LMFDB - Embedded newform 99.2.m.b.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	99.16
Dual form			99.2.m.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.278917 - 0.0592857i) q^{2} +(-1.04736 + 1.37950i) q^{3} +(-1.75281 - 0.780402i) q^{4} +(-2.64954 + 0.563177i) q^{5} +(0.373912 - 0.322674i) q^{6} +(0.425779 + 4.05102i) q^{7} +(0.904002 + 0.656796i) q^{8} +(-0.806061 - 2.88968i) q^{9} +0.772391 q^{10} +(-3.31056 + 0.200500i) q^{11} +(2.91240 - 1.60065i) q^{12} +(2.57679 - 2.86182i) q^{13} +(0.121410 - 1.15514i) q^{14} +(1.99813 - 4.24490i) q^{15} +(2.35451 + 2.61494i) q^{16} +(-1.33502 + 4.10876i) q^{17} +(0.0535075 + 0.853770i) q^{18} +(1.31246 + 0.953561i) q^{19} +(5.08365 + 1.08056i) q^{20} +(-6.03434 - 3.65553i) q^{21} +(0.935259 + 0.140346i) q^{22} +(0.932117 + 1.61447i) q^{23} +(-1.85287 + 0.559170i) q^{24} +(2.13517 - 0.950641i) q^{25} +(-0.888377 + 0.645443i) q^{26} +(4.83057 + 1.91458i) q^{27} +(2.41511 - 7.43295i) q^{28} +(-0.371426 - 3.53388i) q^{29} +(-0.808974 + 1.06552i) q^{30} +(-3.25505 + 3.61509i) q^{31} +(-1.61909 - 2.80435i) q^{32} +(3.19077 - 4.77692i) q^{33} +(0.615950 - 1.06686i) q^{34} +(-3.40956 - 10.4936i) q^{35} +(-0.842241 + 5.69412i) q^{36} +(-6.26542 + 4.55210i) q^{37} +(-0.309536 - 0.343775i) q^{38} +(1.24905 + 6.55206i) q^{39} +(-2.76508 - 1.23109i) q^{40} +(-0.718335 + 6.83450i) q^{41} +(1.46636 + 1.37734i) q^{42} +(-0.492496 + 0.853027i) q^{43} +(5.95925 + 2.23213i) q^{44} +(3.76310 + 7.20238i) q^{45} +(-0.164268 - 0.505566i) q^{46} +(5.35918 - 2.38606i) q^{47} +(-6.07335 + 0.509254i) q^{48} +(-9.38245 + 1.99430i) q^{49} +(-0.651896 + 0.138565i) q^{50} +(-4.26980 - 6.14502i) q^{51} +(-6.75000 + 3.00529i) q^{52} +(-0.485721 - 1.49489i) q^{53} +(-1.23382 - 0.820393i) q^{54} +(8.65855 - 2.39567i) q^{55} +(-2.27579 + 3.94178i) q^{56} +(-2.69007 + 0.811824i) q^{57} +(-0.105911 + 1.00768i) q^{58} +(10.3802 + 4.62154i) q^{59} +(-6.81507 + 5.88117i) q^{60} +(-5.75953 - 6.39660i) q^{61} +(1.12221 - 0.815335i) q^{62} +(11.3630 - 4.49574i) q^{63} +(-1.88937 - 5.81490i) q^{64} +(-5.21561 + 9.03370i) q^{65} +(-1.17316 + 1.14320i) q^{66} +(0.870282 + 1.50737i) q^{67} +(5.54651 - 6.16003i) q^{68} +(-3.20344 - 0.405082i) q^{69} +(0.328868 + 3.12897i) q^{70} +(-1.77418 + 5.46036i) q^{71} +(1.16925 - 3.14170i) q^{72} +(3.27379 - 2.37855i) q^{73} +(2.01741 - 0.898208i) q^{74} +(-0.924890 + 3.94115i) q^{75} +(-1.55634 - 2.69566i) q^{76} +(-2.22180 - 13.3258i) q^{77} +(0.0400613 - 1.90153i) q^{78} +(4.18662 + 0.889893i) q^{79} +(-7.71104 - 5.60240i) q^{80} +(-7.70053 + 4.65852i) q^{81} +(0.605544 - 1.86367i) q^{82} +(-4.34947 - 4.83058i) q^{83} +(7.72429 + 11.1167i) q^{84} +(1.22322 - 11.6382i) q^{85} +(0.187938 - 0.208726i) q^{86} +(5.26402 + 3.18887i) q^{87} +(-3.12444 - 1.99311i) q^{88} +9.26243 q^{89} +(-0.622594 - 2.23196i) q^{90} +(12.6904 + 9.22014i) q^{91} +(-0.373887 - 3.55729i) q^{92} +(-1.57782 - 8.27667i) q^{93} +(-1.63623 + 0.347790i) q^{94} +(-4.01445 - 1.78735i) q^{95} +(5.56439 + 0.703629i) q^{96} +(7.25070 + 1.54118i) q^{97} +2.73516 q^{98} +(3.24790 + 9.40485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) $ 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.278917	−	0.0592857i	−0.197224	−	0.0419213i	0.108240	−	0.994125i	$-0.465478\pi$
$2$	−0.278917	−	0.0592857i	−0.197224	−	0.0419213i	−0.305465	+	0.952203i	$0.598812\pi$
$3$	−1.04736	+	1.37950i	−0.604695	+	0.796457i
$3$	−1.04736	+	1.37950i	−0.604695	+	0.796457i
$4$	−1.75281	−	0.780402i	−0.876405	−	0.390201i
$5$	−2.64954	+	0.563177i	−1.18491	+	0.251861i	−0.757891	−	0.652381i	$-0.773770\pi$
$5$	−2.64954	+	0.563177i	−1.18491	+	0.251861i	−0.427020	+	0.904242i	$0.640437\pi$
$6$	0.373912	−	0.322674i	0.152649	−	0.131731i
$7$	0.425779	+	4.05102i	0.160930	+	1.53114i	0.715268	+	0.698851i	$0.246305\pi$
$7$	0.425779	+	4.05102i	0.160930	+	1.53114i	−0.554338	+	0.832291i	$0.687029\pi$
$8$	0.904002	+	0.656796i	0.319613	+	0.232212i
$9$	−0.806061	−	2.88968i	−0.268687	−	0.963228i
$10$	0.772391			0.244251
$11$	−3.31056	+	0.200500i	−0.998171	+	0.0604531i
$11$	−3.31056	+	0.200500i	−0.998171	+	0.0604531i
$12$	2.91240	−	1.60065i	0.840736	−	0.462066i
$13$	2.57679	−	2.86182i	0.714674	−	0.793726i	−0.270966	−	0.962589i	$-0.587343\pi$
$13$	2.57679	−	2.86182i	0.714674	−	0.793726i	0.985639	+	0.168863i	$0.0540097\pi$
$14$	0.121410	−	1.15514i	0.0324483	−	0.308725i
$15$	1.99813	−	4.24490i	0.515914	−	1.09603i
$16$	2.35451	+	2.61494i	0.588626	+	0.653736i
$17$	−1.33502	+	4.10876i	−0.323789	+	0.996520i	0.648195	+	0.761474i	$0.275524\pi$
$17$	−1.33502	+	4.10876i	−0.323789	+	0.996520i	−0.971984	+	0.235046i	$0.924476\pi$
$18$	0.0535075	+	0.853770i	0.0126118	+	0.201236i
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	0.728068	−	0.685505i	$-0.240418\pi$
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	−0.426968	+	0.904267i	$0.640418\pi$
$20$	5.08365	+	1.08056i	1.13674	+	0.241621i
$21$	−6.03434	−	3.65553i	−1.31680	−	0.797701i
$22$	0.935259	+	0.140346i	0.199398	+	0.0299218i
$23$	0.932117	+	1.61447i	0.194360	+	0.336641i	0.946691	−	0.322145i	$-0.104404\pi$
$23$	0.932117	+	1.61447i	0.194360	+	0.336641i	−0.752331	+	0.658786i	$0.771070\pi$
$24$	−1.85287	+	0.559170i	−0.378216	+	0.114140i
$25$	2.13517	−	0.950641i	0.427035	−	0.190128i
$26$	−0.888377	+	0.645443i	−0.174225	+	0.126582i
$27$	4.83057	+	1.91458i	0.929643	+	0.368462i
$28$	2.41511	−	7.43295i	0.456413	−	1.40470i
$29$	−0.371426	−	3.53388i	−0.0689720	−	0.656225i	−0.973324	−	0.229437i	$-0.926312\pi$
$29$	−0.371426	−	3.53388i	−0.0689720	−	0.656225i	0.904352	−	0.426788i	$-0.140355\pi$
$30$	−0.808974	+	1.06552i	−0.147698	+	0.194536i
$31$	−3.25505	+	3.61509i	−0.584624	+	0.649290i	−0.960795	−	0.277260i	$-0.910574\pi$
$31$	−3.25505	+	3.61509i	−0.584624	+	0.649290i	0.376171	+	0.926550i	$0.377240\pi$
$32$	−1.61909	−	2.80435i	−0.286218	−	0.495744i
$33$	3.19077	−	4.77692i	0.555441	−	0.831556i
$34$	0.615950	−	1.06686i	0.105634	−	0.182964i
$35$	−3.40956	−	10.4936i	−0.576321	−	1.77374i
$36$	−0.842241	+	5.69412i	−0.140373	+	0.949020i
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.968314	−	0.249734i	$-0.919657\pi$
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.0617145	+	0.998094i	$0.519657\pi$
$38$	−0.309536	−	0.343775i	−0.0502134	−	0.0557676i
$39$	1.24905	+	6.55206i	0.200008	+	1.04917i
$40$	−2.76508	−	1.23109i	−0.437198	−	0.194653i
$41$	−0.718335	+	6.83450i	−0.112185	+	1.06737i	0.783106	+	0.621888i	$0.213634\pi$
$41$	−0.718335	+	6.83450i	−0.112185	+	1.06737i	−0.895291	+	0.445481i	$0.853033\pi$
$42$	1.46636	+	1.37734i	0.226265	+	0.212528i
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	−0.901132	−	0.433545i	$-0.857262\pi$
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	0.826027	+	0.563631i	$0.190596\pi$
$44$	5.95925	+	2.23213i	0.898391	+	0.336506i
$45$	3.76310	+	7.20238i	0.560969	+	1.07367i
$46$	−0.164268	−	0.505566i	−0.0242200	−	0.0745416i
$47$	5.35918	−	2.38606i	0.781716	−	0.348042i	0.0232288	−	0.999730i	$-0.492605\pi$
$47$	5.35918	−	2.38606i	0.781716	−	0.348042i	0.758487	+	0.651688i	$0.225939\pi$
$48$	−6.07335	+	0.509254i	−0.876612	+	0.0735045i
$49$	−9.38245	+	1.99430i	−1.34035	+	0.284900i
$50$	−0.651896	+	0.138565i	−0.0921920	+	0.0195960i
$51$	−4.26980	−	6.14502i	−0.597892	−	0.860475i
$52$	−6.75000	+	3.00529i	−0.936056	+	0.416759i
$53$	−0.485721	−	1.49489i	−0.0667189	−	0.205340i	0.912139	−	0.409881i	$-0.134430\pi$
$53$	−0.485721	−	1.49489i	−0.0667189	−	0.205340i	−0.978858	+	0.204541i	$0.934430\pi$
$54$	−1.23382	−	0.820393i	−0.167902	−	0.111641i
$55$	8.65855	−	2.39567i	1.16752	−	0.323032i
$56$	−2.27579	+	3.94178i	−0.304115	+	0.526743i
$57$	−2.69007	+	0.811824i	−0.356308	+	0.107529i
$58$	−0.105911	+	1.00768i	−0.0139069	+	0.132315i
$59$	10.3802	+	4.62154i	1.35138	+	0.601674i	0.949427	−	0.313986i	$-0.101665\pi$
$59$	10.3802	+	4.62154i	1.35138	+	0.601674i	0.401954	+	0.915660i	$0.368331\pi$
$60$	−6.81507	+	5.88117i	−0.879822	+	0.759256i
$61$	−5.75953	−	6.39660i	−0.737432	−	0.819001i	0.251424	−	0.967877i	$-0.419101\pi$
$61$	−5.75953	−	6.39660i	−0.737432	−	0.819001i	−0.988856	+	0.148876i	$0.952434\pi$
$62$	1.12221	−	0.815335i	0.142521	−	0.103548i
$63$	11.3630	−	4.49574i	1.43160	−	0.566410i
$64$	−1.88937	−	5.81490i	−0.236172	−	0.726862i
$65$	−5.21561	+	9.03370i	−0.646916	+	1.12049i
$66$	−1.17316	+	1.14320i	−0.144406	+	0.140718i
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	0.914277	−	0.405088i	$-0.132759\pi$
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	−0.807956	+	0.589243i	$0.799426\pi$
$68$	5.54651	−	6.16003i	0.672614	−	0.747013i
$69$	−3.20344	−	0.405082i	−0.385649	−	0.0487661i
$70$	0.328868	+	3.12897i	0.0393073	+	0.373984i
$71$	−1.77418	+	5.46036i	−0.210556	+	0.648026i	0.788883	+	0.614543i	$0.210660\pi$
$71$	−1.77418	+	5.46036i	−0.210556	+	0.648026i	−0.999439	+	0.0334822i	$0.989340\pi$
$72$	1.16925	−	3.14170i	0.137798	−	0.370253i
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	−0.379482	−	0.925199i	$-0.623898\pi$
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	0.762650	+	0.646811i	$0.223898\pi$
$74$	2.01741	−	0.898208i	0.234519	−	0.104415i
$75$	−0.924890	+	3.94115i	−0.106797	+	0.455084i
$76$	−1.55634	−	2.69566i	−0.178524	−	0.309213i
$77$	−2.22180	−	13.3258i	−0.253198	−	1.51861i
$78$	0.0400613	−	1.90153i	0.00453605	−	0.215306i
$79$	4.18662	+	0.889893i	0.471031	+	0.100121i	0.437311	−	0.899311i	$-0.355931\pi$
$79$	4.18662	+	0.889893i	0.471031	+	0.100121i	0.0337205	+	0.999431i	$0.489264\pi$
$80$	−7.71104	−	5.60240i	−0.862120	−	0.626367i
$81$	−7.70053	+	4.65852i	−0.855615	+	0.517613i
$82$	0.605544	−	1.86367i	0.0668711	−	0.205808i
$83$	−4.34947	−	4.83058i	−0.477417	−	0.530225i	0.455539	−	0.890216i	$-0.349446\pi$
$83$	−4.34947	−	4.83058i	−0.477417	−	0.530225i	−0.932956	+	0.359991i	$0.882780\pi$
$84$	7.72429	+	11.1167i	0.842789	+	1.21293i
$85$	1.22322	−	11.6382i	0.132677	−	1.26234i
$86$	0.187938	−	0.208726i	0.0202659	−	0.0225075i
$87$	5.26402	+	3.18887i	0.564362	+	0.341883i
$88$	−3.12444	−	1.99311i	−0.333066	−	0.212466i
$89$	9.26243			0.981816			0.490908	−	0.871211i	$-0.336665\pi$
$89$	9.26243			0.981816			0.490908	+	0.871211i	$0.336665\pi$
$90$	−0.622594	−	2.23196i	−0.0656272	−	0.235270i
$91$	12.6904	+	9.22014i	1.33032	+	0.966533i
$92$	−0.373887	−	3.55729i	−0.0389804	−	0.370874i
$93$	−1.57782	−	8.27667i	−0.163612	−	0.858250i
$94$	−1.63623	+	0.347790i	−0.168764	+	0.0358718i
$95$	−4.01445	−	1.78735i	−0.411874	−	0.183378i
$96$	5.56439	+	0.703629i	0.567913	+	0.0718138i
$97$	7.25070	+	1.54118i	0.736197	+	0.156483i	0.560726	−	0.828001i	$-0.310522\pi$
$97$	7.25070	+	1.54118i	0.736197	+	0.156483i	0.175470	+	0.984485i	$0.443855\pi$
$98$	2.73516			0.276293
$99$	3.24790	+	9.40485i	0.326426	+	0.945223i
$100$	−4.48444			−0.448444
$101$	13.4178	+	2.85205i	1.33513	+	0.283790i	0.819527	−	0.573041i	$-0.194236\pi$
$101$	13.4178	+	2.85205i	1.33513	+	0.283790i	0.515598	+	0.856830i	$0.327570\pi$
$102$	0.826609	+	1.96709i	0.0818465	+	0.194771i
$103$	4.63647	+	2.06429i	0.456845	+	0.203400i	0.622239	−	0.782827i	$-0.286223\pi$
$103$	4.63647	+	2.06429i	0.456845	+	0.203400i	−0.165395	+	0.986227i	$0.552890\pi$
$104$	4.20906	−	0.894663i	0.412732	−	0.0877289i
$105$	18.0470	+	6.28706i	1.76120	+	0.613554i
$106$	0.0468500	+	0.445748i	0.00455048	+	0.0432949i
$107$	2.24824	+	1.63344i	0.217346	+	0.157911i	0.691131	−	0.722730i	$-0.257113\pi$
$107$	2.24824	+	1.63344i	0.217346	+	0.157911i	−0.473785	+	0.880640i	$0.657113\pi$
$108$	−6.97293	−	7.12568i	−0.670970	−	0.685669i
$109$	−17.3573			−1.66253			−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573			−1.66253			−0.831263	+	0.555879i	$0.812382\pi$
$110$	−2.55705	+	0.154865i	−0.243805	+	0.0147658i
$111$	0.282539	−	13.4109i	0.0268174	−	1.27290i
$112$	−9.59069	+	10.6515i	−0.906235	+	1.00648i
$113$	−0.0986387	+	0.938485i	−0.00927915	+	0.0882852i	−0.998181	−	0.0602828i	$-0.980800\pi$
$113$	−0.0986387	+	0.938485i	−0.00927915	+	0.0882852i	0.988902	+	0.148568i	$0.0474664\pi$
$114$	0.798435	−	0.0669493i	0.0747803	−	0.00627038i
$115$	−3.37892	−	3.75267i	−0.315086	−	0.349938i
$116$	−2.10681	+	6.48408i	−0.195612	+	0.602032i
$117$	−10.3468	−	5.13931i	−0.956562	−	0.475130i
$118$	−2.62121	−	1.90442i	−0.241302	−	0.175316i
$119$	−17.2131	−	3.65876i	−1.57792	−	0.335398i
$120$	4.59435	−	2.52504i	0.419405	−	0.230504i
$121$	10.9196	−	1.32754i	0.992691	−	0.120685i
$122$	1.22720	+	2.12558i	0.111106	+	0.192441i
$123$	−8.67586	−	8.14915i	−0.782276	−	0.734784i
$124$	8.52671	−	3.79633i	0.765721	−	0.340921i
$125$	5.83521	−	4.23953i	0.521917	−	0.379195i
$126$	−3.43586	+	0.580278i	−0.306091	+	0.0516952i
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	−0.911823	−	0.410583i	$-0.865325\pi$
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	0.979015	+	0.203787i	$0.0653251\pi$
$128$	0.859204	+	8.17478i	0.0759436	+	0.722555i
$129$	−0.660933	−	1.57283i	−0.0581919	−	0.138480i
$130$	1.99029	−	2.21044i	0.174560	−	0.193869i
$131$	−1.99869	−	3.46183i	−0.174626	−	0.302461i	0.765406	−	0.643548i	$-0.222538\pi$
$131$	−1.99869	−	3.46183i	−0.174626	−	0.302461i	−0.940032	+	0.341087i	$0.889205\pi$
$132$	−9.32073	+	5.88297i	−0.811265	+	0.512047i
$133$	−3.30407	+	5.72282i	−0.286500	+	0.496232i
$134$	−0.153371	−	0.472027i	−0.0132492	−	0.0407769i
$135$	−13.8770	−	2.35230i	−1.19435	−	0.202454i
$136$	−3.90547	+	2.83749i	−0.334892	+	0.243313i
$137$	0.728855	+	0.809475i	0.0622703	+	0.0691581i	0.773475	−	0.633827i	$-0.218517\pi$
$137$	0.728855	+	0.809475i	0.0622703	+	0.0691581i	−0.711205	+	0.702985i	$0.751850\pi$
$138$	0.869479	+	0.302902i	0.0740149	+	0.0257848i
$139$	2.63551	+	1.17340i	0.223541	+	0.0995269i	0.515451	−	0.856919i	$-0.327624\pi$
$139$	2.63551	+	1.17340i	0.223541	+	0.0995269i	−0.291910	+	0.956446i	$0.594291\pi$
$140$	−2.21287	+	21.0541i	−0.187022	+	1.77939i
$141$	−2.32143	+	9.89207i	−0.195499	+	0.833063i
$142$	0.818570	−	1.41780i	0.0686929	−	0.118980i
$143$	−7.95683	+	9.99087i	−0.665383	+	0.835478i
$144$	5.65848	−	8.91158i	0.471540	−	0.742632i
$145$	2.97431	+	9.15398i	0.247003	+	0.760197i
$146$	−1.05413	+	0.469329i	−0.0872404	+	0.0388419i
$147$	7.07569	−	15.0319i	0.583593	−	1.23981i
$148$	14.5346	−	3.08942i	1.19473	−	0.253948i
$149$	−19.7339	+	4.19458i	−1.61667	+	0.343633i	−0.925408	−	0.378973i	$-0.876277\pi$
$149$	−19.7339	+	4.19458i	−1.61667	+	0.343633i	−0.691260	+	0.722606i	$0.742944\pi$
$150$	0.491621	−	1.04442i	0.0401407	−	0.0852766i
$151$	−10.1206	+	4.50597i	−0.823601	+	0.366691i	−0.774870	−	0.632121i	$-0.782185\pi$
$151$	−10.1206	+	4.50597i	−0.823601	+	0.366691i	−0.0487316	+	0.998812i	$0.515518\pi$
$152$	0.560175	+	1.72404i	0.0454362	+	0.139838i
$153$	12.9491	+	0.545864i	1.04687	+	0.0441305i
$154$	−0.170330	+	3.84851i	−0.0137255	+	0.310122i
$155$	6.58844	−	11.4115i	0.529196	−	0.916595i
$156$	2.92389	−	12.4593i	0.234098	−	0.997541i
$157$	−0.0347854	+	0.330961i	−0.00277618	+	0.0264136i	−0.995822	−	0.0913125i	$-0.970894\pi$
$157$	−0.0347854	+	0.330961i	−0.00277618	+	0.0264136i	0.993046	+	0.117726i	$0.0375605\pi$
$158$	−1.11496	−	0.496413i	−0.0887016	−	0.0394925i
$159$	2.57094	+	0.895644i	0.203889	+	0.0710292i
$160$	5.86920	+	6.51840i	0.464001	+	0.515325i
$161$	−6.14339	+	4.46344i	−0.484167	+	0.351768i
$162$	2.42399	−	0.842810i	0.190447	−	0.0662174i
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	0.972408	+	0.233285i	$0.0749475\pi$
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	−0.649574	+	0.760299i	$0.725053\pi$
$164$	6.59276	−	11.4190i	0.514808	−	0.891674i
$165$	−5.76381	+	14.4536i	−0.448712	+	1.12521i
$166$	0.926759	+	1.60519i	0.0719304	+	0.124587i
$167$	−12.6567	+	14.0567i	−0.979405	+	1.08774i	0.0167258	+	0.999860i	$0.494676\pi$
$167$	−12.6567	+	14.0567i	−0.979405	+	1.08774i	−0.996131	+	0.0878797i	$0.971991\pi$
$168$	−3.05413	−	7.26794i	−0.235631	−	0.560733i
$169$	−0.191273	−	1.81984i	−0.0147133	−	0.139988i
$170$	−1.03115	+	3.17357i	−0.0790860	+	0.243402i
$171$	1.69756	−	4.56123i	0.129816	−	0.348806i
$172$	1.52896	−	1.11085i	0.116582	−	0.0847016i
$173$	−1.38319	+	0.615835i	−0.105162	+	0.0468211i	−0.458643	−	0.888620i	$-0.651664\pi$
$173$	−1.38319	+	0.615835i	−0.105162	+	0.0468211i	0.353481	+	0.935442i	$0.384998\pi$
$174$	−1.27917	−	1.20151i	−0.0969737	−	0.0910864i
$175$	4.76018	+	8.24487i	0.359836	+	0.623254i
$176$	−8.31903	−	8.18485i	−0.627070	−	0.616956i
$177$	−17.2472	+	9.47903i	−1.29638	+	0.712487i
$178$	−2.58345	−	0.549130i	−0.193638	−	0.0411590i
$179$	−10.6703	−	7.75244i	−0.797537	−	0.579445i	0.112653	−	0.993634i	$-0.464065\pi$
$179$	−10.6703	−	7.75244i	−0.797537	−	0.579445i	−0.910191	+	0.414190i	$0.864065\pi$
$180$	−0.975248	−	15.5611i	−0.0726907	−	1.15986i
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	−0.913754	−	0.406267i	$-0.866830\pi$
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	0.978041	+	0.208414i	$0.0668301\pi$
$182$	−2.99296	−	3.32402i	−0.221853	−	0.246392i
$183$	14.8565	−	1.24572i	1.09822	−	0.0920865i
$184$	−0.217744	+	2.07170i	−0.0160523	+	0.152728i
$185$	14.0369	−	15.5895i	1.03201	−	1.14616i
$186$	−0.0506061	+	2.40205i	−0.00371062	+	0.176127i
$187$	3.59584	−	13.8700i	0.262954	−	1.01427i
$188$	−11.2557			−0.820907
$189$	−5.69926	+	20.3839i	−0.414560	+	1.48271i
$190$	1.01374	+	0.736522i	0.0735441	+	0.0534329i
$191$	1.74997	+	16.6498i	0.126623	+	1.20474i	0.854655	+	0.519197i	$0.173769\pi$
$191$	1.74997	+	16.6498i	0.126623	+	1.20474i	−0.728032	+	0.685544i	$0.759565\pi$
$192$	10.0005	+	3.48391i	0.721726	+	0.251430i
$193$	21.5578	−	4.58224i	1.55176	−	0.329837i	0.649275	−	0.760554i	$-0.275073\pi$
$193$	21.5578	−	4.58224i	1.55176	−	0.329837i	0.902487	+	0.430717i	$0.141739\pi$
$194$	−1.93097	−	0.859725i	−0.138636	−	0.0617247i
$195$	−6.99938	−	16.6565i	−0.501236	−	1.19280i
$196$	18.0020	+	3.82645i	1.28586	+	0.273318i
$197$	18.2247			1.29845			0.649227	−	0.760595i	$-0.275093\pi$
$197$	18.2247			1.29845			0.649227	+	0.760595i	$0.275093\pi$
$198$	−0.348321	−	2.81573i	−0.0247541	−	0.200105i
$199$	−25.0958			−1.77899			−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958			−1.77899			−0.889497	+	0.456942i	$0.848945\pi$
$200$	2.55458	+	0.542993i	0.180636	+	0.0383954i
$201$	−2.99093	−	0.378209i	−0.210964	−	0.0266768i
$202$	−3.57338	−	1.59097i	−0.251422	−	0.111940i
$203$	14.1577	−	3.00931i	0.993674	−	0.211212i
$204$	2.68857	+	14.1032i	0.188237	+	0.987423i
$205$	−1.94578	−	18.5128i	−0.135899	−	1.29299i
$206$	−1.17081	−	0.850642i	−0.0815741	−	0.0592670i
$207$	3.91398	−	3.99489i	0.272040	−	0.277664i
$208$	13.5506			0.939563
$209$	−4.53618	−	2.89367i	−0.313774	−	0.200159i
$210$	−4.66087	−	2.82350i	−0.321631	−	0.194840i
$211$	5.53373	−	6.14582i	0.380957	−	0.423096i	−0.521920	−	0.852995i	$-0.674784\pi$
$211$	5.53373	−	6.14582i	0.380957	−	0.423096i	0.902877	+	0.429899i	$0.141451\pi$
$212$	−0.315242	+	2.99933i	−0.0216509	+	0.205995i
$213$	−5.67438	−	8.16647i	−0.388802	−	0.559557i
$214$	−0.530233	−	0.588884i	−0.0362460	−	0.0402552i
$215$	0.824482	−	2.53749i	0.0562292	−	0.173056i
$216$	3.10935	+	4.90348i	0.211565	+	0.333640i
$217$	−16.0308	−	11.6470i	−1.08824	−	0.790652i
$218$	4.84125	+	1.02904i	0.327891	+	0.0696953i
$219$	−0.147631	+	7.00740i	−0.00997600	+	0.473516i
$220$	−17.0464	−	2.55799i	−1.14927	−	0.172460i
$221$	8.31846	+	14.4080i	0.559560	+	0.969187i
$222$	−0.873878	+	3.72377i	−0.0586508	+	0.249923i
$223$	−6.71646	+	2.99036i	−0.449768	+	0.200249i	−0.619104	−	0.785309i	$-0.712504\pi$
$223$	−6.71646	+	2.99036i	−0.449768	+	0.200249i	0.169337	+	0.985558i	$0.445837\pi$
$224$	10.6711	−	7.75301i	0.712993	−	0.518020i
$225$	−4.46813	−	5.40370i	−0.297875	−	0.360247i
$226$	0.0831507	−	0.255912i	0.00553110	−	0.0170230i
$227$	1.97989	+	18.8374i	0.131410	+	1.25028i	0.839185	+	0.543846i	$0.183032\pi$
$227$	1.97989	+	18.8374i	0.131410	+	1.25028i	−0.707775	+	0.706438i	$0.750301\pi$
$228$	5.34873	+	0.676358i	0.354228	+	0.0447929i
$229$	−5.25900	+	5.84071i	−0.347524	+	0.385965i	−0.891412	−	0.453193i	$-0.850285\pi$
$229$	−5.25900	+	5.84071i	−0.347524	+	0.385965i	0.543888	+	0.839158i	$0.316952\pi$
$230$	0.719959	+	1.24701i	0.0474727	+	0.0822251i
$231$	20.7100	+	10.8919i	1.36262	+	0.716637i
$232$	1.98527	−	3.43859i	0.130339	−	0.225754i
$233$	−2.03006	−	6.24789i	−0.132994	−	0.409313i	0.862279	−	0.506434i	$-0.169037\pi$
$233$	−2.03006	−	6.24789i	−0.132994	−	0.409313i	−0.995273	+	0.0971212i	$0.969037\pi$
$234$	2.58121	+	2.04686i	0.168739	+	0.133807i
$235$	−12.8556	+	9.34013i	−0.838606	+	0.609283i
$236$	−14.5878	−	16.2014i	−0.949584	−	1.05462i
$237$	−5.61252	+	4.84341i	−0.364572	+	0.314613i
$238$	4.58412	+	2.04098i	0.297144	+	0.132297i
$239$	2.67031	−	25.4063i	0.172728	−	1.64340i	−0.473889	−	0.880585i	$-0.657150\pi$
$239$	2.67031	−	25.4063i	0.172728	−	1.64340i	0.646617	−	0.762815i	$-0.276183\pi$
$240$	15.8048	−	4.76966i	1.02019	−	0.307880i
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	−0.814000	−	0.580864i	$-0.802715\pi$
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	0.910044	+	0.414513i	$0.136048\pi$
$242$	−3.12437	−	0.277103i	−0.200842	−	0.0178129i
$243$	1.63880	−	15.5021i	0.105129	−	0.994459i
$244$	5.10344	+	15.7068i	0.326714	+	1.00552i
$245$	23.7360	−	10.5680i	1.51644	−	0.675163i
$246$	1.93672	+	2.78729i	0.123481	+	0.177711i
$247$	6.11086	−	1.29890i	0.388825	−	0.0826473i
$248$	−5.31695	+	1.13015i	−0.337627	+	0.0717647i
$249$	11.2193	−	0.940744i	0.710993	−	0.0596172i
$250$	−1.87888	+	0.836532i	−0.118831	+	0.0529070i
$251$	3.60577	+	11.0974i	0.227594	+	0.700463i	0.998018	+	0.0629308i	$0.0200447\pi$
$251$	3.60577	+	11.0974i	0.227594	+	0.700463i	−0.770424	+	0.637532i	$0.779955\pi$
$252$	−23.4256	−	0.987495i	−1.47567	−	0.0622064i
$253$	−3.40953	−	5.15792i	−0.214355	−	0.324276i
$254$	−0.349364	+	0.605116i	−0.0219211	+	0.0379684i
$255$	14.7738	+	13.8768i	0.925168	+	0.869001i
$256$	−1.03320	+	9.83028i	−0.0645752	+	0.614392i
$257$	18.9327	+	8.42939i	1.18099	+	0.525811i	0.900843	−	0.434146i	$-0.142950\pi$
$257$	18.9327	+	8.42939i	1.18099	+	0.525811i	0.280148	+	0.959957i	$0.409616\pi$
$258$	0.0910993	+	0.477873i	0.00567159	+	0.0297511i
$259$	−21.1083	−	23.4432i	−1.31161	−	1.45669i
$260$	16.1919	−	11.7641i	1.00418	−	0.729578i
$261$	−9.91240	+	3.92182i	−0.613562	+	0.242755i
$262$	0.352231	+	1.08406i	0.0217609	+	0.0669732i
$263$	−4.54273	+	7.86823i	−0.280117	+	0.485176i	−0.971413	−	0.237395i	$-0.923706\pi$
$263$	−4.54273	+	7.86823i	−0.280117	+	0.485176i	0.691297	+	0.722571i	$0.257040\pi$
$264$	6.02193	−	2.22267i	0.370624	−	0.136796i
$265$	2.12883	+	3.68724i	0.130773	+	0.226505i
$266$	1.26084	−	1.40031i	0.0773073	−	0.0858585i
$267$	−9.70113	+	12.7776i	−0.593700	+	0.781974i
$268$	−0.349083	−	3.32131i	−0.0213237	−	0.202881i
$269$	2.45399	−	7.55261i	0.149623	−	0.460491i	−0.847954	−	0.530070i	$-0.822166\pi$
$269$	2.45399	−	7.55261i	0.149623	−	0.460491i	0.997576	+	0.0695792i	$0.0221656\pi$
$270$	3.73109	+	1.47881i	0.227067	+	0.0899973i
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	−0.675512	−	0.737349i	$-0.736077\pi$
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	0.492516	+	0.870303i	$0.336077\pi$
$272$	−13.8875	+	6.18310i	−0.842052	+	0.374906i
$273$	−26.0107	+	7.84966i	−1.57424	+	0.475083i
$274$	−0.155300	−	0.268987i	−0.00938201	−	0.0162501i
$275$	−6.87801	+	3.57526i	−0.414760	+	0.215596i
$276$	5.29890	+	3.21000i	0.318956	+	0.193219i
$277$	3.81540	+	0.810988i	0.229245	+	0.0487275i	0.321102	−	0.947045i	$-0.395947\pi$
$277$	3.81540	+	0.810988i	0.229245	+	0.0487275i	−0.0918567	+	0.995772i	$0.529280\pi$
$278$	−0.665523	−	0.483531i	−0.0399154	−	0.0290003i
$279$	13.0702	+	6.49206i	0.782495	+	0.388670i
$280$	3.80987	−	11.7256i	0.227684	−	0.700738i
$281$	0.0265130	+	0.0294457i	0.00158163	+	0.00175658i	0.743935	−	0.668252i	$-0.232957\pi$
$281$	0.0265130	+	0.0294457i	0.00158163	+	0.00175658i	−0.742353	+	0.670008i	$0.766290\pi$
$282$	1.23394	−	2.62144i	0.0734803	−	0.156105i
$283$	−0.668341	+	6.35884i	−0.0397288	+	0.377994i	0.956534	+	0.291621i	$0.0941945\pi$
$283$	−0.668341	+	6.35884i	−0.0397288	+	0.377994i	−0.996263	+	0.0863734i	$0.972472\pi$
$284$	7.37107	−	8.18641i	0.437393	−	0.485774i
$285$	6.67024	−	3.66595i	0.395111	−	0.217152i
$286$	2.81161	−	2.31490i	0.166254	−	0.136883i
$287$	−27.9925			−1.65235
$288$	−6.79859	+	6.93914i	−0.400611	+	0.408893i
$289$	−1.34634	−	0.978174i	−0.0791965	−	0.0575397i
$290$	−0.286886	−	2.72954i	−0.0168465	−	0.160284i
$291$	−9.72018	+	8.38819i	−0.569807	+	0.491724i
$292$	−7.59455	+	1.61427i	−0.444438	+	0.0944681i
$293$	−21.3837	−	9.52066i	−1.24925	−	0.556203i	−0.327819	−	0.944741i	$-0.606314\pi$
$293$	−21.3837	−	9.52066i	−1.24925	−	0.556203i	−0.921433	+	0.388538i	$0.872980\pi$
$294$	−2.86471	+	3.77316i	−0.167073	+	0.220055i
$295$	−30.1054	−	6.39910i	−1.75280	−	0.372570i
$296$	−8.65375			−0.502989
$297$	−16.3757	−	5.36981i	−0.950217	−	0.311588i
$298$	5.75282			0.333252
$299$	7.02221	+	1.49262i	0.406105	+	0.0863202i
$300$	4.69683	−	6.18630i	0.271172	−	0.357166i
$301$	−3.66533	−	1.63191i	−0.211266	−	0.0940616i
$302$	3.08994	−	0.656788i	0.177806	−	0.0377939i
$303$	−17.9878	+	15.5228i	−1.03337	+	0.891763i
$304$	0.596696	+	5.67718i	0.0342229	+	0.325609i
$305$	18.8625	+	13.7044i	1.08007	+	0.784713i
$306$	−3.57937	−	0.919948i	−0.204619	−	0.0525899i
$307$	29.1494			1.66365			0.831823	−	0.555042i	$-0.187298\pi$
$307$	29.1494			1.66365			0.831823	+	0.555042i	$0.187298\pi$
$308$	−6.50506	+	25.0915i	−0.370660	+	1.42972i
$309$	−7.70376	+	4.23397i	−0.438252	+	0.240862i
$310$	−2.51417	+	2.79227i	−0.142795	+	0.158590i
$311$	2.05981	−	19.5978i	0.116801	−	1.11129i	−0.766423	−	0.642337i	$-0.777965\pi$
$311$	2.05981	−	19.5978i	0.116801	−	1.11129i	0.883224	−	0.468952i	$-0.155368\pi$
$312$	−3.17422	+	6.74345i	−0.179705	+	0.381772i
$313$	0.895549	+	0.994608i	0.0506194	+	0.0562185i	0.767923	−	0.640542i	$-0.221290\pi$
$313$	0.895549	+	0.994608i	0.0506194	+	0.0562185i	−0.717303	+	0.696761i	$0.754624\pi$
$314$	0.0293235	−	0.0902485i	0.00165482	−	0.00509302i
$315$	−27.5747	+	18.3110i	−1.55366	+	1.03171i
$316$	−6.64387	−	4.82706i	−0.373747	−	0.271543i
$317$	−3.91346	−	0.831832i	−0.219802	−	0.0467203i	0.0966942	−	0.995314i	$-0.469173\pi$
$317$	−3.91346	−	0.831832i	−0.219802	−	0.0467203i	−0.316496	+	0.948594i	$0.602506\pi$
$318$	−0.663980	−	0.402230i	−0.0372342	−	0.0225560i
$319$	1.93817	+	11.6246i	0.108517	+	0.650855i
$320$	8.28080	+	14.3428i	0.462911	+	0.801785i
$321$	−4.60806	+	1.39065i	−0.257197	+	0.0776184i
$322$	1.97812	−	0.880714i	0.110236	−	0.0490803i
$323$	−5.67011	+	4.11958i	−0.315493	+	0.229219i
$324$	17.1331	−	2.15600i	0.951838	−	0.119778i
$325$	2.78134	−	8.56008i	0.154281	−	0.474828i
$326$	−0.397555	−	3.78248i	−0.0220185	−	0.209492i
$327$	18.1794	−	23.9444i	1.00532	−	1.32413i
$328$	−5.13825	+	5.70660i	−0.283712	+	0.315094i
$329$	11.9478	+	20.6942i	0.658704	+	1.14091i
$330$	2.46452	−	3.68965i	0.135667	−	0.203109i
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	−0.906413	−	0.422393i	$-0.861190\pi$
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	0.819009	+	0.573780i	$0.194524\pi$
$332$	3.85401	+	11.8614i	0.211516	+	0.650980i
$333$	18.2044	+	14.4358i	0.997596	+	0.791078i
$334$	4.36353	−	3.17029i	0.238762	−	0.173471i
$335$	−3.15477	−	3.50372i	−0.172363	−	0.191429i
$336$	−4.64891	−	24.3864i	−0.253619	−	1.33039i
$337$	−16.6245	−	7.40171i	−0.905595	−	0.403197i	−0.0995376	−	0.995034i	$-0.531736\pi$
$337$	−16.6245	−	7.40171i	−0.905595	−	0.403197i	−0.806058	+	0.591837i	$0.798403\pi$
$338$	−0.0545411	+	0.518924i	−0.00296665	+	0.0282258i
$339$	−1.19133	−	1.11901i	−0.0647043	−	0.0607761i
$340$	−11.2265	+	19.4449i	−0.608844	+	1.05455i
$341$	10.0512	−	12.6206i	0.544303	−	0.683445i
$342$	−0.743895	+	1.17156i	−0.0402252	+	0.0633510i
$343$	−3.26270	−	10.0416i	−0.176169	−	0.542193i
$344$	−1.00548	+	0.447669i	−0.0542120	+	0.0241367i
$345$	8.71578	−	0.730824i	0.469242	−	0.0393462i
$346$	0.422305	−	0.0897637i	0.0227033	−	0.00482573i
$347$	26.8150	−	5.69971i	1.43951	−	0.305977i	0.578963	−	0.815354i	$-0.303457\pi$
$347$	26.8150	−	5.69971i	1.43951	−	0.305977i	0.860543	+	0.509377i	$0.170124\pi$
$348$	−6.73823	−	9.69754i	−0.361207	−	0.519843i
$349$	20.9252	−	9.31652i	1.12010	−	0.498702i	0.238712	−	0.971090i	$-0.423275\pi$
$349$	20.9252	−	9.31652i	1.12010	−	0.498702i	0.881390	+	0.472389i	$0.156608\pi$
$350$	−0.838893	−	2.58185i	−0.0448407	−	0.138006i
$351$	17.9266	−	8.89072i	0.956849	−	0.474552i
$352$	5.92237	+	8.95933i	0.315663	+	0.477534i
$353$	14.8524	−	25.7250i	0.790511	−	1.36921i	−0.135140	−	0.990827i	$-0.543148\pi$
$353$	14.8524	−	25.7250i	0.790511	−	1.36921i	0.925651	−	0.378379i	$-0.123518\pi$
$354$	5.37252	−	1.62135i	0.285546	−	0.0861738i
$355$	1.62561	−	15.4666i	0.0862783	−	0.820883i
$356$	−16.2353	−	7.22842i	−0.860469	−	0.383105i
$357$	23.0756	−	19.9135i	1.22129	−	1.05393i
$358$	2.51653	+	2.79489i	0.133003	+	0.147714i
$359$	29.8183	−	21.6643i	1.57375	−	1.14340i	0.650299	−	0.759678i	$-0.274644\pi$
$359$	29.8183	−	21.6643i	1.57375	−	1.14340i	0.923450	−	0.383718i	$-0.125356\pi$
$360$	−1.32865	+	8.98255i	−0.0700258	+	0.473422i
$361$	−5.05804	−	15.5670i	−0.266213	−	0.819318i
$362$	−0.399041	+	0.691159i	−0.0209731	+	0.0363265i
$363$	−9.60544	+	16.4540i	−0.504155	+	0.863613i
$364$	−15.0485	−	26.0648i	−0.788756	−	1.36617i
$365$	−7.33449	+	8.14578i	−0.383905	+	0.426370i
$366$	−4.21757	−	0.533321i	−0.220456	−	0.0278772i
$367$	2.59864	+	24.7244i	0.135648	+	1.29061i	0.824566	+	0.565766i	$0.191419\pi$
$367$	2.59864	+	24.7244i	0.135648	+	1.29061i	−0.688918	+	0.724839i	$0.741914\pi$
$368$	−2.02708	+	6.23872i	−0.105669	+	0.325216i
$369$	20.3286	−	3.43326i	1.05826	−	0.178729i
$370$	−4.83936	+	3.51600i	−0.251586	+	0.182788i
$371$	5.84904	−	2.60416i	0.303667	−	0.135201i
$372$	−3.69350	+	15.7388i	−0.191499	+	0.816017i
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	0.526304	−	0.850297i	$-0.323578\pi$
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	−0.999530	+	0.0306440i	$0.990244\pi$
$374$	−1.82523	+	3.65539i	−0.0943805	+	0.189016i
$375$	−0.263138	+	12.4900i	−0.0135884	+	0.644981i
$376$	6.41186	+	1.36288i	0.330667	+	0.0702853i
$377$	−11.0704	−	8.04312i	−0.570155	−	0.414242i
$378$	2.79810	−	5.34754i	0.143919	−	0.275048i
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	0.310697	+	0.950509i	$0.399438\pi$
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	−0.810054	+	0.586355i	$0.800562\pi$
$380$	5.64172	+	6.26577i	0.289414	+	0.321427i
$381$	2.42181	+	3.48543i	0.124073	+	0.178564i
$382$	0.499001	−	4.74767i	0.0255311	−	0.242912i
$383$	−8.31848	+	9.23861i	−0.425054	+	0.472071i	−0.917191	−	0.398447i	$-0.869549\pi$
$383$	−8.31848	+	9.23861i	−0.425054	+	0.472071i	0.492137	+	0.870518i	$0.336216\pi$
$384$	−12.1770	−	7.37668i	−0.621407	−	0.376440i
$385$	13.3915	+	34.0559i	0.682495	+	1.73565i
$386$	−6.28449			−0.319872
$387$	2.86196	+	0.735564i	0.145482	+	0.0373908i
$388$	−11.5064	−	8.35986i	−0.584147	−	0.424408i
$389$	−0.765115	−	7.27958i	−0.0387929	−	0.369090i	−0.996646	−	0.0818317i	$-0.973923\pi$
$389$	−0.765115	−	7.27958i	−0.0387929	−	0.369090i	0.957853	−	0.287258i	$-0.0927437\pi$
$390$	0.964756	+	5.06075i	0.0488523	+	0.256261i
$391$	−7.87788	+	1.67449i	−0.398401	+	0.0846829i
$392$	−9.79160	−	4.35950i	−0.494551	−	0.220188i
$393$	6.86895	+	0.868594i	0.346493	+	0.0438148i
$394$	−5.08317	−	1.08046i	−0.256087	−	0.0544329i
$395$	−11.5938			−0.583346
$396$	1.64661	−	19.0196i	0.0827455	−	0.955770i
$397$	34.2087			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$398$	6.99965	+	1.48782i	0.350861	+	0.0745777i
$399$	−4.43409	−	10.5519i	−0.221982	−	0.528254i
$400$	7.51315	+	3.34507i	0.375658	+	0.167254i
$401$	−7.31241	+	1.55430i	−0.365164	+	0.0776181i	−0.386840	−	0.922147i	$-0.626433\pi$
$401$	−7.31241	+	1.55430i	−0.365164	+	0.0776181i	0.0216754	+	0.999765i	$0.493100\pi$
$402$	0.811798	+	0.282808i	0.0404888	+	0.0141052i
$403$	1.95817	+	18.6307i	0.0975432	+	0.928061i
$404$	−21.2932	−	15.4704i	−1.05938	−	0.769682i
$405$	17.7793	−	16.6797i	0.883461	−	0.828821i
$406$	−4.12723			−0.204831
$407$	19.8294	−	16.3262i	0.982904	−	0.809260i
$408$	0.176117	−	8.35950i	0.00871910	−	0.413857i
$409$	1.61274	−	1.79113i	0.0797447	−	0.0885655i	−0.701952	−	0.712224i	$-0.747688\pi$
$409$	1.61274	−	1.79113i	0.0797447	−	0.0885655i	0.781697	+	0.623659i	$0.214355\pi$
$410$	−0.554835	+	5.27891i	−0.0274014	+	0.260707i
$411$	−1.88005	+	0.157643i	−0.0927360	+	0.00777598i
$412$	−6.51588	−	7.23662i	−0.321014	−	0.356522i
$413$	−14.3023	+	44.0180i	−0.703771	+	2.16598i
$414$	−1.32851	+	0.882200i	−0.0652929	+	0.0433578i
$415$	14.2446	+	10.3493i	0.699239	+	0.508027i
$416$	−12.1976	−	2.59268i	−0.598037	−	0.127117i
$417$	−4.37905	+	2.40672i	−0.214443	+	0.117857i
$418$	1.09366	+	1.07602i	0.0534929	+	0.0526301i
$419$	5.60088	+	9.70101i	0.273621	+	0.473925i	0.969786	−	0.243956i	$-0.0784453\pi$
$419$	5.60088	+	9.70101i	0.273621	+	0.473925i	−0.696165	+	0.717881i	$0.745112\pi$
$420$	−26.7265	−	25.1039i	−1.30412	−	1.22494i
$421$	−6.30791	+	2.80846i	−0.307429	+	0.136876i	−0.554652	−	0.832083i	$-0.687149\pi$
$421$	−6.30791	+	2.80846i	−0.307429	+	0.136876i	0.247223	+	0.968959i	$0.420482\pi$
$422$	−1.90781	+	1.38611i	−0.0928708	+	0.0674746i
$423$	−11.2148	−	13.5630i	−0.545281	−	0.659456i
$424$	0.542748	−	1.67041i	0.0263582	−	0.0811222i
$425$	1.05546	+	10.0420i	0.0511974	+	0.487110i
$426$	1.09853	+	2.61418i	0.0532238	+	0.126657i
$427$	23.4605	−	26.0555i	1.13533	−	1.26091i
$428$	−2.66600	−	4.61765i	−0.128866	−	0.223202i
$429$	−5.44875	−	21.4405i	−0.263068	−	1.03516i
$430$	−0.380399	+	0.658871i	−0.0183445	+	0.0317736i
$431$	−9.01729	−	27.7524i	−0.434348	−	1.33678i	−0.893754	−	0.448558i	$-0.851938\pi$
$431$	−9.01729	−	27.7524i	−0.434348	−	1.33678i	0.459406	−	0.888226i	$-0.348062\pi$
$432$	6.36707	+	17.1396i	0.306336	+	0.824627i
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.428785	−	0.903407i	$-0.358942\pi$
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.991693	−	0.128630i	$-0.0410581\pi$
$434$	3.78075	+	4.19895i	0.181482	+	0.201556i
$435$	−15.7431	−	5.48447i	−0.754825	−	0.262960i
$436$	30.4240	+	13.5457i	1.45705	+	0.648719i
$437$	−0.316129	+	3.00777i	−0.0151225	+	0.143881i
$438$	0.456616	−	1.94573i	0.0218179	−	0.0929707i
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	−0.486877	−	0.873470i	$-0.661864\pi$
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	0.999886	−	0.0150869i	$-0.00480250\pi$
$440$	9.40081	+	3.52121i	0.448166	+	0.167867i
$441$	13.3257	+	25.5048i	0.634558	+	1.21451i
$442$	−1.46597	−	4.51180i	−0.0697293	−	0.214605i
$443$	−30.5535	+	13.6033i	−1.45164	+	0.646313i	−0.972812	−	0.231595i	$-0.925605\pi$
$443$	−30.5535	+	13.6033i	−1.45164	+	0.646313i	−0.478830	+	0.877908i	$0.658939\pi$
$444$	−10.9611	+	23.2862i	−0.520191	+	1.10512i
$445$	−24.5412	+	5.21639i	−1.16336	+	0.247281i
$446$	2.05062	−	0.435873i	0.0970998	−	0.0206392i
$447$	14.8822	−	31.6163i	0.703902	−	1.49540i
$448$	22.7518	−	10.1298i	1.07492	−	0.478586i
$449$	12.2165	+	37.5984i	0.576530	+	1.77438i	0.630908	+	0.775858i	$0.282682\pi$
$449$	12.2165	+	37.5984i	0.576530	+	1.77438i	−0.0543777	+	0.998520i	$0.517318\pi$
$450$	0.925876	+	1.77208i	0.0436462	+	0.0835367i
$451$	1.00777	−	22.7700i	0.0474540	−	1.07220i
$452$	0.905290	−	1.56801i	0.0425813	−	0.0737529i
$453$	4.38392	−	18.6808i	0.205974	−	0.877699i
$454$	0.564564	−	5.37146i	0.0264963	−	0.252095i
$455$	−38.8164	−	17.2822i	−1.81974	−	0.810201i
$456$	−2.96503	−	1.03293i	−0.138850	−	0.0483716i
$457$	25.1006	+	27.8771i	1.17416	+	1.30404i	0.943642	+	0.330967i	$0.107375\pi$
$457$	25.1006	+	27.8771i	1.17416	+	1.30404i	0.230516	+	0.973069i	$0.425959\pi$
$458$	1.81309	−	1.31729i	0.0847204	−	0.0615529i
$459$	−14.3154	+	17.2916i	−0.668188	+	0.807104i
$460$	2.99402	+	9.21464i	0.139597	+	0.429635i
$461$	−9.68265	+	16.7708i	−0.450966	+	0.781096i	−0.998446	−	0.0557228i	$-0.982254\pi$
$461$	−9.68265	+	16.7708i	−0.450966	+	0.781096i	0.547480	+	0.836818i	$0.315587\pi$
$462$	−5.13063	−	4.26576i	−0.238699	−	0.198461i
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	0.983183	−	0.182625i	$-0.0584594\pi$
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	−0.649749	+	0.760149i	$0.725126\pi$
$464$	8.36637	−	9.29180i	0.388399	−	0.431361i
$465$	8.84174	+	21.0408i	0.410026	+	0.975743i
$466$	0.195809	+	1.86300i	0.00907067	+	0.0863017i
$467$	−6.89755	+	21.2285i	−0.319180	+	0.982336i	0.654819	+	0.755786i	$0.272745\pi$
$467$	−6.89755	+	21.2285i	−0.319180	+	0.982336i	−0.973999	+	0.226551i	$0.927255\pi$
$468$	14.1253	+	17.0829i	0.652940	+	0.789657i
$469$	−5.73585	+	4.16734i	−0.264857	+	0.192430i
$470$	4.13938	−	1.84297i	0.190935	−	0.0850099i
$471$	−0.420129	−	0.394623i	−0.0193585	−	0.0181833i
$472$	6.34827	+	10.9955i	0.292203	+	0.506110i
$473$	1.45940	−	2.92274i	0.0671034	−	0.134388i
$474$	1.85257	−	1.01817i	0.0850915	−	0.0467660i
$475$	3.70883	+	0.788336i	0.170173	+	0.0361714i
$476$	27.3160	+	19.8462i	1.25203	+	0.909651i
$477$	−3.92825	+	2.60856i	−0.179862	+	0.119438i
$478$	−2.25103	+	6.92795i	−0.102960	+	0.316877i
$479$	−15.5651	−	17.2868i	−0.711186	−	0.789852i	0.273929	−	0.961750i	$-0.411677\pi$
$479$	−15.5651	−	17.2868i	−0.711186	−	0.789852i	−0.985115	+	0.171898i	$0.945010\pi$
$480$	−15.1393	+	1.26944i	−0.691013	+	0.0579419i
$481$	−3.11742	+	29.6603i	−0.142142	+	1.35239i
$482$	−0.568967	+	0.631902i	−0.0259157	+	0.0287823i
$483$	0.277036	−	13.1497i	0.0126056	−	0.598331i
$484$	−20.1760	−	6.19475i	−0.917091	−	0.281580i
$485$	−20.0790			−0.911740
$486$	−1.37614	+	4.22664i	−0.0624231	+	0.191724i
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	0.582810	−	0.812608i	$-0.301953\pi$
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	−0.592738	+	0.805395i	$0.701953\pi$
$488$	−1.00536	−	9.56538i	−0.0455106	−	0.433004i
$489$	−21.8162	−	7.60017i	−0.986563	−	0.343691i
$490$	−7.24692	+	1.54038i	−0.327382	+	0.0695873i
$491$	−3.84288	−	1.71096i	−0.173427	−	0.0772146i	0.318187	−	0.948028i	$-0.396926\pi$
$491$	−3.84288	−	1.71096i	−0.173427	−	0.0772146i	−0.491614	+	0.870813i	$0.663593\pi$
$492$	8.84753	+	21.0546i	0.398878	+	0.949213i
$493$	15.0157	+	3.19169i	0.676274	+	0.143746i
$494$	−1.78143			−0.0801504
$495$	−13.9020	−	23.0894i	−0.624850	−	1.03779i
$496$	−17.1173			−0.768589
$497$	−22.8754	−	4.86233i	−1.02610	−	0.218105i
$498$	−3.18502	−	0.402753i	−0.142724	−	0.0180478i
$499$	−14.0359	−	6.24920i	−0.628334	−	0.279752i	0.0677612	−	0.997702i	$-0.478414\pi$
$499$	−14.0359	−	6.24920i	−0.628334	−	0.279752i	−0.696096	+	0.717949i	$0.745081\pi$
$500$	−13.5365	+	2.87728i	−0.605373	+	0.128676i
$501$	−6.13510	−	32.1824i	−0.274096	−	1.43781i
$502$	−0.347793	−	3.30903i	−0.0155228	−	0.147689i
$503$	−3.16786	−	2.30159i	−0.141248	−	0.102623i	0.514917	−	0.857240i	$-0.327823\pi$
$503$	−3.16786	−	2.30159i	−0.141248	−	0.102623i	−0.656165	+	0.754617i	$0.727823\pi$
$504$	13.2249	+	3.39899i	0.589085	+	0.151403i
$505$	−37.1573			−1.65348
$506$	0.645186	+	1.64077i	0.0286820	+	0.0729411i
$507$	2.71081	+	1.64217i	0.120391	+	0.0729314i
$508$	−3.14596	+	3.49394i	−0.139579	+	0.155019i
$509$	−2.98422	+	28.3930i	−0.132273	+	1.25850i	0.704006	+	0.710194i	$0.251393\pi$
$509$	−2.98422	+	28.3930i	−0.132273	+	1.25850i	−0.836280	+	0.548303i	$0.815274\pi$
$510$	−3.29796	−	4.74636i	−0.146036	−	0.210172i
$511$	11.0295	+	12.2494i	0.487914	+	0.541884i
$512$	5.95109	−	18.3156i	0.263004	−	0.809442i
$513$	4.51427	+	7.11906i	0.199310	+	0.314314i
$514$	−4.78092	−	3.47354i	−0.210877	−	0.153211i
$515$	−13.4471	−	2.85826i	−0.592549	−	0.125950i
$516$	−0.0689482	+	3.27266i	−0.00303528	+	0.144071i
$517$	−17.2635	+	8.97371i	−0.759246	+	0.394663i
$518$	4.49763	+	7.79012i	0.197615	+	0.342278i
$519$	0.599153	−	2.55312i	0.0262999	−	0.112069i
$520$	−10.6482	+	4.74089i	−0.466955	+	0.207902i
$521$	11.5485	−	8.39049i	0.505950	−	0.367594i	−0.305335	−	0.952245i	$-0.598768\pi$
$521$	11.5485	−	8.39049i	0.505950	−	0.367594i	0.811285	+	0.584651i	$0.198768\pi$
$522$	2.99725	−	0.506201i	0.131186	−	0.0221558i
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	0.431088	+	0.902310i	$0.358130\pi$
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	−0.879122	+	0.476597i	$0.841870\pi$
$524$	0.801704	+	7.62771i	0.0350226	+	0.333218i
$525$	−16.3595	−	2.06869i	−0.713986	−	0.0902850i
$526$	1.73352	−	1.92527i	0.0755850	−	0.0839456i
$527$	−10.5080	−	18.2004i	−0.457736	−	0.792822i
$528$	20.0041	−	2.90362i	0.870565	−	0.126364i
$529$	9.76231	−	16.9088i	0.424448	−	0.735166i
$530$	−0.375166	−	1.15464i	−0.0162962	−	0.0501545i
$531$	4.98775	−	33.7206i	0.216450	−	1.46335i
$532$	10.2575	−	7.45252i	0.444720	−	0.323108i
$533$	17.7081	+	19.6668i	0.767023	+	0.851865i
$534$	3.46334	−	2.98874i	0.149873	−	0.129336i
$535$	−6.87672	−	3.06171i	−0.297307	−	0.132369i
$536$	−0.203299	+	1.93427i	−0.00878120	+	0.0835475i
$537$	21.8702	−	6.60013i	0.943770	−	0.284816i
$538$	−1.13222	+	1.96107i	−0.0488136	+	0.0845476i
$539$	30.6613	−	8.48344i	1.32068	−	0.365407i
$540$	22.4881	+	14.9528i	0.967733	+	0.643466i
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	−0.941348	−	0.337437i	$-0.890440\pi$
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	0.563226	−	0.826303i	$-0.309560\pi$
$542$	0.969992	−	0.431868i	0.0416647	−	0.0185503i
$543$	2.76618	+	3.98103i	0.118708	+	0.170842i
$544$	13.6839	−	2.90860i	0.586693	−	0.124705i
$545$	45.9888	−	9.77523i	1.96995	−	0.418725i
$546$	7.72020	−	0.647344i	0.330394	−	0.0277038i
$547$	−28.0884	+	12.5058i	−1.20098	+	0.534709i	−0.907011	−	0.421108i	$-0.861641\pi$
$547$	−28.0884	+	12.5058i	−1.20098	+	0.534709i	−0.293965	+	0.955816i	$0.594975\pi$
$548$	−0.645829	−	1.98766i	−0.0275884	−	0.0849085i
$549$	−13.8416	+	21.7993i	−0.590746	+	0.930370i
$550$	2.13036	−	0.589432i	0.0908388	−	0.0251335i
$551$	2.88228	−	4.99226i	0.122789	−	0.212678i
$552$	−2.62986	−	2.47020i	−0.111934	−	0.105139i
$553$	−1.82240	+	17.3390i	−0.0774963	+	0.737328i
$554$	−1.01610	−	0.452397i	−0.0431700	−	0.0192205i
$555$	6.80410	+	35.6918i	0.288818	+	1.51503i
$556$	−3.70382	−	4.11351i	−0.157077	−	0.174452i
$557$	5.90145	−	4.28765i	0.250052	−	0.181674i	−0.455698	−	0.890135i	$-0.650610\pi$
$557$	5.90145	−	4.28765i	0.250052	−	0.181674i	0.705750	+	0.708461i	$0.250610\pi$
$558$	−3.26063	−	2.58563i	−0.138033	−	0.109458i
$559$	1.17215	+	3.60751i	0.0495767	+	0.152581i
$560$	19.4122	−	33.6230i	0.820316	−	1.42083i
$561$	15.3675	+	19.4874i	0.648817	+	0.822757i
$562$	−0.00564923	−	0.00978475i	−0.000238298	−	0.000412745i
$563$	−24.4724	+	27.1794i	−1.03139	+	1.14547i	−0.0421581	+	0.999111i	$0.513423\pi$
$563$	−24.4724	+	27.1794i	−1.03139	+	1.14547i	−0.989231	+	0.146363i	$0.953243\pi$
$564$	11.7888	−	15.5273i	0.496399	−	0.653817i
$565$	−0.267186	−	2.54211i	−0.0112406	−	0.106947i
$566$	0.563400	−	1.73397i	0.0236815	−	0.0728841i
$567$	−22.1505	−	29.2115i	−0.930233	−	1.22677i
$568$	−5.19020	+	3.77090i	−0.217776	+	0.158224i
$569$	0.138387	−	0.0616140i	0.00580150	−	0.00258299i	−0.403834	−	0.914832i	$-0.632323\pi$
$569$	0.138387	−	0.0616140i	0.00580150	−	0.00258299i	0.409635	+	0.912249i	$0.365656\pi$
$570$	−2.07778	+	0.627046i	−0.0870288	+	0.0262641i
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.821637	−	0.570012i	$-0.806939\pi$
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.0828262	−	0.996564i	$-0.526395\pi$
$572$	21.7437	−	11.3026i	0.909150	−	0.472584i
$573$	−24.8014	−	15.0243i	−1.03609	−	0.627651i
$574$	7.80760	+	1.65956i	0.325883	+	0.0692686i
$575$	3.52502	+	2.56108i	0.147003	+	0.106804i
$576$	−15.2803	+	10.1469i	−0.636677	+	0.422786i
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	−0.569011	−	0.822330i	$-0.692674\pi$
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	0.943693	−	0.330822i	$-0.107326\pi$
$578$	0.317526	+	0.352648i	0.0132073	+	0.0146682i
$579$	−16.2576	+	34.5383i	−0.675642	+	1.43536i
$580$	1.93038	−	18.3664i	0.0801547	−	0.762621i
$581$	17.7169	−	19.6766i	0.735019	−	0.816322i
$582$	3.20842	−	1.76334i	0.132993	−	0.0730929i
$583$	1.90773	+	4.85155i	0.0790103	+	0.200931i
$584$	4.52173			0.187111
$585$	30.3086	+	7.78974i	1.25311	+	0.322066i
$586$	5.39985	+	3.92322i	0.223066	+	0.162067i
$587$	2.37226	+	22.5706i	0.0979137	+	0.931586i	0.927655	+	0.373438i	$0.121821\pi$
$587$	2.37226	+	22.5706i	0.0979137	+	0.931586i	−0.829741	+	0.558148i	$0.811512\pi$
$588$	−24.1332	+	20.8262i	−0.995238	+	0.858857i
$589$	−7.71934	+	1.64080i	−0.318070	+	0.0676078i
$590$	8.01754	+	3.56964i	0.330077	+	0.146960i
$591$	−19.0878	+	25.1410i	−0.785169	+	1.03416i
$592$	−26.6554	−	5.66579i	−1.09553	−	0.232863i
$593$	−22.9308			−0.941656			−0.470828	−	0.882225i	$-0.656045\pi$
$593$	−22.9308			−0.941656			−0.470828	+	0.882225i	$0.656045\pi$
$594$	4.24913	+	2.46858i	0.174344	+	0.101287i
$595$	47.6673			1.95417
$596$	37.8633	+	8.04810i	1.55094	+	0.329663i
$597$	26.2844	−	34.6197i	1.07575	−	1.41689i
$598$	−1.87012	−	0.832633i	−0.0764750	−	0.0340489i
$599$	12.2275	−	2.59904i	0.499603	−	0.106194i	0.0487841	−	0.998809i	$-0.484465\pi$
$599$	12.2275	−	2.59904i	0.499603	−	0.106194i	0.450819	+	0.892615i	$0.351132\pi$
$600$	−3.42463	+	2.95534i	−0.139810	+	0.120651i
$601$	−2.34968	−	22.3557i	−0.0958453	−	0.911907i	−0.931767	−	0.363058i	$-0.881733\pi$
$601$	−2.34968	−	22.3557i	−0.0958453	−	0.911907i	0.835921	−	0.548849i	$-0.184934\pi$
$602$	0.925574	+	0.672469i	0.0377236	+	0.0274078i
$603$	3.65433	−	3.72987i	0.148816	−	0.151892i
$604$	21.2559			0.864892
$605$	−28.1843	+	9.66704i	−1.14585	+	0.393021i
$606$	5.93738	−	3.26317i	0.241190	−	0.132557i
$607$	17.8690	−	19.8455i	0.725279	−	0.805504i	−0.261905	−	0.965094i	$-0.584351\pi$
$607$	17.8690	−	19.8455i	0.725279	−	0.805504i	0.987183	+	0.159590i	$0.0510173\pi$
$608$	0.549118	−	5.22451i	0.0222697	−	0.211882i
$609$	−10.6769	+	22.6824i	−0.432649	+	0.919137i
$610$	−4.44861	−	4.94068i	−0.180119	−	0.200042i
$611$	6.98102	−	21.4854i	0.282422	−	0.869205i
$612$	−22.2714	−	11.0623i	−0.900266	−	0.447167i
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.991623	+	0.129163i	$0.0412289\pi$
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.429269	+	0.903176i	$0.358771\pi$
$614$	−8.13027	−	1.72814i	−0.328111	−	0.0697422i
$615$	27.5765	+	16.7055i	1.11199	+	0.673629i
$616$	6.74380	−	13.5058i	0.271716	−	0.544164i
$617$	−20.7128	−	35.8756i	−0.833864	−	1.44430i	−0.894952	−	0.446163i	$-0.852790\pi$
$617$	−20.7128	−	35.8756i	−0.833864	−	1.44430i	0.0610871	−	0.998132i	$-0.480543\pi$
$618$	2.39972	−	0.724203i	0.0965311	−	0.0291317i
$619$	8.14129	−	3.62474i	0.327226	−	0.145690i	−0.236547	−	0.971620i	$-0.576016\pi$
$619$	8.14129	−	3.62474i	0.327226	−	0.145690i	0.563773	+	0.825930i	$0.309349\pi$
$620$	−20.4539	+	14.8606i	−0.821446	+	0.596816i
$621$	1.41161	+	9.58344i	0.0566460	+	0.384570i
$622$	−1.73638	+	5.34404i	−0.0696227	+	0.214277i
$623$	3.94375	+	37.5223i	0.158003	+	1.50330i
$624$	−14.1924	+	18.6931i	−0.568149	+	0.748321i
$625$	−20.8926	+	23.2036i	−0.835704	+	0.928144i
$626$	−0.190818	−	0.330506i	−0.00762662	−	0.0132097i
$627$	8.74285	−	3.22695i	0.349156	−	0.128872i
$628$	0.319255	−	0.552966i	0.0127397	−	0.0220657i
$629$	−10.3390	−	31.8202i	−0.412244	−	1.26876i
$630$	8.77665	−	3.47247i	0.349670	−	0.138346i
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	−0.492716	−	0.870190i	$-0.663996\pi$
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	0.675342	+	0.737504i	$0.263996\pi$
$632$	3.20023	+	3.55422i	0.127298	+	0.141379i
$633$	2.68237	+	14.0707i	0.106615	+	0.559260i
$634$	1.04222	+	0.464025i	0.0413917	+	0.0184288i
$635$	−0.693806	+	6.60113i	−0.0275329	+	0.261958i
$636$	−3.80741	−	3.57626i	−0.150974	−	0.141808i
$637$	−18.4693	+	31.9898i	−0.731780	+	1.26748i
$638$	0.148586	−	3.35722i	0.00588257	−	0.132914i
$639$	17.2088	+	0.725429i	0.680770	+	0.0286975i
$640$	−6.88034	−	21.1755i	−0.271970	−	0.837036i
$641$	24.4996	−	10.9079i	0.967678	−	0.430838i	0.138833	−	0.990316i	$-0.455665\pi$
$641$	24.4996	−	10.9079i	0.967678	−	0.430838i	0.828845	+	0.559478i	$0.188998\pi$
$642$	1.36771	−	0.114684i	0.0539793	−	0.00452620i
$643$	−13.8295	+	2.93955i	−0.545382	+	0.115925i	−0.472360	−	0.881406i	$-0.656598\pi$
$643$	−13.8295	+	2.93955i	−0.545382	+	0.115925i	−0.0730222	+	0.997330i	$0.523264\pi$
$644$	14.2515	−	3.02925i	0.561587	−	0.119369i
$645$	2.63695	+	3.79505i	0.103830	+	0.149430i
$646$	1.82572	−	0.812864i	0.0718321	−	0.0319817i
$647$	−0.393698	−	1.21168i	−0.0154779	−	0.0476360i	0.943019	−	0.332738i	$-0.107973\pi$
$647$	−0.393698	−	1.21168i	−0.0154779	−	0.0476360i	−0.958497	+	0.285102i	$0.907973\pi$
$648$	−10.0210	−	0.846365i	−0.393662	−	0.0332484i
$649$	−35.2907	−	13.2187i	−1.38528	−	0.518878i
$650$	−1.28325	+	2.22266i	−0.0503334	+	0.0871799i
$651$	32.8571	−	9.91582i	1.28777	−	0.388632i
$652$	2.67505	−	25.4514i	0.104763	−	0.996753i
$653$	−4.41090	−	1.96386i	−0.172612	−	0.0768517i	0.318612	−	0.947885i	$-0.396783\pi$
$653$	−4.41090	−	1.96386i	−0.172612	−	0.0768517i	−0.491223	+	0.871034i	$0.663450\pi$
$654$	−6.49010	+	5.60074i	−0.253783	+	0.219006i
$655$	7.24523	+	8.04664i	0.283094	+	0.314408i
$656$	−19.5632	+	14.2135i	−0.763813	+	0.554942i
$657$	−9.51212	−	7.54295i	−0.371103	−	0.294279i
$658$	−2.10558	−	6.48030i	−0.0820840	−	0.252628i
$659$	11.0889	−	19.2065i	0.431961	−	0.748178i	−0.565082	−	0.825035i	$-0.691155\pi$
$659$	11.0889	−	19.2065i	0.431961	−	0.748178i	0.997042	+	0.0768574i	$0.0244886\pi$
$660$	21.3825	−	20.8364i	0.832313	−	0.811055i
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	0.999265	+	0.0383209i	$0.0122009\pi$
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	−0.466446	+	0.884550i	$0.654466\pi$
$662$	0.606812	−	0.673933i	0.0235844	−	0.0261931i
$663$	−28.5883	−	3.61506i	−1.11028	−	0.140397i
$664$	−0.759228	−	7.22357i	−0.0294638	−	0.280329i
$665$	5.53132	−	17.0236i	0.214495	−	0.660148i
$666$	−4.22169	−	5.10566i	−0.163587	−	0.197840i
$667$	5.35915	−	3.89365i	0.207507	−	0.150763i
$668$	33.1547	−	14.7614i	1.28279	−	0.571136i
$669$	2.90936	−	12.3974i	0.112482	−	0.479310i
$670$	0.672198	+	1.16428i	0.0259693	+	0.0449801i
$671$	20.3498	+	20.0215i	0.785594	+	0.772923i
$672$	−0.481213	+	22.8410i	−0.0185632	+	0.881112i
$673$	−34.4734	−	7.32754i	−1.32885	−	0.282456i	−0.511842	−	0.859080i	$-0.671037\pi$
$673$	−34.4734	−	7.32754i	−1.32885	−	0.282456i	−0.817010	+	0.576624i	$0.804370\pi$
$674$	4.19805	+	3.05006i	0.161703	+	0.117484i
$675$	12.1342	−	0.504166i	0.467045	−	0.0194054i
$676$	−1.08494	+	3.33910i	−0.0417285	+	0.128427i
$677$	−29.4752	−	32.7355i	−1.13282	−	1.25813i	−0.962067	−	0.272815i	$-0.912045\pi$
$677$	−29.4752	−	32.7355i	−1.13282	−	1.25813i	−0.170757	−	0.985313i	$-0.554621\pi$
$678$	0.265942	+	0.382739i	0.0102134	+	0.0146990i
$679$	−3.15617	+	30.0289i	−0.121123	+	1.15240i
$680$	8.74970	−	9.71753i	0.335536	−	0.372650i
$681$	−28.0600	−	16.9984i	−1.07526	−	0.651379i
$682$	−3.55167	+	2.92422i	−0.136001	+	0.111974i
$683$	42.2845			1.61797			0.808985	−	0.587829i	$-0.200017\pi$
$683$	42.2845			1.61797			0.808985	+	0.587829i	$0.200017\pi$
$684$	−6.53510	+	6.67020i	−0.249876	+	0.255041i
$685$	−2.38701	−	1.73426i	−0.0912029	−	0.0662628i
$686$	0.314703	+	2.99420i	0.0120154	+	0.114319i
$687$	−2.54920	−	13.3721i	−0.0972580	−	0.510179i
$688$	−3.39020	+	0.720610i	−0.129250	+	0.0274730i
$689$	−5.52972	−	2.46199i	−0.210666	−	0.0937943i
$690$	−2.47431	−	0.312882i	−0.0941953	−	0.0119112i
$691$	8.28186	+	1.76036i	0.315057	+	0.0669674i	0.362726	−	0.931896i	$-0.381846\pi$
$691$	8.28186	+	1.76036i	0.315057	+	0.0669674i	−0.0476694	+	0.998863i	$0.515179\pi$
$692$	2.90507			0.110434
$693$	−36.7164	+	17.1617i	−1.39474	+	0.651918i
$694$	−7.81709			−0.296733
$695$	−7.64373	−	1.62472i	−0.289943	−	0.0616293i
$696$	2.66424	+	6.34013i	0.100988	+	0.240322i
$697$	−27.1223	−	12.0756i	−1.02733	−	0.457397i
$698$	−6.38874	+	1.35797i	−0.241818	+	0.0513999i
$699$	10.7452	+	3.74333i	0.406421	+	0.141586i
$700$	−1.90938	−	18.1666i	−0.0721678	−	0.686631i
$701$	−35.2342	−	25.5991i	−1.33078	−	0.966865i	−0.999730	−	0.0232503i	$-0.992599\pi$
$701$	−35.2342	−	25.5991i	−1.33078	−	0.966865i	−0.331046	−	0.943615i	$-0.607401\pi$
$702$	−5.52712	+	1.41699i	−0.208608	+	0.0534807i
$703$	−12.5638			−0.473854
$704$	7.42078	+	18.8717i	0.279681	+	0.711255i
$705$	0.579722	−	27.5168i	0.0218336	−	1.03634i
$706$	−5.66770	+	6.29462i	−0.213307	+	0.236901i
$707$	−5.84067	+	55.5703i	−0.219661	+	2.08994i
$708$	37.6286	−	3.15518i	1.41417	−	0.118579i
$709$	−4.03304	−	4.47915i	−0.151464	−	0.168218i	0.662638	−	0.748940i	$-0.269437\pi$
$709$	−4.03304	−	4.47915i	−0.151464	−	0.168218i	−0.814102	+	0.580722i	$0.802770\pi$
$710$	−1.37036	+	4.21753i	−0.0514287	+	0.158281i
$711$	−0.803161	−	12.8153i	−0.0301209	−	0.480611i
$712$	8.37326	+	6.08353i	0.313801	+	0.227990i
$713$	−8.87056	−	1.88550i	−0.332205	−	0.0706124i
$714$	−7.61677	+	4.18616i	−0.285051	+	0.156663i
$715$	15.4553	−	30.9523i	0.577996	−	1.15755i
$716$	12.6530	+	21.9157i	0.472866	+	0.819028i
$717$	32.2513	+	30.2934i	1.20445	+	1.13133i
$718$	−9.60122	+	4.27474i	−0.358314	+	0.159532i
$719$	−32.6897	+	23.7504i	−1.21912	+	0.885741i	−0.996027	−	0.0890560i	$-0.971615\pi$
$719$	−32.6897	+	23.7504i	−1.21912	+	0.885741i	−0.223092	+	0.974797i	$0.571615\pi$
$720$	−9.97358	+	26.7983i	−0.371693	+	0.998715i
$721$	−6.38836	+	19.6614i	−0.237915	+	0.732227i
$722$	0.487871	+	4.64179i	0.0181567	+	0.172749i
$723$	2.00092	+	4.76162i	0.0744151	+	0.177086i
$724$	−3.59329	+	3.99075i	−0.133544	+	0.148315i
$725$	−4.15251	−	7.19235i	−0.154220	−	0.267117i
$726$	3.65461	−	4.01985i	0.135635	−	0.149191i
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	−0.985743	−	0.168259i	$-0.946185\pi$
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	0.638588	+	0.769549i	$0.279519\pi$
$728$	5.41643	+	16.6700i	0.200746	+	0.617833i
$729$	19.6687	+	18.4970i	0.728472	+	0.685075i
$730$	2.52864	−	1.83717i	0.0935893	−	0.0679966i
$731$	−2.84739	−	3.16235i	−0.105315	−	0.116964i
$732$	−27.0127	−	9.41048i	−0.998419	−	0.347822i
$733$	0.515414	+	0.229477i	0.0190373	+	0.00847594i	0.416233	−	0.909258i	$-0.363350\pi$
$733$	0.515414	+	0.229477i	0.0190373	+	0.00847594i	−0.397196	+	0.917734i	$0.630017\pi$
$734$	0.740999	−	7.05013i	0.0273508	−	0.260225i
$735$	−10.2817	+	43.8125i	−0.379246	+	1.61605i
$736$	3.01837	−	5.22796i	0.111258	−	0.192705i
$737$	−3.18335	−	4.81575i	−0.117260	−	0.177391i
$738$	−5.87353	−	0.247596i	−0.216208	−	0.00911413i
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	0.961518	−	0.274741i	$-0.0885921\pi$
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	−0.939373	+	0.342896i	$0.888592\pi$
$740$	−36.7700	+	16.3711i	−1.35169	+	0.601813i
$741$	−4.60845	+	9.79038i	−0.169296	+	0.359659i
$742$	−1.78579	+	0.379581i	−0.0655583	+	0.0139349i
$743$	26.6669	−	5.66823i	0.978315	−	0.207947i	0.309111	−	0.951026i	$-0.399968\pi$
$743$	26.6669	−	5.66823i	0.978315	−	0.207947i	0.669204	+	0.743079i	$0.266635\pi$
$744$	4.00973	−	8.51843i	0.147004	−	0.312301i
$745$	49.9236	−	22.2274i	1.82906	−	0.814350i
$746$	1.61067	+	4.95714i	0.0589709	+	0.181494i
$747$	−10.4529	+	16.4623i	−0.382452	+	0.602325i
$748$	−17.1270	+	21.5052i	−0.626224	+	0.786308i
$749$	−5.65985	+	9.80315i	−0.206807	+	0.358199i
$750$	0.813873	−	3.46808i	0.0297184	−	0.126636i
$751$	−3.16787	+	30.1402i	−0.115597	+	1.09983i	0.770854	+	0.637011i	$0.219830\pi$
$751$	−3.16787	+	30.1402i	−0.115597	+	1.09983i	−0.886451	+	0.462822i	$0.846837\pi$
$752$	18.8576	+	8.39595i	0.687667	+	0.306169i
$753$	−19.0855	−	6.64886i	−0.695514	−	0.242298i
$754$	2.61088	+	2.89968i	0.0950828	+	0.105600i
$755$	24.2772	−	17.6384i	0.883539	−	0.641929i
$756$	25.8974	−	31.2814i	0.941878	−	1.13769i
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	0.993855	−	0.110691i	$-0.0353064\pi$
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	−0.869108	+	0.494622i	$0.835306\pi$
$758$	4.48528	−	7.76874i	0.162913	−	0.282173i
$759$	10.6864	+	0.698756i	0.387891	+	0.0253632i
$760$	−2.45515	−	4.25244i	−0.0890576	−	0.154252i
$761$	−22.3095	+	24.7772i	−0.808717	+	0.898171i	−0.996462	−	0.0840467i	$-0.973216\pi$
$761$	−22.3095	+	24.7772i	−0.808717	+	0.898171i	0.187745	+	0.982218i	$0.439882\pi$
$762$	−0.468849	−	1.11573i	−0.0169846	−	0.0404185i
$763$	−7.39038	−	70.3147i	−0.267550	−	2.54556i
$764$	9.92620	−	30.5497i	0.359117	−	1.10525i
$765$	−34.6166	+	5.84636i	−1.25157	+	0.211376i
$766$	2.86788	−	2.08364i	0.103621	−	0.0752849i
$767$	39.9735	−	17.7974i	1.44336	−	0.642625i
$768$	−12.4788	−	11.7212i	−0.450289	−	0.422952i
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.771929	+	0.635709i	$0.219292\pi$
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.164575	+	0.986364i	$0.447375\pi$
$770$	−1.71610	−	10.2927i	−0.0618439	−	0.370923i
$771$	−31.4578	+	17.2891i	−1.13293	+	0.622653i
$772$	−41.3627	−	8.79191i	−1.48868	−	0.316428i
$773$	6.24784	+	4.53932i	0.224719	+	0.163268i	0.694448	−	0.719542i	$-0.255648\pi$
$773$	6.24784	+	4.53932i	0.224719	+	0.163268i	−0.469729	+	0.882811i	$0.655648\pi$
$774$	−0.754641	−	0.374835i	−0.0271250	−	0.0134732i
$775$	−3.51343	+	10.8132i	−0.126206	+	0.388423i
$776$	5.54240	+	6.15546i	0.198961	+	0.220968i
$777$	54.4480	−	4.56550i	1.95331	−	0.163786i
$778$	−0.218171	+	2.07576i	−0.00782182	+	0.0744197i
$779$	−7.45990	+	8.28505i	−0.267279	+	0.296843i
$780$	−0.730173	+	34.6580i	−0.0261444	+	1.24096i
$781$	4.77872	−	18.4326i	0.170996	−	0.659569i
$782$	2.29655			0.0821244
$783$	4.97171	−	17.7818i	0.177674	−	0.635468i
$784$	−27.3060	−	19.8390i	−0.975215	−	0.708535i
$785$	−0.0942245	−	0.896486i	−0.00336301	−	0.0319969i
$786$	−1.86437	−	0.649496i	−0.0665000	−	0.0231668i
$787$	19.2757	−	4.09717i	0.687104	−	0.146048i	0.148886	−	0.988854i	$-0.452431\pi$
$787$	19.2757	−	4.09717i	0.687104	−	0.146048i	0.538218	+	0.842806i	$0.319098\pi$
$788$	−31.9444	−	14.2226i	−1.13797	−	0.506658i
$789$	−6.09637	−	14.5076i	−0.217037	−	0.516484i
$790$	3.23370	+	0.687345i	0.115050	+	0.0244546i
$791$	−3.84382			−0.136670
$792$	−3.24096	+	10.6352i	−0.115163	+	0.377906i
$793$	−33.1470			−1.17709
$794$	−9.54139	−	2.02808i	−0.338611	−	0.0719740i
$795$	−7.31622	−	0.925151i	−0.259479	−	0.0328117i
$796$	43.9882	+	19.5848i	1.55912	+	0.694165i
$797$	−13.7193	+	2.91612i	−0.485961	+	0.103294i	−0.444375	−	0.895841i	$-0.646574\pi$
$797$	−13.7193	+	2.91612i	−0.485961	+	0.103294i	−0.0415860	+	0.999135i	$0.513241\pi$
$798$	0.611170	+	3.20597i	0.0216352	+	0.113490i
$799$	2.64915	+	25.2050i	0.0937202	+	0.891689i
$800$	−6.12297	−	4.44860i	−0.216480	−	0.157282i
$801$	−7.46609	−	26.7655i	−0.263801	−	0.945712i
$802$	2.13170			0.0752731
$803$	−10.3612	+	8.53071i	−0.365638	+	0.301042i
$804$	4.94737	+	2.99705i	0.174480	+	0.105698i
$805$	13.7635	−	15.2859i	0.485099	−	0.538757i
$806$	0.558368	−	5.31251i	0.0196677	−	0.187125i
$807$	7.84863	+	11.2956i	0.276285	+	0.397625i
$808$	10.2565	+	11.3910i	0.360824	+	0.400736i
$809$	−6.46767	+	19.9055i	−0.227391	+	0.699839i	0.770649	+	0.637260i	$0.219932\pi$
$809$	−6.46767	+	19.9055i	−0.227391	+	0.699839i	−0.998040	+	0.0625783i	$0.980068\pi$
$810$	−5.94782	+	3.59820i	−0.208985	+	0.126428i
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	0.559845	−	0.828597i	$-0.310861\pi$
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	−0.615041	+	0.788495i	$0.710861\pi$
$812$	−27.1642	−	5.77393i	−0.953276	−	0.202625i
$813$	0.135848	−	6.44810i	0.00476440	−	0.226145i
$814$	−6.49866	+	3.37806i	−0.227778	+	0.118401i
$815$	−18.0646	−	31.2888i	−0.632775	−	1.09600i
$816$	6.01562	−	25.6338i	0.210589	−	0.897362i
$817$	−1.45980	+	0.649943i	−0.0510718	+	0.0227386i
$818$	−0.556008	+	0.403964i	−0.0194404	+	0.0141243i
$819$	16.4140	−	44.1033i	0.573552	−	1.54109i
$820$	−11.0369	+	33.9680i	−0.385424	+	1.18621i
$821$	−1.13327	−	10.7824i	−0.0395515	−	0.376307i	−0.996337	−	0.0855130i	$-0.972747\pi$
$821$	−1.13327	−	10.7824i	−0.0395515	−	0.376307i	0.956786	−	0.290794i	$-0.0939196\pi$
$822$	0.533724	+	0.0674906i	0.0186158	+	0.00235400i
$823$	31.8960	−	35.4241i	1.11182	−	1.23481i	0.142296	−	0.989824i	$-0.454551\pi$
$823$	31.8960	−	35.4241i	1.11182	−	1.23481i	0.969528	−	0.244982i	$-0.0787819\pi$
$824$	2.83556	+	4.91134i	0.0987815	+	0.171094i
$825$	2.27170	−	13.2328i	0.0790905	−	0.460708i
$826$	6.59880	−	11.4295i	0.229601	−	0.397681i
$827$	11.5619	+	35.5838i	0.402046	+	1.23737i	0.923337	+	0.383991i	$0.125451\pi$
$827$	11.5619	+	35.5838i	0.402046	+	1.23737i	−0.521291	+	0.853379i	$0.674549\pi$
$828$	−9.97808	+	3.94781i	−0.346762	+	0.137196i
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	−0.727959	−	0.685621i	$-0.759531\pi$
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	0.427113	+	0.904198i	$0.359531\pi$
$830$	−3.35949	−	3.73110i	−0.116610	−	0.129508i
$831$	−5.11487	+	4.41396i	−0.177433	+	0.153118i
$832$	−21.5097	−	9.57674i	−0.745715	−	0.332014i
$833$	4.33162	−	41.2126i	0.150082	−	1.42793i
$834$	1.36408	−	0.411659i	0.0472341	−	0.0142546i
$835$	25.6181	−	44.3718i	0.886549	−	1.53555i
$836$	5.69284	+	8.61209i	0.196891	+	0.297856i
$837$	−22.6451	+	11.2309i	−0.782730	+	0.388197i
$838$	−0.987051	−	3.03783i	−0.0340971	−	0.104940i
$839$	14.0334	−	6.24809i	0.484488	−	0.215708i	−0.149932	−	0.988696i	$-0.547906\pi$
$839$	14.0334	−	6.24809i	0.484488	−	0.215708i	0.634420	+	0.772988i	$0.281239\pi$
$840$	12.1852	+	17.5367i	0.420428	+	0.605073i
$841$	16.0159	−	3.40429i	0.552274	−	0.117389i
$842$	1.92589	−	0.409360i	0.0663704	−	0.0141075i
$843$	−0.0683892	+	0.00573448i	−0.00235545	+	0.000197506i
$844$	−14.4958	+	6.45394i	−0.498966	+	0.222154i
$845$	1.53168	+	4.71402i	0.0526913	+	0.162167i
$846$	2.32390	+	4.44783i	0.0798974	+	0.152920i
$847$	10.0272	+	43.6703i	0.344539	+	1.50053i
$848$	2.76543	−	4.78987i	0.0949654	−	0.164485i
$849$	−8.07205	−	7.58200i	−0.277032	−	0.260213i
$850$	0.300963	−	2.86347i	0.0103229	−	0.0982162i
$851$	−13.1894	−	5.87228i	−0.452125	−	0.201299i
$852$	3.57299	+	18.7426i	0.122409	+	0.642110i
$853$	27.7450	+	30.8139i	0.949970	+	1.05505i	0.998418	+	0.0562233i	$0.0179059\pi$
$853$	27.7450	+	30.8139i	0.949970	+	1.05505i	−0.0484478	+	0.998826i	$0.515427\pi$
$854$	−8.08825	+	5.87646i	−0.276774	+	0.201088i
$855$	−1.92898	+	13.0412i	−0.0659696	+	0.446000i
$856$	0.959576	+	2.95327i	0.0327976	+	0.100941i
$857$	−9.20273	+	15.9396i	−0.314359	+	0.544486i	−0.979301	−	0.202409i	$-0.935123\pi$
$857$	−9.20273	+	15.9396i	−0.314359	+	0.544486i	0.664942	+	0.746895i	$0.268456\pi$
$858$	0.248633	+	6.30317i	0.00848818	+	0.215187i
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	0.965363	−	0.260912i	$-0.0840233\pi$
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	−0.708638	+	0.705572i	$0.750690\pi$
$860$	−3.42542	+	3.80432i	−0.116806	+	0.129726i
$861$	29.3184	−	38.6158i	0.999167	−	1.31602i
$862$	0.869760	+	8.27521i	0.0296241	+	0.281855i
$863$	−4.45906	+	13.7236i	−0.151788	+	0.467155i	−0.997821	−	0.0659746i	$-0.978984\pi$
$863$	−4.45906	+	13.7236i	−0.151788	+	0.467155i	0.846033	+	0.533130i	$0.178984\pi$
$864$	−2.45197	−	16.6465i	−0.0834178	−	0.566325i
$865$	3.31799	−	2.41066i	0.112815	−	0.0819649i
$866$	−9.51747	+	4.23745i	−0.323417	+	0.143994i
$867$	2.75950	−	0.832779i	0.0937176	−	0.0282827i
$868$	19.0095	+	32.9255i	0.645225	+	1.11756i
$869$	−14.0385	−	2.10662i	−0.476222	−	0.0714623i
$870$	4.06588	+	2.46306i	0.137846	+	0.0835054i
$871$	6.55636	+	1.39360i	0.222154	+	0.0472202i
$872$	−15.6910	−	11.4002i	−0.531365	−	0.386059i
$873$	−1.39097	−	22.1945i	−0.0470773	−	0.751170i
$874$	0.266492	−	0.820177i	0.00901421	−	0.0277429i
$875$	19.6589	+	21.8334i	0.664593	+	0.738105i
$876$	5.72736	−	12.1674i	0.193510	−	0.411100i
$877$	2.51656	−	23.9435i	0.0849782	−	0.808514i	−0.866164	−	0.499760i	$-0.833421\pi$
$877$	2.51656	−	23.9435i	0.0849782	−	0.808514i	0.951142	−	0.308754i	$-0.0999119\pi$
$878$	−4.10175	+	4.55545i	−0.138427	+	0.153739i
$879$	35.5303	−	19.5274i	1.19841	−	0.658642i
$880$	26.6511	+	17.0010i	0.898409	+	0.573104i
$881$	−10.0956			−0.340129			−0.170064	−	0.985433i	$-0.554398\pi$
$881$	−10.0956			−0.340129			−0.170064	+	0.985433i	$0.554398\pi$
$882$	−2.20471	−	7.90374i	−0.0742363	−	0.266133i
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.996798	−	0.0799659i	$-0.974519\pi$
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.384079	−	0.923300i	$-0.625481\pi$
$884$	−3.33666	−	31.7462i	−0.112224	−	1.06774i
$885$	40.3589	−	34.8283i	1.35665	−	1.17074i
$886$	9.32839	−	1.98281i	0.313393	−	0.0666138i
$887$	−2.35029	−	1.04641i	−0.0789149	−	0.0351352i	0.366900	−	0.930261i	$-0.380419\pi$
$887$	−2.35029	−	1.04641i	−0.0789149	−	0.0351352i	−0.445815	+	0.895125i	$0.647086\pi$
$888$	9.06362	−	11.9379i	0.304155	−	0.400609i
$889$	9.76319	+	2.07523i	0.327447	+	0.0696010i
$890$	7.15422			0.239810
$891$	24.5590	−	16.9663i	0.822758	−	0.568391i
$892$	14.1064			0.472316
$893$	9.30898	+	1.97868i	0.311513	+	0.0662141i
$894$	−6.02529	+	7.93603i	−0.201516	+	0.265421i
$895$	32.6375	+	14.5311i	1.09095	+	0.485722i
$896$	−32.7504	+	6.96130i	−1.09411	+	0.232561i
$897$	−9.41387	+	8.12385i	−0.314320	+	0.271247i
$898$	−1.17833	−	11.2111i	−0.0393215	−	0.374119i
$899$	13.9843	+	10.1602i	0.466403	+	0.338862i
$900$	3.61473	+	12.9586i	0.120491	+	0.431953i
$901$	6.79061			0.226228
$902$	−1.63102	+	6.29121i	−0.0543071	+	0.209474i
$903$	6.09015	−	3.34713i	0.202668	−	0.111386i
$904$	−0.705563	+	0.783607i	−0.0234667	+	0.0260624i
$905$	−0.792460	+	7.53975i	−0.0263423	+	0.250630i
$906$	−2.33025	+	4.95049i	−0.0774174	+	0.164469i
$907$	6.88861	+	7.65058i	0.228733	+	0.254033i	0.846576	−	0.532268i	$-0.178660\pi$
$907$	6.88861	+	7.65058i	0.228733	+	0.254033i	−0.617843	+	0.786301i	$0.711993\pi$
$908$	11.2304	−	34.5636i	0.372693	−	1.14703i
$909$	−2.57408	−	41.0722i	−0.0853768	−	1.36228i
$910$	9.80197	+	7.12155i	0.324932	+	0.236077i
$911$	15.2616	+	3.24395i	0.505639	+	0.107477i	0.453666	−	0.891172i	$-0.350116\pi$
$911$	15.2616	+	3.24395i	0.505639	+	0.107477i	0.0519727	+	0.998649i	$0.483449\pi$
$912$	−8.45665	−	5.12293i	−0.280028	−	0.169637i
$913$	15.3677	+	15.1198i	0.508597	+	0.500394i
$914$	−5.34829	−	9.26351i	−0.176906	−	0.306410i
$915$	−38.6612	+	11.6674i	−1.27810	+	0.385713i
$916$	13.7761	−	6.13353i	0.455176	−	0.202657i
$917$	13.1729	−	9.57070i	0.435009	−	0.316052i
$918$	5.01797	−	3.97423i	0.165618	−	0.131169i
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	−0.877505	−	0.479568i	$-0.840794\pi$
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	0.991799	+	0.127806i	$0.0407935\pi$
$920$	−0.589812	−	5.61168i	−0.0194455	−	0.185012i
$921$	−30.5300	+	40.2117i	−1.00600	+	1.32502i
$922$	3.69493	−	4.10363i	0.121686	−	0.135146i
$923$	11.0549	+	19.1476i	0.363875	+	0.630251i
$924$	−27.8006	−	35.2536i	−0.914573	−	1.15976i
$925$	−9.05036	+	15.6757i	−0.297574	+	0.515413i
$926$	−1.26440	−	3.89141i	−0.0415506	−	0.127880i
$927$	2.22786	−	15.0619i	0.0731726	−	0.494697i
$928$	−9.30886	+	6.76328i	−0.305578	+	0.222016i
$929$	15.7430	+	17.4843i	0.516510	+	0.573643i	0.943819	−	0.330463i	$-0.107205\pi$
$929$	15.7430	+	17.4843i	0.516510	+	0.573643i	−0.427309	+	0.904106i	$0.640538\pi$
$930$	−1.21870	−	6.39282i	−0.0399626	−	0.209629i
$931$	−14.2158	−	6.32929i	−0.465904	−	0.207434i
$932$	−1.31755	+	12.5356i	−0.0431577	+	0.410618i
$933$	24.8778	+	23.3675i	0.814464	+	0.765018i
$934$	3.18239	−	5.51206i	0.104131	−	0.180360i
$935$	−1.71609	+	38.7741i	−0.0561221	+	1.26805i
$936$	−5.97805	−	11.4417i	−0.195399	−	0.373983i
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	0.999990	−	0.00451068i	$-0.00143580\pi$
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	−0.811660	+	0.584130i	$0.801436\pi$
$938$	1.84689	−	0.822288i	0.0603031	−	0.0268487i
$939$	−2.31003	+	0.193697i	−0.0753850	+	0.00632108i
$940$	29.8225	−	6.33896i	0.972702	−	0.206754i
$941$	31.7826	−	6.75560i	1.03608	−	0.220226i	0.341683	−	0.939815i	$-0.389003\pi$
$941$	31.7826	−	6.75560i	1.03608	−	0.220226i	0.694400	+	0.719589i	$0.255670\pi$
$942$	0.0937858	+	0.134975i	0.00305571	+	0.00439772i
$943$	−11.7037	+	5.21082i	−0.381125	+	0.169688i
$944$	12.3551	+	38.0250i	0.402123	+	1.23761i
$945$	3.62066	−	57.2177i	0.117780	−	1.86129i
$946$	−0.580329	+	0.728681i	−0.0188681	+	0.0236915i
$947$	1.92137	−	3.32790i	0.0624360	−	0.108142i	−0.833118	−	0.553096i	$-0.813446\pi$
$947$	1.92137	−	3.32790i	0.0624360	−	0.108142i	0.895554	+	0.444953i	$0.146780\pi$
$948$	13.6175	−	4.10957i	0.442275	−	0.133473i
$949$	1.62891	−	15.4980i	0.0528765	−	0.503087i
$950$	−0.987720	−	0.439761i	−0.0320459	−	0.0142677i
$951$	5.24633	−	4.52741i	0.170124	−	0.146811i
$952$	−13.1576	−	14.6130i	−0.426441	−	0.473610i
$953$	−15.4434	+	11.2203i	−0.500262	+	0.363461i	−0.809117	−	0.587648i	$-0.800054\pi$
$953$	−15.4434	+	11.2203i	−0.500262	+	0.363461i	0.308855	+	0.951109i	$0.400054\pi$
$954$	1.25031	−	0.494682i	0.0404802	−	0.0160159i
$955$	−14.0134	−	43.1289i	−0.453464	−	1.39562i
$956$	−24.5077	+	42.4486i	−0.792636	+	1.37289i
$957$	−18.0662	−	9.50151i	−0.583998	−	0.307140i
$958$	3.31651	+	5.74436i	0.107152	+	0.185592i
$959$	−2.96887	+	3.29726i	−0.0958698	+	0.106474i
$960$	−28.4589	−	3.59869i	−0.918507	−	0.116147i
$961$	0.766796	+	7.29558i	0.0247354	+	0.235341i
$962$	2.62793	−	8.08795i	0.0847280	−	0.260766i
$963$	2.90791	−	7.81335i	0.0937061	−	0.251782i
$964$	−4.62879	+	3.36302i	−0.149083	+	0.108315i
$965$	−54.5376	+	24.2817i	−1.75563	+	0.781655i
$966$	−0.856858	+	3.65125i	−0.0275689	+	0.117477i
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	0.569515	−	0.821981i	$-0.307131\pi$
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	−0.996614	+	0.0822239i	$0.973798\pi$
$968$	10.7433	+	5.97185i	0.345302	+	0.191943i
$969$	0.255693	−	12.1366i	0.00821406	−	0.389885i
$970$	5.60037	+	1.19040i	0.179817	+	0.0382213i
$971$	41.3472	+	30.0405i	1.32689	+	0.964045i	0.999819	+	0.0190472i	$0.00606329\pi$
$971$	41.3472	+	30.0405i	1.32689	+	0.964045i	0.327076	+	0.944998i	$0.393937\pi$
$972$	−14.9704	+	25.8933i	−0.480175	+	0.830527i
$973$	−3.63134	+	11.1761i	−0.116415	+	0.358290i
$974$	0.0516693	+	0.0573846i	0.00165559	+	0.00183872i
$975$	8.89559	+	12.8024i	0.284887	+	0.410004i
$976$	3.16592	−	30.1217i	0.101339	−	0.964171i
$977$	−14.1686	+	15.7358i	−0.453292	+	0.503432i	−0.925862	−	0.377861i	$-0.876660\pi$
$977$	−14.1686	+	15.7358i	−0.453292	+	0.503432i	0.472570	+	0.881293i	$0.343326\pi$
$978$	5.63434	+	3.41321i	0.180166	+	0.109142i
$979$	−30.6638	+	1.85712i	−0.980020	+	0.0593539i
$980$	−49.8521			−1.59247
$981$	13.9910	+	50.1570i	0.446699	+	1.60139i
$982$	0.970410	+	0.705044i	0.0309670	+	0.0224989i
$983$	−5.31375	−	50.5569i	−0.169482	−	1.61252i	−0.666997	−	0.745061i	$-0.732421\pi$
$983$	−5.31375	−	50.5569i	−0.169482	−	1.61252i	0.497515	−	0.867456i	$-0.334246\pi$
$984$	−2.49067	−	13.0651i	−0.0793996	−	0.416501i
$985$	−48.2870	+	10.2637i	−1.53855	+	0.327029i
$986$	−3.99892	−	1.78043i	−0.127352	−	0.0567006i
$987$	−41.0614	−	5.19230i	−1.30700	−	0.165273i
$988$	−11.7249	−	2.49219i	−0.373017	−	0.0792873i
$989$	−1.83625			−0.0583895
$990$	2.50865	+	7.26422i	0.0797300	+	0.230872i
$991$	−13.1480			−0.417662			−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480			−0.417662			−0.208831	+	0.977952i	$0.566966\pi$
$992$	15.4082	+	3.27512i	0.489211	+	0.103985i
$993$	−2.13401	−	5.07834i	−0.0677209	−	0.161156i
$994$	6.09209	+	2.71237i	0.193229	+	0.0860312i
$995$	66.4923	−	14.1334i	2.10795	−	0.448058i
$996$	−20.3994	−	7.10660i	−0.646381	−	0.225181i
$997$	3.88937	+	37.0048i	0.123177	+	1.17195i	0.865146	+	0.501520i	$0.167226\pi$
$997$	3.88937	+	37.0048i	0.123177	+	1.17195i	−0.741969	+	0.670435i	$0.766108\pi$
$998$	3.54437	+	2.57514i	0.112195	+	0.0815146i
$999$	−38.9809	+	9.99353i	−1.23330	+	0.316181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.b.16.5	✓	72
3.2	odd	2		297.2.n.b.181.5		72
9.2	odd	6		891.2.f.e.82.5		36
9.4	even	3	inner	99.2.m.b.49.5	yes	72
9.5	odd	6		297.2.n.b.280.5		72
9.7	even	3		891.2.f.f.82.5		36
11.3	even	5		1089.2.e.p.727.9		36
11.8	odd	10		1089.2.e.o.727.10		36
11.9	even	5	inner	99.2.m.b.97.5	yes	72
33.20	odd	10		297.2.n.b.262.5		72
99.20	odd	30		891.2.f.e.163.5		36
99.25	even	15		9801.2.a.cm.1.10		18
99.31	even	15	inner	99.2.m.b.31.5	yes	72
99.47	odd	30		9801.2.a.cp.1.9		18
99.52	odd	30		9801.2.a.co.1.9		18
99.58	even	15		1089.2.e.p.364.9		36
99.74	even	30		9801.2.a.cn.1.10		18
99.85	odd	30		1089.2.e.o.364.10		36
99.86	odd	30		297.2.n.b.64.5		72
99.97	even	15		891.2.f.f.163.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	1.1	even	1	trivial
99.2.m.b.31.5	yes	72	99.31	even	15	inner
99.2.m.b.49.5	yes	72	9.4	even	3	inner
99.2.m.b.97.5	yes	72	11.9	even	5	inner
297.2.n.b.64.5		72	99.86	odd	30
297.2.n.b.181.5		72	3.2	odd	2
297.2.n.b.262.5		72	33.20	odd	10
297.2.n.b.280.5		72	9.5	odd	6
891.2.f.e.82.5		36	9.2	odd	6
891.2.f.e.163.5		36	99.20	odd	30
891.2.f.f.82.5		36	9.7	even	3
891.2.f.f.163.5		36	99.97	even	15
1089.2.e.o.364.10		36	99.85	odd	30
1089.2.e.o.727.10		36	11.8	odd	10
1089.2.e.p.364.9		36	99.58	even	15
1089.2.e.p.727.9		36	11.3	even	5
9801.2.a.cm.1.10		18	99.25	even	15
9801.2.a.cn.1.10		18	99.74	even	30
9801.2.a.co.1.9		18	99.52	odd	30
9801.2.a.cp.1.9		18	99.47	odd	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.278917 - 0.0592857i) q^{2} +(-1.04736 + 1.37950i) q^{3} +(-1.75281 - 0.780402i) q^{4} +(-2.64954 + 0.563177i) q^{5} +(0.373912 - 0.322674i) q^{6} +(0.425779 + 4.05102i) q^{7} +(0.904002 + 0.656796i) q^{8} +(-0.806061 - 2.88968i) q^{9} +0.772391 q^{10} +(-3.31056 + 0.200500i) q^{11} +(2.91240 - 1.60065i) q^{12} +(2.57679 - 2.86182i) q^{13} +(0.121410 - 1.15514i) q^{14} +(1.99813 - 4.24490i) q^{15} +(2.35451 + 2.61494i) q^{16} +(-1.33502 + 4.10876i) q^{17} +(0.0535075 + 0.853770i) q^{18} +(1.31246 + 0.953561i) q^{19} +(5.08365 + 1.08056i) q^{20} +(-6.03434 - 3.65553i) q^{21} +(0.935259 + 0.140346i) q^{22} +(0.932117 + 1.61447i) q^{23} +(-1.85287 + 0.559170i) q^{24} +(2.13517 - 0.950641i) q^{25} +(-0.888377 + 0.645443i) q^{26} +(4.83057 + 1.91458i) q^{27} +(2.41511 - 7.43295i) q^{28} +(-0.371426 - 3.53388i) q^{29} +(-0.808974 + 1.06552i) q^{30} +(-3.25505 + 3.61509i) q^{31} +(-1.61909 - 2.80435i) q^{32} +(3.19077 - 4.77692i) q^{33} +(0.615950 - 1.06686i) q^{34} +(-3.40956 - 10.4936i) q^{35} +(-0.842241 + 5.69412i) q^{36} +(-6.26542 + 4.55210i) q^{37} +(-0.309536 - 0.343775i) q^{38} +(1.24905 + 6.55206i) q^{39} +(-2.76508 - 1.23109i) q^{40} +(-0.718335 + 6.83450i) q^{41} +(1.46636 + 1.37734i) q^{42} +(-0.492496 + 0.853027i) q^{43} +(5.95925 + 2.23213i) q^{44} +(3.76310 + 7.20238i) q^{45} +(-0.164268 - 0.505566i) q^{46} +(5.35918 - 2.38606i) q^{47} +(-6.07335 + 0.509254i) q^{48} +(-9.38245 + 1.99430i) q^{49} +(-0.651896 + 0.138565i) q^{50} +(-4.26980 - 6.14502i) q^{51} +(-6.75000 + 3.00529i) q^{52} +(-0.485721 - 1.49489i) q^{53} +(-1.23382 - 0.820393i) q^{54} +(8.65855 - 2.39567i) q^{55} +(-2.27579 + 3.94178i) q^{56} +(-2.69007 + 0.811824i) q^{57} +(-0.105911 + 1.00768i) q^{58} +(10.3802 + 4.62154i) q^{59} +(-6.81507 + 5.88117i) q^{60} +(-5.75953 - 6.39660i) q^{61} +(1.12221 - 0.815335i) q^{62} +(11.3630 - 4.49574i) q^{63} +(-1.88937 - 5.81490i) q^{64} +(-5.21561 + 9.03370i) q^{65} +(-1.17316 + 1.14320i) q^{66} +(0.870282 + 1.50737i) q^{67} +(5.54651 - 6.16003i) q^{68} +(-3.20344 - 0.405082i) q^{69} +(0.328868 + 3.12897i) q^{70} +(-1.77418 + 5.46036i) q^{71} +(1.16925 - 3.14170i) q^{72} +(3.27379 - 2.37855i) q^{73} +(2.01741 - 0.898208i) q^{74} +(-0.924890 + 3.94115i) q^{75} +(-1.55634 - 2.69566i) q^{76} +(-2.22180 - 13.3258i) q^{77} +(0.0400613 - 1.90153i) q^{78} +(4.18662 + 0.889893i) q^{79} +(-7.71104 - 5.60240i) q^{80} +(-7.70053 + 4.65852i) q^{81} +(0.605544 - 1.86367i) q^{82} +(-4.34947 - 4.83058i) q^{83} +(7.72429 + 11.1167i) q^{84} +(1.22322 - 11.6382i) q^{85} +(0.187938 - 0.208726i) q^{86} +(5.26402 + 3.18887i) q^{87} +(-3.12444 - 1.99311i) q^{88} +9.26243 q^{89} +(-0.622594 - 2.23196i) q^{90} +(12.6904 + 9.22014i) q^{91} +(-0.373887 - 3.55729i) q^{92} +(-1.57782 - 8.27667i) q^{93} +(-1.63623 + 0.347790i) q^{94} +(-4.01445 - 1.78735i) q^{95} +(5.56439 + 0.703629i) q^{96} +(7.25070 + 1.54118i) q^{97} +2.73516 q^{98} +(3.24790 + 9.40485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more