LMFDB - Embedded newform 690.2.m.h.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, 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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	690.151
Dual form			690.2.m.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-4.28731 - 1.25887i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-4.28731 - 1.25887i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(0.0345508 - 0.0398737i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(-4.11803 + 1.20916i) q^{13} +(-1.85620 - 4.06451i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.686059 + 4.77165i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(-0.891667 + 6.20168i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(-2.92612 - 3.37692i) q^{21} +0.0527605 q^{22} +(-2.00569 + 4.35629i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-3.61056 - 2.32037i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(1.85620 - 4.06451i) q^{28} +(-0.662618 - 4.60861i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(2.42136 - 1.55611i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(0.0506233 - 0.0148644i) q^{33} +(-3.15690 + 3.64325i) q^{34} +(2.92612 - 3.37692i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.733427 - 1.60598i) q^{37} +(-5.27083 + 3.38736i) q^{38} +(-4.11803 - 1.20916i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(4.24660 - 9.29876i) q^{41} +(0.635906 - 4.42282i) q^{42} +(9.31589 + 5.98696i) q^{43} +(0.0345508 + 0.0398737i) q^{44} -1.00000 q^{45} +(-4.60571 + 1.33696i) q^{46} -2.02404 q^{47} +(-0.654861 - 0.755750i) q^{48} +(10.9075 + 7.00982i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-2.00260 + 4.38508i) q^{51} +(-0.610798 - 4.24820i) q^{52} +(1.07346 + 0.315196i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(0.0219175 + 0.0479926i) q^{55} +(4.28731 - 1.25887i) q^{56} +(-4.10300 + 4.73511i) q^{57} +(3.04903 - 3.51877i) q^{58} +(-6.35310 + 1.86544i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(6.79411 - 4.36631i) q^{61} +(2.76168 + 0.810902i) q^{62} +(-0.635906 - 4.42282i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.610798 - 4.24820i) q^{65} +(0.0443850 + 0.0285245i) q^{66} +(7.19410 + 8.30243i) q^{67} -4.82071 q^{68} +(-4.04248 + 2.58038i) q^{69} +4.46831 q^{70} +(6.02569 + 6.95402i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(1.56332 - 10.8732i) q^{73} +(0.733427 - 1.60598i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-6.01166 - 1.76518i) q^{76} +(-0.198326 + 0.127456i) q^{77} +(-1.78291 - 3.90403i) q^{78} +(-11.3725 + 3.33926i) q^{79} +(0.654861 - 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(9.80846 - 2.88002i) q^{82} +(-5.27528 - 11.5513i) q^{83} +(3.75898 - 2.41575i) q^{84} +(-4.62544 - 1.35815i) q^{85} +(1.57597 + 10.9611i) q^{86} +(1.93417 - 4.23525i) q^{87} +(-0.00750860 + 0.0522235i) q^{88} +(10.3471 + 6.64967i) q^{89} +(-0.654861 - 0.755750i) q^{90} +19.1774 q^{91} +(-4.02651 - 2.60524i) q^{92} +2.87827 q^{93} +(-1.32546 - 1.52967i) q^{94} +(-5.27083 - 3.38736i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-5.80480 + 12.7107i) q^{97} +(1.84522 + 12.8338i) q^{98} +(0.0506233 + 0.0148644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−4.28731	−	1.25887i	−1.62045	−	0.475807i	−0.659311	−	0.751871i	$-0.729152\pi$
$7$	−4.28731	−	1.25887i	−1.62045	−	0.475807i	−0.961139	+	0.276064i	$0.910970\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−0.959493	+	0.281733i	−0.303418	+	0.0890917i
$11$	0.0345508	−	0.0398737i	0.0104175	−	0.0120224i	−0.750517	−	0.660851i	$-0.770195\pi$
$11$	0.0345508	−	0.0398737i	0.0104175	−	0.0120224i	0.760934	+	0.648829i	$0.224741\pi$
$12$	−0.654861	+	0.755750i	−0.189042	+	0.218166i
$13$	−4.11803	+	1.20916i	−1.14214	+	0.335361i	−0.797467	−	0.603363i	$-0.793827\pi$
$13$	−4.11803	+	1.20916i	−1.14214	+	0.335361i	−0.344669	+	0.938724i	$0.612009\pi$
$14$	−1.85620	−	4.06451i	−0.496091	−	1.08629i
$15$	−0.841254	+	0.540641i	−0.217211	+	0.139593i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.686059	+	4.77165i	0.166394	+	1.15729i	0.886262	+	0.463184i	$0.153293\pi$
$17$	0.686059	+	4.77165i	0.166394	+	1.15729i	−0.719869	+	0.694110i	$0.755798\pi$
$18$	−0.415415	+	0.909632i	−0.0979143	+	0.214402i
$19$	−0.891667	+	6.20168i	−0.204562	+	1.42276i	0.585965	+	0.810336i	$0.300716\pi$
$19$	−0.891667	+	6.20168i	−0.204562	+	1.42276i	−0.790527	+	0.612427i	$0.790194\pi$
$20$	−0.841254	−	0.540641i	−0.188110	−	0.120891i
$21$	−2.92612	−	3.37692i	−0.638531	−	0.736904i
$22$	0.0527605			0.0112486
$23$	−2.00569	+	4.35629i	−0.418215	+	0.908348i
$23$	−2.00569	+	4.35629i	−0.418215	+	0.908348i
$24$	−1.00000			−0.204124
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−3.61056	−	2.32037i	−0.708089	−	0.455061i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	1.85620	−	4.06451i	0.350789	−	0.768121i
$29$	−0.662618	−	4.60861i	−0.123045	−	0.855797i	−0.954075	−	0.299569i	$-0.903157\pi$
$29$	−0.662618	−	4.60861i	−0.123045	−	0.855797i	0.831030	−	0.556228i	$-0.187752\pi$
$30$	−0.959493	−	0.281733i	−0.175179	−	0.0514371i
$31$	2.42136	−	1.55611i	0.434888	−	0.279486i	−0.304824	−	0.952409i	$-0.598598\pi$
$31$	2.42136	−	1.55611i	0.434888	−	0.279486i	0.739713	+	0.672923i	$0.234961\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	0.0506233	−	0.0148644i	0.00881239	−	0.00258755i
$34$	−3.15690	+	3.64325i	−0.541403	+	0.624813i
$35$	2.92612	−	3.37692i	0.494604	−	0.570804i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−0.733427	−	1.60598i	−0.120575	−	0.264022i	0.839715	−	0.543028i	$-0.182722\pi$
$37$	−0.733427	−	1.60598i	−0.120575	−	0.264022i	−0.960289	+	0.279006i	$0.909995\pi$
$38$	−5.27083	+	3.38736i	−0.855042	+	0.549502i
$39$	−4.11803	−	1.20916i	−0.659413	−	0.193621i
$40$	−0.142315	−	0.989821i	−0.0225020	−	0.156505i
$41$	4.24660	−	9.29876i	0.663207	−	1.45222i	−0.216295	−	0.976328i	$-0.569397\pi$
$41$	4.24660	−	9.29876i	0.663207	−	1.45222i	0.879503	−	0.475894i	$-0.157875\pi$
$42$	0.635906	−	4.42282i	0.0981225	−	0.682457i
$43$	9.31589	+	5.98696i	1.42066	+	0.913003i	0.999983	+	0.00579243i	$0.00184380\pi$
$43$	9.31589	+	5.98696i	1.42066	+	0.913003i	0.420677	+	0.907210i	$0.361793\pi$
$44$	0.0345508	+	0.0398737i	0.00520873	+	0.00601119i
$45$	−1.00000			−0.149071
$46$	−4.60571	+	1.33696i	−0.679074	+	0.197125i
$47$	−2.02404			−0.295236			−0.147618	−	0.989044i	$-0.547161\pi$
$47$	−2.02404			−0.295236			−0.147618	+	0.989044i	$0.547161\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	10.9075	+	7.00982i	1.55821	+	1.00140i
$50$	0.142315	−	0.989821i	0.0201264	−	0.139982i
$51$	−2.00260	+	4.38508i	−0.280420	+	0.614033i
$52$	−0.610798	−	4.24820i	−0.0847025	−	0.589119i
$53$	1.07346	+	0.315196i	0.147451	+	0.0432955i	0.354625	−	0.935009i	$-0.384608\pi$
$53$	1.07346	+	0.315196i	0.147451	+	0.0432955i	−0.207174	+	0.978304i	$0.566427\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	0.0219175	+	0.0479926i	0.00295536	+	0.00647133i
$56$	4.28731	−	1.25887i	0.572916	−	0.168223i
$57$	−4.10300	+	4.73511i	−0.543456	+	0.627181i
$58$	3.04903	−	3.51877i	0.400357	−	0.462037i
$59$	−6.35310	+	1.86544i	−0.827103	+	0.242859i	−0.667772	−	0.744366i	$-0.732752\pi$
$59$	−6.35310	+	1.86544i	−0.827103	+	0.242859i	−0.159331	+	0.987225i	$0.550934\pi$
$60$	−0.415415	−	0.909632i	−0.0536298	−	0.117433i
$61$	6.79411	−	4.36631i	0.869896	−	0.559048i	−0.0278247	−	0.999613i	$-0.508858\pi$
$61$	6.79411	−	4.36631i	0.869896	−	0.559048i	0.897721	+	0.440564i	$0.145222\pi$
$62$	2.76168	+	0.810902i	0.350734	+	0.102985i
$63$	−0.635906	−	4.42282i	−0.0801166	−	0.557224i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.610798	−	4.24820i	0.0757602	−	0.526924i
$66$	0.0443850	+	0.0285245i	0.00546341	+	0.00351112i
$67$	7.19410	+	8.30243i	0.878899	+	1.01430i	0.999766	+	0.0216345i	$0.00688702\pi$
$67$	7.19410	+	8.30243i	0.878899	+	1.01430i	−0.120867	+	0.992669i	$0.538568\pi$
$68$	−4.82071			−0.584597
$69$	−4.04248	+	2.58038i	−0.486657	+	0.310642i
$70$	4.46831			0.534065
$71$	6.02569	+	6.95402i	0.715118	+	0.825290i	0.990711	−	0.135984i	$-0.0434196\pi$
$71$	6.02569	+	6.95402i	0.715118	+	0.825290i	−0.275593	+	0.961274i	$0.588874\pi$
$72$	−0.841254	−	0.540641i	−0.0991427	−	0.0637151i
$73$	1.56332	−	10.8732i	0.182973	−	1.27261i	−0.666712	−	0.745316i	$-0.732299\pi$
$73$	1.56332	−	10.8732i	0.182973	−	1.27261i	0.849685	−	0.527291i	$-0.176792\pi$
$74$	0.733427	−	1.60598i	0.0852592	−	0.186692i
$75$	−0.142315	−	0.989821i	−0.0164331	−	0.114295i
$76$	−6.01166	−	1.76518i	−0.689584	−	0.202480i
$77$	−0.198326	+	0.127456i	−0.0226013	+	0.0145250i
$78$	−1.78291	−	3.90403i	−0.201875	−	0.442045i
$79$	−11.3725	+	3.33926i	−1.27950	+	0.375696i	−0.849719	−	0.527236i	$-0.823229\pi$
$79$	−11.3725	+	3.33926i	−1.27950	+	0.375696i	−0.429784	+	0.902932i	$0.641410\pi$
$80$	0.654861	−	0.755750i	0.0732157	−	0.0844954i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	9.80846	−	2.88002i	1.08316	−	0.318045i
$83$	−5.27528	−	11.5513i	−0.579038	−	1.26792i	−0.941844	−	0.336051i	$-0.890909\pi$
$83$	−5.27528	−	11.5513i	−0.579038	−	1.26792i	0.362806	−	0.931865i	$-0.381819\pi$
$84$	3.75898	−	2.41575i	0.410138	−	0.263580i
$85$	−4.62544	−	1.35815i	−0.501699	−	0.147312i
$86$	1.57597	+	10.9611i	0.169941	+	1.18197i
$87$	1.93417	−	4.23525i	0.207365	−	0.454066i
$88$	−0.00750860	+	0.0522235i	−0.000800420	+	0.00556704i
$89$	10.3471	+	6.64967i	1.09679	+	0.704863i	0.958375	−	0.285511i	$-0.0921635\pi$
$89$	10.3471	+	6.64967i	1.09679	+	0.704863i	0.138413	+	0.990375i	$0.455800\pi$
$90$	−0.654861	−	0.755750i	−0.0690284	−	0.0796630i
$91$	19.1774			2.01034
$92$	−4.02651	−	2.60524i	−0.419792	−	0.271615i
$93$	2.87827			0.298463
$94$	−1.32546	−	1.52967i	−0.136711	−	0.157773i
$95$	−5.27083	−	3.38736i	−0.540776	−	0.347536i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−5.80480	+	12.7107i	−0.589388	+	1.29058i	0.346424	+	0.938078i	$0.387396\pi$
$97$	−5.80480	+	12.7107i	−0.589388	+	1.29058i	−0.935811	+	0.352501i	$0.885331\pi$
$98$	1.84522	+	12.8338i	0.186395	+	1.29641i
$99$	0.0506233	+	0.0148644i	0.00508784	+	0.00149392i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	−1.42313	−	3.11623i	−0.141607	−	0.310076i	0.825519	−	0.564375i	$-0.190883\pi$
$101$	−1.42313	−	3.11623i	−0.141607	−	0.310076i	−0.967126	+	0.254299i	$0.918155\pi$
$102$	−4.62544	+	1.35815i	−0.457987	+	0.134477i
$103$	−4.92488	+	5.68361i	−0.485263	+	0.560023i	−0.944594	−	0.328242i	$-0.893544\pi$
$103$	−4.92488	+	5.68361i	−0.485263	+	0.560023i	0.459331	+	0.888265i	$0.348089\pi$
$104$	2.81058	−	3.24359i	0.275601	−	0.318060i
$105$	4.28731	−	1.25887i	0.418398	−	0.122853i
$106$	0.464757	+	1.01768i	0.0451412	+	0.0988455i
$107$	−15.2510	+	9.80123i	−1.47437	+	0.947520i	−0.476717	+	0.879057i	$0.658173\pi$
$107$	−15.2510	+	9.80123i	−1.47437	+	0.947520i	−0.997654	+	0.0684635i	$0.978190\pi$
$108$	−0.959493	−	0.281733i	−0.0923273	−	0.0271097i
$109$	2.29122	+	15.9358i	0.219459	+	1.52637i	0.740043	+	0.672560i	$0.234805\pi$
$109$	2.29122	+	15.9358i	0.219459	+	1.52637i	−0.520584	+	0.853810i	$0.674286\pi$
$110$	−0.0219175	+	0.0479926i	−0.00208975	+	0.00457592i
$111$	0.251261	−	1.74756i	0.0238486	−	0.165871i
$112$	3.75898	+	2.41575i	0.355190	+	0.228267i
$113$	−3.92299	−	4.52737i	−0.369043	−	0.425899i	0.540606	−	0.841276i	$-0.318195\pi$
$113$	−3.92299	−	4.52737i	−0.369043	−	0.425899i	−0.909649	+	0.415377i	$0.863650\pi$
$114$	−6.26545			−0.586813
$115$	−3.12942	−	3.63410i	−0.291820	−	0.338882i
$116$	4.65600			0.432299
$117$	−2.81058	−	3.24359i	−0.259839	−	0.299870i
$118$	−5.57020	−	3.57975i	−0.512778	−	0.329543i
$119$	3.06552	−	21.3212i	0.281016	−	1.95451i
$120$	0.415415	−	0.909632i	0.0379220	−	0.0830377i
$121$	1.56507	+	10.8853i	0.142279	+	0.989571i
$122$	7.74903	+	2.27532i	0.701564	+	0.205998i
$123$	8.59975	−	5.52673i	0.775414	−	0.498328i
$124$	1.19568	+	2.61817i	0.107375	+	0.235118i
$125$	0.959493	−	0.281733i	0.0858197	−	0.0251989i
$126$	2.92612	−	3.37692i	0.260679	−	0.300840i
$127$	−2.78636	+	3.21564i	−0.247250	+	0.285342i	−0.865786	−	0.500415i	$-0.833181\pi$
$127$	−2.78636	+	3.21564i	−0.247250	+	0.285342i	0.618536	+	0.785757i	$0.287726\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$	4.60023	+	10.0731i	0.405028	+	0.886887i
$130$	3.61056	−	2.32037i	0.316667	−	0.203510i
$131$	−14.9323	−	4.38452i	−1.30464	−	0.383077i	−0.445714	−	0.895175i	$-0.647050\pi$
$131$	−14.9323	−	4.38452i	−1.30464	−	0.383077i	−0.858927	+	0.512098i	$0.828868\pi$
$132$	0.00750860	+	0.0522235i	0.000653540	+	0.00454547i
$133$	11.6299	−	25.4660i	1.00844	−	2.20818i
$134$	−1.56343	+	10.8739i	−0.135059	+	0.939359i
$135$	−0.841254	−	0.540641i	−0.0724036	−	0.0465310i
$136$	−3.15690	−	3.64325i	−0.270702	−	0.312406i
$137$	13.8784			1.18571			0.592857	−	0.805308i	$-0.298000\pi$
$137$	13.8784			1.18571			0.592857	+	0.805308i	$0.298000\pi$
$138$	−4.59738	−	1.36531i	−0.391355	−	0.116223i
$139$	9.91838			0.841266			0.420633	−	0.907231i	$-0.361808\pi$
$139$	9.91838			0.841266			0.420633	+	0.907231i	$0.361808\pi$
$140$	2.92612	+	3.37692i	0.247302	+	0.285402i
$141$	−1.70273	−	1.09428i	−0.143396	−	0.0921548i
$142$	−1.30951	+	9.10783i	−0.109891	+	0.764312i
$143$	−0.0940673	+	0.205979i	−0.00786631	+	0.0172248i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	4.46740	+	1.31175i	0.370997	+	0.108935i
$146$	9.24114	−	5.93892i	0.764802	−	0.491509i
$147$	5.38617	+	11.7941i	0.444244	+	0.972758i
$148$	1.69401	−	0.497407i	0.139247	−	0.0408866i
$149$	6.27512	−	7.24187i	0.514078	−	0.593277i	−0.438060	−	0.898945i	$-0.644334\pi$
$149$	6.27512	−	7.24187i	0.514078	−	0.593277i	0.952138	+	0.305668i	$0.0988799\pi$
$150$	0.654861	−	0.755750i	0.0534692	−	0.0617067i
$151$	16.2984	−	4.78565i	1.32635	−	0.389451i	0.459568	−	0.888143i	$-0.348004\pi$
$151$	16.2984	−	4.78565i	1.32635	−	0.389451i	0.866779	+	0.498692i	$0.166186\pi$
$152$	−2.60276	−	5.69926i	−0.211112	−	0.462271i
$153$	−4.05544	+	2.60627i	−0.327863	+	0.210705i
$154$	−0.226201	−	0.0664185i	−0.0182278	−	0.00535215i
$155$	0.409621	+	2.84897i	0.0329015	+	0.228835i
$156$	1.78291	−	3.90403i	0.142747	−	0.312573i
$157$	−2.20744	+	15.3531i	−0.176173	+	1.22531i	0.689346	+	0.724433i	$0.257898\pi$
$157$	−2.20744	+	15.3531i	−0.176173	+	1.22531i	−0.865519	+	0.500877i	$0.833011\pi$
$158$	−9.97103	−	6.40799i	−0.793253	−	0.509792i
$159$	0.732644	+	0.845516i	0.0581024	+	0.0670538i
$160$	1.00000			0.0790569
$161$	14.0830	−	16.1518i	1.10989	−	1.27294i
$162$	−1.00000			−0.0785674
$163$	−7.42699	−	8.57120i	−0.581727	−	0.671348i	0.386248	−	0.922395i	$-0.373771\pi$
$163$	−7.42699	−	8.57120i	−0.581727	−	0.671348i	−0.967975	+	0.251047i	$0.919225\pi$
$164$	8.59975	+	5.52673i	0.671528	+	0.431565i
$165$	−0.00750860	+	0.0522235i	−0.000584544	+	0.00406559i
$166$	5.27528	−	11.5513i	0.409441	−	0.896551i
$167$	−0.829580	−	5.76985i	−0.0641948	−	0.446485i	−0.996415	−	0.0845943i	$-0.973041\pi$
$167$	−0.829580	−	5.76985i	−0.0641948	−	0.446485i	0.932221	−	0.361890i	$-0.117869\pi$
$168$	4.28731	+	1.25887i	0.330773	+	0.0971237i
$169$	4.55980	−	2.93041i	0.350754	−	0.225416i
$170$	−2.00260	−	4.38508i	−0.153592	−	0.336320i
$171$	−6.01166	+	1.76518i	−0.459723	+	0.134987i
$172$	−7.25181	+	8.36904i	−0.552945	+	0.638133i
$173$	−11.0775	+	12.7842i	−0.842209	+	0.971961i	−0.999879	−	0.0155304i	$-0.995056\pi$
$173$	−11.0775	+	12.7842i	−0.842209	+	0.971961i	0.157670	+	0.987492i	$0.449602\pi$
$174$	4.46740	−	1.31175i	0.338673	−	0.0994432i
$175$	1.85620	+	4.06451i	0.140316	+	0.307248i
$176$	−0.0443850	+	0.0285245i	−0.00334564	+	0.00215011i
$177$	−6.35310	−	1.86544i	−0.477528	−	0.140215i
$178$	1.75042	+	12.1744i	0.131199	+	0.912510i
$179$	−4.85679	+	10.6349i	−0.363014	+	0.794889i	0.636704	+	0.771109i	$0.280297\pi$
$179$	−4.85679	+	10.6349i	−0.363014	+	0.794889i	−0.999717	+	0.0237802i	$0.992430\pi$
$180$	0.142315	−	0.989821i	0.0106075	−	0.0737769i
$181$	−16.0912	−	10.3412i	−1.19605	−	0.768655i	−0.217782	−	0.975997i	$-0.569882\pi$
$181$	−16.0912	−	10.3412i	−1.19605	−	0.768655i	−0.978268	+	0.207342i	$0.933519\pi$
$182$	12.5586	+	14.4933i	0.930902	+	1.07432i
$183$	8.07617			0.597008
$184$	−0.667895	−	4.74910i	−0.0492379	−	0.350108i
$185$	1.76553			0.129804
$186$	1.88487	+	2.17525i	0.138205	+	0.159497i
$187$	0.213967	+	0.137508i	0.0156468	+	0.0100556i
$188$	0.288051	−	2.00344i	0.0210083	−	0.146116i
$189$	1.85620	−	4.06451i	0.135019	−	0.295650i
$190$	−0.891667	−	6.20168i	−0.0646883	−	0.449917i
$191$	−4.47387	−	1.31365i	−0.323718	−	0.0950521i	0.115836	−	0.993268i	$-0.463045\pi$
$191$	−4.47387	−	1.31365i	−0.323718	−	0.0950521i	−0.439554	+	0.898216i	$0.644863\pi$
$192$	0.841254	−	0.540641i	0.0607122	−	0.0390174i
$193$	5.85785	+	12.8269i	0.421657	+	0.923300i	0.994608	+	0.103710i	$0.0330715\pi$
$193$	5.85785	+	12.8269i	0.421657	+	0.923300i	−0.572950	+	0.819590i	$0.694201\pi$
$194$	−13.4075	+	3.93679i	−0.962600	+	0.282645i
$195$	2.81058	−	3.24359i	0.201270	−	0.232278i
$196$	−8.49076	+	9.79886i	−0.606483	+	0.699919i
$197$	14.5251	−	4.26496i	1.03487	−	0.303866i	0.280181	−	0.959947i	$-0.409605\pi$
$197$	14.5251	−	4.26496i	1.03487	−	0.303866i	0.754690	+	0.656081i	$0.227787\pi$
$198$	0.0219175	+	0.0479926i	0.00155761	+	0.00341069i
$199$	6.11663	−	3.93092i	0.433596	−	0.278655i	−0.305581	−	0.952166i	$-0.598851\pi$
$199$	6.11663	−	3.93092i	0.433596	−	0.278655i	0.739178	+	0.673511i	$0.235214\pi$
$200$	0.959493	+	0.281733i	0.0678464	+	0.0199215i
$201$	1.56343	+	10.8739i	0.110276	+	0.766984i
$202$	1.42313	−	3.11623i	0.100131	−	0.219257i
$203$	−2.96078	+	20.5927i	−0.207806	+	1.44532i
$204$	−4.05544	−	2.60627i	−0.283938	−	0.182476i
$205$	6.69434	+	7.72569i	0.467553	+	0.539585i
$206$	−7.52050			−0.523978
$207$	−4.79581	−	0.0147701i	−0.333332	−	0.00102660i
$208$	4.29188			0.297588
$209$	0.216476	+	0.249827i	0.0149740	+	0.0172809i
$210$	3.75898	+	2.41575i	0.259394	+	0.166702i
$211$	−0.884567	+	6.15230i	−0.0608961	+	0.423542i	0.936454	+	0.350790i	$0.114087\pi$
$211$	−0.884567	+	6.15230i	−0.0608961	+	0.423542i	−0.997350	+	0.0727513i	$0.976822\pi$
$212$	−0.464757	+	1.01768i	−0.0319197	+	0.0698943i
$213$	1.30951	+	9.10783i	0.0897260	+	0.624058i
$214$	−17.3946	−	5.10750i	−1.18907	−	0.349142i
$215$	−9.31589	+	5.98696i	−0.635339	+	0.408307i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−12.3400	+	3.62336i	−0.837696	+	0.245970i
$218$	−10.5430	+	12.1673i	−0.714064	+	0.824073i
$219$	7.19362	−	8.30189i	0.486100	−	0.560989i
$220$	−0.0506233	+	0.0148644i	−0.00341302	+	0.00100215i
$221$	−8.59491	−	18.8202i	−0.578156	−	1.26599i
$222$	1.48526	−	0.954517i	0.0996840	−	0.0640630i
$223$	14.9994	+	4.40421i	1.00443	+	0.294928i	0.742273	−	0.670097i	$-0.233748\pi$
$223$	14.9994	+	4.40421i	1.00443	+	0.294928i	0.262158	+	0.965025i	$0.415566\pi$
$224$	0.635906	+	4.42282i	0.0424883	+	0.295512i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	0.852546	−	5.92959i	0.0567105	−	0.394430i
$227$	−0.699806	−	0.449738i	−0.0464477	−	0.0298502i	0.517211	−	0.855858i	$-0.326970\pi$
$227$	−0.699806	−	0.449738i	−0.0464477	−	0.0298502i	−0.563659	+	0.826008i	$0.690607\pi$
$228$	−4.10300	−	4.73511i	−0.271728	−	0.313591i
$229$	2.68945			0.177724			0.0888620	−	0.996044i	$-0.471677\pi$
$229$	2.68945			0.177724			0.0888620	+	0.996044i	$0.471677\pi$
$230$	0.697135	−	4.74489i	0.0459677	−	0.312869i
$231$	−0.235750			−0.0155112
$232$	3.04903	+	3.51877i	0.200179	+	0.231018i
$233$	0.937649	+	0.602590i	0.0614274	+	0.0394770i	0.570994	−	0.820954i	$-0.306558\pi$
$233$	0.937649	+	0.602590i	0.0614274	+	0.0394770i	−0.509567	+	0.860431i	$0.670194\pi$
$234$	0.610798	−	4.24820i	0.0399291	−	0.277713i
$235$	0.840816	−	1.84113i	0.0548488	−	0.120102i
$236$	−0.942310	−	6.55391i	−0.0613392	−	0.426623i
$237$	−11.3725	−	3.33926i	−0.738722	−	0.216908i
$238$	18.1210	−	11.6456i	1.17461	−	0.754874i
$239$	−3.26008	−	7.13858i	−0.210877	−	0.461756i	0.774406	−	0.632689i	$-0.218049\pi$
$239$	−3.26008	−	7.13858i	−0.210877	−	0.461756i	−0.985283	+	0.170933i	$0.945322\pi$
$240$	0.959493	−	0.281733i	0.0619350	−	0.0181858i
$241$	12.2408	−	14.1266i	0.788497	−	0.909974i	−0.209195	−	0.977874i	$-0.567084\pi$
$241$	12.2408	−	14.1266i	0.788497	−	0.909974i	0.997692	+	0.0678998i	$0.0216298\pi$
$242$	−7.20165	+	8.31114i	−0.462939	+	0.534260i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	3.35496	+	7.34634i	0.214779	+	0.470301i
$245$	−10.9075	+	7.00982i	−0.696854	+	0.447841i
$246$	9.80846	+	2.88002i	0.625365	+	0.183624i
$247$	−3.82693	−	26.6169i	−0.243502	−	1.69359i
$248$	−1.19568	+	2.61817i	−0.0759255	+	0.166254i
$249$	1.80723	−	12.5696i	0.114529	−	0.796564i
$250$	0.841254	+	0.540641i	0.0532055	+	0.0341931i
$251$	0.839247	+	0.968542i	0.0529728	+	0.0611338i	0.781618	−	0.623758i	$-0.214395\pi$
$251$	0.839247	+	0.968542i	0.0529728	+	0.0611338i	−0.728645	+	0.684892i	$0.759849\pi$
$252$	4.46831			0.281477
$253$	0.104403	+	0.230487i	0.00656378	+	0.0144906i
$254$	−4.25490			−0.266976
$255$	−3.15690	−	3.64325i	−0.197692	−	0.228149i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−0.0419202	+	0.291562i	−0.00261491	+	0.0181871i	−0.991087	−	0.133215i	$-0.957470\pi$
$257$	−0.0419202	+	0.291562i	−0.00261491	+	0.0181871i	0.988472	+	0.151402i	$0.0483789\pi$
$258$	−4.60023	+	10.0731i	−0.286398	+	0.627124i
$259$	1.12271	+	7.80863i	0.0697619	+	0.485204i
$260$	4.11803	+	1.20916i	0.255389	+	0.0749891i
$261$	3.91688	−	2.51722i	0.242448	−	0.155812i
$262$	−6.46498	−	14.1563i	−0.399408	−	0.874581i
$263$	16.5765	−	4.86731i	1.02215	−	0.300131i	0.272636	−	0.962117i	$-0.412104\pi$
$263$	16.5765	−	4.86731i	1.02215	−	0.300131i	0.749516	+	0.661986i	$0.230286\pi$
$264$	−0.0345508	+	0.0398737i	−0.00212645	+	0.00245406i
$265$	−0.732644	+	0.845516i	−0.0450060	+	0.0519396i
$266$	26.8619	−	7.88737i	1.64701	−	0.483606i
$267$	5.10944	+	11.1881i	0.312693	+	0.684701i
$268$	−9.24175	+	5.93931i	−0.564530	+	0.362801i
$269$	−16.1645	−	4.74633i	−0.985569	−	0.289389i	−0.251048	−	0.967975i	$-0.580775\pi$
$269$	−16.1645	−	4.74633i	−0.985569	−	0.289389i	−0.734521	+	0.678586i	$0.762593\pi$
$270$	−0.142315	−	0.989821i	−0.00866101	−	0.0602386i
$271$	−3.50331	+	7.67117i	−0.212811	+	0.465990i	−0.985691	−	0.168561i	$-0.946088\pi$
$271$	−3.50331	+	7.67117i	−0.212811	+	0.465990i	0.772881	+	0.634552i	$0.218815\pi$
$272$	0.686059	−	4.77165i	0.0415984	−	0.289324i
$273$	16.1331	+	10.3681i	0.976419	+	0.627506i
$274$	9.08843	+	10.4886i	0.549052	+	0.633640i
$275$	−0.0527605			−0.00318158
$276$	−1.97882	−	4.36856i	−0.119111	−	0.262956i
$277$	14.2538			0.856429			0.428215	−	0.903677i	$-0.359143\pi$
$277$	14.2538			0.856429			0.428215	+	0.903677i	$0.359143\pi$
$278$	6.49516	+	7.49581i	0.389554	+	0.449569i
$279$	2.42136	+	1.55611i	0.144963	+	0.0931619i
$280$	−0.635906	+	4.42282i	−0.0380027	+	0.264314i
$281$	9.90319	−	21.6850i	0.590775	−	1.29362i	−0.344198	−	0.938897i	$-0.611849\pi$
$281$	9.90319	−	21.6850i	0.590775	−	1.29362i	0.934973	−	0.354719i	$-0.115424\pi$
$282$	−0.288051	−	2.00344i	−0.0171532	−	0.119303i
$283$	−16.1384	−	4.73866i	−0.959327	−	0.281684i	−0.235662	−	0.971835i	$-0.575726\pi$
$283$	−16.1384	−	4.73866i	−0.959327	−	0.281684i	−0.723665	+	0.690151i	$0.757544\pi$
$284$	−7.74078	+	4.97470i	−0.459331	+	0.295194i
$285$	−2.60276	−	5.69926i	−0.154174	−	0.337595i
$286$	−0.217269	+	0.0637960i	−0.0128474	+	0.00377234i
$287$	−29.9124	+	34.5207i	−1.76567	+	2.03769i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	−5.98654	+	1.75781i	−0.352150	+	0.103400i
$290$	1.93417	+	4.23525i	0.113578	+	0.248702i
$291$	−11.7552	+	7.55464i	−0.689105	+	0.442861i
$292$	10.5400	+	3.09482i	0.616807	+	0.181111i
$293$	0.661190	+	4.59868i	0.0386271	+	0.268658i	0.999978	−	0.00666939i	$-0.00212295\pi$
$293$	0.661190	+	4.59868i	0.0386271	+	0.268658i	−0.961351	+	0.275327i	$0.911214\pi$
$294$	−5.38617	+	11.7941i	−0.314128	+	0.687844i
$295$	0.942310	−	6.55391i	0.0548634	−	0.381583i
$296$	1.48526	+	0.954517i	0.0863289	+	0.0554802i
$297$	0.0345508	+	0.0398737i	0.00200484	+	0.00231371i
$298$	9.58237			0.555092
$299$	2.99202	−	20.3645i	0.173033	−	1.17771i
$300$	1.00000			0.0577350
$301$	−32.4033	−	37.3954i	−1.86770	−	2.15544i
$302$	14.2900	+	9.18359i	0.822294	+	0.528456i
$303$	0.487543	−	3.39094i	0.0280086	−	0.194804i
$304$	2.60276	−	5.69926i	0.149279	−	0.326875i
$305$	1.14936	+	7.99397i	0.0658121	+	0.457733i
$306$	−4.62544	−	1.35815i	−0.264419	−	0.0776404i
$307$	−12.0939	+	7.77228i	−0.690236	+	0.443588i	−0.838170	−	0.545410i	$-0.816374\pi$
$307$	−12.0939	+	7.77228i	−0.690236	+	0.443588i	0.147934	+	0.988997i	$0.452738\pi$
$308$	−0.0979341	−	0.214446i	−0.00558031	−	0.0122192i
$309$	−7.21586	+	2.11877i	−0.410496	+	0.120533i
$310$	−1.88487	+	2.17525i	−0.107053	+	0.123546i
$311$	−1.95558	+	2.25686i	−0.110891	+	0.127975i	−0.808481	−	0.588522i	$-0.799710\pi$
$311$	−1.95558	+	2.25686i	−0.110891	+	0.127975i	0.697590	+	0.716497i	$0.254256\pi$
$312$	4.11803	−	1.20916i	0.233138	−	0.0684554i
$313$	−4.34963	−	9.52435i	−0.245855	−	0.538348i	0.745966	−	0.665984i	$-0.231988\pi$
$313$	−4.34963	−	9.52435i	−0.245855	−	0.538348i	−0.991821	+	0.127636i	$0.959261\pi$
$314$	−13.0487	+	8.38586i	−0.736378	+	0.473241i
$315$	4.28731	+	1.25887i	0.241562	+	0.0709291i
$316$	−1.68680	−	11.7319i	−0.0948899	−	0.659973i
$317$	8.95278	−	19.6038i	0.502838	−	1.10106i	−0.472698	−	0.881224i	$-0.656720\pi$
$317$	8.95278	−	19.6038i	0.502838	−	1.10106i	0.975536	−	0.219838i	$-0.0705527\pi$
$318$	−0.159219	+	1.10739i	−0.00892854	+	0.0620994i
$319$	−0.206656	−	0.132810i	−0.0115705	−	0.00743593i
$320$	0.654861	+	0.755750i	0.0366078	+	0.0422477i
$321$	−18.1289			−1.01186
$322$	21.4291	+	0.0659975i	1.19420	+	0.00367789i
$323$	−30.2040			−1.68059
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	3.61056	+	2.32037i	0.200278	+	0.128711i
$326$	1.61404	−	11.2259i	0.0893933	−	0.621744i
$327$	−6.68803	+	14.6447i	−0.369849	+	0.809856i
$328$	1.45482	+	10.1185i	0.0803290	+	0.558700i
$329$	8.67768	+	2.54800i	0.478416	+	0.140476i
$330$	−0.0443850	+	0.0285245i	−0.00244331	+	0.00157022i
$331$	10.4007	+	22.7744i	0.571676	+	1.25180i	0.945900	+	0.324457i	$0.105182\pi$
$331$	10.4007	+	22.7744i	0.571676	+	1.25180i	−0.374225	+	0.927338i	$0.622091\pi$
$332$	12.1844	−	3.57767i	0.668708	−	0.196350i
$333$	1.15618	−	1.33430i	0.0633580	−	0.0731191i
$334$	3.81730	−	4.40540i	0.208874	−	0.241053i
$335$	−10.5407	+	3.09503i	−0.575899	+	0.169099i
$336$	1.85620	+	4.06451i	0.101264	+	0.221737i
$337$	2.43194	−	1.56291i	0.132476	−	0.0851373i	−0.472724	−	0.881210i	$-0.656729\pi$
$337$	2.43194	−	1.56291i	0.132476	−	0.0851373i	0.605200	+	0.796073i	$0.293093\pi$
$338$	5.20069	+	1.52706i	0.282880	+	0.0830611i
$339$	−0.852546	−	5.92959i	−0.0463040	−	0.322051i
$340$	2.00260	−	4.38508i	0.108606	−	0.237814i
$341$	0.0216118	−	0.150313i	0.00117034	−	0.00813992i
$342$	−5.27083	−	3.38736i	−0.285014	−	0.183167i
$343$	−17.4565	−	20.1459i	−0.942562	−	1.08778i
$344$	−11.0738			−0.597060
$345$	−0.667895	−	4.74910i	−0.0359583	−	0.255683i
$346$	−16.9159			−0.909402
$347$	−13.3726	−	15.4328i	−0.717878	−	0.828476i	0.273172	−	0.961965i	$-0.411927\pi$
$347$	−13.3726	−	15.4328i	−0.717878	−	0.828476i	−0.991050	+	0.133490i	$0.957382\pi$
$348$	3.91688	+	2.51722i	0.209967	+	0.134937i
$349$	4.10249	−	28.5334i	0.219601	−	1.52736i	−0.519914	−	0.854219i	$-0.674036\pi$
$349$	4.10249	−	28.5334i	0.219601	−	1.52736i	0.739515	−	0.673140i	$-0.235055\pi$
$350$	−1.85620	+	4.06451i	−0.0992181	+	0.217257i
$351$	−0.610798	−	4.24820i	−0.0326020	−	0.226752i
$352$	−0.0506233	−	0.0148644i	−0.00269823	−	0.000792273i
$353$	−6.81922	+	4.38245i	−0.362950	+	0.233254i	−0.709387	−	0.704819i	$-0.751028\pi$
$353$	−6.81922	+	4.38245i	−0.362950	+	0.233254i	0.346436	+	0.938073i	$0.387392\pi$
$354$	−2.75059	−	6.02295i	−0.146192	−	0.320116i
$355$	−8.82876	+	2.59236i	−0.468582	+	0.137588i
$356$	−8.05452	+	9.29542i	−0.426889	+	0.492656i
$357$	14.1060	−	16.2792i	0.746567	−	0.861585i
$358$	−11.2178	+	3.29385i	−0.592881	+	0.174086i
$359$	−1.73771	−	3.80505i	−0.0917126	−	0.200823i	0.858217	−	0.513288i	$-0.171573\pi$
$359$	−1.73771	−	3.80505i	−0.0917126	−	0.200823i	−0.949929	+	0.312465i	$0.898845\pi$
$360$	0.841254	−	0.540641i	0.0443380	−	0.0284943i
$361$	−19.4354	−	5.70675i	−1.02292	−	0.300355i
$362$	−2.72215	−	18.9330i	−0.143073	−	0.995095i
$363$	−4.56841	+	10.0034i	−0.239779	+	0.525043i
$364$	−2.72923	+	18.9822i	−0.143051	+	0.994940i
$365$	9.24114	+	5.93892i	0.483704	+	0.310857i
$366$	5.28877	+	6.10356i	0.276448	+	0.319038i
$367$	−29.2737			−1.52808			−0.764038	−	0.645171i	$-0.776786\pi$
$367$	−29.2737			−1.52808			−0.764038	+	0.645171i	$0.776786\pi$
$368$	3.15175	−	3.61476i	0.164296	−	0.188432i
$369$	10.2225			0.532165
$370$	1.15618	+	1.33430i	0.0601067	+	0.0693669i
$371$	−4.20546	−	2.70269i	−0.218337	−	0.140316i
$372$	−0.409621	+	2.84897i	−0.0212378	+	0.147712i
$373$	−3.82777	+	8.38164i	−0.198194	+	0.433985i	−0.982468	−	0.186430i	$-0.940308\pi$
$373$	−3.82777	+	8.38164i	−0.198194	+	0.433985i	0.784274	+	0.620415i	$0.213036\pi$
$374$	0.0361968	+	0.251754i	0.00187169	+	0.0130179i
$375$	0.959493	+	0.281733i	0.0495480	+	0.0145486i
$376$	1.70273	−	1.09428i	0.0878116	−	0.0564331i
$377$	8.30124	+	18.1772i	0.427535	+	0.936172i
$378$	4.28731	−	1.25887i	0.220515	−	0.0647491i
$379$	−11.0746	+	12.7808i	−0.568864	+	0.656504i	−0.965173	−	0.261613i	$-0.915746\pi$
$379$	−11.0746	+	12.7808i	−0.568864	+	0.656504i	0.396309	+	0.918117i	$0.370291\pi$
$380$	4.10300	−	4.73511i	0.210479	−	0.242906i
$381$	−4.08254	+	1.19874i	−0.209155	+	0.0614135i
$382$	−1.93697	−	4.24138i	−0.0991042	−	0.217008i
$383$	−8.72777	+	5.60899i	−0.445968	+	0.286606i	−0.744287	−	0.667860i	$-0.767210\pi$
$383$	−8.72777	+	5.60899i	−0.445968	+	0.286606i	0.298319	+	0.954466i	$0.403574\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	−0.0335507	−	0.233350i	−0.00170990	−	0.0118926i
$386$	−5.85785	+	12.8269i	−0.298157	+	0.652872i
$387$	−1.57597	+	10.9611i	−0.0801110	+	0.557184i
$388$	−11.7552	−	7.55464i	−0.596782	−	0.383529i
$389$	13.5207	+	15.6037i	0.685524	+	0.791137i	0.986721	−	0.162425i	$-0.0519315\pi$
$389$	13.5207	+	15.6037i	0.685524	+	0.791137i	−0.301197	+	0.953562i	$0.597386\pi$
$390$	4.29188			0.217328
$391$	−22.1627	−	6.58176i	−1.12081	−	0.332854i
$392$	−12.9658			−0.654870
$393$	−10.1914	−	11.7615i	−0.514088	−	0.593289i
$394$	12.7352	+	8.18439i	0.641588	+	0.412324i
$395$	1.68680	−	11.7319i	0.0848721	−	0.590298i
$396$	−0.0219175	+	0.0479926i	−0.00110140	+	0.00241172i
$397$	2.72257	+	18.9359i	0.136642	+	0.950365i	0.936623	+	0.350340i	$0.113934\pi$
$397$	2.72257	+	18.9359i	0.136642	+	0.950365i	−0.799981	+	0.600026i	$0.795157\pi$
$398$	6.97633	+	2.04844i	0.349692	+	0.102679i
$399$	23.5517	−	15.1358i	1.17906	−	0.757736i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	24.6165	−	7.22807i	1.22929	−	0.360953i	0.398309	−	0.917251i	$-0.369597\pi$
$401$	24.6165	−	7.22807i	1.22929	−	0.360953i	0.830982	+	0.556299i	$0.187779\pi$
$402$	−7.19410	+	8.30243i	−0.358809	+	0.414088i
$403$	−8.08962	+	9.33592i	−0.402973	+	0.465055i
$404$	3.28704	−	0.965162i	0.163536	−	0.0480186i
$405$	−0.415415	−	0.909632i	−0.0206421	−	0.0452000i
$406$	−17.5018	+	11.2477i	−0.868599	+	0.558215i
$407$	−0.0893770	−	0.0262434i	−0.00443025	−	0.00130084i
$408$	−0.686059	−	4.77165i	−0.0339650	−	0.236232i
$409$	−12.5255	+	27.4270i	−0.619346	+	1.35618i	0.296649	+	0.954987i	$0.404131\pi$
$409$	−12.5255	+	27.4270i	−0.619346	+	1.35618i	−0.915994	+	0.401191i	$0.868596\pi$
$410$	−1.45482	+	10.1185i	−0.0718484	+	0.499717i
$411$	11.6753	+	7.50324i	0.575898	+	0.370107i
$412$	−4.92488	−	5.68361i	−0.242631	−	0.280012i
$413$	29.5860			1.45583
$414$	−3.12942	−	3.63410i	−0.153803	−	0.178606i
$415$	12.6988			0.623361
$416$	2.81058	+	3.24359i	0.137800	+	0.159030i
$417$	8.34387	+	5.36228i	0.408601	+	0.262592i
$418$	−0.0470448	+	0.327204i	−0.00230104	+	0.0160041i
$419$	−8.81703	+	19.3066i	−0.430740	+	0.943189i	0.562466	+	0.826820i	$0.309853\pi$
$419$	−8.81703	+	19.3066i	−0.430740	+	0.943189i	−0.993206	+	0.116369i	$0.962875\pi$
$420$	0.635906	+	4.42282i	0.0310290	+	0.215812i
$421$	11.8508	+	3.47971i	0.577573	+	0.169591i	0.557455	−	0.830207i	$-0.311778\pi$
$421$	11.8508	+	3.47971i	0.577573	+	0.169591i	0.0201174	+	0.999798i	$0.493596\pi$
$422$	−5.22887	+	3.36039i	−0.254537	+	0.163581i
$423$	−0.840816	−	1.84113i	−0.0408819	−	0.0895188i
$424$	−1.07346	+	0.315196i	−0.0521318	+	0.0153073i
$425$	3.15690	−	3.64325i	0.153132	−	0.176724i
$426$	−6.02569	+	6.95402i	−0.291946	+	0.336923i
$427$	−34.6250	+	10.1668i	−1.67562	+	0.492007i
$428$	−7.53102	−	16.4906i	−0.364026	−	0.797105i
$429$	−0.190495	+	0.122424i	−0.00919718	+	0.00591067i
$430$	−10.6253	−	3.11986i	−0.512395	−	0.150453i
$431$	−1.40758	−	9.78992i	−0.0678006	−	0.471564i	−0.995229	−	0.0975636i	$-0.968895\pi$
$431$	−1.40758	−	9.78992i	−0.0678006	−	0.471564i	0.927429	−	0.374000i	$-0.122014\pi$
$432$	0.415415	−	0.909632i	0.0199867	−	0.0437647i
$433$	3.94538	−	27.4407i	0.189603	−	1.31872i	−0.643436	−	0.765500i	$-0.722492\pi$
$433$	3.94538	−	27.4407i	0.189603	−	1.31872i	0.833038	−	0.553215i	$-0.186599\pi$
$434$	−10.8194	−	6.95318i	−0.519346	−	0.333763i
$435$	3.04903	+	3.51877i	0.146190	+	0.168712i
$436$	−16.0996			−0.771033
$437$	−25.2279	−	16.3230i	−1.20681	−	0.780834i
$438$	10.9850			0.524882
$439$	−6.34038	−	7.31719i	−0.302610	−	0.349230i	0.583996	−	0.811757i	$-0.301489\pi$
$439$	−6.34038	−	7.31719i	−0.302610	−	0.349230i	−0.886606	+	0.462526i	$0.846943\pi$
$440$	−0.0443850	−	0.0285245i	−0.00211597	−	0.00135985i
$441$	−1.84522	+	12.8338i	−0.0878676	+	0.611132i
$442$	8.59491	−	18.8202i	0.408818	−	0.895187i
$443$	−0.164355	−	1.14311i	−0.00780872	−	0.0543109i	0.985545	−	0.169417i	$-0.0541884\pi$
$443$	−0.164355	−	1.14311i	−0.00780872	−	0.0543109i	−0.993353	+	0.115106i	$0.963279\pi$
$444$	1.69401	+	0.497407i	0.0803943	+	0.0236059i
$445$	−10.3471	+	6.64967i	−0.490499	+	0.315224i
$446$	6.49401	+	14.2199i	0.307500	+	0.673332i
$447$	9.19421	−	2.69966i	0.434871	−	0.127690i
$448$	−2.92612	+	3.37692i	−0.138246	+	0.159544i
$449$	9.73918	−	11.2396i	0.459620	−	0.530430i	−0.477875	−	0.878428i	$-0.658593\pi$
$449$	9.73918	−	11.2396i	0.459620	−	0.530430i	0.937495	+	0.347998i	$0.113138\pi$
$450$	0.959493	−	0.281733i	0.0452309	−	0.0132810i
$451$	−0.224053	−	0.490607i	−0.0105502	−	0.0231018i
$452$	5.03958	−	3.23874i	0.237042	−	0.152338i
$453$	16.2984	+	4.78565i	0.765767	+	0.224849i
$454$	−0.118386	−	0.823394i	−0.00555614	−	0.0386438i
$455$	−7.96660	+	17.4444i	−0.373480	+	0.817807i
$456$	0.891667	−	6.20168i	0.0417561	−	0.290420i
$457$	−31.1885	−	20.0436i	−1.45894	−	0.937602i	−0.998760	−	0.0497742i	$-0.984150\pi$
$457$	−31.1885	−	20.0436i	−1.45894	−	0.937602i	−0.460176	−	0.887828i	$-0.652214\pi$
$458$	1.76122	+	2.03255i	0.0822963	+	0.0949750i
$459$	−4.82071			−0.225012
$460$	4.04248	−	2.58038i	0.188481	−	0.120311i
$461$	10.7244			0.499486			0.249743	−	0.968312i	$-0.419654\pi$
$461$	10.7244			0.499486			0.249743	+	0.968312i	$0.419654\pi$
$462$	−0.154383	−	0.178168i	−0.00718257	−	0.00828913i
$463$	18.6555	+	11.9891i	0.866993	+	0.557183i	0.896832	−	0.442372i	$-0.145863\pi$
$463$	18.6555	+	11.9891i	0.866993	+	0.557183i	−0.0298383	+	0.999555i	$0.509499\pi$
$464$	−0.662618	+	4.60861i	−0.0307613	+	0.213949i
$465$	−1.19568	+	2.61817i	−0.0554482	+	0.121415i
$466$	0.158622	+	1.10324i	0.00734802	+	0.0511066i
$467$	33.6599	+	9.88343i	1.55759	+	0.457350i	0.943359	−	0.331774i	$-0.107647\pi$
$467$	33.6599	+	9.88343i	1.55759	+	0.457350i	0.614234	+	0.789124i	$0.289465\pi$
$468$	3.61056	−	2.32037i	0.166898	−	0.107259i
$469$	−20.3916	−	44.6515i	−0.941599	−	2.06181i
$470$	1.94205	−	0.570237i	0.0895801	−	0.0263031i
$471$	−10.1575	+	11.7224i	−0.468034	+	0.540140i
$472$	4.33603	−	5.00405i	0.199582	−	0.230330i
$473$	0.560594	−	0.164605i	0.0257761	−	0.00756855i
$474$	−4.92374	−	10.7815i	−0.226155	−	0.495210i
$475$	5.27083	−	3.38736i	0.241842	−	0.155423i
$476$	20.6679	+	6.06864i	0.947311	+	0.278156i
$477$	0.159219	+	1.10739i	0.00729012	+	0.0507039i
$478$	3.26008	−	7.13858i	0.149113	−	0.326511i
$479$	−5.58858	+	38.8695i	−0.255349	+	1.77599i	0.309602	+	0.950866i	$0.399804\pi$
$479$	−5.58858	+	38.8695i	−0.255349	+	1.77599i	−0.564951	+	0.825125i	$0.691105\pi$
$480$	0.841254	+	0.540641i	0.0383978	+	0.0246768i
$481$	4.96217	+	5.72665i	0.226255	+	0.261113i
$482$	18.6922			0.851405
$483$	20.5797	−	5.97396i	0.936409	−	0.271825i
$484$	−10.9972			−0.499873
$485$	−9.15069	−	10.5605i	−0.415511	−	0.479526i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	0.932808	−	6.48782i	0.0422696	−	0.293991i	−0.957711	−	0.287732i	$-0.907099\pi$
$487$	0.932808	−	6.48782i	0.0422696	−	0.293991i	0.999980	−	0.00625885i	$-0.00199227\pi$
$488$	−3.35496	+	7.34634i	−0.151872	+	0.332553i
$489$	−1.61404	−	11.2259i	−0.0729893	−	0.507652i
$490$	−12.4406	−	3.65288i	−0.562007	−	0.165020i
$491$	24.7496	−	15.9056i	1.11693	−	0.717809i	0.154140	−	0.988049i	$-0.450739\pi$
$491$	24.7496	−	15.9056i	1.11693	−	0.717809i	0.962793	+	0.270240i	$0.0871030\pi$
$492$	4.24660	+	9.29876i	0.191451	+	0.419220i
$493$	21.5360	−	6.32355i	0.969935	−	0.284799i
$494$	17.6096	−	20.3225i	0.792293	−	0.914355i
$495$	−0.0345508	+	0.0398737i	−0.00155294	+	0.00179219i
$496$	−2.76168	+	0.810902i	−0.124003	+	0.0364106i
$497$	−17.0798	−	37.3996i	−0.766134	−	1.67760i
$498$	10.6829	−	6.86550i	0.478714	−	0.307651i
$499$	5.09824	+	1.49698i	0.228229	+	0.0670140i	0.393847	−	0.919176i	$-0.371144\pi$
$499$	5.09824	+	1.49698i	0.228229	+	0.0670140i	−0.165619	+	0.986190i	$0.552962\pi$
$500$	0.142315	+	0.989821i	0.00636451	+	0.0442662i
$501$	2.42153	−	5.30241i	0.108186	−	0.236894i
$502$	−0.182386	+	1.26852i	−0.00814027	+	0.0566168i
$503$	10.5044	+	6.75078i	0.468369	+	0.301003i	0.753455	−	0.657499i	$-0.228386\pi$
$503$	10.5044	+	6.75078i	0.468369	+	0.301003i	−0.285086	+	0.958502i	$0.592022\pi$
$504$	2.92612	+	3.37692i	0.130340	+	0.150420i
$505$	3.42581			0.152447
$506$	−0.105821	+	0.229840i	−0.00470432	+	0.0102176i
$507$	5.42025			0.240722
$508$	−2.78636	−	3.21564i	−0.123625	−	0.142671i
$509$	21.3104	+	13.6953i	0.944565	+	0.607035i	0.919686	−	0.392655i	$-0.128443\pi$
$509$	21.3104	+	13.6953i	0.944565	+	0.607035i	0.0248794	+	0.999690i	$0.492080\pi$
$510$	0.686059	−	4.77165i	0.0303792	−	0.211292i
$511$	−20.3903	+	44.6486i	−0.902014	+	1.97514i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−6.01166	−	1.76518i	−0.265421	−	0.0779347i
$514$	−0.247800	+	0.159251i	−0.0109300	+	0.00702426i
$515$	−3.12413	−	6.84089i	−0.137666	−	0.301445i
$516$	−10.6253	+	3.11986i	−0.467751	+	0.137344i
$517$	−0.0699321	+	0.0807059i	−0.00307561	+	0.00354944i
$518$	−5.16615	+	5.96205i	−0.226987	+	0.261958i
$519$	−16.2307	+	4.76575i	−0.712447	+	0.209193i
$520$	1.78291	+	3.90403i	0.0781859	+	0.171203i
$521$	6.75836	−	4.34333i	0.296089	−	0.190285i	−0.384159	−	0.923267i	$-0.625509\pi$
$521$	6.75836	−	4.34333i	0.296089	−	0.190285i	0.680248	+	0.732982i	$0.261872\pi$
$522$	4.46740	+	1.31175i	0.195533	+	0.0574136i
$523$	3.27386	+	22.7702i	0.143156	+	0.995671i	0.927093	+	0.374831i	$0.122299\pi$
$523$	3.27386	+	22.7702i	0.143156	+	0.995671i	−0.783937	+	0.620840i	$0.786792\pi$
$524$	6.46498	−	14.1563i	0.282424	−	0.618422i
$525$	−0.635906	+	4.42282i	−0.0277532	+	0.193028i
$526$	14.5338	+	9.34029i	0.633703	+	0.407256i
$527$	9.08640	+	10.4863i	0.395810	+	0.456789i
$528$	−0.0527605			−0.00229611
$529$	−14.9544	−	17.4747i	−0.650193	−	0.759769i
$530$	−1.11878			−0.0485966
$531$	−4.33603	−	5.00405i	−0.188168	−	0.217157i
$532$	23.5517	+	15.1358i	1.02110	+	0.656218i
$533$	−6.24392	+	43.4274i	−0.270454	+	1.88105i
$534$	−5.10944	+	11.1881i	−0.221107	+	0.484157i
$535$	−2.58001	−	17.9444i	−0.111544	−	0.775803i
$536$	−10.5407	−	3.09503i	−0.455289	−	0.133685i
$537$	−9.83545	+	6.32086i	−0.424431	+	0.272765i
$538$	−6.99848	−	15.3245i	−0.301726	−	0.660687i
$539$	0.656370	−	0.192728i	0.0282718	−	0.00830136i
$540$	0.654861	−	0.755750i	0.0281807	−	0.0325223i
$541$	−19.1726	+	22.1264i	−0.824295	+	0.951288i	−0.999447	−	0.0332538i	$-0.989413\pi$
$541$	−19.1726	+	22.1264i	−0.824295	+	0.951288i	0.175151	+	0.984542i	$0.443958\pi$
$542$	−8.09166	+	2.37593i	−0.347567	+	0.102055i
$543$	−7.94592	−	17.3991i	−0.340992	−	0.746668i
$544$	4.05544	−	2.60627i	0.173876	−	0.111743i
$545$	−15.4475	−	4.53579i	−0.661698	−	0.194292i
$546$	2.72923	+	18.9822i	0.116800	+	0.812365i
$547$	5.97132	−	13.0754i	0.255315	−	0.559062i	−0.737959	−	0.674845i	$-0.764210\pi$
$547$	5.97132	−	13.0754i	0.255315	−	0.559062i	0.993275	+	0.115783i	$0.0369377\pi$
$548$	−1.97510	+	13.7372i	−0.0843723	+	0.586822i
$549$	6.79411	+	4.36631i	0.289965	+	0.186349i
$550$	−0.0345508	−	0.0398737i	−0.00147325	−	0.00170022i
$551$	29.1719			1.24277
$552$	2.00569	−	4.35629i	0.0853677	−	0.185416i
$553$	52.9610			2.25213
$554$	9.33427	+	10.7723i	0.396575	+	0.457672i
$555$	1.48526	+	0.954517i	0.0630457	+	0.0405170i
$556$	−1.41153	+	9.81743i	−0.0598623	+	0.416352i
$557$	4.24280	−	9.29043i	0.179773	−	0.393648i	−0.798196	−	0.602398i	$-0.794212\pi$
$557$	4.24280	−	9.29043i	0.179773	−	0.393648i	0.977969	+	0.208750i	$0.0669393\pi$
$558$	0.409621	+	2.84897i	0.0173406	+	0.120607i
$559$	−45.6023	−	13.3901i	−1.92877	−	0.566339i
$560$	−3.75898	+	2.41575i	−0.158846	+	0.102084i
$561$	0.105658	+	0.231359i	0.00446088	+	0.00976797i
$562$	22.8736	−	6.71630i	0.964865	−	0.283310i
$563$	6.53327	−	7.53980i	0.275345	−	0.317765i	−0.601188	−	0.799108i	$-0.705306\pi$
$563$	6.53327	−	7.53980i	0.275345	−	0.317765i	0.876532	+	0.481343i	$0.159851\pi$
$564$	1.32546	−	1.52967i	0.0558121	−	0.0644106i
$565$	5.74791	−	1.68774i	0.241816	−	0.0710036i
$566$	−6.98715	−	15.2997i	−0.293692	−	0.643096i
$567$	3.75898	−	2.41575i	0.157862	−	0.101452i
$568$	−8.82876	−	2.59236i	−0.370447	−	0.108773i
$569$	−4.60179	−	32.0062i	−0.192917	−	1.34177i	−0.824237	−	0.566246i	$-0.808395\pi$
$569$	−4.60179	−	32.0062i	−0.192917	−	1.34177i	0.631319	−	0.775523i	$-0.282514\pi$
$570$	2.60276	−	5.69926i	0.109018	−	0.238716i
$571$	−0.641494	+	4.46169i	−0.0268457	+	0.186716i	−0.998832	−	0.0483224i	$-0.984613\pi$
$571$	−0.641494	+	4.46169i	−0.0268457	+	0.186716i	0.971986	+	0.235038i	$0.0755216\pi$
$572$	−0.190495	−	0.122424i	−0.00796500	−	0.00511879i
$573$	−3.05345	−	3.52387i	−0.127560	−	0.147212i
$574$	−45.6775			−1.90654
$575$	4.60571	−	1.33696i	0.192071	−	0.0557552i
$576$	1.00000			0.0416667
$577$	−6.44818	−	7.44160i	−0.268441	−	0.309798i	0.605485	−	0.795857i	$-0.292979\pi$
$577$	−6.44818	−	7.44160i	−0.268441	−	0.309798i	−0.873926	+	0.486059i	$0.838434\pi$
$578$	−5.24881	−	3.37321i	−0.218322	−	0.140307i
$579$	−2.00681	+	13.9577i	−0.0834001	+	0.580061i
$580$	−1.93417	+	4.23525i	−0.0803121	+	0.175859i
$581$	8.07526	+	56.1647i	0.335018	+	2.33010i
$582$	−13.4075	−	3.93679i	−0.555757	−	0.163185i
$583$	0.0496569	−	0.0319126i	0.00205658	−	0.00132168i
$584$	4.56332	+	9.99228i	0.188832	+	0.413483i
$585$	4.11803	−	1.20916i	0.170260	−	0.0499927i
$586$	−3.04246	+	3.51119i	−0.125683	+	0.145046i
$587$	19.0944	−	22.0361i	0.788109	−	0.909527i	−0.209558	−	0.977796i	$-0.567202\pi$
$587$	19.0944	−	22.0361i	0.788109	−	0.909527i	0.997667	+	0.0682697i	$0.0217478\pi$
$588$	−12.4406	+	3.65288i	−0.513040	+	0.150642i
$589$	7.49146	+	16.4040i	0.308680	+	0.675915i
$590$	5.57020	−	3.57975i	0.229321	−	0.147376i
$591$	14.5251	+	4.26496i	0.597483	+	0.175437i
$592$	0.251261	+	1.74756i	0.0103268	+	0.0718242i
$593$	−11.8117	+	25.8641i	−0.485050	+	1.06211i	0.495994	+	0.868326i	$0.334804\pi$
$593$	−11.8117	+	25.8641i	−0.485050	+	1.06211i	−0.981044	+	0.193785i	$0.937923\pi$
$594$	−0.00750860	+	0.0522235i	−0.000308082	+	0.00214276i
$595$	18.1210	+	11.6456i	0.742887	+	0.477424i
$596$	6.27512	+	7.24187i	0.257039	+	0.296639i
$597$	7.27085			0.297576
$598$	17.3498	−	11.0747i	0.709487	−	0.452878i
$599$	20.4760			0.836628			0.418314	−	0.908302i	$-0.362621\pi$
$599$	20.4760			0.836628			0.418314	+	0.908302i	$0.362621\pi$
$600$	0.654861	+	0.755750i	0.0267346	+	0.0308533i
$601$	17.9102	+	11.5102i	0.730573	+	0.469511i	0.852300	−	0.523053i	$-0.175207\pi$
$601$	17.9102	+	11.5102i	0.730573	+	0.469511i	−0.121727	+	0.992564i	$0.538843\pi$
$602$	7.04191	−	48.9776i	0.287007	−	1.99618i
$603$	−4.56362	+	9.99293i	−0.185845	+	0.406944i
$604$	2.41743	+	16.8136i	0.0983639	+	0.684136i
$605$	−10.5518	−	3.09827i	−0.428990	−	0.125963i
$606$	2.88197	−	1.85213i	0.117072	−	0.0752377i
$607$	6.37229	+	13.9534i	0.258643	+	0.566350i	0.993753	−	0.111598i	$-0.0355969\pi$
$607$	6.37229	+	13.9534i	0.258643	+	0.566350i	−0.735110	+	0.677948i	$0.762870\pi$
$608$	6.01166	−	1.76518i	0.243805	−	0.0715876i
$609$	−13.6240	+	15.7229i	−0.552072	+	0.637125i
$610$	−5.28877	+	6.10356i	−0.214136	+	0.247126i
$611$	8.33505	−	2.44739i	0.337200	−	0.0990109i
$612$	−2.00260	−	4.38508i	−0.0809502	−	0.177256i
$613$	−14.9807	+	9.62754i	−0.605067	+	0.388853i	−0.807004	−	0.590546i	$-0.798913\pi$
$613$	−14.9807	+	9.62754i	−0.605067	+	0.388853i	0.201938	+	0.979398i	$0.435276\pi$
$614$	−13.7937	−	4.05020i	−0.556669	−	0.163453i
$615$	1.45482	+	10.1185i	0.0586640	+	0.408017i
$616$	0.0979341	−	0.214446i	0.00394588	−	0.00864027i
$617$	0.534474	−	3.71735i	0.0215171	−	0.149655i	−0.976230	−	0.216735i	$-0.930459\pi$
$617$	0.534474	−	3.71735i	0.0215171	−	0.149655i	0.997748	+	0.0670802i	$0.0213683\pi$
$618$	−6.32665	−	4.06589i	−0.254495	−	0.163554i
$619$	27.4537	+	31.6832i	1.10346	+	1.27346i	0.958834	+	0.283969i	$0.0916512\pi$
$619$	27.4537	+	31.6832i	1.10346	+	1.27346i	0.144622	+	0.989487i	$0.453803\pi$
$620$	−2.87827			−0.115594
$621$	−4.02651	−	2.60524i	−0.161578	−	0.104544i
$622$	−2.98626			−0.119738
$623$	−35.9901	−	41.5348i	−1.44191	−	1.66406i
$624$	3.61056	+	2.32037i	0.144538	+	0.0928890i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	4.34963	−	9.52435i	0.173846	−	0.380670i
$627$	0.0470448	+	0.327204i	0.00187879	+	0.0130673i
$628$	−14.8827	−	4.36994i	−0.593883	−	0.174380i
$629$	7.16000	−	4.60145i	0.285488	−	0.183472i
$630$	1.85620	+	4.06451i	0.0739528	+	0.161934i
$631$	25.3715	−	7.44974i	1.01002	−	0.296569i	0.265460	−	0.964122i	$-0.414476\pi$
$631$	25.3715	−	7.44974i	1.01002	−	0.296569i	0.744563	+	0.667552i	$0.232658\pi$
$632$	7.76179	−	8.95759i	0.308748	−	0.356314i
$633$	−4.07033	+	4.69741i	−0.161781	+	0.186705i
$634$	20.6784	−	6.07173i	0.821245	−	0.241139i
$635$	−1.76755	−	3.87039i	−0.0701430	−	0.153592i
$636$	−0.941176	+	0.604857i	−0.0373201	+	0.0239841i
$637$	−53.3934	−	15.6777i	−2.11552	−	0.621173i
$638$	−0.0349600	−	0.243152i	−0.00138408	−	0.00962650i
$639$	−3.82244	+	8.36997i	−0.151213	+	0.331111i
$640$	−0.142315	+	0.989821i	−0.00562549	+	0.0391261i
$641$	−34.9956	−	22.4903i	−1.38224	−	0.888313i	−0.382872	−	0.923801i	$-0.625065\pi$
$641$	−34.9956	−	22.4903i	−1.38224	−	0.888313i	−0.999370	+	0.0354879i	$0.988701\pi$
$642$	−11.8719	−	13.7009i	−0.468547	−	0.540732i
$643$	−18.2634			−0.720238			−0.360119	−	0.932906i	$-0.617264\pi$
$643$	−18.2634			−0.720238			−0.360119	+	0.932906i	$0.617264\pi$
$644$	13.9832	+	16.2383i	0.551016	+	0.639878i
$645$	−11.0738			−0.436031
$646$	−19.7794	−	22.8266i	−0.778209	−	0.898102i
$647$	−17.2875	−	11.1100i	−0.679642	−	0.436779i	0.154748	−	0.987954i	$-0.450543\pi$
$647$	−17.2875	−	11.1100i	−0.679642	−	0.436779i	−0.834390	+	0.551175i	$0.814180\pi$
$648$	0.142315	−	0.989821i	0.00559065	−	0.0388839i
$649$	−0.145123	+	0.317774i	−0.00569656	+	0.0124737i
$650$	0.610798	+	4.24820i	0.0239575	+	0.166628i
$651$	−12.3400	−	3.62336i	−0.483644	−	0.142011i
$652$	9.54093	−	6.13158i	0.373652	−	0.240131i
$653$	12.6327	+	27.6618i	0.494357	+	1.08249i	0.978262	+	0.207371i	$0.0664906\pi$
$653$	12.6327	+	27.6618i	0.494357	+	1.08249i	−0.483905	+	0.875120i	$0.660782\pi$
$654$	−15.4475	+	4.53579i	−0.604045	+	0.177364i
$655$	10.1914	−	11.7615i	0.398211	−	0.459560i
$656$	−6.69434	+	7.72569i	−0.261370	+	0.301637i
$657$	10.5400	−	3.09482i	0.411205	−	0.120741i
$658$	3.75702	+	8.22673i	0.146464	+	0.320711i
$659$	35.9253	−	23.0878i	1.39945	−	0.899373i	0.399601	−	0.916689i	$-0.369149\pi$
$659$	35.9253	−	23.0878i	1.39945	−	0.899373i	0.999850	+	0.0173164i	$0.00551224\pi$
$660$	−0.0506233	−	0.0148644i	−0.00197051	−	0.000578594i
$661$	3.38048	+	23.5118i	0.131486	+	0.914502i	0.943620	+	0.331031i	$0.107397\pi$
$661$	3.38048	+	23.5118i	0.131486	+	0.914502i	−0.812134	+	0.583471i	$0.801694\pi$
$662$	−10.4007	+	22.7744i	−0.404236	+	0.885153i
$663$	2.94448	−	20.4793i	0.114354	−	0.795352i
$664$	10.6829	+	6.86550i	0.414578	+	0.266433i
$665$	18.3335	+	21.1579i	0.710941	+	0.820469i
$666$	1.76553			0.0684129
$667$	21.4054	+	6.35687i	0.828821	+	0.246139i
$668$	5.82919			0.225538
$669$	10.2372	+	11.8143i	0.395792	+	0.456768i
$670$	−9.24175	−	5.93931i	−0.357040	−	0.229456i
$671$	0.0606408	−	0.421766i	0.00234101	−	0.0162821i
$672$	−1.85620	+	4.06451i	−0.0716045	+	0.156792i
$673$	0.803425	+	5.58794i	0.0309697	+	0.215399i	0.999430	−	0.0337702i	$-0.0107514\pi$
$673$	0.803425	+	5.58794i	0.0309697	+	0.215399i	−0.968460	+	0.249170i	$0.919842\pi$
$674$	2.77375	+	0.814447i	0.106841	+	0.0313713i
$675$	0.841254	−	0.540641i	0.0323799	−	0.0208093i
$676$	2.25165	+	4.93043i	0.0866020	+	0.189632i
$677$	45.6297	−	13.3981i	1.75369	−	0.514930i	0.762457	−	0.647039i	$-0.223993\pi$
$677$	45.6297	−	13.3981i	1.75369	−	0.514930i	0.991235	+	0.132109i	$0.0421748\pi$
$678$	3.92299	−	4.52737i	0.150661	−	0.173872i
$679$	40.8881	−	47.1873i	1.56914	−	1.81088i
$680$	4.62544	−	1.35815i	0.177378	−	0.0520827i
$681$	−0.345567	−	0.756687i	−0.0132422	−	0.0289963i
$682$	0.127752	−	0.0821012i	0.00489187	−	0.00314382i
$683$	12.3414	+	3.62377i	0.472232	+	0.138660i	0.509185	−	0.860657i	$-0.329947\pi$
$683$	12.3414	+	3.62377i	0.472232	+	0.138660i	−0.0369530	+	0.999317i	$0.511765\pi$
$684$	−0.891667	−	6.20168i	−0.0340937	−	0.237127i
$685$	−5.76530	+	12.6243i	−0.220281	+	0.482348i
$686$	3.79366	−	26.3855i	0.144843	−	1.00740i
$687$	2.26251	+	1.45403i	0.0863202	+	0.0554746i
$688$	−7.25181	−	8.36904i	−0.276473	−	0.319067i
$689$	−4.80166			−0.182929
$690$	3.15175	−	3.61476i	0.119985	−	0.137611i
$691$	42.1084			1.60188			0.800940	−	0.598745i	$-0.204334\pi$
$691$	42.1084			1.60188			0.800940	+	0.598745i	$0.204334\pi$
$692$	−11.0775	−	12.7842i	−0.421105	−	0.485981i
$693$	−0.198326	−	0.127456i	−0.00753377	−	0.00484166i
$694$	2.90614	−	20.2127i	0.110316	−	0.767262i
$695$	−4.12024	+	9.02208i	−0.156290	+	0.342227i
$696$	0.662618	+	4.60861i	0.0251165	+	0.174689i
$697$	47.2838	+	13.8838i	1.79100	+	0.525885i
$698$	24.2507	−	15.5850i	0.917902	−	0.589900i
$699$	0.463015	+	1.01386i	0.0175129	+	0.0383478i
$700$	−4.28731	+	1.25887i	−0.162045	+	0.0475807i
$701$	−29.0698	+	33.5484i	−1.09795	+	1.26710i	−0.136945	+	0.990579i	$0.543728\pi$
$701$	−29.0698	+	33.5484i	−1.09795	+	1.26710i	−0.961007	+	0.276525i	$0.910817\pi$
$702$	2.81058	−	3.24359i	0.106079	−	0.122421i
$703$	10.6138	−	3.11648i	0.400306	−	0.117540i
$704$	−0.0219175	−	0.0479926i	−0.000826047	−	0.00180879i
$705$	1.70273	−	1.09428i	0.0641285	−	0.0412129i
$706$	−7.77767	−	2.28373i	−0.292716	−	0.0859493i
$707$	2.17849	+	15.1518i	0.0819307	+	0.569840i
$708$	2.75059	−	6.02295i	0.103374	−	0.226356i
$709$	1.86756	−	12.9892i	0.0701376	−	0.487818i	−0.924230	−	0.381835i	$-0.875292\pi$
$709$	1.86756	−	12.9892i	0.0701376	−	0.487818i	0.994368	−	0.105983i	$-0.0337988\pi$
$710$	−7.74078	−	4.97470i	−0.290506	−	0.186697i
$711$	−7.76179	−	8.95759i	−0.291090	−	0.335936i
$712$	−12.2996			−0.460947
$713$	1.92238	+	13.6692i	0.0719938	+	0.511915i
$714$	21.5404			0.806130
$715$	−0.148288	−	0.171133i	−0.00554565	−	0.00640002i
$716$	−9.83545	−	6.32086i	−0.367568	−	0.236222i
$717$	1.11685	−	7.76788i	0.0417096	−	0.290097i
$718$	1.73771	−	3.80505i	0.0648506	−	0.142003i
$719$	−5.45301	−	37.9265i	−0.203363	−	1.41442i	−0.794213	−	0.607639i	$-0.792117\pi$
$719$	−5.45301	−	37.9265i	−0.203363	−	1.41442i	0.590851	−	0.806781i	$-0.298792\pi$
$720$	0.959493	+	0.281733i	0.0357582	+	0.0104996i
$721$	28.2694	−	18.1676i	1.05281	−	0.676598i
$722$	−8.41461	−	18.4254i	−0.313159	−	0.685723i
$723$	17.9350	−	5.26619i	0.667010	−	0.195852i
$724$	12.5260	−	14.4557i	0.465524	−	0.537243i
$725$	−3.04903	+	3.51877i	−0.113238	+	0.130684i
$726$	−10.5518	+	3.09827i	−0.391612	+	0.114988i
$727$	−3.34105	−	7.31588i	−0.123913	−	0.271331i	0.837502	−	0.546434i	$-0.184015\pi$
$727$	−3.34105	−	7.31588i	−0.123913	−	0.271331i	−0.961415	+	0.275103i	$0.911288\pi$
$728$	−16.1331	+	10.3681i	−0.597932	+	0.384268i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	1.56332	+	10.8732i	0.0578612	+	0.402434i
$731$	−22.1764	+	48.5595i	−0.820224	+	1.79604i
$732$	−1.14936	+	7.99397i	−0.0424815	+	0.295466i
$733$	18.1580	+	11.6694i	0.670680	+	0.431020i	0.831170	−	0.556018i	$-0.187671\pi$
$733$	18.1580	+	11.6694i	0.670680	+	0.431020i	−0.160491	+	0.987037i	$0.551308\pi$
$734$	−19.1702	−	22.1236i	−0.707586	−	0.816597i
$735$	−12.9658			−0.478249
$736$	4.79581	+	0.0147701i	0.176776	+	0.000544434i
$737$	0.579610			0.0213502
$738$	6.69434	+	7.72569i	0.246422	+	0.284386i
$739$	10.8994	+	7.00463i	0.400942	+	0.257669i	0.725537	−	0.688184i	$-0.241592\pi$
$739$	10.8994	+	7.00463i	0.400942	+	0.257669i	−0.324595	+	0.945853i	$0.605228\pi$
$740$	−0.251261	+	1.74756i	−0.00923654	+	0.0642415i
$741$	11.1708	−	24.4605i	0.410368	−	0.898580i
$742$	−0.711438	−	4.94816i	−0.0261177	−	0.181653i
$743$	−18.2391	−	5.35548i	−0.669127	−	0.196473i	−0.0705126	−	0.997511i	$-0.522464\pi$
$743$	−18.2391	−	5.35548i	−0.669127	−	0.196473i	−0.598614	+	0.801038i	$0.704282\pi$
$744$	−2.42136	+	1.55611i	−0.0887712	+	0.0570498i
$745$	3.98066	+	8.71643i	0.145840	+	0.319345i
$746$	−8.84108	+	2.59598i	−0.323695	+	0.0950454i
$747$	8.31596	−	9.59713i	0.304265	−	0.351141i
$748$	−0.166559	+	0.192220i	−0.00609002	+	0.00702825i
$749$	77.7242	−	22.8219i	2.83998	−	0.833894i
$750$	0.415415	+	0.909632i	0.0151688	+	0.0332151i
$751$	−6.83179	+	4.39052i	−0.249296	+	0.160212i	−0.659321	−	0.751862i	$-0.729156\pi$
$751$	−6.83179	+	4.39052i	−0.249296	+	0.160212i	0.410025	+	0.912074i	$0.365520\pi$
$752$	1.94205	+	0.570237i	0.0708193	+	0.0207944i
$753$	0.182386	+	1.26852i	0.00664650	+	0.0462275i
$754$	−8.30124	+	18.1772i	−0.302313	+	0.661974i
$755$	−2.41743	+	16.8136i	−0.0879793	+	0.611910i
$756$	3.75898	+	2.41575i	0.136713	+	0.0878599i
$757$	−9.48588	−	10.9473i	−0.344770	−	0.397886i	0.556710	−	0.830707i	$-0.312064\pi$
$757$	−9.48588	−	10.9473i	−0.344770	−	0.397886i	−0.901480	+	0.432821i	$0.857518\pi$
$758$	−16.9114			−0.614249
$759$	−0.0367812	+	0.250343i	−0.00133507	+	0.00908687i
$760$	6.26545			0.227272
$761$	3.04457	+	3.51362i	0.110366	+	0.127369i	0.808244	−	0.588847i	$-0.200418\pi$
$761$	3.04457	+	3.51362i	0.110366	+	0.127369i	−0.697879	+	0.716216i	$0.745873\pi$
$762$	−3.57945	−	2.30037i	−0.129670	−	0.0833336i
$763$	10.2379	−	71.2059i	0.370635	−	2.57783i
$764$	1.93697	−	4.24138i	0.0700772	−	0.153448i
$765$	−0.686059	−	4.77165i	−0.0248045	−	0.172519i
$766$	−9.95447	−	2.92290i	−0.359670	−	0.105608i
$767$	23.9066	−	15.3639i	0.863218	−	0.554757i
$768$	0.415415	+	0.909632i	0.0149900	+	0.0328235i
$769$	19.4224	−	5.70295i	0.700391	−	0.205653i	0.0878984	−	0.996129i	$-0.471985\pi$
$769$	19.4224	−	5.70295i	0.700391	−	0.205653i	0.612493	+	0.790476i	$0.290167\pi$
$770$	0.154383	−	0.178168i	0.00556359	−	0.00642073i
$771$	−0.192896	+	0.222613i	−0.00694697	+	0.00801723i
$772$	−13.5300	+	3.97277i	−0.486955	+	0.142983i
$773$	−9.07041	−	19.8614i	−0.326240	−	0.714365i	0.673451	−	0.739232i	$-0.264811\pi$
$773$	−9.07041	−	19.8614i	−0.326240	−	0.714365i	−0.999691	+	0.0248664i	$0.992084\pi$
$774$	−9.31589	+	5.98696i	−0.334853	+	0.215197i
$775$	−2.76168	−	0.810902i	−0.0992025	−	0.0291285i
$776$	−1.98863	−	13.8313i	−0.0713878	−	0.496513i
$777$	−3.27718	+	7.17602i	−0.117568	+	0.257438i
$778$	−2.93832	+	20.4365i	−0.105344	+	0.732682i
$779$	53.8814	+	34.6274i	1.93050	+	1.24066i
$780$	2.81058	+	3.24359i	0.100635	+	0.116139i
$781$	0.485475			0.0173717
$782$	−9.53930	−	21.0596i	−0.341125	−	0.753088i
$783$	4.65600			0.166392
$784$	−8.49076	−	9.79886i	−0.303242	−	0.349959i
$785$	−13.0487	−	8.38586i	−0.465726	−	0.299304i
$786$	2.21480	−	15.4043i	0.0789994	−	0.549453i
$787$	18.1988	−	39.8499i	0.648718	−	1.42049i	−0.243953	−	0.969787i	$-0.578444\pi$
$787$	18.1988	−	39.8499i	0.648718	−	1.42049i	0.892672	−	0.450708i	$-0.148828\pi$
$788$	2.15441	+	14.9842i	0.0767476	+	0.533791i
$789$	16.5765	+	4.86731i	0.590140	+	0.173281i
$790$	9.97103	−	6.40799i	0.354753	−	0.227986i
$791$	11.1197	+	24.3487i	0.395371	+	0.865741i
$792$	−0.0506233	+	0.0148644i	−0.00179882	+	0.000528182i
$793$	−22.6988	+	26.1958i	−0.806057	+	0.930239i
$794$	−12.5279	+	14.4580i	−0.444598	+	0.513094i
$795$	−1.07346	+	0.315196i	−0.0380717	+	0.0111789i
$796$	3.02042	+	6.61380i	0.107056	+	0.234420i
$797$	−15.7465	+	10.1197i	−0.557771	+	0.358458i	−0.788954	−	0.614453i	$-0.789377\pi$
$797$	−15.7465	+	10.1197i	−0.557771	+	0.358458i	0.231183	+	0.972910i	$0.425740\pi$
$798$	26.8619	+	7.88737i	0.950902	+	0.279210i
$799$	−1.38861	−	9.65799i	−0.0491255	−	0.341675i
$800$	−0.415415	+	0.909632i	−0.0146871	+	0.0321603i
$801$	−1.75042	+	12.1744i	−0.0618479	+	0.430162i
$802$	21.5830	+	13.8706i	0.762123	+	0.489787i
$803$	−0.379539	−	0.438012i	−0.0133936	−	0.0154571i
$804$	−10.9857			−0.387435
$805$	8.84195	+	19.5200i	0.311638	+	0.687991i
$806$	−12.3532			−0.435123
$807$	−11.0324	−	12.7321i	−0.388359	−	0.448190i
$808$	2.88197	+	1.85213i	0.101387	+	0.0651578i
$809$	−2.27767	+	15.8415i	−0.0800785	+	0.556958i	0.909801	+	0.415045i	$0.136234\pi$
$809$	−2.27767	+	15.8415i	−0.0800785	+	0.556958i	−0.989879	+	0.141913i	$0.954675\pi$
$810$	0.415415	−	0.909632i	0.0145962	−	0.0319612i
$811$	−0.989604	−	6.88284i	−0.0347497	−	0.241689i	0.965042	−	0.262095i	$-0.0844134\pi$
$811$	−0.989604	−	6.88284i	−0.0347497	−	0.241689i	−0.999792	+	0.0204056i	$0.993504\pi$
$812$	−19.9617	−	5.86128i	−0.700518	−	0.205691i
$813$	−7.09452	+	4.55937i	−0.248816	+	0.159904i
$814$	−0.0386960	−	0.0847324i	−0.00135629	−	0.00296987i
$815$	10.8819	−	3.19522i	0.381177	−	0.111924i
$816$	3.15690	−	3.64325i	0.110513	−	0.127539i
$817$	−45.4359	+	52.4358i	−1.58960	+	1.83450i
$818$	−28.9304	+	8.49473i	−1.01153	+	0.297011i
$819$	7.96660	+	17.4444i	0.278375	+	0.609557i
$820$	−8.59975	+	5.52673i	−0.300316	+	0.193002i
$821$	−23.4536	−	6.88661i	−0.818537	−	0.240344i	−0.154451	−	0.988000i	$-0.549361\pi$
$821$	−23.4536	−	6.88661i	−0.818537	−	0.240344i	−0.664086	+	0.747656i	$0.731179\pi$
$822$	1.97510	+	13.7372i	0.0688897	+	0.479138i
$823$	22.6547	−	49.6069i	0.789693	−	1.72919i	0.112165	−	0.993690i	$-0.464221\pi$
$823$	22.6547	−	49.6069i	0.789693	−	1.72919i	0.677528	−	0.735497i	$-0.263051\pi$
$824$	1.07028	−	7.44395i	0.0372849	−	0.259322i
$825$	−0.0443850	−	0.0285245i	−0.00154529	−	0.000993095i
$826$	19.3747	+	22.3596i	0.674133	+	0.777991i
$827$	35.4697			1.23340			0.616702	−	0.787197i	$-0.288468\pi$
$827$	35.4697			1.23340			0.616702	+	0.787197i	$0.288468\pi$
$828$	0.697135	−	4.74489i	0.0242271	−	0.164896i
$829$	−31.5209			−1.09477			−0.547384	−	0.836882i	$-0.684376\pi$
$829$	−31.5209			−1.09477			−0.547384	+	0.836882i	$0.684376\pi$
$830$	8.31596	+	9.59713i	0.288651	+	0.333121i
$831$	11.9911	+	7.70620i	0.415966	+	0.267325i
$832$	−0.610798	+	4.24820i	−0.0211756	+	0.147280i
$833$	−25.9652	+	56.8558i	−0.899640	+	1.96994i
$834$	1.41153	+	9.81743i	0.0488774	+	0.339950i
$835$	5.59306	+	1.64227i	0.193556	+	0.0568331i
$836$	−0.278092	+	0.178719i	−0.00961801	+	0.00618112i
$837$	1.19568	+	2.61817i	0.0413286	+	0.0904971i
$838$	−20.3649	+	5.97967i	−0.703493	+	0.206564i
$839$	−31.0288	+	35.8091i	−1.07123	+	1.23627i	−0.100796	+	0.994907i	$0.532139\pi$
$839$	−31.0288	+	35.8091i	−1.07123	+	1.23627i	−0.970436	+	0.241360i	$0.922407\pi$
$840$	−2.92612	+	3.37692i	−0.100961	+	0.116515i
$841$	7.02510	−	2.06276i	0.242245	−	0.0711295i
$842$	5.13084	+	11.2350i	0.176820	+	0.387182i
$843$	20.0549	−	12.8885i	0.690726	−	0.443903i
$844$	−5.96379	−	1.75113i	−0.205282	−	0.0602763i
$845$	0.771382	+	5.36508i	0.0265363	+	0.184564i
$846$	0.840816	−	1.84113i	0.0289078	−	0.0632994i
$847$	6.99320	−	48.6388i	0.240289	−	1.67125i
$848$	−0.941176	−	0.604857i	−0.0323201	−	0.0207709i
$849$	−11.0146	−	12.7115i	−0.378019	−	0.436257i
$850$	4.82071			0.165349
$851$	8.46714	+	0.0260771i	0.290250	+	0.000893911i
$852$	−9.20149			−0.315238
$853$	−16.7167	−	19.2921i	−0.572370	−	0.660550i	0.393577	−	0.919292i	$-0.371238\pi$
$853$	−16.7167	−	19.2921i	−0.572370	−	0.660550i	−0.965947	+	0.258742i	$0.916692\pi$
$854$	−30.3581	−	19.5100i	−1.03883	−	0.667618i
$855$	0.891667	−	6.20168i	0.0304944	−	0.212093i
$856$	7.53102	−	16.4906i	0.257405	−	0.563638i
$857$	−1.81800	−	12.6445i	−0.0621018	−	0.431928i	−0.997025	−	0.0770777i	$-0.975441\pi$
$857$	−1.81800	−	12.6445i	−0.0621018	−	0.431928i	0.934923	−	0.354850i	$-0.115468\pi$
$858$	−0.217269	−	0.0637960i	−0.00741745	−	0.00217796i
$859$	−42.4930	+	27.3086i	−1.44984	+	0.931757i	−0.450604	+	0.892724i	$0.648791\pi$
$859$	−42.4930	+	27.3086i	−1.44984	+	0.931757i	−0.999238	+	0.0390324i	$0.987572\pi$
$860$	−4.60023	−	10.0731i	−0.156867	−	0.343490i
$861$	−43.8272	+	12.8688i	−1.49363	+	0.438568i
$862$	6.47696	−	7.47481i	0.220606	−	0.254593i
$863$	−24.9207	+	28.7600i	−0.848310	+	0.979002i	−0.999956	−	0.00943269i	$-0.996997\pi$
$863$	−24.9207	+	28.7600i	−0.848310	+	0.979002i	0.151645	+	0.988435i	$0.451543\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	−7.02710	−	15.3872i	−0.238929	−	0.523181i
$866$	23.3220	−	14.9881i	0.792512	−	0.509317i
$867$	−5.98654	−	1.75781i	−0.203314	−	0.0596983i
$868$	−1.83031	−	12.7301i	−0.0621248	−	0.432087i
$869$	−0.259779	+	0.568837i	−0.00881240	+	0.0192965i
$870$	−0.662618	+	4.60861i	−0.0224648	+	0.156246i
$871$	−39.6645	−	25.4908i	−1.34398	−	0.863724i
$872$	−10.5430	−	12.1673i	−0.357032	−	0.412037i
$873$	−13.9735			−0.472931
$874$	−4.18466	−	29.7552i	−0.141548	−	1.00649i
$875$	−4.46831			−0.151056
$876$	7.19362	+	8.30189i	0.243050	+	0.280495i
$877$	19.1353	+	12.2975i	0.646153	+	0.415258i	0.822259	−	0.569114i	$-0.192714\pi$
$877$	19.1353	+	12.2975i	0.646153	+	0.415258i	−0.176105	+	0.984371i	$0.556350\pi$
$878$	1.37790	−	9.58348i	0.0465018	−	0.323427i
$879$	−1.93000	+	4.22612i	−0.0650974	+	0.142544i
$880$	−0.00750860	−	0.0522235i	−0.000253115	−	0.00176045i
$881$	9.83198	+	2.88693i	0.331248	+	0.0972631i	0.443127	−	0.896459i	$-0.353869\pi$
$881$	9.83198	+	2.88693i	0.331248	+	0.0972631i	−0.111880	+	0.993722i	$0.535687\pi$
$882$	−10.9075	+	7.00982i	−0.367274	+	0.236033i
$883$	13.8870	+	30.4082i	0.467333	+	1.02332i	0.985754	+	0.168192i	$0.0537928\pi$
$883$	13.8870	+	30.4082i	0.467333	+	1.02332i	−0.518421	+	0.855126i	$0.673480\pi$
$884$	19.8518	−	5.82903i	0.667690	−	0.196051i
$885$	4.33603	−	5.00405i	0.145754	−	0.168209i
$886$	0.756277	−	0.872790i	0.0254076	−	0.0293219i
$887$	9.26429	−	2.72024i	0.311064	−	0.0913367i	−0.122474	−	0.992472i	$-0.539083\pi$
$887$	9.26429	−	2.72024i	0.311064	−	0.0913367i	0.433539	+	0.901135i	$0.357265\pi$
$888$	0.733427	+	1.60598i	0.0246122	+	0.0538932i
$889$	15.9941	−	10.2788i	0.536424	−	0.344739i
$890$	−11.8014	−	3.46520i	−0.395583	−	0.116154i
$891$	0.00750860	+	0.0522235i	0.000251548	+	0.00174955i
$892$	−6.49401	+	14.2199i	−0.217436	+	0.476117i
$893$	1.80477	−	12.5524i	0.0603943	−	0.420051i
$894$	8.06120	+	5.18062i	0.269607	+	0.173266i
$895$	−7.65625	−	8.83578i	−0.255920	−	0.295348i
$896$	−4.46831			−0.149276
$897$	13.5269	−	15.5141i	0.451651	−	0.518001i
$898$	14.8721			0.496289
$899$	−8.77593	−	10.1280i	−0.292694	−	0.337787i
$900$	0.841254	+	0.540641i	0.0280418	+	0.0180214i
$901$	−0.767548	+	5.33841i	−0.0255707	+	0.177848i
$902$	0.224053	−	0.490607i	0.00746014	−	0.0163354i
$903$	−7.04191	−	48.9776i	−0.234340	−	1.62987i
$904$	5.74791	+	1.68774i	0.191172	+	0.0561333i
$905$	16.0912	−	10.3412i	0.534890	−	0.343753i
$906$	7.05645	+	15.4515i	0.234435	+	0.513340i
$907$	−25.7204	+	7.55218i	−0.854031	+	0.250766i	−0.679310	−	0.733852i	$-0.737721\pi$
$907$	−25.7204	+	7.55218i	−0.854031	+	0.250766i	−0.174721	+	0.984618i	$0.555902\pi$
$908$	0.544753	−	0.628678i	0.0180783	−	0.0208634i
$909$	2.24343	−	2.58905i	0.0744098	−	0.0858735i
$910$	−18.4006	+	5.40291i	−0.609975	+	0.179105i
$911$	2.94996	+	6.45951i	0.0977365	+	0.214013i	0.952184	−	0.305524i	$-0.0988316\pi$
$911$	2.94996	+	6.45951i	0.0977365	+	0.214013i	−0.854448	+	0.519537i	$0.826104\pi$
$912$	5.27083	−	3.38736i	0.174535	−	0.112167i
$913$	−0.642857	−	0.188760i	−0.0212755	−	0.00624704i
$914$	−5.27616	−	36.6965i	−0.174520	−	1.21381i
$915$	−3.35496	+	7.34634i	−0.110912	+	0.242863i
$916$	−0.382749	+	2.66208i	−0.0126464	+	0.0879575i
$917$	58.4998	+	37.5956i	1.93183	+	1.24151i
$918$	−3.15690	−	3.64325i	−0.104193	−	0.120245i
$919$	44.6714			1.47357			0.736787	−	0.676125i	$-0.236342\pi$
$919$	44.6714			1.47357			0.736787	+	0.676125i	$0.236342\pi$
$920$	4.59738	+	1.36531i	0.151571	+	0.0450128i
$921$	−14.3761			−0.473707
$922$	7.02301	+	8.10498i	0.231290	+	0.266923i
$923$	−33.2225	−	21.3508i	−1.09353	−	0.702771i
$924$	0.0335507	−	0.233350i	0.00110374	−	0.00767667i
$925$	−0.733427	+	1.60598i	−0.0241149	+	0.0528044i
$926$	3.15595	+	21.9501i	0.103711	+	0.721325i
$927$	−7.21586	−	2.11877i	−0.237000	−	0.0695895i
$928$	−3.91688	+	2.51722i	−0.128578	+	0.0826319i
$929$	−21.2025	−	46.4270i	−0.695631	−	1.52322i	−0.845190	−	0.534467i	$-0.820513\pi$
$929$	−21.2025	−	46.4270i	−0.695631	−	1.52322i	0.149559	−	0.988753i	$-0.452215\pi$
$930$	−2.76168	+	0.810902i	−0.0905591	+	0.0265905i
$931$	−53.1985	+	61.3943i	−1.74351	+	2.01212i
$932$	−0.729898	+	0.842347i	−0.0239086	+	0.0275920i
$933$	−2.86529	+	0.841326i	−0.0938055	+	0.0275438i
$934$	14.5731	+	31.9107i	0.476847	+	1.04415i
$935$	−0.213967	+	0.137508i	−0.00699747	+	0.00449700i
$936$	4.11803	+	1.20916i	0.134602	+	0.0395227i
$937$	−2.10405	−	14.6340i	−0.0687363	−	0.478071i	−0.994893	−	0.100933i	$-0.967817\pi$
$937$	−2.10405	−	14.6340i	−0.0687363	−	0.478071i	0.926157	−	0.377138i	$-0.123092\pi$
$938$	20.3916	−	44.6515i	0.665811	−	1.45792i
$939$	1.49012	−	10.3640i	0.0486281	−	0.338216i
$940$	1.70273	+	1.09428i	0.0555369	+	0.0356914i
$941$	9.02656	+	10.4172i	0.294257	+	0.339591i	0.883557	−	0.468323i	$-0.155142\pi$
$941$	9.02656	+	10.4172i	0.294257	+	0.339591i	−0.589300	+	0.807914i	$0.700596\pi$
$942$	−15.5110			−0.505374
$943$	31.9907	+	37.1498i	1.04176	+	1.20976i
$944$	6.62131			0.215505
$945$	2.92612	+	3.37692i	0.0951866	+	0.109851i
$946$	0.491511	+	0.315875i	0.0159804	+	0.0102700i
$947$	−3.68272	+	25.6139i	−0.119672	+	0.832339i	0.838245	+	0.545294i	$0.183582\pi$
$947$	−3.68272	+	25.6139i	−0.119672	+	0.832339i	−0.957917	+	0.287045i	$0.907327\pi$
$948$	4.92374	−	10.7815i	0.159916	−	0.350167i
$949$	6.70960	+	46.6663i	0.217803	+	1.51485i
$950$	6.01166	+	1.76518i	0.195044	+	0.0572701i
$951$	18.1302	−	11.6516i	0.587912	−	0.377828i
$952$	8.94821	+	19.5939i	0.290013	+	0.635041i
$953$	−13.8682	+	4.07208i	−0.449236	+	0.131908i	−0.498522	−	0.866877i	$-0.666124\pi$
$953$	−13.8682	+	4.07208i	−0.449236	+	0.131908i	0.0492859	+	0.998785i	$0.484305\pi$
$954$	−0.732644	+	0.845516i	−0.0237202	+	0.0273746i
$955$	3.05345	−	3.52387i	0.0988072	−	0.114030i
$956$	7.52987	−	2.21097i	0.243534	−	0.0715079i
$957$	−0.102048	−	0.223454i	−0.00329874	−	0.00722323i
$958$	−33.0353	+	21.2305i	−1.06732	+	0.685927i
$959$	−59.5010	−	17.4711i	−1.92139	−	0.564171i
$960$	0.142315	+	0.989821i	0.00459319	+	0.0319463i
$961$	−9.43638	+	20.6628i	−0.304399	+	0.666542i
$962$	−1.07838	+	7.50032i	−0.0347685	+	0.241820i
$963$	−15.2510	−	9.80123i	−0.491457	−	0.315840i
$964$	12.2408	+	14.1266i	0.394249	+	0.454987i
$965$	−14.1012			−0.453934
$966$	17.9917	+	11.6410i	0.578872	+	0.374543i
$967$	6.60272			0.212329			0.106165	−	0.994349i	$-0.466143\pi$
$967$	6.60272			0.212329			0.106165	+	0.994349i	$0.466143\pi$
$968$	−7.20165	−	8.31114i	−0.231470	−	0.267130i
$969$	−25.4092	−	16.3295i	−0.816261	−	0.524579i
$970$	1.98863	−	13.8313i	0.0638512	−	0.444095i
$971$	−22.7138	+	49.7363i	−0.728921	+	1.59611i	0.0720423	+	0.997402i	$0.477048\pi$
$971$	−22.7138	+	49.7363i	−0.728921	+	1.59611i	−0.800963	+	0.598713i	$0.795679\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	−42.5232	−	12.4859i	−1.36323	−	0.400280i
$974$	5.51403	−	3.54365i	0.176681	−	0.113546i
$975$	1.78291	+	3.90403i	0.0570989	+	0.125029i
$976$	−7.74903	+	2.27532i	−0.248040	+	0.0728312i
$977$	−2.96009	+	3.41613i	−0.0947018	+	0.109292i	−0.801122	−	0.598501i	$-0.795763\pi$
$977$	−2.96009	+	3.41613i	−0.0947018	+	0.109292i	0.706420	+	0.707792i	$0.250309\pi$
$978$	7.42699	−	8.57120i	0.237489	−	0.274077i
$979$	0.622647	−	0.182826i	0.0198999	−	0.00584313i
$980$	−5.38617	−	11.7941i	−0.172055	−	0.376748i
$981$	−13.5439	+	8.70412i	−0.432423	+	0.277901i
$982$	28.2282	+	8.28854i	0.900797	+	0.264498i
$983$	−8.16867	−	56.8144i	−0.260540	−	1.81210i	−0.528796	−	0.848749i	$-0.677356\pi$
$983$	−8.16867	−	56.8144i	−0.260540	−	1.81210i	0.268256	−	0.963348i	$-0.413553\pi$
$984$	−4.24660	+	9.29876i	−0.135377	+	0.296434i
$985$	−2.15441	+	14.9842i	−0.0686451	+	0.477437i
$986$	18.8821	+	12.1348i	0.601330	+	0.386451i
$987$	5.92257	+	6.83502i	0.188518	+	0.217561i
$988$	26.8906			0.855503
$989$	−44.7657	+	28.5747i	−1.42347	+	0.908623i
$990$	−0.0527605			−0.00167684
$991$	17.0968	+	19.7308i	0.543098	+	0.626768i	0.959261	−	0.282522i	$-0.0911709\pi$
$991$	17.0968	+	19.7308i	0.543098	+	0.626768i	−0.416163	+	0.909290i	$0.636625\pi$
$992$	−2.42136	−	1.55611i	−0.0768781	−	0.0494066i
$993$	−3.56313	+	24.7821i	−0.113073	+	0.786437i
$994$	17.0798	−	37.3996i	0.541739	−	1.18624i
$995$	1.03475	+	7.19684i	0.0328038	+	0.228155i
$996$	12.1844	+	3.57767i	0.386079	+	0.113363i
$997$	47.4011	−	30.4628i	1.50121	−	0.964768i	0.506476	−	0.862254i	$-0.330948\pi$
$997$	47.4011	−	30.4628i	1.50121	−	0.964768i	0.994732	−	0.102514i	$-0.0326886\pi$
$998$	2.20730	+	4.83331i	0.0698708	+	0.152996i
$999$	1.69401	−	0.497407i	0.0535962	−	0.0157373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.151.1	✓	30
23.16	even	11	inner	690.2.m.h.361.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.151.1	✓	30	1.1	even	1	trivial
690.2.m.h.361.1	yes	30	23.16	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-4.28731 - 1.25887i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-4.28731 - 1.25887i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(0.0345508 - 0.0398737i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(-4.11803 + 1.20916i) q^{13} +(-1.85620 - 4.06451i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.686059 + 4.77165i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(-0.891667 + 6.20168i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(-2.92612 - 3.37692i) q^{21} +0.0527605 q^{22} +(-2.00569 + 4.35629i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-3.61056 - 2.32037i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(1.85620 - 4.06451i) q^{28} +(-0.662618 - 4.60861i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(2.42136 - 1.55611i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(0.0506233 - 0.0148644i) q^{33} +(-3.15690 + 3.64325i) q^{34} +(2.92612 - 3.37692i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.733427 - 1.60598i) q^{37} +(-5.27083 + 3.38736i) q^{38} +(-4.11803 - 1.20916i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(4.24660 - 9.29876i) q^{41} +(0.635906 - 4.42282i) q^{42} +(9.31589 + 5.98696i) q^{43} +(0.0345508 + 0.0398737i) q^{44} -1.00000 q^{45} +(-4.60571 + 1.33696i) q^{46} -2.02404 q^{47} +(-0.654861 - 0.755750i) q^{48} +(10.9075 + 7.00982i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-2.00260 + 4.38508i) q^{51} +(-0.610798 - 4.24820i) q^{52} +(1.07346 + 0.315196i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(0.0219175 + 0.0479926i) q^{55} +(4.28731 - 1.25887i) q^{56} +(-4.10300 + 4.73511i) q^{57} +(3.04903 - 3.51877i) q^{58} +(-6.35310 + 1.86544i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(6.79411 - 4.36631i) q^{61} +(2.76168 + 0.810902i) q^{62} +(-0.635906 - 4.42282i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.610798 - 4.24820i) q^{65} +(0.0443850 + 0.0285245i) q^{66} +(7.19410 + 8.30243i) q^{67} -4.82071 q^{68} +(-4.04248 + 2.58038i) q^{69} +4.46831 q^{70} +(6.02569 + 6.95402i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(1.56332 - 10.8732i) q^{73} +(0.733427 - 1.60598i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-6.01166 - 1.76518i) q^{76} +(-0.198326 + 0.127456i) q^{77} +(-1.78291 - 3.90403i) q^{78} +(-11.3725 + 3.33926i) q^{79} +(0.654861 - 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(9.80846 - 2.88002i) q^{82} +(-5.27528 - 11.5513i) q^{83} +(3.75898 - 2.41575i) q^{84} +(-4.62544 - 1.35815i) q^{85} +(1.57597 + 10.9611i) q^{86} +(1.93417 - 4.23525i) q^{87} +(-0.00750860 + 0.0522235i) q^{88} +(10.3471 + 6.64967i) q^{89} +(-0.654861 - 0.755750i) q^{90} +19.1774 q^{91} +(-4.02651 - 2.60524i) q^{92} +2.87827 q^{93} +(-1.32546 - 1.52967i) q^{94} +(-5.27083 - 3.38736i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-5.80480 + 12.7107i) q^{97} +(1.84522 + 12.8338i) q^{98} +(0.0506233 + 0.0148644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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