LMFDB - Embedded newform 690.2.q.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(-1.62851 - 0.589888i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.384191 - 1.68890i) q^{6} +(1.12640 - 0.976034i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.30406 + 1.92127i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(-1.62851 - 0.589888i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.384191 - 1.68890i) q^{6} +(1.12640 - 0.976034i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.30406 + 1.92127i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-2.69175 - 1.72988i) q^{11} +(1.21309 - 1.23629i) q^{12} +(-0.301686 + 0.348165i) q^{13} +(1.43007 + 0.419907i) q^{14} +(1.72873 + 0.107190i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.993222 - 2.17485i) q^{17} +(-0.370607 + 2.97702i) q^{18} +(-2.25092 - 1.02796i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.41011 + 0.925025i) q^{21} -3.19969i q^{22} +(1.51739 - 4.54945i) q^{23} +(1.69588 + 0.352123i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.455999 - 0.0655627i) q^{26} +(-2.61885 - 4.48794i) q^{27} +(0.419907 + 1.43007i) q^{28} +(4.48945 - 2.05026i) q^{29} +(0.844448 + 1.51225i) q^{30} +(-0.946047 - 6.57990i) q^{31} +(0.281733 - 0.959493i) q^{32} +(3.36310 + 4.40496i) q^{33} +(1.29263 - 2.01137i) q^{34} +(-0.805795 + 1.25384i) q^{35} +(-2.70479 + 1.29772i) q^{36} +(3.37397 - 11.4907i) q^{37} +(-0.352164 - 2.44935i) q^{38} +(0.696676 - 0.389027i) q^{39} +(0.909632 - 0.415415i) q^{40} +(0.984332 + 3.35233i) q^{41} +(-2.08118 - 1.52740i) q^{42} +(3.53652 + 0.508475i) q^{43} +(2.69175 - 1.72988i) q^{44} +(-2.75202 - 1.19432i) q^{45} +(4.64761 - 1.18311i) q^{46} -2.26918i q^{47} +(0.620637 + 1.61704i) q^{48} +(-0.680062 + 4.72993i) q^{49} +(0.909632 + 0.415415i) q^{50} +(0.334548 + 4.12765i) q^{51} +(-0.191377 - 0.419056i) q^{52} +(-4.51643 - 5.21223i) q^{53} +(2.35964 - 4.62948i) q^{54} +(3.07008 + 0.901458i) q^{55} +(-0.976034 + 1.12640i) q^{56} +(3.05926 + 3.00183i) q^{57} +(4.15197 + 2.66831i) q^{58} +(-4.54854 - 3.94133i) q^{59} +(-0.815645 + 1.52798i) q^{60} +(-6.06637 + 0.872212i) q^{61} +(5.02389 - 4.35323i) q^{62} +(4.47053 - 0.0847166i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.191377 - 0.419056i) q^{65} +(-1.88746 + 5.21072i) q^{66} +(-3.93607 - 6.12464i) q^{67} +2.39092 q^{68} +(-5.15475 + 6.51372i) q^{69} -1.49044 q^{70} +(3.37290 + 5.24833i) q^{71} +(-2.55404 - 1.57381i) q^{72} +(-0.392136 + 0.858657i) q^{73} +(11.4907 - 3.37397i) q^{74} +(-1.68890 + 0.384191i) q^{75} +(1.87013 - 1.62048i) q^{76} +(-4.72043 + 0.678695i) q^{77} +(0.703922 + 0.375757i) q^{78} +(-6.33721 - 5.49123i) q^{79} +(0.841254 + 0.540641i) q^{80} +(1.61742 + 8.85347i) q^{81} +(-2.28799 + 2.64048i) q^{82} +(7.60990 + 2.23447i) q^{83} +(0.159761 - 2.57658i) q^{84} +(1.56572 + 1.80693i) q^{85} +(1.48423 + 3.25001i) q^{86} +(-8.52052 + 0.690592i) q^{87} +(2.91054 + 1.32920i) q^{88} +(-1.46103 + 10.1617i) q^{89} +(-0.483129 - 2.96084i) q^{90} +0.686630i q^{91} +(3.50798 + 3.27018i) q^{92} +(-2.34076 + 11.2735i) q^{93} +(1.90895 - 1.22681i) q^{94} +(2.44935 + 0.352164i) q^{95} +(-1.02480 + 1.39635i) q^{96} +(0.334672 + 1.13979i) q^{97} +(-4.34674 + 1.98509i) q^{98} +(-2.87839 - 9.15736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	−1.62851	−	0.589888i	−0.940218	−	0.340572i
$3$	−1.62851	−	0.589888i	−0.940218	−	0.340572i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.384191	−	1.68890i	−0.156845	−	0.689492i
$7$	1.12640	−	0.976034i	0.425740	−	0.368906i	−0.415477	−	0.909604i	$-0.636385\pi$
$7$	1.12640	−	0.976034i	0.425740	−	0.368906i	0.841217	+	0.540698i	$0.181840\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	2.30406	+	1.92127i	0.768021	+	0.640424i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	−2.69175	−	1.72988i	−0.811594	−	0.521580i	0.0677862	−	0.997700i	$-0.478406\pi$
$11$	−2.69175	−	1.72988i	−0.811594	−	0.521580i	−0.879380	+	0.476120i	$0.842043\pi$
$12$	1.21309	−	1.23629i	0.350188	−	0.356887i
$13$	−0.301686	+	0.348165i	−0.0836727	+	0.0965635i	−0.796042	−	0.605241i	$-0.793077\pi$
$13$	−0.301686	+	0.348165i	−0.0836727	+	0.0965635i	0.712369	+	0.701805i	$0.247622\pi$
$14$	1.43007	+	0.419907i	0.382203	+	0.112225i
$15$	1.72873	+	0.107190i	0.446356	+	0.0276764i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.993222	−	2.17485i	−0.240892	−	0.527479i	0.750112	−	0.661310i	$-0.229999\pi$
$17$	−0.993222	−	2.17485i	−0.240892	−	0.527479i	−0.991004	+	0.133831i	$0.957272\pi$
$18$	−0.370607	+	2.97702i	−0.0873528	+	0.701690i
$19$	−2.25092	−	1.02796i	−0.516397	−	0.235831i	0.140130	−	0.990133i	$-0.455248\pi$
$19$	−2.25092	−	1.02796i	−0.516397	−	0.235831i	−0.656527	+	0.754303i	$0.727975\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−2.41011	+	0.925025i	−0.525928	+	0.201857i
$22$		−	3.19969i		−	0.682177i
$23$	1.51739	−	4.54945i	0.316398	−	0.948626i
$23$	1.51739	−	4.54945i	0.316398	−	0.948626i
$24$	1.69588	+	0.352123i	0.346170	+	0.0718769i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.455999	−	0.0655627i	−0.0894287	−	0.0128579i
$27$	−2.61885	−	4.48794i	−0.503997	−	0.863705i
$28$	0.419907	+	1.43007i	0.0793549	+	0.270258i
$29$	4.48945	−	2.05026i	0.833670	−	0.380724i	0.0476034	−	0.998866i	$-0.484842\pi$
$29$	4.48945	−	2.05026i	0.833670	−	0.380724i	0.786066	+	0.618142i	$0.212114\pi$
$30$	0.844448	+	1.51225i	0.154174	+	0.276098i
$31$	−0.946047	−	6.57990i	−0.169915	−	1.18179i	−0.879056	−	0.476718i	$-0.841826\pi$
$31$	−0.946047	−	6.57990i	−0.169915	−	1.18179i	0.709141	−	0.705067i	$-0.249083\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	3.36310	+	4.40496i	0.585440	+	0.766805i
$34$	1.29263	−	2.01137i	0.221684	−	0.344947i
$35$	−0.805795	+	1.25384i	−0.136204	+	0.211938i
$36$	−2.70479	+	1.29772i	−0.450799	+	0.216287i
$37$	3.37397	−	11.4907i	0.554677	−	1.88906i	0.108539	−	0.994092i	$-0.465383\pi$
$37$	3.37397	−	11.4907i	0.554677	−	1.88906i	0.446138	−	0.894964i	$-0.352799\pi$
$38$	−0.352164	−	2.44935i	−0.0571285	−	0.397338i
$39$	0.696676	−	0.389027i	0.111557	−	0.0622942i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	0.984332	+	3.35233i	0.153727	+	0.523545i	0.999957	−	0.00927203i	$-0.00295142\pi$
$41$	0.984332	+	3.35233i	0.153727	+	0.523545i	−0.846230	+	0.532817i	$0.821133\pi$
$42$	−2.08118	−	1.52740i	−0.321133	−	0.235683i
$43$	3.53652	+	0.508475i	0.539314	+	0.0775417i	0.406589	−	0.913611i	$-0.366718\pi$
$43$	3.53652	+	0.508475i	0.539314	+	0.0775417i	0.132725	+	0.991153i	$0.457627\pi$
$44$	2.69175	−	1.72988i	0.405797	−	0.260790i
$45$	−2.75202	−	1.19432i	−0.410247	−	0.178038i
$46$	4.64761	−	1.18311i	0.685252	−	0.174440i
$47$		−	2.26918i		−	0.330993i	−0.986210	−	0.165497i	$-0.947077\pi$
$47$		−	2.26918i		−	0.330993i	0.986210	−	0.165497i	$-0.0529227\pi$
$48$	0.620637	+	1.61704i	0.0895812	+	0.233399i
$49$	−0.680062	+	4.72993i	−0.0971517	+	0.675705i
$50$	0.909632	+	0.415415i	0.128641	+	0.0587486i
$51$	0.334548	+	4.12765i	0.0468461	+	0.577987i
$52$	−0.191377	−	0.419056i	−0.0265392	−	0.0581127i
$53$	−4.51643	−	5.21223i	−0.620379	−	0.715956i	0.355400	−	0.934714i	$-0.384345\pi$
$53$	−4.51643	−	5.21223i	−0.620379	−	0.715956i	−0.975779	+	0.218759i	$0.929799\pi$
$54$	2.35964	−	4.62948i	0.321107	−	0.629992i
$55$	3.07008	+	0.901458i	0.413970	+	0.121553i
$56$	−0.976034	+	1.12640i	−0.130428	+	0.150522i
$57$	3.05926	+	3.00183i	0.405208	+	0.397603i
$58$	4.15197	+	2.66831i	0.545180	+	0.350366i
$59$	−4.54854	−	3.94133i	−0.592169	−	0.513118i	0.306427	−	0.951894i	$-0.400866\pi$
$59$	−4.54854	−	3.94133i	−0.592169	−	0.513118i	−0.898596	+	0.438777i	$0.855412\pi$
$60$	−0.815645	+	1.52798i	−0.105299	+	0.197261i
$61$	−6.06637	+	0.872212i	−0.776718	+	0.111675i	−0.519263	−	0.854615i	$-0.673793\pi$
$61$	−6.06637	+	0.872212i	−0.776718	+	0.111675i	−0.257456	+	0.966290i	$0.582884\pi$
$62$	5.02389	−	4.35323i	0.638035	−	0.552861i
$63$	4.47053	−	0.0847166i	0.563234	−	0.0106733i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	0.191377	−	0.419056i	0.0237373	−	0.0519775i
$66$	−1.88746	+	5.21072i	−0.232330	+	0.641395i
$67$	−3.93607	−	6.12464i	−0.480867	−	0.748244i	0.513052	−	0.858358i	$-0.328515\pi$
$67$	−3.93607	−	6.12464i	−0.480867	−	0.748244i	−0.993919	+	0.110113i	$0.964879\pi$
$68$	2.39092			0.289941
$69$	−5.15475	+	6.51372i	−0.620559	+	0.784160i
$70$	−1.49044			−0.178142
$71$	3.37290	+	5.24833i	0.400289	+	0.622863i	0.981629	−	0.190798i	$-0.0611077\pi$
$71$	3.37290	+	5.24833i	0.400289	+	0.622863i	−0.581340	+	0.813661i	$0.697471\pi$
$72$	−2.55404	−	1.57381i	−0.300996	−	0.185476i
$73$	−0.392136	+	0.858657i	−0.0458960	+	0.100498i	−0.931191	−	0.364532i	$-0.881229\pi$
$73$	−0.392136	+	0.858657i	−0.0458960	+	0.100498i	0.885295	+	0.465030i	$0.153956\pi$
$74$	11.4907	−	3.37397i	1.33576	−	0.392216i
$75$	−1.68890	+	0.384191i	−0.195018	+	0.0443626i
$76$	1.87013	−	1.62048i	0.214519	−	0.185882i
$77$	−4.72043	+	0.678695i	−0.537942	+	0.0773444i
$78$	0.703922	+	0.375757i	0.0797035	+	0.0425462i
$79$	−6.33721	−	5.49123i	−0.712992	−	0.617811i	0.220929	−	0.975290i	$-0.429091\pi$
$79$	−6.33721	−	5.49123i	−0.712992	−	0.617811i	−0.933921	+	0.357479i	$0.883637\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	1.61742	+	8.85347i	0.179713	+	0.983719i
$82$	−2.28799	+	2.64048i	−0.252666	+	0.291592i
$83$	7.60990	+	2.23447i	0.835296	+	0.245265i	0.671290	−	0.741195i	$-0.265740\pi$
$83$	7.60990	+	2.23447i	0.835296	+	0.245265i	0.164005	+	0.986459i	$0.447559\pi$
$84$	0.159761	−	2.57658i	0.0174314	−	0.281128i
$85$	1.56572	+	1.80693i	0.169826	+	0.195989i
$86$	1.48423	+	3.25001i	0.160049	+	0.350458i
$87$	−8.52052	+	0.690592i	−0.913496	+	0.0740393i
$88$	2.91054	+	1.32920i	0.310265	+	0.141693i
$89$	−1.46103	+	10.1617i	−0.154869	+	1.07714i	0.753042	+	0.657972i	$0.228586\pi$
$89$	−1.46103	+	10.1617i	−0.154869	+	1.07714i	−0.907911	+	0.419163i	$0.862324\pi$
$90$	−0.483129	−	2.96084i	−0.0509263	−	0.312100i
$91$			0.686630i			0.0719783i
$92$	3.50798	+	3.27018i	0.365732	+	0.340940i
$93$	−2.34076	+	11.2735i	−0.242726	+	1.16900i
$94$	1.90895	−	1.22681i	0.196893	−	0.126536i
$95$	2.44935	+	0.352164i	0.251298	+	0.0361313i
$96$	−1.02480	+	1.39635i	−0.104593	+	0.142514i
$97$	0.334672	+	1.13979i	0.0339808	+	0.115728i	0.974737	−	0.223356i	$-0.0717012\pi$
$97$	0.334672	+	1.13979i	0.0339808	+	0.115728i	−0.940756	+	0.339084i	$0.889883\pi$
$98$	−4.34674	+	1.98509i	−0.439087	+	0.200525i
$99$	−2.87839	−	9.15736i	−0.289289	−	0.920349i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−3.16884	+	10.7921i	−0.315311	+	1.07385i	0.637541	+	0.770416i	$0.279952\pi$
$101$	−3.16884	+	10.7921i	−0.315311	+	1.07385i	−0.952852	+	0.303435i	$0.901867\pi$
$102$	−3.29153	+	2.51302i	−0.325910	+	0.248826i
$103$	−8.49723	+	13.2219i	−0.837257	+	1.30280i	0.113713	+	0.993514i	$0.463726\pi$
$103$	−8.49723	+	13.2219i	−0.837257	+	1.30280i	−0.950970	+	0.309283i	$0.899911\pi$
$104$	0.249067	−	0.387555i	0.0244230	−	0.0380029i
$105$	2.05187	−	1.56656i	0.200242	−	0.152881i
$106$	1.94305	−	6.61741i	0.188725	−	0.642739i
$107$	−2.59085	−	18.0197i	−0.250467	−	1.74203i	−0.595421	−	0.803414i	$-0.703015\pi$
$107$	−2.59085	−	18.0197i	−0.250467	−	1.74203i	0.344954	−	0.938619i	$-0.387894\pi$
$108$	5.17029	−	0.517826i	0.497511	−	0.0498279i
$109$	−14.2659	+	6.51502i	−1.36643	+	0.624025i	−0.957471	−	0.288530i	$-0.906834\pi$
$109$	−14.2659	+	6.51502i	−1.36643	+	0.624025i	−0.408954	+	0.912555i	$0.634106\pi$
$110$	0.901458	+	3.07008i	0.0859506	+	0.292721i
$111$	−12.2727	+	16.7224i	−1.16488	+	1.58722i
$112$	−1.47527	−	0.212112i	−0.139400	−	0.0200427i
$113$	6.60972	−	4.24781i	0.621790	−	0.399600i	−0.191472	−	0.981498i	$-0.561326\pi$
$113$	6.60972	−	4.24781i	0.621790	−	0.399600i	0.813262	+	0.581898i	$0.197690\pi$
$114$	−0.871344	+	4.19652i	−0.0816088	+	0.393041i
$115$	−0.174199	+	4.79267i	−0.0162441	+	0.446918i
$116$			4.93546i			0.458246i
$117$	−1.36402	+	0.222572i	−0.126104	+	0.0205768i
$118$	0.856533	−	5.95732i	0.0788503	−	0.548416i
$119$	−3.24150	−	1.48034i	−0.297148	−	0.135703i
$120$	−1.72639	+	0.139925i	−0.157597	+	0.0127733i
$121$	−0.316531	−	0.693107i	−0.0287756	−	0.0630097i
$122$	−4.01348	−	4.63180i	−0.363363	−	0.419343i
$123$	0.374507	−	6.03993i	0.0337682	−	0.544602i
$124$	6.37829	+	1.87283i	0.572787	+	0.168186i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	2.48822	+	3.71505i	0.221668	+	0.330963i
$127$	10.5887	+	6.80493i	0.939593	+	0.603840i	0.918279	−	0.395933i	$-0.129579\pi$
$127$	10.5887	+	6.80493i	0.939593	+	0.603840i	0.0213139	+	0.999773i	$0.493215\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−5.45930	−	2.91420i	−0.480664	−	0.256581i
$130$	0.455999	−	0.0655627i	0.0399937	−	0.00575023i
$131$	2.50812	−	2.17330i	0.219135	−	0.189882i	−0.538374	−	0.842706i	$-0.680961\pi$
$131$	2.50812	−	2.17330i	0.219135	−	0.189882i	0.757510	+	0.652824i	$0.226416\pi$
$132$	−5.40397	+	1.22929i	−0.470356	+	0.106996i
$133$	−3.53877	+	1.03908i	−0.306850	+	0.0900994i
$134$	3.02438	−	6.62246i	0.261266	−	0.572094i
$135$	3.77716	+	3.56834i	0.325087	+	0.307114i
$136$	1.29263	+	2.01137i	0.110842	+	0.172473i
$137$	3.06689			0.262022			0.131011	−	0.991381i	$-0.458178\pi$
$137$	3.06689			0.262022			0.131011	+	0.991381i	$0.458178\pi$
$138$	−8.26656	−	0.814870i	−0.703696	−	0.0693664i
$139$	−3.86632			−0.327937			−0.163969	−	0.986466i	$-0.552430\pi$
$139$	−3.86632			−0.327937			−0.163969	+	0.986466i	$0.552430\pi$
$140$	−0.805795	−	1.25384i	−0.0681021	−	0.105969i
$141$	−1.33856	+	3.69537i	−0.112727	+	0.311206i
$142$	−2.59165	+	5.67493i	−0.217487	+	0.476229i
$143$	1.41435	−	0.415291i	0.118274	−	0.0347283i
$144$	−0.0568398	−	2.99946i	−0.00473665	−	0.249955i
$145$	−3.72997	+	3.23204i	−0.309757	+	0.268406i
$146$	−0.934353	+	0.134340i	−0.0773276	+	0.0111180i
$147$	3.89762	−	7.30157i	0.321470	−	0.602223i
$148$	9.05069	+	7.84247i	0.743962	+	0.644647i
$149$	6.52444	+	4.19300i	0.534503	+	0.343504i	0.779886	−	0.625922i	$-0.215277\pi$
$149$	6.52444	+	4.19300i	0.534503	+	0.343504i	−0.245383	+	0.969426i	$0.578914\pi$
$150$	−1.23629	−	1.21309i	−0.100943	−	0.0990481i
$151$	7.57909	−	8.74674i	0.616778	−	0.711800i	−0.358314	−	0.933601i	$-0.616648\pi$
$151$	7.57909	−	8.74674i	0.616778	−	0.711800i	0.975092	+	0.221802i	$0.0711937\pi$
$152$	2.37430	+	0.697159i	0.192582	+	0.0565470i
$153$	1.89004	−	6.91925i	0.152801	−	0.559388i
$154$	−3.12301	−	3.60414i	−0.251659	−	0.290430i
$155$	2.76150	+	6.04684i	0.221809	+	0.485694i
$156$	0.0644616	+	0.795327i	0.00516106	+	0.0636771i
$157$	2.86966	+	1.31053i	0.229024	+	0.104592i	0.526622	−	0.850100i	$-0.323458\pi$
$157$	2.86966	+	1.31053i	0.229024	+	0.104592i	−0.297598	+	0.954691i	$0.596186\pi$
$158$	1.19336	−	8.29999i	0.0949384	−	0.660311i
$159$	4.28039	+	11.1523i	0.339457	+	0.884438i
$160$			1.00000i			0.0790569i
$161$	−2.73122	−	6.60554i	−0.215251	−	0.520590i
$162$	−6.57357	+	6.14721i	−0.516468	+	0.482970i
$163$	−17.9461	+	11.5333i	−1.40565	+	0.903356i	−0.999943	−	0.0106483i	$-0.996610\pi$
$163$	−17.9461	+	11.5333i	−1.40565	+	0.903356i	−0.405705	+	0.914004i	$0.632974\pi$
$164$	−3.45829	−	0.497227i	−0.270047	−	0.0388269i
$165$	−4.46789	−	3.27903i	−0.347825	−	0.255273i
$166$	2.23447	+	7.60990i	0.173428	+	0.590643i
$167$	22.4942	−	10.2727i	1.74065	−	0.794929i	0.749530	−	0.661971i	$-0.230280\pi$
$167$	22.4942	−	10.2727i	1.74065	−	0.794929i	0.991122	−	0.132958i	$-0.0424477\pi$
$168$	2.25393	−	1.25860i	0.173894	−	0.0971034i
$169$	1.81989	+	12.6576i	0.139991	+	0.973662i
$170$	−0.673599	+	2.29407i	−0.0516627	+	0.175947i
$171$	−3.21127	−	6.69312i	−0.245572	−	0.511836i
$172$	−1.93165	+	3.00570i	−0.147287	+	0.229183i
$173$	4.21538	−	6.55927i	0.320490	−	0.498692i	−0.643207	−	0.765693i	$-0.722396\pi$
$173$	4.21538	−	6.55927i	0.320490	−	0.498692i	0.963696	+	0.267001i	$0.0860327\pi$
$174$	−5.18750	−	6.79456i	−0.393264	−	0.515094i
$175$	0.419907	−	1.43007i	0.0317420	−	0.108103i
$176$	0.455364	+	3.16712i	0.0343243	+	0.238731i
$177$	5.08238	+	9.10161i	0.382015	+	0.684119i
$178$	−9.33844	+	4.26472i	−0.699945	+	0.319654i
$179$	−0.471157	−	1.60461i	−0.0352159	−	0.119934i	0.940009	−	0.341149i	$-0.110816\pi$
$179$	−0.471157	−	1.60461i	−0.0352159	−	0.119934i	−0.975225	+	0.221215i	$0.928998\pi$
$180$	2.22962	−	2.00719i	0.166186	−	0.149607i
$181$	−5.01373	−	0.720865i	−0.372667	−	0.0535815i	−0.0465633	−	0.998915i	$-0.514827\pi$
$181$	−5.01373	−	0.720865i	−0.372667	−	0.0535815i	−0.326104	+	0.945334i	$0.605736\pi$
$182$	−0.577630	+	0.371220i	−0.0428168	+	0.0275167i
$183$	10.3936	+	2.15808i	0.768318	+	0.159530i
$184$	−0.854493	+	4.71909i	−0.0629941	+	0.347896i
$185$			11.9758i			0.880477i
$186$	−10.7494	+	4.12572i	−0.788181	+	0.302513i
$187$	−1.08874	+	7.57233i	−0.0796163	+	0.553744i
$188$	2.06411	+	0.942650i	0.150541	+	0.0687498i
$189$	−7.33026	−	2.49915i	−0.533198	−	0.181787i
$190$	1.02796	+	2.25092i	0.0745762	+	0.163299i
$191$	1.59327	+	1.83873i	0.115285	+	0.133046i	0.810459	−	0.585796i	$-0.199218\pi$
$191$	1.59327	+	1.83873i	0.115285	+	0.133046i	−0.695174	+	0.718842i	$0.744673\pi$
$192$	−1.72873	−	0.107190i	−0.124760	−	0.00773580i
$193$	10.8065	+	3.17308i	0.777870	+	0.228403i	0.646484	−	0.762928i	$-0.276239\pi$
$193$	10.8065	+	3.17308i	0.777870	+	0.228403i	0.131387	+	0.991331i	$0.458057\pi$
$194$	−0.777914	+	0.897760i	−0.0558510	+	0.0644554i
$195$	−0.558854	+	0.569545i	−0.0400204	+	0.0407860i
$196$	−4.01999	−	2.58349i	−0.287142	−	0.184535i
$197$	−15.4010	−	13.3450i	−1.09728	−	0.950795i	−0.0982606	−	0.995161i	$-0.531328\pi$
$197$	−15.4010	−	13.3450i	−1.09728	−	0.950795i	−0.999015	+	0.0443657i	$0.985873\pi$
$198$	6.14748	−	7.37230i	0.436883	−	0.523926i
$199$	1.63691	−	0.235352i	0.116037	−	0.0166836i	−0.0840515	−	0.996461i	$-0.526786\pi$
$199$	1.63691	−	0.235352i	0.116037	−	0.0166836i	0.200089	+	0.979778i	$0.435877\pi$
$200$	−0.755750	+	0.654861i	−0.0534396	+	0.0463056i
$201$	2.79706	+	12.2959i	0.197289	+	0.867283i
$202$	−10.7921	+	3.16884i	−0.759327	+	0.222959i
$203$	3.05580	−	6.69128i	0.214475	−	0.469636i
$204$	−3.89362	−	1.41037i	−0.272608	−	0.0987459i
$205$	−1.88892	−	2.93922i	−0.131928	−	0.205284i
$206$	−15.7170			−1.09505
$207$	12.2369	−	7.56690i	0.850524	−	0.525936i
$208$	0.460688			0.0319429
$209$	4.28067	+	6.66085i	0.296100	+	0.460741i
$210$	2.42720	+	0.879196i	0.167493	+	0.0606703i
$211$	1.39424	−	3.05296i	0.0959833	−	0.210174i	−0.855550	−	0.517721i	$-0.826781\pi$
$211$	1.39424	−	3.05296i	0.0959833	−	0.210174i	0.951533	+	0.307546i	$0.0995080\pi$
$212$	6.61741	−	1.94305i	0.454485	−	0.133449i
$213$	−2.39686	−	10.5366i	−0.164230	−	0.721954i
$214$	13.7584	−	11.9218i	0.940508	−	0.814955i
$215$	−3.53652	+	0.508475i	−0.241189	+	0.0346777i
$216$	3.23089	+	4.06956i	0.219834	+	0.276899i
$217$	−7.48784	−	6.48825i	−0.508307	−	0.440451i
$218$	−13.1935	−	8.47895i	−0.893577	−	0.574267i
$219$	1.14511	−	1.16701i	0.0773792	−	0.0788594i
$220$	−2.09535	+	2.41817i	−0.141269	+	0.163033i
$221$	1.05685	+	0.310319i	0.0710913	+	0.0208743i
$222$	−20.7029	−	1.28369i	−1.38949	−	0.0861556i
$223$	−8.85527	−	10.2195i	−0.592992	−	0.684350i	0.377354	−	0.926069i	$-0.376834\pi$
$223$	−8.85527	−	10.2195i	−0.592992	−	0.684350i	−0.970346	+	0.241719i	$0.922289\pi$
$224$	−0.619153	−	1.35576i	−0.0413689	−	0.0905853i
$225$	2.97702	+	0.370607i	0.198468	+	0.0247071i
$226$	7.14697	+	3.26391i	0.475410	+	0.217112i
$227$	1.94294	−	13.5134i	0.128957	−	0.896917i	−0.817922	−	0.575328i	$-0.804874\pi$
$227$	1.94294	−	13.5134i	0.128957	−	0.896917i	0.946880	−	0.321588i	$-0.104217\pi$
$228$	−4.00142	+	1.53579i	−0.265001	+	0.101710i
$229$		−	1.73080i		−	0.114375i	−0.998363	−	0.0571873i	$-0.981787\pi$
$229$		−	1.73080i		−	0.114375i	0.998363	−	0.0571873i	$-0.0182132\pi$
$230$	−4.12603	+	2.44457i	−0.272062	+	0.161190i
$231$	8.08759	+	1.67926i	0.532125	+	0.110487i
$232$	−4.15197	+	2.66831i	−0.272590	+	0.175183i
$233$	−14.8144	−	2.12999i	−0.970525	−	0.139540i	−0.361224	−	0.932479i	$-0.617641\pi$
$233$	−14.8144	−	2.12999i	−0.970525	−	0.139540i	−0.609302	+	0.792939i	$0.708550\pi$
$234$	−0.924686	−	1.02716i	−0.0604486	−	0.0671474i
$235$	0.639301	+	2.17726i	0.0417034	+	0.142029i
$236$	5.47469	−	2.50021i	0.356372	−	0.162750i
$237$	7.08098	+	12.6807i	0.459959	+	0.823703i
$238$	−0.507143	−	3.52726i	−0.0328732	−	0.228638i
$239$	7.10618	−	24.2014i	0.459661	−	1.56546i	−0.325111	−	0.945676i	$-0.605402\pi$
$239$	7.10618	−	24.2014i	0.459661	−	1.56546i	0.784772	−	0.619785i	$-0.212780\pi$
$240$	−1.05107	−	1.37668i	−0.0678462	−	0.0888645i
$241$	−0.659232	+	1.02579i	−0.0424649	+	0.0660766i	−0.861837	−	0.507185i	$-0.830686\pi$
$241$	−0.659232	+	1.02579i	−0.0424649	+	0.0660766i	0.819372	+	0.573262i	$0.194322\pi$
$242$	0.411949	−	0.641005i	0.0264811	−	0.0412054i
$243$	2.58858	−	15.3720i	0.166057	−	0.986116i
$244$	1.72667	−	5.88049i	0.110539	−	0.376460i
$245$	−0.680062	−	4.72993i	−0.0434476	−	0.302184i
$246$	5.28359	−	2.95038i	0.336869	−	0.188109i
$247$	1.03697	−	0.473569i	0.0659809	−	0.0301325i
$248$	1.87283	+	6.37829i	0.118925	+	0.405022i
$249$	−11.0747	−	8.12784i	−0.701830	−	0.515081i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	−5.36013	+	3.44475i	−0.338328	+	0.217430i	−0.698762	−	0.715355i	$-0.746265\pi$
$251$	−5.36013	+	3.44475i	−0.338328	+	0.217430i	0.360433	+	0.932785i	$0.382629\pi$
$252$	−1.78007	+	4.10173i	−0.112134	+	0.258385i
$253$	−11.9545	+	9.62109i	−0.751571	+	0.604873i
$254$			12.5868i			0.789765i
$255$	−1.48389	−	3.86620i	−0.0929248	−	0.242111i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	6.14023	+	2.80415i	0.383017	+	0.174918i	0.597613	−	0.801785i	$-0.296116\pi$
$257$	6.14023	+	2.80415i	0.383017	+	0.174918i	−0.214596	+	0.976703i	$0.568843\pi$
$258$	−0.499935	−	6.16819i	−0.0311246	−	0.384015i
$259$	−7.41485	−	16.2362i	−0.460736	−	1.00887i
$260$	0.301686	+	0.348165i	0.0187098	+	0.0215922i
$261$	14.2831	+	3.90152i	0.884101	+	0.241498i
$262$	3.18429	+	0.934991i	0.196726	+	0.0577639i
$263$	−4.85550	+	5.60355i	−0.299403	+	0.345530i	−0.885439	−	0.464755i	$-0.846142\pi$
$263$	−4.85550	+	5.60355i	−0.299403	+	0.345530i	0.586036	+	0.810285i	$0.300688\pi$
$264$	−3.95576	−	3.88151i	−0.243460	−	0.238890i
$265$	5.80194	+	3.72868i	0.356410	+	0.229051i
$266$	−2.78733	−	2.41524i	−0.170902	−	0.148088i
$267$	8.37355	−	15.6865i	0.512453	−	0.959999i
$268$	7.20627	−	1.03611i	0.440193	−	0.0632902i
$269$	−19.5675	+	16.9553i	−1.19305	+	1.03379i	−0.194450	+	0.980912i	$0.562292\pi$
$269$	−19.5675	+	16.9553i	−1.19305	+	1.03379i	−0.998601	+	0.0528727i	$0.983162\pi$
$270$	−0.959787	+	5.10674i	−0.0584108	+	0.310786i
$271$	−5.34510	+	1.56946i	−0.324691	+	0.0953380i	−0.440016	−	0.897990i	$-0.645027\pi$
$271$	−5.34510	+	1.56946i	−0.324691	+	0.0953380i	0.115325	+	0.993328i	$0.463209\pi$
$272$	−0.993222	+	2.17485i	−0.0602230	+	0.131870i
$273$	0.405035	−	1.11818i	0.0245138	−	0.0676754i
$274$	1.65809	+	2.58003i	0.100169	+	0.155865i
$275$	−3.19969			−0.192949
$276$	−3.78373	−	7.39482i	−0.227754	−	0.445116i
$277$	17.1356			1.02958			0.514790	−	0.857316i	$-0.327870\pi$
$277$	17.1356			1.02958			0.514790	+	0.857316i	$0.327870\pi$
$278$	−2.09029	−	3.25256i	−0.125367	−	0.195076i
$279$	10.4620	−	16.9781i	0.626345	−	1.01645i
$280$	0.619153	−	1.35576i	0.0370015	−	0.0810219i
$281$	7.96339	−	2.33826i	0.475056	−	0.139489i	−0.0354351	−	0.999372i	$-0.511282\pi$
$281$	7.96339	−	2.33826i	0.475056	−	0.139489i	0.510491	+	0.859883i	$0.329464\pi$
$282$	−3.83242	+	0.871798i	−0.228217	+	0.0519148i
$283$	−17.0131	+	14.7419i	−1.01132	+	0.876317i	−0.992344	−	0.123503i	$-0.960587\pi$
$283$	−17.0131	+	14.7419i	−1.01132	+	0.876317i	−0.0189799	+	0.999820i	$0.506042\pi$
$284$	−6.17520	+	0.887860i	−0.366431	+	0.0526848i
$285$	−3.78105	−	2.01835i	−0.223970	−	0.119556i
$286$	1.11402	+	0.965304i	0.0658734	+	0.0570796i
$287$	4.38074	+	2.81533i	0.258587	+	0.166184i
$288$	2.49258	−	1.66945i	0.146877	−	0.0983732i
$289$	7.38913	−	8.52752i	0.434655	−	0.501619i
$290$	−4.73554	−	1.39048i	−0.278080	−	0.0816517i
$291$	0.127332	−	2.05357i	0.00746435	−	0.120383i
$292$	−0.618163	−	0.713398i	−0.0361753	−	0.0417485i
$293$	12.6712	+	27.7461i	0.740261	+	1.62095i	0.783125	+	0.621865i	$0.213625\pi$
$293$	12.6712	+	27.7461i	0.740261	+	1.62095i	−0.0428636	+	0.999081i	$0.513648\pi$
$294$	8.24968	−	0.668641i	0.481131	−	0.0389959i
$295$	5.47469	+	2.50021i	0.318749	+	0.145568i
$296$	−1.70433	+	11.8539i	−0.0990623	+	0.688993i
$297$	−0.714340	+	16.6107i	−0.0414502	+	0.963853i
$298$			7.75562i			0.449271i
$299$	1.12618	+	1.90081i	0.0651288	+	0.109927i
$300$	0.352123	−	1.69588i	0.0203299	−	0.0979117i
$301$	4.47983	−	2.87901i	0.258213	−	0.165944i
$302$	11.4558	+	1.64709i	0.659207	+	0.0947796i
$303$	11.5266	−	15.7057i	0.662185	−	0.902268i
$304$	0.697159	+	2.37430i	0.0399848	+	0.136176i
$305$	5.57490	−	2.54597i	0.319218	−	0.145782i
$306$	6.84268	−	2.15083i	0.391170	−	0.122955i
$307$	0.215682	+	1.50010i	0.0123096	+	0.0856151i	0.995050	−	0.0993741i	$-0.0316841\pi$
$307$	0.215682	+	1.50010i	0.0123096	+	0.0856151i	−0.982741	+	0.184989i	$0.940775\pi$
$308$	1.34357	−	4.57579i	0.0765572	−	0.260730i
$309$	21.6373	−	16.5196i	1.23090	−	0.939767i
$310$	−3.59394	+	5.59229i	−0.204122	+	0.317620i
$311$	0.504859	−	0.785576i	0.0286279	−	0.0445459i	−0.826645	−	0.562724i	$-0.809753\pi$
$311$	0.504859	−	0.785576i	0.0286279	−	0.0445459i	0.855273	+	0.518178i	$0.173390\pi$
$312$	−0.634221	+	0.484215i	−0.0359057	+	0.0274132i
$313$	7.96321	−	27.1202i	0.450107	−	1.53292i	−0.352148	−	0.935944i	$-0.614549\pi$
$313$	7.96321	−	27.1202i	0.450107	−	1.53292i	0.802256	−	0.596981i	$-0.203633\pi$
$314$	0.448967	+	3.12263i	0.0253367	+	0.176220i
$315$	−4.26558	+	1.34078i	−0.240338	+	0.0755444i
$316$	7.62757	−	3.48339i	0.429084	−	0.195956i
$317$	8.12969	+	27.6872i	0.456609	+	1.55507i	0.790504	+	0.612457i	$0.209819\pi$
$317$	8.12969	+	27.6872i	0.456609	+	1.55507i	−0.333895	+	0.942610i	$0.608363\pi$
$318$	−7.06779	+	9.63031i	−0.396342	+	0.540041i
$319$	−15.6312	−	2.24743i	−0.875180	−	0.125832i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−6.41042	+	30.8736i	−0.357795	+	1.72319i
$322$	4.08033	−	5.86888i	0.227388	−	0.327060i
$323$			5.91642i			0.329198i
$324$	−8.72530	−	2.20661i	−0.484739	−	0.122589i
$325$	−0.0655627	+	0.455999i	−0.00363676	+	0.0252943i
$326$	−19.4048	−	8.86188i	−1.07473	−	0.490814i
$327$	27.0752	−	2.19446i	1.49726	−	0.121354i
$328$	−1.45140	−	3.17812i	−0.0801401	−	0.175482i
$329$	−2.21479	−	2.55601i	−0.122105	−	0.140917i
$330$	0.342976	−	5.53141i	0.0188802	−	0.304494i
$331$	26.6680	+	7.83042i	1.46580	+	0.430399i	0.914733	−	0.404059i	$-0.132401\pi$
$331$	26.6680	+	7.83042i	1.46580	+	0.430399i	0.551071	+	0.834458i	$0.314219\pi$
$332$	−5.19381	+	5.99398i	−0.285048	+	0.328962i
$333$	29.8506	−	19.9929i	1.63580	−	1.09561i
$334$	20.8033	+	13.3694i	1.13830	+	0.731543i
$335$	5.50214	+	4.76763i	0.300614	+	0.260484i
$336$	2.27737	+	1.21567i	0.124241	+	0.0663204i
$337$	27.1460	−	3.90301i	1.47874	−	0.212610i	0.644750	−	0.764393i	$-0.276961\pi$
$337$	27.1460	−	3.90301i	1.47874	−	0.212610i	0.833988	+	0.551783i	$0.186052\pi$
$338$	−9.66435	+	8.37421i	−0.525671	+	0.455497i
$339$	−13.2697	+	3.01859i	−0.720712	+	0.163947i
$340$	−2.29407	+	0.673599i	−0.124413	+	0.0365310i
$341$	−8.83594	+	19.3480i	−0.478493	+	1.04775i
$342$	3.89447	−	6.32007i	0.210589	−	0.341750i
$343$	9.49112	+	14.7685i	0.512472	+	0.797423i
$344$	−3.57289			−0.192637
$345$	3.11082	−	7.70213i	0.167481	−	0.414669i
$346$	7.79701			0.419170
$347$	−6.63793	−	10.3288i	−0.356343	−	0.554480i	0.616086	−	0.787679i	$-0.288717\pi$
$347$	−6.63793	−	10.3288i	−0.356343	−	0.554480i	−0.972429	+	0.233198i	$0.925081\pi$
$348$	2.91137	−	8.03742i	0.156066	−	0.430851i
$349$	5.44380	−	11.9203i	0.291400	−	0.638076i	−0.706148	−	0.708064i	$-0.749569\pi$
$349$	5.44380	−	11.9203i	0.291400	−	0.638076i	0.997548	+	0.0699878i	$0.0222960\pi$
$350$	1.43007	−	0.419907i	0.0764405	−	0.0224450i
$351$	2.35261	+	0.442162i	0.125573	+	0.0236009i
$352$	−2.41817	+	2.09535i	−0.128889	+	0.111683i
$353$	−22.5811	+	3.24668i	−1.20187	+	0.172803i	−0.714022	−	0.700124i	$-0.753128\pi$
$353$	−22.5811	+	3.24668i	−1.20187	+	0.172803i	−0.487851	+	0.872927i	$0.662219\pi$
$354$	−4.90902	+	9.19627i	−0.260912	+	0.488776i
$355$	−4.71490	−	4.08548i	−0.250241	−	0.216835i
$356$	−8.63645	−	5.55031i	−0.457731	−	0.294166i
$357$	4.40556	+	4.32287i	0.233167	+	0.228791i
$358$	1.09516	−	1.26388i	0.0578810	−	0.0667982i
$359$	17.0544	+	5.00762i	0.900096	+	0.264292i	0.698867	−	0.715252i	$-0.253688\pi$
$359$	17.0544	+	5.00762i	0.900096	+	0.264292i	0.201230	+	0.979544i	$0.435506\pi$
$360$	2.89398	+	0.790509i	0.152526	+	0.0416635i
$361$	−8.43241	−	9.73152i	−0.443811	−	0.512185i
$362$	−2.10419	−	4.60754i	−0.110594	−	0.242167i
$363$	0.106618	+	1.31545i	0.00559597	+	0.0690431i
$364$	−0.624580	−	0.285236i	−0.0327369	−	0.0149504i
$365$	0.134340	−	0.934353i	0.00703166	−	0.0489063i
$366$	3.80373	+	9.91041i	0.198824	+	0.518026i
$367$		−	20.4214i		−	1.06599i	−0.846119	−	0.532994i	$-0.821067\pi$
$367$		−	20.4214i		−	1.06599i	0.846119	−	0.532994i	$-0.178933\pi$
$368$	−4.43193	+	1.83249i	−0.231030	+	0.0955251i
$369$	−4.17277	+	9.61514i	−0.217226	+	0.500544i
$370$	−10.0747	+	6.47460i	−0.523757	+	0.336598i
$371$	−10.1746	−	1.46289i	−0.528241	−	0.0759496i
$372$	−9.28232	−	6.81240i	−0.481266	−	0.353207i
$373$	−7.45040	−	25.3737i	−0.385767	−	1.31380i	−0.892246	−	0.451549i	$-0.850871\pi$
$373$	−7.45040	−	25.3737i	−0.385767	−	1.31380i	0.506479	−	0.862252i	$-0.330947\pi$
$374$	−6.95886	+	3.17801i	−0.359834	+	0.164331i
$375$	1.51225	−	0.844448i	0.0780924	−	0.0436071i
$376$	0.322937	+	2.24608i	0.0166542	+	0.115833i
$377$	−0.640576	+	2.18160i	−0.0329914	+	0.112358i
$378$	−1.86062	−	7.51775i	−0.0956999	−	0.386671i
$379$	−1.53770	+	2.39271i	−0.0789864	+	0.122905i	−0.878499	−	0.477744i	$-0.841455\pi$
$379$	−1.53770	+	2.39271i	−0.0789864	+	0.122905i	0.799513	+	0.600649i	$0.205091\pi$
$380$	−1.33784	+	2.08172i	−0.0686296	+	0.106790i
$381$	−13.2296	−	17.3280i	−0.677772	−	0.887741i
$382$	−0.685453	+	2.33444i	−0.0350708	+	0.119440i
$383$	−2.60995	−	18.1526i	−0.133362	−	0.927556i	−0.941128	−	0.338051i	$-0.890232\pi$
$383$	−2.60995	−	18.1526i	−0.133362	−	0.927556i	0.807765	−	0.589504i	$-0.200677\pi$
$384$	−0.844448	−	1.51225i	−0.0430931	−	0.0771718i
$385$	4.33800	−	1.98110i	0.221085	−	0.100966i
$386$	3.17308	+	10.8065i	0.161506	+	0.550037i
$387$	7.17145	+	7.96618i	0.364545	+	0.404943i
$388$	−1.17582	−	0.169057i	−0.0596930	−	0.00858256i
$389$	5.15795	−	3.31482i	0.261519	−	0.168068i	−0.403311	−	0.915063i	$-0.632141\pi$
$389$	5.15795	−	3.31482i	0.261519	−	0.168068i	0.664829	+	0.746995i	$0.268504\pi$
$390$	−0.781271	−	0.162219i	−0.0395612	−	0.00821427i
$391$	−11.4015	+	1.21851i	−0.576599	+	0.0616228i
$392$		−	4.77857i		−	0.241354i
$393$	−5.36649	+	2.05972i	−0.270704	+	0.103899i
$394$	2.90016	−	20.1710i	0.146108	−	1.01620i
$395$	7.62757	+	3.48339i	0.383785	+	0.175269i
$396$	9.52555	+	1.18583i	0.478677	+	0.0595901i
$397$	4.31403	+	9.44640i	0.216515	+	0.474101i	0.986459	−	0.164011i	$-0.0524431\pi$
$397$	4.31403	+	9.44640i	0.216515	+	0.474101i	−0.769944	+	0.638112i	$0.779716\pi$
$398$	1.08297	+	1.24981i	0.0542843	+	0.0626474i
$399$	6.37585	+	0.395336i	0.319192	+	0.0197916i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	10.4864	−	12.1020i	0.523668	−	0.604345i	−0.430878	−	0.902410i	$-0.641796\pi$
$401$	10.4864	−	12.1020i	0.523668	−	0.604345i	0.954545	+	0.298066i	$0.0963414\pi$
$402$	−8.83173	+	9.00068i	−0.440487	+	0.448913i
$403$	2.57630	+	1.65569i	0.128335	+	0.0824756i
$404$	−8.50043	−	7.36566i	−0.422912	−	0.366455i
$405$	−4.04622	−	8.03916i	−0.201058	−	0.399469i
$406$	7.28115	−	1.04687i	0.361358	−	0.0519554i
$407$	−28.9594	+	25.0935i	−1.43547	+	1.24384i
$408$	−0.918569	−	4.03803i	−0.0454760	−	0.199912i
$409$	22.0048	−	6.46120i	1.08807	−	0.319486i	0.311967	−	0.950093i	$-0.399012\pi$
$409$	22.0048	−	6.46120i	1.08807	−	0.319486i	0.776102	+	0.630607i	$0.217194\pi$
$410$	1.45140	−	3.17812i	0.0716795	−	0.156956i
$411$	−4.99445	−	1.80912i	−0.246358	−	0.0892374i
$412$	−8.49723	−	13.2219i	−0.418628	−	0.651398i
$413$	−8.97036			−0.441403
$414$	12.9815	+	6.20337i	0.638004	+	0.304879i
$415$	−7.93117			−0.389326
$416$	0.249067	+	0.387555i	0.0122115	+	0.0190015i
$417$	6.29633	+	2.28070i	0.308333	+	0.111686i
$418$	−3.28916	+	7.20226i	−0.160878	+	0.352274i
$419$	29.0624	−	8.53348i	1.41979	−	0.416888i	0.520357	−	0.853949i	$-0.325799\pi$
$419$	29.0624	−	8.53348i	1.41979	−	0.416888i	0.899432	+	0.437061i	$0.143981\pi$
$420$	0.572616	+	2.51722i	0.0279408	+	0.122828i
$421$	29.3756	−	25.4541i	1.43168	−	1.24056i	0.505850	−	0.862621i	$-0.331179\pi$
$421$	29.3756	−	25.4541i	1.43168	−	1.24056i	0.925831	−	0.377938i	$-0.123367\pi$
$422$	3.32209	−	0.477645i	0.161717	−	0.0232514i
$423$	4.35971	−	5.22833i	0.211976	−	0.254210i
$424$	5.21223	+	4.51643i	0.253128	+	0.219337i
$425$	−2.01137	−	1.29263i	−0.0975656	−	0.0627016i
$426$	7.56809	−	7.71287i	0.366675	−	0.373690i
$427$	−5.98186	+	6.90344i	−0.289483	+	0.334081i
$428$	17.4676	+	5.12895i	0.844328	+	0.247917i
$429$	−2.54825	−	0.158005i	−0.123031	−	0.00762855i
$430$	−2.33974	−	2.70021i	−0.112832	−	0.130216i
$431$	14.9985	+	32.8420i	0.722450	+	1.58195i	0.810438	+	0.585824i	$0.199229\pi$
$431$	14.9985	+	32.8420i	0.722450	+	1.58195i	−0.0879879	+	0.996122i	$0.528044\pi$
$432$	−1.67678	+	4.91817i	−0.0806743	+	0.236626i
$433$	−10.7052	−	4.88890i	−0.514459	−	0.234945i	0.141230	−	0.989977i	$-0.454894\pi$
$433$	−10.7052	−	4.88890i	−0.514459	−	0.234945i	−0.655689	+	0.755031i	$0.727622\pi$
$434$	1.41003	−	9.80698i	0.0676836	−	0.470750i
$435$	7.98082	−	3.06313i	0.382651	−	0.146866i
$436$		−	15.6832i		−	0.751087i
$437$	−8.09219	+	8.68064i	−0.387102	+	0.415251i
$438$	1.60084	+	0.332391i	0.0764913	+	0.0158822i
$439$	−15.1935	+	9.76428i	−0.725147	+	0.466024i	−0.850424	−	0.526098i	$-0.823654\pi$
$439$	−15.1935	+	9.76428i	−0.725147	+	0.466024i	0.125277	+	0.992122i	$0.460018\pi$
$440$	−3.16712	−	0.455364i	−0.150987	−	0.0217086i
$441$	−10.6544	+	9.59149i	−0.507352	+	0.456738i
$442$	0.310319	+	1.05685i	0.0147604	+	0.0502692i
$443$	−4.43826	+	2.02689i	−0.210868	+	0.0963003i	−0.518049	−	0.855351i	$-0.673342\pi$
$443$	−4.43826	+	2.02689i	−0.210868	+	0.0963003i	0.307181	+	0.951651i	$0.400614\pi$
$444$	−10.1129	−	18.1104i	−0.479938	−	0.859482i
$445$	−1.46103	−	10.1617i	−0.0692594	−	0.481710i
$446$	3.80969	−	12.9746i	0.180394	−	0.614366i
$447$	−8.15169	−	10.6770i	−0.385562	−	0.505006i
$448$	0.805795	−	1.25384i	0.0380703	−	0.0592385i
$449$	−19.1070	+	29.7311i	−0.901715	+	1.40310i	0.0134037	+	0.999910i	$0.495733\pi$
$449$	−19.1070	+	29.7311i	−0.901715	+	1.40310i	−0.915118	+	0.403185i	$0.867903\pi$
$450$	1.29772	+	2.70479i	0.0611753	+	0.127505i
$451$	3.14956	−	10.7264i	0.148307	−	0.505087i
$452$	1.11817	+	7.77702i	0.0525941	+	0.365800i
$453$	−17.5022	+	9.77330i	−0.822325	+	0.459190i
$454$	12.4186	−	5.67140i	0.582835	−	0.266172i
$455$	−0.193446	−	0.658816i	−0.00906889	−	0.0308858i
$456$	−3.45532	−	2.53590i	−0.161810	−	0.118754i
$457$	−22.0690	−	3.17305i	−1.03235	−	0.148429i	−0.394741	−	0.918792i	$-0.629166\pi$
$457$	−22.0690	−	3.17305i	−1.03235	−	0.148429i	−0.637605	+	0.770364i	$0.720075\pi$
$458$	1.45604	−	0.935742i	0.0680365	−	0.0437244i
$459$	−7.15953	+	10.1531i	−0.334178	+	0.473908i
$460$	−4.28720	−	2.14940i	−0.199892	−	0.100216i
$461$		−	7.65706i		−	0.356625i	−0.983974	−	0.178312i	$-0.942936\pi$
$461$		−	7.65706i		−	0.356625i	0.983974	−	0.178312i	$-0.0570637\pi$
$462$	2.95980	+	7.71160i	0.137702	+	0.358776i
$463$	−4.90050	+	34.0837i	−0.227746	+	1.58401i	0.479826	+	0.877364i	$0.340700\pi$
$463$	−4.90050	+	34.0837i	−0.227746	+	1.58401i	−0.707572	+	0.706642i	$0.750209\pi$
$464$	−4.48945	−	2.05026i	−0.208417	−	0.0951811i
$465$	−0.930158	−	11.4763i	−0.0431351	−	0.532200i
$466$	−6.21742	−	13.6143i	−0.288016	−	0.630668i
$467$	−15.2617	−	17.6130i	−0.706228	−	0.815030i	0.283352	−	0.959016i	$-0.408554\pi$
$467$	−15.2617	−	17.6130i	−0.706228	−	0.815030i	−0.989580	+	0.143986i	$0.954008\pi$
$468$	0.364178	−	1.33322i	0.0168341	−	0.0616281i
$469$	−10.4115	−	3.05708i	−0.480757	−	0.141163i
$470$	−1.48599	+	1.71493i	−0.0685438	+	0.0791038i
$471$	−3.90019	−	3.82698i	−0.179711	−	0.176338i
$472$	5.06315	+	3.25389i	0.233050	+	0.149772i
$473$	−8.63983	−	7.48646i	−0.397260	−	0.344228i
$474$	−6.83945	+	12.8126i	−0.314147	+	0.588504i
$475$	−2.44935	+	0.352164i	−0.112384	+	0.0161584i
$476$	2.69314	−	2.33361i	0.123440	−	0.106961i
$477$	−0.392011	−	20.6866i	−0.0179490	−	0.947175i
$478$	24.2014	−	7.10618i	1.10695	−	0.325029i
$479$	−2.83658	+	6.21125i	−0.129607	+	0.283799i	−0.963299	−	0.268430i	$-0.913495\pi$
$479$	−2.83658	+	6.21125i	−0.129607	+	0.283799i	0.833692	+	0.552229i	$0.186223\pi$
$480$	0.589888	−	1.62851i	0.0269246	−	0.0743308i
$481$	2.98277	+	4.64128i	0.136003	+	0.211624i
$482$	−1.21935			−0.0555400
$483$	0.551283	+	12.3683i	0.0250842	+	0.562776i
$484$	0.761964			0.0346347
$485$	−0.642231	−	0.999331i	−0.0291622	−	0.0453773i
$486$	14.3313	−	6.13310i	0.650079	−	0.278203i
$487$	5.04845	−	11.0546i	0.228767	−	0.500930i	−0.760086	−	0.649822i	$-0.774843\pi$
$487$	5.04845	−	11.0546i	0.228767	−	0.500930i	0.988853	+	0.148892i	$0.0475707\pi$
$488$	5.88049	−	1.72667i	0.266197	−	0.0781626i
$489$	36.0287	−	8.19580i	1.62927	−	0.370627i
$490$	3.61141	−	3.12930i	0.163147	−	0.141367i
$491$	30.4523	−	4.37837i	1.37429	−	0.197593i	0.584712	−	0.811241i	$-0.301208\pi$
$491$	30.4523	−	4.37837i	1.37429	−	0.197593i	0.789580	+	0.613648i	$0.210299\pi$
$492$	5.33854	+	2.84974i	0.240680	+	0.128476i
$493$	−8.91804	−	7.72753i	−0.401648	−	0.348030i
$494$	0.959021	+	0.616325i	0.0431484	+	0.0277298i
$495$	5.34172	+	7.97548i	0.240093	+	0.358471i
$496$	−4.35323	+	5.02389i	−0.195466	+	0.225579i
$497$	8.92179	+	2.61968i	0.400197	+	0.117508i
$498$	0.850145	−	13.7109i	0.0380959	−	0.614398i
$499$	14.0785	+	16.2475i	0.630241	+	0.727337i	0.977618	−	0.210389i	$-0.0674730\pi$
$499$	14.0785	+	16.2475i	0.630241	+	0.727337i	−0.347377	+	0.937726i	$0.612928\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−42.6917	+	3.46018i	−1.90732	+	0.154589i
$502$	−5.79581	−	2.64686i	−0.258680	−	0.118135i
$503$	3.04247	−	21.1609i	0.135657	−	0.943516i	−0.802338	−	0.596869i	$-0.796411\pi$
$503$	3.04247	−	21.1609i	0.135657	−	0.943516i	0.937996	−	0.346647i	$-0.112680\pi$
$504$	−4.41297	+	0.720077i	−0.196569	+	0.0320748i
$505$		−	11.2477i		−	0.500515i
$506$	−14.5569	−	4.85519i	−0.647131	−	0.215840i
$507$	4.50287	−	21.6865i	0.199980	−	0.963132i
$508$	−10.5887	+	6.80493i	−0.469797	+	0.301920i
$509$	0.606624	+	0.0872193i	0.0268881	+	0.00386593i	0.155746	−	0.987797i	$-0.450222\pi$
$509$	0.606624	+	0.0872193i	0.0268881	+	0.00386593i	−0.128858	+	0.991663i	$0.541131\pi$
$510$	2.45020	−	3.33855i	0.108497	−	0.147834i
$511$	0.396376	+	1.34993i	0.0175346	+	0.0597175i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	1.28138	+	12.7941i	0.0565744	+	0.564873i
$514$	0.960659	+	6.68153i	0.0423728	+	0.294710i
$515$	4.42798	−	15.0803i	0.195120	−	0.664518i
$516$	4.91873	−	3.75535i	0.216535	−	0.165320i
$517$	−3.92541	+	6.10806i	−0.172639	+	0.268632i
$518$	9.65003	−	15.0157i	0.423998	−	0.659754i
$519$	−10.7340	+	8.19520i	−0.471171	+	0.359729i
$520$	−0.129791	+	0.442027i	−0.00569170	+	0.0193842i
$521$	−3.27469	−	22.7760i	−0.143467	−	0.997834i	−0.926618	−	0.376003i	$-0.877298\pi$
$521$	−3.27469	−	22.7760i	−0.143467	−	0.997834i	0.783152	−	0.621831i	$-0.213611\pi$
$522$	4.43985	+	14.1250i	0.194327	+	0.618235i
$523$	−25.8751	+	11.8168i	−1.13144	+	0.516711i	−0.891023	−	0.453958i	$-0.850011\pi$
$523$	−25.8751	+	11.8168i	−1.13144	+	0.516711i	−0.240417	+	0.970670i	$0.577284\pi$
$524$	0.934991	+	3.18429i	0.0408453	+	0.139106i
$525$	−1.52740	+	2.08118i	−0.0666613	+	0.0908302i
$526$	−7.33909	−	1.05520i	−0.320000	−	0.0460090i
$527$	−13.3707	+	8.59282i	−0.582436	+	0.374309i
$528$	1.12669	−	5.42630i	0.0490327	−	0.236149i
$529$	−18.3950	−	13.8066i	−0.799784	−	0.600287i
$530$			6.89677i			0.299577i
$531$	−2.90775	−	17.8201i	−0.126186	−	0.773325i
$532$	0.524881	−	3.65063i	0.0227565	−	0.158275i
$533$	−1.46412	−	0.668642i	−0.0634181	−	0.0289621i
$534$	17.7234	−	1.43649i	0.766967	−	0.0621630i
$535$	7.56264	+	16.5599i	0.326962	+	0.715946i
$536$	4.76763	+	5.50214i	0.205930	+	0.237656i
$537$	−0.179260	+	2.89105i	−0.00773565	+	0.124758i
$538$	−24.8427	−	7.29448i	−1.07105	−	0.314487i
$539$	10.0128	−	11.5554i	0.431282	−	0.497726i
$540$	−4.81496	+	1.95349i	−0.207203	+	0.0840648i
$541$	7.38317	+	4.74487i	0.317427	+	0.203998i	0.689646	−	0.724147i	$-0.257766\pi$
$541$	7.38317	+	4.74487i	0.317427	+	0.203998i	−0.372218	+	0.928145i	$0.621403\pi$
$542$	−4.21009	−	3.64807i	−0.180839	−	0.156698i
$543$	7.73965	+	4.13147i	0.332140	+	0.177298i
$544$	−2.36658	+	0.340263i	−0.101466	+	0.0145886i
$545$	11.8525	−	10.2703i	0.507707	−	0.439930i
$546$	1.15965	−	0.263797i	0.0496285	−	0.0112895i
$547$	−15.7179	+	4.61518i	−0.672048	+	0.197331i	−0.599915	−	0.800064i	$-0.704799\pi$
$547$	−15.7179	+	4.61518i	−0.672048	+	0.197331i	−0.0721330	+	0.997395i	$0.522981\pi$
$548$	−1.27403	+	2.78974i	−0.0544239	+	0.119172i
$549$	−15.6530	−	9.64551i	−0.668056	−	0.411660i
$550$	−1.72988	−	2.69175i	−0.0737625	−	0.114777i
$551$	−12.2130			−0.520291
$552$	4.17528	−	7.18102i	0.177712	−	0.305644i
$553$	−12.4979			−0.531464
$554$	9.26422	+	14.4154i	0.393599	+	0.612452i
$555$	7.06437	−	19.5026i	0.299866	−	0.827841i
$556$	1.60613	−	3.51693i	0.0681151	−	0.149151i
$557$	2.42774	−	0.712847i	0.102866	−	0.0302043i	−0.229894	−	0.973216i	$-0.573838\pi$
$557$	2.42774	−	0.712847i	0.102866	−	0.0302043i	0.332761	+	0.943011i	$0.392020\pi$
$558$	19.9391	−	0.377846i	0.844090	−	0.0159955i
$559$	−1.24395	+	1.07789i	−0.0526136	+	0.0455899i
$560$	1.47527	−	0.212112i	0.0623417	−	0.00896339i
$561$	6.23984	−	11.6894i	0.263446	−	0.493525i
$562$	6.27241	+	5.43507i	0.264586	+	0.229265i
$563$	−25.7404	−	16.5424i	−1.08483	−	0.697178i	−0.129162	−	0.991624i	$-0.541229\pi$
$563$	−25.7404	−	16.5424i	−1.08483	−	0.697178i	−0.955668	+	0.294446i	$0.904865\pi$
$564$	−2.80537	−	2.75271i	−0.118127	−	0.115910i
$565$	−5.14524	+	5.93792i	−0.216462	+	0.249810i
$566$	−21.5997	−	6.34224i	−0.907903	−	0.266584i
$567$	10.4632	+	8.39392i	0.439411	+	0.352511i
$568$	−4.08548	−	4.71490i	−0.171423	−	0.197833i
$569$	1.40975	+	3.08691i	0.0590997	+	0.129410i	0.936878	−	0.349658i	$-0.113702\pi$
$569$	1.40975	+	3.08691i	0.0590997	+	0.129410i	−0.877778	+	0.479068i	$0.840975\pi$
$570$	−0.346249	−	4.27202i	−0.0145028	−	0.178935i
$571$	−7.57671	−	3.46017i	−0.317075	−	0.144803i	0.250519	−	0.968112i	$-0.419399\pi$
$571$	−7.57671	−	3.46017i	−0.317075	−	0.144803i	−0.567595	+	0.823308i	$0.692126\pi$
$572$	−0.209781	+	1.45906i	−0.00877136	+	0.0610062i
$573$	−1.51000	−	3.93424i	−0.0630813	−	0.164355i
$574$			5.20739i			0.217352i
$575$	−1.18311	−	4.64761i	−0.0493390	−	0.193819i
$576$	2.75202	+	1.19432i	0.114667	+	0.0497633i
$577$	31.2127	−	20.0592i	1.29940	−	0.835075i	0.306255	−	0.951950i	$-0.400924\pi$
$577$	31.2127	−	20.0592i	1.29940	−	0.835075i	0.993147	+	0.116875i	$0.0372876\pi$
$578$	11.1687	+	1.60581i	0.464555	+	0.0667930i
$579$	−15.7267	−	11.5420i	−0.653580	−	0.479670i
$580$	−1.39048	−	4.73554i	−0.0577365	−	0.196632i
$581$	10.7527	−	4.91061i	0.446099	−	0.203726i
$582$	1.79642	−	1.00313i	0.0744638	−	0.0415809i
$583$	3.14054	+	21.8429i	0.130068	+	0.904642i
$584$	0.265945	−	0.905724i	0.0110049	−	0.0374791i
$585$	1.24607	−	0.597846i	0.0515185	−	0.0247179i
$586$	−16.4909	+	25.6604i	−0.681234	+	1.06002i
$587$	−22.7267	+	35.3634i	−0.938030	+	1.45960i	−0.0505680	+	0.998721i	$0.516103\pi$
$587$	−22.7267	+	35.3634i	−0.938030	+	1.45960i	−0.887462	+	0.460882i	$0.847533\pi$
$588$	5.02261	+	6.57858i	0.207129	+	0.271296i
$589$	−4.63441	+	15.7833i	−0.190957	+	0.650341i
$590$	0.856533	+	5.95732i	0.0352629	+	0.245259i
$591$	17.2085	+	30.8174i	0.707865	+	1.26766i
$592$	−10.8936	+	4.97492i	−0.447722	+	0.204468i
$593$	7.08148	+	24.1173i	0.290801	+	0.990379i	0.967237	+	0.253876i	$0.0817057\pi$
$593$	7.08148	+	24.1173i	0.290801	+	0.990379i	−0.676435	+	0.736502i	$0.736476\pi$
$594$	−14.3600	+	8.37950i	−0.589200	+	0.343815i
$595$	3.52726	+	0.507143i	0.144603	+	0.0207908i
$596$	−6.52444	+	4.19300i	−0.267251	+	0.171752i
$597$	−2.80454	−	0.582320i	−0.114782	−	0.0238328i
$598$	−0.990203	+	1.97506i	−0.0404924	+	0.0807662i
$599$			35.7148i			1.45927i	0.683838	+	0.729634i	$0.260309\pi$
$599$			35.7148i			1.45927i	−0.683838	+	0.729634i	$0.739691\pi$
$600$	1.61704	−	0.620637i	0.0660153	−	0.0253374i
$601$	−1.44415	+	10.0443i	−0.0589081	+	0.409715i	0.938936	+	0.344091i	$0.111813\pi$
$601$	−1.44415	+	10.0443i	−0.0589081	+	0.409715i	−0.997844	+	0.0656240i	$0.979096\pi$
$602$	4.84396	+	2.21216i	0.197425	+	0.0901611i
$603$	2.69816	−	21.6738i	0.109877	−	0.882627i
$604$	4.80784	+	10.5277i	0.195628	+	0.428367i
$605$	0.498981	+	0.575854i	0.0202864	+	0.0234118i
$606$	19.4442	+	1.20564i	0.789867	+	0.0489759i
$607$	12.4598	+	3.65854i	0.505729	+	0.148496i	0.524638	−	0.851326i	$-0.324201\pi$
$607$	12.4598	+	3.65854i	0.505729	+	0.148496i	−0.0189082	+	0.999821i	$0.506019\pi$
$608$	−1.62048	+	1.87013i	−0.0657191	+	0.0758439i
$609$	−8.92350	+	9.09420i	−0.361598	+	0.368516i
$610$	5.15583	+	3.31345i	0.208753	+	0.134158i
$611$	0.790046	+	0.684579i	0.0319619	+	0.0276951i
$612$	5.50882	+	4.59360i	0.222681	+	0.185685i
$613$	15.2521	−	2.19292i	0.616026	−	0.0885712i	0.172764	−	0.984963i	$-0.444730\pi$
$613$	15.2521	−	2.19292i	0.616026	−	0.0885712i	0.443262	+	0.896392i	$0.353821\pi$
$614$	−1.14536	+	0.992457i	−0.0462228	+	0.0400523i
$615$	1.34231	+	5.90078i	0.0541271	+	0.237942i
$616$	4.57579	−	1.34357i	0.184364	−	0.0541341i
$617$	7.65030	−	16.7518i	0.307989	−	0.674403i	−0.690828	−	0.723019i	$-0.742754\pi$
$617$	7.65030	−	16.7518i	0.307989	−	0.674403i	0.998818	+	0.0486162i	$0.0154811\pi$
$618$	25.5952	+	9.27125i	1.02959	+	0.372944i
$619$	1.24050	+	1.93026i	0.0498600	+	0.0775837i	0.865289	−	0.501274i	$-0.167135\pi$
$619$	1.24050	+	1.93026i	0.0498600	+	0.0775837i	−0.815429	+	0.578858i	$0.803499\pi$
$620$	−6.64756			−0.266973
$621$	−24.3915	+	5.10434i	−0.978798	+	0.204830i
$622$	0.933816			0.0374426
$623$	8.27243	+	12.8722i	0.331428	+	0.515712i
$624$	−0.750233	−	0.271754i	−0.0300333	−	0.0108789i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	27.1202	−	7.96321i	1.08394	−	0.318274i
$627$	−3.04194	−	13.3724i	−0.121483	−	0.534040i
$628$	−2.38420	+	2.06592i	−0.0951398	+	0.0824391i
$629$	−28.3417	+	4.07491i	−1.13006	+	0.162477i
$630$	−3.43408	−	2.86355i	−0.136817	−	0.114087i
$631$	−25.6931	−	22.2632i	−1.02283	−	0.886285i	−0.0292650	−	0.999572i	$-0.509317\pi$
$631$	−25.6931	−	22.2632i	−1.02283	−	0.886285i	−0.993562	+	0.113287i	$0.963862\pi$
$632$	7.05419	+	4.53346i	0.280601	+	0.180331i
$633$	−4.07143	+	4.14931i	−0.161825	+	0.164920i
$634$	−18.8967	+	21.8080i	−0.750484	+	0.866105i
$635$	−12.0769	−	3.54611i	−0.479259	−	0.140723i
$636$	−11.9227	−	0.739268i	−0.472765	−	0.0293139i
$637$	−1.44163	−	1.66373i	−0.0571195	−	0.0659194i
$638$	−6.56021	−	14.3649i	−0.259721	−	0.568710i
$639$	−2.31211	+	18.5728i	−0.0914655	+	0.734727i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	4.16956	−	28.9999i	0.164688	−	1.14543i	−0.724963	−	0.688787i	$-0.758143\pi$
$641$	4.16956	−	28.9999i	0.164688	−	1.14543i	0.889651	−	0.456641i	$-0.150948\pi$
$642$	−29.4382	+	11.2987i	−1.16183	+	0.445925i
$643$			25.0540i			0.988034i	0.869452	+	0.494017i	$0.164472\pi$
$643$			25.0540i			0.988034i	−0.869452	+	0.494017i	$0.835528\pi$
$644$	7.14321	+	0.259633i	0.281482	+	0.0102310i
$645$	6.05919	+	1.25810i	0.238580	+	0.0495375i
$646$	−4.97721	+	3.19866i	−0.195826	+	0.125850i
$647$	−34.5400	−	4.96610i	−1.35791	−	0.195238i	−0.575396	−	0.817875i	$-0.695152\pi$
$647$	−34.5400	−	4.96610i	−1.35791	−	0.195238i	−0.782511	+	0.622637i	$0.786061\pi$
$648$	−2.86094	−	8.53317i	−0.112388	−	0.335215i
$649$	5.42549	+	18.4775i	0.212969	+	0.725307i
$650$	−0.419056	+	0.191377i	−0.0164367	+	0.00750641i
$651$	8.36665	+	14.9831i	0.327915	+	0.587235i
$652$	−3.03595	−	21.1155i	−0.118897	−	0.826945i
$653$	1.01562	−	3.45889i	0.0397443	−	0.135357i	−0.937231	−	0.348709i	$-0.886620\pi$
$653$	1.01562	−	3.45889i	0.0397443	−	0.135357i	0.976975	+	0.213352i	$0.0684383\pi$
$654$	16.4841	+	21.5907i	0.644578	+	0.844264i
$655$	−1.79423	+	2.79188i	−0.0701066	+	0.109088i
$656$	1.88892	−	2.93922i	0.0737499	−	0.114757i
$657$	−2.55322	+	1.22500i	−0.0996106	+	0.0477919i
$658$	0.952842	−	3.24508i	0.0371457	−	0.126507i
$659$	0.272927	+	1.89825i	0.0106317	+	0.0739453i	0.994447	−	0.105243i	$-0.0335620\pi$
$659$	0.272927	+	1.89825i	0.0106317	+	0.0739453i	−0.983815	+	0.179188i	$0.942653\pi$
$660$	4.83874	−	2.70197i	0.188348	−	0.105174i
$661$	0.940382	−	0.429458i	0.0365766	−	0.0167040i	−0.397043	−	0.917800i	$-0.629964\pi$
$661$	0.940382	−	0.429458i	0.0365766	−	0.0167040i	0.433619	+	0.901096i	$0.357236\pi$
$662$	7.83042	+	26.6680i	0.304338	+	1.03648i
$663$	−1.53803	−	1.12878i	−0.0597322	−	0.0438381i
$664$	−7.85044	−	1.12872i	−0.304656	−	0.0438030i
$665$	3.10268	−	1.99397i	0.120317	−	0.0773230i
$666$	32.9576	+	14.3029i	1.27708	+	0.554226i
$667$	−2.51532	−	23.5356i	−0.0973934	−	0.911302i
$668$			24.7289i			0.956789i
$669$	8.39248	+	21.8662i	0.324472	+	0.845395i
$670$	−1.03611	+	7.20627i	−0.0400283	+	0.278403i
$671$	17.8380	+	8.14633i	0.688628	+	0.314486i
$672$	0.208550	+	2.57309i	0.00804499	+	0.0992590i
$673$	12.9075	+	28.2635i	0.497548	+	1.08948i	0.977258	+	0.212052i	$0.0680145\pi$
$673$	12.9075	+	28.2635i	0.497548	+	1.08948i	−0.479710	+	0.877427i	$0.659258\pi$
$674$	17.9597	+	20.7266i	0.691780	+	0.798357i
$675$	−4.62948	−	2.35964i	−0.178189	−	0.0908227i
$676$	−12.2698	−	3.60273i	−0.471914	−	0.138567i
$677$	−19.5229	+	22.5306i	−0.750326	+	0.865923i	−0.994600	−	0.103784i	$-0.966905\pi$
$677$	−19.5229	+	22.5306i	−0.750326	+	0.865923i	0.244274	+	0.969706i	$0.421451\pi$
$678$	−9.71354	−	9.53122i	−0.373046	−	0.366044i
$679$	1.48945	+	0.957210i	0.0571598	+	0.0367344i
$680$	−1.80693	−	1.56572i	−0.0692927	−	0.0600425i
$681$	−11.1355	+	20.8606i	−0.426713	+	0.799378i
$682$	−21.0537	+	3.02706i	−0.806186	+	0.115912i
$683$	−26.4593	+	22.9271i	−1.01244	+	0.877281i	−0.992466	−	0.122519i	$-0.960903\pi$
$683$	−26.4593	+	22.9271i	−1.01244	+	0.877281i	−0.0199702	+	0.999801i	$0.506357\pi$
$684$	7.42229	−	0.140652i	0.283798	−	0.00537798i
$685$	−2.94266	+	0.864042i	−0.112433	+	0.0330134i
$686$	−7.29274	+	15.9689i	−0.278438	+	0.609695i
$687$	−1.02098	+	2.81862i	−0.0389528	+	0.107537i
$688$	−1.93165	−	3.00570i	−0.0736434	−	0.114591i
$689$	3.17726			0.121044
$690$	8.16128	−	1.54710i	0.310695	−	0.0588970i
$691$	40.0560			1.52380			0.761902	−	0.647693i	$-0.224266\pi$
$691$	40.0560			1.52380			0.761902	+	0.647693i	$0.224266\pi$
$692$	4.21538	+	6.55927i	0.160245	+	0.249346i
$693$	−12.1801	−	7.50547i	−0.462684	−	0.285109i
$694$	5.10042	−	11.1684i	0.193609	−	0.423945i
$695$	3.70971	−	1.08927i	0.140717	−	0.0413183i
$696$	8.33551	−	1.89616i	0.315957	−	0.0718737i
$697$	6.31316	−	5.47038i	0.239128	−	0.207206i
$698$	12.9711	−	1.86496i	0.490963	−	0.0705898i
$699$	22.8689	+	12.2076i	0.864982	+	0.461732i
$700$	1.12640	+	0.976034i	0.0425740	+	0.0368906i
$701$	11.1144	+	7.14280i	0.419786	+	0.269780i	0.733436	−	0.679759i	$-0.237915\pi$
$701$	11.1144	+	7.14280i	0.419786	+	0.269780i	−0.313650	+	0.949539i	$0.601552\pi$
$702$	0.899948	+	2.21820i	0.0339664	+	0.0837204i
$703$	−19.4065	+	22.3963i	−0.731931	+	0.844693i
$704$	−3.07008	−	0.901458i	−0.115708	−	0.0339750i
$705$	0.243234	−	3.92279i	0.00916071	−	0.147741i
$706$	−14.9396	−	17.2412i	−0.562258	−	0.648880i
$707$	6.96403	+	15.2491i	0.261909	+	0.573502i
$708$	−10.3904	+	0.842148i	−0.390496	+	0.0316499i
$709$	32.6447	+	14.9083i	1.22600	+	0.559894i	0.919918	−	0.392112i	$-0.128255\pi$
$709$	32.6447	+	14.9083i	1.22600	+	0.559894i	0.306080	+	0.952006i	$0.400983\pi$
$710$	0.887860	−	6.17520i	0.0333208	−	0.231751i
$711$	−4.05120	−	24.8277i	−0.151932	−	0.931110i
$712$		−	10.2662i		−	0.384741i
$713$	−31.3705	−	5.68030i	−1.17483	−	0.212729i
$714$	−1.25480	+	6.04332i	−0.0469598	+	0.226165i
$715$	−1.24006	+	0.796937i	−0.0463755	+	0.0298037i
$716$	1.65533	+	0.238001i	0.0618627	+	0.00889451i
$717$	−25.8486	+	35.2203i	−0.965334	+	1.31533i
$718$	5.00762	+	17.0544i	0.186883	+	0.636464i
$719$	−28.3164	+	12.9317i	−1.05602	+	0.482270i	−0.866278	−	0.499563i	$-0.833494\pi$
$719$	−28.3164	+	12.9317i	−1.05602	+	0.482270i	−0.189747	+	0.981833i	$0.560767\pi$
$720$	0.899583	+	2.86195i	0.0335255	+	0.106659i
$721$	3.33376	+	23.1868i	0.124156	+	0.863522i
$722$	3.62777	−	12.3551i	0.135012	−	0.459807i
$723$	1.67866	−	1.28162i	0.0624301	−	0.0476641i
$724$	2.73850	−	4.26119i	0.101776	−	0.158366i
$725$	2.66831	−	4.15197i	0.0990985	−	0.154200i
$726$	−1.04898	+	0.800877i	−0.0389314	+	0.0297233i
$727$	5.52536	−	18.8176i	0.204924	−	0.697908i	−0.791326	−	0.611394i	$-0.790609\pi$
$727$	5.52536	−	18.8176i	0.204924	−	0.697908i	0.996251	−	0.0865140i	$-0.0275727\pi$
$728$	−0.0977176	−	0.679641i	−0.00362165	−	0.0251892i
$729$	−13.2833	+	23.5065i	−0.491974	+	0.870610i
$730$	0.858657	−	0.392136i	0.0317803	−	0.0145136i
$731$	−2.40669	−	8.19644i	−0.0890147	−	0.303156i
$732$	−6.28072	+	8.55787i	−0.232142	+	0.316308i
$733$	52.1034	+	7.49134i	1.92448	+	0.276699i	0.995602	−	0.0936798i	$-0.0298630\pi$
$733$	52.1034	+	7.49134i	1.92448	+	0.276699i	0.928881	+	0.370379i	$0.120772\pi$
$734$	17.1796	−	11.0406i	0.634110	−	0.407517i
$735$	−1.68265	+	8.10389i	−0.0620654	+	0.298916i
$736$	−3.93767	−	2.73766i	−0.145144	−	0.100911i
$737$			23.2950i			0.858081i
$738$	−10.3447	+	1.68798i	−0.380795	+	0.0621355i
$739$	−1.05168	+	7.31457i	−0.0386865	+	0.269071i	−0.999979	−	0.00645879i	$-0.997944\pi$
$739$	−1.05168	+	7.31457i	−0.0386865	+	0.269071i	0.961293	+	0.275530i	$0.0888532\pi$
$740$	−10.8936	−	4.97492i	−0.400455	−	0.182882i
$741$	−1.96807	+	0.159513i	−0.0722988	+	0.00585985i
$742$	−4.27016	−	9.35035i	−0.156763	−	0.343262i
$743$	28.4811	+	32.8689i	1.04487	+	1.20584i	0.978113	+	0.208074i	$0.0667195\pi$
$743$	28.4811	+	32.8689i	1.04487	+	1.20584i	0.0667563	+	0.997769i	$0.478735\pi$
$744$	0.712555	−	11.4918i	0.0261235	−	0.421312i
$745$	−7.44146	−	2.18501i	−0.272634	−	0.0800525i
$746$	17.3177	−	19.9857i	0.634048	−	0.731730i
$747$	13.2407	+	19.7691i	0.484451	+	0.723312i
$748$	−6.43576	−	4.13601i	−0.235315	−	0.151227i
$749$	−20.5062	−	17.7687i	−0.749280	−	0.649255i
$750$	1.52798	+	0.815645i	0.0557940	+	0.0297831i
$751$	−11.3818	+	1.63645i	−0.415327	+	0.0597150i	−0.346811	−	0.937935i	$-0.612735\pi$
$751$	−11.3818	+	1.63645i	−0.415327	+	0.0597150i	−0.0685159	+	0.997650i	$0.521826\pi$
$752$	−1.71493	+	1.48599i	−0.0625370	+	0.0541886i
$753$	10.7610	−	2.44791i	0.392153	−	0.0892069i
$754$	−2.18160	+	0.640576i	−0.0794493	+	0.0233284i
$755$	−4.80784	+	10.5277i	−0.174975	+	0.383143i
$756$	5.31841	−	5.62966i	0.193429	−	0.204749i
$757$	3.02307	+	4.70399i	0.109875	+	0.170969i	0.891837	−	0.452358i	$-0.149417\pi$
$757$	3.02307	+	4.70399i	0.109875	+	0.170969i	−0.781961	+	0.623327i	$0.785781\pi$
$758$	−2.84422			−0.103307
$759$	25.1433	−	8.61620i	0.912644	−	0.312748i
$760$	−2.47454			−0.0897610
$761$	−24.6505	−	38.3568i	−0.893578	−	1.39043i	−0.920477	−	0.390797i	$-0.872200\pi$
$761$	−24.6505	−	38.3568i	−0.893578	−	1.39043i	0.0268989	−	0.999638i	$-0.491437\pi$
$762$	7.42480	−	20.4977i	0.268972	−	0.742552i
$763$	−9.71027	+	21.2625i	−0.351536	+	0.769755i
$764$	−2.33444	+	0.685453i	−0.0844570	+	0.0247988i
$765$	0.135899	+	7.17146i	0.00491345	+	0.259285i
$766$	13.8599	−	12.0097i	0.500779	−	0.433927i
$767$	2.74446	−	0.394594i	0.0990968	−	0.0142480i
$768$	0.815645	−	1.52798i	0.0294320	−	0.0551362i
$769$	−36.1389	−	31.3146i	−1.30320	−	1.12923i	−0.983342	−	0.181768i	$-0.941818\pi$
$769$	−36.1389	−	31.3146i	−1.30320	−	1.12923i	−0.319862	−	0.947464i	$-0.603636\pi$
$770$	4.01191	+	2.57830i	0.144579	+	0.0929154i
$771$	−8.34527	−	8.18862i	−0.300547	−	0.294906i
$772$	−7.37553	+	8.51181i	−0.265451	+	0.306347i
$773$	31.2031	+	9.16205i	1.12230	+	0.329536i	0.789676	−	0.613525i	$-0.210249\pi$
$773$	31.2031	+	9.16205i	1.12230	+	0.329536i	0.332621	+	0.943061i	$0.392067\pi$
$774$	−2.82440	+	10.3398i	−0.101521	+	0.371658i
$775$	−4.35323	−	5.02389i	−0.156373	−	0.180464i
$776$	−0.493475	−	1.08056i	−0.0177147	−	0.0387898i
$777$	2.49755	+	30.8148i	0.0895991	+	1.10547i
$778$	5.57720	+	2.54702i	0.199952	+	0.0913152i
$779$	1.23041	−	8.55768i	0.0440840	−	0.306611i
$780$	−0.285920	−	0.744949i	−0.0102376	−	0.0266735i
$781$		−	19.9619i		−	0.714294i
$782$	−7.18919	−	8.93278i	−0.257085	−	0.319435i
$783$	−20.9586	−	14.7791i	−0.749001	−	0.528161i
$784$	4.01999	−	2.58349i	0.143571	−	0.0922676i
$785$	−3.12263	−	0.448967i	−0.111452	−	0.0160243i
$786$	−4.63409	−	3.40101i	−0.165293	−	0.121310i
$787$	−1.86703	−	6.35853i	−0.0665525	−	0.226657i	0.919500	−	0.393089i	$-0.128594\pi$
$787$	−1.86703	−	6.35853i	−0.0665525	−	0.226657i	−0.986053	+	0.166432i	$0.946775\pi$
$788$	18.5369	−	8.46551i	0.660349	−	0.301571i
$789$	11.2127	−	6.26121i	0.399182	−	0.222905i
$790$	1.19336	+	8.29999i	0.0424578	+	0.295300i
$791$	3.29921	−	11.2361i	0.117306	−	0.399508i
$792$	4.15232	+	8.65451i	0.147546	+	0.307525i
$793$	1.52647	−	2.37523i	0.0542064	−	0.0843468i
$794$	−5.61448	+	8.73630i	−0.199250	+	0.310040i
$795$	−7.24899	−	9.49467i	−0.257095	−	0.336741i
$796$	−0.465912	+	1.58675i	−0.0165138	+	0.0562409i
$797$	−0.354525	−	2.46578i	−0.0125579	−	0.0873423i	0.982579	−	0.185847i	$-0.0595030\pi$
$797$	−0.354525	−	2.46578i	−0.0125579	−	0.0873423i	−0.995137	+	0.0985051i	$0.968594\pi$
$798$	3.11447	+	5.57744i	0.110251	+	0.197439i
$799$	−4.93512	+	2.25380i	−0.174592	+	0.0797336i
$800$	−0.281733	−	0.959493i	−0.00996075	−	0.0339232i
$801$	−22.8897	+	20.6061i	−0.808766	+	0.728081i
$802$	15.8502	+	2.27892i	0.559692	+	0.0804715i
$803$	2.54091	−	1.63294i	0.0896668	−	0.0576253i
$804$	−12.3466	−	2.56359i	−0.435433	−	0.0904109i
$805$	4.48159	+	5.56850i	0.157955	+	0.196264i
$806$			3.06245i			0.107870i
$807$	41.8675	−	16.0692i	1.47381	−	0.565664i
$808$	1.60071	−	11.1332i	0.0563128	−	0.391664i
$809$	−3.47383	−	1.58645i	−0.122134	−	0.0557765i	0.353411	−	0.935468i	$-0.385022\pi$
$809$	−3.47383	−	1.58645i	−0.122134	−	0.0557765i	−0.475545	+	0.879692i	$0.657749\pi$
$810$	4.57543	−	7.75019i	0.160764	−	0.272314i
$811$	−19.3604	−	42.3935i	−0.679837	−	1.48864i	−0.862816	−	0.505519i	$-0.831301\pi$
$811$	−19.3604	−	42.3935i	−0.679837	−	1.48864i	0.182978	−	0.983117i	$-0.441426\pi$
$812$	4.81717	+	5.55931i	0.169050	+	0.195094i
$813$	9.63033	+	0.597131i	0.337750	+	0.0209423i
$814$	−36.7667	−	10.7957i	−1.28867	−	0.378388i
$815$	13.9699	−	16.1221i	0.489344	−	0.564733i
$816$	2.90039	−	2.95587i	0.101534	−	0.103476i
$817$	−7.43773	−	4.77994i	−0.260213	−	0.167229i
$818$	17.3322	+	15.0185i	0.606007	+	0.525108i
$819$	−1.31920	+	1.58204i	−0.0460967	+	0.0552809i
$820$	3.45829	−	0.497227i	0.120769	−	0.0173639i
$821$	36.1370	−	31.3129i	1.26119	−	1.09283i	0.269658	−	0.962956i	$-0.413089\pi$
$821$	36.1370	−	31.3129i	1.26119	−	1.09283i	0.991531	−	0.129870i	$-0.0414561\pi$
$822$	−1.17827	−	5.17968i	−0.0410970	−	0.180662i
$823$	50.8534	−	14.9319i	1.77264	−	0.520494i	0.778409	−	0.627758i	$-0.216027\pi$
$823$	50.8534	−	14.9319i	1.77264	−	0.520494i	0.994231	+	0.107264i	$0.0342090\pi$
$824$	6.52906	−	14.2966i	0.227451	−	0.498047i
$825$	5.21072	+	1.88746i	0.181414	+	0.0657130i
$826$	−4.84974	−	7.54635i	−0.168744	−	0.262571i
$827$	−2.11165			−0.0734293			−0.0367146	−	0.999326i	$-0.511689\pi$
$827$	−2.11165			−0.0734293			−0.0367146	+	0.999326i	$0.511689\pi$
$828$	1.79970	+	14.2745i	0.0625440	+	0.496073i
$829$	−4.03347			−0.140088			−0.0700442	−	0.997544i	$-0.522314\pi$
$829$	−4.03347			−0.140088			−0.0700442	+	0.997544i	$0.522314\pi$
$830$	−4.28792	−	6.67213i	−0.148836	−	0.231593i
$831$	−27.9055	−	10.1081i	−0.968030	−	0.350646i
$832$	−0.191377	+	0.419056i	−0.00663479	+	0.0145282i
$833$	10.9624	−	3.21884i	0.379824	−	0.111526i
$834$	1.48541	+	6.52985i	0.0514355	+	0.226110i
$835$	−18.6888	+	16.1940i	−0.646754	+	0.560415i
$836$	−7.83718	+	1.12682i	−0.271055	+	0.0389718i
$837$	−27.0527	+	21.4776i	−0.935077	+	0.742373i
$838$	22.8911	+	19.8353i	0.790761	+	0.685198i
$839$	−14.4812	−	9.30653i	−0.499948	−	0.321297i	0.266247	−	0.963905i	$-0.414216\pi$
$839$	−14.4812	−	9.30653i	−0.499948	−	0.321297i	−0.766195	+	0.642608i	$0.777853\pi$
$840$	−1.80804	+	1.84263i	−0.0623833	+	0.0635766i
$841$	−3.03939	+	3.50764i	−0.104806	+	0.120953i
$842$	37.2951	+	10.9508i	1.28527	+	0.377390i
$843$	−14.3477	−	0.889636i	−0.494163	−	0.0306407i
$844$	2.19788	+	2.53649i	0.0756541	+	0.0873095i
$845$	−5.31223	−	11.6322i	−0.182746	−	0.400159i
$846$	6.75538	+	0.840971i	0.232255	+	0.0289132i
$847$	−1.03304	−	0.471773i	−0.0354956	−	0.0162103i
$848$	−0.981513	+	6.82658i	−0.0337053	+	0.234426i
$849$	36.4020	−	13.9715i	1.24931	−	0.479501i
$850$		−	2.39092i		−	0.0820077i
$851$	−47.1567	−	32.7856i	−1.61651	−	1.12388i
$852$	10.5801	+	2.19679i	0.362468	+	0.0752609i
$853$	−4.09969	+	2.63471i	−0.140371	+	0.0902107i	−0.608941	−	0.793215i	$-0.708405\pi$
$853$	−4.09969	+	2.63471i	−0.140371	+	0.0902107i	0.468571	+	0.883426i	$0.344769\pi$
$854$	−9.04158	−	1.29998i	−0.309397	−	0.0444845i
$855$	4.96686	+	5.51728i	0.169863	+	0.188687i
$856$	5.12895	+	17.4676i	0.175304	+	0.597030i
$857$	12.4339	−	5.67836i	0.424733	−	0.193969i	−0.191569	−	0.981479i	$-0.561358\pi$
$857$	12.4339	−	5.67836i	0.424733	−	0.193969i	0.616302	+	0.787510i	$0.288630\pi$
$858$	−1.24477	−	2.22915i	−0.0424956	−	0.0761019i
$859$	5.69801	+	39.6306i	0.194414	+	1.35218i	0.820153	+	0.572145i	$0.193888\pi$
$859$	5.69801	+	39.6306i	0.194414	+	1.35218i	−0.625739	+	0.780032i	$0.715202\pi$
$860$	1.00660	−	3.42816i	0.0343247	−	0.116899i
$861$	−5.47333	−	7.16893i	−0.186531	−	0.244316i
$862$	−19.5197	+	30.3733i	−0.664844	+	1.03452i
$863$	−4.65635	+	7.24542i	−0.158504	+	0.246637i	−0.911418	−	0.411482i	$-0.865011\pi$
$863$	−4.65635	+	7.24542i	−0.158504	+	0.246637i	0.752914	+	0.658119i	$0.228648\pi$
$864$	−5.04397	+	1.24836i	−0.171599	+	0.0424702i
$865$	−2.19667	+	7.48118i	−0.0746891	+	0.254368i
$866$	−1.67486	−	11.6489i	−0.0569141	−	0.395846i
$867$	−17.0635	+	9.52835i	−0.579508	+	0.323600i
$868$	9.01248	−	4.11586i	0.305903	−	0.139701i
$869$	7.55903	+	25.7437i	0.256422	+	0.873295i
$870$	6.89162	+	5.05784i	0.233648	+	0.171477i
$871$	3.31984	+	0.477321i	0.112489	+	0.0161734i
$872$	13.1935	−	8.47895i	0.446789	−	0.287134i
$873$	−1.41874	+	3.26914i	−0.0480170	+	0.110644i
$874$	−11.6776	−	2.11448i	−0.395000	−	0.0715233i
$875$			1.49044i			0.0503862i
$876$	0.585857	+	1.52642i	0.0197943	+	0.0515730i
$877$	−3.35239	+	23.3164i	−0.113202	+	0.787338i	0.851568	+	0.524244i	$0.175652\pi$
$877$	−3.35239	+	23.3164i	−0.113202	+	0.787338i	−0.964770	+	0.263094i	$0.915257\pi$
$878$	−16.4285	−	7.50263i	−0.554434	−	0.253202i
$879$	−4.26806	−	52.6593i	−0.143958	−	1.77616i
$880$	−1.32920	−	2.91054i	−0.0448073	−	0.0981144i
$881$	13.7549	+	15.8740i	0.463414	+	0.534808i	0.938568	−	0.345094i	$-0.112153\pi$
$881$	13.7549	+	15.8740i	0.463414	+	0.534808i	−0.475154	+	0.879903i	$0.657608\pi$
$882$	−13.8291	−	3.77750i	−0.465649	−	0.127195i
$883$	21.4104	+	6.28667i	0.720518	+	0.211563i	0.621379	−	0.783510i	$-0.286573\pi$
$883$	21.4104	+	6.28667i	0.720518	+	0.211563i	0.0991396	+	0.995074i	$0.468391\pi$
$884$	−0.721307	+	0.832432i	−0.0242602	+	0.0279977i
$885$	−7.44073	−	7.30106i	−0.250117	−	0.245422i
$886$	−4.10463	−	2.63789i	−0.137898	−	0.0886215i
$887$	12.8971	+	11.1754i	0.433042	+	0.375233i	0.843931	−	0.536452i	$-0.180236\pi$
$887$	12.8971	+	11.1754i	0.433042	+	0.375233i	−0.410888	+	0.911686i	$0.634781\pi$
$888$	9.76798	−	18.2988i	0.327792	−	0.614066i
$889$	18.5690	−	2.66981i	0.622783	−	0.0895427i
$890$	7.75865	−	6.72291i	0.260071	−	0.225353i
$891$	10.9618	−	26.6293i	0.367234	−	0.892115i
$892$	12.9746	−	3.80969i	0.434422	−	0.127558i
$893$	−2.33262	+	5.10774i	−0.0780583	+	0.170924i
$894$	4.57495	−	12.6301i	0.153009	−	0.422413i
$895$	0.904143	+	1.40687i	0.0302222	+	0.0470266i
$896$	1.49044			0.0497923
$897$	−0.712728	−	3.75980i	−0.0237973	−	0.125536i
$898$	−35.3414			−1.17936
$899$	−17.7378	−	27.6005i	−0.591587	−	0.920528i
$900$	−1.57381	+	2.55404i	−0.0524605	+	0.0851346i
$901$	−6.85003	+	14.9995i	−0.228208	+	0.499705i
$902$	10.7264	−	3.14956i	0.357151	−	0.104869i
$903$	−8.99373	+	2.04589i	−0.299293	+	0.0680830i
$904$	−5.93792	+	5.14524i	−0.197492	+	0.171128i
$905$	5.01373	−	0.720865i	0.166662	−	0.0239624i
$906$	−17.6842	−	9.43994i	−0.587519	−	0.313621i
$907$	6.05708	+	5.24849i	0.201122	+	0.174273i	0.749599	−	0.661893i	$-0.230247\pi$
$907$	6.05708	+	5.24849i	0.201122	+	0.174273i	−0.548477	+	0.836166i	$0.684792\pi$
$908$	11.4851	+	7.38103i	0.381147	+	0.244948i
$909$	−28.0357	+	18.7774i	−0.929886	+	0.622807i
$910$	0.449647	−	0.518920i	0.0149056	−	0.0172020i
$911$	15.5569	+	4.56793i	0.515424	+	0.151342i	0.529092	−	0.848564i	$-0.322533\pi$
$911$	15.5569	+	4.56793i	0.515424	+	0.151342i	−0.0136679	+	0.999907i	$0.504351\pi$
$912$	0.265247	−	4.27781i	0.00878320	−	0.141653i
$913$	−16.6186	−	19.1789i	−0.549996	−	0.634729i
$914$	−9.26208	−	20.2811i	−0.306362	−	0.670840i
$915$	−10.5806	+	0.857563i	−0.349784	+	0.0283502i
$916$	1.57439	+	0.719001i	0.0520194	+	0.0237565i
$917$	0.703941	−	4.89602i	0.0232462	−	0.161681i
$918$	−12.4121	−	0.533778i	−0.409660	−	0.0176173i
$919$		−	10.4529i		−	0.344808i	−0.985026	−	0.172404i	$-0.944847\pi$
$919$		−	10.4529i		−	0.344808i	0.985026	−	0.172404i	$-0.0551535\pi$
$920$	−0.509642	−	4.76868i	−0.0168024	−	0.157219i
$921$	0.533651	−	2.57015i	0.0175844	−	0.0846892i
$922$	6.44153	−	4.13972i	0.212140	−	0.136334i
$923$	−2.84484	−	0.409026i	−0.0936391	−	0.0134633i
$924$	−4.88722	+	6.65914i	−0.160778	+	0.219070i
$925$	−3.37397	−	11.4907i	−0.110935	−	0.377811i
$926$	−31.3225	+	14.3045i	−1.02932	+	0.470075i
$927$	−44.9811	+	14.1387i	−1.47737	+	0.464376i
$928$	−0.702389	−	4.88522i	−0.0230570	−	0.160365i
$929$	4.63240	−	15.7765i	0.151984	−	0.517611i	−0.847938	−	0.530096i	$-0.822156\pi$
$929$	4.63240	−	15.7765i	0.151984	−	0.517611i	0.999922	+	0.0124849i	$0.00397417\pi$
$930$	9.15158	−	6.98705i	0.300092	−	0.229114i
$931$	6.39296	−	9.94763i	0.209521	−	0.326021i
$932$	8.09165	−	12.5908i	0.265051	−	0.412427i
$933$	−1.28557	+	0.981505i	−0.0420876	+	0.0321330i
$934$	6.56586	−	22.3613i	0.214841	−	0.731683i
$935$	−1.08874	−	7.57233i	−0.0356055	−	0.247642i
$936$	1.31846	−	0.414427i	0.0430954	−	0.0135460i
$937$	5.04682	−	2.30481i	0.164872	−	0.0752947i	−0.331269	−	0.943536i	$-0.607477\pi$
$937$	5.04682	−	2.30481i	0.164872	−	0.0752947i	0.496142	+	0.868242i	$0.334750\pi$
$938$	−3.05708	−	10.4115i	−0.0998172	−	0.339946i
$939$	−28.9660	+	39.4680i	−0.945271	+	1.28799i
$940$	−2.24608	−	0.322937i	−0.0732590	−	0.0105331i
$941$	47.9847	−	30.8379i	1.56426	−	1.00529i	0.583023	−	0.812455i	$-0.301870\pi$
$941$	47.9847	−	30.8379i	1.56426	−	1.00529i	0.981232	−	0.192830i	$-0.0617667\pi$
$942$	1.11086	−	5.35007i	0.0361938	−	0.174315i
$943$	16.7449	+	0.608624i	0.545288	+	0.0198195i
$944$			6.01858i			0.195888i
$945$	7.73743	+	0.332746i	0.251699	+	0.0108242i
$946$	1.62696	−	11.3158i	0.0528971	−	0.367908i
$947$	−25.1729	−	11.4961i	−0.818010	−	0.373573i	−0.0379520	−	0.999280i	$-0.512083\pi$
$947$	−25.1729	−	11.4961i	−0.818010	−	0.373573i	−0.780058	+	0.625707i	$0.784811\pi$
$948$	−14.4764	+	1.17332i	−0.470170	+	0.0381075i
$949$	−0.180652	−	0.395573i	−0.00586421	−	0.0128408i
$950$	−1.62048	−	1.87013i	−0.0525753	−	0.0606751i
$951$	3.09309	−	49.8844i	0.100300	−	1.61761i
$952$	3.41918	+	1.00396i	0.110816	+	0.0325386i
$953$	10.4379	−	12.0460i	0.338118	−	0.390209i	−0.561072	−	0.827767i	$-0.689611\pi$
$953$	10.4379	−	12.0460i	0.338118	−	0.390209i	0.899190	+	0.437558i	$0.144156\pi$
$954$	17.1907	−	11.5138i	0.556571	−	0.372773i
$955$	−2.04676	−	1.31537i	−0.0662317	−	0.0425645i
$956$	19.0624	+	16.5176i	0.616522	+	0.534219i
$957$	24.1298	+	12.8806i	0.780005	+	0.416371i
$958$	−6.75881	+	0.971770i	−0.218367	+	0.0313965i
$959$	3.45455	−	2.99339i	0.111553	−	0.0966615i
$960$	1.68890	−	0.384191i	0.0545091	−	0.0123997i
$961$	−12.6558	+	3.71608i	−0.408252	+	0.119874i
$962$	−2.29188	+	5.01853i	−0.0738933	+	0.161804i
$963$	28.6513	−	46.4963i	0.923277	−	1.49832i
$964$	−0.659232	−	1.02579i	−0.0212324	−	0.0330383i
$965$	−11.2627			−0.362560
$966$	−10.1068	+	7.15057i	−0.325182	+	0.230066i
$967$	24.0592			0.773692			0.386846	−	0.922144i	$-0.373565\pi$
$967$	24.0592			0.773692			0.386846	+	0.922144i	$0.373565\pi$
$968$	0.411949	+	0.641005i	0.0132405	+	0.0206027i
$969$	3.49003	−	9.63492i	0.112116	−	0.309518i
$970$	0.493475	−	1.08056i	0.0158445	−	0.0346946i
$971$	35.3126	−	10.3687i	1.13324	−	0.332748i	0.339257	−	0.940694i	$-0.389824\pi$
$971$	35.3126	−	10.3687i	1.13324	−	0.332748i	0.793979	+	0.607946i	$0.208006\pi$
$972$	12.9076	+	8.74042i	0.414010	+	0.280349i
$973$	−4.35504	+	3.77366i	−0.139616	+	0.120978i
$974$	12.0291	−	1.72952i	0.385437	−	0.0554174i
$975$	0.375757	−	0.703922i	0.0120339	−	0.0225435i
$976$	4.63180	+	4.01348i	0.148260	+	0.128468i
$977$	−21.6173	−	13.8926i	−0.691599	−	0.444464i	0.147055	−	0.989128i	$-0.453021\pi$
$977$	−21.6173	−	13.8926i	−0.691599	−	0.444464i	−0.838654	+	0.544665i	$0.816657\pi$
$978$	26.3733	+	25.8783i	0.843326	+	0.827497i
$979$	21.5113	−	24.8253i	0.687503	−	0.793420i
$980$	4.58501	+	1.34628i	0.146463	+	0.0430053i
$981$	−45.3867	−	12.3977i	−1.44908	−	0.395827i
$982$	20.1471	+	23.2509i	0.642918	+	0.741967i
$983$	24.9934	+	54.7280i	0.797167	+	1.74555i	0.654888	+	0.755726i	$0.272716\pi$
$983$	24.9934	+	54.7280i	0.797167	+	1.74555i	0.142279	+	0.989827i	$0.454557\pi$
$984$	0.488876	+	6.03175i	0.0155848	+	0.192285i
$985$	18.5369	+	8.46551i	0.590634	+	0.269734i
$986$	1.67935	−	11.6802i	0.0534815	−	0.371972i
$987$	2.09904	+	5.46895i	0.0668133	+	0.174079i
$988$			1.13999i			0.0362679i
$989$	7.67957	−	15.3177i	0.244196	−	0.487074i
$990$	−3.82145	+	8.80561i	−0.121454	+	0.279861i
$991$	20.8033	−	13.3695i	0.660838	−	0.424695i	−0.166774	−	0.985995i	$-0.553335\pi$
$991$	20.8033	−	13.3695i	0.660838	−	0.424695i	0.827612	+	0.561300i	$0.189699\pi$
$992$	−6.57990	−	0.946047i	−0.208912	−	0.0300370i
$993$	−38.8099	−	28.4830i	−1.23159	−	0.903881i
$994$	2.61968	+	8.92179i	0.0830910	+	0.282982i
$995$	−1.50429	+	0.686988i	−0.0476893	+	0.0217790i
$996$	11.9939	−	6.69746i	0.380042	−	0.212217i
$997$	6.28624	+	43.7218i	0.199087	+	1.38468i	0.806941	+	0.590633i	$0.201122\pi$
$997$	6.28624	+	43.7218i	0.199087	+	1.38468i	−0.607853	+	0.794049i	$0.707969\pi$
$998$	−6.05682	+	20.6276i	−0.191725	+	0.652957i
$999$	−60.4054	+	14.9501i	−1.91114	+	0.473002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.11.9	✓	160
3.2	odd	2		690.2.q.b.11.8	yes	160
23.21	odd	22		690.2.q.b.251.8	yes	160
69.44	even	22	inner	690.2.q.a.251.9	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.9	✓	160	1.1	even	1	trivial
690.2.q.a.251.9	yes	160	69.44	even	22	inner
690.2.q.b.11.8	yes	160	3.2	odd	2
690.2.q.b.251.8	yes	160	23.21	odd	22

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(-1.62851 - 0.589888i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.384191 - 1.68890i) q^{6} +(1.12640 - 0.976034i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.30406 + 1.92127i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(-1.62851 - 0.589888i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.384191 - 1.68890i) q^{6} +(1.12640 - 0.976034i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.30406 + 1.92127i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-2.69175 - 1.72988i) q^{11} +(1.21309 - 1.23629i) q^{12} +(-0.301686 + 0.348165i) q^{13} +(1.43007 + 0.419907i) q^{14} +(1.72873 + 0.107190i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.993222 - 2.17485i) q^{17} +(-0.370607 + 2.97702i) q^{18} +(-2.25092 - 1.02796i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.41011 + 0.925025i) q^{21} -3.19969i q^{22} +(1.51739 - 4.54945i) q^{23} +(1.69588 + 0.352123i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.455999 - 0.0655627i) q^{26} +(-2.61885 - 4.48794i) q^{27} +(0.419907 + 1.43007i) q^{28} +(4.48945 - 2.05026i) q^{29} +(0.844448 + 1.51225i) q^{30} +(-0.946047 - 6.57990i) q^{31} +(0.281733 - 0.959493i) q^{32} +(3.36310 + 4.40496i) q^{33} +(1.29263 - 2.01137i) q^{34} +(-0.805795 + 1.25384i) q^{35} +(-2.70479 + 1.29772i) q^{36} +(3.37397 - 11.4907i) q^{37} +(-0.352164 - 2.44935i) q^{38} +(0.696676 - 0.389027i) q^{39} +(0.909632 - 0.415415i) q^{40} +(0.984332 + 3.35233i) q^{41} +(-2.08118 - 1.52740i) q^{42} +(3.53652 + 0.508475i) q^{43} +(2.69175 - 1.72988i) q^{44} +(-2.75202 - 1.19432i) q^{45} +(4.64761 - 1.18311i) q^{46} -2.26918i q^{47} +(0.620637 + 1.61704i) q^{48} +(-0.680062 + 4.72993i) q^{49} +(0.909632 + 0.415415i) q^{50} +(0.334548 + 4.12765i) q^{51} +(-0.191377 - 0.419056i) q^{52} +(-4.51643 - 5.21223i) q^{53} +(2.35964 - 4.62948i) q^{54} +(3.07008 + 0.901458i) q^{55} +(-0.976034 + 1.12640i) q^{56} +(3.05926 + 3.00183i) q^{57} +(4.15197 + 2.66831i) q^{58} +(-4.54854 - 3.94133i) q^{59} +(-0.815645 + 1.52798i) q^{60} +(-6.06637 + 0.872212i) q^{61} +(5.02389 - 4.35323i) q^{62} +(4.47053 - 0.0847166i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.191377 - 0.419056i) q^{65} +(-1.88746 + 5.21072i) q^{66} +(-3.93607 - 6.12464i) q^{67} +2.39092 q^{68} +(-5.15475 + 6.51372i) q^{69} -1.49044 q^{70} +(3.37290 + 5.24833i) q^{71} +(-2.55404 - 1.57381i) q^{72} +(-0.392136 + 0.858657i) q^{73} +(11.4907 - 3.37397i) q^{74} +(-1.68890 + 0.384191i) q^{75} +(1.87013 - 1.62048i) q^{76} +(-4.72043 + 0.678695i) q^{77} +(0.703922 + 0.375757i) q^{78} +(-6.33721 - 5.49123i) q^{79} +(0.841254 + 0.540641i) q^{80} +(1.61742 + 8.85347i) q^{81} +(-2.28799 + 2.64048i) q^{82} +(7.60990 + 2.23447i) q^{83} +(0.159761 - 2.57658i) q^{84} +(1.56572 + 1.80693i) q^{85} +(1.48423 + 3.25001i) q^{86} +(-8.52052 + 0.690592i) q^{87} +(2.91054 + 1.32920i) q^{88} +(-1.46103 + 10.1617i) q^{89} +(-0.483129 - 2.96084i) q^{90} +0.686630i q^{91} +(3.50798 + 3.27018i) q^{92} +(-2.34076 + 11.2735i) q^{93} +(1.90895 - 1.22681i) q^{94} +(2.44935 + 0.352164i) q^{95} +(-1.02480 + 1.39635i) q^{96} +(0.334672 + 1.13979i) q^{97} +(-4.34674 + 1.98509i) q^{98} +(-2.87839 - 9.15736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

L-functions

Modular forms

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