LMFDB - Embedded newform 945.2.g.b.944.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(944,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("945.944");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			944.12
Character	$\chi$	$=$	945.944
Dual form			945.2.g.b.944.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10299 q^{2} -0.783408 q^{4} +(0.826134 + 2.07786i) q^{5} +(-1.13699 + 2.38899i) q^{7} +3.07008 q^{8} +O(q^{10})$	\(q-1.10299 q^{2} -0.783408 q^{4} +(0.826134 + 2.07786i) q^{5} +(-1.13699 + 2.38899i) q^{7} +3.07008 q^{8} +(-0.911219 - 2.29186i) q^{10} -2.51652i q^{11} +6.14019 q^{13} +(1.25409 - 2.63503i) q^{14} -1.81945 q^{16} -2.69458i q^{17} +2.85713i q^{19} +(-0.647200 - 1.62781i) q^{20} +2.77570i q^{22} +4.90893 q^{23} +(-3.63501 + 3.43318i) q^{25} -6.77258 q^{26} +(0.890727 - 1.87155i) q^{28} -3.39359i q^{29} +3.91879i q^{31} -4.13331 q^{32} +2.97210i q^{34} +(-5.90328 - 0.388883i) q^{35} +6.43269i q^{37} -3.15139i q^{38} +(2.53629 + 6.37919i) q^{40} +0.647200 q^{41} +10.8492i q^{43} +1.97146i q^{44} -5.41451 q^{46} +0.270910i q^{47} +(-4.41451 - 5.43250i) q^{49} +(4.00938 - 3.78677i) q^{50} -4.81027 q^{52} -12.8879 q^{53} +(5.22897 - 2.07898i) q^{55} +(-3.49065 + 7.33437i) q^{56} +3.74310i q^{58} +14.4011 q^{59} -8.83960i q^{61} -4.32239i q^{62} +8.19792 q^{64} +(5.07262 + 12.7584i) q^{65} +6.34657i q^{67} +2.11096i q^{68} +(6.51128 + 0.428934i) q^{70} +13.3887i q^{71} +13.0352 q^{73} -7.09520i q^{74} -2.23830i q^{76} +(6.01192 + 2.86125i) q^{77} -8.30606 q^{79} +(-1.50311 - 3.78057i) q^{80} -0.713857 q^{82} +8.24330i q^{83} +(5.59896 - 2.22608i) q^{85} -11.9665i q^{86} -7.72590i q^{88} +3.46804 q^{89} +(-6.98133 + 14.6688i) q^{91} -3.84570 q^{92} -0.298812i q^{94} +(-5.93671 + 2.36037i) q^{95} -13.2244 q^{97} +(4.86917 + 5.99201i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4}+O(q^{10}) $ 32 * q + 32 * q^4	$ 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) $ 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.10299			−0.779933			−0.389967	−	0.920829i	$-0.627513\pi$
$2$	−1.10299			−0.779933			−0.389967	+	0.920829i	$0.627513\pi$
$3$		0			0
$3$		0			0
$4$	−0.783408			−0.391704
$5$	0.826134	+	2.07786i	0.369458	+	0.929247i
$5$	0.826134	+	2.07786i	0.369458	+	0.929247i
$6$		0			0
$7$	−1.13699	+	2.38899i	−0.429742	+	0.902952i
$7$	−1.13699	+	2.38899i	−0.429742	+	0.902952i
$8$	3.07008			1.08544
$9$		0			0
$10$	−0.911219	−	2.29186i	−0.288153	−	0.724751i
$11$		−	2.51652i		−	0.758758i	−0.925241	−	0.379379i	$-0.876138\pi$
$11$		−	2.51652i		−	0.758758i	0.925241	−	0.379379i	$-0.123862\pi$
$12$		0			0
$13$	6.14019			1.70298			0.851491	−	0.524370i	$-0.175699\pi$
$13$	6.14019			1.70298			0.851491	+	0.524370i	$0.175699\pi$
$14$	1.25409	−	2.63503i	0.335170	−	0.704242i
$15$		0			0
$16$	−1.81945			−0.454864
$17$		−	2.69458i		−	0.653532i	−0.945105	−	0.326766i	$-0.894041\pi$
$17$		−	2.69458i		−	0.653532i	0.945105	−	0.326766i	$-0.105959\pi$
$18$		0			0
$19$			2.85713i			0.655470i	0.944770	+	0.327735i	$0.106285\pi$
$19$			2.85713i			0.655470i	−0.944770	+	0.327735i	$0.893715\pi$
$20$	−0.647200	−	1.62781i	−0.144718	−	0.363990i
$21$		0			0
$22$			2.77570i			0.591781i
$23$	4.90893			1.02358			0.511791	−	0.859110i	$-0.328982\pi$
$23$	4.90893			1.02358			0.511791	+	0.859110i	$0.328982\pi$
$24$		0			0
$25$	−3.63501	+	3.43318i	−0.727001	+	0.686636i
$26$	−6.77258			−1.32821
$27$		0			0
$28$	0.890727	−	1.87155i	0.168332	−	0.353690i
$29$		−	3.39359i		−	0.630174i	−0.949063	−	0.315087i	$-0.897966\pi$
$29$		−	3.39359i		−	0.630174i	0.949063	−	0.315087i	$-0.102034\pi$
$30$		0			0
$31$			3.91879i			0.703835i	0.936031	+	0.351918i	$0.114470\pi$
$31$			3.91879i			0.703835i	−0.936031	+	0.351918i	$0.885530\pi$
$32$	−4.13331			−0.730673
$33$		0			0
$34$			2.97210i			0.509711i
$35$	−5.90328	−	0.388883i	−0.997837	−	0.0657331i
$36$		0			0
$37$			6.43269i			1.05753i	0.848769	+	0.528764i	$0.177344\pi$
$37$			6.43269i			1.05753i	−0.848769	+	0.528764i	$0.822656\pi$
$38$		−	3.15139i		−	0.511223i
$39$		0			0
$40$	2.53629	+	6.37919i	0.401023	+	1.00864i
$41$	0.647200			0.101076			0.0505378	−	0.998722i	$-0.483906\pi$
$41$	0.647200			0.101076			0.0505378	+	0.998722i	$0.483906\pi$
$42$		0			0
$43$			10.8492i			1.65448i	0.561848	+	0.827240i	$0.310091\pi$
$43$			10.8492i			1.65448i	−0.561848	+	0.827240i	$0.689909\pi$
$44$			1.97146i			0.297209i
$45$		0			0
$46$	−5.41451			−0.798326
$47$			0.270910i			0.0395163i	0.999805	+	0.0197581i	$0.00628962\pi$
$47$			0.270910i			0.0395163i	−0.999805	+	0.0197581i	$0.993710\pi$
$48$		0			0
$49$	−4.41451	−	5.43250i	−0.630644	−	0.776072i
$50$	4.00938	−	3.78677i	0.567012	−	0.535530i
$51$		0			0
$52$	−4.81027			−0.667065
$53$	−12.8879			−1.77029			−0.885147	−	0.465311i	$-0.845942\pi$
$53$	−12.8879			−1.77029			−0.885147	+	0.465311i	$0.845942\pi$
$54$		0			0
$55$	5.22897	−	2.07898i	0.705074	−	0.280329i
$56$	−3.49065	+	7.33437i	−0.466457	+	0.980097i
$57$		0			0
$58$			3.74310i			0.491494i
$59$	14.4011			1.87486			0.937430	−	0.348174i	$-0.113198\pi$
$59$	14.4011			1.87486			0.937430	+	0.348174i	$0.113198\pi$
$60$		0			0
$61$		−	8.83960i		−	1.13179i	−0.824476	−	0.565897i	$-0.808530\pi$
$61$		−	8.83960i		−	1.13179i	0.824476	−	0.565897i	$-0.191470\pi$
$62$		−	4.32239i		−	0.548944i
$63$		0			0
$64$	8.19792			1.02474
$65$	5.07262	+	12.7584i	0.629181	+	1.58249i
$66$		0			0
$67$			6.34657i			0.775357i	0.921795	+	0.387679i	$0.126723\pi$
$67$			6.34657i			0.775357i	−0.921795	+	0.387679i	$0.873277\pi$
$68$			2.11096i			0.255991i
$69$		0			0
$70$	6.51128	+	0.428934i	0.778246	+	0.0512675i
$71$			13.3887i			1.58894i	0.607302	+	0.794471i	$0.292252\pi$
$71$			13.3887i			1.58894i	−0.607302	+	0.794471i	$0.707748\pi$
$72$		0			0
$73$	13.0352			1.52566			0.762828	−	0.646601i	$-0.223810\pi$
$73$	13.0352			1.52566			0.762828	+	0.646601i	$0.223810\pi$
$74$		−	7.09520i		−	0.824801i
$75$		0			0
$76$		−	2.23830i		−	0.256750i
$77$	6.01192	+	2.86125i	0.685122	+	0.326070i
$78$		0			0
$79$	−8.30606			−0.934505			−0.467252	−	0.884124i	$-0.654756\pi$
$79$	−8.30606			−0.934505			−0.467252	+	0.884124i	$0.654756\pi$
$80$	−1.50311	−	3.78057i	−0.168053	−	0.422681i
$81$		0			0
$82$	−0.713857			−0.0788323
$83$			8.24330i			0.904820i	0.891810	+	0.452410i	$0.149436\pi$
$83$			8.24330i			0.904820i	−0.891810	+	0.452410i	$0.850564\pi$
$84$		0			0
$85$	5.59896	−	2.22608i	0.607292	−	0.241453i
$86$		−	11.9665i		−	1.29038i
$87$		0			0
$88$		−	7.72590i		−	0.823584i
$89$	3.46804			0.367612			0.183806	−	0.982963i	$-0.441158\pi$
$89$	3.46804			0.367612			0.183806	+	0.982963i	$0.441158\pi$
$90$		0			0
$91$	−6.98133	+	14.6688i	−0.731842	+	1.53771i
$92$	−3.84570			−0.400942
$93$		0			0
$94$		−	0.298812i		−	0.0308201i
$95$	−5.93671	+	2.36037i	−0.609094	+	0.242169i
$96$		0			0
$97$	−13.2244			−1.34274			−0.671369	−	0.741123i	$-0.734293\pi$
$97$	−13.2244			−1.34274			−0.671369	+	0.741123i	$0.734293\pi$
$98$	4.86917	+	5.99201i	0.491860	+	0.605284i
$99$		0			0
$100$	2.84769	−	2.68958i	0.284769	−	0.268958i
$101$	−3.51325			−0.349581			−0.174791	−	0.984606i	$-0.555925\pi$
$101$	−3.51325			−0.349581			−0.174791	+	0.984606i	$0.555925\pi$
$102$		0			0
$103$	−1.86342			−0.183608			−0.0918042	−	0.995777i	$-0.529263\pi$
$103$	−1.86342			−0.183608			−0.0918042	+	0.995777i	$0.529263\pi$
$104$	18.8508			1.84848
$105$		0			0
$106$	14.2153			1.38071
$107$	8.26662			0.799164			0.399582	−	0.916697i	$-0.369155\pi$
$107$	8.26662			0.799164			0.399582	+	0.916697i	$0.369155\pi$
$108$		0			0
$109$	−4.56682			−0.437422			−0.218711	−	0.975790i	$-0.570185\pi$
$109$	−4.56682			−0.437422			−0.218711	+	0.975790i	$0.570185\pi$
$110$	−5.76751	+	2.29310i	−0.549911	+	0.218638i
$111$		0			0
$112$	2.06870	−	4.34665i	0.195474	−	0.410720i
$113$	−12.2406			−1.15149			−0.575747	−	0.817628i	$-0.695289\pi$
$113$	−12.2406			−1.15149			−0.575747	+	0.817628i	$0.695289\pi$
$114$		0			0
$115$	4.05543	+	10.2001i	0.378171	+	0.951161i
$116$			2.65857i			0.246842i
$117$		0			0
$118$	−15.8843			−1.46227
$119$	6.43731	+	3.06371i	0.590108	+	0.280850i
$120$		0			0
$121$	4.66715			0.424286
$122$			9.75000i			0.882724i
$123$		0			0
$124$		−	3.07001i		−	0.275695i
$125$	−10.1367	−	4.71677i	−0.906651	−	0.421880i
$126$		0			0
$127$			11.1889i			0.992855i	0.868078	+	0.496427i	$0.165355\pi$
$127$			11.1889i			0.992855i	−0.868078	+	0.496427i	$0.834645\pi$
$128$	−0.775619			−0.0685556
$129$		0			0
$130$	−5.59506	−	14.0725i	−0.490719	−	1.23424i
$131$	9.07205			0.792628			0.396314	−	0.918115i	$-0.370289\pi$
$131$	9.07205			0.792628			0.396314	+	0.918115i	$0.370289\pi$
$132$		0			0
$133$	−6.82564	−	3.24852i	−0.591858	−	0.281683i
$134$		−	7.00022i		−	0.604727i
$135$		0			0
$136$		−	8.27257i		−	0.709367i
$137$	−0.457202			−0.0390614			−0.0195307	−	0.999809i	$-0.506217\pi$
$137$	−0.457202			−0.0390614			−0.0195307	+	0.999809i	$0.506217\pi$
$138$		0			0
$139$			3.05803i			0.259378i	0.991555	+	0.129689i	$0.0413980\pi$
$139$			3.05803i			0.259378i	−0.991555	+	0.129689i	$0.958602\pi$
$140$	4.62468	+	0.304654i	0.390857	+	0.0257479i
$141$		0			0
$142$		−	14.7676i		−	1.23927i
$143$		−	15.4519i		−	1.29215i
$144$		0			0
$145$	7.05141	−	2.80356i	0.585587	−	0.232823i
$146$	−14.3777			−1.18991
$147$		0			0
$148$		−	5.03942i		−	0.414238i
$149$			4.25094i			0.348251i	0.984724	+	0.174125i	$0.0557098\pi$
$149$			4.25094i			0.348251i	−0.984724	+	0.174125i	$0.944290\pi$
$150$		0			0
$151$	−10.8368			−0.881889			−0.440944	−	0.897534i	$-0.645356\pi$
$151$	−10.8368			−0.881889			−0.440944	+	0.897534i	$0.645356\pi$
$152$			8.77160i			0.711471i
$153$		0			0
$154$	−6.63110	−	3.15594i	−0.534349	−	0.254313i
$155$	−8.14269	+	3.23744i	−0.654037	+	0.260038i
$156$		0			0
$157$	−6.40250			−0.510975			−0.255488	−	0.966812i	$-0.582236\pi$
$157$	−6.40250			−0.510975			−0.255488	+	0.966812i	$0.582236\pi$
$158$	9.16152			0.728851
$159$		0			0
$160$	−3.41467	−	8.58844i	−0.269953	−	0.678976i
$161$	−5.58140	+	11.7274i	−0.439876	+	0.924246i
$162$		0			0
$163$		−	6.43269i		−	0.503847i	−0.967747	−	0.251923i	$-0.918937\pi$
$163$		−	6.43269i		−	0.503847i	0.967747	−	0.251923i	$-0.0810631\pi$
$164$	−0.507022			−0.0395918
$165$		0			0
$166$		−	9.09230i		−	0.705699i
$167$			4.07782i			0.315551i	0.987475	+	0.157775i	$0.0504322\pi$
$167$			4.07782i			0.315551i	−0.987475	+	0.157775i	$0.949568\pi$
$168$		0			0
$169$	24.7019			1.90015
$170$	−6.17561	+	2.45535i	−0.473648	+	0.188317i
$171$		0			0
$172$		−	8.49932i		−	0.648067i
$173$		−	17.0341i		−	1.29508i	−0.762031	−	0.647540i	$-0.775798\pi$
$173$		−	17.0341i		−	1.29508i	0.762031	−	0.647540i	$-0.224202\pi$
$174$		0			0
$175$	−4.06886	−	12.5875i	−0.307577	−	0.951523i
$176$			4.57869i			0.345131i
$177$		0			0
$178$	−3.82522			−0.286713
$179$		−	5.12374i		−	0.382967i	−0.981496	−	0.191483i	$-0.938670\pi$
$179$		−	5.12374i		−	0.382967i	0.981496	−	0.191483i	$-0.0613298\pi$
$180$		0			0
$181$			9.60245i			0.713744i	0.934153	+	0.356872i	$0.116157\pi$
$181$			9.60245i			0.713744i	−0.934153	+	0.356872i	$0.883843\pi$
$182$	7.70035	−	16.1796i	0.570788	−	1.19931i
$183$		0			0
$184$	15.0708			1.11103
$185$	−13.3662	+	5.31426i	−0.982704	+	0.390712i
$186$		0			0
$187$	−6.78095			−0.495872
$188$		−	0.212233i		−	0.0154787i
$189$		0			0
$190$	6.54814	−	2.60347i	0.475052	−	0.188875i
$191$		−	7.71559i		−	0.558281i	−0.960250	−	0.279140i	$-0.909951\pi$
$191$		−	7.71559i		−	0.558281i	0.960250	−	0.279140i	$-0.0900495\pi$
$192$		0			0
$193$		−	3.46300i		−	0.249273i	−0.992203	−	0.124636i	$-0.960224\pi$
$193$		−	3.46300i		−	0.249273i	0.992203	−	0.124636i	$-0.0397764\pi$
$194$	14.5865			1.04725
$195$		0			0
$196$	3.45836	+	4.25587i	0.247026	+	0.303991i
$197$	−13.2153			−0.941552			−0.470776	−	0.882253i	$-0.656026\pi$
$197$	−13.2153			−0.941552			−0.470776	+	0.882253i	$0.656026\pi$
$198$		0			0
$199$		−	15.7475i		−	1.11631i	−0.829735	−	0.558157i	$-0.811509\pi$
$199$		−	15.7475i		−	1.11631i	0.829735	−	0.558157i	$-0.188491\pi$
$200$	−11.1597	+	10.5401i	−0.789113	+	0.745300i
$201$		0			0
$202$	3.87509			0.272650
$203$	8.10724	+	3.85848i	0.569017	+	0.270812i
$204$		0			0
$205$	0.534674	+	1.34479i	0.0373432	+	0.0939243i
$206$	2.05534			0.143202
$207$		0			0
$208$	−11.1718			−0.774624
$209$	7.19000			0.497343
$210$		0			0
$211$	18.9266			1.30296			0.651481	−	0.758665i	$-0.274148\pi$
$211$	18.9266			1.30296			0.651481	+	0.758665i	$0.274148\pi$
$212$	10.0965			0.693432
$213$		0			0
$214$	−9.11802			−0.623295
$215$	−22.5430	+	8.96286i	−1.53742	+	0.611262i
$216$		0			0
$217$	−9.36193	−	4.45562i	−0.635529	−	0.302467i
$218$	5.03716			0.341160
$219$		0			0
$220$	−4.09642	+	1.62869i	−0.276180	+	0.109806i
$221$		−	16.5452i		−	1.11295i
$222$		0			0
$223$	25.5048			1.70793			0.853964	−	0.520332i	$-0.174192\pi$
$223$	25.5048			1.70793			0.853964	+	0.520332i	$0.174192\pi$
$224$	4.69953	−	9.87442i	0.314001	−	0.659763i
$225$		0			0
$226$	13.5012			0.898089
$227$			16.3712i			1.08659i	0.839540	+	0.543297i	$0.182824\pi$
$227$			16.3712i			1.08659i	−0.839540	+	0.543297i	$0.817176\pi$
$228$		0			0
$229$			26.4117i			1.74533i	0.488318	+	0.872666i	$0.337611\pi$
$229$			26.4117i			1.74533i	−0.488318	+	0.872666i	$0.662389\pi$
$230$	−4.47311	−	11.2506i	−0.294948	−	0.741842i
$231$		0			0
$232$		−	10.4186i		−	0.684014i
$233$	13.7123			0.898321			0.449160	−	0.893451i	$-0.351723\pi$
$233$	13.7123			0.898321			0.449160	+	0.893451i	$0.351723\pi$
$234$		0			0
$235$	−0.562913	+	0.223808i	−0.0367204	+	0.0145996i
$236$	−11.2819			−0.734390
$237$		0			0
$238$	−7.10031	−	3.37925i	−0.460244	−	0.219044i
$239$		−	25.5169i		−	1.65055i	−0.564730	−	0.825276i	$-0.691020\pi$
$239$		−	25.5169i		−	1.65055i	0.564730	−	0.825276i	$-0.308980\pi$
$240$		0			0
$241$		−	3.91879i		−	0.252431i	−0.992003	−	0.126216i	$-0.959717\pi$
$241$		−	3.91879i		−	0.252431i	0.992003	−	0.126216i	$-0.0402831\pi$
$242$	−5.14783			−0.330915
$243$		0			0
$244$			6.92501i			0.443329i
$245$	7.64101	−	13.6607i	0.488166	−	0.872751i
$246$		0			0
$247$			17.5433i			1.11625i
$248$			12.0310i			0.763968i
$249$		0			0
$250$	11.1807	+	5.20256i	0.707128	+	0.329039i
$251$	2.19552			0.138580			0.0692900	−	0.997597i	$-0.477927\pi$
$251$	2.19552			0.138580			0.0692900	+	0.997597i	$0.477927\pi$
$252$		0			0
$253$		−	12.3534i		−	0.776651i
$254$		−	12.3413i		−	0.774360i
$255$		0			0
$256$	−15.5403			−0.971271
$257$		−	19.5921i		−	1.22212i	−0.791583	−	0.611062i	$-0.790743\pi$
$257$		−	19.5921i		−	1.22212i	0.791583	−	0.611062i	$-0.209257\pi$
$258$		0			0
$259$	−15.3676	−	7.31390i	−0.954896	−	0.454463i
$260$	−3.97393	−	9.99508i	−0.246453	−	0.619868i
$261$		0			0
$262$	−10.0064			−0.618197
$263$	−8.67351			−0.534832			−0.267416	−	0.963581i	$-0.586170\pi$
$263$	−8.67351			−0.534832			−0.267416	+	0.963581i	$0.586170\pi$
$264$		0			0
$265$	−10.6472	−	26.7793i	−0.654050	−	1.64504i
$266$	7.52862	+	3.58309i	0.461609	+	0.219694i
$267$		0			0
$268$		−	4.97196i		−	0.303711i
$269$	0.483693			0.0294913			0.0147456	−	0.999891i	$-0.495306\pi$
$269$	0.483693			0.0294913			0.0147456	+	0.999891i	$0.495306\pi$
$270$		0			0
$271$		−	21.5291i		−	1.30780i	−0.756581	−	0.653900i	$-0.773132\pi$
$271$		−	21.5291i		−	1.30780i	0.756581	−	0.653900i	$-0.226868\pi$
$272$			4.90267i			0.297268i
$273$		0			0
$274$	0.504290			0.0304653
$275$	8.63965	+	9.14755i	0.520991	+	0.551618i
$276$		0			0
$277$		−	30.9285i		−	1.85831i	−0.369690	−	0.929155i	$-0.620536\pi$
$277$		−	30.9285i		−	1.85831i	0.369690	−	0.929155i	$-0.379464\pi$
$278$		−	3.37298i		−	0.202298i
$279$		0			0
$280$	−18.1235	−	1.19390i	−1.08309	−	0.0713491i
$281$		−	17.0903i		−	1.01952i	−0.860316	−	0.509760i	$-0.829734\pi$
$281$		−	17.0903i		−	1.01952i	0.860316	−	0.509760i	$-0.170266\pi$
$282$		0			0
$283$	−4.09642			−0.243507			−0.121753	−	0.992560i	$-0.538852\pi$
$283$	−4.09642			−0.243507			−0.121753	+	0.992560i	$0.538852\pi$
$284$		−	10.4888i		−	0.622395i
$285$		0			0
$286$			17.0433i			1.00779i
$287$	−0.735860	+	1.54615i	−0.0434364	+	0.0912665i
$288$		0			0
$289$	9.73924			0.572897
$290$	−7.77765	+	3.09230i	−0.456719	+	0.181586i
$291$		0			0
$292$	−10.2119			−0.597606
$293$			12.7535i			0.745070i	0.928018	+	0.372535i	$0.121511\pi$
$293$			12.7535i			0.745070i	−0.928018	+	0.372535i	$0.878489\pi$
$294$		0			0
$295$	11.8972	+	29.9234i	0.692682	+	1.74221i
$296$			19.7488i			1.14788i
$297$		0			0
$298$		−	4.68875i		−	0.271612i
$299$	30.1417			1.74314
$300$		0			0
$301$	−25.9185	−	12.3354i	−1.49392	−	0.710999i
$302$	11.9529			0.687814
$303$		0			0
$304$		−	5.19841i		−	0.298149i
$305$	18.3674	−	7.30269i	1.05172	−	0.418151i
$306$		0			0
$307$	14.9649			0.854092			0.427046	−	0.904230i	$-0.359554\pi$
$307$	14.9649			0.854092			0.427046	+	0.904230i	$0.359554\pi$
$308$	−4.70979	−	2.24153i	−0.268365	−	0.127723i
$309$		0			0
$310$	8.98133	−	3.57087i	0.510105	−	0.202812i
$311$	−14.5269			−0.823745			−0.411872	−	0.911242i	$-0.635125\pi$
$311$	−14.5269			−0.823745			−0.411872	+	0.911242i	$0.635125\pi$
$312$		0			0
$313$	14.7846			0.835673			0.417836	−	0.908522i	$-0.362789\pi$
$313$	14.7846			0.835673			0.417836	+	0.908522i	$0.362789\pi$
$314$	7.06191			0.398527
$315$		0			0
$316$	6.50704			0.366049
$317$	−2.07616			−0.116609			−0.0583043	−	0.998299i	$-0.518569\pi$
$317$	−2.07616			−0.116609			−0.0583043	+	0.998299i	$0.518569\pi$
$318$		0			0
$319$	−8.54002			−0.478150
$320$	6.77258	+	17.0341i	0.378599	+	0.952237i
$321$		0			0
$322$	6.15624	−	12.9352i	0.343074	−	0.720850i
$323$	7.69875			0.428370
$324$		0			0
$325$	−22.3196	+	21.0804i	−1.23807	+	1.16933i
$326$			7.09520i			0.392967i
$327$		0			0
$328$	1.98695			0.109711
$329$	−0.647200	−	0.308022i	−0.0356813	−	0.0169818i
$330$		0			0
$331$	−4.25946			−0.234121			−0.117061	−	0.993125i	$-0.537347\pi$
$331$	−4.25946			−0.234121			−0.117061	+	0.993125i	$0.537347\pi$
$332$		−	6.45787i		−	0.354422i
$333$		0			0
$334$		−	4.49780i		−	0.246109i
$335$	−13.1873	+	5.24312i	−0.720499	+	0.286462i
$336$		0			0
$337$			17.3680i			0.946093i	0.881037	+	0.473046i	$0.156846\pi$
$337$			17.3680i			0.946093i	−0.881037	+	0.473046i	$0.843154\pi$
$338$	−27.2460			−1.48199
$339$		0			0
$340$	−4.38627	+	1.74393i	−0.237879	+	0.0945780i
$341$	9.86169			0.534041
$342$		0			0
$343$	17.9974	−	4.36951i	0.971770	−	0.235931i
$344$			33.3078i			1.79583i
$345$		0			0
$346$			18.7885i			1.01008i
$347$	−22.9829			−1.23378			−0.616892	−	0.787048i	$-0.711609\pi$
$347$	−22.9829			−1.23378			−0.616892	+	0.787048i	$0.711609\pi$
$348$		0			0
$349$			19.5394i			1.04592i	0.852358	+	0.522959i	$0.175172\pi$
$349$			19.5394i			1.04592i	−0.852358	+	0.522959i	$0.824828\pi$
$350$	4.48792	+	13.8839i	0.239889	+	0.742125i
$351$		0			0
$352$			10.4015i			0.554404i
$353$			19.5729i			1.04176i	0.853630	+	0.520880i	$0.174396\pi$
$353$			19.5729i			1.04176i	−0.853630	+	0.520880i	$0.825604\pi$
$354$		0			0
$355$	−27.8198	+	11.0608i	−1.47652	+	0.587048i
$356$	−2.71689			−0.143995
$357$		0			0
$358$			5.65145i			0.298688i
$359$		−	6.38418i		−	0.336944i	−0.985706	−	0.168472i	$-0.946117\pi$
$359$		−	6.38418i		−	0.336944i	0.985706	−	0.168472i	$-0.0538833\pi$
$360$		0			0
$361$	10.8368			0.570359
$362$		−	10.5914i		−	0.556673i
$363$		0			0
$364$	5.46923	−	11.4917i	0.286666	−	0.602328i
$365$	10.7688	+	27.0854i	0.563666	+	1.41771i
$366$		0			0
$367$	5.98307			0.312314			0.156157	−	0.987732i	$-0.450089\pi$
$367$	5.98307			0.312314			0.156157	+	0.987732i	$0.450089\pi$
$368$	−8.93157			−0.465591
$369$		0			0
$370$	14.7428	−	5.86159i	0.766444	−	0.304729i
$371$	14.6534	−	30.7891i	0.760769	−	1.59849i
$372$		0			0
$373$		−	0.447616i		−	0.0231767i	−0.999933	−	0.0115883i	$-0.996311\pi$
$373$		−	0.447616i		−	0.0231767i	0.999933	−	0.0115883i	$-0.00368876\pi$
$374$	7.47934			0.386747
$375$		0			0
$376$			0.831715i			0.0428924i
$377$		−	20.8373i		−	1.07317i
$378$		0			0
$379$	19.2234			0.987440			0.493720	−	0.869621i	$-0.335637\pi$
$379$	19.2234			0.987440			0.493720	+	0.869621i	$0.335637\pi$
$380$	4.65087	−	1.84913i	0.238584	−	0.0948585i
$381$		0			0
$382$			8.51024i			0.435422i
$383$		−	37.5516i		−	1.91880i	−0.282055	−	0.959398i	$-0.591016\pi$
$383$		−	37.5516i		−	1.91880i	0.282055	−	0.959398i	$-0.408984\pi$
$384$		0			0
$385$	−0.978629	+	14.8557i	−0.0498756	+	0.757117i
$386$			3.81967i			0.194416i
$387$		0			0
$388$	10.3601			0.525956
$389$			15.2138i			0.771370i	0.922630	+	0.385685i	$0.126035\pi$
$389$			15.2138i			0.771370i	−0.922630	+	0.385685i	$0.873965\pi$
$390$		0			0
$391$		−	13.2275i		−	0.668943i
$392$	−13.5529	−	16.6782i	−0.684524	−	0.842377i
$393$		0			0
$394$	14.5764			0.734348
$395$	−6.86192	−	17.2588i	−0.345260	−	0.868386i
$396$		0			0
$397$	26.0383			1.30683			0.653413	−	0.757002i	$-0.273337\pi$
$397$	26.0383			1.30683			0.653413	+	0.757002i	$0.273337\pi$
$398$			17.3694i			0.870650i
$399$		0			0
$400$	6.61373	−	6.24652i	0.330686	−	0.312326i
$401$			20.1801i			1.00775i	0.863777	+	0.503874i	$0.168092\pi$
$401$			20.1801i			1.00775i	−0.863777	+	0.503874i	$0.831908\pi$
$402$		0			0
$403$			24.0621i			1.19862i
$404$	2.75231			0.136932
$405$		0			0
$406$	−8.94222	−	4.25587i	−0.443795	−	0.211215i
$407$	16.1880			0.802407
$408$		0			0
$409$		−	17.6119i		−	0.870851i	−0.900225	−	0.435426i	$-0.856598\pi$
$409$		−	17.6119i		−	0.870851i	0.900225	−	0.435426i	$-0.143402\pi$
$410$	−0.589741	−	1.48329i	−0.0291252	−	0.0732547i
$411$		0			0
$412$	1.45982			0.0719202
$413$	−16.3739	+	34.4040i	−0.805705	+	1.69291i
$414$		0			0
$415$	−17.1284	+	6.81007i	−0.840802	+	0.334293i
$416$	−25.3793			−1.24432
$417$		0			0
$418$	−7.93052			−0.387894
$419$	−22.7220			−1.11004			−0.555020	−	0.831837i	$-0.687290\pi$
$419$	−22.7220			−1.11004			−0.555020	+	0.831837i	$0.687290\pi$
$420$		0			0
$421$	10.8984			0.531154			0.265577	−	0.964090i	$-0.414438\pi$
$421$	10.8984			0.531154			0.265577	+	0.964090i	$0.414438\pi$
$422$	−20.8759			−1.01622
$423$		0			0
$424$	−39.5670			−1.92154
$425$	9.25098	+	9.79481i	0.448738	+	0.475118i
$426$		0			0
$427$	21.1177	+	10.0505i	1.02196	+	0.486379i
$428$	−6.47614			−0.313036
$429$		0			0
$430$	24.8648	−	9.88596i	1.19909	−	0.476743i
$431$			23.2417i			1.11951i	0.828657	+	0.559756i	$0.189105\pi$
$431$			23.2417i			1.11951i	−0.828657	+	0.559756i	$0.810895\pi$
$432$		0			0
$433$	−37.1123			−1.78350			−0.891752	−	0.452524i	$-0.850524\pi$
$433$	−37.1123			−1.78350			−0.891752	+	0.452524i	$0.850524\pi$
$434$	10.3261	+	4.91451i	0.495670	+	0.235904i
$435$		0			0
$436$	3.57768			0.171340
$437$			14.0254i			0.670927i
$438$		0			0
$439$		−	3.05648i		−	0.145878i	−0.997336	−	0.0729389i	$-0.976762\pi$
$439$		−	3.05648i		−	0.145878i	0.997336	−	0.0729389i	$-0.0232378\pi$
$440$	16.0533	−	6.38263i	0.765313	−	0.304280i
$441$		0			0
$442$			18.2492i			0.868028i
$443$	19.5456			0.928642			0.464321	−	0.885667i	$-0.346298\pi$
$443$	19.5456			0.928642			0.464321	+	0.885667i	$0.346298\pi$
$444$		0			0
$445$	2.86507	+	7.20611i	0.135817	+	0.341602i
$446$	−28.1316			−1.33207
$447$		0			0
$448$	−9.32095	+	19.5847i	−0.440373	+	0.925291i
$449$		−	15.4551i		−	0.729372i	−0.931131	−	0.364686i	$-0.881176\pi$
$449$		−	15.4551i		−	0.729372i	0.931131	−	0.364686i	$-0.118824\pi$
$450$		0			0
$451$		−	1.62869i		−	0.0766920i
$452$	9.58935			0.451045
$453$		0			0
$454$		−	18.0573i		−	0.847471i
$455$	−36.2473	−	2.38781i	−1.69930	−	0.111942i
$456$		0			0
$457$		−	25.9922i		−	1.21586i	−0.793989	−	0.607932i	$-0.791999\pi$
$457$		−	25.9922i		−	1.21586i	0.793989	−	0.607932i	$-0.208001\pi$
$458$		−	29.1318i		−	1.36124i
$459$		0			0
$460$	−3.17706	−	7.99082i	−0.148131	−	0.372574i
$461$	22.4680			1.04644			0.523221	−	0.852197i	$-0.324730\pi$
$461$	22.4680			1.04644			0.523221	+	0.852197i	$0.324730\pi$
$462$		0			0
$463$			21.3508i			0.992254i	0.868250	+	0.496127i	$0.165245\pi$
$463$			21.3508i			0.992254i	−0.868250	+	0.496127i	$0.834755\pi$
$464$			6.17448i			0.286643i
$465$		0			0
$466$	−15.1245			−0.700630
$467$			39.0462i			1.80684i	0.428755	+	0.903421i	$0.358952\pi$
$467$			39.0462i			1.80684i	−0.428755	+	0.903421i	$0.641048\pi$
$468$		0			0
$469$	−15.1619	−	7.21598i	−0.700110	−	0.333203i
$470$	0.620889	−	0.246858i	0.0286395	−	0.0113867i
$471$		0			0
$472$	44.2124			2.03504
$473$	27.3021			1.25535
$474$		0			0
$475$	−9.80903	−	10.3857i	−0.450069	−	0.476527i
$476$	−5.04304	−	2.40013i	−0.231148	−	0.110010i
$477$		0			0
$478$			28.1449i			1.28732i
$479$	12.8084			0.585229			0.292614	−	0.956231i	$-0.405475\pi$
$479$	12.8084			0.585229			0.292614	+	0.956231i	$0.405475\pi$
$480$		0			0
$481$			39.4979i			1.80095i
$482$			4.32239i			0.196880i
$483$		0			0
$484$	−3.65628			−0.166195
$485$	−10.9252	−	27.4785i	−0.496086	−	1.24774i
$486$		0			0
$487$			31.0146i			1.40540i	0.711484	+	0.702702i	$0.248023\pi$
$487$			31.0146i			1.40540i	−0.711484	+	0.702702i	$0.751977\pi$
$488$		−	27.1382i		−	1.22849i
$489$		0			0
$490$	−8.42797	+	15.0677i	−0.380737	+	0.680687i
$491$		−	6.00082i		−	0.270813i	−0.990790	−	0.135407i	$-0.956766\pi$
$491$		−	6.00082i		−	0.270813i	0.990790	−	0.135407i	$-0.0432341\pi$
$492$		0			0
$493$	−9.14430			−0.411839
$494$		−	19.3501i		−	0.870603i
$495$		0			0
$496$		−	7.13006i		−	0.320149i
$497$	−31.9853	−	15.2228i	−1.43474	−	0.682835i
$498$		0			0
$499$	−17.4241			−0.780009			−0.390004	−	0.920813i	$-0.627527\pi$
$499$	−17.4241			−0.780009			−0.390004	+	0.920813i	$0.627527\pi$
$500$	7.94115	+	3.69515i	0.355139	+	0.165252i
$501$		0			0
$502$	−2.42164			−0.108083
$503$			12.3328i			0.549894i	0.961459	+	0.274947i	$0.0886603\pi$
$503$			12.3328i			0.549894i	−0.961459	+	0.274947i	$0.911340\pi$
$504$		0			0
$505$	−2.90241	−	7.30004i	−0.129156	−	0.324847i
$506$			13.6257i			0.605736i
$507$		0			0
$508$		−	8.76548i		−	0.388905i
$509$	−16.6109			−0.736267			−0.368133	−	0.929773i	$-0.620003\pi$
$509$	−16.6109			−0.736267			−0.368133	+	0.929773i	$0.620003\pi$
$510$		0			0
$511$	−14.8209	+	31.1409i	−0.655638	+	1.37759i
$512$	18.6921			0.826082
$513$		0			0
$514$			21.6100i			0.953175i
$515$	−1.53944	−	3.87193i	−0.0678357	−	0.170618i
$516$		0			0
$517$	0.681749			0.0299833
$518$	16.9503	+	8.06717i	0.744755	+	0.354451i
$519$		0			0
$520$	15.5733	+	39.1694i	0.682935	+	1.71769i
$521$	42.4950			1.86174			0.930870	−	0.365351i	$-0.119051\pi$
$521$	42.4950			1.86174			0.930870	+	0.365351i	$0.119051\pi$
$522$		0			0
$523$	10.5720			0.462282			0.231141	−	0.972920i	$-0.425754\pi$
$523$	10.5720			0.462282			0.231141	+	0.972920i	$0.425754\pi$
$524$	−7.10712			−0.310476
$525$		0			0
$526$	9.56682			0.417133
$527$	10.5595			0.459978
$528$		0			0
$529$	1.09759			0.0477212
$530$	11.7437	+	29.5374i	0.510115	+	1.28302i
$531$		0			0
$532$	5.34726	+	2.54492i	0.231833	+	0.110336i
$533$	3.97393			0.172130
$534$		0			0
$535$	6.82934	+	17.1769i	0.295258	+	0.742621i
$536$			19.4845i			0.841601i
$537$		0			0
$538$	−0.533509			−0.0230012
$539$	−13.6710	+	11.1092i	−0.588851	+	0.478506i
$540$		0			0
$541$	1.72594			0.0742041			0.0371021	−	0.999311i	$-0.488187\pi$
$541$	1.72594			0.0742041			0.0371021	+	0.999311i	$0.488187\pi$
$542$			23.7464i			1.02000i
$543$		0			0
$544$			11.1375i			0.477518i
$545$	−3.77280	−	9.48921i	−0.161609	−	0.406473i
$546$		0			0
$547$		−	22.3570i		−	0.955915i	−0.878383	−	0.477957i	$-0.841377\pi$
$547$		−	22.3570i		−	0.955915i	0.878383	−	0.477957i	$-0.158623\pi$
$548$	0.358176			0.0153005
$549$		0			0
$550$	−9.52947	−	10.0897i	−0.406338	−	0.430225i
$551$	9.69592			0.413060
$552$		0			0
$553$	9.44390	−	19.8431i	0.401595	−	0.843813i
$554$			34.1138i			1.44936i
$555$		0			0
$556$		−	2.39568i		−	0.101600i
$557$	19.1579			0.811747			0.405874	−	0.913929i	$-0.366967\pi$
$557$	19.1579			0.811747			0.405874	+	0.913929i	$0.366967\pi$
$558$		0			0
$559$			66.6159i			2.81755i
$560$	10.7408	+	0.707554i	0.453880	+	0.0298996i
$561$		0			0
$562$			18.8504i			0.795158i
$563$		−	15.7852i		−	0.665268i	−0.943056	−	0.332634i	$-0.892063\pi$
$563$		−	15.7852i		−	0.665268i	0.943056	−	0.332634i	$-0.107937\pi$
$564$		0			0
$565$	−10.1123	−	25.4342i	−0.425429	−	1.07002i
$566$	4.51832			0.189919
$567$		0			0
$568$			41.1042i			1.72470i
$569$		−	19.5204i		−	0.818336i	−0.912459	−	0.409168i	$-0.865819\pi$
$569$		−	19.5204i		−	0.818336i	0.912459	−	0.409168i	$-0.134181\pi$
$570$		0			0
$571$	1.02824			0.0430305			0.0215152	−	0.999769i	$-0.493151\pi$
$571$	1.02824			0.0430305			0.0215152	+	0.999769i	$0.493151\pi$
$572$			12.1051i			0.506141i
$573$		0			0
$574$	0.811647	−	1.70539i	0.0338775	−	0.0711818i
$575$	−17.8440	+	16.8532i	−0.744146	+	0.702829i
$576$		0			0
$577$	22.4849			0.936057			0.468029	−	0.883713i	$-0.344964\pi$
$577$	22.4849			0.936057			0.468029	+	0.883713i	$0.344964\pi$
$578$	−10.7423			−0.446821
$579$		0			0
$580$	−5.52413	+	2.19633i	−0.229377	+	0.0911977i
$581$	−19.6931	−	9.37255i	−0.817009	−	0.388839i
$582$		0			0
$583$			32.4327i			1.34322i
$584$	40.0191			1.65600
$585$		0			0
$586$		−	14.0671i		−	0.581105i
$587$		−	2.36724i		−	0.0977066i	−0.998806	−	0.0488533i	$-0.984443\pi$
$587$		−	2.36724i		−	0.0977066i	0.998806	−	0.0488533i	$-0.0155567\pi$
$588$		0			0
$589$	−11.1965			−0.461343
$590$	−13.1225	−	33.0053i	−0.540246	−	1.35881i
$591$		0			0
$592$		−	11.7040i		−	0.481031i
$593$			6.26402i			0.257232i	0.991694	+	0.128616i	$0.0410535\pi$
$593$			6.26402i			0.257232i	−0.991694	+	0.128616i	$0.958946\pi$
$594$		0			0
$595$	−1.04787	+	15.9069i	−0.0429587	+	0.652118i
$596$		−	3.33022i		−	0.136411i
$597$		0			0
$598$	−33.2461			−1.35953
$599$			21.9813i			0.898130i	0.893499	+	0.449065i	$0.148243\pi$
$599$			21.9813i			0.898130i	−0.893499	+	0.449065i	$0.851757\pi$
$600$		0			0
$601$		−	37.3073i		−	1.52179i	−0.648872	−	0.760897i	$-0.724759\pi$
$601$		−	37.3073i		−	1.52179i	0.648872	−	0.760897i	$-0.275241\pi$
$602$	28.5879	+	13.6058i	1.16516	+	0.554532i
$603$		0			0
$604$	8.48966			0.345439
$605$	3.85569	+	9.69768i	0.156756	+	0.394267i
$606$		0			0
$607$	34.0262			1.38108			0.690541	−	0.723293i	$-0.257372\pi$
$607$	34.0262			1.38108			0.690541	+	0.723293i	$0.257372\pi$
$608$		−	11.8094i		−	0.478934i
$609$		0			0
$610$	−20.2591	+	8.05481i	−0.820269	+	0.326130i
$611$			1.66344i			0.0672955i
$612$		0			0
$613$		−	19.3733i		−	0.782482i	−0.920288	−	0.391241i	$-0.872046\pi$
$613$		−	19.3733i		−	0.782482i	0.920288	−	0.391241i	$-0.127954\pi$
$614$	−16.5062			−0.666135
$615$		0			0
$616$	18.4571	+	8.78426i	0.743656	+	0.353928i
$617$	−4.73198			−0.190502			−0.0952512	−	0.995453i	$-0.530365\pi$
$617$	−4.73198			−0.190502			−0.0952512	+	0.995453i	$0.530365\pi$
$618$		0			0
$619$		−	27.5131i		−	1.10585i	−0.833232	−	0.552923i	$-0.813512\pi$
$619$		−	27.5131i		−	1.10585i	0.833232	−	0.552923i	$-0.186488\pi$
$620$	6.37905	−	2.53624i	0.256189	−	0.101858i
$621$		0			0
$622$	16.0231			0.642466
$623$	−3.94313	+	8.28511i	−0.157978	+	0.331936i
$624$		0			0
$625$	1.42653	−	24.9593i	0.0570614	−	0.998371i
$626$	−16.3073			−0.651769
$627$		0			0
$628$	5.01577			0.200151
$629$	17.3334			0.691127
$630$		0			0
$631$	−1.60012			−0.0636997			−0.0318498	−	0.999493i	$-0.510140\pi$
$631$	−1.60012			−0.0636997			−0.0318498	+	0.999493i	$0.510140\pi$
$632$	−25.5002			−1.01435
$633$		0			0
$634$	2.28998			0.0909469
$635$	−23.2490	+	9.24353i	−0.922607	+	0.366818i
$636$		0			0
$637$	−27.1059	−	33.3566i	−1.07398	−	1.32164i
$638$	9.41958			0.372925
$639$		0			0
$640$	−0.640765	−	1.61163i	−0.0253284	−	0.0637051i
$641$		−	30.1667i		−	1.19151i	−0.803166	−	0.595756i	$-0.796853\pi$
$641$		−	30.1667i		−	1.19151i	0.803166	−	0.595756i	$-0.203147\pi$
$642$		0			0
$643$	14.2826			0.563250			0.281625	−	0.959525i	$-0.409127\pi$
$643$	14.2826			0.563250			0.281625	+	0.959525i	$0.409127\pi$
$644$	4.37252	−	9.18731i	0.172301	−	0.362031i
$645$		0			0
$646$	−8.49167			−0.334100
$647$		−	39.1748i		−	1.54012i	−0.637971	−	0.770060i	$-0.720226\pi$
$647$		−	39.1748i		−	1.54012i	0.637971	−	0.770060i	$-0.279774\pi$
$648$		0			0
$649$		−	36.2405i		−	1.42256i
$650$	24.6184	−	23.2515i	0.965612	−	0.911998i
$651$		0			0
$652$			5.03942i			0.197359i
$653$	−5.31582			−0.208024			−0.104012	−	0.994576i	$-0.533168\pi$
$653$	−5.31582			−0.208024			−0.104012	+	0.994576i	$0.533168\pi$
$654$		0			0
$655$	7.49472	+	18.8504i	0.292843	+	0.736548i
$656$	−1.17755			−0.0459757
$657$		0			0
$658$	0.713857	+	0.339746i	0.0278290	+	0.0132447i
$659$		−	12.2986i		−	0.479084i	−0.970886	−	0.239542i	$-0.923003\pi$
$659$		−	12.2986i		−	0.479084i	0.970886	−	0.239542i	$-0.0769972\pi$
$660$		0			0
$661$		−	13.0189i		−	0.506378i	−0.967417	−	0.253189i	$-0.918521\pi$
$661$		−	13.0189i		−	0.506378i	0.967417	−	0.253189i	$-0.0814794\pi$
$662$	4.69815			0.182599
$663$		0			0
$664$			25.3076i			0.982125i
$665$	1.11109	−	16.8664i	0.0430861	−	0.654052i
$666$		0			0
$667$		−	16.6589i		−	0.645035i
$668$		−	3.19460i		−	0.123603i
$669$		0			0
$670$	14.5455	−	5.78312i	0.561941	−	0.223421i
$671$	−22.2450			−0.858758
$672$		0			0
$673$		−	0.339746i		−	0.0130962i	−0.999979	−	0.00654811i	$-0.997916\pi$
$673$		−	0.339746i		−	0.0130962i	0.999979	−	0.00654811i	$-0.00208434\pi$
$674$		−	19.1567i		−	0.737889i
$675$		0			0
$676$	−19.3517			−0.744295
$677$			3.79745i			0.145948i	0.997334	+	0.0729738i	$0.0232490\pi$
$677$			3.79745i			0.145948i	−0.997334	+	0.0729738i	$0.976751\pi$
$678$		0			0
$679$	15.0360	−	31.5930i	0.577031	−	1.21243i
$680$	17.1892	−	6.83425i	0.659177	−	0.262081i
$681$		0			0
$682$	−10.8774			−0.416516
$683$	26.3437			1.00802			0.504008	−	0.863699i	$-0.331858\pi$
$683$	26.3437			1.00802			0.504008	+	0.863699i	$0.331858\pi$
$684$		0			0
$685$	−0.377710	−	0.950001i	−0.0144316	−	0.0362977i
$686$	−19.8510	+	4.81953i	−0.757916	+	0.184011i
$687$		0			0
$688$		−	19.7396i		−	0.752563i
$689$	−79.1343			−3.01478
$690$		0			0
$691$			5.45879i			0.207662i	0.994595	+	0.103831i	$0.0331101\pi$
$691$			5.45879i			0.207662i	−0.994595	+	0.103831i	$0.966890\pi$
$692$			13.3447i			0.507289i
$693$		0			0
$694$	25.3499			0.962269
$695$	−6.35415	+	2.52634i	−0.241027	+	0.0958295i
$696$		0			0
$697$		−	1.74393i		−	0.0660561i
$698$		−	21.5518i		−	0.815747i
$699$		0			0
$700$	3.18758	+	9.86113i	0.120479	+	0.372716i
$701$		−	31.6400i		−	1.19503i	−0.801858	−	0.597514i	$-0.796155\pi$
$701$		−	31.6400i		−	1.19503i	0.801858	−	0.597514i	$-0.203845\pi$
$702$		0			0
$703$	−18.3790			−0.693177
$704$		−	20.6302i		−	0.777530i
$705$		0			0
$706$		−	21.5888i		−	0.812504i
$707$	3.99453	−	8.39310i	0.150230	−	0.315655i
$708$		0			0
$709$	13.7097			0.514879			0.257439	−	0.966294i	$-0.417121\pi$
$709$	13.7097			0.514879			0.257439	+	0.966294i	$0.417121\pi$
$710$	30.6850	−	12.2000i	1.15159	−	0.457858i
$711$		0			0
$712$	10.6472			0.399019
$713$			19.2371i			0.720433i
$714$		0			0
$715$	32.1068	−	12.7653i	1.20073	−	0.477396i
$716$			4.01398i			0.150010i
$717$		0			0
$718$			7.04170i			0.262794i
$719$	−42.5394			−1.58645			−0.793226	−	0.608928i	$-0.791600\pi$
$719$	−42.5394			−1.58645			−0.793226	+	0.608928i	$0.791600\pi$
$720$		0			0
$721$	2.11869	−	4.45169i	0.0789042	−	0.165790i
$722$	−11.9529			−0.444842
$723$		0			0
$724$		−	7.52264i		−	0.279577i
$725$	11.6508	+	12.3357i	0.432700	+	0.458137i
$726$		0			0
$727$	−20.4569			−0.758706			−0.379353	−	0.925252i	$-0.623853\pi$
$727$	−20.4569			−0.758706			−0.379353	+	0.925252i	$0.623853\pi$
$728$	−21.4332	+	45.0344i	−0.794368	+	1.66909i
$729$		0			0
$730$	−11.8779	−	29.8749i	−0.439622	−	1.10572i
$731$	29.2339			1.08126
$732$		0			0
$733$	−19.7505			−0.729500			−0.364750	−	0.931105i	$-0.618846\pi$
$733$	−19.7505			−0.729500			−0.364750	+	0.931105i	$0.618846\pi$
$734$	−6.59928			−0.243584
$735$		0			0
$736$	−20.2901			−0.747904
$737$	15.9712			0.588308
$738$		0			0
$739$	25.2341			0.928252			0.464126	−	0.885769i	$-0.346369\pi$
$739$	25.2341			0.928252			0.464126	+	0.885769i	$0.346369\pi$
$740$	10.4712	−	4.16324i	0.384929	−	0.153044i
$741$		0			0
$742$	−16.1626	+	33.9601i	−0.593349	+	1.24672i
$743$	−42.1408			−1.54600			−0.772998	−	0.634409i	$-0.781244\pi$
$743$	−42.1408			−1.54600			−0.772998	+	0.634409i	$0.781244\pi$
$744$		0			0
$745$	−8.83286	+	3.51185i	−0.323611	+	0.128664i
$746$			0.493717i			0.0180763i
$747$		0			0
$748$	5.31225			0.194235
$749$	−9.39906	+	19.7488i	−0.343434	+	0.721607i
$750$		0			0
$751$	−22.0602			−0.804990			−0.402495	−	0.915422i	$-0.631857\pi$
$751$	−22.0602			−0.804990			−0.402495	+	0.915422i	$0.631857\pi$
$752$		−	0.492908i		−	0.0179745i
$753$		0			0
$754$			22.9834i			0.837004i
$755$	−8.95267	−	22.5174i	−0.325821	−	0.819493i
$756$		0			0
$757$		−	21.4508i		−	0.779643i	−0.920890	−	0.389821i	$-0.872537\pi$
$757$		−	21.4508i		−	0.779643i	0.920890	−	0.389821i	$-0.127463\pi$
$758$	−21.2033			−0.770138
$759$		0			0
$760$	−18.2262	+	7.24652i	−0.661132	+	0.262859i
$761$	17.8314			0.646389			0.323194	−	0.946333i	$-0.395243\pi$
$761$	17.8314			0.646389			0.323194	+	0.946333i	$0.395243\pi$
$762$		0			0
$763$	5.19242	−	10.9101i	0.187978	−	0.394971i
$764$			6.04446i			0.218681i
$765$		0			0
$766$			41.4191i			1.49653i
$767$	88.4253			3.19285
$768$		0			0
$769$			45.9603i			1.65737i	0.559716	+	0.828685i	$0.310910\pi$
$769$			45.9603i			1.65737i	−0.559716	+	0.828685i	$0.689090\pi$
$770$	1.07942	−	16.3857i	0.0388996	−	0.590501i
$771$		0			0
$772$			2.71295i			0.0976411i
$773$		−	51.1273i		−	1.83892i	−0.393181	−	0.919461i	$-0.628626\pi$
$773$		−	51.1273i		−	1.83892i	0.393181	−	0.919461i	$-0.371374\pi$
$774$		0			0
$775$	−13.4539	−	14.2448i	−0.483279	−	0.511689i
$776$	−40.6001			−1.45746
$777$		0			0
$778$		−	16.7807i		−	0.601617i
$779$			1.84913i			0.0662521i
$780$		0			0
$781$	33.6928			1.20562
$782$			14.5898i			0.521731i
$783$		0			0
$784$	8.03200	+	9.88419i	0.286857	+	0.353007i
$785$	−5.28932	−	13.3035i	−0.188784	−	0.474823i
$786$		0			0
$787$	−19.5203			−0.695822			−0.347911	−	0.937528i	$-0.613109\pi$
$787$	−19.5203			−0.695822			−0.347911	+	0.937528i	$0.613109\pi$
$788$	10.3530			0.368810
$789$		0			0
$790$	7.56864	+	19.0364i	0.269280	+	0.677283i
$791$	13.9174	−	29.2425i	0.494845	−	1.03974i
$792$		0			0
$793$		−	54.2768i		−	1.92742i
$794$	−28.7201			−1.01924
$795$		0			0
$796$			12.3368i			0.437265i
$797$		−	37.0375i		−	1.31194i	−0.754789	−	0.655968i	$-0.772261\pi$
$797$		−	37.0375i		−	1.31194i	0.754789	−	0.655968i	$-0.227739\pi$
$798$		0			0
$799$	0.729988			0.0258251
$800$	15.0246	−	14.1904i	0.531200	−	0.501707i
$801$		0			0
$802$		−	22.2585i		−	0.785975i
$803$		−	32.8033i		−	1.15760i
$804$		0			0
$805$	−28.9788	−	1.90900i	−1.02137	−	0.0672833i
$806$		−	26.5403i		−	0.934842i
$807$		0			0
$808$	−10.7859			−0.379448
$809$			44.2423i			1.55548i	0.628587	+	0.777739i	$0.283633\pi$
$809$			44.2423i			1.55548i	−0.628587	+	0.777739i	$0.716367\pi$
$810$		0			0
$811$		−	24.0599i		−	0.844858i	−0.906396	−	0.422429i	$-0.861177\pi$
$811$		−	24.0599i		−	0.844858i	0.906396	−	0.422429i	$-0.138823\pi$
$812$	−6.35128	−	3.02276i	−0.222886	−	0.106078i
$813$		0			0
$814$	−17.8552			−0.625824
$815$	13.3662	−	5.31426i	0.468198	−	0.186150i
$816$		0			0
$817$	−30.9974			−1.08446
$818$			19.4258i			0.679206i
$819$		0			0
$820$	−0.418868	−	1.05352i	−0.0146275	−	0.0367905i
$821$			18.4260i			0.643071i	0.946898	+	0.321535i	$0.104199\pi$
$821$			18.4260i			0.643071i	−0.946898	+	0.321535i	$0.895801\pi$
$822$		0			0
$823$		−	29.3094i		−	1.02166i	−0.859681	−	0.510831i	$-0.829338\pi$
$823$		−	29.3094i		−	1.02166i	0.859681	−	0.510831i	$-0.170662\pi$
$824$	−5.72085			−0.199295
$825$		0			0
$826$	18.0602	−	37.9473i	0.628396	−	1.32036i
$827$	−24.9515			−0.867650			−0.433825	−	0.900997i	$-0.642836\pi$
$827$	−24.9515			−0.867650			−0.433825	+	0.900997i	$0.642836\pi$
$828$		0			0
$829$		−	42.3566i		−	1.47110i	−0.677468	−	0.735552i	$-0.736923\pi$
$829$		−	42.3566i		−	1.47110i	0.677468	−	0.735552i	$-0.263077\pi$
$830$	18.8925	−	7.51145i	0.655769	−	0.260726i
$831$		0			0
$832$	50.3368			1.74511
$833$	−14.6383	+	11.8952i	−0.507187	+	0.412146i
$834$		0			0
$835$	−8.47313	+	3.36882i	−0.293225	+	0.116583i
$836$	−5.63271			−0.194811
$837$		0			0
$838$	25.0621			0.865758
$839$	7.67143			0.264847			0.132424	−	0.991193i	$-0.457724\pi$
$839$	7.67143			0.264847			0.132424	+	0.991193i	$0.457724\pi$
$840$		0			0
$841$	17.4835			0.602881
$842$	−12.0208			−0.414265
$843$		0			0
$844$	−14.8273			−0.510375
$845$	20.4071	+	51.3271i	0.702025	+	1.76571i
$846$		0			0
$847$	−5.30650	+	11.1498i	−0.182333	+	0.383110i
$848$	23.4490			0.805243
$849$		0			0
$850$	−10.2038	−	10.8036i	−0.349986	−	0.370560i
$851$			31.5776i			1.08247i
$852$		0			0
$853$	−0.0642150			−0.00219868			−0.00109934	−	0.999999i	$-0.500350\pi$
$853$	−0.0642150			−0.00219868			−0.00109934	+	0.999999i	$0.500350\pi$
$854$	−23.2926	−	11.0857i	−0.797057	−	0.379343i
$855$		0			0
$856$	25.3792			0.867442
$857$			40.9321i			1.39821i	0.715017	+	0.699107i	$0.246419\pi$
$857$			40.9321i			1.39821i	−0.715017	+	0.699107i	$0.753581\pi$
$858$		0			0
$859$			3.05648i			0.104286i	0.998640	+	0.0521428i	$0.0166051\pi$
$859$			3.05648i			0.104286i	−0.998640	+	0.0521428i	$0.983395\pi$
$860$	17.6604	−	7.02158i	0.602215	−	0.239434i
$861$		0			0
$862$		−	25.6354i		−	0.873145i
$863$	−45.4719			−1.54788			−0.773941	−	0.633257i	$-0.781718\pi$
$863$	−45.4719			−1.54788			−0.773941	+	0.633257i	$0.781718\pi$
$864$		0			0
$865$	35.3945	−	14.0725i	1.20345	−	0.478478i
$866$	40.9346			1.39101
$867$		0			0
$868$	7.33421	+	3.49057i	0.248939	+	0.118478i
$869$			20.9023i			0.709063i
$870$		0			0
$871$			38.9691i			1.32042i
$872$	−14.0205			−0.474793
$873$		0			0
$874$		−	15.4699i		−	0.523279i
$875$	22.7936	−	18.8535i	0.770564	−	0.637363i
$876$		0			0
$877$		−	12.7296i		−	0.429849i	−0.976631	−	0.214924i	$-0.931049\pi$
$877$		−	12.7296i		−	0.429849i	0.976631	−	0.214924i	$-0.0689505\pi$
$878$			3.37127i			0.113775i
$879$		0			0
$880$	−9.51387	+	3.78261i	−0.320713	+	0.127512i
$881$	42.4279			1.42943			0.714716	−	0.699414i	$-0.246556\pi$
$881$	42.4279			1.42943			0.714716	+	0.699414i	$0.246556\pi$
$882$		0			0
$883$		−	27.1854i		−	0.914860i	−0.889246	−	0.457430i	$-0.848770\pi$
$883$		−	27.1854i		−	0.914860i	0.889246	−	0.457430i	$-0.151230\pi$
$884$			12.9617i			0.435948i
$885$		0			0
$886$	−21.5587			−0.724279
$887$			0.473682i			0.0159047i	0.999968	+	0.00795234i	$0.00253133\pi$
$887$			0.473682i			0.0159047i	−0.999968	+	0.00795234i	$0.997469\pi$
$888$		0			0
$889$	−26.7301	−	12.7217i	−0.896500	−	0.426671i
$890$	−3.16015	−	7.94828i	−0.105928	−	0.266427i
$891$		0			0
$892$	−19.9807			−0.669003
$893$	−0.774024			−0.0259017
$894$		0			0
$895$	10.6464	−	4.23290i	0.355871	−	0.141490i
$896$	0.881870	−	1.85294i	0.0294612	−	0.0619024i
$897$		0			0
$898$			17.0469i			0.568861i
$899$	13.2988			0.443539
$900$		0			0
$901$			34.7276i			1.15694i
$902$			1.79643i			0.0598146i
$903$		0			0
$904$	−37.5794			−1.24987
$905$	−19.9525	+	7.93291i	−0.663245	+	0.263699i
$906$		0			0
$907$		−	22.8581i		−	0.758991i	−0.925194	−	0.379495i	$-0.876098\pi$
$907$		−	22.8581i		−	0.758991i	0.925194	−	0.379495i	$-0.123902\pi$
$908$		−	12.8253i		−	0.425624i
$909$		0			0
$910$	39.9805	+	2.63374i	1.32534	+	0.0873075i
$911$			12.5826i			0.416879i	0.978035	+	0.208440i	$0.0668385\pi$
$911$			12.5826i			0.416879i	−0.978035	+	0.208440i	$0.933161\pi$
$912$		0			0
$913$	20.7444			0.686539
$914$			28.6692i			0.948292i
$915$		0			0
$916$		−	20.6911i		−	0.683653i
$917$	−10.3148	+	21.6730i	−0.340625	+	0.715705i
$918$		0			0
$919$	−48.6017			−1.60322			−0.801611	−	0.597846i	$-0.796024\pi$
$919$	−48.6017			−1.60322			−0.801611	+	0.597846i	$0.796024\pi$
$920$	12.4505	+	31.3150i	0.410481	+	1.03243i
$921$		0			0
$922$	−24.7821			−0.816154
$923$			82.2089i			2.70594i
$924$		0			0
$925$	−22.0846	−	23.3829i	−0.726136	−	0.768823i
$926$		−	23.5497i		−	0.773892i
$927$		0			0
$928$			14.0268i			0.460451i
$929$	−38.0618			−1.24877			−0.624384	−	0.781117i	$-0.714650\pi$
$929$	−38.0618			−1.24877			−0.624384	+	0.781117i	$0.714650\pi$
$930$		0			0
$931$	15.5214	−	12.6128i	0.508692	−	0.413368i
$932$	−10.7423			−0.351876
$933$		0			0
$934$		−	43.0676i		−	1.40922i
$935$	−5.60197	−	14.0899i	−0.183204	−	0.460788i
$936$		0			0
$937$	−28.9516			−0.945807			−0.472904	−	0.881114i	$-0.656794\pi$
$937$	−28.9516			−0.945807			−0.472904	+	0.881114i	$0.656794\pi$
$938$	16.7234	+	7.95917i	0.546039	+	0.259876i
$939$		0			0
$940$	0.440991	−	0.175333i	0.0143835	−	0.00571873i
$941$	48.5089			1.58134			0.790672	−	0.612239i	$-0.209731\pi$
$941$	48.5089			1.58134			0.790672	+	0.612239i	$0.209731\pi$
$942$		0			0
$943$	3.17706			0.103459
$944$	−26.2021			−0.852805
$945$		0			0
$946$	−30.1140			−0.979090
$947$	−35.8278			−1.16425			−0.582124	−	0.813100i	$-0.697778\pi$
$947$	−35.8278			−1.16425			−0.582124	+	0.813100i	$0.697778\pi$
$948$		0			0
$949$	80.0387			2.59816
$950$	10.8193	+	11.4553i	0.351024	+	0.371659i
$951$		0			0
$952$	19.7631	+	9.40582i	0.640524	+	0.304844i
$953$	48.9092			1.58432			0.792161	−	0.610312i	$-0.208956\pi$
$953$	48.9092			1.58432			0.792161	+	0.610312i	$0.208956\pi$
$954$		0			0
$955$	16.0319	−	6.37411i	0.518781	−	0.206261i
$956$			19.9902i			0.646528i
$957$		0			0
$958$	−14.1275			−0.456439
$959$	0.519834	−	1.09225i	0.0167863	−	0.0352706i
$960$		0			0
$961$	15.6431			0.504616
$962$		−	43.5659i		−	1.40462i
$963$		0			0
$964$			3.07001i			0.0988784i
$965$	7.19564	−	2.86091i	0.231636	−	0.0920958i
$966$		0			0
$967$			29.2016i			0.939059i	0.882917	+	0.469530i	$0.155576\pi$
$967$			29.2016i			0.939059i	−0.882917	+	0.469530i	$0.844424\pi$
$968$	14.3285			0.460536
$969$		0			0
$970$	12.0504	+	30.3086i	0.386914	+	0.973151i
$971$	−26.1975			−0.840719			−0.420359	−	0.907358i	$-0.638096\pi$
$971$	−26.1975			−0.840719			−0.420359	+	0.907358i	$0.638096\pi$
$972$		0			0
$973$	−7.30558	−	3.47694i	−0.234206	−	0.111466i
$974$		−	34.2088i		−	1.09612i
$975$		0			0
$976$			16.0832i			0.514812i
$977$	−28.0893			−0.898657			−0.449329	−	0.893367i	$-0.648337\pi$
$977$	−28.0893			−0.898657			−0.449329	+	0.893367i	$0.648337\pi$
$978$		0			0
$979$		−	8.72738i		−	0.278928i
$980$	−5.98603	+	10.7019i	−0.191217	+	0.341860i
$981$		0			0
$982$			6.61885i			0.211216i
$983$			32.6011i			1.03981i	0.854223	+	0.519907i	$0.174033\pi$
$983$			32.6011i			1.03981i	−0.854223	+	0.519907i	$0.825967\pi$
$984$		0			0
$985$	−10.9176	−	27.4596i	−0.347864	−	0.874935i
$986$	10.0861			0.321207
$987$		0			0
$988$		−	13.7436i		−	0.437241i
$989$			53.2577i			1.69350i
$990$		0			0
$991$	39.2582			1.24708			0.623538	−	0.781793i	$-0.285695\pi$
$991$	39.2582			1.24708			0.623538	+	0.781793i	$0.285695\pi$
$992$		−	16.1976i		−	0.514273i
$993$		0			0
$994$	35.2796	+	16.7906i	1.11900	+	0.532565i
$995$	32.7212	−	13.0096i	1.03733	−	0.412431i
$996$		0			0
$997$	−17.2799			−0.547259			−0.273630	−	0.961835i	$-0.588224\pi$
$997$	−17.2799			−0.547259			−0.273630	+	0.961835i	$0.588224\pi$
$998$	19.2186			0.608355
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.g.b.944.12	yes	32
3.2	odd	2	inner	945.2.g.b.944.21	yes	32
5.4	even	2	inner	945.2.g.b.944.23	yes	32
7.6	odd	2	inner	945.2.g.b.944.9	✓	32
15.14	odd	2	inner	945.2.g.b.944.10	yes	32
21.20	even	2	inner	945.2.g.b.944.24	yes	32
35.34	odd	2	inner	945.2.g.b.944.22	yes	32
105.104	even	2	inner	945.2.g.b.944.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.g.b.944.9	✓	32	7.6	odd	2	inner
945.2.g.b.944.10	yes	32	15.14	odd	2	inner
945.2.g.b.944.11	yes	32	105.104	even	2	inner
945.2.g.b.944.12	yes	32	1.1	even	1	trivial
945.2.g.b.944.21	yes	32	3.2	odd	2	inner
945.2.g.b.944.22	yes	32	35.34	odd	2	inner
945.2.g.b.944.23	yes	32	5.4	even	2	inner
945.2.g.b.944.24	yes	32	21.20	even	2	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.10299 q^{2} -0.783408 q^{4} +(0.826134 + 2.07786i) q^{5} +(-1.13699 + 2.38899i) q^{7} +3.07008 q^{8} +O(q^{10})\)	\(q-1.10299 q^{2} -0.783408 q^{4} +(0.826134 + 2.07786i) q^{5} +(-1.13699 + 2.38899i) q^{7} +3.07008 q^{8} +(-0.911219 - 2.29186i) q^{10} -2.51652i q^{11} +6.14019 q^{13} +(1.25409 - 2.63503i) q^{14} -1.81945 q^{16} -2.69458i q^{17} +2.85713i q^{19} +(-0.647200 - 1.62781i) q^{20} +2.77570i q^{22} +4.90893 q^{23} +(-3.63501 + 3.43318i) q^{25} -6.77258 q^{26} +(0.890727 - 1.87155i) q^{28} -3.39359i q^{29} +3.91879i q^{31} -4.13331 q^{32} +2.97210i q^{34} +(-5.90328 - 0.388883i) q^{35} +6.43269i q^{37} -3.15139i q^{38} +(2.53629 + 6.37919i) q^{40} +0.647200 q^{41} +10.8492i q^{43} +1.97146i q^{44} -5.41451 q^{46} +0.270910i q^{47} +(-4.41451 - 5.43250i) q^{49} +(4.00938 - 3.78677i) q^{50} -4.81027 q^{52} -12.8879 q^{53} +(5.22897 - 2.07898i) q^{55} +(-3.49065 + 7.33437i) q^{56} +3.74310i q^{58} +14.4011 q^{59} -8.83960i q^{61} -4.32239i q^{62} +8.19792 q^{64} +(5.07262 + 12.7584i) q^{65} +6.34657i q^{67} +2.11096i q^{68} +(6.51128 + 0.428934i) q^{70} +13.3887i q^{71} +13.0352 q^{73} -7.09520i q^{74} -2.23830i q^{76} +(6.01192 + 2.86125i) q^{77} -8.30606 q^{79} +(-1.50311 - 3.78057i) q^{80} -0.713857 q^{82} +8.24330i q^{83} +(5.59896 - 2.22608i) q^{85} -11.9665i q^{86} -7.72590i q^{88} +3.46804 q^{89} +(-6.98133 + 14.6688i) q^{91} -3.84570 q^{92} -0.298812i q^{94} +(-5.93671 + 2.36037i) q^{95} -13.2244 q^{97} +(4.86917 + 5.99201i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4}+O(q^{10}) \) 32 * q + 32 * q^4	\( 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) \) 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

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