LMFDB - Embedded newform 490.2.s.a.223.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(13,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 22]))

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

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

chi := DirichletCharacter("490.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.s (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			223.20
Character	$\chi$	$=$	490.223
Dual form			490.2.s.a.167.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.330279 - 0.943883i) q^{2} +(-0.362657 - 0.577166i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(1.73060 - 1.41599i) q^{5} +(-0.664555 + 0.151680i) q^{6} +(-2.08663 - 1.62664i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.10005 - 2.28428i) q^{9} +O(q^{10})$	\(q+(0.330279 - 0.943883i) q^{2} +(-0.362657 - 0.577166i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(1.73060 - 1.41599i) q^{5} +(-0.664555 + 0.151680i) q^{6} +(-2.08663 - 1.62664i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.10005 - 2.28428i) q^{9} +(-0.764943 - 2.10116i) q^{10} +(-0.921411 + 0.443728i) q^{11} +(-0.0763201 + 0.677359i) q^{12} +(-0.713313 + 2.03853i) q^{13} +(-2.22453 + 1.43229i) q^{14} +(-1.44487 - 0.485327i) q^{15} +(0.222521 + 0.974928i) q^{16} +(0.178216 - 1.58171i) q^{17} +(-1.79277 - 1.79277i) q^{18} +0.760557 q^{19} +(-2.23589 + 0.0280490i) q^{20} +(-0.182111 + 1.79425i) q^{21} +(0.114505 + 1.01626i) q^{22} +(-3.53697 + 0.398521i) q^{23} +(0.614141 + 0.295755i) q^{24} +(0.989970 - 4.90102i) q^{25} +(1.68854 + 1.34657i) q^{26} +(-3.74943 + 0.422459i) q^{27} +(0.617198 + 2.57275i) q^{28} +(0.279330 - 0.222759i) q^{29} +(-0.935303 + 1.20350i) q^{30} -6.31831i q^{31} +(0.993712 + 0.111964i) q^{32} +(0.590261 + 0.370886i) q^{33} +(-1.43409 - 0.690623i) q^{34} +(-5.91443 + 0.139566i) q^{35} +(-2.28428 + 1.10005i) q^{36} +(2.16667 + 0.244125i) q^{37} +(0.251196 - 0.717877i) q^{38} +(1.43526 - 0.327588i) q^{39} +(-0.711993 + 2.11969i) q^{40} +(2.96817 + 0.677465i) q^{41} +(1.63341 + 0.764493i) q^{42} +(-0.499865 + 0.795530i) q^{43} +(0.997049 + 0.227570i) q^{44} +(-1.33076 - 5.51084i) q^{45} +(-0.792030 + 3.47011i) q^{46} +(1.21133 + 0.423863i) q^{47} +(0.481996 - 0.481996i) q^{48} +(1.70806 + 6.78841i) q^{49} +(-4.29902 - 2.55312i) q^{50} +(-0.977543 + 0.470760i) q^{51} +(1.82869 - 1.14904i) q^{52} +(-6.84697 + 0.771469i) q^{53} +(-0.839605 + 3.67855i) q^{54} +(-0.966284 + 2.07262i) q^{55} +(2.63223 + 0.267164i) q^{56} +(-0.275822 - 0.438967i) q^{57} +(-0.118001 - 0.337228i) q^{58} +(1.52858 + 6.69717i) q^{59} +(0.827051 + 1.28031i) q^{60} +(10.6969 - 8.53047i) q^{61} +(-5.96375 - 2.08681i) q^{62} +(-6.01111 + 2.97706i) q^{63} +(0.433884 - 0.900969i) q^{64} +(1.65207 + 4.53793i) q^{65} +(0.545024 - 0.434642i) q^{66} +(-4.39924 + 4.39924i) q^{67} +(-1.12552 + 1.12552i) q^{68} +(1.51272 + 1.89689i) q^{69} +(-1.82168 + 5.62863i) q^{70} +(10.4537 - 13.1085i) q^{71} +(0.283870 + 2.51942i) q^{72} +(13.6494 - 4.77613i) q^{73} +(0.946031 - 1.96445i) q^{74} +(-3.18772 + 1.20601i) q^{75} +(-0.594628 - 0.474200i) q^{76} +(2.64443 + 0.572911i) q^{77} +(0.164831 - 1.46291i) q^{78} +2.99107i q^{79} +(1.76558 + 1.37213i) q^{80} +(-3.13873 - 3.93584i) q^{81} +(1.61977 - 2.57785i) q^{82} +(2.95370 - 1.03354i) q^{83} +(1.26107 - 1.28925i) q^{84} +(-1.93126 - 2.98967i) q^{85} +(0.585793 + 0.734561i) q^{86} +(-0.229870 - 0.0804349i) q^{87} +(0.544104 - 0.865936i) q^{88} +(10.6936 + 5.14978i) q^{89} +(-5.64111 - 0.564036i) q^{90} +(4.80439 - 3.09336i) q^{91} +(3.01379 + 1.89369i) q^{92} +(-3.64671 + 2.29138i) q^{93} +(0.800154 - 1.00336i) q^{94} +(1.31622 - 1.07694i) q^{95} +(-0.295755 - 0.614141i) q^{96} +(4.64016 + 4.64016i) q^{97} +(6.97160 + 0.629860i) q^{98} +2.59289i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) $ 336 * q + 28 * q^6 + 8 * q^7	$ 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) $ 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.330279	−	0.943883i	0.233543	−	0.667426i
$2$	0.330279	−	0.943883i	0.233543	−	0.667426i
$3$	−0.362657	−	0.577166i	−0.209380	−	0.333227i	0.725480	−	0.688244i	$-0.241618\pi$
$3$	−0.362657	−	0.577166i	−0.209380	−	0.333227i	−0.934860	+	0.355017i	$0.884475\pi$
$4$	−0.781831	−	0.623490i	−0.390916	−	0.311745i
$5$	1.73060	−	1.41599i	0.773949	−	0.633248i
$5$	1.73060	−	1.41599i	0.773949	−	0.633248i
$6$	−0.664555	+	0.151680i	−0.271303	+	0.0619232i
$7$	−2.08663	−	1.62664i	−0.788673	−	0.614814i
$7$	−2.08663	−	1.62664i	−0.788673	−	0.614814i
$8$	−0.846724	+	0.532032i	−0.299362	+	0.188102i
$9$	1.10005	−	2.28428i	0.366684	−	0.761427i
$10$	−0.764943	−	2.10116i	−0.241896	−	0.664444i
$11$	−0.921411	+	0.443728i	−0.277816	+	0.133789i	−0.567604	−	0.823302i	$-0.692129\pi$
$11$	−0.921411	+	0.443728i	−0.277816	+	0.133789i	0.289788	+	0.957091i	$0.406415\pi$
$12$	−0.0763201	+	0.677359i	−0.0220317	+	0.195537i
$13$	−0.713313	+	2.03853i	−0.197837	+	0.565387i	−0.999474	−	0.0324246i	$-0.989677\pi$
$13$	−0.713313	+	2.03853i	−0.197837	+	0.565387i	0.801637	+	0.597811i	$0.203963\pi$
$14$	−2.22453	+	1.43229i	−0.594531	+	0.382796i
$15$	−1.44487	−	0.485327i	−0.373065	−	0.125311i
$16$	0.222521	+	0.974928i	0.0556302	+	0.243732i
$17$	0.178216	−	1.58171i	0.0432238	−	0.383622i	−0.953412	−	0.301670i	$-0.902456\pi$
$17$	0.178216	−	1.58171i	0.0432238	−	0.383622i	0.996636	−	0.0819522i	$-0.0261155\pi$
$18$	−1.79277	−	1.79277i	−0.422560	−	0.422560i
$19$	0.760557			0.174484			0.0872419	−	0.996187i	$-0.472195\pi$
$19$	0.760557			0.174484			0.0872419	+	0.996187i	$0.472195\pi$
$20$	−2.23589	+	0.0280490i	−0.499961	+	0.00627196i
$21$	−0.182111	+	1.79425i	−0.0397399	+	0.391536i
$22$	0.114505	+	1.01626i	0.0244125	+	0.216667i
$23$	−3.53697	+	0.398521i	−0.737509	+	0.0830973i	−0.472724	−	0.881210i	$-0.656729\pi$
$23$	−3.53697	+	0.398521i	−0.737509	+	0.0830973i	−0.264785	+	0.964308i	$0.585301\pi$
$24$	0.614141	+	0.295755i	0.125361	+	0.0603707i
$25$	0.989970	−	4.90102i	0.197994	−	0.980203i
$26$	1.68854	+	1.34657i	0.331151	+	0.264084i
$27$	−3.74943	+	0.422459i	−0.721578	+	0.0813023i
$28$	0.617198	+	2.57275i	0.116640	+	0.486205i
$29$	0.279330	−	0.222759i	0.0518704	−	0.0413652i	−0.597211	−	0.802084i	$-0.703725\pi$
$29$	0.279330	−	0.222759i	0.0518704	−	0.0413652i	0.649082	+	0.760719i	$0.275153\pi$
$30$	−0.935303	+	1.20350i	−0.170762	+	0.219728i
$31$		−	6.31831i		−	1.13480i	−0.823442	−	0.567401i	$-0.807949\pi$
$31$		−	6.31831i		−	1.13480i	0.823442	−	0.567401i	$-0.192051\pi$
$32$	0.993712	+	0.111964i	0.175665	+	0.0197927i
$33$	0.590261	+	0.370886i	0.102751	+	0.0645629i
$34$	−1.43409	−	0.690623i	−0.245945	−	0.118441i
$35$	−5.91443	+	0.139566i	−0.999722	+	0.0235910i
$36$	−2.28428	+	1.10005i	−0.380713	+	0.183342i
$37$	2.16667	+	0.244125i	0.356198	+	0.0401339i	0.288251	−	0.957555i	$-0.406926\pi$
$37$	2.16667	+	0.244125i	0.356198	+	0.0401339i	0.0679476	+	0.997689i	$0.478355\pi$
$38$	0.251196	−	0.717877i	0.0407494	−	0.116455i
$39$	1.43526	−	0.327588i	0.229825	−	0.0524561i
$40$	−0.711993	+	2.11969i	−0.112576	+	0.335152i
$41$	2.96817	+	0.677465i	0.463550	+	0.105802i	0.447916	−	0.894076i	$-0.352166\pi$
$41$	2.96817	+	0.677465i	0.463550	+	0.105802i	0.0156336	+	0.999878i	$0.495023\pi$
$42$	1.63341	+	0.764493i	0.252041	+	0.117964i
$43$	−0.499865	+	0.795530i	−0.0762287	+	0.121317i	−0.882663	−	0.470006i	$-0.844252\pi$
$43$	−0.499865	+	0.795530i	−0.0762287	+	0.121317i	0.806434	+	0.591324i	$0.201394\pi$
$44$	0.997049	+	0.227570i	0.150311	+	0.0343074i
$45$	−1.33076	−	5.51084i	−0.198377	−	0.821507i
$46$	−0.792030	+	3.47011i	−0.116778	+	0.511640i
$47$	1.21133	+	0.423863i	0.176691	+	0.0618267i	0.417175	−	0.908826i	$-0.363020\pi$
$47$	1.21133	+	0.423863i	0.176691	+	0.0618267i	−0.240484	+	0.970653i	$0.577306\pi$
$48$	0.481996	−	0.481996i	0.0695701	−	0.0695701i
$49$	1.70806	+	6.78841i	0.244009	+	0.969773i
$50$	−4.29902	−	2.55312i	−0.607973	−	0.361066i
$51$	−0.977543	+	0.470760i	−0.136883	+	0.0659195i
$52$	1.82869	−	1.14904i	0.253594	−	0.159344i
$53$	−6.84697	+	0.771469i	−0.940504	+	0.105969i	−0.568886	−	0.822416i	$-0.692625\pi$
$53$	−6.84697	+	0.771469i	−0.940504	+	0.105969i	−0.371618	+	0.928386i	$0.621197\pi$
$54$	−0.839605	+	3.67855i	−0.114256	+	0.500587i
$55$	−0.966284	+	2.07262i	−0.130294	+	0.279472i
$56$	2.63223	+	0.267164i	0.351746	+	0.0357013i
$57$	−0.275822	−	0.438967i	−0.0365335	−	0.0581427i
$58$	−0.118001	−	0.337228i	−0.0154943	−	0.0442802i
$59$	1.52858	+	6.69717i	0.199005	+	0.871897i	0.971531	+	0.236914i	$0.0761358\pi$
$59$	1.52858	+	6.69717i	0.199005	+	0.871897i	−0.772526	+	0.634983i	$0.781007\pi$
$60$	0.827051	+	1.28031i	0.106772	+	0.165287i
$61$	10.6969	−	8.53047i	1.36959	−	1.09222i	0.383955	−	0.923352i	$-0.374562\pi$
$61$	10.6969	−	8.53047i	1.36959	−	1.09222i	0.985639	−	0.168863i	$-0.0540096\pi$
$62$	−5.96375	−	2.08681i	−0.757397	−	0.265025i
$63$	−6.01111	+	2.97706i	−0.757329	+	0.375074i
$64$	0.433884	−	0.900969i	0.0542355	−	0.112621i
$65$	1.65207	+	4.53793i	0.204914	+	0.562861i
$66$	0.545024	−	0.434642i	0.0670878	−	0.0535007i
$67$	−4.39924	+	4.39924i	−0.537453	+	0.537453i	−0.922780	−	0.385327i	$-0.874089\pi$
$67$	−4.39924	+	4.39924i	−0.537453	+	0.537453i	0.385327	+	0.922780i	$0.374089\pi$
$68$	−1.12552	+	1.12552i	−0.136489	+	0.136489i
$69$	1.51272	+	1.89689i	0.182110	+	0.228359i
$70$	−1.82168	+	5.62863i	−0.217732	+	0.672750i
$71$	10.4537	−	13.1085i	1.24062	−	1.55569i	0.541477	−	0.840716i	$-0.317865\pi$
$71$	10.4537	−	13.1085i	1.24062	−	1.55569i	0.699147	−	0.714978i	$-0.253563\pi$
$72$	0.283870	+	2.51942i	0.0334544	+	0.296916i
$73$	13.6494	−	4.77613i	1.59754	−	0.559004i	0.622807	−	0.782375i	$-0.285992\pi$
$73$	13.6494	−	4.77613i	1.59754	−	0.559004i	0.974733	+	0.223372i	$0.0717063\pi$
$74$	0.946031	−	1.96445i	0.109974	−	0.228363i
$75$	−3.18772	+	1.20601i	−0.368086	+	0.139258i
$76$	−0.594628	−	0.474200i	−0.0682085	−	0.0543944i
$77$	2.64443	+	0.572911i	0.301361	+	0.0652892i
$78$	0.164831	−	1.46291i	0.0186634	−	0.165642i
$79$			2.99107i			0.336522i	0.985742	+	0.168261i	$0.0538151\pi$
$79$			2.99107i			0.336522i	−0.985742	+	0.168261i	$0.946185\pi$
$80$	1.76558	+	1.37213i	0.197398	+	0.153408i
$81$	−3.13873	−	3.93584i	−0.348748	−	0.437316i
$82$	1.61977	−	2.57785i	0.178874	−	0.284676i
$83$	2.95370	−	1.03354i	0.324210	−	0.113446i	−0.163267	−	0.986582i	$-0.552203\pi$
$83$	2.95370	−	1.03354i	0.324210	−	0.113446i	0.487477	+	0.873136i	$0.337917\pi$
$84$	1.26107	−	1.28925i	0.137594	−	0.140669i
$85$	−1.93126	−	2.98967i	−0.209475	−	0.324275i
$86$	0.585793	+	0.734561i	0.0631677	+	0.0792098i
$87$	−0.229870	−	0.0804349i	−0.0246446	−	0.00862353i
$88$	0.544104	−	0.865936i	0.0580016	−	0.0923091i
$89$	10.6936	+	5.14978i	1.13352	+	0.545875i	0.904044	−	0.427439i	$-0.140584\pi$
$89$	10.6936	+	5.14978i	1.13352	+	0.545875i	0.229477	+	0.973314i	$0.426298\pi$
$90$	−5.64111	−	0.564036i	−0.594625	−	0.0594546i
$91$	4.80439	−	3.09336i	0.503636	−	0.324272i
$92$	3.01379	+	1.89369i	0.314209	+	0.197431i
$93$	−3.64671	+	2.29138i	−0.378146	+	0.237605i
$94$	0.800154	−	1.00336i	0.0825296	−	0.103489i
$95$	1.31622	−	1.07694i	0.135042	−	0.110492i
$96$	−0.295755	−	0.614141i	−0.0301853	−	0.0626805i
$97$	4.64016	+	4.64016i	0.471137	+	0.471137i	0.902283	−	0.431145i	$-0.141890\pi$
$97$	4.64016	+	4.64016i	0.471137	+	0.471137i	−0.431145	+	0.902283i	$0.641890\pi$
$98$	6.97160	+	0.629860i	0.704238	+	0.0636255i
$99$			2.59289i			0.260595i
$100$	−3.82972	+	3.21453i	−0.382972	+	0.321453i
$101$	2.89786	+	0.661418i	0.288348	+	0.0658135i	0.364248	−	0.931302i	$-0.381326\pi$
$101$	2.89786	+	0.661418i	0.288348	+	0.0658135i	−0.0759004	+	0.997115i	$0.524183\pi$
$102$	0.121480	+	1.07817i	0.0120284	+	0.106755i
$103$	4.85437	+	7.72568i	0.478315	+	0.761234i	0.995512	−	0.0946324i	$-0.0301676\pi$
$103$	4.85437	+	7.72568i	0.478315	+	0.761234i	−0.517197	+	0.855866i	$0.673025\pi$
$104$	−0.480585	−	2.10558i	−0.0471252	−	0.206469i
$105$	2.22546	+	3.36299i	0.217183	+	0.328194i
$106$	−1.53324	+	6.71754i	−0.148921	+	0.652466i
$107$	10.2597	−	3.59004i	0.991846	−	0.347062i	0.214905	−	0.976635i	$-0.431056\pi$
$107$	10.2597	−	3.59004i	0.991846	−	0.347062i	0.776941	+	0.629573i	$0.216770\pi$
$108$	3.19482	+	2.00744i	0.307422	+	0.193166i
$109$	5.52045	+	11.4633i	0.528763	+	1.09799i	0.978770	+	0.204962i	$0.0657072\pi$
$109$	5.52045	+	11.4633i	0.528763	+	1.09799i	−0.450007	+	0.893025i	$0.648579\pi$
$110$	1.63717	+	1.59660i	0.156098	+	0.152230i
$111$	−0.644858	−	1.33906i	−0.0612072	−	0.127098i
$112$	1.12154	−	2.39628i	0.105976	−	0.226427i
$113$	−6.31055	−	18.0345i	−0.593646	−	1.69654i	−0.710768	−	0.703427i	$-0.751652\pi$
$113$	−6.31055	−	18.0345i	−0.593646	−	1.69654i	0.117121	−	0.993118i	$-0.462633\pi$
$114$	−0.505432	+	0.115362i	−0.0473381	+	0.0108046i
$115$	−5.55679	+	5.69798i	−0.518173	+	0.531339i
$116$	−0.357277			−0.0331723
$117$	3.87190	+	3.87190i	0.357957	+	0.357957i
$118$	6.82620	+	0.769128i	0.628403	+	0.0708040i
$119$	−2.94476	+	3.01056i	−0.269946	+	0.275978i
$120$	1.48162	−	0.357781i	0.135253	−	0.0326608i
$121$	−6.20628	+	7.78243i	−0.564208	+	0.707494i
$122$	−4.51882	−	12.9140i	−0.409114	−	1.16918i
$123$	−0.685418	−	1.95881i	−0.0618020	−	0.176620i
$124$	−3.93940	+	4.93985i	−0.353769	+	0.443612i
$125$	−5.22652	−	9.88349i	−0.467474	−	0.884007i
$126$	0.824652	+	6.65705i	0.0734658	+	0.593057i
$127$	−5.98359	−	0.674189i	−0.530958	−	0.0598246i	−0.157584	−	0.987506i	$-0.550371\pi$
$127$	−5.98359	−	0.674189i	−0.530958	−	0.0598246i	−0.373374	+	0.927681i	$0.621799\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.640432			0.0563869
$130$	4.82892	−	0.0605783i	0.423524	−	0.00531307i
$131$	19.1041	−	4.36038i	1.66913	−	0.380968i	0.719538	−	0.694453i	$-0.244353\pi$
$131$	19.1041	−	4.36038i	1.66913	−	0.380968i	0.949593	+	0.313484i	$0.101496\pi$
$132$	−0.230241	−	0.657992i	−0.0200399	−	0.0572708i
$133$	−1.58700	−	1.23716i	−0.137611	−	0.107275i
$134$	2.69939	+	5.60535i	0.233192	+	0.484228i
$135$	−5.89057	+	6.04024i	−0.506980	+	0.519861i
$136$	0.690623	+	1.43409i	0.0592204	+	0.122972i
$137$	−9.06525	−	5.69607i	−0.774497	−	0.486648i	0.0858811	−	0.996305i	$-0.472629\pi$
$137$	−9.06525	−	5.69607i	−0.774497	−	0.486648i	−0.860378	+	0.509657i	$0.829772\pi$
$138$	2.29006	−	0.801327i	0.194943	−	0.0682135i
$139$	2.06623	−	9.05274i	0.175255	−	0.767843i	−0.808525	−	0.588462i	$-0.799733\pi$
$139$	2.06623	−	9.05274i	0.175255	−	0.767843i	0.983780	−	0.179381i	$-0.0574094\pi$
$140$	4.71111	+	3.57847i	0.398161	+	0.302436i
$141$	−0.194659	−	0.852855i	−0.0163932	−	0.0718233i
$142$	−8.92027	−	14.1965i	−0.748572	−	1.19135i
$143$	−0.247299	−	2.19484i	−0.0206802	−	0.183542i
$144$	2.47179	+	0.564171i	0.205983	+	0.0470142i
$145$	0.167987	−	0.781034i	0.0139506	−	0.0648614i
$146$		−	14.4609i		−	1.19679i
$147$	3.29860	−	3.44770i	0.272064	−	0.284361i
$148$	−1.54176	−	1.54176i	−0.126732	−	0.126732i
$149$	−3.94152	−	8.18464i	−0.322902	−	0.670512i	0.674820	−	0.737983i	$-0.264221\pi$
$149$	−3.94152	−	8.18464i	−0.322902	−	0.670512i	−0.997721	+	0.0674706i	$0.978507\pi$
$150$	0.0854982	+	3.40715i	0.00698090	+	0.278193i
$151$	−6.54929	+	8.21255i	−0.532973	+	0.668328i	−0.973307	−	0.229507i	$-0.926289\pi$
$151$	−6.54929	+	8.21255i	−0.532973	+	0.668328i	0.440334	+	0.897834i	$0.354860\pi$
$152$	−0.643982	+	0.404641i	−0.0522339	+	0.0328207i
$153$	−3.41703	−	2.14706i	−0.276251	−	0.173580i
$154$	1.41416	−	2.30682i	0.113956	−	0.185889i
$155$	−8.94663	−	10.9345i	−0.718611	−	0.878279i
$156$	−1.32638	−	0.638750i	−0.106195	−	0.0511409i
$157$	5.71387	−	9.09357i	0.456016	−	0.725746i	−0.537018	−	0.843571i	$-0.680449\pi$
$157$	5.71387	−	9.09357i	0.456016	−	0.725746i	0.993034	+	0.117825i	$0.0375922\pi$
$158$	2.82322	+	0.987888i	0.224603	+	0.0785922i
$159$	2.92837	+	3.67206i	0.232235	+	0.291213i
$160$	1.87826	−	1.21332i	0.148490	−	0.0959211i
$161$	8.02860	+	4.92182i	0.632742	+	0.387894i
$162$	−4.75163	+	1.66267i	−0.373323	+	0.130631i
$163$	−8.70554	+	13.8548i	−0.681871	+	1.08519i	0.309089	+	0.951033i	$0.399976\pi$
$163$	−8.70554	+	13.8548i	−0.681871	+	1.08519i	−0.990960	+	0.134158i	$0.957167\pi$
$164$	−1.89821	−	2.38028i	−0.148226	−	0.185869i
$165$	1.54668	−	0.193946i	0.120409	−	0.0150986i
$166$		−	3.12930i		−	0.242881i
$167$	−0.412446	+	3.66056i	−0.0319160	+	0.283262i	0.967609	+	0.252453i	$0.0812372\pi$
$167$	−0.412446	+	3.66056i	−0.0319160	+	0.283262i	−0.999525	+	0.0308098i	$0.990191\pi$
$168$	−0.800398	−	1.61612i	−0.0617521	−	0.124686i
$169$	6.51701	+	5.19715i	0.501309	+	0.399780i
$170$	−3.45976	+	0.835461i	−0.265351	+	0.0640770i
$171$	0.836652	−	1.73733i	0.0639804	−	0.132857i
$172$	0.886815	−	0.310310i	0.0676190	−	0.0236609i
$173$	0.209053	+	1.85540i	0.0158940	+	0.141063i	0.999153	−	0.0411504i	$-0.0131023\pi$
$173$	0.209053	+	1.85540i	0.0158940	+	0.141063i	−0.983259	+	0.182214i	$0.941674\pi$
$174$	−0.151842	+	0.190404i	−0.0115111	+	0.0144345i
$175$	−10.0379	+	8.61629i	−0.758795	+	0.651330i
$176$	−0.637636	−	0.799571i	−0.0480637	−	0.0602699i
$177$	3.31102	−	3.31102i	0.248872	−	0.248872i
$178$	8.39267	−	8.39267i	0.629057	−	0.629057i
$179$	−1.66412	+	1.32710i	−0.124383	+	0.0991918i	−0.683705	−	0.729758i	$-0.739633\pi$
$179$	−1.66412	+	1.32710i	−0.124383	+	0.0991918i	0.559323	+	0.828950i	$0.311061\pi$
$180$	−2.39552	+	5.13826i	−0.178552	+	0.382983i
$181$	−11.3200	+	23.5061i	−0.841406	+	1.74720i	−0.200315	+	0.979732i	$0.564197\pi$
$181$	−11.3200	+	23.5061i	−0.841406	+	1.74720i	−0.641090	+	0.767465i	$0.721518\pi$
$182$	−1.33298	−	5.55645i	−0.0988071	−	0.411871i
$183$	−8.80279	−	3.08023i	−0.650721	−	0.227697i
$184$	2.78281	−	2.21922i	0.205152	−	0.163603i
$185$	4.09532	−	2.64549i	0.301094	−	0.194500i
$186$	0.958363	+	4.19886i	0.0702706	+	0.307876i
$187$	0.537641	+	1.53649i	0.0393162	+	0.112359i
$188$	−0.682782	−	1.08664i	−0.0497970	−	0.0792515i
$189$	8.51086	+	5.21747i	0.619074	+	0.379515i
$190$	−0.581783	−	1.59805i	−0.0422070	−	0.115935i
$191$	−1.39098	+	6.09428i	−0.100648	+	0.440967i	0.899345	+	0.437239i	$0.144044\pi$
$191$	−1.39098	+	6.09428i	−0.100648	+	0.440967i	−0.999993	+	0.00372764i	$0.998813\pi$
$192$	−0.677359	+	0.0763201i	−0.0488842	+	0.00550793i
$193$	−12.7791	+	8.02961i	−0.919856	+	0.577984i	−0.906629	−	0.421928i	$-0.861353\pi$
$193$	−12.7791	+	8.02961i	−0.919856	+	0.577984i	−0.0132273	+	0.999913i	$0.504211\pi$
$194$	5.91232	−	2.84722i	0.424480	−	0.204419i
$195$	2.02000	−	2.59923i	0.144655	−	0.186135i
$196$	2.89709	−	6.37235i	0.206935	−	0.455168i
$197$	5.43314	−	5.43314i	0.387095	−	0.387095i	−0.486555	−	0.873650i	$-0.661747\pi$
$197$	5.43314	−	5.43314i	0.387095	−	0.387095i	0.873650	+	0.486555i	$0.161747\pi$
$198$	2.44738	+	0.856376i	0.173928	+	0.0608600i
$199$	−3.56439	+	15.6166i	−0.252673	+	1.10703i	0.676225	+	0.736695i	$0.263615\pi$
$199$	−3.56439	+	15.6166i	−0.252673	+	1.10703i	−0.928898	+	0.370336i	$0.879243\pi$
$200$	1.76927	+	4.67650i	0.125106	+	0.330679i
$201$	4.13451	+	0.943675i	0.291626	+	0.0665617i
$202$	1.58140	−	2.51679i	0.111267	−	0.177081i
$203$	−0.945208	+	0.0104439i	−0.0663406	+	0.000733022i
$204$	1.05779	+	0.241433i	0.0740599	+	0.0169037i
$205$	6.09600	−	3.03046i	0.425763	−	0.211656i
$206$	8.89543	−	2.03032i	0.619774	−	0.141459i
$207$	−2.98051	+	8.51782i	−0.207160	+	0.592029i
$208$	−2.14615	−	0.241813i	−0.148809	−	0.0167667i
$209$	−0.700786	+	0.337481i	−0.0484744	+	0.0233440i
$210$	3.90930	−	0.989853i	0.269767	−	0.0683063i
$211$	−8.52125	−	4.10362i	−0.586627	−	0.282505i	0.116934	−	0.993140i	$-0.462694\pi$
$211$	−8.52125	−	4.10362i	−0.586627	−	0.282505i	−0.703561	+	0.710635i	$0.748408\pi$
$212$	5.83418	+	3.66586i	0.400693	+	0.251772i
$213$	−11.3569	−	1.27961i	−0.778161	−	0.0876776i
$214$		−	10.8697i		−	0.743038i
$215$	0.261392	+	2.08455i	0.0178268	+	0.142165i
$216$	2.94997	−	2.35252i	0.200720	−	0.160069i
$217$	−10.2776	+	13.1840i	−0.697692	+	0.894987i
$218$	12.6433	−	1.42456i	0.856314	−	0.0964834i
$219$	−7.70667	−	6.14586i	−0.520768	−	0.415299i
$220$	2.04773	−	1.01797i	0.138058	−	0.0686318i
$221$	3.09725	+	1.49156i	0.208344	+	0.100333i
$222$	−1.47690	+	0.166407i	−0.0991230	+	0.0111685i
$223$	−1.96711	−	17.4586i	−0.131728	−	1.16911i	−0.869454	−	0.494014i	$-0.835529\pi$
$223$	−1.96711	−	17.4586i	−0.131728	−	1.16911i	0.737726	−	0.675100i	$-0.235899\pi$
$224$	−1.89138	−	1.85004i	−0.126373	−	0.123611i
$225$	−10.1063	−	7.65274i	−0.673752	−	0.510183i
$226$	−19.1067			−1.27096
$227$	4.97553	+	4.97553i	0.330238	+	0.330238i	0.852677	−	0.522439i	$-0.174978\pi$
$227$	4.97553	+	4.97553i	0.330238	+	0.330238i	−0.522439	+	0.852677i	$0.674978\pi$
$228$	−0.0580458	+	0.515170i	−0.00384418	+	0.0341180i
$229$	0.553497	+	2.42503i	0.0365761	+	0.160251i	0.989918	−	0.141643i	$-0.0452385\pi$
$229$	0.553497	+	2.42503i	0.0365761	+	0.160251i	−0.953342	+	0.301893i	$0.902381\pi$
$230$	3.54294	+	7.12688i	0.233614	+	0.469933i
$231$	−0.628359	−	1.73405i	−0.0413430	−	0.114092i
$232$	−0.118001	+	0.337228i	−0.00774715	+	0.0221401i
$233$	−1.89935	+	16.8572i	−0.124431	+	1.10435i	0.763959	+	0.645265i	$0.223253\pi$
$233$	−1.89935	+	16.8572i	−0.124431	+	1.10435i	−0.888390	+	0.459089i	$0.848176\pi$
$234$	4.93342	−	2.37581i	0.322508	−	0.155312i
$235$	2.69651	−	0.981688i	0.175901	−	0.0640383i
$236$	2.98052	−	6.18911i	0.194015	−	0.402877i
$237$	1.72634	−	1.08473i	0.112138	−	0.0704610i
$238$	1.86903	+	3.77383i	0.121151	+	0.244621i
$239$	−4.79911	+	1.09536i	−0.310428	+	0.0708533i	−0.374897	−	0.927066i	$-0.622322\pi$
$239$	−4.79911	+	1.09536i	−0.310428	+	0.0708533i	0.0644686	+	0.997920i	$0.479465\pi$
$240$	0.151644	−	1.51664i	0.00978859	−	0.0978989i
$241$	−3.50078	−	2.79178i	−0.225505	−	0.179834i	0.504220	−	0.863575i	$-0.331780\pi$
$241$	−3.50078	−	2.79178i	−0.225505	−	0.179834i	−0.729724	+	0.683741i	$0.760352\pi$
$242$	5.29590	+	8.42838i	0.340434	+	0.541797i
$243$	−4.87193	+	13.9232i	−0.312534	+	0.893172i
$244$	−13.6818			−0.875889
$245$	12.5683	+	9.32945i	0.802957	+	0.596037i
$246$	−2.07527			−0.132314
$247$	−0.542515	+	1.55042i	−0.0345194	+	0.0986509i
$248$	3.36154	+	5.34987i	0.213458	+	0.339717i
$249$	−1.66770	−	1.32995i	−0.105686	−	0.0842822i
$250$	−11.0551	+	1.66892i	−0.699184	+	0.105552i
$251$	−4.85433	+	1.10797i	−0.306402	+	0.0699343i	−0.372958	−	0.927848i	$-0.621656\pi$
$251$	−4.85433	+	1.10797i	−0.306402	+	0.0699343i	0.0665552	+	0.997783i	$0.478799\pi$
$252$	6.55584	+	1.42031i	0.412979	+	0.0894710i
$253$	3.08217	−	1.93665i	0.193774	−	0.121756i
$254$	−2.61261	+	5.42514i	−0.163930	+	0.340404i
$255$	−1.02515	+	2.19888i	−0.0641973	+	0.137699i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	2.88587	−	25.6128i	0.180016	−	1.59768i	−0.501021	−	0.865435i	$-0.667042\pi$
$257$	2.88587	−	25.6128i	0.180016	−	1.59768i	0.681036	−	0.732249i	$-0.261529\pi$
$258$	0.211521	−	0.604493i	0.0131687	−	0.0376341i
$259$	−4.12394	−	4.03380i	−0.256249	−	0.250648i
$260$	1.53771	−	4.57794i	0.0953648	−	0.283912i
$261$	−0.201565	−	0.883115i	−0.0124766	−	0.0546634i
$262$	2.19399	−	19.4722i	0.135545	−	1.20299i
$263$	−20.1540	−	20.1540i	−1.24275	−	1.24275i	−0.958857	−	0.283890i	$-0.908375\pi$
$263$	−20.1540	−	20.1540i	−1.24275	−	1.24275i	−0.283890	−	0.958857i	$-0.591625\pi$
$264$	−0.697111			−0.0429042
$265$	−10.7570	+	11.0303i	−0.660797	+	0.677587i
$266$	−1.69188	+	1.08934i	−0.103736	+	0.0667916i
$267$	−0.905845	−	8.03959i	−0.0554368	−	0.492015i
$268$	6.18235	−	0.696584i	0.377647	−	0.0425506i
$269$	−1.42581	−	0.686633i	−0.0869330	−	0.0418647i	0.389912	−	0.920852i	$-0.372505\pi$
$269$	−1.42581	−	0.686633i	−0.0869330	−	0.0418647i	−0.476845	+	0.878987i	$0.658220\pi$
$270$	3.75575	+	7.55498i	0.228568	+	0.459781i
$271$	−15.8601	−	12.6480i	−0.963433	−	0.768312i	0.00936763	−	0.999956i	$-0.497018\pi$
$271$	−15.8601	−	12.6480i	−0.963433	−	0.768312i	−0.972801	+	0.231644i	$0.925590\pi$
$272$	1.58171	−	0.178216i	0.0959055	−	0.0108060i
$273$	−3.52772	−	1.65110i	−0.213508	−	0.0999290i
$274$	−8.37049	+	6.67524i	−0.505680	+	0.403266i
$275$	1.26255	+	4.95513i	0.0761346	+	0.298806i
$276$		−	2.42621i		−	0.146041i
$277$	−5.95820	−	0.671328i	−0.357994	−	0.0403362i	−0.0688637	−	0.997626i	$-0.521937\pi$
$277$	−5.95820	−	0.671328i	−0.357994	−	0.0403362i	−0.289130	+	0.957290i	$0.593366\pi$
$278$	−7.86229	−	4.94021i	−0.471549	−	0.296294i
$279$	−14.4328	−	6.95046i	−0.864068	−	0.416113i
$280$	4.93364	−	3.26484i	0.294841	−	0.195112i
$281$	−1.24678	+	0.600417i	−0.0743766	+	0.0358179i	−0.470702	−	0.882292i	$-0.655999\pi$
$281$	−1.24678	+	0.600417i	−0.0743766	+	0.0358179i	0.396326	+	0.918110i	$0.370285\pi$
$282$	−0.869287	−	0.0979452i	−0.0517653	−	0.00583255i
$283$	−2.16422	+	6.18497i	−0.128649	+	0.367658i	−0.990134	−	0.140125i	$-0.955249\pi$
$283$	−2.16422	+	6.18497i	−0.128649	+	0.367658i	0.861485	+	0.507784i	$0.169535\pi$
$284$	−16.3460	+	3.73088i	−0.969959	+	0.221387i
$285$	−1.09891	−	0.369119i	−0.0650937	−	0.0218647i
$286$	−2.15335	−	0.491489i	−0.127330	−	0.0290623i
$287$	−5.09148	−	6.24177i	−0.300540	−	0.368440i
$288$	1.34889	−	2.14675i	0.0794843	−	0.126498i
$289$	14.1037	+	3.21908i	0.829630	+	0.189358i
$290$	−0.681723	−	0.416519i	−0.0400321	−	0.0244589i
$291$	0.995354	−	4.36093i	0.0583487	−	0.255642i
$292$	−13.6494	−	4.77613i	−0.798770	−	0.279502i
$293$	0.601618	−	0.601618i	0.0351469	−	0.0351469i	−0.689315	−	0.724462i	$-0.742088\pi$
$293$	0.601618	−	0.601618i	0.0351469	−	0.0351469i	0.724462	+	0.689315i	$0.242088\pi$
$294$	−2.16477	−	4.25219i	−0.126252	−	0.247993i
$295$	12.1285	+	9.42568i	0.706146	+	0.548784i
$296$	−1.96445	+	0.946031i	−0.114182	+	0.0549869i
$297$	3.26731	−	2.05299i	0.189588	−	0.119126i
$298$	−9.02715	+	1.01712i	−0.522929	+	0.0589199i
$299$	1.71057	−	7.49449i	0.0989247	−	0.433418i
$300$	3.24419	+	1.04461i	0.187304	+	0.0603107i
$301$	2.33708	−	0.846877i	0.134707	−	0.0488132i
$302$	5.58859	+	8.89420i	0.321587	+	0.511803i
$303$	−0.669182	−	1.91241i	−0.0384435	−	0.109865i
$304$	0.169240	+	0.741489i	0.00970657	+	0.0425273i
$305$	6.43301	−	29.9095i	0.368353	−	1.71261i
$306$	−3.15515	+	2.51615i	−0.180368	+	0.143839i
$307$	15.9897	+	5.59502i	0.912578	+	0.319325i	0.745412	−	0.666604i	$-0.232253\pi$
$307$	15.9897	+	5.59502i	0.912578	+	0.319325i	0.167166	+	0.985929i	$0.446539\pi$
$308$	−1.71030	−	2.09670i	−0.0974533	−	0.119470i
$309$	2.69852	−	5.60354i	0.153514	−	0.318775i
$310$	−13.2758	+	4.83315i	−0.754013	+	0.274504i
$311$	−14.4072	+	11.4894i	−0.816959	+	0.651503i	−0.940105	−	0.340885i	$-0.889273\pi$
$311$	−14.4072	+	11.4894i	−0.816959	+	0.651503i	0.123146	+	0.992389i	$0.460702\pi$
$312$	−1.04098	+	1.04098i	−0.0589339	+	0.0589339i
$313$	−12.4633	+	12.4633i	−0.704469	+	0.704469i	−0.965366	−	0.260898i	$-0.915981\pi$
$313$	−12.4633	+	12.4633i	−0.704469	+	0.704469i	0.260898	+	0.965366i	$0.415981\pi$
$314$	−6.69610	−	8.39664i	−0.377883	−	0.473850i
$315$	−6.18737	+	13.6638i	−0.348619	+	0.769865i
$316$	1.86490	−	2.33851i	0.104909	−	0.131552i
$317$	1.50791	+	13.3831i	0.0846927	+	0.751669i	0.962244	+	0.272187i	$0.0877469\pi$
$317$	1.50791	+	13.3831i	0.0846927	+	0.751669i	−0.877552	+	0.479482i	$0.840825\pi$
$318$	4.43317	−	1.55123i	0.248600	−	0.0869889i
$319$	−0.158534	+	0.329199i	−0.00887620	+	0.0184316i
$320$	−0.524879	−	2.17359i	−0.0293416	−	0.121507i
$321$	−5.79281	−	4.61961i	−0.323323	−	0.257842i
$322$	7.29730	−	5.95249i	0.406663	−	0.331719i
$323$	0.135544	−	1.20298i	0.00754186	−	0.0669359i
$324$			5.03413i			0.279674i
$325$	9.28472	+	5.51404i	0.515023	+	0.305864i
$326$	10.2020	+	12.7930i	0.565039	+	0.708537i
$327$	4.61421	−	7.34347i	0.255166	−	0.406095i
$328$	−2.87365	+	1.00553i	−0.158671	+	0.0555213i
$329$	−1.83813	−	2.85485i	−0.101339	−	0.157393i
$330$	0.327773	−	1.52394i	0.0180433	−	0.0838900i
$331$	−14.3712	−	18.0209i	−0.789911	−	0.990517i	−0.999918	−	0.0128174i	$-0.995920\pi$
$331$	−14.3712	−	18.0209i	−0.789911	−	0.990517i	0.210007	−	0.977700i	$-0.432651\pi$
$332$	−2.95370	−	1.03354i	−0.162105	−	0.0567230i
$333$	2.94110	−	4.68073i	0.161171	−	0.256502i
$334$	3.31892	+	1.59831i	0.181603	+	0.0874554i
$335$	−1.38408	+	13.8426i	−0.0756202	+	0.756302i
$336$	−1.78978	+	0.221712i	−0.0976407	+	0.0120954i
$337$	24.0018	+	15.0813i	1.30746	+	0.821533i	0.991857	−	0.127358i	$-0.0406498\pi$
$337$	24.0018	+	15.0813i	1.30746	+	0.821533i	0.315605	+	0.948891i	$0.397793\pi$
$338$	7.05793	−	4.43479i	0.383901	−	0.241221i
$339$	−8.12033	+	10.1826i	−0.441036	+	0.553042i
$340$	−0.354107	+	3.54154i	−0.0192042	+	0.192067i
$341$	2.80361	+	5.82176i	0.151824	+	0.315266i
$342$	−1.36350	−	1.36350i	−0.0737299	−	0.0737299i
$343$	7.47823	−	16.9433i	0.403787	−	0.914853i
$344$		−	0.939539i		−	0.0506565i
$345$	5.30388	+	1.14077i	0.285552	+	0.0614172i
$346$	1.82033	+	0.415478i	0.0978614	+	0.0223362i
$347$	−0.437691	−	3.88462i	−0.0234965	−	0.208537i	0.976478	−	0.215615i	$-0.0691756\pi$
$347$	−0.437691	−	3.88462i	−0.0234965	−	0.208537i	−0.999975	+	0.00707777i	$0.997747\pi$
$348$	0.129569	+	0.206208i	0.00694563	+	0.0110539i
$349$	−5.59386	−	24.5083i	−0.299432	−	1.31190i	−0.870975	−	0.491327i	$-0.836512\pi$
$349$	−5.59386	−	24.5083i	−0.299432	−	1.31190i	0.571543	−	0.820572i	$-0.306345\pi$
$350$	4.81746	+	12.3204i	0.257504	+	0.658553i
$351$	1.81332	−	7.94467i	0.0967878	−	0.424055i
$352$	−0.965300	+	0.337773i	−0.0514506	+	0.0180034i
$353$	2.85028	+	1.79095i	0.151705	+	0.0953227i	0.605746	−	0.795658i	$-0.292875\pi$
$353$	2.85028	+	1.79095i	0.151705	+	0.0953227i	−0.454040	+	0.890981i	$0.650018\pi$
$354$	−2.03166	−	4.21878i	−0.107981	−	0.224226i
$355$	−0.470282	−	37.4879i	−0.0249600	−	1.98965i
$356$	−5.14978	−	10.6936i	−0.272938	−	0.566761i
$357$	2.80553	+	0.607812i	0.148484	+	0.0321688i
$358$	0.702998	+	2.00905i	0.0371546	+	0.106182i
$359$	33.3678	−	7.61599i	1.76109	−	0.401957i	0.785028	−	0.619460i	$-0.212649\pi$
$359$	33.3678	−	7.61599i	1.76109	−	0.401957i	0.976060	+	0.217504i	$0.0697914\pi$
$360$	4.05873	+	3.95815i	0.213914	+	0.208613i
$361$	−18.4216			−0.969555
$362$	18.4483	+	18.4483i	0.969621	+	0.969621i
$363$	6.74251	+	0.759698i	0.353890	+	0.0398738i
$364$	−5.68490	−	0.577001i	−0.297970	−	0.0302431i
$365$	16.8587	−	27.5929i	0.882427	−	1.44428i
$366$	−5.81476	+	7.29147i	−0.303942	+	0.381131i
$367$	2.24586	+	6.41831i	0.117233	+	0.335033i	0.987516	−	0.157520i	$-0.0503497\pi$
$367$	2.24586	+	6.41831i	0.117233	+	0.335033i	−0.870283	+	0.492552i	$0.836064\pi$
$368$	−1.17558	−	3.35961i	−0.0612813	−	0.175132i
$369$	4.81265	−	6.03488i	0.250537	−	0.314163i
$370$	−1.14443	−	4.73925i	−0.0594963	−	0.246382i
$371$	15.5420	+	9.52782i	0.806901	+	0.494660i
$372$	4.27976	+	0.482214i	0.221895	+	0.0250016i
$373$	15.3662	+	15.3662i	0.795632	+	0.795632i	0.982403	−	0.186772i	$-0.0598025\pi$
$373$	15.3662	+	15.3662i	0.795632	+	0.795632i	−0.186772	+	0.982403i	$0.559802\pi$
$374$	1.62784			0.0841735
$375$	−3.80898	+	6.60089i	−0.196695	+	0.340868i
$376$	−1.25117	+	0.285572i	−0.0645242	+	0.0147272i
$377$	0.254850	+	0.728320i	0.0131255	+	0.0375104i
$378$	7.73564	−	6.31004i	0.397878	−	0.324553i
$379$	15.3837	+	31.9446i	0.790209	+	1.64089i	0.767420	+	0.641145i	$0.221540\pi$
$379$	15.3837	+	31.9446i	0.790209	+	1.64089i	0.0227887	+	0.999740i	$0.492746\pi$
$380$	−1.70052	+	0.0213329i	−0.0872350	+	0.00109435i
$381$	1.78087	+	3.69802i	0.0912369	+	0.189455i
$382$	5.29288	+	3.32574i	0.270807	+	0.170160i
$383$	−20.6081	+	7.21107i	−1.05302	+	0.368469i	−0.800632	−	0.599157i	$-0.795503\pi$
$383$	−20.6081	+	7.21107i	−1.05302	+	0.368469i	−0.252391	+	0.967625i	$0.581217\pi$
$384$	−0.151680	+	0.664555i	−0.00774040	+	0.0339129i
$385$	5.38770	−	2.75300i	0.274582	−	0.140306i
$386$	3.35836	+	14.7139i	0.170936	+	0.748920i
$387$	1.26734	+	2.01696i	0.0644224	+	0.102528i
$388$	−0.734731	−	6.52092i	−0.0373003	−	0.331050i
$389$	−24.7482	−	5.64861i	−1.25478	−	0.286396i	−0.457068	−	0.889432i	$-0.651100\pi$
$389$	−24.7482	−	5.64861i	−1.25478	−	0.286396i	−0.797714	+	0.603036i	$0.793958\pi$
$390$	−1.78621	−	2.76512i	−0.0904480	−	0.140017i
$391$			5.66550i			0.286517i
$392$	−5.05791	−	4.83917i	−0.255463	−	0.244415i
$393$	−9.44490	−	9.44490i	−0.476432	−	0.476432i
$394$	−3.33380	−	6.92270i	−0.167954	−	0.348761i
$395$	4.23531	+	5.17636i	0.213102	+	0.260451i
$396$	1.61664	−	2.02720i	0.0812391	−	0.101871i
$397$	−14.7694	+	9.28021i	−0.741253	+	0.465760i	−0.848983	−	0.528420i	$-0.822785\pi$
$397$	−14.7694	+	9.28021i	−0.741253	+	0.465760i	0.107730	+	0.994180i	$0.465642\pi$
$398$	13.5630	+	8.52220i	0.679852	+	0.427179i
$399$	−0.138506	+	1.36463i	−0.00693396	+	0.0683168i
$400$	4.99843	−	0.125429i	0.249921	−	0.00627146i
$401$	13.4417	+	6.47316i	0.671244	+	0.323254i	0.738278	−	0.674496i	$-0.235639\pi$
$401$	13.4417	+	6.47316i	0.671244	+	0.323254i	−0.0670337	+	0.997751i	$0.521354\pi$
$402$	2.25626	−	3.59082i	0.112532	−	0.179094i
$403$	12.8801	+	4.50693i	0.641602	+	0.224506i
$404$	−1.85325	−	2.32390i	−0.0922027	−	0.115619i
$405$	−11.0050	−	2.36698i	−0.546842	−	0.117616i
$406$	−0.302325	+	0.895616i	−0.0150041	+	0.0444487i
$407$	−2.10472	+	0.736473i	−0.104327	+	0.0365056i
$408$	0.577250	−	0.918688i	0.0285781	−	0.0454818i
$409$	7.88430	+	9.88660i	0.389853	+	0.488861i	0.937567	−	0.347805i	$-0.113073\pi$
$409$	7.88430	+	9.88660i	0.389853	+	0.488861i	−0.547713	+	0.836666i	$0.684502\pi$
$410$	−0.847020	−	6.75481i	−0.0418313	−	0.333596i
$411$			7.29787i			0.359977i
$412$	1.02159	−	9.06683i	0.0503299	−	0.446690i
$413$	7.70431	−	16.4610i	0.379104	−	0.809992i
$414$	7.05543	+	5.62652i	0.346755	+	0.276528i
$415$	3.64819	−	5.97104i	0.179083	−	0.293107i
$416$	−0.937071	+	1.94585i	−0.0459437	+	0.0954030i
$417$	−5.97426	+	2.09048i	−0.292561	+	0.102371i
$418$	0.0870875	+	0.772923i	0.00425959	+	0.0378049i
$419$	−0.966535	+	1.21200i	−0.0472183	+	0.0592099i	−0.804880	−	0.593438i	$-0.797770\pi$
$419$	−0.966535	+	1.21200i	−0.0472183	+	0.0592099i	0.757662	+	0.652648i	$0.226342\pi$
$420$	0.356854	−	4.01685i	0.0174127	−	0.196002i
$421$	−4.59911	−	5.76710i	−0.224147	−	0.281071i	0.657024	−	0.753870i	$-0.271815\pi$
$421$	−4.59911	−	5.76710i	−0.224147	−	0.281071i	−0.881170	+	0.472799i	$0.843244\pi$
$422$	−6.68773	+	6.68773i	−0.325554	+	0.325554i
$423$	2.30075	−	2.30075i	0.111866	−	0.111866i
$424$	5.38705	−	4.29603i	0.261618	−	0.208634i
$425$	−7.57558	−	2.43929i	−0.367470	−	0.118323i
$426$	−4.95875	+	10.2969i	−0.240252	+	0.498888i
$427$	−36.1965	+	0.399948i	−1.75167	+	0.0193548i
$428$	−10.2597	−	3.59004i	−0.495923	−	0.173531i
$429$	−1.17710	+	0.938708i	−0.0568311	+	0.0453213i
$430$	2.05390	+	0.441759i	0.0990480	+	0.0213035i
$431$	−6.56372	−	28.7575i	−0.316163	−	1.38520i	−0.844222	−	0.535993i	$-0.819937\pi$
$431$	−6.56372	−	28.7575i	−0.316163	−	1.38520i	0.528059	−	0.849208i	$-0.322920\pi$
$432$	−1.24619	−	3.56142i	−0.0599575	−	0.171349i
$433$	19.1789	+	30.5230i	0.921677	+	1.46684i	0.883965	+	0.467553i	$0.154864\pi$
$433$	19.1789	+	30.5230i	0.921677	+	1.46684i	0.0377123	+	0.999289i	$0.487993\pi$
$434$	9.04965	+	14.0553i	0.434397	+	0.674675i
$435$	−0.511708	+	0.186291i	−0.0245345	+	0.00893199i
$436$	2.83121	−	12.4043i	0.135590	−	0.594060i
$437$	−2.69007	+	0.303098i	−0.128683	+	0.0144991i
$438$	−8.34633	+	5.24435i	−0.398803	+	0.250585i
$439$	7.39613	−	3.56179i	0.352998	−	0.169995i	−0.248978	−	0.968509i	$-0.580095\pi$
$439$	7.39613	−	3.56179i	0.352998	−	0.169995i	0.601976	+	0.798514i	$0.294380\pi$
$440$	−0.284526	−	2.26903i	−0.0135642	−	0.108172i
$441$	17.3856	+	3.56591i	0.827885	+	0.169805i
$442$	2.43081	−	2.43081i	0.115622	−	0.115622i
$443$	28.8755	+	10.1040i	1.37191	+	0.480054i	0.912830	−	0.408339i	$-0.133892\pi$
$443$	28.8755	+	10.1040i	1.37191	+	0.480054i	0.459084	+	0.888393i	$0.348178\pi$
$444$	−0.330721	+	1.44898i	−0.0156953	+	0.0687656i
$445$	25.7984	−	6.22980i	1.22296	−	0.295321i
$446$	−17.1286	−	3.90949i	−0.811061	−	0.185119i
$447$	−3.29447	+	5.24313i	−0.155823	+	0.247991i
$448$	−2.37091	+	1.17422i	−0.112015	+	0.0554765i
$449$	−12.5580	−	2.86627i	−0.592646	−	0.135268i	−0.0843298	−	0.996438i	$-0.526875\pi$
$449$	−12.5580	−	2.86627i	−0.592646	−	0.135268i	−0.508317	+	0.861170i	$0.669732\pi$
$450$	−10.5612	+	7.01161i	−0.497859	+	0.330530i
$451$	−3.03551	+	0.692836i	−0.142937	+	0.0326244i
$452$	−6.31055	+	18.0345i	−0.296823	+	0.848272i
$453$	7.11514	+	0.801684i	0.334299	+	0.0376664i
$454$	6.33964	−	3.05301i	0.297534	−	0.143285i
$455$	3.93433	−	12.1563i	0.184444	−	0.569897i
$456$	0.467090	+	0.224938i	0.0218735	+	0.0105337i
$457$	5.63505	+	3.54074i	0.263596	+	0.165629i	0.657345	−	0.753589i	$-0.271679\pi$
$457$	5.63505	+	3.54074i	0.263596	+	0.165629i	−0.393749	+	0.919218i	$0.628822\pi$
$458$	2.47175	+	0.278500i	0.115497	+	0.0130134i
$459$			6.00581i			0.280327i
$460$	7.89710	−	0.990258i	0.368204	−	0.0461710i
$461$	−10.1544	+	8.09783i	−0.472936	+	0.377154i	−0.830756	−	0.556637i	$-0.812091\pi$
$461$	−10.1544	+	8.09783i	−0.472936	+	0.377154i	0.357820	+	0.933790i	$0.383520\pi$
$462$	−1.84427	+	0.0203780i	−0.0858033	+	0.000948071i
$463$	−0.0963265	+	0.0108534i	−0.00447667	+	0.000504400i	−0.114203	−	0.993457i	$-0.536431\pi$
$463$	−0.0963265	+	0.0108534i	−0.00447667	+	0.000504400i	0.109726	+	0.993962i	$0.465003\pi$
$464$	0.279330	+	0.222759i	0.0129676	+	0.0103413i
$465$	−3.06645	+	9.12916i	−0.142203	+	0.423355i
$466$	15.2839	+	7.36036i	0.708015	+	0.340962i
$467$	13.9326	−	1.56982i	0.644722	−	0.0726427i	0.216451	−	0.976293i	$-0.430552\pi$
$467$	13.9326	−	1.56982i	0.644722	−	0.0726427i	0.428270	+	0.903651i	$0.359123\pi$
$468$	−0.613082	−	5.44126i	−0.0283397	−	0.251522i
$469$	16.3356	−	2.02360i	0.754308	−	0.0934410i
$470$	−0.0359967	−	2.86943i	−0.00166040	−	0.132357i
$471$	−7.32067			−0.337319
$472$	−4.85740	−	4.85740i	−0.223580	−	0.223580i
$473$	0.107582	−	0.954815i	0.00494662	−	0.0439024i
$474$	−0.453687	−	1.98773i	−0.0208385	−	0.0912995i
$475$	0.752929	−	3.72750i	0.0345467	−	0.171030i
$476$	4.17936	−	0.517724i	0.191561	−	0.0237299i
$477$	−5.76977	+	16.4891i	−0.264180	+	0.754982i
$478$	−0.551148	+	4.89157i	−0.0252089	+	0.223735i
$479$	−31.5214	+	15.1799i	−1.44025	+	0.693587i	−0.980872	−	0.194654i	$-0.937642\pi$
$479$	−31.5214	+	15.1799i	−1.44025	+	0.693587i	−0.459377	+	0.888241i	$0.651927\pi$
$480$	−1.38145	−	0.644050i	−0.0630542	−	0.0293967i
$481$	−2.04317	+	4.24269i	−0.0931605	+	0.193450i
$482$	−3.79134	+	2.38226i	−0.172691	+	0.108509i
$483$	−0.0709233	−	6.41877i	−0.00322712	−	0.292064i
$484$	9.70454	−	2.21500i	0.441115	−	0.100682i
$485$	14.6007	+	1.45987i	0.662983	+	0.0662895i
$486$	11.5328	+	9.19706i	0.523136	+	0.417187i
$487$	6.79699	+	10.8173i	0.308001	+	0.490181i	0.964477	−	0.264166i	$-0.0850967\pi$
$487$	6.79699	+	10.8173i	0.308001	+	0.490181i	−0.656476	+	0.754347i	$0.727954\pi$
$488$	−4.51882	+	12.9140i	−0.204557	+	0.584591i
$489$	11.1536			0.504385
$490$	12.9570	−	8.78165i	0.585335	−	0.396715i
$491$	41.5112			1.87337			0.936687	−	0.350167i	$-0.113875\pi$
$491$	41.5112			1.87337			0.936687	+	0.350167i	$0.113875\pi$
$492$	−0.685418	+	1.95881i	−0.0309010	+	0.0883100i
$493$	−0.302559	−	0.481520i	−0.0136266	−	0.0216866i
$494$	1.28423	+	1.02414i	0.0577804	+	0.0460783i
$495$	3.67149	+	4.48725i	0.165021	+	0.201687i
$496$	6.15990	−	1.40596i	0.276587	−	0.0631293i
$497$	−43.1359	+	10.3482i	−1.93491	+	0.464180i
$498$	−1.80613	+	1.13486i	−0.0809344	+	0.0508545i
$499$	11.1471	−	23.1471i	0.499011	−	1.03621i	−0.487593	−	0.873071i	$-0.662125\pi$
$499$	11.1471	−	23.1471i	0.499011	−	1.03621i	0.986604	−	0.163136i	$-0.0521608\pi$
$500$	−2.07600	+	10.9859i	−0.0928414	+	0.491305i
$501$	2.26232	−	1.08948i	0.101073	−	0.0486743i
$502$	−0.557489	+	4.94786i	−0.0248820	+	0.220834i
$503$	11.4164	−	32.6261i	0.509031	−	1.45473i	−0.347032	−	0.937853i	$-0.612810\pi$
$503$	11.4164	−	32.6261i	0.509031	−	1.45473i	0.856062	−	0.516872i	$-0.172904\pi$
$504$	3.50586	−	5.71885i	0.156164	−	0.254738i
$505$	5.95160	−	2.95868i	0.264843	−	0.131659i
$506$	−0.810000	−	3.54884i	−0.0360089	−	0.157765i
$507$	0.636172	−	5.64618i	0.0282534	−	0.250756i
$508$	4.25781	+	4.25781i	0.188910	+	0.188910i
$509$	27.6904			1.22736			0.613678	−	0.789556i	$-0.289689\pi$
$509$	27.6904			1.22736			0.613678	+	0.789556i	$0.289689\pi$
$510$	1.73690	+	1.69387i	0.0769114	+	0.0750057i
$511$	−36.2503	−	12.2367i	−1.60362	−	0.541319i
$512$	0.111964	+	0.993712i	0.00494818	+	0.0439163i
$513$	−2.85165	+	0.321304i	−0.125904	+	0.0141859i
$514$	−23.2224	−	11.1833i	−1.02430	−	0.493275i
$515$	19.3404	+	6.49637i	0.852241	+	0.286264i
$516$	−0.500710	−	0.399303i	−0.0220425	−	0.0175783i
$517$	−1.30421	+	0.146950i	−0.0573592	+	0.00646283i
$518$	−5.16948	+	2.56023i	−0.227134	+	0.112490i
$519$	0.995058	−	0.793532i	0.0436782	−	0.0348322i
$520$	−3.81317	−	2.96342i	−0.167219	−	0.129955i
$521$		−	2.32206i		−	0.101731i	−0.998706	−	0.0508657i	$-0.983802\pi$
$521$		−	2.32206i		−	0.101731i	0.998706	−	0.0508657i	$-0.0161980\pi$
$522$	−0.900130	−	0.101420i	−0.0393976	−	0.00443905i
$523$	14.8132	+	9.30775i	0.647736	+	0.407000i	0.815443	−	0.578837i	$-0.196493\pi$
$523$	14.8132	+	9.30775i	0.647736	+	0.407000i	−0.167707	+	0.985837i	$0.553636\pi$
$524$	−17.6548	−	8.50212i	−0.771255	−	0.371417i
$525$	8.61334	+	2.66878i	0.375917	+	0.116475i
$526$	−25.6794	+	12.3666i	−1.11968	+	0.539208i
$527$	−9.99376	−	1.12603i	−0.435335	−	0.0490505i
$528$	−0.230241	+	0.657992i	−0.0100200	+	0.0286354i
$529$	−10.0720	+	2.29887i	−0.437914	+	0.0999509i
$530$	6.85852	+	13.7964i	0.297915	+	0.599279i
$531$	16.9797	+	3.87551i	0.736857	+	0.168183i
$532$	0.469415	+	1.95673i	0.0203517	+	0.0848349i
$533$	−3.49826	+	5.56746i	−0.151527	+	0.241153i
$534$	−7.88762	−	1.80030i	−0.341331	−	0.0779065i
$535$	12.6721	−	20.7406i	0.547862	−	0.896693i
$536$	1.38441	−	6.06548i	0.0597973	−	0.261989i
$537$	1.36946	+	0.479195i	0.0590966	+	0.0206788i
$538$	−1.11902	+	1.11902i	−0.0482442	+	0.0482442i
$539$	−4.58604	−	5.49700i	−0.197535	−	0.236773i
$540$	8.37146	−	1.04974i	0.360250	−	0.0451736i
$541$	21.7112	−	10.4556i	0.933437	−	0.449519i	0.0955875	−	0.995421i	$-0.469527\pi$
$541$	21.7112	−	10.4556i	0.933437	−	0.449519i	0.837849	+	0.545902i	$0.183813\pi$
$542$	−17.1765	+	10.7927i	−0.737794	+	0.463587i
$543$	17.6722	−	1.99118i	0.758386	−	0.0854496i
$544$	0.354192	−	1.55182i	0.0151858	−	0.0665335i
$545$	25.7856	+	12.0216i	1.10453	+	0.514948i
$546$	−2.72358	+	2.78444i	−0.116558	+	0.119163i
$547$	14.4581	+	23.0100i	0.618184	+	0.983835i	0.998265	+	0.0588813i	$0.0187534\pi$
$547$	14.4581	+	23.0100i	0.618184	+	0.983835i	−0.380081	+	0.924953i	$0.624104\pi$
$548$	3.53605	+	10.1055i	0.151053	+	0.431684i
$549$	−7.71888	−	33.8186i	−0.329434	−	1.44334i
$550$	5.09406	+	0.444876i	0.217211	+	0.0189696i
$551$	0.212447	−	0.169421i	0.00905054	−	0.00721756i
$552$	−2.29006	−	0.801327i	−0.0974715	−	0.0341068i
$553$	4.86541	−	6.24126i	0.206898	−	0.265405i
$554$	−2.60152	+	5.40212i	−0.110528	+	0.229514i
$555$	−3.01208	−	1.40427i	−0.127856	−	0.0596080i
$556$	−7.25973	+	5.78944i	−0.307881	+	0.245527i
$557$	−8.60835	+	8.60835i	−0.364747	+	0.364747i	−0.865557	−	0.500810i	$-0.833036\pi$
$557$	−8.60835	+	8.60835i	−0.364747	+	0.364747i	0.500810	+	0.865557i	$0.333036\pi$
$558$	−11.3273	+	11.3273i	−0.479522	+	0.479522i
$559$	−1.26515	−	1.58645i	−0.0535103	−	0.0670998i
$560$	−1.45215	−	5.73509i	−0.0613646	−	0.242352i
$561$	0.691830	−	0.867527i	0.0292091	−	0.0366270i
$562$	0.154939	+	1.37512i	0.00653570	+	0.0580059i
$563$	17.0015	−	5.94909i	0.716528	−	0.250724i	0.0527013	−	0.998610i	$-0.483217\pi$
$563$	17.0015	−	5.94909i	0.716528	−	0.250724i	0.663827	+	0.747886i	$0.268931\pi$
$564$	−0.379556	+	0.788157i	−0.0159822	+	0.0331874i
$565$	−36.4577	−	22.2749i	−1.53379	−	0.937113i
$566$	5.12310	+	4.08553i	0.215340	+	0.171728i
$567$	0.147158	+	13.3182i	0.00618006	+	0.559313i
$568$	−1.87724	+	16.6610i	−0.0787673	+	0.699079i
$569$			9.30256i			0.389984i	0.980805	+	0.194992i	$0.0624680\pi$
$569$			9.30256i			0.389984i	−0.980805	+	0.194992i	$0.937532\pi$
$570$	−0.711352	+	0.915330i	−0.0297952	+	0.0383389i
$571$	3.37905	+	4.23719i	0.141409	+	0.177321i	0.847492	−	0.530807i	$-0.178111\pi$
$571$	3.37905	+	4.23719i	0.141409	+	0.177321i	−0.706084	+	0.708128i	$0.749540\pi$
$572$	−1.17512	+	1.87019i	−0.0491341	+	0.0781964i
$573$	4.02186	−	1.40731i	0.168016	−	0.0587912i
$574$	−7.57311	+	2.74423i	−0.316095	+	0.114542i
$575$	−1.54834	+	17.7293i	−0.0645701	+	0.739361i
$576$	−1.58077	−	1.98222i	−0.0658655	−	0.0825927i
$577$	−21.6669	−	7.58158i	−0.902005	−	0.315625i	−0.160865	−	0.986976i	$-0.551429\pi$
$577$	−21.6669	−	7.58158i	−0.902005	−	0.315625i	−0.741139	+	0.671351i	$0.765714\pi$
$578$	7.69660	−	12.2491i	0.320136	−	0.509494i
$579$	9.26883	+	4.46363i	0.385199	+	0.185502i
$580$	−0.618304	+	0.505899i	−0.0256737	+	0.0210063i
$581$	−7.84448	−	2.64799i	−0.325444	−	0.109857i
$582$	−3.78747	−	2.37982i	−0.156996	−	0.0986468i
$583$	5.96656	−	3.74904i	0.247110	−	0.155269i
$584$	−9.01622	+	11.3060i	−0.373094	+	0.467845i
$585$	12.1833	+	1.21816i	0.503716	+	0.0503649i
$586$	−0.369156	−	0.766559i	−0.0152497	−	0.0316663i
$587$	17.7250	+	17.7250i	0.731589	+	0.731589i	0.970934	−	0.239346i	$-0.0769330\pi$
$587$	17.7250	+	17.7250i	0.731589	+	0.731589i	−0.239346	+	0.970934i	$0.576933\pi$
$588$	−4.72855	+	0.638879i	−0.195002	+	0.0263469i
$589$		−	4.80544i		−	0.198005i
$590$	12.9025	−	8.33475i	0.531188	−	0.343136i
$591$	−5.10619	−	1.16545i	−0.210040	−	0.0479404i
$592$	0.244125	+	2.16667i	0.0100335	+	0.0890496i
$593$	−10.5206	−	16.7434i	−0.432028	−	0.687568i	0.557778	−	0.829990i	$-0.311654\pi$
$593$	−10.5206	−	16.7434i	−0.432028	−	0.687568i	−0.989806	+	0.142422i	$0.954511\pi$
$594$	−0.858655	−	3.76202i	−0.0352311	−	0.154357i
$595$	−0.833296	+	9.37982i	−0.0341618	+	0.384535i
$596$	−2.02144	+	8.85651i	−0.0828014	+	0.362777i
$597$	10.3060	−	3.60623i	0.421797	−	0.147593i
$598$	−6.50896	−	4.08985i	−0.266171	−	0.167246i
$599$	−2.18787	−	4.54316i	−0.0893939	−	0.185628i	0.851478	−	0.524390i	$-0.175706\pi$
$599$	−2.18787	−	4.54316i	−0.0893939	−	0.185628i	−0.940872	+	0.338761i	$0.889992\pi$
$600$	2.05748	−	2.71713i	0.0839963	−	0.110926i
$601$	4.54771	+	9.44342i	0.185505	+	0.385205i	0.972894	−	0.231251i	$-0.0742820\pi$
$601$	4.54771	+	9.44342i	0.185505	+	0.385205i	−0.787389	+	0.616456i	$0.788568\pi$
$602$	−0.0274647	−	2.48563i	−0.00111938	−	0.101307i
$603$	5.20971	+	14.8885i	0.212156	+	0.606306i
$604$	10.2409	−	2.33741i	0.416695	−	0.0951080i
$605$	0.279203	+	22.2563i	0.0113512	+	0.904848i
$606$	−2.02611			−0.0823052
$607$	20.5085	+	20.5085i	0.832415	+	0.832415i	0.987847	−	0.155431i	$-0.0496767\pi$
$607$	20.5085	+	20.5085i	0.832415	+	0.832415i	−0.155431	+	0.987847i	$0.549677\pi$
$608$	0.755775	+	0.0851554i	0.0306507	+	0.00345351i
$609$	0.348814	+	0.541754i	0.0141347	+	0.0219530i
$610$	−26.1064	−	15.9505i	−1.05702	−	0.645816i
$611$	−1.72812	+	2.16699i	−0.0699121	+	0.0876669i
$612$	1.33287	+	3.80913i	0.0538781	+	0.153975i
$613$	7.60218	+	21.7258i	0.307049	+	0.877496i	0.989237	+	0.146319i	$0.0467426\pi$
$613$	7.60218	+	21.7258i	0.307049	+	0.877496i	−0.682188	+	0.731176i	$0.738972\pi$
$614$	10.5621	−	13.2444i	0.426251	−	0.534502i
$615$	−3.95983	−	2.41938i	−0.159676	−	0.0975589i
$616$	−2.54391	+	0.921826i	−0.102497	+	0.0371414i
$617$	−24.0472	−	2.70946i	−0.968102	−	0.109079i	−0.386268	−	0.922387i	$-0.626236\pi$
$617$	−24.0472	−	2.70946i	−0.968102	−	0.109079i	−0.581834	+	0.813308i	$0.697665\pi$
$618$	−4.39783	−	4.39783i	−0.176907	−	0.176907i
$619$	−19.2664			−0.774383			−0.387192	−	0.921999i	$-0.626555\pi$
$619$	−19.2664			−0.774383			−0.387192	+	0.921999i	$0.626555\pi$
$620$	0.177222	+	14.1271i	0.00711743	+	0.567356i
$621$	13.0932	−	2.98845i	0.525414	−	0.119922i
$622$	6.08623	+	17.3935i	0.244036	+	0.697414i
$623$	−13.9368	−	28.1404i	−0.558366	−	1.12742i
$624$	0.638750	+	1.32638i	0.0255705	+	0.0530976i
$625$	−23.0399	−	9.70372i	−0.921597	−	0.388149i
$626$	7.64755	+	15.8803i	0.305658	+	0.634704i
$627$	0.448927	+	0.282080i	0.0179284	+	0.0112652i
$628$	−10.1370	+	3.54710i	−0.404511	+	0.141545i
$629$	0.772272	−	3.38355i	0.0307925	−	0.134911i
$630$	10.8534	+	10.3530i	0.432411	+	0.412474i
$631$	1.14765	+	5.02820i	0.0456874	+	0.200169i	0.992621	−	0.121261i	$-0.0386937\pi$
$631$	1.14765	+	5.02820i	0.0456874	+	0.200169i	−0.946933	+	0.321430i	$0.895837\pi$
$632$	−1.59135	−	2.53261i	−0.0633003	−	0.100742i
$633$	0.721826	+	6.40638i	0.0286900	+	0.254631i
$634$	13.1301	+	2.99686i	0.521463	+	0.119021i
$635$	−11.3099	+	7.30593i	−0.448818	+	0.289927i
$636$		−	4.69674i		−	0.186238i
$637$	−15.0568	−	1.36033i	−0.596571	−	0.0538981i
$638$	0.258365	+	0.258365i	0.0102288	+	0.0102288i
$639$	−18.4439	−	38.2992i	−0.729630	−	1.51509i
$640$	−2.22497	−	0.222468i	−0.0879498	−	0.00879381i
$641$	0.717499	−	0.899715i	0.0283395	−	0.0355366i	−0.767460	−	0.641097i	$-0.778480\pi$
$641$	0.717499	−	0.899715i	0.0283395	−	0.0355366i	0.795799	+	0.605560i	$0.207051\pi$
$642$	−6.27362	+	3.94198i	−0.247600	+	0.155577i
$643$	34.9975	+	21.9904i	1.38017	+	0.867216i	0.998372	−	0.0570322i	$-0.0181638\pi$
$643$	34.9975	+	21.9904i	1.38017	+	0.867216i	0.381793	+	0.924248i	$0.375307\pi$
$644$	−3.20831	−	8.85379i	−0.126425	−	0.348888i
$645$	1.10833	−	0.906843i	0.0436406	−	0.0357069i
$646$	−1.09071	−	0.525258i	−0.0429134	−	0.0206660i
$647$	−2.25121	+	3.58279i	−0.0885044	+	0.140854i	−0.888042	−	0.459762i	$-0.847935\pi$
$647$	−2.25121	+	3.58279i	−0.0885044	+	0.140854i	0.799538	+	0.600615i	$0.205078\pi$
$648$	4.75163	+	1.66267i	0.186662	+	0.0653157i
$649$	−4.38018	−	5.49257i	−0.171937	−	0.215602i
$650$	8.27116	−	6.94252i	0.324422	−	0.272308i
$651$	11.3366	+	1.15063i	0.444316	+	0.0450969i
$652$	15.4446	−	5.40429i	0.604857	−	0.211649i
$653$	−14.9661	+	23.8184i	−0.585668	+	0.932086i	0.414093	+	0.910235i	$0.364099\pi$
$653$	−14.9661	+	23.8184i	−0.585668	+	0.932086i	−0.999761	+	0.0218512i	$0.993044\pi$
$654$	−5.40740	−	6.78067i	−0.211446	−	0.265145i
$655$	26.8873	−	34.5972i	1.05058	−	1.35182i
$656$			3.04450i			0.118868i
$657$	4.10502	−	36.4330i	0.160152	−	1.42139i
$658$	−3.30174	+	0.792080i	−0.128715	+	0.0308785i
$659$	−28.1705	−	22.4652i	−1.09737	−	0.875121i	−0.104521	−	0.994523i	$-0.533331\pi$
$659$	−28.1705	−	22.4652i	−1.09737	−	0.875121i	−0.992846	+	0.119402i	$0.961902\pi$
$660$	−1.33016	−	0.812704i	−0.0517765	−	0.0316345i
$661$	−20.7068	+	42.9982i	−0.805402	+	1.67244i	−0.0673136	+	0.997732i	$0.521443\pi$
$661$	−20.7068	+	42.9982i	−0.805402	+	1.67244i	−0.738089	+	0.674704i	$0.764271\pi$
$662$	−21.7561	+	7.61279i	−0.845575	+	0.295880i
$663$	−0.262365	−	2.32855i	−0.0101894	−	0.0904334i
$664$	−1.95109	+	2.44659i	−0.0757169	+	0.0949460i
$665$	−4.49827	+	0.106148i	−0.174435	+	0.00411624i
$666$	−3.44668	−	4.32200i	−0.133556	−	0.167474i
$667$	−0.899209	+	0.899209i	−0.0348175	+	0.0348175i
$668$	2.60478	−	2.60478i	0.100782	−	0.100782i
$669$	−9.36311	+	7.46683i	−0.361999	+	0.288684i
$670$	12.6087	+	5.87833i	0.487116	+	0.227100i
$671$	−6.07101	+	12.6066i	−0.234369	+	0.486672i
$672$	−0.381858	+	1.76257i	−0.0147305	+	0.0679928i
$673$	−41.5445	−	14.5370i	−1.60142	−	0.560361i	−0.625831	−	0.779959i	$-0.715240\pi$
$673$	−41.5445	−	14.5370i	−1.60142	−	0.560361i	−0.975591	+	0.219598i	$0.929526\pi$
$674$	22.1623	−	17.6739i	0.853660	−	0.680771i
$675$	−1.64134	+	18.7942i	−0.0631753	+	0.723390i
$676$	−1.85484	−	8.12658i	−0.0713400	−	0.312561i
$677$	3.62734	+	10.3663i	0.139410	+	0.398410i	0.992328	−	0.123635i	$-0.0394550\pi$
$677$	3.62734	+	10.3663i	0.139410	+	0.398410i	−0.852918	+	0.522045i	$0.825169\pi$
$678$	6.92919	+	11.0277i	0.266114	+	0.423518i
$679$	−2.13442	−	17.2302i	−0.0819115	−	0.661235i
$680$	3.22585	+	1.50393i	0.123706	+	0.0576732i
$681$	1.06729	−	4.67612i	0.0408988	−	0.179189i
$682$	6.42104	−	0.723477i	0.245874	−	0.0277034i
$683$	3.47308	−	2.18228i	0.132894	−	0.0835028i	−0.463944	−	0.885864i	$-0.653566\pi$
$683$	3.47308	−	2.18228i	0.132894	−	0.0835028i	0.596838	+	0.802362i	$0.296423\pi$
$684$	−1.73733	+	0.836652i	−0.0664283	+	0.0319902i
$685$	−23.7539	+	2.97862i	−0.907590	+	0.113807i
$686$	−13.5226	−	12.6546i	−0.516296	−	0.483155i
$687$	1.19891	−	1.19891i	0.0457414	−	0.0457414i
$688$	−0.886815	−	0.310310i	−0.0338095	−	0.0118305i
$689$	3.31137	−	14.5081i	0.126153	−	0.552713i
$690$	2.82852	−	4.62947i	0.107680	−	0.176241i
$691$	−39.7225	−	9.06640i	−1.51112	−	0.344902i	−0.614930	−	0.788582i	$-0.710816\pi$
$691$	−39.7225	−	9.06640i	−1.51112	−	0.344902i	−0.896185	+	0.443680i	$0.853673\pi$
$692$	0.993378	−	1.58095i	0.0377626	−	0.0600988i
$693$	4.21770	−	5.41040i	0.160217	−	0.205524i
$694$	−3.81119	−	0.869879i	−0.144671	−	0.0330201i
$695$	−9.24272	−	18.5924i	−0.350596	−	0.705251i
$696$	0.237430	−	0.0541919i	0.00899977	−	0.00205414i
$697$	1.60053	−	4.57406i	0.0606245	−	0.173255i
$698$	−24.9805	−	2.81463i	−0.945526	−	0.106535i
$699$	10.4182	−	5.01715i	0.394054	−	0.189766i
$700$	13.2201	−	0.477949i	0.499674	−	0.0180648i
$701$	36.0476	+	17.3596i	1.36150	+	0.655664i	0.964971	−	0.262358i	$-0.0845001\pi$
$701$	36.0476	+	17.3596i	1.36150	+	0.655664i	0.396530	+	0.918022i	$0.370214\pi$
$702$	−6.89994	−	4.33552i	−0.260421	−	0.163634i
$703$	1.64788	+	0.185671i	0.0621508	+	0.00700272i
$704$			1.02269i			0.0385441i
$705$	−1.54451	−	1.20032i	−0.0581695	−	0.0452066i
$706$	2.63184	−	2.09882i	0.0990505	−	0.0789901i
$707$	−4.97088	−	6.09392i	−0.186949	−	0.229186i
$708$	−4.65305	+	0.524273i	−0.174872	+	0.0197034i
$709$	−26.3246	−	20.9931i	−0.988640	−	0.788414i	−0.0112668	−	0.999937i	$-0.503586\pi$
$709$	−26.3246	−	20.9931i	−0.988640	−	0.788414i	−0.977373	+	0.211522i	$0.932158\pi$
$710$	−35.5395	−	11.9376i	−1.33377	−	0.448009i
$711$	6.83244	+	3.29033i	0.256237	+	0.123397i
$712$	−11.7944	+	1.32891i	−0.442014	+	0.0498030i
$713$	2.51798	+	22.3477i	0.0942990	+	0.836926i
$714$	1.50031	−	2.44735i	0.0561477	−	0.0915896i
$715$	−3.53584	−	3.44823i	−0.132233	−	0.128956i
$716$	2.12850			0.0795456
$717$	2.37264	+	2.37264i	0.0886078	+	0.0886078i
$718$	3.83209	−	34.0108i	0.143012	−	1.26927i
$719$	−4.55985	−	19.9780i	−0.170054	−	0.745054i	−0.985975	−	0.166892i	$-0.946627\pi$
$719$	−4.55985	−	19.9780i	−0.170054	−	0.745054i	0.815921	−	0.578163i	$-0.196230\pi$
$720$	5.07655	−	2.52367i	0.189192	−	0.0940516i
$721$	2.43766	−	24.0170i	0.0907830	−	0.894439i
$722$	−6.08425	+	17.3878i	−0.226432	+	0.647107i
$723$	−0.341735	+	3.03299i	−0.0127093	+	0.112798i
$724$	23.5061	−	11.3200i	0.873598	−	0.420703i
$725$	−0.815215	−	1.58953i	−0.0302763	−	0.0590336i
$726$	2.94397	−	6.11323i	0.109261	−	0.226883i
$727$	26.0894	−	16.3930i	0.967601	−	0.607984i	0.0471691	−	0.998887i	$-0.484980\pi$
$727$	26.0894	−	16.3930i	0.967601	−	0.607984i	0.920432	+	0.390903i	$0.127837\pi$
$728$	−2.42222	+	5.17531i	−0.0897736	+	0.191810i
$729$	−4.92092	+	1.12317i	−0.182256	+	0.0415988i
$730$	−20.4764	−	25.0261i	−0.757866	−	0.926256i
$731$	1.16922	+	0.932420i	0.0432451	+	0.0344868i
$732$	4.96181	+	7.89667i	0.183394	+	0.291869i
$733$	2.85477	−	8.15847i	0.105443	−	0.301340i	−0.879058	−	0.476714i	$-0.841828\pi$
$733$	2.85477	−	8.15847i	0.105443	−	0.301340i	0.984502	+	0.175374i	$0.0561135\pi$
$734$	6.79989			0.250989
$735$	0.826667	−	10.6374i	0.0304921	−	0.392365i
$736$	−3.55935			−0.131199
$737$	2.10144	−	6.00558i	0.0774077	−	0.221218i
$738$	−4.10670	−	6.53578i	−0.151170	−	0.240585i
$739$	15.4584	+	12.3276i	0.568645	+	0.453480i	0.865123	−	0.501560i	$-0.167240\pi$
$739$	15.4584	+	12.3276i	0.568645	+	0.453480i	−0.296477	+	0.955040i	$0.595812\pi$
$740$	−4.85129	−	0.485064i	−0.178337	−	0.0178313i
$741$	1.09160	−	0.249150i	0.0401008	−	0.00915274i
$742$	14.1263	−	11.5230i	0.518595	−	0.423023i
$743$	−31.8808	+	20.0320i	−1.16959	+	0.734903i	−0.969552	−	0.244885i	$-0.921250\pi$
$743$	−31.8808	+	20.0320i	−1.16959	+	0.734903i	−0.200040	+	0.979788i	$0.564107\pi$
$744$	1.86867	−	3.88033i	0.0685088	−	0.142260i
$745$	−18.4105	−	8.58323i	−0.674510	−	0.314465i
$746$	19.5790	−	9.42877i	0.716839	−	0.345212i
$747$	0.888316	−	7.88402i	0.0325018	−	0.288461i
$748$	0.537641	−	1.53649i	0.0196581	−	0.0561796i
$749$	−27.2480	−	9.19785i	−0.995620	−	0.336082i
$750$	4.97244	+	5.77536i	0.181568	+	0.210886i
$751$	−6.18757	−	27.1095i	−0.225787	−	0.989240i	−0.953034	−	0.302863i	$-0.902057\pi$
$751$	−6.18757	−	27.1095i	−0.225787	−	0.989240i	0.727247	−	0.686376i	$-0.240800\pi$
$752$	−0.143689	+	1.27528i	−0.00523981	+	0.0465046i
$753$	2.39994	+	2.39994i	0.0874586	+	0.0874586i
$754$	0.771621			0.0281008
$755$	0.294634	+	23.4863i	0.0107228	+	0.854756i
$756$	−3.40102	−	9.38561i	−0.123694	−	0.341351i
$757$	−1.63370	−	14.4995i	−0.0593778	−	0.526992i	−0.987830	−	0.155540i	$-0.950288\pi$
$757$	−1.63370	−	14.4995i	−0.0593778	−	0.526992i	0.928452	−	0.371453i	$-0.121140\pi$
$758$	35.2329	−	3.96980i	1.27972	−	0.144190i
$759$	−2.23554	−	1.07658i	−0.0811450	−	0.0390774i
$760$	−0.541512	+	1.61214i	−0.0196427	+	0.0584785i
$761$	−26.9837	−	21.5188i	−0.978160	−	0.780056i	−0.00264631	−	0.999996i	$-0.500842\pi$
$761$	−26.9837	−	21.5188i	−0.978160	−	0.780056i	−0.975513	+	0.219940i	$0.929414\pi$
$762$	4.07869	−	0.459558i	0.147755	−	0.0166480i
$763$	7.12761	−	32.8995i	0.258037	−	1.19104i
$764$	4.88724	−	3.89744i	0.176814	−	0.141004i
$765$	−8.95374	+	1.12275i	−0.323723	+	0.0405933i
$766$			21.8333i			0.788868i
$767$	−14.7427	−	1.66111i	−0.532330	−	0.0599791i
$768$	0.577166	+	0.362657i	0.0208267	+	0.0130863i
$769$	−38.3310	−	18.4592i	−1.38225	−	0.665657i	−0.412773	−	0.910834i	$-0.635440\pi$
$769$	−38.3310	−	18.4592i	−1.38225	−	0.665657i	−0.969478	+	0.245177i	$0.921154\pi$
$770$	−0.819067	−	5.99462i	−0.0295171	−	0.216031i
$771$	−15.8294	+	7.62305i	−0.570083	+	0.274537i
$772$	14.9974	+	1.68981i	0.539770	+	0.0608175i
$773$	12.1765	−	34.7985i	0.437959	−	1.25161i	−0.487619	−	0.873057i	$-0.662134\pi$
$773$	12.1765	−	34.7985i	0.437959	−	1.25161i	0.925578	−	0.378558i	$-0.123580\pi$
$774$	2.32235	−	0.530060i	0.0834750	−	0.0190526i
$775$	−30.9661	−	6.25494i	−1.11234	−	0.224684i
$776$	−6.39766	−	1.46022i	−0.229662	−	0.0524190i
$777$	−0.832594	+	3.84308i	−0.0298692	+	0.137870i
$778$	−13.5054	+	21.4938i	−0.484193	+	0.770589i
$779$	2.25746	+	0.515251i	0.0808819	+	0.0184608i
$780$	−3.19989	+	0.772710i	−0.114575	+	0.0276674i
$781$	−3.81553	+	16.7169i	−0.136530	+	0.598179i
$782$	5.34757	+	1.87120i	0.191229	+	0.0669138i
$783$	−0.953223	+	0.953223i	−0.0340654	+	0.0340654i
$784$	−6.23813	+	3.17580i	−0.222790	+	0.113421i
$785$	−2.98793	−	23.8281i	−0.106644	−	0.850461i
$786$	−12.0343	+	5.79543i	−0.429250	+	0.206716i
$787$	8.79226	−	5.52454i	0.313410	−	0.196929i	−0.366136	−	0.930561i	$-0.619320\pi$
$787$	8.79226	−	5.52454i	0.313410	−	0.196929i	0.679546	+	0.733633i	$0.262177\pi$
$788$	−7.63531	+	0.860292i	−0.271997	+	0.0306466i
$789$	−4.32319	+	18.9412i	−0.153910	+	0.674323i
$790$	6.28471	−	2.28800i	0.223600	−	0.0814034i
$791$	−16.1679	+	47.8964i	−0.574866	+	1.70300i
$792$	−1.37950	−	2.19546i	−0.0490183	−	0.0780122i
$793$	9.75942	+	27.8908i	0.346567	+	0.990432i
$794$	3.88142	+	17.0056i	0.137747	+	0.603507i
$795$	10.2674	+	2.20835i	0.364148	+	0.0783220i
$796$	12.5235	−	9.98719i	0.443885	−	0.353986i
$797$	−40.3333	−	14.1132i	−1.42868	−	0.499916i	−0.498456	−	0.866915i	$-0.666100\pi$
$797$	−40.3333	−	14.1132i	−1.42868	−	0.499916i	−0.930221	+	0.366999i	$0.880385\pi$
$798$	1.24230	+	0.581441i	0.0439770	+	0.0205828i
$799$	0.886309	−	1.84044i	0.0313554	−	0.0651101i
$800$	1.53249	−	4.75936i	0.0541815	−	0.168269i
$801$	23.5271	−	18.7622i	0.831288	−	0.662930i
$802$	10.5494	−	10.5494i	0.372512	−	0.372512i
$803$	−10.4574	+	10.4574i	−0.369034	+	0.369034i
$804$	−2.64412	−	3.31562i	−0.0932508	−	0.116933i
$805$	20.8635	−	2.85066i	0.735343	−	0.100473i
$806$	8.50804	−	10.6687i	0.299683	−	0.375790i
$807$	0.120779	+	1.07194i	0.00425161	+	0.0377341i
$808$	−2.80558	+	0.981717i	−0.0987001	+	0.0345367i
$809$	−6.54958	+	13.6003i	−0.230271	+	0.478162i	−0.983804	−	0.179248i	$-0.942634\pi$
$809$	−6.54958	+	13.6003i	−0.230271	+	0.478162i	0.753533	+	0.657410i	$0.228348\pi$
$810$	−5.86887	+	9.60565i	−0.206211	+	0.337508i
$811$	16.7342	+	13.3451i	0.587617	+	0.468609i	0.871598	−	0.490221i	$-0.163084\pi$
$811$	16.7342	+	13.3451i	0.587617	+	0.468609i	−0.283981	+	0.958830i	$0.591655\pi$
$812$	0.745505	+	0.581162i	0.0261621	+	0.0203948i
$813$	−1.54822	+	13.7408i	−0.0542983	+	0.481911i
$814$			2.22985i			0.0781562i
$815$	4.55235	+	36.3041i	0.159462	+	1.27168i
$816$	−0.676480	−	0.848280i	−0.0236816	−	0.0296957i
$817$	−0.380176	+	0.605046i	−0.0133007	+	0.0211679i
$818$	11.9358	−	4.17652i	0.417326	−	0.146029i
$819$	−1.78102	−	14.3774i	−0.0622340	−	0.502388i
$820$	−6.65550	−	1.43148i	−0.232420	−	0.0499896i
$821$	−25.7498	−	32.2892i	−0.898674	−	1.12690i	−0.991355	−	0.131205i	$-0.958115\pi$
$821$	−25.7498	−	32.2892i	−0.898674	−	1.12690i	0.0926814	−	0.995696i	$-0.470456\pi$
$822$	6.88834	+	2.41033i	0.240258	+	0.0840701i
$823$	9.41652	−	14.9863i	0.328239	−	0.522390i	−0.641311	−	0.767281i	$-0.721609\pi$
$823$	9.41652	−	14.9863i	0.328239	−	0.522390i	0.969551	+	0.244891i	$0.0787522\pi$
$824$	−8.22062	−	3.95884i	−0.286379	−	0.137913i
$825$	2.40206	−	2.52571i	0.0836289	−	0.0879341i
$826$	−12.9927	−	12.7087i	−0.452073	−	0.442192i
$827$	46.3016	+	29.0932i	1.61006	+	1.01167i	0.969923	+	0.243412i	$0.0782669\pi$
$827$	46.3016	+	29.0932i	1.61006	+	1.01167i	0.640141	+	0.768258i	$0.278876\pi$
$828$	7.64103	−	4.80118i	0.265544	−	0.166853i
$829$	−0.177623	+	0.222733i	−0.00616912	+	0.00773583i	−0.784906	−	0.619614i	$-0.787289\pi$
$829$	−0.177623	+	0.222733i	−0.00616912	+	0.00773583i	0.778737	+	0.627350i	$0.215860\pi$
$830$	−4.43105	−	5.41558i	−0.153804	−	0.187977i
$831$	1.77332	+	3.68233i	0.0615157	+	0.127739i
$832$	1.52716	+	1.52716i	0.0529447	+	0.0529447i
$833$	11.0417	−	1.49186i	0.382573	−	0.0516898i
$834$			6.32945i			0.219171i
$835$	4.46952	+	6.91899i	0.154674	+	0.239441i
$836$	0.758313	+	0.173080i	0.0262268	+	0.00598609i
$837$	2.66923	+	23.6900i	0.0922620	+	0.818848i
$838$	0.824757	+	1.31259i	0.0284908	+	0.0453428i
$839$	7.87002	+	34.4808i	0.271703	+	1.19041i	0.908001	+	0.418967i	$0.137608\pi$
$839$	7.87002	+	34.4808i	0.271703	+	1.19041i	−0.636298	+	0.771443i	$0.719535\pi$
$840$	−3.67357	−	1.66351i	−0.126750	−	0.0573965i
$841$	−6.42470	+	28.1485i	−0.221541	+	0.970637i
$842$	−6.96246	+	2.43627i	−0.239942	+	0.0839594i
$843$	0.798693	+	0.501852i	0.0275085	+	0.0172847i
$844$	4.10362	+	8.52125i	0.141252	+	0.293314i
$845$	18.6374	−	0.233805i	0.641148	−	0.00804313i
$846$	−1.41175	−	2.93153i	−0.0485369	−	0.100788i
$847$	25.6095	−	6.14366i	0.879952	−	0.211099i
$848$	−2.27572	−	6.50364i	−0.0781486	−	0.223336i
$849$	4.35462	−	0.993914i	0.149450	−	0.0341110i
$850$	−4.80446	+	6.34482i	−0.164792	+	0.217625i
$851$	−7.76073			−0.266034
$852$	8.08134	+	8.08134i	0.276862	+	0.276862i
$853$	−14.5258	−	1.63667i	−0.497355	−	0.0560385i	−0.140276	−	0.990112i	$-0.544799\pi$
$853$	−14.5258	−	1.63667i	−0.497355	−	0.0560385i	−0.357080	+	0.934074i	$0.616228\pi$
$854$	−11.5774	+	34.2973i	−0.396172	+	1.17363i
$855$	−1.01212	−	4.19131i	−0.0346136	−	0.143340i
$856$	−6.77715	+	8.49828i	−0.231638	+	0.290465i
$857$	−0.0202464	−	0.0578608i	−0.000691603	−	0.00197649i	0.943537	−	0.331267i	$-0.107476\pi$
$857$	−0.0202464	−	0.0578608i	−0.000691603	−	0.00197649i	−0.944229	+	0.329291i	$0.893190\pi$
$858$	0.497259	+	1.42108i	0.0169761	+	0.0485150i
$859$	−22.5672	+	28.2983i	−0.769982	+	0.965526i	−0.999971	−	0.00766686i	$-0.997560\pi$
$859$	−22.5672	+	28.2983i	−0.769982	+	0.965526i	0.229989	+	0.973193i	$0.426131\pi$
$860$	1.09533	−	1.79274i	0.0373504	−	0.0611320i
$861$	−1.75607	+	5.20225i	−0.0598468	+	0.177292i
$862$	−29.3116	−	3.30262i	−0.998357	−	0.112488i
$863$	−36.0843	−	36.0843i	−1.22832	−	1.22832i	−0.964598	−	0.263725i	$-0.915049\pi$
$863$	−36.0843	−	36.0843i	−1.22832	−	1.22832i	−0.263725	−	0.964598i	$-0.584951\pi$
$864$	−3.77315			−0.128365
$865$	2.98901	+	2.91494i	0.101629	+	0.0991110i
$866$	35.1445	−	8.02151i	1.19426	−	0.272582i
$867$	−3.25687	−	9.30760i	−0.110609	−	0.316103i
$868$	16.2555	−	3.89965i	0.551746	−	0.132363i
$869$	−1.32722	−	2.75601i	−0.0450230	−	0.0934911i
$870$	0.00683095	+	0.544521i	0.000231591	+	0.0184610i
$871$	−5.82996	−	12.1060i	−0.197541	−	0.410197i
$872$	−10.7732	−	6.76922i	−0.364825	−	0.229235i
$873$	15.7039	−	5.49502i	0.531495	−	0.185978i
$874$	−0.602384	+	2.63922i	−0.0203759	+	0.0892728i
$875$	−5.17110	+	29.1249i	−0.174815	+	0.984601i
$876$	2.19343	+	9.61006i	0.0741092	+	0.324694i
$877$	−19.9133	−	31.6919i	−0.672425	−	1.07016i	−0.992438	−	0.122745i	$-0.960830\pi$
$877$	−19.9133	−	31.6919i	−0.672425	−	1.07016i	0.320013	−	0.947413i	$-0.396313\pi$
$878$	−0.919125	−	8.15746i	−0.0310190	−	0.275301i
$879$	−0.565414	−	0.129052i	−0.0190710	−	0.00435282i
$880$	−2.23568	−	0.480855i	−0.0753646	−	0.0162096i
$881$			30.7357i			1.03551i	0.855528	+	0.517756i	$0.173233\pi$
$881$			30.7357i			1.03551i	−0.855528	+	0.517756i	$0.826767\pi$
$882$	9.10790	−	15.2322i	0.306679	−	0.512896i
$883$	40.8810	+	40.8810i	1.37576	+	1.37576i	0.851659	+	0.524097i	$0.175597\pi$
$883$	40.8810	+	40.8810i	1.37576	+	1.37576i	0.524097	+	0.851659i	$0.324403\pi$
$884$	−1.49156	−	3.09725i	−0.0501665	−	0.104172i
$885$	1.04170	−	10.4184i	0.0350165	−	0.350211i
$886$	19.0739	−	23.9179i	0.640801	−	0.803539i
$887$	−3.64628	+	2.29111i	−0.122430	+	0.0769280i	−0.591855	−	0.806044i	$-0.701604\pi$
$887$	−3.64628	+	2.29111i	−0.122430	+	0.0769280i	0.469425	+	0.882972i	$0.344461\pi$
$888$	1.25844	+	0.790730i	0.0422305	+	0.0265352i
$889$	11.3889	+	11.1400i	0.381971	+	0.373622i
$890$	2.64048	−	26.4083i	0.0885090	−	0.885207i
$891$	4.63850	+	2.23379i	0.155396	+	0.0748346i
$892$	−9.34731	+	14.8762i	−0.312971	+	0.498090i
$893$	0.921286	+	0.322372i	0.0308297	+	0.0107878i
$894$	3.86080	+	4.84129i	0.129125	+	0.161917i
$895$	−1.00079	+	4.65305i	−0.0334528	+	0.155534i
$896$	0.325260	+	2.62568i	0.0108662	+	0.0877179i
$897$	−4.94591	+	1.73065i	−0.165139	+	0.0577847i
$898$	−6.85305	+	10.9066i	−0.228689	+	0.363957i
$899$	−1.40746	−	1.76490i	−0.0469413	−	0.0588626i
$900$	3.13000	+	12.2843i	0.104333	+	0.409477i
$901$			10.9674i			0.365379i
$902$	−0.348610	+	3.09400i	−0.0116074	+	0.103019i
$903$	−1.33635	−	1.04176i	−0.0444708	−	0.0346674i
$904$	14.9382	+	11.9128i	0.496838	+	0.396215i
$905$	13.6940	+	56.7087i	0.455204	+	1.88506i
$906$	3.10668	−	6.45109i	0.103213	−	0.214323i
$907$	23.5514	−	8.24099i	0.782011	−	0.273637i	0.0903979	−	0.995906i	$-0.471186\pi$
$907$	23.5514	−	8.24099i	0.782011	−	0.273637i	0.691613	+	0.722268i	$0.256900\pi$
$908$	−0.787834	−	6.99222i	−0.0261452	−	0.232045i
$909$	4.69866	−	5.89193i	0.155845	−	0.195423i
$910$	−10.1747	−	7.72853i	−0.337288	−	0.256198i
$911$	−15.6682	−	19.6473i	−0.519110	−	0.650944i	0.451310	−	0.892367i	$-0.350957\pi$
$911$	−15.6682	−	19.6473i	−0.519110	−	0.650944i	−0.970420	+	0.241424i	$0.922386\pi$
$912$	0.366586	−	0.366586i	0.0121389	−	0.0121389i
$913$	−2.26296	+	2.26296i	−0.0748930	+	0.0748930i
$914$	5.20318	−	4.14940i	0.172106	−	0.137250i
$915$	−19.5957	+	7.13397i	−0.647814	+	0.235842i
$916$	1.07924	−	2.24106i	0.0356591	−	0.0740469i
$917$	−46.9560	−	21.9770i	−1.55062	−	0.725745i
$918$	5.66879	+	1.98359i	0.187098	+	0.0654684i
$919$	17.7131	−	14.1257i	0.584300	−	0.465964i	−0.286174	−	0.958178i	$-0.592384\pi$
$919$	17.7131	−	14.1257i	0.584300	−	0.465964i	0.870474	+	0.492214i	$0.163812\pi$
$920$	1.67356	−	7.78100i	0.0551756	−	0.256532i
$921$	−2.56951	−	11.2578i	−0.0846682	−	0.370956i
$922$	4.28964	+	12.2591i	0.141272	+	0.403731i
$923$	19.2654	+	30.6606i	0.634127	+	1.00921i
$924$	−0.589890	+	1.74751i	−0.0194059	+	0.0574888i
$925$	3.34140	−	10.3772i	0.109864	−	0.341200i
$926$	−0.0215703	+	0.0945056i	−0.000708843	+	0.00310565i
$927$	22.9877	−	2.59009i	0.755014	−	0.0850696i
$928$	0.302515	−	0.190083i	0.00993054	−	0.00623977i
$929$	32.5652	−	15.6826i	1.06843	−	0.514528i	0.184829	−	0.982771i	$-0.440827\pi$
$929$	32.5652	−	15.6826i	1.06843	−	0.514528i	0.883600	+	0.468243i	$0.155113\pi$
$930$	7.60408	+	5.90954i	0.249347	+	0.193781i
$931$	1.29908	+	5.16298i	0.0425756	+	0.169210i
$932$	11.9953	−	11.9953i	0.392919	−	0.392919i
$933$	11.8562	+	4.14865i	0.388153	+	0.135821i
$934$	3.11990	−	13.6692i	0.102086	−	0.447269i
$935$	3.10609	+	1.89776i	0.101580	+	0.0620634i
$936$	−5.33840	−	1.21846i	−0.174491	−	0.0398265i
$937$	18.5792	−	29.5687i	0.606957	−	0.965967i	−0.391985	−	0.919972i	$-0.628211\pi$
$937$	18.5792	−	29.5687i	0.606957	−	0.965967i	0.998942	−	0.0459950i	$-0.0146458\pi$
$938$	3.48527	−	16.0873i	0.113798	−	0.525267i
$939$	11.7133	+	2.67349i	0.382250	+	0.0872460i
$940$	−2.72029	−	0.913735i	−0.0887262	−	0.0298027i
$941$	−28.1652	+	6.42853i	−0.918161	+	0.209564i	−0.655387	−	0.755293i	$-0.727494\pi$
$941$	−28.1652	+	6.42853i	−0.918161	+	0.209564i	−0.262774	+	0.964857i	$0.584637\pi$
$942$	−2.41786	+	6.90986i	−0.0787782	+	0.225135i
$943$	−10.7683	−	1.21330i	−0.350664	−	0.0395103i
$944$	−6.18911	+	2.98052i	−0.201438	+	0.0970076i
$945$	22.1168	−	3.02190i	0.719459	−	0.0983023i
$946$	−0.865702	−	0.416900i	−0.0281464	−	0.0135546i
$947$	40.8078	+	25.6412i	1.32608	+	0.833228i	0.993932	−	0.110001i	$-0.0350853\pi$
$947$	40.8078	+	25.6412i	1.32608	+	0.833228i	0.332144	+	0.943229i	$0.392228\pi$
$948$	−2.02603	−	0.228279i	−0.0658024	−	0.00741415i
$949$			31.2316i			1.01382i
$950$	−3.26965	−	1.94179i	−0.106082	−	0.0630001i
$951$	7.17740	−	5.72379i	0.232743	−	0.185606i
$952$	0.891683	−	4.11582i	0.0288996	−	0.133395i
$953$	−29.3868	+	3.31110i	−0.951932	+	0.107257i	−0.574252	−	0.818679i	$-0.694707\pi$
$953$	−29.3868	+	3.31110i	−0.951932	+	0.107257i	−0.377681	+	0.925936i	$0.623278\pi$
$954$	13.6581	+	10.8920i	0.442198	+	0.352641i
$955$	6.22218	+	12.5164i	0.201345	+	0.405021i
$956$	4.43504	+	2.13580i	0.143439	+	0.0690768i
$957$	0.247496	−	0.0278861i	0.00800040	−	0.000901429i
$958$	3.91720	+	34.7661i	0.126559	+	1.12324i
$959$	9.65035	+	26.6315i	0.311626	+	0.859977i
$960$	−1.06417	+	1.09121i	−0.0343460	+	0.0352187i
$961$	−8.92103			−0.287775
$962$	3.32978	+	3.32978i	0.107357	+	0.107357i
$963$	3.08559	−	27.3853i	0.0994316	−	0.882480i
$964$	0.996373	+	4.36540i	0.0320910	+	0.140600i
$965$	−10.7456	+	31.9910i	−0.345915	+	1.02983i
$966$	−6.08199	−	2.05304i	−0.195685	−	0.0660555i
$967$	−14.7740	+	42.2217i	−0.475100	+	1.35776i	0.418224	+	0.908344i	$0.362653\pi$
$967$	−14.7740	+	42.2217i	−0.475100	+	1.35776i	−0.893324	+	0.449413i	$0.851633\pi$
$968$	1.11451	−	9.89152i	0.0358216	−	0.317925i
$969$	−0.743477	+	0.358040i	−0.0238839	+	0.0115019i
$970$	6.20025	−	13.2992i	0.199078	−	0.427011i
$971$	−6.00303	+	12.4654i	−0.192646	+	0.400034i	−0.974809	−	0.223039i	$-0.928402\pi$
$971$	−6.00303	+	12.4654i	−0.192646	+	0.400034i	0.782163	+	0.623074i	$0.214116\pi$
$972$	12.4900	−	7.84798i	0.400616	−	0.251724i
$973$	−19.0370	+	15.5287i	−0.610299	+	0.497827i
$974$	12.4552	−	2.84282i	0.399091	−	0.0910898i
$975$	−0.184653	−	7.35853i	−0.00591363	−	0.235661i
$976$	10.6969	+	8.53047i	0.342399	+	0.273054i
$977$	−24.5092	−	39.0061i	−0.784118	−	1.24792i	−0.964438	−	0.264308i	$-0.914856\pi$
$977$	−24.5092	−	39.0061i	−0.784118	−	1.24792i	0.180321	−	0.983608i	$-0.442286\pi$
$978$	3.68381	−	10.5277i	0.117795	−	0.336640i
$979$	−12.1383			−0.387943
$980$	−4.00945	−	15.1302i	−0.128077	−	0.483318i
$981$	32.2582			1.02993
$982$	13.7103	−	39.1817i	0.437513	−	1.25034i
$983$	−1.18901	−	1.89230i	−0.0379235	−	0.0603550i	0.827224	−	0.561872i	$-0.189918\pi$
$983$	−1.18901	−	1.89230i	−0.0379235	−	0.0603550i	−0.865148	+	0.501517i	$0.832776\pi$
$984$	1.62251	+	1.29391i	0.0517237	+	0.0412483i
$985$	1.70936	−	17.0959i	0.0544647	−	0.544719i
$986$	−0.554428	+	0.126545i	−0.0176566	+	0.00403000i
$987$	−0.981111	+	2.09623i	−0.0312291	+	0.0667239i
$988$	1.39083	−	0.873914i	0.0442481	−	0.0278029i
$989$	1.45097	−	3.01297i	0.0461382	−	0.0958069i
$990$	5.44806	−	1.98341i	0.173151	−	0.0630369i
$991$	15.3169	−	7.37625i	0.486559	−	0.234314i	−0.174488	−	0.984659i	$-0.555827\pi$
$991$	15.3169	−	7.37625i	0.486559	−	0.234314i	0.661046	+	0.750345i	$0.270113\pi$
$992$	0.707426	−	6.27858i	0.0224608	−	0.199345i
$993$	−5.18922	+	14.8299i	−0.164675	+	0.470614i
$994$	−4.47938	+	44.1330i	−0.142077	+	1.39981i
$995$	15.9443	+	32.0732i	0.505469	+	1.01679i
$996$	0.474654	+	2.07959i	0.0150400	+	0.0658944i
$997$	−1.73067	+	15.3601i	−0.0548109	+	0.486461i	0.936079	+	0.351789i	$0.114427\pi$
$997$	−1.73067	+	15.3601i	−0.0548109	+	0.486461i	−0.990890	+	0.134672i	$0.957002\pi$
$998$	−18.1665	−	18.1665i	−0.575051	−	0.575051i
$999$	−8.22690			−0.260288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.s.a.223.20	yes	336
5.2	odd	4	inner	490.2.s.a.27.20	✓	336
49.20	odd	14	inner	490.2.s.a.363.20	yes	336
245.167	even	28	inner	490.2.s.a.167.20	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.s.a.27.20	✓	336	5.2	odd	4	inner
490.2.s.a.167.20	yes	336	245.167	even	28	inner
490.2.s.a.223.20	yes	336	1.1	even	1	trivial
490.2.s.a.363.20	yes	336	49.20	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.330279 - 0.943883i) q^{2} +(-0.362657 - 0.577166i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(1.73060 - 1.41599i) q^{5} +(-0.664555 + 0.151680i) q^{6} +(-2.08663 - 1.62664i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.10005 - 2.28428i) q^{9} +O(q^{10})\)	\(q+(0.330279 - 0.943883i) q^{2} +(-0.362657 - 0.577166i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(1.73060 - 1.41599i) q^{5} +(-0.664555 + 0.151680i) q^{6} +(-2.08663 - 1.62664i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.10005 - 2.28428i) q^{9} +(-0.764943 - 2.10116i) q^{10} +(-0.921411 + 0.443728i) q^{11} +(-0.0763201 + 0.677359i) q^{12} +(-0.713313 + 2.03853i) q^{13} +(-2.22453 + 1.43229i) q^{14} +(-1.44487 - 0.485327i) q^{15} +(0.222521 + 0.974928i) q^{16} +(0.178216 - 1.58171i) q^{17} +(-1.79277 - 1.79277i) q^{18} +0.760557 q^{19} +(-2.23589 + 0.0280490i) q^{20} +(-0.182111 + 1.79425i) q^{21} +(0.114505 + 1.01626i) q^{22} +(-3.53697 + 0.398521i) q^{23} +(0.614141 + 0.295755i) q^{24} +(0.989970 - 4.90102i) q^{25} +(1.68854 + 1.34657i) q^{26} +(-3.74943 + 0.422459i) q^{27} +(0.617198 + 2.57275i) q^{28} +(0.279330 - 0.222759i) q^{29} +(-0.935303 + 1.20350i) q^{30} -6.31831i q^{31} +(0.993712 + 0.111964i) q^{32} +(0.590261 + 0.370886i) q^{33} +(-1.43409 - 0.690623i) q^{34} +(-5.91443 + 0.139566i) q^{35} +(-2.28428 + 1.10005i) q^{36} +(2.16667 + 0.244125i) q^{37} +(0.251196 - 0.717877i) q^{38} +(1.43526 - 0.327588i) q^{39} +(-0.711993 + 2.11969i) q^{40} +(2.96817 + 0.677465i) q^{41} +(1.63341 + 0.764493i) q^{42} +(-0.499865 + 0.795530i) q^{43} +(0.997049 + 0.227570i) q^{44} +(-1.33076 - 5.51084i) q^{45} +(-0.792030 + 3.47011i) q^{46} +(1.21133 + 0.423863i) q^{47} +(0.481996 - 0.481996i) q^{48} +(1.70806 + 6.78841i) q^{49} +(-4.29902 - 2.55312i) q^{50} +(-0.977543 + 0.470760i) q^{51} +(1.82869 - 1.14904i) q^{52} +(-6.84697 + 0.771469i) q^{53} +(-0.839605 + 3.67855i) q^{54} +(-0.966284 + 2.07262i) q^{55} +(2.63223 + 0.267164i) q^{56} +(-0.275822 - 0.438967i) q^{57} +(-0.118001 - 0.337228i) q^{58} +(1.52858 + 6.69717i) q^{59} +(0.827051 + 1.28031i) q^{60} +(10.6969 - 8.53047i) q^{61} +(-5.96375 - 2.08681i) q^{62} +(-6.01111 + 2.97706i) q^{63} +(0.433884 - 0.900969i) q^{64} +(1.65207 + 4.53793i) q^{65} +(0.545024 - 0.434642i) q^{66} +(-4.39924 + 4.39924i) q^{67} +(-1.12552 + 1.12552i) q^{68} +(1.51272 + 1.89689i) q^{69} +(-1.82168 + 5.62863i) q^{70} +(10.4537 - 13.1085i) q^{71} +(0.283870 + 2.51942i) q^{72} +(13.6494 - 4.77613i) q^{73} +(0.946031 - 1.96445i) q^{74} +(-3.18772 + 1.20601i) q^{75} +(-0.594628 - 0.474200i) q^{76} +(2.64443 + 0.572911i) q^{77} +(0.164831 - 1.46291i) q^{78} +2.99107i q^{79} +(1.76558 + 1.37213i) q^{80} +(-3.13873 - 3.93584i) q^{81} +(1.61977 - 2.57785i) q^{82} +(2.95370 - 1.03354i) q^{83} +(1.26107 - 1.28925i) q^{84} +(-1.93126 - 2.98967i) q^{85} +(0.585793 + 0.734561i) q^{86} +(-0.229870 - 0.0804349i) q^{87} +(0.544104 - 0.865936i) q^{88} +(10.6936 + 5.14978i) q^{89} +(-5.64111 - 0.564036i) q^{90} +(4.80439 - 3.09336i) q^{91} +(3.01379 + 1.89369i) q^{92} +(-3.64671 + 2.29138i) q^{93} +(0.800154 - 1.00336i) q^{94} +(1.31622 - 1.07694i) q^{95} +(-0.295755 - 0.614141i) q^{96} +(4.64016 + 4.64016i) q^{97} +(6.97160 + 0.629860i) q^{98} +2.59289i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) \) 336 * q + 28 * q^6 + 8 * q^7	\( 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) \) 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

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