LMFDB - Embedded newform 728.2.h.a.27.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(27,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("728.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, 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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.18
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.27.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.629285 + 1.26649i) q^{2} -2.38356i q^{3} +(-1.20800 - 1.59397i) q^{4} -1.68057 q^{5} +(3.01876 + 1.49994i) q^{6} +(1.10198 - 2.40533i) q^{7} +(2.77892 - 0.526865i) q^{8} -2.68138 q^{9} +(1.05755 - 2.12842i) q^{10} +6.45771 q^{11} +(-3.79932 + 2.87935i) q^{12} -1.00000 q^{13} +(2.35287 + 2.90929i) q^{14} +4.00574i q^{15} +(-1.08146 + 3.85103i) q^{16} -0.816850i q^{17} +(1.68735 - 3.39594i) q^{18} -5.75603i q^{19} +(2.03013 + 2.67877i) q^{20} +(-5.73327 - 2.62665i) q^{21} +(-4.06373 + 8.17863i) q^{22} +0.878221i q^{23} +(-1.25582 - 6.62374i) q^{24} -2.17570 q^{25} +(0.629285 - 1.26649i) q^{26} -0.759458i q^{27} +(-5.16522 + 1.14912i) q^{28} +0.973834i q^{29} +(-5.07323 - 2.52075i) q^{30} -3.89496 q^{31} +(-4.19675 - 3.79306i) q^{32} -15.3924i q^{33} +(1.03453 + 0.514031i) q^{34} +(-1.85195 + 4.04232i) q^{35} +(3.23911 + 4.27403i) q^{36} -2.19900i q^{37} +(7.28996 + 3.62218i) q^{38} +2.38356i q^{39} +(-4.67016 + 0.885431i) q^{40} +4.21071i q^{41} +(6.93448 - 5.60823i) q^{42} +3.91987 q^{43} +(-7.80092 - 10.2934i) q^{44} +4.50623 q^{45} +(-1.11226 - 0.552651i) q^{46} -9.01192 q^{47} +(9.17918 + 2.57774i) q^{48} +(-4.57127 - 5.30128i) q^{49} +(1.36913 - 2.75550i) q^{50} -1.94702 q^{51} +(1.20800 + 1.59397i) q^{52} -9.57202i q^{53} +(0.961847 + 0.477915i) q^{54} -10.8526 q^{55} +(1.79504 - 7.26484i) q^{56} -13.7199 q^{57} +(-1.23335 - 0.612818i) q^{58} -0.722834i q^{59} +(6.38501 - 4.83894i) q^{60} +1.45484 q^{61} +(2.45104 - 4.93293i) q^{62} +(-2.95483 + 6.44961i) q^{63} +(7.44483 - 2.92823i) q^{64} +1.68057 q^{65} +(19.4943 + 9.68617i) q^{66} -5.83289 q^{67} +(-1.30203 + 0.986757i) q^{68} +2.09330 q^{69} +(-3.95416 - 4.88926i) q^{70} +5.00020i q^{71} +(-7.45134 + 1.41272i) q^{72} +8.53527i q^{73} +(2.78502 + 1.38380i) q^{74} +5.18592i q^{75} +(-9.17492 + 6.95329i) q^{76} +(7.11628 - 15.5329i) q^{77} +(-3.01876 - 1.49994i) q^{78} +14.3010i q^{79} +(1.81747 - 6.47191i) q^{80} -9.85435 q^{81} +(-5.33282 - 2.64973i) q^{82} -10.7679i q^{83} +(2.73901 + 12.3116i) q^{84} +1.37277i q^{85} +(-2.46672 + 4.96449i) q^{86} +2.32119 q^{87} +(17.9455 - 3.40234i) q^{88} -17.9213i q^{89} +(-2.83570 + 5.70710i) q^{90} +(-1.10198 + 2.40533i) q^{91} +(1.39986 - 1.06089i) q^{92} +9.28389i q^{93} +(5.67106 - 11.4135i) q^{94} +9.67338i q^{95} +(-9.04100 + 10.0032i) q^{96} +13.1424i q^{97} +(9.59065 - 2.45346i) q^{98} -17.3155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.629285	+	1.26649i	−0.444971	+	0.895545i
$2$	−0.629285	+	1.26649i	−0.444971	+	0.895545i
$3$		−	2.38356i		−	1.37615i	−0.725639	−	0.688076i	$-0.758456\pi$
$3$		−	2.38356i		−	1.37615i	0.725639	−	0.688076i	$-0.241544\pi$
$4$	−1.20800	−	1.59397i	−0.604001	−	0.796984i
$5$	−1.68057			−0.751572			−0.375786	−	0.926707i	$-0.622627\pi$
$5$	−1.68057			−0.751572			−0.375786	+	0.926707i	$0.622627\pi$
$6$	3.01876	+	1.49994i	1.23241	+	0.612348i
$7$	1.10198	−	2.40533i	0.416510	−	0.909131i
$7$	1.10198	−	2.40533i	0.416510	−	0.909131i
$8$	2.77892	−	0.526865i	0.982498	−	0.186275i
$9$	−2.68138			−0.893792
$10$	1.05755	−	2.12842i	0.334428	−	0.673066i
$11$	6.45771			1.94707			0.973536	−	0.228535i	$-0.0733935\pi$
$11$	6.45771			1.94707			0.973536	+	0.228535i	$0.0733935\pi$
$12$	−3.79932	+	2.87935i	−1.09677	+	0.831197i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.35287	+	2.90929i	0.628832	+	0.777541i
$15$			4.00574i			1.03428i
$16$	−1.08146	+	3.85103i	−0.270366	+	0.962758i
$17$		−	0.816850i		−	0.198115i	−0.995082	−	0.0990577i	$-0.968417\pi$
$17$		−	0.816850i		−	0.198115i	0.995082	−	0.0990577i	$-0.0315828\pi$
$18$	1.68735	−	3.39594i	0.397712	−	0.800431i
$19$		−	5.75603i		−	1.32052i	−0.751036	−	0.660262i	$-0.770445\pi$
$19$		−	5.75603i		−	1.32052i	0.751036	−	0.660262i	$-0.229555\pi$
$20$	2.03013	+	2.67877i	0.453950	+	0.598990i
$21$	−5.73327	−	2.62665i	−1.25110	−	0.573181i
$22$	−4.06373	+	8.17863i	−0.866391	+	1.74369i
$23$			0.878221i			0.183122i	0.995799	+	0.0915609i	$0.0291856\pi$
$23$			0.878221i			0.183122i	−0.995799	+	0.0915609i	$0.970814\pi$
$24$	−1.25582	−	6.62374i	−0.256342	−	1.35207i
$25$	−2.17570			−0.435140
$26$	0.629285	−	1.26649i	0.123413	−	0.248379i
$27$		−	0.759458i		−	0.146158i
$28$	−5.16522	+	1.14912i	−0.976135	+	0.217164i
$29$			0.973834i			0.180836i	0.995904	+	0.0904182i	$0.0288204\pi$
$29$			0.973834i			0.180836i	−0.995904	+	0.0904182i	$0.971180\pi$
$30$	−5.07323	−	2.52075i	−0.926241	−	0.460224i
$31$	−3.89496			−0.699555			−0.349778	−	0.936833i	$-0.613743\pi$
$31$	−3.89496			−0.699555			−0.349778	+	0.936833i	$0.613743\pi$
$32$	−4.19675	−	3.79306i	−0.741887	−	0.670524i
$33$		−	15.3924i		−	2.67946i
$34$	1.03453	+	0.514031i	0.177421	+	0.0881557i
$35$	−1.85195	+	4.04232i	−0.313037	+	0.683277i
$36$	3.23911	+	4.27403i	0.539851	+	0.712338i
$37$		−	2.19900i		−	0.361514i	−0.983528	−	0.180757i	$-0.942145\pi$
$37$		−	2.19900i		−	0.361514i	0.983528	−	0.180757i	$-0.0578547\pi$
$38$	7.28996	+	3.62218i	1.18259	+	0.587595i
$39$			2.38356i			0.381676i
$40$	−4.67016	+	0.885431i	−0.738418	+	0.139999i
$41$			4.21071i			0.657602i	0.944399	+	0.328801i	$0.106645\pi$
$41$			4.21071i			0.657602i	−0.944399	+	0.328801i	$0.893355\pi$
$42$	6.93448	−	5.60823i	1.07001	−	0.865368i
$43$	3.91987			0.597775			0.298887	−	0.954288i	$-0.403384\pi$
$43$	3.91987			0.597775			0.298887	+	0.954288i	$0.403384\pi$
$44$	−7.80092	−	10.2934i	−1.17603	−	1.55178i
$45$	4.50623			0.671749
$46$	−1.11226	−	0.552651i	−0.163994	−	0.0814839i
$47$	−9.01192			−1.31452			−0.657262	−	0.753662i	$-0.728285\pi$
$47$	−9.01192			−1.31452			−0.657262	+	0.753662i	$0.728285\pi$
$48$	9.17918	+	2.57774i	1.32490	+	0.372064i
$49$	−4.57127	−	5.30128i	−0.653038	−	0.757325i
$50$	1.36913	−	2.75550i	0.193625	−	0.389687i
$51$	−1.94702			−0.272637
$52$	1.20800	+	1.59397i	0.167520	+	0.221043i
$53$		−	9.57202i		−	1.31482i	−0.753534	−	0.657409i	$-0.771652\pi$
$53$		−	9.57202i		−	1.31482i	0.753534	−	0.657409i	$-0.228348\pi$
$54$	0.961847	+	0.477915i	0.130891	+	0.0650360i
$55$	−10.8526			−1.46336
$56$	1.79504	−	7.26484i	0.239872	−	0.970804i
$57$	−13.7199			−1.81724
$58$	−1.23335	−	0.612818i	−0.161947	−	0.0804670i
$59$		−	0.722834i		−	0.0941050i	−0.998892	−	0.0470525i	$-0.985017\pi$
$59$		−	0.722834i		−	0.0941050i	0.998892	−	0.0470525i	$-0.0149828\pi$
$60$	6.38501	−	4.83894i	0.824302	−	0.624704i
$61$	1.45484			0.186273			0.0931365	−	0.995653i	$-0.470311\pi$
$61$	1.45484			0.186273			0.0931365	+	0.995653i	$0.470311\pi$
$62$	2.45104	−	4.93293i	0.311282	−	0.626483i
$63$	−2.95483	+	6.44961i	−0.372274	+	0.812574i
$64$	7.44483	−	2.92823i	0.930603	−	0.366029i
$65$	1.68057			0.208449
$66$	19.4943	+	9.68617i	2.39958	+	1.19229i
$67$	−5.83289			−0.712600			−0.356300	−	0.934372i	$-0.615962\pi$
$67$	−5.83289			−0.712600			−0.356300	+	0.934372i	$0.615962\pi$
$68$	−1.30203	+	0.986757i	−0.157895	+	0.119662i
$69$	2.09330			0.252003
$70$	−3.95416	−	4.88926i	−0.472613	−	0.584378i
$71$			5.00020i			0.593414i	0.954969	+	0.296707i	$0.0958885\pi$
$71$			5.00020i			0.593414i	−0.954969	+	0.296707i	$0.904111\pi$
$72$	−7.45134	+	1.41272i	−0.878149	+	0.166491i
$73$			8.53527i			0.998978i	0.866320	+	0.499489i	$0.166479\pi$
$73$			8.53527i			0.998978i	−0.866320	+	0.499489i	$0.833521\pi$
$74$	2.78502	+	1.38380i	0.323752	+	0.160863i
$75$			5.18592i			0.598818i
$76$	−9.17492	+	6.95329i	−1.05244	+	0.797597i
$77$	7.11628	−	15.5329i	0.810976	−	1.77014i
$78$	−3.01876	−	1.49994i	−0.341808	−	0.169835i
$79$			14.3010i			1.60899i	0.593962	+	0.804493i	$0.297563\pi$
$79$			14.3010i			1.60899i	−0.593962	+	0.804493i	$0.702437\pi$
$80$	1.81747	−	6.47191i	0.203199	−	0.723582i
$81$	−9.85435			−1.09493
$82$	−5.33282	−	2.64973i	−0.588912	−	0.292614i
$83$		−	10.7679i		−	1.18193i	−0.806696	−	0.590967i	$-0.798746\pi$
$83$		−	10.7679i		−	1.18193i	0.806696	−	0.590967i	$-0.201254\pi$
$84$	2.73901	+	12.3116i	0.298850	+	1.34331i
$85$			1.37277i			0.148898i
$86$	−2.46672	+	4.96449i	−0.265993	+	0.535334i
$87$	2.32119			0.248858
$88$	17.9455	−	3.40234i	1.91299	−	0.362690i
$89$		−	17.9213i		−	1.89965i	−0.312782	−	0.949825i	$-0.601261\pi$
$89$		−	17.9213i		−	1.89965i	0.312782	−	0.949825i	$-0.398739\pi$
$90$	−2.83570	+	5.70710i	−0.298909	+	0.601581i
$91$	−1.10198	+	2.40533i	−0.115519	+	0.252148i
$92$	1.39986	−	1.06089i	0.145945	−	0.110606i
$93$			9.28389i			0.962694i
$94$	5.67106	−	11.4135i	0.584926	−	1.17722i
$95$			9.67338i			0.992468i
$96$	−9.04100	+	10.0032i	−0.922743	+	1.02095i
$97$			13.1424i			1.33441i	0.744874	+	0.667206i	$0.232510\pi$
$97$			13.1424i			1.33441i	−0.744874	+	0.667206i	$0.767490\pi$
$98$	9.59065	−	2.45346i	0.968802	−	0.247837i
$99$	−17.3155			−1.74028
$100$	2.62825	+	3.46799i	0.262825	+	0.346799i
$101$	16.8120			1.67286			0.836429	−	0.548075i	$-0.184639\pi$
$101$	16.8120			1.67286			0.836429	+	0.548075i	$0.184639\pi$
$102$	1.22523	−	2.46588i	0.121316	−	0.244158i
$103$	7.83407			0.771914			0.385957	−	0.922517i	$-0.373871\pi$
$103$	7.83407			0.771914			0.385957	+	0.922517i	$0.373871\pi$
$104$	−2.77892	+	0.526865i	−0.272496	+	0.0516634i
$105$	9.63513	+	4.41425i	0.940293	+	0.430787i
$106$	12.1229	+	6.02353i	1.17748	+	0.585057i
$107$	9.20742			0.890115			0.445057	−	0.895502i	$-0.353183\pi$
$107$	9.20742			0.890115			0.445057	+	0.895502i	$0.353183\pi$
$108$	−1.21055	+	0.917426i	−0.116485	+	0.0882794i
$109$			2.51531i			0.240923i	0.992718	+	0.120461i	$0.0384374\pi$
$109$			2.51531i			0.240923i	−0.992718	+	0.120461i	$0.961563\pi$
$110$	6.82937	−	13.7447i	0.651155	−	1.31051i
$111$	−5.24146			−0.497498
$112$	8.07126	+	6.84505i	0.762663	+	0.646797i
$113$	−4.54621			−0.427671			−0.213836	−	0.976870i	$-0.568596\pi$
$113$	−4.54621			−0.427671			−0.213836	+	0.976870i	$0.568596\pi$
$114$	8.63370	−	17.3761i	0.808620	−	1.62742i
$115$		−	1.47591i		−	0.137629i
$116$	1.55226	−	1.17639i	0.144124	−	0.109225i
$117$	2.68138			0.247893
$118$	0.915463	+	0.454868i	0.0842752	+	0.0418740i
$119$	−1.96480	−	0.900155i	−0.180113	−	0.0825171i
$120$	2.11048	+	11.1316i	0.192660	+	1.01617i
$121$	30.7020			2.79109
$122$	−0.915507	+	1.84254i	−0.0828861	+	0.166816i
$123$	10.0365			0.904960
$124$	4.70512	+	6.20844i	0.422532	+	0.557534i
$125$	12.0592			1.07861
$126$	−6.30895	−	7.80091i	−0.562045	−	0.694960i
$127$		−	15.5388i		−	1.37884i	−0.724360	−	0.689422i	$-0.757865\pi$
$127$		−	15.5388i		−	1.37884i	0.724360	−	0.689422i	$-0.242135\pi$
$128$	−0.976331	+	11.2715i	−0.0862963	+	0.996270i
$129$		−	9.34327i		−	0.822629i
$130$	−1.05755	+	2.12842i	−0.0927536	+	0.186675i
$131$			13.0448i			1.13973i	0.821738	+	0.569865i	$0.193005\pi$
$131$			13.0448i			1.13973i	−0.821738	+	0.569865i	$0.806995\pi$
$132$	−24.5349	+	18.5940i	−2.13549	+	1.61840i
$133$	−13.8452	−	6.34304i	−1.20053	−	0.550012i
$134$	3.67055	−	7.38730i	0.317087	−	0.638166i
$135$			1.27632i			0.109848i
$136$	−0.430370	−	2.26996i	−0.0369039	−	0.194648i
$137$	5.11894			0.437341			0.218670	−	0.975799i	$-0.429828\pi$
$137$	5.11894			0.437341			0.218670	+	0.975799i	$0.429828\pi$
$138$	−1.31728	+	2.65114i	−0.112134	+	0.225680i
$139$		−	0.246340i		−	0.0208943i	−0.999945	−	0.0104471i	$-0.996675\pi$
$139$		−	0.246340i		−	0.0208943i	0.999945	−	0.0104471i	$-0.00332549\pi$
$140$	8.68049	−	1.93118i	0.733636	−	0.163214i
$141$			21.4805i			1.80898i
$142$	−6.33271	−	3.14655i	−0.531429	−	0.264052i
$143$	−6.45771			−0.540020
$144$	2.89981	−	10.3261i	0.241651	−	0.860505i
$145$		−	1.63659i		−	0.135912i
$146$	−10.8098	−	5.37111i	−0.894629	−	0.444516i
$147$	−12.6359	+	10.8959i	−1.04219	+	0.898679i
$148$	−3.50514	+	2.65640i	−0.288121	+	0.218355i
$149$		−	0.552841i		−	0.0452905i	−0.999744	−	0.0226452i	$-0.992791\pi$
$149$		−	0.552841i		−	0.0452905i	0.999744	−	0.0226452i	$-0.00720882\pi$
$150$	−6.56792	−	3.26342i	−0.536268	−	0.266457i
$151$		−	5.10249i		−	0.415235i	−0.978210	−	0.207617i	$-0.933429\pi$
$151$		−	5.10249i		−	0.415235i	0.978210	−	0.207617i	$-0.0665709\pi$
$152$	−3.03265	−	15.9956i	−0.245980	−	1.29741i
$153$			2.19028i			0.177074i
$154$	15.1942	+	18.7874i	1.22438	+	1.51393i
$155$	6.54574			0.525766
$156$	3.79932	−	2.87935i	0.304189	−	0.230532i
$157$	−19.7641			−1.57735			−0.788675	−	0.614810i	$-0.789233\pi$
$157$	−19.7641			−1.57735			−0.788675	+	0.614810i	$0.789233\pi$
$158$	−18.1121	−	8.99939i	−1.44092	−	0.715953i
$159$	−22.8155			−1.80939
$160$	7.05291	+	6.37448i	0.557582	+	0.503947i
$161$	2.11242	+	0.967785i	0.166482	+	0.0762721i
$162$	6.20119	−	12.4804i	0.487211	−	0.980557i
$163$	−9.64780			−0.755674			−0.377837	−	0.925872i	$-0.623332\pi$
$163$	−9.64780			−0.755674			−0.377837	+	0.925872i	$0.623332\pi$
$164$	6.71173	−	5.08654i	0.524098	−	0.397192i
$165$			25.8679i			2.01381i
$166$	13.6375	+	6.77610i	1.05848	+	0.525927i
$167$	20.9545			1.62150			0.810752	−	0.585390i	$-0.199058\pi$
$167$	20.9545			1.62150			0.810752	+	0.585390i	$0.199058\pi$
$168$	−17.3162	−	4.27859i	−1.33597	−	0.330101i
$169$	1.00000			0.0769231
$170$	−1.73860	−	0.863864i	−0.133345	−	0.0662553i
$171$			15.4341i			1.18027i
$172$	−4.73521	−	6.24815i	−0.361057	−	0.476417i
$173$	−12.0936			−0.919456			−0.459728	−	0.888060i	$-0.652053\pi$
$173$	−12.0936			−0.919456			−0.459728	+	0.888060i	$0.652053\pi$
$174$	−1.46069	+	2.93977i	−0.110735	+	0.222864i
$175$	−2.39758	+	5.23328i	−0.181240	+	0.395599i
$176$	−6.98377	+	24.8688i	−0.526422	+	1.87456i
$177$	−1.72292			−0.129503
$178$	22.6971	+	11.2776i	1.70122	+	0.845290i
$179$	2.49636			0.186587			0.0932934	−	0.995639i	$-0.470261\pi$
$179$	2.49636			0.186587			0.0932934	+	0.995639i	$0.470261\pi$
$180$	−5.44353	−	7.18278i	−0.405737	−	0.535373i
$181$	13.0487			0.969903			0.484951	−	0.874541i	$-0.338837\pi$
$181$	13.0487			0.969903			0.484951	+	0.874541i	$0.338837\pi$
$182$	−2.35287	−	2.90929i	−0.174407	−	0.215651i
$183$		−	3.46770i		−	0.256340i
$184$	0.462704	+	2.44051i	0.0341110	+	0.179917i
$185$			3.69557i			0.271704i
$186$	−11.7580	−	5.84221i	−0.862136	−	0.428371i
$187$		−	5.27498i		−	0.385745i
$188$	10.8864	+	14.3647i	0.793974	+	1.04765i
$189$	−1.82675	−	0.836909i	−0.132876	−	0.0608762i
$190$	−12.2513	−	6.08731i	−0.888800	−	0.441620i
$191$			5.23967i			0.379129i	0.981868	+	0.189565i	$0.0607076\pi$
$191$			5.23967i			0.379129i	−0.981868	+	0.189565i	$0.939292\pi$
$192$	−6.97963	−	17.7452i	−0.503712	−	1.28065i
$193$	−16.4515			−1.18420			−0.592102	−	0.805863i	$-0.701702\pi$
$193$	−16.4515			−1.18420			−0.592102	+	0.805863i	$0.701702\pi$
$194$	−16.6448	−	8.27033i	−1.19502	−	0.593775i
$195$		−	4.00574i		−	0.286857i
$196$	−2.92796	+	13.6904i	−0.209140	+	0.977886i
$197$		−	18.0122i		−	1.28331i	−0.766991	−	0.641657i	$-0.778247\pi$
$197$		−	18.0122i		−	1.28331i	0.766991	−	0.641657i	$-0.221753\pi$
$198$	10.8964	−	21.9300i	0.774374	−	1.55850i
$199$	−9.12392			−0.646778			−0.323389	−	0.946266i	$-0.604822\pi$
$199$	−9.12392			−0.646778			−0.323389	+	0.946266i	$0.604822\pi$
$200$	−6.04610	+	1.14630i	−0.427524	+	0.0810556i
$201$			13.9031i			0.980646i
$202$	−10.5795	+	21.2923i	−0.744374	+	1.49812i
$203$	2.34240	+	1.07315i	0.164404	+	0.0753202i
$204$	2.35200	+	3.10348i	0.164673	+	0.217287i
$205$		−	7.07637i		−	0.494235i
$206$	−4.92986	+	9.92179i	−0.343480	+	0.691284i
$207$		−	2.35484i		−	0.163673i
$208$	1.08146	−	3.85103i	0.0749860	−	0.267021i
$209$		−	37.1707i		−	2.57115i
$210$	−11.6539	+	9.42500i	−0.804192	+	0.650386i
$211$	17.3894			1.19713			0.598567	−	0.801073i	$-0.295737\pi$
$211$	17.3894			1.19713			0.598567	+	0.801073i	$0.295737\pi$
$212$	−15.2575	+	11.5630i	−1.04789	+	0.794152i
$213$	11.9183			0.816628
$214$	−5.79409	+	11.6611i	−0.396076	+	0.797138i
$215$	−6.58760			−0.449271
$216$	−0.400132	−	2.11047i	−0.0272255	−	0.143600i
$217$	−4.29218	+	9.36868i	−0.291372	+	0.635987i
$218$	−3.18562	−	1.58284i	−0.215757	−	0.107204i
$219$	20.3444			1.37474
$220$	13.1100	+	17.2987i	0.883873	+	1.16628i
$221$			0.816850i			0.0549473i
$222$	3.29837	−	6.63827i	0.221372	−	0.445531i
$223$	−2.74027			−0.183502			−0.0917510	−	0.995782i	$-0.529246\pi$
$223$	−2.74027			−0.183502			−0.0917510	+	0.995782i	$0.529246\pi$
$224$	−13.7483	+	5.91470i	−0.918598	+	0.395192i
$225$	5.83387			0.388925
$226$	2.86086	−	5.75773i	0.190301	−	0.382999i
$227$			16.9588i			1.12559i	0.826595	+	0.562797i	$0.190275\pi$
$227$			16.9588i			1.12559i	−0.826595	+	0.562797i	$0.809725\pi$
$228$	16.5736	+	21.8690i	1.09761	+	1.44831i
$229$	−20.6306			−1.36331			−0.681655	−	0.731674i	$-0.738739\pi$
$229$	−20.6306			−1.36331			−0.681655	+	0.731674i	$0.738739\pi$
$230$	1.86923	+	0.928766i	0.123253	+	0.0612410i
$231$	−37.0238	−	16.9621i	−2.43598	−	1.11603i
$232$	0.513079	+	2.70621i	0.0336853	+	0.177671i
$233$	20.2350			1.32564			0.662821	−	0.748778i	$-0.269359\pi$
$233$	20.2350			1.32564			0.662821	+	0.748778i	$0.269359\pi$
$234$	−1.68735	+	3.39594i	−0.110305	+	0.222000i
$235$	15.1451			0.987959
$236$	−1.15217	+	0.873185i	−0.0750002	+	0.0568395i
$237$	34.0873			2.21421
$238$	2.37646	−	1.92195i	0.154043	−	0.124581i
$239$		−	18.8318i		−	1.21813i	−0.793122	−	0.609063i	$-0.791546\pi$
$239$		−	18.8318i		−	1.21813i	0.793122	−	0.609063i	$-0.208454\pi$
$240$	−15.4262	−	4.33206i	−0.995758	−	0.279633i
$241$			4.30150i			0.277084i	0.990357	+	0.138542i	$0.0442415\pi$
$241$			4.30150i			0.277084i	−0.990357	+	0.138542i	$0.955758\pi$
$242$	−19.3203	+	38.8838i	−1.24195	+	2.49954i
$243$			21.2101i			1.36063i
$244$	−1.75745	−	2.31896i	−0.112509	−	0.148456i
$245$	7.68231	+	8.90914i	0.490805	+	0.569184i
$246$	−6.31581	+	12.7111i	−0.402681	+	0.810432i
$247$			5.75603i			0.366247i
$248$	−10.8238	+	2.05212i	−0.687312	+	0.130310i
$249$	−25.6661			−1.62652
$250$	−7.58869	+	15.2729i	−0.479951	+	0.965944i
$251$			7.40762i			0.467565i	0.972289	+	0.233782i	$0.0751103\pi$
$251$			7.40762i			0.467565i	−0.972289	+	0.233782i	$0.924890\pi$
$252$	13.8499	−	3.08123i	0.872462	−	0.194099i
$253$			5.67129i			0.356551i
$254$	19.6797	+	9.77831i	1.23482	+	0.613546i
$255$	3.27209			0.204906
$256$	−13.6609	−	8.32950i	−0.853805	−	0.520594i
$257$			8.82159i			0.550276i	0.961405	+	0.275138i	$0.0887235\pi$
$257$			8.82159i			0.550276i	−0.961405	+	0.275138i	$0.911277\pi$
$258$	11.8332	+	5.87957i	0.736701	+	0.366046i
$259$	−5.28933	−	2.42326i	−0.328663	−	0.150574i
$260$	−2.03013	−	2.67877i	−0.125903	−	0.166130i
$261$		−	2.61122i		−	0.161630i
$262$	−16.5212	−	8.20890i	−1.02068	−	0.507148i
$263$		−	17.8426i		−	1.10022i	−0.835092	−	0.550110i	$-0.814586\pi$
$263$		−	17.8426i		−	1.10022i	0.835092	−	0.550110i	$-0.185414\pi$
$264$	−8.10969	−	42.7742i	−0.499117	−	2.63257i
$265$			16.0864i			0.988181i
$266$	16.7460	−	13.5432i	1.02676	−	0.830388i
$267$	−42.7165			−2.61421
$268$	7.04614	+	9.29743i	0.430411	+	0.567931i
$269$	22.2065			1.35395			0.676976	−	0.736005i	$-0.263290\pi$
$269$	22.2065			1.35395			0.676976	+	0.736005i	$0.263290\pi$
$270$	−1.61645	−	0.803168i	−0.0983738	−	0.0488792i
$271$	10.1511			0.616635			0.308318	−	0.951283i	$-0.400234\pi$
$271$	10.1511			0.616635			0.308318	+	0.951283i	$0.400234\pi$
$272$	3.14572	+	0.883394i	0.190737	+	0.0535636i
$273$	5.73327	+	2.62665i	0.346993	+	0.158972i
$274$	−3.22127	+	6.48309i	−0.194604	+	0.391658i
$275$	−14.0500			−0.847248
$276$	−2.52871	−	3.33665i	−0.152210	−	0.200842i
$277$		−	18.4917i		−	1.11106i	−0.831497	−	0.555530i	$-0.812516\pi$
$277$		−	18.4917i		−	1.11106i	0.831497	−	0.555530i	$-0.187484\pi$
$278$	0.311988	+	0.155018i	0.0187118	+	0.00929736i
$279$	10.4439			0.625257
$280$	−3.01668	+	12.2090i	−0.180281	+	0.729629i
$281$	−2.67691			−0.159691			−0.0798456	−	0.996807i	$-0.525443\pi$
$281$	−2.67691			−0.159691			−0.0798456	+	0.996807i	$0.525443\pi$
$282$	−27.2049	−	13.5173i	−1.62003	−	0.804946i
$283$			22.6633i			1.34719i	0.739100	+	0.673596i	$0.235251\pi$
$283$			22.6633i			1.34719i	−0.739100	+	0.673596i	$0.764749\pi$
$284$	7.97015	−	6.04025i	0.472942	−	0.358423i
$285$	23.0571			1.36579
$286$	4.06373	−	8.17863i	0.240294	−	0.483612i
$287$	10.1282	+	4.64013i	0.597846	+	0.273898i
$288$	11.2531	+	10.1706i	0.663093	+	0.599310i
$289$	16.3328			0.960750
$290$	2.07273	+	1.02988i	0.121715	+	0.0604767i
$291$	31.3258			1.83635
$292$	13.6049	−	10.3106i	0.796169	−	0.603383i
$293$	33.5920			1.96247			0.981234	−	0.192821i	$-0.0617636\pi$
$293$	33.5920			1.96247			0.981234	+	0.192821i	$0.0617636\pi$
$294$	−5.84798	−	22.8599i	−0.341061	−	1.33322i
$295$			1.21477i			0.0707267i
$296$	−1.15858	−	6.11086i	−0.0673409	−	0.355186i
$297$		−	4.90435i		−	0.284579i
$298$	0.700168	+	0.347894i	0.0405597	+	0.0201530i
$299$		−	0.878221i		−	0.0507888i
$300$	8.26618	−	6.26460i	0.477248	−	0.361687i
$301$	4.31963	−	9.42860i	0.248980	−	0.543456i
$302$	6.46226	+	3.21092i	0.371861	+	0.184768i
$303$		−	40.0725i		−	2.30211i
$304$	22.1666	+	6.22493i	1.27134	+	0.357024i
$305$	−2.44495			−0.139997
$306$	−2.77398	−	1.37831i	−0.158578	−	0.0787929i
$307$		−	22.5430i		−	1.28660i	−0.765616	−	0.643298i	$-0.777566\pi$
$307$		−	22.5430i		−	1.28660i	0.765616	−	0.643298i	$-0.222434\pi$
$308$	−33.3555	+	7.42070i	−1.90060	+	0.422834i
$309$		−	18.6730i		−	1.06227i
$310$	−4.11913	+	8.29012i	−0.233951	+	0.470847i
$311$	14.5078			0.822663			0.411332	−	0.911486i	$-0.365064\pi$
$311$	14.5078			0.822663			0.411332	+	0.911486i	$0.365064\pi$
$312$	1.25582	+	6.62374i	0.0710966	+	0.374995i
$313$		−	28.4797i		−	1.60977i	−0.593433	−	0.804883i	$-0.702228\pi$
$313$		−	28.4797i		−	1.60977i	0.593433	−	0.804883i	$-0.297772\pi$
$314$	12.4373	−	25.0311i	0.701876	−	1.41259i
$315$	4.96579	−	10.8390i	0.279791	−	0.610708i
$316$	22.7953	−	17.2756i	1.28234	−	0.971829i
$317$		−	9.99512i		−	0.561382i	−0.959798	−	0.280691i	$-0.909436\pi$
$317$		−	9.99512i		−	0.561382i	0.959798	−	0.280691i	$-0.0905636\pi$
$318$	14.3575	−	28.8957i	0.805126	−	1.62039i
$319$			6.28873i			0.352101i
$320$	−12.5115	+	4.92109i	−0.699415	+	0.275097i
$321$		−	21.9465i		−	1.22493i
$322$	−2.55500	+	2.06634i	−0.142385	+	0.115153i
$323$	−4.70181			−0.261616
$324$	11.9041	+	15.7075i	0.661337	+	0.872639i
$325$	2.17570			0.120686
$326$	6.07121	−	12.2189i	0.336253	−	0.676740i
$327$	5.99540			0.331546
$328$	2.21847	+	11.7012i	0.122495	+	0.646092i
$329$	−9.93098	+	21.6767i	−0.547513	+	1.19507i
$330$	−32.7614	−	16.2782i	−1.80346	−	0.896088i
$331$	−5.10543			−0.280620			−0.140310	−	0.990108i	$-0.544810\pi$
$331$	−5.10543			−0.280620			−0.140310	+	0.990108i	$0.544810\pi$
$332$	−17.1637	+	13.0077i	−0.941982	+	0.713889i
$333$			5.89635i			0.323118i
$334$	−13.1863	+	26.5386i	−0.721523	+	1.45213i
$335$	9.80255			0.535570
$336$	16.3156	−	19.2384i	0.890090	−	1.04954i
$337$	12.5235			0.682200			0.341100	−	0.940027i	$-0.389200\pi$
$337$	12.5235			0.682200			0.341100	+	0.940027i	$0.389200\pi$
$338$	−0.629285	+	1.26649i	−0.0342286	+	0.0688881i
$339$			10.8362i			0.588540i
$340$	2.18815	−	1.65831i	0.118669	−	0.0899345i
$341$	−25.1525			−1.36208
$342$	−19.5471	−	9.71243i	−1.05699	−	0.525188i
$343$	−17.7888	+	5.15351i	−0.960505	+	0.278263i
$344$	10.8930	−	2.06524i	0.587313	−	0.111350i
$345$	−3.51792			−0.189399
$346$	7.61029	−	15.3164i	0.409132	−	0.823414i
$347$	27.2021			1.46029			0.730143	−	0.683295i	$-0.239454\pi$
$347$	27.2021			1.46029			0.730143	+	0.683295i	$0.239454\pi$
$348$	−2.80401	−	3.69991i	−0.150311	−	0.198336i
$349$	−16.8525			−0.902096			−0.451048	−	0.892500i	$-0.648950\pi$
$349$	−16.8525			−0.902096			−0.451048	+	0.892500i	$0.648950\pi$
$350$	−5.11915	−	6.32974i	−0.273630	−	0.338339i
$351$			0.759458i			0.0405369i
$352$	−27.1014	−	24.4945i	−1.44451	−	1.30556i
$353$			5.53986i			0.294857i	0.989073	+	0.147429i	$0.0470996\pi$
$353$			5.53986i			0.294857i	−0.989073	+	0.147429i	$0.952900\pi$
$354$	1.08421	−	2.18207i	0.0576250	−	0.115975i
$355$		−	8.40316i		−	0.445993i
$356$	−28.5659	+	21.6489i	−1.51399	+	1.14739i
$357$	−2.14558	+	4.68322i	−0.113556	+	0.247862i
$358$	−1.57092	+	3.16162i	−0.0830258	+	0.167097i
$359$			18.2949i			0.965567i	0.875740	+	0.482784i	$0.160374\pi$
$359$			18.2949i			0.965567i	−0.875740	+	0.482784i	$0.839626\pi$
$360$	12.5225	−	2.37417i	0.659992	−	0.125130i
$361$	−14.1319			−0.743782
$362$	−8.21135	+	16.5261i	−0.431579	+	0.868592i
$363$		−	73.1801i		−	3.84096i
$364$	5.16522	−	1.14912i	0.270731	−	0.0602304i
$365$		−	14.3441i		−	0.750803i
$366$	4.39181	+	2.18217i	0.229564	+	0.114064i
$367$	32.4218			1.69240			0.846202	−	0.532862i	$-0.178884\pi$
$367$	32.4218			1.69240			0.846202	+	0.532862i	$0.178884\pi$
$368$	−3.38206	−	0.949764i	−0.176302	−	0.0495099i
$369$		−	11.2905i		−	0.587760i
$370$	−4.68040	−	2.32556i	−0.243323	−	0.120900i
$371$	−23.0239	−	10.5482i	−1.19534	−	0.547636i
$372$	14.7982	−	11.2150i	0.767251	−	0.581468i
$373$			12.6232i			0.653604i	0.945093	+	0.326802i	$0.105971\pi$
$373$			12.6232i			0.653604i	−0.945093	+	0.326802i	$0.894029\pi$
$374$	6.68072	+	3.31946i	0.345452	+	0.171645i
$375$		−	28.7440i		−	1.48433i
$376$	−25.0434	+	4.74807i	−1.29152	+	0.244863i
$377$		−	0.973834i		−	0.0501550i
$378$	2.20948	−	1.78691i	0.113644	−	0.0919087i
$379$	18.1976			0.934746			0.467373	−	0.884060i	$-0.345200\pi$
$379$	18.1976			0.934746			0.467373	+	0.884060i	$0.345200\pi$
$380$	15.4191	−	11.6855i	0.790981	−	0.599452i
$381$	−37.0377			−1.89750
$382$	−6.63600	−	3.29724i	−0.339527	−	0.168702i
$383$	18.4321			0.941835			0.470917	−	0.882177i	$-0.343923\pi$
$383$	18.4321			0.941835			0.470917	+	0.882177i	$0.343923\pi$
$384$	26.8663	+	2.32715i	1.37102	+	0.118757i
$385$	−11.9594	+	26.1041i	−0.609506	+	1.33039i
$386$	10.3527	−	20.8357i	0.526937	−	1.06051i
$387$	−10.5107			−0.534287
$388$	20.9486	−	15.8761i	1.06350	−	0.805985i
$389$			19.8567i			1.00678i	0.864060	+	0.503388i	$0.167914\pi$
$389$			19.8567i			1.00678i	−0.864060	+	0.503388i	$0.832086\pi$
$390$	5.07323	+	2.52075i	0.256893	+	0.127643i
$391$	0.717375			0.0362792
$392$	−15.4963	−	12.3234i	−0.782679	−	0.622425i
$393$	31.0932			1.56844
$394$	22.8123	+	11.3348i	1.14927	+	0.571038i
$395$		−	24.0337i		−	1.20927i
$396$	20.9172	+	27.6004i	1.05113	+	1.38697i
$397$	7.46775			0.374796			0.187398	−	0.982284i	$-0.439995\pi$
$397$	7.46775			0.374796			0.187398	+	0.982284i	$0.439995\pi$
$398$	5.74154	−	11.5554i	0.287798	−	0.579218i
$399$	−15.1191	+	33.0008i	−0.756899	+	1.65211i
$400$	2.35294	−	8.37868i	0.117647	−	0.418934i
$401$	−3.95952			−0.197729			−0.0988644	−	0.995101i	$-0.531521\pi$
$401$	−3.95952			−0.197729			−0.0988644	+	0.995101i	$0.531521\pi$
$402$	−17.6081	−	8.74898i	−0.878212	−	0.436359i
$403$	3.89496			0.194022
$404$	−20.3089	−	26.7978i	−1.01041	−	1.33324i
$405$	16.5609			0.822917
$406$	−2.83317	+	2.29131i	−0.140608	+	0.113716i
$407$		−	14.2005i		−	0.703893i
$408$	−5.41061	+	1.02581i	−0.267865	+	0.0507854i
$409$			18.5513i			0.917303i	0.888616	+	0.458652i	$0.151667\pi$
$409$			18.5513i			0.917303i	−0.888616	+	0.458652i	$0.848333\pi$
$410$	8.96216	+	4.45305i	0.442610	+	0.219920i
$411$		−	12.2013i		−	0.601847i
$412$	−9.46357	−	12.4873i	−0.466237	−	0.615203i
$413$	−1.73866	−	0.796551i	−0.0855538	−	0.0391957i
$414$	2.98239	+	1.48187i	0.146576	+	0.0728297i
$415$			18.0962i			0.888309i
$416$	4.19675	+	3.79306i	0.205763	+	0.185970i
$417$	−0.587167			−0.0287537
$418$	47.0764	+	23.3910i	2.30258	+	1.14409i
$419$			40.1301i			1.96048i	0.197800	+	0.980242i	$0.436620\pi$
$419$			40.1301i			1.96048i	−0.197800	+	0.980242i	$0.563380\pi$
$420$	−4.60308	−	20.6905i	−0.224608	−	1.00959i
$421$		−	7.51607i		−	0.366311i	−0.983084	−	0.183155i	$-0.941369\pi$
$421$		−	7.51607i		−	0.366311i	0.983084	−	0.183155i	$-0.0586311\pi$
$422$	−10.9429	+	22.0235i	−0.532690	+	1.07209i
$423$	24.1644			1.17491
$424$	−5.04316	−	26.5999i	−0.244918	−	1.29181i
$425$			1.77722i			0.0862079i
$426$	−7.50000	+	15.0944i	−0.363376	+	0.731327i
$427$	1.60321	−	3.49937i	0.0775846	−	0.169346i
$428$	−11.1226	−	14.6763i	−0.537630	−	0.709407i
$429$			15.3924i			0.743150i
$430$	4.14548	−	8.34314i	0.199913	−	0.402342i
$431$			23.2557i			1.12019i	0.828429	+	0.560095i	$0.189235\pi$
$431$			23.2557i			1.12019i	−0.828429	+	0.560095i	$0.810765\pi$
$432$	2.92469	+	0.821326i	0.140714	+	0.0395161i
$433$		−	12.0026i		−	0.576809i	−0.957509	−	0.288404i	$-0.906875\pi$
$433$		−	12.0026i		−	0.576809i	0.957509	−	0.288404i	$-0.0931247\pi$
$434$	−9.16435	−	11.3316i	−0.439903	−	0.543933i
$435$	−3.90092			−0.187035
$436$	4.00932	−	3.03850i	0.192012	−	0.145518i
$437$	5.05506			0.241817
$438$	−12.8024	+	25.7660i	−0.611722	+	1.23115i
$439$	19.8600			0.947867			0.473933	−	0.880561i	$-0.342834\pi$
$439$	19.8600			0.947867			0.473933	+	0.880561i	$0.342834\pi$
$440$	−30.1585	+	5.71785i	−1.43775	+	0.272588i
$441$	12.2573	+	14.2147i	0.583681	+	0.676891i
$442$	−1.03453	−	0.514031i	−0.0492078	−	0.0244500i
$443$	−36.9563			−1.75585			−0.877924	−	0.478800i	$-0.841072\pi$
$443$	−36.9563			−1.75585			−0.877924	+	0.478800i	$0.841072\pi$
$444$	6.33170	+	8.35472i	0.300489	+	0.396497i
$445$			30.1179i			1.42772i
$446$	1.72441	−	3.47053i	0.0816532	−	0.164334i
$447$	−1.31773			−0.0623266
$448$	1.16069	−	21.1342i	0.0548374	−	0.998495i
$449$	−27.0181			−1.27506			−0.637531	−	0.770425i	$-0.720044\pi$
$449$	−27.0181			−1.27506			−0.637531	+	0.770425i	$0.720044\pi$
$450$	−3.67116	+	7.38855i	−0.173060	+	0.348299i
$451$			27.1915i			1.28040i
$452$	5.49182	+	7.24650i	0.258314	+	0.340847i
$453$	−12.1621			−0.571426
$454$	−21.4782	−	10.6719i	−1.00802	−	0.500857i
$455$	1.85195	−	4.04232i	0.0868210	−	0.189507i
$456$	−38.1264	+	7.22851i	−1.78543	+	0.338506i
$457$	−18.2396			−0.853214			−0.426607	−	0.904437i	$-0.640291\pi$
$457$	−18.2396			−0.853214			−0.426607	+	0.904437i	$0.640291\pi$
$458$	12.9825	−	26.1285i	0.606634	−	1.22091i
$459$	−0.620363			−0.0289561
$460$	−2.35255	+	1.78290i	−0.109688	+	0.0831281i
$461$	−29.4658			−1.37236			−0.686179	−	0.727432i	$-0.740713\pi$
$461$	−29.4658			−1.37236			−0.686179	+	0.727432i	$0.740713\pi$
$462$	44.7809	−	36.2163i	2.08339	−	1.68493i
$463$		−	34.1247i		−	1.58591i	−0.609280	−	0.792955i	$-0.708541\pi$
$463$		−	34.1247i		−	1.58591i	0.609280	−	0.792955i	$-0.291459\pi$
$464$	−3.75026	−	1.05317i	−0.174102	−	0.0488920i
$465$		−	15.6022i		−	0.723534i
$466$	−12.7336	+	25.6275i	−0.589872	+	1.18717i
$467$		−	10.3935i		−	0.480952i	−0.970655	−	0.240476i	$-0.922696\pi$
$467$		−	10.3935i		−	0.480952i	0.970655	−	0.240476i	$-0.0773036\pi$
$468$	−3.23911	−	4.27403i	−0.149728	−	0.197567i
$469$	−6.42774	+	14.0300i	−0.296806	+	0.647847i
$470$	−9.53060	+	19.1812i	−0.439614	+	0.884762i
$471$			47.1091i			2.17067i
$472$	−0.380836	−	2.00870i	−0.0175294	−	0.0924579i
$473$	25.3134			1.16391
$474$	−21.4506	+	43.1713i	−0.985259	+	1.98292i
$475$			12.5234i			0.574612i
$476$	0.938662	+	4.21921i	0.0430235	+	0.193387i
$477$			25.6662i			1.17517i
$478$	23.8503	+	11.8505i	1.09089	+	0.542031i
$479$	25.5721			1.16842			0.584210	−	0.811602i	$-0.301404\pi$
$479$	25.5721			1.16842			0.584210	+	0.811602i	$0.301404\pi$
$480$	15.1940	−	16.8111i	0.693508	−	0.767317i
$481$			2.19900i			0.100266i
$482$	−5.44781	−	2.70687i	−0.248141	−	0.123294i
$483$	2.30678	−	5.03508i	0.104962	−	0.229104i
$484$	−37.0880	−	48.9379i	−1.68582	−	2.22445i
$485$		−	22.0867i		−	1.00291i
$486$	−26.8624	−	13.3472i	−1.21850	−	0.605441i
$487$			37.3038i			1.69040i	0.534453	+	0.845198i	$0.320518\pi$
$487$			37.3038i			1.69040i	−0.534453	+	0.845198i	$0.679482\pi$
$488$	4.04288	−	0.766503i	0.183013	−	0.0346980i
$489$			22.9961i			1.03992i
$490$	−16.1177	+	4.12320i	−0.728124	+	0.186267i
$491$	36.8751			1.66415			0.832075	−	0.554663i	$-0.187153\pi$
$491$	36.8751			1.66415			0.832075	+	0.554663i	$0.187153\pi$
$492$	−12.1241	−	15.9978i	−0.546596	−	0.721238i
$493$	0.795476			0.0358265
$494$	−7.28996	−	3.62218i	−0.327991	−	0.162970i
$495$	29.0999			1.30794
$496$	4.21226	−	14.9996i	0.189136	−	0.673502i
$497$	12.0271	+	5.51013i	0.539491	+	0.247163i
$498$	16.1513	−	32.5059i	0.723755	−	1.45662i
$499$	−26.1293			−1.16971			−0.584854	−	0.811139i	$-0.698848\pi$
$499$	−26.1293			−1.16971			−0.584854	+	0.811139i	$0.698848\pi$
$500$	−14.5676	−	19.2220i	−0.651482	−	0.859635i
$501$		−	49.9463i		−	2.23144i
$502$	−9.38168	−	4.66150i	−0.418725	−	0.208053i
$503$	24.5290			1.09370			0.546848	−	0.837232i	$-0.315828\pi$
$503$	24.5290			1.09370			0.546848	+	0.837232i	$0.315828\pi$
$504$	−4.81318	+	19.4798i	−0.214396	+	0.867698i
$505$	−28.2537			−1.25727
$506$	−7.18264	−	3.56886i	−0.319307	−	0.158655i
$507$		−	2.38356i		−	0.105858i
$508$	−24.7683	+	18.7709i	−1.09892	+	0.832823i
$509$	9.69607			0.429771			0.214885	−	0.976639i	$-0.431062\pi$
$509$	9.69607			0.429771			0.214885	+	0.976639i	$0.431062\pi$
$510$	−2.05907	+	4.14407i	−0.0911773	+	0.183503i
$511$	20.5302	+	9.40572i	0.908201	+	0.416085i
$512$	19.1458	−	12.0598i	0.846134	−	0.532971i
$513$	−4.37146			−0.193005
$514$	−11.1725	−	5.55129i	−0.492796	−	0.244857i
$515$	−13.1657			−0.580149
$516$	−14.8929	+	11.2867i	−0.655622	+	0.496869i
$517$	−58.1963			−2.55947
$518$	6.39754	−	5.17398i	0.281092	−	0.227331i
$519$			28.8258i			1.26531i
$520$	4.67016	−	0.885431i	0.204800	−	0.0388287i
$521$			23.8145i			1.04333i	0.853149	+	0.521667i	$0.174690\pi$
$521$			23.8145i			1.04333i	−0.853149	+	0.521667i	$0.825310\pi$
$522$	3.30708	+	1.64320i	0.144747	+	0.0719208i
$523$			12.8009i			0.559746i	0.960037	+	0.279873i	$0.0902923\pi$
$523$			12.8009i			0.559746i	−0.960037	+	0.279873i	$0.909708\pi$
$524$	20.7930	−	15.7582i	0.908347	−	0.688398i
$525$	12.4739	+	5.71479i	0.544404	+	0.249414i
$526$	22.5975	+	11.2281i	0.985296	+	0.489566i
$527$			3.18160i			0.138593i
$528$	59.2764	+	16.6463i	2.57968	+	0.724436i
$529$	22.2287			0.966466
$530$	−20.3733	−	10.1229i	−0.884960	−	0.439712i
$531$			1.93819i			0.0841103i
$532$	6.61439	+	29.7312i	0.286770	+	1.28901i
$533$		−	4.21071i		−	0.182386i
$534$	26.8808	−	54.1001i	1.16325	−	2.34114i
$535$	−15.4737			−0.668985
$536$	−16.2091	+	3.07314i	−0.700128	+	0.132740i
$537$		−	5.95023i		−	0.256772i
$538$	−13.9742	+	28.1243i	−0.602470	+	1.21253i
$539$	−29.5199	−	34.2341i	−1.27151	−	1.47457i
$540$	2.03441	−	1.54179i	0.0875471	−	0.0663483i
$541$		−	42.8431i		−	1.84197i	−0.389597	−	0.920985i	$-0.627386\pi$
$541$		−	42.8431i		−	1.84197i	0.389597	−	0.920985i	$-0.372614\pi$
$542$	−6.38793	+	12.8563i	−0.274385	+	0.552225i
$543$		−	31.1024i		−	1.33473i
$544$	−3.09836	+	3.42812i	−0.132841	+	0.146979i
$545$		−	4.22714i		−	0.181071i
$546$	−6.93448	+	5.60823i	−0.296769	+	0.240010i
$547$	34.8819			1.49144			0.745721	−	0.666258i	$-0.232105\pi$
$547$	34.8819			1.49144			0.745721	+	0.666258i	$0.232105\pi$
$548$	−6.18369	−	8.15942i	−0.264154	−	0.348553i
$549$	−3.90097			−0.166489
$550$	8.84146	−	17.7942i	0.377001	−	0.758749i
$551$	5.60541			0.238799
$552$	5.81711	−	1.10288i	0.247593	−	0.0469419i
$553$	34.3986	+	15.7594i	1.46278	+	0.670159i
$554$	23.4196	+	11.6366i	0.995003	+	0.494390i
$555$	8.80862			0.373905
$556$	−0.392658	+	0.297579i	−0.0166524	+	0.0126202i
$557$		−	21.8138i		−	0.924281i	−0.886807	−	0.462141i	$-0.847082\pi$
$557$		−	21.8138i		−	0.924281i	0.886807	−	0.462141i	$-0.152918\pi$
$558$	−6.57216	+	13.2271i	−0.278222	+	0.559946i
$559$	−3.91987			−0.165793
$560$	−13.5643	−	11.5036i	−0.573196	−	0.486114i
$561$	−12.5733			−0.530843
$562$	1.68454	−	3.39029i	0.0710580	−	0.143011i
$563$			40.3058i			1.69869i	0.527842	+	0.849343i	$0.323001\pi$
$563$			40.3058i			1.69869i	−0.527842	+	0.849343i	$0.676999\pi$
$564$	34.2392	−	25.9485i	1.44173	−	1.09263i
$565$	7.64020			0.321426
$566$	−28.7028	−	14.2616i	−1.20647	−	0.599462i
$567$	−10.8593	+	23.7030i	−0.456049	+	0.995432i
$568$	2.63443	+	13.8952i	0.110538	+	0.583028i
$569$	−43.5399			−1.82529			−0.912644	−	0.408756i	$-0.865963\pi$
$569$	−43.5399			−1.82529			−0.912644	+	0.408756i	$0.865963\pi$
$570$	−14.5095	+	29.2017i	−0.607736	+	1.22312i
$571$	−3.15835			−0.132173			−0.0660865	−	0.997814i	$-0.521051\pi$
$571$	−3.15835			−0.132173			−0.0660865	+	0.997814i	$0.521051\pi$
$572$	7.80092	+	10.2934i	0.326173	+	0.430387i
$573$	12.4891			0.521739
$574$	−12.2502	+	9.90727i	−0.511312	+	0.413521i
$575$		−	1.91074i		−	0.0796836i
$576$	−19.9624	+	7.85170i	−0.831766	+	0.327154i
$577$			8.84506i			0.368225i	0.982905	+	0.184112i	$0.0589410\pi$
$577$			8.84506i			0.368225i	−0.982905	+	0.184112i	$0.941059\pi$
$578$	−10.2780	+	20.6853i	−0.427506	+	0.860395i
$579$			39.2132i			1.62964i
$580$	−2.60867	+	1.97701i	−0.108319	+	0.0820907i
$581$	−25.9005	−	11.8661i	−1.07453	−	0.492288i
$582$	−19.7129	+	39.6739i	−0.817124	+	1.64453i
$583$		−	61.8133i		−	2.56005i
$584$	4.49693	+	23.7189i	0.186084	+	0.981493i
$585$	−4.50623			−0.186310
$586$	−21.1390	+	42.5440i	−0.873242	+	1.75748i
$587$		−	25.8252i		−	1.06592i	−0.846140	−	0.532960i	$-0.821080\pi$
$587$		−	25.8252i		−	1.06592i	0.846140	−	0.532960i	$-0.178920\pi$
$588$	32.6319	+	6.97898i	1.34572	+	0.287808i
$589$			22.4195i			0.923779i
$590$	−1.53850	−	0.764436i	−0.0633389	−	0.0314713i
$591$	−42.9332			−1.76604
$592$	8.46842	+	2.37814i	0.348050	+	0.0977410i
$593$			2.47895i			0.101798i	0.998704	+	0.0508992i	$0.0162087\pi$
$593$			2.47895i			0.101798i	−0.998704	+	0.0508992i	$0.983791\pi$
$594$	6.21132	+	3.08623i	0.254854	+	0.126630i
$595$	3.30197	+	1.51277i	0.135368	+	0.0620175i
$596$	−0.881210	+	0.667833i	−0.0360958	+	0.0273555i
$597$			21.7474i			0.890064i
$598$	1.11226	+	0.552651i	0.0454837	+	0.0225996i
$599$		−	4.73676i		−	0.193539i	−0.995307	−	0.0967695i	$-0.969149\pi$
$599$		−	4.73676i		−	0.193539i	0.995307	−	0.0967695i	$-0.0308510\pi$
$600$	2.73228	+	14.4113i	0.111545	+	0.588337i
$601$			13.4825i			0.549963i	0.961450	+	0.274981i	$0.0886717\pi$
$601$			13.4825i			0.549963i	−0.961450	+	0.274981i	$0.911328\pi$
$602$	9.22297	+	11.4041i	0.375900	+	0.464795i
$603$	15.6402			0.636917
$604$	−8.13320	+	6.16382i	−0.330935	+	0.250802i
$605$	−51.5967			−2.09770
$606$	50.7515	+	25.2170i	2.06164	+	1.02437i
$607$	12.6426			0.513148			0.256574	−	0.966525i	$-0.417406\pi$
$607$	12.6426			0.513148			0.256574	+	0.966525i	$0.417406\pi$
$608$	−21.8329	+	24.1566i	−0.885443	+	0.979680i
$609$	2.55792	−	5.58325i	0.103652	−	0.226245i
$610$	1.53857	−	3.09651i	0.0622949	−	0.125374i
$611$	9.01192			0.364583
$612$	3.49124	−	2.64587i	0.141125	−	0.106953i
$613$			11.8220i			0.477487i	0.971083	+	0.238743i	$0.0767355\pi$
$613$			11.8220i			0.477487i	−0.971083	+	0.238743i	$0.923265\pi$
$614$	28.5505	+	14.1859i	1.15220	+	0.572498i
$615$	−16.8670			−0.680142
$616$	11.5918	−	46.9142i	0.467048	−	1.89023i
$617$	26.8587			1.08129			0.540645	−	0.841251i	$-0.318180\pi$
$617$	26.8587			1.08129			0.540645	+	0.841251i	$0.318180\pi$
$618$	23.6492	+	11.7506i	0.951311	+	0.472680i
$619$		−	22.1068i		−	0.888546i	−0.895891	−	0.444273i	$-0.853462\pi$
$619$		−	22.1068i		−	0.888546i	0.895891	−	0.444273i	$-0.146538\pi$
$620$	−7.90726	−	10.4337i	−0.317563	−	0.419027i
$621$	0.666972			0.0267647
$622$	−9.12955	+	18.3740i	−0.366062	+	0.736732i
$623$	−43.1066	−	19.7489i	−1.72703	−	0.791224i
$624$	−9.17918	−	2.57774i	−0.367461	−	0.103192i
$625$	−9.38784			−0.375514
$626$	36.0693	+	17.9218i	1.44162	+	0.716300i
$627$	−88.5988			−3.53830
$628$	23.8751	+	31.5034i	0.952721	+	1.25712i
$629$	−1.79626			−0.0716214
$630$	10.6026	+	13.1099i	0.422418	+	0.522313i
$631$			24.0898i			0.958999i	0.877542	+	0.479500i	$0.159182\pi$
$631$			24.0898i			0.958999i	−0.877542	+	0.479500i	$0.840818\pi$
$632$	7.53469	+	39.7413i	0.299714	+	1.58083i
$633$		−	41.4487i		−	1.64744i
$634$	12.6587	+	6.28978i	0.502743	+	0.249799i
$635$			26.1139i			1.03630i
$636$	27.5612	+	36.3672i	1.09287	+	1.44205i
$637$	4.57127	+	5.30128i	0.181120	+	0.210044i
$638$	−7.96462	−	3.95740i	−0.315322	−	0.156675i
$639$		−	13.4074i		−	0.530389i
$640$	1.64079	−	18.9425i	0.0648579	−	0.748768i
$641$	−41.5721			−1.64200			−0.821000	−	0.570929i	$-0.806583\pi$
$641$	−41.5721			−1.64200			−0.821000	+	0.570929i	$0.806583\pi$
$642$	27.7950	+	13.8106i	1.09698	+	0.545060i
$643$		−	32.7452i		−	1.29134i	−0.763615	−	0.645672i	$-0.776577\pi$
$643$		−	32.7452i		−	1.29134i	0.763615	−	0.645672i	$-0.223423\pi$
$644$	−1.00918	−	4.53621i	−0.0397674	−	0.178752i
$645$			15.7020i			0.618265i
$646$	2.95878	−	5.95481i	0.116412	−	0.234289i
$647$	−48.6201			−1.91145			−0.955727	−	0.294254i	$-0.904929\pi$
$647$	−48.6201			−1.91145			−0.955727	+	0.294254i	$0.904929\pi$
$648$	−27.3845	+	5.19191i	−1.07576	+	0.203957i
$649$		−	4.66785i		−	0.183229i
$650$	−1.36913	+	2.75550i	−0.0537018	+	0.108080i
$651$	22.3309	+	10.2307i	0.875215	+	0.400972i
$652$	11.6546	+	15.3783i	0.456428	+	0.602260i
$653$		−	29.9679i		−	1.17273i	−0.810045	−	0.586367i	$-0.800558\pi$
$653$		−	29.9679i		−	1.17273i	0.810045	−	0.586367i	$-0.199442\pi$
$654$	−3.77281	+	7.59312i	−0.147529	+	0.296914i
$655$		−	21.9227i		−	0.856590i
$656$	−16.2156	−	4.55373i	−0.633111	−	0.177793i
$657$		−	22.8863i		−	0.892879i
$658$	−21.2039	−	26.2183i	−0.826615	−	1.02210i
$659$	−2.82799			−0.110163			−0.0550814	−	0.998482i	$-0.517542\pi$
$659$	−2.82799			−0.110163			−0.0550814	+	0.998482i	$0.517542\pi$
$660$	41.2325	−	31.2484i	1.60497	−	1.21634i
$661$	−15.6250			−0.607742			−0.303871	−	0.952713i	$-0.598279\pi$
$661$	−15.6250			−0.607742			−0.303871	+	0.952713i	$0.598279\pi$
$662$	3.21277	−	6.46598i	0.124868	−	0.251308i
$663$	1.94702			0.0756158
$664$	−5.67325	−	29.9233i	−0.220165	−	1.16125i
$665$	23.2677	+	10.6599i	0.902283	+	0.413373i
$666$	−7.46768	−	3.71048i	−0.289367	−	0.143778i
$667$	−0.855241			−0.0331151
$668$	−25.3130	−	33.4007i	−0.979390	−	1.29231i
$669$			6.53161i			0.252527i
$670$	−6.16859	+	12.4148i	−0.238314	+	0.479627i
$671$	9.39491			0.362687
$672$	14.0981	+	32.7700i	0.543845	+	1.26413i
$673$	−33.9631			−1.30918			−0.654590	−	0.755984i	$-0.727159\pi$
$673$	−33.9631			−1.30918			−0.654590	+	0.755984i	$0.727159\pi$
$674$	−7.88086	+	15.8609i	−0.303560	+	0.610941i
$675$			1.65235i			0.0635990i
$676$	−1.20800	−	1.59397i	−0.0464616	−	0.0613064i
$677$	−11.9305			−0.458525			−0.229262	−	0.973365i	$-0.573631\pi$
$677$	−11.9305			−0.458525			−0.229262	+	0.973365i	$0.573631\pi$
$678$	−13.7239	−	6.81904i	−0.527064	−	0.261884i
$679$	31.6119	+	14.4827i	1.21315	+	0.555796i
$680$	0.723265	+	3.81482i	0.0277359	+	0.146292i
$681$	40.4224			1.54899
$682$	15.8281	−	31.8554i	0.606089	−	1.21981i
$683$	16.8447			0.644545			0.322273	−	0.946647i	$-0.395553\pi$
$683$	16.8447			0.644545			0.322273	+	0.946647i	$0.395553\pi$
$684$	24.6014	−	18.6444i	0.940659	−	0.712886i
$685$	−8.60272			−0.328693
$686$	4.66734	−	25.7724i	0.178200	−	0.983994i
$687$			49.1744i			1.87612i
$688$	−4.23920	+	15.0955i	−0.161618	+	0.575512i
$689$			9.57202i			0.364665i
$690$	2.21377	−	4.45542i	0.0842769	−	0.169615i
$691$		−	14.3162i		−	0.544616i	−0.962210	−	0.272308i	$-0.912213\pi$
$691$		−	14.3162i		−	0.544616i	0.962210	−	0.272308i	$-0.0877869\pi$
$692$	14.6090	+	19.2767i	0.555352	+	0.732791i
$693$	−19.0814	+	41.6497i	−0.724844	+	1.58214i
$694$	−17.1179	+	34.4512i	−0.649785	+	1.30775i
$695$			0.413991i			0.0157036i
$696$	6.45042	−	1.22296i	0.244503	−	0.0463560i
$697$	3.43952			0.130281
$698$	10.6050	−	21.3436i	0.401407	−	0.807867i
$699$		−	48.2315i		−	1.82428i
$700$	11.2380	−	2.50015i	0.424755	−	0.0944967i
$701$			14.5603i			0.549935i	0.961454	+	0.274967i	$0.0886670\pi$
$701$			14.5603i			0.549935i	−0.961454	+	0.274967i	$0.911333\pi$
$702$	−0.961847	−	0.477915i	−0.0363026	−	0.0180377i
$703$	−12.6575			−0.477387
$704$	48.0765	−	18.9097i	1.81195	−	0.712685i
$705$		−	36.0994i		−	1.35958i
$706$	−7.01619	−	3.48615i	−0.264058	−	0.131203i
$707$	18.5266	−	40.4385i	0.696763	−	1.52085i
$708$	2.08129	+	2.74628i	0.0782198	+	0.103212i
$709$			35.4973i			1.33313i	0.745448	+	0.666564i	$0.232236\pi$
$709$			35.4973i			1.33313i	−0.745448	+	0.666564i	$0.767764\pi$
$710$	10.6425	+	5.28798i	0.399407	+	0.198454i
$711$		−	38.3463i		−	1.43810i
$712$	−9.44208	−	49.8018i	−0.353857	−	1.86640i
$713$		−	3.42064i		−	0.128104i
$714$	−4.58108	−	5.66444i	−0.171443	−	0.211986i
$715$	10.8526			0.405864
$716$	−3.01561	−	3.97912i	−0.112699	−	0.148707i
$717$	−44.8867			−1.67633
$718$	−23.1703	−	11.5127i	−0.864709	−	0.429650i
$719$	23.4197			0.873406			0.436703	−	0.899606i	$-0.356146\pi$
$719$	23.4197			0.873406			0.436703	+	0.899606i	$0.356146\pi$
$720$	−4.87332	+	17.3536i	−0.181618	+	0.646732i
$721$	8.63301	−	18.8436i	0.321510	−	0.701771i
$722$	8.89296	−	17.8979i	0.330962	−	0.666090i
$723$	10.2529			0.381309
$724$	−15.7629	−	20.7992i	−0.585822	−	0.772997i
$725$		−	2.11877i		−	0.0786891i
$726$	92.6820	+	46.0511i	3.43975	+	1.70912i
$727$	19.4068			0.719757			0.359879	−	0.932999i	$-0.382818\pi$
$727$	19.4068			0.719757			0.359879	+	0.932999i	$0.382818\pi$
$728$	−1.79504	+	7.26484i	−0.0665286	+	0.269253i
$729$	20.9926			0.777503
$730$	18.1667	+	9.02651i	0.672378	+	0.334086i
$731$		−	3.20195i		−	0.118428i
$732$	−5.52740	+	4.18899i	−0.204299	+	0.154829i
$733$	−13.5804			−0.501603			−0.250802	−	0.968038i	$-0.580694\pi$
$733$	−13.5804			−0.501603			−0.250802	+	0.968038i	$0.580694\pi$
$734$	−20.4025	+	41.0619i	−0.753071	+	1.51562i
$735$	21.2355	−	18.3113i	0.783284	−	0.675422i
$736$	3.33114	−	3.68567i	0.122788	−	0.135856i
$737$	−37.6671			−1.38748
$738$	14.2993	+	7.10493i	0.526365	+	0.261536i
$739$	17.3365			0.637734			0.318867	−	0.947800i	$-0.396698\pi$
$739$	17.3365			0.637734			0.318867	+	0.947800i	$0.396698\pi$
$740$	5.89061	−	4.46425i	0.216543	−	0.164109i
$741$	13.7199			0.504012
$742$	27.8478	−	22.5218i	1.02233	−	0.826800i
$743$		−	9.07974i		−	0.333104i	−0.986033	−	0.166552i	$-0.946737\pi$
$743$		−	9.07974i		−	0.333104i	0.986033	−	0.166552i	$-0.0532633\pi$
$744$	4.89135	+	25.7992i	0.179326	+	0.945845i
$745$			0.929085i			0.0340390i
$746$	−15.9872	−	7.94357i	−0.585331	−	0.290835i
$747$			28.8729i			1.05640i
$748$	−8.40815	+	6.37218i	−0.307432	+	0.232990i
$749$	10.1464	−	22.1469i	0.370742	−	0.809231i
$750$	36.4040	+	18.0881i	1.32929	+	0.660485i
$751$			7.78993i			0.284259i	0.989848	+	0.142129i	$0.0453949\pi$
$751$			7.78993i			0.284259i	−0.989848	+	0.142129i	$0.954605\pi$
$752$	9.74607	−	34.7052i	0.355402	−	1.26557i
$753$	17.6565			0.643440
$754$	1.23335	+	0.612818i	0.0449160	+	0.0223175i
$755$			8.57507i			0.312079i
$756$	0.872711	+	3.92277i	0.0317402	+	0.142670i
$757$		−	44.2936i		−	1.60988i	−0.593357	−	0.804939i	$-0.702198\pi$
$757$		−	44.2936i		−	1.60988i	0.593357	−	0.804939i	$-0.297802\pi$
$758$	−11.4514	+	23.0471i	−0.415935	+	0.837107i
$759$	13.5179			0.490668
$760$	5.09657	+	26.8816i	0.184872	+	0.975098i
$761$			8.33939i			0.302303i	0.988511	+	0.151151i	$0.0482981\pi$
$761$			8.33939i			0.302303i	−0.988511	+	0.151151i	$0.951702\pi$
$762$	23.3072	−	46.9079i	0.844332	−	1.69929i
$763$	6.05016	+	2.77183i	0.219030	+	0.100347i
$764$	8.35186	−	6.32953i	0.302160	−	0.228994i
$765$		−	3.68092i		−	0.133084i
$766$	−11.5990	+	23.3441i	−0.419090	+	0.843455i
$767$			0.722834i			0.0261000i
$768$	−19.8539	+	32.5616i	−0.716416	+	1.17496i
$769$			25.5540i			0.921500i	0.887530	+	0.460750i	$0.152419\pi$
$769$			25.5540i			0.921500i	−0.887530	+	0.460750i	$0.847581\pi$
$770$	−25.5348	−	31.5734i	−0.920210	−	1.13783i
$771$	21.0268			0.757262
$772$	19.8734	+	26.2231i	0.715260	+	0.943791i
$773$	15.7192			0.565381			0.282690	−	0.959211i	$-0.408773\pi$
$773$	15.7192			0.565381			0.282690	+	0.959211i	$0.408773\pi$
$774$	6.61420	−	13.3117i	0.237742	−	0.478478i
$775$	8.47426			0.304404
$776$	6.92428	+	36.5218i	0.248567	+	1.31106i
$777$	−5.77600	+	12.6075i	−0.207213	+	0.452290i
$778$	−25.1484	−	12.4955i	−0.901614	−	0.447987i
$779$	24.2369			0.868379
$780$	−6.38501	+	4.83894i	−0.228620	+	0.173262i
$781$			32.2898i			1.15542i
$782$	−0.451433	+	0.908550i	−0.0161432	+	0.0324897i
$783$	0.739585			0.0264306
$784$	25.3590	−	11.8710i	0.905680	−	0.423963i
$785$	33.2149			1.18549
$786$	−19.5664	+	39.3792i	−0.697912	+	1.40461i
$787$		−	40.7884i		−	1.45395i	−0.686665	−	0.726974i	$-0.740926\pi$
$787$		−	40.7884i		−	1.45395i	0.686665	−	0.726974i	$-0.259074\pi$
$788$	−28.7108	+	21.7587i	−1.02278	+	0.775123i
$789$	−42.5289			−1.51407
$790$	30.4385	+	15.1241i	1.08295	+	0.538090i
$791$	−5.00984	+	10.9351i	−0.178129	+	0.388809i
$792$	−48.1186	+	9.12295i	−1.70982	+	0.324170i
$793$	−1.45484			−0.0516628
$794$	−4.69934	+	9.45784i	−0.166773	+	0.335646i
$795$	38.3430			1.35989
$796$	11.0217	+	14.5432i	0.390654	+	0.515471i
$797$	29.9750			1.06177			0.530884	−	0.847444i	$-0.321860\pi$
$797$	29.9750			1.06177			0.530884	+	0.847444i	$0.321860\pi$
$798$	−32.2811	−	39.9151i	−1.14274	−	1.41298i
$799$			7.36139i			0.260427i
$800$	9.13086	+	8.25255i	0.322825	+	0.291772i
$801$			48.0537i			1.69789i
$802$	2.49166	−	5.01470i	0.0879837	−	0.177075i
$803$			55.1182i			1.94508i
$804$	22.1610	−	16.7949i	0.781559	−	0.592311i
$805$	−3.55005	−	1.62643i	−0.125123	−	0.0573240i
$806$	−2.45104	+	4.93293i	−0.0863341	+	0.173755i
$807$		−	52.9306i		−	1.86324i
$808$	46.7193	−	8.85766i	1.64358	−	0.311611i
$809$	28.3634			0.997205			0.498603	−	0.866831i	$-0.333847\pi$
$809$	28.3634			0.997205			0.498603	+	0.866831i	$0.333847\pi$
$810$	−10.4215	+	20.9742i	−0.366174	+	0.736959i
$811$			17.8449i			0.626619i	0.949651	+	0.313309i	$0.101438\pi$
$811$			17.8449i			0.626619i	−0.949651	+	0.313309i	$0.898562\pi$
$812$	−1.11905	−	5.03007i	−0.0392711	−	0.176521i
$813$		−	24.1958i		−	0.848584i
$814$	17.9848	+	8.93616i	0.630368	+	0.313212i
$815$	16.2138			0.567943
$816$	2.10563	−	7.49802i	0.0737117	−	0.262483i
$817$		−	22.5629i		−	0.789376i
$818$	−23.4951	−	11.6741i	−0.821486	−	0.408174i
$819$	2.95483	−	6.44961i	0.103250	−	0.225368i
$820$	−11.2795	+	8.54827i	−0.393897	+	0.298518i
$821$		−	4.62357i		−	0.161364i	−0.996740	−	0.0806818i	$-0.974290\pi$
$821$		−	4.62357i		−	0.161364i	0.996740	−	0.0806818i	$-0.0257098\pi$
$822$	15.4529	+	7.67810i	0.538981	+	0.267805i
$823$			47.4508i			1.65403i	0.562178	+	0.827016i	$0.309964\pi$
$823$			47.4508i			1.65403i	−0.562178	+	0.827016i	$0.690036\pi$
$824$	21.7703	−	4.12750i	0.758404	−	0.143788i
$825$			33.4891i			1.16594i
$826$	2.10294	−	1.70074i	0.0731705	−	0.0591763i
$827$	−21.4189			−0.744807			−0.372404	−	0.928071i	$-0.621466\pi$
$827$	−21.4189			−0.744807			−0.372404	+	0.928071i	$0.621466\pi$
$828$	−3.75354	+	2.84465i	−0.130445	+	0.0988585i
$829$	−15.5176			−0.538947			−0.269474	−	0.963008i	$-0.586850\pi$
$829$	−15.5176			−0.538947			−0.269474	+	0.963008i	$0.586850\pi$
$830$	−22.9187	−	11.3877i	−0.795520	−	0.395272i
$831$	−44.0762			−1.52899
$832$	−7.44483	+	2.92823i	−0.258103	+	0.101518i
$833$	−4.33035	+	3.73404i	−0.150038	+	0.129377i
$834$	0.369495	−	0.743642i	0.0127946	−	0.0257502i
$835$	−35.2153			−1.21868
$836$	−59.2489	+	44.9023i	−2.04917	+	1.55298i
$837$			2.95806i			0.102245i
$838$	−50.8245	−	25.2533i	−1.75570	−	0.872360i
$839$	8.76582			0.302630			0.151315	−	0.988486i	$-0.451649\pi$
$839$	8.76582			0.302630			0.151315	+	0.988486i	$0.451649\pi$
$840$	29.1010	+	7.19045i	1.00408	+	0.248094i
$841$	28.0516			0.967298
$842$	9.51903	+	4.72974i	0.328048	+	0.162998i
$843$			6.38059i			0.219759i
$844$	−21.0064	−	27.7181i	−0.723070	−	0.954096i
$845$	−1.68057			−0.0578132
$846$	−15.2063	+	30.6040i	−0.522802	+	1.05219i
$847$	33.8330	−	73.8485i	1.16252	−	2.53746i
$848$	36.8622	+	10.3518i	1.26585	+	0.355482i
$849$	54.0193			1.85394
$850$	−2.25083	−	1.11838i	−0.0772030	−	0.0383600i
$851$	1.93121			0.0662010
$852$	−14.3973	−	18.9974i	−0.493244	−	0.650839i
$853$	21.4369			0.733985			0.366992	−	0.930224i	$-0.380387\pi$
$853$	21.4369			0.733985			0.366992	+	0.930224i	$0.380387\pi$
$854$	3.42305	+	4.23255i	0.117134	+	0.144835i
$855$		−	25.9380i		−	0.887060i
$856$	25.5867	−	4.85107i	0.874536	−	0.165806i
$857$			48.0166i			1.64021i	0.572210	+	0.820107i	$0.306086\pi$
$857$			48.0166i			1.64021i	−0.572210	+	0.820107i	$0.693914\pi$
$858$	−19.4943	−	9.68617i	−0.665524	−	0.330680i
$859$			11.4813i			0.391738i	0.980630	+	0.195869i	$0.0627527\pi$
$859$			11.4813i			0.391738i	−0.980630	+	0.195869i	$0.937247\pi$
$860$	7.95784	+	10.5004i	0.271360	+	0.358062i
$861$	11.0600	−	24.1411i	0.376925	−	0.822727i
$862$	−29.4532	−	14.6345i	−1.00318	−	0.498452i
$863$			14.5463i			0.495163i	0.968867	+	0.247581i	$0.0796358\pi$
$863$			14.5463i			0.495163i	−0.968867	+	0.247581i	$0.920364\pi$
$864$	−2.88067	+	3.18725i	−0.0980023	+	0.108433i
$865$	20.3240			0.691037
$866$	15.2012	+	7.55306i	0.516558	+	0.256663i
$867$		−	38.9302i		−	1.32214i
$868$	20.1183	−	4.47579i	0.682861	−	0.151918i
$869$			92.3515i			3.13281i
$870$	2.45479	−	4.94048i	0.0832251	−	0.167498i
$871$	5.83289			0.197640
$872$	1.32523	+	6.98985i	0.0448779	+	0.236706i
$873$		−	35.2398i		−	1.19269i
$874$	−3.18107	+	6.40220i	−0.107601	+	0.216558i
$875$	13.2891	−	29.0065i	0.449253	−	0.980598i
$876$	−24.5760	−	32.4282i	−0.830347	−	1.09565i
$877$			48.2621i			1.62969i	0.579675	+	0.814847i	$0.303179\pi$
$877$			48.2621i			1.62969i	−0.579675	+	0.814847i	$0.696821\pi$
$878$	−12.4976	+	25.1525i	−0.421774	+	0.848857i
$879$		−	80.0688i		−	2.70065i
$880$	11.7367	−	41.7937i	0.395644	−	1.40886i
$881$			3.34804i			0.112798i	0.998408	+	0.0563991i	$0.0179619\pi$
$881$			3.34804i			0.112798i	−0.998408	+	0.0563991i	$0.982038\pi$
$882$	−25.7161	+	6.57865i	−0.865908	+	0.221515i
$883$	−39.7732			−1.33847			−0.669237	−	0.743049i	$-0.733379\pi$
$883$	−39.7732			−1.33847			−0.669237	+	0.743049i	$0.733379\pi$
$884$	1.30203	−	0.986757i	0.0437921	−	0.0331882i
$885$	2.89548			0.0973306
$886$	23.2560	−	46.8049i	0.781302	−	1.57244i
$887$	1.92704			0.0647036			0.0323518	−	0.999477i	$-0.489700\pi$
$887$	1.92704			0.0647036			0.0323518	+	0.999477i	$0.489700\pi$
$888$	−14.5656	+	2.76154i	−0.488790	+	0.0926713i
$889$	−37.3760	−	17.1235i	−1.25355	−	0.574303i
$890$	−38.1440	−	18.9527i	−1.27859	−	0.635296i
$891$	−63.6365			−2.13190
$892$	3.31025	+	4.36790i	0.110835	+	0.146248i
$893$			51.8729i			1.73586i
$894$	0.829228	−	1.66890i	0.0277335	−	0.0558162i
$895$	−4.19530			−0.140233
$896$	26.0358	+	14.7694i	0.869796	+	0.493411i
$897$	−2.09330			−0.0698931
$898$	17.0021	−	34.2182i	0.567366	−	1.14188i
$899$		−	3.79304i		−	0.126505i
$900$	−7.04732	−	9.29900i	−0.234911	−	0.309967i
$901$	−7.81891			−0.260486
$902$	−34.4378	−	17.1112i	−1.14665	−	0.569740i
$903$	−22.4737	−	10.2961i	−0.747877	−	0.342633i
$904$	−12.6336	+	2.39524i	−0.420186	+	0.0796644i
$905$	−21.9292			−0.728952
$906$	7.65343	−	15.4032i	0.254268	−	0.511737i
$907$	−47.2726			−1.56966			−0.784831	−	0.619710i	$-0.787250\pi$
$907$	−47.2726			−1.56966			−0.784831	+	0.619710i	$0.787250\pi$
$908$	27.0318	−	20.4862i	0.897080	−	0.679860i
$909$	−45.0794			−1.49519
$910$	3.95416	+	4.88926i	0.131079	+	0.162077i
$911$			57.2072i			1.89536i	0.319222	+	0.947680i	$0.396578\pi$
$911$			57.2072i			1.89536i	−0.319222	+	0.947680i	$0.603422\pi$
$912$	14.8375	−	52.8356i	0.491320	−	1.74956i
$913$		−	69.5362i		−	2.30131i
$914$	11.4779	−	23.1003i	0.379656	−	0.764091i
$915$			5.82770i			0.192658i
$916$	24.9218	+	32.8845i	0.823440	+	1.08654i
$917$	31.3771	+	14.3752i	1.03616	+	0.474710i
$918$	0.390385	−	0.785685i	0.0128846	−	0.0259315i
$919$		−	11.7893i		−	0.388894i	−0.980913	−	0.194447i	$-0.937709\pi$
$919$		−	11.7893i		−	0.388894i	0.980913	−	0.194447i	$-0.0622912\pi$
$920$	−0.777604	−	4.10144i	−0.0256369	−	0.135220i
$921$	−53.7326			−1.77055
$922$	18.5424	−	37.3182i	0.610660	−	1.22901i
$923$		−	5.00020i		−	0.164584i
$924$	17.6877	+	79.5049i	0.581883	+	2.61552i
$925$			4.78437i			0.157309i
$926$	43.2187	+	21.4742i	1.42025	+	0.705685i
$927$	−21.0061			−0.689931
$928$	3.69381	−	4.08694i	0.121255	−	0.134160i
$929$		−	6.11545i		−	0.200641i	−0.994955	−	0.100321i	$-0.968013\pi$
$929$		−	6.11545i		−	0.200641i	0.994955	−	0.100321i	$-0.0319869\pi$
$930$	19.7600	+	9.81821i	0.647957	+	0.321952i
$931$	−30.5143	+	26.3123i	−1.00007	+	0.862352i
$932$	−24.4440	−	32.2540i	−0.800688	−	1.05651i
$933$		−	34.5803i		−	1.13211i
$934$	13.1632	+	6.54045i	0.430714	+	0.214010i
$935$			8.86495i			0.289915i
$936$	7.45134	−	1.41272i	0.243555	−	0.0461763i
$937$		−	13.1924i		−	0.430978i	−0.976506	−	0.215489i	$-0.930866\pi$
$937$		−	13.1924i		−	0.430978i	0.976506	−	0.215489i	$-0.0691345\pi$
$938$	−13.7241	−	16.9696i	−0.448106	−	0.554076i
$939$	−67.8831			−2.21528
$940$	−18.2953	−	24.1408i	−0.596728	−	0.787387i
$941$	1.98071			0.0645694			0.0322847	−	0.999479i	$-0.489722\pi$
$941$	1.98071			0.0645694			0.0322847	+	0.999479i	$0.489722\pi$
$942$	−59.6633	−	29.6450i	−1.94393	−	0.965887i
$943$	−3.69793			−0.120421
$944$	2.78366	+	0.781719i	0.0906003	+	0.0254428i
$945$	3.06997	+	1.40648i	0.0998662	+	0.0457528i
$946$	−15.9293	+	32.0592i	−0.517907	+	1.04233i
$947$	37.0962			1.20547			0.602733	−	0.797943i	$-0.294079\pi$
$947$	37.0962			1.20547			0.602733	+	0.797943i	$0.294079\pi$
$948$	−41.1775	−	54.3340i	−1.33738	−	1.76469i
$949$		−	8.53527i		−	0.277067i
$950$	−15.8608	−	7.88077i	−0.514591	−	0.255686i
$951$	−23.8240			−0.772547
$952$	−5.93428	−	1.46628i	−0.192331	−	0.0475224i
$953$	1.46318			0.0473971			0.0236985	−	0.999719i	$-0.492456\pi$
$953$	1.46318			0.0473971			0.0236985	+	0.999719i	$0.492456\pi$
$954$	−32.5060	−	16.1513i	−1.05242	−	0.522919i
$955$		−	8.80561i		−	0.284943i
$956$	−30.0172	+	22.7488i	−0.970826	+	0.735749i
$957$	14.9896			0.484545
$958$	−16.0921	+	32.3869i	−0.519914	+	1.04637i
$959$	5.64098	−	12.3128i	0.182157	−	0.397600i
$960$	11.7297	+	29.8220i	0.378575	+	0.962501i
$961$	−15.8293			−0.510622
$962$	−2.78502	−	1.38380i	−0.0897926	−	0.0446154i
$963$	−24.6886			−0.795578
$964$	6.85644	−	5.19621i	0.220831	−	0.167359i
$965$	27.6478			0.890014
$966$	4.92526	+	6.09001i	0.158468	+	0.195943i
$967$			0.345097i			0.0110976i	0.999985	+	0.00554878i	$0.00176624\pi$
$967$			0.345097i			0.0110976i	−0.999985	+	0.00554878i	$0.998234\pi$
$968$	85.3184	−	16.1758i	2.74224	−	0.519909i
$969$			11.2071i			0.360023i
$970$	27.9726	+	13.8988i	0.898147	+	0.446264i
$971$		−	6.24436i		−	0.200391i	−0.994968	−	0.100195i	$-0.968053\pi$
$971$		−	6.24436i		−	0.200391i	0.994968	−	0.100195i	$-0.0319468\pi$
$972$	33.8082	−	25.6218i	1.08440	−	0.821821i
$973$	−0.592530	−	0.271462i	−0.0189956	−	0.00870269i
$974$	−47.2450	−	23.4747i	−1.51383	−	0.752178i
$975$		−	5.18592i		−	0.166082i
$976$	−1.57335	+	5.60263i	−0.0503618	+	0.179336i
$977$	21.5410			0.689157			0.344578	−	0.938758i	$-0.388022\pi$
$977$	21.5410			0.689157			0.344578	+	0.938758i	$0.388022\pi$
$978$	−29.1244	−	14.4711i	−0.931297	−	0.462735i
$979$		−	115.730i		−	3.69875i
$980$	4.92063	−	23.0076i	0.157184	−	0.734951i
$981$		−	6.74449i		−	0.215335i
$982$	−23.2049	+	46.7020i	−0.740499	+	1.49032i
$983$	−31.1862			−0.994684			−0.497342	−	0.867555i	$-0.665691\pi$
$983$	−31.1862			−0.994684			−0.497342	+	0.867555i	$0.665691\pi$
$984$	27.8906	−	5.28787i	0.889121	−	0.168571i
$985$			30.2707i			0.964503i
$986$	−0.500581	+	1.00746i	−0.0159417	+	0.0320842i
$987$	51.6678	+	23.6711i	1.64460	+	0.753461i
$988$	9.17492	−	6.95329i	0.291893	−	0.221214i
$989$			3.44251i			0.109466i
$990$	−18.3121	+	36.8548i	−0.581998	+	1.17132i
$991$			7.02945i			0.223298i	0.993748	+	0.111649i	$0.0356132\pi$
$991$			7.02945i			0.223298i	−0.993748	+	0.111649i	$0.964387\pi$
$992$	16.3462	+	14.7738i	0.518991	+	0.469069i
$993$			12.1691i			0.386175i
$994$	−14.5470	+	11.7648i	−0.461404	+	0.373158i
$995$	15.3333			0.486100
$996$	31.0047	+	40.9109i	0.982420	+	1.29631i
$997$	30.9954			0.981636			0.490818	−	0.871262i	$-0.336698\pi$
$997$	30.9954			0.981636			0.490818	+	0.871262i	$0.336698\pi$
$998$	16.4428	−	33.0925i	0.520487	−	1.04753i
$999$	−1.67005			−0.0528380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.a.27.18	yes	48
4.3	odd	2		2912.2.h.a.2575.41		48
7.6	odd	2		728.2.h.b.27.18	yes	48
8.3	odd	2		728.2.h.b.27.17	yes	48
8.5	even	2		2912.2.h.b.2575.41		48
28.27	even	2		2912.2.h.b.2575.8		48
56.13	odd	2		2912.2.h.a.2575.8		48
56.27	even	2	inner	728.2.h.a.27.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.17	✓	48	56.27	even	2	inner
728.2.h.a.27.18	yes	48	1.1	even	1	trivial
728.2.h.b.27.17	yes	48	8.3	odd	2
728.2.h.b.27.18	yes	48	7.6	odd	2
2912.2.h.a.2575.8		48	56.13	odd	2
2912.2.h.a.2575.41		48	4.3	odd	2
2912.2.h.b.2575.8		48	28.27	even	2
2912.2.h.b.2575.41		48	8.5	even	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.629285 + 1.26649i) q^{2} -2.38356i q^{3} +(-1.20800 - 1.59397i) q^{4} -1.68057 q^{5} +(3.01876 + 1.49994i) q^{6} +(1.10198 - 2.40533i) q^{7} +(2.77892 - 0.526865i) q^{8} -2.68138 q^{9} +(1.05755 - 2.12842i) q^{10} +6.45771 q^{11} +(-3.79932 + 2.87935i) q^{12} -1.00000 q^{13} +(2.35287 + 2.90929i) q^{14} +4.00574i q^{15} +(-1.08146 + 3.85103i) q^{16} -0.816850i q^{17} +(1.68735 - 3.39594i) q^{18} -5.75603i q^{19} +(2.03013 + 2.67877i) q^{20} +(-5.73327 - 2.62665i) q^{21} +(-4.06373 + 8.17863i) q^{22} +0.878221i q^{23} +(-1.25582 - 6.62374i) q^{24} -2.17570 q^{25} +(0.629285 - 1.26649i) q^{26} -0.759458i q^{27} +(-5.16522 + 1.14912i) q^{28} +0.973834i q^{29} +(-5.07323 - 2.52075i) q^{30} -3.89496 q^{31} +(-4.19675 - 3.79306i) q^{32} -15.3924i q^{33} +(1.03453 + 0.514031i) q^{34} +(-1.85195 + 4.04232i) q^{35} +(3.23911 + 4.27403i) q^{36} -2.19900i q^{37} +(7.28996 + 3.62218i) q^{38} +2.38356i q^{39} +(-4.67016 + 0.885431i) q^{40} +4.21071i q^{41} +(6.93448 - 5.60823i) q^{42} +3.91987 q^{43} +(-7.80092 - 10.2934i) q^{44} +4.50623 q^{45} +(-1.11226 - 0.552651i) q^{46} -9.01192 q^{47} +(9.17918 + 2.57774i) q^{48} +(-4.57127 - 5.30128i) q^{49} +(1.36913 - 2.75550i) q^{50} -1.94702 q^{51} +(1.20800 + 1.59397i) q^{52} -9.57202i q^{53} +(0.961847 + 0.477915i) q^{54} -10.8526 q^{55} +(1.79504 - 7.26484i) q^{56} -13.7199 q^{57} +(-1.23335 - 0.612818i) q^{58} -0.722834i q^{59} +(6.38501 - 4.83894i) q^{60} +1.45484 q^{61} +(2.45104 - 4.93293i) q^{62} +(-2.95483 + 6.44961i) q^{63} +(7.44483 - 2.92823i) q^{64} +1.68057 q^{65} +(19.4943 + 9.68617i) q^{66} -5.83289 q^{67} +(-1.30203 + 0.986757i) q^{68} +2.09330 q^{69} +(-3.95416 - 4.88926i) q^{70} +5.00020i q^{71} +(-7.45134 + 1.41272i) q^{72} +8.53527i q^{73} +(2.78502 + 1.38380i) q^{74} +5.18592i q^{75} +(-9.17492 + 6.95329i) q^{76} +(7.11628 - 15.5329i) q^{77} +(-3.01876 - 1.49994i) q^{78} +14.3010i q^{79} +(1.81747 - 6.47191i) q^{80} -9.85435 q^{81} +(-5.33282 - 2.64973i) q^{82} -10.7679i q^{83} +(2.73901 + 12.3116i) q^{84} +1.37277i q^{85} +(-2.46672 + 4.96449i) q^{86} +2.32119 q^{87} +(17.9455 - 3.40234i) q^{88} -17.9213i q^{89} +(-2.83570 + 5.70710i) q^{90} +(-1.10198 + 2.40533i) q^{91} +(1.39986 - 1.06089i) q^{92} +9.28389i q^{93} +(5.67106 - 11.4135i) q^{94} +9.67338i q^{95} +(-9.04100 + 10.0032i) q^{96} +13.1424i q^{97} +(9.59065 - 2.45346i) q^{98} -17.3155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Introduction

L-functions

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