LMFDB - Embedded newform 1445.2.d.j.866.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, not 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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.2
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.35190 q^{2} -1.56935i q^{3} +3.53144 q^{4} +1.00000i q^{5} +3.69096i q^{6} +3.58212i q^{7} -3.60181 q^{8} +0.537139 q^{9} -2.35190i q^{10} +2.48259i q^{11} -5.54207i q^{12} -1.25948 q^{13} -8.42480i q^{14} +1.56935 q^{15} +1.40821 q^{16} -1.26330 q^{18} +3.63431 q^{19} +3.53144i q^{20} +5.62161 q^{21} -5.83882i q^{22} +8.83293i q^{23} +5.65249i q^{24} -1.00000 q^{25} +2.96218 q^{26} -5.55101i q^{27} +12.6501i q^{28} +8.75919i q^{29} -3.69096 q^{30} -2.44403i q^{31} +3.89165 q^{32} +3.89606 q^{33} -3.58212 q^{35} +1.89688 q^{36} -4.60155i q^{37} -8.54755 q^{38} +1.97657i q^{39} -3.60181i q^{40} -4.32497i q^{41} -13.2215 q^{42} -7.54720 q^{43} +8.76714i q^{44} +0.537139i q^{45} -20.7742i q^{46} -11.3322 q^{47} -2.20997i q^{48} -5.83161 q^{49} +2.35190 q^{50} -4.44779 q^{52} -5.69139 q^{53} +13.0554i q^{54} -2.48259 q^{55} -12.9021i q^{56} -5.70351i q^{57} -20.6008i q^{58} +4.47000 q^{59} +5.54207 q^{60} -0.242871i q^{61} +5.74812i q^{62} +1.92410i q^{63} -11.9692 q^{64} -1.25948i q^{65} -9.16315 q^{66} -7.23278 q^{67} +13.8620 q^{69} +8.42480 q^{70} -1.83778i q^{71} -1.93467 q^{72} +5.47256i q^{73} +10.8224i q^{74} +1.56935i q^{75} +12.8344 q^{76} -8.89296 q^{77} -4.64870i q^{78} -9.03570i q^{79} +1.40821i q^{80} -7.10006 q^{81} +10.1719i q^{82} -7.31575 q^{83} +19.8524 q^{84} +17.7503 q^{86} +13.7462 q^{87} -8.94182i q^{88} -2.19350 q^{89} -1.26330i q^{90} -4.51162i q^{91} +31.1930i q^{92} -3.83554 q^{93} +26.6522 q^{94} +3.63431i q^{95} -6.10736i q^{96} -9.82039i q^{97} +13.7154 q^{98} +1.33350i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.35190	−1.66305	−0.831523	−	0.555490i	$-0.812531\pi$
$2$	−2.35190	−1.66305	−0.831523	+	0.555490i	$0.812531\pi$
$3$	− 1.56935i	− 0.906065i	−0.891494	−	0.453032i	$-0.850342\pi$
$3$	− 1.56935i	− 0.906065i	0.891494	−	0.453032i	$-0.149658\pi$
$4$	3.53144	1.76572
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	3.69096i	1.50683i
$7$	3.58212i	1.35392i	0.736022	+	0.676958i	$0.236702\pi$
$7$	3.58212i	1.35392i	−0.736022	+	0.676958i	$0.763298\pi$
$8$	−3.60181	−1.27343
$9$	0.537139	0.179046
$10$	− 2.35190i	− 0.743737i
$11$	2.48259i	0.748530i	0.927322	+	0.374265i	$0.122105\pi$
$11$	2.48259i	0.748530i	−0.927322	+	0.374265i	$0.877895\pi$
$12$	− 5.54207i	− 1.59986i
$13$	−1.25948	−0.349317	−0.174659	−	0.984629i	$-0.555882\pi$
$13$	−1.25948	−0.349317	−0.174659	+	0.984629i	$0.555882\pi$
$14$	− 8.42480i	− 2.25162i
$15$	1.56935	0.405205
$16$	1.40821	0.352052
$17$	0	0
$17$	0	0
$18$	−1.26330	−0.297762
$19$	3.63431	0.833768	0.416884	−	0.908960i	$-0.363122\pi$
$19$	3.63431	0.833768	0.416884	+	0.908960i	$0.363122\pi$
$20$	3.53144i	0.789655i
$21$	5.62161	1.22674
$22$	− 5.83882i	− 1.24484i
$23$	8.83293i	1.84179i	0.389808	+	0.920896i	$0.372541\pi$
$23$	8.83293i	1.84179i	−0.389808	+	0.920896i	$0.627459\pi$
$24$	5.65249i	1.15381i
$25$	−1.00000	−0.200000
$26$	2.96218	0.580931
$27$	− 5.55101i	− 1.06829i
$28$	12.6501i	2.39064i
$29$	8.75919i	1.62654i	0.581885	+	0.813271i	$0.302315\pi$
$29$	8.75919i	1.62654i	−0.581885	+	0.813271i	$0.697685\pi$
$30$	−3.69096	−0.673874
$31$	− 2.44403i	− 0.438961i	−0.975617	−	0.219480i	$-0.929564\pi$
$31$	− 2.44403i	− 0.438961i	0.975617	−	0.219480i	$-0.0704362\pi$
$32$	3.89165	0.687953
$33$	3.89606	0.678217
$34$	0	0
$35$	−3.58212	−0.605489
$36$	1.89688	0.316146
$37$	− 4.60155i	− 0.756490i	−0.925705	−	0.378245i	$-0.876528\pi$
$37$	− 4.60155i	− 0.756490i	0.925705	−	0.378245i	$-0.123472\pi$
$38$	−8.54755	−1.38660
$39$	1.97657i	0.316504i
$40$	− 3.60181i	− 0.569495i
$41$	− 4.32497i	− 0.675447i	−0.941245	−	0.337724i	$-0.890343\pi$
$41$	− 4.32497i	− 0.675447i	0.941245	−	0.337724i	$-0.109657\pi$
$42$	−13.2215	−2.04012
$43$	−7.54720	−1.15094	−0.575469	−	0.817824i	$-0.695180\pi$
$43$	−7.54720	−1.15094	−0.575469	+	0.817824i	$0.695180\pi$
$44$	8.76714i	1.32170i
$45$	0.537139i	0.0800720i
$46$	− 20.7742i	− 3.06299i
$47$	−11.3322	−1.65297	−0.826484	−	0.562961i	$-0.809662\pi$
$47$	−11.3322	−1.65297	−0.826484	+	0.562961i	$0.809662\pi$
$48$	− 2.20997i	− 0.318982i
$49$	−5.83161	−0.833087
$50$	2.35190	0.332609
$51$	0	0
$52$	−4.44779	−0.616797
$53$	−5.69139	−0.781772	−0.390886	−	0.920439i	$-0.627831\pi$
$53$	−5.69139	−0.781772	−0.390886	+	0.920439i	$0.627831\pi$
$54$	13.0554i	1.77662i
$55$	−2.48259	−0.334753
$56$	− 12.9021i	− 1.72412i
$57$	− 5.70351i	− 0.755448i
$58$	− 20.6008i	− 2.70501i
$59$	4.47000	0.581945	0.290972	−	0.956731i	$-0.406021\pi$
$59$	4.47000	0.581945	0.290972	+	0.956731i	$0.406021\pi$
$60$	5.54207	0.715478
$61$	− 0.242871i	− 0.0310964i	−0.999879	−	0.0155482i	$-0.995051\pi$
$61$	− 0.242871i	− 0.0310964i	0.999879	−	0.0155482i	$-0.00494935\pi$
$62$	5.74812i	0.730012i
$63$	1.92410i	0.242414i
$64$	−11.9692	−1.49615
$65$	− 1.25948i	− 0.156220i
$66$	−9.16315	−1.12791
$67$	−7.23278	−0.883625	−0.441812	−	0.897108i	$-0.645664\pi$
$67$	−7.23278	−0.883625	−0.441812	+	0.897108i	$0.645664\pi$
$68$	0	0
$69$	13.8620	1.66878
$70$	8.42480	1.00696
$71$	− 1.83778i	− 0.218105i	−0.994036	−	0.109052i	$-0.965218\pi$
$71$	− 1.83778i	− 0.218105i	0.994036	−	0.109052i	$-0.0347816\pi$
$72$	−1.93467	−0.228003
$73$	5.47256i	0.640515i	0.947331	+	0.320257i	$0.103769\pi$
$73$	5.47256i	0.640515i	−0.947331	+	0.320257i	$0.896231\pi$
$74$	10.8224i	1.25808i
$75$	1.56935i	0.181213i
$76$	12.8344	1.47220
$77$	−8.89296	−1.01345
$78$	− 4.64870i	− 0.526361i
$79$	− 9.03570i	− 1.01660i	−0.861181	−	0.508298i	$-0.830275\pi$
$79$	− 9.03570i	− 1.01660i	0.861181	−	0.508298i	$-0.169725\pi$
$80$	1.40821i	0.157442i
$81$	−7.10006	−0.788896
$82$	10.1719i	1.12330i
$83$	−7.31575	−0.803008	−0.401504	−	0.915857i	$-0.631512\pi$
$83$	−7.31575	−0.803008	−0.401504	+	0.915857i	$0.631512\pi$
$84$	19.8524	2.16607
$85$	0	0
$86$	17.7503	1.91406
$87$	13.7462	1.47375
$88$	− 8.94182i	− 0.953201i
$89$	−2.19350	−0.232510	−0.116255	−	0.993219i	$-0.537089\pi$
$89$	−2.19350	−0.232510	−0.116255	+	0.993219i	$0.537089\pi$
$90$	− 1.26330i	− 0.133163i
$91$	− 4.51162i	− 0.472946i
$92$	31.1930i	3.25209i
$93$	−3.83554	−0.397727
$94$	26.6522	2.74896
$95$	3.63431i	0.372873i
$96$	− 6.10736i	− 0.623330i
$97$	− 9.82039i	− 0.997110i	−0.866858	−	0.498555i	$-0.833864\pi$
$97$	− 9.82039i	− 0.997110i	0.866858	−	0.498555i	$-0.166136\pi$
$98$	13.7154	1.38546
$99$	1.33350i	0.134022i
$100$	−3.53144	−0.353144
$101$	−5.46415	−0.543704	−0.271852	−	0.962339i	$-0.587636\pi$
$101$	−5.46415	−0.543704	−0.271852	+	0.962339i	$0.587636\pi$
$102$	0	0
$103$	7.16074	0.705568	0.352784	−	0.935705i	$-0.385235\pi$
$103$	7.16074	0.705568	0.352784	+	0.935705i	$0.385235\pi$
$104$	4.53641	0.444832
$105$	5.62161i	0.548613i
$106$	13.3856	1.30012
$107$	0.623156i	0.0602427i	0.999546	+	0.0301214i	$0.00958938\pi$
$107$	0.623156i	0.0602427i	−0.999546	+	0.0301214i	$0.990411\pi$
$108$	− 19.6031i	− 1.88631i
$109$	6.18952i	0.592848i	0.955056	+	0.296424i	$0.0957942\pi$
$109$	6.18952i	0.592848i	−0.955056	+	0.296424i	$0.904206\pi$
$110$	5.83882	0.556710
$111$	−7.22144	−0.685429
$112$	5.04437i	0.476648i
$113$	16.0596i	1.51076i	0.655287	+	0.755380i	$0.272548\pi$
$113$	16.0596i	1.51076i	−0.655287	+	0.755380i	$0.727452\pi$
$114$	13.4141i	1.25635i
$115$	−8.83293	−0.823675
$116$	30.9326i	2.87202i
$117$	−0.676517	−0.0625440
$118$	−10.5130	−0.967801
$119$	0	0
$120$	−5.65249	−0.516000
$121$	4.83672	0.439702
$122$	0.571208i	0.0517147i
$123$	−6.78740	−0.611999
$124$	− 8.63096i	− 0.775083i
$125$	− 1.00000i	− 0.0894427i
$126$	− 4.52529i	− 0.403145i
$127$	5.91786	0.525125	0.262563	−	0.964915i	$-0.415432\pi$
$127$	5.91786	0.525125	0.262563	+	0.964915i	$0.415432\pi$
$128$	20.3671	1.80021
$129$	11.8442i	1.04282i
$130$	2.96218i	0.259800i
$131$	16.1207i	1.40848i	0.709964	+	0.704238i	$0.248711\pi$
$131$	16.1207i	1.40848i	−0.709964	+	0.704238i	$0.751289\pi$
$132$	13.7587	1.19754
$133$	13.0186i	1.12885i
$134$	17.0108	1.46951
$135$	5.55101	0.477755
$136$	0	0
$137$	−17.1320	−1.46369	−0.731843	−	0.681473i	$-0.761339\pi$
$137$	−17.1320	−1.46369	−0.731843	+	0.681473i	$0.761339\pi$
$138$	−32.6020	−2.77526
$139$	2.13307i	0.180925i	0.995900	+	0.0904624i	$0.0288345\pi$
$139$	2.13307i	0.180925i	−0.995900	+	0.0904624i	$0.971165\pi$
$140$	−12.6501	−1.06913
$141$	17.7842i	1.49770i
$142$	4.32229i	0.362718i
$143$	− 3.12678i	− 0.261475i
$144$	0.756403	0.0630335
$145$	−8.75919	−0.727412
$146$	− 12.8709i	− 1.06521i
$147$	9.15184i	0.754831i
$148$	− 16.2501i	− 1.33575i
$149$	18.5384	1.51872	0.759362	−	0.650669i	$-0.225511\pi$
$149$	18.5384	1.51872	0.759362	+	0.650669i	$0.225511\pi$
$150$	− 3.69096i	− 0.301366i
$151$	−8.91261	−0.725298	−0.362649	−	0.931926i	$-0.618128\pi$
$151$	−8.91261	−0.725298	−0.362649	+	0.931926i	$0.618128\pi$
$152$	−13.0901	−1.06175
$153$	0	0
$154$	20.9154	1.68541
$155$	2.44403	0.196309
$156$	6.98014i	0.558859i
$157$	18.2426	1.45592	0.727960	−	0.685620i	$-0.240469\pi$
$157$	18.2426	1.45592	0.727960	+	0.685620i	$0.240469\pi$
$158$	21.2511i	1.69064i
$159$	8.93178i	0.708337i
$160$	3.89165i	0.307662i
$161$	−31.6406	−2.49363
$162$	16.6987	1.31197
$163$	9.36510i	0.733531i	0.930313	+	0.366766i	$0.119535\pi$
$163$	9.36510i	0.733531i	−0.930313	+	0.366766i	$0.880465\pi$
$164$	− 15.2734i	− 1.19265i
$165$	3.89606i	0.303308i
$166$	17.2059	1.33544
$167$	9.28133i	0.718211i	0.933297	+	0.359106i	$0.116918\pi$
$167$	9.28133i	0.718211i	−0.933297	+	0.359106i	$0.883082\pi$
$168$	−20.2479	−1.56216
$169$	−11.4137	−0.877977
$170$	0	0
$171$	1.95213	0.149283
$172$	−26.6525	−2.03224
$173$	− 4.29978i	− 0.326906i	−0.986551	−	0.163453i	$-0.947737\pi$
$173$	− 4.29978i	− 0.326906i	0.986551	−	0.163453i	$-0.0522632\pi$
$174$	−32.3298	−2.45092
$175$	− 3.58212i	− 0.270783i
$176$	3.49601i	0.263521i
$177$	− 7.01500i	− 0.527280i
$178$	5.15889	0.386675
$179$	0.117678	0.00879567	0.00439783	−	0.999990i	$-0.498600\pi$
$179$	0.117678	0.00879567	0.00439783	+	0.999990i	$0.498600\pi$
$180$	1.89688i	0.141385i
$181$	− 2.32364i	− 0.172715i	−0.996264	−	0.0863574i	$-0.972477\pi$
$181$	− 2.32364i	− 0.172715i	0.996264	−	0.0863574i	$-0.0275227\pi$
$182$	10.6109i	0.786531i
$183$	−0.381149	−0.0281754
$184$	− 31.8145i	− 2.34539i
$185$	4.60155	0.338313
$186$	9.02082	0.661438
$187$	0	0
$188$	−40.0189	−2.91868
$189$	19.8844	1.44638
$190$	− 8.54755i	− 0.620104i
$191$	−14.6622	−1.06092	−0.530461	−	0.847710i	$-0.677981\pi$
$191$	−14.6622	−1.06092	−0.530461	+	0.847710i	$0.677981\pi$
$192$	18.7838i	1.35561i
$193$	− 8.39606i	− 0.604362i	−0.953251	−	0.302181i	$-0.902285\pi$
$193$	− 8.39606i	− 0.604362i	0.953251	−	0.302181i	$-0.0977146\pi$
$194$	23.0966i	1.65824i
$195$	−1.97657	−0.141545
$196$	−20.5940	−1.47100
$197$	6.68150i	0.476037i	0.971261	+	0.238019i	$0.0764979\pi$
$197$	6.68150i	0.476037i	−0.971261	+	0.238019i	$0.923502\pi$
$198$	− 3.13626i	− 0.222884i
$199$	18.8718i	1.33779i	0.743359	+	0.668893i	$0.233232\pi$
$199$	18.8718i	1.33779i	−0.743359	+	0.668893i	$0.766768\pi$
$200$	3.60181	0.254686
$201$	11.3508i	0.800621i
$202$	12.8512	0.904204
$203$	−31.3765	−2.20220
$204$	0	0
$205$	4.32497	0.302069
$206$	−16.8414	−1.17339
$207$	4.74451i	0.329766i
$208$	−1.77361	−0.122978
$209$	9.02252i	0.624101i
$210$	− 13.2215i	− 0.912368i
$211$	6.61973i	0.455721i	0.973694	+	0.227860i	$0.0731730\pi$
$211$	6.61973i	0.455721i	−0.973694	+	0.227860i	$0.926827\pi$
$212$	−20.0988	−1.38039
$213$	−2.88413	−0.197617
$214$	− 1.46560i	− 0.100186i
$215$	− 7.54720i	− 0.514715i
$216$	19.9937i	1.36040i
$217$	8.75482	0.594316
$218$	− 14.5571i	− 0.985934i
$219$	8.58836	0.580348
$220$	−8.76714	−0.591081
$221$	0	0
$222$	16.9841	1.13990
$223$	−2.94266	−0.197055	−0.0985275	−	0.995134i	$-0.531413\pi$
$223$	−2.94266	−0.197055	−0.0985275	+	0.995134i	$0.531413\pi$
$224$	13.9404i	0.931429i
$225$	−0.537139	−0.0358093
$226$	− 37.7706i	− 2.51246i
$227$	21.5256i	1.42871i	0.699786	+	0.714353i	$0.253279\pi$
$227$	21.5256i	1.42871i	−0.699786	+	0.714353i	$0.746721\pi$
$228$	− 20.1416i	− 1.33391i
$229$	11.9409	0.789075	0.394537	−	0.918880i	$-0.370905\pi$
$229$	11.9409	0.789075	0.394537	+	0.918880i	$0.370905\pi$
$230$	20.7742	1.36981
$231$	13.9562i	0.918249i
$232$	− 31.5489i	− 2.07129i
$233$	− 10.0687i	− 0.659623i	−0.944047	−	0.329812i	$-0.893015\pi$
$233$	− 10.0687i	− 0.659623i	0.944047	−	0.329812i	$-0.106985\pi$
$234$	1.59110	0.104014
$235$	− 11.3322i	− 0.739230i
$236$	15.7856	1.02755
$237$	−14.1802	−0.921101
$238$	0	0
$239$	−16.6253	−1.07540	−0.537701	−	0.843135i	$-0.680707\pi$
$239$	−16.6253	−1.07540	−0.537701	+	0.843135i	$0.680707\pi$
$240$	2.20997	0.142653
$241$	5.92200i	0.381470i	0.981642	+	0.190735i	$0.0610871\pi$
$241$	5.92200i	0.381470i	−0.981642	+	0.190735i	$0.938913\pi$
$242$	−11.3755	−0.731245
$243$	− 5.51054i	− 0.353502i
$244$	− 0.857684i	− 0.0549076i
$245$	− 5.83161i	− 0.372568i
$246$	15.9633	1.01778
$247$	−4.57735	−0.291250
$248$	8.80292i	0.558986i
$249$	11.4810i	0.727577i
$250$	2.35190i	0.148747i
$251$	7.77270	0.490608	0.245304	−	0.969446i	$-0.421112\pi$
$251$	7.77270	0.490608	0.245304	+	0.969446i	$0.421112\pi$
$252$	6.79484i	0.428035i
$253$	−21.9286	−1.37864
$254$	−13.9182	−0.873307
$255$	0	0
$256$	−23.9630	−1.49768
$257$	8.06588	0.503135	0.251568	−	0.967840i	$-0.419054\pi$
$257$	8.06588	0.503135	0.251568	+	0.967840i	$0.419054\pi$
$258$	− 27.8564i	− 1.73426i
$259$	16.4833	1.02422
$260$	− 4.44779i	− 0.275840i
$261$	4.70491i	0.291226i
$262$	− 37.9144i	− 2.34236i
$263$	21.3252	1.31497	0.657483	−	0.753469i	$-0.271621\pi$
$263$	21.3252	1.31497	0.657483	+	0.753469i	$0.271621\pi$
$264$	−14.0329	−0.863662
$265$	− 5.69139i	− 0.349619i
$266$	− 30.6184i	− 1.87733i
$267$	3.44237i	0.210670i
$268$	−25.5422	−1.56024
$269$	− 4.20185i	− 0.256191i	−0.991762	−	0.128096i	$-0.959114\pi$
$269$	− 4.20185i	− 0.256191i	0.991762	−	0.128096i	$-0.0408864\pi$
$270$	−13.0554	−0.794528
$271$	24.7136	1.50124	0.750621	−	0.660733i	$-0.229755\pi$
$271$	24.7136	1.50124	0.750621	+	0.660733i	$0.229755\pi$
$272$	0	0
$273$	−7.08031	−0.428520
$274$	40.2928	2.43418
$275$	− 2.48259i	− 0.149706i
$276$	48.9527	2.94661
$277$	− 20.0627i	− 1.20545i	−0.797949	−	0.602725i	$-0.794082\pi$
$277$	− 20.0627i	− 1.20545i	0.797949	−	0.602725i	$-0.205918\pi$
$278$	− 5.01678i	− 0.300886i
$279$	− 1.31278i	− 0.0785943i
$280$	12.9021	0.771049
$281$	−25.1805	−1.50215	−0.751073	−	0.660219i	$-0.770463\pi$
$281$	−25.1805	−1.50215	−0.751073	+	0.660219i	$0.770463\pi$
$282$	− 41.8266i	− 2.49074i
$283$	8.48659i	0.504476i	0.967665	+	0.252238i	$0.0811665\pi$
$283$	8.48659i	0.504476i	−0.967665	+	0.252238i	$0.918833\pi$
$284$	− 6.49003i	− 0.385112i
$285$	5.70351	0.337847
$286$	7.35389i	0.434845i
$287$	15.4926	0.914499
$288$	2.09036	0.123175
$289$	0	0
$290$	20.6008	1.20972
$291$	−15.4116	−0.903446
$292$	19.3260i	1.13097i
$293$	25.9873	1.51820	0.759098	−	0.650977i	$-0.225640\pi$
$293$	25.9873	1.51820	0.759098	+	0.650977i	$0.225640\pi$
$294$	− 21.5242i	− 1.25532i
$295$	4.47000i	0.260254i
$296$	16.5739i	0.963338i
$297$	13.7809	0.799649
$298$	−43.6005	−2.52571
$299$	− 11.1249i	− 0.643370i
$300$	5.54207i	0.319972i
$301$	− 27.0350i	− 1.55827i
$302$	20.9616	1.20620
$303$	8.57517i	0.492631i
$304$	5.11786	0.293529
$305$	0.242871	0.0139067
$306$	0	0
$307$	16.9475	0.967245	0.483622	−	0.875277i	$-0.339321\pi$
$307$	16.9475	0.967245	0.483622	+	0.875277i	$0.339321\pi$
$308$	−31.4050	−1.78947
$309$	− 11.2377i	− 0.639291i
$310$	−5.74812	−0.326471
$311$	17.1905i	0.974782i	0.873184	+	0.487391i	$0.162051\pi$
$311$	17.1905i	0.974782i	−0.873184	+	0.487391i	$0.837949\pi$
$312$	− 7.11922i	− 0.403046i
$313$	− 5.91487i	− 0.334328i	−0.985929	−	0.167164i	$-0.946539\pi$
$313$	− 5.91487i	− 0.334328i	0.985929	−	0.167164i	$-0.0534610\pi$
$314$	−42.9049	−2.42126
$315$	−1.92410	−0.108411
$316$	− 31.9090i	− 1.79502i
$317$	− 0.640574i	− 0.0359782i	−0.999838	−	0.0179891i	$-0.994274\pi$
$317$	− 0.640574i	− 0.0359782i	0.999838	−	0.0179891i	$-0.00572642\pi$
$318$	− 21.0067i	− 1.17800i
$319$	−21.7455	−1.21752
$320$	− 11.9692i	− 0.669098i
$321$	0.977950	0.0545838
$322$	74.4157	4.14702
$323$	0	0
$324$	−25.0735	−1.39297
$325$	1.25948	0.0698635
$326$	− 22.0258i	− 1.21990i
$327$	9.71352	0.537159
$328$	15.5777i	0.860135i
$329$	− 40.5932i	− 2.23798i
$330$	− 9.16315i	− 0.504415i
$331$	−11.6609	−0.640939	−0.320469	−	0.947259i	$-0.603841\pi$
$331$	−11.6609	−0.640939	−0.320469	+	0.947259i	$0.603841\pi$
$332$	−25.8352	−1.41789
$333$	− 2.47167i	− 0.135447i
$334$	− 21.8288i	− 1.19442i
$335$	− 7.23278i	− 0.395169i
$336$	7.91638	0.431874
$337$	− 30.8806i	− 1.68217i	−0.540900	−	0.841087i	$-0.681916\pi$
$337$	− 30.8806i	− 1.68217i	0.540900	−	0.841087i	$-0.318084\pi$
$338$	26.8439	1.46012
$339$	25.2031	1.36885
$340$	0	0
$341$	6.06754	0.328576
$342$	−4.59122	−0.248265
$343$	4.18533i	0.225986i
$344$	27.1836	1.46564
$345$	13.8620i	0.746303i
$346$	10.1127i	0.543660i
$347$	− 0.0149992i	0 0.000805197i	−1.00000		0.000402598i	$-0.999872\pi$
$347$	− 0.0149992i	0 0.000805197i	1.00000		0.000402598i	$-0.000128151\pi$
$348$	48.5441	2.60224
$349$	3.65491	0.195643	0.0978215	−	0.995204i	$-0.468813\pi$
$349$	3.65491	0.195643	0.0978215	+	0.995204i	$0.468813\pi$
$350$	8.42480i	0.450325i
$351$	6.99140i	0.373173i
$352$	9.66138i	0.514953i
$353$	3.82333	0.203495	0.101748	−	0.994810i	$-0.467557\pi$
$353$	3.82333	0.203495	0.101748	+	0.994810i	$0.467557\pi$
$354$	16.4986i	0.876891i
$355$	1.83778	0.0975395
$356$	−7.74622	−0.410549
$357$	0	0
$358$	−0.276767	−0.0146276
$359$	6.69675	0.353441	0.176721	−	0.984261i	$-0.443451\pi$
$359$	6.69675	0.353441	0.176721	+	0.984261i	$0.443451\pi$
$360$	− 1.93467i	− 0.101966i
$361$	−5.79178	−0.304830
$362$	5.46497i	0.287232i
$363$	− 7.59052i	− 0.398399i
$364$	− 15.9325i	− 0.835092i
$365$	−5.47256	−0.286447
$366$	0.896426	0.0468569
$367$	23.0276i	1.20203i	0.799238	+	0.601015i	$0.205237\pi$
$367$	23.0276i	1.20203i	−0.799238	+	0.601015i	$0.794763\pi$
$368$	12.4386i	0.648406i
$369$	− 2.32311i	− 0.120936i
$370$	−10.8224	−0.562630
$371$	− 20.3873i	− 1.05845i
$372$	−13.5450	−0.702275
$373$	23.7303	1.22871	0.614355	−	0.789030i	$-0.289416\pi$
$373$	23.7303	1.22871	0.614355	+	0.789030i	$0.289416\pi$
$374$	0	0
$375$	−1.56935	−0.0810409
$376$	40.8163	2.10494
$377$	− 11.0320i	− 0.568179i
$378$	−46.7662	−2.40539
$379$	− 2.97819i	− 0.152979i	−0.997070	−	0.0764897i	$-0.975629\pi$
$379$	− 2.97819i	− 0.152979i	0.997070	−	0.0764897i	$-0.0243712\pi$
$380$	12.8344i	0.658389i
$381$	− 9.28720i	− 0.475798i
$382$	34.4841	1.76436
$383$	24.4222	1.24791	0.623957	−	0.781459i	$-0.285524\pi$
$383$	24.4222	1.24791	0.623957	+	0.781459i	$0.285524\pi$
$384$	− 31.9631i	− 1.63111i
$385$	− 8.89296i	− 0.453227i
$386$	19.7467i	1.00508i
$387$	−4.05390	−0.206071
$388$	− 34.6802i	− 1.76062i
$389$	−1.68867	−0.0856191	−0.0428095	−	0.999083i	$-0.513631\pi$
$389$	−1.68867	−0.0856191	−0.0428095	+	0.999083i	$0.513631\pi$
$390$	4.64870	0.235396
$391$	0	0
$392$	21.0043	1.06088
$393$	25.2991	1.27617
$394$	− 15.7142i	− 0.791671i
$395$	9.03570	0.454635
$396$	4.70917i	0.236645i
$397$	31.5256i	1.58222i	0.611671	+	0.791112i	$0.290498\pi$
$397$	31.5256i	1.58222i	−0.611671	+	0.791112i	$0.709502\pi$
$398$	− 44.3846i	− 2.22480i
$399$	20.4307	1.02281
$400$	−1.40821	−0.0704103
$401$	− 5.06607i	− 0.252987i	−0.991967	−	0.126494i	$-0.959628\pi$
$401$	− 5.06607i	− 0.252987i	0.991967	−	0.126494i	$-0.0403724\pi$
$402$	− 26.6959i	− 1.33147i
$403$	3.07821i	0.153337i
$404$	−19.2964	−0.960029
$405$	− 7.10006i	− 0.352805i
$406$	73.7945	3.66236
$407$	11.4238	0.566256
$408$	0	0
$409$	−26.1178	−1.29144	−0.645722	−	0.763573i	$-0.723443\pi$
$409$	−26.1178	−1.29144	−0.645722	+	0.763573i	$0.723443\pi$
$410$	−10.1719	−0.502355
$411$	26.8861i	1.32619i
$412$	25.2877	1.24584
$413$	16.0121i	0.787904i
$414$	− 11.1586i	− 0.548416i
$415$	− 7.31575i	− 0.359116i
$416$	−4.90146	−0.240314
$417$	3.34754	0.163930
$418$	− 21.2201i	− 1.03791i
$419$	7.29855i	0.356557i	0.983980	+	0.178279i	$0.0570529\pi$
$419$	7.29855i	0.356557i	−0.983980	+	0.178279i	$0.942947\pi$
$420$	19.8524i	0.968697i
$421$	−21.0644	−1.02662	−0.513309	−	0.858204i	$-0.671580\pi$
$421$	−21.0644	−1.02662	−0.513309	+	0.858204i	$0.671580\pi$
$422$	− 15.5690i	− 0.757885i
$423$	−6.08695	−0.295958
$424$	20.4993	0.995533
$425$	0	0
$426$	6.78319	0.328646
$427$	0.869993	0.0421019
$428$	2.20064i	0.106372i
$429$	−4.90702	−0.236913
$430$	17.7503i	0.855995i
$431$	21.0432i	1.01362i	0.862059	+	0.506809i	$0.169175\pi$
$431$	21.0432i	1.01362i	−0.862059	+	0.506809i	$0.830825\pi$
$432$	− 7.81697i	− 0.376094i
$433$	−37.1262	−1.78417	−0.892084	−	0.451869i	$-0.850758\pi$
$433$	−37.1262	−1.78417	−0.892084	+	0.451869i	$0.850758\pi$
$434$	−20.5905	−0.988375
$435$	13.7462i	0.659082i
$436$	21.8579i	1.04680i
$437$	32.1016i	1.53563i
$438$	−20.1990	−0.965145
$439$	− 0.471326i	− 0.0224952i	−0.999937	−	0.0112476i	$-0.996420\pi$
$439$	− 0.471326i	− 0.0224952i	0.999937	−	0.0112476i	$-0.00358029\pi$
$440$	8.94182	0.426285
$441$	−3.13238	−0.149161
$442$	0	0
$443$	−11.0249	−0.523808	−0.261904	−	0.965094i	$-0.584350\pi$
$443$	−11.0249	−0.523808	−0.261904	+	0.965094i	$0.584350\pi$
$444$	−25.5021	−1.21028
$445$	− 2.19350i	− 0.103982i
$446$	6.92084	0.327711
$447$	− 29.0932i	− 1.37606i
$448$	− 42.8751i	− 2.02566i
$449$	17.2633i	0.814703i	0.913271	+	0.407352i	$0.133548\pi$
$449$	17.2633i	0.814703i	−0.913271	+	0.407352i	$0.866452\pi$
$450$	1.26330	0.0595525
$451$	10.7372	0.505593
$452$	56.7136i	2.66758i
$453$	13.9870i	0.657167i
$454$	− 50.6262i	− 2.37600i
$455$	4.51162	0.211508
$456$	20.5429i	0.962011i
$457$	−11.2676	−0.527078	−0.263539	−	0.964649i	$-0.584890\pi$
$457$	−11.2676	−0.527078	−0.263539	+	0.964649i	$0.584890\pi$
$458$	−28.0837	−1.31227
$459$	0	0
$460$	−31.1930	−1.45438
$461$	−30.0075	−1.39759	−0.698794	−	0.715323i	$-0.746280\pi$
$461$	−30.0075	−1.39759	−0.698794	+	0.715323i	$0.746280\pi$
$462$	− 32.8235i	− 1.52709i
$463$	−17.1592	−0.797457	−0.398728	−	0.917069i	$-0.630548\pi$
$463$	−17.1592	−0.797457	−0.398728	+	0.917069i	$0.630548\pi$
$464$	12.3348i	0.572627i
$465$	− 3.83554i	− 0.177869i
$466$	23.6806i	1.09698i
$467$	26.5914	1.23051	0.615253	−	0.788330i	$-0.289054\pi$
$467$	26.5914	1.23051	0.615253	+	0.788330i	$0.289054\pi$
$468$	−2.38908	−0.110435
$469$	− 25.9087i	− 1.19635i
$470$	26.6522i	1.22937i
$471$	− 28.6291i	− 1.31916i
$472$	−16.1001	−0.741066
$473$	− 18.7366i	− 0.861512i
$474$	33.3504	1.53183
$475$	−3.63431	−0.166754
$476$	0	0
$477$	−3.05707	−0.139974
$478$	39.1011	1.78844
$479$	− 22.9101i	− 1.04679i	−0.852090	−	0.523395i	$-0.824665\pi$
$479$	− 22.9101i	− 1.04679i	0.852090	−	0.523395i	$-0.175335\pi$
$480$	6.10736	0.278761
$481$	5.79557i	0.264255i
$482$	− 13.9280i	− 0.634402i
$483$	49.6552i	2.25939i
$484$	17.0806	0.776392
$485$	9.82039	0.445921
$486$	12.9603i	0.587889i
$487$	15.7135i	0.712048i	0.934477	+	0.356024i	$0.115868\pi$
$487$	15.7135i	0.712048i	−0.934477	+	0.356024i	$0.884132\pi$
$488$	0.874773i	0.0395991i
$489$	14.6971	0.664627
$490$	13.7154i	0.619597i
$491$	0.859183	0.0387744	0.0193872	−	0.999812i	$-0.493828\pi$
$491$	0.859183	0.0387744	0.0193872	+	0.999812i	$0.493828\pi$
$492$	−23.9693	−1.08062
$493$	0	0
$494$	10.7655	0.484362
$495$	−1.33350	−0.0599363
$496$	− 3.44170i	− 0.154537i
$497$	6.58317	0.295296
$498$	− 27.0021i	− 1.20999i
$499$	22.6396i	1.01349i	0.862097	+	0.506744i	$0.169151\pi$
$499$	22.6396i	1.01349i	−0.862097	+	0.506744i	$0.830849\pi$
$500$	− 3.53144i	− 0.157931i
$501$	14.5657	0.650746
$502$	−18.2806	−0.815904
$503$	− 17.1150i	− 0.763121i	−0.924344	−	0.381560i	$-0.875387\pi$
$503$	− 17.1150i	− 0.763121i	0.924344	−	0.381560i	$-0.124613\pi$
$504$	− 6.93023i	− 0.308697i
$505$	− 5.46415i	− 0.243152i
$506$	51.5739	2.29274
$507$	17.9121i	0.795504i
$508$	20.8986	0.927225
$509$	−29.7081	−1.31679	−0.658393	−	0.752674i	$-0.728764\pi$
$509$	−29.7081	−1.31679	−0.658393	+	0.752674i	$0.728764\pi$
$510$	0	0
$511$	−19.6034	−0.867203
$512$	15.6244	0.690508
$513$	− 20.1741i	− 0.890709i
$514$	−18.9701	−0.836737
$515$	7.16074i	0.315540i
$516$	41.8271i	1.84134i
$517$	− 28.1332i	− 1.23730i
$518$	−38.7672	−1.70333
$519$	−6.74786	−0.296198
$520$	4.53641i	0.198935i
$521$	− 38.6564i	− 1.69357i	−0.531936	−	0.846784i	$-0.678535\pi$
$521$	− 38.6564i	− 1.69357i	0.531936	−	0.846784i	$-0.321465\pi$
$522$	− 11.0655i	− 0.484323i
$523$	0.599508	0.0262147	0.0131073	−	0.999914i	$-0.495828\pi$
$523$	0.599508	0.0262147	0.0131073	+	0.999914i	$0.495828\pi$
$524$	56.9295i	2.48698i
$525$	−5.62161	−0.245347
$526$	−50.1547	−2.18685
$527$	0	0
$528$	5.48646	0.238767
$529$	−55.0206	−2.39220
$530$	13.3856i	0.581433i
$531$	2.40101	0.104195
$532$	45.9743i	1.99324i
$533$	5.44723i	0.235946i
$534$	− 8.09611i	− 0.350353i
$535$	−0.623156	−0.0269414
$536$	26.0511	1.12523
$537$	− 0.184678i	− 0.00796945i
$538$	9.88234i	0.426058i
$539$	− 14.4775i	− 0.623591i
$540$	19.6031	0.843582
$541$	− 39.7072i	− 1.70715i	−0.520973	−	0.853573i	$-0.674431\pi$
$541$	− 39.7072i	− 1.70715i	0.520973	−	0.853573i	$-0.325569\pi$
$542$	−58.1239	−2.49663
$543$	−3.64660	−0.156491
$544$	0	0
$545$	−6.18952	−0.265130
$546$	16.6522	0.712649
$547$	− 4.03770i	− 0.172639i	−0.996267	−	0.0863197i	$-0.972489\pi$
$547$	− 4.03770i	− 0.172639i	0.996267	−	0.0863197i	$-0.0275107\pi$
$548$	−60.5007	−2.58446
$549$	− 0.130455i	− 0.00556770i
$550$	5.83882i	0.248968i
$551$	31.8336i	1.35616i
$552$	−49.9281	−2.12508
$553$	32.3670	1.37638
$554$	47.1854i	2.00472i
$555$	− 7.22144i	− 0.306533i
$556$	7.53283i	0.319463i
$557$	5.42781	0.229984	0.114992	−	0.993366i	$-0.463316\pi$
$557$	5.42781	0.229984	0.114992	+	0.993366i	$0.463316\pi$
$558$	3.08754i	0.130706i
$559$	9.50557	0.402043
$560$	−5.04437	−0.213163
$561$	0	0
$562$	59.2222	2.49814
$563$	5.18858	0.218673	0.109336	−	0.994005i	$-0.465127\pi$
$563$	5.18858	0.218673	0.109336	+	0.994005i	$0.465127\pi$
$564$	62.8037i	2.64451i
$565$	−16.0596	−0.675632
$566$	− 19.9596i	− 0.838966i
$567$	− 25.4333i	− 1.06810i
$568$	6.61934i	0.277741i
$569$	11.9963	0.502911	0.251455	−	0.967869i	$-0.419091\pi$
$569$	11.9963	0.502911	0.251455	+	0.967869i	$0.419091\pi$
$570$	−13.4141	−0.561855
$571$	43.5118i	1.82091i	0.413606	+	0.910456i	$0.364269\pi$
$571$	43.5118i	1.82091i	−0.413606	+	0.910456i	$0.635731\pi$
$572$	− 11.0421i	− 0.461692i
$573$	23.0102i	0.961263i
$574$	−36.4371	−1.52085
$575$	− 8.83293i	− 0.368358i
$576$	−6.42912	−0.267880
$577$	−27.7097	−1.15357	−0.576784	−	0.816897i	$-0.695693\pi$
$577$	−27.7097	−1.15357	−0.576784	+	0.816897i	$0.695693\pi$
$578$	0	0
$579$	−13.1764	−0.547591
$580$	−30.9326	−1.28441
$581$	− 26.2059i	− 1.08720i
$582$	36.2467	1.50247
$583$	− 14.1294i	− 0.585180i
$584$	− 19.7111i	− 0.815651i
$585$	− 0.676517i	− 0.0279705i
$586$	−61.1196	−2.52483
$587$	−4.37916	−0.180747	−0.0903736	−	0.995908i	$-0.528806\pi$
$587$	−4.37916	−0.180747	−0.0903736	+	0.995908i	$0.528806\pi$
$588$	32.3192i	1.33282i
$589$	− 8.88237i	− 0.365992i
$590$	− 10.5130i	− 0.432814i
$591$	10.4856	0.431320
$592$	− 6.47993i	− 0.266324i
$593$	35.8783	1.47335	0.736673	−	0.676250i	$-0.236396\pi$
$593$	35.8783	1.47335	0.736673	+	0.676250i	$0.236396\pi$
$594$	−32.4114	−1.32985
$595$	0	0
$596$	65.4673	2.68164
$597$	29.6165	1.21212
$598$	26.1647i	1.06995i
$599$	11.1415	0.455230	0.227615	−	0.973751i	$-0.426907\pi$
$599$	11.1415	0.455230	0.227615	+	0.973751i	$0.426907\pi$
$600$	− 5.65249i	− 0.230762i
$601$	− 20.4505i	− 0.834193i	−0.908862	−	0.417096i	$-0.863048\pi$
$601$	− 20.4505i	− 0.834193i	0.908862	−	0.417096i	$-0.136952\pi$
$602$	63.5837i	2.59148i
$603$	−3.88501	−0.158210
$604$	−31.4744	−1.28067
$605$	4.83672i	0.196641i
$606$	− 20.1680i	− 0.819268i
$607$	1.57554i	0.0639492i	0.999489	+	0.0319746i	$0.0101796\pi$
$607$	1.57554i	0.0639492i	−0.999489	+	0.0319746i	$0.989820\pi$
$608$	14.1435	0.573593
$609$	49.2407i	1.99534i
$610$	−0.571208	−0.0231275
$611$	14.2727	0.577410
$612$	0	0
$613$	−22.4800	−0.907959	−0.453980	−	0.891012i	$-0.649996\pi$
$613$	−22.4800	−0.907959	−0.453980	+	0.891012i	$0.649996\pi$
$614$	−39.8589	−1.60857
$615$	− 6.78740i	− 0.273694i
$616$	32.0307	1.29055
$617$	− 27.1976i	− 1.09493i	−0.836827	−	0.547467i	$-0.815592\pi$
$617$	− 27.1976i	− 1.09493i	0.836827	−	0.547467i	$-0.184408\pi$
$618$	26.4300i	1.06317i
$619$	14.3702i	0.577588i	0.957391	+	0.288794i	$0.0932542\pi$
$619$	14.3702i	0.577588i	−0.957391	+	0.288794i	$0.906746\pi$
$620$	8.63096	0.346628
$621$	49.0317	1.96757
$622$	− 40.4303i	− 1.62111i
$623$	− 7.85738i	− 0.314799i
$624$	2.78342i	0.111426i
$625$	1.00000	0.0400000
$626$	13.9112i	0.556003i
$627$	14.1595	0.565476
$628$	64.4228	2.57075
$629$	0	0
$630$	4.52529	0.180292
$631$	23.2691	0.926330	0.463165	−	0.886272i	$-0.346714\pi$
$631$	23.2691	0.926330	0.463165	+	0.886272i	$0.346714\pi$
$632$	32.5448i	1.29456i
$633$	10.3887	0.412913
$634$	1.50657i	0.0598334i
$635$	5.91786i	0.234843i
$636$	31.5421i	1.25073i
$637$	7.34480	0.291012
$638$	51.1434	2.02478
$639$	− 0.987146i	− 0.0390509i
$640$	20.3671i	0.805079i
$641$	− 5.38403i	− 0.212656i	−0.994331	−	0.106328i	$-0.966091\pi$
$641$	− 5.38403i	− 0.212656i	0.994331	−	0.106328i	$-0.0339094\pi$
$642$	−2.30004	−0.0907754
$643$	− 16.1891i	− 0.638438i	−0.947681	−	0.319219i	$-0.896580\pi$
$643$	− 16.1891i	− 0.638438i	0.947681	−	0.319219i	$-0.103420\pi$
$644$	−111.737	−4.40306
$645$	−11.8442	−0.466365
$646$	0	0
$647$	−25.8383	−1.01581	−0.507904	−	0.861413i	$-0.669580\pi$
$647$	−25.8383	−1.01581	−0.507904	+	0.861413i	$0.669580\pi$
$648$	25.5730	1.00460
$649$	11.0972i	0.435604i
$650$	−2.96218	−0.116186
$651$	− 13.7394i	− 0.538489i
$652$	33.0723i	1.29521i
$653$	− 12.4784i	− 0.488319i	−0.969735	−	0.244159i	$-0.921488\pi$
$653$	− 12.4784i	− 0.488319i	0.969735	−	0.244159i	$-0.0785120\pi$
$654$	−22.8452	−0.893320
$655$	−16.1207	−0.629889
$656$	− 6.09045i	− 0.237792i
$657$	2.93953i	0.114682i
$658$	95.4713i	3.72186i
$659$	41.7109	1.62483	0.812413	−	0.583082i	$-0.198153\pi$
$659$	41.7109	1.62483	0.812413	+	0.583082i	$0.198153\pi$
$660$	13.7587i	0.535557i
$661$	−18.1720	−0.706808	−0.353404	−	0.935471i	$-0.614976\pi$
$661$	−18.1720	−0.706808	−0.353404	+	0.935471i	$0.614976\pi$
$662$	27.4252	1.06591
$663$	0	0
$664$	26.3499	1.02257
$665$	−13.0186	−0.504838
$666$	5.81313i	0.225254i
$667$	−77.3693	−2.99575
$668$	32.7765i	1.26816i
$669$	4.61806i	0.178545i
$670$	17.0108i	0.657184i
$671$	0.602949	0.0232766
$672$	21.8773	0.843936
$673$	− 6.39677i	− 0.246577i	−0.992371	−	0.123289i	$-0.960656\pi$
$673$	− 6.39677i	− 0.246577i	0.992371	−	0.123289i	$-0.0393441\pi$
$674$	72.6282i	2.79753i
$675$	5.55101i	0.213659i
$676$	−40.3069	−1.55026
$677$	41.8887i	1.60991i	0.593334	+	0.804957i	$0.297811\pi$
$677$	41.8887i	1.60991i	−0.593334	+	0.804957i	$0.702189\pi$
$678$	−59.2753	−2.27645
$679$	35.1779	1.35000
$680$	0	0
$681$	33.7812	1.29450
$682$	−14.2703	−0.546436
$683$	30.3064i	1.15964i	0.814744	+	0.579820i	$0.196877\pi$
$683$	30.3064i	1.15964i	−0.814744	+	0.579820i	$0.803123\pi$
$684$	6.89384	0.263593
$685$	− 17.1320i	− 0.654580i
$686$	− 9.84348i	− 0.375826i
$687$	− 18.7394i	− 0.714953i
$688$	−10.6280	−0.405189
$689$	7.16820	0.273087
$690$	− 32.6020i	− 1.24114i
$691$	5.79281i	0.220369i	0.993911	+	0.110184i	$0.0351441\pi$
$691$	5.79281i	0.220369i	−0.993911	+	0.110184i	$0.964856\pi$
$692$	− 15.1844i	− 0.577225i
$693$	−4.77676	−0.181454
$694$	0.0352765i	0.00133908i
$695$	−2.13307	−0.0809121
$696$	−49.5113	−1.87672
$697$	0	0
$698$	−8.59600	−0.325363
$699$	−15.8013	−0.597662
$700$	− 12.6501i	− 0.478128i
$701$	5.24783	0.198208	0.0991039	−	0.995077i	$-0.468402\pi$
$701$	5.24783	0.198208	0.0991039	+	0.995077i	$0.468402\pi$
$702$	− 16.4431i	− 0.620604i
$703$	− 16.7235i	− 0.630738i
$704$	− 29.7146i	− 1.11991i
$705$	−17.7842	−0.669790
$706$	−8.99209	−0.338422
$707$	− 19.5733i	− 0.736129i
$708$	− 24.7731i	− 0.931030i
$709$	41.7572i	1.56823i	0.620618	+	0.784113i	$0.286882\pi$
$709$	41.7572i	1.56823i	−0.620618	+	0.784113i	$0.713118\pi$
$710$	−4.32229	−0.162213
$711$	− 4.85343i	− 0.182018i
$712$	7.90055	0.296086
$713$	21.5879	0.808475
$714$	0	0
$715$	3.12678	0.116935
$716$	0.415573	0.0155307
$717$	26.0910i	0.974385i
$718$	−15.7501	−0.587789
$719$	− 10.1819i	− 0.379719i	−0.981811	−	0.189860i	$-0.939197\pi$
$719$	− 10.1819i	− 0.379719i	0.981811	−	0.189860i	$-0.0608033\pi$
$720$	0.756403i	0.0281895i
$721$	25.6506i	0.955280i
$722$	13.6217	0.506947
$723$	9.29370	0.345636
$724$	− 8.20580i	− 0.304966i
$725$	− 8.75919i	− 0.325308i
$726$	17.8521i	0.662555i
$727$	46.0182	1.70672	0.853361	−	0.521321i	$-0.174561\pi$
$727$	46.0182	1.70672	0.853361	+	0.521321i	$0.174561\pi$
$728$	16.2500i	0.602264i
$729$	−29.9482	−1.10919
$730$	12.8709	0.476374
$731$	0	0
$732$	−1.34601	−0.0497498
$733$	2.55919	0.0945257	0.0472629	−	0.998882i	$-0.484950\pi$
$733$	2.55919	0.0945257	0.0472629	+	0.998882i	$0.484950\pi$
$734$	− 54.1586i	− 1.99903i
$735$	−9.15184	−0.337571
$736$	34.3746i	1.26707i
$737$	− 17.9561i	− 0.661420i
$738$	5.46373i	0.201123i
$739$	2.47667	0.0911057	0.0455528	−	0.998962i	$-0.485495\pi$
$739$	2.47667	0.0911057	0.0455528	+	0.998962i	$0.485495\pi$
$740$	16.2501	0.597366
$741$	7.18347i	0.263891i
$742$	47.9488i	1.76026i
$743$	1.59477i	0.0585064i	0.999572	+	0.0292532i	$0.00931291\pi$
$743$	1.59477i	0.0585064i	−0.999572	+	0.0292532i	$0.990687\pi$
$744$	13.8149	0.506478
$745$	18.5384i	0.679194i
$746$	−55.8114	−2.04340
$747$	−3.92957	−0.143776
$748$	0	0
$749$	−2.23222	−0.0815636
$750$	3.69096	0.134775
$751$	12.7441i	0.465041i	0.972592	+	0.232520i	$0.0746972\pi$
$751$	12.7441i	0.465041i	−0.972592	+	0.232520i	$0.925303\pi$
$752$	−15.9580	−0.581930
$753$	− 12.1981i	− 0.444523i
$754$	25.9463i	0.944908i
$755$	− 8.91261i	− 0.324363i
$756$	70.2207	2.55390
$757$	46.0573	1.67398	0.836991	−	0.547217i	$-0.184313\pi$
$757$	46.0573	1.67398	0.836991	+	0.547217i	$0.184313\pi$
$758$	7.00441i	0.254412i
$759$	34.4136i	1.24914i
$760$	− 13.0901i	− 0.474827i
$761$	−29.7003	−1.07664	−0.538318	−	0.842742i	$-0.680940\pi$
$761$	−29.7003	−1.07664	−0.538318	+	0.842742i	$0.680940\pi$
$762$	21.8426i	0.791273i
$763$	−22.1716	−0.802666
$764$	−51.7788	−1.87329
$765$	0	0
$766$	−57.4385	−2.07534
$767$	−5.62989	−0.203284
$768$	37.6063i	1.35700i
$769$	43.8299	1.58055	0.790273	−	0.612755i	$-0.209939\pi$
$769$	43.8299	1.58055	0.790273	+	0.612755i	$0.209939\pi$
$770$	20.9154i	0.753738i
$771$	− 12.6582i	− 0.455873i
$772$	− 29.6502i	− 1.06713i
$773$	27.9122	1.00393	0.501966	−	0.864887i	$-0.332610\pi$
$773$	27.9122	1.00393	0.501966	+	0.864887i	$0.332610\pi$
$774$	9.53437	0.342706
$775$	2.44403i	0.0877922i
$776$	35.3711i	1.26975i
$777$	− 25.8681i	− 0.928013i
$778$	3.97159	0.142388
$779$	− 15.7183i	− 0.563167i
$780$	−6.98014	−0.249929
$781$	4.56247	0.163258
$782$	0	0
$783$	48.6224	1.73762
$784$	−8.21211	−0.293289
$785$	18.2426i	0.651107i
$786$	−59.5010	−2.12233
$787$	− 30.0226i	− 1.07019i	−0.844792	−	0.535096i	$-0.820276\pi$
$787$	− 30.0226i	− 1.07019i	0.844792	−	0.535096i	$-0.179724\pi$
$788$	23.5953i	0.840549i
$789$	− 33.4667i	− 1.19144i
$790$	−21.2511	−0.756079
$791$	−57.5275	−2.04544
$792$	− 4.80300i	− 0.170667i
$793$	0.305891i	0.0108625i
$794$	− 74.1451i	− 2.63131i
$795$	−8.93178	−0.316778
$796$	66.6447i	2.36216i
$797$	5.16206	0.182850	0.0914249	−	0.995812i	$-0.470858\pi$
$797$	5.16206	0.182850	0.0914249	+	0.995812i	$0.470858\pi$
$798$	−48.0509	−1.70099
$799$	0	0
$800$	−3.89165	−0.137591
$801$	−1.17821	−0.0416301
$802$	11.9149i	0.420730i
$803$	−13.5861	−0.479445
$804$	40.0846i	1.41367i
$805$	− 31.6406i	− 1.11519i
$806$	− 7.23966i	− 0.255006i
$807$	−6.59417	−0.232126
$808$	19.6808	0.692369
$809$	− 22.2343i	− 0.781717i	−0.920451	−	0.390859i	$-0.872178\pi$
$809$	− 22.2343i	− 0.781717i	0.920451	−	0.390859i	$-0.127822\pi$
$810$	16.6987i	0.586731i
$811$	− 15.6644i	− 0.550051i	−0.961437	−	0.275026i	$-0.911314\pi$
$811$	− 15.6644i	− 0.550051i	0.961437	−	0.275026i	$-0.0886863\pi$
$812$	−110.804	−3.88847
$813$	− 38.7842i	− 1.36022i
$814$	−26.8676	−0.941710
$815$	−9.36510	−0.328045
$816$	0	0
$817$	−27.4289	−0.959615
$818$	61.4266	2.14773
$819$	− 2.42337i	− 0.0846793i
$820$	15.2734	0.533370
$821$	− 34.9393i	− 1.21939i	−0.792637	−	0.609694i	$-0.791292\pi$
$821$	− 34.9393i	− 1.21939i	0.792637	−	0.609694i	$-0.208708\pi$
$822$	− 63.2335i	− 2.20552i
$823$	2.44416i	0.0851980i	0.999092	+	0.0425990i	$0.0135638\pi$
$823$	2.44416i	0.0851980i	−0.999092	+	0.0425990i	$0.986436\pi$
$824$	−25.7916	−0.898492
$825$	−3.89606	−0.135643
$826$	− 37.6589i	− 1.31032i
$827$	− 50.8219i	− 1.76725i	−0.468194	−	0.883626i	$-0.655095\pi$
$827$	− 50.8219i	− 1.76725i	0.468194	−	0.883626i	$-0.344905\pi$
$828$	16.7550i	0.582275i
$829$	41.5846	1.44429	0.722147	−	0.691740i	$-0.243156\pi$
$829$	41.5846	1.44429	0.722147	+	0.691740i	$0.243156\pi$
$830$	17.2059i	0.597226i
$831$	−31.4854	−1.09222
$832$	15.0750	0.522631
$833$	0	0
$834$	−7.87308	−0.272623
$835$	−9.28133	−0.321194
$836$	31.8625i	1.10199i
$837$	−13.5668	−0.468939
$838$	− 17.1655i	− 0.592971i
$839$	− 4.44768i	− 0.153551i	−0.997048	−	0.0767755i	$-0.975538\pi$
$839$	− 4.44768i	− 0.153551i	0.997048	−	0.0767755i	$-0.0244625\pi$
$840$	− 20.2479i	− 0.698620i
$841$	−47.7235	−1.64564
$842$	49.5415	1.70731
$843$	39.5171i	1.36104i
$844$	23.3772i	0.804676i
$845$	− 11.4137i	− 0.392643i
$846$	14.3159	0.492191
$847$	17.3257i	0.595320i
$848$	−8.01465	−0.275224
$849$	13.3184	0.457088
$850$	0	0
$851$	40.6451	1.39330
$852$	−10.1851	−0.348937
$853$	17.8866i	0.612426i	0.951963	+	0.306213i	$0.0990619\pi$
$853$	17.8866i	0.612426i	−0.951963	+	0.306213i	$0.900938\pi$
$854$	−2.04614	−0.0700174
$855$	1.95213i	0.0667615i
$856$	− 2.24449i	− 0.0767150i
$857$	38.5585i	1.31713i	0.752523	+	0.658566i	$0.228837\pi$
$857$	38.5585i	1.31713i	−0.752523	+	0.658566i	$0.771163\pi$
$858$	11.5408	0.393997
$859$	−3.50985	−0.119755	−0.0598773	−	0.998206i	$-0.519071\pi$
$859$	−3.50985	−0.119755	−0.0598773	+	0.998206i	$0.519071\pi$
$860$	− 26.6525i	− 0.908843i
$861$	− 24.3133i	− 0.828595i
$862$	− 49.4916i	− 1.68569i
$863$	−21.9552	−0.747365	−0.373683	−	0.927557i	$-0.621905\pi$
$863$	−21.9552	−0.747365	−0.373683	+	0.927557i	$0.621905\pi$
$864$	− 21.6026i	− 0.734935i
$865$	4.29978	0.146197
$866$	87.3171	2.96715
$867$	0	0
$868$	30.9171	1.04940
$869$	22.4320	0.760952
$870$	− 32.3298i	− 1.09608i
$871$	9.10956	0.308666
$872$	− 22.2934i	− 0.754951i
$873$	− 5.27492i	− 0.178529i
$874$	− 75.4998i	− 2.55382i
$875$	3.58212	0.121098
$876$	30.3293	1.02473
$877$	− 5.65595i	− 0.190988i	−0.995430	−	0.0954939i	$-0.969557\pi$
$877$	− 5.65595i	− 0.190988i	0.995430	−	0.0954939i	$-0.0304431\pi$
$878$	1.10851i	0.0374105i
$879$	− 40.7832i	− 1.37558i
$880$	−3.49601	−0.117850
$881$	− 34.3915i	− 1.15868i	−0.815086	−	0.579340i	$-0.803311\pi$
$881$	− 34.3915i	− 1.15868i	0.815086	−	0.579340i	$-0.196689\pi$
$882$	7.36706	0.248062
$883$	58.3115	1.96234	0.981170	−	0.193148i	$-0.0618697\pi$
$883$	58.3115	1.96234	0.981170	+	0.193148i	$0.0618697\pi$
$884$	0	0
$885$	7.01500	0.235807
$886$	25.9295	0.871117
$887$	44.5012i	1.49420i	0.664710	+	0.747102i	$0.268555\pi$
$887$	44.5012i	1.49420i	−0.664710	+	0.747102i	$0.731445\pi$
$888$	26.0102	0.872846
$889$	21.1985i	0.710975i
$890$	5.15889i	0.172927i
$891$	− 17.6266i	− 0.590513i
$892$	−10.3918	−0.347944
$893$	−41.1847	−1.37819
$894$	68.4244i	2.28845i
$895$	0.117678i	0.00393354i
$896$	72.9573i	2.43733i
$897$	−17.4589	−0.582935
$898$	− 40.6015i	− 1.35489i
$899$	21.4077	0.713988
$900$	−1.89688	−0.0632292
$901$	0	0
$902$	−25.2527	−0.840824
$903$	−42.4274	−1.41190
$904$	− 57.8436i	− 1.92385i
$905$	2.32364	0.0772404
$906$	− 32.8961i	− 1.09290i
$907$	35.3726i	1.17453i	0.809396	+	0.587264i	$0.199795\pi$
$907$	35.3726i	1.17453i	−0.809396	+	0.587264i	$0.800205\pi$
$908$	76.0165i	2.52270i
$909$	−2.93501	−0.0973482
$910$	−10.6109	−0.351748
$911$	49.1810i	1.62944i	0.579856	+	0.814719i	$0.303109\pi$
$911$	49.1810i	1.62944i	−0.579856	+	0.814719i	$0.696891\pi$
$912$	− 8.03172i	− 0.265957i
$913$	− 18.1620i	− 0.601076i
$914$	26.5004	0.876554
$915$	− 0.381149i	− 0.0126004i
$916$	42.1685	1.39329
$917$	−57.7465	−1.90696
$918$	0	0
$919$	49.6635	1.63825	0.819123	−	0.573618i	$-0.194460\pi$
$919$	49.6635	1.63825	0.819123	+	0.573618i	$0.194460\pi$
$920$	31.8145	1.04889
$921$	− 26.5966i	− 0.876387i
$922$	70.5747	2.32425
$923$	2.31466i	0.0761878i
$924$	49.2854i	1.62137i
$925$	4.60155i	0.151298i
$926$	40.3568	1.32621
$927$	3.84631	0.126329
$928$	34.0877i	1.11898i
$929$	− 34.1165i	− 1.11933i	−0.828720	−	0.559664i	$-0.810930\pi$
$929$	− 34.1165i	− 1.11933i	0.828720	−	0.559664i	$-0.189070\pi$
$930$	9.02082i	0.295804i
$931$	−21.1939	−0.694601
$932$	− 35.5571i	− 1.16471i
$933$	26.9779	0.883216
$934$	−62.5405	−2.04639
$935$	0	0
$936$	2.43668	0.0796455
$937$	38.5275	1.25864	0.629319	−	0.777147i	$-0.283334\pi$
$937$	38.5275	1.25864	0.629319	+	0.777147i	$0.283334\pi$
$938$	60.9347i	1.98959i
$939$	−9.28250	−0.302923
$940$	− 40.0189i	− 1.30527i
$941$	− 37.1363i	− 1.21061i	−0.795994	−	0.605305i	$-0.793051\pi$
$941$	− 37.1363i	− 1.21061i	0.795994	−	0.605305i	$-0.206949\pi$
$942$	67.3328i	2.19382i
$943$	38.2022	1.24403
$944$	6.29469	0.204875
$945$	19.8844i	0.646840i
$946$	44.0667i	1.43273i
$947$	− 2.23113i	− 0.0725021i	−0.999343	−	0.0362510i	$-0.988458\pi$
$947$	− 2.23113i	− 0.0725021i	0.999343	−	0.0362510i	$-0.0115416\pi$
$948$	−50.0765	−1.62641
$949$	− 6.89259i	− 0.223743i
$950$	8.54755	0.277319
$951$	−1.00528	−0.0325986
$952$	0	0
$953$	25.8280	0.836651	0.418326	−	0.908297i	$-0.362617\pi$
$953$	25.8280	0.836651	0.418326	+	0.908297i	$0.362617\pi$
$954$	7.18992	0.232782
$955$	− 14.6622i	− 0.474458i
$956$	−58.7114	−1.89886
$957$	34.1264i	1.10315i
$958$	53.8823i	1.74086i
$959$	− 61.3689i	− 1.98171i
$960$	−18.7838	−0.606246
$961$	25.0267	0.807313
$962$	− 13.6306i	− 0.439469i
$963$	0.334721i	0.0107862i
$964$	20.9132i	0.673569i
$965$	8.39606	0.270279
$966$	− 116.784i	− 3.75747i
$967$	31.4013	1.00980	0.504899	−	0.863178i	$-0.331530\pi$
$967$	31.4013	1.00980	0.504899	+	0.863178i	$0.331530\pi$
$968$	−17.4209	−0.559930
$969$	0	0
$970$	−23.0966	−0.741587
$971$	−41.1265	−1.31981	−0.659906	−	0.751348i	$-0.729404\pi$
$971$	−41.1265	−1.31981	−0.659906	+	0.751348i	$0.729404\pi$
$972$	− 19.4602i	− 0.624185i
$973$	−7.64093	−0.244957
$974$	− 36.9567i	− 1.18417i
$975$	− 1.97657i	− 0.0633009i
$976$	− 0.342012i	− 0.0109475i
$977$	−27.8890	−0.892250	−0.446125	−	0.894971i	$-0.647196\pi$
$977$	−27.8890	−0.892250	−0.446125	+	0.894971i	$0.647196\pi$
$978$	−34.5662	−1.10530
$979$	− 5.44557i	− 0.174041i
$980$	− 20.5940i	− 0.657851i
$981$	3.32463i	0.106147i
$982$	−2.02071	−0.0644836
$983$	56.6933i	1.80824i	0.427283	+	0.904118i	$0.359471\pi$
$983$	56.6933i	1.80824i	−0.427283	+	0.904118i	$0.640529\pi$
$984$	24.4469	0.779338
$985$	−6.68150	−0.212890
$986$	0	0
$987$	−63.7050	−2.02775
$988$	−16.1647	−0.514266
$989$	− 66.6639i	− 2.11979i
$990$	3.13626	0.0996768
$991$	35.8868i	1.13998i	0.821651	+	0.569991i	$0.193053\pi$
$991$	35.8868i	1.13998i	−0.821651	+	0.569991i	$0.806947\pi$
$992$	− 9.51130i	− 0.301984i
$993$	18.3000i	0.580732i
$994$	−15.4830	−0.491090
$995$	−18.8718	−0.598276
$996$	40.5444i	1.28470i
$997$	32.9550i	1.04370i	0.853038	+	0.521848i	$0.174757\pi$
$997$	32.9550i	1.04370i	−0.853038	+	0.521848i	$0.825243\pi$
$998$	− 53.2461i	− 1.68548i
$999$	−25.5433	−0.808153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.2		24
17.4	even	4		1445.2.a.p.1.12		12
17.7	odd	16		85.2.l.a.36.6	yes	24
17.12	odd	16		85.2.l.a.26.6	✓	24
17.13	even	4		1445.2.a.q.1.12		12
17.16	even	2	inner	1445.2.d.j.866.1		24
51.29	even	16		765.2.be.b.451.1		24
51.41	even	16		765.2.be.b.631.1		24
85.4	even	4		7225.2.a.bs.1.1		12
85.7	even	16		425.2.n.c.274.1		24
85.12	even	16		425.2.n.f.349.6		24
85.24	odd	16		425.2.m.b.376.1		24
85.29	odd	16		425.2.m.b.26.1		24
85.58	even	16		425.2.n.f.274.6		24
85.63	even	16		425.2.n.c.349.1		24
85.64	even	4		7225.2.a.bq.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.6	✓	24	17.12	odd	16
85.2.l.a.36.6	yes	24	17.7	odd	16
425.2.m.b.26.1		24	85.29	odd	16
425.2.m.b.376.1		24	85.24	odd	16
425.2.n.c.274.1		24	85.7	even	16
425.2.n.c.349.1		24	85.63	even	16
425.2.n.f.274.6		24	85.58	even	16
425.2.n.f.349.6		24	85.12	even	16
765.2.be.b.451.1		24	51.29	even	16
765.2.be.b.631.1		24	51.41	even	16
1445.2.a.p.1.12		12	17.4	even	4
1445.2.a.q.1.12		12	17.13	even	4
1445.2.d.j.866.1		24	17.16	even	2	inner
1445.2.d.j.866.2		24	1.1	even	1	trivial
7225.2.a.bq.1.1		12	85.64	even	4
7225.2.a.bs.1.1		12	85.4	even	4

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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.35190 q^{2} -1.56935i q^{3} +3.53144 q^{4} +1.00000i q^{5} +3.69096i q^{6} +3.58212i q^{7} -3.60181 q^{8} +0.537139 q^{9} -2.35190i q^{10} +2.48259i q^{11} -5.54207i q^{12} -1.25948 q^{13} -8.42480i q^{14} +1.56935 q^{15} +1.40821 q^{16} -1.26330 q^{18} +3.63431 q^{19} +3.53144i q^{20} +5.62161 q^{21} -5.83882i q^{22} +8.83293i q^{23} +5.65249i q^{24} -1.00000 q^{25} +2.96218 q^{26} -5.55101i q^{27} +12.6501i q^{28} +8.75919i q^{29} -3.69096 q^{30} -2.44403i q^{31} +3.89165 q^{32} +3.89606 q^{33} -3.58212 q^{35} +1.89688 q^{36} -4.60155i q^{37} -8.54755 q^{38} +1.97657i q^{39} -3.60181i q^{40} -4.32497i q^{41} -13.2215 q^{42} -7.54720 q^{43} +8.76714i q^{44} +0.537139i q^{45} -20.7742i q^{46} -11.3322 q^{47} -2.20997i q^{48} -5.83161 q^{49} +2.35190 q^{50} -4.44779 q^{52} -5.69139 q^{53} +13.0554i q^{54} -2.48259 q^{55} -12.9021i q^{56} -5.70351i q^{57} -20.6008i q^{58} +4.47000 q^{59} +5.54207 q^{60} -0.242871i q^{61} +5.74812i q^{62} +1.92410i q^{63} -11.9692 q^{64} -1.25948i q^{65} -9.16315 q^{66} -7.23278 q^{67} +13.8620 q^{69} +8.42480 q^{70} -1.83778i q^{71} -1.93467 q^{72} +5.47256i q^{73} +10.8224i q^{74} +1.56935i q^{75} +12.8344 q^{76} -8.89296 q^{77} -4.64870i q^{78} -9.03570i q^{79} +1.40821i q^{80} -7.10006 q^{81} +10.1719i q^{82} -7.31575 q^{83} +19.8524 q^{84} +17.7503 q^{86} +13.7462 q^{87} -8.94182i q^{88} -2.19350 q^{89} -1.26330i q^{90} -4.51162i q^{91} +31.1930i q^{92} -3.83554 q^{93} +26.6522 q^{94} +3.63431i q^{95} -6.10736i q^{96} -9.82039i q^{97} +13.7154 q^{98} +1.33350i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

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