LMFDB - Embedded newform 95.2.p.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(4,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("95.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (of order $18$, degree $6$, 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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	95.4
Dual form			95.2.p.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.810919 + 2.22798i) q^{2} +(2.25040 - 0.396806i) q^{3} +(-2.77422 - 2.32785i) q^{4} +(2.12266 + 0.703088i) q^{5} +(-0.940815 + 5.33563i) q^{6} +(-1.41749 - 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(2.08777 - 0.759885i) q^{9} +O(q^{10})$	\(q+(-0.810919 + 2.22798i) q^{2} +(2.25040 - 0.396806i) q^{3} +(-2.77422 - 2.32785i) q^{4} +(2.12266 + 0.703088i) q^{5} +(-0.940815 + 5.33563i) q^{6} +(-1.41749 - 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(2.08777 - 0.759885i) q^{9} +(-3.28777 + 4.15909i) q^{10} +(-1.36374 - 2.36206i) q^{11} +(-7.16682 - 4.13776i) q^{12} +(-6.10515 - 1.07650i) q^{13} +(2.97282 - 2.49449i) q^{14} +(5.05581 + 0.739946i) q^{15} +(0.325107 + 1.84377i) q^{16} +(-1.06864 + 2.93608i) q^{17} +5.26771i q^{18} +(3.46824 + 2.64032i) q^{19} +(-4.25204 - 6.89175i) q^{20} +(-3.51465 - 1.27923i) q^{21} +(6.36852 - 1.12294i) q^{22} +(4.69173 - 5.59139i) q^{23} +(6.72981 - 5.64698i) q^{24} +(4.01134 + 2.98483i) q^{25} +(7.34921 - 12.7292i) q^{26} +(-1.54012 + 0.889189i) q^{27} +(2.02734 + 5.57008i) q^{28} +(2.09149 - 0.761241i) q^{29} +(-5.74844 + 10.6642i) q^{30} +(-2.21333 + 3.83360i) q^{31} +(3.20067 + 0.564364i) q^{32} +(-4.00624 - 4.77445i) q^{33} +(-5.67494 - 4.76184i) q^{34} +(-2.43344 - 2.73377i) q^{35} +(-7.56083 - 2.75192i) q^{36} -2.04016i q^{37} +(-8.69505 + 5.58609i) q^{38} -14.1662 q^{39} +(8.41876 - 1.73939i) q^{40} +(0.681538 + 3.86519i) q^{41} +(5.70020 - 6.79323i) q^{42} +(-0.303946 - 0.362229i) q^{43} +(-1.71522 + 9.72747i) q^{44} +(4.96588 - 0.145091i) q^{45} +(8.65289 + 14.9872i) q^{46} +(-0.787194 - 2.16280i) q^{47} +(1.46324 + 4.02022i) q^{48} +(-2.16049 - 3.74208i) q^{49} +(-9.90301 + 6.51673i) q^{50} +(-1.23982 + 7.03139i) q^{51} +(14.4311 + 17.1983i) q^{52} +(-4.09062 + 4.87501i) q^{53} +(-0.732183 - 4.15242i) q^{54} +(-1.23401 - 5.97268i) q^{55} -6.29258 q^{56} +(8.85263 + 4.56556i) q^{57} +5.27711i q^{58} +(11.5263 + 4.19524i) q^{59} +(-12.3035 - 13.8220i) q^{60} +(-3.66993 - 3.07944i) q^{61} +(-6.74636 - 8.03999i) q^{62} +(-3.58126 - 0.631473i) q^{63} +(-5.72509 + 9.91615i) q^{64} +(-12.2023 - 6.57750i) q^{65} +(13.8861 - 5.05414i) q^{66} +(0.229482 + 0.630496i) q^{67} +(9.79940 - 5.65769i) q^{68} +(8.33957 - 14.4446i) q^{69} +(8.06411 - 3.20479i) q^{70} +(2.01848 - 1.69370i) q^{71} +(5.49040 - 6.54321i) q^{72} +(-6.41403 + 1.13097i) q^{73} +(4.54543 + 1.65440i) q^{74} +(10.2115 + 5.12533i) q^{75} +(-3.47540 - 15.3984i) q^{76} +4.46426i q^{77} +(11.4876 - 31.5620i) q^{78} +(-0.715459 - 4.05757i) q^{79} +(-0.606244 + 4.14227i) q^{80} +(-8.21894 + 6.89651i) q^{81} +(-9.16425 - 1.61590i) q^{82} +(5.56331 + 3.21198i) q^{83} +(6.77258 + 11.7304i) q^{84} +(-4.33268 + 5.48093i) q^{85} +(1.05351 - 0.383448i) q^{86} +(4.40463 - 2.54302i) q^{87} +(-9.08097 - 5.24290i) q^{88} +(-3.00487 + 17.0415i) q^{89} +(-3.70367 + 11.1815i) q^{90} +(7.77297 + 6.52229i) q^{91} +(-26.0318 + 4.59011i) q^{92} +(-3.45968 + 9.50539i) q^{93} +5.45702 q^{94} +(5.50550 + 8.04297i) q^{95} +7.42673 q^{96} +(-0.0444434 + 0.122107i) q^{97} +(10.0893 - 1.77901i) q^{98} +(-4.64207 - 3.89516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−0.810919	+	2.22798i	−0.573406	+	1.57542i	0.225678	+	0.974202i	$0.427540\pi$
$2$	−0.810919	+	2.22798i	−0.573406	+	1.57542i	−0.799084	+	0.601219i	$0.794682\pi$
$3$	2.25040	−	0.396806i	1.29927	−	0.229096i	0.519126	−	0.854698i	$-0.326257\pi$
$3$	2.25040	−	0.396806i	1.29927	−	0.229096i	0.780143	+	0.625601i	$0.215146\pi$
$4$	−2.77422	−	2.32785i	−1.38711	−	1.16392i
$5$	2.12266	+	0.703088i	0.949281	+	0.314430i
$5$	2.12266	+	0.703088i	0.949281	+	0.314430i
$6$	−0.940815	+	5.33563i	−0.384086	+	2.17826i
$7$	−1.41749	−	0.818386i	−0.535759	−	0.309321i	0.207599	−	0.978214i	$-0.433435\pi$
$7$	−1.41749	−	0.818386i	−0.535759	−	0.309321i	−0.743359	+	0.668893i	$0.766768\pi$
$8$	3.32944	−	1.92225i	1.17713	−	0.679619i
$9$	2.08777	−	0.759885i	0.695923	−	0.253295i
$10$	−3.28777	+	4.15909i	−1.03968	+	1.31522i
$11$	−1.36374	−	2.36206i	−0.411183	−	0.712189i	0.583837	−	0.811871i	$-0.301551\pi$
$11$	−1.36374	−	2.36206i	−0.411183	−	0.712189i	−0.995019	+	0.0996818i	$0.968218\pi$
$12$	−7.16682	−	4.13776i	−2.06888	−	1.19447i
$13$	−6.10515	−	1.07650i	−1.69326	−	0.298568i	−0.757930	−	0.652336i	$-0.773789\pi$
$13$	−6.10515	−	1.07650i	−1.69326	−	0.298568i	−0.935333	+	0.353768i	$0.884900\pi$
$14$	2.97282	−	2.49449i	0.794518	−	0.666680i
$15$	5.05581	+	0.739946i	1.30541	+	0.191053i
$16$	0.325107	+	1.84377i	0.0812767	+	0.460943i
$17$	−1.06864	+	2.93608i	−0.259184	+	0.712103i	0.740034	+	0.672570i	$0.234809\pi$
$17$	−1.06864	+	2.93608i	−0.259184	+	0.712103i	−0.999218	+	0.0395336i	$0.987413\pi$
$18$			5.26771i			1.24161i
$19$	3.46824	+	2.64032i	0.795669	+	0.605732i
$19$	3.46824	+	2.64032i	0.795669	+	0.605732i
$20$	−4.25204	−	6.89175i	−0.950785	−	1.54104i
$21$	−3.51465	−	1.27923i	−0.766960	−	0.279151i
$22$	6.36852	−	1.12294i	1.35777	−	0.239412i
$23$	4.69173	−	5.59139i	0.978293	−	1.16588i	−0.00784655	−	0.999969i	$-0.502498\pi$
$23$	4.69173	−	5.59139i	0.978293	−	1.16588i	0.986140	−	0.165915i	$-0.0530579\pi$
$24$	6.72981	−	5.64698i	1.37372	−	1.15268i
$25$	4.01134	+	2.98483i	0.802267	+	0.596965i
$26$	7.34921	−	12.7292i	1.44130	−	2.49640i
$27$	−1.54012	+	0.889189i	−0.296396	+	0.171124i
$28$	2.02734	+	5.57008i	0.383132	+	1.05265i
$29$	2.09149	−	0.761241i	0.388381	−	0.141359i	−0.140447	−	0.990088i	$-0.544854\pi$
$29$	2.09149	−	0.761241i	0.388381	−	0.141359i	0.528828	+	0.848729i	$0.322632\pi$
$30$	−5.74844	+	10.6642i	−1.04952	+	1.94701i
$31$	−2.21333	+	3.83360i	−0.397526	+	0.688535i	−0.993420	−	0.114528i	$-0.963464\pi$
$31$	−2.21333	+	3.83360i	−0.397526	+	0.688535i	0.595894	+	0.803063i	$0.296798\pi$
$32$	3.20067	+	0.564364i	0.565804	+	0.0997665i
$33$	−4.00624	−	4.77445i	−0.697397	−	0.831125i
$34$	−5.67494	−	4.76184i	−0.973244	−	0.816649i
$35$	−2.43344	−	2.73377i	−0.411326	−	0.462091i
$36$	−7.56083	−	2.75192i	−1.26014	−	0.458653i
$37$		−	2.04016i		−	0.335400i	−0.985838	−	0.167700i	$-0.946366\pi$
$37$		−	2.04016i		−	0.335400i	0.985838	−	0.167700i	$-0.0536339\pi$
$38$	−8.69505	+	5.58609i	−1.41052	+	0.906183i
$39$	−14.1662			−2.26841
$40$	8.41876	−	1.73939i	1.33112	−	0.275022i
$41$	0.681538	+	3.86519i	0.106438	+	0.603642i	0.990636	+	0.136529i	$0.0435947\pi$
$41$	0.681538	+	3.86519i	0.106438	+	0.603642i	−0.884198	+	0.467113i	$0.845294\pi$
$42$	5.70020	−	6.79323i	0.879559	−	1.04822i
$43$	−0.303946	−	0.362229i	−0.0463513	−	0.0552394i	0.742371	−	0.669989i	$-0.233701\pi$
$43$	−0.303946	−	0.362229i	−0.0463513	−	0.0552394i	−0.788722	+	0.614750i	$0.789257\pi$
$44$	−1.71522	+	9.72747i	−0.258579	+	1.46647i
$45$	4.96588	−	0.145091i	0.740270	−	0.0216289i
$46$	8.65289	+	14.9872i	1.27580	+	2.20975i
$47$	−0.787194	−	2.16280i	−0.114824	−	0.315477i	0.868947	−	0.494905i	$-0.164797\pi$
$47$	−0.787194	−	2.16280i	−0.114824	−	0.315477i	−0.983771	+	0.179429i	$0.942575\pi$
$48$	1.46324	+	4.02022i	0.211201	+	0.580269i
$49$	−2.16049	−	3.74208i	−0.308641	−	0.534582i
$50$	−9.90301	+	6.51673i	−1.40050	+	0.921605i
$51$	−1.23982	+	7.03139i	−0.173610	+	0.984592i
$52$	14.4311	+	17.1983i	2.00123	+	2.38498i
$53$	−4.09062	+	4.87501i	−0.561890	+	0.669634i	−0.969945	−	0.243323i	$-0.921762\pi$
$53$	−4.09062	+	4.87501i	−0.561890	+	0.669634i	0.408056	+	0.912957i	$0.366207\pi$
$54$	−0.732183	−	4.15242i	−0.0996375	−	0.565073i
$55$	−1.23401	−	5.97268i	−0.166394	−	0.805356i
$56$	−6.29258			−0.840881
$57$	8.85263	+	4.56556i	1.17256	+	0.604724i
$58$			5.27711i			0.692919i
$59$	11.5263	+	4.19524i	1.50060	+	0.546174i	0.956216	−	0.292661i	$-0.0945407\pi$
$59$	11.5263	+	4.19524i	1.50060	+	0.546174i	0.544385	+	0.838835i	$0.316763\pi$
$60$	−12.3035	−	13.8220i	−1.58837	−	1.78441i
$61$	−3.66993	−	3.07944i	−0.469887	−	0.394282i	0.376867	−	0.926268i	$-0.377002\pi$
$61$	−3.66993	−	3.07944i	−0.469887	−	0.394282i	−0.846753	+	0.531986i	$0.821446\pi$
$62$	−6.74636	−	8.03999i	−0.856788	−	1.02108i
$63$	−3.58126	−	0.631473i	−0.451197	−	0.0795581i
$64$	−5.72509	+	9.91615i	−0.715637	+	1.23952i
$65$	−12.2023	−	6.57750i	−1.51350	−	0.815838i
$66$	13.8861	−	5.05414i	1.70926	−	0.622121i
$67$	0.229482	+	0.630496i	0.0280357	+	0.0770274i	0.952921	−	0.303219i	$-0.0980614\pi$
$67$	0.229482	+	0.630496i	0.0280357	+	0.0770274i	−0.924885	+	0.380246i	$0.875839\pi$
$68$	9.79940	−	5.65769i	1.18835	−	0.686095i
$69$	8.33957	−	14.4446i	1.00397	−	1.73892i
$70$	8.06411	−	3.20479i	0.963845	−	0.383046i
$71$	2.01848	−	1.69370i	0.239549	−	0.201006i	−0.515107	−	0.857126i	$-0.672248\pi$
$71$	2.01848	−	1.69370i	0.239549	−	0.201006i	0.754657	+	0.656120i	$0.227803\pi$
$72$	5.49040	−	6.54321i	0.647050	−	0.771124i
$73$	−6.41403	+	1.13097i	−0.750706	+	0.132370i	−0.535893	−	0.844286i	$-0.680025\pi$
$73$	−6.41403	+	1.13097i	−0.750706	+	0.132370i	−0.214812	+	0.976655i	$0.568914\pi$
$74$	4.54543	+	1.65440i	0.528395	+	0.192320i
$75$	10.2115	+	5.12533i	1.17912	+	0.591822i
$76$	−3.47540	−	15.3984i	−0.398656	−	1.76632i
$77$			4.46426i			0.508750i
$78$	11.4876	−	31.5620i	1.30072	−	3.57369i
$79$	−0.715459	−	4.05757i	−0.0804954	−	0.456512i	−0.998238	−	0.0593365i	$-0.981101\pi$
$79$	−0.715459	−	4.05757i	−0.0804954	−	0.456512i	0.917743	−	0.397176i	$-0.130010\pi$
$80$	−0.606244	+	4.14227i	−0.0677801	+	0.463120i
$81$	−8.21894	+	6.89651i	−0.913216	+	0.766279i
$82$	−9.16425	−	1.61590i	−1.01202	−	0.178447i
$83$	5.56331	+	3.21198i	0.610653	+	0.352560i	0.773221	−	0.634137i	$-0.218644\pi$
$83$	5.56331	+	3.21198i	0.610653	+	0.352560i	−0.162568	+	0.986697i	$0.551978\pi$
$84$	6.77258	+	11.7304i	0.738949	+	1.27990i
$85$	−4.33268	+	5.48093i	−0.469946	+	0.594490i
$86$	1.05351	−	0.383448i	0.113603	−	0.0413483i
$87$	4.40463	−	2.54302i	0.472226	−	0.272640i
$88$	−9.08097	−	5.24290i	−0.968034	−	0.558895i
$89$	−3.00487	+	17.0415i	−0.318516	+	1.80639i	0.233276	+	0.972411i	$0.425056\pi$
$89$	−3.00487	+	17.0415i	−0.318516	+	1.80639i	−0.551791	+	0.833982i	$0.686056\pi$
$90$	−3.70367	+	11.1815i	−0.390401	+	1.17864i
$91$	7.77297	+	6.52229i	0.814828	+	0.683722i
$92$	−26.0318	+	4.59011i	−2.71400	+	0.478552i
$93$	−3.45968	+	9.50539i	−0.358752	+	0.985664i
$94$	5.45702			0.562849
$95$	5.50550	+	8.04297i	0.564853	+	0.825192i
$96$	7.42673			0.757988
$97$	−0.0444434	+	0.122107i	−0.00451254	+	0.0123981i	−0.941928	−	0.335814i	$-0.890989\pi$
$97$	−0.0444434	+	0.122107i	−0.00451254	+	0.0123981i	0.937416	+	0.348212i	$0.113211\pi$
$98$	10.0893	−	1.77901i	1.01917	−	0.179707i
$99$	−4.64207	−	3.89516i	−0.466546	−	0.391478i
$100$	−4.18011	−	17.6184i	−0.418011	−	1.76184i
$101$	0.648657	−	3.67872i	0.0645438	−	0.366046i	−0.935379	−	0.353646i	$-0.884942\pi$
$101$	0.648657	−	3.67872i	0.0645438	−	0.366046i	0.999923	−	0.0123999i	$-0.00394711\pi$
$102$	−14.6604	−	8.46419i	−1.45160	−	0.838080i
$103$	5.71537	−	3.29977i	0.563152	−	0.325136i	−0.191258	−	0.981540i	$-0.561257\pi$
$103$	5.71537	−	3.29977i	0.563152	−	0.325136i	0.754410	+	0.656404i	$0.227923\pi$
$104$	−22.3960	+	8.15148i	−2.19611	+	0.799319i
$105$	−6.56099	−	5.18647i	−0.640287	−	0.506148i
$106$	−7.54427	−	13.0671i	−0.732764	−	1.26918i
$107$	10.2150	+	5.89764i	0.987522	+	0.570146i	0.904533	−	0.426404i	$-0.140220\pi$
$107$	10.2150	+	5.89764i	0.987522	+	0.570146i	0.0829897	+	0.996550i	$0.473553\pi$
$108$	6.34253	+	1.11836i	0.610310	+	0.107614i
$109$	−5.54468	+	4.65254i	−0.531084	+	0.445632i	−0.868475	−	0.495732i	$-0.834900\pi$
$109$	−5.54468	+	4.65254i	−0.531084	+	0.445632i	0.337392	+	0.941364i	$0.390455\pi$
$110$	14.3077	+	2.09401i	1.36419	+	0.199656i
$111$	−0.809547	−	4.59117i	−0.0768388	−	0.435774i
$112$	1.04808	−	2.87958i	0.0990345	−	0.272095i
$113$		−	13.2879i		−	1.25002i	−0.780616	−	0.625010i	$-0.785095\pi$
$113$		−	13.2879i		−	1.25002i	0.780616	−	0.625010i	$-0.214905\pi$
$114$	−17.3508	+	16.0212i	−1.62505	+	1.50052i
$115$	13.8902	−	8.56989i	1.29526	−	0.799146i
$116$	−7.57432	−	2.75683i	−0.703258	−	0.255965i
$117$	−13.5642	+	2.39173i	−1.25401	+	0.221115i
$118$	−18.6939	+	22.2785i	−1.72091	+	2.05090i
$119$	3.91763	−	3.28728i	0.359129	−	0.301345i
$120$	18.2554	−	7.25495i	1.66648	−	0.662283i
$121$	1.78043	−	3.08380i	0.161858	−	0.280345i
$122$	9.83695	−	5.67937i	0.890596	−	0.514186i
$123$	3.06747	+	8.42779i	0.276584	+	0.759909i
$124$	15.0643	−	5.48296i	1.35282	−	0.492384i
$125$	6.41609	+	9.15608i	0.573872	+	0.818945i
$126$	4.31102	−	7.46691i	0.384057	−	0.665205i
$127$	−8.56161	−	1.50964i	−0.759720	−	0.133959i	−0.219650	−	0.975579i	$-0.570491\pi$
$127$	−8.56161	−	1.50964i	−0.759720	−	0.133959i	−0.540071	+	0.841620i	$0.681603\pi$
$128$	−13.2722	−	15.8172i	−1.17311	−	1.39806i
$129$	−0.827735	−	0.694552i	−0.0728780	−	0.0611519i
$130$	24.5496	−	21.8526i	2.15314	−	1.91660i
$131$	−9.90994	−	3.60692i	−0.865835	−	0.315138i	−0.129356	−	0.991598i	$-0.541291\pi$
$131$	−9.90994	−	3.60692i	−0.865835	−	0.315138i	−0.736479	+	0.676460i	$0.763513\pi$
$132$			22.5713i			1.96458i
$133$	−2.75538	−	6.58098i	−0.238922	−	0.570643i
$134$	−1.59083			−0.137426
$135$	−3.89432	+	0.804602i	−0.335170	+	0.0692491i
$136$	2.08589	+	11.8297i	0.178864	+	1.01439i
$137$	−0.255327	+	0.304287i	−0.0218141	+	0.0259970i	−0.776841	−	0.629697i	$-0.783179\pi$
$137$	−0.255327	+	0.304287i	−0.0218141	+	0.0259970i	0.755027	+	0.655694i	$0.227624\pi$
$138$	25.4195	+	30.2938i	2.16385	+	2.57878i
$139$	1.30330	−	7.39141i	0.110545	−	0.626931i	−0.878315	−	0.478082i	$-0.841332\pi$
$139$	1.30330	−	7.39141i	0.110545	−	0.626931i	0.988860	−	0.148849i	$-0.0475568\pi$
$140$	0.387097	+	13.2488i	0.0327157	+	1.11972i
$141$	−2.62971	−	4.55480i	−0.221462	−	0.383583i
$142$	2.13672	+	5.87059i	0.179310	+	0.492649i
$143$	5.78306	+	15.8888i	0.483604	+	1.32869i
$144$	2.07980	+	3.60232i	0.173317	+	0.300194i
$145$	4.97474	−	0.145350i	0.413130	−	0.0120707i
$146$	2.68149	−	15.2075i	0.221922	−	1.25858i
$147$	−6.34684	−	7.56387i	−0.523479	−	0.623858i
$148$	−4.74918	+	5.65985i	−0.390380	+	0.465237i
$149$	0.640034	+	3.62981i	0.0524336	+	0.297366i	0.999736	−	0.0229749i	$-0.00731377\pi$
$149$	0.640034	+	3.62981i	0.0524336	+	0.297366i	−0.947302	+	0.320341i	$0.896203\pi$
$150$	−19.6998	+	18.5948i	−1.60849	+	1.51826i
$151$	−4.49051			−0.365433			−0.182716	−	0.983166i	$-0.558489\pi$
$151$	−4.49051			−0.365433			−0.182716	+	0.983166i	$0.558489\pi$
$152$	16.6227	+	2.12396i	1.34828	+	0.172276i
$153$			6.94189i			0.561219i
$154$	−9.94629	−	3.62015i	−0.801495	−	0.291720i
$155$	−7.39349	+	6.58125i	−0.593860	+	0.528618i
$156$	39.3002	+	32.9768i	3.14653	+	2.64025i
$157$	−13.0262	−	15.5240i	−1.03960	−	1.23895i	−0.970439	−	0.241345i	$-0.922411\pi$
$157$	−13.0262	−	15.5240i	−1.03960	−	1.23895i	−0.0691635	−	0.997605i	$-0.522033\pi$
$158$	9.62037	+	1.69633i	0.765355	+	0.134953i
$159$	−7.27109	+	12.5939i	−0.576635	+	0.998761i
$160$	6.39712	+	3.44830i	0.505737	+	0.272612i
$161$	−11.2264	+	4.08607i	−0.884762	+	0.322027i
$162$	−8.70040	−	23.9042i	−0.683568	−	1.87809i
$163$	13.5611	−	7.82949i	1.06219	−	0.613253i	0.136149	−	0.990688i	$-0.456527\pi$
$163$	13.5611	−	7.82949i	1.06219	−	0.613253i	0.926036	+	0.377436i	$0.123194\pi$
$164$	7.10685	−	12.3094i	0.554952	−	0.961205i
$165$	−5.14701	−	12.9513i	−0.400694	−	1.00825i
$166$	−11.6676	+	9.79030i	−0.905583	+	0.759875i
$167$	3.88610	−	4.63128i	0.300716	−	0.358379i	−0.594434	−	0.804144i	$-0.702624\pi$
$167$	3.88610	−	4.63128i	0.300716	−	0.358379i	0.895150	+	0.445765i	$0.147068\pi$
$168$	−14.1608	+	2.49693i	−1.09253	+	0.192643i
$169$	23.8980	+	8.69815i	1.83831	+	0.669088i
$170$	−8.69795	−	14.0977i	−0.667103	−	1.08125i
$171$	9.24723	+	2.87692i	0.707153	+	0.220003i
$172$			1.71244i			0.130573i
$173$	0.561050	−	1.54147i	0.0426558	−	0.117196i	−0.916536	−	0.399952i	$-0.869027\pi$
$173$	0.561050	−	1.54147i	0.0426558	−	0.117196i	0.959192	+	0.282757i	$0.0912489\pi$
$174$	2.09399	+	11.8756i	0.158745	+	0.900288i
$175$	−3.24327	−	7.51377i	−0.245168	−	0.567988i
$176$	3.91175	−	3.28235i	0.294859	−	0.247416i
$177$	27.6036	+	4.86726i	2.07481	+	0.365845i
$178$	−35.5314	−	20.5141i	−2.66319	−	1.53759i
$179$	−7.09424	−	12.2876i	−0.530248	−	0.918417i	−0.999377	−	0.0352872i	$-0.988765\pi$
$179$	−7.09424	−	12.2876i	−0.530248	−	0.918417i	0.469129	−	0.883130i	$-0.344568\pi$
$180$	−14.1142	−	11.1573i	−1.05201	−	0.831616i
$181$	−21.5620	+	7.84794i	−1.60269	+	0.583333i	−0.979976	−	0.199113i	$-0.936194\pi$
$181$	−21.5620	+	7.84794i	−1.60269	+	0.583333i	−0.622718	+	0.782446i	$0.713972\pi$
$182$	−20.8348	+	12.0290i	−1.54438	+	0.891647i
$183$	−9.48076	−	5.47372i	−0.700838	−	0.404629i
$184$	4.87277	−	27.6349i	0.359226	−	2.03727i
$185$	1.43441	−	4.33055i	0.105460	−	0.318388i
$186$	−18.3723	−	15.4162i	−1.34712	−	1.13037i
$187$	8.39256	−	1.47983i	0.613724	−	0.108216i
$188$	−2.85082	+	7.83255i	−0.207917	+	0.571248i
$189$	2.91080			0.211729
$190$	−22.3841	+	5.74396i	−1.62391	+	0.416710i
$191$	10.2099			0.738762			0.369381	−	0.929278i	$-0.379570\pi$
$191$	10.2099			0.738762			0.369381	+	0.929278i	$0.379570\pi$
$192$	−8.94896	+	24.5871i	−0.645835	+	1.77442i
$193$	11.6515	−	2.05447i	0.838693	−	0.147884i	0.262228	−	0.965006i	$-0.415543\pi$
$193$	11.6515	−	2.05447i	0.838693	−	0.147884i	0.576465	+	0.817122i	$0.304432\pi$
$194$	−0.236012	−	0.198038i	−0.0169447	−	0.0142183i
$195$	−30.0699	−	9.96007i	−2.15335	−	0.713256i
$196$	−2.71731	+	15.4106i	−0.194094	+	1.10076i
$197$	2.36143	+	1.36337i	0.168245	+	0.0971363i	0.581758	−	0.813362i	$-0.302365\pi$
$197$	2.36143	+	1.36337i	0.168245	+	0.0971363i	−0.413513	+	0.910498i	$0.635698\pi$
$198$	12.4427	−	7.18379i	0.884263	−	0.510529i
$199$	4.20830	−	1.53170i	0.298319	−	0.108579i	−0.188525	−	0.982068i	$-0.560371\pi$
$199$	4.20830	−	1.53170i	0.298319	−	0.108579i	0.486843	+	0.873489i	$0.338148\pi$
$200$	19.0931	+	2.22700i	1.35008	+	0.157473i
$201$	0.766611	+	1.32781i	0.0540726	+	0.0936564i
$202$	7.67010	+	4.42834i	0.539666	+	0.311577i
$203$	−3.58765	−	0.632600i	−0.251804	−	0.0443998i
$204$	19.8076	−	16.6205i	1.38681	−	1.16367i
$205$	−1.27090	+	8.68366i	−0.0887635	+	0.606493i
$206$	2.71712	+	15.4096i	0.189311	+	1.07364i
$207$	5.54643	−	15.2387i	0.385504	−	1.05916i
$208$		−	11.6065i		−	0.804764i
$209$	1.50684	−	11.7929i	0.104230	−	0.815733i
$210$	16.8758	−	10.4119i	1.16454	−	0.718493i
$211$	6.89756	+	2.51051i	0.474847	+	0.172830i	0.568347	−	0.822789i	$-0.307583\pi$
$211$	6.89756	+	2.51051i	0.474847	+	0.172830i	−0.0934995	+	0.995619i	$0.529805\pi$
$212$	22.6966	−	4.00202i	1.55881	−	0.274860i
$213$	3.87031	−	4.61246i	0.265189	−	0.316041i
$214$	−21.4234	+	17.9763i	−1.46447	+	1.22884i
$215$	−0.390494	−	0.982588i	−0.0266315	−	0.0670119i
$216$	−3.41849	+	5.92100i	−0.232599	+	0.402873i
$217$	6.27473	−	3.62272i	0.425956	−	0.245926i
$218$	−5.86948	−	16.1263i	−0.397532	−	1.09221i
$219$	−13.9854	+	5.09026i	−0.945044	+	0.343968i
$220$	−10.4801	+	19.4421i	−0.706567	+	1.31079i
$221$	9.68493	−	16.7748i	0.651479	−	1.12839i
$222$	10.8855	+	1.91941i	0.730588	+	0.128822i
$223$	10.6581	+	12.7019i	0.713721	+	0.850580i	0.994005	−	0.109338i	$-0.0348730\pi$
$223$	10.6581	+	12.7019i	0.713721	+	0.850580i	−0.280284	+	0.959917i	$0.590429\pi$
$224$	−4.07504	−	3.41936i	−0.272275	−	0.228466i
$225$	10.6429	+	3.18347i	0.709524	+	0.212231i
$226$	29.6052	+	10.7754i	1.96931	+	0.716770i
$227$			11.7828i			0.782052i	0.920380	+	0.391026i	$0.127880\pi$
$227$			11.7828i			0.782052i	−0.920380	+	0.391026i	$0.872120\pi$
$228$	−13.9312	−	33.2735i	−0.922617	−	2.20359i
$229$	7.82331			0.516979			0.258490	−	0.966014i	$-0.416775\pi$
$229$	7.82331			0.516979			0.258490	+	0.966014i	$0.416775\pi$
$230$	7.82976	+	37.8965i	0.516279	+	2.49882i
$231$	1.77145	+	10.0464i	0.116553	+	0.661003i
$232$	5.50020	−	6.55488i	0.361106	−	0.430349i
$233$	4.31937	+	5.14763i	0.282971	+	0.337232i	0.888742	−	0.458407i	$-0.151580\pi$
$233$	4.31937	+	5.14763i	0.282971	+	0.337232i	−0.605771	+	0.795639i	$0.707135\pi$
$234$	5.67071	−	32.1602i	0.370706	−	2.10238i
$235$	−0.150305	−	5.14434i	−0.00980484	−	0.335580i
$236$	−22.2107	−	38.4701i	−1.44580	−	2.50419i
$237$	−3.22014	−	8.84726i	−0.209170	−	0.574691i
$238$	4.14713	+	11.3941i	0.268818	+	0.738572i
$239$	−7.98728	−	13.8344i	−0.516654	−	0.894871i	−0.999813	−	0.0193382i	$-0.993844\pi$
$239$	−7.98728	−	13.8344i	−0.516654	−	0.894871i	0.483159	−	0.875533i	$-0.339489\pi$
$240$	0.279388	+	9.56233i	0.0180344	+	0.617246i
$241$	1.81557	−	10.2966i	0.116951	−	0.663261i	−0.868815	−	0.495137i	$-0.835118\pi$
$241$	1.81557	−	10.2966i	0.116951	−	0.663261i	0.985766	−	0.168124i	$-0.0537710\pi$
$242$	5.42686	+	6.46748i	0.348852	+	0.415746i
$243$	−12.3300	+	14.6943i	−0.790968	+	0.942639i
$244$	3.01274	+	17.0861i	0.192871	+	1.09383i
$245$	−1.95497	−	9.46215i	−0.124898	−	0.604515i
$246$	−21.2644			−1.35577
$247$	−18.3318	−	19.8531i	−1.16642	−	1.26322i
$248$			17.0183i			1.08066i
$249$	13.7942	+	5.02068i	0.874172	+	0.318173i
$250$	−25.6025	+	6.87009i	−1.61924	+	0.434503i
$251$	−9.08999	−	7.62741i	−0.573755	−	0.481438i	0.309135	−	0.951018i	$-0.399961\pi$
$251$	−9.08999	−	7.62741i	−0.573755	−	0.481438i	−0.882890	+	0.469581i	$0.844405\pi$
$252$	8.46525	+	10.0885i	0.533260	+	0.635515i
$253$	−19.6055	−	3.45698i	−1.23259	−	0.217339i
$254$	10.3062	−	17.8509i	0.646670	−	1.12007i
$255$	−7.57541	+	14.0535i	−0.474390	+	0.880066i
$256$	24.4839	−	8.91141i	1.53024	−	0.556963i
$257$	−1.30525	−	3.58614i	−0.0814191	−	0.223697i	0.892303	−	0.451437i	$-0.149089\pi$
$257$	−1.30525	−	3.58614i	−0.0814191	−	0.223697i	−0.973722	+	0.227740i	$0.926866\pi$
$258$	2.21868	−	1.28095i	0.138129	−	0.0797486i
$259$	−1.66963	+	2.89189i	−0.103746	+	0.179693i
$260$	18.5403	+	46.6525i	1.14982	+	2.89326i
$261$	3.78810	−	3.17859i	0.234477	−	0.196750i
$262$	16.0723	−	19.1542i	0.992951	−	1.18335i
$263$	2.08737	−	0.368060i	0.128713	−	0.0226956i	−0.108921	−	0.994050i	$-0.534739\pi$
$263$	2.08737	−	0.368060i	0.128713	−	0.0226956i	0.237633	+	0.971355i	$0.423628\pi$
$264$	−22.5162	−	8.19524i	−1.38578	−	0.504382i
$265$	−12.1105	+	7.47190i	−0.743944	+	0.458995i
$266$	16.8967	−	0.802292i	1.03600	−	0.0491917i
$267$			39.5425i			2.41996i
$268$	0.831067	−	2.28334i	0.0507655	−	0.139477i
$269$	0.682137	+	3.86859i	0.0415906	+	0.235872i	0.998516	−	0.0544625i	$-0.0173445\pi$
$269$	0.682137	+	3.86859i	0.0415906	+	0.235872i	−0.956925	+	0.290335i	$0.906233\pi$
$270$	1.36534	−	9.32894i	0.0830920	−	0.567741i
$271$	14.5057	−	12.1717i	0.881159	−	0.739380i	−0.0852584	−	0.996359i	$-0.527172\pi$
$271$	14.5057	−	12.1717i	0.881159	−	0.739380i	0.966417	+	0.256979i	$0.0827271\pi$
$272$	−5.76088	−	1.01580i	−0.349305	−	0.0615918i
$273$	20.0804	+	11.5934i	1.21532	+	0.701665i
$274$	−0.470897	−	0.815617i	−0.0284479	−	0.0492732i
$275$	1.57994	−	13.5456i	0.0952740	−	0.816828i
$276$	−56.7606	+	20.6592i	−3.41659	+	1.24354i
$277$	−13.0141	+	7.51370i	−0.781942	+	0.451454i	−0.837118	−	0.547022i	$-0.815761\pi$
$277$	−13.0141	+	7.51370i	−0.781942	+	0.451454i	0.0551762	+	0.998477i	$0.482428\pi$
$278$	15.4110	+	8.89757i	0.924293	+	0.533641i
$279$	−1.70782	+	9.68554i	−0.102245	+	0.579858i
$280$	−13.3570	−	4.42423i	−0.798232	−	0.264399i
$281$	21.0532	+	17.6657i	1.25593	+	1.05385i	0.996103	+	0.0881948i	$0.0281098\pi$
$281$	21.0532	+	17.6657i	1.25593	+	1.05385i	0.259826	+	0.965655i	$0.416335\pi$
$282$	12.2805	−	2.16538i	0.731292	−	0.128947i
$283$	6.95521	−	19.1093i	0.413444	−	1.13593i	−0.541902	−	0.840442i	$-0.682296\pi$
$283$	6.95521	−	19.1093i	0.413444	−	1.13593i	0.955347	−	0.295488i	$-0.0954821\pi$
$284$	−9.54240			−0.566237
$285$	15.5811	+	15.9153i	0.922944	+	0.942741i
$286$	−40.0896			−2.37055
$287$	2.19715	−	6.03662i	0.129694	−	0.356330i
$288$	7.11111	−	1.25388i	0.419026	−	0.0738856i
$289$	5.54421	+	4.65214i	0.326130	+	0.273656i
$290$	−3.71027	+	11.2015i	−0.217875	+	0.657775i
$291$	−0.0515625	+	0.292425i	−0.00302265	+	0.0171423i
$292$	20.4267	+	11.7934i	1.19538	+	0.690154i
$293$	3.97210	−	2.29329i	0.232053	−	0.133976i	−0.379466	−	0.925206i	$-0.623892\pi$
$293$	3.97210	−	2.29329i	0.232053	−	0.133976i	0.611519	+	0.791230i	$0.290559\pi$
$294$	21.9989	−	8.00696i	1.28300	−	0.466975i
$295$	21.5168	+	17.0091i	1.25276	+	0.990308i
$296$	−3.92169	−	6.79257i	−0.227944	−	0.394810i
$297$	4.20064	+	2.42524i	0.243746	+	0.140727i
$298$	−8.60617	−	1.51750i	−0.498542	−	0.0879064i
$299$	−34.6628	+	29.0856i	−2.00460	+	1.68206i
$300$	−16.3980	−	37.9897i	−0.946739	−	2.19333i
$301$	0.134396	+	0.762200i	0.00774648	+	0.0439325i
$302$	3.64144	−	10.0048i	0.209541	−	0.575710i
$303$		−	8.53597i		−	0.490379i
$304$	−3.74061	+	7.25303i	−0.214538	+	0.415990i
$305$	−5.62489	−	9.11687i	−0.322080	−	0.522031i
$306$	−15.4664	−	5.62931i	−0.884156	−	0.321806i
$307$	−23.9533	+	4.22361i	−1.36709	+	0.241054i	−0.808551	−	0.588426i	$-0.799748\pi$
$307$	−23.9533	+	4.22361i	−1.36709	+	0.241054i	−0.558536	+	0.829480i	$0.688637\pi$
$308$	10.3921	−	12.3849i	0.592146	−	0.705692i
$309$	11.5525	−	9.69369i	0.657198	−	0.551455i
$310$	−8.66737	−	21.8094i	−0.492274	−	1.23869i
$311$	−11.0103	+	19.0703i	−0.624334	+	1.08138i	0.364335	+	0.931268i	$0.381296\pi$
$311$	−11.0103	+	19.0703i	−0.624334	+	1.08138i	−0.988669	+	0.150111i	$0.952037\pi$
$312$	−47.1654	+	27.2310i	−2.67022	+	1.54165i
$313$	10.0833	+	27.7037i	0.569943	+	1.56591i	0.804593	+	0.593827i	$0.202384\pi$
$313$	10.0833	+	27.7037i	0.569943	+	1.56591i	−0.234649	+	0.972080i	$0.575394\pi$
$314$	45.1504	−	16.4334i	2.54798	−	0.927390i
$315$	−7.15781	−	3.85834i	−0.403297	−	0.217393i
$316$	−7.46057	+	12.9221i	−0.419690	+	0.726924i
$317$	−7.92095	−	1.39668i	−0.444885	−	0.0784452i	−0.0532818	−	0.998580i	$-0.516968\pi$
$317$	−7.92095	−	1.39668i	−0.444885	−	0.0784452i	−0.391603	+	0.920134i	$0.628079\pi$
$318$	−22.1627	−	26.4125i	−1.24282	−	1.48114i
$319$	−4.65035	−	3.90211i	−0.260370	−	0.218476i
$320$	−19.1243	+	17.0233i	−1.06908	+	0.951633i
$321$	25.3281	+	9.21867i	1.41368	+	0.514536i
$322$		−	28.3256i		−	1.57853i
$323$	−11.4585	+	7.36145i	−0.637568	+	0.409602i
$324$	38.8552			2.15862
$325$	−21.2766	−	22.5410i	−1.18021	−	1.25035i
$326$	6.44702	+	36.5629i	0.357068	+	2.02503i
$327$	−10.6316	+	12.6702i	−0.587928	+	0.700666i
$328$	9.69901	+	11.5588i	0.535538	+	0.638230i
$329$	−0.654167	+	3.70997i	−0.0360654	+	0.204537i
$330$	33.0290	−	0.965027i	1.81818	−	0.0531230i
$331$	−9.10916	−	15.7775i	−0.500685	−	0.867212i	−1.00000		0.000790925i	$-0.999748\pi$
$331$	−9.10916	−	15.7775i	−0.500685	−	0.867212i	0.499315	−	0.866421i	$-0.333585\pi$
$332$	−7.95686	−	21.8613i	−0.436689	−	1.19979i
$333$	−1.55028	−	4.25937i	−0.0849551	−	0.233412i
$334$	7.16709	+	12.4138i	0.392166	+	0.679251i
$335$	0.0438168	+	1.49967i	0.00239397	+	0.0819359i
$336$	1.21597	−	6.89610i	0.0663365	−	0.376213i
$337$	6.17287	+	7.35654i	0.336258	+	0.400736i	0.907505	−	0.420042i	$-0.137985\pi$
$337$	6.17287	+	7.35654i	0.336258	+	0.400736i	−0.571247	+	0.820778i	$0.693540\pi$
$338$	−38.7586	+	46.1907i	−2.10819	+	2.51244i
$339$	−5.27272	−	29.9031i	−0.286375	−	1.62411i
$340$	24.7786	−	5.11948i	1.34381	−	0.277643i
$341$	12.0736			0.653823
$342$	−13.9085	+	18.2697i	−0.752084	+	0.987912i
$343$			18.5299i			1.00052i
$344$	−1.70826	−	0.621757i	−0.0921035	−	0.0335229i
$345$	27.8578	−	24.7974i	1.49982	−	1.33505i
$346$	2.97940	+	2.50002i	0.160174	+	0.134402i
$347$	0.813944	+	0.970021i	0.0436948	+	0.0520734i	0.787449	−	0.616379i	$-0.211401\pi$
$347$	0.813944	+	0.970021i	0.0436948	+	0.0520734i	−0.743754	+	0.668453i	$0.766957\pi$
$348$	−18.1392	−	3.19843i	−0.972363	−	0.171454i
$349$	13.3074	−	23.0491i	0.712330	−	1.23379i	−0.251650	−	0.967818i	$-0.580973\pi$
$349$	13.3074	−	23.0491i	0.712330	−	1.23379i	0.963980	−	0.265974i	$-0.0856934\pi$
$350$	19.3706	−	1.13289i	1.03540	−	0.0605556i
$351$	10.3599	−	3.77068i	0.552969	−	0.201264i
$352$	−3.03181	−	8.32983i	−0.161596	−	0.443982i
$353$	23.2738	−	13.4371i	1.23874	−	0.715187i	0.269903	−	0.962888i	$-0.413008\pi$
$353$	23.2738	−	13.4371i	1.23874	−	0.715187i	0.968837	+	0.247701i	$0.0796751\pi$
$354$	−33.2284	+	57.5533i	−1.76607	+	3.05892i
$355$	5.47536	−	2.17598i	0.290602	−	0.115489i
$356$	48.0062	−	40.2820i	2.54432	−	2.13494i
$357$	7.51183	−	8.95225i	0.397568	−	0.473803i
$358$	33.1294	−	5.84160i	1.75094	−	0.308738i
$359$	−19.7868	−	7.20180i	−1.04431	−	0.380097i	−0.237795	−	0.971315i	$-0.576425\pi$
$359$	−19.7868	−	7.20180i	−1.04431	−	0.380097i	−0.806511	+	0.591219i	$0.798647\pi$
$360$	16.2547	−	10.0287i	0.856697	−	0.528561i
$361$	5.05739	+	18.3146i	0.266178	+	0.963924i
$362$		−	54.4039i		−	2.85940i
$363$	2.78302	−	7.64627i	0.146070	−	0.401325i
$364$	−6.38103	−	36.1886i	−0.334457	−	1.89680i
$365$	−14.4100	−	2.10897i	−0.754252	−	0.110389i
$366$	19.8835	−	16.6842i	1.03933	−	0.872098i
$367$	−10.8503	−	1.91320i	−0.566381	−	0.0998682i	−0.116877	−	0.993146i	$-0.537288\pi$
$367$	−10.8503	−	1.91320i	−0.566381	−	0.0998682i	−0.449504	+	0.893278i	$0.648399\pi$
$368$	11.8346	+	6.83268i	0.616919	+	0.356178i
$369$	4.36000	+	7.55174i	0.226972	+	0.393128i
$370$	8.48519	+	6.70756i	0.441124	+	0.348709i
$371$	9.78803	−	3.56255i	0.508169	−	0.184959i
$372$	31.7251	−	18.3165i	1.64487	−	0.949665i
$373$	4.18558	+	2.41654i	0.216721	+	0.125124i	0.604431	−	0.796657i	$-0.293401\pi$
$373$	4.18558	+	2.41654i	0.216721	+	0.125124i	−0.387710	+	0.921781i	$0.626734\pi$
$374$	−3.50864	+	19.8985i	−0.181427	+	1.02893i
$375$	18.0720	+	18.0589i	0.933232	+	0.932558i
$376$	−6.77836	−	5.68772i	−0.349567	−	0.293322i
$377$	−13.5884	+	2.39599i	−0.699836	+	0.123400i
$378$	−2.36042	+	6.48520i	−0.121407	+	0.333563i
$379$	−2.03721			−0.104644			−0.0523221	−	0.998630i	$-0.516662\pi$
$379$	−2.03721			−0.104644			−0.0523221	+	0.998630i	$0.516662\pi$
$380$	3.44934	−	35.1290i	0.176948	−	1.80208i
$381$	−19.8661			−1.01777
$382$	−8.27940	+	22.7475i	−0.423611	+	1.16386i
$383$	−34.0551	+	6.00483i	−1.74013	+	0.306833i	−0.951413	−	0.307918i	$-0.900368\pi$
$383$	−34.0551	+	6.00483i	−1.74013	+	0.306833i	−0.788721	+	0.614751i	$0.789257\pi$
$384$	−36.1442	−	30.3286i	−1.84448	−	1.54770i
$385$	−3.13877	+	9.47609i	−0.159966	+	0.482946i
$386$	−4.87109	+	27.6253i	−0.247932	+	1.40609i
$387$	−0.909821	−	0.525286i	−0.0462488	−	0.0267018i
$388$	0.407543	−	0.235295i	0.0206899	−	0.0119453i
$389$	−4.25700	+	1.54942i	−0.215839	+	0.0785588i	−0.447676	−	0.894196i	$-0.647748\pi$
$389$	−4.25700	+	1.54942i	−0.215839	+	0.0785588i	0.231838	+	0.972754i	$0.425526\pi$
$390$	46.5751	−	58.9185i	2.35842	−	2.98345i
$391$	11.4029	+	19.7505i	0.576672	+	0.998825i
$392$	−14.3864	−	8.30601i	−0.726624	−	0.419517i
$393$	−23.7326	−	4.18469i	−1.19715	−	0.211090i
$394$	−4.95250	+	4.15564i	−0.249503	+	0.209358i
$395$	1.33415	−	9.11585i	0.0671286	−	0.458668i
$396$	3.81079	+	21.6121i	0.191500	+	1.08605i
$397$	−8.59660	+	23.6190i	−0.431451	+	1.18540i	0.513471	+	0.858107i	$0.328359\pi$
$397$	−8.59660	+	23.6190i	−0.431451	+	1.18540i	−0.944922	+	0.327295i	$0.893863\pi$
$398$			10.6181i			0.532237i
$399$	−8.81208	−	13.7165i	−0.441156	−	0.686683i
$400$	−4.19923	+	8.36637i	−0.209961	+	0.418319i
$401$	−27.1680	−	9.88834i	−1.35671	−	0.493800i	−0.441671	−	0.897177i	$-0.645614\pi$
$401$	−27.1680	−	9.88834i	−1.35671	−	0.493800i	−0.915034	+	0.403377i	$0.867836\pi$
$402$	−3.57999	+	0.631249i	−0.178554	+	0.0314839i
$403$	17.6396	−	21.0220i	0.878690	−	1.04718i
$404$	−10.3630	+	8.69560i	−0.515579	+	0.432622i
$405$	−22.2948	+	8.86028i	−1.10784	+	0.440271i
$406$	4.31872	−	7.48024i	0.214334	−	0.371238i
$407$	−4.81898	+	2.78224i	−0.238868	+	0.137910i
$408$	9.38819	+	25.7938i	0.464785	+	1.27699i
$409$	−21.5769	+	7.85333i	−1.06691	+	0.388322i	−0.815019	−	0.579434i	$-0.803274\pi$
$409$	−21.5769	+	7.85333i	−1.06691	+	0.388322i	−0.251888	+	0.967756i	$0.581051\pi$
$410$	−18.3164	−	9.87328i	−0.904584	−	0.487607i
$411$	−0.453845	+	0.786083i	−0.0223865	+	0.0387746i
$412$	−23.5371	−	4.15022i	−1.15959	−	0.204467i
$413$	−12.9051	−	15.3797i	−0.635018	−	0.756785i
$414$	29.4538	+	24.7147i	1.44758	+	1.21466i
$415$	9.55069	+	10.7294i	0.468825	+	0.526687i
$416$	−18.9330	−	6.89106i	−0.928268	−	0.337862i
$417$		−	17.1508i		−	0.839877i
$418$	25.0525	+	12.9203i	1.22536	+	0.631953i
$419$	−8.98058			−0.438730			−0.219365	−	0.975643i	$-0.570399\pi$
$419$	−8.98058			−0.438730			−0.219365	+	0.975643i	$0.570399\pi$
$420$	6.12832	+	29.6614i	0.299031	+	1.44733i
$421$	−5.91109	−	33.5235i	−0.288089	−	1.63383i	−0.694038	−	0.719938i	$-0.744170\pi$
$421$	−5.91109	−	33.5235i	−0.288089	−	1.63383i	0.405949	−	0.913896i	$-0.366941\pi$
$422$	−11.1867	+	13.3318i	−0.544561	+	0.648983i
$423$	−3.28696	−	3.91724i	−0.159817	−	0.190463i
$424$	−4.24846	+	24.0942i	−0.206324	+	1.17012i
$425$	−13.0504	+	8.58787i	−0.633036	+	0.416573i
$426$	7.13796	+	12.3633i	0.345835	+	0.599005i
$427$	2.68191	+	7.36848i	0.129787	+	0.356586i
$428$	−14.6099	−	40.1404i	−0.706196	−	1.94026i
$429$	19.3190	+	33.4615i	0.932729	+	1.61553i
$430$	2.50585	−	0.0732148i	0.120843	−	0.00353073i
$431$	6.59394	−	37.3961i	0.317619	−	1.80131i	−0.239525	−	0.970890i	$-0.576992\pi$
$431$	6.59394	−	37.3961i	0.317619	−	1.80131i	0.557144	−	0.830416i	$-0.311897\pi$
$432$	−2.14016	−	2.55055i	−0.102969	−	0.122713i
$433$	23.7703	−	28.3283i	1.14233	−	1.36137i	0.219749	−	0.975556i	$-0.429476\pi$
$433$	23.7703	−	28.3283i	1.14233	−	1.36137i	0.922576	−	0.385814i	$-0.126079\pi$
$434$	2.98305	+	16.9177i	0.143191	+	0.812076i
$435$	11.1375	−	2.30110i	0.534001	−	0.110329i
$436$	26.2126			1.25535
$437$	31.0351	−	7.00459i	1.48461	−	0.335075i
$438$		−	35.2869i		−	1.68607i
$439$	20.8452	+	7.58705i	0.994889	+	0.362110i	0.787611	−	0.616172i	$-0.211318\pi$
$439$	20.8452	+	7.58705i	0.994889	+	0.362110i	0.207277	+	0.978282i	$0.433540\pi$
$440$	−15.5896	−	17.5136i	−0.743203	−	0.834928i
$441$	−7.35415	−	6.17086i	−0.350198	−	0.293851i
$442$	29.5202	+	35.1808i	1.40413	+	1.67338i
$443$	−9.69917	−	1.71023i	−0.460822	−	0.0812553i	−0.0615822	−	0.998102i	$-0.519615\pi$
$443$	−9.69917	−	1.71023i	−0.460822	−	0.0812553i	−0.399239	+	0.916847i	$0.630726\pi$
$444$	−8.44168	+	14.6214i	−0.400625	+	0.693902i
$445$	−18.3600	+	34.0605i	−0.870346	+	1.61462i
$446$	−36.9424	+	13.4459i	−1.74927	+	0.636683i
$447$	2.88066	+	7.91456i	0.136251	+	0.374346i
$448$	16.2305	−	9.37067i	0.766818	−	0.442723i
$449$	−18.6520	+	32.3061i	−0.880240	+	1.52462i	−0.0291671	+	0.999575i	$0.509285\pi$
$449$	−18.6520	+	32.3061i	−0.880240	+	1.52462i	−0.851073	+	0.525047i	$0.824048\pi$
$450$	−15.7232	+	21.1306i	−0.741199	+	0.996105i
$451$	8.20040	−	6.88095i	0.386142	−	0.324011i
$452$	−30.9322	+	36.8636i	−1.45493	+	1.73392i
$453$	−10.1054	+	1.78186i	−0.474795	+	0.0837192i
$454$	−26.2519	−	9.55490i	−1.23206	−	0.448434i
$455$	11.9136	+	19.3097i	0.558518	+	0.905251i
$456$	38.2504	−	1.81622i	1.79124	−	0.0850521i
$457$		−	14.0343i		−	0.656498i	−0.944591	−	0.328249i	$-0.893542\pi$
$457$		−	14.0343i		−	0.656498i	0.944591	−	0.328249i	$-0.106458\pi$
$458$	−6.34407	+	17.4302i	−0.296439	+	0.814460i
$459$	−0.964885	−	5.47214i	−0.0450370	−	0.255417i
$460$	−58.4838	−	8.55942i	−2.72682	−	0.399085i
$461$	−7.76457	+	6.51525i	−0.361632	+	0.303445i	−0.805441	−	0.592676i	$-0.798071\pi$
$461$	−7.76457	+	6.51525i	−0.361632	+	0.303445i	0.443809	+	0.896122i	$0.353627\pi$
$462$	−23.8196	−	4.20004i	−1.10819	−	0.195404i
$463$	0.625383	+	0.361065i	0.0290640	+	0.0167801i	0.514462	−	0.857513i	$-0.327992\pi$
$463$	0.625383	+	0.361065i	0.0290640	+	0.0167801i	−0.485398	+	0.874294i	$0.661325\pi$
$464$	2.08351	+	3.60875i	0.0967247	+	0.167532i
$465$	−14.0268	+	17.7442i	−0.650479	+	0.822869i
$466$	−14.9715	+	5.44917i	−0.693540	+	0.252428i
$467$	30.3258	−	17.5086i	1.40331	−	0.810201i	0.408579	−	0.912723i	$-0.366024\pi$
$467$	30.3258	−	17.5086i	1.40331	−	0.810201i	0.994731	+	0.102522i	$0.0326911\pi$
$468$	43.1976	+	24.9401i	1.99681	+	1.15286i
$469$	0.190702	−	1.08152i	0.00880580	−	0.0499402i
$470$	11.5834	+	3.83677i	0.534302	+	0.176977i
$471$	−35.4742	−	29.7664i	−1.63456	−	1.37156i
$472$	46.4406	−	8.18872i	2.13760	−	0.376917i
$473$	−0.441105	+	1.21193i	−0.0202820	+	0.0557244i
$474$	22.3228			1.02532
$475$	6.03137	+	20.9433i	0.276738	+	0.960945i
$476$	−18.5207			−0.848895
$477$	−4.83581	+	13.2863i	−0.221417	+	0.608337i
$478$	37.2997	−	6.57695i	1.70605	−	0.300823i
$479$	20.6527	+	17.3296i	0.943645	+	0.791812i	0.978216	−	0.207590i	$-0.0665621\pi$
$479$	20.6527	+	17.3296i	0.943645	+	0.791812i	−0.0345713	+	0.999402i	$0.511007\pi$
$480$	15.7644	+	5.22164i	0.719543	+	0.238334i
$481$	−2.19623	+	12.4555i	−0.100140	+	0.567920i
$482$	21.4683	+	12.3947i	0.977855	+	0.564565i
$483$	−23.6425	+	13.6500i	−1.07577	+	0.621096i
$484$	−12.1179	+	4.41057i	−0.550816	+	0.200480i
$485$	−0.180190	+	0.227944i	−0.00818201	+	0.0103504i
$486$	−22.7400	−	39.3868i	−1.03151	−	1.78662i
$487$	2.65660	+	1.53379i	0.120382	+	0.0695026i	0.558982	−	0.829180i	$-0.311192\pi$
$487$	2.65660	+	1.53379i	0.120382	+	0.0695026i	−0.438600	+	0.898682i	$0.644525\pi$
$488$	−18.1383	−	3.19827i	−0.821081	−	0.144779i
$489$	27.4110	−	23.0006i	1.23957	−	1.04012i
$490$	22.6668	+	3.31741i	1.02398	+	0.149865i
$491$	0.216866	+	1.22991i	0.00978703	+	0.0555050i	0.989310	−	0.145827i	$-0.0465842\pi$
$491$	0.216866	+	1.22991i	0.00978703	+	0.0555050i	−0.979523	+	0.201332i	$0.935473\pi$
$492$	11.1088	−	30.5212i	0.500823	−	1.37600i
$493$			6.95428i			0.313205i
$494$	59.0980	−	24.7436i	2.65895	−	1.11327i
$495$	−7.11488	−	11.5319i	−0.319790	−	0.518319i
$496$	−7.78785	−	2.83455i	−0.349685	−	0.127275i
$497$	−4.24727	+	0.748908i	−0.190516	+	0.0335931i
$498$	−22.3720	+	26.6619i	−1.00251	+	1.19475i
$499$	−14.9931	+	12.5807i	−0.671181	+	0.563188i	−0.913415	−	0.407030i	$-0.866564\pi$
$499$	−14.9931	+	12.5807i	−0.671181	+	0.563188i	0.242233	+	0.970218i	$0.422120\pi$
$500$	3.51431	−	40.3367i	0.157165	−	1.80391i
$501$	6.90757	−	11.9643i	0.308607	−	0.534524i
$502$	24.3650	−	14.0671i	1.08746	−	0.627846i
$503$	1.75066	+	4.80990i	0.0780581	+	0.214463i	0.972583	−	0.232555i	$-0.0747084\pi$
$503$	1.75066	+	4.80990i	0.0780581	+	0.214463i	−0.894525	+	0.447017i	$0.852486\pi$
$504$	−13.1374	+	4.78164i	−0.585188	+	0.212991i
$505$	3.96333	−	7.35258i	0.176366	−	0.327186i
$506$	23.6006	−	40.8774i	1.04917	−	1.81722i
$507$	57.2315	+	10.0915i	2.54174	+	0.448177i
$508$	20.2376	+	24.1182i	0.897898	+	1.07007i
$509$	12.1303	+	10.1785i	0.537664	+	0.451154i	0.870738	−	0.491747i	$-0.163641\pi$
$509$	12.1303	+	10.1785i	0.537664	+	0.451154i	−0.333074	+	0.942901i	$0.608086\pi$
$510$	−25.1679	−	28.2741i	−1.11446	−	1.25200i
$511$	10.0174	+	3.64603i	0.443143	+	0.161291i
$512$			20.4803i			0.905108i
$513$	−7.68925	−	0.982494i	−0.339489	−	0.0433782i
$514$	9.04830			0.399103
$515$	14.4518	−	2.98587i	0.636822	−	0.131573i
$516$	0.679509	+	3.85368i	0.0299137	+	0.169649i
$517$	−4.03514	+	4.80890i	−0.177465	+	0.211495i
$518$	−5.08914	−	6.06501i	−0.223604	−	0.266481i
$519$	0.650921	−	3.69156i	0.0285723	−	0.162041i
$520$	−53.2702	+	1.55643i	−2.33605	+	0.0682539i
$521$	14.9866	+	25.9576i	0.656575	+	1.13722i	0.981496	+	0.191481i	$0.0613289\pi$
$521$	14.9866	+	25.9576i	0.656575	+	1.13722i	−0.324921	+	0.945741i	$0.605338\pi$
$522$	4.01000	+	11.0174i	0.175513	+	0.482218i
$523$	−10.3894	−	28.5446i	−0.454296	−	1.24817i	−0.929673	−	0.368386i	$-0.879910\pi$
$523$	−10.3894	−	28.5446i	−0.454296	−	1.24817i	0.475377	−	0.879782i	$-0.342312\pi$
$524$	19.0960	+	33.0752i	0.834213	+	1.44490i
$525$	−10.2802	−	15.6220i	−0.448663	−	0.681802i
$526$	−0.872659	+	4.94909i	−0.0380497	+	0.215791i
$527$	−8.89048	−	10.5953i	−0.387275	−	0.461537i
$528$	7.50054	−	8.93880i	0.326419	−	0.389011i
$529$	−5.25736	−	29.8160i	−0.228581	−	1.29635i
$530$	−6.82660	−	33.0411i	−0.296528	−	1.43522i
$531$	27.2522			1.18265
$532$	−7.67550	+	24.6712i	−0.332775	+	1.06963i
$533$		−	24.3313i		−	1.05390i
$534$	−88.0999	−	32.0658i	−3.81246	−	1.38762i
$535$	17.5364	+	19.7007i	0.758164	+	0.851736i
$536$	1.97602	+	1.65808i	0.0853510	+	0.0716180i
$537$	−20.8407	−	24.8369i	−0.899341	−	1.07179i
$538$	−9.17230	−	1.61732i	−0.395446	−	0.0697278i
$539$	−5.89268	+	10.2064i	−0.253816	+	0.439622i
$540$	12.6767	+	6.83325i	0.545519	+	0.294056i
$541$	22.4204	−	8.16035i	0.963927	−	0.350841i	0.188356	−	0.982101i	$-0.439684\pi$
$541$	22.4204	−	8.16035i	0.963927	−	0.350841i	0.775571	+	0.631260i	$0.217462\pi$
$542$	15.3554	+	42.1887i	0.659573	+	1.81216i
$543$	−45.4091	+	26.2170i	−1.94869	+	1.12508i
$544$	−5.07740	+	8.79431i	−0.217692	+	0.377053i
$545$	−15.0406	+	5.97734i	−0.644268	+	0.256041i
$546$	−42.1135	+	35.3374i	−1.80229	+	1.51230i
$547$	−8.83204	+	10.5256i	−0.377631	+	0.450043i	−0.921065	−	0.389409i	$-0.872679\pi$
$547$	−8.83204	+	10.5256i	−0.377631	+	0.450043i	0.543434	+	0.839452i	$0.317124\pi$
$548$	1.41667	−	0.249797i	0.0605171	−	0.0106708i
$549$	−10.0020	−	3.64043i	−0.426874	−	0.155370i
$550$	28.8980	+	14.5044i	1.23222	+	0.618471i
$551$	9.26373	+	2.88205i	0.394648	+	0.122779i
$552$		−	64.1230i		−	2.72926i
$553$	−2.30650	+	6.33707i	−0.0980826	+	0.269480i
$554$	−6.18699	−	35.0882i	−0.262860	−	1.49075i
$555$	1.50960	−	10.3146i	0.0640791	−	0.437832i
$556$	−20.8217	+	17.4715i	−0.883038	+	0.740957i
$557$	26.6208	+	4.69396i	1.12796	+	0.198889i	0.706332	−	0.707881i	$-0.250349\pi$
$557$	26.6208	+	4.69396i	1.12796	+	0.198889i	0.421626	+	0.906770i	$0.361460\pi$
$558$	−20.1943	−	11.6592i	−0.854893	−	0.493573i
$559$	1.46570	+	2.53866i	0.0619923	+	0.107374i
$560$	4.24932	−	5.37547i	0.179567	−	0.227155i
$561$	18.2994	−	6.66044i	0.772601	−	0.281204i
$562$	−56.4314	+	32.5807i	−2.38042	+	1.37433i
$563$	−33.0543	−	19.0839i	−1.39307	−	0.804290i	−0.399417	−	0.916769i	$-0.630787\pi$
$563$	−33.0543	−	19.0839i	−1.39307	−	0.804290i	−0.993654	+	0.112479i	$0.964121\pi$
$564$	−3.30747	+	18.7576i	−0.139270	+	0.789838i
$565$	9.34256	−	28.2056i	0.393044	−	1.18662i
$566$	36.9350	+	30.9922i	1.55250	+	1.30270i
$567$	17.2942	−	3.04944i	0.726290	−	0.128065i
$568$	3.46467	−	9.51911i	0.145374	−	0.399413i
$569$	−2.28061			−0.0956082			−0.0478041	−	0.998857i	$-0.515222\pi$
$569$	−2.28061			−0.0956082			−0.0478041	+	0.998857i	$0.515222\pi$
$570$	−48.0940	+	21.8084i	−2.01444	+	0.913452i
$571$	−14.4656			−0.605367			−0.302683	−	0.953091i	$-0.597883\pi$
$571$	−14.4656			−0.605367			−0.302683	+	0.953091i	$0.597883\pi$
$572$	20.9433	−	57.5412i	0.875683	−	2.40592i
$573$	22.9764	−	4.05135i	0.959851	−	0.169248i
$574$	11.6678	+	9.79042i	0.487003	+	0.408644i
$575$	35.5094	−	8.42492i	1.48085	−	0.351344i
$576$	−4.41753	+	25.0530i	−0.184064	+	1.04388i
$577$	7.08262	+	4.08915i	0.294853	+	0.170234i	0.640128	−	0.768268i	$-0.278881\pi$
$577$	7.08262	+	4.08915i	0.294853	+	0.170234i	−0.345275	+	0.938501i	$0.612214\pi$
$578$	−14.8608	+	8.57989i	−0.618128	+	0.356876i
$579$	25.4053	−	9.24678i	1.05581	−	0.384283i
$580$	−14.1394	−	11.1772i	−0.587106	−	0.464109i
$581$	−5.25728	−	9.10587i	−0.218109	−	0.377775i
$582$	−0.609705	−	0.352014i	−0.0252731	−	0.0145914i
$583$	17.0936	+	3.01407i	0.707945	+	0.124830i
$584$	−19.1811	+	16.0949i	−0.793721	+	0.666011i
$585$	−30.4736	−	4.45998i	−1.25993	−	0.184397i
$586$	1.88836	+	10.7094i	0.0780076	+	0.442403i
$587$	−11.7776	+	32.3587i	−0.486114	+	1.33559i	0.418058	+	0.908420i	$0.362711\pi$
$587$	−11.7776	+	32.3587i	−0.486114	+	1.33559i	−0.904172	+	0.427168i	$0.859511\pi$
$588$			35.7584i			1.47465i
$589$	−17.7983	+	7.45194i	−0.733366	+	0.307052i
$590$	−55.3443	+	34.1461i	−2.27849	+	1.40577i
$591$	5.85516	+	2.13110i	0.240849	+	0.0876619i
$592$	3.76158	−	0.663268i	0.154600	−	0.0272602i
$593$	1.70415	−	2.03093i	0.0699812	−	0.0834003i	−0.729918	−	0.683535i	$-0.760442\pi$
$593$	1.70415	−	2.03093i	0.0699812	−	0.0834003i	0.799899	+	0.600134i	$0.204886\pi$
$594$	−8.80977	+	7.39228i	−0.361469	+	0.303309i
$595$	10.6270	−	4.22333i	0.435666	−	0.173140i
$596$	6.67406	−	11.5598i	0.273380	−	0.473508i
$597$	8.86258	−	5.11681i	0.362721	−	0.209417i
$598$	−36.6934	−	100.814i	−1.50050	−	4.12260i
$599$	−2.30660	+	0.839535i	−0.0942453	+	0.0343025i	−0.388712	−	0.921359i	$-0.627080\pi$
$599$	−2.30660	+	0.839535i	−0.0942453	+	0.0343025i	0.294467	+	0.955662i	$0.404858\pi$
$600$	43.8508	−	2.56462i	1.79020	−	0.104700i
$601$	−7.48153	+	12.9584i	−0.305178	+	0.528584i	−0.977301	−	0.211856i	$-0.932049\pi$
$601$	−7.48153	+	12.9584i	−0.305178	+	0.528584i	0.672123	+	0.740440i	$0.265383\pi$
$602$	−1.80715	−	0.318649i	−0.0736540	−	0.0129872i
$603$	0.958210	+	1.14195i	0.0390213	+	0.0465038i
$604$	12.4577	+	10.4532i	0.506896	+	0.425336i
$605$	5.94743	−	5.29405i	0.241797	−	0.215234i
$606$	19.0180	+	6.92198i	0.772553	+	0.281186i
$607$		−	43.0431i		−	1.74706i	−0.486767	−	0.873532i	$-0.661824\pi$
$607$		−	43.0431i		−	1.74706i	0.486767	−	0.873532i	$-0.338176\pi$
$608$	9.61059	+	10.4082i	0.389761	+	0.422106i
$609$	−8.32467			−0.337333
$610$	24.8736	−	5.13910i	1.00710	−	0.208076i
$611$	2.47768	+	14.0516i	0.100236	+	0.568468i
$612$	16.1597	−	19.2584i	0.653217	−	0.778473i
$613$	25.1922	+	30.0229i	1.01750	+	1.21261i	0.976957	+	0.213437i	$0.0684659\pi$
$613$	25.1922	+	30.0229i	1.01750	+	1.21261i	0.0405478	+	0.999178i	$0.487090\pi$
$614$	10.0141	−	56.7925i	0.404134	−	2.29196i
$615$	0.585696	+	20.0460i	0.0236176	+	0.808333i
$616$	8.58143	+	14.8635i	0.345756	+	0.598866i
$617$	−9.54332	−	26.2201i	−0.384200	−	1.05558i	−0.969570	−	0.244814i	$-0.921273\pi$
$617$	−9.54332	−	26.2201i	−0.384200	−	1.05558i	0.585370	−	0.810766i	$-0.300949\pi$
$618$	12.2292	+	33.5995i	0.491932	+	1.35157i
$619$	−12.4298	−	21.5291i	−0.499597	−	0.865327i	0.500403	−	0.865792i	$-0.333185\pi$
$619$	−12.4298	−	21.5291i	−0.499597	−	0.865327i	−1.00000		0.000465813i	$0.999852\pi$
$620$	35.8313	−	1.04691i	1.43902	−	0.0420448i
$621$	−2.25403	+	12.7832i	−0.0904511	+	0.512974i
$622$	−33.5599	−	39.9951i	−1.34563	−	1.60366i
$623$	18.2059	−	21.6969i	0.729403	−	0.869268i
$624$	−4.60552	−	26.1192i	−0.184368	−	1.04561i
$625$	7.18162	+	23.9463i	0.287265	+	0.957851i
$626$	−69.9001			−2.79377
$627$	−1.28851	−	27.1367i	−0.0514582	−	1.08374i
$628$			73.3901i			2.92858i
$629$	5.99005	+	2.18020i	0.238839	+	0.0869303i
$630$	14.4007	−	12.8187i	0.573738	−	0.510708i
$631$	33.9105	+	28.4543i	1.34995	+	1.13275i	0.978947	+	0.204116i	$0.0654320\pi$
$631$	33.9105	+	28.4543i	1.34995	+	1.13275i	0.371007	+	0.928630i	$0.379012\pi$
$632$	−10.1817	−	12.1341i	−0.405008	−	0.482670i
$633$	16.5184	+	2.91265i	0.656549	+	0.115767i
$634$	9.53501	−	16.5151i	0.378684	−	0.655900i
$635$	−17.1119	−	9.22402i	−0.679067	−	0.366044i
$636$	49.4883	−	18.0123i	1.96234	−	0.714233i
$637$	9.16175	+	25.1717i	0.363002	+	0.997339i
$638$	12.4649	−	7.19661i	0.493490	−	0.284916i
$639$	2.92709	−	5.06988i	0.115794	−	0.200561i
$640$	−17.0515	−	42.9061i	−0.674019	−	1.69601i
$641$	15.5815	−	13.0744i	0.615432	−	0.516409i	−0.280932	−	0.959728i	$-0.590644\pi$
$641$	15.5815	−	13.0744i	0.615432	−	0.516409i	0.896364	+	0.443319i	$0.146199\pi$
$642$	−41.0780	+	48.9549i	−1.62122	+	1.93210i
$643$	−29.9093	+	5.27382i	−1.17951	+	0.207979i	−0.728822	−	0.684703i	$-0.759932\pi$
$643$	−29.9093	+	5.27382i	−1.17951	+	0.207979i	−0.450686	+	0.892682i	$0.648821\pi$
$644$	40.6562	+	14.7977i	1.60208	+	0.583109i
$645$	−1.26867	−	2.05627i	−0.0499536	−	0.0809654i
$646$	−7.10926	−	31.4989i	−0.279710	−	1.23931i
$647$			48.5913i			1.91032i	0.296087	+	0.955161i	$0.404318\pi$
$647$			48.5913i			1.91032i	−0.296087	+	0.955161i	$0.595682\pi$
$648$	−14.1076	+	38.7604i	−0.554200	+	1.52265i
$649$	−5.80948	−	32.9472i	−0.228042	−	1.29329i
$650$	67.4746	−	29.1250i	2.64657	−	1.14238i
$651$	12.6831	−	10.6424i	0.497091	−	0.417109i
$652$	−55.8473	−	9.84739i	−2.18715	−	0.385653i
$653$	17.2820	+	9.97774i	0.676295	+	0.390459i	0.798458	−	0.602051i	$-0.205650\pi$
$653$	17.2820	+	9.97774i	0.676295	+	0.390459i	−0.122163	+	0.992510i	$0.538983\pi$
$654$	−19.6077	−	33.9615i	−0.766721	−	1.32800i
$655$	−18.4994	−	14.6238i	−0.722831	−	0.571399i
$656$	−6.90496	+	2.51320i	−0.269594	+	0.0981240i
$657$	−12.5316	+	7.23513i	−0.488905	+	0.282269i
$658$	−7.73526	−	4.46595i	−0.301552	−	0.174101i
$659$	2.95696	−	16.7698i	0.115187	−	0.653257i	−0.871471	−	0.490448i	$-0.836833\pi$
$659$	2.95696	−	16.7698i	0.115187	−	0.653257i	0.986658	−	0.162810i	$-0.0520556\pi$
$660$	−15.8696	+	47.9111i	−0.617724	+	1.86494i
$661$	−21.0919	−	17.6982i	−0.820379	−	0.688380i	0.132682	−	0.991159i	$-0.457641\pi$
$661$	−21.0919	−	17.6982i	−0.820379	−	0.688380i	−0.953061	+	0.302779i	$0.902086\pi$
$662$	42.5388	−	7.50074i	1.65332	−	0.291525i
$663$	15.1386	−	41.5930i	0.587935	−	1.61534i
$664$	24.6969			0.958427
$665$	−1.22172	−	15.9064i	−0.0473761	−	0.616825i
$666$	10.7470			0.416436
$667$	5.55633	−	15.2659i	0.215142	−	0.591098i
$668$	−21.5618	+	3.80193i	−0.834253	+	0.147101i
$669$	29.0252	+	24.3551i	1.12218	+	0.941621i
$670$	−3.37677	−	1.11849i	−0.130456	−	0.0432110i
$671$	−2.26901	+	12.8682i	−0.0875940	+	0.496770i
$672$	−10.5273	−	6.07793i	−0.406099	−	0.234461i
$673$	−32.2647	+	18.6280i	−1.24371	+	0.718057i	−0.969848	−	0.243711i	$-0.921635\pi$
$673$	−32.2647	+	18.6280i	−1.24371	+	0.718057i	−0.273864	+	0.961768i	$0.588302\pi$
$674$	−21.3959	+	7.78748i	−0.824140	+	0.299962i
$675$	−8.83201	−	1.03016i	−0.339944	−	0.0396508i
$676$	−46.0503	−	79.7615i	−1.77117	−	3.06775i
$677$	19.7350	+	11.3940i	0.758478	+	0.437907i	0.828749	−	0.559621i	$-0.189053\pi$
$677$	19.7350	+	11.3940i	0.758478	+	0.437907i	−0.0702711	+	0.997528i	$0.522386\pi$
$678$	70.8993	+	12.5015i	2.72287	+	0.480116i
$679$	0.162929	−	0.136713i	0.00625263	−	0.00524658i
$680$	−3.88968	+	26.5769i	−0.149162	+	1.01918i
$681$	4.67549	+	26.5160i	0.179165	+	1.01610i
$682$	−9.79072	+	26.8998i	−0.374906	+	1.03005i
$683$		−	4.61408i		−	0.176553i	−0.996096	−	0.0882764i	$-0.971864\pi$
$683$		−	4.61408i		−	0.176553i	0.996096	−	0.0882764i	$-0.0281359\pi$
$684$	−18.9568	−	29.5074i	−0.724833	−	1.12824i
$685$	−0.755912	+	0.466379i	−0.0288819	+	0.0178194i
$686$	−41.2842	−	15.0262i	−1.57624	−	0.573704i
$687$	17.6056	−	3.10434i	0.671695	−	0.118438i
$688$	0.569052	−	0.678170i	0.0216949	−	0.0258550i
$689$	30.2218	−	25.3591i	1.15136	−	0.966104i
$690$	32.6577	+	82.1754i	1.24326	+	3.12837i
$691$	−17.8800	+	30.9690i	−0.680186	+	1.17812i	0.294738	+	0.955578i	$0.404768\pi$
$691$	−17.8800	+	30.9690i	−0.680186	+	1.17812i	−0.974924	+	0.222538i	$0.928566\pi$
$692$	−5.14479	+	2.97035i	−0.195576	+	0.112916i
$693$	3.39233	+	9.32034i	0.128864	+	0.354050i
$694$	−2.82123	+	1.02684i	−0.107092	+	0.0389785i
$695$	7.96327	−	14.7731i	0.302064	−	0.560375i
$696$	9.77663	−	16.9336i	0.370582	−	0.641867i
$697$	−12.0768	−	2.12947i	−0.457442	−	0.0806594i
$698$	40.5618	+	48.3397i	1.53529	+	1.82968i
$699$	11.7629	+	9.87026i	0.444915	+	0.373328i
$700$	−8.49337	+	28.3947i	−0.321019	+	1.07322i
$701$	−30.8939	−	11.2444i	−1.16685	−	0.424697i	−0.315307	−	0.948990i	$-0.602108\pi$
$701$	−30.8939	−	11.2444i	−1.16685	−	0.424697i	−0.851538	+	0.524293i	$0.824330\pi$
$702$			26.1393i			0.986565i
$703$	5.38667	−	7.07575i	0.203162	−	0.266867i
$704$	31.2301			1.17703
$705$	−2.37955	−	11.5172i	−0.0896192	−	0.433762i
$706$	11.0645	+	62.7500i	0.416419	+	2.36163i
$707$	−3.93007	+	4.68368i	−0.147806	+	0.176148i
$708$	−65.2482	−	77.7598i	−2.45218	−	2.92239i
$709$	−7.71396	+	43.7480i	−0.289704	+	1.64299i	0.398279	+	0.917264i	$0.369608\pi$
$709$	−7.71396	+	43.7480i	−0.289704	+	1.64299i	−0.687983	+	0.725727i	$0.741504\pi$
$710$	0.407981	+	13.9635i	0.0153113	+	0.524043i
$711$	−4.57700	−	7.92760i	−0.171651	−	0.297308i
$712$	22.7535	+	62.5147i	0.852723	+	2.34284i
$713$	11.0508	+	30.3618i	0.413855	+	1.13706i
$714$	13.8540	+	23.9958i	0.518471	+	0.898019i
$715$	1.10421	+	37.7925i	0.0412950	+	1.41336i
$716$	−8.92264	+	50.6028i	−0.333455	+	1.89112i
$717$	−23.4641	−	27.9635i	−0.876284	−	1.04431i
$718$	32.0910	−	38.2445i	1.19762	−	1.42727i
$719$	3.48789	+	19.7808i	0.130076	+	0.737699i	0.978163	+	0.207841i	$0.0666436\pi$
$719$	3.48789	+	19.7808i	0.130076	+	0.737699i	−0.848086	+	0.529858i	$0.822245\pi$
$720$	1.88196	+	9.10878i	0.0701363	+	0.339464i
$721$	−10.8019			−0.402285
$722$	−44.9056	−	3.58385i	−1.67121	−	0.133377i
$723$		−	23.8919i		−	0.888548i
$724$	78.0868	+	28.4213i	2.90207	+	1.05627i
$725$	10.6619	+	3.18915i	0.395971	+	0.118442i
$726$	14.7790	+	12.4010i	0.548498	+	0.460245i
$727$	0.469102	+	0.559054i	0.0173980	+	0.0207342i	0.774673	−	0.632362i	$-0.217914\pi$
$727$	0.469102	+	0.559054i	0.0173980	+	0.0207342i	−0.757275	+	0.653096i	$0.773470\pi$
$728$	38.4171	+	6.77397i	1.42383	+	0.251060i
$729$	−5.82299	+	10.0857i	−0.215666	+	0.373545i
$730$	16.3841	−	30.3949i	0.606401	−	1.12497i
$731$	1.38834	−	0.505315i	0.0513497	−	0.0186898i
$732$	13.5597	+	37.2551i	0.501183	+	1.37699i
$733$	−25.5432	+	14.7474i	−0.943461	+	0.544707i	−0.891043	−	0.453918i	$-0.850026\pi$
$733$	−25.5432	+	14.7474i	−0.943461	+	0.544707i	−0.0524171	+	0.998625i	$0.516693\pi$
$734$	13.0613	−	22.6228i	0.482101	−	0.835023i
$735$	−8.15410	−	20.5179i	−0.300768	−	0.756814i
$736$	18.1723	−	15.2483i	0.669838	−	0.562061i
$737$	1.17632	−	1.40188i	0.0433303	−	0.0516390i
$738$	−20.3607	+	3.59015i	−0.749489	+	0.132155i
$739$	−38.0572	−	13.8517i	−1.39996	−	0.509542i	−0.471790	−	0.881711i	$-0.656392\pi$
$739$	−38.0572	−	13.8517i	−1.39996	−	0.509542i	−0.928165	+	0.372169i	$0.878614\pi$
$740$	−14.0602	+	8.67482i	−0.516864	+	0.318893i
$741$	−49.1318	−	37.4033i	−1.80490	−	1.37405i
$742$			24.6965i			0.906637i
$743$	−6.64673	+	18.2617i	−0.243845	+	0.669958i	0.756036	+	0.654530i	$0.227133\pi$
$743$	−6.64673	+	18.2617i	−0.243845	+	0.669958i	−0.999881	+	0.0154284i	$0.995089\pi$
$744$	6.75297	+	38.2980i	0.247576	+	1.40407i
$745$	−1.19350	+	8.15484i	−0.0437266	+	0.298770i
$746$	−8.77818	+	7.36576i	−0.321392	+	0.269680i
$747$	14.0556	+	2.47839i	0.514269	+	0.0906795i
$748$	−26.7277	−	15.4312i	−0.977260	−	0.564221i
$749$	−9.65309	−	16.7196i	−0.352716	−	0.610923i
$750$	−54.8898	+	25.6197i	−2.00429	+	0.935499i
$751$	−5.32221	+	1.93713i	−0.194210	+	0.0706868i	−0.437294	−	0.899318i	$-0.644063\pi$
$751$	−5.32221	+	1.93713i	−0.194210	+	0.0706868i	0.243084	+	0.970005i	$0.421841\pi$
$752$	3.73178	−	2.15455i	0.136084	−	0.0785682i
$753$	−23.4827	−	13.5578i	−0.855758	−	0.494072i
$754$	5.68082	−	32.2176i	0.206883	−	1.17329i
$755$	−9.53181	−	3.15722i	−0.346898	−	0.114903i
$756$	−8.07520	−	6.77590i	−0.293692	−	0.246437i
$757$	−12.3875	+	2.18425i	−0.450231	+	0.0793879i	−0.394166	−	0.919039i	$-0.628967\pi$
$757$	−12.3875	+	2.18425i	−0.450231	+	0.0793879i	−0.0560650	+	0.998427i	$0.517855\pi$
$758$	1.65201	−	4.53886i	0.0600037	−	0.164859i
$759$	−45.4920			−1.65126
$760$	33.7909	+	16.1956i	1.22572	+	0.587477i
$761$	50.0335			1.81371			0.906857	−	0.421439i	$-0.138475\pi$
$761$	50.0335			1.81371			0.906857	+	0.421439i	$0.138475\pi$
$762$	16.1098	−	44.2613i	0.583596	−	1.60342i
$763$	11.6671	−	2.05722i	0.422377	−	0.0744764i
$764$	−28.3245	−	23.7671i	−1.02475	−	0.859864i
$765$	−4.88076	+	14.7353i	−0.176464	+	0.532754i
$766$	14.2373	−	80.7436i	0.514413	−	2.91738i
$767$	−65.8538	−	38.0207i	−2.37784	−	1.37285i
$768$	51.5625	−	29.7696i	1.86060	−	1.07422i
$769$	−29.8303	+	10.8573i	−1.07571	+	0.391525i	−0.818308	−	0.574780i	$-0.805088\pi$
$769$	−29.8303	+	10.8573i	−1.07571	+	0.391525i	−0.257399	+	0.966305i	$0.582865\pi$
$770$	−18.5673	−	14.6775i	−0.669118	−	0.528939i
$771$	−4.36033	−	7.55231i	−0.157033	−	0.271990i
$772$	−37.1064	−	21.4234i	−1.33549	−	0.771044i
$773$	−11.2636	−	1.98608i	−0.405124	−	0.0714342i	−0.0326266	−	0.999468i	$-0.510387\pi$
$773$	−11.2636	−	1.98608i	−0.405124	−	0.0714342i	−0.372497	+	0.928033i	$0.621498\pi$
$774$	1.90812	−	1.60110i	0.0685859	−	0.0575504i
$775$	−20.3210	+	8.77145i	−0.729953	+	0.315080i
$776$	0.0867493	+	0.491980i	0.00311412	+	0.0176610i
$777$	−2.60983	+	7.17044i	−0.0936270	+	0.257238i
$778$		−	10.7410i		−	0.385083i
$779$	−7.84162	+	15.2049i	−0.280955	+	0.544772i
$780$	60.2352	+	97.6298i	2.15677	+	3.49571i
$781$	−6.75332	−	2.45801i	−0.241653	−	0.0879544i
$782$	−53.2506	+	9.38951i	−1.90424	+	0.335768i
$783$	−2.54426	+	3.03213i	−0.0909246	+	0.108360i
$784$	6.19714	−	5.20002i	0.221327	−	0.185715i
$785$	−16.7354	−	42.1107i	−0.597311	−	1.50299i
$786$	28.5686	−	49.4823i	1.01901	−	1.76497i
$787$	5.75062	−	3.32012i	0.204987	−	0.118350i	−0.393992	−	0.919114i	$-0.628906\pi$
$787$	5.75062	−	3.32012i	0.204987	−	0.118350i	0.598980	+	0.800764i	$0.295573\pi$
$788$	−3.37741	−	9.27935i	−0.120315	−	0.330563i
$789$	4.55138	−	1.65657i	0.162033	−	0.0589753i
$790$	19.2281	+	10.3647i	0.684104	+	0.368759i
$791$	−10.8746	+	18.8354i	−0.386657	+	0.669710i
$792$	−22.9430	−	4.04546i	−0.815242	−	0.143749i
$793$	19.0905	+	22.7511i	0.677922	+	0.807916i
$794$	−45.6515	−	38.3061i	−1.62011	−	1.35943i
$795$	−24.2886	+	21.6203i	−0.861429	+	0.766793i
$796$	−15.2403	−	5.54703i	−0.540179	−	0.196609i
$797$		−	0.186468i		−	0.00660502i	−0.999995	−	0.00330251i	$-0.998949\pi$
$797$		−	0.186468i		−	0.00660502i	0.999995	−	0.00330251i	$-0.00105122\pi$
$798$	37.7060	−	8.51019i	1.33478	−	0.301258i
$799$	7.19137			0.254412
$800$	11.1544	+	11.8173i	0.394369	+	0.417805i
$801$	6.67609	+	37.8620i	0.235888	+	1.33779i
$802$	44.0621	−	52.5112i	1.55589	−	1.85423i
$803$	11.4185	+	13.6080i	0.402950	+	0.480217i
$804$	0.964190	−	5.46819i	0.0340044	−	0.192848i
$805$	−26.7026	+	0.780186i	−0.941143	+	0.0274979i
$806$	32.5324	+	56.3478i	1.14591	+	1.98477i
$807$	3.07016	+	8.43520i	0.108075	+	0.296933i
$808$	−4.91176	−	13.4949i	−0.172795	−	0.474750i
$809$	0.609985	+	1.05652i	0.0214459	+	0.0371454i	0.876549	−	0.481312i	$-0.159840\pi$
$809$	0.609985	+	1.05652i	0.0214459	+	0.0371454i	−0.855103	+	0.518458i	$0.826506\pi$
$810$	−1.66124	−	56.8575i	−0.0583700	−	1.99777i
$811$	−3.31560	+	18.8037i	−0.116427	+	0.660288i	0.869608	+	0.493744i	$0.164372\pi$
$811$	−3.31560	+	18.8037i	−0.116427	+	0.660288i	−0.986034	+	0.166544i	$0.946739\pi$
$812$	8.48035	+	10.1065i	0.297602	+	0.354668i
$813$	27.8138	−	33.1472i	0.975473	−	1.16252i
$814$	−2.29098	−	12.9928i	−0.0802987	−	0.455396i
$815$	34.2903	−	7.08469i	1.20114	−	0.248166i
$816$	−13.3674			−0.467951
$817$	−0.0977570	−	2.05881i	−0.00342008	−	0.0720287i
$818$		−	54.4413i		−	1.90349i
$819$	21.1844	+	7.71047i	0.740241	+	0.269426i
$820$	23.7400	−	21.1319i	0.829037	−	0.737959i
$821$	−7.64305	−	6.41328i	−0.266744	−	0.223825i	0.499598	−	0.866257i	$-0.333481\pi$
$821$	−7.64305	−	6.41328i	−0.266744	−	0.223825i	−0.766343	+	0.642432i	$0.777925\pi$
$822$	−1.38335	−	1.64861i	−0.0482498	−	0.0575019i
$823$	27.7792	+	4.89822i	0.968322	+	0.170741i	0.635375	−	0.772204i	$-0.280846\pi$
$823$	27.7792	+	4.89822i	0.968322	+	0.170741i	0.332948	+	0.942945i	$0.391957\pi$
$824$	12.6860	−	21.9727i	0.441937	−	0.765457i
$825$	−1.81946	−	31.1099i	−0.0633456	−	1.08311i
$826$	44.7307	−	16.2806i	1.55638	−	0.566476i
$827$	−3.02789	−	8.31907i	−0.105290	−	0.289283i	0.875849	−	0.482585i	$-0.160302\pi$
$827$	−3.02789	−	8.31907i	−0.105290	−	0.289283i	−0.981139	+	0.193303i	$0.938080\pi$
$828$	−50.8604	+	29.3643i	−1.76752	+	1.02048i
$829$	22.8446	−	39.5680i	0.793425	−	1.37425i	−0.130409	−	0.991460i	$-0.541629\pi$
$829$	22.8446	−	39.5680i	0.793425	−	1.37425i	0.923834	−	0.382793i	$-0.125038\pi$
$830$	−31.6498	+	12.5781i	−1.09858	+	0.436591i
$831$	−26.3055	+	22.0729i	−0.912526	+	0.765701i
$832$	45.6273	−	54.3765i	1.58184	−	1.88517i
$833$	13.2958	−	2.34441i	0.460673	−	0.0812290i
$834$	38.2116	+	13.9079i	1.32316	+	0.481591i
$835$	11.5051	−	7.09834i	0.398149	−	0.245648i
$836$	−31.6325	+	29.2085i	−1.09403	+	1.01020i
$837$		−	7.87227i		−	0.272105i
$838$	7.28252	−	20.0086i	0.251570	−	0.691184i
$839$	−0.0317008	−	0.179784i	−0.00109443	−	0.00620684i	0.984256	−	0.176751i	$-0.0565586\pi$
$839$	−0.0317008	−	0.179784i	−0.00109443	−	0.00620684i	−0.985350	+	0.170544i	$0.945448\pi$
$840$	−31.8141	−	4.65616i	−1.09769	−	0.160653i
$841$	−18.4204	+	15.4566i	−0.635187	+	0.532985i
$842$	79.4831	+	14.0150i	2.73917	+	0.482989i
$843$	54.3880	+	31.4010i	1.87322	+	1.08151i
$844$	−13.2913	−	23.0212i	−0.457505	−	0.792422i
$845$	44.6116	+	35.2655i	1.53469	+	1.21317i
$846$	11.3930	−	4.14671i	0.391699	−	0.142567i
$847$	−5.04748	+	2.91416i	−0.173433	+	0.100132i
$848$	−10.3183	−	5.95727i	−0.354332	−	0.204573i
$849$	8.06933	−	45.7634i	0.276939	−	1.57060i
$850$	−8.55082	−	36.0401i	−0.293291	−	1.23616i
$851$	−11.4073	−	9.57186i	−0.391037	−	0.328119i
$852$	−21.4742	+	3.78648i	−0.735695	+	0.129723i
$853$	−16.8337	+	46.2501i	−0.576374	+	1.58357i	0.217872	+	0.975977i	$0.430089\pi$
$853$	−16.8337	+	46.2501i	−0.576374	+	1.58357i	−0.794246	+	0.607597i	$0.792134\pi$
$854$	−18.5917			−0.636193
$855$	17.6060	+	12.6083i	0.602111	+	0.431195i
$856$	45.3470			1.54993
$857$	−10.7975	+	29.6660i	−0.368837	+	1.01337i	0.606968	+	0.794727i	$0.292386\pi$
$857$	−10.7975	+	29.6660i	−0.368837	+	1.01337i	−0.975805	+	0.218645i	$0.929836\pi$
$858$	−90.2176	+	15.9078i	−3.07998	+	0.543083i
$859$	8.18869	+	6.87112i	0.279394	+	0.234440i	0.771706	−	0.635979i	$-0.219404\pi$
$859$	8.18869	+	6.87112i	0.279394	+	0.234440i	−0.492312	+	0.870419i	$0.663848\pi$
$860$	−1.20400	+	3.63493i	−0.0410560	+	0.123950i
$861$	2.54910	−	14.4567i	0.0868730	−	0.492681i
$862$	77.9706	+	45.0164i	2.65569	+	1.53326i
$863$	22.1552	−	12.7913i	0.754170	−	0.435420i	−0.0730285	−	0.997330i	$-0.523266\pi$
$863$	22.1552	−	12.7913i	0.754170	−	0.435420i	0.827199	+	0.561909i	$0.189933\pi$
$864$	−5.43124	+	1.97681i	−0.184775	+	0.0672524i
$865$	2.27470	−	2.87755i	0.0773423	−	0.0978395i
$866$	43.8392	+	75.9316i	1.48971	+	2.58026i
$867$	14.3227	+	8.26921i	0.486424	+	0.280837i
$868$	−25.8406	−	4.55640i	−0.877088	−	0.154654i
$869$	−8.60854	+	7.22342i	−0.292025	+	0.245038i
$870$	−3.90478	+	26.6801i	−0.132384	+	0.904540i
$871$	−0.722290	−	4.09631i	−0.0244739	−	0.138798i
$872$	−9.51731	+	26.1486i	−0.322297	+	0.885503i
$873$			0.288703i			0.00977113i
$874$	−9.56087	+	74.8258i	−0.323401	+	2.53102i
$875$	−1.60151	−	18.2295i	−0.0541409	−	0.616268i
$876$	50.6479	+	18.4343i	1.71123	+	0.622838i
$877$	−30.6228	+	5.39963i	−1.03406	+	0.182332i	−0.664821	−	0.747003i	$-0.731492\pi$
$877$	−30.6228	+	5.39963i	−1.03406	+	0.182332i	−0.369237	+	0.929335i	$0.620381\pi$
$878$	−33.8076	+	40.2903i	−1.14095	+	1.35973i
$879$	8.02882	−	6.73698i	0.270805	−	0.227233i
$880$	10.6111	−	4.21699i	0.357699	−	0.142155i
$881$	23.7233	−	41.0899i	0.799257	−	1.38435i	−0.120844	−	0.992672i	$-0.538560\pi$
$881$	23.7233	−	41.0899i	0.799257	−	1.38435i	0.920101	−	0.391682i	$-0.128107\pi$
$882$	19.7122	−	11.3808i	0.663744	−	0.383213i
$883$	−4.97065	−	13.6568i	−0.167276	−	0.459586i	0.827525	−	0.561429i	$-0.189748\pi$
$883$	−4.97065	−	13.6568i	−0.167276	−	0.459586i	−0.994801	+	0.101843i	$0.967526\pi$
$884$	−65.9173	+	23.9919i	−2.21704	+	0.806936i
$885$	55.1708	+	29.7392i	1.85455	+	0.999674i
$886$	11.6756	−	20.2227i	0.392249	−	0.679396i
$887$	36.5629	+	6.44703i	1.22766	+	0.216470i	0.749621	−	0.661867i	$-0.230236\pi$
$887$	36.5629	+	6.44703i	1.22766	+	0.216470i	0.478042	+	0.878337i	$0.341347\pi$
$888$	−11.5207	−	13.7299i	−0.386610	−	0.460744i
$889$	10.9005	+	9.14660i	0.365591	+	0.306767i
$890$	−60.9977	−	68.5260i	−2.04465	−	2.29700i
$891$	27.4985	+	10.0086i	0.921234	+	0.335302i
$892$		−	60.0483i		−	2.01057i
$893$	2.98031	−	9.57955i	0.0997322	−	0.320567i
$894$	−19.9695			−0.667879
$895$	−6.41938	−	31.0702i	−0.214576	−	1.03856i
$896$	5.86861	+	33.2825i	0.196056	+	1.11189i
$897$	−66.4639	+	79.2086i	−2.21917	+	2.64470i
$898$	−56.8523	−	67.7539i	−1.89718	−	2.26098i
$899$	−1.71087	+	9.70283i	−0.0570607	+	0.323607i
$900$	−22.1150	−	33.6066i	−0.737168	−	1.12022i
$901$	−9.94198	−	17.2200i	−0.331215	−	0.573682i
$902$	8.68077	+	23.8502i	0.289038	+	0.794126i
$903$	0.604891	+	1.66192i	0.0201295	+	0.0553054i
$904$	−25.5427	−	44.2412i	−0.849537	−	1.47144i
$905$	−51.2866	+	1.49847i	−1.70482	+	0.0498109i
$906$	4.22474	−	23.9597i	0.140358	−	0.796007i
$907$	−6.98432	−	8.32358i	−0.231910	−	0.276380i	0.637522	−	0.770432i	$-0.279960\pi$
$907$	−6.98432	−	8.32358i	−0.231910	−	0.276380i	−0.869432	+	0.494052i	$0.835515\pi$
$908$	27.4286	−	32.6881i	0.910250	−	1.08479i
$909$	−1.44116	−	8.17321i	−0.0478002	−	0.271088i
$910$	−52.6825	+	10.8847i	−1.74641	+	0.360824i
$911$	−39.5522			−1.31042			−0.655211	−	0.755446i	$-0.727420\pi$
$911$	−39.5522			−1.31042			−0.655211	+	0.755446i	$0.727420\pi$
$912$	−5.53981	+	17.8065i	−0.183441	+	0.589633i
$913$		−	17.5212i		−	0.579867i
$914$	31.2682	+	11.3807i	1.03426	+	0.376440i
$915$	−16.2759	−	18.2846i	−0.538064	−	0.604471i
$916$	−21.7036	−	18.2115i	−0.717108	−	0.601725i
$917$	11.0953	+	13.2229i	0.366400	+	0.436659i
$918$	12.9743	+	2.28771i	0.428214	+	0.0755058i
$919$	16.0782	−	27.8483i	0.530372	−	0.918631i	−0.469000	−	0.883198i	$-0.655386\pi$
$919$	16.0782	−	27.8483i	0.530372	−	0.918631i	0.999372	−	0.0354331i	$-0.0112811\pi$
$920$	29.7730	−	55.2333i	0.981585	−	1.82099i
$921$	−52.2286	+	19.0096i	−1.72099	+	0.626389i
$922$	−8.21942	−	22.5827i	−0.270692	−	0.743720i
$923$	−14.1464	+	8.16742i	−0.465634	+	0.268834i
$924$	18.4721	−	31.9945i	0.607686	−	1.05254i
$925$	6.08951	−	8.18375i	0.200222	−	0.269080i
$926$	−1.31158	+	1.10055i	−0.0431012	+	0.0361662i
$927$	9.42491	−	11.2322i	0.309555	−	0.368913i
$928$	7.12380	−	1.25612i	0.233850	−	0.0412341i
$929$	−10.2742	−	3.73950i	−0.337085	−	0.122689i	0.167931	−	0.985799i	$-0.446291\pi$
$929$	−10.2742	−	3.73950i	−0.337085	−	0.122689i	−0.505016	+	0.863110i	$0.668514\pi$
$930$	−28.1592	−	45.6407i	−0.923376	−	1.49662i
$931$	2.38720	−	18.6828i	0.0782372	−	0.612304i
$932$		−	24.3355i		−	0.797136i
$933$	−17.2103	+	47.2848i	−0.563439	+	1.54803i
$934$	14.4171	+	81.7633i	0.471741	+	2.67538i
$935$	18.8550	+	2.75952i	0.616623	+	0.0902461i
$936$	−40.5635	+	34.0368i	−1.32586	+	1.11253i
$937$	44.3460	+	7.81940i	1.44872	+	0.255449i	0.842005	−	0.539470i	$-0.181375\pi$
$937$	44.3460	+	7.81940i	1.44872	+	0.255449i	0.606716	+	0.794918i	$0.292486\pi$
$938$	2.25497	+	1.30191i	0.0736275	+	0.0425088i
$939$	33.6845	+	58.3433i	1.09925	+	1.90396i
$940$	−11.5583	+	14.6214i	−0.376989	+	0.476899i
$941$	40.0794	−	14.5877i	1.30655	−	0.475545i	0.407426	−	0.913238i	$-0.366427\pi$
$941$	40.0794	−	14.5877i	1.30655	−	0.475545i	0.899125	+	0.437693i	$0.144204\pi$
$942$	95.0855	−	54.8977i	3.09805	−	1.78866i
$943$	24.8094	+	14.3237i	0.807905	+	0.466444i
$944$	−3.98778	+	22.6158i	−0.129791	+	0.736083i
$945$	6.17862	+	2.04655i	0.200991	+	0.0665742i
$946$	−2.34245	−	1.96555i	−0.0761596	−	0.0639055i
$947$	−24.3377	+	4.29139i	−0.790869	+	0.139452i	−0.554469	−	0.832204i	$-0.687079\pi$
$947$	−24.3377	+	4.29139i	−0.790869	+	0.139452i	−0.236400	+	0.971656i	$0.575968\pi$
$948$	−11.6617	+	32.0403i	−0.378754	+	1.04062i
$949$	40.3761			1.31066
$950$	−51.5523	−	3.54555i	−1.67258	−	0.115033i
$951$	−18.3795			−0.595996
$952$	6.72453	−	18.4755i	0.217943	−	0.598794i
$953$	−15.2813	+	2.69451i	−0.495010	+	0.0872836i	−0.415580	−	0.909557i	$-0.636421\pi$
$953$	−15.2813	+	2.69451i	−0.495010	+	0.0872836i	−0.0794303	+	0.996840i	$0.525310\pi$
$954$	−25.6801	−	21.5482i	−0.831426	−	0.697649i
$955$	21.6721	+	7.17845i	0.701293	+	0.232289i
$956$	−10.0458	+	56.9728i	−0.324906	+	1.84263i
$957$	−12.0135	−	6.93602i	−0.388342	−	0.224210i
$958$	−55.3578	+	31.9608i	−1.78853	+	1.03261i
$959$	0.610947	−	0.222367i	0.0197285	−	0.00718059i
$960$	−36.2824	+	45.8980i	−1.17101	+	1.48135i
$961$	5.70235	+	9.87675i	0.183947	+	0.318605i
$962$	−25.9695	−	14.9935i	−0.837292	−	0.483411i
$963$	25.8081	+	4.55067i	0.831655	+	0.146643i
$964$	−29.0057	+	24.3387i	−0.934210	+	0.783895i
$965$	26.1766	+	3.83109i	0.842654	+	0.123327i
$966$	−11.2398	−	63.7440i	−0.361634	−	2.05093i
$967$	5.48978	−	15.0830i	0.176539	−	0.485038i	−0.819589	−	0.572952i	$-0.805798\pi$
$967$	5.48978	−	15.0830i	0.176539	−	0.485038i	0.996128	+	0.0879145i	$0.0280202\pi$
$968$		−	13.6898i		−	0.440006i
$969$	−22.8652	+	21.1130i	−0.734535	+	0.678248i
$970$	−0.361735	−	0.586304i	−0.0116146	−	0.0188251i
$971$	5.42132	+	1.97320i	0.173978	+	0.0633230i	0.427541	−	0.903996i	$-0.359380\pi$
$971$	5.42132	+	1.97320i	0.173978	+	0.0633230i	−0.253562	+	0.967319i	$0.581602\pi$
$972$	68.4122	−	12.0629i	2.19432	−	0.386918i
$973$	−7.89644	+	9.41061i	−0.253148	+	0.301690i
$974$	−5.57154	+	4.67507i	−0.178524	+	0.149799i
$975$	−56.8253	−	42.2836i	−1.81987	−	1.35416i
$976$	4.48466	−	7.76766i	0.143551	−	0.248637i
$977$	40.5060	−	23.3862i	1.29590	−	0.748190i	0.316209	−	0.948689i	$-0.397590\pi$
$977$	40.5060	−	23.3862i	1.29590	−	0.748190i	0.979694	+	0.200499i	$0.0642565\pi$
$978$	29.0168	+	79.7229i	0.927854	+	2.54926i
$979$	44.3509	−	16.1424i	1.41746	−	0.515914i
$980$	−16.6030	+	30.8010i	−0.530362	+	0.983901i
$981$	−8.04061	+	13.9267i	−0.256717	+	0.444647i
$982$	−2.91607	−	0.514183i	−0.0930557	−	0.0164082i
$983$	21.6002	+	25.7421i	0.688939	+	0.821046i	0.991227	−	0.132171i	$-0.0421947\pi$
$983$	21.6002	+	25.7421i	0.688939	+	0.821046i	−0.302288	+	0.953217i	$0.597750\pi$
$984$	26.4133	+	22.1634i	0.842025	+	0.706543i
$985$	4.05393	+	4.55426i	0.129169	+	0.145111i
$986$	−15.4940	−	5.63936i	−0.493430	−	0.179594i
$987$			8.60848i			0.274011i
$988$	4.64142	+	97.7507i	0.147663	+	3.10986i
$989$	−3.45139			−0.109748
$990$	31.4624	−	6.50041i	0.999940	−	0.206597i
$991$	−7.91905	−	44.9112i	−0.251557	−	1.42665i	−0.804758	−	0.593602i	$-0.797705\pi$
$991$	−7.91905	−	44.9112i	−0.251557	−	1.42665i	0.553202	−	0.833047i	$-0.313406\pi$
$992$	−9.24768	+	11.0210i	−0.293614	+	0.349916i
$993$	−26.7599	−	31.8912i	−0.849199	−	1.01204i
$994$	1.77564	−	10.0701i	0.0563198	−	0.319406i
$995$	10.0097	−	0.292459i	0.317329	−	0.00927158i
$996$	−26.5808	−	46.0393i	−0.842246	−	1.45881i
$997$	−1.64213	−	4.51171i	−0.0520067	−	0.142887i	0.910969	−	0.412474i	$-0.135335\pi$
$997$	−1.64213	−	4.51171i	−0.0520067	−	0.142887i	−0.962976	+	0.269587i	$0.913113\pi$
$998$	−15.8713	−	43.6062i	−0.502399	−	1.38033i
$999$	1.81408	+	3.14208i	0.0573950	+	0.0994111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.4.1	✓	48
3.2	odd	2		855.2.da.b.289.8		48
5.2	odd	4		475.2.l.f.251.1		48
5.3	odd	4		475.2.l.f.251.8		48
5.4	even	2	inner	95.2.p.a.4.8	yes	48
15.14	odd	2		855.2.da.b.289.1		48
19.5	even	9	inner	95.2.p.a.24.8	yes	48
19.9	even	9		1805.2.b.k.1084.2		24
19.10	odd	18		1805.2.b.l.1084.23		24
57.5	odd	18		855.2.da.b.784.1		48
95.9	even	18		1805.2.b.k.1084.23		24
95.24	even	18	inner	95.2.p.a.24.1	yes	48
95.28	odd	36		9025.2.a.cu.1.2		24
95.29	odd	18		1805.2.b.l.1084.2		24
95.43	odd	36		475.2.l.f.176.8		48
95.47	odd	36		9025.2.a.cu.1.23		24
95.48	even	36		9025.2.a.ct.1.23		24
95.62	odd	36		475.2.l.f.176.1		48
95.67	even	36		9025.2.a.ct.1.2		24
285.119	odd	18		855.2.da.b.784.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.1	✓	48	1.1	even	1	trivial
95.2.p.a.4.8	yes	48	5.4	even	2	inner
95.2.p.a.24.1	yes	48	95.24	even	18	inner
95.2.p.a.24.8	yes	48	19.5	even	9	inner
475.2.l.f.176.1		48	95.62	odd	36
475.2.l.f.176.8		48	95.43	odd	36
475.2.l.f.251.1		48	5.2	odd	4
475.2.l.f.251.8		48	5.3	odd	4
855.2.da.b.289.1		48	15.14	odd	2
855.2.da.b.289.8		48	3.2	odd	2
855.2.da.b.784.1		48	57.5	odd	18
855.2.da.b.784.8		48	285.119	odd	18
1805.2.b.k.1084.2		24	19.9	even	9
1805.2.b.k.1084.23		24	95.9	even	18
1805.2.b.l.1084.2		24	95.29	odd	18
1805.2.b.l.1084.23		24	19.10	odd	18
9025.2.a.ct.1.2		24	95.67	even	36
9025.2.a.ct.1.23		24	95.48	even	36
9025.2.a.cu.1.2		24	95.28	odd	36
9025.2.a.cu.1.23		24	95.47	odd	36

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.810919 + 2.22798i) q^{2} +(2.25040 - 0.396806i) q^{3} +(-2.77422 - 2.32785i) q^{4} +(2.12266 + 0.703088i) q^{5} +(-0.940815 + 5.33563i) q^{6} +(-1.41749 - 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(2.08777 - 0.759885i) q^{9} +O(q^{10})\)	\(q+(-0.810919 + 2.22798i) q^{2} +(2.25040 - 0.396806i) q^{3} +(-2.77422 - 2.32785i) q^{4} +(2.12266 + 0.703088i) q^{5} +(-0.940815 + 5.33563i) q^{6} +(-1.41749 - 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(2.08777 - 0.759885i) q^{9} +(-3.28777 + 4.15909i) q^{10} +(-1.36374 - 2.36206i) q^{11} +(-7.16682 - 4.13776i) q^{12} +(-6.10515 - 1.07650i) q^{13} +(2.97282 - 2.49449i) q^{14} +(5.05581 + 0.739946i) q^{15} +(0.325107 + 1.84377i) q^{16} +(-1.06864 + 2.93608i) q^{17} +5.26771i q^{18} +(3.46824 + 2.64032i) q^{19} +(-4.25204 - 6.89175i) q^{20} +(-3.51465 - 1.27923i) q^{21} +(6.36852 - 1.12294i) q^{22} +(4.69173 - 5.59139i) q^{23} +(6.72981 - 5.64698i) q^{24} +(4.01134 + 2.98483i) q^{25} +(7.34921 - 12.7292i) q^{26} +(-1.54012 + 0.889189i) q^{27} +(2.02734 + 5.57008i) q^{28} +(2.09149 - 0.761241i) q^{29} +(-5.74844 + 10.6642i) q^{30} +(-2.21333 + 3.83360i) q^{31} +(3.20067 + 0.564364i) q^{32} +(-4.00624 - 4.77445i) q^{33} +(-5.67494 - 4.76184i) q^{34} +(-2.43344 - 2.73377i) q^{35} +(-7.56083 - 2.75192i) q^{36} -2.04016i q^{37} +(-8.69505 + 5.58609i) q^{38} -14.1662 q^{39} +(8.41876 - 1.73939i) q^{40} +(0.681538 + 3.86519i) q^{41} +(5.70020 - 6.79323i) q^{42} +(-0.303946 - 0.362229i) q^{43} +(-1.71522 + 9.72747i) q^{44} +(4.96588 - 0.145091i) q^{45} +(8.65289 + 14.9872i) q^{46} +(-0.787194 - 2.16280i) q^{47} +(1.46324 + 4.02022i) q^{48} +(-2.16049 - 3.74208i) q^{49} +(-9.90301 + 6.51673i) q^{50} +(-1.23982 + 7.03139i) q^{51} +(14.4311 + 17.1983i) q^{52} +(-4.09062 + 4.87501i) q^{53} +(-0.732183 - 4.15242i) q^{54} +(-1.23401 - 5.97268i) q^{55} -6.29258 q^{56} +(8.85263 + 4.56556i) q^{57} +5.27711i q^{58} +(11.5263 + 4.19524i) q^{59} +(-12.3035 - 13.8220i) q^{60} +(-3.66993 - 3.07944i) q^{61} +(-6.74636 - 8.03999i) q^{62} +(-3.58126 - 0.631473i) q^{63} +(-5.72509 + 9.91615i) q^{64} +(-12.2023 - 6.57750i) q^{65} +(13.8861 - 5.05414i) q^{66} +(0.229482 + 0.630496i) q^{67} +(9.79940 - 5.65769i) q^{68} +(8.33957 - 14.4446i) q^{69} +(8.06411 - 3.20479i) q^{70} +(2.01848 - 1.69370i) q^{71} +(5.49040 - 6.54321i) q^{72} +(-6.41403 + 1.13097i) q^{73} +(4.54543 + 1.65440i) q^{74} +(10.2115 + 5.12533i) q^{75} +(-3.47540 - 15.3984i) q^{76} +4.46426i q^{77} +(11.4876 - 31.5620i) q^{78} +(-0.715459 - 4.05757i) q^{79} +(-0.606244 + 4.14227i) q^{80} +(-8.21894 + 6.89651i) q^{81} +(-9.16425 - 1.61590i) q^{82} +(5.56331 + 3.21198i) q^{83} +(6.77258 + 11.7304i) q^{84} +(-4.33268 + 5.48093i) q^{85} +(1.05351 - 0.383448i) q^{86} +(4.40463 - 2.54302i) q^{87} +(-9.08097 - 5.24290i) q^{88} +(-3.00487 + 17.0415i) q^{89} +(-3.70367 + 11.1815i) q^{90} +(7.77297 + 6.52229i) q^{91} +(-26.0318 + 4.59011i) q^{92} +(-3.45968 + 9.50539i) q^{93} +5.45702 q^{94} +(5.50550 + 8.04297i) q^{95} +7.42673 q^{96} +(-0.0444434 + 0.122107i) q^{97} +(10.0893 - 1.77901i) q^{98} +(-4.64207 - 3.89516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

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