LMFDB - Embedded newform 819.2.et.c.514.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			514.4
Character	$\chi$	$=$	819.514
Dual form			819.2.et.c.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430820 - 0.430820i) q^{2} -1.62879i q^{4} +(-1.97745 - 0.529856i) q^{5} +(-1.23433 - 2.34018i) q^{7} +(-1.56335 + 1.56335i) q^{8} +O(q^{10})$	\(q+(-0.430820 - 0.430820i) q^{2} -1.62879i q^{4} +(-1.97745 - 0.529856i) q^{5} +(-1.23433 - 2.34018i) q^{7} +(-1.56335 + 1.56335i) q^{8} +(0.623652 + 1.08020i) q^{10} +(0.0981532 + 0.0263001i) q^{11} +(3.09469 - 1.85010i) q^{13} +(-0.476419 + 1.53997i) q^{14} -1.91053 q^{16} -3.63007 q^{17} +(0.374251 + 1.39672i) q^{19} +(-0.863023 + 3.22084i) q^{20} +(-0.0309558 - 0.0536170i) q^{22} -4.80660i q^{23} +(-0.700572 - 0.404476i) q^{25} +(-2.13032 - 0.536194i) q^{26} +(-3.81165 + 2.01047i) q^{28} +(-3.79375 + 6.57097i) q^{29} +(1.73499 + 6.47506i) q^{31} +(3.94980 + 3.94980i) q^{32} +(1.56391 + 1.56391i) q^{34} +(1.20088 + 5.28159i) q^{35} +(-2.15422 + 2.15422i) q^{37} +(0.440501 - 0.762971i) q^{38} +(3.91981 - 2.26310i) q^{40} +(0.872020 + 3.25442i) q^{41} +(-7.21579 + 4.16604i) q^{43} +(0.0428372 - 0.159871i) q^{44} +(-2.07078 + 2.07078i) q^{46} +(0.529965 - 1.97786i) q^{47} +(-3.95284 + 5.77711i) q^{49} +(0.127564 + 0.476077i) q^{50} +(-3.01343 - 5.04060i) q^{52} +(5.27832 - 9.14232i) q^{53} +(-0.180158 - 0.104014i) q^{55} +(5.58823 + 1.72882i) q^{56} +(4.46533 - 1.19648i) q^{58} +(1.58843 + 1.58843i) q^{59} +(-5.15531 - 2.97642i) q^{61} +(2.04212 - 3.53706i) q^{62} +0.417744i q^{64} +(-7.09988 + 2.01874i) q^{65} +(-1.62200 + 6.05338i) q^{67} +5.91262i q^{68} +(1.75806 - 2.79278i) q^{70} +(0.0733605 - 0.273785i) q^{71} +(4.17396 - 1.11841i) q^{73} +1.85616 q^{74} +(2.27496 - 0.609575i) q^{76} +(-0.0596070 - 0.262159i) q^{77} +(-5.01725 - 8.69014i) q^{79} +(3.77797 + 1.01230i) q^{80} +(1.02639 - 1.77775i) q^{82} +(-3.74842 + 3.74842i) q^{83} +(7.17828 + 1.92342i) q^{85} +(4.90352 + 1.31389i) q^{86} +(-0.194565 + 0.112332i) q^{88} +(-5.75005 - 5.75005i) q^{89} +(-8.14945 - 4.95848i) q^{91} -7.82893 q^{92} +(-1.08042 + 0.623781i) q^{94} -2.96025i q^{95} +(16.5697 + 4.43983i) q^{97} +(4.19186 - 0.785934i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.430820	−	0.430820i	−0.304636	−	0.304636i	0.538189	−	0.842824i	$-0.319109\pi$
$2$	−0.430820	−	0.430820i	−0.304636	−	0.304636i	−0.842824	+	0.538189i	$0.819109\pi$
$3$		0			0
$3$		0			0
$4$		−	1.62879i		−	0.814394i
$5$	−1.97745	−	0.529856i	−0.884342	−	0.236959i	−0.212062	−	0.977256i	$-0.568018\pi$
$5$	−1.97745	−	0.529856i	−0.884342	−	0.236959i	−0.672279	+	0.740297i	$0.734685\pi$
$6$		0			0
$7$	−1.23433	−	2.34018i	−0.466534	−	0.884503i
$7$	−1.23433	−	2.34018i	−0.466534	−	0.884503i
$8$	−1.56335	+	1.56335i	−0.552729	+	0.552729i
$9$		0			0
$10$	0.623652	+	1.08020i	0.197216	+	0.341588i
$11$	0.0981532	+	0.0263001i	0.0295943	+	0.00792977i	0.273586	−	0.961848i	$-0.411790\pi$
$11$	0.0981532	+	0.0263001i	0.0295943	+	0.00792977i	−0.243992	+	0.969777i	$0.578457\pi$
$12$		0			0
$13$	3.09469	−	1.85010i	0.858313	−	0.513126i
$13$	3.09469	−	1.85010i	0.858313	−	0.513126i
$14$	−0.476419	+	1.53997i	−0.127328	+	0.411574i
$15$		0			0
$16$	−1.91053			−0.477632
$17$	−3.63007			−0.880422			−0.440211	−	0.897894i	$-0.645096\pi$
$17$	−3.63007			−0.880422			−0.440211	+	0.897894i	$0.645096\pi$
$18$		0			0
$19$	0.374251	+	1.39672i	0.0858590	+	0.320430i	0.995475	−	0.0950189i	$-0.0302911\pi$
$19$	0.374251	+	1.39672i	0.0858590	+	0.320430i	−0.909616	+	0.415449i	$0.863624\pi$
$20$	−0.863023	+	3.22084i	−0.192978	+	0.720203i
$21$		0			0
$22$	−0.0309558	−	0.0536170i	−0.00659979	−	0.0114312i
$23$		−	4.80660i		−	1.00224i	−0.865376	−	0.501122i	$-0.832921\pi$
$23$		−	4.80660i		−	1.00224i	0.865376	−	0.501122i	$-0.167079\pi$
$24$		0			0
$25$	−0.700572	−	0.404476i	−0.140114	−	0.0808951i
$26$	−2.13032	−	0.536194i	−0.417790	−	0.105156i
$27$		0			0
$28$	−3.81165	+	2.01047i	−0.720334	+	0.379943i
$29$	−3.79375	+	6.57097i	−0.704482	+	1.22020i	0.262397	+	0.964960i	$0.415487\pi$
$29$	−3.79375	+	6.57097i	−0.704482	+	1.22020i	−0.966878	+	0.255238i	$0.917846\pi$
$30$		0			0
$31$	1.73499	+	6.47506i	0.311613	+	1.16296i	0.927102	+	0.374810i	$0.122292\pi$
$31$	1.73499	+	6.47506i	0.311613	+	1.16296i	−0.615489	+	0.788146i	$0.711041\pi$
$32$	3.94980	+	3.94980i	0.698233	+	0.698233i
$33$		0			0
$34$	1.56391	+	1.56391i	0.268208	+	0.268208i
$35$	1.20088	+	5.28159i	0.202985	+	0.892752i
$36$		0			0
$37$	−2.15422	+	2.15422i	−0.354152	+	0.354152i	−0.861652	−	0.507500i	$-0.830570\pi$
$37$	−2.15422	+	2.15422i	−0.354152	+	0.354152i	0.507500	+	0.861652i	$0.330570\pi$
$38$	0.440501	−	0.762971i	0.0714588	−	0.123770i
$39$		0			0
$40$	3.91981	−	2.26310i	0.619776	−	0.357828i
$41$	0.872020	+	3.25442i	0.136187	+	0.508256i	0.999990	+	0.00442675i	$0.00140908\pi$
$41$	0.872020	+	3.25442i	0.136187	+	0.508256i	−0.863804	+	0.503829i	$0.831924\pi$
$42$		0			0
$43$	−7.21579	+	4.16604i	−1.10040	+	0.635315i	−0.936326	−	0.351133i	$-0.885796\pi$
$43$	−7.21579	+	4.16604i	−1.10040	+	0.635315i	−0.164073	+	0.986448i	$0.552463\pi$
$44$	0.0428372	−	0.159871i	0.00645796	−	0.0241014i
$45$		0			0
$46$	−2.07078	+	2.07078i	−0.305320	+	0.305320i
$47$	0.529965	−	1.97786i	0.0773034	−	0.288500i	−0.916442	−	0.400167i	$-0.868952\pi$
$47$	0.529965	−	1.97786i	0.0773034	−	0.288500i	0.993746	+	0.111667i	$0.0356189\pi$
$48$		0			0
$49$	−3.95284	+	5.77711i	−0.564692	+	0.825302i
$50$	0.127564	+	0.476077i	0.0180403	+	0.0673275i
$51$		0			0
$52$	−3.01343	−	5.04060i	−0.417887	−	0.699005i
$53$	5.27832	−	9.14232i	0.725033	−	1.25579i	−0.233927	−	0.972254i	$-0.575158\pi$
$53$	5.27832	−	9.14232i	0.725033	−	1.25579i	0.958960	−	0.283540i	$-0.0915089\pi$
$54$		0			0
$55$	−0.180158	−	0.104014i	−0.0242924	−	0.0140252i
$56$	5.58823	+	1.72882i	0.746758	+	0.231024i
$57$		0			0
$58$	4.46533	−	1.19648i	0.586326	−	0.157106i
$59$	1.58843	+	1.58843i	0.206796	+	0.206796i	0.802904	−	0.596108i	$-0.203287\pi$
$59$	1.58843	+	1.58843i	0.206796	+	0.206796i	−0.596108	+	0.802904i	$0.703287\pi$
$60$		0			0
$61$	−5.15531	−	2.97642i	−0.660070	−	0.381091i	0.132234	−	0.991219i	$-0.457785\pi$
$61$	−5.15531	−	2.97642i	−0.660070	−	0.381091i	−0.792303	+	0.610127i	$0.791118\pi$
$62$	2.04212	−	3.53706i	0.259349	−	0.449206i
$63$		0			0
$64$			0.417744i			0.0522180i
$65$	−7.09988	+	2.01874i	−0.880632	+	0.250394i
$66$		0			0
$67$	−1.62200	+	6.05338i	−0.198158	+	0.739537i	0.793268	+	0.608872i	$0.208378\pi$
$67$	−1.62200	+	6.05338i	−0.198158	+	0.739537i	−0.991427	+	0.130665i	$0.958289\pi$
$68$			5.91262i			0.717011i
$69$		0			0
$70$	1.75806	−	2.79278i	0.210128	−	0.333801i
$71$	0.0733605	−	0.273785i	0.00870629	−	0.0324923i	−0.961436	−	0.275029i	$-0.911313\pi$
$71$	0.0733605	−	0.273785i	0.00870629	−	0.0324923i	0.970142	+	0.242536i	$0.0779793\pi$
$72$		0			0
$73$	4.17396	−	1.11841i	0.488525	−	0.130900i	−0.00614434	−	0.999981i	$-0.501956\pi$
$73$	4.17396	−	1.11841i	0.488525	−	0.130900i	0.494669	+	0.869081i	$0.335289\pi$
$74$	1.85616			0.215775
$75$		0			0
$76$	2.27496	−	0.609575i	0.260956	−	0.0699230i
$77$	−0.0596070	−	0.262159i	−0.00679285	−	0.0298758i
$78$		0			0
$79$	−5.01725	−	8.69014i	−0.564485	−	0.977717i	−0.997097	−	0.0761370i	$-0.975741\pi$
$79$	−5.01725	−	8.69014i	−0.564485	−	0.977717i	0.432612	−	0.901580i	$-0.357592\pi$
$80$	3.77797	+	1.01230i	0.422390	+	0.113179i
$81$		0			0
$82$	1.02639	−	1.77775i	0.113346	−	0.196320i
$83$	−3.74842	+	3.74842i	−0.411442	+	0.411442i	−0.882241	−	0.470798i	$-0.843966\pi$
$83$	−3.74842	+	3.74842i	−0.411442	+	0.411442i	0.470798	+	0.882241i	$0.343966\pi$
$84$		0			0
$85$	7.17828	+	1.92342i	0.778594	+	0.208624i
$86$	4.90352	+	1.31389i	0.528760	+	0.141681i
$87$		0			0
$88$	−0.194565	+	0.112332i	−0.0207407	+	0.0119746i
$89$	−5.75005	−	5.75005i	−0.609504	−	0.609504i	0.333312	−	0.942817i	$-0.391834\pi$
$89$	−5.75005	−	5.75005i	−0.609504	−	0.609504i	−0.942817	+	0.333312i	$0.891834\pi$
$90$		0			0
$91$	−8.14945	−	4.95848i	−0.854294	−	0.519790i
$92$	−7.82893			−0.816222
$93$		0			0
$94$	−1.08042	+	0.623781i	−0.111437	+	0.0643381i
$95$		−	2.96025i		−	0.303715i
$96$		0			0
$97$	16.5697	+	4.43983i	1.68239	+	0.450796i	0.968410	−	0.249365i	$-0.0802219\pi$
$97$	16.5697	+	4.43983i	1.68239	+	0.450796i	0.713985	+	0.700161i	$0.246889\pi$
$98$	4.19186	−	0.785934i	0.423442	−	0.0793913i
$99$		0			0
$100$	−0.658805	+	1.14108i	−0.0658805	+	0.114108i
$101$	−9.40508	−	16.2901i	−0.935840	−	1.62092i	−0.773129	−	0.634249i	$-0.781309\pi$
$101$	−9.40508	−	16.2901i	−0.935840	−	1.62092i	−0.162711	−	0.986674i	$-0.552024\pi$
$102$		0			0
$103$	0.800311	+	1.38618i	0.0788569	+	0.136584i	0.902757	−	0.430151i	$-0.141540\pi$
$103$	0.800311	+	1.38618i	0.0788569	+	0.136584i	−0.823900	+	0.566735i	$0.808206\pi$
$104$	−1.94574	+	7.73047i	−0.190795	+	0.758035i
$105$		0			0
$106$	−6.21270	+	1.66469i	−0.603431	+	0.161689i
$107$	−18.1365			−1.75333			−0.876663	−	0.481105i	$-0.840236\pi$
$107$	−18.1365			−1.75333			−0.876663	+	0.481105i	$0.840236\pi$
$108$		0			0
$109$	−11.6210	+	3.11385i	−1.11309	+	0.298252i	−0.768085	−	0.640347i	$-0.778790\pi$
$109$	−11.6210	+	3.11385i	−1.11309	+	0.298252i	−0.345008	+	0.938600i	$0.612124\pi$
$110$	0.0328042	+	0.122427i	0.00312776	+	0.0116729i
$111$		0			0
$112$	2.35823	+	4.47097i	0.222832	+	0.422467i
$113$	−5.06433	−	8.77167i	−0.476412	−	0.825170i	0.523223	−	0.852196i	$-0.324730\pi$
$113$	−5.06433	−	8.77167i	−0.476412	−	0.825170i	−0.999635	+	0.0270263i	$0.991396\pi$
$114$		0			0
$115$	−2.54680	+	9.50480i	−0.237491	+	0.886327i
$116$	10.7027	+	6.17921i	0.993722	+	0.573726i
$117$		0			0
$118$		−	1.36865i		−	0.125995i
$119$	4.48072	+	8.49501i	0.410747	+	0.778736i
$120$		0			0
$121$	−9.51734	−	5.49484i	−0.865212	−	0.499531i
$122$	0.938710	+	3.50331i	0.0849868	+	0.317175i
$123$		0			0
$124$	10.5465	−	2.82593i	0.947104	−	0.253776i
$125$	8.40900	+	8.40900i	0.752123	+	0.752123i
$126$		0			0
$127$	7.73205	+	4.46410i	0.686108	+	0.396125i	0.802152	−	0.597119i	$-0.203688\pi$
$127$	7.73205	+	4.46410i	0.686108	+	0.396125i	−0.116044	+	0.993244i	$0.537021\pi$
$128$	8.07958	−	8.07958i	0.714141	−	0.714141i
$129$		0			0
$130$	3.92849	+	2.18906i	0.344551	+	0.191993i
$131$	16.4911	−	9.52114i	1.44083	−	0.831866i	0.442929	−	0.896557i	$-0.353939\pi$
$131$	16.4911	−	9.52114i	1.44083	−	0.831866i	0.997905	+	0.0646904i	$0.0206060\pi$
$132$		0			0
$133$	2.80663	−	2.59983i	0.243365	−	0.225434i
$134$	3.30670	−	1.90913i	0.285656	−	0.164923i
$135$		0			0
$136$	5.67509	−	5.67509i	0.486635	−	0.486635i
$137$	−2.60936	+	2.60936i	−0.222933	+	0.222933i	−0.809732	−	0.586800i	$-0.800388\pi$
$137$	−2.60936	+	2.60936i	−0.222933	+	0.222933i	0.586800	+	0.809732i	$0.300388\pi$
$138$		0			0
$139$	−3.25815	+	1.88110i	−0.276353	+	0.159552i	−0.631771	−	0.775155i	$-0.717672\pi$
$139$	−3.25815	+	1.88110i	−0.276353	+	0.159552i	0.355418	+	0.934707i	$0.384338\pi$
$140$	8.60260	−	1.95597i	0.727052	−	0.165310i
$141$		0			0
$142$	−0.149557	+	0.0863470i	−0.0125506	+	0.00724608i
$143$	0.352412	−	0.100203i	0.0294701	−	0.00837938i
$144$		0			0
$145$	10.9836	−	10.9836i	0.912139	−	0.912139i
$146$	−2.28006	−	1.31639i	−0.188699	−	0.108945i
$147$		0			0
$148$	3.50877	+	3.50877i	0.288419	+	0.288419i
$149$	−14.7434	+	3.95049i	−1.20783	+	0.323636i	−0.805909	−	0.592039i	$-0.798323\pi$
$149$	−14.7434	+	3.95049i	−1.20783	+	0.323636i	−0.401918	+	0.915676i	$0.631656\pi$
$150$		0			0
$151$	−3.29330	−	12.2908i	−0.268005	−	1.00021i	−0.960385	−	0.278676i	$-0.910105\pi$
$151$	−3.29330	−	12.2908i	−0.268005	−	1.00021i	0.692380	−	0.721533i	$-0.256562\pi$
$152$	−2.76866	−	1.59849i	−0.224568	−	0.129654i
$153$		0			0
$154$	−0.0872633	+	0.138623i	−0.00703188	+	0.0111706i
$155$		−	13.7234i		−	1.10229i
$156$		0			0
$157$	15.3520	+	8.86346i	1.22522	+	0.707381i	0.966026	−	0.258444i	$-0.0832096\pi$
$157$	15.3520	+	8.86346i	1.22522	+	0.707381i	0.259194	+	0.965825i	$0.416543\pi$
$158$	−1.58235	+	5.90542i	−0.125885	+	0.469810i
$159$		0			0
$160$	−5.71771	−	9.90336i	−0.452024	−	0.782929i
$161$	−11.2483	+	5.93295i	−0.886489	+	0.467582i
$162$		0			0
$163$	−6.17370	−	23.0406i	−0.483562	−	1.80468i	−0.586452	−	0.809984i	$-0.699476\pi$
$163$	−6.17370	−	23.0406i	−0.483562	−	1.80468i	0.102891	−	0.994693i	$-0.467191\pi$
$164$	5.30077	−	1.42034i	0.413920	−	0.110910i
$165$		0			0
$166$	3.22979			0.250680
$167$	−6.81217	+	1.82532i	−0.527141	+	0.141247i	−0.512568	−	0.858647i	$-0.671306\pi$
$167$	−6.81217	+	1.82532i	−0.527141	+	0.141247i	−0.0145735	+	0.999894i	$0.504639\pi$
$168$		0			0
$169$	6.15424	−	11.4510i	0.473403	−	0.880846i
$170$	−2.26390	−	3.92119i	−0.173633	−	0.300742i
$171$		0			0
$172$	6.78560	+	11.7530i	0.517397	+	0.896158i
$173$	11.1650	−	19.3383i	0.848859	−	1.47027i	−0.0333684	−	0.999443i	$-0.510623\pi$
$173$	11.1650	−	19.3383i	0.848859	−	1.47027i	0.882227	−	0.470824i	$-0.156043\pi$
$174$		0			0
$175$	−0.0818039	+	2.13872i	−0.00618379	+	0.161672i
$176$	−0.187524	−	0.0502470i	−0.0141352	−	0.00378751i
$177$		0			0
$178$			4.95448i			0.371354i
$179$	−8.47154	+	4.89104i	−0.633192	+	0.365574i	−0.781987	−	0.623294i	$-0.785794\pi$
$179$	−8.47154	+	4.89104i	−0.633192	+	0.365574i	0.148795	+	0.988868i	$0.452461\pi$
$180$		0			0
$181$	−14.1944			−1.05506			−0.527530	−	0.849536i	$-0.676882\pi$
$181$	−14.1944			−1.05506			−0.527530	+	0.849536i	$0.676882\pi$
$182$	1.37473	+	5.64716i	0.101902	+	0.418595i
$183$		0			0
$184$	7.51442	+	7.51442i	0.553970	+	0.553970i
$185$	5.40128	−	3.11843i	0.397110	−	0.229272i
$186$		0			0
$187$	−0.356303	−	0.0954712i	−0.0260555	−	0.00698154i
$188$	−3.22151	−	0.863201i	−0.234953	−	0.0629554i
$189$		0			0
$190$	−1.27533	+	1.27533i	−0.0925224	+	0.0925224i
$191$	−2.33347	+	4.04168i	−0.168844	+	0.292446i	−0.938014	−	0.346598i	$-0.887337\pi$
$191$	−2.33347	+	4.04168i	−0.168844	+	0.292446i	0.769170	+	0.639044i	$0.220670\pi$
$192$		0			0
$193$	−5.08020	−	1.36124i	−0.365681	−	0.0979839i	0.0712994	−	0.997455i	$-0.477285\pi$
$193$	−5.08020	−	1.36124i	−0.365681	−	0.0979839i	−0.436980	+	0.899471i	$0.643952\pi$
$194$	−5.22578	−	9.05131i	−0.375189	−	0.649846i
$195$		0			0
$196$	9.40969	+	6.43834i	0.672121	+	0.459881i
$197$	11.0378	−	2.95757i	0.786411	−	0.210718i	0.156802	−	0.987630i	$-0.449882\pi$
$197$	11.0378	−	2.95757i	0.786411	−	0.210718i	0.629609	+	0.776912i	$0.283215\pi$
$198$		0			0
$199$	−6.97182			−0.494219			−0.247110	−	0.968987i	$-0.579481\pi$
$199$	−6.97182			−0.494219			−0.247110	+	0.968987i	$0.579481\pi$
$200$	1.72758	−	0.462904i	0.122159	−	0.0327323i
$201$		0			0
$202$	−2.96619	+	11.0700i	−0.208701	+	0.778881i
$203$	20.0600	+	0.767273i	1.40793	+	0.0538520i
$204$		0			0
$205$		−	6.89750i		−	0.481742i
$206$	0.252404	−	0.941984i	0.0175858	−	0.0656311i
$207$		0			0
$208$	−5.91249	+	3.53467i	−0.409958	+	0.245085i
$209$			0.146936i			0.0101637i
$210$		0			0
$211$	3.94886	−	6.83963i	0.271851	−	0.470860i	−0.697485	−	0.716600i	$-0.745698\pi$
$211$	3.94886	−	6.83963i	0.271851	−	0.470860i	0.969336	+	0.245740i	$0.0790309\pi$
$212$	−14.8909	−	8.59727i	−1.02271	−	0.590463i
$213$		0			0
$214$	7.81359	+	7.81359i	0.534126	+	0.534126i
$215$	16.4763	−	4.41480i	1.12367	−	0.301087i
$216$		0			0
$217$	13.0112	−	12.0526i	0.883260	−	0.818181i
$218$	6.34808	+	3.66507i	0.429946	+	0.248230i
$219$		0			0
$220$	−0.169417	+	0.293439i	−0.0114221	+	0.0197836i
$221$	−11.2340	+	6.71601i	−0.755678	+	0.451768i
$222$		0			0
$223$	−3.02363	−	11.2843i	−0.202477	−	0.755654i	−0.990204	−	0.139630i	$-0.955409\pi$
$223$	−3.02363	−	11.2843i	−0.202477	−	0.755654i	0.787727	−	0.616025i	$-0.211258\pi$
$224$	4.36786	−	14.1186i	0.291840	−	0.943339i
$225$		0			0
$226$	−1.59720	+	5.96083i	−0.106244	+	0.396508i
$227$	−7.36360	+	7.36360i	−0.488739	+	0.488739i	−0.907908	−	0.419169i	$-0.862322\pi$
$227$	−7.36360	+	7.36360i	−0.488739	+	0.488739i	0.419169	+	0.907908i	$0.362322\pi$
$228$		0			0
$229$	−0.194192	+	0.724734i	−0.0128326	+	0.0478918i	−0.972045	−	0.234794i	$-0.924559\pi$
$229$	−0.194192	+	0.724734i	−0.0128326	+	0.0478918i	0.959213	+	0.282685i	$0.0912252\pi$
$230$	5.19207	−	2.99764i	0.342355	−	0.197659i
$231$		0			0
$232$	−4.34178	−	16.2037i	−0.285052	−	1.06383i
$233$	22.2901	−	12.8692i	1.46028	−	0.843091i	0.461252	−	0.887269i	$-0.347400\pi$
$233$	22.2901	−	12.8692i	1.46028	−	0.843091i	0.999024	+	0.0441785i	$0.0140670\pi$
$234$		0			0
$235$	−2.09596	+	3.63031i	−0.136725	+	0.236815i
$236$	2.58721	−	2.58721i	0.168413	−	0.168413i
$237$		0			0
$238$	1.72944	−	5.59021i	0.112103	−	0.362359i
$239$	8.82009	+	8.82009i	0.570524	+	0.570524i	0.932275	−	0.361751i	$-0.117821\pi$
$239$	8.82009	+	8.82009i	0.570524	+	0.570524i	−0.361751	+	0.932275i	$0.617821\pi$
$240$		0			0
$241$	−20.8684	−	20.8684i	−1.34425	−	1.34425i	−0.891777	−	0.452474i	$-0.850541\pi$
$241$	−20.8684	−	20.8684i	−1.34425	−	1.34425i	−0.452474	−	0.891777i	$-0.649459\pi$
$242$	1.73297	+	6.46755i	0.111400	+	0.415750i
$243$		0			0
$244$	−4.84796	+	8.39690i	−0.310359	+	0.537557i
$245$	10.8776	−	9.32951i	0.694943	−	0.596040i
$246$		0			0
$247$	3.74227	+	3.63002i	0.238115	+	0.230973i
$248$	−12.8352	−	7.41042i	−0.815038	−	0.470562i
$249$		0			0
$250$		−	7.24553i		−	0.458247i
$251$	3.38771	+	5.86769i	0.213831	+	0.370365i	0.952910	−	0.303253i	$-0.0980726\pi$
$251$	3.38771	+	5.86769i	0.213831	+	0.370365i	−0.739080	+	0.673618i	$0.764739\pi$
$252$		0			0
$253$	0.126414	−	0.471783i	0.00794757	−	0.0296607i
$254$	−1.40790	−	5.25435i	−0.0883394	−	0.329687i
$255$		0			0
$256$	−6.12620			−0.382888
$257$	12.9504			0.807822			0.403911	−	0.914798i	$-0.367651\pi$
$257$	12.9504			0.807822			0.403911	+	0.914798i	$0.367651\pi$
$258$		0			0
$259$	7.70028	+	2.38223i	0.478472	+	0.148024i
$260$	3.28810	+	11.5642i	0.203919	+	0.717181i
$261$		0			0
$262$	−11.2066	−	3.00280i	−0.692346	−	0.185514i
$263$	−2.76188	−	4.78372i	−0.170305	−	0.294977i	0.768222	−	0.640184i	$-0.221142\pi$
$263$	−2.76188	−	4.78372i	−0.170305	−	0.294977i	−0.938526	+	0.345207i	$0.887809\pi$
$264$		0			0
$265$	−15.2817	+	15.2817i	−0.938748	+	0.938748i
$266$	−2.32921	−	0.0890900i	−0.142813	−	0.00546246i
$267$		0			0
$268$	9.85967	+	2.64189i	0.602275	+	0.161379i
$269$			12.1333i			0.739778i	0.929076	+	0.369889i	$0.120604\pi$
$269$			12.1333i			0.739778i	−0.929076	+	0.369889i	$0.879396\pi$
$270$		0			0
$271$	−1.61558	−	1.61558i	−0.0981395	−	0.0981395i	0.656332	−	0.754472i	$-0.272107\pi$
$271$	−1.61558	−	1.61558i	−0.0981395	−	0.0981395i	−0.754472	+	0.656332i	$0.772107\pi$
$272$	6.93535			0.420518
$273$		0			0
$274$	2.24833			0.135827
$275$	−0.0581257	−	0.0581257i	−0.00350511	−	0.00350511i
$276$		0			0
$277$		−	5.18421i		−	0.311489i	−0.987797	−	0.155745i	$-0.950222\pi$
$277$		−	5.18421i		−	0.311489i	0.987797	−	0.155745i	$-0.0497777\pi$
$278$	2.21409	+	0.593264i	0.132792	+	0.0355816i
$279$		0			0
$280$	−10.1344	−	6.37961i	−0.605646	−	0.381255i
$281$	−13.5499	+	13.5499i	−0.808321	+	0.808321i	−0.984380	−	0.176059i	$-0.943665\pi$
$281$	−13.5499	+	13.5499i	−0.808321	+	0.808321i	0.176059	+	0.984380i	$0.443665\pi$
$282$		0			0
$283$	6.84696	+	11.8593i	0.407009	+	0.704961i	0.994553	−	0.104232i	$-0.0332383\pi$
$283$	6.84696	+	11.8593i	0.407009	+	0.704961i	−0.587544	+	0.809192i	$0.699905\pi$
$284$	−0.445938	−	0.119489i	−0.0264615	−	0.00709035i
$285$		0			0
$286$	−0.194995	−	0.108657i	−0.0115303	−	0.00642500i
$287$	6.53956	−	6.05772i	0.386018	−	0.357576i
$288$		0			0
$289$	−3.82256			−0.224857
$290$	−9.46392			−0.555740
$291$		0			0
$292$	−1.82165	−	6.79850i	−0.106604	−	0.397852i
$293$	5.35275	−	19.9768i	0.312711	−	1.16705i	−0.613390	−	0.789780i	$-0.710195\pi$
$293$	5.35275	−	19.9768i	0.312711	−	1.16705i	0.926102	−	0.377274i	$-0.123139\pi$
$294$		0			0
$295$	−2.29940	−	3.98267i	−0.133876	−	0.231880i
$296$		−	6.73562i		−	0.391500i
$297$		0			0
$298$	8.05371	+	4.64981i	0.466539	+	0.269356i
$299$	−8.89270	−	14.8749i	−0.514278	−	0.860240i
$300$		0			0
$301$	18.6560	+	11.7439i	1.07531	+	0.676909i
$302$	−3.87629	+	6.71393i	−0.223055	+	0.386343i
$303$		0			0
$304$	−0.715016	−	2.66848i	−0.0410090	−	0.153048i
$305$	8.61728	+	8.61728i	0.493424	+	0.493424i
$306$		0			0
$307$	12.7621	+	12.7621i	0.728370	+	0.728370i	0.970295	−	0.241925i	$-0.0777788\pi$
$307$	12.7621	+	12.7621i	0.728370	+	0.728370i	−0.241925	+	0.970295i	$0.577779\pi$
$308$	−0.427001	+	0.0970872i	−0.0243306	+	0.00553206i
$309$		0			0
$310$	−5.91232	+	5.91232i	−0.335797	+	0.335797i
$311$	3.99213	−	6.91458i	0.226373	−	0.392090i	−0.730357	−	0.683065i	$-0.760646\pi$
$311$	3.99213	−	6.91458i	0.226373	−	0.392090i	0.956731	+	0.290975i	$0.0939798\pi$
$312$		0			0
$313$	−16.6125	+	9.59123i	−0.938994	+	0.542129i	−0.889645	−	0.456653i	$-0.849048\pi$
$313$	−16.6125	+	9.59123i	−0.938994	+	0.542129i	−0.0493493	+	0.998782i	$0.515715\pi$
$314$	−2.79538	−	10.4325i	−0.157752	−	0.588740i
$315$		0			0
$316$	−14.1544	+	8.17204i	−0.796247	+	0.459713i
$317$	−6.86941	+	25.6370i	−0.385824	+	1.43992i	0.451039	+	0.892504i	$0.351053\pi$
$317$	−6.86941	+	25.6370i	−0.385824	+	1.43992i	−0.836864	+	0.547412i	$0.815613\pi$
$318$		0			0
$319$	−0.545185	+	0.545185i	−0.0305245	+	0.0305245i
$320$	0.221344	−	0.826067i	0.0123735	−	0.0461785i
$321$		0			0
$322$	7.40202	+	2.28995i	0.412498	+	0.127614i
$323$	−1.35856	−	5.07021i	−0.0755922	−	0.282114i
$324$		0			0
$325$	−2.91638	+	0.0444031i	−0.161772	+	0.00246304i
$326$	−7.26659	+	12.5861i	−0.402459	+	0.697079i
$327$		0			0
$328$	−6.45110	−	3.72454i	−0.356202	−	0.205653i
$329$	−5.28269	+	1.20112i	−0.291244	+	0.0662201i
$330$		0			0
$331$	−32.6825	+	8.75726i	−1.79639	+	0.481343i	−0.993406	−	0.114651i	$-0.963425\pi$
$331$	−32.6825	+	8.75726i	−1.79639	+	0.481343i	−0.802989	+	0.595994i	$0.796758\pi$
$332$	6.10538	+	6.10538i	0.335076	+	0.335076i
$333$		0			0
$334$	3.72120	+	2.14844i	0.203615	+	0.117557i
$335$	6.41483	−	11.1108i	0.350480	−	0.607049i
$336$		0			0
$337$			4.82368i			0.262763i	0.991332	+	0.131381i	$0.0419412\pi$
$337$			4.82368i			0.262763i	−0.991332	+	0.131381i	$0.958059\pi$
$338$	−7.58469	+	2.28195i	−0.412553	+	0.124122i
$339$		0			0
$340$	3.13284	−	11.6919i	0.169902	−	0.634082i
$341$			0.681178i			0.0368879i
$342$		0			0
$343$	18.3986	+	2.11945i	0.993430	+	0.114440i
$344$	4.76785	−	17.7938i	0.257065	−	0.959380i
$345$		0			0
$346$	−13.1415	+	3.52124i	−0.706489	+	0.189303i
$347$	−30.0530			−1.61333			−0.806664	−	0.591010i	$-0.798729\pi$
$347$	−30.0530			−1.61333			−0.806664	+	0.591010i	$0.798729\pi$
$348$		0			0
$349$	29.5463	−	7.91691i	1.58158	−	0.423782i	0.642164	−	0.766567i	$-0.278037\pi$
$349$	29.5463	−	7.91691i	1.58158	−	0.423782i	0.939414	+	0.342785i	$0.111370\pi$
$350$	0.956647	−	0.886161i	0.0511349	−	0.0473673i
$351$		0			0
$352$	0.283806	+	0.491566i	0.0151269	+	0.0262005i
$353$	−30.1693	−	8.08384i	−1.60575	−	0.430260i	−0.658978	−	0.752162i	$-0.729011\pi$
$353$	−30.1693	−	8.08384i	−1.60575	−	0.430260i	−0.946773	+	0.321903i	$0.895678\pi$
$354$		0			0
$355$	−0.290133	+	0.502525i	−0.0153987	+	0.0266713i
$356$	−9.36562	+	9.36562i	−0.496377	+	0.496377i
$357$		0			0
$358$	5.75687	+	1.54255i	0.304260	+	0.0815262i
$359$	−12.8721	−	3.44908i	−0.679366	−	0.182035i	−0.0973957	−	0.995246i	$-0.531051\pi$
$359$	−12.8721	−	3.44908i	−0.679366	−	0.182035i	−0.581970	+	0.813210i	$0.697718\pi$
$360$		0			0
$361$	14.6437	−	8.45455i	0.770722	−	0.444976i
$362$	6.11523	+	6.11523i	0.321409	+	0.321409i
$363$		0			0
$364$	−8.07631	+	13.2737i	−0.423314	+	0.695732i
$365$	−8.84639			−0.463041
$366$		0			0
$367$	−20.0733	+	11.5893i	−1.04782	+	0.604957i	−0.922037	−	0.387101i	$-0.873476\pi$
$367$	−20.0733	+	11.5893i	−1.04782	+	0.604957i	−0.125779	+	0.992058i	$0.540143\pi$
$368$			9.18313i			0.478704i
$369$		0			0
$370$	−3.67047	−	0.983498i	−0.190818	−	0.0511296i
$371$	−27.9098	−	1.06752i	−1.44901	−	0.0554230i
$372$		0			0
$373$	−0.724254	+	1.25444i	−0.0375004	+	0.0649527i	−0.884166	−	0.467172i	$-0.845273\pi$
$373$	−0.724254	+	1.25444i	−0.0375004	+	0.0649527i	0.846666	+	0.532125i	$0.178606\pi$
$374$	0.112372	+	0.194634i	0.00581060	+	0.0100643i
$375$		0			0
$376$	2.26357	+	3.92062i	0.116735	+	0.202190i
$377$	0.416476	+	27.3539i	0.0214496	+	1.40880i
$378$		0			0
$379$	−2.31805	+	0.621121i	−0.119070	+	0.0319048i	−0.317862	−	0.948137i	$-0.602965\pi$
$379$	−2.31805	+	0.621121i	−0.119070	+	0.0319048i	0.198792	+	0.980042i	$0.436298\pi$
$380$	−4.82161			−0.247343
$381$		0			0
$382$	2.74654	−	0.735934i	0.140525	−	0.0376537i
$383$	7.48482	+	27.9337i	0.382456	+	1.42735i	0.842137	+	0.539263i	$0.181297\pi$
$383$	7.48482	+	27.9337i	0.382456	+	1.42735i	−0.459681	+	0.888084i	$0.652036\pi$
$384$		0			0
$385$	−0.0210365	+	0.549988i	−0.00107212	+	0.0280300i
$386$	1.60221	+	2.77510i	0.0815501	+	0.141249i
$387$		0			0
$388$	7.23154	−	26.9885i	0.367126	−	1.37013i
$389$	26.2815	+	15.1736i	1.33252	+	0.769332i	0.985686	−	0.168593i	$-0.0539223\pi$
$389$	26.2815	+	15.1736i	1.33252	+	0.769332i	0.346837	+	0.937925i	$0.387256\pi$
$390$		0			0
$391$			17.4483i			0.882399i
$392$	−2.85199	−	15.2114i	−0.144047	−	0.768290i
$393$		0			0
$394$	−6.02949	−	3.48113i	−0.303761	−	0.175377i
$395$	5.31684	+	19.8427i	0.267519	+	0.998396i
$396$		0			0
$397$	16.6187	−	4.45296i	0.834068	−	0.223488i	0.183580	−	0.983005i	$-0.441231\pi$
$397$	16.6187	−	4.45296i	0.834068	−	0.223488i	0.650488	+	0.759517i	$0.274565\pi$
$398$	3.00360	+	3.00360i	0.150557	+	0.150557i
$399$		0			0
$400$	1.33846	+	0.772762i	0.0669231	+	0.0386381i
$401$	10.6544	−	10.6544i	0.532056	−	0.532056i	−0.389128	−	0.921184i	$-0.627224\pi$
$401$	10.6544	−	10.6544i	0.532056	−	0.532056i	0.921184	+	0.389128i	$0.127224\pi$
$402$		0			0
$403$	17.3488	+	16.8284i	0.864205	+	0.838283i
$404$	−26.5331	+	15.3189i	−1.32007	+	0.762143i
$405$		0			0
$406$	−8.31168	−	8.97279i	−0.412502	−	0.445312i
$407$	−0.268100	+	0.154787i	−0.0132892	+	0.00767253i
$408$		0			0
$409$	12.7272	−	12.7272i	0.629320	−	0.629320i	−0.318577	−	0.947897i	$-0.603205\pi$
$409$	12.7272	−	12.7272i	0.629320	−	0.629320i	0.947897	+	0.318577i	$0.103205\pi$
$410$	−2.97158	+	2.97158i	−0.146756	+	0.146756i
$411$		0			0
$412$	2.25779	−	1.30354i	0.111233	−	0.0642206i
$413$	1.75655	−	5.67785i	0.0864341	−	0.279389i
$414$		0			0
$415$	9.39842	−	5.42618i	0.461351	−	0.266361i
$416$	19.5310	+	4.91588i	0.957584	+	0.241021i
$417$		0			0
$418$	0.0633028	−	0.0633028i	0.00309624	−	0.00309624i
$419$	−13.0716	−	7.54692i	−0.638592	−	0.368691i	0.145480	−	0.989361i	$-0.453527\pi$
$419$	−13.0716	−	7.54692i	−0.638592	−	0.368691i	−0.784072	+	0.620670i	$0.786861\pi$
$420$		0			0
$421$	−13.2298	−	13.2298i	−0.644780	−	0.644780i	0.306947	−	0.951727i	$-0.400693\pi$
$421$	−13.2298	−	13.2298i	−0.644780	−	0.644780i	−0.951727	+	0.306947i	$0.900693\pi$
$422$	−4.64790	+	1.24540i	−0.226256	+	0.0606252i
$423$		0			0
$424$	6.04080	+	22.5446i	0.293367	+	1.09486i
$425$	2.54313	+	1.46828i	0.123360	+	0.0712219i
$426$		0			0
$427$	−0.601971	+	15.7382i	−0.0291314	+	0.761626i
$428$			29.5406i			1.42790i
$429$		0			0
$430$	−9.00029	−	5.19632i	−0.434032	−	0.250589i
$431$	−10.5271	+	39.2876i	−0.507072	+	1.89242i	−0.0593708	+	0.998236i	$0.518909\pi$
$431$	−10.5271	+	39.2876i	−0.507072	+	1.89242i	−0.447701	+	0.894183i	$0.647757\pi$
$432$		0			0
$433$	−1.94157	−	3.36289i	−0.0933058	−	0.161610i	0.815594	−	0.578624i	$-0.196410\pi$
$433$	−1.94157	−	3.36289i	−0.0933058	−	0.161610i	−0.908900	+	0.417014i	$0.863077\pi$
$434$	−10.7980	−	0.413012i	−0.518320	−	0.0198252i
$435$		0			0
$436$	5.07180	+	18.9282i	0.242895	+	0.906496i
$437$	6.71348	−	1.79887i	0.321149	−	0.0860517i
$438$		0			0
$439$	−23.3601			−1.11491			−0.557457	−	0.830206i	$-0.688223\pi$
$439$	−23.3601			−1.11491			−0.557457	+	0.830206i	$0.688223\pi$
$440$	0.444261	−	0.119039i	0.0211793	−	0.00567498i
$441$		0			0
$442$	7.73321	+	1.94642i	0.367831	+	0.0925820i
$443$	7.62370	+	13.2046i	0.362213	+	0.627371i	0.988325	−	0.152362i	$-0.0486880\pi$
$443$	7.62370	+	13.2046i	0.362213	+	0.627371i	−0.626112	+	0.779733i	$0.715355\pi$
$444$		0			0
$445$	8.32374	+	14.4171i	0.394583	+	0.683438i
$446$	−3.55888	+	6.16415i	−0.168518	+	0.291881i
$447$		0			0
$448$	0.977594	−	0.515635i	0.0461870	−	0.0243615i
$449$	−22.2529	−	5.96266i	−1.05018	−	0.281395i	−0.307855	−	0.951433i	$-0.599611\pi$
$449$	−22.2529	−	5.96266i	−1.05018	−	0.281395i	−0.742327	+	0.670038i	$0.766278\pi$
$450$		0			0
$451$			0.342366i			0.0161214i
$452$	−14.2872	+	8.24872i	−0.672013	+	0.387987i
$453$		0			0
$454$	6.34478			0.297775
$455$	13.4878	+	14.1232i	0.632319	+	0.662104i
$456$		0			0
$457$	−2.86607	−	2.86607i	−0.134069	−	0.134069i	0.636887	−	0.770957i	$-0.280222\pi$
$457$	−2.86607	−	2.86607i	−0.134069	−	0.134069i	−0.770957	+	0.636887i	$0.780222\pi$
$458$	0.395892	−	0.228568i	0.0184988	−	0.0106803i
$459$		0			0
$460$	15.4813	+	4.14820i	0.721819	+	0.193411i
$461$	14.2239	+	3.81128i	0.662473	+	0.177509i	0.574362	−	0.818601i	$-0.305250\pi$
$461$	14.2239	+	3.81128i	0.662473	+	0.177509i	0.0881113	+	0.996111i	$0.471917\pi$
$462$		0			0
$463$	3.88913	−	3.88913i	0.180743	−	0.180743i	−0.610936	−	0.791680i	$-0.709207\pi$
$463$	3.88913	−	3.88913i	0.180743	−	0.180743i	0.791680	+	0.610936i	$0.209207\pi$
$464$	7.24806	−	12.5540i	0.336483	−	0.582805i
$465$		0			0
$466$	−15.1474	−	4.05872i	−0.701688	−	0.188017i
$467$	−2.18755	−	3.78894i	−0.101228	−	0.175331i	0.810963	−	0.585097i	$-0.198944\pi$
$467$	−2.18755	−	3.78894i	−0.101228	−	0.175331i	−0.912191	+	0.409766i	$0.865610\pi$
$468$		0			0
$469$	16.1680	−	3.67613i	0.746571	−	0.169748i
$470$	2.46699	−	0.661028i	0.113794	−	0.0304909i
$471$		0			0
$472$	−4.96655			−0.228604
$473$	−0.817820	+	0.219134i	−0.0376034	+	0.0100758i
$474$		0			0
$475$	0.302751	−	1.12988i	0.0138912	−	0.0518425i
$476$	13.8366	−	7.29815i	0.634198	−	0.334510i
$477$		0			0
$478$		−	7.59974i		−	0.347604i
$479$	−8.19394	+	30.5802i	−0.374391	+	1.39724i	0.479843	+	0.877355i	$0.340694\pi$
$479$	−8.19394	+	30.5802i	−0.374391	+	1.39724i	−0.854233	+	0.519890i	$0.825973\pi$
$480$		0			0
$481$	−2.68112	+	10.6522i	−0.122249	+	0.485697i
$482$			17.9811i			0.819015i
$483$		0			0
$484$	−8.94993	+	15.5017i	−0.406815	+	0.704624i
$485$	−30.4132	−	17.5591i	−1.38099	−	0.797316i
$486$		0			0
$487$	−22.4600	−	22.4600i	−1.01776	−	1.01776i	−0.999839	−	0.0179183i	$-0.994296\pi$
$487$	−22.4600	−	22.4600i	−1.01776	−	1.01776i	−0.0179183	−	0.999839i	$-0.505704\pi$
$488$	12.7128	−	3.40638i	0.575480	−	0.154199i
$489$		0			0
$490$	−8.70562	−	0.666938i	−0.393280	−	0.0301292i
$491$	−3.19371	−	1.84389i	−0.144130	−	0.0832136i	0.426201	−	0.904629i	$-0.359852\pi$
$491$	−3.19371	−	1.84389i	−0.144130	−	0.0832136i	−0.570331	+	0.821415i	$0.693185\pi$
$492$		0			0
$493$	13.7716	−	23.8531i	0.620241	−	1.07429i
$494$	−0.0483580	−	3.17613i	−0.00217573	−	0.142901i
$495$		0			0
$496$	−3.31474	−	12.3708i	−0.148836	−	0.555464i
$497$	−0.731257	+	0.166266i	−0.0328013	+	0.00745804i
$498$		0			0
$499$	−7.61668	+	28.4258i	−0.340969	+	1.27252i	0.556281	+	0.830994i	$0.312228\pi$
$499$	−7.61668	+	28.4258i	−0.340969	+	1.27252i	−0.897251	+	0.441521i	$0.854439\pi$
$500$	13.6965	−	13.6965i	0.612525	−	0.612525i
$501$		0			0
$502$	1.06842	−	3.98741i	0.0476861	−	0.177967i
$503$	12.1149	−	6.99455i	0.540178	−	0.311872i	−0.204973	−	0.978768i	$-0.565711\pi$
$503$	12.1149	−	6.99455i	0.540178	−	0.311872i	0.745151	+	0.666896i	$0.232377\pi$
$504$		0			0
$505$	9.96667	+	37.1961i	0.443511	+	1.65520i
$506$	−0.257715	+	0.148792i	−0.0114568	+	0.00661461i
$507$		0			0
$508$	7.27107	−	12.5939i	0.322602	−	0.558763i
$509$	26.6190	−	26.6190i	1.17987	−	1.17987i	0.200090	−	0.979777i	$-0.435877\pi$
$509$	26.6190	−	26.6190i	1.17987	−	1.17987i	0.979777	−	0.200090i	$-0.0641235\pi$
$510$		0			0
$511$	−7.76933	−	8.38731i	−0.343695	−	0.371033i
$512$	−13.5199	−	13.5199i	−0.597499	−	0.597499i
$513$		0			0
$514$	−5.57928	−	5.57928i	−0.246092	−	0.246092i
$515$	−0.848098	−	3.16515i	−0.0373717	−	0.139473i
$516$		0			0
$517$	0.104036	−	0.180195i	0.00457548	−	0.00792496i
$518$	−2.29112	−	4.34375i	−0.100666	−	0.190853i
$519$		0			0
$520$	7.94362	−	14.2556i	0.348351	−	0.625151i
$521$	6.79737	+	3.92446i	0.297798	+	0.171934i	0.641453	−	0.767162i	$-0.278332\pi$
$521$	6.79737	+	3.92446i	0.297798	+	0.171934i	−0.343655	+	0.939096i	$0.611665\pi$
$522$		0			0
$523$		−	13.2423i		−	0.579043i	−0.957171	−	0.289522i	$-0.906504\pi$
$523$		−	13.2423i		−	0.579043i	0.957171	−	0.289522i	$-0.0934962\pi$
$524$	−15.5079	−	26.8605i	−0.677467	−	1.17341i
$525$		0			0
$526$	−0.871048	+	3.25079i	−0.0379795	+	0.141741i
$527$	−6.29813	−	23.5050i	−0.274351	−	1.02389i
$528$		0			0
$529$	−0.103385			−0.00449500
$530$	13.1673			0.571953
$531$		0			0
$532$	−4.23458	−	4.57140i	−0.183592	−	0.198195i
$533$	8.71965	+	8.45811i	0.377690	+	0.366362i
$534$		0			0
$535$	35.8641	+	9.60975i	1.55054	+	0.415466i
$536$	−6.92782	−	11.9993i	−0.299236	−	0.518292i
$537$		0			0
$538$	5.22726	−	5.22726i	0.225363	−	0.225363i
$539$	−0.539922	+	0.463082i	−0.0232561	+	0.0199464i
$540$		0			0
$541$	23.6349	+	6.33296i	1.01614	+	0.272275i	0.728195	−	0.685370i	$-0.240360\pi$
$541$	23.6349	+	6.33296i	1.01614	+	0.272275i	0.287950	+	0.957645i	$0.407026\pi$
$542$			1.39205i			0.0597936i
$543$		0			0
$544$	−14.3381	−	14.3381i	−0.614740	−	0.614740i
$545$	24.6299			1.05503
$546$		0			0
$547$	−39.7857			−1.70111			−0.850557	−	0.525883i	$-0.823735\pi$
$547$	−39.7857			−1.70111			−0.850557	+	0.525883i	$0.823735\pi$
$548$	4.25009	+	4.25009i	0.181555	+	0.181555i
$549$		0			0
$550$			0.0500834i			0.00213556i
$551$	−10.5976	−	2.83963i	−0.451474	−	0.120972i
$552$		0			0
$553$	−14.1435	+	22.4678i	−0.601442	+	0.955428i
$554$	−2.23346	+	2.23346i	−0.0948908	+	0.0948908i
$555$		0			0
$556$	3.06391	+	5.30684i	0.129939	+	0.225060i
$557$	0.380110	+	0.101850i	0.0161058	+	0.00431553i	0.266863	−	0.963734i	$-0.414013\pi$
$557$	0.380110	+	0.101850i	0.0161058	+	0.00431553i	−0.250757	+	0.968050i	$0.580680\pi$
$558$		0			0
$559$	−14.6231	+	26.2426i	−0.618489	+	1.10994i
$560$	−2.29431	−	10.0906i	−0.0969521	−	0.426407i
$561$		0			0
$562$	11.6752			0.492487
$563$	−27.7772			−1.17067			−0.585335	−	0.810792i	$-0.699037\pi$
$563$	−27.7772			−1.17067			−0.585335	+	0.810792i	$0.699037\pi$
$564$		0			0
$565$	5.36673	+	20.0289i	0.225780	+	0.842622i
$566$	2.15941	−	8.05902i	0.0907667	−	0.338746i
$567$		0			0
$568$	0.313335	+	0.542712i	0.0131472	+	0.0227717i
$569$			0.573198i			0.0240297i	0.999928	+	0.0120149i	$0.00382454\pi$
$569$			0.573198i			0.0240297i	−0.999928	+	0.0120149i	$0.996175\pi$
$570$		0			0
$571$	26.2481	+	15.1543i	1.09845	+	0.634189i	0.935813	−	0.352497i	$-0.114667\pi$
$571$	26.2481	+	15.1543i	1.09845	+	0.634189i	0.162635	+	0.986686i	$0.448001\pi$
$572$	−0.163209	−	0.574004i	−0.00682412	−	0.0240003i
$573$		0			0
$574$	−5.42716	−	0.207583i	−0.226525	−	0.00866437i
$575$	−1.94415	+	3.36737i	−0.0810768	+	0.140429i
$576$		0			0
$577$	−10.1337	−	37.8193i	−0.421870	−	1.57444i	−0.770665	−	0.637240i	$-0.780076\pi$
$577$	−10.1337	−	37.8193i	−0.421870	−	1.57444i	0.348795	−	0.937199i	$-0.386591\pi$
$578$	1.64684	+	1.64684i	0.0684994	+	0.0684994i
$579$		0			0
$580$	−17.8900	−	17.8900i	−0.742841	−	0.742841i
$581$	13.3988	+	4.14516i	0.555874	+	0.171970i
$582$		0			0
$583$	0.758528	−	0.758528i	0.0314150	−	0.0314150i
$584$	−4.77691	+	8.27385i	−0.197670	+	0.342374i
$585$		0			0
$586$	−10.9125	+	6.30031i	−0.450790	+	0.260264i
$587$	−4.30312	−	16.0595i	−0.177609	−	0.662845i	−0.996093	−	0.0883156i	$-0.971852\pi$
$587$	−4.30312	−	16.0595i	−0.177609	−	0.662845i	0.818484	−	0.574530i	$-0.194815\pi$
$588$		0			0
$589$	−8.39455	+	4.84659i	−0.345891	+	0.199700i
$590$	−0.725188	+	2.70644i	−0.0298555	+	0.111422i
$591$		0			0
$592$	4.11569	−	4.11569i	0.169154	−	0.169154i
$593$	1.93471	−	7.22043i	0.0794489	−	0.296507i	−0.914756	−	0.404006i	$-0.867617\pi$
$593$	1.93471	−	7.22043i	0.0794489	−	0.296507i	0.994205	+	0.107499i	$0.0342841\pi$
$594$		0			0
$595$	−4.35927	−	19.1726i	−0.178713	−	0.785999i
$596$	6.43450	+	24.0139i	0.263568	+	0.983647i
$597$		0			0
$598$	−2.57727	+	10.2396i	−0.105392	+	0.418727i
$599$	−2.38287	+	4.12725i	−0.0973613	+	0.168635i	−0.910592	−	0.413307i	$-0.864374\pi$
$599$	−2.38287	+	4.12725i	−0.0973613	+	0.168635i	0.813230	+	0.581942i	$0.197707\pi$
$600$		0			0
$601$	−15.7639	−	9.10131i	−0.643024	−	0.371250i	0.142754	−	0.989758i	$-0.454404\pi$
$601$	−15.7639	−	9.10131i	−0.643024	−	0.371250i	−0.785778	+	0.618508i	$0.787737\pi$
$602$	−2.97784	−	13.0969i	−0.121368	−	0.533789i
$603$		0			0
$604$	−20.0191	+	5.36409i	−0.814564	+	0.218262i
$605$	15.9086	+	15.9086i	0.646775	+	0.646775i
$606$		0			0
$607$	−25.1421	−	14.5158i	−1.02048	−	0.589177i	−0.106240	−	0.994340i	$-0.533881\pi$
$607$	−25.1421	−	14.5158i	−1.02048	−	0.589177i	−0.914244	+	0.405163i	$0.867215\pi$
$608$	−4.03856	+	6.99499i	−0.163785	+	0.283685i
$609$		0			0
$610$		−	7.42500i		−	0.300629i
$611$	−2.01916	−	7.10135i	−0.0816865	−	0.287290i
$612$		0			0
$613$	2.94070	−	10.9749i	0.118774	−	0.443270i	−0.880768	−	0.473549i	$-0.842973\pi$
$613$	2.94070	−	10.9749i	0.118774	−	0.443270i	0.999542	+	0.0302784i	$0.00963940\pi$
$614$		−	10.9963i		−	0.443775i
$615$		0			0
$616$	0.503034	+	0.316660i	0.0202678	+	0.0127586i
$617$	5.32917	−	19.8887i	0.214544	−	0.800690i	−0.771782	−	0.635887i	$-0.780635\pi$
$617$	5.32917	−	19.8887i	0.214544	−	0.800690i	0.986327	−	0.164803i	$-0.0526988\pi$
$618$		0			0
$619$	−0.198576	+	0.0532082i	−0.00798143	+	0.00213862i	−0.262808	−	0.964848i	$-0.584648\pi$
$619$	−0.198576	+	0.0532082i	−0.00798143	+	0.00213862i	0.254826	+	0.966987i	$0.417982\pi$
$620$	−22.3525			−0.897698
$621$		0			0
$622$	−4.69883	+	1.25905i	−0.188406	+	0.0504832i
$623$	−6.35865	+	20.5536i	−0.254754	+	0.823463i
$624$		0			0
$625$	−10.1504	−	17.5810i	−0.406017	−	0.703242i
$626$	11.2891	+	3.02490i	0.451203	+	0.120899i
$627$		0			0
$628$	14.4367	−	25.0051i	0.576087	−	0.997812i
$629$	7.81998	−	7.81998i	0.311803	−	0.311803i
$630$		0			0
$631$	28.5113	+	7.63958i	1.13502	+	0.304127i	0.776946	−	0.629568i	$-0.216768\pi$
$631$	28.5113	+	7.63958i	1.13502	+	0.304127i	0.358071	+	0.933694i	$0.383435\pi$
$632$	21.4295	+	5.74202i	0.852421	+	0.228405i
$633$		0			0
$634$	14.0044	−	8.08544i	0.556186	−	0.321114i
$635$	−12.9244	−	12.9244i	−0.512889	−	0.512889i
$636$		0			0
$637$	−1.54457	+	25.1916i	−0.0611982	+	0.998126i
$638$	0.469754			0.0185977
$639$		0			0
$640$	−20.2580	+	11.6959i	−0.800766	+	0.462323i
$641$		−	47.3075i		−	1.86853i	−0.356575	−	0.934267i	$-0.616056\pi$
$641$		−	47.3075i		−	1.86853i	0.356575	−	0.934267i	$-0.383944\pi$
$642$		0			0
$643$	19.6736	+	5.27154i	0.775853	+	0.207889i	0.624955	−	0.780660i	$-0.285117\pi$
$643$	19.6736	+	5.27154i	0.775853	+	0.207889i	0.150897	+	0.988549i	$0.451784\pi$
$644$	9.66351	+	18.3211i	0.380796	+	0.721951i
$645$		0			0
$646$	−1.59905	+	2.76964i	−0.0629139	+	0.108970i
$647$	1.56833	+	2.71643i	0.0616576	+	0.106794i	0.895206	−	0.445652i	$-0.147028\pi$
$647$	1.56833	+	2.71643i	0.0616576	+	0.106794i	−0.833549	+	0.552446i	$0.813695\pi$
$648$		0			0
$649$	0.114133	+	0.197685i	0.00448013	+	0.00775981i
$650$	1.27556	+	1.23730i	0.0500317	+	0.0485311i
$651$		0			0
$652$	−37.5282	+	10.0557i	−1.46972	+	0.393810i
$653$	4.18468			0.163759			0.0818795	−	0.996642i	$-0.473908\pi$
$653$	4.18468			0.163759			0.0818795	+	0.996642i	$0.473908\pi$
$654$		0			0
$655$	−37.6551	+	10.0897i	−1.47131	+	0.394236i
$656$	−1.66602	−	6.21766i	−0.0650471	−	0.242759i
$657$		0			0
$658$	2.79336	+	1.75842i	0.108896	+	0.0685503i
$659$	8.69927	+	15.0676i	0.338875	+	0.586949i	0.984221	−	0.176941i	$-0.0566202\pi$
$659$	8.69927	+	15.0676i	0.338875	+	0.586949i	−0.645346	+	0.763890i	$0.723287\pi$
$660$		0			0
$661$	−7.68938	+	28.6972i	−0.299082	+	1.11619i	0.638839	+	0.769341i	$0.279415\pi$
$661$	−7.68938	+	28.6972i	−0.299082	+	1.11619i	−0.937921	+	0.346849i	$0.887252\pi$
$662$	17.8531	+	10.3075i	0.693880	+	0.400612i
$663$		0			0
$664$		−	11.7202i		−	0.454833i
$665$	−6.92749	+	3.65393i	−0.268637	+	0.141693i
$666$		0			0
$667$	31.5840	+	18.2350i	1.22294	+	0.706063i
$668$	2.97305	+	11.0956i	0.115031	+	0.429301i
$669$		0			0
$670$	−7.55040	+	2.02312i	−0.291697	+	0.0781601i
$671$	−0.427730	−	0.427730i	−0.0165123	−	0.0165123i
$672$		0			0
$673$	−22.9048	−	13.2241i	−0.882917	−	0.509752i	−0.0112978	−	0.999936i	$-0.503596\pi$
$673$	−22.9048	−	13.2241i	−0.882917	−	0.509752i	−0.871619	+	0.490184i	$0.836930\pi$
$674$	2.07814	−	2.07814i	0.0800469	−	0.0800469i
$675$		0			0
$676$	−18.6512	−	10.0240i	−0.717356	−	0.385537i
$677$	8.72930	−	5.03986i	0.335494	−	0.193698i	−0.322783	−	0.946473i	$-0.604619\pi$
$677$	8.72930	−	5.03986i	0.335494	−	0.193698i	0.658278	+	0.752775i	$0.271285\pi$
$678$		0			0
$679$	−10.0625	−	44.2561i	−0.386164	−	1.69839i
$680$	−14.2292	+	8.21522i	−0.545664	+	0.315039i
$681$		0			0
$682$	0.293465	−	0.293465i	0.0112374	−	0.0112374i
$683$	31.5016	−	31.5016i	1.20537	−	1.20537i	0.232864	−	0.972509i	$-0.425190\pi$
$683$	31.5016	−	31.5016i	1.20537	−	1.20537i	0.972509	−	0.232864i	$-0.0748097\pi$
$684$		0			0
$685$	6.54246	−	3.77729i	0.249974	−	0.144323i
$686$	−7.01338	−	8.83958i	−0.267772	−	0.337497i
$687$		0			0
$688$	13.7860	−	7.95933i	0.525585	−	0.303447i
$689$	−0.579451	−	38.0581i	−0.0220753	−	1.44990i
$690$		0			0
$691$	−2.87952	+	2.87952i	−0.109542	+	0.109542i	−0.759753	−	0.650211i	$-0.774680\pi$
$691$	−2.87952	+	2.87952i	−0.109542	+	0.109542i	0.650211	+	0.759753i	$0.274680\pi$
$692$	−31.4981	−	18.1854i	−1.19738	−	0.691306i
$693$		0			0
$694$	12.9474	+	12.9474i	0.491478	+	0.491478i
$695$	7.43954	−	1.99342i	0.282198	−	0.0756146i
$696$		0			0
$697$	−3.16550	−	11.8138i	−0.119902	−	0.447479i
$698$	−16.1399	−	9.31838i	−0.610905	−	0.352706i
$699$		0			0
$700$	3.48352	+	0.133241i	0.131665	+	0.00503604i
$701$		−	19.7829i		−	0.747191i	−0.927592	−	0.373596i	$-0.878125\pi$
$701$		−	19.7829i		−	0.747191i	0.927592	−	0.373596i	$-0.121875\pi$
$702$		0			0
$703$	−3.81507	−	2.20263i	−0.143888	−	0.0830737i
$704$	−0.0109867	+	0.0410029i	−0.000414076	+	0.00154535i
$705$		0			0
$706$	9.51487	+	16.4802i	0.358097	+	0.620242i
$707$	−26.5126	+	42.1169i	−0.997110	+	1.58397i
$708$		0			0
$709$	−1.08628	−	4.05405i	−0.0407960	−	0.152253i	0.942523	−	0.334140i	$-0.108446\pi$
$709$	−1.08628	−	4.05405i	−0.0407960	−	0.152253i	−0.983319	+	0.181888i	$0.941779\pi$
$710$	0.341493	−	0.0915029i	0.0128160	−	0.00343404i
$711$		0			0
$712$	17.9787			0.673782
$713$	31.1230	−	8.33939i	1.16557	−	0.312313i
$714$		0			0
$715$	−0.749969	+	0.0114186i	−0.0280472	+	0.000427032i
$716$	7.96647	+	13.7983i	0.297721	+	0.515668i
$717$		0			0
$718$	4.05964	+	7.03151i	0.151505	+	0.262414i
$719$	−10.3212	+	17.8769i	−0.384918	+	0.666697i	−0.991758	−	0.128127i	$-0.959103\pi$
$719$	−10.3212	+	17.8769i	−0.384918	+	0.666697i	0.606840	+	0.794824i	$0.292437\pi$
$720$		0			0
$721$	2.25605	−	3.58387i	0.0840197	−	0.133470i
$722$	−9.95120	−	2.66642i	−0.370345	−	0.0992337i
$723$		0			0
$724$			23.1196i			0.859235i
$725$	5.31559	−	3.06896i	0.197416	−	0.113978i
$726$		0			0
$727$	14.8265			0.549885			0.274942	−	0.961461i	$-0.411341\pi$
$727$	14.8265			0.549885			0.274942	+	0.961461i	$0.411341\pi$
$728$	20.4923	−	4.98862i	0.759497	−	0.184890i
$729$		0			0
$730$	3.81120	+	3.81120i	0.141059	+	0.141059i
$731$	26.1939	−	15.1230i	0.968815	−	0.559346i
$732$		0			0
$733$	38.1303	+	10.2170i	1.40838	+	0.377373i	0.881345	−	0.472473i	$-0.156639\pi$
$733$	38.1303	+	10.2170i	1.40838	+	0.377373i	0.527031	+	0.849846i	$0.323305\pi$
$734$	13.6409	+	3.65506i	0.503494	+	0.134911i
$735$		0			0
$736$	18.9851	−	18.9851i	0.699801	−	0.699801i
$737$	−0.318408	+	0.551499i	−0.0117287	+	0.0203147i
$738$		0			0
$739$	10.3718	+	2.77912i	0.381533	+	0.102232i	0.444488	−	0.895785i	$-0.353386\pi$
$739$	10.3718	+	2.77912i	0.381533	+	0.102232i	−0.0629547	+	0.998016i	$0.520052\pi$
$740$	−5.07927	−	8.79755i	−0.186718	−	0.323404i
$741$		0			0
$742$	11.5642	+	12.4840i	0.424536	+	0.458303i
$743$	23.5602	−	6.31294i	0.864340	−	0.231599i	0.200701	−	0.979652i	$-0.435678\pi$
$743$	23.5602	−	6.31294i	0.864340	−	0.231599i	0.663639	+	0.748053i	$0.269011\pi$
$744$		0			0
$745$	31.2475			1.14482
$746$	0.852463	−	0.228417i	0.0312109	−	0.00836293i
$747$		0			0
$748$	−0.155502	+	0.580343i	−0.00568573	+	0.0212194i
$749$	22.3865	+	42.4427i	0.817987	+	1.55082i
$750$		0			0
$751$		−	44.0350i		−	1.60686i	−0.595398	−	0.803431i	$-0.703006\pi$
$751$		−	44.0350i		−	1.60686i	0.595398	−	0.803431i	$-0.296994\pi$
$752$	−1.01251	+	3.77875i	−0.0369225	+	0.137797i
$753$		0			0
$754$	11.6052	−	11.9641i	0.422637	−	0.435705i
$755$			26.0493i			0.948032i
$756$		0			0
$757$	15.1721	−	26.2788i	0.551438	−	0.955119i	−0.446733	−	0.894667i	$-0.647413\pi$
$757$	15.1721	−	26.2788i	0.551438	−	0.955119i	0.998171	−	0.0604518i	$-0.0192542\pi$
$758$	1.26626	+	0.731073i	0.0459925	+	0.0265538i
$759$		0			0
$760$	4.62791	+	4.62791i	0.167872	+	0.167872i
$761$	−30.3847	+	8.14155i	−1.10144	+	0.295131i	−0.763353	−	0.645982i	$-0.776448\pi$
$761$	−30.3847	+	8.14155i	−1.10144	+	0.295131i	−0.338092	+	0.941113i	$0.609781\pi$
$762$		0			0
$763$	21.6312	+	23.3517i	0.783101	+	0.845389i
$764$	6.58305	+	3.80072i	0.238166	+	0.137505i
$765$		0			0
$766$	8.80980	−	15.2590i	0.318311	−	0.551331i
$767$	7.85445	+	1.97694i	0.283608	+	0.0713832i
$768$		0			0
$769$	−6.01297	−	22.4407i	−0.216833	−	0.809232i	−0.985513	−	0.169599i	$-0.945753\pi$
$769$	−6.01297	−	22.4407i	−0.216833	−	0.809232i	0.768680	−	0.639633i	$-0.220914\pi$
$770$	0.246009	−	0.227883i	0.00886555	−	0.00821234i
$771$		0			0
$772$	−2.21717	+	8.27457i	−0.0797975	+	0.297808i
$773$	38.0766	−	38.0766i	1.36952	−	1.36952i	0.508394	−	0.861125i	$-0.330239\pi$
$773$	38.0766	−	38.0766i	1.36952	−	1.36952i	0.861125	−	0.508394i	$-0.169761\pi$
$774$		0			0
$775$	1.40352	−	5.23801i	0.0504160	−	0.188155i
$776$	−32.8453	+	18.9632i	−1.17908	+	0.680741i
$777$		0			0
$778$	−4.78549	−	17.8597i	−0.171568	−	0.640300i
$779$	−4.21917	+	2.43594i	−0.151168	+	0.0872766i
$780$		0			0
$781$	0.0144011	−	0.0249435i	0.000515313	−	0.000892548i
$782$	7.51708	−	7.51708i	0.268810	−	0.268810i
$783$		0			0
$784$	7.55201	−	11.0373i	0.269715	−	0.394190i
$785$	−25.6614	−	25.6614i	−0.915894	−	0.915894i
$786$		0			0
$787$	14.8317	+	14.8317i	0.528695	+	0.528695i	0.920183	−	0.391488i	$-0.128040\pi$
$787$	14.8317	+	14.8317i	0.528695	+	0.528695i	−0.391488	+	0.920183i	$0.628040\pi$
$788$	−4.81726	−	17.9783i	−0.171608	−	0.640449i
$789$		0			0
$790$	6.25804	−	10.8392i	0.222651	−	0.385643i
$791$	−14.2762	+	22.6786i	−0.507603	+	0.806358i
$792$		0			0
$793$	−21.4608	+	0.326750i	−0.762094	+	0.0116032i
$794$	−9.07809	−	5.24124i	−0.322169	−	0.186005i
$795$		0			0
$796$			11.3556i			0.402489i
$797$	9.47306	+	16.4078i	0.335553	+	0.581195i	0.983591	−	0.180413i	$-0.0577434\pi$
$797$	9.47306	+	16.4078i	0.335553	+	0.581195i	−0.648038	+	0.761608i	$0.724410\pi$
$798$		0			0
$799$	−1.92381	+	7.17977i	−0.0680596	+	0.254002i
$800$	−1.16952	−	4.36472i	−0.0413489	−	0.154316i
$801$		0			0
$802$	−9.18027			−0.324167
$803$	0.439102			0.0154956
$804$		0			0
$805$	25.3865	−	5.77213i	0.894757	−	0.203441i
$806$	−0.224183	−	14.7242i	−0.00789650	−	0.518639i
$807$		0			0
$808$	40.1706	+	10.7637i	1.41320	+	0.378665i
$809$	−20.9032	−	36.2055i	−0.734918	−	1.27292i	−0.954759	−	0.297380i	$-0.903887\pi$
$809$	−20.9032	−	36.2055i	−0.734918	−	1.27292i	0.219841	−	0.975536i	$-0.429446\pi$
$810$		0			0
$811$	−16.4161	+	16.4161i	−0.576448	+	0.576448i	−0.933923	−	0.357475i	$-0.883638\pi$
$811$	−16.4161	+	16.4161i	−0.576448	+	0.576448i	0.357475	+	0.933923i	$0.383638\pi$
$812$	1.24973	−	32.6734i	0.0438568	−	1.14661i
$813$		0			0
$814$	0.182188	+	0.0488172i	0.00638570	+	0.00171104i
$815$			48.8327i			1.71053i
$816$		0			0
$817$	−8.51932	−	8.51932i	−0.298053	−	0.298053i
$818$	−10.9663			−0.383427
$819$		0			0
$820$	−11.2346			−0.392328
$821$	28.3759	+	28.3759i	0.990327	+	0.990327i	0.999954	−	0.00962644i	$-0.00306424\pi$
$821$	28.3759	+	28.3759i	0.990327	+	0.990327i	−0.00962644	+	0.999954i	$0.503064\pi$
$822$		0			0
$823$		−	26.5127i		−	0.924176i	−0.886834	−	0.462088i	$-0.847100\pi$
$823$		−	26.5127i		−	0.924176i	0.886834	−	0.462088i	$-0.152900\pi$
$824$	−3.41826	−	0.915920i	−0.119081	−	0.0319076i
$825$		0			0
$826$	−3.20289	+	1.68937i	−0.111443	+	0.0587808i
$827$	9.55537	−	9.55537i	0.332273	−	0.332273i	−0.521176	−	0.853449i	$-0.674507\pi$
$827$	9.55537	−	9.55537i	0.332273	−	0.332273i	0.853449	+	0.521176i	$0.174507\pi$
$828$		0			0
$829$	−3.75261	−	6.49971i	−0.130333	−	0.225744i	0.793472	−	0.608607i	$-0.208271\pi$
$829$	−3.75261	−	6.49971i	−0.130333	−	0.225744i	−0.923805	+	0.382863i	$0.874938\pi$
$830$	−6.38674	−	1.71132i	−0.221687	−	0.0594008i
$831$		0			0
$832$	0.772869	+	1.29279i	0.0267944	+	0.0448194i
$833$	14.3491	−	20.9714i	0.497167	−	0.726614i
$834$		0			0
$835$	14.4379			0.499643
$836$	0.239327			0.00827729
$837$		0			0
$838$	2.38016	+	8.88289i	0.0822214	+	0.306854i
$839$	3.08672	−	11.5198i	0.106566	−	0.397708i	−0.891953	−	0.452129i	$-0.850665\pi$
$839$	3.08672	−	11.5198i	0.106566	−	0.397708i	0.998518	+	0.0544211i	$0.0173313\pi$
$840$		0			0
$841$	−14.2851	−	24.7425i	−0.492589	−	0.853189i
$842$			11.3993i			0.392846i
$843$		0			0
$844$	−11.1403	−	6.43186i	−0.383465	−	0.221394i
$845$	−18.2371	+	19.3829i	−0.627374	+	0.666792i
$846$		0			0
$847$	−1.11131	+	29.0547i	−0.0381852	+	0.998331i
$848$	−10.0844	+	17.4666i	−0.346299	+	0.599807i
$849$		0			0
$850$	−0.463068	−	1.72819i	−0.0158831	−	0.0592766i
$851$	10.3545	+	10.3545i	0.354947	+	0.354947i
$852$		0			0
$853$	−3.51458	−	3.51458i	−0.120337	−	0.120337i	0.644374	−	0.764711i	$-0.277118\pi$
$853$	−3.51458	−	3.51458i	−0.120337	−	0.120337i	−0.764711	+	0.644374i	$0.777118\pi$
$854$	7.03968	−	6.52100i	0.240893	−	0.223144i
$855$		0			0
$856$	28.3539	−	28.3539i	0.969115	−	0.969115i
$857$	27.7599	−	48.0815i	0.948259	−	1.64243i	0.199168	−	0.979965i	$-0.436176\pi$
$857$	27.7599	−	48.0815i	0.948259	−	1.64243i	0.749091	−	0.662467i	$-0.230491\pi$
$858$		0			0
$859$	23.3968	−	13.5082i	0.798289	−	0.460892i	−0.0445837	−	0.999006i	$-0.514196\pi$
$859$	23.3968	−	13.5082i	0.798289	−	0.460892i	0.842872	+	0.538113i	$0.180863\pi$
$860$	−7.19077	−	26.8363i	−0.245203	−	0.915111i
$861$		0			0
$862$	21.4612	−	12.3906i	0.730971	−	0.422026i
$863$	0.273598	−	1.02108i	0.00931338	−	0.0347580i	−0.961113	−	0.276156i	$-0.910939\pi$
$863$	0.273598	−	1.02108i	0.00931338	−	0.0347580i	0.970426	+	0.241398i	$0.0776060\pi$
$864$		0			0
$865$	−32.3247	+	32.3247i	−1.09907	+	1.09907i
$866$	−0.612336	+	2.28527i	−0.0208080	+	0.0776566i
$867$		0			0
$868$	−19.6311	−	21.1925i	−0.666322	−	0.719321i
$869$	−0.263908	−	0.984919i	−0.00895247	−	0.0334111i
$870$		0			0
$871$	6.17978	+	21.7342i	0.209394	+	0.736435i
$872$	13.2998	−	23.0358i	0.450386	−	0.780092i
$873$		0			0
$874$	−3.66729	−	2.11731i	−0.124048	−	0.0716192i
$875$	9.29902	−	30.0580i	0.314364	−	1.01615i
$876$		0			0
$877$	−23.6254	+	6.33040i	−0.797772	+	0.213762i	−0.634606	−	0.772836i	$-0.718837\pi$
$877$	−23.6254	+	6.33040i	−0.797772	+	0.213762i	−0.163167	+	0.986599i	$0.552171\pi$
$878$	10.0640	+	10.0640i	0.339643	+	0.339643i
$879$		0			0
$880$	0.344196	+	0.198722i	0.0116028	+	0.00669890i
$881$	−11.6797	+	20.2298i	−0.393498	+	0.681558i	−0.992908	−	0.118884i	$-0.962068\pi$
$881$	−11.6797	+	20.2298i	−0.393498	+	0.681558i	0.599411	+	0.800442i	$0.295402\pi$
$882$		0			0
$883$			52.8083i			1.77714i	0.458739	+	0.888571i	$0.348301\pi$
$883$			52.8083i			1.77714i	−0.458739	+	0.888571i	$0.651699\pi$
$884$	10.9390	+	18.2977i	0.367917	+	0.615420i
$885$		0			0
$886$	2.40438	−	8.97326i	0.0807767	−	0.301463i
$887$			43.8954i			1.47386i	0.675966	+	0.736932i	$0.263726\pi$
$887$			43.8954i			1.47386i	−0.675966	+	0.736932i	$0.736274\pi$
$888$		0			0
$889$	0.902850	−	23.6045i	0.0302806	−	0.791671i
$890$	2.62516	−	9.79722i	0.0879955	−	0.328404i
$891$		0			0
$892$	−18.3798	+	4.92485i	−0.615400	+	0.164896i
$893$	2.96086			0.0990813
$894$		0			0
$895$	19.3436	−	5.18309i	0.646584	−	0.173252i
$896$	−28.8805	−	8.93473i	−0.964831	−	0.298489i
$897$		0			0
$898$	7.01818	+	12.1559i	0.234200	+	0.405646i
$899$	−49.1295	−	13.1642i	−1.63856	−	0.439051i
$900$		0			0
$901$	−19.1607	+	33.1873i	−0.638335	+	1.10563i
$902$	0.147498	−	0.147498i	0.00491115	−	0.00491115i
$903$		0			0
$904$	21.6306	+	5.79590i	0.719422	+	0.192769i
$905$	28.0687	+	7.52098i	0.933034	+	0.250006i
$906$		0			0
$907$	17.0797	−	9.86098i	0.567123	−	0.327429i	−0.188876	−	0.982001i	$-0.560485\pi$
$907$	17.0797	−	9.86098i	0.567123	−	0.327429i	0.755999	+	0.654572i	$0.227151\pi$
$908$	11.9937	+	11.9937i	0.398026	+	0.398026i
$909$		0			0
$910$	0.273714	−	11.8954i	0.00907354	−	0.394328i
$911$	32.0257			1.06106			0.530529	−	0.847667i	$-0.321993\pi$
$911$	32.0257			1.06106			0.530529	+	0.847667i	$0.321993\pi$
$912$		0			0
$913$	−0.466503	+	0.269336i	−0.0154390	+	0.00891371i
$914$			2.46953i			0.0816846i
$915$		0			0
$916$	1.18044	+	0.316297i	0.0390028	+	0.0104508i
$917$	−42.6367	−	26.8398i	−1.40799	−	0.886329i
$918$		0			0
$919$	−12.8209	+	22.2064i	−0.422922	+	0.732523i	−0.996224	−	0.0868215i	$-0.972329\pi$
$919$	−12.8209	+	22.2064i	−0.422922	+	0.732523i	0.573302	+	0.819344i	$0.305662\pi$
$920$	−10.8778	−	18.8409i	−0.358631	−	0.621167i
$921$		0			0
$922$	−4.48597	−	7.76992i	−0.147737	−	0.255889i
$923$	−0.279502	−	0.983005i	−0.00919993	−	0.0323560i
$924$		0			0
$925$	2.38052	−	0.637858i	0.0782709	−	0.0209726i
$926$	−3.35103			−0.110122
$927$		0			0
$928$	−40.9386	+	10.9695i	−1.34388	+	0.360090i
$929$	4.40197	+	16.4284i	0.144424	+	0.538998i	0.999780	+	0.0209579i	$0.00667159\pi$
$929$	4.40197	+	16.4284i	0.144424	+	0.538998i	−0.855356	+	0.518040i	$0.826662\pi$
$930$		0			0
$931$	−9.54838	−	3.35893i	−0.312935	−	0.110085i
$932$	−20.9612	−	36.3059i	−0.686608	−	1.18924i
$933$		0			0
$934$	−0.689913	+	2.57479i	−0.0225747	+	0.0842498i
$935$	0.653985	+	0.377579i	0.0213876	+	0.0123481i
$936$		0			0
$937$		−	23.7513i		−	0.775922i	−0.921676	−	0.387961i	$-0.873180\pi$
$937$		−	23.7513i		−	0.775922i	0.921676	−	0.387961i	$-0.126820\pi$
$938$	−8.54927	−	5.38177i	−0.279144	−	0.175721i
$939$		0			0
$940$	5.91300	+	3.41387i	0.192861	+	0.111348i
$941$	4.82733	+	18.0159i	0.157367	+	0.587300i	0.998891	+	0.0470811i	$0.0149919\pi$
$941$	4.82733	+	18.0159i	0.157367	+	0.587300i	−0.841525	+	0.540219i	$0.818341\pi$
$942$		0			0
$943$	15.6427	−	4.19145i	0.509397	−	0.136492i
$944$	−3.03473	−	3.03473i	−0.0987721	−	0.0987721i
$945$		0			0
$946$	0.446741	+	0.257926i	0.0145248	+	0.00838589i
$947$	−34.1328	+	34.1328i	−1.10917	+	1.10917i	−0.115906	+	0.993260i	$0.536977\pi$
$947$	−34.1328	+	34.1328i	−1.10917	+	1.10917i	−0.993260	+	0.115906i	$0.963023\pi$
$948$		0			0
$949$	10.8480	−	11.1834i	0.352139	−	0.363028i
$950$	−0.617206	+	0.356344i	−0.0200248	+	0.0115613i
$951$		0			0
$952$	−20.2857	−	6.27576i	−0.657462	−	0.203398i
$953$	5.68926	−	3.28470i	0.184293	−	0.106402i	−0.405015	−	0.914310i	$-0.632734\pi$
$953$	5.68926	−	3.28470i	0.184293	−	0.106402i	0.589308	+	0.807908i	$0.299400\pi$
$954$		0			0
$955$	6.75582	−	6.75582i	0.218613	−	0.218613i
$956$	14.3661	−	14.3661i	0.464631	−	0.464631i
$957$		0			0
$958$	16.7047	−	9.64445i	0.539704	−	0.311598i
$959$	9.32718	+	2.88554i	0.301190	+	0.0931789i
$960$		0			0
$961$	−12.0695	+	6.96831i	−0.389338	+	0.224784i
$962$	5.74425	−	3.43409i	0.185202	−	0.110720i
$963$		0			0
$964$	−33.9902	+	33.9902i	−1.09475	+	1.09475i
$965$	9.32458	+	5.38355i	0.300169	+	0.173303i
$966$		0			0
$967$	−3.29098	−	3.29098i	−0.105831	−	0.105831i	0.652209	−	0.758039i	$-0.273843\pi$
$967$	−3.29098	−	3.29098i	−0.105831	−	0.105831i	−0.758039	+	0.652209i	$0.773843\pi$
$968$	23.4694	−	6.28860i	0.754334	−	0.202123i
$969$		0			0
$970$	5.53781	+	20.6674i	0.177809	+	0.663590i
$971$	−8.75030	−	5.05199i	−0.280811	−	0.162126i	0.352980	−	0.935631i	$-0.385168\pi$
$971$	−8.75030	−	5.05199i	−0.280811	−	0.162126i	−0.633790	+	0.773505i	$0.718502\pi$
$972$		0			0
$973$	8.42374	+	5.30275i	0.270053	+	0.169998i
$974$			19.3524i			0.620091i
$975$		0			0
$976$	9.84935	+	5.68653i	0.315270	+	0.182021i
$977$	3.55718	−	13.2756i	0.113804	−	0.424723i	−0.885390	−	0.464848i	$-0.846109\pi$
$977$	3.55718	−	13.2756i	0.113804	−	0.424723i	0.999195	+	0.0401249i	$0.0127756\pi$
$978$		0			0
$979$	−0.413159	−	0.715613i	−0.0132046	−	0.0228711i
$980$	−15.1958	−	17.7173i	−0.485412	−	0.565957i
$981$		0			0
$982$	0.581530	+	2.17030i	0.0185574	+	0.0692571i
$983$	−45.8389	+	12.2825i	−1.46203	+	0.391751i	−0.900192	−	0.435494i	$-0.856574\pi$
$983$	−45.8389	+	12.2825i	−1.46203	+	0.391751i	−0.561842	+	0.827244i	$0.689907\pi$
$984$		0			0
$985$	−23.3938			−0.745388
$986$	−16.2095	+	4.34332i	−0.516215	+	0.138319i
$987$		0			0
$988$	5.91254	−	6.09537i	0.188103	−	0.193919i
$989$	20.0245	+	34.6834i	0.636741	+	1.10287i
$990$		0			0
$991$	4.62262	+	8.00661i	0.146842	+	0.254338i	0.930059	−	0.367411i	$-0.119756\pi$
$991$	4.62262	+	8.00661i	0.146842	+	0.254338i	−0.783216	+	0.621749i	$0.786422\pi$
$992$	−18.7224	+	32.4281i	−0.594436	+	1.02959i
$993$		0			0
$994$	0.386671	+	0.243409i	0.0122644	+	0.00772048i
$995$	13.7864	+	3.69406i	0.437059	+	0.117110i
$996$		0			0
$997$			38.4529i			1.21782i	0.793241	+	0.608908i	$0.208392\pi$
$997$			38.4529i			1.21782i	−0.793241	+	0.608908i	$0.791608\pi$
$998$	15.5278	−	8.96500i	0.491525	−	0.283782i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.514.4		36
3.2	odd	2		273.2.bt.a.241.6	yes	36
7.5	odd	6		819.2.gh.c.397.4		36
13.2	odd	12		819.2.gh.c.262.4		36
21.5	even	6		273.2.cg.a.124.6	yes	36
39.2	even	12		273.2.cg.a.262.6	yes	36
91.54	even	12	inner	819.2.et.c.145.4		36
273.236	odd	12		273.2.bt.a.145.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.6	✓	36	273.236	odd	12
273.2.bt.a.241.6	yes	36	3.2	odd	2
273.2.cg.a.124.6	yes	36	21.5	even	6
273.2.cg.a.262.6	yes	36	39.2	even	12
819.2.et.c.145.4		36	91.54	even	12	inner
819.2.et.c.514.4		36	1.1	even	1	trivial
819.2.gh.c.262.4		36	13.2	odd	12
819.2.gh.c.397.4		36	7.5	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.430820 - 0.430820i) q^{2} -1.62879i q^{4} +(-1.97745 - 0.529856i) q^{5} +(-1.23433 - 2.34018i) q^{7} +(-1.56335 + 1.56335i) q^{8} +O(q^{10})\)	\(q+(-0.430820 - 0.430820i) q^{2} -1.62879i q^{4} +(-1.97745 - 0.529856i) q^{5} +(-1.23433 - 2.34018i) q^{7} +(-1.56335 + 1.56335i) q^{8} +(0.623652 + 1.08020i) q^{10} +(0.0981532 + 0.0263001i) q^{11} +(3.09469 - 1.85010i) q^{13} +(-0.476419 + 1.53997i) q^{14} -1.91053 q^{16} -3.63007 q^{17} +(0.374251 + 1.39672i) q^{19} +(-0.863023 + 3.22084i) q^{20} +(-0.0309558 - 0.0536170i) q^{22} -4.80660i q^{23} +(-0.700572 - 0.404476i) q^{25} +(-2.13032 - 0.536194i) q^{26} +(-3.81165 + 2.01047i) q^{28} +(-3.79375 + 6.57097i) q^{29} +(1.73499 + 6.47506i) q^{31} +(3.94980 + 3.94980i) q^{32} +(1.56391 + 1.56391i) q^{34} +(1.20088 + 5.28159i) q^{35} +(-2.15422 + 2.15422i) q^{37} +(0.440501 - 0.762971i) q^{38} +(3.91981 - 2.26310i) q^{40} +(0.872020 + 3.25442i) q^{41} +(-7.21579 + 4.16604i) q^{43} +(0.0428372 - 0.159871i) q^{44} +(-2.07078 + 2.07078i) q^{46} +(0.529965 - 1.97786i) q^{47} +(-3.95284 + 5.77711i) q^{49} +(0.127564 + 0.476077i) q^{50} +(-3.01343 - 5.04060i) q^{52} +(5.27832 - 9.14232i) q^{53} +(-0.180158 - 0.104014i) q^{55} +(5.58823 + 1.72882i) q^{56} +(4.46533 - 1.19648i) q^{58} +(1.58843 + 1.58843i) q^{59} +(-5.15531 - 2.97642i) q^{61} +(2.04212 - 3.53706i) q^{62} +0.417744i q^{64} +(-7.09988 + 2.01874i) q^{65} +(-1.62200 + 6.05338i) q^{67} +5.91262i q^{68} +(1.75806 - 2.79278i) q^{70} +(0.0733605 - 0.273785i) q^{71} +(4.17396 - 1.11841i) q^{73} +1.85616 q^{74} +(2.27496 - 0.609575i) q^{76} +(-0.0596070 - 0.262159i) q^{77} +(-5.01725 - 8.69014i) q^{79} +(3.77797 + 1.01230i) q^{80} +(1.02639 - 1.77775i) q^{82} +(-3.74842 + 3.74842i) q^{83} +(7.17828 + 1.92342i) q^{85} +(4.90352 + 1.31389i) q^{86} +(-0.194565 + 0.112332i) q^{88} +(-5.75005 - 5.75005i) q^{89} +(-8.14945 - 4.95848i) q^{91} -7.82893 q^{92} +(-1.08042 + 0.623781i) q^{94} -2.96025i q^{95} +(16.5697 + 4.43983i) q^{97} +(4.19186 - 0.785934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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