LMFDB - Embedded newform 525.2.bm.a.131.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.17
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.352641 + 1.65904i) q^{2} +(-1.23560 + 1.21379i) q^{3} +(-0.800979 - 0.356619i) q^{4} +(-2.12372 - 0.699871i) q^{5} +(-1.57801 - 2.47795i) q^{6} +(-1.86600 + 1.87565i) q^{7} +(-1.11979 + 1.54126i) q^{8} +(0.0534131 - 2.99952i) q^{9} +O(q^{10})$	\(q+(-0.352641 + 1.65904i) q^{2} +(-1.23560 + 1.21379i) q^{3} +(-0.800979 - 0.356619i) q^{4} +(-2.12372 - 0.699871i) q^{5} +(-1.57801 - 2.47795i) q^{6} +(-1.86600 + 1.87565i) q^{7} +(-1.11979 + 1.54126i) q^{8} +(0.0534131 - 2.99952i) q^{9} +(1.91003 - 3.27654i) q^{10} +(-1.63151 - 1.46902i) q^{11} +(1.42255 - 0.531584i) q^{12} +(2.63489 + 0.856127i) q^{13} +(-2.45375 - 3.75720i) q^{14} +(3.47356 - 1.71299i) q^{15} +(-3.33549 - 3.70444i) q^{16} +(-0.120494 + 1.14642i) q^{17} +(4.95751 + 1.14637i) q^{18} +(0.582481 + 1.30827i) q^{19} +(1.45147 + 1.31794i) q^{20} +(0.0289797 - 4.58248i) q^{21} +(3.01251 - 2.18871i) q^{22} +(1.32216 - 6.22025i) q^{23} +(-0.487157 - 3.26357i) q^{24} +(4.02036 + 2.97266i) q^{25} +(-2.34952 + 4.06949i) q^{26} +(3.57480 + 3.77104i) q^{27} +(2.16352 - 0.836903i) q^{28} +(-5.01558 - 6.90335i) q^{29} +(1.61701 + 6.36687i) q^{30} +(4.17491 + 0.438801i) q^{31} +(4.02233 - 2.32229i) q^{32} +(3.79898 - 0.165197i) q^{33} +(-1.85947 - 0.604179i) q^{34} +(5.27557 - 2.67739i) q^{35} +(-1.11247 + 2.38351i) q^{36} +(-6.12804 - 6.80588i) q^{37} +(-2.37589 + 0.505011i) q^{38} +(-4.29483 + 2.14038i) q^{39} +(3.45680 - 2.48949i) q^{40} +(-2.68196 + 8.25424i) q^{41} +(7.59232 + 1.66405i) q^{42} -4.94699 q^{43} +(0.782926 + 1.75848i) q^{44} +(-2.21272 + 6.33276i) q^{45} +(9.85342 + 4.38703i) q^{46} +(0.392378 + 3.73322i) q^{47} +(8.61776 + 0.528607i) q^{48} +(-0.0361019 - 6.99991i) q^{49} +(-6.34951 + 5.62167i) q^{50} +(-1.24264 - 1.56277i) q^{51} +(-1.80518 - 1.62539i) q^{52} +(0.253006 - 0.568260i) q^{53} +(-7.51695 + 4.60093i) q^{54} +(2.43675 + 4.26163i) q^{55} +(-0.801331 - 4.97632i) q^{56} +(-2.30769 - 0.909491i) q^{57} +(13.2217 - 5.88666i) q^{58} +(-2.03225 + 0.431968i) q^{59} +(-3.39314 + 0.133333i) q^{60} +(0.917392 - 4.31599i) q^{61} +(-2.20023 + 6.77162i) q^{62} +(5.52638 + 5.69729i) q^{63} +(-0.646440 - 1.98954i) q^{64} +(-4.99658 - 3.66226i) q^{65} +(-1.06561 + 6.36093i) q^{66} +(-1.01995 + 9.70418i) q^{67} +(0.505348 - 0.875288i) q^{68} +(5.91644 + 9.29057i) q^{69} +(2.58152 + 9.69655i) q^{70} +(8.03467 + 11.0588i) q^{71} +(4.56323 + 3.44116i) q^{72} +(-8.68851 - 7.82317i) q^{73} +(13.4522 - 7.76665i) q^{74} +(-8.57575 + 1.20687i) q^{75} -1.25562i q^{76} +(5.79976 - 0.318952i) q^{77} +(-2.03645 - 7.88009i) q^{78} +(-1.54978 - 14.7452i) q^{79} +(4.49102 + 10.2016i) q^{80} +(-8.99429 - 0.320428i) q^{81} +(-12.7484 - 7.36028i) q^{82} +(-2.07400 - 1.50685i) q^{83} +(-1.65741 + 3.66014i) q^{84} +(1.05824 - 2.35034i) q^{85} +(1.74451 - 8.20727i) q^{86} +(14.5765 + 2.44190i) q^{87} +(4.09109 - 0.869588i) q^{88} +(-10.5774 - 2.24831i) q^{89} +(-9.72604 - 5.90418i) q^{90} +(-6.52249 + 3.34459i) q^{91} +(-3.27728 + 4.51079i) q^{92} +(-5.69113 + 4.52529i) q^{93} +(-6.33195 - 0.665514i) q^{94} +(-0.321402 - 3.18607i) q^{95} +(-2.15120 + 7.75169i) q^{96} +(-6.22524 - 8.56831i) q^{97} +(11.6259 + 2.40856i) q^{98} +(-4.49351 + 4.81530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.352641	+	1.65904i	−0.249355	+	1.17312i	0.658087	+	0.752942i	$0.271366\pi$
$2$	−0.352641	+	1.65904i	−0.249355	+	1.17312i	−0.907441	+	0.420179i	$0.861967\pi$
$3$	−1.23560	+	1.21379i	−0.713374	+	0.700784i
$3$	−1.23560	+	1.21379i	−0.713374	+	0.700784i
$4$	−0.800979	−	0.356619i	−0.400489	−	0.178309i
$5$	−2.12372	−	0.699871i	−0.949756	−	0.312992i
$5$	−2.12372	−	0.699871i	−0.949756	−	0.312992i
$6$	−1.57801	−	2.47795i	−0.644221	−	1.01162i
$7$	−1.86600	+	1.87565i	−0.705281	+	0.708928i
$7$	−1.86600	+	1.87565i	−0.705281	+	0.708928i
$8$	−1.11979	+	1.54126i	−0.395906	+	0.544917i
$9$	0.0534131	−	2.99952i	0.0178044	−	0.999841i
$10$	1.91003	−	3.27654i	0.604003	−	1.03613i
$11$	−1.63151	−	1.46902i	−0.491919	−	0.442926i	0.385459	−	0.922725i	$-0.374043\pi$
$11$	−1.63151	−	1.46902i	−0.491919	−	0.442926i	−0.877379	+	0.479799i	$0.840710\pi$
$12$	1.42255	−	0.531584i	0.410655	−	0.153455i
$13$	2.63489	+	0.856127i	0.730787	+	0.237447i	0.650694	−	0.759340i	$-0.274478\pi$
$13$	2.63489	+	0.856127i	0.730787	+	0.237447i	0.0800931	+	0.996787i	$0.474478\pi$
$14$	−2.45375	−	3.75720i	−0.655793	−	1.00415i
$15$	3.47356	−	1.71299i	0.896871	−	0.442293i
$16$	−3.33549	−	3.70444i	−0.833873	−	0.926110i
$17$	−0.120494	+	1.14642i	−0.0292240	+	0.278048i	0.970145	+	0.242526i	$0.0779760\pi$
$17$	−0.120494	+	1.14642i	−0.0292240	+	0.278048i	−0.999369	+	0.0355218i	$0.988691\pi$
$18$	4.95751	+	1.14637i	1.16850	+	0.270202i
$19$	0.582481	+	1.30827i	0.133630	+	0.300139i	0.967950	−	0.251142i	$-0.0808061\pi$
$19$	0.582481	+	1.30827i	0.133630	+	0.300139i	−0.834320	+	0.551280i	$0.814139\pi$
$20$	1.45147	+	1.31794i	0.324558	+	0.294700i
$21$	0.0289797	−	4.58248i	0.00632389	−	0.999980i
$22$	3.01251	−	2.18871i	0.642268	−	0.466635i
$23$	1.32216	−	6.22025i	0.275689	−	1.29701i	−0.594421	−	0.804154i	$-0.702619\pi$
$23$	1.32216	−	6.22025i	0.275689	−	1.29701i	0.870110	−	0.492858i	$-0.164048\pi$
$24$	−0.487157	−	3.26357i	−0.0994405	−	0.666174i
$25$	4.02036	+	2.97266i	0.804072	+	0.594532i
$26$	−2.34952	+	4.06949i	−0.460779	+	0.798093i
$27$	3.57480	+	3.77104i	0.687971	+	0.725738i
$28$	2.16352	−	0.836903i	0.408866	−	0.158160i
$29$	−5.01558	−	6.90335i	−0.931369	−	1.28192i	−0.959323	−	0.282311i	$-0.908899\pi$
$29$	−5.01558	−	6.90335i	−0.931369	−	1.28192i	0.0279537	−	0.999609i	$-0.491101\pi$
$30$	1.61701	+	6.36687i	0.295224	+	1.16243i
$31$	4.17491	+	0.438801i	0.749836	+	0.0788109i	0.471734	−	0.881741i	$-0.343628\pi$
$31$	4.17491	+	0.438801i	0.749836	+	0.0788109i	0.278102	+	0.960552i	$0.410295\pi$
$32$	4.02233	−	2.32229i	0.711054	−	0.410527i
$33$	3.79898	−	0.165197i	0.661318	−	0.0287571i
$34$	−1.85947	−	0.604179i	−0.318897	−	0.103616i
$35$	5.27557	−	2.67739i	0.891733	−	0.452561i
$36$	−1.11247	+	2.38351i	−0.185412	+	0.397251i
$37$	−6.12804	−	6.80588i	−1.00744	−	1.11888i	−0.992896	−	0.118985i	$-0.962036\pi$
$37$	−6.12804	−	6.80588i	−1.00744	−	1.11888i	−0.0145471	−	0.999894i	$-0.504631\pi$
$38$	−2.37589	+	0.505011i	−0.385420	+	0.0819236i
$39$	−4.29483	+	2.14038i	−0.687723	+	0.342735i
$40$	3.45680	−	2.48949i	0.546568	−	0.393623i
$41$	−2.68196	+	8.25424i	−0.418853	+	1.28910i	0.489907	+	0.871775i	$0.337031\pi$
$41$	−2.68196	+	8.25424i	−0.418853	+	1.28910i	−0.908759	+	0.417321i	$0.862969\pi$
$42$	7.59232	+	1.66405i	1.17152	+	0.256768i
$43$	−4.94699			−0.754409			−0.377205	−	0.926130i	$-0.623115\pi$
$43$	−4.94699			−0.754409			−0.377205	+	0.926130i	$0.623115\pi$
$44$	0.782926	+	1.75848i	0.118031	+	0.265101i
$45$	−2.21272	+	6.33276i	−0.329852	+	0.944033i
$46$	9.85342	+	4.38703i	1.45281	+	0.646832i
$47$	0.392378	+	3.73322i	0.0572341	+	0.544546i	0.985143	+	0.171738i	$0.0549384\pi$
$47$	0.392378	+	3.73322i	0.0572341	+	0.544546i	−0.927908	+	0.372808i	$0.878395\pi$
$48$	8.61776	+	0.528607i	1.24387	+	0.0762979i
$49$	−0.0361019	−	6.99991i	−0.00515741	−	0.999987i
$50$	−6.34951	+	5.62167i	−0.897957	+	0.795024i
$51$	−1.24264	−	1.56277i	−0.174004	−	0.218832i
$52$	−1.80518	−	1.62539i	−0.250333	−	0.225401i
$53$	0.253006	−	0.568260i	0.0347530	−	0.0780566i	−0.895335	−	0.445394i	$-0.853064\pi$
$53$	0.253006	−	0.568260i	0.0347530	−	0.0780566i	0.930088	+	0.367337i	$0.119730\pi$
$54$	−7.51695	+	4.60093i	−1.02293	+	0.626108i
$55$	2.43675	+	4.26163i	0.328571	+	0.574639i
$56$	−0.801331	−	4.97632i	−0.107082	−	0.664988i
$57$	−2.30769	−	0.909491i	−0.305661	−	0.120465i
$58$	13.2217	−	5.88666i	1.73609	−	0.772956i
$59$	−2.03225	+	0.431968i	−0.264576	+	0.0562374i	−0.338290	−	0.941042i	$-0.609848\pi$
$59$	−2.03225	+	0.431968i	−0.264576	+	0.0562374i	0.0737134	+	0.997279i	$0.476515\pi$
$60$	−3.39314	+	0.133333i	−0.438052	+	0.0172133i
$61$	0.917392	−	4.31599i	0.117460	−	0.552606i	−0.879582	−	0.475747i	$-0.842178\pi$
$61$	0.917392	−	4.31599i	0.117460	−	0.552606i	0.997042	−	0.0768587i	$-0.0244890\pi$
$62$	−2.20023	+	6.77162i	−0.279430	+	0.859996i
$63$	5.52638	+	5.69729i	0.696258	+	0.717791i
$64$	−0.646440	−	1.98954i	−0.0808050	−	0.248692i
$65$	−4.99658	−	3.66226i	−0.619750	−	0.454247i
$66$	−1.06561	+	6.36093i	−0.131167	+	0.782976i
$67$	−1.01995	+	9.70418i	−0.124607	+	1.18555i	0.736251	+	0.676709i	$0.236594\pi$
$67$	−1.01995	+	9.70418i	−0.124607	+	1.18555i	−0.860858	+	0.508846i	$0.830072\pi$
$68$	0.505348	−	0.875288i	0.0612824	−	0.106144i
$69$	5.91644	+	9.29057i	0.712256	+	1.11845i
$70$	2.58152	+	9.69655i	0.308551	+	1.15896i
$71$	8.03467	+	11.0588i	0.953539	+	1.31243i	0.949937	+	0.312441i	$0.101147\pi$
$71$	8.03467	+	11.0588i	0.953539	+	1.31243i	0.00360210	+	0.999994i	$0.498853\pi$
$72$	4.56323	+	3.44116i	0.537782	+	0.405545i
$73$	−8.68851	−	7.82317i	−1.01691	−	0.915633i	−0.0204608	−	0.999791i	$-0.506513\pi$
$73$	−8.68851	−	7.82317i	−1.01691	−	0.915633i	−0.996452	+	0.0841579i	$0.973180\pi$
$74$	13.4522	−	7.76665i	1.56379	−	0.902855i
$75$	−8.57575	+	1.20687i	−0.990242	+	0.139357i
$76$		−	1.25562i		−	0.144030i
$77$	5.79976	−	0.318952i	0.660944	−	0.0363479i
$78$	−2.03645	−	7.88009i	−0.230583	−	0.892245i
$79$	−1.54978	−	14.7452i	−0.174364	−	1.65896i	−0.635848	−	0.771814i	$-0.719350\pi$
$79$	−1.54978	−	14.7452i	−0.174364	−	1.65896i	0.461484	−	0.887148i	$-0.347317\pi$
$80$	4.49102	+	10.2016i	0.502111	+	1.14057i
$81$	−8.99429	−	0.320428i	−0.999366	−	0.0356031i
$82$	−12.7484	−	7.36028i	−1.40782	−	0.812807i
$83$	−2.07400	−	1.50685i	−0.227651	−	0.165398i	0.468113	−	0.883669i	$-0.344934\pi$
$83$	−2.07400	−	1.50685i	−0.227651	−	0.165398i	−0.695764	+	0.718271i	$0.744934\pi$
$84$	−1.65741	+	3.66014i	−0.180838	+	0.399354i
$85$	1.05824	−	2.35034i	0.114782	−	0.254931i
$86$	1.74451	−	8.20727i	0.188115	−	0.885013i
$87$	14.5765	+	2.44190i	1.56276	+	0.261800i
$88$	4.09109	−	0.869588i	0.436112	−	0.0926984i
$89$	−10.5774	−	2.24831i	−1.12121	−	0.238320i	−0.390227	−	0.920719i	$-0.627603\pi$
$89$	−10.5774	−	2.24831i	−1.12121	−	0.238320i	−0.730980	+	0.682399i	$0.760937\pi$
$90$	−9.72604	−	5.90418i	−1.02521	−	0.622355i
$91$	−6.52249	+	3.34459i	−0.683743	+	0.350608i
$92$	−3.27728	+	4.51079i	−0.341680	+	0.470282i
$93$	−5.69113	+	4.52529i	−0.590143	+	0.469251i
$94$	−6.33195	−	0.665514i	−0.653090	−	0.0686426i
$95$	−0.321402	−	3.18607i	−0.0329752	−	0.326884i
$96$	−2.15120	+	7.75169i	−0.219556	+	0.791154i
$97$	−6.22524	−	8.56831i	−0.632078	−	0.869980i	0.366084	−	0.930582i	$-0.380698\pi$
$97$	−6.22524	−	8.56831i	−0.632078	−	0.869980i	−0.998162	+	0.0606015i	$0.980698\pi$
$98$	11.6259	+	2.40856i	1.17439	+	0.243301i
$99$	−4.49351	+	4.81530i	−0.451614	+	0.483955i
$100$	−2.16012	−	3.81477i	−0.216012	−	0.381477i
$101$	−2.87011	−	4.97117i	−0.285586	−	0.494650i	0.687165	−	0.726502i	$-0.258855\pi$
$101$	−2.87011	−	4.97117i	−0.285586	−	0.494650i	−0.972751	+	0.231851i	$0.925522\pi$
$102$	3.03091	−	1.51049i	0.300105	−	0.149561i
$103$	−18.5079	+	1.94526i	−1.82364	+	0.191672i	−0.953552	−	0.301227i	$-0.902604\pi$
$103$	−18.5079	+	1.94526i	−1.82364	+	0.191672i	−0.870086	+	0.492899i	$0.835937\pi$
$104$	−4.27004	+	3.10236i	−0.418712	+	0.304212i
$105$	−3.26869	+	9.71162i	−0.318992	+	0.947757i
$106$	0.853548	+	0.620139i	0.0829040	+	0.0602333i
$107$	−11.2732	−	6.50858i	−1.08982	−	0.629208i	−0.156291	−	0.987711i	$-0.549954\pi$
$107$	−11.2732	−	6.50858i	−1.08982	−	0.629208i	−0.933528	+	0.358503i	$0.883287\pi$
$108$	−1.51852	−	4.29537i	−0.146119	−	0.413322i
$109$	−10.6648	+	2.26687i	−1.02150	+	0.217126i	−0.688067	−	0.725647i	$-0.741540\pi$
$109$	−10.6648	+	2.26687i	−1.02150	+	0.217126i	−0.333433	+	0.942774i	$0.608207\pi$
$110$	−7.92953	+	2.53984i	−0.756051	+	0.242165i
$111$	15.8327	+	0.971168i	1.50278	+	0.0921792i
$112$	13.1722	+	0.656272i	1.24466	+	0.0620119i
$113$	1.59470	+	0.518149i	0.150017	+	0.0487434i	0.383063	−	0.923722i	$-0.374869\pi$
$113$	1.59470	+	0.518149i	0.150017	+	0.0487434i	−0.233046	+	0.972466i	$0.574869\pi$
$114$	2.32267	−	3.50783i	0.217538	−	0.328538i
$115$	−7.16126	+	12.2847i	−0.667791	+	1.14556i
$116$	1.55551	+	7.31808i	0.144425	+	0.679467i
$117$	2.70871	−	7.85769i	0.250421	−	0.726443i
$118$		−	3.52392i		−	0.324403i
$119$	−1.92544	−	2.36522i	−0.176505	−	0.216820i
$120$	−1.24950	+	7.27186i	−0.114063	+	0.663827i
$121$	−0.646001	−	6.14629i	−0.0587274	−	0.558754i
$122$	6.83691	+	3.04399i	0.618985	+	0.275590i
$123$	−6.70510	−	13.4543i	−0.604579	−	1.21313i
$124$	−3.18753	−	1.84032i	−0.286249	−	0.165266i
$125$	−6.45763	−	9.12683i	−0.577588	−	0.816328i
$126$	−11.4009	+	7.15941i	−1.01567	+	0.637811i
$127$	5.04533	+	15.5279i	0.447701	+	1.37788i	0.879495	+	0.475909i	$0.157881\pi$
$127$	5.04533	+	15.5279i	0.447701	+	1.37788i	−0.431794	+	0.901972i	$0.642119\pi$
$128$	12.7670	−	1.34186i	1.12845	−	0.118605i
$129$	6.11250	−	6.00462i	0.538176	−	0.528678i
$130$	7.83784	−	6.99809i	0.687424	−	0.613773i
$131$	−2.02909	+	0.903409i	−0.177282	+	0.0789312i	−0.493459	−	0.869769i	$-0.664268\pi$
$131$	−2.02909	+	0.903409i	−0.177282	+	0.0789312i	0.316176	+	0.948700i	$0.397601\pi$
$132$	−3.10182	−	1.22247i	−0.269978	−	0.106402i
$133$	−3.54077	−	1.34871i	−0.307023	−	0.116948i
$134$	−15.7400	−	5.11423i	−1.35973	−	0.441802i
$135$	−4.95263	−	10.5105i	−0.426255	−	0.904603i
$136$	−1.63200	−	1.46946i	−0.139943	−	0.126005i
$137$	1.36986	+	6.44469i	0.117035	+	0.550607i	0.997123	+	0.0757967i	$0.0241500\pi$
$137$	1.36986	+	6.44469i	0.117035	+	0.550607i	−0.880088	+	0.474810i	$0.842517\pi$
$138$	−17.4998	+	6.53941i	−1.48968	+	0.556671i
$139$	11.4009	−	3.70438i	0.967012	−	0.314201i	0.217403	−	0.976082i	$-0.430241\pi$
$139$	11.4009	−	3.70438i	0.967012	−	0.314201i	0.749609	+	0.661881i	$0.230241\pi$
$140$	−5.18042	+	0.263164i	−0.437826	+	0.0222415i
$141$	−5.01618	−	4.13650i	−0.422439	−	0.348356i
$142$	−21.1803	+	9.43009i	−1.77741	+	0.791355i
$143$	−3.04119	−	5.26749i	−0.254317	−	0.440489i
$144$	−11.2897	+	9.80703i	−0.940810	+	0.817252i
$145$	5.82022	+	18.1710i	0.483343	+	1.50902i
$146$	16.0429	−	11.6558i	1.32772	−	0.964645i
$147$	8.54105	+	8.60526i	0.704454	+	0.709750i
$148$	2.48133	+	7.63673i	0.203964	+	0.627736i
$149$	2.27491	+	1.31342i	0.186368	+	0.107600i	0.590281	−	0.807198i	$-0.299017\pi$
$149$	2.27491	+	1.31342i	0.186368	+	0.107600i	−0.403913	+	0.914797i	$0.632350\pi$
$150$	1.02191	−	14.6531i	0.0834387	−	1.19642i
$151$	5.24888	+	9.09133i	0.427148	+	0.739842i	0.996618	−	0.0821702i	$-0.0261851\pi$
$151$	5.24888	+	9.09133i	0.427148	+	0.739842i	−0.569471	+	0.822012i	$0.692852\pi$
$152$	−2.66865	−	0.567238i	−0.216456	−	0.0460091i
$153$	3.43228	+	0.422658i	0.277483	+	0.0341698i
$154$	−1.51608	+	9.73453i	−0.122169	+	0.784431i
$155$	−8.55923	−	3.85379i	−0.687494	−	0.309544i
$156$	4.20337	−	0.182782i	0.336539	−	0.0146343i
$157$	9.26216	−	5.34751i	0.739201	−	0.426778i	−0.0825777	−	0.996585i	$-0.526315\pi$
$157$	9.26216	−	5.34751i	0.739201	−	0.426778i	0.821779	+	0.569807i	$0.192982\pi$
$158$	25.0094	+	2.62860i	1.98964	+	0.209120i
$159$	0.377137	+	1.00924i	0.0299089	+	0.0800379i
$160$	−10.1676	+	2.11678i	−0.803819	+	0.167346i
$161$	9.19986	+	14.0869i	0.725050	+	1.11020i
$162$	3.70336	−	14.8089i	0.290963	−	1.16350i
$163$	0.594098	+	0.659813i	0.0465334	+	0.0516806i	0.765962	−	0.642886i	$-0.222263\pi$
$163$	0.594098	+	0.659813i	0.0465334	+	0.0516806i	−0.719429	+	0.694566i	$0.755596\pi$
$164$	5.09181	−	5.65503i	0.397604	−	0.441584i
$165$	−8.18358	−	2.30797i	−0.637091	−	0.179675i
$166$	3.23130	−	2.90947i	0.250797	−	0.225819i
$167$	6.59219	+	4.78950i	0.510119	+	0.370623i	0.812869	−	0.582447i	$-0.197905\pi$
$167$	6.59219	+	4.78950i	0.510119	+	0.370623i	−0.302750	+	0.953070i	$0.597905\pi$
$168$	7.03034	+	5.17609i	0.542403	+	0.399344i
$169$	−4.30753	−	3.12961i	−0.331349	−	0.240739i
$170$	3.52614	+	2.58450i	0.270443	+	0.198222i
$171$	3.95531	−	1.67729i	0.302470	−	0.128265i
$172$	3.96243	+	1.76419i	0.302133	+	0.134518i
$173$	7.46343	+	1.58640i	0.567434	+	0.120612i	0.482690	−	0.875791i	$-0.339660\pi$
$173$	7.46343	+	1.58640i	0.567434	+	0.120612i	0.0847434	+	0.996403i	$0.472993\pi$
$174$	−9.19148	+	23.3219i	−0.696805	+	1.76803i
$175$	−13.0776	+	1.99380i	−0.988577	+	0.150717i
$176$			10.9437i			0.824916i
$177$	1.98673	−	3.00047i	0.149331	−	0.225529i
$178$	7.46007	−	16.7556i	0.559156	−	1.25589i
$179$	1.74343	−	3.91581i	0.130310	−	0.292681i	−0.836593	−	0.547825i	$-0.815456\pi$
$179$	1.74343	−	3.91581i	0.130310	−	0.292681i	0.966903	+	0.255143i	$0.0821227\pi$
$180$	4.03072	−	4.28331i	0.300432	−	0.319259i
$181$	−8.45024	+	11.6308i	−0.628101	+	0.864507i	−0.997911	−	0.0646001i	$-0.979423\pi$
$181$	−8.45024	+	11.6308i	−0.628101	+	0.864507i	0.369810	+	0.929107i	$0.379423\pi$
$182$	−3.24872	−	12.0005i	−0.240811	−	0.889539i
$183$	4.10519	+	6.44636i	0.303464	+	0.476529i
$184$	8.10649	+	9.00316i	0.597618	+	0.663722i
$185$	8.25099	+	18.7426i	0.606625	+	1.37798i
$186$	−5.50074	−	11.0376i	−0.403334	−	0.809319i
$187$	1.88070	−	1.69339i	0.137531	−	0.123833i
$188$	1.01705	−	3.13016i	0.0741761	−	0.228290i
$189$	−13.7437	−	0.331690i	−0.999709	−	0.0241269i
$190$	5.39916	+	0.590316i	0.391696	+	0.0428260i
$191$	−18.4695	+	16.6300i	−1.33641	+	1.20331i	−0.375374	+	0.926873i	$0.622486\pi$
$191$	−18.4695	+	16.6300i	−1.33641	+	1.20331i	−0.961033	+	0.276433i	$0.910848\pi$
$192$	3.21363	+	1.67363i	0.231924	+	0.120784i
$193$	−5.50456	−	9.53418i	−0.396227	−	0.686285i	0.597030	−	0.802219i	$-0.296347\pi$
$193$	−5.50456	−	9.53418i	−0.396227	−	0.686285i	−0.993257	+	0.115934i	$0.963014\pi$
$194$	16.4105	−	7.30641i	1.17820	−	0.524570i
$195$	10.6190	−	1.53973i	0.760442	−	0.110263i
$196$	−2.46738	+	5.61965i	−0.176241	+	0.401404i
$197$	−5.62015	−	7.73547i	−0.400419	−	0.551130i	0.560430	−	0.828202i	$-0.310636\pi$
$197$	−5.62015	−	7.73547i	−0.400419	−	0.551130i	−0.960849	+	0.277072i	$0.910636\pi$
$198$	−6.40419	−	9.15299i	−0.455126	−	0.650475i
$199$	1.67222	−	0.965456i	0.118540	−	0.0684393i	−0.439557	−	0.898214i	$-0.644865\pi$
$199$	1.67222	−	0.965456i	0.118540	−	0.0684393i	0.558098	+	0.829775i	$0.311531\pi$
$200$	−9.08360	+	2.86766i	−0.642307	+	0.202774i
$201$	−10.5186	−	13.2285i	−0.741926	−	0.933066i
$202$	9.25951	−	3.00860i	0.651497	−	0.211684i
$203$	22.3073	+	3.47419i	1.56567	+	0.243840i
$204$	0.438011	+	1.69489i	0.0306669	+	0.118666i
$205$	11.4726	−	15.6527i	0.801284	−	1.09323i
$206$	3.29937	−	31.3914i	0.229878	−	2.18714i
$207$	−18.5872	−	4.29808i	−1.29190	−	0.298737i
$208$	−5.61718	−	12.6164i	−0.389482	−	0.874790i
$209$	0.971555	−	2.99014i	0.0672039	−	0.206832i
$210$	−14.9593	−	8.84762i	−1.03229	−	0.610544i
$211$	0.0475288	+	0.146279i	0.00327202	+	0.0100702i	0.952679	−	0.303978i	$-0.0983148\pi$
$211$	0.0475288	+	0.146279i	0.00327202	+	0.0100702i	−0.949407	+	0.314048i	$0.898315\pi$
$212$	−0.405305	+	0.364938i	−0.0278364	+	0.0250640i
$213$	−23.3507	−	3.91179i	−1.59996	−	0.268031i
$214$	14.7734	−	16.4075i	1.00989	−	1.12159i
$215$	10.5060	+	3.46226i	0.716504	+	0.236124i
$216$	−9.81519	+	1.28692i	−0.667839	+	0.0875640i
$217$	−8.61341	+	7.01186i	−0.584716	+	0.475996i
$218$		−	18.4927i		−	1.25248i
$219$	20.2312	−	0.879747i	1.36710	−	0.0594478i
$220$	−0.432004	−	4.28247i	−0.0291257	−	0.288724i
$221$	−1.29897	+	2.91753i	−0.0873782	+	0.196255i
$222$	−7.19447	+	25.9247i	−0.482861	+	1.73995i
$223$	−18.7463	+	6.09103i	−1.25534	+	0.407885i	−0.859832	−	0.510576i	$-0.829432\pi$
$223$	−18.7463	+	6.09103i	−1.25534	+	0.407885i	−0.395510	+	0.918462i	$0.629432\pi$
$224$	−3.14986	+	11.8779i	−0.210459	+	0.793623i
$225$	9.13131	−	11.9004i	0.608754	−	0.793359i
$226$	−1.42199	+	2.46295i	−0.0945892	+	0.163833i
$227$	−1.47171	+	1.63450i	−0.0976809	+	0.108486i	−0.790003	−	0.613103i	$-0.789921\pi$
$227$	−1.47171	+	1.63450i	−0.0976809	+	0.108486i	0.692322	+	0.721589i	$0.256588\pi$
$228$	1.52407	+	1.55145i	0.100934	+	0.102747i
$229$	14.9393	−	1.57018i	0.987216	−	0.103761i	0.402863	−	0.915260i	$-0.368015\pi$
$229$	14.9393	−	1.57018i	0.987216	−	0.103761i	0.584353	+	0.811500i	$0.301348\pi$
$230$	−17.8555	−	16.2129i	−1.17736	−	1.06905i
$231$	−6.77904	+	7.43381i	−0.446028	+	0.489109i
$232$	16.2562			1.06727
$233$	6.71541	+	15.0831i	0.439941	+	0.988124i	0.988390	+	0.151940i	$0.0485520\pi$
$233$	6.71541	+	15.0831i	0.439941	+	0.988124i	−0.548449	+	0.836184i	$0.684781\pi$
$234$	12.0810	+	7.26481i	0.789762	+	0.474916i
$235$	1.77948	−	8.20293i	0.116080	−	0.535100i
$236$	1.78184	+	0.378741i	0.115988	+	0.0246539i
$237$	19.8125	+	16.3380i	1.28696	+	1.06127i
$238$	4.60299	−	2.36031i	0.298368	−	0.152996i
$239$	19.3843	−	6.29834i	1.25387	−	0.407406i	0.394562	−	0.918870i	$-0.370896\pi$
$239$	19.3843	−	6.29834i	1.25387	−	0.407406i	0.859305	+	0.511464i	$0.170896\pi$
$240$	−17.9317	−	7.15394i	−1.15749	−	0.461785i
$241$	2.87441	+	13.5230i	0.185157	+	0.871096i	0.968404	+	0.249385i	$0.0802286\pi$
$241$	2.87441	+	13.5230i	0.185157	+	0.871096i	−0.783247	+	0.621710i	$0.786438\pi$
$242$	10.4248	+	1.09569i	0.670130	+	0.0704335i
$243$	11.5023	−	10.5213i	0.737872	−	0.674941i
$244$	−2.27397	+	3.12986i	−0.145576	+	0.200369i
$245$	−4.82236	+	14.8911i	−0.308090	+	0.951357i
$246$	24.6857	−	6.37953i	1.57391	−	0.406744i
$247$	0.414724	+	3.94583i	0.0263882	+	0.251067i
$248$	−5.35133	+	5.94325i	−0.339810	+	0.377397i
$249$	4.39163	−	0.655543i	0.278308	−	0.0415434i
$250$	17.4190	−	7.49500i	1.10168	−	0.474026i
$251$	5.06529			0.319718			0.159859	−	0.987140i	$-0.448896\pi$
$251$	5.06529			0.319718			0.159859	+	0.987140i	$0.448896\pi$
$252$	−2.39475	−	6.53422i	−0.150855	−	0.411617i
$253$	−11.2948	+	8.20614i	−0.710097	+	0.515916i
$254$	−27.5407	+	2.89464i	−1.72806	+	0.181626i
$255$	1.54527	+	4.18857i	0.0967685	+	0.262299i
$256$	−1.83861	+	17.4932i	−0.114913	+	1.09333i
$257$	−12.2397	+	21.1998i	−0.763493	+	1.32241i	0.177547	+	0.984112i	$0.443184\pi$
$257$	−12.2397	+	21.1998i	−0.763493	+	1.32241i	−0.941040	+	0.338296i	$0.890149\pi$
$258$	7.80641	+	12.2584i	0.486006	+	0.763173i
$259$	24.2003	+	1.20572i	1.50374	+	0.0749196i
$260$	2.69613	+	4.71527i	0.167207	+	0.292428i
$261$	−20.9747	+	14.6756i	−1.29830	+	0.908398i
$262$	−0.783255	−	3.68493i	−0.0483897	−	0.227656i
$263$	1.98895	+	9.35729i	0.122644	+	0.576995i	0.995957	+	0.0898349i	$0.0286339\pi$
$263$	1.98895	+	9.35729i	0.122644	+	0.576995i	−0.873313	+	0.487160i	$0.838033\pi$
$264$	−3.99945	+	6.04020i	−0.246149	+	0.371749i
$265$	−0.935022	+	1.02975i	−0.0574380	+	0.0632573i
$266$	3.48618	−	5.39868i	0.213752	−	0.331014i
$267$	15.7985	−	10.0608i	0.966850	−	0.615712i
$268$	4.27765	−	7.40911i	0.261299	−	0.452583i
$269$	−0.861707	+	8.19859i	−0.0525392	+	0.499877i	0.936333	+	0.351112i	$0.114196\pi$
$269$	−0.861707	+	8.19859i	−0.0525392	+	0.499877i	−0.988873	+	0.148765i	$0.952470\pi$
$270$	19.1839	−	4.51019i	1.16750	−	0.274481i
$271$	22.2176	−	2.33517i	1.34963	−	0.141851i	0.598029	−	0.801474i	$-0.295951\pi$
$271$	22.2176	−	2.33517i	1.34963	−	0.141851i	0.751597	+	0.659623i	$0.229284\pi$
$272$	4.64875	−	3.37752i	0.281872	−	0.204792i
$273$	3.99955	−	12.0495i	0.242064	−	0.729271i
$274$	−11.1751			−0.675112
$275$	−2.19237	−	10.7559i	−0.132205	−	0.648606i
$276$	−1.42576	−	9.55146i	−0.0858205	−	0.574930i
$277$	−0.00693943	+	0.00770702i	−0.000416950	+	0.000463070i	−0.743353	−	0.668899i	$-0.766766\pi$
$277$	−0.00693943	+	0.00770702i	−0.000416950	+	0.000463070i	0.742936	+	0.669362i	$0.233433\pi$
$278$	2.12530	+	20.2209i	0.127467	+	1.21277i
$279$	1.53919	−	12.4993i	0.0921488	−	0.748314i
$280$	−1.78098	+	11.1291i	−0.106434	+	0.665093i
$281$	11.7300	−	16.1450i	0.699756	−	0.963132i	−0.300201	−	0.953876i	$-0.597054\pi$
$281$	11.7300	−	16.1450i	0.699756	−	0.963132i	0.999957	−	0.00925569i	$-0.00294622\pi$
$282$	8.63155	−	6.86336i	0.514001	−	0.408707i
$283$	−2.53931	−	0.266892i	−0.150946	−	0.0158651i	0.0287539	−	0.999587i	$-0.490846\pi$
$283$	−2.53931	−	0.266892i	−0.150946	−	0.0158651i	−0.179700	+	0.983721i	$0.557513\pi$
$284$	−2.49183	−	11.7231i	−0.147863	−	0.695641i
$285$	4.26435	+	3.54659i	0.252598	+	0.210082i
$286$	9.81143	−	3.18793i	0.580162	−	0.188506i
$287$	−10.4775	−	20.4328i	−0.618467	−	1.20611i
$288$	−6.75092	−	12.1891i	−0.397802	−	0.718250i
$289$	15.3287	+	3.25823i	0.901691	+	0.191660i
$290$	−32.1990	+	3.24815i	−1.89079	+	0.190738i
$291$	18.0921	+	3.03085i	1.06058	+	0.177671i
$292$	4.16942	+	9.36468i	0.243997	+	0.548026i
$293$	−21.9055			−1.27973			−0.639867	−	0.768486i	$-0.721011\pi$
$293$	−21.9055			−1.27973			−0.639867	+	0.768486i	$0.721011\pi$
$294$	−17.2884	+	11.1354i	−1.00828	+	0.649430i
$295$	4.61824	+	0.504935i	0.268885	+	0.0293984i
$296$	17.3517	−	1.82374i	1.00855	−	0.106003i
$297$	−0.292598	−	11.4040i	−0.0169782	−	0.661725i
$298$	−2.98125	+	3.31101i	−0.172699	+	0.191802i
$299$	8.80906	−	15.2577i	0.509441	−	0.882378i
$300$	7.29938	+	2.09160i	0.421430	+	0.120758i
$301$	9.23108	−	9.27881i	0.532070	−	0.534822i
$302$	−16.9339	+	5.50215i	−0.974435	+	0.316613i
$303$	9.58028	+	2.65866i	0.550373	+	0.152736i
$304$	2.90356	−	6.52150i	0.166531	−	0.374034i
$305$	−4.96892	+	8.52389i	−0.284520	+	0.488077i
$306$	−1.91157	+	5.54526i	−0.109277	+	0.317001i
$307$		−	16.3011i		−	0.930351i	−0.885219	−	0.465175i	$-0.845991\pi$
$307$		−	16.3011i		−	0.930351i	0.885219	−	0.465175i	$-0.154009\pi$
$308$	−4.75923	−	1.81283i	−0.271182	−	0.103296i
$309$	20.5072	−	24.8683i	1.16662	−	1.41471i
$310$	9.41194	−	12.8411i	0.534562	−	0.729327i
$311$	−10.8199	+	12.0167i	−0.613540	+	0.681405i	−0.967214	−	0.253964i	$-0.918266\pi$
$311$	−10.8199	+	12.0167i	−0.613540	+	0.681405i	0.353674	+	0.935369i	$0.384932\pi$
$312$	1.51043	−	9.01622i	0.0855112	−	0.510443i
$313$	−10.2862	+	9.26177i	−0.581413	+	0.523506i	−0.906516	−	0.422172i	$-0.861268\pi$
$313$	−10.2862	+	9.26177i	−0.581413	+	0.523506i	0.325103	+	0.945679i	$0.394601\pi$
$314$	5.60554	+	17.2521i	0.316339	+	0.973591i
$315$	−7.74910	−	15.9672i	−0.436613	−	0.899650i
$316$	−4.01707	+	12.3633i	−0.225978	+	0.695488i
$317$	−2.31766	−	5.20555i	−0.130173	−	0.292373i	0.836687	−	0.547682i	$-0.184490\pi$
$317$	−2.31766	−	5.20555i	−0.130173	−	0.292373i	−0.966860	+	0.255309i	$0.917823\pi$
$318$	−1.80736	+	0.269787i	−0.101352	+	0.0151289i
$319$	−1.95818	+	18.6309i	−0.109637	+	1.04313i
$320$	−0.0195640	+	4.67764i	−0.00109366	+	0.261488i
$321$	21.8292	−	5.64132i	1.21839	−	0.314868i
$322$	−26.6150	+	10.2954i	−1.48320	+	0.573738i
$323$	−1.57002	+	0.510130i	−0.0873581	+	0.0283844i
$324$	7.08997	+	3.46419i	0.393887	+	0.192455i
$325$	8.04823	+	11.2746i	0.446435	+	0.625401i
$326$	−1.30416	+	0.752958i	−0.0722308	+	0.0417025i
$327$	10.4259	−	15.7458i	0.576552	−	0.870743i
$328$	−9.71868	−	13.3766i	−0.536625	−	0.738600i
$329$	−7.73438	−	6.23022i	−0.426410	−	0.343483i
$330$	6.71488	−	12.7630i	0.369642	−	0.702582i
$331$	−27.0994	+	12.0654i	−1.48952	+	0.663176i	−0.980309	−	0.197467i	$-0.936728\pi$
$331$	−27.0994	+	12.0654i	−1.48952	+	0.663176i	−0.509208	+	0.860643i	$0.670062\pi$
$332$	1.12386	+	1.94658i	0.0616797	+	0.106832i
$333$	−20.7417	+	18.0177i	−1.13664	+	0.987363i
$334$	−10.2707	+	9.24775i	−0.561986	+	0.506014i
$335$	8.95776	−	19.8951i	0.489415	−	1.08699i
$336$	−17.0722	+	15.1775i	−0.931365	+	0.828000i
$337$	−2.13539	+	6.57206i	−0.116322	+	0.358003i	−0.992220	−	0.124493i	$-0.960270\pi$
$337$	−2.13539	+	6.57206i	−0.116322	+	0.358003i	0.875898	+	0.482496i	$0.160270\pi$
$338$	6.71116	−	6.04276i	0.365039	−	0.328683i
$339$	−2.59934	+	1.29541i	−0.141177	+	0.0703570i
$340$	−1.68581	+	1.50519i	−0.0914257	+	0.0816302i
$341$	−6.16681	−	6.84894i	−0.333951	−	0.370891i
$342$	1.38789	+	7.15351i	0.0750484	+	0.386818i
$343$	13.1967	+	12.9941i	0.712556	+	0.701615i
$344$	5.53959	−	7.62460i	0.298675	−	0.411091i
$345$	−6.06266	−	23.8713i	−0.326403	−	1.28519i
$346$	−5.26381	+	11.8227i	−0.282984	+	0.635593i
$347$	10.4804	−	23.5393i	0.562615	−	1.26365i	−0.378511	−	0.925597i	$-0.623564\pi$
$347$	10.4804	−	23.5393i	0.562615	−	1.26365i	0.941126	−	0.338057i	$-0.109770\pi$
$348$	−10.8046	−	7.15416i	−0.579189	−	0.383503i
$349$			18.3171i			0.980492i	0.871584	+	0.490246i	$0.163093\pi$
$349$			18.3171i			0.980492i	−0.871584	+	0.490246i	$0.836907\pi$
$350$	1.30391	−	22.3995i	0.0696969	−	1.19730i
$351$	6.19072	+	12.9968i	0.330436	+	0.693716i
$352$	−9.97397	−	2.12003i	−0.531614	−	0.112998i
$353$	−17.4742	−	7.78001i	−0.930058	−	0.414088i	−0.114933	−	0.993373i	$-0.536665\pi$
$353$	−17.4742	−	7.78001i	−0.930058	−	0.414088i	−0.815125	+	0.579285i	$0.803332\pi$
$354$	4.27731	+	4.35415i	0.227336	+	0.231420i
$355$	−9.32365	−	29.1089i	−0.494848	−	1.54494i
$356$	7.67052	+	5.57296i	0.406537	+	0.295366i
$357$	5.24996	+	0.585383i	0.277857	+	0.0309818i
$358$	5.88170	+	4.27330i	0.310857	+	0.225851i
$359$	19.4648	−	17.5262i	1.02731	−	0.924996i	0.0300947	−	0.999547i	$-0.490419\pi$
$359$	19.4648	−	17.5262i	1.02731	−	0.924996i	0.997217	+	0.0745512i	$0.0237524\pi$
$360$	−7.28265	−	10.5017i	−0.383829	−	0.553490i
$361$	11.3412	−	12.5957i	0.596905	−	0.662930i
$362$	−16.3160	−	18.1208i	−0.857552	−	0.952408i
$363$	8.25853	+	6.81025i	0.433460	+	0.357445i
$364$	6.41712	−	0.352903i	0.336348	−	0.0184971i
$365$	12.9767	+	22.6951i	0.679233	+	1.18791i
$366$	−12.1425	+	4.53744i	−0.634696	+	0.237176i
$367$	28.8102	+	3.02808i	1.50388	+	0.158064i	0.820353	−	0.571858i	$-0.193777\pi$
$367$	28.8102	+	3.02808i	1.50388	+	0.158064i	0.683530	+	0.729923i	$0.260444\pi$
$368$	−27.4526	+	15.8498i	−1.43107	+	0.826226i
$369$	24.6155	+	8.48550i	1.28143	+	0.441738i
$370$	−34.0044	+	7.07935i	−1.76781	+	0.368038i
$371$	0.593747	+	1.53492i	0.0308258	+	0.0796892i
$372$	6.17228	−	1.59510i	0.320018	−	0.0827021i
$373$	−8.14114	−	1.73045i	−0.421532	−	0.0895994i	−0.00773831	−	0.999970i	$-0.502463\pi$
$373$	−8.14114	−	1.73045i	−0.421532	−	0.0895994i	−0.413794	+	0.910371i	$0.635797\pi$
$374$	2.14620	+	3.71732i	0.110977	+	0.192218i
$375$	19.0571	+	3.43887i	0.984106	+	0.177583i
$376$	−6.19324	−	3.57567i	−0.319392	−	0.184401i
$377$	−7.30534	−	22.4835i	−0.376244	−	1.15796i
$378$	5.39688	−	22.6845i	0.277586	−	1.16676i
$379$	−21.1439	+	15.3619i	−1.08609	+	0.789089i	−0.978734	−	0.205132i	$-0.934238\pi$
$379$	−21.1439	+	15.3619i	−1.08609	+	0.789089i	−0.107353	+	0.994221i	$0.534238\pi$
$380$	−0.878775	+	2.66659i	−0.0450802	+	0.136793i
$381$	−25.0817	−	13.0623i	−1.28497	−	0.669203i
$382$	−21.0768	−	36.5061i	−1.07838	−	1.86782i
$383$	−7.82988	+	3.48609i	−0.400088	+	0.178131i	−0.596909	−	0.802309i	$-0.703605\pi$
$383$	−7.82988	+	3.48609i	−0.400088	+	0.178131i	0.196821	+	0.980439i	$0.436938\pi$
$384$	−14.1461	+	17.1545i	−0.721891	+	0.875410i
$385$	−12.5403	−	3.38172i	−0.639112	−	0.172349i
$386$	17.7587	−	5.77017i	0.903896	−	0.293694i
$387$	−0.264234	+	14.8386i	−0.0134318	+	0.754289i
$388$	1.93067	+	9.08307i	0.0980148	+	0.461123i
$389$	−18.2141	−	16.4001i	−0.923492	−	0.831516i	0.0625452	−	0.998042i	$-0.480078\pi$
$389$	−18.2141	−	16.4001i	−0.923492	−	0.831516i	−0.986037	+	0.166526i	$0.946745\pi$
$390$	−1.19020	+	18.1604i	−0.0602683	+	0.919585i
$391$	6.97172	+	2.26525i	0.352575	+	0.114559i
$392$	10.8291	+	7.78279i	0.546952	+	0.393090i
$393$	1.41059	−	3.57915i	0.0711549	−	0.180544i
$394$	14.8154	−	6.59623i	0.746388	−	0.332313i
$395$	−7.02843	+	32.3993i	−0.353639	+	1.63018i
$396$	5.31643	−	2.25448i	0.267160	−	0.113292i
$397$	3.76986	−	0.396228i	0.189204	−	0.0198861i	−0.00945256	−	0.999955i	$-0.503009\pi$
$397$	3.76986	−	0.396228i	0.189204	−	0.0198861i	0.198656	+	0.980069i	$0.436342\pi$
$398$	1.01204	+	3.11474i	0.0507290	+	0.156128i
$399$	6.01202	−	2.63130i	0.300978	−	0.131730i
$400$	−2.39784	−	24.8085i	−0.119892	−	1.24042i
$401$	2.81269	+	1.62391i	0.140459	+	0.0810942i	0.568583	−	0.822626i	$-0.307492\pi$
$401$	2.81269	+	1.62391i	0.140459	+	0.0810942i	−0.428124	+	0.903720i	$0.640825\pi$
$402$	25.6559	−	12.7859i	1.27960	−	0.637705i
$403$	10.6248	+	4.73045i	0.529257	+	0.235640i
$404$	0.526082	+	5.00534i	0.0261736	+	0.249025i
$405$	18.8771	+	6.97535i	0.938010	+	0.346608i
$406$	−13.6303	+	35.7836i	−0.676460	+	1.77591i
$407$			20.1061i			0.996621i
$408$	3.80013	−	0.165247i	0.188134	−	0.00818095i
$409$	−2.29776	−	10.8101i	−0.113617	−	0.534525i	−0.997735	−	0.0672623i	$-0.978574\pi$
$409$	−2.29776	−	10.8101i	−0.113617	−	0.534525i	0.884119	−	0.467263i	$-0.154760\pi$
$410$	21.9227	+	24.5534i	1.08269	+	1.21260i
$411$	−9.51512	−	6.30033i	−0.469346	−	0.310772i
$412$	15.5182	+	5.04216i	0.764525	+	0.248409i
$413$	2.98195	−	4.61783i	0.146732	−	0.227229i
$414$	13.6853	−	29.3213i	0.672596	−	1.44106i
$415$	3.34999	+	4.65165i	0.164444	+	0.228340i
$416$	12.5866	−	2.67536i	0.617107	−	0.131170i
$417$	−9.59060	+	18.4155i	−0.469654	+	0.901809i
$418$	4.61816	+	2.66630i	0.225882	+	0.130413i
$419$	−22.1848	−	16.1182i	−1.08380	−	0.787427i	−0.105459	−	0.994424i	$-0.533631\pi$
$419$	−22.1848	−	16.1182i	−1.08380	−	0.787427i	−0.978342	+	0.206997i	$0.933631\pi$
$420$	6.08150	−	6.61313i	0.296747	−	0.322688i
$421$	−16.4944	+	11.9839i	−0.803889	+	0.584060i	−0.912053	−	0.410073i	$-0.865503\pi$
$421$	−16.4944	+	11.9839i	−0.803889	+	0.584060i	0.108163	+	0.994133i	$0.465503\pi$
$422$	−0.259443	+	0.0272686i	−0.0126295	+	0.00132741i
$423$	11.2189	−	0.977543i	0.545479	−	0.0475298i
$424$	0.592523	+	1.02628i	0.0287755	+	0.0498406i
$425$	−3.89235	+	4.25084i	−0.188807	+	0.206196i
$426$	14.7242	−	37.3603i	0.713391	−	1.81011i
$427$	6.38342	+	9.77434i	0.308915	+	0.473013i
$428$	6.70850	+	9.23346i	0.324268	+	0.446316i
$429$	10.1513	+	2.81714i	0.490111	+	0.136013i
$430$	−9.44888	+	16.2090i	−0.455666	+	0.781668i
$431$	−4.72620	−	0.496744i	−0.227653	−	0.0239273i	−0.00998506	−	0.999950i	$-0.503178\pi$
$431$	−4.72620	−	0.496744i	−0.227653	−	0.0239273i	−0.217668	+	0.976023i	$0.569845\pi$
$432$	2.04587	−	25.8209i	0.0984320	−	1.24231i
$433$	−11.3453	+	15.6155i	−0.545221	+	0.750432i	−0.989354	−	0.145529i	$-0.953512\pi$
$433$	−11.3453	+	15.6155i	−0.545221	+	0.750432i	0.444133	+	0.895961i	$0.353512\pi$
$434$	−8.59554	−	16.7627i	−0.412599	−	0.804635i
$435$	−29.2473	−	15.3876i	−1.40230	−	0.737778i
$436$	9.35066	+	1.98754i	0.447815	+	0.0951861i
$437$	8.90792	−	1.89344i	0.426124	−	0.0905754i
$438$	−5.67481	+	33.8747i	−0.271153	+	1.61860i
$439$	−6.27314	+	29.5128i	−0.299401	+	1.40857i	0.529090	+	0.848566i	$0.322533\pi$
$439$	−6.27314	+	29.5128i	−0.299401	+	1.40857i	−0.828491	+	0.560003i	$0.810800\pi$
$440$	−9.29693	−	1.01648i	−0.443214	−	0.0484587i
$441$	−20.9983	−	0.265598i	−0.999920	−	0.0126475i
$442$	−4.38225	−	3.18389i	−0.208442	−	0.151442i
$443$	−29.5165	−	17.0414i	−1.40237	−	0.809660i	−0.407736	−	0.913100i	$-0.633682\pi$
$443$	−29.5165	−	17.0414i	−1.40237	−	0.809660i	−0.994636	+	0.103440i	$0.967015\pi$
$444$	−12.3353	−	6.42413i	−0.585409	−	0.304876i
$445$	20.8900	+	12.1776i	0.990281	+	0.577274i
$446$	−3.49459	−	33.2488i	−0.165474	−	1.57438i
$447$	−4.40510	+	1.13841i	−0.208354	+	0.0538449i
$448$	4.93792	+	2.49998i	0.233295	+	0.118113i
$449$		−	12.1777i		−	0.574701i	−0.957825	−	0.287351i	$-0.907226\pi$
$449$		−	12.1777i		−	0.574701i	0.957825	−	0.287351i	$-0.0927745\pi$
$450$	16.5232	+	19.3458i	0.778911	+	0.911969i
$451$	16.5013	−	9.52703i	0.777016	−	0.448610i
$452$	−1.09254	−	0.983726i	−0.0513887	−	0.0462706i
$453$	−17.5205	−	4.86219i	−0.823185	−	0.228445i
$454$	−2.19272	−	3.01803i	−0.102910	−	0.141643i
$455$	16.1927	−	2.53806i	0.759126	−	0.118986i
$456$	3.98589	−	2.53830i	0.186656	−	0.118867i
$457$	−7.17108	+	12.4207i	−0.335449	+	0.581015i	−0.983571	−	0.180522i	$-0.942221\pi$
$457$	−7.17108	+	12.4207i	−0.335449	+	0.581015i	0.648122	+	0.761536i	$0.275555\pi$
$458$	−2.66320	+	25.3386i	−0.124443	+	1.18400i
$459$	−4.75394	+	3.64384i	−0.221895	+	0.170080i
$460$	10.1170	−	7.28596i	0.471707	−	0.339710i
$461$	−4.89388	−	15.0618i	−0.227931	−	0.701499i	−0.997981	−	0.0635153i	$-0.979769\pi$
$461$	−4.89388	−	15.0618i	−0.227931	−	0.701499i	0.770050	−	0.637983i	$-0.220231\pi$
$462$	−9.94244	−	13.8682i	−0.462564	−	0.645206i
$463$	4.33962	−	13.3560i	0.201679	−	0.620704i	−0.798154	−	0.602453i	$-0.794190\pi$
$463$	4.33962	−	13.3560i	0.201679	−	0.620704i	0.999833	−	0.0182514i	$-0.00580992\pi$
$464$	−8.84363	+	41.6060i	−0.410555	+	1.93151i
$465$	15.2535	−	5.62739i	0.707363	−	0.260964i
$466$	−27.3916	+	5.82226i	−1.26889	+	0.269711i
$467$	−28.2552	+	12.5800i	−1.30749	+	0.582134i	−0.937850	−	0.347040i	$-0.887187\pi$
$467$	−28.2552	+	12.5800i	−1.30749	+	0.582134i	−0.369643	+	0.929174i	$0.620520\pi$
$468$	−4.97182	+	5.32786i	−0.229822	+	0.246280i
$469$	−16.2984	−	20.0210i	−0.752590	−	0.924486i
$470$	12.9815	+	5.84491i	0.598792	+	0.269606i
$471$	−4.95355	+	17.8497i	−0.228248	+	0.822472i
$472$	1.60992	−	3.61593i	0.0741025	−	0.166437i
$473$	8.07108	+	7.26723i	0.371108	+	0.334148i
$474$	−34.0922	+	27.1084i	−1.56591	+	1.24513i
$475$	−1.54727	+	6.99125i	−0.0709936	+	0.320780i
$476$	0.698753	+	2.58114i	0.0320273	+	0.118306i
$477$	−1.69100	−	0.789250i	−0.0774254	−	0.0361373i
$478$	3.61353	+	34.3805i	0.165279	+	1.57253i
$479$	11.4080	+	5.07918i	0.521245	+	0.232073i	0.650456	−	0.759544i	$-0.274578\pi$
$479$	11.4080	+	5.07918i	0.521245	+	0.232073i	−0.129211	+	0.991617i	$0.541244\pi$
$480$	9.99374	−	14.9568i	0.456150	−	0.682684i
$481$	−10.3200	−	23.1791i	−0.470552	−	1.05688i
$482$	−23.4489			−1.06807
$483$	−28.4659	−	6.23902i	−1.29524	−	0.283885i
$484$	−1.67445	+	5.15343i	−0.0761114	+	0.234247i
$485$	7.22395	+	22.5535i	0.328022	+	1.02410i
$486$	13.3991	+	22.7930i	0.607796	+	1.03391i
$487$	27.8983	−	5.92996i	1.26419	−	0.268712i	0.473427	−	0.880833i	$-0.343017\pi$
$487$	27.8983	−	5.92996i	1.26419	−	0.268712i	0.790764	+	0.612121i	$0.209683\pi$
$488$	5.62477	+	6.24694i	0.254622	+	0.282786i
$489$	−1.53494	−	0.0941524i	−0.0694126	−	0.00425772i
$490$	−23.0044	−	13.2517i	−1.03923	−	0.598652i
$491$	6.45330	+	2.09680i	0.291233	+	0.0946274i	0.450990	−	0.892529i	$-0.351071\pi$
$491$	6.45330	+	2.09680i	0.291233	+	0.0946274i	−0.159757	+	0.987156i	$0.551071\pi$
$492$	0.572595	+	13.1678i	0.0258146	+	0.593649i
$493$	8.51849	−	4.91815i	0.383653	−	0.221502i
$494$	−6.69256	−	0.703416i	−0.301112	−	0.0316482i
$495$	12.9130	−	7.08146i	0.580397	−	0.318288i
$496$	−12.2999	−	16.9293i	−0.552281	−	0.760149i
$497$	−35.7350	−	5.56545i	−1.60293	−	0.249644i
$498$	−0.461092	+	7.51707i	−0.0206620	+	0.336848i
$499$	7.46908	−	12.9368i	0.334362	−	0.579132i	−0.649000	−	0.760788i	$-0.724813\pi$
$499$	7.46908	−	12.9368i	0.334362	−	0.579132i	0.983362	+	0.181657i	$0.0581459\pi$
$500$	1.91763	+	9.61331i	0.0857590	+	0.429920i
$501$	−13.9588	+	2.08364i	−0.623632	+	0.0930902i
$502$	−1.78623	+	8.40354i	−0.0797232	+	0.375068i
$503$	16.4449	−	11.9479i	0.733244	−	0.532733i	−0.157344	−	0.987544i	$-0.550293\pi$
$503$	16.4449	−	11.9479i	0.733244	−	0.532733i	0.890588	+	0.454811i	$0.150293\pi$
$504$	−14.9694	+	2.13781i	−0.666790	+	0.0952257i
$505$	2.61612	+	12.5661i	0.116416	+	0.559183i
$506$	−9.63135	−	21.6324i	−0.428166	−	0.961676i
$507$	9.12108	−	1.36151i	0.405082	−	0.0604670i
$508$	1.49635	−	14.2368i	0.0663897	−	0.631656i
$509$	22.0552	+	24.4947i	0.977578	+	1.08571i	0.996305	+	0.0858859i	$0.0273720\pi$
$509$	22.0552	+	24.4947i	0.977578	+	1.08571i	−0.0187269	+	0.999825i	$0.505961\pi$
$510$	−7.49395	+	1.08661i	−0.331838	+	0.0481158i
$511$	30.8862	−	1.69856i	1.36633	−	0.0751397i
$512$	−3.95567	−	1.28527i	−0.174817	−	0.0568016i
$513$	−2.85130	+	6.87338i	−0.125888	+	0.303467i
$514$	−30.8552	−	27.7822i	−1.36096	−	1.22542i
$515$	40.6670	+	8.82197i	1.79200	+	0.388743i
$516$	−7.03734	+	2.62974i	−0.309802	+	0.115768i
$517$	4.84401	−	6.66721i	0.213039	−	0.293223i
$518$	−10.5344	+	39.7242i	−0.462853	+	1.74538i
$519$	−11.1474	+	7.09890i	−0.489315	+	0.311607i
$520$	11.2396	−	3.60007i	0.492890	−	0.157874i
$521$	−12.5685	−	5.59587i	−0.550637	−	0.245159i	0.112507	−	0.993651i	$-0.464112\pi$
$521$	−12.5685	−	5.59587i	−0.550637	−	0.245159i	−0.663144	+	0.748491i	$0.730778\pi$
$522$	−16.9510	−	39.9731i	−0.741924	−	1.74957i
$523$	−0.293109	+	1.37897i	−0.0128168	+	0.0602981i	−0.984091	−	0.177664i	$-0.943146\pi$
$523$	−0.293109	+	1.37897i	−0.0128168	+	0.0602981i	0.971274	+	0.237962i	$0.0764794\pi$
$524$	1.94743			0.0850739
$525$	13.7387	−	18.3371i	0.599605	−	0.800296i
$526$	−16.2255			−0.707467
$527$	−1.00610	+	4.73333i	−0.0438264	+	0.206187i
$528$	−13.2834	−	13.5221i	−0.578088	−	0.588473i
$529$	−15.9319	−	7.09334i	−0.692692	−	0.308406i
$530$	−1.37868	−	1.91438i	−0.0598860	−	0.0831552i
$531$	1.18715	+	6.11885i	0.0515179	+	0.265535i
$532$	2.35511	+	2.34299i	0.102107	+	0.101581i
$533$	−14.1334	+	19.4529i	−0.612184	+	0.842599i
$534$	11.1202	+	29.7582i	0.481217	+	1.28776i
$535$	19.3859	+	21.7122i	0.838126	+	0.938699i
$536$	−13.8145	−	12.4387i	−0.596697	−	0.537268i
$537$	2.59880	+	6.95454i	0.112147	+	0.300111i
$538$	−13.2979	−	4.32076i	−0.573315	−	0.186281i
$539$	−10.2241	+	11.4735i	−0.440383	+	0.494197i
$540$	0.218699	+	10.1849i	0.00941129	+	0.438289i
$541$	−13.6401	−	15.1489i	−0.586435	−	0.651302i	0.374776	−	0.927115i	$-0.377720\pi$
$541$	−13.6401	−	15.1489i	−0.586435	−	0.651302i	−0.961211	+	0.275813i	$0.911053\pi$
$542$	−3.96070	+	37.6835i	−0.170127	+	1.61865i
$543$	−3.67622	−	24.6278i	−0.157762	−	1.05688i
$544$	2.17766	+	4.89110i	0.0933663	+	0.209704i
$545$	24.2355	+	2.64978i	1.03813	+	0.113504i
$546$	18.5803	+	10.8846i	0.795163	+	0.465817i
$547$	−19.5434	+	14.1991i	−0.835615	+	0.607109i	−0.921142	−	0.389226i	$-0.872742\pi$
$547$	−19.5434	+	14.1991i	−0.835615	+	0.607109i	0.0855276	+	0.996336i	$0.472742\pi$
$548$	1.20107	−	5.65058i	0.0513071	−	0.241381i
$549$	−12.8969	−	2.98227i	−0.550427	−	0.127280i
$550$	18.6177	+	0.155738i	0.793859	+	0.00664068i
$551$	6.10999	−	10.5828i	0.260294	−	0.450843i
$552$	−20.9443	−	1.28471i	−0.891451	−	0.0546809i
$553$	30.5486	+	24.6076i	1.29906	+	1.04642i
$554$	−0.0103392	−	0.0142306i	−0.000439268	−	0.000604601i
$555$	−32.9446	−	13.1434i	−1.39842	−	0.557905i
$556$	−10.4529	−	1.09865i	−0.443303	−	0.0465930i
$557$	13.5239	−	7.80806i	0.573028	−	0.330838i	−0.185330	−	0.982676i	$-0.559335\pi$
$557$	13.5239	−	7.80806i	0.573028	−	0.330838i	0.758358	+	0.651838i	$0.226002\pi$
$558$	20.1941	+	6.96134i	0.854885	+	0.294697i
$559$	−13.0348	−	4.23525i	−0.551312	−	0.179132i
$560$	−27.5148	−	10.6126i	−1.16271	−	0.448465i
$561$	−0.268368	+	4.37514i	−0.0113305	+	0.184718i
$562$	22.6488	+	25.1541i	0.955382	+	1.06106i
$563$	28.5534	−	6.06922i	1.20338	−	0.255787i	0.437770	−	0.899087i	$-0.355768\pi$
$563$	28.5534	−	6.06922i	1.20338	−	0.255787i	0.765614	+	0.643300i	$0.222435\pi$
$564$	2.54270	+	5.10212i	0.107067	+	0.214838i
$565$	−3.02405	−	2.21649i	−0.127223	−	0.0932483i
$566$	1.33825	−	4.11871i	0.0562508	−	0.173122i
$567$	17.3843	−	16.2722i	0.730074	−	0.683368i
$568$	−26.0416			−1.09268
$569$	−0.950793	−	2.13552i	−0.0398593	−	0.0895255i	0.892518	−	0.451011i	$-0.148936\pi$
$569$	−0.950793	−	2.13552i	−0.0398593	−	0.0895255i	−0.932378	+	0.361485i	$0.882270\pi$
$570$	−7.38772	+	5.82407i	−0.309438	+	0.243943i
$571$	−33.8921	−	15.0897i	−1.41834	−	0.631486i	−0.452770	−	0.891627i	$-0.649564\pi$
$571$	−33.8921	−	15.0897i	−1.41834	−	0.631486i	−0.965571	+	0.260141i	$0.916231\pi$
$572$	0.557440	+	5.30369i	0.0233077	+	0.221758i
$573$	2.63552	−	42.9662i	0.110100	−	1.79494i
$574$	37.5937	−	10.1772i	1.56913	−	0.424787i
$575$	23.8062	−	21.0773i	0.992789	−	0.878986i
$576$	−6.00219	+	1.83274i	−0.250091	+	0.0763643i
$577$	−31.2888	−	28.1726i	−1.30257	−	1.17284i	−0.973539	−	0.228519i	$-0.926612\pi$
$577$	−31.2888	−	28.1726i	−1.30257	−	1.17284i	−0.329030	−	0.944319i	$-0.606722\pi$
$578$	−10.8111	+	24.2821i	−0.449681	+	1.01000i
$579$	18.3739	+	5.09903i	0.763595	+	0.211908i
$580$	1.81826	−	16.6302i	0.0754991	−	0.690532i
$581$	6.69638	−	1.07831i	0.277813	−	0.0447359i
$582$	−11.4083	+	28.9467i	−0.472889	+	1.19988i
$583$	−1.24757	+	0.555453i	−0.0516690	+	0.0230045i
$584$	21.7868	−	4.63094i	0.901546	−	0.191630i
$585$	−11.2519	+	14.7918i	−0.465209	+	0.611564i
$586$	7.72477	−	36.3422i	0.319107	−	1.50128i
$587$	−5.32570	+	16.3908i	−0.219815	+	0.676522i	0.778961	+	0.627072i	$0.215747\pi$
$587$	−5.32570	+	16.3908i	−0.219815	+	0.676522i	−0.998777	+	0.0494499i	$0.984253\pi$
$588$	−3.77240	−	9.93853i	−0.155571	−	0.409858i
$589$	1.85773	+	5.71752i	0.0765466	+	0.235586i
$590$	−2.46629	+	7.48381i	−0.101535	+	0.308103i
$591$	16.3335	+	2.73625i	0.671871	+	0.112554i
$592$	−4.77193	+	45.4019i	−0.196125	+	1.86601i
$593$	−4.41829	+	7.65271i	−0.181438	+	0.314259i	−0.942370	−	0.334572i	$-0.891408\pi$
$593$	−4.41829	+	7.65271i	−0.181438	+	0.314259i	0.760933	+	0.648831i	$0.224742\pi$
$594$	19.0229	+	3.53607i	0.780517	+	0.145087i
$595$	2.43374	+	6.37063i	0.0997736	+	0.261170i
$596$	−1.35376	−	1.86330i	−0.0554524	−	0.0763236i
$597$	−0.894329	+	3.22264i	−0.0366024	+	0.131894i
$598$	22.2068	+	19.9951i	0.908105	+	0.817661i
$599$	−16.3736	+	9.45330i	−0.669007	+	0.386251i	−0.795700	−	0.605691i	$-0.792897\pi$
$599$	−16.3736	+	9.45330i	−0.669007	+	0.386251i	0.126693	+	0.991942i	$0.459564\pi$
$600$	7.74295	−	14.5689i	0.316104	−	0.594772i
$601$		−	6.60099i		−	0.269260i	−0.990896	−	0.134630i	$-0.957015\pi$
$601$		−	6.60099i		−	0.269260i	0.990896	−	0.134630i	$-0.0429846\pi$
$602$	12.1387	+	18.5868i	0.494736	+	0.757543i
$603$	29.0534	+	3.57770i	1.18315	+	0.145695i
$604$	−0.962104	−	9.15381i	−0.0391475	−	0.372463i
$605$	−2.92969	+	13.5051i	−0.119109	+	0.549061i
$606$	−7.78923	+	14.9565i	−0.316416	+	0.607568i
$607$	−10.8778	−	6.28032i	−0.441518	−	0.254910i	0.262723	−	0.964871i	$-0.415379\pi$
$607$	−10.8778	−	6.28032i	−0.441518	−	0.254910i	−0.704241	+	0.709961i	$0.748713\pi$
$608$	5.38112	+	3.90961i	0.218233	+	0.158556i
$609$	−31.7798	+	22.7837i	−1.28778	+	0.923244i
$610$	−12.3893	−	11.2495i	−0.501627	−	0.455480i
$611$	−2.16224	+	10.1726i	−0.0874750	+	0.411537i
$612$	−2.59846	−	1.56256i	−0.105036	−	0.0631626i
$613$	10.1493	−	2.15730i	0.409926	−	0.0871324i	0.00166677	−	0.999999i	$-0.499469\pi$
$613$	10.1493	−	2.15730i	0.409926	−	0.0871324i	0.408259	+	0.912866i	$0.366136\pi$
$614$	27.0442	+	5.74842i	1.09141	+	0.231987i
$615$	4.82348	+	33.2658i	0.194502	+	1.34141i
$616$	−6.00293	+	9.29609i	−0.241865	+	0.374550i
$617$	20.4154	−	28.0994i	0.821895	−	1.13124i	−0.167483	−	0.985875i	$-0.553564\pi$
$617$	20.4154	−	28.0994i	0.821895	−	1.13124i	0.989378	−	0.145366i	$-0.0464360\pi$
$618$	34.0260	+	42.7920i	1.36873	+	1.72135i
$619$	−39.7910	−	4.18220i	−1.59933	−	0.168097i	−0.737521	−	0.675324i	$-0.764004\pi$
$619$	−39.7910	−	4.18220i	−1.59933	−	0.168097i	−0.861812	+	0.507227i	$0.830670\pi$
$620$	5.48143	+	6.13918i	0.220139	+	0.246556i
$621$	28.1833	−	17.2503i	1.13096	−	0.692230i
$622$	−16.1207	−	22.1883i	−0.646382	−	0.889668i
$623$	23.9545	−	15.6442i	0.959718	−	0.626772i
$624$	22.2543	+	8.77072i	0.890884	+	0.351110i
$625$	7.32659	+	23.9023i	0.293064	+	0.956093i
$626$	−11.7383	−	20.3314i	−0.469158	−	0.812606i
$627$	2.42896	+	4.87388i	0.0970032	+	0.194644i
$628$	−9.32582	+	0.980183i	−0.372141	+	0.0391136i
$629$	8.54079	−	6.20524i	0.340543	−	0.247419i
$630$	29.2229	−	7.22542i	1.16427	−	0.287868i
$631$	23.5436	+	17.1054i	0.937255	+	0.680955i	0.947758	−	0.318990i	$-0.103343\pi$
$631$	23.5436	+	17.1054i	0.937255	+	0.680955i	−0.0105037	+	0.999945i	$0.503343\pi$
$632$	24.4616	+	14.1229i	0.973029	+	0.561779i
$633$	−0.236278	−	0.123052i	−0.00939122	−	0.00489086i
$634$	9.45354	−	2.00941i	0.375448	−	0.0798039i
$635$	0.152693	−	36.5080i	0.00605945	−	1.44878i
$636$	0.0578351	−	0.942873i	0.00229331	−	0.0373873i
$637$	5.89769	−	18.4749i	0.233675	−	0.732002i
$638$	−30.2189	−	9.81872i	−1.19638	−	0.388727i
$639$	33.6002	−	23.5095i	1.32920	−	0.930021i
$640$	−28.0526	−	6.08550i	−1.10888	−	0.240550i
$641$	8.59923	+	40.4562i	0.339649	+	1.59792i	0.734123	+	0.679017i	$0.237594\pi$
$641$	8.59923	+	40.4562i	0.339649	+	1.59792i	−0.394474	+	0.918907i	$0.629073\pi$
$642$	1.66133	+	38.2050i	0.0655674	+	1.50783i
$643$		−	2.07578i		−	0.0818606i	−0.999162	−	0.0409303i	$-0.986968\pi$
$643$		−	2.07578i		−	0.0818606i	0.999162	−	0.0409303i	$-0.0130322\pi$
$644$	−2.34525	−	14.5641i	−0.0924157	−	0.573907i
$645$	−17.1837	+	8.47416i	−0.676607	+	0.333670i
$646$	−0.292675	−	2.78462i	−0.0115152	−	0.109559i
$647$	−27.3273	−	12.1669i	−1.07435	−	0.478331i	−0.208184	−	0.978090i	$-0.566755\pi$
$647$	−27.3273	−	12.1669i	−1.07435	−	0.478331i	−0.866165	+	0.499759i	$0.833422\pi$
$648$	10.5656	−	13.5037i	0.415055	−	0.530476i
$649$	3.95021	+	2.28065i	0.155059	+	0.0895234i
$650$	−21.5431	+	9.37649i	−0.844991	+	0.367776i
$651$	2.13179	−	19.1187i	0.0835512	−	0.749323i
$652$	−0.240558	−	0.740363i	−0.00942100	−	0.0289948i
$653$	21.7976	−	2.29102i	0.853007	−	0.0896546i	0.332075	−	0.943253i	$-0.392251\pi$
$653$	21.7976	−	2.29102i	0.853007	−	0.0896546i	0.520932	+	0.853598i	$0.325585\pi$
$654$	22.4463	+	22.8496i	0.877720	+	0.893489i
$655$	4.94149	−	0.498484i	0.193080	−	0.0194774i
$656$	39.5230	−	17.5968i	1.54311	−	0.687039i
$657$	−23.9299	+	25.6435i	−0.933593	+	1.00045i
$658$	13.0637	−	10.6346i	0.509275	−	0.414582i
$659$	0.285267	+	0.0926887i	0.0111124	+	0.00361064i	0.314568	−	0.949235i	$-0.398140\pi$
$659$	0.285267	+	0.0926887i	0.0111124	+	0.00361064i	−0.303456	+	0.952846i	$0.598140\pi$
$660$	5.73181	+	4.76705i	0.223111	+	0.185557i
$661$	−2.71042	−	2.44047i	−0.105423	−	0.0949234i	0.614734	−	0.788735i	$-0.289263\pi$
$661$	−2.71042	−	2.44047i	−0.105423	−	0.0949234i	−0.720157	+	0.693811i	$0.755930\pi$
$662$	−10.4607	−	49.2138i	−0.406568	−	1.91275i
$663$	−1.93628	−	5.18158i	−0.0751987	−	0.201236i
$664$	4.64488	−	1.50921i	0.180256	−	0.0585688i
$665$	6.57567	+	5.34236i	0.254994	+	0.207168i
$666$	−22.5777	−	40.7652i	−0.874870	−	1.57962i
$667$	−49.5720	+	22.0709i	−1.91943	+	0.854587i
$668$	−3.57217	−	6.18719i	−0.138212	−	0.239390i
$669$	15.7696	−	30.2802i	0.609689	−	1.17070i
$670$	29.8480	+	21.8771i	1.15313	+	0.845188i
$671$	−7.83701	+	5.69392i	−0.302545	+	0.219812i
$672$	−10.5253	−	18.4995i	−0.406022	−	0.713636i
$673$	3.03537	+	9.34192i	0.117005	+	0.360104i	0.992360	−	0.123376i	$-0.0393723\pi$
$673$	3.03537	+	9.34192i	0.117005	+	0.360104i	−0.875355	+	0.483481i	$0.839372\pi$
$674$	−10.1503	−	5.86028i	−0.390975	−	0.225730i
$675$	3.16197	+	25.7876i	0.121704	+	0.992566i
$676$	2.33417	+	4.04290i	0.0897757	+	0.155496i
$677$	−12.9281	−	2.74795i	−0.496866	−	0.105612i	−0.0473393	−	0.998879i	$-0.515074\pi$
$677$	−12.9281	−	2.74795i	−0.496866	−	0.105612i	−0.449527	+	0.893267i	$0.648408\pi$
$678$	−1.23251	−	4.76922i	−0.0473342	−	0.183161i
$679$	27.6874	+	4.31210i	1.06255	+	0.165483i
$680$	2.43748	+	4.26292i	0.0934732	+	0.163475i
$681$	−0.165500	−	3.80594i	−0.00634197	−	0.145844i
$682$	13.5373	−	7.81579i	0.518372	−	0.299282i
$683$	8.84556	+	0.929706i	0.338466	+	0.0355742i	0.272237	−	0.962230i	$-0.412237\pi$
$683$	8.84556	+	0.929706i	0.338466	+	0.0355742i	0.0662291	+	0.997804i	$0.478903\pi$
$684$	−3.76627	−	0.0670667i	−0.144007	−	0.00256436i
$685$	1.60125	−	14.6454i	0.0611808	−	0.559573i
$686$	−26.2115	+	17.3117i	−1.00076	+	0.660963i
$687$	−16.5531	+	20.0733i	−0.631540	+	0.765845i
$688$	16.5007	+	18.3258i	0.629082	+	0.698666i
$689$	1.15315	−	1.28070i	0.0439313	−	0.0487907i
$690$	41.7415	−	1.64023i	1.58907	−	0.0624425i
$691$	1.41852	−	1.27724i	0.0539630	−	0.0485885i	−0.641708	−	0.766949i	$-0.721774\pi$
$691$	1.41852	−	1.27724i	0.0539630	−	0.0485885i	0.695671	+	0.718361i	$0.255107\pi$
$692$	−5.41231	−	3.93227i	−0.205745	−	0.149482i
$693$	−0.646920	−	17.4136i	−0.0245745	−	0.661487i
$694$	35.3569	+	25.6883i	1.34213	+	0.975113i
$695$	−26.8049	−	0.112110i	−1.01677	−	0.00425259i
$696$	−20.0862	+	19.7317i	−0.761366	+	0.747929i
$697$	−9.13967	−	4.06924i	−0.346190	−	0.154134i
$698$	−30.3889	−	6.45935i	−1.15024	−	0.244490i
$699$	−26.6053	−	10.4855i	−1.00630	−	0.396598i
$700$	11.1859	+	3.06674i	0.422789	+	0.115912i
$701$		−	43.3280i		−	1.63647i	−0.574881	−	0.818237i	$-0.694952\pi$
$701$		−	43.3280i		−	1.63647i	0.574881	−	0.818237i	$-0.305048\pi$
$702$	−23.7453	+	5.68748i	−0.896209	+	0.214660i
$703$	5.33448	−	11.9814i	0.201194	−	0.451889i
$704$	−1.86800	+	4.19559i	−0.0704027	+	0.158127i
$705$	7.75794	+	12.2955i	0.292181	+	0.463073i
$706$	19.0695	−	26.2469i	0.717690	−	0.987815i
$707$	14.6798	+	3.89289i	0.552090	+	0.146407i
$708$	−2.66135	+	1.69481i	−0.100020	+	0.0636948i
$709$	−2.53727	−	2.81792i	−0.0952892	−	0.105829i	0.693614	−	0.720347i	$-0.256017\pi$
$709$	−2.53727	−	2.81792i	−0.0952892	−	0.105829i	−0.788903	+	0.614518i	$0.789351\pi$
$710$	51.5809	−	5.20335i	1.93580	−	0.195278i
$711$	−44.3113	+	3.86102i	−1.66180	+	0.144800i
$712$	15.3097	−	13.7850i	0.573757	−	0.516613i
$713$	8.24933	−	25.3888i	0.308940	−	0.950819i
$714$	−2.82253	+	8.50349i	−0.105630	+	0.318235i
$715$	2.77206	+	13.3151i	0.103669	+	0.497956i
$716$	−2.79290	+	2.51474i	−0.104376	+	0.0939803i
$717$	−16.3064	+	31.3108i	−0.608972	+	1.16932i
$718$	22.2126	+	38.4734i	0.828967	+	1.43581i
$719$	2.54099	−	1.13132i	0.0947630	−	0.0421912i	−0.358808	−	0.933412i	$-0.616817\pi$
$719$	2.54099	−	1.13132i	0.0947630	−	0.0421912i	0.453571	+	0.891220i	$0.350150\pi$
$720$	30.8398	−	12.9260i	1.14933	−	0.481724i
$721$	30.8871	−	38.3442i	1.15030	−	1.42801i
$722$	16.8974	+	23.2573i	0.628856	+	0.865546i
$723$	−19.9658	−	13.2201i	−0.742536	−	0.491662i
$724$	10.9162	−	6.30248i	0.405698	−	0.234230i
$725$	0.356883	−	42.6636i	0.0132543	−	1.58448i
$726$	−14.2108	+	11.2997i	−0.527412	+	0.419371i
$727$	−34.8219	+	11.3143i	−1.29147	+	0.419625i	−0.872607	−	0.488423i	$-0.837572\pi$
$727$	−34.8219	+	11.3143i	−1.29147	+	0.419625i	−0.418866	+	0.908048i	$0.637572\pi$
$728$	2.14894	−	13.7981i	0.0796451	−	0.511391i
$729$	−1.44154	+	26.9615i	−0.0533905	+	0.998574i
$730$	−42.2282	+	13.5258i	−1.56294	+	0.500611i
$731$	0.596081	−	5.67133i	0.0220469	−	0.209762i
$732$	−0.989277	−	6.62739i	−0.0365647	−	0.244955i
$733$	3.68396	+	8.27430i	0.136070	+	0.305618i	0.968710	−	0.248197i	$-0.0798380\pi$
$733$	3.68396	+	8.27430i	0.136070	+	0.305618i	−0.832640	+	0.553815i	$0.813171\pi$
$734$	−15.1834	+	46.7296i	−0.560429	+	1.72482i
$735$	−12.1162	−	24.2528i	−0.446913	−	0.894578i
$736$	−9.12710	−	28.0903i	−0.336429	−	1.03542i
$737$	15.9197	−	14.3342i	0.586409	−	0.528005i
$738$	−22.7583	+	37.8459i	−0.837743	+	1.39313i
$739$	−30.7093	+	34.1061i	−1.12966	+	1.25461i	−0.166393	+	0.986059i	$0.553212\pi$
$739$	−30.7093	+	34.1061i	−1.12966	+	1.25461i	−0.963265	+	0.268553i	$0.913455\pi$
$740$	0.0750955	−	17.9549i	0.00276057	−	0.660035i
$741$	−5.30186	−	4.37208i	−0.194769	−	0.160612i
$742$	−2.75588	+	0.443777i	−0.101172	+	0.0162916i
$743$			6.83822i			0.250870i	0.992102	+	0.125435i	$0.0400326\pi$
$743$			6.83822i			0.250870i	−0.992102	+	0.125435i	$0.959967\pi$
$744$	−0.601779	−	13.8389i	−0.0220623	−	0.507358i
$745$	−3.91204	−	4.38148i	−0.143326	−	0.160525i
$746$	5.74179	−	12.8963i	0.210222	−	0.472166i
$747$	−4.63060	+	6.14052i	−0.169425	+	0.224670i
$748$	−2.11030	+	0.685677i	−0.0771601	+	0.0250708i
$749$	33.2435	−	8.99952i	1.21469	−	0.328835i
$750$	−12.4256	+	30.4039i	−0.453717	+	1.11019i
$751$	24.4185	−	42.2941i	0.891044	−	1.54333i	0.0524186	−	0.998625i	$-0.483307\pi$
$751$	24.4185	−	42.2941i	0.891044	−	1.54333i	0.838625	−	0.544708i	$-0.183360\pi$
$752$	12.5207	−	13.9057i	0.456584	−	0.507088i
$753$	−6.25867	+	6.14821i	−0.228079	+	0.224053i
$754$	39.8773	−	4.19128i	1.45225	−	0.152637i
$755$	−4.78438	−	22.9810i	−0.174122	−	0.836363i
$756$	10.8901	+	5.16695i	0.396071	+	0.187920i
$757$	28.7424			1.04466			0.522330	−	0.852743i	$-0.325063\pi$
$757$	28.7424			1.04466			0.522330	+	0.852743i	$0.325063\pi$
$758$	−18.0299	−	40.4958i	−0.654876	−	1.47087i
$759$	3.99528	−	23.8490i	0.145019	−	0.865666i
$760$	5.27046	+	3.07236i	0.191180	+	0.111446i
$761$	26.1206	+	5.55210i	0.946871	+	0.201264i	0.655371	−	0.755307i	$-0.272512\pi$
$761$	26.1206	+	5.55210i	0.946871	+	0.201264i	0.291500	+	0.956571i	$0.405846\pi$
$762$	30.5158	−	37.0053i	1.10547	−	1.34056i
$763$	15.6486	−	24.2333i	0.566517	−	0.877305i
$764$	20.7243	−	6.73372i	0.749778	−	0.243618i
$765$	−6.99339	−	3.29976i	−0.252847	−	0.119303i
$766$	−3.02244	−	14.2195i	−0.109205	−	0.513770i
$767$	−5.72457	−	0.601676i	−0.206702	−	0.0217253i
$768$	−18.9614	−	23.8463i	−0.684209	−	0.860480i
$769$	13.3220	−	18.3362i	0.480405	−	0.661220i	−0.498178	−	0.867075i	$-0.665997\pi$
$769$	13.3220	−	18.3362i	0.480405	−	0.661220i	0.978583	+	0.205855i	$0.0659974\pi$
$770$	10.0326	−	19.6123i	0.361551	−	0.706780i
$771$	−10.6088	−	41.0510i	−0.382067	−	1.47842i
$772$	1.00897	+	9.59970i	0.0363136	+	0.345501i
$773$	−3.33122	+	3.69969i	−0.119816	+	0.133069i	−0.800068	−	0.599909i	$-0.795203\pi$
$773$	−3.33122	+	3.69969i	−0.119816	+	0.133069i	0.680253	+	0.732978i	$0.261870\pi$
$774$	−24.5247	−	5.67108i	−0.881523	−	0.203843i
$775$	15.4802	+	14.1747i	0.556067	+	0.509171i
$776$	20.1770			0.724310
$777$	−31.3654	+	27.8844i	−1.12523	+	1.00035i
$778$	33.6314	−	24.4347i	1.20575	−	0.876025i
$779$	−12.3610	+	1.29919i	−0.442879	+	0.0465484i
$780$	−9.05469	−	2.55364i	−0.324210	−	0.0914349i
$781$	3.13690	−	29.8456i	0.112247	−	1.06796i
$782$	−6.21665	+	10.7676i	−0.222307	+	0.385047i
$783$	8.10313	−	43.5921i	0.289582	−	1.55785i
$784$	−25.8103	+	23.4819i	−0.921797	+	0.838639i
$785$	−23.4128	+	4.87429i	−0.835638	+	0.173971i
$786$	5.44053	+	3.60238i	0.194057	+	0.128493i
$787$	−4.13159	−	19.4376i	−0.147275	−	0.692876i	−0.988380	−	0.152003i	$-0.951428\pi$
$787$	−4.13159	−	19.4376i	−0.147275	−	0.692876i	0.841105	−	0.540872i	$-0.181906\pi$
$788$	1.74301	+	8.20020i	0.0620920	+	0.292120i
$789$	−13.8154	−	9.14769i	−0.491840	−	0.325666i
$790$	−51.2733	−	23.0858i	−1.82422	−	0.821355i
$791$	−3.94757	+	2.02423i	−0.140359	+	0.0719732i
$792$	−2.38983	−	12.3178i	−0.0849191	−	0.437693i
$793$	6.11227	−	10.5868i	0.217053	−	0.375947i
$794$	−0.672046	+	6.39409i	−0.0238500	+	0.226918i
$795$	−0.0945943	−	2.40729i	−0.00335492	−	0.0853777i
$796$	−1.68371	+	0.176965i	−0.0596775	+	0.00627236i
$797$	−32.0432	+	23.2807i	−1.13503	+	0.824645i	−0.986419	−	0.164251i	$-0.947479\pi$
$797$	−32.0432	+	23.2807i	−1.13503	+	0.824645i	−0.148608	+	0.988896i	$0.547479\pi$
$798$	2.24535	+	10.9021i	0.0794846	+	0.385930i
$799$	−4.32712			−0.153083
$800$	23.0746	+	2.62056i	0.815810	+	0.0926508i
$801$	−7.30882	+	31.6072i	−0.258244	+	1.11679i
$802$	−3.68601	+	4.09373i	−0.130157	+	0.144555i
$803$	2.68302	+	25.5272i	0.0946816	+	0.900835i
$804$	3.70766	+	14.3469i	0.130759	+	0.505975i
$805$	−9.67891	−	36.3553i	−0.341137	−	1.28136i
$806$	−11.5947	+	15.9588i	−0.408407	+	0.562124i
$807$	−8.88667	−	11.1761i	−0.312826	−	0.393418i
$808$	10.8758	+	1.14309i	0.382609	+	0.0402138i
$809$	−3.93376	−	18.5069i	−0.138303	−	0.650667i	−0.991611	−	0.129259i	$-0.958740\pi$
$809$	−3.93376	−	18.5069i	−0.138303	−	0.650667i	0.853307	−	0.521408i	$-0.174593\pi$
$810$	−18.2292	+	28.8581i	−0.640510	+	1.01397i
$811$	21.7566	−	7.06915i	0.763978	−	0.248232i	0.0989931	−	0.995088i	$-0.468438\pi$
$811$	21.7566	−	7.06915i	0.763978	−	0.248232i	0.664985	+	0.746857i	$0.268438\pi$
$812$	−16.6287	−	10.7380i	−0.583554	−	0.376828i
$813$	−24.6177	+	29.8530i	−0.863381	+	1.04699i
$814$	−33.3569	−	7.09022i	−1.16916	−	0.248512i
$815$	−0.799913	−	1.81705i	−0.0280197	−	0.0636485i
$816$	−1.64439	+	9.81588i	−0.0575652	+	0.343625i
$817$	−2.88153	−	6.47202i	−0.100812	−	0.226427i
$818$	18.7447			0.655393
$819$	9.68379	+	19.7430i	0.338379	+	0.689877i
$820$	−14.7714	+	8.44608i	−0.515839	+	0.294950i
$821$	48.6017	−	5.10825i	1.69621	−	0.178279i	0.793514	−	0.608553i	$-0.208250\pi$
$821$	48.6017	−	5.10825i	1.69621	−	0.178279i	0.902699	+	0.430273i	$0.141583\pi$
$822$	13.8079	−	13.5642i	0.481607	−	0.473107i
$823$	5.68973	−	6.31909i	0.198332	−	0.220270i	−0.635773	−	0.771876i	$-0.719318\pi$
$823$	5.68973	−	6.31909i	0.198332	−	0.220270i	0.834104	+	0.551607i	$0.185985\pi$
$824$	17.7268	−	30.7038i	0.617543	−	1.06962i
$825$	15.7644	+	10.6289i	0.548844	+	0.370052i
$826$	6.60962	+	6.57562i	0.229978	+	0.228795i
$827$	−39.2032	+	12.7379i	−1.36323	+	0.442940i	−0.897120	−	0.441787i	$-0.854345\pi$
$827$	−39.2032	+	12.7379i	−1.36323	+	0.442940i	−0.466110	+	0.884727i	$0.654345\pi$
$828$	13.3552	+	10.0712i	0.464124	+	0.349999i
$829$	−9.22714	+	20.7245i	−0.320472	+	0.719792i	−0.999903	−	0.0139479i	$-0.995560\pi$
$829$	−9.22714	+	20.7245i	−0.320472	+	0.719792i	0.679431	+	0.733740i	$0.262227\pi$
$830$	−8.89863	+	3.91741i	−0.308876	+	0.135975i
$831$	−0.000780367	−	0.0179458i	−2.70706e−5	−	0.000622534i
$832$		−	5.79564i		−	0.200928i
$833$	8.02919	+	0.802057i	0.278195	+	0.0277896i
$834$	−27.1700	−	22.4053i	−0.940821	−	0.775831i
$835$	−10.6479	−	14.7852i	−0.368486	−	0.511664i
$836$	−1.84454	+	2.04856i	−0.0637946	+	0.0708511i
$837$	13.2698	+	17.3124i	0.458670	+	0.598404i
$838$	34.5641	−	31.1217i	1.19400	−	1.07508i
$839$	12.3305	+	37.9494i	0.425696	+	1.31016i	0.902326	+	0.431054i	$0.141858\pi$
$839$	12.3305	+	37.9494i	0.425696	+	1.31016i	−0.476630	+	0.879104i	$0.658142\pi$
$840$	−11.3079	−	15.9129i	−0.390159	−	0.549047i
$841$	−13.5387	+	41.6679i	−0.466853	+	1.43683i
$842$	−14.0652	−	31.5910i	−0.484719	−	1.08870i
$843$	5.10308	+	34.1866i	0.175759	+	1.17745i
$844$	0.0140961	−	0.134116i	0.000485208	−	0.00461645i
$845$	6.95767	+	9.66112i	0.239351	+	0.332353i
$846$	−2.33444	+	18.9573i	−0.0802595	+	0.651765i
$847$	12.7337	+	10.2573i	0.437536	+	0.352445i
$848$	−2.94899	+	0.958184i	−0.101269	+	0.0329042i
$849$	3.46152	−	2.75242i	0.118799	−	0.0944630i
$850$	−5.67972	−	7.95659i	−0.194813	−	0.272909i
$851$	−50.4365	+	29.1195i	−1.72894	+	0.998204i
$852$	17.3084	+	11.4606i	0.592975	+	0.392632i
$853$	−16.4568	−	22.6509i	−0.563471	−	0.775552i	0.428291	−	0.903641i	$-0.359116\pi$
$853$	−16.4568	−	22.6509i	−0.563471	−	0.775552i	−0.991763	+	0.128089i	$0.959116\pi$
$854$	−18.4671	+	7.14355i	−0.631931	+	0.244447i
$855$	−9.57385	+	0.793876i	−0.327419	+	0.0271500i
$856$	22.6550	−	10.0867i	0.774332	−	0.344755i
$857$	−7.16953	−	12.4180i	−0.244906	−	0.424190i	0.717199	−	0.696868i	$-0.245424\pi$
$857$	−7.16953	−	12.4180i	−0.244906	−	0.424190i	−0.962105	+	0.272678i	$0.912091\pi$
$858$	−8.25352	+	15.8481i	−0.281771	+	0.541044i
$859$	27.3862	−	24.6586i	0.934405	−	0.841342i	−0.0531545	−	0.998586i	$-0.516928\pi$
$859$	27.3862	−	24.6586i	0.934405	−	0.841342i	0.987560	+	0.157244i	$0.0502609\pi$
$860$	−7.18039	−	6.51984i	−0.244849	−	0.222325i
$861$	37.7472	+	12.5293i	1.28642	+	0.426996i
$862$	2.49077	−	7.66581i	0.0848360	−	0.261098i
$863$	0.211385	−	0.190332i	0.00719562	−	0.00647896i	−0.665525	−	0.746376i	$-0.731792\pi$
$863$	0.211385	−	0.190332i	0.00719562	−	0.00647896i	0.672721	+	0.739897i	$0.265126\pi$
$864$	23.1365	+	6.86663i	0.787120	+	0.233608i
$865$	−14.7399	−	8.59251i	−0.501173	−	0.292154i
$866$	−21.9059	−	24.3290i	−0.744394	−	0.826733i
$867$	−22.8950	+	14.5801i	−0.777555	+	0.495165i
$868$	9.39972	−	2.54464i	0.319047	−	0.0863709i
$869$	−19.1325	+	26.3336i	−0.649025	+	0.893306i
$870$	35.8425	−	43.0963i	1.21517	−	1.46110i
$871$	−10.9955	+	24.6962i	−0.372567	+	0.836800i
$872$	8.44848	−	18.9756i	0.286102	−	0.642595i
$873$	−26.0334	+	18.2151i	−0.881096	+	0.616488i
$874$			15.4463i			0.522480i
$875$	29.1686	+	4.91840i	0.986080	+	0.166272i
$876$	−16.5185	−	6.51018i	−0.558109	−	0.219958i
$877$	24.5346	+	5.21499i	0.828474	+	0.176098i	0.602584	−	0.798055i	$-0.294138\pi$
$877$	24.5346	+	5.21499i	0.828474	+	0.176098i	0.225890	+	0.974153i	$0.427471\pi$
$878$	−46.7508	−	20.8148i	−1.57776	−	0.702466i
$879$	27.0665	−	26.5888i	0.912929	−	0.896817i
$880$	7.65922	−	23.2414i	0.258192	−	0.783469i
$881$	33.7345	+	24.5095i	1.13654	+	0.825747i	0.986634	−	0.162953i	$-0.0521020\pi$
$881$	33.7345	+	24.5095i	1.13654	+	0.825747i	0.149909	+	0.988700i	$0.452102\pi$
$882$	7.84550	−	34.7435i	0.264172	−	1.16987i
$883$	−46.0564	−	33.4619i	−1.54992	−	1.12608i	−0.943707	−	0.330783i	$-0.892687\pi$
$883$	−46.0564	−	33.4619i	−1.54992	−	1.12608i	−0.606214	−	0.795301i	$-0.707313\pi$
$884$	2.08089	−	1.87365i	0.0699880	−	0.0630175i
$885$	−6.31919	+	4.98170i	−0.212417	+	0.167458i
$886$	38.6811	−	42.9597i	1.29952	−	1.44326i
$887$	−13.1321	−	14.5847i	−0.440932	−	0.489705i	0.481183	−	0.876620i	$-0.340207\pi$
$887$	−13.1321	−	14.5847i	−0.440932	−	0.489705i	−0.922115	+	0.386915i	$0.873541\pi$
$888$	−19.2262	+	23.3148i	−0.645188	+	0.782394i
$889$	−38.5395	−	19.5118i	−1.29257	−	0.654406i
$890$	−27.5699	+	30.3631i	−0.924144	+	1.01777i
$891$	14.2036	+	13.7356i	0.475838	+	0.460159i
$892$	17.1875	+	1.80648i	0.575481	+	0.0604855i
$893$	−4.65552	+	2.68787i	−0.155791	+	0.0899461i
$894$	−0.335253	−	7.70970i	−0.0112125	−	0.257851i
$895$	−6.44312	+	7.09590i	−0.215370	+	0.237190i
$896$	−21.3063	+	26.4502i	−0.711793	+	0.883640i
$897$	7.63527	+	29.5448i	0.254934	+	0.986474i
$898$	20.2033	+	4.29435i	0.674194	+	0.143304i
$899$	−17.9104	−	31.0217i	−0.597345	−	1.03463i
$900$	−11.5579	+	6.27556i	−0.385263	+	0.209185i
$901$	0.620980	+	0.358523i	0.0206878	+	0.0119441i
$902$	9.98673	+	30.7360i	0.332522	+	1.02340i
$903$	−0.143362	+	22.6695i	−0.00477080	+	0.754394i
$904$	−2.58433	+	1.87763i	−0.0859536	+	0.0624489i
$905$	26.0860	−	18.7864i	0.867127	−	0.624480i
$906$	14.2450	−	27.3527i	0.473259	−	0.908731i
$907$	−5.28890	−	9.16065i	−0.175615	−	0.304174i	0.764759	−	0.644317i	$-0.222858\pi$
$907$	−5.28890	−	9.16065i	−0.175615	−	0.304174i	−0.940374	+	0.340142i	$0.889525\pi$
$908$	1.76170	−	0.784361i	0.0584642	−	0.0260299i
$909$	−15.0645	+	8.34343i	−0.499656	+	0.276734i
$910$	−1.49946	+	27.7594i	−0.0497065	+	0.920217i
$911$	14.3596	−	4.66573i	0.475756	−	0.154583i	−0.0613168	−	0.998118i	$-0.519530\pi$
$911$	14.3596	−	4.66573i	0.475756	−	0.154583i	0.537073	+	0.843536i	$0.319530\pi$
$912$	4.32812	+	11.5823i	0.143318	+	0.383528i
$913$	1.17016	+	5.50518i	0.0387267	+	0.182195i
$914$	−18.0776	−	16.2772i	−0.597955	−	0.538401i
$915$	−4.20664	−	16.5634i	−0.139067	−	0.547568i
$916$	−12.5260	−	4.06995i	−0.413871	−	0.134475i
$917$	2.09180	−	5.49161i	0.0690774	−	0.181349i
$918$	−4.36886	−	9.17197i	−0.144194	−	0.302720i
$919$	−43.0035	+	19.1464i	−1.41856	+	0.631582i	−0.965619	−	0.259961i	$-0.916290\pi$
$919$	−43.0035	+	19.1464i	−1.41856	+	0.631582i	−0.452936	+	0.891543i	$0.649624\pi$
$920$	−10.9148	−	24.7937i	−0.359851	−	0.817424i
$921$	19.7861	+	20.1416i	0.651975	+	0.663688i
$922$	26.7140	−	2.80775i	0.879778	−	0.0924684i
$923$	11.7027	+	36.0173i	0.385200	+	1.18552i
$924$	8.08090	−	3.53679i	0.265842	−	0.116352i
$925$	−4.40537	−	45.5786i	−0.144848	−	1.49862i
$926$	20.6278	+	11.9095i	0.677872	+	0.391369i
$927$	4.84629	+	55.6188i	0.159173	+	1.82676i
$928$	−36.2059	−	16.1199i	−1.18852	−	0.529162i
$929$	5.63279	+	53.5924i	0.184806	+	1.75831i	0.557334	+	0.830289i	$0.311824\pi$
$929$	5.63279	+	53.5924i	0.184806	+	1.75831i	−0.372528	+	0.928021i	$0.621509\pi$
$930$	3.95709	+	27.2906i	0.129758	+	0.894895i
$931$	9.13676	−	4.12454i	0.299445	−	0.135176i
$932$		−	14.4760i		−	0.474179i
$933$	−1.21674	−	27.9810i	−0.0398343	−	0.916056i
$934$	−10.9069	−	51.3128i	−0.356884	−	1.67901i
$935$	−5.17924	+	2.28004i	−0.169379	+	0.0745652i
$936$	9.07754	+	12.9738i	0.296709	+	0.424062i
$937$	54.3024	+	17.6439i	1.77398	+	0.576401i	0.998489	−	0.0549556i	$-0.0175017\pi$
$937$	54.3024	+	17.6439i	1.77398	+	0.576401i	0.775492	+	0.631357i	$0.217502\pi$
$938$	38.9633	−	19.9795i	1.27220	−	0.652354i
$939$	1.46780	−	23.9292i	0.0478999	−	0.780900i
$940$	−4.35064	+	5.93578i	−0.141902	+	0.193604i
$941$	52.9048	−	11.2453i	1.72465	−	0.366585i	0.764186	−	0.644996i	$-0.223141\pi$
$941$	52.9048	−	11.2453i	1.72465	−	0.366585i	0.960462	+	0.278410i	$0.0898074\pi$
$942$	−27.8667	−	14.5127i	−0.907945	−	0.472849i
$943$	47.7975	+	27.5959i	1.55650	+	0.898646i
$944$	8.37875	+	6.08752i	0.272705	+	0.198132i
$945$	28.9557	+	10.3233i	0.941928	+	0.335816i
$946$	−14.9028	+	10.8275i	−0.484533	+	0.352034i
$947$	21.1767	−	2.22576i	0.688150	−	0.0723275i	0.246002	−	0.969269i	$-0.420883\pi$
$947$	21.1767	−	2.22576i	0.688150	−	0.0723275i	0.442148	+	0.896942i	$0.354216\pi$
$948$	−10.0430	−	20.1519i	−0.326180	−	0.654504i
$949$	−16.1956	−	28.0517i	−0.525732	−	0.910595i
$950$	−11.0532	−	5.03238i	−0.358612	−	0.163272i
$951$	9.18216	+	3.61882i	0.297752	+	0.117348i
$952$	5.80151	−	0.319048i	0.188028	−	0.0103404i
$953$	−12.7030	−	17.4841i	−0.411489	−	0.566366i	0.552092	−	0.833783i	$-0.313830\pi$
$953$	−12.7030	−	17.4841i	−0.411489	−	0.566366i	−0.963581	+	0.267417i	$0.913830\pi$
$954$	1.90571	−	2.52712i	0.0616998	−	0.0818184i
$955$	50.8629	−	22.3912i	1.64589	−	0.724562i
$956$	−17.7725	−	1.86797i	−0.574804	−	0.0604144i
$957$	−20.1945	−	25.3971i	−0.652796	−	0.820973i
$958$	−12.4495	+	17.1353i	−0.402225	+	0.553615i
$959$	−14.6441	−	9.45640i	−0.472883	−	0.305363i
$960$	−5.65351	−	5.80344i	−0.182466	−	0.187305i
$961$	−13.0852	−	2.78135i	−0.422105	−	0.0897211i
$962$	42.0944	−	8.94744i	1.35718	−	0.288477i
$963$	−20.1248	+	33.4665i	−0.648512	+	1.07844i
$964$	2.52023	−	11.8567i	0.0811711	−	0.381880i
$965$	5.01744	+	24.1004i	0.161517	+	0.775819i
$966$	20.3890	−	45.0260i	0.656006	−	1.44869i
$967$	41.8265	+	30.3887i	1.34505	+	0.977235i	0.999242	+	0.0389288i	$0.0123946\pi$
$967$	41.8265	+	30.3887i	1.34505	+	0.977235i	0.345806	+	0.938306i	$0.387605\pi$
$968$	10.1964	+	5.88690i	0.327725	+	0.189212i
$969$	1.32072	−	2.53599i	0.0424277	−	0.0814678i
$970$	−39.9648	+	4.03154i	−1.28319	+	0.129445i
$971$	0.384526	+	3.65852i	0.0123400	+	0.117408i	0.998958	−	0.0456424i	$-0.0145335\pi$
$971$	0.384526	+	3.65852i	0.0123400	+	0.117408i	−0.986618	+	0.163050i	$0.947867\pi$
$972$	−12.9652	+	4.32540i	−0.415858	+	0.138737i
$973$	−14.3260	+	28.2964i	−0.459269	+	0.907142i
$974$			48.3756i			1.55005i
$975$	−23.6294	−	4.16197i	−0.756746	−	0.133290i
$976$	−19.0483	+	10.9975i	−0.609721	+	0.352023i
$977$	24.7782	+	22.3104i	0.792724	+	0.713772i	0.962373	−	0.271732i	$-0.0875966\pi$
$977$	24.7782	+	22.3104i	0.792724	+	0.713772i	−0.169649	+	0.985505i	$0.554263\pi$
$978$	0.697487	−	2.51334i	0.0223032	−	0.0803677i
$979$	13.9544	+	19.2066i	0.445985	+	0.613846i
$980$	9.17306	−	10.2077i	0.293023	−	0.326073i
$981$	6.22988	+	32.1103i	0.198905	+	1.02520i
$982$	−5.75438	+	9.96688i	−0.183630	+	0.318056i
$983$	2.84143	−	27.0344i	0.0906274	−	0.862263i	−0.850900	−	0.525327i	$-0.823943\pi$
$983$	2.84143	−	27.0344i	0.0906274	−	0.862263i	0.941528	−	0.336935i	$-0.109390\pi$
$984$	28.2449	+	4.73168i	0.900413	+	0.150840i
$985$	6.52178	+	20.3613i	0.207801	+	0.648766i
$986$	5.15546	+	15.8669i	0.164183	+	0.505304i
$987$	17.1188	−	1.68988i	0.544898	−	0.0537893i
$988$	1.07497	−	3.30843i	0.0341995	−	0.105255i
$989$	−6.54069	+	30.7715i	−0.207982	+	0.978478i
$990$	7.19478	+	23.9205i	0.228665	+	0.760243i
$991$	−22.3443	+	4.74942i	−0.709789	+	0.150870i	−0.548639	−	0.836060i	$-0.684854\pi$
$991$	−22.3443	+	4.74942i	−0.709789	+	0.150870i	−0.161150	+	0.986930i	$0.551520\pi$
$992$	17.8119	−	7.93036i	0.565528	−	0.251789i
$993$	18.8391	−	47.8011i	0.597840	−	1.51692i
$994$	21.8349	−	57.3233i	0.692562	−	1.81819i
$995$	−4.22702	+	0.880018i	−0.134005	+	0.0278985i
$996$	−3.75138	−	1.04106i	−0.118867	−	0.0329873i
$997$	−7.62009	+	17.1150i	−0.241331	+	0.542038i	−0.993084	−	0.117407i	$-0.962542\pi$
$997$	−7.62009	+	17.1150i	−0.241331	+	0.542038i	0.751753	+	0.659445i	$0.229209\pi$
$998$	18.8288	+	16.9536i	0.596017	+	0.536656i
$999$	3.75872	−	47.4388i	0.118921	−	1.50090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.17	✓	608
3.2	odd	2	inner	525.2.bm.a.131.60	yes	608
7.3	odd	6	inner	525.2.bm.a.206.17	yes	608
21.17	even	6	inner	525.2.bm.a.206.60	yes	608
25.21	even	5	inner	525.2.bm.a.446.60	yes	608
75.71	odd	10	inner	525.2.bm.a.446.17	yes	608
175.171	odd	30	inner	525.2.bm.a.521.60	yes	608
525.521	even	30	inner	525.2.bm.a.521.17	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.17	✓	608	1.1	even	1	trivial
525.2.bm.a.131.60	yes	608	3.2	odd	2	inner
525.2.bm.a.206.17	yes	608	7.3	odd	6	inner
525.2.bm.a.206.60	yes	608	21.17	even	6	inner
525.2.bm.a.446.17	yes	608	75.71	odd	10	inner
525.2.bm.a.446.60	yes	608	25.21	even	5	inner
525.2.bm.a.521.17	yes	608	525.521	even	30	inner
525.2.bm.a.521.60	yes	608	175.171	odd	30	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.352641 + 1.65904i) q^{2} +(-1.23560 + 1.21379i) q^{3} +(-0.800979 - 0.356619i) q^{4} +(-2.12372 - 0.699871i) q^{5} +(-1.57801 - 2.47795i) q^{6} +(-1.86600 + 1.87565i) q^{7} +(-1.11979 + 1.54126i) q^{8} +(0.0534131 - 2.99952i) q^{9} +O(q^{10})\)	\(q+(-0.352641 + 1.65904i) q^{2} +(-1.23560 + 1.21379i) q^{3} +(-0.800979 - 0.356619i) q^{4} +(-2.12372 - 0.699871i) q^{5} +(-1.57801 - 2.47795i) q^{6} +(-1.86600 + 1.87565i) q^{7} +(-1.11979 + 1.54126i) q^{8} +(0.0534131 - 2.99952i) q^{9} +(1.91003 - 3.27654i) q^{10} +(-1.63151 - 1.46902i) q^{11} +(1.42255 - 0.531584i) q^{12} +(2.63489 + 0.856127i) q^{13} +(-2.45375 - 3.75720i) q^{14} +(3.47356 - 1.71299i) q^{15} +(-3.33549 - 3.70444i) q^{16} +(-0.120494 + 1.14642i) q^{17} +(4.95751 + 1.14637i) q^{18} +(0.582481 + 1.30827i) q^{19} +(1.45147 + 1.31794i) q^{20} +(0.0289797 - 4.58248i) q^{21} +(3.01251 - 2.18871i) q^{22} +(1.32216 - 6.22025i) q^{23} +(-0.487157 - 3.26357i) q^{24} +(4.02036 + 2.97266i) q^{25} +(-2.34952 + 4.06949i) q^{26} +(3.57480 + 3.77104i) q^{27} +(2.16352 - 0.836903i) q^{28} +(-5.01558 - 6.90335i) q^{29} +(1.61701 + 6.36687i) q^{30} +(4.17491 + 0.438801i) q^{31} +(4.02233 - 2.32229i) q^{32} +(3.79898 - 0.165197i) q^{33} +(-1.85947 - 0.604179i) q^{34} +(5.27557 - 2.67739i) q^{35} +(-1.11247 + 2.38351i) q^{36} +(-6.12804 - 6.80588i) q^{37} +(-2.37589 + 0.505011i) q^{38} +(-4.29483 + 2.14038i) q^{39} +(3.45680 - 2.48949i) q^{40} +(-2.68196 + 8.25424i) q^{41} +(7.59232 + 1.66405i) q^{42} -4.94699 q^{43} +(0.782926 + 1.75848i) q^{44} +(-2.21272 + 6.33276i) q^{45} +(9.85342 + 4.38703i) q^{46} +(0.392378 + 3.73322i) q^{47} +(8.61776 + 0.528607i) q^{48} +(-0.0361019 - 6.99991i) q^{49} +(-6.34951 + 5.62167i) q^{50} +(-1.24264 - 1.56277i) q^{51} +(-1.80518 - 1.62539i) q^{52} +(0.253006 - 0.568260i) q^{53} +(-7.51695 + 4.60093i) q^{54} +(2.43675 + 4.26163i) q^{55} +(-0.801331 - 4.97632i) q^{56} +(-2.30769 - 0.909491i) q^{57} +(13.2217 - 5.88666i) q^{58} +(-2.03225 + 0.431968i) q^{59} +(-3.39314 + 0.133333i) q^{60} +(0.917392 - 4.31599i) q^{61} +(-2.20023 + 6.77162i) q^{62} +(5.52638 + 5.69729i) q^{63} +(-0.646440 - 1.98954i) q^{64} +(-4.99658 - 3.66226i) q^{65} +(-1.06561 + 6.36093i) q^{66} +(-1.01995 + 9.70418i) q^{67} +(0.505348 - 0.875288i) q^{68} +(5.91644 + 9.29057i) q^{69} +(2.58152 + 9.69655i) q^{70} +(8.03467 + 11.0588i) q^{71} +(4.56323 + 3.44116i) q^{72} +(-8.68851 - 7.82317i) q^{73} +(13.4522 - 7.76665i) q^{74} +(-8.57575 + 1.20687i) q^{75} -1.25562i q^{76} +(5.79976 - 0.318952i) q^{77} +(-2.03645 - 7.88009i) q^{78} +(-1.54978 - 14.7452i) q^{79} +(4.49102 + 10.2016i) q^{80} +(-8.99429 - 0.320428i) q^{81} +(-12.7484 - 7.36028i) q^{82} +(-2.07400 - 1.50685i) q^{83} +(-1.65741 + 3.66014i) q^{84} +(1.05824 - 2.35034i) q^{85} +(1.74451 - 8.20727i) q^{86} +(14.5765 + 2.44190i) q^{87} +(4.09109 - 0.869588i) q^{88} +(-10.5774 - 2.24831i) q^{89} +(-9.72604 - 5.90418i) q^{90} +(-6.52249 + 3.34459i) q^{91} +(-3.27728 + 4.51079i) q^{92} +(-5.69113 + 4.52529i) q^{93} +(-6.33195 - 0.665514i) q^{94} +(-0.321402 - 3.18607i) q^{95} +(-2.15120 + 7.75169i) q^{96} +(-6.22524 - 8.56831i) q^{97} +(11.6259 + 2.40856i) q^{98} +(-4.49351 + 4.81530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

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