LMFDB - Embedded newform 285.2.bi.a.233.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(17,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("285.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bi (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$36$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.35
Character	$\chi$	$=$	285.233
Dual form			285.2.bi.a.137.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29521 + 1.07028i) q^{2} +(0.116537 + 1.72813i) q^{3} +(2.83694 + 3.38094i) q^{4} +(-1.19209 - 1.89180i) q^{5} +(-1.58209 + 4.09115i) q^{6} +(-1.25451 - 0.336146i) q^{7} +(1.58194 + 5.90389i) q^{8} +(-2.97284 + 0.402780i) q^{9} +O(q^{10})$	\(q+(2.29521 + 1.07028i) q^{2} +(0.116537 + 1.72813i) q^{3} +(2.83694 + 3.38094i) q^{4} +(-1.19209 - 1.89180i) q^{5} +(-1.58209 + 4.09115i) q^{6} +(-1.25451 - 0.336146i) q^{7} +(1.58194 + 5.90389i) q^{8} +(-2.97284 + 0.402780i) q^{9} +(-0.711347 - 5.61796i) q^{10} +(3.04712 + 1.75926i) q^{11} +(-5.51207 + 5.29660i) q^{12} +(1.60756 - 2.29584i) q^{13} +(-2.51961 - 2.11420i) q^{14} +(3.13035 - 2.28055i) q^{15} +(-1.15510 + 6.55091i) q^{16} +(2.30214 + 1.07351i) q^{17} +(-7.25439 - 2.25729i) q^{18} +(-2.79661 - 3.34349i) q^{19} +(3.01418 - 9.39731i) q^{20} +(0.434705 - 2.20713i) q^{21} +(5.11090 + 7.29913i) q^{22} +(0.497076 - 5.68160i) q^{23} +(-10.0183 + 3.42181i) q^{24} +(-2.15785 + 4.51040i) q^{25} +(6.14688 - 3.54890i) q^{26} +(-1.04250 - 5.09050i) q^{27} +(-2.42249 - 5.19505i) q^{28} +(3.39948 + 1.23731i) q^{29} +(9.62564 - 1.88400i) q^{30} +(-2.43171 - 4.21185i) q^{31} +(-2.65091 + 3.78589i) q^{32} +(-2.68511 + 5.47083i) q^{33} +(4.13496 + 4.92786i) q^{34} +(0.859569 + 2.77401i) q^{35} +(-9.79554 - 8.90831i) q^{36} +(-7.43438 + 7.43438i) q^{37} +(-2.84036 - 10.6672i) q^{38} +(4.15483 + 2.51052i) q^{39} +(9.28318 - 10.0307i) q^{40} +(-3.46983 - 0.611825i) q^{41} +(3.35998 - 4.60058i) q^{42} +(-0.226718 - 2.59140i) q^{43} +(2.69657 + 15.2930i) q^{44} +(4.30587 + 5.14388i) q^{45} +(7.22177 - 12.5085i) q^{46} +(3.58571 + 7.68957i) q^{47} +(-11.4554 - 1.23274i) q^{48} +(-4.60137 - 2.65660i) q^{49} +(-9.78009 + 8.04284i) q^{50} +(-1.58687 + 4.10350i) q^{51} +(12.3226 - 1.07809i) q^{52} +(-1.19119 + 13.6154i) q^{53} +(3.05548 - 12.7996i) q^{54} +(-0.304272 - 7.86175i) q^{55} -7.93826i q^{56} +(5.45207 - 5.22254i) q^{57} +(6.47827 + 6.47827i) q^{58} +(5.48561 - 1.99660i) q^{59} +(16.5910 + 4.11375i) q^{60} +(4.19756 - 3.52217i) q^{61} +(-1.07346 - 12.2697i) q^{62} +(3.86486 + 0.494014i) q^{63} +(1.38520 - 0.799744i) q^{64} +(-6.25963 - 0.304351i) q^{65} +(-12.0182 + 9.68290i) q^{66} +(-11.1761 + 5.21149i) q^{67} +(2.90159 + 10.8289i) q^{68} +(9.87645 + 0.196894i) q^{69} +(-0.996058 + 7.28692i) q^{70} +(7.10233 - 8.46423i) q^{71} +(-7.08083 - 16.9141i) q^{72} +(-7.18468 + 5.03077i) q^{73} +(-25.0203 + 9.10666i) q^{74} +(-8.04601 - 3.20340i) q^{75} +(3.37031 - 18.9405i) q^{76} +(-3.23128 - 3.23128i) q^{77} +(6.84928 + 10.2090i) q^{78} +(-5.37968 - 0.948582i) q^{79} +(13.7700 - 5.62404i) q^{80} +(8.67554 - 2.39480i) q^{81} +(-7.30918 - 5.11795i) q^{82} +(-13.8880 - 3.72127i) q^{83} +(8.69539 - 4.79179i) q^{84} +(-0.713495 - 5.63492i) q^{85} +(2.25315 - 6.19047i) q^{86} +(-1.74206 + 6.01892i) q^{87} +(-5.56608 + 20.7729i) q^{88} +(1.10014 + 6.23923i) q^{89} +(4.37752 + 16.4148i) q^{90} +(-2.78844 + 2.33978i) q^{91} +(20.6193 - 14.4378i) q^{92} +(6.99523 - 4.69314i) q^{93} +21.4869i q^{94} +(-2.99143 + 9.27639i) q^{95} +(-6.85142 - 4.13991i) q^{96} +(-1.61322 + 3.45955i) q^{97} +(-7.71783 - 11.0222i) q^{98} +(-9.76719 - 4.00266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	2.29521	+	1.07028i	1.62296	+	0.756799i	0.999682	−	0.0252003i	$-0.00802235\pi$
$2$	2.29521	+	1.07028i	1.62296	+	0.756799i	0.623279	+	0.782000i	$0.285800\pi$
$3$	0.116537	+	1.72813i	0.0672825	+	0.997734i
$3$	0.116537	+	1.72813i	0.0672825	+	0.997734i
$4$	2.83694	+	3.38094i	1.41847	+	1.69047i
$5$	−1.19209	−	1.89180i	−0.533119	−	0.846041i
$5$	−1.19209	−	1.89180i	−0.533119	−	0.846041i
$6$	−1.58209	+	4.09115i	−0.645887	+	1.67020i
$7$	−1.25451	−	0.336146i	−0.474161	−	0.127051i	0.0138214	−	0.999904i	$-0.495600\pi$
$7$	−1.25451	−	0.336146i	−0.474161	−	0.127051i	−0.487983	+	0.872853i	$0.662267\pi$
$8$	1.58194	+	5.90389i	0.559301	+	2.08734i
$9$	−2.97284	+	0.402780i	−0.990946	+	0.134260i
$10$	−0.711347	−	5.61796i	−0.224948	−	1.77655i
$11$	3.04712	+	1.75926i	0.918741	+	0.530436i	0.883233	−	0.468934i	$-0.155362\pi$
$11$	3.04712	+	1.75926i	0.918741	+	0.530436i	0.0355081	+	0.999369i	$0.488695\pi$
$12$	−5.51207	+	5.29660i	−1.59120	+	1.52900i
$13$	1.60756	−	2.29584i	0.445857	−	0.636750i	−0.531821	−	0.846857i	$-0.678492\pi$
$13$	1.60756	−	2.29584i	0.445857	−	0.636750i	0.977679	+	0.210106i	$0.0673810\pi$
$14$	−2.51961	−	2.11420i	−0.673393	−	0.565044i
$15$	3.13035	−	2.28055i	0.808254	−	0.588834i
$16$	−1.15510	+	6.55091i	−0.288775	+	1.63773i
$17$	2.30214	+	1.07351i	0.558352	+	0.260364i	0.681244	−	0.732056i	$-0.261439\pi$
$17$	2.30214	+	1.07351i	0.558352	+	0.260364i	−0.122892	+	0.992420i	$0.539217\pi$
$18$	−7.25439	−	2.25729i	−1.70988	−	0.532048i
$19$	−2.79661	−	3.34349i	−0.641587	−	0.767050i
$19$	−2.79661	−	3.34349i	−0.641587	−	0.767050i
$20$	3.01418	−	9.39731i	0.673991	−	2.10130i
$21$	0.434705	−	2.20713i	0.0948604	−	0.481635i
$22$	5.11090	+	7.29913i	1.08965	+	1.55618i
$23$	0.497076	−	5.68160i	0.103647	−	1.18470i	−0.749131	−	0.662422i	$-0.769529\pi$
$23$	0.497076	−	5.68160i	0.103647	−	1.18470i	0.852778	−	0.522273i	$-0.174916\pi$
$24$	−10.0183	+	3.42181i	−2.04498	+	0.698475i
$25$	−2.15785	+	4.51040i	−0.431569	+	0.902080i
$26$	6.14688	−	3.54890i	1.20550	−	0.695997i
$27$	−1.04250	−	5.09050i	−0.200629	−	0.979667i
$28$	−2.42249	−	5.19505i	−0.457808	−	0.981772i
$29$	3.39948	+	1.23731i	0.631268	+	0.229763i	0.637783	−	0.770216i	$-0.279852\pi$
$29$	3.39948	+	1.23731i	0.631268	+	0.229763i	−0.00651533	+	0.999979i	$0.502074\pi$
$30$	9.62564	−	1.88400i	1.75739	−	0.343969i
$31$	−2.43171	−	4.21185i	−0.436749	−	0.756471i	0.560688	−	0.828027i	$-0.310537\pi$
$31$	−2.43171	−	4.21185i	−0.436749	−	0.756471i	−0.997437	+	0.0715563i	$0.977203\pi$
$32$	−2.65091	+	3.78589i	−0.468619	+	0.669257i
$33$	−2.68511	+	5.47083i	−0.467418	+	0.952349i
$34$	4.13496	+	4.92786i	0.709140	+	0.845121i
$35$	0.859569	+	2.77401i	0.145294	+	0.468893i
$36$	−9.79554	−	8.90831i	−1.63259	−	1.48472i
$37$	−7.43438	+	7.43438i	−1.22220	+	1.22220i	−0.255358	+	0.966847i	$0.582193\pi$
$37$	−7.43438	+	7.43438i	−1.22220	+	1.22220i	−0.966847	+	0.255358i	$0.917807\pi$
$38$	−2.84036	−	10.6672i	−0.460768	−	1.73045i
$39$	4.15483	+	2.51052i	0.665306	+	0.402005i
$40$	9.28318	−	10.0307i	1.46780	−	1.58599i
$41$	−3.46983	−	0.611825i	−0.541897	−	0.0955510i	−0.104002	−	0.994577i	$-0.533165\pi$
$41$	−3.46983	−	0.611825i	−0.541897	−	0.0955510i	−0.437895	+	0.899026i	$0.644276\pi$
$42$	3.35998	−	4.60058i	0.518456	−	0.709885i
$43$	−0.226718	−	2.59140i	−0.0345742	−	0.395185i	−0.993689	−	0.112168i	$-0.964220\pi$
$43$	−0.226718	−	2.59140i	−0.0345742	−	0.395185i	0.959115	−	0.283017i	$-0.0913351\pi$
$44$	2.69657	+	15.2930i	0.406524	+	2.30551i
$45$	4.30587	+	5.14388i	0.641881	+	0.766804i
$46$	7.22177	−	12.5085i	1.06479	−	1.84427i
$47$	3.58571	+	7.68957i	0.523029	+	1.12164i	0.973466	+	0.228831i	$0.0734904\pi$
$47$	3.58571	+	7.68957i	0.523029	+	1.12164i	−0.450437	+	0.892808i	$0.648732\pi$
$48$	−11.4554	−	1.23274i	−1.65345	−	0.177931i
$49$	−4.60137	−	2.65660i	−0.657339	−	0.379515i
$50$	−9.78009	+	8.04284i	−1.38311	+	1.13743i
$51$	−1.58687	+	4.10350i	−0.222206	+	0.574604i
$52$	12.3226	−	1.07809i	1.70884	−	0.149504i
$53$	−1.19119	+	13.6154i	−0.163622	+	1.87021i	0.261671	+	0.965157i	$0.415727\pi$
$53$	−1.19119	+	13.6154i	−0.163622	+	1.87021i	−0.425293	+	0.905056i	$0.639829\pi$
$54$	3.05548	−	12.7996i	0.415798	−	1.74180i
$55$	−0.304272	−	7.86175i	−0.0410280	−	1.06008i
$56$		−	7.93826i		−	1.06080i
$57$	5.45207	−	5.22254i	0.722145	−	0.691742i
$58$	6.47827	+	6.47827i	0.850639	+	0.850639i
$59$	5.48561	−	1.99660i	0.714165	−	0.259935i	0.0407184	−	0.999171i	$-0.487035\pi$
$59$	5.48561	−	1.99660i	0.714165	−	0.259935i	0.673447	+	0.739236i	$0.264813\pi$
$60$	16.5910	+	4.11375i	2.14189	+	0.531083i
$61$	4.19756	−	3.52217i	0.537443	−	0.450968i	−0.333219	−	0.942849i	$-0.608135\pi$
$61$	4.19756	−	3.52217i	0.537443	−	0.450968i	0.870662	+	0.491881i	$0.163691\pi$
$62$	−1.07346	−	12.2697i	−0.136330	−	1.55825i
$63$	3.86486	+	0.494014i	0.486926	+	0.0622399i
$64$	1.38520	−	0.799744i	0.173150	−	0.0999680i
$65$	−6.25963	−	0.304351i	−0.776411	−	0.0377500i
$66$	−12.0182	+	9.68290i	−1.47934	+	1.19188i
$67$	−11.1761	+	5.21149i	−1.36537	+	0.636684i	−0.960652	−	0.277755i	$-0.910410\pi$
$67$	−11.1761	+	5.21149i	−1.36537	+	0.636684i	−0.404722	+	0.914440i	$0.632632\pi$
$68$	2.90159	+	10.8289i	0.351869	+	1.31319i
$69$	9.87645	+	0.196894i	1.18898	+	0.0237032i
$70$	−0.996058	+	7.28692i	−0.119052	+	0.870953i
$71$	7.10233	−	8.46423i	0.842892	−	1.00452i	−0.156965	−	0.987604i	$-0.550171\pi$
$71$	7.10233	−	8.46423i	0.842892	−	1.00452i	0.999857	−	0.0169151i	$-0.00538451\pi$
$72$	−7.08083	−	16.9141i	−0.834484	−	1.99335i
$73$	−7.18468	+	5.03077i	−0.840903	+	0.588807i	−0.912708	−	0.408612i	$-0.866013\pi$
$73$	−7.18468	+	5.03077i	−0.840903	+	0.588807i	0.0718051	+	0.997419i	$0.477124\pi$
$74$	−25.0203	+	9.10666i	−2.90855	+	1.05863i
$75$	−8.04601	−	3.20340i	−0.929073	−	0.369897i
$76$	3.37031	−	18.9405i	0.386601	−	2.17262i
$77$	−3.23128	−	3.23128i	−0.368239	−	0.368239i
$78$	6.84928	+	10.2090i	0.775529	+	1.15594i
$79$	−5.37968	−	0.948582i	−0.605261	−	0.106724i	−0.137385	−	0.990518i	$-0.543870\pi$
$79$	−5.37968	−	0.948582i	−0.605261	−	0.106724i	−0.467876	+	0.883794i	$0.654981\pi$
$80$	13.7700	−	5.62404i	1.53953	−	0.628787i
$81$	8.67554	−	2.39480i	0.963948	−	0.266089i
$82$	−7.30918	−	5.11795i	−0.807164	−	0.565183i
$83$	−13.8880	−	3.72127i	−1.52440	−	0.408462i	−0.603214	−	0.797580i	$-0.706113\pi$
$83$	−13.8880	−	3.72127i	−1.52440	−	0.408462i	−0.921188	+	0.389117i	$0.872780\pi$
$84$	8.69539	−	4.79179i	0.948745	−	0.522827i
$85$	−0.713495	−	5.63492i	−0.0773894	−	0.611193i
$86$	2.25315	−	6.19047i	0.242963	−	0.667536i
$87$	−1.74206	+	6.01892i	−0.186769	+	0.645296i
$88$	−5.56608	+	20.7729i	−0.593346	+	2.21440i
$89$	1.10014	+	6.23923i	0.116615	+	0.661357i	0.985938	+	0.167112i	$0.0534443\pi$
$89$	1.10014	+	6.23923i	0.116615	+	0.661357i	−0.869323	+	0.494245i	$0.835445\pi$
$90$	4.37752	+	16.4148i	0.461432	+	1.73027i
$91$	−2.78844	+	2.33978i	−0.292308	+	0.245276i
$92$	20.6193	−	14.4378i	2.14971	−	1.50524i
$93$	6.99523	−	4.69314i	0.725371	−	0.486656i
$94$			21.4869i			2.21621i
$95$	−2.99143	+	9.27639i	−0.306914	+	0.951737i
$96$	−6.85142	−	4.13991i	−0.699270	−	0.422527i
$97$	−1.61322	+	3.45955i	−0.163797	+	0.351265i	−0.971026	−	0.238975i	$-0.923189\pi$
$97$	−1.61322	+	3.45955i	−0.163797	+	0.351265i	0.807228	+	0.590239i	$0.200967\pi$
$98$	−7.71783	−	11.0222i	−0.779619	−	1.11341i
$99$	−9.76719	−	4.00266i	−0.981640	−	0.402283i
$100$	−21.3711	+	5.50020i	−2.13711	+	0.550020i
$101$	2.02208	−	0.356548i	0.201205	−	0.0354778i	−0.0721374	−	0.997395i	$-0.522982\pi$
$101$	2.02208	−	0.356548i	0.201205	−	0.0354778i	0.273342	+	0.961917i	$0.411871\pi$
$102$	−8.03408	+	7.72001i	−0.795493	+	0.764395i
$103$	9.22632	−	2.47219i	0.909096	−	0.243592i	0.226178	−	0.974086i	$-0.427377\pi$
$103$	9.22632	−	2.47219i	0.909096	−	0.243592i	0.682919	+	0.730494i	$0.260710\pi$
$104$	16.0974	+	5.85898i	1.57848	+	0.574521i
$105$	−4.69366	+	1.80872i	−0.458055	+	0.176513i
$106$	−17.3062	+	29.9753i	−1.68093	+	2.91145i
$107$	−2.98842	+	11.1529i	−0.288901	+	1.07819i	0.657040	+	0.753856i	$0.271808\pi$
$107$	−2.98842	+	11.1529i	−0.288901	+	1.07819i	−0.945941	+	0.324339i	$0.894858\pi$
$108$	14.2531	−	17.9661i	1.37151	−	1.72879i
$109$	5.73789	−	6.83815i	0.549590	−	0.654976i	−0.417719	−	0.908576i	$-0.637170\pi$
$109$	5.73789	−	6.83815i	0.549590	−	0.654976i	0.967309	+	0.253600i	$0.0816148\pi$
$110$	7.71587	−	18.3700i	0.735679	−	1.75151i
$111$	−13.7139	−	11.9812i	−1.30167	−	1.13720i
$112$	3.65115	−	7.82991i	0.345001	−	0.739857i
$113$	0.490668	−	0.490668i	0.0461581	−	0.0461581i	−0.683651	−	0.729809i	$-0.739609\pi$
$113$	0.490668	−	0.490668i	0.0461581	−	0.0461581i	0.729809	+	0.683651i	$0.239609\pi$
$114$	18.1032	−	6.15162i	1.69552	−	0.576152i
$115$	−11.3410	+	5.83260i	−1.05756	+	0.543893i
$116$	5.46086	+	15.0036i	0.507028	+	1.39305i
$117$	−3.85430	+	7.47264i	−0.356330	+	0.690846i
$118$	14.7275	+	1.28849i	1.35578	+	0.118615i
$119$	−2.52721	−	2.12058i	−0.231669	−	0.194394i
$120$	18.4161	+	14.8736i	1.68115	+	1.35776i
$121$	0.689963	+	1.19505i	0.0627239	+	0.108641i
$122$	13.4040	−	3.59159i	1.21354	−	0.325168i
$123$	0.652948	−	6.06761i	0.0588743	−	0.547098i
$124$	7.34137	−	20.1702i	0.659274	−	1.81134i
$125$	11.1051	−	1.29457i	0.993274	−	0.115790i
$126$	8.34194	+	5.27033i	0.743159	+	0.469518i
$127$	4.83532	+	3.38573i	0.429065	+	0.300435i	0.768089	−	0.640343i	$-0.221208\pi$
$127$	4.83532	+	3.38573i	0.429065	+	0.300435i	−0.339024	+	0.940778i	$0.610097\pi$
$128$	13.2435	−	1.15866i	1.17057	−	0.102412i
$129$	4.45185	−	0.693791i	0.391963	−	0.0610849i
$130$	−14.0414	−	7.39808i	−1.23152	−	0.648854i
$131$	−5.03994	−	13.8471i	−0.440342	−	1.20983i	−0.939268	−	0.343184i	$-0.888494\pi$
$131$	−5.03994	−	13.8471i	−0.440342	−	1.20983i	0.498926	−	0.866644i	$-0.333728\pi$
$132$	−26.1140	+	6.44222i	−2.27293	+	0.560723i
$133$	2.38448	+	5.13452i	0.206761	+	0.445220i
$134$	−31.2292			−2.69779
$135$	−8.38748	+	8.04054i	−0.721879	+	0.692019i
$136$	−2.69601	+	15.2898i	−0.231181	+	1.31109i
$137$	−1.95005	−	0.170608i	−0.166604	−	0.0145760i	0.00354829	−	0.999994i	$-0.498871\pi$
$137$	−1.95005	−	0.170608i	−0.166604	−	0.0145760i	−0.170153	+	0.985418i	$0.554426\pi$
$138$	22.4578	+	11.0224i	1.91174	+	0.938292i
$139$	−1.81184	+	0.319476i	−0.153678	+	0.0270976i	−0.249958	−	0.968257i	$-0.580417\pi$
$139$	−1.81184	+	0.319476i	−0.153678	+	0.0270976i	0.0962798	+	0.995354i	$0.469306\pi$
$140$	−6.94019	+	10.7758i	−0.586553	+	0.910725i
$141$	−12.8707	+	7.09267i	−1.08391	+	0.597311i
$142$	25.3604	−	11.8258i	2.12820	−	0.992396i
$143$	8.93740	−	4.16758i	0.747383	−	0.348510i
$144$	0.795354	−	19.9400i	0.0662795	−	1.66167i
$145$	−1.71174	−	7.90613i	−0.142152	−	0.656569i
$146$	−21.8747	+	3.85710i	−1.81036	+	0.319216i
$147$	4.05471	−	8.26134i	0.334427	−	0.681384i
$148$	−46.2261	−	4.04426i	−3.79976	−	0.332436i
$149$	−1.38354	+	7.84645i	−0.113344	+	0.642806i	0.874213	+	0.485543i	$0.161378\pi$
$149$	−1.38354	+	7.84645i	−0.113344	+	0.642806i	−0.987557	+	0.157263i	$0.949733\pi$
$150$	−15.0388	−	15.9639i	−1.22791	−	1.30345i
$151$	−0.887249			−0.0722033			−0.0361016	−	0.999348i	$-0.511494\pi$
$151$	−0.887249			−0.0722033			−0.0361016	+	0.999348i	$0.511494\pi$
$152$	15.3155	−	21.8001i	1.24225	−	1.76822i
$153$	−7.27629	−	2.26410i	−0.588253	−	0.183042i
$154$	−3.95812	−	10.8749i	−0.318955	−	0.876321i
$155$	−5.06918	+	9.62123i	−0.407166	+	0.772796i
$156$	3.29912	+	21.1694i	0.264141	+	1.69491i
$157$	7.76436	−	0.679294i	0.619664	−	0.0542135i	0.226999	−	0.973895i	$-0.427109\pi$
$157$	7.76436	−	0.679294i	0.619664	−	0.0542135i	0.392665	+	0.919682i	$0.371553\pi$
$158$	−11.3323	−	7.93494i	−0.901547	−	0.631270i
$159$	−23.6679	−	0.471836i	−1.87698	−	0.0374190i
$160$	10.3223	+	0.501881i	0.816048	+	0.0396772i
$161$	−2.53343	+	6.96055i	−0.199662	+	0.548568i
$162$	22.4753	+	3.78863i	1.76583	+	0.297663i
$163$	21.2530	−	5.69473i	1.66466	−	0.446046i	0.701000	−	0.713161i	$-0.252737\pi$
$163$	21.2530	−	5.69473i	1.66466	−	0.446046i	0.963665	+	0.267115i	$0.0860705\pi$
$164$	−7.77517	−	13.4670i	−0.607139	−	1.05160i
$165$	13.5506	−	1.44200i	1.05491	−	0.112260i
$166$	−27.8931	−	23.4051i	−2.16492	−	1.81658i
$167$	3.71984	+	0.325444i	0.287850	+	0.0251836i	0.230166	−	0.973151i	$-0.426073\pi$
$167$	3.71984	+	0.325444i	0.287850	+	0.0251836i	0.0576838	+	0.998335i	$0.481628\pi$
$168$	13.7183	−	0.925099i	1.05839	−	0.0713730i
$169$	1.75965	+	4.83461i	0.135358	+	0.371893i
$170$	4.39330	−	13.6970i	0.336950	−	1.05051i
$171$	9.66057	+	8.81325i	0.738762	+	0.673966i
$172$	8.11817	−	8.11817i	0.619005	−	0.619005i
$173$	4.33294	−	9.29202i	0.329427	−	0.706459i	−0.669925	−	0.742428i	$-0.733674\pi$
$173$	4.33294	−	9.29202i	0.329427	−	0.706459i	0.999353	+	0.0359689i	$0.0114517\pi$
$174$	−10.4403	+	11.9502i	−0.791478	+	0.905944i
$175$	4.22320	−	4.93300i	0.319244	−	0.372900i
$176$	−15.0445	+	17.9293i	−1.13402	+	1.35147i
$177$	4.08965	+	9.24714i	0.307397	+	0.695058i
$178$	−4.15263	+	15.4978i	−0.311253	+	1.16161i
$179$	3.49438	−	6.05245i	0.261182	−	0.452381i	−0.705374	−	0.708835i	$-0.749221\pi$
$179$	3.49438	−	6.05245i	0.261182	−	0.452381i	0.966556	+	0.256454i	$0.0825543\pi$
$180$	−5.17562	+	29.1507i	−0.385768	+	2.17277i
$181$	9.61845	+	3.50083i	0.714933	+	0.260214i	0.673773	−	0.738938i	$-0.264672\pi$
$181$	9.61845	+	3.50083i	0.714933	+	0.260214i	0.0411601	+	0.999153i	$0.486895\pi$
$182$	−8.90428	+	2.38589i	−0.660029	+	0.176854i
$183$	6.57593	+	6.84346i	0.486107	+	0.505883i
$184$	34.3299	−	6.05328i	2.53083	−	0.446254i
$185$	22.9268	+	5.20195i	1.68561	+	0.382455i
$186$	21.0785	−	3.28495i	1.54555	−	0.240864i
$187$	5.12634	+	7.32117i	0.374875	+	0.535377i
$188$	−15.8255	+	33.9379i	−1.15419	+	2.47518i
$189$	−0.403320	+	6.73653i	−0.0293372	+	0.490010i
$190$	−16.7943	+	18.0896i	−1.21838	+	1.31236i
$191$			24.8382i			1.79723i	0.438739	+	0.898614i	$0.355425\pi$
$191$			24.8382i			1.79723i	−0.438739	+	0.898614i	$0.644575\pi$
$192$	1.54348	+	2.30060i	0.111391	+	0.166031i
$193$	−10.5854	+	7.41198i	−0.761954	+	0.533526i	−0.888744	−	0.458404i	$-0.848421\pi$
$193$	−10.5854	+	7.41198i	−0.761954	+	0.533526i	0.126790	+	0.991930i	$0.459533\pi$
$194$	−7.40536	+	6.21383i	−0.531674	+	0.446127i
$195$	−0.203521	−	10.8529i	−0.0145744	−	0.777192i
$196$	−4.07202	−	23.0936i	−0.290858	−	1.64954i
$197$	−0.908670	+	3.39120i	−0.0647400	+	0.241613i	−0.990712	−	0.135980i	$-0.956582\pi$
$197$	−0.908670	+	3.39120i	−0.0647400	+	0.241613i	0.925972	+	0.377593i	$0.123248\pi$
$198$	−18.1338	−	19.6406i	−1.28872	−	1.39579i
$199$	−2.29640	+	6.30930i	−0.162787	+	0.447254i	−0.994089	−	0.108567i	$-0.965374\pi$
$199$	−2.29640	+	6.30930i	−0.162787	+	0.447254i	0.831302	+	0.555821i	$0.187596\pi$
$200$	−30.0425	−	5.60449i	−2.12432	−	0.396298i
$201$	−10.3085	−	18.7063i	−0.727108	−	1.31944i
$202$	5.02272	+	1.34583i	0.353397	+	0.0946925i
$203$	−3.84877	−	2.69494i	−0.270131	−	0.189148i
$204$	−18.3755	+	6.27627i	−1.28654	+	0.439427i
$205$	2.97890	+	7.29359i	0.208055	+	0.509407i
$206$	23.8223	+	4.20051i	1.65978	+	0.292664i
$207$	0.810711	+	17.0907i	0.0563483	+	1.18788i
$208$	13.1829	+	13.1829i	0.914070	+	0.914070i
$209$	−2.63955	−	15.1080i	−0.182582	−	1.04504i
$210$	−12.7088	−	0.872120i	−0.876990	−	0.0601820i
$211$	10.4984	−	3.82111i	0.722740	−	0.263056i	0.0456515	−	0.998957i	$-0.485464\pi$
$211$	10.4984	−	3.82111i	0.722740	−	0.263056i	0.677089	+	0.735902i	$0.263241\pi$
$212$	−49.4120	+	34.5986i	−3.39363	+	2.37624i
$213$	15.4549	+	11.2873i	1.05895	+	0.773395i
$214$	−18.7958	+	22.3999i	−1.28485	+	1.53123i
$215$	−4.63215	+	3.51809i	−0.315910	+	0.239932i
$216$	28.4046	−	14.2077i	1.93269	−	0.966710i
$217$	1.63482	+	6.10123i	0.110979	+	0.414179i
$218$	20.4884	−	9.55389i	1.38765	−	0.647071i
$219$	−9.53108	−	11.8298i	−0.644051	−	0.799381i
$220$	25.7169	−	23.3320i	1.73383	−	1.57305i
$221$	6.16543	−	3.55961i	0.414732	−	0.239446i
$222$	−18.6532	−	42.1770i	−1.25192	−	2.83074i
$223$	0.554848	+	6.34194i	0.0371554	+	0.424688i	0.991878	+	0.127191i	$0.0405961\pi$
$223$	0.554848	+	6.34194i	0.0371554	+	0.424688i	−0.954723	+	0.297497i	$0.903848\pi$
$224$	4.59821	−	3.85835i	0.307231	−	0.257797i
$225$	4.59823	−	14.2778i	0.306549	−	0.951855i
$226$	1.65134	−	0.601037i	0.109845	−	0.0399804i
$227$	8.66241	+	8.66241i	0.574944	+	0.574944i	0.933506	−	0.358562i	$-0.116733\pi$
$227$	8.66241	+	8.66241i	0.574944	+	0.574944i	−0.358562	+	0.933506i	$0.616733\pi$
$228$	33.1243	+	3.61706i	2.19371	+	0.239546i
$229$		−	3.60011i		−	0.237902i	−0.992900	−	0.118951i	$-0.962047\pi$
$229$		−	3.60011i		−	0.237902i	0.992900	−	0.118951i	$-0.0379531\pi$
$230$	−32.2726	+	1.24904i	−2.12799	+	0.0823593i
$231$	5.20750	−	5.96063i	0.342629	−	0.392181i
$232$	−1.92716	+	22.0275i	−0.126524	+	1.44618i
$233$	−4.20002	+	0.367454i	−0.275153	+	0.0240727i	−0.223897	−	0.974613i	$-0.571878\pi$
$233$	−4.20002	+	0.367454i	−0.275153	+	0.0240727i	−0.0512557	+	0.998686i	$0.516322\pi$
$234$	−16.8442	+	13.0261i	−1.10114	+	0.851546i
$235$	10.2727	−	15.9501i	0.670116	−	1.04047i
$236$	22.3127	+	12.8822i	1.45243	+	0.838563i
$237$	1.01234	−	9.40731i	0.0657585	−	0.611070i
$238$	−3.53089	−	7.57201i	−0.228873	−	0.490820i
$239$	0.279956	−	0.484897i	0.0181088	−	0.0313654i	−0.856829	−	0.515601i	$-0.827569\pi$
$239$	0.279956	−	0.484897i	0.0181088	−	0.0313654i	0.874938	+	0.484235i	$0.160902\pi$
$240$	11.3238	+	23.1409i	0.730946	+	1.49374i
$241$	4.06831	+	23.0725i	0.262063	+	1.48623i	0.777270	+	0.629167i	$0.216604\pi$
$241$	4.06831	+	23.0725i	0.262063	+	1.48623i	−0.515208	+	0.857065i	$0.672285\pi$
$242$	0.304579	+	3.48135i	0.0195791	+	0.223790i
$243$	5.14954	+	14.7133i	0.330343	+	0.943861i
$244$	23.8165	+	4.19949i	1.52469	+	0.268845i
$245$	0.459472	+	11.8718i	0.0293546	+	0.758461i
$246$	7.99267	−	13.2276i	0.509594	−	0.843362i
$247$	−12.1718	+	1.04569i	−0.774476	+	0.0665357i
$248$	21.0195	−	21.0195i	1.33474	−	1.33474i
$249$	4.81236	−	24.4338i	0.304971	−	1.54843i
$250$	26.8742	+	8.91423i	1.69967	+	0.563786i
$251$	−15.2022	−	18.1172i	−0.959552	−	1.14355i	−0.989578	−	0.144000i	$-0.954004\pi$
$251$	−15.2022	−	18.1172i	−0.959552	−	1.14355i	0.0300262	−	0.999549i	$-0.490441\pi$
$252$	9.29414	+	14.4683i	0.585476	+	0.911418i
$253$	11.5100	−	16.4380i	0.723630	−	1.03345i
$254$	7.47443	+	12.9461i	0.468988	+	0.812310i
$255$	9.65470	−	1.88968i	0.604601	−	0.118337i
$256$	28.6308	+	10.4207i	1.78942	+	0.651297i
$257$	−3.10796	−	6.66504i	−0.193869	−	0.415754i	0.785211	−	0.619228i	$-0.212554\pi$
$257$	−3.10796	−	6.66504i	−0.193869	−	0.415754i	−0.979080	+	0.203474i	$0.934777\pi$
$258$	10.9605	+	3.17230i	0.682370	+	0.197499i
$259$	11.8256	−	6.82749i	0.734804	−	0.424239i
$260$	−16.7292	−	22.0268i	−1.03750	−	1.36605i
$261$	−10.6045	−	2.30908i	−0.656400	−	0.142928i
$262$	3.25250	−	37.1762i	0.200940	−	2.29676i
$263$	−11.4702	−	16.3811i	−0.707281	−	1.01010i	−0.998570	−	0.0534668i	$-0.982973\pi$
$263$	−11.4702	−	16.3811i	−0.707281	−	1.01010i	0.291289	−	0.956635i	$-0.405916\pi$
$264$	−36.5468	−	7.19808i	−2.24930	−	0.443011i
$265$	27.1776	−	13.9772i	1.66951	−	0.858614i
$266$	−0.0224552	+	14.3369i	−0.00137682	+	0.879051i
$267$	−10.6540	+	2.62829i	−0.652012	+	0.160849i
$268$	−49.3256	−	23.0009i	−3.01304	−	1.40500i
$269$	4.54921	−	25.7998i	0.277370	−	1.57304i	−0.453961	−	0.891022i	$-0.649989\pi$
$269$	4.54921	−	25.7998i	0.277370	−	1.57304i	0.731331	−	0.682023i	$-0.238899\pi$
$270$	−27.8566	+	9.47784i	−1.69530	+	0.576803i
$271$	−8.35306	−	7.00905i	−0.507412	−	0.425769i	0.352805	−	0.935697i	$-0.385228\pi$
$271$	−8.35306	−	7.00905i	−0.507412	−	0.425769i	−0.860217	+	0.509927i	$0.829672\pi$
$272$	−9.69166	+	13.8411i	−0.587643	+	0.839241i
$273$	−4.36839	−	4.54611i	−0.264387	−	0.275143i
$274$	−4.29320	−	2.47868i	−0.259361	−	0.149742i
$275$	−14.5102	+	9.94753i	−0.874996	+	0.599858i
$276$	27.3532	+	33.9502i	1.64647	+	2.04356i
$277$	−6.56685	−	24.5078i	−0.394564	−	1.47253i	−0.822522	−	0.568733i	$-0.807434\pi$
$277$	−6.56685	−	24.5078i	−0.394564	−	1.47253i	0.427959	−	0.903798i	$-0.359233\pi$
$278$	−4.50048	−	1.20590i	−0.269921	−	0.0723251i
$279$	8.92554	+	11.5417i	0.534358	+	0.690984i
$280$	−15.0176	+	9.46312i	−0.897476	+	0.565529i
$281$	12.4124	+	14.7926i	0.740464	+	0.882450i	0.996446	−	0.0842310i	$-0.0268434\pi$
$281$	12.4124	+	14.7926i	0.740464	+	0.882450i	−0.255982	+	0.966681i	$0.582399\pi$
$282$	−37.1321	+	2.50401i	−2.21118	+	0.149112i
$283$	−26.2237	−	12.2283i	−1.55884	−	0.726898i	−0.563754	−	0.825943i	$-0.690644\pi$
$283$	−26.2237	−	12.2283i	−1.55884	−	0.726898i	−0.995083	+	0.0990448i	$0.968421\pi$
$284$	48.7659			2.89372
$285$	−16.3794	−	4.08852i	−0.970231	−	0.242183i
$286$	24.9737			1.47673
$287$	4.14728	+	1.93391i	0.244806	+	0.114155i
$288$	6.35584	−	12.3226i	0.374521	−	0.726114i
$289$	−6.77994	−	8.08002i	−0.398820	−	0.475295i
$290$	4.53294	−	19.9783i	0.266184	−	1.17317i
$291$	−6.16655	−	2.38468i	−0.361489	−	0.139792i
$292$	−37.3912	−	10.0189i	−2.18816	−	0.586314i
$293$	4.88256	+	18.2220i	0.285242	+	1.06454i	0.948662	+	0.316291i	$0.102438\pi$
$293$	4.88256	+	18.2220i	0.285242	+	1.06454i	−0.663420	+	0.748247i	$0.730896\pi$
$294$	18.1483	−	14.6219i	1.05843	−	0.852765i
$295$	−10.3165	−	7.99757i	−0.600650	−	0.465637i
$296$	−55.6525	−	32.1310i	−3.23474	−	1.86758i
$297$	5.77887	−	17.3454i	0.335324	−	1.00648i
$298$	−11.5734	+	16.5285i	−0.670428	+	0.957471i
$299$	−12.2449	−	10.2747i	−0.708143	−	0.594203i
$300$	−11.9955	−	36.2909i	−0.692563	−	2.09526i
$301$	−0.586667	+	3.32715i	−0.0338149	+	0.191774i
$302$	−2.03643	−	0.949601i	−0.117183	−	0.0546434i
$303$	0.851806	+	3.45286i	0.0489350	+	0.198362i
$304$	25.1333	−	14.4583i	1.44149	−	0.829239i
$305$	−11.6671	−	3.74222i	−0.668058	−	0.214279i
$306$	−14.2774	−	12.9842i	−0.816186	−	0.742260i
$307$	6.01990	+	8.59731i	0.343574	+	0.490674i	0.953337	−	0.301910i	$-0.0976241\pi$
$307$	6.01990	+	8.59731i	0.343574	+	0.490674i	−0.609763	+	0.792584i	$0.708735\pi$
$308$	1.75780	−	20.0917i	0.100160	−	1.14483i
$309$	5.34745	+	15.6561i	0.304206	+	0.890647i
$310$	−21.9322	+	16.6574i	−1.24567	+	0.946075i
$311$	18.8891	−	10.9056i	1.07110	−	0.618400i	0.142618	−	0.989778i	$-0.454448\pi$
$311$	18.8891	−	10.9056i	1.07110	−	0.618400i	0.928482	+	0.371378i	$0.121114\pi$
$312$	−8.24912	+	28.5012i	−0.467014	+	1.61356i
$313$	9.70460	+	20.8116i	0.548537	+	1.17634i	0.963797	+	0.266638i	$0.0859128\pi$
$313$	9.70460	+	20.8116i	0.548537	+	1.17634i	−0.415260	+	0.909703i	$0.636309\pi$
$314$	18.5479	+	6.75089i	1.04672	+	0.380975i
$315$	−3.67268	−	7.90046i	−0.206932	−	0.445140i
$316$	−12.0547	−	20.8794i	−0.678132	−	1.17456i
$317$	8.05870	−	11.5090i	0.452622	−	0.646411i	−0.526383	−	0.850247i	$-0.676452\pi$
$317$	8.05870	−	11.5090i	0.452622	−	0.646411i	0.979005	+	0.203837i	$0.0653411\pi$
$318$	−53.8178	−	26.4141i	−3.01795	−	1.48123i
$319$	8.18188	+	9.75079i	0.458097	+	0.545939i
$320$	−3.16424	−	1.66716i	−0.176886	−	0.0931969i
$321$	−19.6219	−	3.86464i	−1.09519	−	0.215703i
$322$	−13.2645	+	13.2645i	−0.739200	+	0.739200i
$323$	−2.84894	−	10.6994i	−0.158519	−	0.595330i
$324$	32.7087	+	22.5375i	1.81715	+	1.25208i
$325$	6.88626	+	12.2048i	0.381981	+	0.677001i
$326$	54.8752	+	9.67597i	3.03925	+	0.535902i
$327$	12.4859	+	9.11890i	0.690469	+	0.504276i
$328$	−1.87693	−	21.4534i	−0.103636	−	1.18456i
$329$	−1.91350	−	10.8520i	−0.105495	−	0.598289i
$330$	32.6449	+	11.1932i	1.79704	+	0.616166i
$331$	−6.84169	+	11.8502i	−0.376053	+	0.651343i	−0.990484	−	0.137627i	$-0.956052\pi$
$331$	−6.84169	+	11.8502i	−0.376053	+	0.651343i	0.614431	+	0.788971i	$0.289386\pi$
$332$	−26.8180	−	57.5113i	−1.47183	−	3.15634i
$333$	19.1068	−	25.0956i	1.04705	−	1.37523i
$334$	8.18952	+	4.72822i	0.448111	+	0.258717i
$335$	23.1820	+	14.9304i	1.26657	+	0.815734i
$336$	13.9566	+	5.39717i	0.761393	+	0.294440i
$337$	9.89464	−	0.865669i	0.538995	−	0.0471560i	0.185592	−	0.982627i	$-0.440580\pi$
$337$	9.89464	−	0.865669i	0.538995	−	0.0471560i	0.353404	+	0.935471i	$0.385024\pi$
$338$	−1.13558	+	12.9798i	−0.0617676	+	0.706007i
$339$	0.905116	+	0.790754i	0.0491592	+	0.0429479i
$340$	17.0272	−	18.3982i	0.923427	−	0.997784i
$341$		−	17.1120i		−	0.926668i
$342$	12.7405	+	30.5678i	0.688926	+	1.65292i
$343$	11.3080	+	11.3080i	0.610577	+	0.610577i
$344$	14.9407	−	5.43796i	0.805548	−	0.293195i
$345$	−11.4011	−	18.9190i	−0.613816	−	1.01857i
$346$	19.8901	−	16.6897i	1.06930	−	0.897246i
$347$	−0.0372280	−	0.425518i	−0.00199850	−	0.0228430i	0.995130	−	0.0985715i	$-0.0314273\pi$
$347$	−0.0372280	−	0.425518i	−0.00199850	−	0.0228430i	−0.997128	+	0.0757285i	$0.975872\pi$
$348$	−25.2917	+	11.1855i	−1.35578	+	0.599607i
$349$	−8.04440	+	4.64444i	−0.430607	+	0.248611i	−0.699605	−	0.714530i	$-0.746641\pi$
$349$	−8.04440	+	4.64444i	−0.430607	+	0.248611i	0.268998	+	0.963141i	$0.413307\pi$
$350$	14.9728	−	6.80231i	0.800330	−	0.363599i
$351$	−13.3628	−	5.78988i	−0.713255	−	0.309041i
$352$	−14.7380	+	6.87243i	−0.785537	+	0.366302i
$353$	5.91386	+	22.0708i	0.314763	+	1.17471i	0.924210	+	0.381885i	$0.124725\pi$
$353$	5.91386	+	22.0708i	0.314763	+	1.17471i	−0.609447	+	0.792827i	$0.708608\pi$
$354$	−0.510378	+	25.6012i	−0.0271263	+	1.36069i
$355$	−24.4793	−	3.34610i	−1.29923	−	0.177593i
$356$	−17.9734	+	21.4199i	−0.952588	+	1.13525i
$357$	3.37012	−	4.61447i	0.178366	−	0.244224i
$358$	14.4981	−	10.1517i	0.766251	−	0.536534i
$359$	29.7799	−	10.8390i	1.57172	−	0.572061i	0.598340	−	0.801242i	$-0.295827\pi$
$359$	29.7799	−	10.8390i	1.57172	−	0.572061i	0.973384	+	0.229181i	$0.0736048\pi$
$360$	−23.5572	+	33.5587i	−1.24158	+	1.76870i
$361$	−3.35791	+	18.7009i	−0.176732	+	0.984259i
$362$	18.3295	+	18.3295i	0.963379	+	0.963379i
$363$	−1.98479	+	1.33161i	−0.104175	+	0.0698914i
$364$	−15.8213	−	2.78972i	−0.829261	−	0.146221i
$365$	18.0820	+	7.59488i	0.946455	+	0.397534i
$366$	7.76878	+	22.7453i	0.406081	+	1.18891i
$367$	−10.2028	−	7.14405i	−0.532580	−	0.372916i	0.276134	−	0.961119i	$-0.410947\pi$
$367$	−10.2028	−	7.14405i	−0.532580	−	0.372916i	−0.808713	+	0.588203i	$0.799836\pi$
$368$	36.6455	+	9.81912i	1.91028	+	0.511857i
$369$	10.5617	+	0.421277i	0.549819	+	0.0219308i
$370$	47.0545	+	36.4776i	2.44625	+	1.89638i
$371$	6.07110	−	16.6802i	0.315196	−	0.865994i
$372$	35.7123	+	10.3362i	1.85159	+	0.535909i
$373$	1.36070	−	5.07820i	0.0704544	−	0.262939i	−0.921710	−	0.387880i	$-0.873207\pi$
$373$	1.36070	−	5.07820i	0.0704544	−	0.262939i	0.992164	+	0.124941i	$0.0398741\pi$
$374$	3.93037	+	22.2902i	0.203235	+	1.15260i
$375$	3.53134	+	19.0402i	0.182358	+	0.983232i
$376$	−39.7260	+	33.3341i	−2.04871	+	1.71907i
$377$	8.30553	−	5.81560i	0.427757	−	0.299518i
$378$	−8.13565	+	15.0301i	−0.418453	+	0.773065i
$379$		−	19.7601i		−	1.01501i	−0.861649	−	0.507504i	$-0.830568\pi$
$379$		−	19.7601i		−	1.01501i	0.861649	−	0.507504i	$-0.169432\pi$
$380$	−39.8494	+	16.2028i	−2.04423	+	0.831184i
$381$	−5.28747	+	8.75060i	−0.270885	+	0.448307i
$382$	−26.5837	+	57.0090i	−1.36014	+	2.91683i
$383$	−8.99650	−	12.8483i	−0.459700	−	0.656519i	0.520654	−	0.853768i	$-0.325688\pi$
$383$	−8.99650	−	12.8483i	−0.459700	−	0.656519i	−0.980353	+	0.197249i	$0.936799\pi$
$384$	3.54567	+	22.7515i	0.180939	+	1.16103i
$385$	−2.26098	+	9.96494i	−0.115230	+	0.507860i
$386$	−32.2286	+	5.68278i	−1.64039	+	0.289246i
$387$	1.71776	+	7.61250i	0.0873187	+	0.386965i
$388$	−16.2731	+	4.36037i	−0.826143	+	0.221364i
$389$	3.51070	+	1.27779i	0.178000	+	0.0647866i	0.429483	−	0.903075i	$-0.358696\pi$
$389$	3.51070	+	1.27779i	0.178000	+	0.0647866i	−0.251483	+	0.967862i	$0.580918\pi$
$390$	11.1485	−	25.1275i	0.564525	−	1.27238i
$391$	7.24358	−	12.5462i	0.366323	−	0.634491i
$392$	8.40518	−	31.3686i	0.424526	−	1.58435i
$393$	23.3422	−	10.3233i	1.17746	−	0.520744i
$394$	−5.71511	+	6.81101i	−0.287923	+	0.343134i
$395$	4.61852	+	11.3081i	0.232383	+	0.568972i
$396$	−14.1762	−	44.3776i	−0.712381	−	2.23006i
$397$	11.9845	−	25.7009i	0.601485	−	1.28989i	−0.335999	−	0.941862i	$-0.609074\pi$
$397$	11.9845	−	25.7009i	0.601485	−	1.28989i	0.937484	−	0.348027i	$-0.113148\pi$
$398$	−12.0234	+	12.0234i	−0.602679	+	0.602679i
$399$	−8.59522	+	4.71905i	−0.430299	+	0.236248i
$400$	−27.0547	−	19.3458i	−1.35273	−	0.967291i
$401$	2.58548	+	7.10354i	0.129113	+	0.354734i	0.987358	−	0.158506i	$-0.0506676\pi$
$401$	2.58548	+	7.10354i	0.129113	+	0.354734i	−0.858246	+	0.513239i	$0.828445\pi$
$402$	−3.63935	−	53.9680i	−0.181514	−	2.69168i
$403$	−13.5788	−	1.18800i	−0.676411	−	0.0591783i
$404$	6.94199	+	5.82502i	0.345377	+	0.289806i
$405$	−14.8725	−	13.5576i	−0.739021	−	0.673682i
$406$	−5.94943	−	10.3047i	−0.295265	−	0.511414i
$407$	−35.7324	+	9.57448i	−1.77119	+	0.474589i
$408$	−26.7369	−	2.87722i	−1.32367	−	0.142443i
$409$	−0.0555899	+	0.152732i	−0.00274874	+	0.00755211i	−0.941059	−	0.338241i	$-0.890168\pi$
$409$	−0.0555899	+	0.152732i	−0.00274874	+	0.00755211i	0.938311	+	0.345793i	$0.112390\pi$
$410$	−0.968952	+	19.9286i	−0.0478531	+	0.984203i
$411$	0.0675785	−	3.38982i	0.00333340	−	0.167208i
$412$	34.5328	+	24.1801i	1.70131	+	1.19127i
$413$	−7.55291	+	0.660794i	−0.371654	+	0.0325155i
$414$	−16.4310	+	40.0945i	−0.807539	+	1.97054i
$415$	9.51578	+	30.7094i	0.467111	+	1.50746i
$416$	4.43028	+	12.1721i	0.217212	+	0.596786i
$417$	−0.763240	−	3.09385i	−0.0373760	−	0.151507i
$418$	10.1114	−	37.5011i	0.494563	−	1.83424i
$419$	−3.66313			−0.178955			−0.0894777	−	0.995989i	$-0.528520\pi$
$419$	−3.66313			−0.178955			−0.0894777	+	0.995989i	$0.528520\pi$
$420$	−19.4308	−	10.7377i	−0.948126	−	0.523948i
$421$	1.85434	−	10.5165i	0.0903749	−	0.512542i	−0.905692	−	0.423936i	$-0.860648\pi$
$421$	1.85434	−	10.5165i	0.0903749	−	0.512542i	0.996067	−	0.0886051i	$-0.0282409\pi$
$422$	28.1857	+	2.46593i	1.37206	+	0.120040i
$423$	−13.7569	−	21.4156i	−0.668885	−	1.04126i
$424$	−82.2679	+	14.5061i	−3.99528	+	0.704476i
$425$	−9.80962	+	8.06712i	−0.475836	+	0.391313i
$426$	23.3918	+	42.4479i	1.13334	+	2.05661i
$427$	−6.44986	+	3.00762i	−0.312131	+	0.145549i
$428$	−46.1853	+	21.5366i	−2.23245	+	1.04101i
$429$	8.24363	+	14.9593i	0.398006	+	0.722240i
$430$	−14.3971	+	3.11708i	−0.694290	+	0.150319i
$431$	−6.81601	+	1.20185i	−0.328316	+	0.0578909i	−0.335377	−	0.942084i	$-0.608864\pi$
$431$	−6.81601	+	1.20185i	−0.328316	+	0.0578909i	0.00706087	+	0.999975i	$0.497752\pi$
$432$	34.5516	−	0.949276i	1.66236	−	0.0456721i
$433$	−7.76218	−	0.679103i	−0.373027	−	0.0326356i	−0.100899	−	0.994897i	$-0.532172\pi$
$433$	−7.76218	−	0.679103i	−0.373027	−	0.0326356i	−0.272128	+	0.962261i	$0.587727\pi$
$434$	−2.77774	+	15.7533i	−0.133336	+	0.756184i
$435$	13.4633	−	3.87945i	0.645517	−	0.186005i
$436$	39.3974			1.88679
$437$	−20.3865	+	14.2273i	−0.975220	+	0.680582i
$438$	−9.21475	−	37.3527i	−0.440298	−	1.78478i
$439$	1.59434	+	4.38042i	0.0760938	+	0.209066i	0.971907	−	0.235364i	$-0.0756284\pi$
$439$	1.59434	+	4.38042i	0.0760938	+	0.209066i	−0.895813	+	0.444430i	$0.853406\pi$
$440$	45.9335	−	14.2332i	2.18979	−	0.678542i
$441$	14.7492	+	6.04431i	0.702341	+	0.287824i
$442$	17.9608	−	1.57136i	0.854306	−	0.0747421i
$443$	11.4084	+	7.98825i	0.542030	+	0.379533i	0.812290	−	0.583254i	$-0.198221\pi$
$443$	11.4084	+	7.98825i	0.542030	+	0.379533i	−0.270260	+	0.962787i	$0.587110\pi$
$444$	1.60195	−	80.3558i	0.0760251	−	3.81352i
$445$	10.4919	−	9.51898i	0.497365	−	0.451243i
$446$	−5.51413	+	15.1499i	−0.261102	+	0.717371i
$447$	−13.7209	−	1.47653i	−0.648975	−	0.0698376i
$448$	−2.00658	+	0.537661i	−0.0948019	+	0.0254021i
$449$	5.57855	+	9.66232i	0.263268	+	0.455993i	0.967108	−	0.254365i	$-0.0818664\pi$
$449$	5.57855	+	9.66232i	0.263268	+	0.455993i	−0.703841	+	0.710358i	$0.748533\pi$
$450$	25.8351	−	27.8493i	1.21788	−	1.31283i
$451$	−9.49664	−	7.96863i	−0.447179	−	0.375228i
$452$	3.05091	+	0.266920i	0.143503	+	0.0125549i
$453$	−0.103397	−	1.53328i	−0.00485802	−	0.0720397i
$454$	10.6109	+	29.1532i	0.497995	+	1.36823i
$455$	7.75048	+	2.48596i	0.363348	+	0.116544i
$456$	39.4581	+	23.9267i	1.84780	+	1.12047i
$457$	−14.3309	+	14.3309i	−0.670373	+	0.670373i	−0.957802	−	0.287429i	$-0.907200\pi$
$457$	−14.3309	+	14.3309i	−0.670373	+	0.670373i	0.287429	+	0.957802i	$0.407200\pi$
$458$	3.85311	−	8.26302i	0.180044	−	0.386106i
$459$	3.06470	−	12.8382i	0.143048	−	0.599236i
$460$	−51.8935	−	21.7965i	−2.41955	−	1.01627i
$461$	−16.1635	+	19.2630i	−0.752811	+	0.897166i	−0.997371	−	0.0724687i	$-0.976912\pi$
$461$	−16.1635	+	19.2630i	−0.752811	+	0.897166i	0.244559	+	0.969634i	$0.421357\pi$
$462$	18.3319	−	8.10746i	0.852875	−	0.377193i
$463$	−8.97342	+	33.4893i	−0.417030	+	1.55638i	0.363704	+	0.931515i	$0.381512\pi$
$463$	−8.97342	+	33.4893i	−0.417030	+	1.55638i	−0.780734	+	0.624863i	$0.785155\pi$
$464$	−12.0322	+	20.8405i	−0.558583	+	0.967494i
$465$	−17.2174	−	7.63895i	−0.798440	−	0.354248i
$466$	−10.0332	−	3.65180i	−0.464780	−	0.169166i
$467$	−21.4622	+	5.75079i	−0.993154	+	0.266115i	−0.718575	−	0.695450i	$-0.755205\pi$
$467$	−21.4622	+	5.75079i	−0.993154	+	0.266115i	−0.274579	+	0.961565i	$0.588539\pi$
$468$	−36.1990	+	8.16830i	−1.67330	+	0.377580i
$469$	15.7723	−	2.78109i	0.728299	−	0.128419i
$470$	40.6490	−	25.6143i	1.87500	−	1.18150i
$471$	2.07874	+	13.3386i	0.0957832	+	0.614612i
$472$	20.4656	+	29.2279i	0.942005	+	1.34532i
$473$	3.86810	−	8.29517i	0.177855	−	0.381412i
$474$	12.3919	−	20.5083i	0.569181	−	0.941977i
$475$	21.1152	−	5.39909i	0.968830	−	0.247727i
$476$		−	14.5603i		−	0.667371i
$477$	−1.94278	−	40.9560i	−0.0889540	−	1.87525i
$478$	1.16153	−	0.813313i	0.0531272	−	0.0372001i
$479$	−0.716636	+	0.601329i	−0.0327439	+	0.0274754i	−0.659013	−	0.752132i	$-0.729026\pi$
$479$	−0.716636	+	0.601329i	−0.0327439	+	0.0274754i	0.626269	+	0.779607i	$0.284581\pi$
$480$	0.335610	+	17.8967i	0.0153185	+	0.816868i
$481$	5.11689	+	29.0193i	0.233310	+	1.32317i
$482$	−15.3563	+	57.3106i	−0.699462	+	2.61043i
$483$	−12.3239	−	3.56693i	−0.560759	−	0.162301i
$484$	−2.08301	+	5.72301i	−0.0946821	+	0.260137i
$485$	8.46790	−	1.07221i	0.384507	−	0.0486864i
$486$	−3.92804	+	39.2817i	−0.178179	+	1.78185i
$487$	4.54139	+	1.21686i	0.205790	+	0.0551412i	0.360241	−	0.932859i	$-0.382694\pi$
$487$	4.54139	+	1.21686i	0.205790	+	0.0551412i	−0.154451	+	0.988000i	$0.549361\pi$
$488$	27.4348	+	19.2101i	1.24192	+	0.869599i
$489$	12.3180	+	36.0642i	0.557038	+	1.63088i
$490$	−11.6515	+	27.7401i	−0.526362	+	1.25317i
$491$	12.0423	+	2.12338i	0.543461	+	0.0958269i	0.438638	−	0.898664i	$-0.355461\pi$
$491$	12.0423	+	2.12338i	0.543461	+	0.0958269i	0.104823	+	0.994491i	$0.466572\pi$
$492$	22.3666	−	15.0059i	1.00836	−	0.676517i
$493$	6.49783	+	6.49783i	0.292648	+	0.292648i
$494$	−29.0562	−	10.6271i	−1.30730	−	0.478138i
$495$	4.07111	+	23.2491i	0.182983	+	1.04497i
$496$	30.4003	−	11.0648i	1.36502	−	0.496825i
$497$	−11.7552	+	8.23106i	−0.527292	+	0.369214i
$498$	37.1963	−	50.9303i	1.66681	−	2.28224i
$499$	1.56404	−	1.86395i	0.0700162	−	0.0834420i	−0.729899	−	0.683555i	$-0.760433\pi$
$499$	1.56404	−	1.86395i	0.0700162	−	0.0834420i	0.799916	+	0.600113i	$0.204878\pi$
$500$	35.8815	+	33.8731i	1.60467	+	1.51485i
$501$	−0.128910	+	6.46629i	−0.00575927	+	0.288892i
$502$	−15.5018	−	57.8534i	−0.691878	−	2.58212i
$503$	−6.20691	+	2.89433i	−0.276752	+	0.129052i	−0.556039	−	0.831156i	$-0.687680\pi$
$503$	−6.20691	+	2.89433i	−0.276752	+	0.129052i	0.279287	+	0.960208i	$0.409902\pi$
$504$	3.19738	+	23.5992i	0.142422	+	1.05119i
$505$	−3.08502	−	3.40035i	−0.137282	−	0.151313i
$506$	44.0112	−	25.4099i	1.95654	−	1.12961i
$507$	−8.14975	+	3.60431i	−0.361943	+	0.160073i
$508$	2.27059	+	25.9530i	0.100741	+	1.15148i
$509$	−16.0374	+	13.4570i	−0.710844	+	0.596469i	−0.924836	−	0.380366i	$-0.875798\pi$
$509$	−16.0374	+	13.4570i	−0.710844	+	0.596469i	0.213992	+	0.976835i	$0.431353\pi$
$510$	24.1821	+	5.99597i	1.07080	+	0.265506i
$511$	10.7043	−	3.89606i	0.473532	−	0.172352i
$512$	35.7599	+	35.7599i	1.58038	+	1.58038i
$513$	−14.1046	+	17.7218i	−0.622733	+	0.782434i
$514$		−	18.6241i		−	0.821473i
$515$	−15.6755	−	14.5073i	−0.690745	−	0.639269i
$516$	14.9753	+	13.0832i	0.659250	+	0.575954i
$517$	−2.60185	+	29.7392i	−0.114429	+	1.30793i
$518$	34.4495	−	3.01394i	1.51362	−	0.132425i
$519$	16.5627	+	6.40501i	0.727023	+	0.281149i
$520$	−8.10552	−	37.4376i	−0.355450	−	1.64175i
$521$	−25.4811	−	14.7115i	−1.11635	−	0.644523i	−0.175880	−	0.984412i	$-0.556277\pi$
$521$	−25.4811	−	14.7115i	−1.11635	−	0.644523i	−0.940466	+	0.339889i	$0.889610\pi$
$522$	−21.8682	−	16.6495i	−0.957144	−	0.728730i
$523$	−0.596818	−	1.27988i	−0.0260970	−	0.0559653i	0.892827	−	0.450399i	$-0.148718\pi$
$523$	−0.596818	−	1.27988i	−0.0260970	−	0.0559653i	−0.918924	+	0.394434i	$0.870941\pi$
$524$	32.5182	−	56.3232i	1.42056	−	2.46049i
$525$	9.01700	+	6.72334i	0.393534	+	0.293431i
$526$	−8.79420	−	49.8744i	−0.383445	−	2.17463i
$527$	−1.07670	−	12.3067i	−0.0469018	−	0.536090i
$528$	−32.7373	−	23.9093i	−1.42471	−	1.04052i
$529$	−9.38291	−	1.65446i	−0.407952	−	0.0719330i
$530$	77.3379	−	2.99320i	3.35934	−	0.130016i
$531$	−15.5036	+	8.14505i	−0.672800	+	0.353465i
$532$	−10.5949	+	22.6281i	−0.459345	+	0.981054i
$533$	−6.98262	+	6.98262i	−0.302451	+	0.302451i
$534$	−27.2661	−	5.37020i	−1.17992	−	0.232391i
$535$	24.6616	−	7.64179i	1.06622	−	0.330383i
$536$	−48.4479	−	57.7380i	−2.09263	−	2.49390i
$537$	10.8666	+	5.33340i	0.468929	+	0.230153i
$538$	38.0544	−	54.3473i	1.64064	−	2.34308i
$539$	−9.34729	−	16.1900i	−0.402616	−	0.697352i
$540$	−50.9793	−	5.54698i	−2.19380	−	0.238704i
$541$	−15.8377	−	5.76444i	−0.680914	−	0.247833i	−0.0216742	−	0.999765i	$-0.506900\pi$
$541$	−15.8377	−	5.76444i	−0.680914	−	0.247833i	−0.659240	+	0.751933i	$0.729122\pi$
$542$	−11.6704	−	25.0273i	−0.501288	−	1.07502i
$543$	−4.92897	+	17.0299i	−0.211522	+	0.730821i
$544$	−10.1669	+	5.86989i	−0.435904	+	0.251669i
$545$	−19.7765	−	2.70328i	−0.847133	−	0.115796i
$546$	−5.16080	−	15.1097i	−0.220862	−	0.646634i
$547$	1.97726	−	22.6002i	0.0845414	−	0.966313i	−0.828915	−	0.559375i	$-0.811041\pi$
$547$	1.97726	−	22.6002i	0.0845414	−	0.966313i	0.913456	−	0.406938i	$-0.133403\pi$
$548$	−4.95538	−	7.07701i	−0.211683	−	0.302315i
$549$	−11.0600	+	12.1616i	−0.472030	+	0.519042i
$550$	−43.9505	+	7.30182i	−1.87406	+	0.311351i
$551$	−5.37009	−	14.8264i	−0.228774	−	0.631627i
$552$	14.4615	+	58.6209i	0.615523	+	2.49507i
$553$	6.43001	+	2.99836i	0.273432	+	0.127503i
$554$	11.1578	−	63.2790i	0.474049	−	2.68847i
$555$	−6.31780	+	40.2267i	−0.268176	+	1.70753i
$556$	−6.22020	−	5.21937i	−0.263795	−	0.221351i
$557$	6.78038	−	9.68339i	0.287294	−	0.410298i	−0.649400	−	0.760447i	$-0.724980\pi$
$557$	6.78038	−	9.68339i	0.287294	−	0.410298i	0.936694	+	0.350148i	$0.113869\pi$
$558$	8.13322	+	36.0435i	0.344307	+	1.52584i
$559$	−6.31389	−	3.64533i	−0.267049	−	0.154181i
$560$	−19.1652	+	2.42670i	−0.809876	+	0.102547i
$561$	−12.0545	+	9.71214i	−0.508941	+	0.410047i
$562$	12.6571	+	47.2368i	0.533906	+	1.99257i
$563$	14.6737	+	3.93180i	0.618422	+	0.165706i	0.554410	−	0.832243i	$-0.312944\pi$
$563$	14.6737	+	3.93180i	0.618422	+	0.165706i	0.0640117	+	0.997949i	$0.479610\pi$
$564$	−60.4932	−	23.3935i	−2.54722	−	0.985042i
$565$	−1.51317	−	0.343327i	−0.0636594	−	0.0144439i
$566$	−47.1013	−	56.1332i	−1.97982	−	2.35945i
$567$	−11.6886	+	0.0880656i	−0.490874	+	0.00369841i
$568$	61.2073	+	28.5415i	2.56820	+	1.19757i
$569$	−18.9340			−0.793753			−0.396876	−	0.917872i	$-0.629906\pi$
$569$	−18.9340			−0.793753			−0.396876	+	0.917872i	$0.629906\pi$
$570$	−33.2183	−	26.9145i	−1.39136	−	1.12732i
$571$	43.1074			1.80399			0.901994	−	0.431749i	$-0.142103\pi$
$571$	43.1074			1.80399			0.901994	+	0.431749i	$0.142103\pi$
$572$	39.4452	+	18.3936i	1.64929	+	0.769075i
$573$	−42.9235	+	2.89456i	−1.79316	+	0.120922i
$574$	7.44909	+	8.87748i	0.310919	+	0.370539i
$575$	24.5537	+	14.5020i	1.02396	+	0.604776i
$576$	−3.79585	+	2.93544i	−0.158160	+	0.122310i
$577$	3.10516	+	0.832024i	0.129269	+	0.0346376i	0.322874	−	0.946442i	$-0.395351\pi$
$577$	3.10516	+	0.832024i	0.129269	+	0.0346376i	−0.193604	+	0.981080i	$0.562018\pi$
$578$	−6.91357	−	25.8018i	−0.287566	−	1.07321i
$579$	−14.0424	−	17.4291i	−0.583583	−	0.724331i
$580$	21.8740	−	28.2165i	0.908270	−	1.17163i
$581$	16.1717	+	9.33675i	0.670916	+	0.387354i
$582$	−11.6013	−	12.0732i	−0.480889	−	0.500452i
$583$	−27.5826	+	39.3920i	−1.14235	+	1.63145i
$584$	−41.0668	−	34.4592i	−1.69936	−	1.42593i
$585$	18.7314	−	1.61647i	0.774450	−	0.0668328i
$586$	−8.29601	+	47.0490i	−0.342705	+	1.94358i
$587$	−10.9090	−	5.08693i	−0.450261	−	0.209960i	0.184242	−	0.982881i	$-0.441017\pi$
$587$	−10.9090	−	5.08693i	−0.450261	−	0.209960i	−0.634502	+	0.772921i	$0.718795\pi$
$588$	39.4340	−	9.72821i	1.62623	−	0.401185i
$589$	−7.28174	+	19.9093i	−0.300039	+	0.820350i
$590$	−15.1190	−	29.3976i	−0.622438	−	1.21028i
$591$	−5.96632	−	1.17510i	−0.245421	−	0.0483370i
$592$	−40.1145	−	57.2894i	−1.64869	−	2.35458i
$593$	−2.99019	+	34.1780i	−0.122792	+	1.40352i	0.645664	+	0.763622i	$0.276581\pi$
$593$	−2.99019	+	34.1780i	−0.122792	+	1.40352i	−0.768456	+	0.639902i	$0.778975\pi$
$594$	31.8281	−	33.6264i	1.30592	−	1.37971i
$595$	−0.999065	+	7.30892i	−0.0409577	+	0.299636i
$596$	−30.4534	+	17.5823i	−1.24742	+	0.720197i
$597$	−11.1709	−	3.23320i	−0.457194	−	0.132326i
$598$	−17.1080	−	36.6882i	−0.699597	−	1.50029i
$599$	15.5124	+	5.64606i	0.633821	+	0.230692i	0.638893	−	0.769295i	$-0.279392\pi$
$599$	15.5124	+	5.64606i	0.633821	+	0.230692i	−0.00507274	+	0.999987i	$0.501615\pi$
$600$	6.18422	−	52.5703i	0.252470	−	2.14617i
$601$	−10.2343	−	17.7264i	−0.417468	−	0.723075i	0.578216	−	0.815884i	$-0.303749\pi$
$601$	−10.2343	−	17.7264i	−0.417468	−	0.723075i	−0.995684	+	0.0928081i	$0.970416\pi$
$602$	−4.90750	+	7.00864i	−0.200015	+	0.285651i
$603$	31.1256	−	19.9944i	1.26753	−	0.814235i
$604$	−2.51707	−	2.99973i	−0.102418	−	0.122057i
$605$	1.43831	−	2.72988i	0.0584754	−	0.110986i
$606$	−1.74044	+	8.83672i	−0.0707004	+	0.358967i
$607$	14.0018	−	14.0018i	0.568317	−	0.568317i	−0.363339	−	0.931657i	$-0.618363\pi$
$607$	14.0018	−	14.0018i	0.568317	−	0.568317i	0.931657	+	0.363339i	$0.118363\pi$
$608$	20.0717	−	1.72437i	0.814013	−	0.0699324i
$609$	4.20867	−	6.96523i	0.170544	−	0.282245i
$610$	−22.7734	−	21.0763i	−0.922067	−	0.853353i
$611$	23.4182	+	4.12927i	0.947401	+	0.167052i
$612$	−12.9876	−	31.0238i	−0.524993	−	1.25406i
$613$	−3.47901	−	39.7652i	−0.140516	−	1.60610i	−0.659760	−	0.751476i	$-0.729342\pi$
$613$	−3.47901	−	39.7652i	−0.140516	−	1.60610i	0.519244	−	0.854626i	$-0.326213\pi$
$614$	4.61547	+	26.1756i	0.186265	+	1.05636i
$615$	−12.2571	+	5.99788i	−0.494254	+	0.241858i
$616$	13.9654	−	24.1888i	0.562683	−	0.974596i
$617$	−4.15376	−	8.90776i	−0.167224	−	0.358613i	0.804782	−	0.593571i	$-0.202282\pi$
$617$	−4.15376	−	8.90776i	−0.167224	−	0.358613i	−0.972005	+	0.234958i	$0.924505\pi$
$618$	−4.48284	+	41.6575i	−0.180326	+	1.67571i
$619$	−9.10631	−	5.25753i	−0.366014	−	0.211318i	0.305702	−	0.952127i	$-0.401109\pi$
$619$	−9.10631	−	5.25753i	−0.366014	−	0.211318i	−0.671715	+	0.740809i	$0.734442\pi$
$620$	−46.9097	+	10.1563i	−1.88394	+	0.407887i
$621$	−29.4404	+	3.39270i	−1.18140	+	0.136145i
$622$	55.0264	−	4.81419i	2.20636	−	0.193031i
$623$	0.717145	−	8.19700i	0.0287318	−	0.328406i
$624$	−21.2454	+	24.3180i	−0.850498	+	0.973500i
$625$	−15.6874	−	19.4655i	−0.627496	−	0.778620i
$626$			58.1537i			2.32429i
$627$	25.8009	−	6.32212i	1.03039	−	0.252481i
$628$	24.3237	+	24.3237i	0.970621	+	0.970621i
$629$	−25.0959	+	9.13415i	−1.00064	+	0.364202i
$630$	0.0260930	−	22.0640i	0.00103957	−	0.879052i
$631$	−2.98070	+	2.50110i	−0.118660	+	0.0995672i	−0.700187	−	0.713960i	$-0.746900\pi$
$631$	−2.98070	+	2.50110i	−0.118660	+	0.0995672i	0.581527	+	0.813527i	$0.302455\pi$
$632$	−2.91001	−	33.2616i	−0.115754	−	1.32308i
$633$	7.82680	+	17.6973i	0.311088	+	0.703403i
$634$	30.8143	−	17.7906i	1.22379	−	0.706556i
$635$	0.641001	−	13.1836i	0.0254373	−	0.523174i
$636$	−65.5491	−	81.3581i	−2.59919	−	3.22606i
$637$	−13.4961	+	6.29334i	−0.534735	+	0.249351i
$638$	8.34314	+	31.1370i	0.330308	+	1.23273i
$639$	−17.7049	+	28.0235i	−0.700393	+	1.10859i
$640$	−17.9794	−	23.6729i	−0.710699	−	0.935755i
$641$	−3.66237	+	4.36465i	−0.144655	+	0.172393i	−0.833507	−	0.552509i	$-0.813671\pi$
$641$	−3.66237	+	4.36465i	−0.144655	+	0.172393i	0.688852	+	0.724902i	$0.258115\pi$
$642$	−40.9003	−	29.8711i	−1.61421	−	1.17892i
$643$	5.85877	−	4.10236i	0.231047	−	0.161781i	−0.452320	−	0.891856i	$-0.649404\pi$
$643$	5.85877	−	4.10236i	0.231047	−	0.161781i	0.683368	+	0.730075i	$0.260515\pi$
$644$	−30.7204	+	11.1813i	−1.21055	+	0.440605i
$645$	−6.61951	−	7.59496i	−0.260643	−	0.299051i
$646$	4.91237	−	27.6065i	0.193275	−	1.08616i
$647$	5.77360	+	5.77360i	0.226983	+	0.226983i	0.811431	−	0.584448i	$-0.198689\pi$
$647$	5.77360	+	5.77360i	0.226983	+	0.226983i	−0.584448	+	0.811431i	$0.698689\pi$
$648$	27.8628	+	47.4310i	1.09456	+	1.86326i
$649$	20.2278	+	3.56671i	0.794012	+	0.140006i
$650$	2.74294	+	35.3828i	0.107587	+	1.38783i
$651$	−10.3532	+	3.53619i	−0.405773	+	0.138594i
$652$	79.5471	+	55.6995i	3.11530	+	2.18136i
$653$	−0.563992	−	0.151121i	−0.0220707	−	0.00591383i	0.247767	−	0.968820i	$-0.420303\pi$
$653$	−0.563992	−	0.151121i	−0.0220707	−	0.00591383i	−0.269838	+	0.962906i	$0.586970\pi$
$654$	18.8980	+	34.2931i	0.738969	+	1.34097i
$655$	−20.1880	+	26.0416i	−0.788810	+	1.01753i
$656$	8.01602	−	22.0238i	0.312973	−	0.859886i
$657$	19.3326	−	17.8495i	0.754236	−	0.696375i
$658$	7.22273	−	26.9556i	0.281571	−	1.05084i
$659$	−4.61581	−	26.1776i	−0.179807	−	1.01973i	−0.932448	−	0.361304i	$-0.882332\pi$
$659$	−4.61581	−	26.1776i	−0.179807	−	1.01973i	0.752642	−	0.658430i	$-0.228779\pi$
$660$	43.3177	+	41.7229i	1.68614	+	1.62406i
$661$	−35.4630	+	29.7570i	−1.37935	+	1.15741i	−0.409901	+	0.912130i	$0.634437\pi$
$661$	−35.4630	+	29.7570i	−1.37935	+	1.15741i	−0.969451	+	0.245284i	$0.921119\pi$
$662$	−28.3861	+	19.8761i	−1.10326	+	0.772508i
$663$	6.86996	+	10.2398i	0.266807	+	0.397682i
$664$		−	87.8798i		−	3.41040i
$665$	6.87100	−	10.6318i	0.266446	−	0.412283i
$666$	70.7134	−	37.1503i	2.74009	−	1.43955i
$667$	8.71970	−	18.6994i	0.337628	−	0.724045i
$668$	9.45268	+	13.4998i	0.365735	+	0.522324i
$669$	−10.8950	+	1.69792i	−0.421225	+	0.0656452i
$670$	37.2280	+	59.0795i	1.43824	+	2.28244i
$671$	18.9869	−	3.34790i	0.732981	−	0.129244i
$672$	7.20358	+	7.49664i	0.277884	+	0.289189i
$673$	19.6844	−	5.27443i	0.758779	−	0.203314i	0.141370	−	0.989957i	$-0.454849\pi$
$673$	19.6844	−	5.27443i	0.758779	−	0.203314i	0.617409	+	0.786643i	$0.288183\pi$
$674$	23.6368	+	8.60310i	0.910456	+	0.331379i
$675$	25.2097	+	6.28243i	0.970323	+	0.241811i
$676$	−11.3535	+	19.6648i	−0.436672	+	0.756338i
$677$	9.17300	−	34.2341i	0.352547	−	1.31572i	−0.530996	−	0.847374i	$-0.678182\pi$
$677$	9.17300	−	34.2341i	0.352547	−	1.31572i	0.883543	−	0.468350i	$-0.155151\pi$
$678$	1.23111	+	2.78367i	0.0472805	+	0.106906i
$679$	3.18671	−	3.79778i	0.122295	−	0.145745i
$680$	32.1392	−	13.1265i	1.23248	−	0.503379i
$681$	−13.9602	+	15.9792i	−0.534958	+	0.612325i
$682$	18.3146	−	39.2758i	0.701302	−	1.50395i
$683$	−7.02322	+	7.02322i	−0.268736	+	0.268736i	−0.828591	−	0.559855i	$-0.810857\pi$
$683$	−7.02322	+	7.02322i	−0.268736	+	0.268736i	0.559855	+	0.828591i	$0.310857\pi$
$684$	−2.39054	+	57.6644i	−0.0914047	+	2.20485i
$685$	2.00188	+	3.89250i	0.0764880	+	0.148725i
$686$	13.8516	+	38.0571i	0.528858	+	1.45303i
$687$	6.22144	−	0.419545i	0.237363	−	0.0160066i
$688$	17.2379	+	1.50812i	0.657189	+	0.0574966i
$689$	29.3437	+	24.6223i	1.11791	+	0.938035i
$690$	−5.91944	−	55.6255i	−0.225349	−	2.11763i
$691$	−2.72506	−	4.71994i	−0.103666	−	0.179555i	0.809526	−	0.587084i	$-0.199724\pi$
$691$	−2.72506	−	4.71994i	−0.103666	−	0.179555i	−0.913192	+	0.407529i	$0.866391\pi$
$692$	43.7080	−	11.7115i	1.66153	−	0.445206i
$693$	10.9076	+	8.30459i	0.414345	+	0.315465i
$694$	0.369975	−	1.01650i	0.0140441	−	0.0385857i
$695$	2.76426	+	3.04680i	0.104854	+	0.115572i
$696$	−38.2909	−	0.763356i	−1.45141	−	0.0289349i
$697$	−7.33125	−	5.13340i	−0.277691	−	0.194441i
$698$	−23.4344	+	2.05025i	−0.887007	+	0.0776030i
$699$	−1.12446	−	7.21534i	−0.0425311	−	0.272909i
$700$	28.6591	+	0.283717i	1.08321	+	0.0107235i
$701$	−2.13761	−	5.87305i	−0.0807366	−	0.221822i	0.892756	−	0.450540i	$-0.148769\pi$
$701$	−2.13761	−	5.87305i	−0.0807366	−	0.221822i	−0.973493	+	0.228718i	$0.926546\pi$
$702$	−24.4738	−	27.5909i	−0.923704	−	1.04135i
$703$	45.6479	+	4.06573i	1.72164	+	0.153342i
$704$	5.62782			0.212106
$705$	28.7609	+	15.8937i	1.08320	+	0.598592i
$706$	−10.0483	+	56.9867i	−0.378173	+	2.14472i
$707$	−2.65658	−	0.232421i	−0.0999109	−	0.00874108i
$708$	−19.6619	+	40.0604i	−0.738939	+	1.50556i
$709$	5.36244	−	0.945543i	0.201391	−	0.0355106i	−0.0720428	−	0.997402i	$-0.522952\pi$
$709$	5.36244	−	0.945543i	0.201391	−	0.0355106i	0.273433	+	0.961891i	$0.411841\pi$
$710$	−52.6039	−	33.8796i	−1.97419	−	1.27148i
$711$	16.3750	+	0.653153i	0.614110	+	0.0244952i
$712$	−35.0954	+	16.3652i	−1.31525	+	0.613313i
$713$	−25.1388	+	11.7224i	−0.941455	+	0.439008i
$714$	12.6739	−	6.98423i	0.474309	−	0.261378i
$715$	−18.5384	−	11.9397i	−0.693297	−	0.446519i
$716$	30.3763	−	5.35616i	1.13522	−	0.200169i
$717$	0.870589	+	0.427290i	0.0325127	+	0.0159574i
$718$	79.9520	+	6.99490i	2.98378	+	0.261047i
$719$	1.10049	−	6.24118i	0.0410413	−	0.232757i	−0.957386	−	0.288810i	$-0.906740\pi$
$719$	1.10049	−	6.24118i	0.0410413	−	0.232757i	0.998428	+	0.0560530i	$0.0178516\pi$
$720$	−38.6708	+	22.2657i	−1.44118	+	0.829792i
$721$	−12.4055			−0.462007
$722$	−27.7223	+	39.3287i	−1.03172	+	1.46366i
$723$	−39.3981	+	9.71935i	−1.46523	+	0.361466i
$724$	15.4509	+	42.4510i	0.574228	+	1.57768i
$725$	−12.9163	+	12.6631i	−0.479700	+	0.470295i
$726$	−5.98071	+	0.932055i	−0.221965	+	0.0345918i
$727$	−36.0960	+	3.15799i	−1.33873	+	0.117123i	−0.733913	−	0.679243i	$-0.762308\pi$
$727$	−36.0960	+	3.15799i	−1.33873	+	0.117123i	−0.604814	+	0.796367i	$0.706753\pi$
$728$	−18.2249	−	12.7612i	−0.675462	−	0.472963i
$729$	−24.8264	+	10.6137i	−0.919496	+	0.393100i
$730$	33.3734	+	36.7846i	1.23521	+	1.36146i
$731$	2.25995	−	6.20916i	0.0835872	−	0.229654i
$732$	−4.48175	+	41.6473i	−0.165650	+	1.53933i
$733$	−12.7950	+	3.42840i	−0.472593	+	0.126631i	−0.487251	−	0.873262i	$-0.662000\pi$
$733$	−12.7950	+	3.42840i	−0.472593	+	0.126631i	0.0146587	+	0.999893i	$0.495334\pi$
$734$	−15.7714	−	27.3169i	−0.582133	−	1.00828i
$735$	−20.4624	+	2.17753i	−0.754768	+	0.0803193i
$736$	20.1922	+	16.9433i	0.744294	+	0.624537i
$737$	−43.2232	−	3.78154i	−1.59215	−	0.139295i
$738$	23.7904	+	12.2708i	0.875738	+	0.451696i
$739$	−11.0482	−	30.3548i	−0.406416	−	1.11662i	−0.959060	−	0.283201i	$-0.908604\pi$
$739$	−11.0482	−	30.3548i	−0.406416	−	1.11662i	0.552645	−	0.833417i	$-0.313619\pi$
$740$	47.4546	+	92.2718i	1.74447	+	3.39198i
$741$	−3.22555	−	20.9126i	−0.118494	−	0.768244i
$742$	31.7869	−	31.7869i	1.16693	−	1.16693i
$743$	17.1304	−	36.7362i	0.628452	−	1.34772i	−0.291833	−	0.956469i	$-0.594265\pi$
$743$	17.1304	−	36.7362i	0.628452	−	1.34772i	0.920285	−	0.391250i	$-0.127957\pi$
$744$	38.7738	+	33.8748i	1.42152	+	1.24191i
$745$	16.4932	−	6.73628i	0.604266	−	0.246798i
$746$	8.55818	−	10.1992i	0.313337	−	0.373421i
$747$	42.7855	+	5.46893i	1.56544	+	0.200098i
$748$	−10.2093	+	38.1015i	−0.373288	+	1.39313i
$749$	7.49802	−	12.9870i	0.273972	−	0.474533i
$750$	−12.2731	+	47.4809i	−0.448150	+	1.73376i
$751$	−42.7652	−	15.5653i	−1.56052	−	0.567985i	−0.589668	−	0.807646i	$-0.700742\pi$
$751$	−42.7652	−	15.5653i	−1.56052	−	0.567985i	−0.970857	+	0.239661i	$0.922964\pi$
$752$	−54.5155	+	14.6074i	−1.98798	+	0.532677i
$753$	29.5372	−	28.3826i	1.07640	−	1.03432i
$754$	25.2873	−	4.45883i	0.920908	−	0.162381i
$755$	1.05768	+	1.67850i	0.0384929	+	0.0610869i
$756$	−23.9200	+	17.7475i	−0.869960	+	0.645472i
$757$	−4.20662	−	6.00768i	−0.152892	−	0.218353i	0.735398	−	0.677636i	$-0.236995\pi$
$757$	−4.20662	−	6.00768i	−0.152892	−	0.218353i	−0.888290	+	0.459283i	$0.848106\pi$
$758$	21.1488	−	45.3537i	0.768157	−	1.64732i
$759$	29.7483	+	17.9752i	1.07980	+	0.652457i
$760$	−59.4990	−	2.98633i	−2.15826	−	0.108326i
$761$		−	1.90258i		−	0.0689684i	−0.999405	−	0.0344842i	$-0.989021\pi$
$761$		−	1.90258i		−	0.0689684i	0.999405	−	0.0344842i	$-0.0109788\pi$
$762$	−21.5014	+	14.4255i	−0.778915	+	0.522579i
$763$	−9.49686	+	6.64978i	−0.343810	+	0.240738i
$764$	−83.9763	+	70.4645i	−3.03816	+	2.54932i
$765$	4.39074	+	16.4643i	0.158748	+	0.595269i
$766$	−6.89763	−	39.1184i	−0.249222	−	1.41341i
$767$	4.23459	−	15.8037i	0.152902	−	0.570639i
$768$	−14.6718	+	50.6920i	−0.529424	+	1.82919i
$769$	−8.74217	+	24.0189i	−0.315251	+	0.866144i	0.676324	+	0.736605i	$0.263572\pi$
$769$	−8.74217	+	24.0189i	−0.315251	+	0.866144i	−0.991574	+	0.129540i	$0.958650\pi$
$770$	−15.8547	+	20.4518i	−0.571362	+	0.737031i
$771$	11.1558	−	6.14767i	0.401768	−	0.221403i
$772$	−55.0896	−	14.7612i	−1.98272	−	0.531268i
$773$	18.4916	+	12.9480i	0.665097	+	0.465706i	0.856733	−	0.515760i	$-0.172491\pi$
$773$	18.4916	+	12.9480i	0.665097	+	0.465706i	−0.191636	+	0.981466i	$0.561379\pi$
$774$	−4.20484	+	19.3108i	−0.151140	+	0.694112i
$775$	24.2444	−	1.87947i	0.870884	−	0.0675125i
$776$	−22.9768	−	4.05144i	−0.824820	−	0.145438i
$777$	13.1769	+	19.6404i	0.472718	+	0.704595i
$778$	6.69023	+	6.69023i	0.239856	+	0.239856i
$779$	7.65814	+	13.3124i	0.274381	+	0.476966i
$780$	36.1156	−	31.4771i	1.29314	−	1.12706i
$781$	36.5324	−	13.2967i	1.30723	−	0.475794i
$782$	30.0535	−	21.0437i	1.07471	−	0.752521i
$783$	2.75457	−	18.5949i	0.0984402	−	0.664529i
$784$	22.7182	−	27.0745i	0.811364	−	0.966947i
$785$	−10.5409	−	13.8789i	−0.376221	−	0.495358i
$786$	64.6242	+	1.28833i	2.30507	+	0.0459532i
$787$	−10.2577	−	38.2823i	−0.365648	−	1.36462i	−0.866540	−	0.499108i	$-0.833661\pi$
$787$	−10.2577	−	38.2823i	−0.365648	−	1.36462i	0.500892	−	0.865510i	$-0.333005\pi$
$788$	−14.0433	+	6.54849i	−0.500271	+	0.233280i
$789$	26.9719	−	21.7309i	0.960225	−	0.773641i
$790$	−1.50228	+	30.8976i	−0.0534486	+	1.09929i
$791$	−0.780484	+	0.450613i	−0.0277508	+	0.0160219i
$792$	8.18014	−	63.9964i	0.290669	−	2.27401i
$793$	−1.33849	−	15.2990i	−0.0475312	−	0.543285i
$794$	55.0140	−	46.1623i	1.95238	−	1.63824i
$795$	27.3216	+	45.3374i	0.968997	+	1.60795i
$796$	−27.8461	+	10.1351i	−0.986978	+	0.359231i
$797$	22.5716	+	22.5716i	0.799526	+	0.799526i	0.983021	−	0.183495i	$-0.0587410\pi$
$797$	22.5716	+	22.5716i	0.799526	+	0.799526i	−0.183495	+	0.983021i	$0.558741\pi$
$798$	−24.7786	+	1.63197i	−0.877152	+	0.0577711i
$799$			21.5518i			0.762447i
$800$	−11.3556	−	20.1260i	−0.401482	−	0.711562i
$801$	−5.78359	−	18.1051i	−0.204353	−	0.639713i
$802$	−1.66852	+	19.0713i	−0.0589176	+	0.673431i
$803$	−30.7430	+	2.68966i	−1.08490	+	0.0949162i
$804$	34.0002	−	87.9212i	1.19909	−	3.10074i
$805$	16.1881	−	3.50484i	0.570554	−	0.123529i
$806$	−29.8949	−	17.2598i	−1.05300	−	0.607951i
$807$	45.1155	+	4.85497i	1.58814	+	0.170903i
$808$	5.30383	+	11.3741i	0.186588	+	0.400140i
$809$	−13.0026	+	22.5212i	−0.457149	+	0.791805i	−0.998809	−	0.0487928i	$-0.984463\pi$
$809$	−13.0026	+	22.5212i	−0.457149	+	0.791805i	0.541660	+	0.840597i	$0.317796\pi$
$810$	−19.6252	−	47.0353i	−0.689560	−	1.65265i
$811$	4.11887	+	23.3593i	0.144633	+	0.820254i	0.967661	+	0.252254i	$0.0811718\pi$
$811$	4.11887	+	23.3593i	0.144633	+	0.820254i	−0.823028	+	0.568001i	$0.807717\pi$
$812$	−1.80733	−	20.6578i	−0.0634247	−	0.724948i
$813$	11.1391	−	15.2519i	0.390665	−	0.534909i
$814$	−92.2609	−	16.2681i	−3.23374	−	0.570196i
$815$	−36.1088	−	33.4179i	−1.26484	−	1.17058i
$816$	−25.0486	−	15.1354i	−0.876877	−	0.529845i
$817$	−8.03029	+	8.00518i	−0.280944	+	0.280066i
$818$	−0.291056	+	0.291056i	−0.0101765	+	0.0101765i
$819$	7.34717	−	8.07892i	0.256731	−	0.282300i
$820$	−16.2082	+	30.7629i	−0.566015	+	1.07429i
$821$	25.4084	+	30.2805i	0.886758	+	1.05680i	0.998013	+	0.0630049i	$0.0200684\pi$
$821$	25.4084	+	30.2805i	0.886758	+	1.05680i	−0.111255	+	0.993792i	$0.535487\pi$
$822$	3.78315	−	7.70804i	0.131953	−	0.268849i
$823$	−27.3248	+	39.0239i	−0.952484	+	1.36029i	−0.0197179	+	0.999806i	$0.506277\pi$
$823$	−27.3248	+	39.0239i	−0.952484	+	1.36029i	−0.932766	+	0.360482i	$0.882612\pi$
$824$	29.1910	+	50.5603i	1.01692	+	1.76135i
$825$	−18.8815	−	23.9161i	−0.657371	−	0.832653i
$826$	−18.0428	−	6.56703i	−0.627788	−	0.228496i
$827$	15.8288	+	33.9450i	0.550422	+	1.18038i	0.963010	+	0.269466i	$0.0868472\pi$
$827$	15.8288	+	33.9450i	0.550422	+	1.18038i	−0.412588	+	0.910918i	$0.635375\pi$
$828$	−55.4826	+	51.2262i	−1.92815	+	1.78024i
$829$	33.6249	−	19.4134i	1.16784	−	0.674254i	0.214671	−	0.976686i	$-0.431132\pi$
$829$	33.6249	−	19.4134i	1.16784	−	0.674254i	0.953171	+	0.302433i	$0.0977988\pi$
$830$	−11.0268	+	80.6691i	−0.382745	+	2.80007i
$831$	41.5873	−	14.2044i	1.44265	−	0.492745i
$832$	0.390709	−	4.46582i	0.0135454	−	0.154825i
$833$	−7.74113	−	11.0555i	−0.268214	−	0.383050i
$834$	1.55948	−	7.91793i	0.0540002	−	0.274175i
$835$	−3.81871	−	7.42518i	−0.132152	−	0.256959i
$836$	43.5909	−	51.7846i	1.50762	−	1.79101i
$837$	−18.9054	+	16.7695i	−0.653465	+	0.579639i
$838$	−8.40766	−	3.92056i	−0.290438	−	0.135433i
$839$	1.26540	−	7.17643i	0.0436864	−	0.247758i	−0.955142	−	0.296148i	$-0.904298\pi$
$839$	1.26540	−	7.17643i	0.0436864	−	0.247758i	0.998829	+	0.0483899i	$0.0154090\pi$
$840$	−18.1036	−	24.8496i	−0.624632	−	0.857392i
$841$	−12.1898	−	10.2284i	−0.420337	−	0.352704i
$842$	15.5116	−	22.1529i	0.534566	−	0.763439i
$843$	−24.1169	+	23.1741i	−0.830630	+	0.798159i
$844$	42.7023	+	24.6542i	1.46987	+	0.848632i
$845$	7.04847	−	9.09221i	0.242475	−	0.312781i
$846$	−8.65451	−	63.8771i	−0.297548	−	2.19614i
$847$	−0.463856	−	1.73113i	−0.0159383	−	0.0594825i
$848$	−87.8170	−	23.5305i	−3.01565	−	0.808040i
$849$	18.0760	−	46.7429i	0.620368	−	1.60421i
$850$	−31.1492	+	8.01677i	−1.06841	+	0.274973i
$851$	38.5437	+	45.9346i	1.32126	+	1.57462i
$852$	5.68302	+	84.2736i	0.194697	+	2.88717i
$853$	−28.4651	−	13.2735i	−0.974627	−	0.454476i	−0.130986	−	0.991384i	$-0.541814\pi$
$853$	−28.4651	−	13.2735i	−0.974627	−	0.454476i	−0.843641	+	0.536908i	$0.819592\pi$
$854$	−18.0228			−0.616727
$855$	5.15668	−	28.7821i	0.176355	−	0.984327i
$856$	−70.5732			−2.41214
$857$	−36.8459	−	17.1815i	−1.25863	−	0.586909i	−0.325193	−	0.945648i	$-0.605429\pi$
$857$	−36.8459	−	17.1815i	−1.25863	−	0.586909i	−0.933438	+	0.358739i	$0.883207\pi$
$858$	2.91035	+	43.1577i	0.0993578	+	1.47338i
$859$	−5.62167	−	6.69964i	−0.191809	−	0.228589i	0.661566	−	0.749887i	$-0.269892\pi$
$859$	−5.62167	−	6.69964i	−0.191809	−	0.228589i	−0.853374	+	0.521298i	$0.825448\pi$
$860$	−25.0356	−	5.68041i	−0.853706	−	0.193700i
$861$	−2.85873	+	7.39240i	−0.0974253	+	0.251932i
$862$	−16.9305	−	4.53652i	−0.576656	−	0.154514i
$863$	−1.27655	−	4.76415i	−0.0434543	−	0.162174i	0.940789	−	0.338992i	$-0.110086\pi$
$863$	−1.27655	−	4.76415i	−0.0434543	−	0.162174i	−0.984243	+	0.176819i	$0.943419\pi$
$864$	22.0356	+	9.54766i	0.749668	+	0.324818i
$865$	−22.7439	+	2.87984i	−0.773317	+	0.0979176i
$866$	−17.0890	−	9.86637i	−0.580709	−	0.335273i
$867$	13.1732	−	12.6582i	0.447385	−	0.429895i
$868$	−15.9900	+	22.8361i	−0.542735	+	0.775106i
$869$	−14.7237	−	12.3547i	−0.499468	−	0.419104i
$870$	35.0533	+	5.50529i	1.18842	+	0.186647i
$871$	−6.00150	+	34.0362i	−0.203353	+	1.15327i
$872$	49.4487	+	23.0583i	1.67454	+	0.780852i
$873$	3.40239	−	10.9345i	0.115154	−	0.370076i
$874$	−62.0185	+	10.8354i	−2.09781	+	0.366513i
$875$	−14.3667	−	2.10888i	−0.485683	−	0.0712933i
$876$	12.9565	−	65.7843i	0.437761	−	2.22265i
$877$	−27.1383	−	38.7575i	−0.916396	−	1.30875i	−0.950949	−	0.309346i	$-0.899890\pi$
$877$	−27.1383	−	38.7575i	−0.916396	−	1.30875i	0.0345533	−	0.999403i	$-0.488999\pi$
$878$	−1.02890	+	11.7604i	−0.0347237	+	0.396894i
$879$	−30.9208	+	10.5612i	−1.04293	+	0.356221i
$880$	51.8530	+	7.08786i	1.74797	+	0.238932i
$881$	−7.60268	+	4.38941i	−0.256141	+	0.147883i	−0.622573	−	0.782562i	$-0.713913\pi$
$881$	−7.60268	+	4.38941i	−0.256141	+	0.147883i	0.366432	+	0.930445i	$0.380579\pi$
$882$	27.3834	+	29.6586i	0.922047	+	0.998659i
$883$	−12.3179	−	26.4158i	−0.414531	−	0.888964i	−0.997094	−	0.0761786i	$-0.975728\pi$
$883$	−12.3179	−	26.4158i	−0.414531	−	0.888964i	0.582564	−	0.812785i	$-0.302050\pi$
$884$	29.5258	+	10.7465i	0.993060	+	0.361444i
$885$	12.6186	−	18.7602i	0.424168	−	0.630618i
$886$	17.6351	+	30.5449i	0.592463	+	1.02618i
$887$	2.03278	−	2.90312i	0.0682542	−	0.0974771i	−0.783574	−	0.621299i	$-0.786605\pi$
$887$	2.03278	−	2.90312i	0.0682542	−	0.0974771i	0.851828	+	0.523822i	$0.175494\pi$
$888$	49.0408	−	99.9190i	1.64570	−	3.35306i
$889$	−4.92787	−	5.87281i	−0.165276	−	0.196968i
$890$	34.2692	−	10.6188i	1.14871	−	0.355944i
$891$	30.6485	+	7.96524i	1.02676	+	0.266846i
$892$	−19.8676	+	19.8676i	−0.665217	+	0.665217i
$893$	15.6822	−	33.4936i	0.524785	−	1.12082i
$894$	−29.9121	−	18.0741i	−1.00041	−	0.604488i
$895$	−15.6157	+	0.604370i	−0.521974	+	0.0202019i
$896$	−17.0036	−	2.99820i	−0.568052	−	0.100163i
$897$	16.3290	−	22.3582i	0.545210	−	0.746518i
$898$	2.46260	+	28.1477i	0.0821781	+	0.939300i
$899$	−3.05520	−	17.3269i	−0.101897	−	0.577884i
$900$	61.3173	−	24.9590i	2.04391	−	0.831968i
$901$	−17.3585	+	30.0658i	−0.578294	+	1.00164i
$902$	−13.2682	−	28.4537i	−0.441782	−	0.947405i
$903$	−5.81811	−	0.626099i	−0.193615	−	0.0208353i
$904$	3.67305	+	2.12064i	0.122164	+	0.0705314i
$905$	−4.84316	−	22.3695i	−0.160992	−	0.743588i
$906$	1.40371	−	3.62986i	0.0466352	−	0.120594i
$907$	38.4016	−	3.35970i	1.27510	−	0.111557i	0.570582	−	0.821240i	$-0.306718\pi$
$907$	38.4016	−	3.35970i	1.27510	−	0.111557i	0.704521	+	0.709683i	$0.251162\pi$
$908$	−4.71230	+	53.8618i	−0.156383	+	1.78747i
$909$	−5.86771	+	1.87441i	−0.194620	+	0.0621704i
$910$	15.1283	+	14.0010i	0.501500	+	0.464127i
$911$		−	45.7871i		−	1.51699i	−0.651677	−	0.758496i	$-0.725934\pi$
$911$		−	45.7871i		−	1.51699i	0.651677	−	0.758496i	$-0.274066\pi$
$912$	27.9147	+	41.7486i	0.924347	+	1.38243i
$913$	−35.7716	−	35.7716i	−1.18387	−	1.18387i
$914$	−48.2306	+	17.5545i	−1.59533	+	0.580652i
$915$	5.10738	−	20.5984i	0.168845	−	0.680962i
$916$	12.1717	−	10.2133i	0.402166	−	0.337457i
$917$	1.66802	+	19.0655i	0.0550828	+	0.629600i
$918$	20.7746	−	26.1863i	0.685663	−	0.864277i
$919$	36.7249	−	21.2031i	1.21144	−	0.699426i	0.248368	−	0.968666i	$-0.420106\pi$
$919$	36.7249	−	21.2031i	1.21144	−	0.699426i	0.963073	+	0.269239i	$0.0867723\pi$
$920$	−52.3759	−	57.7293i	−1.72678	−	1.90328i
$921$	−14.1557	+	11.4051i	−0.466446	+	0.375809i
$922$	−57.7155	+	26.9132i	−1.90076	+	0.886338i
$923$	−8.01505	−	29.9126i	−0.263818	−	0.984584i
$924$	34.9259	+	0.696272i	1.14898	+	0.0229057i
$925$	−17.4898	−	49.5743i	−0.575060	−	1.62999i
$926$	−56.4387	+	67.2610i	−1.85469	+	2.21033i
$927$	−26.4326	+	11.0656i	−0.868161	+	0.363442i
$928$	−13.6960	+	9.59006i	−0.449594	+	0.314809i
$929$	22.6009	−	8.22606i	0.741512	−	0.269888i	0.0564825	−	0.998404i	$-0.482011\pi$
$929$	22.6009	−	8.22606i	0.741512	−	0.269888i	0.685030	+	0.728515i	$0.259789\pi$
$930$	−31.3419	−	35.9604i	−1.02774	−	1.17919i
$931$	3.98592	+	22.8141i	0.130633	+	0.747703i
$932$	−13.1576	−	13.1576i	−0.430990	−	0.430990i
$933$	21.0475	+	31.3718i	0.689065	+	1.02707i
$934$	−55.4154	−	9.77122i	−1.81325	−	0.319724i
$935$	7.73916	−	18.4255i	0.253098	−	0.602578i
$936$	−50.2149	−	10.9341i	−1.64133	−	0.357392i
$937$	−14.6263	−	10.2415i	−0.477821	−	0.334574i	0.309728	−	0.950825i	$-0.399762\pi$
$937$	−14.6263	−	10.2415i	−0.477821	−	0.334574i	−0.787550	+	0.616251i	$0.788651\pi$
$938$	39.1774	+	10.4976i	1.27919	+	0.342757i
$939$	−34.8341	+	19.1961i	−1.13677	+	0.626441i
$940$	83.0693	−	10.5183i	2.70942	−	0.343068i
$941$	1.15784	−	3.18113i	0.0377444	−	0.103702i	−0.919389	−	0.393350i	$-0.871316\pi$
$941$	1.15784	−	3.18113i	0.0377444	−	0.103702i	0.957133	+	0.289648i	$0.0935383\pi$
$942$	−9.50487	+	32.8398i	−0.309685	+	1.06998i
$943$	−5.20091	+	19.4101i	−0.169365	+	0.632079i
$944$	6.74309	+	38.2420i	0.219469	+	1.24467i
$945$	13.2250	−	7.26754i	0.430209	−	0.236413i
$946$	17.7562	−	14.8992i	0.577305	−	0.484416i
$947$	−1.10444	+	0.773334i	−0.0358893	+	0.0251300i	−0.591383	−	0.806390i	$-0.701418\pi$
$947$	−1.10444	+	0.773334i	−0.0358893	+	0.0251300i	0.555494	+	0.831520i	$0.312529\pi$
$948$	34.6774	−	23.2653i	1.12627	−	0.755622i
$949$			24.5821i			0.797969i
$950$	54.2423	+	10.2070i	1.75985	+	0.331158i
$951$	20.8282	+	12.5852i	0.675400	+	0.408104i
$952$	8.52178	−	18.2750i	0.276193	−	0.592297i
$953$	32.3288	+	46.1703i	1.04723	+	1.49560i	0.857986	+	0.513673i	$0.171716\pi$
$953$	32.3288	+	46.1703i	1.04723	+	1.49560i	0.189246	+	0.981930i	$0.439395\pi$
$954$	39.3752	−	96.0822i	1.27482	−	3.11078i
$955$	46.9890	−	29.6093i	1.52053	−	0.958136i
$956$	2.43362	−	0.429114i	0.0787090	−	0.0138785i
$957$	−15.8971	+	15.2756i	−0.513880	+	0.493792i
$958$	−2.28842	+	0.613181i	−0.0739355	+	0.0198110i
$959$	2.38902	+	0.869532i	0.0771454	+	0.0280786i
$960$	2.51231	−	5.66249i	0.0810843	−	0.182756i
$961$	3.67353	−	6.36275i	0.118501	−	0.205250i
$962$	−19.3143	+	72.0821i	−0.622719	+	2.32402i
$963$	4.39191	−	34.3595i	0.141527	−	1.10722i
$964$	−66.4652	+	79.2101i	−2.14070	+	2.55119i
$965$	26.6408	+	11.1898i	0.857597	+	0.360212i
$966$	−24.4685	−	21.3769i	−0.787260	−	0.687790i
$967$	−20.5374	+	44.0426i	−0.660438	+	1.41631i	0.235385	+	0.971902i	$0.424365\pi$
$967$	−20.5374	+	44.0426i	−0.660438	+	1.41631i	−0.895823	+	0.444411i	$0.853413\pi$
$968$	−5.96397	+	5.96397i	−0.191689	+	0.191689i
$969$	18.1579	−	6.17020i	0.583315	−	0.198215i
$970$	20.5832	+	6.60204i	0.660887	+	0.211979i
$971$	4.13642	+	11.3647i	0.132744	+	0.364711i	0.988201	−	0.153163i	$-0.0489459\pi$
$971$	4.13642	+	11.3647i	0.132744	+	0.364711i	−0.855457	+	0.517874i	$0.826724\pi$
$972$	−35.1359	+	59.1511i	−1.12698	+	1.89727i
$973$	2.38036	+	0.208255i	0.0763109	+	0.00667634i
$974$	9.12108	+	7.65349i	0.292258	+	0.245234i
$975$	−20.2889	+	13.3226i	−0.649766	+	0.426666i
$976$	18.2248	+	31.5663i	0.583362	+	1.01041i
$977$	47.9134	−	12.8383i	1.53288	−	0.410735i	0.608925	−	0.793227i	$-0.291601\pi$
$977$	47.9134	−	12.8383i	1.53288	−	0.410735i	0.923959	+	0.382492i	$0.124934\pi$
$978$	−10.3263	+	95.9588i	−0.330199	+	3.06842i
$979$	−7.62413	+	20.9471i	−0.243668	+	0.669473i
$980$	−38.8343	+	35.2330i	−1.24052	+	1.12548i
$981$	−14.3035	+	22.6398i	−0.456677	+	0.722834i
$982$	25.3670	+	17.7622i	0.809495	+	0.566814i
$983$	−27.4174	+	2.39871i	−0.874479	+	0.0765070i	−0.515552	−	0.856858i	$-0.672413\pi$
$983$	−27.4174	+	2.39871i	−0.874479	+	0.0765070i	−0.358928	+	0.933365i	$0.616857\pi$
$984$	36.8554	−	5.74367i	1.17491	−	0.183102i
$985$	7.49870	−	2.32359i	0.238929	−	0.0740357i
$986$	7.95944	+	21.8684i	0.253480	+	0.696431i
$987$	18.5306	−	4.57142i	0.589836	−	0.145510i
$988$	−38.0662	−	38.1856i	−1.21105	−	1.21485i
$989$	−14.8360			−0.471757
$990$	−15.5389	+	57.7190i	−0.493860	+	1.83443i
$991$	7.73953	−	43.8931i	0.245854	−	1.39431i	−0.572646	−	0.819803i	$-0.694083\pi$
$991$	7.73953	−	43.8931i	0.245854	−	1.39431i	0.818500	−	0.574506i	$-0.194806\pi$
$992$	22.3918	+	1.95903i	0.710942	+	0.0621994i
$993$	−21.2759	−	10.4423i	−0.675169	−	0.331377i
$994$	−35.7902	+	6.31077i	−1.13519	+	0.200165i
$995$	14.6735	−	3.17691i	0.465180	−	0.100715i
$996$	96.2615	−	53.0470i	3.05016	−	1.68086i
$997$	17.1774	−	8.00995i	0.544013	−	0.253678i	−0.131129	−	0.991365i	$-0.541860\pi$
$997$	17.1774	−	8.00995i	0.544013	−	0.253678i	0.675142	+	0.737688i	$0.264082\pi$
$998$	5.58476	−	2.60422i	0.176782	−	0.0824350i
$999$	45.5951	+	30.0944i	1.44256	+	0.952144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bi.a.233.35	yes	432
3.2	odd	2	inner	285.2.bi.a.233.2	yes	432
5.2	odd	4	inner	285.2.bi.a.62.2	yes	432
15.2	even	4	inner	285.2.bi.a.62.35	yes	432
19.4	even	9	inner	285.2.bi.a.23.35	yes	432
57.23	odd	18	inner	285.2.bi.a.23.2	✓	432
95.42	odd	36	inner	285.2.bi.a.137.2	yes	432
285.137	even	36	inner	285.2.bi.a.137.35	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bi.a.23.2	✓	432	57.23	odd	18	inner
285.2.bi.a.23.35	yes	432	19.4	even	9	inner
285.2.bi.a.62.2	yes	432	5.2	odd	4	inner
285.2.bi.a.62.35	yes	432	15.2	even	4	inner
285.2.bi.a.137.2	yes	432	95.42	odd	36	inner
285.2.bi.a.137.35	yes	432	285.137	even	36	inner
285.2.bi.a.233.2	yes	432	3.2	odd	2	inner
285.2.bi.a.233.35	yes	432	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29521 + 1.07028i) q^{2} +(0.116537 + 1.72813i) q^{3} +(2.83694 + 3.38094i) q^{4} +(-1.19209 - 1.89180i) q^{5} +(-1.58209 + 4.09115i) q^{6} +(-1.25451 - 0.336146i) q^{7} +(1.58194 + 5.90389i) q^{8} +(-2.97284 + 0.402780i) q^{9} +O(q^{10})\)	\(q+(2.29521 + 1.07028i) q^{2} +(0.116537 + 1.72813i) q^{3} +(2.83694 + 3.38094i) q^{4} +(-1.19209 - 1.89180i) q^{5} +(-1.58209 + 4.09115i) q^{6} +(-1.25451 - 0.336146i) q^{7} +(1.58194 + 5.90389i) q^{8} +(-2.97284 + 0.402780i) q^{9} +(-0.711347 - 5.61796i) q^{10} +(3.04712 + 1.75926i) q^{11} +(-5.51207 + 5.29660i) q^{12} +(1.60756 - 2.29584i) q^{13} +(-2.51961 - 2.11420i) q^{14} +(3.13035 - 2.28055i) q^{15} +(-1.15510 + 6.55091i) q^{16} +(2.30214 + 1.07351i) q^{17} +(-7.25439 - 2.25729i) q^{18} +(-2.79661 - 3.34349i) q^{19} +(3.01418 - 9.39731i) q^{20} +(0.434705 - 2.20713i) q^{21} +(5.11090 + 7.29913i) q^{22} +(0.497076 - 5.68160i) q^{23} +(-10.0183 + 3.42181i) q^{24} +(-2.15785 + 4.51040i) q^{25} +(6.14688 - 3.54890i) q^{26} +(-1.04250 - 5.09050i) q^{27} +(-2.42249 - 5.19505i) q^{28} +(3.39948 + 1.23731i) q^{29} +(9.62564 - 1.88400i) q^{30} +(-2.43171 - 4.21185i) q^{31} +(-2.65091 + 3.78589i) q^{32} +(-2.68511 + 5.47083i) q^{33} +(4.13496 + 4.92786i) q^{34} +(0.859569 + 2.77401i) q^{35} +(-9.79554 - 8.90831i) q^{36} +(-7.43438 + 7.43438i) q^{37} +(-2.84036 - 10.6672i) q^{38} +(4.15483 + 2.51052i) q^{39} +(9.28318 - 10.0307i) q^{40} +(-3.46983 - 0.611825i) q^{41} +(3.35998 - 4.60058i) q^{42} +(-0.226718 - 2.59140i) q^{43} +(2.69657 + 15.2930i) q^{44} +(4.30587 + 5.14388i) q^{45} +(7.22177 - 12.5085i) q^{46} +(3.58571 + 7.68957i) q^{47} +(-11.4554 - 1.23274i) q^{48} +(-4.60137 - 2.65660i) q^{49} +(-9.78009 + 8.04284i) q^{50} +(-1.58687 + 4.10350i) q^{51} +(12.3226 - 1.07809i) q^{52} +(-1.19119 + 13.6154i) q^{53} +(3.05548 - 12.7996i) q^{54} +(-0.304272 - 7.86175i) q^{55} -7.93826i q^{56} +(5.45207 - 5.22254i) q^{57} +(6.47827 + 6.47827i) q^{58} +(5.48561 - 1.99660i) q^{59} +(16.5910 + 4.11375i) q^{60} +(4.19756 - 3.52217i) q^{61} +(-1.07346 - 12.2697i) q^{62} +(3.86486 + 0.494014i) q^{63} +(1.38520 - 0.799744i) q^{64} +(-6.25963 - 0.304351i) q^{65} +(-12.0182 + 9.68290i) q^{66} +(-11.1761 + 5.21149i) q^{67} +(2.90159 + 10.8289i) q^{68} +(9.87645 + 0.196894i) q^{69} +(-0.996058 + 7.28692i) q^{70} +(7.10233 - 8.46423i) q^{71} +(-7.08083 - 16.9141i) q^{72} +(-7.18468 + 5.03077i) q^{73} +(-25.0203 + 9.10666i) q^{74} +(-8.04601 - 3.20340i) q^{75} +(3.37031 - 18.9405i) q^{76} +(-3.23128 - 3.23128i) q^{77} +(6.84928 + 10.2090i) q^{78} +(-5.37968 - 0.948582i) q^{79} +(13.7700 - 5.62404i) q^{80} +(8.67554 - 2.39480i) q^{81} +(-7.30918 - 5.11795i) q^{82} +(-13.8880 - 3.72127i) q^{83} +(8.69539 - 4.79179i) q^{84} +(-0.713495 - 5.63492i) q^{85} +(2.25315 - 6.19047i) q^{86} +(-1.74206 + 6.01892i) q^{87} +(-5.56608 + 20.7729i) q^{88} +(1.10014 + 6.23923i) q^{89} +(4.37752 + 16.4148i) q^{90} +(-2.78844 + 2.33978i) q^{91} +(20.6193 - 14.4378i) q^{92} +(6.99523 - 4.69314i) q^{93} +21.4869i q^{94} +(-2.99143 + 9.27639i) q^{95} +(-6.85142 - 4.13991i) q^{96} +(-1.61322 + 3.45955i) q^{97} +(-7.71783 - 11.0222i) q^{98} +(-9.76719 - 4.00266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Introduction

L-functions

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