	2.46514i	−0.0713603	+	0.0840119i
$862$	31.9222	−	19.2070i	1.08728	−	0.654192i
$863$	−22.0597	−	2.39914i	−0.750922	−	0.0816677i	−0.275350	−	0.961344i	$-0.588794\pi$
$863$	−22.0597	−	2.39914i	−0.750922	−	0.0816677i	−0.475573	+	0.879676i	$0.657759\pi$
$864$	0.161782	−	0.986827i	0.00550394	−	0.0335725i
$865$	29.6030	+	28.0414i	1.00653	+	0.953438i
$866$	15.4303	−	5.19906i	0.524342	−	0.176671i
$867$	21.5249	+	12.9511i	0.731024	+	0.439843i
$868$	−0.528894	−	0.402055i	−0.0179518	−	0.0136466i
$869$	−2.48180	+	6.22885i	−0.0841893	+	0.211299i
$870$	−3.11621	+	4.59607i	−0.105650	+	0.155821i
$871$	−1.83711	−	11.2058i	−0.0622479	−	0.379696i
$872$	−0.117551	−	2.16810i	−0.00398078	−	0.0734212i
$873$	−6.58084	−	1.44855i	−0.222728	−	0.0490260i
$874$	3.18960	+	8.00528i	0.107890	+	0.270783i
$875$	1.12754	−	4.06102i	0.0381177	−	0.137288i
$876$	0.530979	−	9.79332i	0.0179401	−	0.330886i
$877$	13.6424	−	1.48370i	0.460671	−	0.0501010i	0.125158	−	0.992137i	$-0.460056\pi$
$877$	13.6424	−	1.48370i	0.460671	−	0.0501010i	0.335512	+	0.942036i	$0.391091\pi$
$878$	−13.9568	+	10.6097i	−0.471021	+	0.358061i
$879$	3.89199	+	14.0177i	0.131274	+	0.472805i
$880$	9.84123	−	2.16622i	0.331748	−	0.0730232i
$881$	−20.2199	−	29.8221i	−0.681225	−	1.00473i	−0.998410	−	0.0563683i	$-0.982048\pi$
$881$	−20.2199	−	29.8221i	−0.681225	−	1.00473i	0.317185	−	0.948364i	$-0.397262\pi$
$882$	4.98901	−	4.72584i	0.167989	−	0.159127i
$883$	20.6122	−	38.8788i	0.693657	−	1.30838i	−0.246999	−	0.969016i	$-0.579444\pi$
$883$	20.6122	−	38.8788i	0.693657	−	1.30838i	0.940656	−	0.339361i	$-0.110211\pi$
$884$	8.12464			0.273261
$885$	15.4023	−	4.45956i	0.517741	−	0.149906i
$886$	32.4441			1.08998
$887$	12.1521	−	22.9213i	0.408027	−	0.769621i	−0.591294	−	0.806456i	$-0.701383\pi$
$887$	12.1521	−	22.9213i	0.408027	−	0.769621i	0.999321	+	0.0368351i	$0.0117276\pi$
$888$	7.10268	−	6.72802i	0.238350	−	0.225777i
$889$	0.208409	+	0.307380i	0.00698980	+	0.0103092i
$890$	−0.560324	+	0.123337i	−0.0187821	+	0.00413425i
$891$	1.29138	+	4.65113i	0.0432628	+	0.155819i
$892$	−6.96339	+	5.29343i	−0.233151	+	0.177237i
$893$	26.4551	−	2.87717i	0.885287	−	0.0962807i
$894$	−0.974350	+	17.9708i	−0.0325871	+	0.601035i
$895$	3.75832	−	13.5362i	0.125627	−	0.452467i
$896$	0.132448	+	0.332420i	0.00442478	+	0.0111054i
$897$	−3.93182	−	0.865459i	−0.131280	−	0.0288968i
$898$	0.568211	+	10.4800i	0.0189614	+	0.349723i
$899$	0.798975	+	4.87353i	0.0266473	+	0.162541i
$900$	0.360328	−	0.531444i	0.0120109	−	0.0177148i
$901$	−17.8919	+	44.9053i	−0.596066	+	1.49601i
$902$	−34.7345	−	26.4044i	−1.15653	−	0.879172i
$903$	−0.129362	−	0.0778348i	−0.00430491	−	0.00259018i
$904$	−19.2899	+	6.49951i	−0.641571	+	0.216171i
$905$	−13.1796	−	12.4844i	−0.438104	−	0.414994i
$906$	−3.60855	+	22.0112i	−0.119886	+	0.731272i
$907$	−23.2575	−	2.52940i	−0.772252	−	0.0839874i	−0.286495	−	0.958082i	$-0.592490\pi$
$907$	−23.2575	−	2.52940i	−0.772252	−	0.0839874i	−0.485756	+	0.874094i	$0.661456\pi$
$908$	−15.3810	+	9.25442i	−0.510436	+	0.307119i
$909$	−3.46088	+	4.07447i	−0.114790	+	0.135142i
$910$	−0.848713	+	0.392656i	−0.0281345	+	0.0130164i
$911$	24.5818	+	11.3727i	0.814430	+	0.376795i	0.782466	−	0.622694i	$-0.213962\pi$
$911$	24.5818	+	11.3727i	0.814430	+	0.376795i	0.0319643	+	0.999489i	$0.489824\pi$
$912$	1.73470	+	2.04224i	0.0574416	+	0.0676255i
$913$	35.7665	+	12.0511i	1.18370	+	0.398834i
$914$	0.288389	+	0.543959i	0.00953906	+	0.0179926i
$915$	−5.23312	−	9.87072i	−0.173002	−	0.326316i
$916$	22.0295	+	7.42261i	0.727876	+	0.245250i
$917$	2.61341	+	3.07674i	0.0863023	+	0.101603i
$918$	−5.89021	−	2.72510i	−0.194406	−	0.0899418i
$919$	19.8318	−	9.17519i	0.654192	−	0.302662i	−0.0645745	−	0.997913i	$-0.520569\pi$
$919$	19.8318	−	9.17519i	0.654192	−	0.302662i	0.718767	+	0.695251i	$0.244707\pi$
$920$	4.34625	−	5.11680i	0.143292	−	0.168696i
$921$	17.1796	−	10.3366i	0.566086	−	0.340603i
$922$	−31.1711	−	3.39006i	−1.02657	−	0.111646i
$923$	−0.271092	+	1.65359i	−0.00892310	+	0.0544285i
$924$	−1.25401	−	1.18786i	−0.0412538	−	0.0390777i
$925$	5.95290	−	2.00576i	0.195730	−	0.0659491i
$926$	−7.54906	−	4.54212i	−0.248077	−	0.149263i
$927$	−0.300409	−	0.228365i	−0.00986671	−	0.00750048i
$928$	0.984564	−	2.47107i	0.0323199	−	0.0811168i
$929$	11.6906	−	17.2424i	0.383557	−	0.565704i	−0.586080	−	0.810253i	$-0.699330\pi$
$929$	11.6906	−	17.2424i	0.383557	−	0.565704i	0.969637	+	0.244549i	$0.0786399\pi$
$930$	0.627036	+	3.82475i	0.0205613	+	0.125419i
$931$	0.996897	+	18.3867i	0.0326720	+	0.602599i
$932$	−24.6722	−	5.43076i	−0.808165	−	0.177891i
$933$	5.62426	+	14.1158i	0.184130	+	0.462132i
$934$	9.18929	−	33.0968i	0.300683	−	1.08296i
$935$	3.54063	−	65.3032i	0.115791	−	2.13564i
$936$	−1.24452	+	0.135350i	−0.0406785	+	0.00442405i
$937$	−30.7489	+	23.3747i	−1.00452	+	0.763619i	−0.971791	−	0.235845i	$-0.924214\pi$
$937$	−30.7489	+	23.3747i	−1.00452	+	0.763619i	−0.0327328	+	0.999464i	$0.510421\pi$
$938$	−0.868360	−	3.12755i	−0.0283530	−	0.102118i
$939$	29.2821	−	6.44548i	0.955586	−	0.210340i
$940$	−11.6346	−	17.1597i	−0.379477	−	0.559687i
$941$	−9.34267	+	8.84985i	−0.304562	+	0.288497i	−0.824682	−	0.565597i	$-0.808646\pi$
$941$	−9.34267	+	8.84985i	−0.304562	+	0.288497i	0.520120	+	0.854093i	$0.325887\pi$
$942$	0.821452	−	1.54942i	0.0267643	−	0.0504829i
$943$	−29.0686			−0.946604
$944$	−6.74638	+	3.67238i	−0.219576	+	0.119526i
$945$	0.747002			0.0243000
$946$	0.953951	−	1.79934i	0.0310156	−	0.0585017i
$947$	38.8819	−	36.8309i	1.26349	−	1.19684i	0.292893	−	0.956145i	$-0.405382\pi$
$947$	38.8819	−	36.8309i	1.26349	−	1.19684i	0.970600	−	0.240699i	$-0.0773767\pi$
$948$	0.779519	+	1.14970i	0.0253176	+	0.0373406i
$949$	−11.9908	+	2.63938i	−0.389239	+	0.0856780i
$950$	0.460279	+	1.65777i	0.0149334	+	0.0537853i
$951$	3.84228	−	2.92083i	0.124595	−	0.0947143i
$952$	2.30875	−	0.251092i	0.0748270	−	0.00813793i
$953$	0.830511	−	15.3179i	0.0269029	−	0.496194i	−0.953770	−	0.300538i	$-0.902834\pi$
$953$	0.830511	−	15.3179i	0.0269029	−	0.496194i	0.980673	−	0.195656i	$-0.0626836\pi$
$954$	1.99258	−	7.17661i	0.0645120	−	0.232351i
$955$	−14.2074	−	35.6578i	−0.459740	−	1.15386i
$956$	2.45557	+	0.540511i	0.0794187	+	0.0174814i
$957$	0.695142	+	12.8211i	0.0224707	+	0.414449i
$958$	2.19450	+	13.3859i	0.0709010	+	0.432477i
$959$	3.29495	−	4.85968i	0.106399	−	0.156927i
$960$	0.772687	−	1.93930i	0.0249384	−	0.0625905i
$961$	−21.9347	−	16.6743i	−0.707572	−	0.537882i
$962$	−10.4943	−	6.31420i	−0.338349	−	0.203578i
$963$	−9.91239	+	3.33987i	−0.319422	+	0.107626i
$964$	−0.717601	−	0.679748i	−0.0231124	−	0.0218932i
$965$	−0.730050	+	4.45311i	−0.0235011	+	0.143351i
$966$	−1.14404	−	0.124422i	−0.0368088	−	0.00400320i
$967$	16.7440	−	10.0746i	0.538452	−	0.323976i	−0.220218	−	0.975451i	$-0.570677\pi$
$967$	16.7440	−	10.0746i	0.538452	−	0.323976i	0.758670	+	0.651475i	$0.225849\pi$
$968$	7.96326	−	9.37508i	0.255949	−	0.301326i
$969$	15.7831	−	7.30202i	0.507025	−	0.234575i
$970$	−12.7667	−	5.90649i	−0.409913	−	0.189646i
$971$	−26.2175	−	30.8656i	−0.841360	−	0.990526i	−0.999995	−	0.00318833i	$-0.998985\pi$
$971$	−26.2175	−	30.8656i	−0.841360	−	0.990526i	0.158635	−	0.987337i	$-0.449291\pi$
$972$	0.947653	+	0.319302i	0.0303960	+	0.0102416i
$973$	0.633971	+	1.19580i	0.0203242	+	0.0383355i
$974$	17.1783	+	32.4017i	0.550428	+	1.03822i
$975$	−0.761721	−	0.256654i	−0.0243946	−	0.00821950i
$976$	3.46466	+	4.07891i	0.110901	+	0.130563i
$977$	13.5924	+	6.28854i	0.434861	+	0.201188i	0.625092	−	0.780551i	$-0.285062\pi$
$977$	13.5924	+	6.28854i	0.434861	+	0.201188i	−0.190231	+	0.981739i	$0.560924\pi$
$978$	−5.52443	+	2.55587i	−0.176652	+	0.0817278i
$979$	−0.858857	+	1.01113i	−0.0274492	+	0.0323157i
$980$	12.2922	−	7.39595i	0.392659	−	0.236255i
$981$	2.15856	+	0.234757i	0.0689175	+	0.00749523i
$982$	2.10541	−	12.8425i	0.0671864	−	0.409819i
$983$	−16.6783	−	15.7985i	−0.531954	−	0.503893i	0.373909	−	0.927466i	$-0.378017\pi$
$983$	−16.6783	−	15.7985i	−0.531954	−	0.503893i	−0.905862	+	0.423572i	$0.860776\pi$
$984$	−8.56569	+	2.88612i	−0.273064	+	0.0920060i
$985$	−44.9697	−	27.0574i	−1.43285	−	0.862120i
$986$	−13.7433	−	10.4474i	−0.437677	−	0.332713i
$987$	−1.31537	+	3.30134i	−0.0418688	+	0.105083i
$988$	1.88245	−	2.77641i	0.0598888	−	0.0883294i
$989$	−0.219512	−	1.33897i	−0.00698009	−	0.0425767i
$990$	0.545548	+	10.0620i	0.0173387	+	0.319793i
$991$	−5.05985	−	1.11376i	−0.160731	−	0.0353796i	0.133876	−	0.990998i	$-0.457258\pi$
$991$	−5.05985	−	1.11376i	−0.160731	−	0.0353796i	−0.294607	+	0.955618i	$0.595189\pi$
$992$	−0.687206	−	1.72476i	−0.0218188	−	0.0547611i
$993$	4.39796	−	15.8400i	0.139565	−	0.502668i
$994$	−0.0259312	+	0.478272i	−0.000822486	+	0.0151699i
$995$	16.6026	−	1.80564i	0.526337	−	0.0572426i
$996$	6.22453	−	4.73176i	0.197232	−	0.149932i
$997$	2.00862	+	7.23438i	0.0636135	+	0.229115i	0.988523	−	0.151073i	$-0.0482729\pi$
$997$	2.00862	+	7.23438i	0.0636135	+	0.229115i	−0.924909	+	0.380188i	$0.875859\pi$
$998$	−7.81791	+	1.72085i	−0.247472	+	0.0544726i
$999$	5.49030	+	8.09758i	0.173705	+	0.256196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.19.3	✓	84
59.28	even	29	inner	354.2.e.c.205.3	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.19.3	✓	84	1.1	even	1	trivial
354.2.e.c.205.3	yes	84	59.28	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(2.03876 - 0.448764i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-0.284870 + 0.216552i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(2.03876 - 0.448764i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-0.284870 + 0.216552i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.558482 - 2.01147i) q^{10} +(-1.78668 - 4.48424i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(0.0677744 + 1.25003i) q^{13} +(0.0578912 + 0.353121i) q^{14} +(1.17151 - 1.72785i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(5.16669 + 3.92761i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(2.53928 - 0.855582i) q^{19} +(-1.51556 - 1.43562i) q^{20} +(-0.0578912 + 0.353121i) q^{21} +(-4.79878 - 0.521898i) q^{22} +(-2.75562 + 1.65800i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(-0.582738 + 0.269603i) q^{25} +(1.13616 + 0.525643i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(0.339103 + 0.114257i) q^{28} +(-1.24596 - 2.35013i) q^{29} +(-0.977832 - 1.84439i) q^{30} +(-1.75943 - 0.592822i) q^{31} +(0.647386 + 0.762162i) q^{32} +(-4.38093 - 2.02684i) q^{33} +(5.89021 - 2.72510i) q^{34} +(-0.483599 + 0.569337i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-9.72602 - 1.05777i) q^{37} +(0.433502 - 2.64424i) q^{38} +(0.908845 + 0.860904i) q^{39} +(-1.97829 + 0.666562i) q^{40} +(7.74500 + 4.66001i) q^{41} +(0.284870 + 0.216552i) q^{42} +(-0.156164 + 0.391943i) q^{43} +(-2.70889 + 3.99532i) q^{44} +(-0.337730 - 2.06006i) q^{45} +(0.174109 + 3.21125i) q^{46} +(9.69903 + 2.13492i) q^{47} +(0.370138 + 0.928977i) q^{48} +(-1.83844 + 6.62147i) q^{49} +(-0.0347616 + 0.641140i) q^{50} +(6.45201 - 0.701698i) q^{51} +(0.996598 - 0.757594i) q^{52} +(1.99258 + 7.17661i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(-5.65498 - 8.34047i) q^{55} +(0.259786 - 0.246083i) q^{56} +(1.25512 - 2.36741i) q^{57} -2.65999 q^{58} +(5.90865 + 4.90794i) q^{59} -2.08756 q^{60} +(2.50681 - 4.72835i) q^{61} +(-1.34790 + 1.27680i) q^{62} +(0.200812 + 0.296176i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.699142 + 2.51808i) q^{65} +(-3.84280 + 2.92122i) q^{66} +(-9.01767 + 0.980731i) q^{67} +(0.351364 - 6.48053i) q^{68} +(-0.860362 + 3.09874i) q^{69} +(0.276494 + 0.693947i) q^{70} +(1.30724 + 0.287746i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(1.58671 + 9.67851i) q^{73} +(-5.49030 + 8.09758i) q^{74} +(-0.237659 + 0.596479i) q^{75} +(-2.13316 - 1.62159i) q^{76} +(1.48004 + 0.890513i) q^{77} +(1.18633 - 0.399721i) q^{78} +(-1.00845 - 0.955251i) q^{79} +(-0.337730 + 2.06006i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(7.74500 - 4.66001i) q^{82} +(-5.06181 + 5.95923i) q^{83} +(0.324762 - 0.150251i) q^{84} +(12.2962 + 5.68882i) q^{85} +(0.273137 + 0.321562i) q^{86} +(-2.52075 - 0.849339i) q^{87} +(2.26104 + 4.26478i) q^{88} +(-0.128736 - 0.242821i) q^{89} +(-1.97829 - 0.666562i) q^{90} +(-0.290003 - 0.341417i) q^{91} +(2.91873 + 1.35035i) q^{92} +(-1.68502 + 0.779574i) q^{93} +(6.42933 - 7.56920i) q^{94} +(4.79301 - 2.88386i) q^{95} +(0.994138 + 0.108119i) q^{96} +(1.09015 - 6.64961i) q^{97} +(4.98901 + 4.72584i) q^{98} +(-4.57439 + 1.54129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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