LMFDB - Embedded newform 75.3.k.a.67.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.7
Character	$\chi$	$=$	75.67
Dual form			75.3.k.a.28.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.670302 - 1.31554i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(1.06979 + 1.47245i) q^{4} +(0.953987 + 4.90815i) q^{5} +(2.06891 + 1.50315i) q^{6} +(0.393993 + 0.393993i) q^{7} +(8.48731 - 1.34426i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(0.670302 - 1.31554i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(1.06979 + 1.47245i) q^{4} +(0.953987 + 4.90815i) q^{5} +(2.06891 + 1.50315i) q^{6} +(0.393993 + 0.393993i) q^{7} +(8.48731 - 1.34426i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(7.09633 + 2.03493i) q^{10} +(-6.51400 - 20.0480i) q^{11} +(-2.80882 + 1.43116i) q^{12} +(5.40231 + 10.6026i) q^{13} +(0.782409 - 0.254220i) q^{14} +(-8.65498 + 0.302135i) q^{15} +(1.67094 - 5.14262i) q^{16} +(-1.72521 - 10.8926i) q^{17} +(-3.13206 + 3.13206i) q^{18} +(1.70989 - 2.35346i) q^{19} +(-6.20641 + 6.65540i) q^{20} +(-0.780768 + 0.567261i) q^{21} +(-30.7404 - 4.86880i) q^{22} +(6.44790 + 3.28537i) q^{23} +14.8837i q^{24} +(-23.1798 + 9.36461i) q^{25} +17.5694 q^{26} +(2.35900 - 4.62981i) q^{27} +(-0.158642 + 1.00163i) q^{28} +(-24.8443 - 34.1952i) q^{29} +(-5.40398 + 11.5885i) q^{30} +(6.35836 + 4.61962i) q^{31} +(18.6597 + 18.6597i) q^{32} +(36.0617 - 5.71161i) q^{33} +(-15.4860 - 5.03172i) q^{34} +(-1.55791 + 2.30964i) q^{35} +(-1.68727 - 5.19289i) q^{36} +(-43.5956 + 22.2131i) q^{37} +(-1.94993 - 3.82695i) q^{38} +(-19.6020 + 6.36907i) q^{39} +(14.6946 + 40.3746i) q^{40} +(10.4762 - 32.2425i) q^{41} +(0.222906 + 1.40737i) q^{42} +(49.3109 - 49.3109i) q^{43} +(22.5510 - 31.0388i) q^{44} +(1.82822 - 14.8882i) q^{45} +(8.64408 - 6.28029i) q^{46} +(4.14042 + 0.655778i) q^{47} +(8.34487 + 4.25192i) q^{48} -48.6895i q^{49} +(-3.21794 + 36.7712i) q^{50} +19.1016 q^{51} +(-9.83244 + 19.2973i) q^{52} +(-14.6290 + 92.3640i) q^{53} +(-4.50946 - 6.20674i) q^{54} +(92.1844 - 51.0972i) q^{55} +(3.87357 + 2.81431i) q^{56} +(3.56282 + 3.56282i) q^{57} +(-61.6384 + 9.76256i) q^{58} +(12.2094 + 3.96708i) q^{59} +(-9.70393 - 12.4208i) q^{60} +(30.8453 + 94.9322i) q^{61} +(10.3393 - 5.26815i) q^{62} +(-0.758878 - 1.48938i) q^{63} +(57.6257 - 18.7237i) q^{64} +(-46.8856 + 36.6301i) q^{65} +(16.6584 - 51.2692i) q^{66} +(4.00146 + 25.2642i) q^{67} +(14.1931 - 14.1931i) q^{68} +(-7.36744 + 10.1404i) q^{69} +(1.99416 + 3.59766i) q^{70} +(-67.9173 + 49.3448i) q^{71} +(-25.4619 - 4.03277i) q^{72} +(-17.6189 - 8.97729i) q^{73} +72.2414i q^{74} +(-9.73966 - 42.1917i) q^{75} +5.29457 q^{76} +(5.33232 - 10.4653i) q^{77} +(-4.76047 + 30.0564i) q^{78} +(-40.2257 - 55.3659i) q^{79} +(26.8348 + 3.29522i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-35.3941 - 35.3941i) q^{82} +(-24.2550 + 3.84162i) q^{83} +(-1.67052 - 0.542786i) q^{84} +(51.8165 - 18.8590i) q^{85} +(-31.8174 - 97.9238i) q^{86} +(65.2302 - 33.2365i) q^{87} +(-82.2361 - 161.397i) q^{88} +(-105.862 + 34.3966i) q^{89} +(-18.3606 - 12.3847i) q^{90} +(-2.04889 + 6.30584i) q^{91} +(2.06040 + 13.0089i) q^{92} +(-9.62572 + 9.62572i) q^{93} +(3.63804 - 5.00733i) q^{94} +(13.1823 + 6.14721i) q^{95} +(-36.9775 + 26.8657i) q^{96} +(-28.1525 - 4.45891i) q^{97} +(-64.0531 - 32.6367i) q^{98} +63.2392i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.670302	−	1.31554i	0.335151	−	0.657771i	−0.660511	−	0.750817i	$-0.729660\pi$
$2$	0.670302	−	1.31554i	0.335151	−	0.657771i	0.995662	+	0.0930455i	$0.0296602\pi$
$3$	−0.270952	+	1.71073i	−0.0903175	+	0.570242i
$3$	−0.270952	+	1.71073i	−0.0903175	+	0.570242i
$4$	1.06979	+	1.47245i	0.267449	+	0.368112i
$5$	0.953987	+	4.90815i	0.190797	+	0.981629i
$5$	0.953987	+	4.90815i	0.190797	+	0.981629i
$6$	2.06891	+	1.50315i	0.344819	+	0.250526i
$7$	0.393993	+	0.393993i	0.0562848	+	0.0562848i	0.734689	−	0.678404i	$-0.237328\pi$
$7$	0.393993	+	0.393993i	0.0562848	+	0.0562848i	−0.678404	+	0.734689i	$0.737328\pi$
$8$	8.48731	−	1.34426i	1.06091	−	0.168032i
$9$	−2.85317	−	0.927051i	−0.317019	−	0.103006i
$10$	7.09633	+	2.03493i	0.709633	+	0.203493i
$11$	−6.51400	−	20.0480i	−0.592182	−	1.82255i	−0.568282	−	0.822834i	$-0.692392\pi$
$11$	−6.51400	−	20.0480i	−0.592182	−	1.82255i	−0.0238997	−	0.999714i	$-0.507608\pi$
$12$	−2.80882	+	1.43116i	−0.234068	+	0.119264i
$13$	5.40231	+	10.6026i	0.415563	+	0.815587i	0.999991	+	0.00414246i	$0.00131859\pi$
$13$	5.40231	+	10.6026i	0.415563	+	0.815587i	−0.584429	+	0.811445i	$0.698681\pi$
$14$	0.782409	−	0.254220i	0.0558864	−	0.0181586i
$15$	−8.65498	+	0.302135i	−0.576999	+	0.0201424i
$16$	1.67094	−	5.14262i	0.104434	−	0.321414i
$17$	−1.72521	−	10.8926i	−0.101483	−	0.640739i	−0.985028	−	0.172393i	$-0.944850\pi$
$17$	−1.72521	−	10.8926i	−0.101483	−	0.640739i	0.883545	−	0.468346i	$-0.155150\pi$
$18$	−3.13206	+	3.13206i	−0.174003	+	0.174003i
$19$	1.70989	−	2.35346i	0.0899940	−	0.123866i	−0.761646	−	0.647993i	$-0.775608\pi$
$19$	1.70989	−	2.35346i	0.0899940	−	0.123866i	0.851640	+	0.524127i	$0.175608\pi$
$20$	−6.20641	+	6.65540i	−0.310321	+	0.332770i
$21$	−0.780768	+	0.567261i	−0.0371794	+	0.0270124i
$22$	−30.7404	−	4.86880i	−1.39729	−	0.221309i
$23$	6.44790	+	3.28537i	0.280343	+	0.142842i	0.588509	−	0.808491i	$-0.299715\pi$
$23$	6.44790	+	3.28537i	0.280343	+	0.142842i	−0.308166	+	0.951333i	$0.599715\pi$
$24$			14.8837i			0.620154i
$25$	−23.1798	+	9.36461i	−0.927193	+	0.374585i
$26$	17.5694			0.675746
$27$	2.35900	−	4.62981i	0.0873705	−	0.171474i
$28$	−0.158642	+	1.00163i	−0.00566578	+	0.0357724i
$29$	−24.8443	−	34.1952i	−0.856698	−	1.17914i	−0.982347	−	0.187069i	$-0.940101\pi$
$29$	−24.8443	−	34.1952i	−0.856698	−	1.17914i	0.125648	−	0.992075i	$-0.459899\pi$
$30$	−5.40398	+	11.5885i	−0.180133	+	0.386284i
$31$	6.35836	+	4.61962i	0.205109	+	0.149020i	0.685598	−	0.727981i	$-0.259541\pi$
$31$	6.35836	+	4.61962i	0.205109	+	0.149020i	−0.480489	+	0.877001i	$0.659541\pi$
$32$	18.6597	+	18.6597i	0.583115	+	0.583115i
$33$	36.0617	−	5.71161i	1.09278	−	0.173079i
$34$	−15.4860	−	5.03172i	−0.455472	−	0.147992i
$35$	−1.55791	+	2.30964i	−0.0445118	+	0.0659898i
$36$	−1.68727	−	5.19289i	−0.0468687	−	0.144247i
$37$	−43.5956	+	22.2131i	−1.17826	+	0.600354i	−0.929720	−	0.368268i	$-0.879951\pi$
$37$	−43.5956	+	22.2131i	−1.17826	+	0.600354i	−0.248541	+	0.968621i	$0.579951\pi$
$38$	−1.94993	−	3.82695i	−0.0513140	−	0.100709i
$39$	−19.6020	+	6.36907i	−0.502615	+	0.163309i
$40$	14.6946	+	40.3746i	0.367365	+	1.00936i
$41$	10.4762	−	32.2425i	0.255517	−	0.786402i	−0.738210	−	0.674571i	$-0.764329\pi$
$41$	10.4762	−	32.2425i	0.255517	−	0.786402i	0.993727	−	0.111831i	$-0.0356714\pi$
$42$	0.222906	+	1.40737i	0.00530727	+	0.0335088i
$43$	49.3109	−	49.3109i	1.14677	−	1.14677i	0.159581	−	0.987185i	$-0.448986\pi$
$43$	49.3109	−	49.3109i	1.14677	−	1.14677i	0.987185	−	0.159581i	$-0.0510142\pi$
$44$	22.5510	−	31.0388i	0.512523	−	0.705427i
$45$	1.82822	−	14.8882i	0.0406271	−	0.330848i
$46$	8.64408	−	6.28029i	0.187915	−	0.136528i
$47$	4.14042	+	0.655778i	0.0880940	+	0.0139527i	0.200326	−	0.979729i	$-0.435800\pi$
$47$	4.14042	+	0.655778i	0.0880940	+	0.0139527i	−0.112232	+	0.993682i	$0.535800\pi$
$48$	8.34487	+	4.25192i	0.173851	+	0.0885817i
$49$		−	48.6895i		−	0.993664i
$50$	−3.21794	+	36.7712i	−0.0643588	+	0.735423i
$51$	19.1016			0.374542
$52$	−9.83244	+	19.2973i	−0.189085	+	0.371101i
$53$	−14.6290	+	92.3640i	−0.276019	+	1.74272i	0.327032	+	0.945013i	$0.393952\pi$
$53$	−14.6290	+	92.3640i	−0.276019	+	1.74272i	−0.603051	+	0.797703i	$0.706048\pi$
$54$	−4.50946	−	6.20674i	−0.0835085	−	0.114940i
$55$	92.1844	−	51.0972i	1.67608	−	0.929040i
$56$	3.87357	+	2.81431i	0.0691709	+	0.0502556i
$57$	3.56282	+	3.56282i	0.0625057	+	0.0625057i
$58$	−61.6384	+	9.76256i	−1.06273	+	0.168320i
$59$	12.2094	+	3.96708i	0.206939	+	0.0672387i	0.410652	−	0.911792i	$-0.365301\pi$
$59$	12.2094	+	3.96708i	0.206939	+	0.0672387i	−0.203713	+	0.979031i	$0.565301\pi$
$60$	−9.70393	−	12.4208i	−0.161732	−	0.207013i
$61$	30.8453	+	94.9322i	0.505661	+	1.55627i	0.799656	+	0.600459i	$0.205015\pi$
$61$	30.8453	+	94.9322i	0.505661	+	1.55627i	−0.293994	+	0.955807i	$0.594985\pi$
$62$	10.3393	−	5.26815i	0.166763	−	0.0849702i
$63$	−0.758878	−	1.48938i	−0.0120457	−	0.0236410i
$64$	57.6257	−	18.7237i	0.900401	−	0.292558i
$65$	−46.8856	+	36.6301i	−0.721316	+	0.563540i
$66$	16.6584	−	51.2692i	0.252399	−	0.776806i
$67$	4.00146	+	25.2642i	0.0597233	+	0.377078i	0.999388	+	0.0349811i	$0.0111371\pi$
$67$	4.00146	+	25.2642i	0.0597233	+	0.377078i	−0.939665	+	0.342097i	$0.888863\pi$
$68$	14.1931	−	14.1931i	0.208722	−	0.208722i
$69$	−7.36744	+	10.1404i	−0.106775	+	0.146963i
$70$	1.99416	+	3.59766i	0.0284880	+	0.0513951i
$71$	−67.9173	+	49.3448i	−0.956581	+	0.694997i	−0.952354	−	0.304994i	$-0.901345\pi$
$71$	−67.9173	+	49.3448i	−0.956581	+	0.694997i	−0.00422699	+	0.999991i	$0.501345\pi$
$72$	−25.4619	−	4.03277i	−0.353638	−	0.0560107i
$73$	−17.6189	−	8.97729i	−0.241355	−	0.122977i	0.329130	−	0.944285i	$-0.393245\pi$
$73$	−17.6189	−	8.97729i	−0.241355	−	0.122977i	−0.570485	+	0.821308i	$0.693245\pi$
$74$			72.2414i			0.976235i
$75$	−9.73966	−	42.1917i	−0.129862	−	0.562556i
$76$	5.29457			0.0696653
$77$	5.33232	−	10.4653i	0.0692509	−	0.135912i
$78$	−4.76047	+	30.0564i	−0.0610317	+	0.385339i
$79$	−40.2257	−	55.3659i	−0.509186	−	0.700834i	0.474596	−	0.880204i	$-0.342594\pi$
$79$	−40.2257	−	55.3659i	−0.509186	−	0.700834i	−0.983782	+	0.179370i	$0.942594\pi$
$80$	26.8348	+	3.29522i	0.335435	+	0.0411903i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	−35.3941	−	35.3941i	−0.431636	−	0.431636i
$83$	−24.2550	+	3.84162i	−0.292229	+	0.0462845i	−0.300828	−	0.953678i	$-0.597263\pi$
$83$	−24.2550	+	3.84162i	−0.292229	+	0.0462845i	0.00859867	+	0.999963i	$0.497263\pi$
$84$	−1.67052	−	0.542786i	−0.0198872	−	0.00646174i
$85$	51.8165	−	18.8590i	0.609606	−	0.221870i
$86$	−31.8174	−	97.9238i	−0.369970	−	1.13865i
$87$	65.2302	−	33.2365i	0.749773	−	0.382028i
$88$	−82.2361	−	161.397i	−0.934501	−	1.83406i
$89$	−105.862	+	34.3966i	−1.18946	+	0.386478i	−0.835872	−	0.548924i	$-0.815038\pi$
$89$	−105.862	+	34.3966i	−1.18946	+	0.386478i	−0.353586	+	0.935402i	$0.615038\pi$
$90$	−18.3606	−	12.3847i	−0.204006	−	0.137607i
$91$	−2.04889	+	6.30584i	−0.0225153	+	0.0692950i
$92$	2.06040	+	13.0089i	0.0223957	+	0.141401i
$93$	−9.62572	+	9.62572i	−0.103502	+	0.103502i
$94$	3.63804	−	5.00733i	0.0387025	−	0.0532694i
$95$	13.1823	+	6.14721i	0.138761	+	0.0647075i
$96$	−36.9775	+	26.8657i	−0.385182	+	0.279851i
$97$	−28.1525	−	4.45891i	−0.290231	−	0.0459682i	0.00962105	−	0.999954i	$-0.496937\pi$
$97$	−28.1525	−	4.45891i	−0.290231	−	0.0459682i	−0.299853	+	0.953986i	$0.596937\pi$
$98$	−64.0531	−	32.6367i	−0.653604	−	0.333028i
$99$			63.2392i			0.638780i
$100$	−38.5865	−	24.1128i	−0.385865	−	0.241128i
$101$	−66.1639			−0.655088			−0.327544	−	0.944836i	$-0.606221\pi$
$101$	−66.1639			−0.655088			−0.327544	+	0.944836i	$0.606221\pi$
$102$	12.8039	−	25.1290i	0.125528	−	0.246363i
$103$	−8.56735	+	54.0921i	−0.0831781	+	0.525166i	0.910555	+	0.413388i	$0.135655\pi$
$103$	−8.56735	+	54.0921i	−0.0831781	+	0.525166i	−0.993733	+	0.111778i	$0.964345\pi$
$104$	60.1038	+	82.7258i	0.577921	+	0.795440i
$105$	−3.52904	−	3.29097i	−0.0336099	−	0.0313425i
$106$	111.703	+	81.1569i	1.05380	+	0.765631i
$107$	16.8454	+	16.8454i	0.157434	+	0.157434i	0.781429	−	0.623995i	$-0.214491\pi$
$107$	16.8454	+	16.8454i	0.157434	+	0.157434i	−0.623995	+	0.781429i	$0.714491\pi$
$108$	9.34079	−	1.47944i	0.0864888	−	0.0136985i
$109$	173.684	+	56.4335i	1.59344	+	0.517739i	0.965473	−	0.260505i	$-0.0838890\pi$
$109$	173.684	+	56.4335i	1.59344	+	0.517739i	0.627963	+	0.778243i	$0.283889\pi$
$110$	−5.42913	−	155.523i	−0.0493557	−	1.41385i
$111$	−26.1882	−	80.5989i	−0.235929	−	0.726116i
$112$	2.68450	−	1.36782i	0.0239687	−	0.0122127i
$113$	35.1536	+	68.9928i	0.311094	+	0.610555i	0.992624	−	0.121234i	$-0.0386853\pi$
$113$	35.1536	+	68.9928i	0.311094	+	0.610555i	−0.681530	+	0.731790i	$0.738685\pi$
$114$	7.07521	−	2.29888i	0.0620633	−	0.0201656i
$115$	−9.97387	+	34.7814i	−0.0867293	+	0.302447i
$116$	23.7723	−	73.1637i	0.204934	−	0.630721i
$117$	−5.58453	−	35.2593i	−0.0477310	−	0.301362i
$118$	13.4029	−	13.4029i	0.113584	−	0.113584i
$119$	3.61188	−	4.97132i	0.0303519	−	0.0417758i
$120$	−73.0514	+	14.1988i	−0.608761	+	0.118324i
$121$	−261.600	+	190.064i	−2.16199	+	1.57077i
$122$	145.563	+	23.0549i	1.19314	+	0.188975i
$123$	52.3195	+	26.6581i	0.425362	+	0.216733i
$124$			14.3044i			0.115358i
$125$	−68.0761	−	104.836i	−0.544609	−	0.838690i
$126$	−2.46802			−0.0195875
$127$	45.4714	−	89.2427i	0.358043	−	0.702698i	−0.639787	−	0.768553i	$-0.720977\pi$
$127$	45.4714	−	89.2427i	0.358043	−	0.702698i	0.997829	+	0.0658545i	$0.0209773\pi$
$128$	−2.51767	+	15.8959i	−0.0196693	+	0.124187i
$129$	70.9966	+	97.7184i	0.550361	+	0.757507i
$130$	16.7610	+	86.2332i	0.128931	+	0.663332i
$131$	166.681	+	121.101i	1.27237	+	0.924433i	0.999294	−	0.0375590i	$-0.0119582\pi$
$131$	166.681	+	121.101i	1.27237	+	0.924433i	0.273078	+	0.961992i	$0.411958\pi$
$132$	46.9886	+	46.9886i	0.355974	+	0.355974i
$133$	1.60093	−	0.253562i	0.0120371	−	0.00190648i
$134$	35.9183	+	11.6706i	0.268047	+	0.0870938i
$135$	24.9742	+	7.16157i	0.184994	+	0.0530486i
$136$	−29.2848	−	90.1294i	−0.215330	−	0.662716i
$137$	83.3000	−	42.4434i	0.608029	−	0.309806i	−0.122732	−	0.992440i	$-0.539166\pi$
$137$	83.3000	−	42.4434i	0.608029	−	0.309806i	0.730761	+	0.682634i	$0.239166\pi$
$138$	8.40173	+	16.4893i	0.0608821	+	0.119488i
$139$	−56.9994	+	18.5202i	−0.410068	+	0.133239i	−0.506784	−	0.862073i	$-0.669166\pi$
$139$	−56.9994	+	18.5202i	−0.410068	+	0.133239i	0.0967167	+	0.995312i	$0.469166\pi$
$140$	−5.06747	+	0.176900i	−0.0361962	+	0.00126357i
$141$	−2.24371	+	6.90544i	−0.0159129	+	0.0489748i
$142$	19.3900	+	122.424i	0.136550	+	0.862141i
$143$	177.371	−	177.371i	1.24036	−	1.24036i
$144$	−9.53494	+	13.1237i	−0.0662148	+	0.0911369i
$145$	144.134	−	154.561i	0.994027	−	1.06594i
$146$	−23.6200	+	17.1609i	−0.161781	+	0.117541i
$147$	83.2945	+	13.1925i	0.566629	+	0.0897452i
$148$	−79.3460	−	40.4288i	−0.536121	−	0.273168i
$149$			104.435i			0.700905i	0.936580	+	0.350453i	$0.113972\pi$
$149$			104.435i			0.700905i	−0.936580	+	0.350453i	$0.886028\pi$
$150$	−62.0335	−	15.4683i	−0.413556	−	0.103122i
$151$	−50.7197			−0.335892			−0.167946	−	0.985796i	$-0.553713\pi$
$151$	−50.7197			−0.335892			−0.167946	+	0.985796i	$0.553713\pi$
$152$	11.3487	−	22.2730i	0.0746624	−	0.146533i
$153$	−5.17564	+	32.6777i	−0.0338277	+	0.213580i
$154$	−10.1932	−	14.0298i	−0.0661898	−	0.0911025i
$155$	−16.6080	+	35.6148i	−0.107148	+	0.229773i
$156$	−30.3482	−	22.0493i	−0.194540	−	0.141341i
$157$	14.5163	+	14.5163i	0.0924608	+	0.0924608i	0.751824	−	0.659364i	$-0.229174\pi$
$157$	14.5163	+	14.5163i	0.0924608	+	0.0924608i	−0.659364	+	0.751824i	$0.729174\pi$
$158$	−99.7996	+	15.8067i	−0.631643	+	0.100042i
$159$	−154.046	−	50.0525i	−0.968841	−	0.314795i
$160$	−73.7834	+	109.386i	−0.461146	+	0.683659i
$161$	1.24602	+	3.83484i	0.00773923	+	0.0238189i
$162$	11.8399	−	6.03272i	0.0730857	−	0.0372390i
$163$	−101.124	−	198.466i	−0.620390	−	1.21758i	−0.960783	−	0.277301i	$-0.910560\pi$
$163$	−101.124	−	198.466i	−0.620390	−	1.21758i	0.340393	−	0.940283i	$-0.389440\pi$
$164$	58.6827	−	19.0672i	0.357821	−	0.116263i
$165$	62.4358	+	171.547i	0.378399	+	1.03968i
$166$	−11.2044	+	34.4835i	−0.0674963	+	0.207732i
$167$	−51.4260	−	324.691i	−0.307940	−	1.94426i	−0.328592	−	0.944472i	$-0.606574\pi$
$167$	−51.4260	−	324.691i	−0.307940	−	1.94426i	0.0206519	−	0.999787i	$-0.493426\pi$
$168$	−5.86408	+	5.86408i	−0.0349052	+	0.0349052i
$169$	16.1048	−	22.1664i	0.0952947	−	0.131162i
$170$	9.92295	−	80.8080i	0.0583703	−	0.475341i
$171$	−7.06037	+	5.12966i	−0.0412887	+	0.0299980i
$172$	125.360	+	19.8551i	0.728839	+	0.115437i
$173$	98.9952	+	50.4406i	0.572227	+	0.291564i	0.716061	−	0.698038i	$-0.245943\pi$
$173$	98.9952	+	50.4406i	0.572227	+	0.291564i	−0.143834	+	0.989602i	$0.545943\pi$
$174$		−	108.092i		−	0.621216i
$175$	−12.8223	−	5.44310i	−0.0732702	−	0.0311034i
$176$	−113.984			−0.647635
$177$	−10.0948	+	19.8121i	−0.0570326	+	0.111933i
$178$	−25.7092	+	162.322i	−0.144434	+	0.911920i
$179$	−41.9277	−	57.7085i	−0.234233	−	0.322394i	0.675679	−	0.737196i	$-0.263851\pi$
$179$	−41.9277	−	57.7085i	−0.234233	−	0.322394i	−0.909912	+	0.414802i	$0.863851\pi$
$180$	23.8778	−	13.2353i	0.132655	−	0.0735296i
$181$	88.8537	+	64.5560i	0.490904	+	0.356663i	0.805532	−	0.592552i	$-0.201880\pi$
$181$	88.8537	+	64.5560i	0.490904	+	0.356663i	−0.314628	+	0.949215i	$0.601880\pi$
$182$	6.92223	+	6.92223i	0.0380342	+	0.0380342i
$183$	−170.761	+	27.0458i	−0.933119	+	0.147791i
$184$	59.1417	+	19.2163i	0.321422	+	0.104436i
$185$	−150.615	−	192.783i	−0.814134	−	1.04207i
$186$	6.21090	+	19.1152i	0.0333919	+	0.102770i
$187$	−207.136	+	105.541i	−1.10768	+	0.564392i
$188$	3.46380	+	6.79809i	0.0184245	+	0.0361601i
$189$	2.75354	−	0.894681i	0.0145690	−	0.00473376i
$190$	16.9231	−	13.2214i	0.0890687	−	0.0695864i
$191$	−3.32599	+	10.2364i	−0.0174136	+	0.0535935i	−0.959386	−	0.282098i	$-0.908970\pi$
$191$	−3.32599	+	10.2364i	−0.0174136	+	0.0535935i	0.941972	+	0.335691i	$0.108970\pi$
$192$	16.4173	+	103.655i	0.0855070	+	0.539870i
$193$	−165.738	+	165.738i	−0.858747	+	0.858747i	−0.991191	−	0.132444i	$-0.957718\pi$
$193$	−165.738	+	165.738i	−0.858747	+	0.858747i	0.132444	+	0.991191i	$0.457718\pi$
$194$	−24.7365	+	34.0469i	−0.127508	+	0.175500i
$195$	−49.9604	−	90.1334i	−0.256207	−	0.462223i
$196$	71.6927	−	52.0878i	0.365779	−	0.265754i
$197$	−189.915	−	30.0796i	−0.964035	−	0.152688i	−0.345477	−	0.938427i	$-0.612283\pi$
$197$	−189.915	−	30.0796i	−0.964035	−	0.152688i	−0.618558	+	0.785739i	$0.712283\pi$
$198$	83.1939	+	42.3894i	0.420171	+	0.214088i
$199$		−	250.497i		−	1.25878i	−0.777090	−	0.629390i	$-0.783305\pi$
$199$		−	250.497i		−	1.25878i	0.777090	−	0.629390i	$-0.216695\pi$
$200$	−184.146	+	110.640i	−0.920729	+	0.553200i
$201$	−44.3044			−0.220420
$202$	−44.3498	+	87.0415i	−0.219554	+	0.430898i
$203$	3.68420	−	23.2611i	0.0181488	−	0.114587i
$204$	20.4348	+	28.1261i	0.100171	+	0.137873i
$205$	168.245	+	20.6599i	0.820707	+	0.100780i
$206$	65.4177	+	47.5288i	0.317562	+	0.230722i
$207$	−15.3512	−	15.3512i	−0.0741606	−	0.0741606i
$208$	63.5522	−	10.0657i	0.305540	−	0.0483927i
$209$	−58.3204	−	18.9494i	−0.279045	−	0.0906672i
$210$	−6.69493	+	2.43667i	−0.0318806	+	0.0116032i
$211$	−69.5547	−	214.067i	−0.329643	−	1.01454i	−0.969301	−	0.245877i	$-0.920924\pi$
$211$	−69.5547	−	214.067i	−0.329643	−	1.01454i	0.639658	−	0.768660i	$-0.279076\pi$
$212$	−151.651	+	77.2700i	−0.715335	+	0.364481i
$213$	−66.0131	−	129.558i	−0.309921	−	0.608253i
$214$	33.4524	−	10.8693i	0.156320	−	0.0507913i
$215$	289.067	+	194.983i	1.34450	+	0.906899i
$216$	13.7979	−	42.4657i	0.0638794	−	0.196600i
$217$	0.685053	+	4.32525i	0.00315693	+	0.0199320i
$218$	190.662	−	190.662i	0.874595	−	0.874595i
$219$	20.1316	−	27.7088i	0.0919251	−	0.126524i
$220$	173.856	+	81.0730i	0.790256	+	0.368514i
$221$	106.170	−	77.1368i	0.480406	−	0.349035i
$222$	−123.585	−	19.5740i	−0.556690	−	0.0881711i
$223$	336.307	+	171.357i	1.50811	+	0.768418i	0.995901	−	0.0904458i	$-0.0288292\pi$
$223$	336.307	+	171.357i	1.50811	+	0.768418i	0.512204	+	0.858864i	$0.328829\pi$
$224$			14.7036i			0.0656410i
$225$	74.8174	−	5.22995i	0.332522	−	0.0232442i
$226$	114.326			0.505869
$227$	−143.467	+	281.569i	−0.632011	+	1.24039i	0.323721	+	0.946153i	$0.395066\pi$
$227$	−143.467	+	281.569i	−0.632011	+	1.24039i	−0.955732	+	0.294239i	$0.904934\pi$
$228$	−1.43458	+	9.05755i	−0.00629200	+	0.0397261i
$229$	−23.3868	−	32.1891i	−0.102126	−	0.140564i	0.754896	−	0.655845i	$-0.227688\pi$
$229$	−23.3868	−	32.1891i	−0.102126	−	0.140564i	−0.857021	+	0.515281i	$0.827688\pi$
$230$	39.0710	+	36.4351i	0.169874	+	0.158414i
$231$	16.4584	+	11.9577i	0.0712485	+	0.0517650i
$232$	−256.828	−	256.828i	−1.10702	−	1.10702i
$233$	−297.145	+	47.0631i	−1.27530	+	0.201988i	−0.757116	−	0.653281i	$-0.773392\pi$
$233$	−297.145	+	47.0631i	−1.27530	+	0.201988i	−0.518185	+	0.855269i	$0.673392\pi$
$234$	−50.1285	−	16.2877i	−0.214224	−	0.0696057i
$235$	0.731249	+	20.9474i	0.00311170	+	0.0891378i
$236$	7.22026	+	22.2217i	0.0305943	+	0.0941597i
$237$	105.615	−	53.8136i	0.445634	−	0.227062i
$238$	−4.11893	−	8.08386i	−0.0173064	−	0.0339658i
$239$	−215.295	+	69.9535i	−0.900815	+	0.292693i	−0.722573	−	0.691294i	$-0.757041\pi$
$239$	−215.295	+	69.9535i	−0.900815	+	0.292693i	−0.178242	+	0.983987i	$0.557041\pi$
$240$	−12.9082	+	45.0141i	−0.0537840	+	0.187559i
$241$	95.8777	−	295.081i	0.397833	−	1.22440i	−0.528900	−	0.848684i	$-0.677396\pi$
$241$	95.8777	−	295.081i	0.397833	−	1.22440i	0.926733	−	0.375720i	$-0.122604\pi$
$242$	74.6856	+	471.546i	0.308618	+	1.94854i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$	−106.784	+	146.976i	−0.437641	+	0.602361i
$245$	238.975	−	46.4492i	0.975410	−	0.189588i
$246$	70.1398	−	50.9595i	0.285121	−	0.207153i
$247$	34.1902	+	5.41519i	0.138422	+	0.0219239i
$248$	60.1754	+	30.6609i	0.242643	+	0.123633i
$249$		−	42.5346i		−	0.170822i
$250$	−183.548	+	19.2851i	−0.734192	+	0.0771402i
$251$	373.505			1.48807			0.744034	−	0.668142i	$-0.232910\pi$
$251$	373.505			1.48807			0.744034	+	0.668142i	$0.232910\pi$
$252$	1.38119	−	2.71074i	0.00548092	−	0.0107569i
$253$	23.8636	−	150.669i	0.0943224	−	0.595528i
$254$	−86.9229	−	119.639i	−0.342216	−	0.471020i
$255$	18.2227	+	93.7537i	0.0714616	+	0.367662i
$256$	215.302	+	156.426i	0.841022	+	0.611038i
$257$	−156.641	−	156.641i	−0.609499	−	0.609499i	0.333316	−	0.942815i	$-0.391832\pi$
$257$	−156.641	−	156.641i	−0.609499	−	0.609499i	−0.942815	+	0.333316i	$0.891832\pi$
$258$	176.142	−	27.8981i	0.682720	−	0.108132i
$259$	−25.9282	−	8.42458i	−0.100109	−	0.0325274i
$260$	−104.094	−	29.8498i	−0.400361	−	0.114807i
$261$	39.1842	+	120.597i	0.150131	+	0.462056i
$262$	271.040	−	138.102i	1.03450	−	0.527105i
$263$	116.163	+	227.982i	0.441683	+	0.866852i	0.999324	+	0.0367698i	$0.0117068\pi$
$263$	116.163	+	227.982i	0.441683	+	0.866852i	−0.557640	+	0.830083i	$0.688293\pi$
$264$	298.389	−	96.9524i	1.13026	−	0.367244i
$265$	−467.292	+	16.3126i	−1.76337	+	0.0615571i
$266$	0.739535	−	2.27605i	0.00278021	−	0.00855660i
$267$	−30.1596	−	190.420i	−0.112957	−	0.713185i
$268$	−32.9195	+	32.9195i	−0.122834	+	0.122834i
$269$	178.232	−	245.316i	0.662573	−	0.911954i	−0.336990	−	0.941508i	$-0.609409\pi$
$269$	178.232	−	245.316i	0.662573	−	0.911954i	0.999563	+	0.0295543i	$0.00940881\pi$
$270$	26.1616	−	28.0542i	0.0968949	−	0.103905i
$271$	−163.460	+	118.761i	−0.603173	+	0.438231i	−0.847004	−	0.531587i	$-0.821596\pi$
$271$	−163.460	+	118.761i	−0.603173	+	0.438231i	0.243830	+	0.969818i	$0.421596\pi$
$272$	−58.8990	−	9.32869i	−0.216540	−	0.0342966i
$273$	−10.2324	−	5.21368i	−0.0374814	−	0.0190977i
$274$		−	138.035i		−	0.503776i
$275$	338.735	+	403.709i	1.23177	+	1.46803i
$276$	−22.8129			−0.0826553
$277$	−4.98529	+	9.78418i	−0.0179974	+	0.0353220i	−0.899830	−	0.436240i	$-0.856310\pi$
$277$	−4.98529	+	9.78418i	−0.0179974	+	0.0353220i	0.881833	+	0.471562i	$0.156310\pi$
$278$	−13.8427	+	87.3992i	−0.0497938	+	0.314386i
$279$	−13.8589	−	19.0751i	−0.0496734	−	0.0683695i
$280$	−10.1177	+	21.6969i	−0.0361348	+	0.0774889i
$281$	120.286	+	87.3927i	0.428063	+	0.311006i	0.780874	−	0.624689i	$-0.214774\pi$
$281$	120.286	+	87.3927i	0.428063	+	0.311006i	−0.352811	+	0.935695i	$0.614774\pi$
$282$	7.58043	+	7.58043i	0.0268810	+	0.0268810i
$283$	124.962	−	19.7920i	0.441560	−	0.0699363i	0.0683040	−	0.997665i	$-0.478241\pi$
$283$	124.962	−	19.7920i	0.441560	−	0.0699363i	0.373256	+	0.927728i	$0.378241\pi$
$284$	−145.315	−	47.2157i	−0.511673	−	0.166253i
$285$	−14.0880	+	20.8857i	−0.0494315	+	0.0732833i
$286$	−114.447	−	352.232i	−0.400165	−	1.23158i
$287$	16.8309	−	8.57576i	0.0586442	−	0.0298807i
$288$	−35.9407	−	70.5377i	−0.124794	−	0.244923i
$289$	159.184	−	51.7219i	0.550809	−	0.178969i
$290$	−106.718	−	293.217i	−0.367994	−	1.01109i
$291$	15.2560	−	46.9530i	0.0524260	−	0.161350i
$292$	−5.63006	−	35.5468i	−0.0192810	−	0.121736i
$293$	41.4386	−	41.4386i	0.141429	−	0.141429i	−0.632848	−	0.774276i	$-0.718114\pi$
$293$	41.4386	−	41.4386i	0.141429	−	0.141429i	0.774276	+	0.632848i	$0.218114\pi$
$294$	73.1878	−	100.734i	0.248938	−	0.342634i
$295$	−7.82340	+	63.7102i	−0.0265200	+	0.215967i
$296$	−340.150	+	247.133i	−1.14915	+	0.834909i
$297$	−108.185	−	17.1348i	−0.364259	−	0.0576930i
$298$	137.389	+	70.0030i	0.461035	+	0.234909i
$299$			86.1133i			0.288004i
$300$	51.7056	−	59.4776i	0.172352	−	0.198259i
$301$	38.8563			0.129091
$302$	−33.9975	+	66.7239i	−0.112575	+	0.220940i
$303$	17.9273	−	113.188i	0.0591659	−	0.373559i
$304$	−9.24581	−	12.7258i	−0.0304139	−	0.0418611i
$305$	−436.515	+	241.958i	−1.43120	+	0.793304i
$306$	39.5196	+	28.7127i	0.129149	+	0.0938324i
$307$	226.358	+	226.358i	0.737321	+	0.737321i	0.972059	−	0.234738i	$-0.0754231\pi$
$307$	226.358	+	226.358i	0.737321	+	0.737321i	−0.234738	+	0.972059i	$0.575423\pi$
$308$	21.1140	−	3.34413i	0.0685520	−	0.0108576i
$309$	−90.2154	−	29.3128i	−0.291959	−	0.0948633i
$310$	35.7205	+	45.7212i	0.115227	+	0.147488i
$311$	−87.6519	−	269.765i	−0.281839	−	0.867411i	−0.987328	−	0.158690i	$-0.949273\pi$
$311$	−87.6519	−	269.765i	−0.281839	−	0.867411i	0.705490	−	0.708720i	$-0.250727\pi$
$312$	−157.806	+	80.4064i	−0.505790	+	0.257713i
$313$	234.750	+	460.724i	0.750001	+	1.47196i	0.877222	+	0.480086i	$0.159394\pi$
$313$	234.750	+	460.724i	0.750001	+	1.47196i	−0.127220	+	0.991874i	$0.540606\pi$
$314$	28.8272	−	9.36653i	0.0918064	−	0.0298297i
$315$	6.58615	−	5.14553i	0.0209084	−	0.0163350i
$316$	38.4901	−	118.460i	0.121804	−	0.374874i
$317$	−33.8794	−	213.906i	−0.106875	−	0.674784i	−0.981713	−	0.190367i	$-0.939032\pi$
$317$	−33.8794	−	213.906i	−0.106875	−	0.674784i	0.874838	−	0.484416i	$-0.160968\pi$
$318$	−169.103	+	169.103i	−0.531771	+	0.531771i
$319$	−523.711	+	720.826i	−1.64173	+	2.25964i
$320$	146.873	+	264.973i	0.458978	+	0.828041i
$321$	−33.3822	+	24.2536i	−0.103995	+	0.0755564i
$322$	5.88011	+	0.931317i	0.0182612	+	0.00289229i
$323$	−28.5851	−	14.5648i	−0.0884987	−	0.0450924i
$324$			16.3804i			0.0505568i
$325$	−224.514	−	195.177i	−0.690813	−	0.600543i
$326$	−328.874			−1.00882
$327$	−143.603	+	281.836i	−0.439151	+	0.861883i
$328$	45.5727	−	287.735i	0.138941	−	0.877240i
$329$	1.37293	+	1.88967i	0.00417303	+	0.00574368i
$330$	267.528	+	32.8516i	0.810692	+	0.0995503i
$331$	−329.061	−	239.077i	−0.994143	−	0.722287i	−0.0333183	−	0.999445i	$-0.510608\pi$
$331$	−329.061	−	239.077i	−0.994143	−	0.722287i	−0.960824	+	0.277158i	$0.910608\pi$
$332$	−31.6045	−	31.6045i	−0.0951942	−	0.0951942i
$333$	144.978	−	22.9623i	0.435371	−	0.0689559i
$334$	−461.616	−	149.988i	−1.38208	−	0.449066i
$335$	−120.183	+	43.7415i	−0.358756	+	0.130572i
$336$	1.61259	+	4.96305i	0.00479938	+	0.0147710i
$337$	26.5837	−	13.5451i	0.0788833	−	0.0401930i	−0.414104	−	0.910230i	$-0.635905\pi$
$337$	26.5837	−	13.5451i	0.0788833	−	0.0401930i	0.492987	+	0.870037i	$0.335905\pi$
$338$	−18.3657	−	36.0447i	−0.0543364	−	0.106641i
$339$	−127.553	+	41.4444i	−0.376262	+	0.122255i
$340$	83.2018	+	56.1218i	0.244711	+	0.165064i
$341$	51.1959	−	157.565i	0.150135	−	0.462067i
$342$	2.01570	+	12.7266i	0.00589386	+	0.0372124i
$343$	38.4890	−	38.4890i	0.112213	−	0.112213i
$344$	352.230	−	484.804i	1.02393	−	1.40931i
$345$	−56.7991	−	26.4867i	−0.164635	−	0.0767730i
$346$	132.713	−	96.4220i	0.383565	−	0.278676i
$347$	11.9494	+	1.89259i	0.0344362	+	0.00545416i	0.173629	−	0.984811i	$-0.444451\pi$
$347$	11.9494	+	1.89259i	0.0344362	+	0.00545416i	−0.139193	+	0.990265i	$0.544451\pi$
$348$	118.722	+	60.4918i	0.341155	+	0.173827i
$349$		−	206.289i		−	0.591086i	−0.955329	−	0.295543i	$-0.904499\pi$
$349$		−	206.289i		−	0.591086i	0.955329	−	0.295543i	$-0.0955006\pi$
$350$	−15.7554	+	13.2197i	−0.0450155	+	0.0377707i
$351$	61.8322			0.176160
$352$	252.541	−	495.639i	0.717445	−	1.40806i
$353$	26.1311	−	164.985i	0.0740258	−	0.467381i	−0.922631	−	0.385683i	$-0.873966\pi$
$353$	26.1311	−	164.985i	0.0740258	−	0.467381i	0.996657	−	0.0816976i	$-0.0260342\pi$
$354$	19.2971	+	26.5602i	0.0545116	+	0.0750288i
$355$	−306.984	−	286.274i	−0.864743	−	0.806405i
$356$	−163.897	−	119.078i	−0.460386	−	0.334490i
$357$	7.52592	+	7.52592i	0.0210810	+	0.0210810i
$358$	−104.022	+	16.4755i	−0.290565	+	0.0460209i
$359$	342.021	+	111.129i	0.952704	+	0.309552i	0.743814	−	0.668387i	$-0.233015\pi$
$359$	342.021	+	111.129i	0.952704	+	0.309552i	0.208890	+	0.977939i	$0.433015\pi$
$360$	−4.49689	−	128.818i	−0.0124914	−	0.357828i
$361$	108.940	+	335.283i	0.301773	+	0.928762i
$362$	144.485	−	73.6187i	0.399130	−	0.203367i
$363$	−254.266	−	499.025i	−0.700457	−	1.37472i
$364$	−11.4769	+	3.72907i	−0.0315300	+	0.0102447i
$365$	27.2537	−	95.0405i	0.0746676	−	0.260385i
$366$	−78.8813	+	242.772i	−0.215523	+	0.663311i
$367$	16.1515	+	101.976i	0.0440094	+	0.277865i	0.999873	−	0.0159468i	$-0.00507624\pi$
$367$	16.1515	+	101.976i	0.0440094	+	0.277865i	−0.955863	+	0.293811i	$0.905076\pi$
$368$	27.6694	−	27.6694i	0.0751887	−	0.0751887i
$369$	−59.7808	+	82.2813i	−0.162008	+	0.222984i
$370$	−354.571	+	68.9173i	−0.958301	+	0.186263i
$371$	−42.1545	+	30.6270i	−0.113624	+	0.0825527i
$372$	−24.4709	−	3.87581i	−0.0657820	−	0.0104188i
$373$	421.303	+	214.665i	1.12950	+	0.575509i	0.915898	−	0.401412i	$-0.131480\pi$
$373$	421.303	+	214.665i	1.12950	+	0.575509i	0.213602	+	0.976921i	$0.431480\pi$
$374$			343.241i			0.917757i
$375$	197.792	−	88.0540i	0.527444	−	0.234811i
$376$	36.0226			0.0958047
$377$	228.343	−	448.148i	0.605683	−	1.18872i
$378$	0.668717	−	4.22211i	0.00176909	−	0.0111696i
$379$	241.950	+	333.015i	0.638390	+	0.878668i	0.998528	−	0.0542306i	$-0.0172706\pi$
$379$	241.950	+	333.015i	0.638390	+	0.878668i	−0.360139	+	0.932899i	$0.617271\pi$
$380$	5.05094	+	25.9865i	0.0132920	+	0.0683855i
$381$	140.349	+	101.970i	0.368371	+	0.267637i
$382$	11.2369	+	11.2369i	0.0294161	+	0.0294161i
$383$	−565.560	+	89.5759i	−1.47666	+	0.233880i	−0.842237	−	0.539108i	$-0.818761\pi$
$383$	−565.560	+	89.5759i	−1.47666	+	0.233880i	−0.634421	+	0.772988i	$0.718761\pi$
$384$	−26.5114	−	8.61408i	−0.0690402	−	0.0224325i
$385$	56.4520	+	16.1881i	0.146629	+	0.0420470i
$386$	106.941	+	329.130i	0.277049	+	0.852669i
$387$	−186.406	+	94.9787i	−0.481670	+	0.245423i
$388$	−23.5518	−	46.2231i	−0.0607006	−	0.119132i
$389$	304.232	−	98.8510i	0.782087	−	0.254116i	0.109356	−	0.994003i	$-0.465121\pi$
$389$	304.232	−	98.8510i	0.782087	−	0.254116i	0.672731	+	0.739887i	$0.265121\pi$
$390$	−152.063	+	5.30834i	−0.389905	+	0.0136111i
$391$	24.6621	−	75.9021i	0.0630744	−	0.194123i
$392$	−65.4513	−	413.243i	−0.166968	−	1.05419i
$393$	−252.333	+	252.333i	−0.642068	+	0.642068i
$394$	−166.871	+	229.679i	−0.423531	+	0.582941i
$395$	233.369	−	250.252i	0.590808	−	0.633549i
$396$	−93.1164	+	67.6530i	−0.235142	+	0.170841i
$397$	490.179	+	77.6368i	1.23471	+	0.195559i	0.739465	−	0.673195i	$-0.235079\pi$
$397$	490.179	+	77.6368i	1.23471	+	0.195559i	0.495244	+	0.868754i	$0.335079\pi$
$398$	−329.540	−	167.909i	−0.827989	−	0.421881i
$399$			2.80746i			0.00703623i
$400$	9.42659	+	134.853i	0.0235665	+	0.337132i
$401$	113.589			0.283264			0.141632	−	0.989919i	$-0.454765\pi$
$401$	113.589			0.283264			0.141632	+	0.989919i	$0.454765\pi$
$402$	−29.6973	+	58.2843i	−0.0738739	+	0.144986i
$403$	−14.6303	+	92.3721i	−0.0363035	+	0.229211i
$404$	−70.7818	−	97.4228i	−0.175203	−	0.241146i
$405$	−19.0183	+	40.7836i	−0.0469588	+	0.100700i
$406$	−28.1315	−	20.4387i	−0.0692894	−	0.0503417i
$407$	729.311	+	729.311i	1.79192	+	1.79192i
$408$	162.122	−	25.6775i	0.397357	−	0.0629351i
$409$	463.198	+	150.502i	1.13251	+	0.367976i	0.814530	−	0.580121i	$-0.196995\pi$
$409$	463.198	+	150.502i	1.13251	+	0.367976i	0.317982	+	0.948097i	$0.396995\pi$
$410$	139.954	−	207.485i	0.341351	−	0.506061i
$411$	50.0388	+	154.004i	0.121749	+	0.374705i
$412$	−88.8130	+	45.2525i	−0.215565	+	0.109836i
$413$	3.24743	+	6.37344i	0.00786302	+	0.0154320i
$414$	−30.4852	+	9.90524i	−0.0736357	+	0.0239257i
$415$	−41.9942	−	115.382i	−0.101191	−	0.278030i
$416$	−97.0363	+	298.647i	−0.233260	+	0.717902i
$417$	−16.2389	−	102.528i	−0.0389422	−	0.245872i
$418$	−64.0211	+	64.0211i	−0.153160	+	0.153160i
$419$	0.447207	−	0.615528i	0.00106732	−	0.00146904i	−0.808483	−	0.588520i	$-0.799711\pi$
$419$	0.447207	−	0.615528i	0.00106732	−	0.00146904i	0.809550	+	0.587050i	$0.199711\pi$
$420$	1.07042	−	8.71699i	0.00254861	−	0.0207547i
$421$	435.667	−	316.531i	1.03484	−	0.751854i	0.0655671	−	0.997848i	$-0.479114\pi$
$421$	435.667	−	316.531i	1.03484	−	0.751854i	0.969271	+	0.245994i	$0.0791143\pi$
$422$	−328.237	−	51.9877i	−0.777814	−	0.123194i
$423$	−11.2054	−	5.70943i	−0.0264903	−	0.0134975i
$424$			803.587i			1.89525i
$425$	141.995	+	236.332i	0.334105	+	0.556075i
$426$	−214.688			−0.503962
$427$	−25.2498	+	49.5555i	−0.0591330	+	0.116055i
$428$	−6.78284	+	42.8252i	−0.0158478	+	0.100059i
$429$	255.375	+	351.493i	0.595279	+	0.819331i
$430$	450.271	−	249.582i	1.04714	−	0.580424i
$431$	−324.711	−	235.916i	−0.753389	−	0.547369i	0.143487	−	0.989652i	$-0.454169\pi$
$431$	−324.711	−	235.916i	−0.753389	−	0.547369i	−0.896875	+	0.442283i	$0.854169\pi$
$432$	−19.8676	−	19.8676i	−0.0459897	−	0.0459897i
$433$	−266.919	+	42.2758i	−0.616441	+	0.0976347i	−0.456843	−	0.889547i	$-0.651020\pi$
$433$	−266.919	+	42.2758i	−0.616441	+	0.0976347i	−0.159598	+	0.987182i	$0.551020\pi$
$434$	6.14925	+	1.99801i	0.0141688	+	0.00460371i
$435$	225.358	+	288.452i	0.518065	+	0.663109i
$436$	102.711	+	316.113i	0.235577	+	0.725030i
$437$	18.7572	−	9.55725i	0.0429225	−	0.0218701i
$438$	−22.9578	−	45.0572i	−0.0524150	−	0.102870i
$439$	152.256	−	49.4710i	0.346825	−	0.112690i	−0.130424	−	0.991458i	$-0.541634\pi$
$439$	152.256	−	49.4710i	0.346825	−	0.112690i	0.477249	+	0.878768i	$0.341634\pi$
$440$	713.710	−	557.598i	1.62207	−	1.26727i
$441$	−45.1377	+	138.920i	−0.102353	+	0.315010i
$442$	−30.3109	−	191.376i	−0.0685768	−	0.432977i
$443$	226.750	−	226.750i	0.511851	−	0.511851i	−0.403242	−	0.915093i	$-0.632117\pi$
$443$	226.750	−	226.750i	0.511851	−	0.511851i	0.915093	+	0.403242i	$0.132117\pi$
$444$	90.6616	−	124.785i	0.204193	−	0.281047i
$445$	−269.814	−	486.771i	−0.606324	−	1.09387i
$446$	450.855	−	327.566i	1.01089	−	0.734452i
$447$	−178.660	−	28.2969i	−0.399686	−	0.0633040i
$448$	30.0812	+	15.3271i	0.0671454	+	0.0342123i
$449$		−	431.199i		−	0.960355i	−0.877171	−	0.480178i	$-0.840572\pi$
$449$		−	431.199i		−	0.960355i	0.877171	−	0.480178i	$-0.159428\pi$
$450$	43.2701	−	101.931i	0.0961557	−	0.226514i
$451$	−714.640			−1.58457
$452$	−63.9810	+	125.570i	−0.141551	+	0.277809i
$453$	13.7426	−	86.7675i	0.0303369	−	0.191540i
$454$	274.250	+	377.473i	0.604075	+	0.831437i
$455$	−32.9046	−	4.04058i	−0.0723179	−	0.00888039i
$456$	35.0281	+	25.4494i	0.0768161	+	0.0558101i
$457$	82.9758	+	82.9758i	0.181566	+	0.181566i	0.792038	−	0.610472i	$-0.209020\pi$
$457$	82.9758	+	82.9758i	0.181566	+	0.181566i	−0.610472	+	0.792038i	$0.709020\pi$
$458$	−58.0223	+	9.18984i	−0.126686	+	0.0200651i
$459$	−54.5002	−	17.7082i	−0.118737	−	0.0385800i
$460$	−61.8838	+	22.5230i	−0.134530	+	0.0489631i
$461$	131.921	+	406.011i	0.286163	+	0.880718i	0.986048	+	0.166463i	$0.0532346\pi$
$461$	131.921	+	406.011i	0.286163	+	0.880718i	−0.699885	+	0.714256i	$0.746765\pi$
$462$	26.7630	−	13.6364i	0.0579286	−	0.0295161i
$463$	−179.084	−	351.473i	−0.386791	−	0.759121i	0.612723	−	0.790298i	$-0.290074\pi$
$463$	−179.084	−	351.473i	−0.386791	−	0.759121i	−0.999514	+	0.0311774i	$0.990074\pi$
$464$	−217.366	+	70.6265i	−0.468461	+	0.152212i
$465$	−56.4273	−	38.0617i	−0.121349	−	0.0818530i
$466$	−137.263	+	422.453i	−0.294557	+	0.906552i
$467$	123.720	+	781.139i	0.264926	+	1.67267i	0.657885	+	0.753118i	$0.271451\pi$
$467$	123.720	+	781.139i	0.264926	+	1.67267i	−0.392959	+	0.919556i	$0.628549\pi$
$468$	45.9432	−	45.9432i	0.0981692	−	0.0981692i
$469$	−8.37739	+	11.5305i	−0.0178622	+	0.0245853i
$470$	28.0473	+	13.0791i	0.0596752	+	0.0278279i
$471$	−28.7667	+	20.9003i	−0.0610759	+	0.0443742i
$472$	108.958	+	17.2572i	0.230843	+	0.0365620i
$473$	−1309.80	−	667.375i	−2.76913	−	1.41094i
$474$		−	175.013i		−	0.369225i
$475$	−17.5956	+	70.5651i	−0.0370435	+	0.148558i
$476$	11.1840			0.0234957
$477$	127.365	−	249.968i	0.267013	−	0.524042i
$478$	−52.2858	+	330.119i	−0.109384	+	0.690626i
$479$	−314.782	−	433.260i	−0.657165	−	0.904510i	0.342219	−	0.939620i	$-0.388822\pi$
$479$	−314.782	−	433.260i	−0.657165	−	0.904510i	−0.999383	+	0.0351107i	$0.988822\pi$
$480$	−167.137	−	155.861i	−0.348202	−	0.324711i
$481$	−471.035	−	342.227i	−0.979282	−	0.711490i
$482$	−323.925	−	323.925i	−0.672043	−	0.672043i
$483$	−6.89798	+	1.09253i	−0.0142815	+	0.00226197i
$484$	−559.717	−	181.863i	−1.15644	−	0.375750i
$485$	−4.97207	−	142.430i	−0.0102517	−	0.293670i
$486$	7.11229	+	21.8894i	0.0146343	+	0.0450399i
$487$	−232.335	+	118.381i	−0.477074	+	0.243081i	−0.675956	−	0.736942i	$-0.736269\pi$
$487$	−232.335	+	118.381i	−0.477074	+	0.243081i	0.198882	+	0.980024i	$0.436269\pi$
$488$	389.407	+	764.255i	0.797966	+	1.56610i
$489$	366.921	−	119.220i	0.750350	−	0.243803i
$490$	99.0799	−	345.517i	0.202204	−	0.705137i
$491$	−72.8185	+	224.112i	−0.148307	+	0.456440i	−0.997421	−	0.0717677i	$-0.977136\pi$
$491$	−72.8185	+	224.112i	−0.148307	+	0.456440i	0.849115	+	0.528208i	$0.177136\pi$
$492$	16.7185	+	105.556i	0.0339807	+	0.214545i
$493$	−329.612	+	329.612i	−0.668583	+	0.668583i
$494$	30.0417	−	41.3488i	0.0608131	−	0.0837021i
$495$	−310.387	+	60.3294i	−0.627045	+	0.121878i
$496$	34.3814	−	24.9795i	0.0693173	−	0.0503620i
$497$	−46.2005	−	7.31743i	−0.0929587	−	0.0147232i
$498$	−55.9560	−	28.5110i	−0.112362	−	0.0572511i
$499$		−	587.043i		−	1.17644i	−0.808701	−	0.588220i	$-0.799829\pi$
$499$		−	587.043i		−	1.17644i	0.808701	−	0.588220i	$-0.200171\pi$
$500$	81.5382	−	212.392i	0.163076	−	0.424783i
$501$	569.392			1.13651
$502$	250.361	−	491.361i	0.498727	−	0.978808i
$503$	73.2923	−	462.750i	0.145710	−	0.919979i	−0.801180	−	0.598423i	$-0.795794\pi$
$503$	73.2923	−	462.750i	0.145710	−	0.919979i	0.946891	−	0.321556i	$-0.104206\pi$
$504$	−8.44294	−	11.6207i	−0.0167519	−	0.0230570i
$505$	−63.1195	−	324.742i	−0.124989	−	0.643054i
$506$	−182.215	−	132.387i	−0.360109	−	0.261634i
$507$	33.5569	+	33.5569i	0.0661873	+	0.0661873i
$508$	180.050	−	28.5171i	0.354429	−	0.0561361i
$509$	819.001	+	266.110i	1.60904	+	0.522809i	0.969321	−	0.245800i	$-0.0790507\pi$
$509$	819.001	+	266.110i	1.60904	+	0.522809i	0.639719	+	0.768609i	$0.279051\pi$
$510$	135.552	+	38.8706i	0.265788	+	0.0762168i
$511$	−3.40475	−	10.4787i	−0.00666291	−	0.0205063i
$512$	292.742	−	149.159i	0.571762	−	0.291327i
$513$	−6.86242	−	13.4683i	−0.0133770	−	0.0262539i
$514$	−311.065	+	101.071i	−0.605186	+	0.196637i
$515$	−273.665	+	9.55333i	−0.531388	+	0.0185502i
$516$	−67.9333	+	209.077i	−0.131654	+	0.405189i
$517$	−13.8236	−	87.2790i	−0.0267382	−	0.168818i
$518$	−28.4626	+	28.4626i	−0.0549472	+	0.0549472i
$519$	−113.113	+	155.687i	−0.217944	+	0.299974i
$520$	−348.692	+	373.917i	−0.670562	+	0.719072i
$521$	−403.189	+	292.934i	−0.773876	+	0.562254i	−0.903135	−	0.429357i	$-0.858740\pi$
$521$	−403.189	+	292.934i	−0.773876	+	0.562254i	0.129259	+	0.991611i	$0.458740\pi$
$522$	184.915	+	29.2877i	0.354244	+	0.0561067i
$523$	−442.160	−	225.292i	−0.845430	−	0.430768i	−0.0230688	−	0.999734i	$-0.507344\pi$
$523$	−442.160	−	225.292i	−0.845430	−	0.430768i	−0.822361	+	0.568966i	$0.807344\pi$
$524$			374.981i			0.715613i
$525$	12.7859	−	20.4606i	0.0243541	−	0.0389726i
$526$	377.784			0.718221
$527$	39.3500	−	77.2287i	0.0746679	−	0.146544i
$528$	30.8842	−	194.995i	0.0584928	−	0.369309i
$529$	−280.157	−	385.603i	−0.529597	−	0.728927i
$530$	−291.767	+	625.676i	−0.550503	+	1.18052i
$531$	−31.1579	−	22.6375i	−0.0586777	−	0.0426319i
$532$	2.08602	+	2.08602i	0.00392110	+	0.00392110i
$533$	398.451	−	63.1084i	0.747563	−	0.118402i
$534$	−270.722	−	87.9629i	−0.506970	−	0.164725i
$535$	−66.6096	+	98.7502i	−0.124504	+	0.184580i
$536$	67.9233	+	209.046i	0.126722	+	0.390012i
$537$	110.084	−	56.0905i	0.204998	−	0.104452i
$538$	−203.254	−	398.908i	−0.377795	−	0.741464i
$539$	−976.129	+	317.164i	−1.81100	+	0.588430i
$540$	16.1723	+	44.4346i	0.0299487	+	0.0822863i
$541$	−119.778	+	368.639i	−0.221401	+	0.681402i	0.777236	+	0.629209i	$0.216621\pi$
$541$	−119.778	+	368.639i	−0.221401	+	0.681402i	−0.998637	+	0.0521931i	$0.983379\pi$
$542$	46.6670	+	294.644i	0.0861015	+	0.543624i
$543$	−134.513	+	134.513i	−0.247721	+	0.247721i
$544$	171.060	−	235.444i	0.314448	−	0.432801i
$545$	−111.291	+	906.306i	−0.204204	+	1.66295i
$546$	−13.7176	+	9.96644i	−0.0251239	+	0.0182536i
$547$	−123.231	−	19.5179i	−0.225285	−	0.0356817i	0.0427711	−	0.999085i	$-0.486381\pi$
$547$	−123.231	−	19.5179i	−0.225285	−	0.0356817i	−0.268056	+	0.963403i	$0.586381\pi$
$548$	151.610	+	77.2489i	0.276660	+	0.140965i
$549$		−	299.453i		−	0.545452i
$550$	758.151	−	175.014i	1.37846	−	0.318207i
$551$	−122.958			−0.223154
$552$	−48.8984	+	95.9686i	−0.0885841	+	0.173856i
$553$	5.96515	−	37.6624i	0.0107869	−	0.0681057i
$554$	9.52986	+	13.1167i	0.0172019	+	0.0236764i
$555$	370.608	−	205.426i	0.667762	−	0.370136i
$556$	−88.2477	−	64.1157i	−0.158719	−	0.115316i
$557$	−196.710	−	196.710i	−0.353159	−	0.353159i	0.508124	−	0.861284i	$-0.330339\pi$
$557$	−196.710	−	196.710i	−0.353159	−	0.353159i	−0.861284	+	0.508124i	$0.830339\pi$
$558$	−34.3837	+	5.44585i	−0.0616196	+	0.00975958i
$559$	789.219	+	256.433i	1.41184	+	0.458735i
$560$	9.27443	+	11.8710i	0.0165615	+	0.0211982i
$561$	−124.428	−	382.950i	−0.221797	−	0.682621i
$562$	195.597	−	99.6614i	0.348037	−	0.177334i
$563$	339.903	+	667.098i	0.603736	+	1.18490i	0.967373	+	0.253358i	$0.0815349\pi$
$563$	339.903	+	667.098i	0.603736	+	1.18490i	−0.363637	+	0.931541i	$0.618465\pi$
$564$	−12.5682	+	4.08366i	−0.0222840	+	0.00724053i
$565$	−305.091	+	238.357i	−0.539983	+	0.421871i
$566$	57.7249	−	177.659i	0.101987	−	0.313885i
$567$	0.784474	+	4.95298i	0.00138355	+	0.00873541i
$568$	−510.103	+	510.103i	−0.898068	+	0.898068i
$569$	49.8222	−	68.5744i	0.0875611	−	0.120517i	−0.762989	−	0.646411i	$-0.776269\pi$
$569$	49.8222	−	68.5744i	0.0875611	−	0.120517i	0.850550	+	0.525894i	$0.176269\pi$
$570$	18.0329	+	32.5331i	0.0316366	+	0.0570756i
$571$	559.772	−	406.698i	0.980336	−	0.712256i	0.0225521	−	0.999746i	$-0.492821\pi$
$571$	559.772	−	406.698i	0.980336	−	0.712256i	0.957784	+	0.287490i	$0.0928208\pi$
$572$	450.921	+	71.4188i	0.788323	+	0.124858i
$573$	−16.6104	−	8.46343i	−0.0289885	−	0.0147704i
$574$		−	27.8901i		−	0.0485890i
$575$	−180.227	−	15.7722i	−0.313439	−	0.0274299i
$576$	−181.774			−0.315579
$577$	−496.404	+	974.249i	−0.860320	+	1.68847i	−0.145278	+	0.989391i	$0.546408\pi$
$577$	−496.404	+	974.249i	−0.860320	+	1.68847i	−0.715042	+	0.699081i	$0.753592\pi$
$578$	38.6588	−	244.082i	0.0668838	−	0.422288i
$579$	−238.626	−	328.440i	−0.412134	−	0.567254i
$580$	381.776	+	46.8809i	0.658235	+	0.0808291i
$581$	−11.0699	−	8.04274i	−0.0190532	−	0.0138429i
$582$	−51.5425	−	51.5425i	−0.0885611	−	0.0885611i
$583$	1947.01	−	308.376i	3.33964	−	0.528947i
$584$	−161.605	−	52.5087i	−0.276721	−	0.0899121i
$585$	167.730	−	61.0466i	0.286719	−	0.104353i
$586$	−26.7379	−	82.2907i	−0.0456278	−	0.140428i
$587$	−384.734	+	196.032i	−0.655423	+	0.333955i	−0.749880	−	0.661574i	$-0.769889\pi$
$587$	−384.734	+	196.032i	−0.655423	+	0.333955i	0.0944564	+	0.995529i	$0.469889\pi$
$588$	69.6827	+	136.760i	0.118508	+	0.232585i
$589$	21.7442	−	7.06511i	0.0369171	−	0.0119951i
$590$	78.5694	+	52.9971i	0.133169	+	0.0898256i
$591$	102.916	−	316.742i	0.174138	−	0.535943i
$592$	41.3878	+	261.312i	0.0699119	+	0.441406i
$593$	323.721	−	323.721i	0.545904	−	0.545904i	−0.379349	−	0.925254i	$-0.623852\pi$
$593$	323.721	−	323.721i	0.545904	−	0.545904i	0.925254	+	0.379349i	$0.123852\pi$
$594$	−95.0583	+	130.836i	−0.160031	+	0.220263i
$595$	27.8456	+	12.9850i	0.0467994	+	0.0218236i
$596$	−153.775	+	111.724i	−0.258011	+	0.187456i
$597$	428.532	+	67.8728i	0.717809	+	0.113690i
$598$	113.286	+	57.7220i	0.189441	+	0.0965250i
$599$			730.113i			1.21889i	0.792829	+	0.609444i	$0.208607\pi$
$599$			730.113i			1.21889i	−0.792829	+	0.609444i	$0.791393\pi$
$600$	−139.380	−	345.001i	−0.232300	−	0.575002i
$601$	572.492			0.952566			0.476283	−	0.879292i	$-0.341984\pi$
$601$	572.492			0.952566			0.476283	+	0.879292i	$0.341984\pi$
$602$	26.0455	−	51.1172i	0.0432649	−	0.0849122i
$603$	12.0044	−	75.7927i	0.0199078	−	0.125693i
$604$	−54.2597	−	74.6820i	−0.0898339	−	0.123646i
$605$	−1182.42	−	1102.65i	−1.95442	−	1.82257i
$606$	−136.887	−	99.4545i	−0.225887	−	0.164116i
$607$	−100.061	−	100.061i	−0.164845	−	0.164845i	0.619864	−	0.784709i	$-0.287188\pi$
$607$	−100.061	−	100.061i	−0.164845	−	0.164845i	−0.784709	+	0.619864i	$0.787188\pi$
$608$	75.8207	−	12.0088i	0.124705	−	0.0197513i
$609$	38.7952	+	12.6053i	0.0637031	+	0.0206984i
$610$	25.7082	+	736.439i	0.0421447	+	1.20728i
$611$	15.4149	+	47.4421i	0.0252289	+	0.0776466i
$612$	−53.6530	+	27.3376i	−0.0876683	+	0.0446692i
$613$	−9.06541	−	17.7919i	−0.0147886	−	0.0290243i	0.883494	−	0.468442i	$-0.155185\pi$
$613$	−9.06541	−	17.7919i	−0.0147886	−	0.0290243i	−0.898283	+	0.439418i	$0.855185\pi$
$614$	449.511	−	146.055i	0.732102	−	0.237875i
$615$	−80.9299	+	282.223i	−0.131593	+	0.458900i
$616$	31.1890	−	95.9899i	0.0506315	−	0.155828i
$617$	−102.375	−	646.368i	−0.165923	−	1.04760i	−0.920316	−	0.391175i	$-0.872069\pi$
$617$	−102.375	−	646.368i	−0.165923	−	1.04760i	0.754393	−	0.656423i	$-0.227931\pi$
$618$	−99.0338	+	99.0338i	−0.160249	+	0.160249i
$619$	544.455	−	749.377i	0.879571	−	1.21063i	−0.0969683	−	0.995287i	$-0.530915\pi$
$619$	544.455	−	749.377i	0.879571	−	1.21063i	0.976539	−	0.215338i	$-0.0690855\pi$
$620$	−70.2081	+	13.6462i	−0.113239	+	0.0220100i
$621$	30.4212	−	22.1023i	0.0489875	−	0.0355915i
$622$	−413.640	−	65.5142i	−0.665016	−	0.105328i
$623$	−55.2609	−	28.1568i	−0.0887012	−	0.0451955i
$624$			111.448i			0.178602i
$625$	449.608	−	434.140i	0.719373	−	0.694624i
$626$	763.455			1.21958
$627$	48.2193	−	94.6358i	0.0769049	−	0.150934i
$628$	−5.84503	+	36.9040i	−0.00930737	+	0.0587644i
$629$	317.169	+	436.546i	0.504244	+	0.694032i
$630$	−2.35446	−	12.1134i	−0.00373724	−	0.0192276i
$631$	−568.505	−	413.043i	−0.900959	−	0.654585i	0.0377534	−	0.999287i	$-0.487980\pi$
$631$	−568.505	−	413.043i	−0.900959	−	0.654585i	−0.938712	+	0.344702i	$0.887980\pi$
$632$	−415.834	−	415.834i	−0.657965	−	0.657965i
$633$	385.057	−	60.9870i	0.608304	−	0.0963459i
$634$	−304.112	−	98.8121i	−0.479672	−	0.155855i
$635$	481.395	+	138.044i	0.758103	+	0.217392i
$636$	−91.0977	−	280.370i	−0.143235	−	0.440833i
$637$	516.237	−	263.036i	0.810420	−	0.412930i
$638$	597.232	+	1172.13i	0.936101	+	1.83720i
$639$	239.525	−	77.8263i	0.374843	−	0.121794i
$640$	−80.4214	+	2.80742i	−0.125658	+	0.00438659i
$641$	−106.870	+	328.912i	−0.166724	+	0.513124i	−0.999159	−	0.0409986i	$-0.986946\pi$
$641$	−106.870	+	328.912i	−0.166724	+	0.513124i	0.832435	+	0.554122i	$0.186946\pi$
$642$	9.53047	+	60.1730i	0.0148450	+	0.0937274i
$643$	0.555827	−	0.555827i	0.000864428	−	0.000864428i	−0.706674	−	0.707539i	$-0.749805\pi$
$643$	0.555827	−	0.555827i	0.000864428	−	0.000864428i	0.707539	+	0.706674i	$0.249805\pi$
$644$	−4.31362	+	5.93719i	−0.00669817	+	0.00921923i
$645$	−411.887	+	441.684i	−0.638584	+	0.684781i
$646$	−38.3213	+	27.8421i	−0.0593209	+	0.0430992i
$647$	−590.648	−	93.5494i	−0.912902	−	0.144590i	−0.317724	−	0.948183i	$-0.602919\pi$
$647$	−590.648	−	93.5494i	−0.912902	−	0.144590i	−0.595178	+	0.803594i	$0.702919\pi$
$648$	68.9086	+	35.1107i	0.106340	+	0.0541832i
$649$		−	270.617i		−	0.416975i
$650$	−407.255	+	164.531i	−0.626547	+	0.253124i
$651$	−7.58494			−0.0116512
$652$	184.049	−	361.217i	0.282284	−	0.554014i
$653$	−75.2906	+	475.366i	−0.115299	+	0.727972i	0.860524	+	0.509410i	$0.170137\pi$
$653$	−75.2906	+	475.366i	−0.115299	+	0.727972i	−0.975823	+	0.218562i	$0.929863\pi$
$654$	274.510	+	377.830i	0.419740	+	0.577722i
$655$	−435.369	+	933.622i	−0.664685	+	1.42538i
$656$	−148.306	−	107.750i	−0.226076	−	0.164254i
$657$	41.9474	+	41.9474i	0.0638469	+	0.0638469i
$658$	3.40622	−	0.539492i	0.00517662	−	0.000819896i
$659$	−201.815	−	65.5738i	−0.306245	−	0.0995050i	0.151863	−	0.988402i	$-0.451473\pi$
$659$	−201.815	−	65.5738i	−0.306245	−	0.0995050i	−0.458108	+	0.888897i	$0.651473\pi$
$660$	−185.801	+	275.454i	−0.281516	+	0.417354i
$661$	156.455	+	481.518i	0.236694	+	0.728469i	0.996892	+	0.0787777i	$0.0251017\pi$
$661$	156.455	+	481.518i	0.236694	+	0.728469i	−0.760198	+	0.649691i	$0.774898\pi$
$662$	−535.086	+	272.640i	−0.808288	+	0.411843i
$663$	103.193	+	202.528i	0.155646	+	0.305472i
$664$	−200.696	+	65.2100i	−0.302253	+	0.0982078i
$665$	2.77179	+	7.61570i	0.00416810	+	0.0114522i
$666$	66.9715	−	206.117i	0.100558	−	0.309485i
$667$	−47.8495	−	302.110i	−0.0717383	−	0.452938i
$668$	423.075	−	423.075i	0.633346	−	0.633346i
$669$	−384.269	+	528.900i	−0.574393	+	0.790584i
$670$	−23.0153	+	187.426i	−0.0343512	+	0.279740i
$671$	1702.28	−	1236.78i	2.53693	−	1.84318i
$672$	−25.1538	−	3.98397i	−0.0374312	−	0.00592853i
$673$	−571.178	−	291.029i	−0.848704	−	0.432436i	−0.0251562	−	0.999684i	$-0.508008\pi$
$673$	−571.178	−	291.029i	−0.848704	−	0.432436i	−0.823547	+	0.567247i	$0.808008\pi$
$674$		−	44.0512i		−	0.0653579i
$675$	−11.3249	+	129.409i	−0.0167777	+	0.191717i
$676$	49.8676			0.0737686
$677$	−168.114	+	329.942i	−0.248322	+	0.487359i	−0.981198	−	0.193003i	$-0.938177\pi$
$677$	−168.114	+	329.942i	−0.248322	+	0.487359i	0.732876	+	0.680362i	$0.238177\pi$
$678$	−30.9770	+	195.581i	−0.0456888	+	0.288468i
$679$	−9.33510	−	12.8487i	−0.0137483	−	0.0189229i
$680$	414.431	−	229.717i	0.609458	−	0.337818i
$681$	−442.815	−	321.724i	−0.650242	−	0.472428i
$682$	−172.967	−	172.967i	−0.253617	−	0.253617i
$683$	68.3866	−	10.8314i	0.100127	−	0.0158585i	−0.106170	−	0.994348i	$-0.533859\pi$
$683$	68.3866	−	10.8314i	0.100127	−	0.0158585i	0.206297	+	0.978489i	$0.433859\pi$
$684$	−15.1063	−	4.90833i	−0.0220852	−	0.00717592i
$685$	287.786	+	368.358i	0.420125	+	0.537749i
$686$	−24.8347	−	76.4332i	−0.0362021	−	0.111419i
$687$	61.4035	−	31.2866i	0.0893791	−	0.0455410i
$688$	−171.192	−	335.983i	−0.248825	−	0.488347i
$689$	−1058.33	+	343.873i	−1.53604	+	0.499090i
$690$	−72.9169	+	56.9675i	−0.105677	+	0.0825616i
$691$	18.7005	−	57.5541i	0.0270629	−	0.0832910i	−0.936613	−	0.350366i	$-0.886057\pi$
$691$	18.7005	−	57.5541i	0.0270629	−	0.0832910i	0.963676	+	0.267075i	$0.0860572\pi$
$692$	31.6335	+	199.726i	0.0457132	+	0.288622i
$693$	−24.9158	+	24.9158i	−0.0359536	+	0.0359536i
$694$	10.4995	−	14.4513i	0.0151289	−	0.0208232i
$695$	−145.277	−	262.093i	−0.209031	−	0.377113i
$696$	508.951	−	369.774i	0.731251	−	0.531285i
$697$	−369.277	−	58.4877i	−0.529809	−	0.0839135i
$698$	−271.382	−	138.276i	−0.388800	−	0.198103i
$699$		−	521.086i		−	0.745473i
$700$	−5.70255	−	24.7031i	−0.00814650	−	0.0352902i
$701$	−163.588			−0.233364			−0.116682	−	0.993169i	$-0.537226\pi$
$701$	−163.588			−0.233364			−0.116682	+	0.993169i	$0.537226\pi$
$702$	41.4463	−	81.3429i	0.0590403	−	0.115873i
$703$	−22.2661	+	140.582i	−0.0316729	+	0.199975i
$704$	−750.747	−	1033.32i	−1.06640	−	1.46778i
$705$	−36.0334	−	4.42478i	−0.0511112	−	0.00627628i
$706$	−199.530	−	144.967i	−0.282620	−	0.205335i
$707$	−26.0682	−	26.0682i	−0.0368715	−	0.0368715i
$708$	−39.9716	+	6.33088i	−0.0564570	+	0.00894191i
$709$	−407.029	−	132.252i	−0.574088	−	0.186533i	0.00756218	−	0.999971i	$-0.497593\pi$
$709$	−407.029	−	132.252i	−0.574088	−	0.186533i	−0.581651	+	0.813439i	$0.697593\pi$
$710$	−582.377	+	211.960i	−0.820249	+	0.298535i
$711$	63.4437	+	195.260i	0.0892316	+	0.274627i
$712$	−852.244	+	434.240i	−1.19697	+	0.609888i
$713$	25.8209	+	50.6764i	0.0362145	+	0.0710749i
$714$	14.9453	−	4.85603i	0.0209318	−	0.00680116i
$715$	1039.77	+	701.355i	1.45423	+	0.980916i
$716$	40.1186	−	123.472i	0.0560316	−	0.172448i
$717$	−61.3367	−	387.265i	−0.0855463	−	0.540118i
$718$	375.453	−	375.453i	0.522914	−	0.522914i
$719$	−86.8817	+	119.582i	−0.120837	+	0.166318i	−0.865150	−	0.501513i	$-0.832777\pi$
$719$	−86.8817	+	119.582i	−0.120837	+	0.166318i	0.744313	+	0.667831i	$0.232777\pi$
$720$	−73.5093	−	34.2790i	−0.102096	−	0.0476098i
$721$	−24.6874	+	17.9364i	−0.0342405	+	0.0248772i
$722$	514.102	+	81.4257i	0.712052	+	0.112778i
$723$	478.825	+	243.974i	0.662275	+	0.337446i
$724$			199.894i			0.276097i
$725$	896.110	+	559.981i	1.23601	+	0.772388i
$726$	−826.923			−1.13901
$727$	−628.670	+	1233.83i	−0.864745	+	1.69716i	−0.160700	+	0.987003i	$0.551375\pi$
$727$	−628.670	+	1233.83i	−0.864745	+	1.69716i	−0.704045	+	0.710155i	$0.748625\pi$
$728$	−8.91291	+	56.2739i	−0.0122430	+	0.0772993i
$729$	−15.8702	−	21.8435i	−0.0217698	−	0.0299636i
$730$	−106.762	−	99.5592i	−0.146249	−	0.136382i
$731$	−622.194	−	452.051i	−0.851155	−	0.618400i
$732$	−222.502	−	222.502i	−0.303965	−	0.303965i
$733$	−423.531	+	67.0807i	−0.577805	+	0.0915153i	−0.438495	−	0.898734i	$-0.644488\pi$
$733$	−423.531	+	67.0807i	−0.577805	+	0.0915153i	−0.139310	+	0.990249i	$0.544488\pi$
$734$	144.980	+	47.1070i	0.197521	+	0.0641785i
$735$	14.7108	+	421.407i	0.0200147	+	0.573343i
$736$	59.0118	+	181.620i	0.0801791	+	0.246766i
$737$	480.432	−	244.793i	0.651876	−	0.332147i
$738$	68.1733	+	133.798i	0.0923757	+	0.181297i
$739$	209.279	−	67.9988i	0.283192	−	0.0920146i	−0.163977	−	0.986464i	$-0.552432\pi$
$739$	209.279	−	67.9988i	0.283192	−	0.0920146i	0.447169	+	0.894450i	$0.352432\pi$
$740$	122.735	−	428.010i	0.165859	−	0.578392i
$741$	−18.5278	+	57.0228i	−0.0250038	+	0.0769538i
$742$	12.0349	+	75.9854i	0.0162196	+	0.102406i
$743$	336.000	−	336.000i	0.452221	−	0.452221i	−0.443870	−	0.896091i	$-0.646395\pi$
$743$	336.000	−	336.000i	0.452221	−	0.452221i	0.896091	+	0.443870i	$0.146395\pi$
$744$	−68.7571	+	94.6360i	−0.0924154	+	0.127199i
$745$	−512.582	+	99.6295i	−0.688029	+	0.133731i
$746$	564.801	−	410.352i	0.757106	−	0.550070i
$747$	72.7650	+	11.5249i	0.0974097	+	0.0154282i
$748$	−376.997	−	192.090i	−0.504007	−	0.256804i
$749$			13.2740i			0.0177223i
$750$	16.7414	−	319.226i	0.0223218	−	0.425635i
$751$	−1104.53			−1.47074			−0.735370	−	0.677666i	$-0.762991\pi$
$751$	−1104.53			−1.47074			−0.735370	+	0.677666i	$0.762991\pi$
$752$	10.2908	−	20.1968i	0.0136846	−	0.0268575i
$753$	−101.202	+	638.965i	−0.134398	+	0.848559i
$754$	−436.499	−	600.789i	−0.578911	−	0.796802i
$755$	−48.3859	−	248.940i	−0.0640873	−	0.329721i
$756$	4.26310	+	3.09732i	0.00563902	+	0.00409699i
$757$	−69.8417	−	69.8417i	−0.0922612	−	0.0922612i	0.659470	−	0.751731i	$-0.270781\pi$
$757$	−69.8417	−	69.8417i	−0.0922612	−	0.0922612i	−0.751731	+	0.659470i	$0.770781\pi$
$758$	600.275	−	95.0742i	0.791920	−	0.125428i
$759$	251.287	+	81.6480i	0.331076	+	0.107573i
$760$	120.146	+	34.4528i	0.158087	+	0.0453327i
$761$	−134.619	−	414.314i	−0.176897	−	0.544433i	0.822818	−	0.568305i	$-0.192401\pi$
$761$	−134.619	−	414.314i	−0.176897	−	0.544433i	−0.999715	+	0.0238717i	$0.992401\pi$
$762$	228.222	−	116.285i	0.299504	−	0.152605i
$763$	46.1961	+	90.6649i	0.0605453	+	0.118827i
$764$	−18.6306	+	6.05345i	−0.0243856	+	0.00792337i
$765$	−165.324	+	5.77129i	−0.216110	+	0.00754416i
$766$	−261.255	+	804.061i	−0.341064	+	1.04969i
$767$	23.8976	+	150.884i	0.0311572	+	0.196719i
$768$	−325.938	+	325.938i	−0.424399	+	0.424399i
$769$	683.879	−	941.278i	0.889309	−	1.22403i	−0.0844452	−	0.996428i	$-0.526912\pi$
$769$	683.879	−	941.278i	0.889309	−	1.22403i	0.973754	−	0.227601i	$-0.0730882\pi$
$770$	59.1360	−	63.4141i	0.0768000	−	0.0823560i
$771$	310.413	−	225.528i	0.402611	−	0.292514i
$772$	−421.346	−	66.7347i	−0.545785	−	0.0864439i
$773$	250.662	+	127.718i	0.324271	+	0.165224i	0.608546	−	0.793518i	$-0.291753\pi$
$773$	250.662	+	127.718i	0.324271	+	0.165224i	−0.284275	+	0.958743i	$0.591753\pi$
$774$			308.890i			0.399082i
$775$	−190.647	−	47.5384i	−0.245996	−	0.0613399i
$776$	−244.933			−0.315635
$777$	21.4375	−	42.0734i	0.0275900	−	0.0541485i
$778$	73.8848	−	466.490i	0.0949676	−	0.599602i
$779$	−57.9681	−	79.7863i	−0.0744135	−	0.102421i
$780$	79.2692	−	169.988i	0.101627	−	0.217934i
$781$	1431.68	+	1040.18i	1.83314	+	1.33185i
$782$	−83.3214	−	83.3214i	−0.106549	−	0.106549i
$783$	−216.925	+	34.3575i	−0.277043	+	0.0438793i
$784$	−250.392	−	81.3572i	−0.319377	−	0.103772i
$785$	−57.4000	+	85.0968i	−0.0731210	+	0.108404i
$786$	162.815	+	501.094i	0.207144	+	0.637524i
$787$	173.456	−	88.3803i	0.220402	−	0.112300i	−0.340304	−	0.940316i	$-0.610530\pi$
$787$	173.456	−	88.3803i	0.220402	−	0.112300i	0.560706	+	0.828015i	$0.310530\pi$
$788$	−158.879	−	311.818i	−0.201624	−	0.395709i
$789$	−421.490	+	136.950i	−0.534207	+	0.173575i
$790$	−172.789	−	474.752i	−0.218720	−	0.600951i
$791$	−13.3324	+	41.0330i	−0.0168551	+	0.0518748i
$792$	85.0098	+	536.731i	0.107336	+	0.677691i
$793$	−839.896	+	839.896i	−1.05914	+	1.05914i
$794$	430.703	−	592.812i	0.542447	−	0.746614i
$795$	98.7074	−	803.828i	0.124160	−	1.01110i
$796$	368.843	−	267.980i	0.463371	−	0.336659i
$797$	−555.916	−	88.0484i	−0.697510	−	0.110475i	−0.202398	−	0.979303i	$-0.564873\pi$
$797$	−555.916	−	88.0484i	−0.697510	−	0.110475i	−0.495113	+	0.868829i	$0.664873\pi$
$798$	3.69333	+	1.88184i	0.00462823	+	0.00235820i
$799$		−	46.2311i		−	0.0578613i
$800$	−607.269	−	257.787i	−0.759086	−	0.322234i
$801$	333.929			0.416890
$802$	76.1389	−	149.431i	0.0949363	−	0.186323i
$803$	−65.2073	+	411.703i	−0.0812047	+	0.512706i
$804$	−47.3966	−	65.2358i	−0.0589510	−	0.0811391i
$805$	−17.6333	+	9.77402i	−0.0219047	+	0.0121416i
$806$	111.713	+	81.1640i	0.138601	+	0.100700i
$807$	371.375	+	371.375i	0.460193	+	0.460193i
$808$	−561.554	+	88.9414i	−0.694992	+	0.110076i
$809$	922.167	+	299.630i	1.13988	+	0.370371i	0.817324	−	0.576178i	$-0.195456\pi$
$809$	922.167	+	299.630i	1.13988	+	0.370371i	0.322560	+	0.946549i	$0.395456\pi$
$810$	40.9046	+	52.3567i	0.0504995	+	0.0646380i
$811$	232.124	+	714.404i	0.286219	+	0.880892i	0.986031	+	0.166564i	$0.0532674\pi$
$811$	232.124	+	714.404i	0.286219	+	0.880892i	−0.699811	+	0.714328i	$0.746733\pi$
$812$	38.1921	−	19.4599i	0.0470346	−	0.0239653i
$813$	−158.877	−	311.814i	−0.195421	−	0.383535i
$814$	1448.30	−	470.580i	1.77924	−	0.578109i
$815$	877.631	−	685.664i	1.07685	−	0.841305i
$816$	31.9177	−	98.2325i	0.0391148	−	0.120383i
$817$	−31.7350	−	200.367i	−0.0388434	−	0.245247i
$818$	508.474	−	508.474i	0.621607	−	0.621607i
$819$	11.6917	−	16.0922i	0.0142756	−	0.0196486i
$820$	149.567	+	269.834i	0.182399	+	0.329065i
$821$	−533.904	+	387.904i	−0.650309	+	0.472477i	−0.863377	−	0.504560i	$-0.831655\pi$
$821$	−533.904	+	387.904i	−0.650309	+	0.472477i	0.213067	+	0.977038i	$0.431655\pi$
$822$	236.139	+	37.4008i	0.287274	+	0.0454998i
$823$	−305.539	−	155.680i	−0.371251	−	0.189162i	0.258404	−	0.966037i	$-0.416804\pi$
$823$	−305.539	−	155.680i	−0.371251	−	0.189162i	−0.629655	+	0.776875i	$0.716804\pi$
$824$			470.613i			0.571132i
$825$	−782.416	+	470.098i	−0.948383	+	0.569815i
$826$	10.5613			0.0127861
$827$	319.358	−	626.774i	0.386164	−	0.757889i	−0.613326	−	0.789830i	$-0.710169\pi$
$827$	319.358	−	626.774i	0.386164	−	0.757889i	0.999490	+	0.0319407i	$0.0101688\pi$
$828$	6.18120	−	39.0266i	0.00746522	−	0.0471335i
$829$	284.477	+	391.550i	0.343157	+	0.472315i	0.945360	−	0.326028i	$-0.105710\pi$
$829$	284.477	+	391.550i	0.343157	+	0.472315i	−0.602203	+	0.798343i	$0.705710\pi$
$830$	−179.939	−	22.0959i	−0.216794	−	0.0266216i
$831$	−15.3873	−	11.1795i	−0.0185166	−	0.0134531i
$832$	509.833	+	509.833i	0.612780	+	0.612780i
$833$	−530.354	+	83.9998i	−0.636679	+	0.100840i
$834$	−145.765	−	47.3621i	−0.174779	−	0.0567891i
$835$	1544.57	−	562.158i	1.84979	−	0.673243i
$836$	−34.4888	−	106.146i	−0.0412545	−	0.126968i
$837$	36.3874	−	18.5403i	0.0434735	−	0.0221509i
$838$	−0.509989	−	1.00091i	−0.000608579	−	0.00119440i
$839$	102.878	−	33.4272i	0.122620	−	0.0398417i	−0.247064	−	0.968999i	$-0.579466\pi$
$839$	102.878	−	33.4272i	0.122620	−	0.0398417i	0.369684	+	0.929157i	$0.379466\pi$
$840$	−34.3760	−	23.1875i	−0.0409238	−	0.0276042i
$841$	−292.190	+	899.269i	−0.347432	+	1.06929i
$842$	−124.381	−	785.310i	−0.147721	−	0.932672i
$843$	−182.097	+	182.097i	−0.216010	+	0.216010i
$844$	240.793	−	331.424i	0.285300	−	0.392682i
$845$	124.160	+	57.8983i	0.146934	+	0.0685187i
$846$	−15.0220	+	10.9141i	−0.0177565	+	0.0129008i
$847$	−177.953	−	28.1849i	−0.210098	−	0.0332762i
$848$	450.548	+	229.566i	0.531307	+	0.270714i
$849$			219.138i			0.258113i
$850$	406.084	−	28.3864i	0.477746	−	0.0333958i
$851$	−354.079			−0.416074
$852$	120.147	−	235.801i	0.141017	−	0.276762i
$853$	154.582	−	975.995i	0.181222	−	1.14419i	−0.714519	−	0.699616i	$-0.753355\pi$
$853$	154.582	−	975.995i	0.181222	−	1.14419i	0.895741	−	0.444575i	$-0.146645\pi$
$854$	48.2674	+	66.4344i	0.0565192	+	0.0777920i
$855$	−31.9126	−	29.7597i	−0.0373247	−	0.0348067i
$856$	165.617	+	120.328i	0.193478	+	0.140570i
$857$	796.776	+	796.776i	0.929727	+	0.929727i	0.997688	−	0.0679611i	$-0.0216494\pi$
$857$	796.776	+	796.776i	0.929727	+	0.929727i	−0.0679611	+	0.997688i	$0.521649\pi$
$858$	633.582	−	100.350i	0.738441	−	0.116957i
$859$	−1498.52	−	486.899i	−1.74449	−	0.566820i	−0.749080	−	0.662480i	$-0.769504\pi$
$859$	−1498.52	−	486.899i	−1.74449	−	0.566820i	−0.995414	+	0.0956596i	$0.969504\pi$
$860$	22.1402	+	634.228i	0.0257444	+	0.737474i
$861$	10.1104	+	31.1167i	0.0117426	+	0.0361401i
$862$	−528.012	+	269.035i	−0.612543	+	0.312106i
$863$	−257.875	−	506.109i	−0.298813	−	0.586453i	0.691968	−	0.721928i	$-0.256744\pi$
$863$	−257.875	−	506.109i	−0.298813	−	0.586453i	−0.990781	+	0.135475i	$0.956744\pi$
$864$	130.409	−	42.3724i	0.150936	−	0.0490422i
$865$	−153.130	+	534.003i	−0.177029	+	0.617344i
$866$	−123.301	+	379.481i	−0.142380	+	0.438200i
$867$	45.3509	+	286.334i	0.0523078	+	0.330258i
$868$	−5.63584	+	5.63584i	−0.00649290	+	0.00649290i
$869$	−847.947	+	1167.10i	−0.975774	+	1.34304i
$870$	530.529	−	103.118i	0.609804	−	0.118526i
$871$	−246.250	+	178.911i	−0.282721	+	0.205409i
$872$	1549.97	+	245.492i	1.77749	+	0.281527i
$873$	76.1901	+	38.8208i	0.0872739	+	0.0444683i
$874$		−	31.0821i		−	0.0355630i
$875$	14.4832	−	68.1263i	0.0165523	−	0.0778587i
$876$	62.3363			0.0711602
$877$	−184.787	+	362.665i	−0.210703	+	0.413529i	−0.972036	−	0.234833i	$-0.924546\pi$
$877$	−184.787	+	362.665i	−0.210703	+	0.413529i	0.761332	+	0.648362i	$0.224546\pi$
$878$	36.9764	−	233.460i	0.0421143	−	0.265899i
$879$	59.6623	+	82.1181i	0.0678752	+	0.0934222i
$880$	−108.739	−	559.449i	−0.123567	−	0.635738i
$881$	614.164	+	446.216i	0.697122	+	0.506489i	0.878994	−	0.476834i	$-0.158216\pi$
$881$	614.164	+	446.216i	0.697122	+	0.506489i	−0.181872	+	0.983322i	$0.558216\pi$
$882$	152.499	+	152.499i	0.172901	+	0.172901i
$883$	511.058	−	80.9437i	0.578775	−	0.0916690i	0.139818	−	0.990177i	$-0.455348\pi$
$883$	511.058	−	80.9437i	0.578775	−	0.0916690i	0.438957	+	0.898508i	$0.355348\pi$
$884$	227.160	+	73.8087i	0.256968	+	0.0834940i
$885$	−106.871	−	30.6461i	−0.120758	−	0.0346284i
$886$	−146.308	−	450.291i	−0.165133	−	0.508229i
$887$	676.295	−	344.590i	0.762453	−	0.388489i	−0.0291107	−	0.999576i	$-0.509268\pi$
$887$	676.295	−	344.590i	0.762453	−	0.388489i	0.791563	+	0.611087i	$0.209268\pi$
$888$	−330.613	−	648.864i	−0.372312	−	0.730703i
$889$	53.0764	−	17.2456i	0.0597035	−	0.0193989i
$890$	−821.225	+	28.6680i	−0.922725	+	0.0322113i
$891$	58.6260	−	180.432i	0.0657980	−	0.202505i
$892$	107.466	+	678.512i	0.120477	+	0.760663i
$893$	8.62299	−	8.62299i	0.00965621	−	0.00965621i
$894$	−156.982	+	216.067i	−0.175595	+	0.241685i
$895$	243.243	−	260.840i	0.271780	−	0.291442i
$896$	−7.25484	+	5.27095i	−0.00809692	+	0.00588275i
$897$	−147.316	−	23.3326i	−0.164232	−	0.0260118i
$898$	−567.261	−	289.034i	−0.631694	−	0.321864i
$899$		−	332.197i		−	0.369518i
$900$	87.7401	+	104.570i	0.0974890	+	0.116189i
$901$	1031.32			1.14464
$902$	−479.025	+	940.139i	−0.531070	+	1.04228i
$903$	−10.5282	+	66.4726i	−0.0116592	+	0.0736130i
$904$	391.103	+	538.308i	0.432636	+	0.595473i
$905$	−232.085	+	497.692i	−0.256448	+	0.549936i
$906$	−104.935	−	76.2395i	−0.115822	−	0.0841495i
$907$	−238.082	−	238.082i	−0.262493	−	0.262493i	0.563573	−	0.826066i	$-0.309426\pi$
$907$	−238.082	−	238.082i	−0.262493	−	0.262493i	−0.826066	+	0.563573i	$0.809426\pi$
$908$	−568.075	+	89.9742i	−0.625633	+	0.0990905i
$909$	188.777	+	61.3373i	0.207675	+	0.0674778i
$910$	−27.3716	+	40.5790i	−0.0300787	+	0.0445923i
$911$	14.8379	+	45.6663i	0.0162875	+	0.0501277i	0.958870	−	0.283846i	$-0.0916104\pi$
$911$	14.8379	+	45.6663i	0.0162875	+	0.0501277i	−0.942582	+	0.333974i	$0.891610\pi$
$912$	24.2755	−	12.3690i	0.0266179	−	0.0135625i
$913$	235.014	+	461.241i	0.257409	+	0.505193i
$914$	164.777	−	53.5393i	0.180281	−	0.0585769i
$915$	−295.648	−	812.317i	−0.323113	−	0.887778i
$916$	22.3777	−	68.8715i	0.0244298	−	0.0751872i
$917$	17.9583	+	113.384i	0.0195837	+	0.123647i
$918$	−59.8275	+	59.8275i	−0.0651716	+	0.0651716i
$919$	−685.407	+	943.382i	−0.745818	+	1.02653i	0.252445	+	0.967611i	$0.418765\pi$
$919$	−685.407	+	943.382i	−0.745818	+	1.02653i	−0.998263	+	0.0589192i	$0.981235\pi$
$920$	−37.8961	+	308.608i	−0.0411914	+	0.335444i
$921$	−448.568	+	325.904i	−0.487045	+	0.353859i
$922$	622.552	+	98.6025i	0.675219	+	0.106944i
$923$	−890.095	−	453.526i	−0.964350	−	0.491361i
$924$			37.0264i			0.0400719i
$925$	802.522	−	923.152i	0.867592	−	0.998002i
$926$	−582.418			−0.628961
$927$	74.5902	−	146.392i	0.0804641	−	0.157920i
$928$	174.485	−	1101.66i	0.188023	−	1.18713i
$929$	−296.480	−	408.070i	−0.319139	−	0.439257i	0.619065	−	0.785340i	$-0.287512\pi$
$929$	−296.480	−	408.070i	−0.319139	−	0.439257i	−0.938204	+	0.346083i	$0.887512\pi$
$930$	−87.8951	+	48.7197i	−0.0945108	+	0.0523867i
$931$	−114.589	−	83.2536i	−0.123081	−	0.0894238i
$932$	−387.182	−	387.182i	−0.415431	−	0.415431i
$933$	485.243	−	76.8550i	0.520089	−	0.0823740i
$934$	1110.55	+	360.840i	1.18903	+	0.386338i
$935$	−715.617	−	915.971i	−0.765366	−	0.979648i
$936$	−94.7953	−	291.750i	−0.101277	−	0.311699i
$937$	721.832	−	367.792i	0.770365	−	0.392521i	−0.0241942	−	0.999707i	$-0.507702\pi$
$937$	721.832	−	367.792i	0.770365	−	0.392521i	0.794559	+	0.607187i	$0.207702\pi$
$938$	9.55346	+	18.7497i	0.0101849	+	0.0199890i
$939$	−851.778	+	276.760i	−0.907112	+	0.294739i
$940$	−30.0616	+	23.4861i	−0.0319804	+	0.0249853i
$941$	−67.1154	+	206.560i	−0.0713235	+	0.219511i	−0.980364	−	0.197197i	$-0.936816\pi$
$941$	−67.1154	+	206.560i	−0.0713235	+	0.219511i	0.909040	+	0.416708i	$0.136816\pi$
$942$	8.21276	+	51.8533i	0.00871843	+	0.0550460i
$943$	173.478	−	173.478i	0.183964	−	0.183964i
$944$	40.8024	−	56.1597i	0.0432229	−	0.0594912i
$945$	7.01807	+	12.6613i	0.00742653	+	0.0133982i
$946$	−1755.92	+	1275.75i	−1.85615	+	1.34857i
$947$	425.771	+	67.4355i	0.449600	+	0.0712096i	0.377129	−	0.926161i	$-0.376911\pi$
$947$	425.771	+	67.4355i	0.449600	+	0.0712096i	0.0724712	+	0.997371i	$0.476911\pi$
$948$	192.224	+	97.9431i	0.202768	+	0.103316i
$949$		−	235.305i		−	0.247951i
$950$	81.0370	+	70.4478i	0.0853021	+	0.0741556i
$951$	375.115			0.394443
$952$	23.9724	−	47.0484i	0.0251811	−	0.0494206i
$953$	−167.899	+	1060.07i	−0.176180	+	1.11236i	0.728117	+	0.685452i	$0.240396\pi$
$953$	−167.899	+	1060.07i	−0.176180	+	1.11236i	−0.904297	+	0.426903i	$0.859604\pi$
$954$	−243.471	−	335.108i	−0.255210	−	0.351267i
$955$	−53.4145	−	6.55912i	−0.0559314	−	0.00686819i
$956$	−333.324	−	242.174i	−0.348665	−	0.253320i
$957$	−1091.24	−	1091.24i	−1.14027	−	1.14027i
$958$	−780.971	+	123.694i	−0.815210	+	0.129117i
$959$	49.5421	+	16.0972i	0.0516601	+	0.0167854i
$960$	−493.092	+	179.464i	−0.513638	+	0.186942i
$961$	−277.877	−	855.219i	−0.289154	−	0.889926i
$962$	−765.949	+	390.271i	−0.796205	+	0.405687i
$963$	−32.4463	−	63.6795i	−0.0336929	−	0.0661261i
$964$	537.061	−	174.502i	0.557117	−	0.181018i
$965$	−971.579	−	655.355i	−1.00682	−	0.679125i
$966$	−3.18646	+	9.80691i	−0.00329861	+	0.0101521i
$967$	−252.438	−	1593.83i	−0.261053	−	1.64822i	−0.674924	−	0.737887i	$-0.735824\pi$
$967$	−252.438	−	1593.83i	−0.261053	−	1.64822i	0.413871	−	0.910335i	$-0.364176\pi$
$968$	−1964.79	+	1964.79i	−2.02974	+	2.02974i
$969$	32.6616	−	44.9549i	0.0337065	−	0.0463931i
$970$	−190.706	−	88.9303i	−0.196604	−	0.0916807i
$971$	−815.526	+	592.515i	−0.839883	+	0.610211i	−0.922338	−	0.386384i	$-0.873724\pi$
$971$	−815.526	+	592.515i	−0.839883	+	0.610211i	0.0824550	+	0.996595i	$0.473724\pi$
$972$	−28.0224	−	4.43831i	−0.0288296	−	0.00456616i
$973$	−29.7542	−	15.1605i	−0.0305799	−	0.0155812i
$974$			384.998i			0.395275i
$975$	394.726	−	331.199i	0.404848	−	0.339691i
$976$	539.741			0.553013
$977$	612.098	−	1201.31i	0.626508	−	1.22959i	−0.331664	−	0.943397i	$-0.607610\pi$
$977$	612.098	−	1201.31i	0.626508	−	1.22959i	0.958172	−	0.286193i	$-0.0923898\pi$
$978$	89.1092	−	562.614i	0.0911137	−	0.575269i
$979$	1379.17	+	1898.26i	1.40875	+	1.93898i
$980$	324.049	+	302.187i	0.330662	+	0.308354i
$981$	−443.234	−	322.029i	−0.451819	−	0.328266i
$982$	246.019	+	246.019i	0.250528	+	0.250528i
$983$	−324.809	+	51.4447i	−0.330426	+	0.0523344i	−0.319444	−	0.947605i	$-0.603496\pi$
$983$	−324.809	+	51.4447i	−0.330426	+	0.0523344i	−0.0109828	+	0.999940i	$0.503496\pi$
$984$	479.887	+	155.925i	0.487690	+	0.158460i
$985$	−33.5413	−	960.826i	−0.0340521	−	0.975458i
$986$	212.679	+	654.557i	0.215698	+	0.663851i
$987$	−3.60471	+	1.83669i	−0.00365218	+	0.00186088i
$988$	28.6029	+	56.1363i	0.0289503	+	0.0568182i
$989$	479.956	−	155.947i	0.485295	−	0.157682i
$990$	−128.688	+	448.767i	−0.129987	+	0.453300i
$991$	387.220	−	1191.74i	0.390736	−	1.20256i	−0.541496	−	0.840703i	$-0.682142\pi$
$991$	387.220	−	1191.74i	0.390736	−	1.20256i	0.932233	−	0.361859i	$-0.117858\pi$
$992$	32.4444	+	204.846i	0.0327060	+	0.206498i
$993$	498.155	−	498.155i	0.501667	−	0.501667i
$994$	−40.5947	+	55.8738i	−0.0408397	+	0.0562110i
$995$	1229.48	−	238.971i	1.23565	−	0.240172i
$996$	62.6299	−	45.5033i	0.0628814	−	0.0456860i
$997$	−1543.84	−	244.519i	−1.54848	−	0.245255i	−0.677110	−	0.735881i	$-0.736768\pi$
$997$	−1543.84	−	244.519i	−1.54848	−	0.245255i	−0.871370	+	0.490626i	$0.836768\pi$
$998$	−772.280	−	393.496i	−0.773828	−	0.394285i
$999$			254.240i			0.254495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.67.7	yes	80
3.2	odd	2		225.3.r.b.217.4		80
5.2	odd	4		375.3.k.b.268.7		80
5.3	odd	4		375.3.k.c.268.4		80
5.4	even	2		375.3.k.a.232.4		80
25.3	odd	20	inner	75.3.k.a.28.7	✓	80
25.4	even	10		375.3.k.b.7.7		80
25.21	even	5		375.3.k.c.7.4		80
25.22	odd	20		375.3.k.a.118.4		80
75.53	even	20		225.3.r.b.28.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.7	✓	80	25.3	odd	20	inner
75.3.k.a.67.7	yes	80	1.1	even	1	trivial
225.3.r.b.28.4		80	75.53	even	20
225.3.r.b.217.4		80	3.2	odd	2
375.3.k.a.118.4		80	25.22	odd	20
375.3.k.a.232.4		80	5.4	even	2
375.3.k.b.7.7		80	25.4	even	10
375.3.k.b.268.7		80	5.2	odd	4
375.3.k.c.7.4		80	25.21	even	5
375.3.k.c.268.4		80	5.3	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.670302 - 1.31554i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(1.06979 + 1.47245i) q^{4} +(0.953987 + 4.90815i) q^{5} +(2.06891 + 1.50315i) q^{6} +(0.393993 + 0.393993i) q^{7} +(8.48731 - 1.34426i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(0.670302 - 1.31554i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(1.06979 + 1.47245i) q^{4} +(0.953987 + 4.90815i) q^{5} +(2.06891 + 1.50315i) q^{6} +(0.393993 + 0.393993i) q^{7} +(8.48731 - 1.34426i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(7.09633 + 2.03493i) q^{10} +(-6.51400 - 20.0480i) q^{11} +(-2.80882 + 1.43116i) q^{12} +(5.40231 + 10.6026i) q^{13} +(0.782409 - 0.254220i) q^{14} +(-8.65498 + 0.302135i) q^{15} +(1.67094 - 5.14262i) q^{16} +(-1.72521 - 10.8926i) q^{17} +(-3.13206 + 3.13206i) q^{18} +(1.70989 - 2.35346i) q^{19} +(-6.20641 + 6.65540i) q^{20} +(-0.780768 + 0.567261i) q^{21} +(-30.7404 - 4.86880i) q^{22} +(6.44790 + 3.28537i) q^{23} +14.8837i q^{24} +(-23.1798 + 9.36461i) q^{25} +17.5694 q^{26} +(2.35900 - 4.62981i) q^{27} +(-0.158642 + 1.00163i) q^{28} +(-24.8443 - 34.1952i) q^{29} +(-5.40398 + 11.5885i) q^{30} +(6.35836 + 4.61962i) q^{31} +(18.6597 + 18.6597i) q^{32} +(36.0617 - 5.71161i) q^{33} +(-15.4860 - 5.03172i) q^{34} +(-1.55791 + 2.30964i) q^{35} +(-1.68727 - 5.19289i) q^{36} +(-43.5956 + 22.2131i) q^{37} +(-1.94993 - 3.82695i) q^{38} +(-19.6020 + 6.36907i) q^{39} +(14.6946 + 40.3746i) q^{40} +(10.4762 - 32.2425i) q^{41} +(0.222906 + 1.40737i) q^{42} +(49.3109 - 49.3109i) q^{43} +(22.5510 - 31.0388i) q^{44} +(1.82822 - 14.8882i) q^{45} +(8.64408 - 6.28029i) q^{46} +(4.14042 + 0.655778i) q^{47} +(8.34487 + 4.25192i) q^{48} -48.6895i q^{49} +(-3.21794 + 36.7712i) q^{50} +19.1016 q^{51} +(-9.83244 + 19.2973i) q^{52} +(-14.6290 + 92.3640i) q^{53} +(-4.50946 - 6.20674i) q^{54} +(92.1844 - 51.0972i) q^{55} +(3.87357 + 2.81431i) q^{56} +(3.56282 + 3.56282i) q^{57} +(-61.6384 + 9.76256i) q^{58} +(12.2094 + 3.96708i) q^{59} +(-9.70393 - 12.4208i) q^{60} +(30.8453 + 94.9322i) q^{61} +(10.3393 - 5.26815i) q^{62} +(-0.758878 - 1.48938i) q^{63} +(57.6257 - 18.7237i) q^{64} +(-46.8856 + 36.6301i) q^{65} +(16.6584 - 51.2692i) q^{66} +(4.00146 + 25.2642i) q^{67} +(14.1931 - 14.1931i) q^{68} +(-7.36744 + 10.1404i) q^{69} +(1.99416 + 3.59766i) q^{70} +(-67.9173 + 49.3448i) q^{71} +(-25.4619 - 4.03277i) q^{72} +(-17.6189 - 8.97729i) q^{73} +72.2414i q^{74} +(-9.73966 - 42.1917i) q^{75} +5.29457 q^{76} +(5.33232 - 10.4653i) q^{77} +(-4.76047 + 30.0564i) q^{78} +(-40.2257 - 55.3659i) q^{79} +(26.8348 + 3.29522i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-35.3941 - 35.3941i) q^{82} +(-24.2550 + 3.84162i) q^{83} +(-1.67052 - 0.542786i) q^{84} +(51.8165 - 18.8590i) q^{85} +(-31.8174 - 97.9238i) q^{86} +(65.2302 - 33.2365i) q^{87} +(-82.2361 - 161.397i) q^{88} +(-105.862 + 34.3966i) q^{89} +(-18.3606 - 12.3847i) q^{90} +(-2.04889 + 6.30584i) q^{91} +(2.06040 + 13.0089i) q^{92} +(-9.62572 + 9.62572i) q^{93} +(3.63804 - 5.00733i) q^{94} +(13.1823 + 6.14721i) q^{95} +(-36.9775 + 26.8657i) q^{96} +(-28.1525 - 4.45891i) q^{97} +(-64.0531 - 32.6367i) q^{98} +63.2392i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

L-functions

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