LMFDB - Embedded newform 345.2.m.c.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	345.16
Dual form			345.2.m.c.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45237 - 1.67613i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.415386 - 2.88907i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.315630 - 2.19526i) q^{6} +(-1.14822 + 0.337148i) q^{7} +(-1.71422 - 1.10166i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(1.45237 - 1.67613i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.415386 - 2.88907i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.315630 - 2.19526i) q^{6} +(-1.14822 + 0.337148i) q^{7} +(-1.71422 - 1.10166i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-2.12799 - 0.624835i) q^{10} +(-1.24933 - 1.44181i) q^{11} +(-1.91139 - 2.20587i) q^{12} +(1.06836 + 0.313700i) q^{13} +(-1.10254 + 2.41423i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(1.26489 - 0.371404i) q^{16} +(0.404389 - 2.81259i) q^{17} +(-0.921321 - 2.01741i) q^{18} +(0.743567 + 5.17162i) q^{19} +(-2.45543 + 1.57801i) q^{20} +(-0.783669 + 0.904402i) q^{21} -4.23115 q^{22} +(1.92677 + 4.39176i) q^{23} -2.03770 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.07746 - 1.33510i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.45100 + 3.17724i) q^{28} +(-0.516816 + 3.59454i) q^{29} +(-2.12799 + 0.624835i) q^{30} +(3.80710 + 2.44667i) q^{31} +(2.90755 - 6.36664i) q^{32} +(-1.83051 - 0.537485i) q^{33} +(-4.12693 - 4.76273i) q^{34} +(0.783669 + 0.904402i) q^{35} +(-2.80055 - 0.822315i) q^{36} +(-1.35198 + 2.96043i) q^{37} +(9.74822 + 6.26480i) q^{38} +(1.06836 - 0.313700i) q^{39} +(-0.289995 + 2.01696i) q^{40} +(-2.05888 - 4.50832i) q^{41} +(0.377714 + 2.62706i) q^{42} +(-3.15508 + 2.02764i) q^{43} +(-3.64653 + 4.20832i) q^{44} -1.00000 q^{45} +(10.1595 + 3.14895i) q^{46} +9.16361 q^{47} +(0.863294 - 0.996295i) q^{48} +(-4.68403 + 3.01024i) q^{49} +(0.315630 + 2.19526i) q^{50} +(-1.18041 - 2.58473i) q^{51} +(0.462518 - 3.21689i) q^{52} +(3.35984 - 0.986538i) q^{53} +(-1.86576 - 1.19905i) q^{54} +(-0.792522 + 1.73538i) q^{55} +(2.33973 + 0.687006i) q^{56} +(3.42152 + 3.94864i) q^{57} +(5.27428 + 6.08685i) q^{58} +(-4.67952 - 1.37403i) q^{59} +(-1.21250 + 2.65501i) q^{60} +(-6.76838 - 4.34977i) q^{61} +(9.63025 - 2.82770i) q^{62} +(-0.170308 + 1.18451i) q^{63} +(-5.35318 - 11.7218i) q^{64} +(-0.158463 - 1.10213i) q^{65} +(-3.55947 + 2.28753i) q^{66} +(-3.91161 + 4.51424i) q^{67} -8.29374 q^{68} +(3.99527 + 2.65289i) q^{69} +2.65407 q^{70} +(3.58893 - 4.14184i) q^{71} +(-1.71422 + 1.10166i) q^{72} +(0.943464 + 6.56193i) q^{73} +(2.99847 + 6.56573i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(14.6323 - 4.29643i) q^{76} +(1.92061 + 1.23430i) q^{77} +(1.02586 - 2.24632i) q^{78} +(-9.78739 - 2.87384i) q^{79} +(-0.863294 - 0.996295i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.5468 - 3.09681i) q^{82} +(2.44164 - 5.34644i) q^{83} +(2.93841 + 1.88840i) q^{84} +(-2.72641 + 0.800546i) q^{85} +(-1.18375 + 8.23320i) q^{86} +(1.50858 + 3.30333i) q^{87} +(0.553247 + 3.84792i) q^{88} +(-7.19727 + 4.62541i) q^{89} +(-1.45237 + 1.67613i) q^{90} -1.33248 q^{91} +(11.8877 - 7.39086i) q^{92} +4.52551 q^{93} +(13.3090 - 15.3594i) q^{94} +(4.39538 - 2.82474i) q^{95} +(-0.996081 - 6.92789i) q^{96} +(0.672143 + 1.47179i) q^{97} +(-1.75740 + 12.2230i) q^{98} +(-1.83051 + 0.537485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.45237	−	1.67613i	1.02698	−	1.18520i	0.0444675	−	0.999011i	$-0.485841\pi$
$2$	1.45237	−	1.67613i	1.02698	−	1.18520i	0.982514	−	0.186189i	$-0.0596137\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.415386	−	2.88907i	−0.207693	−	1.44454i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.315630	−	2.19526i	0.128856	−	0.896210i
$7$	−1.14822	+	0.337148i	−0.433987	+	0.127430i	−0.491427	−	0.870919i	$-0.663524\pi$
$7$	−1.14822	+	0.337148i	−0.433987	+	0.127430i	0.0574399	+	0.998349i	$0.481706\pi$
$8$	−1.71422	−	1.10166i	−0.606068	−	0.389497i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−2.12799	−	0.624835i	−0.672931	−	0.197590i
$11$	−1.24933	−	1.44181i	−0.376688	−	0.434721i	0.535473	−	0.844552i	$-0.320133\pi$
$11$	−1.24933	−	1.44181i	−0.376688	−	0.434721i	−0.912162	+	0.409831i	$0.865588\pi$
$12$	−1.91139	−	2.20587i	−0.551772	−	0.636779i
$13$	1.06836	+	0.313700i	0.296311	+	0.0870047i	0.426509	−	0.904483i	$-0.359743\pi$
$13$	1.06836	+	0.313700i	0.296311	+	0.0870047i	−0.130198	+	0.991488i	$0.541561\pi$
$14$	−1.10254	+	2.41423i	−0.294666	+	0.645229i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	1.26489	−	0.371404i	0.316222	−	0.0928511i
$17$	0.404389	−	2.81259i	0.0980788	−	0.682153i	−0.880161	−	0.474675i	$-0.842565\pi$
$17$	0.404389	−	2.81259i	0.0980788	−	0.682153i	0.978240	−	0.207478i	$-0.0665254\pi$
$18$	−0.921321	−	2.01741i	−0.217157	−	0.475508i
$19$	0.743567	+	5.17162i	0.170586	+	1.18645i	0.877650	+	0.479302i	$0.159110\pi$
$19$	0.743567	+	5.17162i	0.170586	+	1.18645i	−0.707064	+	0.707149i	$0.749981\pi$
$20$	−2.45543	+	1.57801i	−0.549052	+	0.352854i
$21$	−0.783669	+	0.904402i	−0.171011	+	0.197357i
$22$	−4.23115			−0.902083
$23$	1.92677	+	4.39176i	0.401760	+	0.915745i
$23$	1.92677	+	4.39176i	0.401760	+	0.915745i
$24$	−2.03770			−0.415943
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	2.07746	−	1.33510i	0.407424	−	0.261835i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	1.45100	+	3.17724i	0.274213	+	0.600443i
$29$	−0.516816	+	3.59454i	−0.0959704	+	0.667489i	0.883874	+	0.467725i	$0.154926\pi$
$29$	−0.516816	+	3.59454i	−0.0959704	+	0.667489i	−0.979844	+	0.199763i	$0.935983\pi$
$30$	−2.12799	+	0.624835i	−0.388517	+	0.114079i
$31$	3.80710	+	2.44667i	0.683775	+	0.439436i	0.835868	−	0.548931i	$-0.184965\pi$
$31$	3.80710	+	2.44667i	0.683775	+	0.439436i	−0.152093	+	0.988366i	$0.548601\pi$
$32$	2.90755	−	6.36664i	0.513986	−	1.12547i
$33$	−1.83051	−	0.537485i	−0.318650	−	0.0935641i
$34$	−4.12693	−	4.76273i	−0.707762	−	0.816801i
$35$	0.783669	+	0.904402i	0.132464	+	0.152872i
$36$	−2.80055	−	0.822315i	−0.466758	−	0.137053i
$37$	−1.35198	+	2.96043i	−0.222264	+	0.486691i	−0.987610	−	0.156928i	$-0.949841\pi$
$37$	−1.35198	+	2.96043i	−0.222264	+	0.486691i	0.765346	+	0.643620i	$0.222568\pi$
$38$	9.74822	+	6.26480i	1.58137	+	1.01628i
$39$	1.06836	−	0.313700i	0.171075	−	0.0502322i
$40$	−0.289995	+	2.01696i	−0.0458522	+	0.318909i
$41$	−2.05888	−	4.50832i	−0.321543	−	0.704081i	0.677976	−	0.735084i	$-0.262857\pi$
$41$	−2.05888	−	4.50832i	−0.321543	−	0.704081i	−0.999519	+	0.0310028i	$0.990130\pi$
$42$	0.377714	+	2.62706i	0.0582825	+	0.405363i
$43$	−3.15508	+	2.02764i	−0.481145	+	0.309213i	−0.758635	−	0.651515i	$-0.774134\pi$
$43$	−3.15508	+	2.02764i	−0.481145	+	0.309213i	0.277491	+	0.960728i	$0.410497\pi$
$44$	−3.64653	+	4.20832i	−0.549735	+	0.634428i
$45$	−1.00000			−0.149071
$46$	10.1595	+	3.14895i	1.49794	+	0.464287i
$47$	9.16361			1.33665			0.668325	−	0.743869i	$-0.267012\pi$
$47$	9.16361			1.33665			0.668325	+	0.743869i	$0.267012\pi$
$48$	0.863294	−	0.996295i	0.124606	−	0.143803i
$49$	−4.68403	+	3.01024i	−0.669147	+	0.430035i
$50$	0.315630	+	2.19526i	0.0446369	+	0.310456i
$51$	−1.18041	−	2.58473i	−0.165290	−	0.361934i
$52$	0.462518	−	3.21689i	0.0641397	−	0.446102i
$53$	3.35984	−	0.986538i	0.461509	−	0.135511i	−0.0427090	−	0.999088i	$-0.513599\pi$
$53$	3.35984	−	0.986538i	0.461509	−	0.135511i	0.504218	+	0.863576i	$0.331781\pi$
$54$	−1.86576	−	1.19905i	−0.253898	−	0.163170i
$55$	−0.792522	+	1.73538i	−0.106864	+	0.233999i
$56$	2.33973	+	0.687006i	0.312659	+	0.0918050i
$57$	3.42152	+	3.94864i	0.453191	+	0.523010i
$58$	5.27428	+	6.08685i	0.692548	+	0.799242i
$59$	−4.67952	−	1.37403i	−0.609222	−	0.178884i	−0.0374531	−	0.999298i	$-0.511924\pi$
$59$	−4.67952	−	1.37403i	−0.609222	−	0.178884i	−0.571769	+	0.820415i	$0.693743\pi$
$60$	−1.21250	+	2.65501i	−0.156534	+	0.342761i
$61$	−6.76838	−	4.34977i	−0.866602	−	0.556931i	0.0301098	−	0.999547i	$-0.490414\pi$
$61$	−6.76838	−	4.34977i	−0.866602	−	0.556931i	−0.896712	+	0.442616i	$0.854051\pi$
$62$	9.63025	−	2.82770i	1.22304	−	0.359118i
$63$	−0.170308	+	1.18451i	−0.0214567	+	0.149235i
$64$	−5.35318	−	11.7218i	−0.669147	−	1.46523i
$65$	−0.158463	−	1.10213i	−0.0196549	−	0.136703i
$66$	−3.55947	+	2.28753i	−0.438140	+	0.281575i
$67$	−3.91161	+	4.51424i	−0.477880	+	0.551502i	−0.942586	−	0.333962i	$-0.891614\pi$
$67$	−3.91161	+	4.51424i	−0.477880	+	0.551502i	0.464707	+	0.885465i	$0.346160\pi$
$68$	−8.29374			−1.00576
$69$	3.99527	+	2.65289i	0.480974	+	0.319370i
$70$	2.65407			0.317222
$71$	3.58893	−	4.14184i	0.425927	−	0.491546i	−0.501706	−	0.865038i	$-0.667294\pi$
$71$	3.58893	−	4.14184i	0.425927	−	0.491546i	0.927633	+	0.373492i	$0.121840\pi$
$72$	−1.71422	+	1.10166i	−0.202023	+	0.129832i
$73$	0.943464	+	6.56193i	0.110424	+	0.768016i	0.967508	+	0.252840i	$0.0813646\pi$
$73$	0.943464	+	6.56193i	0.110424	+	0.768016i	−0.857084	+	0.515177i	$0.827726\pi$
$74$	2.99847	+	6.56573i	0.348565	+	0.763251i
$75$	−0.142315	+	0.989821i	−0.0164331	+	0.114295i
$76$	14.6323	−	4.29643i	1.67844	−	0.492835i
$77$	1.92061	+	1.23430i	0.218874	+	0.140662i
$78$	1.02586	−	2.24632i	0.116156	−	0.254346i
$79$	−9.78739	−	2.87384i	−1.10117	−	0.323332i	−0.319851	−	0.947468i	$-0.603633\pi$
$79$	−9.78739	−	2.87384i	−1.10117	−	0.323332i	−0.781316	+	0.624136i	$0.785451\pi$
$80$	−0.863294	−	0.996295i	−0.0965192	−	0.111389i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−10.5468	−	3.09681i	−1.16470	−	0.341985i
$83$	2.44164	−	5.34644i	0.268004	−	0.586848i	−0.727005	−	0.686633i	$-0.759088\pi$
$83$	2.44164	−	5.34644i	0.268004	−	0.586848i	0.995009	+	0.0997848i	$0.0318154\pi$
$84$	2.93841	+	1.88840i	0.320606	+	0.206041i
$85$	−2.72641	+	0.800546i	−0.295721	+	0.0868314i
$86$	−1.18375	+	8.23320i	−0.127648	+	0.887808i
$87$	1.50858	+	3.30333i	0.161737	+	0.354154i
$88$	0.553247	+	3.84792i	0.0589763	+	0.410190i
$89$	−7.19727	+	4.62541i	−0.762909	+	0.490292i	−0.863322	−	0.504654i	$-0.831620\pi$
$89$	−7.19727	+	4.62541i	−0.762909	+	0.490292i	0.100412	+	0.994946i	$0.467984\pi$
$90$	−1.45237	+	1.67613i	−0.153093	+	0.176679i
$91$	−1.33248			−0.139682
$92$	11.8877	−	7.39086i	1.23938	−	0.770550i
$93$	4.52551			0.469273
$94$	13.3090	−	15.3594i	1.37271	−	1.58420i
$95$	4.39538	−	2.82474i	0.450957	−	0.289812i
$96$	−0.996081	−	6.92789i	−0.101662	−	0.707075i
$97$	0.672143	+	1.47179i	0.0682458	+	0.149437i	0.940681	−	0.339292i	$-0.110188\pi$
$97$	0.672143	+	1.47179i	0.0682458	+	0.149437i	−0.872435	+	0.488730i	$0.837460\pi$
$98$	−1.75740	+	12.2230i	−0.177525	+	1.23471i
$99$	−1.83051	+	0.537485i	−0.183973	+	0.0540193i
$100$	2.45543	+	1.57801i	0.245543	+	0.157801i
$101$	5.52561	−	12.0994i	0.549819	−	1.20394i	−0.407047	−	0.913407i	$-0.633442\pi$
$101$	5.52561	−	12.0994i	0.549819	−	1.20394i	0.956866	−	0.290529i	$-0.0938311\pi$
$102$	−6.04672	−	1.77548i	−0.598714	−	0.175798i
$103$	−9.93522	−	11.4659i	−0.978946	−	1.12976i	−0.991535	−	0.129843i	$-0.958553\pi$
$103$	−9.93522	−	11.4659i	−0.978946	−	1.12976i	0.0125883	−	0.999921i	$-0.495993\pi$
$104$	−1.48582	−	1.71473i	−0.145697	−	0.168143i
$105$	1.14822	+	0.337148i	0.112055	+	0.0329023i
$106$	3.22617	−	7.06433i	0.313354	−	0.686149i
$107$	16.1047	+	10.3499i	1.55690	+	1.00056i	0.983420	+	0.181341i	$0.0580438\pi$
$107$	16.1047	+	10.3499i	1.55690	+	1.00056i	0.573481	+	0.819219i	$0.305593\pi$
$108$	−2.80055	+	0.822315i	−0.269483	+	0.0791273i
$109$	0.209897	−	1.45986i	0.0201045	−	0.139830i	−0.977297	−	0.211874i	$-0.932043\pi$
$109$	0.209897	−	1.45986i	0.0201045	−	0.139830i	0.997401	+	0.0720445i	$0.0229524\pi$
$110$	1.75768	+	3.84879i	0.167588	+	0.366967i
$111$	0.463168	+	3.22141i	0.0439620	+	0.305762i
$112$	−1.32715	+	0.852909i	−0.125404	+	0.0805923i
$113$	−9.03874	+	10.4313i	−0.850293	+	0.981291i	−0.999972	−	0.00744391i	$-0.997631\pi$
$113$	−9.03874	+	10.4313i	−0.850293	+	0.981291i	0.149679	+	0.988735i	$0.452176\pi$
$114$	11.5877			1.08529
$115$	3.19447	−	3.57706i	0.297886	−	0.333562i
$116$	10.5995			0.984143
$117$	0.729166	−	0.841502i	0.0674114	−	0.0777969i
$118$	−9.09946	+	5.84786i	−0.837673	+	0.538340i
$119$	0.483931	+	3.36581i	0.0443619	+	0.308543i
$120$	0.846490	+	1.85355i	0.0772736	+	0.169206i
$121$	1.04749	−	7.28544i	0.0952262	−	0.662313i
$122$	−17.1210	+	5.02717i	−1.55006	+	0.455138i
$123$	−4.16942	−	2.67952i	−0.375944	−	0.241605i
$124$	5.48720	−	12.0153i	0.492765	−	1.07900i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	1.73805	+	2.00581i	0.154837	+	0.178692i
$127$	6.97127	+	8.04528i	0.618600	+	0.713903i	0.975441	−	0.220263i	$-0.0706914\pi$
$127$	6.97127	+	8.04528i	0.618600	+	0.713903i	−0.356840	+	0.934165i	$0.616146\pi$
$128$	−13.9908	−	4.10807i	−1.23662	−	0.363105i
$129$	−1.55799	+	3.41153i	−0.137174	+	0.300368i
$130$	−2.07746	−	1.33510i	−0.182205	−	0.117096i
$131$	−17.8336	+	5.23642i	−1.55813	+	0.457508i	−0.943518	−	0.331322i	$-0.892505\pi$
$131$	−17.8336	+	5.23642i	−1.55813	+	0.457508i	−0.614611	+	0.788830i	$0.710687\pi$
$132$	−0.792466	+	5.51172i	−0.0689753	+	0.479734i
$133$	−2.59738	−	5.68747i	−0.225221	−	0.493166i
$134$	1.88532	+	13.1127i	0.162867	+	1.13277i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	−3.79174	+	4.37590i	−0.325139	+	0.375230i
$137$	−5.29724			−0.452574			−0.226287	−	0.974061i	$-0.572659\pi$
$137$	−5.29724			−0.452574			−0.226287	+	0.974061i	$0.572659\pi$
$138$	10.2492	−	2.84359i	0.872469	−	0.242063i
$139$	16.3788			1.38923			0.694616	−	0.719381i	$-0.255574\pi$
$139$	16.3788			1.38923			0.694616	+	0.719381i	$0.255574\pi$
$140$	2.28736	−	2.63975i	0.193317	−	0.223100i
$141$	7.70892	−	4.95422i	0.649208	−	0.417221i
$142$	−1.72979	−	12.0310i	−0.145161	−	1.00962i
$143$	−0.882448	−	1.93229i	−0.0737940	−	0.161586i
$144$	0.187612	−	1.30487i	0.0156343	−	0.108739i
$145$	3.48440	−	1.02311i	0.289364	−	0.0849648i
$146$	12.3689	+	7.94900i	1.02366	+	0.657864i
$147$	−2.31300	+	5.06476i	−0.190773	+	0.417734i
$148$	9.11448	+	2.67625i	0.749205	+	0.219987i
$149$	−4.00647	−	4.62371i	−0.328222	−	0.378789i	0.567522	−	0.823358i	$-0.307902\pi$
$149$	−4.00647	−	4.62371i	−0.328222	−	0.378789i	−0.895744	+	0.444569i	$0.853357\pi$
$150$	1.45237	+	1.67613i	0.118586	+	0.136855i
$151$	−13.3156	−	3.90980i	−1.08361	−	0.318175i	−0.309285	−	0.950969i	$-0.600090\pi$
$151$	−13.3156	−	3.90980i	−1.08361	−	0.318175i	−0.774320	+	0.632794i	$0.781908\pi$
$152$	4.42274	−	9.68445i	0.358732	−	0.785513i
$153$	−2.39043	−	1.53624i	−0.193255	−	0.124197i
$154$	4.85829	−	1.42652i	0.391492	−	0.114952i
$155$	0.644047	−	4.47944i	0.0517311	−	0.359798i
$156$	−1.35008	−	2.95627i	−0.108093	−	0.236691i
$157$	1.15830	+	8.05618i	0.0924427	+	0.642953i	0.982383	+	0.186877i	$0.0598365\pi$
$157$	1.15830	+	8.05618i	0.0924427	+	0.642953i	−0.889941	+	0.456076i	$0.849254\pi$
$158$	−19.0318	+	12.2310i	−1.51409	+	0.973047i
$159$	2.29311	−	2.64639i	0.181856	−	0.209873i
$160$	−6.99913			−0.553330
$161$	−3.69304	−	4.39310i	−0.291052	−	0.346225i
$162$	−2.21783			−0.174249
$163$	−12.4828	+	14.4059i	−0.977727	+	1.12836i	0.0139886	+	0.999902i	$0.495547\pi$
$163$	−12.4828	+	14.4059i	−0.977727	+	1.12836i	−0.991715	+	0.128455i	$0.958998\pi$
$164$	−12.1696	+	7.82094i	−0.950288	+	0.610713i
$165$	0.271506	+	1.88837i	0.0211367	+	0.147009i
$166$	−5.41514	−	11.8575i	−0.420296	−	0.920321i
$167$	1.98003	−	13.7714i	0.153219	−	1.06566i	−0.757559	−	0.652767i	$-0.773608\pi$
$167$	1.98003	−	13.7714i	0.153219	−	1.06566i	0.910778	−	0.412896i	$-0.135483\pi$
$168$	2.33973	−	0.687006i	0.180514	−	0.0530037i
$169$	−9.89330	−	6.35804i	−0.761023	−	0.489080i
$170$	−2.61794	+	5.73250i	−0.200787	+	0.439662i
$171$	5.01316	+	1.47200i	0.383366	+	0.112566i
$172$	7.16858	+	8.27298i	0.546599	+	0.630809i
$173$	−9.15609	−	10.5667i	−0.696125	−	0.803371i	0.292099	−	0.956388i	$-0.405646\pi$
$173$	−9.15609	−	10.5667i	−0.696125	−	0.803371i	−0.988223	+	0.153018i	$0.951101\pi$
$174$	7.72781	+	2.26909i	0.585844	+	0.172019i
$175$	0.497125	−	1.08855i	0.0375791	−	0.0822868i
$176$	−2.11576	−	1.35972i	−0.159481	−	0.102492i
$177$	−4.67952	+	1.37403i	−0.351735	+	0.103279i
$178$	−2.70035	+	18.7813i	−0.202400	+	1.40772i
$179$	4.64265	+	10.1660i	0.347008	+	0.759841i	0.999997	+	0.00247357i	$0.000787362\pi$
$179$	4.64265	+	10.1660i	0.347008	+	0.759841i	−0.652989	+	0.757367i	$0.726485\pi$
$180$	0.415386	+	2.88907i	0.0309610	+	0.215339i
$181$	−9.87413	+	6.34572i	−0.733938	+	0.471673i	−0.853460	−	0.521158i	$-0.825500\pi$
$181$	−9.87413	+	6.34572i	−0.733938	+	0.471673i	0.119522	+	0.992832i	$0.461864\pi$
$182$	−1.93526	+	2.23341i	−0.143451	+	0.165551i
$183$	−8.04558			−0.594747
$184$	1.53532	−	9.65110i	0.113185	−	0.711488i
$185$	3.25453			0.239278
$186$	6.57272	−	7.58532i	0.481935	−	0.556183i
$187$	−4.56043	+	2.93081i	−0.333491	+	0.214322i
$188$	−3.80643	−	26.4743i	−0.277613	−	1.93084i
$189$	0.497125	+	1.08855i	0.0361605	+	0.0791805i
$190$	1.64911	−	11.4698i	0.119639	−	0.832106i
$191$	2.27011	−	0.666564i	0.164259	−	0.0482309i	−0.198569	−	0.980087i	$-0.563629\pi$
$191$	2.27011	−	0.666564i	0.164259	−	0.0482309i	0.362828	+	0.931856i	$0.381811\pi$
$192$	−10.8407	−	6.96688i	−0.782358	−	0.502791i
$193$	−2.52804	+	5.53563i	−0.181972	+	0.398463i	−0.978532	−	0.206097i	$-0.933924\pi$
$193$	−2.52804	+	5.53563i	−0.181972	+	0.398463i	0.796560	+	0.604560i	$0.206651\pi$
$194$	3.44310	+	1.01099i	0.247200	+	0.0725846i
$195$	−0.729166	−	0.841502i	−0.0522167	−	0.0602612i
$196$	10.6425	+	12.2821i	0.760178	+	0.877292i
$197$	−15.2752	−	4.48521i	−1.08831	−	0.319558i	−0.312114	−	0.950045i	$-0.601037\pi$
$197$	−15.2752	−	4.48521i	−1.08831	−	0.319558i	−0.776200	+	0.630487i	$0.782855\pi$
$198$	−1.75768	+	3.84879i	−0.124913	+	0.273521i
$199$	−0.710448	−	0.456577i	−0.0503623	−	0.0323659i	0.515217	−	0.857060i	$-0.327711\pi$
$199$	−0.710448	−	0.456577i	−0.0503623	−	0.0323659i	−0.565580	+	0.824694i	$0.691348\pi$
$200$	1.95516	−	0.574086i	0.138250	−	0.0405940i
$201$	−0.850075	+	5.91240i	−0.0599596	+	0.417028i
$202$	−12.2549	−	26.8344i	−0.862250	−	1.88806i
$203$	−0.618472	−	4.30157i	−0.0434082	−	0.301911i
$204$	−6.97714	+	4.48394i	−0.488498	+	0.313938i
$205$	−3.24562	+	3.74565i	−0.226684	+	0.261607i
$206$	−33.6478			−2.34436
$207$	4.79529	+	0.0717463i	0.333296	+	0.00498671i
$208$	1.46787			0.101778
$209$	6.52752	−	7.53315i	0.451518	−	0.521079i
$210$	2.23275	−	1.43490i	0.154074	−	0.0990174i
$211$	2.98974	+	20.7941i	0.205822	+	1.43153i	0.786599	+	0.617464i	$0.211840\pi$
$211$	2.98974	+	20.7941i	0.205822	+	1.43153i	−0.580777	+	0.814063i	$0.697251\pi$
$212$	−4.24581	−	9.29702i	−0.291603	−	0.638522i
$213$	0.779948	−	5.42466i	0.0534412	−	0.371692i
$214$	40.7377	−	11.9617i	2.78477	−	0.817683i
$215$	3.15508	+	2.02764i	0.215174	+	0.138284i
$216$	−0.846490	+	1.85355i	−0.0575964	+	0.126118i
$217$	−5.19628	−	1.52577i	−0.352747	−	0.103576i
$218$	−2.14207	−	2.47208i	−0.145079	−	0.167430i
$219$	4.34134	+	5.01018i	0.293361	+	0.338556i
$220$	5.34284	+	1.56880i	0.360214	+	0.105768i
$221$	1.31434	−	2.87801i	0.0884123	−	0.193596i
$222$	6.07217	+	3.90235i	0.407538	+	0.261909i
$223$	7.37900	−	2.16667i	0.494134	−	0.145091i	−0.0251652	−	0.999683i	$-0.508011\pi$
$223$	7.37900	−	2.16667i	0.494134	−	0.145091i	0.519299	+	0.854592i	$0.326193\pi$
$224$	−1.19201	+	8.29058i	−0.0796442	+	0.553938i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	4.35650	+	30.3001i	0.289790	+	2.01553i
$227$	9.54343	−	6.13319i	0.633420	−	0.407074i	−0.184154	−	0.982897i	$-0.558955\pi$
$227$	9.54343	−	6.13319i	0.633420	−	0.407074i	0.817574	+	0.575823i	$0.195318\pi$
$228$	9.98665	−	11.5252i	0.661382	−	0.763276i
$229$	13.3843			0.884462			0.442231	−	0.896901i	$-0.354187\pi$
$229$	13.3843			0.884462			0.442231	+	0.896901i	$0.354187\pi$
$230$	−1.35604	−	10.5496i	−0.0894146	−	0.695617i
$231$	2.28304			0.150213
$232$	4.84590	−	5.59247i	0.318149	−	0.367164i
$233$	−6.00181	+	3.85713i	−0.393192	+	0.252689i	−0.722266	−	0.691615i	$-0.756900\pi$
$233$	−6.00181	+	3.85713i	−0.393192	+	0.252689i	0.329075	+	0.944304i	$0.393263\pi$
$234$	−0.351444	−	2.44435i	−0.0229746	−	0.159792i
$235$	−3.80670	−	8.33551i	−0.248322	−	0.543749i
$236$	−2.02587	+	14.0902i	−0.131873	+	0.917195i
$237$	−9.78739	+	2.87384i	−0.635759	+	0.186676i
$238$	6.34437	+	4.07728i	0.411244	+	0.264291i
$239$	10.0694	−	22.0490i	0.651337	−	1.42623i	−0.239042	−	0.971009i	$-0.576833\pi$
$239$	10.0694	−	22.0490i	0.651337	−	1.42623i	0.890379	−	0.455220i	$-0.150439\pi$
$240$	−1.26489	−	0.371404i	−0.0816481	−	0.0239740i
$241$	−13.3924	−	15.4556i	−0.862680	−	0.995585i	−0.999987	−	0.00505698i	$-0.998390\pi$
$241$	−13.3924	−	15.4556i	−0.862680	−	0.995585i	0.137308	−	0.990528i	$-0.456155\pi$
$242$	−10.6900	−	12.3369i	−0.687177	−	0.793045i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−9.75531	+	21.3611i	−0.624520	+	1.36751i
$245$	4.68403	+	3.01024i	0.299252	+	0.192317i
$246$	−10.5468	+	3.09681i	−0.672437	+	0.197445i
$247$	−0.827937	+	5.75843i	−0.0526804	+	0.366400i
$248$	−3.83080	−	8.38828i	−0.243256	−	0.532656i
$249$	−0.836467	−	5.81776i	−0.0530090	−	0.368685i
$250$	1.86576	−	1.19905i	0.118001	−	0.0758346i
$251$	14.0464	−	16.2104i	0.886602	−	1.02319i	−0.112960	−	0.993600i	$-0.536033\pi$
$251$	14.0464	−	16.2104i	0.886602	−	1.02319i	0.999562	−	0.0295936i	$-0.00942132\pi$
$252$	3.49289			0.220031
$253$	3.92489	−	8.26481i	0.246755	−	0.519604i
$254$	23.6098			1.48141
$255$	−1.86079	+	2.14747i	−0.116527	+	0.134480i
$256$	−5.52413	+	3.55014i	−0.345258	+	0.221884i
$257$	−1.89886	−	13.2069i	−0.118448	−	0.823822i	−0.959266	−	0.282504i	$-0.908835\pi$
$257$	−1.89886	−	13.2069i	−0.118448	−	0.823822i	0.840818	−	0.541317i	$-0.182074\pi$
$258$	3.45536	+	7.56619i	0.215122	+	0.471051i
$259$	0.554272	−	3.85504i	0.0344408	−	0.239541i
$260$	−3.11832	+	0.915621i	−0.193390	+	0.0567844i
$261$	3.05501	+	1.96334i	0.189100	+	0.121527i
$262$	−17.1241	+	37.4966i	−1.05793	+	2.31655i
$263$	24.3964	+	7.16342i	1.50434	+	0.441715i	0.927087	−	0.374847i	$-0.122305\pi$
$263$	24.3964	+	7.16342i	1.50434	+	0.441715i	0.577257	+	0.816562i	$0.304123\pi$
$264$	2.54576	+	2.93797i	0.156681	+	0.180819i
$265$	−2.29311	−	2.64639i	−0.140865	−	0.162567i
$266$	−13.3053	−	3.90678i	−0.815799	−	0.239540i
$267$	−3.55405	+	7.78228i	−0.217504	+	0.476268i
$268$	14.6668	+	9.42577i	0.895917	+	0.575771i
$269$	−17.4944	+	5.13683i	−1.06665	+	0.313198i	−0.767528	−	0.641015i	$-0.778513\pi$
$269$	−17.4944	+	5.13683i	−1.06665	+	0.313198i	−0.299127	+	0.954213i	$0.596695\pi$
$270$	−0.315630	+	2.19526i	−0.0192087	+	0.133599i
$271$	−0.261101	−	0.571731i	−0.0158608	−	0.0347302i	0.901536	−	0.432704i	$-0.142441\pi$
$271$	−0.261101	−	0.571731i	−0.0158608	−	0.0347302i	−0.917397	+	0.397974i	$0.869713\pi$
$272$	−0.533101	−	3.70780i	−0.0323240	−	0.224818i
$273$	−1.12095	+	0.720394i	−0.0678433	+	0.0436002i
$274$	−7.69355	+	8.87884i	−0.464785	+	0.536390i
$275$	1.90778			0.115044
$276$	6.00480	−	12.6446i	0.361447	−	0.761115i
$277$	28.9915			1.74193			0.870967	−	0.491342i	$-0.163494\pi$
$277$	28.9915			1.74193			0.870967	+	0.491342i	$0.163494\pi$
$278$	23.7881	−	27.4529i	1.42671	−	1.64652i
$279$	3.80710	−	2.44667i	0.227925	−	0.146479i
$280$	−0.347035	−	2.41368i	−0.0207393	−	0.144245i
$281$	−12.7748	−	27.9730i	−0.762083	−	1.66873i	−0.743348	−	0.668905i	$-0.766763\pi$
$281$	−12.7748	−	27.9730i	−0.762083	−	1.66873i	−0.0187354	−	0.999824i	$-0.505964\pi$
$282$	2.89231	−	20.1165i	0.172235	−	1.19792i
$283$	20.9832	−	6.16123i	1.24732	−	0.366247i	0.409561	−	0.912283i	$-0.365682\pi$
$283$	20.9832	−	6.16123i	1.24732	−	0.366247i	0.837762	+	0.546036i	$0.183864\pi$
$284$	−13.4569	−	8.64820i	−0.798518	−	0.513176i
$285$	2.17046	−	4.75265i	0.128567	−	0.281522i
$286$	−4.52040	−	1.32731i	−0.267297	−	0.0784855i
$287$	3.88402	+	4.48240i	0.229266	+	0.264588i
$288$	−4.58346	−	5.28959i	−0.270083	−	0.311692i
$289$	8.56426	+	2.51469i	0.503780	+	0.147923i
$290$	3.34578	−	7.32623i	0.196471	−	0.430211i
$291$	1.36115	+	0.874759i	0.0797921	+	0.0512793i
$292$	18.5660	−	5.45147i	1.08649	−	0.319023i
$293$	−0.384063	+	2.67122i	−0.0224372	+	0.156054i	−0.997960	−	0.0638449i	$-0.979664\pi$
$293$	−0.384063	+	2.67122i	−0.0224372	+	0.156054i	0.975523	+	0.219899i	$0.0705728\pi$
$294$	5.12984	+	11.2328i	0.299178	+	0.655109i
$295$	0.694081	+	4.82744i	0.0404109	+	0.281064i
$296$	5.57899	−	3.58540i	0.324272	−	0.208397i
$297$	−1.24933	+	1.44181i	−0.0724937	+	0.0836621i
$298$	−13.5688			−0.786019
$299$	0.680802	+	5.29643i	0.0393718	+	0.306300i
$300$	2.91878			0.168516
$301$	2.93911	−	3.39191i	0.169407	−	0.195507i
$302$	−25.8925	+	16.6401i	−1.48994	+	0.957529i
$303$	−1.89299	−	13.1660i	−0.108749	−	0.756369i
$304$	2.86129	+	6.26535i	0.164106	+	0.359342i
$305$	−1.14501	+	7.96369i	−0.0655628	+	0.456000i
$306$	−6.04672	+	1.77548i	−0.345668	+	0.101497i
$307$	22.8299	+	14.6719i	1.30297	+	0.837371i	0.993533	−	0.113548i	$-0.0362215\pi$
$307$	22.8299	+	14.6719i	1.30297	+	0.837371i	0.309442	+	0.950918i	$0.399858\pi$
$308$	2.76819	−	6.06150i	0.157732	−	0.345386i
$309$	−14.5569	−	4.27431i	−0.828116	−	0.243157i
$310$	−6.57272	−	7.58532i	−0.373305	−	0.430817i
$311$	−4.69352	−	5.41661i	−0.266145	−	0.307148i	0.606909	−	0.794771i	$-0.292409\pi$
$311$	−4.69352	−	5.41661i	−0.266145	−	0.307148i	−0.873054	+	0.487624i	$0.837864\pi$
$312$	−2.17700	−	0.639226i	−0.123249	−	0.0361890i
$313$	−8.26805	+	18.1045i	−0.467338	+	1.02333i	0.518415	+	0.855129i	$0.326522\pi$
$313$	−8.26805	+	18.1045i	−0.467338	+	1.02333i	−0.985753	+	0.168198i	$0.946205\pi$
$314$	15.1855	+	9.75910i	0.856965	+	0.550738i
$315$	1.14822	−	0.337148i	0.0646949	−	0.0189961i
$316$	−4.23718	+	29.4702i	−0.238360	+	1.65783i
$317$	4.29763	+	9.41049i	0.241379	+	0.528546i	0.991086	−	0.133224i	$-0.0425330\pi$
$317$	4.29763	+	9.41049i	0.241379	+	0.528546i	−0.749707	+	0.661770i	$0.769806\pi$
$318$	−1.10524	−	7.68709i	−0.0619786	−	0.431071i
$319$	5.82830	−	3.74562i	0.326322	−	0.209715i
$320$	−8.43875	+	9.73884i	−0.471741	+	0.544418i
$321$	19.1437			1.06850
$322$	−12.7270	−	0.190420i	−0.709251	−	0.0106117i
$323$	14.8463			0.826072
$324$	−1.91139	+	2.20587i	−0.106189	+	0.122548i
$325$	−0.936708	+	0.601986i	−0.0519592	+	0.0333922i
$326$	6.01646	+	41.8454i	0.333221	+	2.31760i
$327$	−0.612686	−	1.34160i	−0.0338816	−	0.0741904i
$328$	−1.43727	+	9.99644i	−0.0793600	+	0.551961i
$329$	−10.5219	+	3.08949i	−0.580088	+	0.170329i
$330$	3.55947	+	2.28753i	0.195942	+	0.125924i
$331$	−7.37798	+	16.1555i	−0.405530	+	0.887988i	0.591149	+	0.806562i	$0.298674\pi$
$331$	−7.37798	+	16.1555i	−0.405530	+	0.887988i	−0.996679	+	0.0814254i	$0.974053\pi$
$332$	−16.4605	−	4.83323i	−0.903385	−	0.265258i
$333$	2.13127	+	2.45961i	0.116793	+	0.134786i
$334$	−20.2069	−	23.3199i	−1.10567	−	1.27601i
$335$	5.73124	+	1.68284i	0.313131	+	0.0919436i
$336$	−0.655354	+	1.43502i	−0.0357525	+	0.0782870i
$337$	24.9997	+	16.0663i	1.36182	+	0.875189i	0.998406	−	0.0564388i	$-0.0179746\pi$
$337$	24.9997	+	16.0663i	1.36182	+	0.875189i	0.363414	+	0.931628i	$0.381611\pi$
$338$	−25.0256	+	7.34818i	−1.36121	+	0.399689i
$339$	−1.96431	+	13.6620i	−0.106686	+	0.742021i
$340$	3.44535	+	7.54425i	0.186850	+	0.409145i
$341$	−1.22870	−	8.54581i	−0.0665380	−	0.462782i
$342$	9.74822	−	6.26480i	0.527123	−	0.338762i
$343$	9.84909	−	11.3665i	0.531801	−	0.613731i
$344$	7.64228			0.412044
$345$	0.753458	−	4.73628i	0.0405648	−	0.254992i
$346$	−31.0091			−1.66706
$347$	−12.7678	+	14.7348i	−0.685412	+	0.791007i	−0.986705	−	0.162524i	$-0.948036\pi$
$347$	−12.7678	+	14.7348i	−0.685412	+	0.791007i	0.301293	+	0.953532i	$0.402582\pi$
$348$	8.91690	−	5.73055i	0.477996	−	0.307190i
$349$	−0.935278	−	6.50500i	−0.0500643	−	0.348205i	−0.999422	−	0.0340062i	$-0.989173\pi$
$349$	−0.935278	−	6.50500i	−0.0500643	−	0.348205i	0.949357	−	0.314198i	$-0.101736\pi$
$350$	−1.10254	−	2.41423i	−0.0589333	−	0.129046i
$351$	0.158463	−	1.10213i	0.00845813	−	0.0588276i
$352$	−12.8120	+	3.76193i	−0.682880	+	0.200512i
$353$	−3.80065	−	2.44253i	−0.202288	−	0.130003i	0.435575	−	0.900152i	$-0.356545\pi$
$353$	−3.80065	−	2.44253i	−0.202288	−	0.130003i	−0.637863	+	0.770150i	$0.720181\pi$
$354$	−4.49335	+	9.83907i	−0.238819	+	0.522941i
$355$	−5.25845	−	1.54402i	−0.279089	−	0.0819480i
$356$	16.3528	+	18.8721i	0.866695	+	1.00022i
$357$	2.22680	+	2.56987i	0.117855	+	0.136012i
$358$	23.7823	+	6.98311i	1.25693	+	0.369069i
$359$	−12.6861	+	27.7788i	−0.669549	+	1.46611i	0.203800	+	0.979013i	$0.434671\pi$
$359$	−12.6861	+	27.7788i	−0.669549	+	1.46611i	−0.873349	+	0.487095i	$0.838056\pi$
$360$	1.71422	+	1.10166i	0.0903473	+	0.0580627i
$361$	−7.96239	+	2.33797i	−0.419073	+	0.123051i
$362$	−3.70468	+	25.7666i	−0.194714	+	1.35426i
$363$	−3.05760	−	6.69522i	−0.160483	−	0.351408i
$364$	0.553494	+	3.84963i	0.0290109	+	0.201776i
$365$	5.57702	−	3.58413i	0.291914	−	0.187602i
$366$	−11.6852	+	13.4854i	−0.610794	+	0.704894i
$367$	25.6759			1.34027			0.670137	−	0.742238i	$-0.266236\pi$
$367$	25.6759			1.34027			0.670137	+	0.742238i	$0.266236\pi$
$368$	4.06827	+	4.83947i	0.212073	+	0.252275i
$369$	−4.95620			−0.258009
$370$	4.72679	−	5.45501i	0.245734	−	0.283592i
$371$	−3.52523	+	2.26553i	−0.183021	+	0.117620i
$372$	−1.87983	−	13.0745i	−0.0974647	−	0.677882i
$373$	−4.62838	−	10.1347i	−0.239648	−	0.524756i	0.751146	−	0.660137i	$-0.229502\pi$
$373$	−4.62838	−	10.1347i	−0.239648	−	0.524756i	−0.990794	+	0.135380i	$0.956774\pi$
$374$	−1.71103	+	11.9005i	−0.0884752	+	0.615359i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	−15.7084	−	10.0952i	−0.810101	−	0.520621i
$377$	−1.67975	+	3.67815i	−0.0865117	+	0.189434i
$378$	2.54656	+	0.747738i	0.130981	+	0.0384595i
$379$	−4.67590	−	5.39627i	−0.240185	−	0.277188i	0.622840	−	0.782349i	$-0.285979\pi$
$379$	−4.67590	−	5.39627i	−0.240185	−	0.277188i	−0.863025	+	0.505161i	$0.831433\pi$
$380$	−9.98665	−	11.5252i	−0.512304	−	0.591231i
$381$	10.2142	+	2.99916i	0.523290	+	0.153652i
$382$	2.17979	−	4.77308i	0.111528	−	0.244212i
$383$	13.5830	+	8.72926i	0.694059	+	0.446044i	0.839527	−	0.543319i	$-0.182832\pi$
$383$	13.5830	+	8.72926i	0.694059	+	0.446044i	−0.145468	+	0.989363i	$0.546469\pi$
$384$	−13.9908	+	4.10807i	−0.713965	+	0.209639i
$385$	0.324910	−	2.25980i	0.0165589	−	0.115170i
$386$	5.60676	+	12.2771i	0.285377	+	0.624887i
$387$	0.533744	+	3.71227i	0.0271317	+	0.188705i
$388$	3.97290	−	2.55323i	0.201694	−	0.129621i
$389$	16.2239	−	18.7233i	0.822583	−	0.949311i	−0.176807	−	0.984246i	$-0.556577\pi$
$389$	16.2239	−	18.7233i	0.822583	−	0.949311i	0.999390	+	0.0349343i	$0.0111222\pi$
$390$	−2.46948			−0.125047
$391$	13.1314	−	3.64324i	0.664082	−	0.184247i
$392$	11.3457			0.573046
$393$	−12.1716	+	14.0467i	−0.613974	+	0.708564i
$394$	−29.7030	+	19.0890i	−1.49642	+	0.961689i
$395$	1.45169	+	10.0968i	0.0730427	+	0.508023i
$396$	2.31320	+	5.06520i	0.116243	+	0.254536i
$397$	3.03100	−	21.0811i	0.152122	−	1.05803i	−0.760533	−	0.649299i	$-0.775062\pi$
$397$	3.03100	−	21.0811i	0.152122	−	1.05803i	0.912655	−	0.408731i	$-0.134028\pi$
$398$	−1.79711	+	0.527680i	−0.0900812	+	0.0264502i
$399$	−5.25993	−	3.38035i	−0.263326	−	0.169229i
$400$	−0.547636	+	1.19916i	−0.0273818	+	0.0599578i
$401$	24.5279	+	7.20203i	1.22486	+	0.359652i	0.829309	−	0.558791i	$-0.188734\pi$
$401$	24.5279	+	7.20203i	1.22486	+	0.359652i	0.395554	+	0.918443i	$0.370553\pi$
$402$	8.67530	+	10.0118i	0.432685	+	0.499345i
$403$	3.29985	+	3.80823i	0.164377	+	0.189701i
$404$	−37.2513	−	10.9380i	−1.85332	−	0.544184i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−8.10821	−	5.21083i	−0.402404	−	0.258609i
$407$	5.95744	−	1.74926i	0.295299	−	0.0867077i
$408$	−0.824023	+	5.73120i	−0.0407952	+	0.283737i
$409$	−8.63558	−	18.9093i	−0.427002	−	0.935004i	−0.993804	−	0.111150i	$-0.964547\pi$
$409$	−8.63558	−	18.9093i	−0.427002	−	0.935004i	0.566802	−	0.823854i	$-0.308181\pi$
$410$	1.56433	+	10.8801i	0.0772566	+	0.537332i
$411$	−4.45632	+	2.86390i	−0.219814	+	0.141266i
$412$	−28.9987	+	33.4663i	−1.42866	+	1.64877i
$413$	5.83638			0.287189
$414$	7.08480	−	7.93331i	0.348199	−	0.389901i
$415$	−5.87758			−0.288519
$416$	5.10353	−	5.88979i	0.250221	−	0.288771i
$417$	13.7787	−	8.85504i	0.674747	−	0.433633i
$418$	−3.14614	−	21.8819i	−0.153883	−	1.07028i
$419$	−4.40667	−	9.64926i	−0.215280	−	0.471397i	0.770925	−	0.636926i	$-0.219794\pi$
$419$	−4.40667	−	9.64926i	−0.215280	−	0.471397i	−0.986205	+	0.165529i	$0.947067\pi$
$420$	0.497090	−	3.45734i	0.0242555	−	0.168701i
$421$	32.1340	−	9.43540i	1.56612	−	0.459853i	0.620249	−	0.784405i	$-0.287032\pi$
$421$	32.1340	−	9.43540i	1.56612	−	0.459853i	0.945868	+	0.324552i	$0.105213\pi$
$422$	39.1958	+	25.1896i	1.90802	+	1.22621i
$423$	3.80670	−	8.33551i	0.185088	−	0.405287i
$424$	−6.84634	−	2.01027i	−0.332488	−	0.0976271i
$425$	1.86079	+	2.14747i	0.0902618	+	0.104168i
$426$	−7.95964	−	9.18591i	−0.385646	−	0.445059i
$427$	9.23811	+	2.71255i	0.447063	+	0.131270i
$428$	23.2118	−	50.8268i	1.12199	−	2.45681i
$429$	−1.78704	−	1.14846i	−0.0862790	−	0.0554481i
$430$	7.98093	−	2.34341i	0.384875	−	0.113009i
$431$	−5.06780	+	35.2473i	−0.244107	+	1.69780i	0.386977	+	0.922089i	$0.373519\pi$
$431$	−5.06780	+	35.2473i	−0.244107	+	1.69780i	−0.631085	+	0.775714i	$0.717390\pi$
$432$	−0.547636	−	1.19916i	−0.0263482	−	0.0576944i
$433$	−4.60553	−	32.0322i	−0.221328	−	1.53937i	−0.733025	−	0.680202i	$-0.761892\pi$
$433$	−4.60553	−	32.0322i	−0.221328	−	1.53937i	0.511697	−	0.859166i	$-0.329017\pi$
$434$	−10.1043	+	6.49364i	−0.485022	+	0.311705i
$435$	2.37813	−	2.74450i	0.114022	−	0.131589i
$436$	−4.30484			−0.206164
$437$	−21.2798	+	13.2301i	−1.01795	+	0.632882i
$438$	14.7029			0.702533
$439$	−0.147768	+	0.170533i	−0.00705257	+	0.00813910i	−0.759265	−	0.650782i	$-0.774441\pi$
$439$	−0.147768	+	0.170533i	−0.00705257	+	0.00813910i	0.752212	+	0.658921i	$0.228987\pi$
$440$	3.27036	−	2.10173i	0.155908	−	0.100196i
$441$	0.792398	+	5.51125i	0.0377332	+	0.262440i
$442$	−2.91499	−	6.38295i	−0.138652	−	0.303606i
$443$	−2.14575	+	14.9240i	−0.101948	+	0.709062i	0.873177	+	0.487404i	$0.162056\pi$
$443$	−2.14575	+	14.9240i	−0.101948	+	0.709062i	−0.975124	+	0.221658i	$0.928853\pi$
$444$	9.11448	−	2.67625i	0.432554	−	0.127009i
$445$	7.19727	+	4.62541i	0.341183	+	0.219265i
$446$	7.08543	−	15.5149i	0.335505	−	0.734653i
$447$	−5.87022	−	1.72365i	−0.277652	−	0.0815259i
$448$	10.0986	+	11.6544i	0.477115	+	0.550620i
$449$	−16.0852	−	18.5633i	−0.759106	−	0.876055i	0.236312	−	0.971677i	$-0.424061\pi$
$449$	−16.0852	−	18.5633i	−0.759106	−	0.876055i	−0.995418	+	0.0956225i	$0.969516\pi$
$450$	2.12799	+	0.624835i	0.100315	+	0.0294550i
$451$	−3.92790	+	8.60090i	−0.184958	+	0.405001i
$452$	33.8912	+	21.7806i	1.59411	+	1.02447i
$453$	−13.3156	+	3.90980i	−0.625620	+	0.183699i
$454$	3.58061	−	24.9037i	0.168046	−	1.16879i
$455$	0.553533	+	1.21207i	0.0259500	+	0.0568226i
$456$	−1.51516	−	10.5382i	−0.0709540	−	0.493496i
$457$	24.8311	−	15.9580i	1.16155	−	0.746483i	0.189645	−	0.981853i	$-0.439266\pi$
$457$	24.8311	−	15.9580i	1.16155	−	0.746483i	0.971906	+	0.235370i	$0.0756300\pi$
$458$	19.4390	−	22.4338i	0.908326	−	1.04826i
$459$	−2.84151			−0.132630
$460$	−11.6613	−	7.74320i	−0.543711	−	0.361028i
$461$	−7.71446			−0.359298			−0.179649	−	0.983731i	$-0.557496\pi$
$461$	−7.71446			−0.359298			−0.179649	+	0.983731i	$0.557496\pi$
$462$	3.31582	−	3.82666i	0.154266	−	0.178032i
$463$	−14.2456	+	9.15510i	−0.662050	+	0.425474i	−0.828052	−	0.560652i	$-0.810551\pi$
$463$	−14.2456	+	9.15510i	−0.662050	+	0.425474i	0.166002	+	0.986125i	$0.446914\pi$
$464$	0.681312	+	4.73863i	0.0316291	+	0.219985i
$465$	−1.87996	−	4.11655i	−0.0871812	−	0.190900i
$466$	−2.25182	+	15.6618i	−0.104314	+	0.725518i
$467$	−12.2112	+	3.58555i	−0.565069	+	0.165919i	−0.551776	−	0.833992i	$-0.686050\pi$
$467$	−12.2112	+	3.58555i	−0.565069	+	0.165919i	−0.0132931	+	0.999912i	$0.504231\pi$
$468$	−2.73404	−	1.75706i	−0.126381	−	0.0812203i
$469$	2.96943	−	6.50214i	0.137115	−	0.300241i
$470$	−19.5001	−	5.72575i	−0.899473	−	0.264109i
$471$	5.32992	+	6.15106i	0.245590	+	0.283426i
$472$	6.50801	+	7.51065i	0.299556	+	0.345706i
$473$	6.86521	+	2.01581i	0.315663	+	0.0926870i
$474$	−9.39801	+	20.5788i	−0.431665	+	0.945214i
$475$	−4.39538	−	2.82474i	−0.201674	−	0.129608i
$476$	9.52305	−	2.79622i	0.436488	−	0.128165i
$477$	0.498341	−	3.46604i	0.0228175	−	0.158699i
$478$	−22.3323	−	48.9009i	−1.02146	−	2.23668i
$479$	−4.98805	−	34.6927i	−0.227910	−	1.58515i	−0.706891	−	0.707323i	$-0.749903\pi$
$479$	−4.98805	−	34.6927i	−0.227910	−	1.58515i	0.478981	−	0.877825i	$-0.341006\pi$
$480$	−5.88805	+	3.78402i	−0.268751	+	0.172716i
$481$	−2.37310	+	2.73870i	−0.108204	+	0.124874i
$482$	−45.3563			−2.06592
$483$	−5.48187	−	1.69911i	−0.249434	−	0.0773120i
$484$	−21.4833			−0.976512
$485$	1.05957	−	1.22281i	0.0481125	−	0.0555248i
$486$	−1.86576	+	1.19905i	−0.0846325	+	0.0543900i
$487$	−2.48766	−	17.3020i	−0.112726	−	0.784030i	−0.965248	−	0.261337i	$-0.915837\pi$
$487$	−2.48766	−	17.3020i	−0.112726	−	0.784030i	0.852521	−	0.522693i	$-0.175072\pi$
$488$	6.81051	+	14.9129i	0.308297	+	0.675077i
$489$	−2.71277	+	18.8677i	−0.122676	+	0.853227i
$490$	11.8485	−	3.47903i	0.535261	−	0.157167i
$491$	22.1694	+	14.2474i	1.00049	+	0.642977i	0.934916	−	0.354870i	$-0.115475\pi$
$491$	22.1694	+	14.2474i	1.00049	+	0.642977i	0.0655767	+	0.997848i	$0.479111\pi$
$492$	−6.00942	+	13.1588i	−0.270925	+	0.593244i
$493$	9.90096	+	2.90718i	0.445917	+	0.130933i
$494$	8.44938	+	9.75110i	0.380156	+	0.438723i
$495$	1.24933	+	1.44181i	0.0561533	+	0.0648044i
$496$	5.72426	+	1.68079i	0.257027	+	0.0754698i
$497$	−2.72447	+	5.96575i	−0.122209	+	0.267600i
$498$	−10.9662	−	7.04752i	−0.491405	−	0.315807i
$499$	−20.3179	+	5.96589i	−0.909556	+	0.267070i	−0.702854	−	0.711334i	$-0.748091\pi$
$499$	−20.3179	+	5.96589i	−0.909556	+	0.267070i	−0.206702	+	0.978404i	$0.566273\pi$
$500$	0.415386	−	2.88907i	0.0185766	−	0.129203i
$501$	−5.77967	−	12.6557i	−0.258217	−	0.565416i
$502$	−6.77011	−	47.0871i	−0.302165	−	2.10160i
$503$	37.6156	−	24.1741i	1.67720	−	1.07787i	0.795672	−	0.605727i	$-0.207118\pi$
$503$	37.6156	−	24.1741i	1.67720	−	1.07787i	0.881523	−	0.472141i	$-0.156519\pi$
$504$	1.59688	−	1.84290i	0.0711307	−	0.0820892i
$505$	−13.3014			−0.591906
$506$	−8.15246	−	18.5822i	−0.362421	−	0.826078i
$507$	−11.7602			−0.522288
$508$	20.3476	−	23.4824i	0.902779	−	1.04186i
$509$	−11.7079	+	7.52422i	−0.518944	+	0.333505i	−0.773754	−	0.633486i	$-0.781623\pi$
$509$	−11.7079	+	7.52422i	−0.518944	+	0.333505i	0.254810	+	0.966991i	$0.417987\pi$
$510$	0.896867	+	6.23785i	0.0397140	+	0.276217i
$511$	−3.29565	−	7.21646i	−0.145791	−	0.319238i
$512$	2.07771	−	14.4508i	0.0918228	−	0.638641i
$513$	5.01316	−	1.47200i	0.221336	−	0.0649902i
$514$	−24.8942	−	15.9985i	−1.09804	−	0.705666i
$515$	−6.30247	+	13.8005i	−0.277720	+	0.608122i
$516$	10.5033	+	3.08405i	0.462382	+	0.135768i
$517$	−11.4484	−	13.2122i	−0.503500	−	0.581070i
$518$	−5.65653	−	6.52798i	−0.248534	−	0.286823i
$519$	−13.4154	−	3.93911i	−0.588870	−	0.172908i
$520$	−0.942539	+	2.06387i	−0.0413331	+	0.0905068i
$521$	−32.4683	−	20.8661i	−1.42246	−	0.914161i	−0.999970	−	0.00779439i	$-0.997519\pi$
$521$	−32.4683	−	20.8661i	−1.42246	−	0.914161i	−0.422492	−	0.906366i	$-0.638845\pi$
$522$	7.72781	−	2.26909i	0.338237	−	0.0993154i
$523$	−0.122002	+	0.848545i	−0.00533479	+	0.0371043i	−0.992315	−	0.123738i	$-0.960512\pi$
$523$	−0.122002	+	0.848545i	−0.00533479	+	0.0371043i	0.986980	+	0.160842i	$0.0514209\pi$
$524$	22.5362	+	49.3474i	0.984499	+	2.15575i
$525$	−0.170308	−	1.18451i	−0.00743283	−	0.0516965i
$526$	47.4393	−	30.4874i	2.06845	−	1.32931i
$527$	8.42104	−	9.71839i	0.366826	−	0.423340i
$528$	−2.51501			−0.109452
$529$	−15.5751	+	16.9239i	−0.677177	+	0.735820i
$530$	−7.76614			−0.337340
$531$	−3.19381	+	3.68585i	−0.138599	+	0.159952i
$532$	−15.3526	+	9.86651i	−0.665619	+	0.427767i
$533$	−0.785374	−	5.46240i	−0.0340183	−	0.236603i
$534$	7.88228	+	17.2598i	0.341100	+	0.746904i
$535$	2.72443	−	18.9489i	0.117788	−	0.819230i
$536$	11.6785	−	3.42913i	0.504436	−	0.148116i
$537$	9.40178	+	6.04216i	0.405717	+	0.260738i
$538$	−16.7984	+	36.7835i	−0.724232	+	1.58585i
$539$	10.1921	+	2.99267i	0.439005	+	0.128904i
$540$	1.91139	+	2.20587i	0.0822533	+	0.0949254i
$541$	0.656242	+	0.757343i	0.0282140	+	0.0325607i	0.769681	−	0.638428i	$-0.220415\pi$
$541$	0.656242	+	0.757343i	0.0282140	+	0.0325607i	−0.741467	+	0.670989i	$0.765870\pi$
$542$	−1.33751	−	0.392728i	−0.0574509	−	0.0168691i
$543$	−4.87589	+	10.6767i	−0.209245	+	0.458182i
$544$	−16.7309	−	10.7523i	−0.717333	−	0.461002i
$545$	−1.41513	+	0.415521i	−0.0606177	+	0.0177990i
$546$	−0.420572	+	2.92514i	−0.0179988	+	0.125184i
$547$	−6.47780	−	14.1844i	−0.276971	−	0.606482i	0.719113	−	0.694893i	$-0.244548\pi$
$547$	−6.47780	−	14.1844i	−0.276971	−	0.606482i	−0.996084	+	0.0884114i	$0.971821\pi$
$548$	2.20040	+	15.3041i	0.0939963	+	0.653758i
$549$	−6.76838	+	4.34977i	−0.288867	+	0.185644i
$550$	2.77081	−	3.19769i	0.118148	−	0.136350i
$551$	−18.9739			−0.808314
$552$	−3.92618	−	8.94908i	−0.167110	−	0.380898i
$553$	12.2070			0.519094
$554$	42.1065	−	48.5935i	1.78893	−	2.06454i
$555$	2.73789	−	1.75953i	0.116217	−	0.0746880i
$556$	−6.80351	−	47.3195i	−0.288533	−	2.00679i
$557$	1.84368	+	4.03710i	0.0781193	+	0.171057i	0.944662	−	0.328046i	$-0.106390\pi$
$557$	1.84368	+	4.03710i	0.0781193	+	0.171057i	−0.866542	+	0.499103i	$0.833663\pi$
$558$	1.42839	−	9.93466i	0.0604685	−	0.420567i
$559$	−4.00684	+	1.17652i	−0.169471	+	0.0497613i
$560$	1.32715	+	0.852909i	0.0560824	+	0.0360420i
$561$	−2.25196	+	4.93111i	−0.0950779	+	0.208191i
$562$	−65.4401	−	19.2149i	−2.76042	−	0.810533i
$563$	−6.42681	−	7.41693i	−0.270858	−	0.312586i	0.603983	−	0.796997i	$-0.293579\pi$
$563$	−6.42681	−	7.41693i	−0.270858	−	0.312586i	−0.874841	+	0.484411i	$0.839034\pi$
$564$	−17.5153	−	20.2137i	−0.737526	−	0.851150i
$565$	13.2434	+	3.88862i	0.557156	+	0.163596i
$566$	20.1484	−	44.1189i	0.846902	−	1.85446i
$567$	1.00672	+	0.646982i	0.0422784	+	0.0271707i
$568$	−10.7151	+	3.14624i	−0.449597	+	0.132013i
$569$	1.16169	−	8.07976i	0.0487008	−	0.338721i	−0.950874	−	0.309577i	$-0.899813\pi$
$569$	1.16169	−	8.07976i	0.0487008	−	0.338721i	0.999575	−	0.0291445i	$-0.00927829\pi$
$570$	−4.81372	−	10.5406i	−0.201624	−	0.441496i
$571$	5.00315	+	34.7977i	0.209375	+	1.45624i	0.775203	+	0.631713i	$0.217648\pi$
$571$	5.00315	+	34.7977i	0.209375	+	1.45624i	−0.565827	+	0.824524i	$0.691443\pi$
$572$	−5.21597	+	3.35210i	−0.218091	+	0.140158i
$573$	1.54936	−	1.78806i	0.0647256	−	0.0746974i
$574$	13.1541			0.549042
$575$	−4.58084	−	1.41983i	−0.191034	−	0.0592110i
$576$	−12.8863			−0.536930
$577$	−11.7525	+	13.5631i	−0.489264	+	0.564641i	−0.945669	−	0.325131i	$-0.894592\pi$
$577$	−11.7525	+	13.5631i	−0.489264	+	0.564641i	0.456405	+	0.889772i	$0.349137\pi$
$578$	16.6534	−	10.7025i	0.692691	−	0.445165i
$579$	0.866066	+	6.02362i	0.0359925	+	0.250333i
$580$	−4.40321	−	9.64168i	−0.182833	−	0.400349i
$581$	−1.00100	+	6.96208i	−0.0415283	+	0.288836i
$582$	3.44310	−	1.01099i	0.142721	−	0.0419067i
$583$	−5.61996	−	3.61173i	−0.232755	−	0.149582i
$584$	5.61173	−	12.2880i	0.232215	−	0.508480i
$585$	−1.06836	−	0.313700i	−0.0441714	−	0.0129699i
$586$	3.91949	+	4.52333i	0.161913	+	0.186857i
$587$	−4.29804	−	4.96020i	−0.177399	−	0.204729i	0.660085	−	0.751191i	$-0.270520\pi$
$587$	−4.29804	−	4.96020i	−0.177399	−	0.204729i	−0.837484	+	0.546461i	$0.815975\pi$
$588$	15.5932	+	4.57858i	0.643054	+	0.188818i
$589$	−9.82243	+	21.5081i	−0.404726	+	0.886227i
$590$	9.09946	+	5.84786i	0.374619	+	0.240753i
$591$	−15.2752	+	4.48521i	−0.628338	+	0.184497i
$592$	−0.610589	+	4.24674i	−0.0250950	+	0.174540i
$593$	4.87992	+	10.6855i	0.200394	+	0.438802i	0.982973	−	0.183749i	$-0.0588234\pi$
$593$	4.87992	+	10.6855i	0.200394	+	0.438802i	−0.782579	+	0.622551i	$0.786096\pi$
$594$	0.602155	+	4.18808i	0.0247067	+	0.171839i
$595$	2.86062	−	1.83841i	0.117274	−	0.0753674i
$596$	−11.6940	+	13.4956i	−0.479004	+	0.552800i
$597$	−0.844511			−0.0345635
$598$	9.86625	+	6.55127i	0.403461	+	0.267901i
$599$	8.55732			0.349643			0.174821	−	0.984600i	$-0.444065\pi$
$599$	8.55732			0.349643			0.174821	+	0.984600i	$0.444065\pi$
$600$	1.33441	−	1.53999i	0.0544770	−	0.0628698i
$601$	18.3083	−	11.7661i	0.746813	−	0.479947i	−0.111057	−	0.993814i	$-0.535424\pi$
$601$	18.3083	−	11.7661i	0.746813	−	0.479947i	0.857870	+	0.513867i	$0.171787\pi$
$602$	−1.41659	−	9.85263i	−0.0577361	−	0.401563i
$603$	2.48136	+	5.43341i	0.101049	+	0.221266i
$604$	−5.76460	+	40.0937i	−0.234558	+	1.63139i
$605$	−7.06221	+	2.07365i	−0.287120	+	0.0843060i
$606$	−24.8173	−	15.9491i	−1.00813	−	0.647887i
$607$	11.2435	−	24.6199i	0.456360	−	0.999289i	−0.531942	−	0.846781i	$-0.678538\pi$
$607$	11.2435	−	24.6199i	0.456360	−	0.999289i	0.988302	−	0.152508i	$-0.0487351\pi$
$608$	35.0878	+	10.3027i	1.42300	+	0.417830i
$609$	−2.84589	−	3.28434i	−0.115321	−	0.133088i
$610$	11.6852	+	13.4854i	0.473119	+	0.546008i
$611$	9.79007	+	2.87462i	0.396064	+	0.116295i
$612$	−3.44535	+	7.54425i	−0.139270	+	0.304958i
$613$	−27.4806	−	17.6607i	−1.10993	−	0.713309i	−0.148653	−	0.988889i	$-0.547494\pi$
$613$	−27.4806	−	17.6607i	−1.10993	−	0.713309i	−0.961278	+	0.275580i	$0.911130\pi$
$614$	57.7495	−	16.9568i	2.33058	−	0.684321i
$615$	−0.705341	+	4.90575i	−0.0284421	+	0.197819i
$616$	−1.93257	−	4.23173i	−0.0778654	−	0.170501i
$617$	−1.92500	−	13.3886i	−0.0774974	−	0.539006i	−0.991174	−	0.132565i	$-0.957679\pi$
$617$	−1.92500	−	13.3886i	−0.0774974	−	0.539006i	0.913677	−	0.406441i	$-0.133230\pi$
$618$	−28.3064	+	18.1914i	−1.13865	+	0.731765i
$619$	−6.20781	+	7.16419i	−0.249513	+	0.287953i	−0.866665	−	0.498891i	$-0.833741\pi$
$619$	−6.20781	+	7.16419i	−0.249513	+	0.287953i	0.617152	+	0.786844i	$0.288286\pi$
$620$	−13.2090			−0.530484
$621$	4.07285	−	2.53218i	0.163438	−	0.101613i
$622$	−15.8956			−0.637357
$623$	6.70461	−	7.73754i	0.268615	−	0.309998i
$624$	1.23485	−	0.793590i	0.0494336	−	0.0317690i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	18.3372	+	40.1528i	0.732900	+	1.60483i
$627$	1.41856	−	9.86633i	0.0566520	−	0.394023i
$628$	22.7937	−	6.69284i	0.909568	−	0.267073i
$629$	7.77974	+	4.99973i	0.310198	+	0.199352i
$630$	1.10254	−	2.41423i	0.0439263	−	0.0961851i
$631$	−1.30771	−	0.383978i	−0.0520591	−	0.0152859i	0.255599	−	0.966783i	$-0.417727\pi$
$631$	−1.30771	−	0.383978i	−0.0520591	−	0.0152859i	−0.307658	+	0.951497i	$0.599545\pi$
$632$	13.6117	+	15.7088i	0.541446	+	0.624862i
$633$	13.7573	+	15.8768i	0.546803	+	0.631044i
$634$	22.0149	+	6.46416i	0.874324	+	0.256725i
$635$	4.42227	−	9.68342i	0.175492	−	0.384275i
$636$	−8.59815	−	5.52569i	−0.340939	−	0.219108i
$637$	−5.94857	+	1.74666i	−0.235691	+	0.0692050i
$638$	2.18672	−	15.2090i	0.0865733	−	0.602130i
$639$	−2.27666	−	4.98519i	−0.0900632	−	0.197211i
$640$	2.07516	+	14.4330i	0.0820278	+	0.570516i
$641$	−11.3511	+	7.29494i	−0.448343	+	0.288133i	−0.745264	−	0.666769i	$-0.767677\pi$
$641$	−11.3511	+	7.29494i	−0.448343	+	0.288133i	0.296921	+	0.954902i	$0.404040\pi$
$642$	27.8038	−	32.0873i	1.09733	−	1.26638i
$643$	−10.4820			−0.413369			−0.206684	−	0.978408i	$-0.566267\pi$
$643$	−10.4820			−0.413369			−0.206684	+	0.978408i	$0.566267\pi$
$644$	−11.1579	+	12.4943i	−0.439684	+	0.492343i
$645$	3.75045			0.147674
$646$	21.5624	−	24.8843i	0.848360	−	0.979060i
$647$	−22.8798	+	14.7039i	−0.899496	+	0.578071i	−0.906641	−	0.421903i	$-0.861362\pi$
$647$	−22.8798	+	14.7039i	−0.899496	+	0.578071i	0.00714442	+	0.999974i	$0.497726\pi$
$648$	0.289995	+	2.01696i	0.0113921	+	0.0792335i
$649$	3.86519	+	8.46359i	0.151722	+	0.332225i
$650$	−0.351444	+	2.44435i	−0.0137848	+	0.0958752i
$651$	−5.19628	+	1.52577i	−0.203658	+	0.0597995i
$652$	46.8048	+	30.0796i	1.83302	+	1.17801i
$653$	−15.1559	+	33.1867i	−0.593095	+	1.29870i	0.340459	+	0.940259i	$0.389418\pi$
$653$	−15.1559	+	33.1867i	−0.593095	+	1.29870i	−0.933554	+	0.358437i	$0.883310\pi$
$654$	−3.13853	−	0.921555i	−0.122726	−	0.0360357i
$655$	12.1716	+	14.0467i	0.475582	+	0.548851i
$656$	−4.27866	−	4.93784i	−0.167054	−	0.192790i
$657$	6.36088	+	1.86772i	0.248161	+	0.0728668i
$658$	−10.1033	+	22.1230i	−0.393866	+	0.862446i
$659$	−3.31705	−	2.13174i	−0.129214	−	0.0830407i	0.474437	−	0.880289i	$-0.342652\pi$
$659$	−3.31705	−	2.13174i	−0.129214	−	0.0830407i	−0.603651	+	0.797249i	$0.706288\pi$
$660$	5.34284	−	1.56880i	0.207970	−	0.0610655i
$661$	−1.04478	+	7.26663i	−0.0406373	+	0.282639i	0.959363	+	0.282176i	$0.0910563\pi$
$661$	−1.04478	+	7.26663i	−0.0406373	+	0.282639i	−1.00000		0.000462594i	$0.999853\pi$
$662$	16.3631	+	35.8302i	0.635971	+	1.39258i
$663$	−0.450274	−	3.13173i	−0.0174872	−	0.121626i
$664$	−10.0755	+	6.47511i	−0.391004	+	0.251283i
$665$	−4.09451	+	4.72532i	−0.158778	+	0.183240i
$666$	7.21801			0.279692
$667$	−16.7821	+	4.65613i	−0.649806	+	0.180286i
$668$	−40.6090			−1.57121
$669$	5.03622	−	5.81210i	0.194711	−	0.224709i
$670$	11.1445	−	7.16217i	0.430551	−	0.276699i
$671$	2.18442	+	15.1930i	0.0843288	+	0.586519i
$672$	3.47945	+	7.61893i	0.134223	+	0.293906i
$673$	−6.80044	+	47.2981i	−0.262138	+	1.82321i	0.254580	+	0.967052i	$0.418063\pi$
$673$	−6.80044	+	47.2981i	−0.262138	+	1.82321i	−0.516718	+	0.856156i	$0.672846\pi$
$674$	63.2380	−	18.5684i	2.43584	−	0.715227i
$675$	0.841254	+	0.540641i	0.0323799	+	0.0208093i
$676$	−14.2593	+	31.2235i	−0.548434	+	1.20090i
$677$	−30.8964	−	9.07200i	−1.18744	−	0.348665i	−0.372405	−	0.928070i	$-0.621467\pi$
$677$	−30.8964	−	9.07200i	−1.18744	−	0.348665i	−0.815040	+	0.579405i	$0.803285\pi$
$678$	20.0464	+	23.1348i	0.769878	+	0.888486i
$679$	−1.26798	−	1.46333i	−0.0486606	−	0.0561573i
$680$	5.55560	+	1.63127i	0.213047	+	0.0625564i
$681$	4.71259	−	10.3191i	0.180587	−	0.395430i
$682$	−16.1084	−	10.3522i	−0.616822	−	0.396408i
$683$	−0.0283866	+	0.00833507i	−0.00108618	+	0.000318933i	−0.282276	−	0.959333i	$-0.591089\pi$
$683$	−0.0283866	+	0.00833507i	−0.00108618	+	0.000318933i	0.281189	+	0.959652i	$0.409271\pi$
$684$	2.17031	−	15.0948i	0.0829837	−	0.577165i
$685$	2.20055	+	4.81854i	0.0840788	+	0.184107i
$686$	−4.74707	−	33.0166i	−0.181244	−	1.26058i
$687$	11.2596	−	7.23612i	0.429581	−	0.276075i
$688$	−3.23774	+	3.73655i	−0.123438	+	0.142455i
$689$	3.89901			0.148540
$690$	−6.84429	−	8.14172i	−0.260558	−	0.309950i
$691$	−51.0504			−1.94205			−0.971024	−	0.238984i	$-0.923186\pi$
$691$	−51.0504			−1.94205			−0.971024	+	0.238984i	$0.923186\pi$
$692$	−26.7246	+	30.8418i	−1.01592	+	1.17243i
$693$	1.92061	−	1.23430i	0.0729581	−	0.0468873i
$694$	6.15384	+	42.8009i	0.233597	+	1.62470i
$695$	−6.80400	−	14.8987i	−0.258090	−	0.565139i
$696$	1.05312	−	7.32458i	0.0399182	−	0.277637i
$697$	−13.5126	+	3.96767i	−0.511827	+	0.150286i
$698$	−12.2616	−	7.88003i	−0.464107	−	0.298264i
$699$	−2.96372	+	6.48965i	−0.112098	+	0.245461i
$700$	−3.35140	−	0.984061i	−0.126671	−	0.0371940i
$701$	5.66584	+	6.53872i	0.213996	+	0.246964i	0.852591	−	0.522578i	$-0.175030\pi$
$701$	5.66584	+	6.53872i	0.213996	+	0.246964i	−0.638596	+	0.769542i	$0.720484\pi$
$702$	−1.61717	−	1.86631i	−0.0610361	−	0.0704394i
$703$	−16.3155	−	4.79066i	−0.615350	−	0.180683i
$704$	−10.2127	+	22.3627i	−0.384906	+	0.842826i
$705$	−7.70892	−	4.95422i	−0.290335	−	0.186587i
$706$	−9.61394	+	2.82291i	−0.361825	+	0.106241i
$707$	−2.26533	+	15.7557i	−0.0851966	+	0.592555i
$708$	5.91348	+	12.9487i	0.222242	+	0.486643i
$709$	0.191349	+	1.33086i	0.00718625	+	0.0499815i	0.993099	−	0.117279i	$-0.0374171\pi$
$709$	0.191349	+	1.33086i	0.00718625	+	0.0499815i	−0.985913	+	0.167260i	$0.946508\pi$
$710$	−10.2252	+	6.57133i	−0.383744	+	0.246618i
$711$	−6.67996	+	7.70909i	−0.250518	+	0.289113i
$712$	17.4333			0.653342
$713$	−3.40978	+	21.4340i	−0.127697	+	0.802711i
$714$	7.54157			0.282236
$715$	−1.39109	+	1.60541i	−0.0520239	+	0.0600388i
$716$	27.4417	−	17.6357i	1.02555	−	0.659078i
$717$	−3.44963	−	23.9927i	−0.128829	−	0.896024i
$718$	28.1357	+	61.6087i	1.05002	+	2.29921i
$719$	−6.74426	+	46.9074i	−0.251519	+	1.74935i	0.337587	+	0.941294i	$0.390389\pi$
$719$	−6.74426	+	46.9074i	−0.251519	+	1.74935i	−0.589106	+	0.808056i	$0.700520\pi$
$720$	−1.26489	+	0.371404i	−0.0471396	+	0.0138414i
$721$	15.2735	+	9.81569i	0.568815	+	0.365556i
$722$	−7.64561	+	16.7416i	−0.284540	+	0.623056i
$723$	−19.6223	−	5.76164i	−0.729763	−	0.214278i
$724$	22.4348	+	25.8911i	0.833782	+	0.962236i
$725$	−2.37813	−	2.74450i	−0.0883214	−	0.101928i
$726$	−15.6628	−	4.59901i	−0.581301	−	0.170685i
$727$	13.1063	−	28.6988i	0.486085	−	1.06438i	−0.494660	−	0.869087i	$-0.664707\pi$
$727$	13.1063	−	28.6988i	0.486085	−	1.06438i	0.980745	−	0.195292i	$-0.0625653\pi$
$728$	2.28417	+	1.46794i	0.0846568	+	0.0544057i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	2.09244	−	14.5533i	0.0774448	−	0.538641i
$731$	4.42705	+	9.69389i	0.163740	+	0.358541i
$732$	3.34202	+	23.2443i	0.123525	+	0.859132i
$733$	−1.83037	+	1.17631i	−0.0676064	+	0.0434480i	−0.574007	−	0.818850i	$-0.694612\pi$
$733$	−1.83037	+	1.17631i	−0.0676064	+	0.0434480i	0.506401	+	0.862298i	$0.330976\pi$
$734$	37.2910	−	43.0361i	1.37644	−	1.58849i
$735$	5.56792			0.205376
$736$	33.5629	+	0.502162i	1.23715	+	0.0185099i
$737$	11.3956			0.419761
$738$	−7.19824	+	8.30721i	−0.264971	+	0.305793i
$739$	20.4835	−	13.1639i	0.753497	−	0.484243i	−0.106646	−	0.994297i	$-0.534011\pi$
$739$	20.4835	−	13.1639i	0.753497	−	0.484243i	0.860142	+	0.510054i	$0.170375\pi$
$740$	−1.35189	−	9.40257i	−0.0496963	−	0.345646i
$741$	2.41674	+	5.29192i	0.0887810	+	0.194403i
$742$	−1.32263	+	9.19911i	−0.0485554	+	0.337710i
$743$	−38.9981	+	11.4509i	−1.43070	+	0.420091i	−0.903111	−	0.429408i	$-0.858722\pi$
$743$	−38.9981	+	11.4509i	−1.43070	+	0.420091i	−0.527590	+	0.849499i	$0.676904\pi$
$744$	−7.75772	−	4.98558i	−0.284412	−	0.182780i
$745$	−2.54153	+	5.56517i	−0.0931143	+	0.203892i
$746$	−23.7092	−	6.96165i	−0.868055	−	0.254884i
$747$	−3.84900	−	4.44198i	−0.140827	−	0.162524i
$748$	10.3616	+	11.9580i	0.378859	+	0.437227i
$749$	−21.9812	−	6.45427i	−0.803176	−	0.235834i
$750$	0.921321	−	2.01741i	0.0336419	−	0.0736654i
$751$	24.5103	+	15.7518i	0.894394	+	0.574792i	0.905123	−	0.425151i	$-0.139779\pi$
$751$	24.5103	+	15.7518i	0.894394	+	0.574792i	−0.0107290	+	0.999942i	$0.503415\pi$
$752$	11.5909	−	3.40341i	0.422678	−	0.124109i
$753$	3.05258	−	21.2311i	0.111242	−	0.773706i
$754$	3.72541	+	8.15751i	0.135671	+	0.297079i
$755$	1.97500	+	13.7365i	0.0718778	+	0.499921i
$756$	2.93841	−	1.88840i	0.106869	−	0.0686804i
$757$	−17.1427	+	19.7838i	−0.623064	+	0.719054i	−0.976286	−	0.216486i	$-0.930541\pi$
$757$	−17.1427	+	19.7838i	−0.623064	+	0.719054i	0.353222	+	0.935539i	$0.385086\pi$
$758$	−15.8360			−0.575188
$759$	−1.16647	−	9.07475i	−0.0423401	−	0.329393i
$760$	−10.6466			−0.386191
$761$	−28.5397	+	32.9366i	−1.03456	+	1.19395i	−0.0538406	+	0.998550i	$0.517146\pi$
$761$	−28.5397	+	32.9366i	−1.03456	+	1.19395i	−0.980723	+	0.195401i	$0.937399\pi$
$762$	19.8618	−	12.7644i	0.719517	−	0.462405i
$763$	0.251183	+	1.74701i	0.00909342	+	0.0632461i
$764$	−2.86872	−	6.28162i	−0.103787	−	0.227261i
$765$	−0.404389	+	2.81259i	−0.0146207	+	0.101689i
$766$	34.3589	−	10.0887i	1.24144	−	0.364519i
$767$	−4.56840	−	2.93593i	−0.164955	−	0.106010i
$768$	−2.72784	+	5.97314i	−0.0984325	+	0.215537i
$769$	19.1077	+	5.61054i	0.689043	+	0.202321i	0.607466	−	0.794346i	$-0.292186\pi$
$769$	19.1077	+	5.61054i	0.689043	+	0.202321i	0.0815770	+	0.996667i	$0.474004\pi$
$770$	−3.31582	−	3.82666i	−0.119494	−	0.137903i
$771$	−8.73760	−	10.0837i	−0.314677	−	0.363156i
$772$	17.0429	+	5.00425i	0.613388	+	0.180107i
$773$	−10.7776	+	23.5997i	−0.387644	+	0.848823i	0.610731	+	0.791838i	$0.290876\pi$
$773$	−10.7776	+	23.5997i	−0.387644	+	0.848823i	−0.998375	+	0.0569843i	$0.981852\pi$
$774$	6.99743	+	4.49697i	0.251517	+	0.161640i
$775$	−4.34219	+	1.27498i	−0.155976	+	0.0457987i
$776$	0.469213	−	3.26345i	0.0168437	−	0.117151i
$777$	−1.61791	−	3.54273i	−0.0580422	−	0.127095i
$778$	−7.81960	−	54.3865i	−0.280346	−	1.94985i
$779$	21.7844	−	14.0000i	0.780507	−	0.501601i
$780$	−2.12827	+	2.45616i	−0.0762045	+	0.0879446i
$781$	−10.4555			−0.374127
$782$	12.9651	−	27.3012i	0.463631	−	0.976288i
$783$	3.63150			0.129779
$784$	−4.80675	+	5.54729i	−0.171670	+	0.198117i
$785$	6.84698	−	4.40029i	0.244379	−	0.157053i
$786$	5.86646	+	40.8021i	0.209250	+	1.45536i
$787$	−1.09586	−	2.39959i	−0.0390631	−	0.0855363i	0.889094	−	0.457724i	$-0.151335\pi$
$787$	−1.09586	−	2.39959i	−0.0390631	−	0.0855363i	−0.928158	+	0.372187i	$0.878608\pi$
$788$	−6.61297	+	45.9942i	−0.235577	+	1.63848i
$789$	24.3964	−	7.16342i	0.868533	−	0.255024i
$790$	19.0318	+	12.2310i	0.677122	+	0.435160i
$791$	6.86159	−	15.0248i	0.243970	−	0.534220i
$792$	3.73002	+	1.09523i	0.132540	+	0.0389174i
$793$	−5.86657	−	6.77038i	−0.208328	−	0.240423i
$794$	−30.9324	−	35.6979i	−1.09775	−	1.26687i
$795$	−3.35984	−	0.986538i	−0.119161	−	0.0349889i
$796$	−1.02397	+	2.24219i	−0.0362938	+	0.0794723i
$797$	1.10524	+	0.710292i	0.0391495	+	0.0251598i	0.560069	−	0.828446i	$-0.310775\pi$
$797$	1.10524	+	0.710292i	0.0391495	+	0.0251598i	−0.520920	+	0.853606i	$0.674411\pi$
$798$	−13.3053	+	3.90678i	−0.471002	+	0.138299i
$799$	3.70567	−	25.7735i	0.131097	−	0.911800i
$800$	2.90755	+	6.36664i	0.102797	+	0.225095i
$801$	1.21756	+	8.46833i	0.0430205	+	0.299214i
$802$	47.6951	−	30.6518i	1.68417	−	1.08235i
$803$	8.28234	−	9.55834i	0.292278	−	0.337306i
$804$	17.4344			0.614865
$805$	−2.46196	+	5.18426i	−0.0867728	+	0.182721i
$806$	11.1757			0.393646
$807$	−11.9401	+	13.7796i	−0.420311	+	0.485064i
$808$	−22.8016	+	14.6537i	−0.802157	+	0.515515i
$809$	−0.647513	−	4.50355i	−0.0227654	−	0.158336i	0.975268	−	0.221027i	$-0.0709409\pi$
$809$	−0.647513	−	4.50355i	−0.0227654	−	0.158336i	−0.998033	+	0.0626907i	$0.980032\pi$
$810$	0.921321	+	2.01741i	0.0323719	+	0.0708846i
$811$	−3.52923	+	24.5463i	−0.123928	+	0.861937i	0.829110	+	0.559086i	$0.188848\pi$
$811$	−3.52923	+	24.5463i	−0.123928	+	0.861937i	−0.953038	+	0.302852i	$0.902061\pi$
$812$	−12.1706	+	3.57362i	−0.427105	+	0.125409i
$813$	−0.528754	−	0.339809i	−0.0185442	−	0.0119176i
$814$	5.72043	−	12.5260i	0.200501	−	0.439036i
$815$	18.2896	+	5.37031i	0.640657	+	0.188114i
$816$	−2.45306	−	2.83098i	−0.0858743	−	0.0991042i
$817$	−12.8322	−	14.8092i	−0.448942	−	0.518107i
$818$	−44.2364	−	12.9890i	−1.54669	−	0.454149i
$819$	−0.553533	+	1.21207i	−0.0193420	+	0.0423531i
$820$	12.1696	+	7.82094i	0.424981	+	0.273119i
$821$	−11.1443	+	3.27227i	−0.388940	+	0.114203i	−0.470355	−	0.882477i	$-0.655874\pi$
$821$	−11.1443	+	3.27227i	−0.388940	+	0.114203i	0.0814151	+	0.996680i	$0.474056\pi$
$822$	−1.67197	+	11.6288i	−0.0583166	+	0.405601i
$823$	−3.21777	−	7.04592i	−0.112164	−	0.245605i	0.845222	−	0.534415i	$-0.179468\pi$
$823$	−3.21777	−	7.04592i	−0.112164	−	0.245605i	−0.957387	+	0.288809i	$0.906741\pi$
$824$	4.39965	+	30.6003i	0.153269	+	1.06601i
$825$	1.60493	−	1.03143i	0.0558765	−	0.0359096i
$826$	8.47659	−	9.78250i	0.294938	−	0.340377i
$827$	−46.1134			−1.60352			−0.801759	−	0.597647i	$-0.796102\pi$
$827$	−46.1134			−1.60352			−0.801759	+	0.597647i	$0.796102\pi$
$828$	−1.78462	−	13.8837i	−0.0620197	−	0.482494i
$829$	51.5451			1.79024			0.895118	−	0.445830i	$-0.147091\pi$
$829$	51.5451			1.79024			0.895118	+	0.445830i	$0.147091\pi$
$830$	−8.53643	+	9.85157i	−0.296304	+	0.341953i
$831$	24.3892	−	15.6740i	0.846053	−	0.543726i
$832$	−2.04201	−	14.2025i	−0.0707938	−	0.492382i
$833$	6.57241	+	14.3916i	0.227720	+	0.498638i
$834$	5.16965	−	35.9557i	0.179010	−	1.24504i
$835$	−13.3494	+	3.91975i	−0.461976	+	0.135648i
$836$	−24.4752	−	15.7293i	−0.846494	−	0.544009i
$837$	1.87996	−	4.11655i	0.0649811	−	0.142289i
$838$	−22.5735	−	6.62818i	−0.779789	−	0.228967i
$839$	−12.5920	−	14.5319i	−0.434724	−	0.501698i	0.495542	−	0.868584i	$-0.334969\pi$
$839$	−12.5920	−	14.5319i	−0.434724	−	0.501698i	−0.930266	+	0.366886i	$0.880424\pi$
$840$	−1.59688	−	1.84290i	−0.0550976	−	0.0635860i
$841$	15.1717	+	4.45481i	0.523162	+	0.153614i
$842$	30.8556	−	67.5644i	1.06335	−	2.32842i
$843$	−25.8702	−	16.6258i	−0.891018	−	0.572623i
$844$	58.8338	−	17.2752i	2.02514	−	0.594636i
$845$	−1.67365	+	11.6405i	−0.0575753	+	0.400445i
$846$	−8.44263	−	18.4868i	−0.290263	−	0.635588i
$847$	1.25352	+	8.71845i	0.0430716	+	0.299570i
$848$	3.88341	−	2.49572i	0.133357	−	0.0857033i
$849$	14.3212	−	16.5275i	0.491502	−	0.567224i
$850$	6.30199			0.216157
$851$	−15.6064	−	0.233501i	−0.534982	−	0.00800430i
$852$	−15.9962			−0.548021
$853$	−16.7285	+	19.3057i	−0.572771	+	0.661014i	−0.966035	−	0.258412i	$-0.916801\pi$
$853$	−16.7285	+	19.3057i	−0.572771	+	0.661014i	0.393263	+	0.919426i	$0.371346\pi$
$854$	17.9637	−	11.5446i	0.614707	−	0.395048i
$855$	−0.743567	−	5.17162i	−0.0254294	−	0.176866i
$856$	−16.2050	−	35.4839i	−0.553874	−	1.21282i
$857$	6.31511	−	43.9225i	0.215720	−	1.50037i	−0.537874	−	0.843025i	$-0.680772\pi$
$857$	6.31511	−	43.9225i	0.215720	−	1.50037i	0.753594	−	0.657340i	$-0.228319\pi$
$858$	−4.52040	+	1.32731i	−0.154324	+	0.0453136i
$859$	−37.7152	−	24.2381i	−1.28683	−	0.826994i	−0.295114	−	0.955462i	$-0.595358\pi$
$859$	−37.7152	−	24.2381i	−1.28683	−	0.826994i	−0.991714	+	0.128468i	$0.958994\pi$
$860$	4.54743	−	9.95749i	0.155066	−	0.339548i
$861$	5.69081	+	1.67097i	0.193942	+	0.0569466i
$862$	51.7186	+	59.6864i	1.76154	+	2.03293i
$863$	−28.6781	−	33.0963i	−0.976213	−	1.12661i	−0.991937	−	0.126733i	$-0.959551\pi$
$863$	−28.6781	−	33.0963i	−0.976213	−	1.12661i	0.0157239	−	0.999876i	$-0.494995\pi$
$864$	−6.71562	−	1.97188i	−0.228470	−	0.0670849i
$865$	−5.80822	+	12.7182i	−0.197485	+	0.432433i
$866$	−60.3789	−	38.8032i	−2.05176	−	1.31859i
$867$	8.56426	−	2.51469i	0.290857	−	0.0854034i
$868$	−2.24958	+	15.6462i	−0.0763559	+	0.531067i
$869$	8.08419	+	17.7019i	0.274237	+	0.600496i
$870$	−1.14621	−	7.97208i	−0.0388602	−	0.270279i
$871$	−5.59514	+	3.59578i	−0.189584	+	0.121838i
$872$	−1.96809	+	2.27129i	−0.0666479	+	0.0769157i
$873$	1.61800			0.0547612
$874$	−8.73086	+	54.8827i	−0.295326	+	1.85643i
$875$	−1.19670			−0.0404557
$876$	12.6714	−	14.6236i	0.428128	−	0.494086i
$877$	48.4939	−	31.1651i	1.63752	−	1.05237i	0.694581	−	0.719414i	$-0.255590\pi$
$877$	48.4939	−	31.1651i	1.63752	−	1.05237i	0.942942	−	0.332958i	$-0.108047\pi$
$878$	0.0712212	+	0.495355i	0.00240360	+	0.0167174i
$879$	1.12107	+	2.45481i	0.0378129	+	0.0827987i
$880$	−0.357923	+	2.48941i	−0.0120656	+	0.0839179i
$881$	42.4933	−	12.4772i	1.43164	−	0.420366i	0.528212	−	0.849113i	$-0.322863\pi$
$881$	42.4933	−	12.4772i	1.43164	−	0.420366i	0.903425	+	0.428746i	$0.141045\pi$
$882$	10.3884	+	6.67622i	0.349796	+	0.224800i
$883$	23.5137	−	51.4877i	0.791298	−	1.73270i	0.118399	−	0.992966i	$-0.462224\pi$
$883$	23.5137	−	51.4877i	0.791298	−	1.73270i	0.672899	−	0.739734i	$-0.265049\pi$
$884$	−8.86074	−	2.60175i	−0.298019	−	0.0875062i
$885$	3.19381	+	3.68585i	0.107359	+	0.123899i
$886$	21.8981	+	25.2718i	0.735682	+	0.849022i
$887$	38.7866	+	11.3888i	1.30233	+	0.382397i	0.858084	−	0.513509i	$-0.171655\pi$
$887$	38.7866	+	11.3888i	1.30233	+	0.382397i	0.444242	+	0.895907i	$0.353473\pi$
$888$	2.75493	−	6.03246i	0.0924494	−	0.202436i
$889$	−10.7170	−	6.88740i	−0.359437	−	0.230996i
$890$	18.2059	−	5.34573i	0.610262	−	0.179189i
$891$	−0.271506	+	1.88837i	−0.00909579	+	0.0632626i
$892$	−9.32479	−	20.4184i	−0.312217	−	0.683660i
$893$	6.81376	+	47.3907i	0.228014	+	1.58587i
$894$	−11.4148	+	7.33584i	−0.381768	+	0.245347i
$895$	7.31867	−	8.44620i	0.244636	−	0.282325i
$896$	17.4496			0.582949
$897$	3.43619	+	4.08757i	0.114731	+	0.136480i
$898$	−54.4760			−1.81789
$899$	−10.7622	+	12.4203i	−0.358940	+	0.414239i
$900$	2.45543	−	1.57801i	0.0818478	−	0.0526004i
$901$	−1.41604	−	9.84879i	−0.0471752	−	0.328111i
$902$	8.71142	+	19.0753i	0.290059	+	0.635140i
$903$	0.638729	−	4.44246i	0.0212556	−	0.147836i
$904$	26.9861	−	7.92384i	0.897545	−	0.263543i
$905$	9.87413	+	6.34572i	0.328227	+	0.210939i
$906$	−12.7858	+	27.9971i	−0.424781	+	0.930140i
$907$	−40.3434	−	11.8459i	−1.33958	−	0.393336i	−0.468061	−	0.883696i	$-0.655047\pi$
$907$	−40.3434	−	11.8459i	−1.33958	−	0.393336i	−0.871520	+	0.490360i	$0.836865\pi$
$908$	−21.6834	−	25.0240i	−0.719590	−	0.830451i
$909$	−8.71058	−	10.0525i	−0.288912	−	0.333422i
$910$	2.83551	+	0.832582i	0.0939963	+	0.0275998i
$911$	13.2875	−	29.0955i	0.440234	−	0.963978i	−0.551321	−	0.834293i	$-0.685876\pi$
$911$	13.2875	−	29.0955i	0.440234	−	0.963978i	0.991555	−	0.129685i	$-0.0413966\pi$
$912$	5.79437	+	3.72382i	0.191871	+	0.123308i
$913$	−10.7589	+	3.15911i	−0.356069	+	0.104551i
$914$	9.31640	−	64.7970i	0.308159	−	2.14329i
$915$	3.34226	+	7.31852i	0.110492	+	0.241943i
$916$	−5.55966	−	38.6683i	−0.183696	−	1.27764i
$917$	18.7115	−	12.0251i	0.617907	−	0.397105i
$918$	−4.12693	+	4.76273i	−0.136209	+	0.157193i
$919$	3.14092			0.103609			0.0518047	−	0.998657i	$-0.483503\pi$
$919$	3.14092			0.103609			0.0518047	+	0.998657i	$0.483503\pi$
$920$	−9.41674	+	2.61264i	−0.310461	+	0.0861360i
$921$	27.1380			0.894228
$922$	−11.2043	+	12.9304i	−0.368993	+	0.425840i
$923$	5.13358	−	3.29915i	0.168974	−	0.108593i
$924$	−0.948341	−	6.59585i	−0.0311981	−	0.216988i
$925$	−1.35198	−	2.96043i	−0.0444529	−	0.0973383i
$926$	−5.34482	+	37.1740i	−0.175642	+	1.22162i
$927$	−14.5569	+	4.27431i	−0.478113	+	0.140387i
$928$	21.3824	+	13.7417i	0.701913	+	0.451092i
$929$	11.4888	−	25.1569i	0.376934	−	0.825371i	−0.622163	−	0.782888i	$-0.713746\pi$
$929$	11.4888	−	25.1569i	0.376934	−	0.825371i	0.999097	−	0.0424833i	$-0.0135269\pi$
$930$	−9.63025	−	2.82770i	−0.315788	−	0.0927239i
$931$	−19.0507	−	21.9857i	−0.624362	−	0.720553i
$932$	13.6366	+	15.7375i	0.446681	+	0.515498i
$933$	−6.87688	−	2.01923i	−0.225139	−	0.0661067i
$934$	−11.7254	+	25.6751i	−0.383668	+	0.840116i
$935$	4.56043	+	2.93081i	0.149142	+	0.0958477i
$936$	−2.17700	+	0.639226i	−0.0711576	+	0.0208937i
$937$	−6.73251	+	46.8257i	−0.219942	+	1.52973i	0.518304	+	0.855196i	$0.326563\pi$
$937$	−6.73251	+	46.8257i	−0.219942	+	1.52973i	−0.738246	+	0.674532i	$0.764346\pi$
$938$	−6.58569	−	14.4207i	−0.215030	−	0.470851i
$939$	2.83251	+	19.7005i	0.0924354	+	0.642903i
$940$	−22.5006	+	14.4603i	−0.733890	+	0.471642i
$941$	20.4881	−	23.6445i	0.667893	−	0.770790i	−0.316152	−	0.948709i	$-0.602391\pi$
$941$	20.4881	−	23.6445i	0.667893	−	0.770790i	0.984045	+	0.177919i	$0.0569363\pi$
$942$	18.0510			0.588133
$943$	15.8324	−	17.7286i	0.515575	−	0.577323i
$944$	−6.42939			−0.209259
$945$	0.783669	−	0.904402i	0.0254928	−	0.0294202i
$946$	13.3496	−	8.57926i	0.434033	−	0.278936i
$947$	3.24073	+	22.5398i	0.105310	+	0.732445i	0.972235	+	0.234007i	$0.0751838\pi$
$947$	3.24073	+	22.5398i	0.105310	+	0.732445i	−0.866925	+	0.498438i	$0.833907\pi$
$948$	12.3683	+	27.0827i	0.401702	+	0.879605i
$949$	−1.05052	+	7.30650i	−0.0341012	+	0.237179i
$950$	−11.1183	+	3.26464i	−0.360727	+	0.105919i
$951$	8.70309	+	5.59313i	0.282217	+	0.181370i
$952$	2.87843	−	6.30287i	0.0932903	−	0.204277i
$953$	24.2902	+	7.13223i	0.786835	+	0.231036i	0.650378	−	0.759610i	$-0.274610\pi$
$953$	24.2902	+	7.13223i	0.786835	+	0.231036i	0.136457	+	0.990646i	$0.456428\pi$
$954$	−5.08574	−	5.86926i	−0.164657	−	0.190024i
$955$	−1.54936	−	1.78806i	−0.0501363	−	0.0578603i
$956$	−67.8837	−	19.9325i	−2.19552	−	0.644662i
$957$	2.87804	−	6.30204i	0.0930340	−	0.203716i
$958$	−65.3937	−	42.0260i	−2.11278	−	1.35780i
$959$	6.08240	−	1.78595i	0.196411	−	0.0576714i
$960$	−1.83392	+	12.7552i	−0.0591894	+	0.411671i
$961$	−4.37008	−	9.56913i	−0.140970	−	0.308682i
$962$	1.14379	+	7.95521i	0.0368772	+	0.256486i
$963$	16.1047	−	10.3499i	0.518967	−	0.333520i
$964$	−39.0894	+	45.1116i	−1.25899	+	1.45295i
$965$	6.08557			0.195901
$966$	−10.8096	+	6.72057i	−0.347794	+	0.216231i
$967$	46.4454			1.49358			0.746791	−	0.665058i	$-0.231593\pi$
$967$	46.4454			1.49358			0.746791	+	0.665058i	$0.231593\pi$
$968$	−9.82172	+	11.3349i	−0.315682	+	0.364317i
$969$	12.4895	−	8.02653i	0.401221	−	0.257849i
$970$	−0.510691	−	3.55194i	−0.0163973	−	0.114046i
$971$	18.2012	+	39.8551i	0.584105	+	1.27901i	0.938939	+	0.344083i	$0.111810\pi$
$971$	18.2012	+	39.8551i	0.584105	+	1.27901i	−0.354834	+	0.934929i	$0.615463\pi$
$972$	−0.415386	+	2.88907i	−0.0133235	+	0.0926670i
$973$	−18.8065	+	5.52208i	−0.602908	+	0.177030i
$974$	−32.6134	−	20.9593i	−1.04500	−	0.671581i
$975$	−0.462551	+	1.01285i	−0.0148135	+	0.0324370i
$976$	−10.1768	−	2.98816i	−0.325750	−	0.0956488i
$977$	−15.3486	−	17.7132i	−0.491044	−	0.566695i	0.455100	−	0.890440i	$-0.349603\pi$
$977$	−15.3486	−	17.7132i	−0.491044	−	0.566695i	−0.946144	+	0.323745i	$0.895058\pi$
$978$	27.6847	+	31.9499i	0.885259	+	1.02164i
$979$	15.6607	+	4.59841i	0.500519	+	0.146966i
$980$	6.75113	−	14.7829i	0.215657	−	0.472223i
$981$	−1.24075	−	0.797379i	−0.0396139	−	0.0254583i
$982$	56.0787	−	16.4662i	1.78954	−	0.525457i
$983$	1.79032	−	12.4520i	0.0571023	−	0.397156i	−0.941146	−	0.337999i	$-0.890250\pi$
$983$	1.79032	−	12.4520i	0.0571023	−	0.397156i	0.998249	−	0.0591563i	$-0.0188410\pi$
$984$	4.19537	+	9.18659i	0.133744	+	0.292858i
$985$	2.26566	+	15.7580i	0.0721901	+	0.502093i
$986$	19.2527	−	12.3729i	0.613130	−	0.394035i
$987$	−7.18124	+	8.28759i	−0.228581	+	0.263797i
$988$	16.9804			0.540219
$989$	−14.9840	−	9.94952i	−0.476465	−	0.316376i
$990$	4.23115			0.134475
$991$	−34.1750	+	39.4401i	−1.08561	+	1.25286i	−0.120020	+	0.992771i	$0.538296\pi$
$991$	−34.1750	+	39.4401i	−1.08561	+	1.25286i	−0.965586	+	0.260085i	$0.916249\pi$
$992$	26.6464	−	17.1246i	0.846024	−	0.543707i
$993$	2.52758	+	17.5797i	0.0802104	+	0.557876i
$994$	6.04241	+	13.2310i	0.191654	+	0.419663i
$995$	−0.120186	+	0.835915i	−0.00381017	+	0.0265003i
$996$	−16.4605	+	4.83323i	−0.521569	+	0.153147i
$997$	−13.2949	−	8.54409i	−0.421053	−	0.270594i	0.312912	−	0.949782i	$-0.398696\pi$
$997$	−13.2949	−	8.54409i	−0.421053	−	0.270594i	−0.733964	+	0.679188i	$0.762332\pi$
$998$	−19.5096	+	42.7201i	−0.617566	+	1.35228i
$999$	3.12270	+	0.916908i	0.0987979	+	0.0290097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.16.5	✓	50
23.6	even	11		7935.2.a.bv.1.3		25
23.13	even	11	inner	345.2.m.c.151.5	yes	50
23.17	odd	22		7935.2.a.bw.1.3		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.5	✓	50	1.1	even	1	trivial
345.2.m.c.151.5	yes	50	23.13	even	11	inner
7935.2.a.bv.1.3		25	23.6	even	11
7935.2.a.bw.1.3		25	23.17	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45237 - 1.67613i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.415386 - 2.88907i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.315630 - 2.19526i) q^{6} +(-1.14822 + 0.337148i) q^{7} +(-1.71422 - 1.10166i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(1.45237 - 1.67613i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.415386 - 2.88907i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.315630 - 2.19526i) q^{6} +(-1.14822 + 0.337148i) q^{7} +(-1.71422 - 1.10166i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-2.12799 - 0.624835i) q^{10} +(-1.24933 - 1.44181i) q^{11} +(-1.91139 - 2.20587i) q^{12} +(1.06836 + 0.313700i) q^{13} +(-1.10254 + 2.41423i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(1.26489 - 0.371404i) q^{16} +(0.404389 - 2.81259i) q^{17} +(-0.921321 - 2.01741i) q^{18} +(0.743567 + 5.17162i) q^{19} +(-2.45543 + 1.57801i) q^{20} +(-0.783669 + 0.904402i) q^{21} -4.23115 q^{22} +(1.92677 + 4.39176i) q^{23} -2.03770 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.07746 - 1.33510i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.45100 + 3.17724i) q^{28} +(-0.516816 + 3.59454i) q^{29} +(-2.12799 + 0.624835i) q^{30} +(3.80710 + 2.44667i) q^{31} +(2.90755 - 6.36664i) q^{32} +(-1.83051 - 0.537485i) q^{33} +(-4.12693 - 4.76273i) q^{34} +(0.783669 + 0.904402i) q^{35} +(-2.80055 - 0.822315i) q^{36} +(-1.35198 + 2.96043i) q^{37} +(9.74822 + 6.26480i) q^{38} +(1.06836 - 0.313700i) q^{39} +(-0.289995 + 2.01696i) q^{40} +(-2.05888 - 4.50832i) q^{41} +(0.377714 + 2.62706i) q^{42} +(-3.15508 + 2.02764i) q^{43} +(-3.64653 + 4.20832i) q^{44} -1.00000 q^{45} +(10.1595 + 3.14895i) q^{46} +9.16361 q^{47} +(0.863294 - 0.996295i) q^{48} +(-4.68403 + 3.01024i) q^{49} +(0.315630 + 2.19526i) q^{50} +(-1.18041 - 2.58473i) q^{51} +(0.462518 - 3.21689i) q^{52} +(3.35984 - 0.986538i) q^{53} +(-1.86576 - 1.19905i) q^{54} +(-0.792522 + 1.73538i) q^{55} +(2.33973 + 0.687006i) q^{56} +(3.42152 + 3.94864i) q^{57} +(5.27428 + 6.08685i) q^{58} +(-4.67952 - 1.37403i) q^{59} +(-1.21250 + 2.65501i) q^{60} +(-6.76838 - 4.34977i) q^{61} +(9.63025 - 2.82770i) q^{62} +(-0.170308 + 1.18451i) q^{63} +(-5.35318 - 11.7218i) q^{64} +(-0.158463 - 1.10213i) q^{65} +(-3.55947 + 2.28753i) q^{66} +(-3.91161 + 4.51424i) q^{67} -8.29374 q^{68} +(3.99527 + 2.65289i) q^{69} +2.65407 q^{70} +(3.58893 - 4.14184i) q^{71} +(-1.71422 + 1.10166i) q^{72} +(0.943464 + 6.56193i) q^{73} +(2.99847 + 6.56573i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(14.6323 - 4.29643i) q^{76} +(1.92061 + 1.23430i) q^{77} +(1.02586 - 2.24632i) q^{78} +(-9.78739 - 2.87384i) q^{79} +(-0.863294 - 0.996295i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.5468 - 3.09681i) q^{82} +(2.44164 - 5.34644i) q^{83} +(2.93841 + 1.88840i) q^{84} +(-2.72641 + 0.800546i) q^{85} +(-1.18375 + 8.23320i) q^{86} +(1.50858 + 3.30333i) q^{87} +(0.553247 + 3.84792i) q^{88} +(-7.19727 + 4.62541i) q^{89} +(-1.45237 + 1.67613i) q^{90} -1.33248 q^{91} +(11.8877 - 7.39086i) q^{92} +4.52551 q^{93} +(13.3090 - 15.3594i) q^{94} +(4.39538 - 2.82474i) q^{95} +(-0.996081 - 6.92789i) q^{96} +(0.672143 + 1.47179i) q^{97} +(-1.75740 + 12.2230i) q^{98} +(-1.83051 + 0.537485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

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