LMFDB - Embedded newform 900.2.bj.f.127.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.19
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.510574 + 1.31883i) q^{2} +(-1.47863 + 1.34672i) q^{4} +(-0.968294 - 2.01554i) q^{5} +(-2.67499 + 2.67499i) q^{7} +(-2.53105 - 1.26246i) q^{8} +O(q^{10})$	\(q+(0.510574 + 1.31883i) q^{2} +(-1.47863 + 1.34672i) q^{4} +(-0.968294 - 2.01554i) q^{5} +(-2.67499 + 2.67499i) q^{7} +(-2.53105 - 1.26246i) q^{8} +(2.16377 - 2.30610i) q^{10} +(-1.87313 - 2.57815i) q^{11} +(5.65630 - 0.895870i) q^{13} +(-4.89364 - 2.16208i) q^{14} +(0.372689 - 3.98260i) q^{16} +(2.03694 - 3.99773i) q^{17} +(-0.869130 - 2.67491i) q^{19} +(4.14612 + 1.67622i) q^{20} +(2.44377 - 3.78668i) q^{22} +(5.81945 + 0.921710i) q^{23} +(-3.12481 + 3.90327i) q^{25} +(4.06946 + 7.00230i) q^{26} +(0.352856 - 7.55779i) q^{28} +(-8.67000 - 2.81705i) q^{29} +(6.80347 - 2.21058i) q^{31} +(5.44266 - 1.54190i) q^{32} +(6.31233 + 0.645250i) q^{34} +(7.98173 + 2.80138i) q^{35} +(-0.906743 - 5.72495i) q^{37} +(3.08399 - 2.51197i) q^{38} +(-0.0937491 + 6.32386i) q^{40} +(6.17980 + 4.48988i) q^{41} +(-4.72744 - 4.72744i) q^{43} +(6.24171 + 1.28954i) q^{44} +(1.75568 + 8.14547i) q^{46} +(-2.06198 - 4.04686i) q^{47} -7.31116i q^{49} +(-6.74320 - 2.12819i) q^{50} +(-7.15709 + 8.94212i) q^{52} +(-1.95228 - 3.83156i) q^{53} +(-3.38262 + 6.27178i) q^{55} +(10.1476 - 3.39345i) q^{56} +(-0.711456 - 12.8726i) q^{58} +(-5.25683 - 3.81931i) q^{59} +(3.90898 - 2.84004i) q^{61} +(6.38905 + 7.84396i) q^{62} +(4.81238 + 6.39070i) q^{64} +(-7.28263 - 10.5330i) q^{65} +(-8.86745 - 4.51819i) q^{67} +(2.37193 + 8.65435i) q^{68} +(0.380718 + 11.9569i) q^{70} +(-2.55860 - 0.831340i) q^{71} +(0.818638 - 5.16868i) q^{73} +(7.08728 - 4.11885i) q^{74} +(4.88747 + 2.78472i) q^{76} +(11.9071 + 1.88591i) q^{77} +(-1.62208 + 4.99225i) q^{79} +(-8.38797 + 3.10516i) q^{80} +(-2.76616 + 10.4425i) q^{82} +(0.853734 - 1.67555i) q^{83} +(-10.0299 - 0.234570i) q^{85} +(3.82099 - 8.64841i) q^{86} +(1.48617 + 8.89017i) q^{88} +(6.51253 + 8.96373i) q^{89} +(-12.7341 + 17.5270i) q^{91} +(-9.84610 + 6.47430i) q^{92} +(4.28434 - 4.78562i) q^{94} +(-4.54981 + 4.34186i) q^{95} +(-4.14245 + 2.11068i) q^{97} +(9.64219 - 3.73289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.510574	+	1.31883i	0.361030	+	0.932554i
$2$	0.510574	+	1.31883i	0.361030	+	0.932554i
$3$		0			0
$3$		0			0
$4$	−1.47863	+	1.34672i	−0.739315	+	0.673360i
$5$	−0.968294	−	2.01554i	−0.433034	−	0.901377i
$5$	−0.968294	−	2.01554i	−0.433034	−	0.901377i
$6$		0			0
$7$	−2.67499	+	2.67499i	−1.01105	+	1.01105i	−0.0111136	+	0.999938i	$0.503538\pi$
$7$	−2.67499	+	2.67499i	−1.01105	+	1.01105i	−0.999938	+	0.0111136i	$0.996462\pi$
$8$	−2.53105	−	1.26246i	−0.894860	−	0.446348i
$9$		0			0
$10$	2.16377	−	2.30610i	0.684245	−	0.729252i
$11$	−1.87313	−	2.57815i	−0.564771	−	0.777341i	0.427152	−	0.904180i	$-0.359517\pi$
$11$	−1.87313	−	2.57815i	−0.564771	−	0.777341i	−0.991923	+	0.126839i	$0.959517\pi$
$12$		0			0
$13$	5.65630	−	0.895870i	1.56878	−	0.248470i	0.689323	−	0.724455i	$-0.257908\pi$
$13$	5.65630	−	0.895870i	1.56878	−	0.248470i	0.879453	+	0.475985i	$0.157908\pi$
$14$	−4.89364	−	2.16208i	−1.30788	−	0.577841i
$15$		0			0
$16$	0.372689	−	3.98260i	0.0931723	−	0.995650i
$17$	2.03694	−	3.99773i	0.494031	−	0.969591i	−0.500558	−	0.865703i	$-0.666872\pi$
$17$	2.03694	−	3.99773i	0.494031	−	0.969591i	0.994589	−	0.103888i	$-0.0331283\pi$
$18$		0			0
$19$	−0.869130	−	2.67491i	−0.199392	−	0.613665i	−0.999897	−	0.0143397i	$-0.995435\pi$
$19$	−0.869130	−	2.67491i	−0.199392	−	0.613665i	0.800505	−	0.599326i	$-0.204565\pi$
$20$	4.14612	+	1.67622i	0.927100	+	0.374814i
$21$		0			0
$22$	2.44377	−	3.78668i	0.521013	−	0.807323i
$23$	5.81945	+	0.921710i	1.21344	+	0.192190i	0.730160	−	0.683276i	$-0.239446\pi$
$23$	5.81945	+	0.921710i	1.21344	+	0.192190i	0.483279	+	0.875466i	$0.339446\pi$
$24$		0			0
$25$	−3.12481	+	3.90327i	−0.624963	+	0.780655i
$26$	4.06946	+	7.00230i	0.798087	+	1.37326i
$27$		0			0
$28$	0.352856	−	7.55779i	0.0666835	−	1.42829i
$29$	−8.67000	−	2.81705i	−1.60998	−	0.523114i	−0.640431	−	0.768016i	$-0.721244\pi$
$29$	−8.67000	−	2.81705i	−1.60998	−	0.523114i	−0.969548	+	0.244902i	$0.921244\pi$
$30$		0			0
$31$	6.80347	−	2.21058i	1.22194	−	0.397032i	0.374151	−	0.927368i	$-0.377934\pi$
$31$	6.80347	−	2.21058i	1.22194	−	0.397032i	0.847788	+	0.530336i	$0.177934\pi$
$32$	5.44266	−	1.54190i	0.962136	−	0.272571i
$33$		0			0
$34$	6.31233	+	0.645250i	1.08256	+	0.110659i
$35$	7.98173	+	2.80138i	1.34916	+	0.473519i
$36$		0			0
$37$	−0.906743	−	5.72495i	−0.149068	−	0.941176i	−0.942909	−	0.333051i	$-0.891922\pi$
$37$	−0.906743	−	5.72495i	−0.149068	−	0.941176i	0.793841	−	0.608125i	$-0.208078\pi$
$38$	3.08399	−	2.51197i	0.500290	−	0.407496i
$39$		0			0
$40$	−0.0937491	+	6.32386i	−0.0148230	+	0.999890i
$41$	6.17980	+	4.48988i	0.965122	+	0.701202i	0.954335	−	0.298740i	$-0.0965662\pi$
$41$	6.17980	+	4.48988i	0.965122	+	0.701202i	0.0107873	+	0.999942i	$0.496566\pi$
$42$		0			0
$43$	−4.72744	−	4.72744i	−0.720928	−	0.720928i	0.247866	−	0.968794i	$-0.420271\pi$
$43$	−4.72744	−	4.72744i	−0.720928	−	0.720928i	−0.968794	+	0.247866i	$0.920271\pi$
$44$	6.24171	+	1.28954i	0.940974	+	0.194405i
$45$		0			0
$46$	1.75568	+	8.14547i	0.258861	+	1.20098i
$47$	−2.06198	−	4.04686i	−0.300771	−	0.590296i	0.690317	−	0.723507i	$-0.257471\pi$
$47$	−2.06198	−	4.04686i	−0.300771	−	0.590296i	−0.991088	+	0.133211i	$0.957471\pi$
$48$		0			0
$49$		−	7.31116i		−	1.04445i
$50$	−6.74320	−	2.12819i	−0.953633	−	0.300972i
$51$		0			0
$52$	−7.15709	+	8.94212i	−0.992509	+	1.24005i
$53$	−1.95228	−	3.83156i	−0.268166	−	0.526305i	0.717177	−	0.696891i	$-0.245434\pi$
$53$	−1.95228	−	3.83156i	−0.268166	−	0.526305i	−0.985343	+	0.170586i	$0.945434\pi$
$54$		0			0
$55$	−3.38262	+	6.27178i	−0.456112	+	0.845687i
$56$	10.1476	−	3.39345i	1.35603	−	0.453469i
$57$		0			0
$58$	−0.711456	−	12.8726i	−0.0934187	−	1.69025i
$59$	−5.25683	−	3.81931i	−0.684381	−	0.497232i	0.190427	−	0.981701i	$-0.439013\pi$
$59$	−5.25683	−	3.81931i	−0.684381	−	0.497232i	−0.874808	+	0.484469i	$0.839013\pi$
$60$		0			0
$61$	3.90898	−	2.84004i	0.500493	−	0.363630i	−0.308712	−	0.951156i	$-0.599898\pi$
$61$	3.90898	−	2.84004i	0.500493	−	0.363630i	0.809205	+	0.587526i	$0.199898\pi$
$62$	6.38905	+	7.84396i	0.811411	+	0.996184i
$63$		0			0
$64$	4.81238	+	6.39070i	0.601547	+	0.798837i
$65$	−7.28263	−	10.5330i	−0.903299	−	1.30646i
$66$		0			0
$67$	−8.86745	−	4.51819i	−1.08333	−	0.551985i	−0.181200	−	0.983446i	$-0.557998\pi$
$67$	−8.86745	−	4.51819i	−1.08333	−	0.551985i	−0.902132	+	0.431461i	$0.857998\pi$
$68$	2.37193	+	8.65435i	0.287639	+	1.04949i
$69$		0			0
$70$	0.380718	+	11.9569i	0.0455046	+	1.42912i
$71$	−2.55860	−	0.831340i	−0.303650	−	0.0986619i	0.153229	−	0.988191i	$-0.451033\pi$
$71$	−2.55860	−	0.831340i	−0.303650	−	0.0986619i	−0.456879	+	0.889529i	$0.651033\pi$
$72$		0			0
$73$	0.818638	−	5.16868i	0.0958143	−	0.604948i	−0.892326	−	0.451392i	$-0.850928\pi$
$73$	0.818638	−	5.16868i	0.0958143	−	0.604948i	0.988140	−	0.153556i	$-0.0490724\pi$
$74$	7.08728	−	4.11885i	0.823880	−	0.478806i
$75$		0			0
$76$	4.88747	+	2.78472i	0.560631	+	0.319429i
$77$	11.9071	+	1.88591i	1.35694	+	0.214919i
$78$		0			0
$79$	−1.62208	+	4.99225i	−0.182498	+	0.561672i	−0.999896	−	0.0144014i	$-0.995416\pi$
$79$	−1.62208	+	4.99225i	−0.182498	+	0.561672i	0.817398	+	0.576073i	$0.195416\pi$
$80$	−8.38797	+	3.10516i	−0.937803	+	0.347167i
$81$		0			0
$82$	−2.76616	+	10.4425i	−0.305471	+	1.15318i
$83$	0.853734	−	1.67555i	0.0937094	−	0.183915i	−0.839394	−	0.543524i	$-0.817090\pi$
$83$	0.853734	−	1.67555i	0.0937094	−	0.183915i	0.933103	+	0.359609i	$0.117090\pi$
$84$		0			0
$85$	−10.0299	−	0.234570i	−1.08790	−	0.0254426i
$86$	3.82099	−	8.64841i	0.412028	−	0.932582i
$87$		0			0
$88$	1.48617	+	8.89017i	0.158427	+	0.947695i
$89$	6.51253	+	8.96373i	0.690327	+	0.950153i	1.00000		0.000689768i	$-0.000219560\pi$
$89$	6.51253	+	8.96373i	0.690327	+	0.950153i	−0.309673	+	0.950843i	$0.600220\pi$
$90$		0			0
$91$	−12.7341	+	17.5270i	−1.33490	+	1.83733i
$92$	−9.84610	+	6.47430i	−1.02653	+	0.674993i
$93$		0			0
$94$	4.28434	−	4.78562i	0.441895	−	0.493599i
$95$	−4.54981	+	4.34186i	−0.466801	+	0.445466i
$96$		0			0
$97$	−4.14245	+	2.11068i	−0.420602	+	0.214307i	−0.651465	−	0.758679i	$-0.725845\pi$
$97$	−4.14245	+	2.11068i	−0.420602	+	0.214307i	0.230863	+	0.972986i	$0.425845\pi$
$98$	9.64219	−	3.73289i	0.974008	−	0.377078i
$99$		0			0
$100$	−0.636175	−	9.97974i	−0.0636175	−	0.997974i
$101$	−5.39783			−0.537104			−0.268552	−	0.963265i	$-0.586545\pi$
$101$	−5.39783			−0.537104			−0.268552	+	0.963265i	$0.586545\pi$
$102$		0			0
$103$	10.7306	−	5.46751i	1.05732	−	0.538730i	0.163213	−	0.986591i	$-0.447814\pi$
$103$	10.7306	−	5.46751i	1.05732	−	0.538730i	0.894103	+	0.447861i	$0.147814\pi$
$104$	−15.4474	−	4.87338i	−1.51474	−	0.477874i
$105$		0			0
$106$	4.05640	−	4.53101i	0.393992	−	0.440091i
$107$	−6.85755	+	6.85755i	−0.662945	+	0.662945i	−0.956073	−	0.293128i	$-0.905304\pi$
$107$	−6.85755	+	6.85755i	−0.662945	+	0.662945i	0.293128	+	0.956073i	$0.405304\pi$
$108$		0			0
$109$	−3.08613	+	4.24770i	−0.295598	+	0.406856i	−0.930822	−	0.365472i	$-0.880908\pi$
$109$	−3.08613	+	4.24770i	−0.295598	+	0.406856i	0.635224	+	0.772328i	$0.280908\pi$
$110$	−9.99849	−	1.25890i	−0.953319	−	0.120031i
$111$		0			0
$112$	9.65648	+	11.6504i	0.912452	+	1.10086i
$113$	4.10283	−	0.649824i	0.385962	−	0.0611303i	0.0395615	−	0.999217i	$-0.487404\pi$
$113$	4.10283	−	0.649824i	0.385962	−	0.0611303i	0.346400	+	0.938087i	$0.387404\pi$
$114$		0			0
$115$	−3.77719	−	12.6218i	−0.352225	−	1.17699i
$116$	16.6135	−	7.51069i	1.54253	−	0.697350i
$117$		0			0
$118$	2.35303	−	8.88291i	0.216614	−	0.817739i
$119$	5.24508	+	16.1427i	0.480815	+	1.47980i
$120$		0			0
$121$	0.260974	−	0.803195i	0.0237249	−	0.0730177i
$122$	5.74135	+	3.70523i	0.519798	+	0.335456i
$123$		0			0
$124$	−7.08278	+	12.4310i	−0.636052	+	1.11634i
$125$	10.8929	+	2.51868i	0.974295	+	0.225277i
$126$		0			0
$127$	1.81207	−	11.4410i	0.160795	−	1.01522i	−0.766869	−	0.641804i	$-0.778186\pi$
$127$	1.81207	−	11.4410i	0.160795	−	1.01522i	0.927664	−	0.373417i	$-0.121814\pi$
$128$	−5.97117	+	9.60963i	−0.527782	+	0.849380i
$129$		0			0
$130$	10.1730	−	14.9824i	0.892230	−	1.31405i
$131$	−10.4381	+	3.39154i	−0.911981	+	0.296321i	−0.727173	−	0.686454i	$-0.759166\pi$
$131$	−10.4381	+	3.39154i	−0.911981	+	0.296321i	−0.184808	+	0.982775i	$0.559166\pi$
$132$		0			0
$133$	9.48027	+	4.83044i	0.822043	+	0.418852i
$134$	1.43124	−	14.0015i	0.123641	−	1.20955i
$135$		0			0
$136$	−10.2026	+	7.54686i	−0.874863	+	0.647138i
$137$	1.12464	+	7.10069i	0.0960844	+	0.606653i	0.988000	+	0.154452i	$0.0493612\pi$
$137$	1.12464	+	7.10069i	0.0960844	+	0.606653i	−0.891916	+	0.452201i	$0.850639\pi$
$138$		0			0
$139$	−0.371124	+	0.269638i	−0.0314784	+	0.0228704i	−0.603413	−	0.797429i	$-0.706193\pi$
$139$	−0.371124	+	0.269638i	−0.0314784	+	0.0228704i	0.571935	+	0.820299i	$0.306193\pi$
$140$	−15.5747	+	6.60696i	−1.31630	+	0.558390i
$141$		0			0
$142$	−0.209957	−	3.79882i	−0.0176192	−	0.318790i
$143$	−12.9047	−	12.9047i	−1.07914	−	1.07914i
$144$		0			0
$145$	2.71722	+	20.2025i	0.225653	+	1.67773i
$146$	7.23458	−	1.55934i	0.598738	−	0.129052i
$147$		0			0
$148$	9.05064	+	7.24395i	0.743958	+	0.595449i
$149$			7.21619i			0.591173i	0.955316	+	0.295587i	$0.0955151\pi$
$149$			7.21619i			0.591173i	−0.955316	+	0.295587i	$0.904485\pi$
$150$		0			0
$151$		−	6.00455i		−	0.488643i	−0.969694	−	0.244322i	$-0.921435\pi$
$151$		−	6.00455i		−	0.488643i	0.969694	−	0.244322i	$-0.0785653\pi$
$152$	−1.17716	+	7.86755i	−0.0954804	+	0.638143i
$153$		0			0
$154$	3.59228	+	16.6664i	0.289474	+	1.34302i
$155$	−11.0433	−	11.5722i	−0.887017	−	0.929500i
$156$		0			0
$157$	−5.17494	−	5.17494i	−0.413005	−	0.413005i	0.469779	−	0.882784i	$-0.344334\pi$
$157$	−5.17494	−	5.17494i	−0.413005	−	0.413005i	−0.882784	+	0.469779i	$0.844334\pi$
$158$	−7.41212	+	0.409661i	−0.589677	+	0.0325909i
$159$		0			0
$160$	−8.37785	−	9.47690i	−0.662327	−	0.749215i
$161$	−18.0326	+	13.1014i	−1.42116	+	1.03254i
$162$		0			0
$163$	1.30952	+	8.26801i	0.102570	+	0.647601i	0.984388	+	0.176011i	$0.0563195\pi$
$163$	1.30952	+	8.26801i	0.102570	+	0.647601i	−0.881818	+	0.471589i	$0.843680\pi$
$164$	−15.1842	+	1.68358i	−1.18569	+	0.131466i
$165$		0			0
$166$	2.64566	+	0.270440i	0.205343	+	0.0209902i
$167$	−2.24832	−	1.14558i	−0.173980	−	0.0886475i	0.364831	−	0.931074i	$-0.381127\pi$
$167$	−2.24832	−	1.14558i	−0.173980	−	0.0886475i	−0.538812	+	0.842426i	$0.681127\pi$
$168$		0			0
$169$	18.8274	−	6.11740i	1.44826	−	0.470570i
$170$	−4.81166	−	13.3476i	−0.369038	−	1.02371i
$171$		0			0
$172$	13.3567	+	0.623593i	1.01844	+	0.0475485i
$173$	1.71345	−	10.8183i	0.130271	−	0.822498i	−0.832864	−	0.553478i	$-0.813300\pi$
$173$	1.71345	−	10.8183i	0.130271	−	0.822498i	0.963135	−	0.269020i	$-0.0866997\pi$
$174$		0			0
$175$	−2.08237	−	18.8001i	−0.157412	−	1.42115i
$176$	−10.9658	+	6.49909i	−0.826580	+	0.489888i
$177$		0			0
$178$	−8.49652	+	13.1656i	−0.636841	+	0.986801i
$179$	−1.95273	+	6.00987i	−0.145954	+	0.449199i	−0.997132	−	0.0756768i	$-0.975888\pi$
$179$	−1.95273	+	6.00987i	−0.145954	+	0.449199i	0.851179	+	0.524876i	$0.175888\pi$
$180$		0			0
$181$	−6.77451	−	20.8498i	−0.503545	−	1.54975i	−0.803203	−	0.595706i	$-0.796873\pi$
$181$	−6.77451	−	20.8498i	−0.503545	−	1.54975i	0.299658	−	0.954047i	$-0.403127\pi$
$182$	−29.6169	−	7.84532i	−2.19535	−	0.581534i
$183$		0			0
$184$	−13.5657	−	9.67973i	−1.00007	−	0.713599i
$185$	−10.6609	+	7.37101i	−0.783804	+	0.541928i
$186$		0			0
$187$	−14.1222	+	2.23674i	−1.03272	+	0.163566i
$188$	8.49890	+	3.20690i	0.619846	+	0.233887i
$189$		0			0
$190$	−8.04919	−	3.78359i	−0.583950	−	0.274491i
$191$	−2.31470	+	3.18591i	−0.167486	+	0.230524i	−0.884507	−	0.466527i	$-0.845505\pi$
$191$	−2.31470	+	3.18591i	−0.167486	+	0.230524i	0.717021	+	0.697051i	$0.245505\pi$
$192$		0			0
$193$	−0.560677	+	0.560677i	−0.0403584	+	0.0403584i	−0.726998	−	0.686640i	$-0.759085\pi$
$193$	−0.560677	+	0.560677i	−0.0403584	+	0.0403584i	0.686640	+	0.726998i	$0.259085\pi$
$194$	−4.89865	−	4.38553i	−0.351703	−	0.314862i
$195$		0			0
$196$	9.84609	+	10.8105i	0.703292	+	0.772179i
$197$	14.5597	−	7.41854i	1.03734	−	0.528549i	0.149525	−	0.988758i	$-0.452225\pi$
$197$	14.5597	−	7.41854i	1.03734	−	0.528549i	0.887811	+	0.460209i	$0.152225\pi$
$198$		0			0
$199$	8.83105			0.626017			0.313008	−	0.949750i	$-0.398663\pi$
$199$	8.83105			0.626017			0.313008	+	0.949750i	$0.398663\pi$
$200$	12.8368	−	5.93440i	0.907697	−	0.419625i
$201$		0			0
$202$	−2.75599	−	7.11882i	−0.193911	−	0.500878i
$203$	30.7278	−	15.6566i	2.15667	−	1.09888i
$204$		0			0
$205$	3.06569	−	16.8032i	0.214117	−	1.17358i
$206$	12.6895	+	11.3603i	0.884118	+	0.791507i
$207$		0			0
$208$	−1.45985	−	22.8607i	−0.101222	−	1.58510i
$209$	−5.26830	+	7.25120i	−0.364416	+	0.501576i
$210$		0			0
$211$	7.83691	+	10.7866i	0.539515	+	0.742578i	0.988543	−	0.150939i	$-0.0482297\pi$
$211$	7.83691	+	10.7866i	0.539515	+	0.742578i	−0.449028	+	0.893518i	$0.648230\pi$
$212$	8.04673	+	3.03628i	0.552652	+	0.208533i
$213$		0			0
$214$	−12.5452	−	5.54267i	−0.857575	−	0.378889i
$215$	−4.95080	+	14.1059i	−0.337642	+	0.962015i
$216$		0			0
$217$	−12.2859	+	24.1125i	−0.834024	+	1.63686i
$218$	−7.17769	−	1.90133i	−0.486135	−	0.128774i
$219$		0			0
$220$	−3.44470	−	13.8291i	−0.232241	−	0.932356i
$221$	7.94012	−	24.4372i	0.534110	−	1.64382i
$222$		0			0
$223$	−7.44805	−	1.17966i	−0.498758	−	0.0789956i	−0.0980131	−	0.995185i	$-0.531249\pi$
$223$	−7.44805	−	1.17966i	−0.498758	−	0.0789956i	−0.400745	+	0.916190i	$0.631249\pi$
$224$	−10.4345	+	18.6836i	−0.697185	+	1.24835i
$225$		0			0
$226$	2.95181	+	5.07916i	0.196351	+	0.337860i
$227$	1.55633	−	9.82630i	0.103297	−	0.652194i	−0.880654	−	0.473759i	$-0.842897\pi$
$227$	1.55633	−	9.82630i	0.103297	−	0.652194i	0.983952	−	0.178435i	$-0.0571034\pi$
$228$		0			0
$229$	−14.7309	−	4.78636i	−0.973446	−	0.316292i	−0.221240	−	0.975219i	$-0.571010\pi$
$229$	−14.7309	−	4.78636i	−0.973446	−	0.316292i	−0.752206	+	0.658928i	$0.771010\pi$
$230$	14.7175	−	11.4259i	0.970445	−	0.753398i
$231$		0			0
$232$	18.3877	+	18.0756i	1.20721	+	1.18672i
$233$	−6.23351	−	3.17613i	−0.408371	−	0.208075i	0.237723	−	0.971333i	$-0.423599\pi$
$233$	−6.23351	−	3.17613i	−0.408371	−	0.208075i	−0.646094	+	0.763257i	$0.723599\pi$
$234$		0			0
$235$	−6.16002	+	8.07456i	−0.401835	+	0.526726i
$236$	12.9165	−	1.43214i	0.840790	−	0.0932241i
$237$		0			0
$238$	−18.6115	+	15.1594i	−1.20640	+	0.982638i
$239$	4.50266	−	3.27138i	0.291253	−	0.211608i	−0.432558	−	0.901606i	$-0.642389\pi$
$239$	4.50266	−	3.27138i	0.291253	−	0.211608i	0.723811	+	0.689998i	$0.242389\pi$
$240$		0			0
$241$	4.28091	+	3.11026i	0.275757	+	0.200350i	0.717065	−	0.697006i	$-0.245485\pi$
$241$	4.28091	+	3.11026i	0.275757	+	0.200350i	−0.441307	+	0.897356i	$0.645485\pi$
$242$	1.19252	−	0.0659097i	0.0766584	−	0.00423684i
$243$		0			0
$244$	−1.95519	+	9.46367i	−0.125168	+	0.605849i
$245$	−14.7360	+	7.07935i	−0.941445	+	0.452283i
$246$		0			0
$247$	−7.31243	−	14.3514i	−0.465279	−	0.913161i
$248$	−20.0107	−	2.99404i	−1.27068	−	0.190122i
$249$		0			0
$250$	2.23994	+	15.6519i	0.141666	+	0.989914i
$251$			15.3609i			0.969572i	0.874633	+	0.484786i	$0.161102\pi$
$251$			15.3609i			0.969572i	−0.874633	+	0.484786i	$0.838898\pi$
$252$		0			0
$253$	−8.52430	−	16.7299i	−0.535918	−	1.05180i
$254$	16.0139	−	3.45164i	1.00480	−	0.216575i
$255$		0			0
$256$	−15.7222	−	2.96854i	−0.982638	−	0.185534i
$257$	12.1799	+	12.1799i	0.759760	+	0.759760i	0.976278	−	0.216519i	$-0.0694703\pi$
$257$	12.1799	+	12.1799i	0.759760	+	0.759760i	−0.216519	+	0.976278i	$0.569470\pi$
$258$		0			0
$259$	17.7397	+	12.8887i	1.10229	+	0.800863i
$260$	24.9534	+	5.76681i	1.54754	+	0.357642i
$261$		0			0
$262$	−9.80229	−	12.0345i	−0.605588	−	0.743491i
$263$	−3.97405	−	25.0911i	−0.245050	−	1.54719i	−0.736595	−	0.676334i	$-0.763568\pi$
$263$	−3.97405	−	25.0911i	−0.245050	−	1.54719i	0.491545	−	0.870852i	$-0.336432\pi$
$264$		0			0
$265$	−5.83229	+	7.64497i	−0.358275	+	0.469627i
$266$	−1.53016	+	14.9692i	−0.0938199	+	0.917818i
$267$		0			0
$268$	19.1964	−	5.26125i	1.17261	−	0.321382i
$269$	18.7336	−	6.08693i	1.14221	−	0.371126i	0.324006	−	0.946055i	$-0.394970\pi$
$269$	18.7336	−	6.08693i	1.14221	−	0.371126i	0.818204	+	0.574928i	$0.194970\pi$
$270$		0			0
$271$	24.1214	+	7.83752i	1.46527	+	0.476095i	0.929676	−	0.368379i	$-0.120087\pi$
$271$	24.1214	+	7.83752i	1.46527	+	0.476095i	0.535595	+	0.844475i	$0.320087\pi$
$272$	−15.1622	−	9.60224i	−0.919343	−	0.582221i
$273$		0			0
$274$	−8.79040	+	5.10864i	−0.531048	+	0.308624i
$275$	15.9164	+	0.744879i	0.959795	+	0.0449179i
$276$		0			0
$277$	28.7725	+	4.55711i	1.72877	+	0.273810i	0.940073	−	0.340973i	$-0.110756\pi$
$277$	28.7725	+	4.55711i	1.72877	+	0.273810i	0.788696	+	0.614783i	$0.210756\pi$
$278$	−0.545093	−	0.351780i	−0.0326925	−	0.0210984i
$279$		0			0
$280$	−16.6655	−	17.1671i	−0.995954	−	1.02593i
$281$	0.728710	+	2.24274i	0.0434712	+	0.133790i	0.970437	−	0.241356i	$-0.0775923\pi$
$281$	0.728710	+	2.24274i	0.0434712	+	0.133790i	−0.926965	+	0.375147i	$0.877592\pi$
$282$		0			0
$283$	5.68103	−	11.1496i	0.337702	−	0.662777i	−0.658237	−	0.752811i	$-0.728697\pi$
$283$	5.68103	−	11.1496i	0.337702	−	0.662777i	0.995939	+	0.0900336i	$0.0286974\pi$
$284$	4.90280	−	2.21648i	0.290928	−	0.131524i
$285$		0			0
$286$	10.4303	−	23.6079i	0.616757	−	1.39596i
$287$	−28.5413	+	4.52050i	−1.68474	+	0.266837i
$288$		0			0
$289$	−1.84032	−	2.53299i	−0.108254	−	0.148999i
$290$	−25.2563	+	13.8984i	−1.48310	+	0.816143i
$291$		0			0
$292$	5.75030	+	8.74503i	0.336511	+	0.511764i
$293$	−9.39519	+	9.39519i	−0.548873	+	0.548873i	−0.926115	−	0.377242i	$-0.876873\pi$
$293$	−9.39519	+	9.39519i	−0.548873	+	0.548873i	0.377242	+	0.926115i	$0.376873\pi$
$294$		0			0
$295$	−2.60782	+	14.2936i	−0.151833	+	0.832205i
$296$	−4.93253	+	15.6348i	−0.286697	+	0.908756i
$297$		0			0
$298$	−9.51693	+	3.68439i	−0.551301	+	0.213431i
$299$	33.7423			1.95137
$300$		0			0
$301$	25.2917			1.45779
$302$	7.91898	−	3.06576i	0.455686	−	0.176415i
$303$		0			0
$304$	−10.9770	+	2.46449i	−0.629574	+	0.141348i
$305$	−9.50926	−	5.12872i	−0.544498	−	0.293669i
$306$		0			0
$307$	−5.71466	+	5.71466i	−0.326153	+	0.326153i	−0.851122	−	0.524969i	$-0.824077\pi$
$307$	−5.71466	+	5.71466i	−0.326153	+	0.326153i	0.524969	+	0.851122i	$0.324077\pi$
$308$	−20.1460	+	13.2470i	−1.14793	+	0.754820i
$309$		0			0
$310$	9.62335	−	20.4727i	0.546569	−	1.16277i
$311$	1.83300	+	2.52291i	0.103940	+	0.143061i	0.857819	−	0.513953i	$-0.171819\pi$
$311$	1.83300	+	2.52291i	0.103940	+	0.143061i	−0.753879	+	0.657014i	$0.771819\pi$
$312$		0			0
$313$	−19.3284	+	3.06132i	−1.09251	+	0.173036i	−0.676586	−	0.736364i	$-0.736541\pi$
$313$	−19.3284	+	3.06132i	−1.09251	+	0.173036i	−0.415922	+	0.909400i	$0.636541\pi$
$314$	4.18268	−	9.46706i	0.236042	−	0.534257i
$315$		0			0
$316$	−4.32471	−	9.56618i	−0.243284	−	0.538139i
$317$	4.91849	−	9.65308i	0.276250	−	0.542171i	−0.710642	−	0.703554i	$-0.751595\pi$
$317$	4.91849	−	9.65308i	0.276250	−	0.542171i	0.986892	+	0.161383i	$0.0515954\pi$
$318$		0			0
$319$	8.97729	+	27.6293i	0.502632	+	1.54694i
$320$	8.22092	−	15.8876i	0.459563	−	0.888145i
$321$		0			0
$322$	−26.4855	−	17.0926i	−1.47598	−	0.952536i
$323$	−12.4639	−	1.97409i	−0.693510	−	0.109841i
$324$		0			0
$325$	−14.1781	+	24.8775i	−0.786458	+	1.37996i
$326$	−10.2355	+	5.94847i	−0.566892	+	0.329455i
$327$		0			0
$328$	−9.97303	−	19.1659i	−0.550669	−	1.05826i
$329$	16.3411	+	5.30955i	0.900914	+	0.292725i
$330$		0			0
$331$	−25.3803	+	8.24655i	−1.39503	+	0.453271i	−0.907579	−	0.419881i	$-0.862072\pi$
$331$	−25.3803	+	8.24655i	−1.39503	+	0.453271i	−0.487447	+	0.873153i	$0.662072\pi$
$332$	0.994137	+	3.62725i	0.0545604	+	0.199071i
$333$		0			0
$334$	0.362889	−	3.55006i	0.0198564	−	0.194251i
$335$	−0.520304	+	22.2477i	−0.0284273	+	1.21552i
$336$		0			0
$337$	0.384015	+	2.42457i	0.0209186	+	0.132075i	0.995938	−	0.0900470i	$-0.0287017\pi$
$337$	0.384015	+	2.42457i	0.0209186	+	0.132075i	−0.975019	+	0.222122i	$0.928702\pi$
$338$	17.6806	+	21.7068i	0.961699	+	1.18070i
$339$		0			0
$340$	15.1465	−	13.1607i	0.821432	−	0.713738i
$341$	−18.4430	−	13.3996i	−0.998745	−	0.725631i
$342$		0			0
$343$	0.832357	+	0.832357i	0.0449431	+	0.0449431i
$344$	5.99715	+	17.9336i	0.323345	+	0.966915i
$345$		0			0
$346$	15.1423	−	3.26378i	0.814055	−	0.175462i
$347$	−11.8684	−	23.2931i	−0.637129	−	1.25044i	−0.953383	−	0.301762i	$-0.902425\pi$
$347$	−11.8684	−	23.2931i	−0.637129	−	1.25044i	0.316254	−	0.948675i	$-0.397575\pi$
$348$		0			0
$349$			26.9516i			1.44269i	0.692578	+	0.721343i	$0.256475\pi$
$349$			26.9516i			1.44269i	−0.692578	+	0.721343i	$0.743525\pi$
$350$	23.7309	−	12.3451i	1.26847	−	0.659874i
$351$		0			0
$352$	−14.1701	−	11.1438i	−0.755267	−	0.593967i
$353$	−1.86058	−	3.65160i	−0.0990289	−	0.194355i	0.836177	−	0.548460i	$-0.184786\pi$
$353$	−1.86058	−	3.65160i	−0.0990289	−	0.194355i	−0.935206	+	0.354105i	$0.884786\pi$
$354$		0			0
$355$	0.801878	+	5.96195i	0.0425593	+	0.316427i
$356$	−21.7013	−	4.48348i	−1.15016	−	0.237624i
$357$		0			0
$358$	−8.92302	+	0.493167i	−0.471596	+	0.0260647i
$359$	0.119029	+	0.0864800i	0.00628213	+	0.00456424i	0.590922	−	0.806729i	$-0.298764\pi$
$359$	0.119029	+	0.0864800i	0.00628213	+	0.00456424i	−0.584640	+	0.811293i	$0.698764\pi$
$360$		0			0
$361$	8.97159	−	6.51824i	0.472189	−	0.343065i
$362$	24.0385	−	19.5798i	1.26343	−	1.02909i
$363$		0			0
$364$	−4.77494	−	43.0652i	−0.250275	−	2.25723i
$365$	−11.2104	+	3.35480i	−0.586777	+	0.175598i
$366$		0			0
$367$	4.01183	+	2.04413i	0.209416	+	0.106703i	0.555553	−	0.831481i	$-0.312507\pi$
$367$	4.01183	+	2.04413i	0.209416	+	0.106703i	−0.346137	+	0.938184i	$0.612507\pi$
$368$	5.83965	−	22.8330i	0.304413	−	1.19025i
$369$		0			0
$370$	−15.1643	−	10.2965i	−0.788354	−	0.535287i
$371$	15.4717	+	5.02706i	0.803251	+	0.260992i
$372$		0			0
$373$	−3.30218	+	20.8491i	−0.170980	+	1.07953i	0.741664	+	0.670772i	$0.234037\pi$
$373$	−3.30218	+	20.8491i	−0.170980	+	1.07953i	−0.912644	+	0.408755i	$0.865963\pi$
$374$	−10.1603	−	17.4828i	−0.525376	−	0.904012i
$375$		0			0
$376$	0.109952	+	12.8460i	0.00567036	+	0.662480i
$377$	−51.5639	−	8.16691i	−2.65567	−	0.420618i
$378$		0			0
$379$	4.41385	−	13.5844i	0.226724	−	0.697786i	−0.771388	−	0.636366i	$-0.780437\pi$
$379$	4.41385	−	13.5844i	0.226724	−	0.697786i	0.998112	−	0.0614203i	$-0.0195630\pi$
$380$	0.880210	−	12.5473i	0.0451538	−	0.643664i
$381$		0			0
$382$	−5.38350	−	1.42605i	−0.275444	−	0.0729633i
$383$	−1.28672	+	2.52534i	−0.0657485	+	0.129039i	−0.921542	−	0.388279i	$-0.873070\pi$
$383$	−1.28672	+	2.52534i	−0.0657485	+	0.129039i	0.855793	+	0.517318i	$0.173070\pi$
$384$		0			0
$385$	−7.72849	−	25.8254i	−0.393880	−	1.31619i
$386$	−1.02570	−	0.453171i	−0.0522070	−	0.0230658i
$387$		0			0
$388$	3.28264	−	8.69963i	0.166651	−	0.441657i
$389$	5.93355	+	8.16684i	0.300843	+	0.414075i	0.932498	−	0.361174i	$-0.117624\pi$
$389$	5.93355	+	8.16684i	0.300843	+	0.414075i	−0.631655	+	0.775250i	$0.717624\pi$
$390$		0			0
$391$	15.5386	−	21.3871i	0.785823	−	1.08159i
$392$	−9.23007	+	18.5049i	−0.466189	+	0.934638i
$393$		0			0
$394$	17.2176	+	15.4141i	0.867410	+	0.776550i
$395$	11.6327	−	1.56459i	0.585306	−	0.0787233i
$396$		0			0
$397$	22.5436	−	11.4865i	1.13143	−	0.576492i	0.214970	−	0.976621i	$-0.431035\pi$
$397$	22.5436	−	11.4865i	1.13143	−	0.576492i	0.916459	+	0.400129i	$0.131035\pi$
$398$	4.50890	+	11.6467i	0.226011	+	0.583794i
$399$		0			0
$400$	14.3806	+	13.8996i	0.719029	+	0.694980i
$401$	−17.2518			−0.861514			−0.430757	−	0.902468i	$-0.641753\pi$
$401$	−17.2518			−0.861514			−0.430757	+	0.902468i	$0.641753\pi$
$402$		0			0
$403$	36.5021	−	18.5987i	1.81830	−	0.926469i
$404$	7.98138	−	7.26936i	0.397089	−	0.361664i
$405$		0			0
$406$	36.3372	+	32.5309i	1.80338	+	1.61448i
$407$	−13.0613	+	13.0613i	−0.647425	+	0.647425i
$408$		0			0
$409$	−21.0539	+	28.9783i	−1.04105	+	1.43288i	−0.144732	+	0.989471i	$0.546232\pi$
$409$	−21.0539	+	28.9783i	−1.04105	+	1.43288i	−0.896318	+	0.443412i	$0.853768\pi$
$410$	23.7258	−	4.53612i	1.17173	−	0.224023i
$411$		0			0
$412$	−8.50336	+	22.5355i	−0.418931	+	1.11025i
$413$	24.2786	−	3.84536i	1.19467	−	0.189218i
$414$		0			0
$415$	−4.20380	−	0.0983139i	−0.206356	−	0.00482604i
$416$	29.4040	−	13.5973i	1.44165	−	0.666665i
$417$		0			0
$418$	−12.2530	−	3.24573i	−0.599312	−	0.158754i
$419$	0.811971	+	2.49899i	0.0396674	+	0.122084i	0.968929	−	0.247338i	$-0.0795558\pi$
$419$	0.811971	+	2.49899i	0.0396674	+	0.122084i	−0.929262	+	0.369422i	$0.879556\pi$
$420$		0			0
$421$	−10.6553	+	32.7937i	−0.519308	+	1.59827i	0.255996	+	0.966678i	$0.417596\pi$
$421$	−10.6553	+	32.7937i	−0.519308	+	1.59827i	−0.775304	+	0.631588i	$0.782404\pi$
$422$	−10.2244	+	15.8429i	−0.497714	+	0.771220i
$423$		0			0
$424$	0.104103	+	12.1625i	0.00505567	+	0.590664i
$425$	9.23915	+	20.4429i	0.448164	+	0.991626i
$426$		0			0
$427$	−2.85940	+	18.0536i	−0.138376	+	0.873673i
$428$	0.904574	−	19.3750i	0.0437242	−	0.936525i
$429$		0			0
$430$	−21.1311	+	0.672834i	−1.01903	+	0.0324469i
$431$	−17.2790	+	5.61428i	−0.832299	+	0.270430i	−0.694014	−	0.719962i	$-0.744159\pi$
$431$	−17.2790	+	5.61428i	−0.832299	+	0.270430i	−0.138286	+	0.990392i	$0.544159\pi$
$432$		0			0
$433$	29.5954	+	15.0796i	1.42226	+	0.724679i	0.984659	−	0.174490i	$-0.0558276\pi$
$433$	29.5954	+	15.0796i	1.42226	+	0.724679i	0.437603	+	0.899168i	$0.355828\pi$
$434$	−38.0732	−	3.89186i	−1.82757	−	0.186815i
$435$		0			0
$436$	−1.15721	−	10.4369i	−0.0554205	−	0.499838i
$437$	−2.59237	−	16.3676i	−0.124010	−	0.782967i
$438$		0			0
$439$	−20.3567	+	14.7900i	−0.971575	+	0.705890i	−0.955810	−	0.293986i	$-0.905018\pi$
$439$	−20.3567	+	14.7900i	−0.971575	+	0.705890i	−0.0157647	+	0.999876i	$0.505018\pi$
$440$	16.4794	−	11.6037i	0.785627	−	0.553186i
$441$		0			0
$442$	36.2825	−	2.00530i	1.72578	−	0.0953825i
$443$	26.7805	+	26.7805i	1.27238	+	1.27238i	0.944837	+	0.327541i	$0.106220\pi$
$443$	26.7805	+	26.7805i	1.27238	+	1.27238i	0.327541	+	0.944837i	$0.393780\pi$
$444$		0			0
$445$	11.7607	−	21.8058i	0.557512	−	1.03369i
$446$	−2.24701	−	10.4250i	−0.106399	−	0.493639i
$447$		0			0
$448$	−29.9681	−	4.22199i	−1.41586	−	0.199470i
$449$			13.0315i			0.614996i	0.951549	+	0.307498i	$0.0994918\pi$
$449$			13.0315i			0.614996i	−0.951549	+	0.307498i	$0.900508\pi$
$450$		0			0
$451$		−	24.3426i		−	1.14625i
$452$	−5.19143	+	6.48621i	−0.244184	+	0.305086i
$453$		0			0
$454$	13.7538	−	2.96451i	0.645500	−	0.139131i
$455$	47.6568	+	8.69484i	2.23418	+	0.407621i
$456$		0			0
$457$	2.56587	+	2.56587i	0.120026	+	0.120026i	0.764569	−	0.644542i	$-0.222952\pi$
$457$	2.56587	+	2.56587i	0.120026	+	0.120026i	−0.644542	+	0.764569i	$0.722952\pi$
$458$	−1.20881	−	21.8714i	−0.0564840	−	1.02198i
$459$		0			0
$460$	22.5831	+	13.5762i	1.05294	+	0.632993i
$461$	24.2919	−	17.6491i	1.13138	−	0.821999i	0.145489	−	0.989360i	$-0.453524\pi$
$461$	24.2919	−	17.6491i	1.13138	−	0.821999i	0.985896	+	0.167361i	$0.0535244\pi$
$462$		0			0
$463$	−1.50581	−	9.50734i	−0.0699811	−	0.441844i	−0.997654	−	0.0684508i	$-0.978194\pi$
$463$	−1.50581	−	9.50734i	−0.0699811	−	0.441844i	0.927673	−	0.373393i	$-0.121806\pi$
$464$	−14.4504	+	33.4793i	−0.670844	+	1.55424i
$465$		0			0
$466$	1.00612	−	9.84260i	0.0466074	−	0.455950i
$467$	21.9563	+	11.1873i	1.01602	+	0.517686i	0.880980	−	0.473154i	$-0.156885\pi$
$467$	21.9563	+	11.1873i	1.01602	+	0.517686i	0.135037	+	0.990841i	$0.456885\pi$
$468$		0			0
$469$	35.8065	−	11.6342i	1.65339	−	0.537219i
$470$	−13.7941	−	4.00137i	−0.636275	−	0.184569i
$471$		0			0
$472$	8.48355	+	16.3034i	0.390487	+	0.750425i
$473$	−3.33291	+	21.0432i	−0.153247	+	0.967566i
$474$		0			0
$475$	13.1568	+	4.96613i	0.603673	+	0.227862i
$476$	−29.4952	−	16.8054i	−1.35191	−	0.770274i
$477$		0			0
$478$	6.61334	+	4.26797i	0.302487	+	0.195213i
$479$	10.8575	−	33.4159i	0.496091	−	1.52681i	−0.319159	−	0.947701i	$-0.603400\pi$
$479$	10.8575	−	33.4159i	0.496091	−	1.52681i	0.815250	−	0.579110i	$-0.196600\pi$
$480$		0			0
$481$	−10.2576	−	31.5697i	−0.467707	−	1.43946i
$482$	−1.91619	+	7.23381i	−0.0872801	+	0.329491i
$483$		0			0
$484$	0.695795	+	1.53909i	0.0316271	+	0.0699585i
$485$	8.26527	+	6.30551i	0.375307	+	0.286318i
$486$		0			0
$487$	30.0414	−	4.75809i	1.36131	−	0.215610i	0.567296	−	0.823514i	$-0.307990\pi$
$487$	30.0414	−	4.75809i	1.36131	−	0.215610i	0.794010	+	0.607904i	$0.207990\pi$
$488$	−13.4792	+	2.25333i	−0.610177	+	0.102003i
$489$		0			0
$490$	−16.8603	−	15.8197i	−0.761669	−	0.714661i
$491$	4.57417	−	6.29580i	0.206429	−	0.284125i	−0.693232	−	0.720715i	$-0.743814\pi$
$491$	4.57417	−	6.29580i	0.206429	−	0.284125i	0.899661	+	0.436589i	$0.143814\pi$
$492$		0			0
$493$	−28.9221	+	28.9221i	−1.30259	+	1.30259i
$494$	15.1936	−	16.9713i	0.683592	−	0.763576i
$495$		0			0
$496$	−6.26828	−	27.9194i	−0.281454	−	1.25362i
$497$	9.06806	−	4.62041i	0.406758	−	0.207254i
$498$		0			0
$499$	21.1079			0.944921			0.472461	−	0.881352i	$-0.343366\pi$
$499$	21.1079			0.944921			0.472461	+	0.881352i	$0.343366\pi$
$500$	−19.4986	+	10.9456i	−0.872003	+	0.489500i
$501$		0			0
$502$	−20.2584	+	7.84287i	−0.904178	+	0.350044i
$503$	29.0339	−	14.7935i	1.29456	−	0.659610i	0.335291	−	0.942115i	$-0.391165\pi$
$503$	29.0339	−	14.7935i	1.29456	−	0.659610i	0.959266	+	0.282505i	$0.0911653\pi$
$504$		0			0
$505$	5.22668	+	10.8795i	0.232584	+	0.484133i
$506$	17.7116	−	19.7840i	0.787377	−	0.879504i
$507$		0			0
$508$	12.7284	+	19.3573i	0.564731	+	0.858840i
$509$	−9.07044	+	12.4844i	−0.402040	+	0.553361i	−0.961255	−	0.275662i	$-0.911103\pi$
$509$	−9.07044	+	12.4844i	−0.402040	+	0.553361i	0.559214	+	0.829023i	$0.311103\pi$
$510$		0			0
$511$	11.6363	+	16.0160i	0.514760	+	0.708507i
$512$	−4.11233	−	22.2506i	−0.181741	−	0.983346i
$513$		0			0
$514$	−9.84447	+	22.2819i	−0.434221	+	0.982813i
$515$	−21.4104	−	16.3338i	−0.943453	−	0.719753i
$516$		0			0
$517$	−6.57105	+	12.8964i	−0.288994	+	0.567183i
$518$	−7.94053	+	29.9763i	−0.348887	+	1.31708i
$519$		0			0
$520$	5.13508	+	35.8537i	0.225188	+	1.57229i
$521$	11.0271	−	33.9378i	0.483104	−	1.48684i	−0.351603	−	0.936149i	$-0.614363\pi$
$521$	11.0271	−	33.9378i	0.483104	−	1.48684i	0.834708	−	0.550693i	$-0.185637\pi$
$522$		0			0
$523$	22.2177	+	3.51894i	0.971512	+	0.153872i	0.621964	−	0.783046i	$-0.286335\pi$
$523$	22.2177	+	3.51894i	0.971512	+	0.153872i	0.349548	+	0.936918i	$0.386335\pi$
$524$	10.8666	−	19.0720i	0.474711	−	0.833166i
$525$		0			0
$526$	31.0619	−	18.0520i	1.35436	−	0.787103i
$527$	5.02098	−	31.7012i	0.218717	−	1.38093i
$528$		0			0
$529$	11.1422	+	3.62031i	0.484442	+	0.157405i
$530$	−13.0602	−	3.78848i	−0.567300	−	0.164561i
$531$		0			0
$532$	−20.5230	+	5.62484i	−0.889787	+	0.243868i
$533$	38.9771	+	19.8598i	1.68829	+	0.860226i
$534$		0			0
$535$	20.4618	+	7.18156i	0.884641	+	0.310486i
$536$	16.7399	+	22.6306i	0.723052	+	0.977492i
$537$		0			0
$538$	17.5925	+	21.5987i	0.758468	+	0.931185i
$539$	−18.8493	+	13.6948i	−0.811895	+	0.589876i
$540$		0			0
$541$	−26.2427	−	19.0664i	−1.12826	−	0.819730i	−0.142820	−	0.989749i	$-0.545617\pi$
$541$	−26.2427	−	19.0664i	−1.12826	−	0.819730i	−0.985441	+	0.170019i	$0.945617\pi$
$542$	1.97939	+	35.8137i	0.0850220	+	1.53833i
$543$		0			0
$544$	4.92231	−	24.8990i	0.211042	−	1.06754i
$545$	11.5497	+	2.10721i	0.494735	+	0.0902629i
$546$		0			0
$547$	8.08784	+	15.8733i	0.345811	+	0.678692i	0.996760	−	0.0804289i	$-0.0256290\pi$
$547$	8.08784	+	15.8733i	0.345811	+	0.678692i	−0.650949	+	0.759121i	$0.725629\pi$
$548$	−11.2256	−	8.98472i	−0.479533	−	0.383808i
$549$		0			0
$550$	7.14413	+	21.3714i	0.304627	+	0.911278i
$551$			25.6398i			1.09229i
$552$		0			0
$553$	−9.01518	−	17.6933i	−0.383364	−	0.752395i
$554$	8.68040	+	40.2727i	0.368795	+	1.71102i
$555$		0			0
$556$	0.185629	−	0.898495i	0.00787242	−	0.0381047i
$557$	−1.21960	−	1.21960i	−0.0516762	−	0.0516762i	0.680796	−	0.732473i	$-0.261634\pi$
$557$	−1.21960	−	1.21960i	−0.0516762	−	0.0516762i	−0.732473	+	0.680796i	$0.761634\pi$
$558$		0			0
$559$	−30.9750	−	22.5047i	−1.31010	−	0.951846i
$560$	14.1315	−	30.7440i	0.597164	−	1.29917i
$561$		0			0
$562$	−2.58573	+	2.10613i	−0.109072	+	0.0888416i
$563$	3.05112	+	19.2640i	0.128589	+	0.811882i	0.964706	+	0.263330i	$0.0848207\pi$
$563$	3.05112	+	19.2640i	0.128589	+	0.811882i	−0.836116	+	0.548552i	$0.815179\pi$
$564$		0			0
$565$	−5.28249	−	7.64020i	−0.222236	−	0.321426i
$566$	17.6051	+	1.79960i	0.739996	+	0.0756428i
$567$		0			0
$568$	5.42640	+	5.33430i	0.227687	+	0.223822i
$569$	−7.24903	+	2.35535i	−0.303895	+	0.0987415i	−0.456995	−	0.889469i	$-0.651074\pi$
$569$	−7.24903	+	2.35535i	−0.303895	+	0.0987415i	0.153100	+	0.988211i	$0.451074\pi$
$570$		0			0
$571$	2.36607	+	0.768784i	0.0990171	+	0.0321726i	0.358107	−	0.933681i	$-0.383422\pi$
$571$	2.36607	+	0.768784i	0.0990171	+	0.0321726i	−0.259089	+	0.965853i	$0.583422\pi$
$572$	36.4603	+	1.70225i	1.52448	+	0.0711745i
$573$		0			0
$574$	−20.5342	−	35.3331i	−0.857081	−	1.47478i
$575$	−21.7824	+	19.8347i	−0.908388	+	0.827165i
$576$		0			0
$577$	−36.6621	−	5.80671i	−1.52626	−	0.241736i	−0.663821	−	0.747891i	$-0.731066\pi$
$577$	−36.6621	−	5.80671i	−1.52626	−	0.241736i	−0.862443	+	0.506155i	$0.831066\pi$
$578$	2.40096	−	3.72035i	0.0998669	−	0.154746i
$579$		0			0
$580$	−31.2249	−	26.2127i	−1.29654	−	1.08842i
$581$	2.19834	+	6.76580i	0.0912026	+	0.280693i
$582$		0			0
$583$	−6.22145	+	12.2103i	−0.257666	+	0.505698i
$584$	−8.59727	+	12.0487i	−0.355757	+	0.498577i
$585$		0			0
$586$	−17.1876	−	7.59373i	−0.710013	−	0.313694i
$587$	11.9115	−	1.88659i	0.491638	−	0.0778678i	0.0943071	−	0.995543i	$-0.469936\pi$
$587$	11.9115	−	1.88659i	0.491638	−	0.0778678i	0.397331	+	0.917675i	$0.369936\pi$
$588$		0			0
$589$	−11.8262	−	16.2774i	−0.487290	−	0.670697i
$590$	−20.1823	+	3.85865i	−0.830892	+	0.158858i
$591$		0			0
$592$	−23.1381	+	1.47757i	−0.950971	+	0.0607277i
$593$	−22.6034	+	22.6034i	−0.928211	+	0.928211i	−0.997590	−	0.0693792i	$-0.977898\pi$
$593$	−22.6034	+	22.6034i	−0.928211	+	0.928211i	0.0693792	+	0.997590i	$0.477898\pi$
$594$		0			0
$595$	27.4575	−	26.2025i	1.12565	−	1.07420i
$596$	−9.71819	−	10.6701i	−0.398072	−	0.437063i
$597$		0			0
$598$	17.2279	+	44.5004i	0.704502	+	1.81976i
$599$	33.3121			1.36109			0.680547	−	0.732705i	$-0.261742\pi$
$599$	33.3121			1.36109			0.680547	+	0.732705i	$0.261742\pi$
$600$		0			0
$601$	−26.4204			−1.07771			−0.538856	−	0.842398i	$-0.681143\pi$
$601$	−26.4204			−1.07771			−0.538856	+	0.842398i	$0.681143\pi$
$602$	12.9133	+	33.3555i	0.526307	+	1.35947i
$603$		0			0
$604$	8.08645	+	8.87850i	0.329033	+	0.361261i
$605$	−1.87157	+	0.251725i	−0.0760902	+	0.0102341i
$606$		0			0
$607$	20.2216	−	20.2216i	0.820768	−	0.820768i	−0.165450	−	0.986218i	$-0.552908\pi$
$607$	20.2216	−	20.2216i	0.820768	−	0.820768i	0.986218	+	0.165450i	$0.0529076\pi$
$608$	−8.85480	−	13.2185i	−0.359110	−	0.536081i
$609$		0			0
$610$	1.90873	−	15.1597i	0.0772823	−	0.613798i
$611$	−15.2886	−	21.0430i	−0.618512	−	0.851309i
$612$		0			0
$613$	40.0338	−	6.34074i	1.61695	−	0.256100i	0.718615	−	0.695408i	$-0.244776\pi$
$613$	40.0338	−	6.34074i	1.61695	−	0.256100i	0.898336	+	0.439308i	$0.144776\pi$
$614$	−10.4544	−	4.61891i	−0.421906	−	0.186404i
$615$		0			0
$616$	−27.7566	−	19.8056i	−1.11835	−	0.797991i
$617$	5.90249	−	11.5843i	0.237625	−	0.466366i	−0.741140	−	0.671351i	$-0.765714\pi$
$617$	5.90249	−	11.5843i	0.237625	−	0.466366i	0.978765	+	0.204985i	$0.0657144\pi$
$618$		0			0
$619$	−5.82642	−	17.9319i	−0.234183	−	0.720743i	−0.997229	−	0.0743975i	$-0.976297\pi$
$619$	−5.82642	−	17.9319i	−0.234183	−	0.720743i	0.763045	−	0.646345i	$-0.223703\pi$
$620$	31.9134	+	2.23876i	1.28167	+	0.0899109i
$621$		0			0
$622$	−2.39141	+	3.70555i	−0.0958868	+	0.148579i
$623$	−41.3989	−	6.55694i	−1.65861	−	0.262698i
$624$		0			0
$625$	−5.47108	−	24.3940i	−0.218843	−	0.975760i
$626$	−13.9060	−	23.9279i	−0.555794	−	0.956352i
$627$		0			0
$628$	14.6210	+	0.682622i	0.583442	+	0.0272396i
$629$	−24.7338	−	8.03649i	−0.986200	−	0.320436i
$630$		0			0
$631$	−43.8376	+	14.2437i	−1.74515	+	0.567032i	−0.995496	−	0.0948030i	$-0.969778\pi$
$631$	−43.8376	+	14.2437i	−1.74515	+	0.567032i	−0.749649	+	0.661835i	$0.769778\pi$
$632$	10.4081	−	10.5878i	0.414011	−	0.421160i
$633$		0			0
$634$	15.2420	+	1.55805i	0.605338	+	0.0618780i
$635$	−24.8143	+	7.42591i	−0.984727	+	0.294688i
$636$		0			0
$637$	−6.54985	−	41.3541i	−0.259515	−	1.63851i
$638$	−31.8548	+	25.9463i	−1.26114	+	1.02722i
$639$		0			0
$640$	25.1505	+	2.73020i	0.994160	+	0.107921i
$641$	−0.312769	−	0.227240i	−0.0123537	−	0.00897545i	0.581591	−	0.813481i	$-0.302430\pi$
$641$	−0.312769	−	0.227240i	−0.0123537	−	0.00897545i	−0.593945	+	0.804506i	$0.702430\pi$
$642$		0			0
$643$	−13.3778	−	13.3778i	−0.527569	−	0.527569i	0.392278	−	0.919847i	$-0.371687\pi$
$643$	−13.3778	−	13.3778i	−0.527569	−	0.527569i	−0.919847	+	0.392278i	$0.871687\pi$
$644$	9.01952	−	43.6569i	0.355419	−	1.72032i
$645$		0			0
$646$	−3.76025	−	17.4457i	−0.147945	−	0.686392i
$647$	−6.16863	−	12.1066i	−0.242514	−	0.475960i	0.737380	−	0.675478i	$-0.236063\pi$
$647$	−6.16863	−	12.1066i	−0.242514	−	0.475960i	−0.979894	+	0.199518i	$0.936063\pi$
$648$		0			0
$649$			20.7070i			0.812820i
$650$	−40.0482	−	5.99667i	−1.57082	−	0.235209i
$651$		0			0
$652$	−13.0710	−	10.4618i	−0.511900	−	0.409714i
$653$	17.6758	+	34.6908i	0.691709	+	1.35755i	0.923049	+	0.384682i	$0.125689\pi$
$653$	17.6758	+	34.6908i	0.691709	+	1.35755i	−0.231341	+	0.972873i	$0.574311\pi$
$654$		0			0
$655$	16.9429	+	17.7544i	0.662016	+	0.693722i
$656$	20.1846	−	22.9383i	0.788075	−	0.895591i
$657$		0			0
$658$	1.34094	+	24.2621i	0.0522754	+	0.945834i
$659$	19.0465	+	13.8381i	0.741948	+	0.539057i	0.893320	−	0.449420i	$-0.148369\pi$
$659$	19.0465	+	13.8381i	0.741948	+	0.539057i	−0.151373	+	0.988477i	$0.548369\pi$
$660$		0			0
$661$	−15.6894	+	11.3990i	−0.610249	+	0.443372i	−0.849502	−	0.527586i	$-0.823097\pi$
$661$	−15.6894	+	11.3990i	−0.610249	+	0.443372i	0.239253	+	0.970957i	$0.423097\pi$
$662$	−23.8343	−	29.2618i	−0.926346	−	1.13729i
$663$		0			0
$664$	−4.27615	+	3.16308i	−0.165947	+	0.122751i
$665$	0.556262	−	23.7852i	0.0215709	−	0.922349i
$666$		0			0
$667$	−47.8581	−	24.3849i	−1.85307	−	0.944189i
$668$	4.86721	−	1.33398i	0.188318	−	0.0516131i
$669$		0			0
$670$	−29.6065	+	10.6729i	−1.14380	+	0.412329i
$671$	−14.6441	−	4.75815i	−0.565328	−	0.183686i
$672$		0			0
$673$	4.78582	−	30.2165i	0.184480	−	1.16476i	−0.705483	−	0.708726i	$-0.749270\pi$
$673$	4.78582	−	30.2165i	0.184480	−	1.16476i	0.889963	−	0.456033i	$-0.150730\pi$
$674$	−3.00153	+	1.74437i	−0.115615	+	0.0671907i
$675$		0			0
$676$	−19.6004	+	34.4007i	−0.753860	+	1.32310i
$677$	−37.1215	−	5.87947i	−1.42670	−	0.225966i	−0.605151	−	0.796111i	$-0.706887\pi$
$677$	−37.1215	−	5.87947i	−1.42670	−	0.225966i	−0.821545	+	0.570144i	$0.806887\pi$
$678$		0			0
$679$	5.43495	−	16.7271i	0.208574	−	0.641926i
$680$	25.0901	+	13.2561i	0.962161	+	0.508349i
$681$		0			0
$682$	8.25533	−	31.1647i	0.316113	−	1.19336i
$683$	2.82681	−	5.54792i	0.108165	−	0.212285i	−0.830579	−	0.556900i	$-0.811991\pi$
$683$	2.82681	−	5.54792i	0.108165	−	0.212285i	0.938744	+	0.344615i	$0.111991\pi$
$684$		0			0
$685$	13.2228	−	9.14232i	0.505216	−	0.349310i
$686$	−0.672759	+	1.52272i	−0.0256861	+	0.0581377i
$687$		0			0
$688$	−20.5894	+	17.0657i	−0.784963	+	0.650622i
$689$	−14.4752	−	19.9235i	−0.551463	−	0.759024i
$690$		0			0
$691$	−27.7225	+	38.1568i	−1.05462	+	1.45155i	−0.169877	+	0.985465i	$0.554337\pi$
$691$	−27.7225	+	38.1568i	−1.05462	+	1.45155i	−0.884738	+	0.466088i	$0.845663\pi$
$692$	12.0356	+	18.3037i	0.457526	+	0.695804i
$693$		0			0
$694$	24.6599	−	27.5452i	0.936077	−	1.04560i
$695$	0.902823	+	0.486928i	0.0342460	+	0.0184702i
$696$		0			0
$697$	30.5372	−	15.5595i	1.15668	−	0.589358i
$698$	−35.5446	+	13.7608i	−1.34538	+	0.520853i
$699$		0			0
$700$	28.3975	+	24.9940i	1.07332	+	0.944683i
$701$	32.9433			1.24425			0.622126	−	0.782917i	$-0.286269\pi$
$701$	32.9433			1.24425			0.622126	+	0.782917i	$0.286269\pi$
$702$		0			0
$703$	−14.5256	+	7.40118i	−0.547844	+	0.279141i
$704$	7.46193	−	24.3776i	0.281232	−	0.918767i
$705$		0			0
$706$	3.86588	−	4.31821i	0.145494	−	0.162518i
$707$	14.4391	−	14.4391i	0.543040	−	0.543040i
$708$		0			0
$709$	3.33723	−	4.59330i	0.125332	−	0.172505i	−0.741740	−	0.670688i	$-0.765999\pi$
$709$	3.33723	−	4.59330i	0.125332	−	0.172505i	0.867072	+	0.498183i	$0.165999\pi$
$710$	−7.45338	+	4.10155i	−0.279720	+	0.153929i
$711$		0			0
$712$	−5.16714	−	30.9094i	−0.193647	−	1.15838i
$713$	41.6300	−	6.59354i	1.55905	−	0.246930i
$714$		0			0
$715$	−13.5144	+	38.5055i	−0.505410	+	1.44002i
$716$	−5.20626	−	11.5162i	−0.194567	−	0.430379i
$717$		0			0
$718$	−0.0532791	+	0.201134i	−0.00198836	+	0.00750626i
$719$	10.8641	+	33.4362i	0.405162	+	1.24696i	0.920760	+	0.390130i	$0.127570\pi$
$719$	10.8641	+	33.4362i	0.405162	+	1.24696i	−0.515597	+	0.856831i	$0.672430\pi$
$720$		0			0
$721$	−14.0787	+	43.3298i	−0.524318	+	1.61369i
$722$	13.1771	+	8.50397i	0.490401	+	0.316485i
$723$		0			0
$724$	38.0958	+	21.7057i	1.41582	+	0.806687i
$725$	38.0879	−	25.0386i	1.41455	−	0.929911i
$726$		0			0
$727$	−5.97044	+	37.6959i	−0.221432	+	1.39806i	0.587054	+	0.809548i	$0.300288\pi$
$727$	−5.97044	+	37.6959i	−0.221432	+	1.39806i	−0.808486	+	0.588516i	$0.799712\pi$
$728$	54.3578	−	28.2853i	2.01463	−	1.04832i
$729$		0			0
$730$	−10.1481	−	13.0717i	−0.375599	−	0.483805i
$731$	−28.5286	+	9.26949i	−1.05517	+	0.342844i
$732$		0			0
$733$	−33.2393	−	16.9363i	−1.22772	−	0.625555i	−0.284805	−	0.958586i	$-0.591929\pi$
$733$	−33.2393	−	16.9363i	−1.22772	−	0.625555i	−0.942916	+	0.333031i	$0.891929\pi$
$734$	−0.647527	+	6.33460i	−0.0239006	+	0.233815i
$735$		0			0
$736$	33.0945	−	3.95643i	1.21988	−	0.145836i
$737$	4.96136	+	31.3248i	0.182754	+	1.15386i
$738$		0			0
$739$	18.6572	−	13.5552i	0.686316	−	0.498638i	−0.189131	−	0.981952i	$-0.560567\pi$
$739$	18.6572	−	13.5552i	0.686316	−	0.498638i	0.875447	+	0.483314i	$0.160567\pi$
$740$	5.83680	−	25.2562i	0.214565	−	0.928437i
$741$		0			0
$742$	1.26960	+	22.9713i	0.0466085	+	0.843301i
$743$	−27.6530	−	27.6530i	−1.01449	−	1.01449i	−0.999893	−	0.0145985i	$-0.995353\pi$
$743$	−27.6530	−	27.6530i	−1.01449	−	1.01449i	−0.0145985	−	0.999893i	$-0.504647\pi$
$744$		0			0
$745$	14.5445	−	6.98739i	0.532870	−	0.255998i
$746$	−29.1825	+	6.29000i	−1.06845	+	0.230293i
$747$		0			0
$748$	17.8692	−	22.3259i	0.653364	−	0.816317i
$749$		−	36.6878i		−	1.34054i
$750$		0			0
$751$		−	46.4576i		−	1.69526i	−0.530586	−	0.847631i	$-0.678028\pi$
$751$		−	46.4576i		−	1.69526i	0.530586	−	0.847631i	$-0.321972\pi$
$752$	−16.8855	+	6.70382i	−0.615751	+	0.244463i
$753$		0			0
$754$	−15.5564	−	72.1738i	−0.566530	−	2.62842i
$755$	−12.1024	+	5.81417i	−0.440452	+	0.211599i
$756$		0			0
$757$	−9.68302	−	9.68302i	−0.351935	−	0.351935i	0.508894	−	0.860829i	$-0.330055\pi$
$757$	−9.68302	−	9.68302i	−0.351935	−	0.351935i	−0.860829	+	0.508894i	$0.830055\pi$
$758$	20.1692	−	1.11473i	0.732578	−	0.0404889i
$759$		0			0
$760$	16.9972	−	5.24548i	0.616554	−	0.190274i
$761$	−10.6853	+	7.76333i	−0.387342	+	0.281420i	−0.764365	−	0.644783i	$-0.776948\pi$
$761$	−10.6853	+	7.76333i	−0.387342	+	0.281420i	0.377023	+	0.926204i	$0.376948\pi$
$762$		0			0
$763$	−3.10718	−	19.6179i	−0.112487	−	0.710217i
$764$	−0.867947	−	7.82803i	−0.0314012	−	0.283208i
$765$		0			0
$766$	−3.98746	−	0.407600i	−0.144073	−	0.0147272i
$767$	−33.1559	−	16.8937i	−1.19719	−	0.609998i
$768$		0			0
$769$	−22.2437	+	7.22741i	−0.802128	+	0.260627i	−0.681260	−	0.732041i	$-0.738568\pi$
$769$	−22.2437	+	7.22741i	−0.802128	+	0.260627i	−0.120868	+	0.992669i	$0.538568\pi$
$770$	30.1134	−	23.3784i	1.08521	−	0.842497i
$771$		0			0
$772$	0.0739584	−	1.58411i	0.00266182	−	0.0570133i
$773$	3.05840	−	19.3100i	0.110003	−	0.694533i	−0.869625	−	0.493713i	$-0.835639\pi$
$773$	3.05840	−	19.3100i	0.110003	−	0.694533i	0.979628	−	0.200820i	$-0.0643606\pi$
$774$		0			0
$775$	−12.6311	+	33.4635i	−0.453722	+	1.20204i
$776$	13.1494	−	0.112549i	0.472035	−	0.00404029i
$777$		0			0
$778$	−7.74116	+	11.9951i	−0.277534	+	0.430046i
$779$	6.63897	−	20.4327i	0.237866	−	0.732076i
$780$		0			0
$781$	2.64928	+	8.15366i	0.0947989	+	0.291761i
$782$	36.1396	+	9.57314i	1.29235	+	0.342335i
$783$		0			0
$784$	−29.1174	−	2.72479i	−1.03991	−	0.0973140i
$785$	−5.41944	+	15.4412i	−0.193428	+	0.551119i
$786$		0			0
$787$	2.84772	−	0.451034i	0.101510	−	0.0160776i	−0.105473	−	0.994422i	$-0.533636\pi$
$787$	2.84772	−	0.451034i	0.101510	−	0.0160776i	0.206983	+	0.978345i	$0.433636\pi$
$788$	−11.5377	+	30.5771i	−0.411014	+	1.08926i
$789$		0			0
$790$	8.00280	+	14.5428i	0.284727	+	0.517409i
$791$	−9.23676	+	12.7133i	−0.328421	+	0.452033i
$792$		0			0
$793$	19.5661	−	19.5661i	0.694811	−	0.694811i
$794$	26.6589	+	23.8664i	0.946090	+	0.846988i
$795$		0			0
$796$	−13.0578	+	11.8930i	−0.462823	+	0.421535i
$797$	−28.2728	+	14.4057i	−1.00147	+	0.510276i	−0.876252	−	0.481853i	$-0.839964\pi$
$797$	−28.2728	+	14.4057i	−1.00147	+	0.510276i	−0.125221	+	0.992129i	$0.539964\pi$
$798$		0			0
$799$	−20.3784			−0.720935
$800$	−10.9889	+	26.0623i	−0.388515	+	0.921442i
$801$		0			0
$802$	−8.80832	−	22.7522i	−0.311033	−	0.803409i
$803$	−14.8590	+	7.57105i	−0.524364	+	0.267177i
$804$		0			0
$805$	43.8673	+	23.6593i	1.54612	+	0.833882i
$806$	43.1656	+	38.6440i	1.52044	+	1.36118i
$807$		0			0
$808$	13.6621	+	6.81455i	0.480632	+	0.239735i
$809$	−20.9392	+	28.8204i	−0.736184	+	1.01327i	0.262645	+	0.964892i	$0.415405\pi$
$809$	−20.9392	+	28.8204i	−0.736184	+	1.01327i	−0.998829	+	0.0483777i	$0.984595\pi$
$810$		0			0
$811$	−9.94055	−	13.6820i	−0.349060	−	0.480440i	0.598000	−	0.801496i	$-0.295962\pi$
$811$	−9.94055	−	13.6820i	−0.349060	−	0.480440i	−0.947060	+	0.321056i	$0.895962\pi$
$812$	−24.3500	+	64.5320i	−0.854516	+	2.26463i
$813$		0			0
$814$	−23.8944	−	10.5569i	−0.837499	−	0.370019i
$815$	15.3965	−	10.6453i	0.539316	−	0.372887i
$816$		0			0
$817$	−8.53671	+	16.7542i	−0.298662	+	0.586156i
$818$	−48.9670	−	12.9710i	−1.71209	−	0.453522i
$819$		0			0
$820$	18.0961	+	28.9743i	0.631945	+	1.01183i
$821$	−11.9857	+	36.8881i	−0.418303	+	1.28740i	0.490961	+	0.871182i	$0.336646\pi$
$821$	−11.9857	+	36.8881i	−0.418303	+	1.28740i	−0.909263	+	0.416221i	$0.863354\pi$
$822$		0			0
$823$	−43.9738	−	6.96477i	−1.53283	−	0.242777i	−0.667741	−	0.744393i	$-0.732739\pi$
$823$	−43.9738	−	6.96477i	−1.53283	−	0.242777i	−0.865090	+	0.501617i	$0.832739\pi$
$824$	−34.0621	+	0.291548i	−1.18661	+	0.0101566i
$825$		0			0
$826$	17.4674	+	30.0561i	0.607768	+	1.04578i
$827$	−3.77162	+	23.8130i	−0.131152	+	0.828061i	0.831144	+	0.556057i	$0.187686\pi$
$827$	−3.77162	+	23.8130i	−0.131152	+	0.828061i	−0.962296	+	0.272004i	$0.912314\pi$
$828$		0			0
$829$	16.9774	+	5.51628i	0.589648	+	0.191588i	0.588618	−	0.808411i	$-0.299672\pi$
$829$	16.9774	+	5.51628i	0.589648	+	0.191588i	0.00103007	+	0.999999i	$0.499672\pi$
$830$	−2.01669	−	5.59430i	−0.0700003	−	0.194181i
$831$		0			0
$832$	32.9455	+	31.8364i	1.14218	+	1.10373i
$833$	−29.2280	−	14.8924i	−1.01269	−	0.515992i
$834$		0			0
$835$	−0.131922	+	5.64085i	−0.00456535	+	0.195209i
$836$	−1.97547	−	17.8168i	−0.0683230	−	0.616206i
$837$		0			0
$838$	−2.88117	+	2.34677i	−0.0995285	+	0.0810679i
$839$	29.6949	−	21.5746i	1.02518	−	0.744838i	0.0578434	−	0.998326i	$-0.481578\pi$
$839$	29.6949	−	21.5746i	1.02518	−	0.744838i	0.967339	+	0.253487i	$0.0815776\pi$
$840$		0			0
$841$	43.7717	+	31.8020i	1.50937	+	1.09662i
$842$	−48.6896	+	2.69103i	−1.67796	+	0.0927390i
$843$		0			0
$844$	−26.1144	−	5.39523i	−0.898894	−	0.185711i
$845$	−30.5604	−	32.0240i	−1.05131	−	1.10166i
$846$		0			0
$847$	1.45044	+	2.84664i	0.0498376	+	0.0978118i
$848$	−15.9872	+	6.34716i	−0.549001	+	0.217962i
$849$		0			0
$850$	−22.2435	+	22.6225i	−0.762944	+	0.775944i
$851$		−	34.1518i		−	1.17071i
$852$		0			0
$853$	17.8328	+	34.9989i	0.610584	+	1.19834i	0.964753	+	0.263157i	$0.0847637\pi$
$853$	17.8328	+	34.9989i	0.610584	+	1.19834i	−0.354169	+	0.935181i	$0.615236\pi$
$854$	−25.2695	+	5.44660i	−0.864706	+	0.186379i
$855$		0			0
$856$	26.0142	−	8.69938i	0.889146	−	0.297339i
$857$	10.9795	+	10.9795i	0.375051	+	0.375051i	0.869313	−	0.494262i	$-0.164562\pi$
$857$	10.9795	+	10.9795i	0.375051	+	0.375051i	−0.494262	+	0.869313i	$0.664562\pi$
$858$		0			0
$859$	−3.93540	−	2.85923i	−0.134274	−	0.0975558i	0.518621	−	0.855004i	$-0.326446\pi$
$859$	−3.93540	−	2.85923i	−0.134274	−	0.0975558i	−0.652895	+	0.757449i	$0.726446\pi$
$860$	−11.6763	−	27.5248i	−0.398159	−	0.938587i
$861$		0			0
$862$	−16.2265	−	19.9216i	−0.552676	−	0.678531i
$863$	8.04227	+	50.7769i	0.273762	+	1.72847i	0.615034	+	0.788501i	$0.289142\pi$
$863$	8.04227	+	50.7769i	0.273762	+	1.72847i	−0.341272	+	0.939965i	$0.610858\pi$
$864$		0			0
$865$	−23.4638	+	7.02174i	−0.797793	+	0.238746i
$866$	−4.77682	+	46.7305i	−0.162323	+	1.58797i
$867$		0			0
$868$	−14.3065	−	52.1992i	−0.485593	−	1.77176i
$869$	15.9091	−	5.16919i	0.539680	−	0.175353i
$870$		0			0
$871$	−54.2047	−	17.6122i	−1.83666	−	0.596766i
$872$	13.1737	−	6.85499i	0.446118	−	0.232139i
$873$		0			0
$874$	20.2625	−	11.7757i	0.685388	−	0.398320i
$875$	−35.8760	+	22.4011i	−1.21283	+	0.757295i
$876$		0			0
$877$	38.6996	+	6.12942i	1.30679	+	0.206976i	0.770708	−	0.637188i	$-0.219903\pi$
$877$	38.6996	+	6.12942i	1.30679	+	0.206976i	0.536085	+	0.844164i	$0.319903\pi$
$878$	−29.8992	−	19.2957i	−1.00905	−	0.651198i
$879$		0			0
$880$	23.7173	+	15.8090i	0.799511	+	0.532923i
$881$	−2.79199	−	8.59285i	−0.0940645	−	0.289501i	0.892944	−	0.450167i	$-0.148636\pi$
$881$	−2.79199	−	8.59285i	−0.0940645	−	0.289501i	−0.987009	+	0.160667i	$0.948636\pi$
$882$		0			0
$883$	−7.91111	+	15.5264i	−0.266230	+	0.522506i	−0.984960	−	0.172784i	$-0.944724\pi$
$883$	−7.91111	+	15.5264i	−0.266230	+	0.522506i	0.718730	+	0.695289i	$0.244724\pi$
$884$	21.1695	+	46.8267i	0.712009	+	1.57495i
$885$		0			0
$886$	−21.6455	+	48.9923i	−0.727195	+	1.64593i
$887$	29.1515	−	4.61715i	0.978812	−	0.155029i	0.353526	−	0.935425i	$-0.384983\pi$
$887$	29.1515	−	4.61715i	0.978812	−	0.155029i	0.625286	+	0.780396i	$0.284983\pi$
$888$		0			0
$889$	25.7572	+	35.4517i	0.863868	+	1.18901i
$890$	34.7629	+	4.37694i	1.16525	+	0.146715i
$891$		0			0
$892$	12.6016	−	8.28617i	0.421932	−	0.277441i
$893$	−9.03285	+	9.03285i	−0.302273	+	0.302273i
$894$		0			0
$895$	14.0040	−	1.88352i	0.468101	−	0.0629592i
$896$	−9.73285	−	41.6785i	−0.325152	−	1.39238i
$897$		0			0
$898$	−17.1864	+	6.65356i	−0.573517	+	0.222032i
$899$	−65.2134			−2.17499
$900$		0			0
$901$	−19.2942			−0.642783
$902$	32.1037	−	12.4287i	1.06894	−	0.413830i
$903$		0			0
$904$	−11.2048	−	3.53493i	−0.372667	−	0.117570i
$905$	−35.4639	+	33.8430i	−1.17886	+	1.12498i
$906$		0			0
$907$	20.1655	−	20.1655i	0.669586	−	0.669586i	−0.288034	−	0.957620i	$-0.593002\pi$
$907$	20.1655	−	20.1655i	0.669586	−	0.669586i	0.957620	+	0.288034i	$0.0930018\pi$
$908$	10.9320	+	16.6254i	0.362792	+	0.551733i
$909$		0			0
$910$	12.8653	+	67.2906i	0.426479	+	2.23066i
$911$	20.6077	+	28.3641i	0.682764	+	0.939744i	0.999963	−	0.00861519i	$-0.00274233\pi$
$911$	20.6077	+	28.3641i	0.682764	+	0.939744i	−0.317199	+	0.948359i	$0.602742\pi$
$912$		0			0
$913$	−5.91896	+	0.937472i	−0.195889	+	0.0310258i
$914$	−2.07388	+	4.69401i	−0.0685980	+	0.155264i
$915$		0			0
$916$	28.2275	−	12.7612i	0.932661	−	0.421641i
$917$	18.8495	−	36.9942i	0.622465	−	1.22166i
$918$		0			0
$919$	9.59985	+	29.5453i	0.316670	+	0.974609i	0.975062	+	0.221934i	$0.0712369\pi$
$919$	9.59985	+	29.5453i	0.316670	+	0.974609i	−0.658392	+	0.752675i	$0.728763\pi$
$920$	−6.37434	+	36.7150i	−0.210156	+	1.21046i
$921$		0			0
$922$	35.6789	+	23.0257i	1.17502	+	0.758311i
$923$	−15.2170	−	2.41013i	−0.500873	−	0.0793306i
$924$		0			0
$925$	25.1794	+	14.3501i	0.827895	+	0.471830i
$926$	11.7697	−	6.84011i	0.386778	−	0.224780i
$927$		0			0
$928$	−51.5315	−	1.96403i	−1.69160	−	0.0644724i
$929$	−9.92021	−	3.22327i	−0.325472	−	0.105752i	0.141724	−	0.989906i	$-0.454736\pi$
$929$	−9.92021	−	3.22327i	−0.325472	−	0.105752i	−0.467195	+	0.884154i	$0.654736\pi$
$930$		0			0
$931$	−19.5567	+	6.35435i	−0.640944	+	0.208255i
$932$	13.4944	−	3.69847i	0.442024	−	0.121148i
$933$		0			0
$934$	−3.54384	+	34.6686i	−0.115958	+	1.13439i
$935$	18.1827	+	26.2980i	0.594637	+	0.860038i
$936$		0			0
$937$	−6.36346	−	40.1773i	−0.207885	−	1.31254i	−0.842076	−	0.539359i	$-0.818666\pi$
$937$	−6.36346	−	40.1773i	−0.207885	−	1.31254i	0.634190	−	0.773177i	$-0.281334\pi$
$938$	33.6254	+	41.2826i	1.09791	+	1.34792i
$939$		0			0
$940$	−1.76579	−	20.2351i	−0.0575937	−	0.659996i
$941$	−11.2321	−	8.16062i	−0.366157	−	0.266028i	0.389459	−	0.921044i	$-0.372662\pi$
$941$	−11.2321	−	8.16062i	−0.366157	−	0.266028i	−0.755615	+	0.655015i	$0.772662\pi$
$942$		0			0
$943$	31.8246	+	31.8246i	1.03635	+	1.03635i
$944$	−17.1700	+	19.5124i	−0.558835	+	0.635076i
$945$		0			0
$946$	−29.4541	+	6.34854i	−0.957635	+	0.206409i
$947$	0.980303	+	1.92395i	0.0318556	+	0.0625201i	0.906386	−	0.422451i	$-0.138830\pi$
$947$	0.980303	+	1.92395i	0.0318556	+	0.0625201i	−0.874530	+	0.484971i	$0.838830\pi$
$948$		0			0
$949$		−	29.9690i		−	0.972834i
$950$	0.168002	+	19.8871i	0.00545069	+	0.645223i
$951$		0			0
$952$	7.10401	−	47.4796i	0.230242	−	1.53882i
$953$	−14.3483	−	28.1601i	−0.464786	−	0.912194i	−0.997813	−	0.0660958i	$-0.978946\pi$
$953$	−14.3483	−	28.1601i	−0.464786	−	0.912194i	0.533027	−	0.846098i	$-0.321054\pi$
$954$		0			0
$955$	8.66264	+	1.58047i	0.280316	+	0.0511429i
$956$	−2.25214	+	10.9010i	−0.0728395	+	0.352563i
$957$		0			0
$958$	49.6135	−	2.74209i	1.60294	−	0.0885929i
$959$	−22.0027	−	15.9859i	−0.710504	−	0.516212i
$960$		0			0
$961$	16.3210	−	11.8579i	0.526484	−	0.382513i
$962$	36.3979	−	29.6467i	1.17351	−	0.955849i
$963$		0			0
$964$	−10.5185	+	1.16626i	−0.338779	+	0.0375627i
$965$	1.67297	+	0.587167i	0.0538547	+	0.0189016i
$966$		0			0
$967$	−19.6084	−	9.99098i	−0.630564	−	0.321288i	0.109337	−	0.994005i	$-0.465127\pi$
$967$	−19.6084	−	9.99098i	−0.630564	−	0.321288i	−0.739900	+	0.672717i	$0.765127\pi$
$968$	−1.67454	+	1.70345i	−0.0538217	+	0.0547511i
$969$		0			0
$970$	−4.09587	+	14.1199i	−0.131511	+	0.453363i
$971$	−20.8080	−	6.76092i	−0.667759	−	0.216968i	−0.0445309	−	0.999008i	$-0.514179\pi$
$971$	−20.8080	−	6.76092i	−0.667759	−	0.216968i	−0.623228	+	0.782040i	$0.714179\pi$
$972$		0			0
$973$	0.271476	−	1.71403i	0.00870313	−	0.0549494i
$974$	21.6135	+	37.1902i	0.692540	+	1.19165i
$975$		0			0
$976$	−9.85391	−	16.6263i	−0.315416	−	0.532196i
$977$	6.40242	+	1.01404i	0.204832	+	0.0324421i	0.258007	−	0.966143i	$-0.416934\pi$
$977$	6.40242	+	1.01404i	0.204832	+	0.0324421i	−0.0531754	+	0.998585i	$0.516934\pi$
$978$		0			0
$979$	10.9110	−	33.5805i	0.348716	−	1.07324i
$980$	12.2551	−	30.3129i	0.391475	−	0.968311i
$981$		0			0
$982$	10.6385	+	2.81808i	0.339489	+	0.0899286i
$983$	14.9685	−	29.3774i	0.477422	−	0.936994i	−0.519183	−	0.854663i	$-0.673764\pi$
$983$	14.9685	−	29.3774i	0.477422	−	0.936994i	0.996605	−	0.0823306i	$-0.0262364\pi$
$984$		0			0
$985$	−29.0504	−	22.1624i	−0.925624	−	0.706151i
$986$	−52.9102	−	23.3765i	−1.68501	−	0.744460i
$987$		0			0
$988$	30.1398	+	11.3727i	0.958873	+	0.361813i
$989$	−23.1538	−	31.8685i	−0.736248	−	1.01336i
$990$		0			0
$991$	19.0778	−	26.2584i	0.606027	−	0.834124i	−0.390216	−	0.920723i	$-0.627600\pi$
$991$	19.0778	−	26.2584i	0.606027	−	0.834124i	0.996243	+	0.0865988i	$0.0275998\pi$
$992$	33.6205	−	22.5217i	1.06745	−	0.715064i
$993$		0			0
$994$	10.7235	+	9.60018i	0.340127	+	0.304499i
$995$	−8.55105	−	17.7993i	−0.271087	−	0.564277i
$996$		0			0
$997$	2.62660	−	1.33832i	0.0831852	−	0.0423850i	−0.411903	−	0.911228i	$-0.635136\pi$
$997$	2.62660	−	1.33832i	0.0831852	−	0.0423850i	0.495088	+	0.868843i	$0.335136\pi$
$998$	10.7772	+	27.8378i	0.341145	+	0.881190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.19		240
3.2	odd	2		300.2.w.a.127.12	yes	240
4.3	odd	2	inner	900.2.bj.f.127.22		240
12.11	even	2		300.2.w.a.127.9	✓	240
25.13	odd	20	inner	900.2.bj.f.163.22		240
75.38	even	20		300.2.w.a.163.9	yes	240
100.63	even	20	inner	900.2.bj.f.163.19		240
300.263	odd	20		300.2.w.a.163.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.9	✓	240	12.11	even	2
300.2.w.a.127.12	yes	240	3.2	odd	2
300.2.w.a.163.9	yes	240	75.38	even	20
300.2.w.a.163.12	yes	240	300.263	odd	20
900.2.bj.f.127.19		240	1.1	even	1	trivial
900.2.bj.f.127.22		240	4.3	odd	2	inner
900.2.bj.f.163.19		240	100.63	even	20	inner
900.2.bj.f.163.22		240	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.510574 + 1.31883i) q^{2} +(-1.47863 + 1.34672i) q^{4} +(-0.968294 - 2.01554i) q^{5} +(-2.67499 + 2.67499i) q^{7} +(-2.53105 - 1.26246i) q^{8} +O(q^{10})\)	\(q+(0.510574 + 1.31883i) q^{2} +(-1.47863 + 1.34672i) q^{4} +(-0.968294 - 2.01554i) q^{5} +(-2.67499 + 2.67499i) q^{7} +(-2.53105 - 1.26246i) q^{8} +(2.16377 - 2.30610i) q^{10} +(-1.87313 - 2.57815i) q^{11} +(5.65630 - 0.895870i) q^{13} +(-4.89364 - 2.16208i) q^{14} +(0.372689 - 3.98260i) q^{16} +(2.03694 - 3.99773i) q^{17} +(-0.869130 - 2.67491i) q^{19} +(4.14612 + 1.67622i) q^{20} +(2.44377 - 3.78668i) q^{22} +(5.81945 + 0.921710i) q^{23} +(-3.12481 + 3.90327i) q^{25} +(4.06946 + 7.00230i) q^{26} +(0.352856 - 7.55779i) q^{28} +(-8.67000 - 2.81705i) q^{29} +(6.80347 - 2.21058i) q^{31} +(5.44266 - 1.54190i) q^{32} +(6.31233 + 0.645250i) q^{34} +(7.98173 + 2.80138i) q^{35} +(-0.906743 - 5.72495i) q^{37} +(3.08399 - 2.51197i) q^{38} +(-0.0937491 + 6.32386i) q^{40} +(6.17980 + 4.48988i) q^{41} +(-4.72744 - 4.72744i) q^{43} +(6.24171 + 1.28954i) q^{44} +(1.75568 + 8.14547i) q^{46} +(-2.06198 - 4.04686i) q^{47} -7.31116i q^{49} +(-6.74320 - 2.12819i) q^{50} +(-7.15709 + 8.94212i) q^{52} +(-1.95228 - 3.83156i) q^{53} +(-3.38262 + 6.27178i) q^{55} +(10.1476 - 3.39345i) q^{56} +(-0.711456 - 12.8726i) q^{58} +(-5.25683 - 3.81931i) q^{59} +(3.90898 - 2.84004i) q^{61} +(6.38905 + 7.84396i) q^{62} +(4.81238 + 6.39070i) q^{64} +(-7.28263 - 10.5330i) q^{65} +(-8.86745 - 4.51819i) q^{67} +(2.37193 + 8.65435i) q^{68} +(0.380718 + 11.9569i) q^{70} +(-2.55860 - 0.831340i) q^{71} +(0.818638 - 5.16868i) q^{73} +(7.08728 - 4.11885i) q^{74} +(4.88747 + 2.78472i) q^{76} +(11.9071 + 1.88591i) q^{77} +(-1.62208 + 4.99225i) q^{79} +(-8.38797 + 3.10516i) q^{80} +(-2.76616 + 10.4425i) q^{82} +(0.853734 - 1.67555i) q^{83} +(-10.0299 - 0.234570i) q^{85} +(3.82099 - 8.64841i) q^{86} +(1.48617 + 8.89017i) q^{88} +(6.51253 + 8.96373i) q^{89} +(-12.7341 + 17.5270i) q^{91} +(-9.84610 + 6.47430i) q^{92} +(4.28434 - 4.78562i) q^{94} +(-4.54981 + 4.34186i) q^{95} +(-4.14245 + 2.11068i) q^{97} +(9.64219 - 3.73289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

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