LMFDB - Embedded newform 135.2.k.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(16,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("135.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.k (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	135.16
Dual form			135.2.k.a.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25101 + 1.04972i) q^{2} +(-0.905836 + 1.47630i) q^{3} +(0.115814 + 0.656812i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.68292 + 0.895989i) q^{6} +(-0.576430 + 3.26909i) q^{7} +(1.08849 - 1.88532i) q^{8} +(-1.35892 - 2.67457i) q^{9} +O(q^{10})$	\(q+(1.25101 + 1.04972i) q^{2} +(-0.905836 + 1.47630i) q^{3} +(0.115814 + 0.656812i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.68292 + 0.895989i) q^{6} +(-0.576430 + 3.26909i) q^{7} +(1.08849 - 1.88532i) q^{8} +(-1.35892 - 2.67457i) q^{9} +(0.816539 + 1.41429i) q^{10} +(-3.04687 + 1.10897i) q^{11} +(-1.07456 - 0.423989i) q^{12} +(4.99824 - 4.19402i) q^{13} +(-4.15276 + 3.48458i) q^{14} +(-1.35613 + 1.07745i) q^{15} +(4.59423 - 1.67216i) q^{16} +(-0.561583 - 0.972691i) q^{17} +(1.10753 - 4.77241i) q^{18} +(0.0708761 - 0.122761i) q^{19} +(-0.115814 + 0.656812i) q^{20} +(-4.30401 - 3.81225i) q^{21} +(-4.97577 - 1.81103i) q^{22} +(-0.0812647 - 0.460875i) q^{23} +(1.79731 + 3.31473i) q^{24} +(0.766044 + 0.642788i) q^{25} +10.6554 q^{26} +(5.17943 + 0.416551i) q^{27} -2.21394 q^{28} +(-1.61158 - 1.35227i) q^{29} +(-2.82756 - 0.0756567i) q^{30} +(-1.58476 - 8.98762i) q^{31} +(3.41134 + 1.24163i) q^{32} +(1.12279 - 5.50263i) q^{33} +(0.318509 - 1.80635i) q^{34} +(-1.65976 + 2.87479i) q^{35} +(1.59931 - 1.20231i) q^{36} +(3.89752 + 6.75070i) q^{37} +(0.217532 - 0.0791751i) q^{38} +(1.66404 + 11.1780i) q^{39} +(1.66767 - 1.39934i) q^{40} +(-9.42272 + 7.90660i) q^{41} +(-1.38256 - 9.28718i) q^{42} +(-2.68125 + 0.975897i) q^{43} +(-1.08125 - 1.87279i) q^{44} +(-0.362210 - 2.97805i) q^{45} +(0.382128 - 0.661865i) q^{46} +(0.226235 - 1.28304i) q^{47} +(-1.69301 + 8.29716i) q^{48} +(-3.77686 - 1.37466i) q^{49} +(0.283581 + 1.60827i) q^{50} +(1.94469 + 0.0520337i) q^{51} +(3.33355 + 2.79718i) q^{52} -10.6122 q^{53} +(6.04226 + 5.95807i) q^{54} -3.24241 q^{55} +(5.53586 + 4.64514i) q^{56} +(0.117030 + 0.215836i) q^{57} +(-0.596588 - 3.38342i) q^{58} +(-4.34027 - 1.57973i) q^{59} +(-0.864743 - 0.765940i) q^{60} +(0.313991 - 1.78073i) q^{61} +(7.45195 - 12.9072i) q^{62} +(9.52675 - 2.90074i) q^{63} +(-1.92481 - 3.33388i) q^{64} +(6.13125 - 2.23159i) q^{65} +(7.18086 - 5.70523i) q^{66} +(-9.22089 + 7.73725i) q^{67} +(0.573836 - 0.481506i) q^{68} +(0.754002 + 0.297506i) q^{69} +(-5.09412 + 1.85411i) q^{70} +(0.293127 + 0.507712i) q^{71} +(-6.52161 - 0.349245i) q^{72} +(1.15209 - 1.99548i) q^{73} +(-2.21052 + 12.5365i) q^{74} +(-1.64286 + 0.548651i) q^{75} +(0.0888393 + 0.0323349i) q^{76} +(-1.86902 - 10.5997i) q^{77} +(-9.65206 + 15.7306i) q^{78} +(8.47739 + 7.11338i) q^{79} +4.88907 q^{80} +(-5.30667 + 7.26906i) q^{81} -20.0877 q^{82} +(1.76441 + 1.48051i) q^{83} +(2.00547 - 3.26844i) q^{84} +(-0.195036 - 1.10610i) q^{85} +(-4.37870 - 1.59372i) q^{86} +(3.45619 - 1.15423i) q^{87} +(-1.22573 + 6.95143i) q^{88} +(3.01777 - 5.22692i) q^{89} +(2.67300 - 4.10580i) q^{90} +(10.8295 + 18.7573i) q^{91} +(0.293297 - 0.106751i) q^{92} +(14.7039 + 5.80173i) q^{93} +(1.62986 - 1.36761i) q^{94} +(0.108588 - 0.0911165i) q^{95} +(-4.92313 + 3.91145i) q^{96} +(9.81310 - 3.57168i) q^{97} +(-3.28188 - 5.68438i) q^{98} +(7.10647 + 6.64206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.25101	+	1.04972i	0.884598	+	0.742266i	0.967119	−	0.254323i	$-0.0818528\pi$
$2$	1.25101	+	1.04972i	0.884598	+	0.742266i	−0.0825212	+	0.996589i	$0.526297\pi$
$3$	−0.905836	+	1.47630i	−0.522985	+	0.852342i
$3$	−0.905836	+	1.47630i	−0.522985	+	0.852342i
$4$	0.115814	+	0.656812i	0.0579068	+	0.328406i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$	−2.68292	+	0.895989i	−1.09530	+	0.365786i
$7$	−0.576430	+	3.26909i	−0.217870	+	1.23560i	0.657986	+	0.753030i	$0.271408\pi$
$7$	−0.576430	+	3.26909i	−0.217870	+	1.23560i	−0.875856	+	0.482572i	$0.839703\pi$
$8$	1.08849	−	1.88532i	0.384840	−	0.666562i
$9$	−1.35892	−	2.67457i	−0.452974	−	0.891524i
$10$	0.816539	+	1.41429i	0.258212	+	0.447237i
$11$	−3.04687	+	1.10897i	−0.918665	+	0.334367i	−0.757707	−	0.652595i	$-0.773680\pi$
$11$	−3.04687	+	1.10897i	−0.918665	+	0.334367i	−0.160958	+	0.986961i	$0.551458\pi$
$12$	−1.07456	−	0.423989i	−0.310199	−	0.122395i
$13$	4.99824	−	4.19402i	1.38626	−	1.16321i	0.419434	−	0.907786i	$-0.362229\pi$
$13$	4.99824	−	4.19402i	1.38626	−	1.16321i	0.966829	−	0.255426i	$-0.0822158\pi$
$14$	−4.15276	+	3.48458i	−1.10987	+	0.931293i
$15$	−1.35613	+	1.07745i	−0.350152	+	0.278197i
$16$	4.59423	−	1.67216i	1.14856	−	0.418040i
$17$	−0.561583	−	0.972691i	−0.136204	−	0.235912i	0.789853	−	0.613297i	$-0.210157\pi$
$17$	−0.561583	−	0.972691i	−0.136204	−	0.235912i	−0.926057	+	0.377384i	$0.876824\pi$
$18$	1.10753	−	4.77241i	0.261048	−	1.12487i
$19$	0.0708761	−	0.122761i	0.0162601	−	0.0281633i	−0.857781	−	0.514016i	$-0.828157\pi$
$19$	0.0708761	−	0.122761i	0.0162601	−	0.0281633i	0.874041	+	0.485852i	$0.161491\pi$
$20$	−0.115814	+	0.656812i	−0.0258967	+	0.146868i
$21$	−4.30401	−	3.81225i	−0.939212	−	0.831901i
$22$	−4.97577	−	1.81103i	−1.06084	−	0.386113i
$23$	−0.0812647	−	0.460875i	−0.0169449	−	0.0960990i	0.975162	−	0.221491i	$-0.0710923\pi$
$23$	−0.0812647	−	0.460875i	−0.0169449	−	0.0960990i	−0.992107	+	0.125392i	$0.959981\pi$
$24$	1.79731	+	3.31473i	0.366874	+	0.676617i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	10.6554			2.08970
$27$	5.17943	+	0.416551i	0.996782	+	0.0801653i
$28$	−2.21394			−0.418395
$29$	−1.61158	−	1.35227i	−0.299263	−	0.251111i	0.480775	−	0.876844i	$-0.340356\pi$
$29$	−1.61158	−	1.35227i	−0.299263	−	0.251111i	−0.780037	+	0.625733i	$0.784800\pi$
$30$	−2.82756	−	0.0756567i	−0.516240	−	0.0138130i
$31$	−1.58476	−	8.98762i	−0.284631	−	1.61422i	−0.706600	−	0.707613i	$-0.749772\pi$
$31$	−1.58476	−	8.98762i	−0.284631	−	1.61422i	0.421969	−	0.906610i	$-0.361339\pi$
$32$	3.41134	+	1.24163i	0.603045	+	0.219491i
$33$	1.12279	−	5.50263i	0.195453	−	0.957885i
$34$	0.318509	−	1.80635i	0.0546238	−	0.309787i
$35$	−1.65976	+	2.87479i	−0.280551	+	0.485929i
$36$	1.59931	−	1.20231i	0.266552	−	0.200385i
$37$	3.89752	+	6.75070i	0.640748	+	1.10981i	0.985266	+	0.171029i	$0.0547090\pi$
$37$	3.89752	+	6.75070i	0.640748	+	1.10981i	−0.344518	+	0.938780i	$0.611958\pi$
$38$	0.217532	−	0.0791751i	0.0352883	−	0.0128439i
$39$	1.66404	+	11.1780i	0.266460	+	1.78991i
$40$	1.66767	−	1.39934i	0.263681	−	0.221255i
$41$	−9.42272	+	7.90660i	−1.47158	+	1.23480i	−0.556930	+	0.830560i	$0.688021\pi$
$41$	−9.42272	+	7.90660i	−1.47158	+	1.23480i	−0.914651	+	0.404244i	$0.867535\pi$
$42$	−1.38256	−	9.28718i	−0.213334	−	1.43304i
$43$	−2.68125	+	0.975897i	−0.408887	+	0.148823i	−0.538271	−	0.842772i	$-0.680922\pi$
$43$	−2.68125	+	0.975897i	−0.408887	+	0.148823i	0.129384	+	0.991595i	$0.458700\pi$
$44$	−1.08125	−	1.87279i	−0.163005	−	0.282333i
$45$	−0.362210	−	2.97805i	−0.0539951	−	0.443942i
$46$	0.382128	−	0.661865i	0.0563417	−	0.0975866i
$47$	0.226235	−	1.28304i	0.0329997	−	0.187151i	−0.963852	−	0.266438i	$-0.914153\pi$
$47$	0.226235	−	1.28304i	0.0329997	−	0.187151i	0.996852	+	0.0792872i	$0.0252644\pi$
$48$	−1.69301	+	8.29716i	−0.244364	+	1.19759i
$49$	−3.77686	−	1.37466i	−0.539551	−	0.196381i
$50$	0.283581	+	1.60827i	0.0401044	+	0.227443i
$51$	1.94469	+	0.0520337i	0.272311	+	0.00728617i
$52$	3.33355	+	2.79718i	0.462280	+	0.387899i
$53$	−10.6122			−1.45770			−0.728851	−	0.684673i	$-0.759945\pi$
$53$	−10.6122			−1.45770			−0.728851	+	0.684673i	$0.759945\pi$
$54$	6.04226	+	5.95807i	0.822247	+	0.810791i
$55$	−3.24241			−0.437206
$56$	5.53586	+	4.64514i	0.739761	+	0.620733i
$57$	0.117030	+	0.215836i	0.0155010	+	0.0285881i
$58$	−0.596588	−	3.38342i	−0.0783359	−	0.444265i
$59$	−4.34027	−	1.57973i	−0.565056	−	0.205663i	0.0436675	−	0.999046i	$-0.486096\pi$
$59$	−4.34027	−	1.57973i	−0.565056	−	0.205663i	−0.608723	+	0.793383i	$0.708318\pi$
$60$	−0.864743	−	0.765940i	−0.111638	−	0.0988824i
$61$	0.313991	−	1.78073i	0.0402024	−	0.227999i	−0.958086	−	0.286480i	$-0.907515\pi$
$61$	0.313991	−	1.78073i	0.0402024	−	0.227999i	0.998289	+	0.0584812i	$0.0186258\pi$
$62$	7.45195	−	12.9072i	0.946399	−	1.63921i
$63$	9.52675	−	2.90074i	1.20026	−	0.365459i
$64$	−1.92481	−	3.33388i	−0.240602	−	0.416735i
$65$	6.13125	−	2.23159i	0.760488	−	0.276795i
$66$	7.18086	−	5.70523i	0.883903	−	0.702265i
$67$	−9.22089	+	7.73725i	−1.12651	+	0.945255i	−0.998915	−	0.0465708i	$-0.985171\pi$
$67$	−9.22089	+	7.73725i	−1.12651	+	0.945255i	−0.127596	+	0.991826i	$0.540726\pi$
$68$	0.573836	−	0.481506i	0.0695879	−	0.0583911i
$69$	0.754002	+	0.297506i	0.0907712	+	0.0358155i
$70$	−5.09412	+	1.85411i	−0.608863	+	0.221608i
$71$	0.293127	+	0.507712i	0.0347878	+	0.0602543i	0.882895	−	0.469570i	$-0.155591\pi$
$71$	0.293127	+	0.507712i	0.0347878	+	0.0602543i	−0.848107	+	0.529824i	$0.822258\pi$
$72$	−6.52161	−	0.349245i	−0.768579	−	0.0411590i
$73$	1.15209	−	1.99548i	0.134842	−	0.233554i	−0.790695	−	0.612210i	$-0.790281\pi$
$73$	1.15209	−	1.99548i	0.134842	−	0.233554i	0.925537	+	0.378657i	$0.123614\pi$
$74$	−2.21052	+	12.5365i	−0.256968	+	1.45734i
$75$	−1.64286	+	0.548651i	−0.189701	+	0.0633527i
$76$	0.0888393	+	0.0323349i	0.0101906	+	0.00370906i
$77$	−1.86902	−	10.5997i	−0.212995	−	1.20795i
$78$	−9.65206	+	15.7306i	−1.09288	+	1.78114i
$79$	8.47739	+	7.11338i	0.953781	+	0.800317i	0.979930	−	0.199341i	$-0.0638801\pi$
$79$	8.47739	+	7.11338i	0.953781	+	0.800317i	−0.0261493	+	0.999658i	$0.508325\pi$
$80$	4.88907			0.546615
$81$	−5.30667	+	7.26906i	−0.589630	+	0.807673i
$82$	−20.0877			−2.21831
$83$	1.76441	+	1.48051i	0.193669	+	0.162507i	0.734466	−	0.678646i	$-0.237433\pi$
$83$	1.76441	+	1.48051i	0.193669	+	0.162507i	−0.540797	+	0.841153i	$0.681877\pi$
$84$	2.00547	−	3.26844i	0.218814	−	0.356616i
$85$	−0.195036	−	1.10610i	−0.0211546	−	0.119974i
$86$	−4.37870	−	1.59372i	−0.472167	−	0.171855i
$87$	3.45619	−	1.15423i	0.370542	−	0.123747i
$88$	−1.22573	+	6.95143i	−0.130663	+	0.741025i
$89$	3.01777	−	5.22692i	0.319882	−	0.554053i	−0.660581	−	0.750755i	$-0.729690\pi$
$89$	3.01777	−	5.22692i	0.319882	−	0.554053i	0.980463	+	0.196702i	$0.0630232\pi$
$90$	2.67300	−	4.10580i	0.281759	−	0.432789i
$91$	10.8295	+	18.7573i	1.13524	+	1.96630i
$92$	0.293297	−	0.106751i	0.0305783	−	0.0111296i
$93$	14.7039	+	5.80173i	1.52473	+	0.601612i
$94$	1.62986	−	1.36761i	0.168107	−	0.141059i
$95$	0.108588	−	0.0911165i	0.0111409	−	0.00934836i
$96$	−4.92313	+	3.91145i	−0.502465	+	0.399211i
$97$	9.81310	−	3.57168i	0.996369	−	0.362649i	0.208186	−	0.978089i	$-0.433244\pi$
$97$	9.81310	−	3.57168i	0.996369	−	0.362649i	0.788183	+	0.615440i	$0.211022\pi$
$98$	−3.28188	−	5.68438i	−0.331519	−	0.574209i
$99$	7.10647	+	6.64206i	0.714227	+	0.667553i
$100$	−0.333472	+	0.577591i	−0.0333472	+	0.0577591i
$101$	0.645925	−	3.66322i	0.0642719	−	0.364504i	−0.935661	−	0.352901i	$-0.885195\pi$
$101$	0.645925	−	3.66322i	0.0642719	−	0.364504i	0.999933	−	0.0116034i	$-0.00369357\pi$
$102$	2.37820	+	2.10648i	0.235477	+	0.208572i
$103$	8.27883	+	3.01325i	0.815737	+	0.296904i	0.715992	−	0.698109i	$-0.245975\pi$
$103$	8.27883	+	3.01325i	0.815737	+	0.296904i	0.0997455	+	0.995013i	$0.468197\pi$
$104$	−2.46654	−	13.9885i	−0.241864	−	1.37168i
$105$	−2.74058	−	5.05440i	−0.267453	−	0.493259i
$106$	−13.2760	−	11.1399i	−1.28948	−	1.08200i
$107$	2.97570			0.287672			0.143836	−	0.989602i	$-0.454056\pi$
$107$	2.97570			0.287672			0.143836	+	0.989602i	$0.454056\pi$
$108$	0.326253	+	3.45015i	0.0313937	+	0.331991i
$109$	−5.86067			−0.561350			−0.280675	−	0.959803i	$-0.590558\pi$
$109$	−5.86067			−0.561350			−0.280675	+	0.959803i	$0.590558\pi$
$110$	−4.05629	−	3.40363i	−0.386752	−	0.324523i
$111$	−13.4966	−	0.361126i	−1.28104	−	0.0342765i
$112$	2.81821	+	15.9828i	0.266296	+	1.51024i
$113$	9.95986	+	3.62509i	0.936945	+	0.341020i	0.764959	−	0.644079i	$-0.222759\pi$
$113$	9.95986	+	3.62509i	0.936945	+	0.341020i	0.171986	+	0.985099i	$0.444982\pi$
$114$	−0.0801620	+	0.392862i	−0.00750786	+	0.0367949i
$115$	0.0812647	−	0.460875i	0.00757797	−	0.0429768i
$116$	0.701548	−	1.21512i	0.0651371	−	0.112821i
$117$	−18.0094	−	7.66881i	−1.66497	−	0.708982i
$118$	−3.77145	−	6.53234i	−0.347190	−	0.601351i
$119$	3.50353	−	1.27518i	0.321168	−	0.116896i
$120$	0.555209	+	3.72955i	0.0506834	+	0.340459i
$121$	−0.372904	+	0.312903i	−0.0339003	+	0.0284458i
$122$	2.26208	−	1.89811i	0.204799	−	0.171847i
$123$	−3.13707	−	21.0728i	−0.282860	−	1.90007i
$124$	5.71964	−	2.08178i	0.513639	−	0.186949i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	14.9630	+	6.37159i	1.33301	+	0.567626i
$127$	1.64109	−	2.84245i	0.145623	−	0.252227i	−0.783982	−	0.620783i	$-0.786815\pi$
$127$	1.64109	−	2.84245i	0.145623	−	0.252227i	0.929605	+	0.368557i	$0.120148\pi$
$128$	2.35246	−	13.3415i	0.207930	−	1.17923i
$129$	0.988062	−	4.84234i	0.0869940	−	0.426344i
$130$	10.0128	+	3.64436i	0.878181	+	0.319632i
$131$	−3.28994	−	18.6582i	−0.287444	−	1.63017i	−0.696424	−	0.717631i	$-0.745227\pi$
$131$	−3.28994	−	18.6582i	−0.287444	−	1.63017i	0.408980	−	0.912543i	$-0.365885\pi$
$132$	3.74423	+	0.100184i	0.325893	+	0.00871988i
$133$	0.360462	+	0.302464i	0.0312560	+	0.0262269i
$134$	−19.6574			−1.69814
$135$	4.72460	+	2.16290i	0.406629	+	0.186153i
$136$	−2.44512			−0.209667
$137$	14.0842	+	11.8180i	1.20329	+	1.00968i	0.999530	+	0.0306625i	$0.00976172\pi$
$137$	14.0842	+	11.8180i	1.20329	+	1.00968i	0.203763	+	0.979020i	$0.434683\pi$
$138$	0.630965	+	1.16368i	0.0537113	+	0.0990587i
$139$	−1.41765	−	8.03987i	−0.120243	−	0.681933i	−0.984020	−	0.178058i	$-0.943019\pi$
$139$	−1.41765	−	8.03987i	−0.120243	−	0.681933i	0.863777	−	0.503874i	$-0.168093\pi$
$140$	−2.08042	−	0.757212i	−0.175828	−	0.0639961i
$141$	1.68922	+	1.49622i	0.142258	+	0.126004i
$142$	−0.166251	+	0.942855i	−0.0139515	+	0.0791226i
$143$	−10.5779	+	18.3215i	−0.884571	+	1.53212i
$144$	−10.7155	−	10.0153i	−0.892959	−	0.834605i
$145$	−1.05188	−	1.82192i	−0.0873541	−	0.151302i
$146$	3.53599	−	1.28699i	0.292640	−	0.106512i
$147$	5.45063	−	4.33056i	0.449561	−	0.357178i
$148$	−3.98256	+	3.34176i	−0.327364	+	0.274691i
$149$	4.68447	−	3.93074i	0.383767	−	0.322019i	−0.430412	−	0.902632i	$-0.641632\pi$
$149$	4.68447	−	3.93074i	0.383767	−	0.322019i	0.814179	+	0.580614i	$0.197187\pi$
$150$	−2.63116	−	1.03818i	−0.214834	−	0.0847668i
$151$	0.562722	−	0.204814i	0.0457936	−	0.0166675i	−0.319022	−	0.947747i	$-0.603354\pi$
$151$	0.562722	−	0.204814i	0.0457936	−	0.0166675i	0.364815	+	0.931080i	$0.381132\pi$
$152$	−0.154296	−	0.267249i	−0.0125151	−	0.0216767i
$153$	−1.83839	+	2.82381i	−0.148625	+	0.228291i
$154$	8.78862	−	15.2223i	0.708207	−	1.22665i
$155$	1.58476	−	8.98762i	0.127291	−	0.721903i
$156$	−7.14912	+	2.38753i	−0.572388	+	0.191155i
$157$	−6.09122	−	2.21702i	−0.486133	−	0.176938i	0.0873139	−	0.996181i	$-0.472172\pi$
$157$	−6.09122	−	2.21702i	−0.486133	−	0.176938i	−0.573446	+	0.819243i	$0.694394\pi$
$158$	3.13823	+	17.7978i	0.249665	+	1.41592i
$159$	9.61294	−	15.6668i	0.762356	−	1.24246i
$160$	2.78095	+	2.33349i	0.219853	+	0.184479i
$161$	1.55349			0.122432
$162$	−14.2692	+	3.52314i	−1.12109	+	0.276804i
$163$	−19.6457			−1.53877			−0.769386	−	0.638784i	$-0.779438\pi$
$163$	−19.6457			−1.53877			−0.769386	+	0.638784i	$0.779438\pi$
$164$	−6.28443	−	5.27326i	−0.490731	−	0.411773i
$165$	2.93709	−	4.78677i	0.228652	−	0.372649i
$166$	0.653163	+	3.70427i	0.0506953	+	0.287507i
$167$	15.1191	+	5.50290i	1.16995	+	0.425827i	0.852642	−	0.522495i	$-0.174999\pi$
$167$	15.1191	+	5.50290i	1.16995	+	0.425827i	0.317309	+	0.948322i	$0.397221\pi$
$168$	−11.8722	+	3.96485i	−0.915960	+	0.305895i
$169$	5.13516	−	29.1229i	0.395012	−	2.24023i
$170$	0.917110	−	1.58848i	0.0703391	−	0.121831i
$171$	−0.424648	−	0.0227408i	−0.0324736	−	0.00173903i
$172$	−0.951507	−	1.64806i	−0.0725517	−	0.125663i
$173$	−11.5284	+	4.19599i	−0.876487	+	0.319015i	−0.740791	−	0.671735i	$-0.765549\pi$
$173$	−11.5284	+	4.19599i	−0.876487	+	0.319015i	−0.135696	+	0.990751i	$0.543327\pi$
$174$	5.53535	+	2.18408i	0.419634	+	0.165575i
$175$	−2.54290	+	2.13375i	−0.192225	+	0.161296i
$176$	−12.1436	+	10.1897i	−0.915360	+	0.768078i
$177$	6.26374	−	4.97657i	0.470811	−	0.374062i
$178$	9.26207	−	3.37112i	0.694222	−	0.252676i
$179$	2.94426	+	5.09960i	0.220064	+	0.381162i	0.954827	−	0.297162i	$-0.0960400\pi$
$179$	2.94426	+	5.09960i	0.220064	+	0.381162i	−0.734763	+	0.678324i	$0.762707\pi$
$180$	1.91407	−	0.582803i	0.142667	−	0.0434396i
$181$	−6.83565	+	11.8397i	−0.508090	+	0.880037i	0.491866	+	0.870671i	$0.336315\pi$
$181$	−6.83565	+	11.8397i	−0.508090	+	0.880037i	−0.999956	+	0.00936669i	$0.997018\pi$
$182$	−6.14209	+	34.8335i	−0.455282	+	2.58203i
$183$	2.34447	+	2.07660i	0.173308	+	0.153506i
$184$	−0.957354	−	0.348448i	−0.0705771	−	0.0256880i
$185$	1.35359	+	7.67661i	0.0995182	+	0.564396i
$186$	12.3046	+	22.6931i	0.902216	+	1.66394i
$187$	2.78975	+	2.34088i	0.204007	+	0.171182i
$188$	0.868918			0.0633723
$189$	−4.34732	+	16.6919i	−0.316221	+	1.21416i
$190$	0.231492			0.0167942
$191$	−7.57309	−	6.35458i	−0.547970	−	0.459801i	0.326283	−	0.945272i	$-0.394204\pi$
$191$	−7.57309	−	6.35458i	−0.547970	−	0.459801i	−0.874253	+	0.485471i	$0.838648\pi$
$192$	6.66537	+	0.178344i	0.481032	+	0.0128709i
$193$	0.441336	+	2.50294i	0.0317681	+	0.180166i	0.996563	−	0.0828374i	$-0.0263982\pi$
$193$	0.441336	+	2.50294i	0.0317681	+	0.180166i	−0.964795	+	0.263003i	$0.915287\pi$
$194$	16.0256	+	5.83283i	1.15057	+	0.418773i
$195$	−2.25941	+	11.0730i	−0.161800	+	0.792955i
$196$	0.465484	−	2.63989i	0.0332489	−	0.188564i
$197$	−13.4027	+	23.2141i	−0.954901	+	1.65394i	−0.220308	+	0.975430i	$0.570706\pi$
$197$	−13.4027	+	23.2141i	−0.954901	+	1.65394i	−0.734594	+	0.678507i	$0.762627\pi$
$198$	1.91794	+	15.7691i	0.136302	+	1.12066i
$199$	2.76917	+	4.79634i	0.196301	+	0.340004i	0.947326	−	0.320270i	$-0.103774\pi$
$199$	2.76917	+	4.79634i	0.196301	+	0.340004i	−0.751025	+	0.660274i	$0.770440\pi$
$200$	2.04570	−	0.744572i	0.144653	−	0.0526492i
$201$	−3.06987	−	20.6215i	−0.216532	−	1.45453i
$202$	4.65343	−	3.90469i	0.327414	−	0.274733i
$203$	5.34968	−	4.48891i	0.375474	−	0.315060i
$204$	0.191045	+	1.28332i	0.0133758	+	0.0898503i
$205$	−11.5587	+	4.20701i	−0.807293	+	0.293831i
$206$	7.19383	+	12.4601i	0.501218	+	0.868134i
$207$	−1.12221	+	0.843641i	−0.0779990	+	0.0586371i
$208$	15.9500	−	27.6262i	1.10593	−	1.91553i
$209$	−0.0798119	+	0.452636i	−0.00552070	+	0.0313095i
$210$	1.87722	−	9.19996i	0.129540	−	0.634857i
$211$	6.77888	+	2.46731i	0.466677	+	0.169857i	0.564647	−	0.825333i	$-0.309012\pi$
$211$	6.77888	+	2.46731i	0.466677	+	0.169857i	−0.0979693	+	0.995189i	$0.531235\pi$
$212$	−1.22904	−	6.97024i	−0.0844109	−	0.478718i
$213$	−1.01506	−	0.0271598i	−0.0695508	−	0.00186096i
$214$	3.72263	+	3.12366i	0.254474	+	0.213529i
$215$	−2.85333			−0.194596
$216$	6.42310	−	9.31149i	0.437037	−	0.633566i
$217$	30.2949			2.05655
$218$	−7.33176	−	6.15208i	−0.496569	−	0.416671i
$219$	1.90232	+	3.50842i	0.128547	+	0.237077i
$220$	−0.375515	−	2.12965i	−0.0253172	−	0.143581i
$221$	−6.88642	−	2.50645i	−0.463230	−	0.168602i
$222$	−16.5053	−	14.6194i	−1.10776	−	0.981192i
$223$	−4.45618	+	25.2723i	−0.298408	+	1.69236i	0.354610	+	0.935014i	$0.384614\pi$
$223$	−4.45618	+	25.2723i	−0.298408	+	1.69236i	−0.653018	+	0.757343i	$0.726497\pi$
$224$	−6.02539	+	10.4363i	−0.402588	+	0.697304i
$225$	0.678188	−	2.92234i	0.0452125	−	0.194823i
$226$	8.65455	+	14.9901i	0.575692	+	0.997128i
$227$	−2.29801	+	0.836409i	−0.152525	+	0.0555144i	−0.417154	−	0.908836i	$-0.636973\pi$
$227$	−2.29801	+	0.836409i	−0.152525	+	0.0555144i	0.264630	+	0.964350i	$0.414750\pi$
$228$	−0.128210	+	0.101863i	−0.00849090	+	0.00674606i
$229$	−4.19172	+	3.51727i	−0.276997	+	0.232428i	−0.770693	−	0.637206i	$-0.780090\pi$
$229$	−4.19172	+	3.51727i	−0.276997	+	0.232428i	0.493696	+	0.869634i	$0.335645\pi$
$230$	0.585454	−	0.491254i	0.0386037	−	0.0323923i
$231$	17.3414	+	6.84240i	1.14098	+	0.450197i
$232$	−4.30367	+	1.56641i	−0.282550	+	0.102840i
$233$	6.57769	+	11.3929i	0.430919	+	0.746373i	0.996953	−	0.0780090i	$-0.0248563\pi$
$233$	6.57769	+	11.3929i	0.430919	+	0.746373i	−0.566034	+	0.824382i	$0.691523\pi$
$234$	−14.4799	−	28.4987i	−0.946578	−	1.86302i
$235$	0.651417	−	1.12829i	0.0424937	−	0.0736013i
$236$	0.534923	−	3.03370i	0.0348205	−	0.197477i
$237$	−18.1806	+	6.07161i	−1.18096	+	0.394394i
$238$	5.72154	+	2.08247i	0.370873	+	0.134987i
$239$	3.15714	+	17.9050i	0.204218	+	1.15818i	0.898665	+	0.438635i	$0.144538\pi$
$239$	3.15714	+	17.9050i	0.204218	+	1.15818i	−0.694447	+	0.719544i	$0.744351\pi$
$240$	−4.42870	+	7.21774i	−0.285871	+	0.465903i
$241$	−14.1473	−	11.8710i	−0.911309	−	0.764679i	0.0610589	−	0.998134i	$-0.480552\pi$
$241$	−14.1473	−	11.8710i	−0.911309	−	0.764679i	−0.972367	+	0.233455i	$0.924997\pi$
$242$	−0.794968			−0.0511025
$243$	−5.92434	−	14.4188i	−0.380046	−	0.924967i
$244$	1.20597			0.0772043
$245$	−3.07892	−	2.58352i	−0.196705	−	0.165055i
$246$	18.1961	−	29.6554i	1.16014	−	1.89076i
$247$	−0.160606	−	0.910845i	−0.0102191	−	0.0579557i
$248$	−18.6696	−	6.79516i	−1.18552	−	0.431493i
$249$	−3.78394	+	1.26369i	−0.239798	+	0.0800831i
$250$	−0.283581	+	1.60827i	−0.0179352	+	0.101716i
$251$	5.06089	−	8.76572i	0.319441	−	0.553288i	−0.660931	−	0.750447i	$-0.729838\pi$
$251$	5.06089	−	8.76572i	0.319441	−	0.553288i	0.980371	+	0.197159i	$0.0631716\pi$
$252$	3.00857	+	5.92134i	0.189522	+	0.373009i
$253$	0.758698	+	1.31410i	0.0476990	+	0.0826170i
$254$	5.03681	−	1.83325i	0.316037	−	0.115028i
$255$	1.80961	+	0.714018i	0.113322	+	0.0447135i
$256$	11.0498	−	9.27191i	0.690614	−	0.579494i
$257$	12.2529	−	10.2814i	0.764316	−	0.641338i	−0.174930	−	0.984581i	$-0.555970\pi$
$257$	12.2529	−	10.2814i	0.764316	−	0.641338i	0.939247	+	0.343243i	$0.111526\pi$
$258$	6.31919	−	5.02062i	0.393415	−	0.312570i
$259$	−24.3153	+	8.85005i	−1.51088	+	0.549916i
$260$	2.17582	+	3.76863i	0.134939	+	0.233720i
$261$	−1.42675	+	6.14792i	−0.0883136	+	0.380547i
$262$	15.4702	−	26.7951i	0.955751	−	1.65541i
$263$	3.10956	−	17.6352i	0.191743	−	1.08743i	−0.725237	−	0.688499i	$-0.758270\pi$
$263$	3.10956	−	17.6352i	0.191743	−	1.08743i	0.916980	−	0.398932i	$-0.130619\pi$
$264$	−9.15209	−	8.10640i	−0.563272	−	0.498914i
$265$	−9.97223	−	3.62959i	−0.612589	−	0.222964i
$266$	0.133439	+	0.756770i	0.00818167	+	0.0464006i
$267$	4.98290	+	9.18986i	0.304949	+	0.562410i
$268$	−6.14982	−	5.16031i	−0.375660	−	0.315216i
$269$	15.6959			0.956993			0.478496	−	0.878089i	$-0.341182\pi$
$269$	15.6959			0.956993			0.478496	+	0.878089i	$0.341182\pi$
$270$	3.64008	+	7.66533i	0.221528	+	0.466497i
$271$	0.686673			0.0417124			0.0208562	−	0.999782i	$-0.493361\pi$
$271$	0.686673			0.0417124			0.0208562	+	0.999782i	$0.493361\pi$
$272$	−4.20654	−	3.52971i	−0.255059	−	0.214020i
$273$	−37.5011	−	1.00341i	−2.26967	−	0.0607293i
$274$	5.21381	+	29.5690i	0.314978	+	1.78633i
$275$	−3.04687	−	1.10897i	−0.183733	−	0.0668733i
$276$	−0.108082	+	0.529693i	−0.00650577	+	0.0318838i
$277$	1.82173	−	10.3315i	0.109457	−	0.620762i	−0.879889	−	0.475179i	$-0.842383\pi$
$277$	1.82173	−	10.3315i	0.109457	−	0.620762i	0.989346	−	0.145582i	$-0.0465056\pi$
$278$	6.66614	−	11.5461i	0.399808	−	0.692488i
$279$	−21.8845	+	16.4520i	−1.31019	+	0.984956i
$280$	3.61328	+	6.25838i	0.215935	+	0.374010i
$281$	0.178327	−	0.0649058i	0.0106381	−	0.00387195i	−0.336696	−	0.941614i	$-0.609309\pi$
$281$	0.178327	−	0.0649058i	0.0106381	−	0.00387195i	0.347334	+	0.937742i	$0.387087\pi$
$282$	0.542622	+	3.64499i	0.0323127	+	0.217056i
$283$	6.65226	−	5.58191i	0.395436	−	0.331810i	−0.423291	−	0.905994i	$-0.639125\pi$
$283$	6.65226	−	5.58191i	0.395436	−	0.331810i	0.818726	+	0.574184i	$0.194681\pi$
$284$	−0.299523	+	0.251330i	−0.0177734	+	0.0149137i
$285$	0.0361519	+	0.242846i	0.00214145	+	0.0143849i
$286$	−32.4656	+	11.8165i	−1.91973	+	0.698725i
$287$	−20.4159	−	35.3613i	−1.20511	−	2.08731i
$288$	−1.31492	−	10.8111i	−0.0774825	−	0.637053i
$289$	7.86925	−	13.6299i	0.462897	−	0.801761i
$290$	0.596588	−	3.38342i	0.0350329	−	0.198681i
$291$	−3.61620	+	17.7224i	−0.211985	+	1.03891i
$292$	1.44409	+	0.525605i	0.0845088	+	0.0307587i
$293$	4.13097	+	23.4279i	0.241334	+	1.36867i	0.828855	+	0.559464i	$0.188993\pi$
$293$	4.13097	+	23.4279i	0.241334	+	1.36867i	−0.587521	+	0.809209i	$0.699896\pi$
$294$	11.3647	+	0.304083i	0.662802	+	0.0177345i
$295$	−3.53822	−	2.96892i	−0.206003	−	0.172857i
$296$	16.9697			0.986342
$297$	−16.2430	+	4.47465i	−0.942513	+	0.259646i
$298$	9.98651			0.578503
$299$	−2.33910	−	1.96274i	−0.135274	−	0.113508i
$300$	−0.550626	−	1.01551i	−0.0317904	−	0.0586304i
$301$	−1.64474	−	9.32781i	−0.0948015	−	0.537646i
$302$	0.918968	+	0.334477i	0.0528807	+	0.0192470i
$303$	4.82291	+	4.27186i	0.277069	+	0.245412i
$304$	0.120345	−	0.682508i	0.00690223	−	0.0391445i
$305$	0.904101	−	1.56595i	0.0517687	−	0.0896660i
$306$	−5.26405	+	1.60282i	−0.300926	+	0.0916269i
$307$	−13.8291	−	23.9527i	−0.789269	−	1.36705i	−0.926416	−	0.376503i	$-0.877127\pi$
$307$	−13.8291	−	23.9527i	−0.789269	−	1.36705i	0.137147	−	0.990551i	$-0.456207\pi$
$308$	6.74558	−	2.45519i	0.384365	−	0.139897i
$309$	−11.9477	+	9.49252i	−0.679682	+	0.540011i
$310$	11.4171	−	9.58005i	0.648445	−	0.544110i
$311$	0.213412	−	0.179074i	0.0121015	−	0.0101543i	−0.636717	−	0.771098i	$-0.719708\pi$
$311$	0.213412	−	0.179074i	0.0121015	−	0.0101543i	0.648818	+	0.760943i	$0.275264\pi$
$312$	22.8854	+	9.02990i	1.29563	+	0.511217i
$313$	14.0772	−	5.12369i	0.795692	−	0.289608i	0.0879921	−	0.996121i	$-0.471955\pi$
$313$	14.0772	−	5.12369i	0.795692	−	0.289608i	0.707700	+	0.706513i	$0.249733\pi$
$314$	−5.29292	−	9.16761i	−0.298697	−	0.517358i
$315$	9.94433	+	0.532539i	0.560299	+	0.0300052i
$316$	−3.69035	+	6.39188i	−0.207599	+	0.359571i
$317$	3.84554	−	21.8092i	0.215987	−	1.22492i	−0.663198	−	0.748444i	$-0.730801\pi$
$317$	3.84554	−	21.8092i	0.215987	−	1.22492i	0.879185	−	0.476480i	$-0.158088\pi$
$318$	28.4717	−	9.50844i	1.59661	−	0.533207i
$319$	6.40990	+	2.33301i	0.358885	+	0.130624i
$320$	−0.668481	−	3.79114i	−0.0373692	−	0.211931i
$321$	−2.69550	+	4.39302i	−0.150448	+	0.245195i
$322$	1.94343	+	1.63073i	0.108303	+	0.0908770i
$323$	−0.159211			−0.00885876
$324$	−5.38899	−	2.64363i	−0.299388	−	0.146868i
$325$	6.52474			0.361927
$326$	−24.5770	−	20.6226i	−1.36119	−	1.14218i
$327$	5.30881	−	8.65211i	0.293578	−	0.478463i
$328$	4.64994	+	26.3711i	0.256750	+	1.45610i
$329$	4.06397	+	1.47917i	0.224054	+	0.0815490i
$330$	8.69911	−	2.90516i	0.478870	−	0.159924i
$331$	−0.315100	+	1.78702i	−0.0173194	+	0.0982234i	−0.992242	−	0.124320i	$-0.960325\pi$
$331$	−0.315100	+	1.78702i	−0.0173194	+	0.0982234i	0.974923	+	0.222544i	$0.0714360\pi$
$332$	−0.768076	+	1.33035i	−0.0421536	+	0.0730122i
$333$	12.7588	−	19.5979i	0.699179	−	1.07396i
$334$	13.1376	+	22.7550i	0.718859	+	1.24510i
$335$	−11.3111	+	4.11690i	−0.617991	+	0.224930i
$336$	−26.1483	−	10.3173i	−1.42651	−	0.562856i
$337$	−16.3799	+	13.7444i	−0.892271	+	0.748705i	−0.968664	−	0.248373i	$-0.920104\pi$
$337$	−16.3799	+	13.7444i	−0.892271	+	0.748705i	0.0763931	+	0.997078i	$0.475660\pi$
$338$	36.9952	−	31.0426i	2.01227	−	1.68850i
$339$	−14.3737	+	11.4200i	−0.780674	+	0.620249i
$340$	0.703914	−	0.256204i	0.0381751	−	0.0138946i
$341$	14.7955	+	25.6266i	0.801223	+	1.38776i
$342$	−0.507368	−	0.474211i	−0.0274353	−	0.0256424i
$343$	−4.94734	+	8.56904i	−0.267131	+	0.462685i
$344$	−1.07864	+	6.11729i	−0.0581565	+	0.329822i
$345$	0.606777	+	0.537448i	0.0326678	+	0.0289352i
$346$	−18.8268	−	6.85238i	−1.01213	−	0.368386i
$347$	4.43463	+	25.1500i	0.238063	+	1.35012i	0.836066	+	0.548629i	$0.184850\pi$
$347$	4.43463	+	25.1500i	0.238063	+	1.35012i	−0.598003	+	0.801494i	$0.704039\pi$
$348$	1.15839	+	2.13639i	0.0620961	+	0.114523i
$349$	25.9602	+	21.7832i	1.38962	+	1.16603i	0.965494	+	0.260424i	$0.0838624\pi$
$349$	25.9602	+	21.7832i	1.38962	+	1.16603i	0.424124	+	0.905604i	$0.360582\pi$
$350$	−5.42105			−0.289767
$351$	27.6351	−	19.6406i	1.47505	−	1.04834i
$352$	−11.7708			−0.627387
$353$	9.36489	+	7.85807i	0.498443	+	0.418243i	0.857040	−	0.515249i	$-0.172301\pi$
$353$	9.36489	+	7.85807i	0.498443	+	0.418243i	−0.358598	+	0.933492i	$0.616745\pi$
$354$	13.0600	+	0.349445i	0.694132	+	0.0185728i
$355$	0.101802	+	0.577348i	0.00540309	+	0.0306425i
$356$	3.78260	+	1.37676i	0.200478	+	0.0729679i
$357$	−1.29108	+	6.32737i	−0.0683311	+	0.334880i
$358$	−1.66987	+	9.47031i	−0.0882554	+	0.500521i
$359$	5.83763	−	10.1111i	0.308099	−	0.533642i	−0.669848	−	0.742498i	$-0.733641\pi$
$359$	5.83763	−	10.1111i	0.308099	−	0.533642i	0.977946	+	0.208856i	$0.0669740\pi$
$360$	−6.00886	−	2.55870i	−0.316695	−	0.134856i
$361$	9.48995	+	16.4371i	0.499471	+	0.865110i
$362$	−20.9799	+	7.63604i	−1.10268	+	0.401342i
$363$	−0.124149	−	0.833957i	−0.00651615	−	0.0437714i
$364$	−11.0658	+	9.28531i	−0.580005	+	0.486682i
$365$	1.76511	−	1.48110i	0.0923901	−	0.0775245i
$366$	0.753105	+	5.05888i	0.0393654	+	0.264432i
$367$	23.7108	−	8.63004i	1.23770	−	0.450484i	0.361469	−	0.932384i	$-0.382275\pi$
$367$	23.7108	−	8.63004i	1.23770	−	0.450484i	0.876226	+	0.481900i	$0.160053\pi$
$368$	−1.14401	−	1.98148i	−0.0596354	−	0.103292i
$369$	33.9515	+	14.4573i	1.76744	+	0.752617i
$370$	−6.36495	+	11.0244i	−0.330898	+	0.573132i
$371$	6.11720	−	34.6924i	0.317589	−	1.80114i
$372$	−2.10773	+	10.3296i	−0.109281	+	0.535567i
$373$	−21.6760	−	7.88942i	−1.12234	−	0.408498i	−0.286834	−	0.957980i	$-0.592603\pi$
$373$	−21.6760	−	7.88942i	−1.12234	−	0.408498i	−0.835506	+	0.549482i	$0.814825\pi$
$374$	1.03274	+	5.85694i	0.0534015	+	0.302855i
$375$	−1.73143	−	0.0463276i	−0.0894107	−	0.00239235i
$376$	−2.17269	−	1.82310i	−0.112048	−	0.0940195i
$377$	−13.7265			−0.706952
$378$	−22.9604	+	16.3183i	−1.18096	+	0.839323i
$379$	−25.4066			−1.30505			−0.652526	−	0.757766i	$-0.726291\pi$
$379$	−25.4066			−1.30505			−0.652526	+	0.757766i	$0.726291\pi$
$380$	0.0724225	+	0.0607697i	0.00371519	+	0.00311742i
$381$	2.70975	+	4.99754i	0.138825	+	0.256032i
$382$	−2.80347	−	15.8993i	−0.143438	−	0.813479i
$383$	−10.9165	−	3.97330i	−0.557809	−	0.203026i	0.0477034	−	0.998862i	$-0.484810\pi$
$383$	−10.9165	−	3.97330i	−0.557809	−	0.203026i	−0.605513	+	0.795835i	$0.707032\pi$
$384$	17.5651	+	15.5581i	0.896364	+	0.793948i
$385$	1.86902	−	10.5997i	0.0952541	−	0.540213i
$386$	−2.07528	+	3.59449i	−0.105629	+	0.182954i
$387$	6.25372	+	5.84504i	0.317894	+	0.297120i
$388$	3.48241	+	6.03171i	0.176793	+	0.306214i
$389$	−29.5550	+	10.7571i	−1.49850	+	0.545409i	−0.955671	−	0.294436i	$-0.904868\pi$
$389$	−29.5550	+	10.7571i	−1.49850	+	0.545409i	−0.542827	+	0.839845i	$0.682646\pi$
$390$	−14.4501	+	11.4807i	−0.731711	+	0.581348i
$391$	−0.402652	+	0.337865i	−0.0203630	+	0.0170866i
$392$	−6.70277	+	5.62429i	−0.338541	+	0.284070i
$393$	30.5252	+	12.0443i	1.53979	+	0.607556i
$394$	−41.1353	+	14.9720i	−2.07237	+	0.754279i
$395$	5.53322	+	9.58382i	0.278407	+	0.482215i
$396$	−3.53956	+	5.43685i	−0.177870	+	0.273212i
$397$	−6.19763	+	10.7346i	−0.311050	+	0.538755i	−0.978590	−	0.205819i	$-0.934014\pi$
$397$	−6.19763	+	10.7346i	−0.311050	+	0.538755i	0.667540	+	0.744574i	$0.267347\pi$
$398$	−1.57057	+	8.90713i	−0.0787254	+	0.446474i
$399$	−0.773047	+	0.258167i	−0.0387007	+	0.0129245i
$400$	4.59423	+	1.67216i	0.229711	+	0.0836081i
$401$	−1.14056	−	6.46841i	−0.0569566	−	0.323017i	0.942995	−	0.332806i	$-0.107995\pi$
$401$	−1.14056	−	6.46841i	−0.0569566	−	0.323017i	−0.999952	+	0.00978852i	$0.996884\pi$
$402$	17.8064	−	29.0202i	0.888102	−	1.44740i
$403$	−45.6153	−	38.2758i	−2.27226	−	1.90665i
$404$	2.48086			0.123427
$405$	−7.47280	+	5.01570i	−0.371327	+	0.249232i
$406$	11.4046			0.566001
$407$	−19.3615	−	16.2463i	−0.959716	−	0.805297i
$408$	2.21488	−	3.60972i	0.109653	−	0.178708i
$409$	−3.35273	−	19.0143i	−0.165782	−	0.940195i	−0.948255	−	0.317511i	$-0.897153\pi$
$409$	−3.35273	−	19.0143i	−0.165782	−	0.940195i	0.782473	−	0.622685i	$-0.213958\pi$
$410$	−18.8762	−	6.87038i	−0.932230	−	0.339304i
$411$	−30.2049	+	10.0873i	−1.48990	+	0.497568i
$412$	−1.02034	+	5.78661i	−0.0502683	+	0.285086i
$413$	7.66615	−	13.2782i	0.377227	−	0.653376i
$414$	−2.28949	−	0.122607i	−0.112522	−	0.00602579i
$415$	1.15163	+	1.99469i	0.0565315	+	0.0979154i
$416$	22.2581	−	8.10129i	1.09129	−	0.397198i
$417$	13.1534	+	5.18993i	0.644125	+	0.254152i
$418$	−0.574987	+	0.482472i	−0.0281235	+	0.0235985i
$419$	24.2397	−	20.3395i	1.18419	−	0.993650i	0.184244	−	0.982881i	$-0.441016\pi$
$419$	24.2397	−	20.3395i	1.18419	−	0.993650i	0.999942	−	0.0107695i	$-0.00342810\pi$
$420$	3.00239	−	2.38542i	0.146502	−	0.116396i
$421$	21.6889	−	7.89413i	1.05705	−	0.384736i	0.245734	−	0.969337i	$-0.420971\pi$
$421$	21.6889	−	7.89413i	1.05705	−	0.384736i	0.811321	+	0.584601i	$0.198749\pi$
$422$	5.89046	+	10.2026i	0.286743	+	0.496654i
$423$	−3.73902	+	1.13847i	−0.181797	+	0.0553543i
$424$	−11.5513	+	20.0075i	−0.560982	+	0.971649i
$425$	0.195036	−	1.10610i	0.00946063	−	0.0536539i
$426$	−1.24134	−	1.09951i	−0.0601431	−	0.0532714i
$427$	5.64039	+	2.05293i	0.272957	+	0.0993484i
$428$	0.344627	+	1.95448i	0.0166582	+	0.0944731i
$429$	−17.4662	−	32.2125i	−0.843275	−	1.55523i
$430$	−3.56955	−	2.99521i	−0.172139	−	0.144442i
$431$	−22.6904			−1.09296			−0.546479	−	0.837473i	$-0.684032\pi$
$431$	−22.6904			−1.09296			−0.546479	+	0.837473i	$0.684032\pi$
$432$	24.4920	−	6.74711i	1.17837	−	0.324621i
$433$	7.13506			0.342889			0.171445	−	0.985194i	$-0.445157\pi$
$433$	7.13506			0.342889			0.171445	+	0.985194i	$0.445157\pi$
$434$	37.8992	+	31.8012i	1.81922	+	1.52651i
$435$	3.64253	+	0.0974625i	0.174646	+	0.00467297i
$436$	−0.678746	−	3.84936i	−0.0325060	−	0.184351i
$437$	−0.0623372	−	0.0226889i	−0.00298199	−	0.00108536i
$438$	−1.30304	+	6.38598i	−0.0622615	+	0.305134i
$439$	−6.24652	+	35.4257i	−0.298130	+	1.69078i	0.356072	+	0.934459i	$0.384116\pi$
$439$	−6.24652	+	35.4257i	−0.298130	+	1.69078i	−0.654202	+	0.756320i	$0.726995\pi$
$440$	−3.52933	+	6.11299i	−0.168254	+	0.291425i
$441$	1.45581	+	11.9695i	0.0693244	+	0.569978i
$442$	−5.98390	−	10.3644i	−0.284625	−	0.492985i
$443$	11.7031	−	4.25958i	0.556031	−	0.202379i	−0.0486928	−	0.998814i	$-0.515506\pi$
$443$	11.7031	−	4.25958i	0.556031	−	0.202379i	0.604724	+	0.796435i	$0.293283\pi$
$444$	−1.32590	−	8.90653i	−0.0629242	−	0.422685i
$445$	4.62348	−	3.87956i	0.219174	−	0.183909i
$446$	−32.1036	+	26.9381i	−1.52015	+	1.27556i
$447$	1.55958	+	10.4763i	0.0737657	+	0.495512i
$448$	12.0083	−	4.37066i	0.567338	−	0.206494i
$449$	−3.67280	−	6.36147i	−0.173330	−	0.300216i	0.766252	−	0.642540i	$-0.222119\pi$
$449$	−3.67280	−	6.36147i	−0.173330	−	0.300216i	−0.939582	+	0.342324i	$0.888786\pi$
$450$	3.91606	−	2.94397i	0.184605	−	0.138780i
$451$	19.9416	−	34.5398i	0.939013	−	1.62642i
$452$	−1.22752	+	6.96159i	−0.0577375	+	0.327446i
$453$	−0.207367	+	1.01627i	−0.00974295	+	0.0477487i
$454$	−3.75284	−	1.36592i	−0.176129	−	0.0641058i
$455$	3.76105	+	21.3300i	0.176321	+	0.999965i
$456$	0.534306	+	0.0142963i	0.0250212	+	0.000669488i
$457$	−0.723908	−	0.607431i	−0.0338630	−	0.0284144i	0.625699	−	0.780065i	$-0.284814\pi$
$457$	−0.723908	−	0.607431i	−0.0338630	−	0.0284144i	−0.659562	+	0.751650i	$0.729258\pi$
$458$	−8.93605			−0.417554
$459$	−2.50351	−	5.27191i	−0.116854	−	0.246072i
$460$	0.312120			0.0145527
$461$	14.8867	+	12.4914i	0.693342	+	0.581783i	0.919871	−	0.392221i	$-0.128293\pi$
$461$	14.8867	+	12.4914i	0.693342	+	0.581783i	−0.226529	+	0.974004i	$0.572738\pi$
$462$	14.5117	+	26.7636i	0.675144	+	1.24515i
$463$	−4.42656	−	25.1043i	−0.205720	−	1.16669i	−0.896303	−	0.443441i	$-0.853757\pi$
$463$	−4.42656	−	25.1043i	−0.205720	−	1.16669i	0.690584	−	0.723252i	$-0.257354\pi$
$464$	−9.66518	−	3.51784i	−0.448695	−	0.163312i
$465$	11.8329	+	10.4809i	0.548737	+	0.486040i
$466$	−3.73061	+	21.1574i	−0.172817	+	0.980096i
$467$	−4.61685	+	7.99663i	−0.213643	+	0.370040i	−0.952852	−	0.303436i	$-0.901866\pi$
$467$	−4.61685	+	7.99663i	−0.213643	+	0.370040i	0.739209	+	0.673476i	$0.235199\pi$
$468$	2.95123	−	12.7170i	0.136421	−	0.587842i
$469$	−19.9786	−	34.6040i	−0.922526	−	1.59786i
$470$	1.99932	−	0.727692i	0.0922216	−	0.0335659i
$471$	8.79064	−	6.98421i	0.405051	−	0.321815i
$472$	−7.70266	+	6.46330i	−0.354544	+	0.297497i
$473$	7.08719	−	5.94685i	0.325869	−	0.273437i
$474$	−29.1176	−	11.4889i	−1.33742	−	0.527704i
$475$	0.133203	−	0.0484821i	0.00611179	−	0.00222451i
$476$	1.24331	+	2.15348i	0.0569871	+	0.0987046i
$477$	14.4212	+	28.3832i	0.660300	+	1.29958i
$478$	−14.8457	+	25.7135i	−0.679026	+	1.17611i
$479$	1.38311	−	7.84399i	0.0631958	−	0.358401i	−0.936769	−	0.349950i	$-0.886199\pi$
$479$	1.38311	−	7.84399i	0.0631958	−	0.358401i	0.999964	−	0.00845138i	$-0.00269019\pi$
$480$	−5.96402	+	1.99175i	−0.272219	+	0.0909106i
$481$	47.7933	+	17.3953i	2.17919	+	0.793159i
$482$	−5.23718	−	29.7015i	−0.238547	−	1.35287i
$483$	−1.40721	+	2.29341i	−0.0640300	+	0.104354i
$484$	−0.248706	−	0.208689i	−0.0113048	−	0.00948587i
$485$	10.4429			0.474187
$486$	7.72435	−	24.2570i	0.350383	−	1.10032i
$487$	−14.2155			−0.644164			−0.322082	−	0.946712i	$-0.604383\pi$
$487$	−14.2155			−0.644164			−0.322082	+	0.946712i	$0.604383\pi$
$488$	−3.01548	−	2.53029i	−0.136504	−	0.114541i
$489$	17.7958	−	29.0030i	0.804754	−	1.31156i
$490$	−1.13978	−	6.46403i	−0.0514902	−	0.292015i
$491$	23.4229	+	8.52523i	1.05706	+	0.384738i	0.811323	−	0.584598i	$-0.198748\pi$
$491$	23.4229	+	8.52523i	1.05706	+	0.384738i	0.245737	+	0.969337i	$0.420970\pi$
$492$	13.4776	−	4.50099i	0.607616	−	0.202920i
$493$	−0.410310	+	2.32698i	−0.0184794	+	0.104802i
$494$	0.755214	−	1.30807i	0.0339787	−	0.0588528i
$495$	4.40617	+	8.67205i	0.198043	+	0.389780i
$496$	−22.3095	−	38.6412i	−1.00173	−	1.73504i
$497$	−1.82872	+	0.665601i	−0.0820295	+	0.0298563i
$498$	−6.06027	−	2.39120i	−0.271567	−	0.107152i
$499$	−16.3030	+	13.6798i	−0.729821	+	0.612393i	−0.930083	−	0.367350i	$-0.880265\pi$
$499$	−16.3030	+	13.6798i	−0.729821	+	0.612393i	0.200262	+	0.979742i	$0.435821\pi$
$500$	−0.510909	+	0.428704i	−0.0228485	+	0.0191722i
$501$	−21.8194	+	17.3356i	−0.974817	+	0.774497i
$502$	15.5328	−	5.65348i	0.693263	−	0.252327i
$503$	−6.05280	−	10.4838i	−0.269881	−	0.467448i	0.698950	−	0.715171i	$-0.253651\pi$
$503$	−6.05280	−	10.4838i	−0.269881	−	0.467448i	−0.968831	+	0.247723i	$0.920318\pi$
$504$	4.90096	−	21.1184i	0.218306	−	0.940690i
$505$	1.85987	−	3.22138i	0.0827630	−	0.143350i
$506$	−0.430305	+	2.44038i	−0.0191294	+	0.108488i
$507$	38.3426	+	33.9617i	1.70285	+	1.50829i
$508$	2.05702	+	0.748693i	0.0912654	+	0.0332179i
$509$	−3.60661	−	20.4541i	−0.159860	−	0.906613i	−0.954207	−	0.299148i	$-0.903298\pi$
$509$	−3.60661	−	20.4541i	−0.159860	−	0.906613i	0.794347	−	0.607465i	$-0.207813\pi$
$510$	1.51432	+	2.79283i	0.0670553	+	0.123669i
$511$	5.85933	+	4.91656i	0.259201	+	0.217496i
$512$	−3.53820			−0.156368
$513$	0.418234	−	0.606308i	0.0184655	−	0.0267692i
$514$	26.1212			1.15216
$515$	6.74896	+	5.66305i	0.297395	+	0.249544i
$516$	3.29494	+	0.0881621i	0.145051	+	0.00388112i
$517$	0.733545	+	4.16014i	0.0322613	+	0.182963i
$518$	−39.7088	−	14.4528i	−1.74471	−	0.635021i
$519$	4.24830	−	20.8202i	0.186480	−	0.913907i
$520$	2.46654	−	13.9885i	0.108165	−	0.613434i
$521$	8.34325	−	14.4509i	0.365524	−	0.633107i	−0.623336	−	0.781954i	$-0.714223\pi$
$521$	8.34325	−	14.4509i	0.365524	−	0.633107i	0.988860	+	0.148848i	$0.0475564\pi$
$522$	−8.23848	+	6.19342i	−0.360589	+	0.271079i
$523$	6.37442	+	11.0408i	0.278734	+	0.482781i	0.971070	−	0.238794i	$-0.0767519\pi$
$523$	6.37442	+	11.0408i	0.278734	+	0.482781i	−0.692337	+	0.721575i	$0.743419\pi$
$524$	11.8739	−	4.32175i	0.518714	−	0.188796i
$525$	−0.846599	−	5.68692i	−0.0369486	−	0.248197i
$526$	22.4021	−	18.7976i	0.976779	−	0.819615i
$527$	−7.85220	+	6.58878i	−0.342047	+	0.287012i
$528$	−4.04293	−	27.1578i	−0.175946	−	1.18189i
$529$	21.4071	−	7.79156i	0.930745	−	0.338763i
$530$	−8.66530	−	15.0087i	−0.376396	−	0.651938i
$531$	1.67298	+	13.7551i	0.0726014	+	0.596921i
$532$	−0.156915	+	0.271785i	−0.00680314	+	0.0117834i
$533$	−13.9366	+	79.0381i	−0.603659	+	3.42352i
$534$	−3.41314	+	16.7273i	−0.147701	+	0.723860i
$535$	2.79624	+	1.01775i	0.120892	+	0.0440011i
$536$	4.55035	+	25.8063i	0.196545	+	1.11466i
$537$	−10.1956	−	0.272801i	−0.439971	−	0.0117722i
$538$	19.6357	+	16.4763i	0.846554	+	0.710343i
$539$	13.0321			0.561330
$540$	−0.873445	+	3.35367i	−0.0375871	+	0.144319i
$541$	−16.5825			−0.712936			−0.356468	−	0.934307i	$-0.616019\pi$
$541$	−16.5825			−0.712936			−0.356468	+	0.934307i	$0.616019\pi$
$542$	0.859035	+	0.720816i	0.0368987	+	0.0309617i
$543$	−11.2870	−	20.8163i	−0.484369	−	0.893313i
$544$	−0.708033	−	4.01546i	−0.0303567	−	0.172161i
$545$	−5.50723	−	2.00447i	−0.235904	−	0.0858619i
$546$	−45.8610	−	40.6211i	−1.96267	−	1.73842i
$547$	3.24404	−	18.3979i	0.138705	−	0.786636i	−0.833503	−	0.552516i	$-0.813668\pi$
$547$	3.24404	−	18.3979i	0.138705	−	0.786636i	0.972208	−	0.234120i	$-0.0752209\pi$
$548$	−6.13109	+	10.6194i	−0.261907	+	0.453636i
$549$	−5.18938	+	1.58008i	−0.221477	+	0.0674362i
$550$	−2.64755	−	4.58570i	−0.112892	−	0.195535i
$551$	−0.280229	+	0.101995i	−0.0119382	+	0.00434513i
$552$	1.38162	−	1.09770i	0.0588057	−	0.0467214i
$553$	−28.1409	+	23.6130i	−1.19667	+	1.00413i
$554$	13.1242	−	11.0125i	0.557596	−	0.467878i
$555$	−12.5591	−	4.95545i	−0.533105	−	0.210347i
$556$	5.11650	−	1.86225i	0.216988	−	0.0789771i
$557$	0.729857	+	1.26415i	0.0309250	+	0.0535637i	0.881074	−	0.472979i	$-0.156821\pi$
$557$	0.729857	+	1.26415i	0.0309250	+	0.0535637i	−0.850149	+	0.526543i	$0.823488\pi$
$558$	−44.6477	−	2.39098i	−1.89009	−	0.101218i
$559$	−9.30862	+	16.1230i	−0.393713	+	0.681930i
$560$	−2.81821	+	15.9828i	−0.119091	+	0.675398i
$561$	−5.98290	+	1.99806i	−0.252598	+	0.0843580i
$562$	0.291222	+	0.105996i	0.0122845	+	0.00447118i
$563$	−3.05801	−	17.3428i	−0.128880	−	0.730914i	−0.978927	−	0.204208i	$-0.934538\pi$
$563$	−3.05801	−	17.3428i	−0.128880	−	0.730914i	0.850048	−	0.526706i	$-0.176573\pi$
$564$	−0.787097	+	1.28278i	−0.0331428	+	0.0540149i
$565$	8.11935	+	6.81295i	0.341584	+	0.286623i
$566$	14.1815			0.596093
$567$	−20.7043	−	21.5381i	−0.869500	−	0.904516i
$568$	1.27627			0.0535510
$569$	−4.98741	−	4.18493i	−0.209083	−	0.175442i	0.532232	−	0.846598i	$-0.321353\pi$
$569$	−4.98741	−	4.18493i	−0.209083	−	0.175442i	−0.741315	+	0.671157i	$0.765798\pi$
$570$	−0.209694	+	0.341752i	−0.00878312	+	0.0143144i
$571$	2.13227	+	12.0927i	0.0892326	+	0.506063i	0.996363	+	0.0852130i	$0.0271571\pi$
$571$	2.13227	+	12.0927i	0.0892326	+	0.506063i	−0.907130	+	0.420850i	$0.861732\pi$
$572$	−13.2589	−	4.82583i	−0.554381	−	0.201778i
$573$	16.2413	−	5.42394i	0.678488	−	0.226589i
$574$	11.5791	−	65.6684i	0.483303	−	2.74095i
$575$	0.233992	−	0.405287i	0.00975815	−	0.0169016i
$576$	−6.30102	+	9.67853i	−0.262543	+	0.403272i
$577$	4.31665	+	7.47666i	0.179705	+	0.311258i	0.941779	−	0.336232i	$-0.109152\pi$
$577$	4.31665	+	7.47666i	0.179705	+	0.311258i	−0.762075	+	0.647489i	$0.775819\pi$
$578$	24.1522	−	8.79067i	1.00460	−	0.365644i
$579$	−4.09487	−	1.61571i	−0.170177	−	0.0671466i
$580$	1.07483	−	0.901892i	0.0446300	−	0.0374490i
$581$	−5.85699	+	4.91460i	−0.242989	+	0.203892i
$582$	−23.1275	+	18.3749i	−0.958667	+	0.761666i
$583$	32.3340	−	11.7686i	1.33914	−	0.487407i
$584$	−2.50809	−	4.34414i	−0.103785	−	0.179762i
$585$	−14.3004	−	13.3659i	−0.591250	−	0.552612i
$586$	−19.4249	+	33.6449i	−0.802436	+	1.38986i
$587$	0.420297	−	2.38362i	0.0173475	−	0.0983826i	−0.974905	−	0.222623i	$-0.928538\pi$
$587$	0.420297	−	2.38362i	0.0173475	−	0.0983826i	0.992252	+	0.124240i	$0.0396493\pi$
$588$	3.47562	+	3.07851i	0.143332	+	0.126955i
$589$	−1.21565	−	0.442460i	−0.0500900	−	0.0182313i
$590$	−1.30981	−	7.42831i	−0.0539241	−	0.305819i
$591$	−22.1304	−	40.8146i	−0.910321	−	1.67889i
$592$	29.1943	+	24.4970i	1.19988	+	1.00682i
$593$	26.6840			1.09578			0.547890	−	0.836550i	$-0.315431\pi$
$593$	26.6840			1.09578			0.547890	+	0.836550i	$0.315431\pi$
$594$	−25.0173	−	11.4528i	−1.02647	−	0.469913i
$595$	3.72838			0.152849
$596$	3.12428	+	2.62158i	0.127976	+	0.107384i
$597$	−9.58925	−	0.256578i	−0.392462	−	0.0105010i
$598$	−0.865908	−	4.91081i	−0.0354096	−	0.200818i
$599$	−4.62484	−	1.68330i	−0.188966	−	0.0687780i	0.245804	−	0.969320i	$-0.420948\pi$
$599$	−4.62484	−	1.68330i	−0.188966	−	0.0687780i	−0.434770	+	0.900542i	$0.643170\pi$
$600$	−0.753854	+	3.69452i	−0.0307760	+	0.150828i
$601$	−0.0589830	+	0.334509i	−0.00240597	+	0.0136449i	−0.985987	−	0.166822i	$-0.946650\pi$
$601$	−0.0589830	+	0.334509i	−0.00240597	+	0.0136449i	0.983581	+	0.180466i	$0.0577607\pi$
$602$	7.73402	−	13.3957i	0.315215	−	0.545968i
$603$	33.2243	+	14.1476i	1.35300	+	0.576136i
$604$	0.199695	+	0.345882i	0.00812548	+	0.0140737i
$605$	−0.457434	+	0.166492i	−0.0185973	+	0.00676888i
$606$	1.54925	+	10.4069i	0.0629338	+	0.422750i
$607$	7.28068	−	6.10922i	0.295514	−	0.247965i	−0.482960	−	0.875642i	$-0.660438\pi$
$607$	7.28068	−	6.10922i	0.295514	−	0.247965i	0.778474	+	0.627677i	$0.215994\pi$
$608$	0.394206	−	0.330778i	0.0159872	−	0.0134148i
$609$	1.78105	+	11.9639i	0.0721716	+	0.484803i
$610$	2.77485	−	1.00996i	0.112350	−	0.0408922i
$611$	−4.25032	−	7.36178i	−0.171950	−	0.297826i
$612$	−2.06762	−	0.880438i	−0.0835786	−	0.0355896i
$613$	−15.3952	+	26.6653i	−0.621806	+	1.07700i	0.367343	+	0.930086i	$0.380268\pi$
$613$	−15.3952	+	26.6653i	−0.621806	+	1.07700i	−0.989149	+	0.146915i	$0.953066\pi$
$614$	7.84334	−	44.4818i	0.316532	−	1.79514i
$615$	4.25946	−	20.8749i	0.171758	−	0.841758i
$616$	−22.0183	−	8.01402i	−0.887145	−	0.322894i
$617$	−2.70601	−	15.3465i	−0.108940	−	0.617828i	−0.989573	−	0.144030i	$-0.953994\pi$
$617$	−2.70601	−	15.3465i	−0.108940	−	0.617828i	0.880634	−	0.473798i	$-0.157117\pi$
$618$	−24.9112	−	0.666546i	−1.00208	−	0.0268124i
$619$	30.1586	+	25.3060i	1.21218	+	1.01714i	0.999197	+	0.0400790i	$0.0127609\pi$
$619$	30.1586	+	25.3060i	1.21218	+	1.01714i	0.212979	+	0.977057i	$0.431683\pi$
$620$	6.08671			0.244448
$621$	−0.228927	−	2.42092i	−0.00918651	−	0.0971482i
$622$	0.454958			0.0182422
$623$	15.3478	+	12.8783i	0.614896	+	0.515959i
$624$	26.3364	+	48.5717i	1.05430	+	1.94442i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	22.9892	+	8.36739i	0.918834	+	0.334428i
$627$	−0.595929	−	0.527840i	−0.0237991	−	0.0210799i
$628$	0.750721	−	4.25755i	0.0299570	−	0.169895i
$629$	4.37756	−	7.58216i	0.174545	−	0.302321i
$630$	11.8814	+	11.1050i	0.473368	+	0.442434i
$631$	−9.30130	−	16.1103i	−0.370279	−	0.641342i	0.619329	−	0.785131i	$-0.287405\pi$
$631$	−9.30130	−	16.1103i	−0.370279	−	0.641342i	−0.989608	+	0.143789i	$0.954071\pi$
$632$	22.6386	−	8.23977i	0.900515	−	0.327760i
$633$	−9.78305	+	7.77268i	−0.388841	+	0.308936i
$634$	27.7044	−	23.2467i	1.10028	−	0.923246i
$635$	2.51430	−	2.10974i	0.0997768	−	0.0837227i
$636$	11.4035	+	4.49946i	0.452177	+	0.178415i
$637$	−24.6430	+	8.96933i	−0.976392	+	0.355378i
$638$	5.56983	+	9.64723i	0.220512	+	0.381938i
$639$	0.959574	−	1.47393i	0.0379602	−	0.0583078i
$640$	6.77365	−	11.7323i	0.267752	−	0.463760i
$641$	−5.14183	+	29.1608i	−0.203090	+	1.15178i	0.697327	+	0.716753i	$0.254373\pi$
$641$	−5.14183	+	29.1608i	−0.203090	+	1.15178i	−0.900417	+	0.435028i	$0.856738\pi$
$642$	−7.98355	+	2.66619i	−0.315086	+	0.105226i
$643$	18.0063	+	6.55375i	0.710099	+	0.258455i	0.671717	−	0.740808i	$-0.265557\pi$
$643$	18.0063	+	6.55375i	0.710099	+	0.258455i	0.0383823	+	0.999263i	$0.487780\pi$
$644$	0.179915	+	1.02035i	0.00708965	+	0.0402074i
$645$	2.58465	−	4.21237i	0.101771	−	0.165862i
$646$	−0.199175	−	0.167128i	−0.00783644	−	0.00657555i
$647$	−48.1204			−1.89181			−0.945904	−	0.324448i	$-0.894822\pi$
$647$	−48.1204			−1.89181			−0.945904	+	0.324448i	$0.894822\pi$
$648$	7.92826	+	17.9171i	0.311452	+	0.703850i
$649$	14.9761			0.587864
$650$	8.16252	+	6.84916i	0.320160	+	0.268646i
$651$	−27.4422	+	44.7243i	−1.07554	+	1.75288i
$652$	−2.27524	−	12.9035i	−0.0891054	−	0.505342i
$653$	−42.1586	−	15.3445i	−1.64979	−	0.600476i	−0.661082	−	0.750313i	$-0.729903\pi$
$653$	−42.1586	−	15.3445i	−1.64979	−	0.600476i	−0.988711	+	0.149838i	$0.952125\pi$
$654$	15.7237	−	5.25110i	0.614845	−	0.205334i
$655$	3.28994	−	18.6582i	0.128549	−	0.729036i
$656$	−30.0690	+	52.0810i	−1.17400	+	2.03342i
$657$	−6.90267	−	0.369652i	−0.269299	−	0.0144215i
$658$	3.53136	+	6.11649i	0.137667	+	0.238446i
$659$	17.3182	−	6.30332i	0.674623	−	0.245543i	0.0180857	−	0.999836i	$-0.494243\pi$
$659$	17.3182	−	6.30332i	0.674623	−	0.245543i	0.656537	+	0.754294i	$0.272021\pi$
$660$	3.48416	+	1.37474i	0.135621	+	0.0535118i
$661$	23.9670	−	20.1107i	0.932209	−	0.782217i	−0.0440034	−	0.999031i	$-0.514011\pi$
$661$	23.9670	−	20.1107i	0.932209	−	0.782217i	0.976213	+	0.216815i	$0.0695668\pi$
$662$	−2.27007	+	1.90481i	−0.0882286	+	0.0740326i
$663$	9.93824	−	7.89598i	0.385969	−	0.306654i
$664$	4.71179	−	1.71495i	0.182853	−	0.0665530i
$665$	0.235275	+	0.407508i	0.00912357	+	0.0158025i
$666$	36.5337	−	11.1239i	1.41565	−	0.431043i
$667$	−0.492265	+	0.852628i	−0.0190606	+	0.0330139i
$668$	−1.86337	+	10.5677i	−0.0720961	+	0.408877i
$669$	−33.2729	−	29.4712i	−1.28640	−	1.13942i
$670$	−18.4719	−	6.72323i	−0.713632	−	0.259741i
$671$	1.01809	+	5.77386i	0.0393028	+	0.222897i
$672$	−9.94906	−	18.3488i	−0.383793	−	0.707822i
$673$	8.18259	+	6.86601i	0.315416	+	0.264665i	0.786726	−	0.617302i	$-0.211774\pi$
$673$	8.18259	+	6.86601i	0.315416	+	0.264665i	−0.471310	+	0.881967i	$0.656219\pi$
$674$	−34.9193			−1.34504
$675$	3.69992	+	3.64837i	0.142410	+	0.140426i
$676$	19.7230			0.758578
$677$	24.4700	+	20.5327i	0.940458	+	0.789138i	0.977665	−	0.210170i	$-0.0674017\pi$
$677$	24.4700	+	20.5327i	0.940458	+	0.789138i	−0.0372073	+	0.999308i	$0.511846\pi$
$678$	−29.9695	−	0.801890i	−1.15097	−	0.0307964i
$679$	6.01959	+	34.1388i	0.231011	+	1.31013i
$680$	−2.29766	−	0.836279i	−0.0881112	−	0.0320698i
$681$	0.846835	−	4.15021i	0.0324508	−	0.159036i
$682$	−8.39147	+	47.5904i	−0.321326	+	1.82233i
$683$	10.7963	−	18.6997i	0.413108	−	0.715525i	−0.582119	−	0.813103i	$-0.697776\pi$
$683$	10.7963	−	18.6997i	0.413108	−	0.715525i	0.995228	+	0.0975785i	$0.0311097\pi$
$684$	−0.0342436	−	0.281548i	−0.00130934	−	0.0107652i
$685$	9.19280	+	15.9224i	0.351239	+	0.608363i
$686$	−15.1843	+	5.52663i	−0.579739	+	0.211008i
$687$	−1.39553	−	9.37432i	−0.0532429	−	0.357653i
$688$	−10.6864	+	8.96698i	−0.407416	+	0.341863i
$689$	−53.0424	+	44.5079i	−2.02076	+	1.69562i
$690$	0.194913	+	1.30930i	0.00742020	+	0.0498442i
$691$	−4.28596	+	1.55996i	−0.163045	+	0.0593437i	−0.422253	−	0.906478i	$-0.638761\pi$
$691$	−4.28596	+	1.55996i	−0.163045	+	0.0593437i	0.259208	+	0.965822i	$0.416539\pi$
$692$	−4.09112	−	7.08603i	−0.155521	−	0.269371i
$693$	−25.8099	+	19.4030i	−0.980438	+	0.737060i
$694$	−20.8528	+	36.1181i	−0.791560	+	1.37102i
$695$	1.41765	−	8.03987i	0.0537743	−	0.304969i
$696$	1.58593	−	7.77241i	0.0601146	−	0.294612i
$697$	12.9823	+	4.72518i	0.491740	+	0.178979i
$698$	9.61018	+	54.5020i	0.363751	+	2.06293i
$699$	−22.7776	−	0.609457i	−0.861529	−	0.0230518i
$700$	−1.69598	−	1.42309i	−0.0641019	−	0.0537878i
$701$	0.461138			0.0174170			0.00870848	−	0.999962i	$-0.497228\pi$
$701$	0.461138			0.0174170			0.00870848	+	0.999962i	$0.497228\pi$
$702$	55.1889	+	4.43852i	2.08297	+	0.167521i
$703$	1.10496			0.0416745
$704$	9.56182	+	8.02332i	0.360375	+	0.302390i
$705$	1.07561	+	1.98373i	0.0405099	+	0.0747116i
$706$	3.46678	+	19.6611i	0.130474	+	0.739954i
$707$	11.6031	+	4.22318i	0.436379	+	0.158829i
$708$	3.99410	+	3.53774i	0.150107	+	0.132956i
$709$	0.100255	−	0.568575i	0.00376516	−	0.0213533i	−0.982867	−	0.184315i	$-0.940993\pi$
$709$	0.100255	−	0.568575i	0.00376516	−	0.0213533i	0.986632	+	0.162961i	$0.0521046\pi$
$710$	−0.478700	+	0.829133i	−0.0179653	+	0.0311168i
$711$	7.50513	−	32.3399i	0.281464	−	1.21284i
$712$	−6.56963	−	11.3789i	−0.246207	−	0.426443i
$713$	−4.01338	+	1.46075i	−0.150302	+	0.0547056i
$714$	−8.25713	+	6.56033i	−0.309015	+	0.245514i
$715$	−16.2063	+	13.5987i	−0.606082	+	0.508564i
$716$	−3.00849	+	2.52443i	−0.112433	+	0.0943422i
$717$	−29.2930	−	11.5581i	−1.09397	−	0.431647i
$718$	17.9168	−	6.52117i	0.668648	−	0.243368i
$719$	10.6586	+	18.4613i	0.397500	+	0.688491i	0.993417	−	0.114556i	$-0.0365445\pi$
$719$	10.6586	+	18.4613i	0.397500	+	0.688491i	−0.595917	+	0.803046i	$0.703211\pi$
$720$	−6.64386	−	13.0762i	−0.247602	−	0.487320i
$721$	−14.6227	+	25.3273i	−0.544580	+	0.943240i
$722$	−5.38234	+	30.5248i	−0.200310	+	1.13601i
$723$	30.3403	−	10.1325i	1.12837	−	0.376831i
$724$	−8.56811	−	3.11854i	−0.318431	−	0.115900i
$725$	−0.365315	−	2.07181i	−0.0135675	−	0.0769449i
$726$	0.720111	−	1.17361i	0.0267258	−	0.0435568i
$727$	−27.4476	−	23.0313i	−1.01798	−	0.854183i	−0.0286038	−	0.999591i	$-0.509106\pi$
$727$	−27.4476	−	23.0313i	−1.01798	−	0.854183i	−0.989372	+	0.145408i	$0.953551\pi$
$728$	47.1514			1.74755
$729$	26.6530	+	4.31499i	0.987147	+	0.159815i
$730$	3.76292			0.139272
$731$	2.45499	+	2.05998i	0.0908012	+	0.0761913i
$732$	−1.09241	+	1.78037i	−0.0403767	+	0.0658045i
$733$	−3.31929	−	18.8246i	−0.122601	−	0.695304i	−0.982704	−	0.185184i	$-0.940712\pi$
$733$	−3.31929	−	18.8246i	−0.122601	−	0.695304i	0.860103	−	0.510120i	$-0.170399\pi$
$734$	38.7217	+	14.0935i	1.42924	+	0.520202i
$735$	6.60306	−	2.20516i	0.243557	−	0.0813387i
$736$	0.295013	−	1.67310i	0.0108743	−	0.0616713i
$737$	19.5145	−	33.8000i	0.718825	−	1.24504i
$738$	27.2975	+	53.7259i	1.00484	+	1.97768i
$739$	−13.0940	−	22.6794i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$739$	−13.0940	−	22.6794i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$740$	−4.88533	+	1.77811i	−0.179588	+	0.0653648i
$741$	1.49016	+	0.587973i	0.0547425	+	0.0215997i
$742$	44.0700	−	36.9792i	1.61786	−	1.35755i
$743$	21.6719	−	18.1849i	0.795066	−	0.667140i	−0.151928	−	0.988392i	$-0.548548\pi$
$743$	21.6719	−	18.1849i	0.795066	−	0.667140i	0.946994	+	0.321252i	$0.104104\pi$
$744$	26.9433	−	21.4066i	0.987788	−	0.784802i
$745$	5.74636	−	2.09150i	0.210530	−	0.0766267i
$746$	−18.8352	−	32.6235i	−0.689605	−	1.19443i
$747$	1.56205	−	6.73093i	0.0571524	−	0.246272i
$748$	−1.21443	+	2.10345i	−0.0444039	+	0.0769098i
$749$	−1.71528	+	9.72784i	−0.0626750	+	0.355448i
$750$	−2.11741	−	1.87548i	−0.0773168	−	0.0684828i
$751$	−26.5665	−	9.66942i	−0.969425	−	0.352842i	−0.191705	−	0.981453i	$-0.561402\pi$
$751$	−26.5665	−	9.66942i	−0.969425	−	0.352842i	−0.777720	+	0.628611i	$0.783624\pi$
$752$	−1.10608	−	6.27288i	−0.0403345	−	0.228748i
$753$	8.35649	+	15.4117i	0.304527	+	0.561634i
$754$	−17.1720	−	14.4090i	−0.625368	−	0.524746i
$755$	0.598836			0.0217939
$756$	−11.4669	−	0.922219i	−0.417049	−	0.0335408i
$757$	8.77707			0.319008			0.159504	−	0.987197i	$-0.449011\pi$
$757$	8.77707			0.319008			0.159504	+	0.987197i	$0.449011\pi$
$758$	−31.7840	−	26.6699i	−1.15445	−	0.968695i
$759$	−2.62727	−	0.0702974i	−0.0953638	−	0.00255163i
$760$	−0.0535865	−	0.303904i	−0.00194379	−	0.0110238i
$761$	16.9405	+	6.16585i	0.614094	+	0.223512i	0.630293	−	0.776357i	$-0.282935\pi$
$761$	16.9405	+	6.16585i	0.614094	+	0.223512i	−0.0161998	+	0.999869i	$0.505157\pi$
$762$	−1.85610	+	9.09646i	−0.0672394	+	0.329530i
$763$	3.37826	−	19.1591i	0.122301	−	0.693606i
$764$	3.29670	−	5.71005i	0.119270	−	0.206582i
$765$	−2.69332	+	2.02474i	−0.0973770	+	0.0732048i
$766$	−9.48585	−	16.4300i	−0.342738	−	0.593639i
$767$	−28.3192	+	10.3073i	−1.02255	+	0.372176i
$768$	3.67877	+	24.7117i	0.132746	+	0.891706i
$769$	−13.7946	+	11.5751i	−0.497447	+	0.417408i	−0.856686	−	0.515838i	$-0.827481\pi$
$769$	−13.7946	+	11.5751i	−0.497447	+	0.417408i	0.359239	+	0.933246i	$0.383036\pi$
$770$	13.4649	−	11.2984i	0.485243	−	0.407167i
$771$	4.07932	+	27.4023i	0.146913	+	0.986869i
$772$	−1.59285	+	0.579750i	−0.0573279	+	0.0208656i
$773$	−5.79943	−	10.0449i	−0.208591	−	0.361290i	0.742680	−	0.669647i	$-0.233554\pi$
$773$	−5.79943	−	10.0449i	−0.208591	−	0.361290i	−0.951271	+	0.308356i	$0.900221\pi$
$774$	1.68780	+	13.8769i	0.0606665	+	0.498794i
$775$	4.56313	−	7.90358i	0.163913	−	0.283905i
$776$	3.94772	−	22.3886i	0.141715	−	0.803704i
$777$	8.96038	−	43.9134i	0.321452	−	1.57538i
$778$	−48.2656	−	17.5673i	−1.73041	−	0.629817i
$779$	0.302776	+	1.71713i	0.0108481	+	0.0615226i
$780$	−7.53456	−	0.201601i	−0.269781	−	0.00721848i
$781$	−1.45616	−	1.22186i	−0.0521054	−	0.0437216i
$782$	−0.858386			−0.0306958
$783$	−7.78377	−	7.67532i	−0.278169	−	0.274293i
$784$	−19.6504			−0.701801
$785$	−4.96561	−	4.16664i	−0.177230	−	0.148714i
$786$	25.5442	+	47.1106i	0.911131	+	1.68038i
$787$	−1.22634	−	6.95490i	−0.0437142	−	0.247915i	0.955118	−	0.296225i	$-0.0957278\pi$
$787$	−1.22634	−	6.95490i	−0.0437142	−	0.247915i	−0.998832	+	0.0483094i	$0.984617\pi$
$788$	−16.7995	−	6.11453i	−0.598458	−	0.217821i
$789$	23.2180	+	20.5652i	0.826584	+	0.732141i
$790$	−3.13823	+	17.7978i	−0.111653	+	0.633218i
$791$	−17.5919	+	30.4701i	−0.625497	+	1.08339i
$792$	20.2578	−	6.16815i	0.719829	−	0.219176i
$793$	−5.89902	−	10.2174i	−0.209480	−	0.362831i
$794$	−19.0217	+	6.92332i	−0.675053	+	0.245699i
$795$	14.3916	−	11.4342i	0.510417	−	0.405529i
$796$	−2.82959	+	2.37430i	−0.100292	+	0.0841550i
$797$	−22.7353	+	19.0772i	−0.805326	+	0.675749i	−0.949487	−	0.313805i	$-0.898396\pi$
$797$	−22.7353	+	19.0772i	−0.805326	+	0.675749i	0.144161	+	0.989554i	$0.453952\pi$
$798$	−1.23809	−	0.488514i	−0.0438280	−	0.0172932i
$799$	−1.37505	+	0.500478i	−0.0486458	+	0.0177056i
$800$	1.81514	+	3.14391i	0.0641748	+	0.111154i
$801$	−18.0807	−	0.968258i	−0.638850	−	0.0342117i
$802$	5.36319	−	9.28932i	0.189381	−	0.328017i
$803$	−1.29735	+	7.35761i	−0.0457823	+	0.259645i
$804$	13.1889	−	4.40458i	0.465137	−	0.155338i
$805$	1.45980	+	0.531324i	0.0514512	+	0.0187267i
$806$	−16.8863	−	95.7667i	−0.594793	−	3.37324i
$807$	−14.2179	+	23.1718i	−0.500493	+	0.815685i
$808$	−6.20327	−	5.20517i	−0.218230	−	0.183117i
$809$	23.8087			0.837068			0.418534	−	0.908201i	$-0.362544\pi$
$809$	23.8087			0.837068			0.418534	+	0.908201i	$0.362544\pi$
$810$	−14.6136	−	1.56968i	−0.513471	−	0.0551530i
$811$	−17.3795			−0.610277			−0.305139	−	0.952308i	$-0.598703\pi$
$811$	−17.3795			−0.610277			−0.305139	+	0.952308i	$0.598703\pi$
$812$	3.56794	+	2.99385i	0.125210	+	0.105064i
$813$	−0.622014	+	1.01374i	−0.0218150	+	0.0355532i
$814$	−7.16742	−	40.6485i	−0.251218	−	1.42473i
$815$	−18.4609	−	6.71923i	−0.646658	−	0.235364i
$816$	9.02134	−	3.01278i	0.315810	−	0.105468i
$817$	−0.0702348	+	0.398321i	−0.00245720	+	0.0139355i
$818$	15.7654	−	27.3065i	0.551225	−	0.954749i
$819$	35.4512	−	54.4540i	1.23877	−	1.90278i
$820$	−4.10187	−	7.10465i	−0.143243	−	0.248105i
$821$	23.9764	−	8.72670i	0.836782	−	0.304564i	0.112143	−	0.993692i	$-0.464229\pi$
$821$	23.9764	−	8.72670i	0.836782	−	0.304564i	0.724639	+	0.689128i	$0.242006\pi$
$822$	−48.3755	−	19.0875i	−1.68729	−	0.665753i
$823$	2.23773	−	1.87767i	0.0780022	−	0.0654516i	−0.602953	−	0.797777i	$-0.706009\pi$
$823$	2.23773	−	1.87767i	0.0780022	−	0.0654516i	0.680955	+	0.732325i	$0.261565\pi$
$824$	14.6924	−	12.3284i	0.511833	−	0.429479i
$825$	4.39713	−	3.49354i	0.153089	−	0.121630i
$826$	23.5288	−	8.56379i	0.818673	−	0.297972i
$827$	5.75613	+	9.96991i	0.200160	+	0.346688i	0.948580	−	0.316538i	$-0.102520\pi$
$827$	5.75613	+	9.96991i	0.200160	+	0.346688i	−0.748420	+	0.663225i	$0.769187\pi$
$828$	−0.684081	−	0.639376i	−0.0237734	−	0.0222199i
$829$	10.5843	−	18.3326i	0.367608	−	0.636717i	−0.621583	−	0.783349i	$-0.713510\pi$
$829$	10.5843	−	18.3326i	0.367608	−	0.636717i	0.989191	+	0.146632i	$0.0468433\pi$
$830$	−0.653163	+	3.70427i	−0.0226716	+	0.128577i
$831$	13.6022	+	12.0481i	0.471857	+	0.417944i
$832$	−23.6030	−	8.59080i	−0.818288	−	0.297832i
$833$	0.783898	+	4.44571i	0.0271605	+	0.154035i
$834$	11.0071	+	20.3001i	0.381143	+	0.702935i
$835$	12.3252	+	10.3421i	0.426531	+	0.357902i
$836$	−0.306540			−0.0106019
$837$	−4.46435	−	47.2109i	−0.154310	−	1.63185i
$838$	51.6749			1.78508
$839$	−16.5465	−	13.8842i	−0.571249	−	0.479335i	0.310811	−	0.950472i	$-0.399399\pi$
$839$	−16.5465	−	13.8842i	−0.571249	−	0.479335i	−0.882060	+	0.471137i	$0.843844\pi$
$840$	−12.5123	−	0.334789i	−0.431715	−	0.0115513i
$841$	−4.26726	−	24.2008i	−0.147147	−	0.834511i
$842$	35.4197	+	12.8917i	1.22064	+	0.444278i
$843$	−0.0657149	+	0.322058i	−0.00226334	+	0.0110923i
$844$	−0.835472	+	4.73820i	−0.0287581	+	0.163096i
$845$	14.7861	−	25.6103i	0.508658	−	0.881021i
$846$	−5.87263	−	2.50070i	−0.201905	−	0.0859757i
$847$	−0.807958	−	1.39942i	−0.0277618	−	0.0480848i
$848$	−48.7550	+	17.7454i	−1.67425	+	0.609378i
$849$	2.21471	+	14.8770i	0.0760086	+	0.510578i
$850$	1.40509	−	1.17901i	0.0481943	−	0.0404398i
$851$	2.79450	−	2.34486i	0.0957941	−	0.0803808i
$852$	−0.0997189	−	0.669849i	−0.00341631	−	0.0229486i
$853$	−34.1880	+	12.4434i	−1.17057	+	0.426054i	−0.852864	−	0.522134i	$-0.825136\pi$
$853$	−34.1880	+	12.4434i	−1.17057	+	0.426054i	−0.317711	+	0.948188i	$0.602914\pi$
$854$	4.90117	+	8.48908i	0.167715	+	0.290490i
$855$	−0.391261	−	0.166608i	−0.0133808	−	0.00569786i
$856$	3.23903	−	5.61016i	0.110708	−	0.191751i
$857$	7.66544	−	43.4729i	0.261846	−	1.48500i	−0.516021	−	0.856576i	$-0.672587\pi$
$857$	7.66544	−	43.4729i	0.261846	−	1.48500i	0.777867	−	0.628429i	$-0.216302\pi$
$858$	11.9638	−	58.6328i	0.408438	−	2.00169i
$859$	15.6677	+	5.70257i	0.534575	+	0.194569i	0.595180	−	0.803593i	$-0.297081\pi$
$859$	15.6677	+	5.70257i	0.534575	+	0.194569i	−0.0606051	+	0.998162i	$0.519303\pi$
$860$	−0.330455	−	1.87410i	−0.0112684	−	0.0639064i
$861$	70.6974	+	1.89164i	2.40936	+	0.0644669i
$862$	−28.3859	−	23.8186i	−0.966828	−	0.811265i
$863$	−3.15701			−0.107466			−0.0537329	−	0.998555i	$-0.517112\pi$
$863$	−3.15701			−0.107466			−0.0537329	+	0.998555i	$0.517112\pi$
$864$	17.1516	+	7.85191i	0.583509	+	0.267127i
$865$	−12.2683			−0.417133
$866$	8.92604	+	7.48984i	0.303319	+	0.254515i
$867$	12.9936	+	23.9639i	0.441286	+	0.813855i
$868$	3.50856	+	19.8980i	0.119088	+	0.675383i
$869$	−33.7180	−	12.2723i	−1.14380	−	0.416311i
$870$	4.45453	+	3.94557i	0.151023	+	0.133767i
$871$	−13.6381	+	77.3452i	−0.462108	+	2.62074i
$872$	−6.37929	+	11.0493i	−0.216030	+	0.374175i
$873$	−22.8879	−	21.3922i	−0.774639	−	0.724017i
$874$	−0.0541674	−	0.0938207i	−0.00183224	−	0.00317353i
$875$	−3.11933	+	1.13534i	−0.105453	+	0.0383817i
$876$	−2.08406	+	1.65579i	−0.0704137	+	0.0559441i
$877$	−28.3641	+	23.8003i	−0.957787	+	0.803679i	−0.980592	−	0.196061i	$-0.937185\pi$
$877$	−28.3641	+	23.8003i	−0.957787	+	0.803679i	0.0228043	+	0.999740i	$0.492741\pi$
$878$	−45.0017	+	37.7609i	−1.51873	+	1.27437i
$879$	−38.3286	−	15.1233i	−1.29279	−	0.510096i
$880$	−14.8964	+	5.42183i	−0.502156	+	0.182770i
$881$	−27.8086	−	48.1660i	−0.936897	−	1.62275i	−0.771216	−	0.636573i	$-0.780351\pi$
$881$	−27.8086	−	48.1660i	−0.936897	−	1.62275i	−0.165680	−	0.986179i	$-0.552982\pi$
$882$	−10.7435	+	16.5022i	−0.361751	+	0.555659i
$883$	−7.39606	+	12.8103i	−0.248897	+	0.431103i	−0.963220	−	0.268714i	$-0.913401\pi$
$883$	−7.39606	+	12.8103i	−0.248897	+	0.431103i	0.714323	+	0.699816i	$0.246735\pi$
$884$	0.848726	−	4.81336i	0.0285457	−	0.161891i
$885$	7.58807	−	2.53412i	0.255070	−	0.0851835i
$886$	19.1121	+	6.95623i	0.642083	+	0.233699i
$887$	3.34540	+	18.9727i	0.112328	+	0.637041i	0.988039	+	0.154206i	$0.0492819\pi$
$887$	3.34540	+	18.9727i	0.112328	+	0.637041i	−0.875711	+	0.482835i	$0.839607\pi$
$888$	−15.3717	+	25.0523i	−0.515842	+	0.840701i
$889$	8.34627	+	7.00335i	0.279925	+	0.234885i
$890$	9.85649			0.330390
$891$	8.10755	−	28.0328i	0.271613	−	0.939134i
$892$	−17.1152			−0.573060
$893$	−0.141473	−	0.118710i	−0.00473420	−	0.00397247i
$894$	−9.04614	+	14.7431i	−0.302548	+	0.493082i
$895$	1.02253	+	5.79905i	0.0341794	+	0.193841i
$896$	42.2585	+	15.3808i	1.41176	+	0.513838i
$897$	5.01643	−	1.67529i	0.167494	−	0.0559364i
$898$	2.08307	−	11.8137i	0.0695130	−	0.394228i
$899$	−9.59976	+	16.6273i	−0.320170	+	0.554551i
$900$	1.99797	+	0.106995i	0.0665990	+	0.00356651i
$901$	5.95965	+	10.3224i	0.198545	+	0.343890i
$902$	61.2044	−	22.2766i	2.03788	−	0.741729i
$903$	15.2605	+	6.02133i	0.507838	+	0.200377i
$904$	17.6757	−	14.8317i	0.587885	−	0.493294i
$905$	−10.4728	+	8.78774i	−0.348128	+	0.292114i
$906$	−1.32622	+	1.05369i	−0.0440608	+	0.0350065i
$907$	−41.4725	+	15.0948i	−1.37707	+	0.501213i	−0.921289	−	0.388878i	$-0.872863\pi$
$907$	−41.4725	+	15.0948i	−1.37707	+	0.501213i	−0.455783	+	0.890091i	$0.650641\pi$
$908$	−0.815505	−	1.41250i	−0.0270635	−	0.0468753i
$909$	−10.6753	+	3.25046i	−0.354078	+	0.107811i
$910$	−17.6855	+	30.6321i	−0.586267	+	1.01544i
$911$	−0.459647	+	2.60679i	−0.0152288	+	0.0863667i	−0.991475	−	0.130298i	$-0.958407\pi$
$911$	−0.459647	+	2.60679i	−0.0152288	+	0.0863667i	0.976246	+	0.216665i	$0.0695178\pi$
$912$	0.898574	+	0.795905i	0.0297547	+	0.0263551i
$913$	−7.01775	−	2.55425i	−0.232254	−	0.0845334i
$914$	−0.267983	−	1.51981i	−0.00886408	−	0.0502707i
$915$	1.49284	+	2.75322i	0.0493518	+	0.0910186i
$916$	−2.79565	−	2.34583i	−0.0923708	−	0.0775083i
$917$	62.8918			2.07687
$918$	2.40213	−	9.22321i	0.0792822	−	0.304411i
$919$	51.3752			1.69471			0.847355	−	0.531026i	$-0.178193\pi$
$919$	51.3752			1.69471			0.847355	+	0.531026i	$0.178193\pi$
$920$	−0.780442	−	0.654869i	−0.0257304	−	0.0215904i
$921$	47.8883	+	1.28134i	1.57797	+	0.0422216i
$922$	5.51088	+	31.2538i	0.181491	+	1.02929i
$923$	3.59447	+	1.30828i	0.118314	+	0.0430626i
$924$	−2.48580	+	12.1825i	−0.0817767	+	0.400775i
$925$	−1.35359	+	7.67661i	−0.0445059	+	0.252405i
$926$	20.8148	−	36.0523i	0.684018	−	1.18475i
$927$	−3.19112	−	26.2371i	−0.104810	−	0.861739i
$928$	−3.81862	−	6.61405i	−0.125352	−	0.217117i
$929$	−15.7950	+	5.74890i	−0.518217	+	0.188615i	−0.587869	−	0.808956i	$-0.700033\pi$
$929$	−15.7950	+	5.74890i	−0.518217	+	0.188615i	0.0696528	+	0.997571i	$0.477811\pi$
$930$	3.80103	+	25.5329i	0.124641	+	0.837258i
$931$	−0.436444	+	0.366220i	−0.0143039	+	0.0120024i
$932$	−6.72120	+	5.63976i	−0.220160	+	0.184736i
$933$	0.0710504	+	0.477272i	0.00232608	+	0.0156252i
$934$	−14.1700	+	5.15745i	−0.463656	+	0.168757i
$935$	1.82088	+	3.15386i	0.0595492	+	0.103142i
$936$	−34.0613	+	25.6061i	−1.11333	+	0.836963i
$937$	−19.9272	+	34.5149i	−0.650992	+	1.12755i	0.331891	+	0.943318i	$0.392314\pi$
$937$	−19.9272	+	34.5149i	−0.650992	+	1.12755i	−0.982883	+	0.184233i	$0.941020\pi$
$938$	11.3311	−	64.2619i	0.369974	−	2.09823i
$939$	−5.18757	+	25.4234i	−0.169290	+	0.829663i
$940$	0.816515	+	0.297187i	0.0266318	+	0.00969318i
$941$	−3.91468	−	22.2012i	−0.127615	−	0.723740i	−0.979720	−	0.200370i	$-0.935786\pi$
$941$	−3.91468	−	22.2012i	−0.127615	−	0.723740i	0.852105	−	0.523370i	$-0.175325\pi$
$942$	18.3287	+	0.490417i	0.597180	+	0.0159787i
$943$	4.40969	+	3.70017i	0.143599	+	0.120494i
$944$	−22.5818			−0.734974
$945$	−9.79412	+	14.1984i	−0.318603	+	0.461874i
$946$	15.1087			0.491226
$947$	−25.0170	−	20.9918i	−0.812944	−	0.682141i	0.138364	−	0.990381i	$-0.455815\pi$
$947$	−25.0170	−	20.9918i	−0.812944	−	0.682141i	−0.951309	+	0.308240i	$0.900260\pi$
$948$	−6.09347	−	11.2381i	−0.197907	−	0.364995i
$949$	−2.61067	−	14.8058i	−0.0847458	−	0.480617i
$950$	0.217532	+	0.0791751i	0.00705766	+	0.00256878i
$951$	28.7134	+	25.4327i	0.931096	+	0.824712i
$952$	1.40944	−	7.99332i	0.0456801	−	0.259065i
$953$	−4.11444	+	7.12642i	−0.133280	+	0.230847i	−0.924939	−	0.380115i	$-0.875884\pi$
$953$	−4.11444	+	7.12642i	−0.133280	+	0.230847i	0.791659	+	0.610963i	$0.209218\pi$
$954$	−11.7534	+	50.6459i	−0.380530	+	1.63972i
$955$	−4.94299	−	8.56150i	−0.159951	−	0.277044i
$956$	−11.3946	+	4.14729i	−0.368528	+	0.134133i
$957$	−9.25054	+	7.34960i	−0.299028	+	0.237579i
$958$	9.96429	−	8.36103i	0.321932	−	0.270133i
$959$	−46.7528	+	39.2303i	−1.50973	+	1.26681i
$960$	6.20240	+	2.44728i	0.200182	+	0.0789856i
$961$	−49.1353	+	17.8838i	−1.58501	+	0.576897i
$962$	41.5297	+	71.9315i	1.33897	+	2.31916i
$963$	−4.04374	−	7.95872i	−0.130308	−	0.256466i
$964$	6.15857	−	10.6670i	0.198354	−	0.343559i
$965$	−0.441336	+	2.50294i	−0.0142071	+	0.0805725i
$966$	−4.16787	+	1.39191i	−0.134099	+	0.0447839i
$967$	47.4670	+	17.2766i	1.52644	+	0.555577i	0.962745	−	0.270410i	$-0.0871592\pi$
$967$	47.4670	+	17.2766i	1.52644	+	0.555577i	0.563690	+	0.825987i	$0.309381\pi$
$968$	0.184021	+	1.04364i	0.00591467	+	0.0335438i
$969$	0.144219	−	0.235044i	0.00463300	−	0.00755069i
$970$	13.0642	+	10.9621i	0.419465	+	0.351973i
$971$	−18.3764			−0.589726			−0.294863	−	0.955540i	$-0.595274\pi$
$971$	−18.3764			−0.589726			−0.294863	+	0.955540i	$0.595274\pi$
$972$	8.78433	−	5.56107i	0.281758	−	0.178371i
$973$	27.1003			0.868794
$974$	−17.7837	−	14.9223i	−0.569826	−	0.478141i
$975$	−5.91035	+	9.63247i	−0.189283	+	0.308486i
$976$	−1.53513	−	8.70613i	−0.0491382	−	0.278676i
$977$	43.3549	+	15.7799i	1.38705	+	0.504844i	0.924307	−	0.381650i	$-0.124644\pi$
$977$	43.3549	+	15.7799i	1.38705	+	0.504844i	0.462740	+	0.886494i	$0.346866\pi$
$978$	52.7078	−	17.6024i	1.68541	−	0.562861i
$979$	−3.39823	+	19.2723i	−0.108608	+	0.615947i
$980$	1.34031	−	2.32148i	0.0428146	−	0.0741570i
$981$	7.96419	+	15.6748i	0.254277	+	0.500457i
$982$	20.3531	+	35.2527i	0.649495	+	1.12496i
$983$	22.0552	−	8.02744i	0.703452	−	0.256036i	0.0345681	−	0.999402i	$-0.488994\pi$
$983$	22.0552	−	8.02744i	0.703452	−	0.256036i	0.668884	+	0.743367i	$0.266772\pi$
$984$	−43.1438	−	17.0232i	−1.37537	−	0.542681i
$985$	−20.5341	+	17.2302i	−0.654271	+	0.548998i
$986$	−2.95599	+	2.48037i	−0.0941379	+	0.0789910i
$987$	−5.86499	+	4.65976i	−0.186685	+	0.148322i
$988$	0.579653	−	0.210977i	0.0184412	−	0.00671206i
$989$	0.667657	+	1.15642i	0.0212303	+	0.0367719i
$990$	−3.59108	+	15.4741i	−0.114132	+	0.491799i
$991$	5.17587	−	8.96488i	0.164417	−	0.284779i	−0.772031	−	0.635585i	$-0.780759\pi$
$991$	5.17587	−	8.96488i	0.164417	−	0.284779i	0.936448	+	0.350806i	$0.114092\pi$
$992$	5.75311	−	32.6275i	0.182661	−	1.03592i
$993$	−2.35275	−	2.08393i	−0.0746621	−	0.0661314i
$994$	−2.98645	−	1.08698i	−0.0947244	−	0.0344769i
$995$	0.961722	+	5.45420i	0.0304886	+	0.172910i
$996$	−1.26824	−	2.33899i	−0.0401857	−	0.0741136i
$997$	11.6634	+	9.78672i	0.369382	+	0.309948i	0.808517	−	0.588473i	$-0.200271\pi$
$997$	11.6634	+	9.78672i	0.369382	+	0.309948i	−0.439135	+	0.898421i	$0.644715\pi$
$998$	−34.7552			−1.10016
$999$	17.3749	+	36.5883i	0.549718	+	1.15760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.k.a.16.4	✓	30
3.2	odd	2		405.2.k.a.46.2		30
5.2	odd	4		675.2.u.c.124.3		60
5.3	odd	4		675.2.u.c.124.8		60
5.4	even	2		675.2.l.d.151.2		30
27.5	odd	18		405.2.k.a.361.2		30
27.7	even	9		3645.2.a.h.1.12		15
27.20	odd	18		3645.2.a.g.1.4		15
27.22	even	9	inner	135.2.k.a.76.4	yes	30
135.22	odd	36		675.2.u.c.49.8		60
135.49	even	18		675.2.l.d.76.2		30
135.103	odd	36		675.2.u.c.49.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.4	✓	30	1.1	even	1	trivial
135.2.k.a.76.4	yes	30	27.22	even	9	inner
405.2.k.a.46.2		30	3.2	odd	2
405.2.k.a.361.2		30	27.5	odd	18
675.2.l.d.76.2		30	135.49	even	18
675.2.l.d.151.2		30	5.4	even	2
675.2.u.c.49.3		60	135.103	odd	36
675.2.u.c.49.8		60	135.22	odd	36
675.2.u.c.124.3		60	5.2	odd	4
675.2.u.c.124.8		60	5.3	odd	4
3645.2.a.g.1.4		15	27.20	odd	18
3645.2.a.h.1.12		15	27.7	even	9

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25101 + 1.04972i) q^{2} +(-0.905836 + 1.47630i) q^{3} +(0.115814 + 0.656812i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.68292 + 0.895989i) q^{6} +(-0.576430 + 3.26909i) q^{7} +(1.08849 - 1.88532i) q^{8} +(-1.35892 - 2.67457i) q^{9} +O(q^{10})\)	\(q+(1.25101 + 1.04972i) q^{2} +(-0.905836 + 1.47630i) q^{3} +(0.115814 + 0.656812i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.68292 + 0.895989i) q^{6} +(-0.576430 + 3.26909i) q^{7} +(1.08849 - 1.88532i) q^{8} +(-1.35892 - 2.67457i) q^{9} +(0.816539 + 1.41429i) q^{10} +(-3.04687 + 1.10897i) q^{11} +(-1.07456 - 0.423989i) q^{12} +(4.99824 - 4.19402i) q^{13} +(-4.15276 + 3.48458i) q^{14} +(-1.35613 + 1.07745i) q^{15} +(4.59423 - 1.67216i) q^{16} +(-0.561583 - 0.972691i) q^{17} +(1.10753 - 4.77241i) q^{18} +(0.0708761 - 0.122761i) q^{19} +(-0.115814 + 0.656812i) q^{20} +(-4.30401 - 3.81225i) q^{21} +(-4.97577 - 1.81103i) q^{22} +(-0.0812647 - 0.460875i) q^{23} +(1.79731 + 3.31473i) q^{24} +(0.766044 + 0.642788i) q^{25} +10.6554 q^{26} +(5.17943 + 0.416551i) q^{27} -2.21394 q^{28} +(-1.61158 - 1.35227i) q^{29} +(-2.82756 - 0.0756567i) q^{30} +(-1.58476 - 8.98762i) q^{31} +(3.41134 + 1.24163i) q^{32} +(1.12279 - 5.50263i) q^{33} +(0.318509 - 1.80635i) q^{34} +(-1.65976 + 2.87479i) q^{35} +(1.59931 - 1.20231i) q^{36} +(3.89752 + 6.75070i) q^{37} +(0.217532 - 0.0791751i) q^{38} +(1.66404 + 11.1780i) q^{39} +(1.66767 - 1.39934i) q^{40} +(-9.42272 + 7.90660i) q^{41} +(-1.38256 - 9.28718i) q^{42} +(-2.68125 + 0.975897i) q^{43} +(-1.08125 - 1.87279i) q^{44} +(-0.362210 - 2.97805i) q^{45} +(0.382128 - 0.661865i) q^{46} +(0.226235 - 1.28304i) q^{47} +(-1.69301 + 8.29716i) q^{48} +(-3.77686 - 1.37466i) q^{49} +(0.283581 + 1.60827i) q^{50} +(1.94469 + 0.0520337i) q^{51} +(3.33355 + 2.79718i) q^{52} -10.6122 q^{53} +(6.04226 + 5.95807i) q^{54} -3.24241 q^{55} +(5.53586 + 4.64514i) q^{56} +(0.117030 + 0.215836i) q^{57} +(-0.596588 - 3.38342i) q^{58} +(-4.34027 - 1.57973i) q^{59} +(-0.864743 - 0.765940i) q^{60} +(0.313991 - 1.78073i) q^{61} +(7.45195 - 12.9072i) q^{62} +(9.52675 - 2.90074i) q^{63} +(-1.92481 - 3.33388i) q^{64} +(6.13125 - 2.23159i) q^{65} +(7.18086 - 5.70523i) q^{66} +(-9.22089 + 7.73725i) q^{67} +(0.573836 - 0.481506i) q^{68} +(0.754002 + 0.297506i) q^{69} +(-5.09412 + 1.85411i) q^{70} +(0.293127 + 0.507712i) q^{71} +(-6.52161 - 0.349245i) q^{72} +(1.15209 - 1.99548i) q^{73} +(-2.21052 + 12.5365i) q^{74} +(-1.64286 + 0.548651i) q^{75} +(0.0888393 + 0.0323349i) q^{76} +(-1.86902 - 10.5997i) q^{77} +(-9.65206 + 15.7306i) q^{78} +(8.47739 + 7.11338i) q^{79} +4.88907 q^{80} +(-5.30667 + 7.26906i) q^{81} -20.0877 q^{82} +(1.76441 + 1.48051i) q^{83} +(2.00547 - 3.26844i) q^{84} +(-0.195036 - 1.10610i) q^{85} +(-4.37870 - 1.59372i) q^{86} +(3.45619 - 1.15423i) q^{87} +(-1.22573 + 6.95143i) q^{88} +(3.01777 - 5.22692i) q^{89} +(2.67300 - 4.10580i) q^{90} +(10.8295 + 18.7573i) q^{91} +(0.293297 - 0.106751i) q^{92} +(14.7039 + 5.80173i) q^{93} +(1.62986 - 1.36761i) q^{94} +(0.108588 - 0.0911165i) q^{95} +(-4.92313 + 3.91145i) q^{96} +(9.81310 - 3.57168i) q^{97} +(-3.28188 - 5.68438i) q^{98} +(7.10647 + 6.64206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Introduction

L-functions

Modular forms

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