LMFDB - Embedded newform 1050.2.j.c.407.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.j (of order $4$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.3
Root			$-2.80721i$ of defining polynomial
Character	$\chi$	$=$	1050.407
Dual form			1050.2.j.c.743.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.799269 + 1.53661i) q^{3} -1.00000i q^{4} +(-1.65172 - 0.521378i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.72234 + 2.45633i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.799269 + 1.53661i) q^{3} -1.00000i q^{4} +(-1.65172 - 0.521378i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.72234 + 2.45633i) q^{9} +1.70489i q^{11} +(1.53661 - 0.799269i) q^{12} +(-0.921665 + 0.921665i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.76445 + 4.76445i) q^{17} +(-0.519010 - 2.95476i) q^{18} -5.94473i q^{19} +(-0.521378 + 1.65172i) q^{21} +(-1.20554 - 1.20554i) q^{22} +(2.49622 + 2.49622i) q^{23} +(-0.521378 + 1.65172i) q^{24} -1.30343i q^{26} +(-5.15103 - 0.683293i) q^{27} +(0.707107 - 0.707107i) q^{28} +5.19708 q^{29} -3.40667 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.61976 + 1.36267i) q^{33} -6.73795i q^{34} +(2.45633 + 1.72234i) q^{36} +(1.02910 + 1.02910i) q^{37} +(4.20356 + 4.20356i) q^{38} +(-2.15290 - 0.679581i) q^{39} +10.9749i q^{41} +(-0.799269 - 1.53661i) q^{42} +(-8.17020 + 8.17020i) q^{43} +1.70489 q^{44} -3.53019 q^{46} +(-0.436661 + 0.436661i) q^{47} +(-0.799269 - 1.53661i) q^{48} +1.00000i q^{49} +(-11.1292 - 3.51302i) q^{51} +(0.921665 + 0.921665i) q^{52} +(-6.87196 - 6.87196i) q^{53} +(4.12549 - 3.15917i) q^{54} +1.00000i q^{56} +(9.13472 - 4.75144i) q^{57} +(-3.67489 + 3.67489i) q^{58} -0.686337 q^{59} -1.74994 q^{61} +(2.40888 - 2.40888i) q^{62} +(-2.95476 + 0.519010i) q^{63} +1.00000i q^{64} +(0.888895 - 2.81600i) q^{66} +(-1.03802 - 1.03802i) q^{67} +(4.76445 + 4.76445i) q^{68} +(-1.84056 + 5.83087i) q^{69} +12.2611i q^{71} +(-2.95476 + 0.519010i) q^{72} +(4.59693 - 4.59693i) q^{73} -1.45536 q^{74} -5.94473 q^{76} +(-1.20554 + 1.20554i) q^{77} +(2.00286 - 1.04179i) q^{78} -7.19515i q^{79} +(-3.06710 - 8.46126i) q^{81} +(-7.76040 - 7.76040i) q^{82} +(6.64687 + 6.64687i) q^{83} +(1.65172 + 0.521378i) q^{84} -11.5544i q^{86} +(4.15386 + 7.98588i) q^{87} +(-1.20554 + 1.20554i) q^{88} +2.25517 q^{89} -1.30343 q^{91} +(2.49622 - 2.49622i) q^{92} +(-2.72285 - 5.23472i) q^{93} -0.617532i q^{94} +(1.65172 + 0.521378i) q^{96} +(-13.2182 - 13.2182i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.18778 - 2.93640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3}+O(q^{10}) $ 12 * q - 4 * q^3	$ 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.799269	+	1.53661i	0.461458	+	0.887162i
$3$	0.799269	+	1.53661i	0.461458	+	0.887162i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−1.65172	−	0.521378i	−0.674310	−	0.212852i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.72234	+	2.45633i	−0.574113	+	0.818776i
$10$		0			0
$11$			1.70489i			0.514045i	0.966405	+	0.257022i	$0.0827414\pi$
$11$			1.70489i			0.514045i	−0.966405	+	0.257022i	$0.917259\pi$
$12$	1.53661	−	0.799269i	0.443581	−	0.230729i
$13$	−0.921665	+	0.921665i	−0.255624	+	0.255624i	−0.823272	−	0.567648i	$-0.807854\pi$
$13$	−0.921665	+	0.921665i	−0.255624	+	0.255624i	0.567648	+	0.823272i	$0.307854\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.76445	+	4.76445i	−1.15555	+	1.15555i	−0.170128	+	0.985422i	$0.554418\pi$
$17$	−4.76445	+	4.76445i	−1.15555	+	1.15555i	−0.985422	+	0.170128i	$0.945582\pi$
$18$	−0.519010	−	2.95476i	−0.122332	−	0.696444i
$19$		−	5.94473i		−	1.36381i	−0.731439	−	0.681907i	$-0.761151\pi$
$19$		−	5.94473i		−	1.36381i	0.731439	−	0.681907i	$-0.238849\pi$
$20$		0			0
$21$	−0.521378	+	1.65172i	−0.113774	+	0.360434i
$22$	−1.20554	−	1.20554i	−0.257022	−	0.257022i
$23$	2.49622	+	2.49622i	0.520498	+	0.520498i	0.917722	−	0.397224i	$-0.130026\pi$
$23$	2.49622	+	2.49622i	0.520498	+	0.520498i	−0.397224	+	0.917722i	$0.630026\pi$
$24$	−0.521378	+	1.65172i	−0.106426	+	0.337155i
$25$		0			0
$26$		−	1.30343i		−	0.255624i
$27$	−5.15103	−	0.683293i	−0.991316	−	0.131500i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	5.19708			0.965073			0.482536	−	0.875876i	$-0.339716\pi$
$29$	5.19708			0.965073			0.482536	+	0.875876i	$0.339716\pi$
$30$		0			0
$31$	−3.40667			−0.611856			−0.305928	−	0.952055i	$-0.598967\pi$
$31$	−3.40667			−0.611856			−0.305928	+	0.952055i	$0.598967\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.61976	+	1.36267i	−0.456041	+	0.237210i
$34$		−	6.73795i		−	1.15555i
$35$		0			0
$36$	2.45633	+	1.72234i	0.409388	+	0.287056i
$37$	1.02910	+	1.02910i	0.169183	+	0.169183i	0.786620	−	0.617437i	$-0.211829\pi$
$37$	1.02910	+	1.02910i	0.169183	+	0.169183i	−0.617437	+	0.786620i	$0.711829\pi$
$38$	4.20356	+	4.20356i	0.681907	+	0.681907i
$39$	−2.15290	−	0.679581i	−0.344740	−	0.108820i
$40$		0			0
$41$			10.9749i			1.71399i	0.515328	+	0.856993i	$0.327670\pi$
$41$			10.9749i			1.71399i	−0.515328	+	0.856993i	$0.672330\pi$
$42$	−0.799269	−	1.53661i	−0.123330	−	0.237104i
$43$	−8.17020	+	8.17020i	−1.24594	+	1.24594i	−0.288449	+	0.957495i	$0.593139\pi$
$43$	−8.17020	+	8.17020i	−1.24594	+	1.24594i	−0.957495	+	0.288449i	$0.906861\pi$
$44$	1.70489			0.257022
$45$		0			0
$46$	−3.53019			−0.520498
$47$	−0.436661	+	0.436661i	−0.0636935	+	0.0636935i	−0.738236	−	0.674542i	$-0.764341\pi$
$47$	−0.436661	+	0.436661i	−0.0636935	+	0.0636935i	0.674542	+	0.738236i	$0.264341\pi$
$48$	−0.799269	−	1.53661i	−0.115365	−	0.221790i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−11.1292	−	3.51302i	−1.55840	−	0.491922i
$52$	0.921665	+	0.921665i	0.127812	+	0.127812i
$53$	−6.87196	−	6.87196i	−0.943937	−	0.943937i	0.0545729	−	0.998510i	$-0.482620\pi$
$53$	−6.87196	−	6.87196i	−0.943937	−	0.943937i	−0.998510	+	0.0545729i	$0.982620\pi$
$54$	4.12549	−	3.15917i	0.561408	−	0.429908i
$55$		0			0
$56$			1.00000i			0.133631i
$57$	9.13472	−	4.75144i	1.20992	−	0.629343i
$58$	−3.67489	+	3.67489i	−0.482536	+	0.482536i
$59$	−0.686337			−0.0893535			−0.0446767	−	0.999001i	$-0.514226\pi$
$59$	−0.686337			−0.0893535			−0.0446767	+	0.999001i	$0.514226\pi$
$60$		0			0
$61$	−1.74994			−0.224056			−0.112028	−	0.993705i	$-0.535735\pi$
$61$	−1.74994			−0.224056			−0.112028	+	0.993705i	$0.535735\pi$
$62$	2.40888	−	2.40888i	0.305928	−	0.305928i
$63$	−2.95476	+	0.519010i	−0.372265	+	0.0653891i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.888895	−	2.81600i	0.109415	−	0.346625i
$67$	−1.03802	−	1.03802i	−0.126814	−	0.126814i	0.640851	−	0.767665i	$-0.278582\pi$
$67$	−1.03802	−	1.03802i	−0.126814	−	0.126814i	−0.767665	+	0.640851i	$0.778582\pi$
$68$	4.76445	+	4.76445i	0.577775	+	0.577775i
$69$	−1.84056	+	5.83087i	−0.221578	+	0.701954i
$70$		0			0
$71$			12.2611i			1.45513i	0.686040	+	0.727564i	$0.259348\pi$
$71$			12.2611i			1.45513i	−0.686040	+	0.727564i	$0.740652\pi$
$72$	−2.95476	+	0.519010i	−0.348222	+	0.0611659i
$73$	4.59693	−	4.59693i	0.538030	−	0.538030i	−0.384920	−	0.922950i	$-0.625771\pi$
$73$	4.59693	−	4.59693i	0.538030	−	0.538030i	0.922950	+	0.384920i	$0.125771\pi$
$74$	−1.45536			−0.169183
$75$		0			0
$76$	−5.94473			−0.681907
$77$	−1.20554	+	1.20554i	−0.137384	+	0.137384i
$78$	2.00286	−	1.04179i	0.226780	−	0.117960i
$79$		−	7.19515i		−	0.809517i	−0.914424	−	0.404759i	$-0.867356\pi$
$79$		−	7.19515i		−	0.809517i	0.914424	−	0.404759i	$-0.132644\pi$
$80$		0			0
$81$	−3.06710	−	8.46126i	−0.340789	−	0.940140i
$82$	−7.76040	−	7.76040i	−0.856993	−	0.856993i
$83$	6.64687	+	6.64687i	0.729589	+	0.729589i	0.970538	−	0.240949i	$-0.0774587\pi$
$83$	6.64687	+	6.64687i	0.729589	+	0.729589i	−0.240949	+	0.970538i	$0.577459\pi$
$84$	1.65172	+	0.521378i	0.180217	+	0.0568871i
$85$		0			0
$86$		−	11.5544i		−	1.24594i
$87$	4.15386	+	7.98588i	0.445341	+	0.856176i
$88$	−1.20554	+	1.20554i	−0.128511	+	0.128511i
$89$	2.25517			0.239048			0.119524	−	0.992831i	$-0.461863\pi$
$89$	2.25517			0.239048			0.119524	+	0.992831i	$0.461863\pi$
$90$		0			0
$91$	−1.30343			−0.136637
$92$	2.49622	−	2.49622i	0.260249	−	0.260249i
$93$	−2.72285	−	5.23472i	−0.282346	−	0.542815i
$94$		−	0.617532i		−	0.0636935i
$95$		0			0
$96$	1.65172	+	0.521378i	0.168578	+	0.0532130i
$97$	−13.2182	−	13.2182i	−1.34210	−	1.34210i	−0.893967	−	0.448133i	$-0.852089\pi$
$97$	−13.2182	−	13.2182i	−1.34210	−	1.34210i	−0.448133	−	0.893967i	$-0.647911\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−4.18778	−	2.93640i	−0.420888	−	0.295120i
$100$		0			0
$101$		−	17.8429i		−	1.77544i	−0.460385	−	0.887719i	$-0.652289\pi$
$101$		−	17.8429i		−	1.77544i	0.460385	−	0.887719i	$-0.347711\pi$
$102$	10.3536	−	5.38544i	1.02516	−	0.533238i
$103$	11.9006	−	11.9006i	1.17260	−	1.17260i	0.191013	−	0.981587i	$-0.438823\pi$
$103$	11.9006	−	11.9006i	1.17260	−	1.17260i	0.981587	−	0.191013i	$-0.0611774\pi$
$104$	−1.30343			−0.127812
$105$		0			0
$106$	9.71842			0.943937
$107$	−3.96954	+	3.96954i	−0.383750	+	0.383750i	−0.872451	−	0.488701i	$-0.837471\pi$
$107$	−3.96954	+	3.96954i	−0.383750	+	0.383750i	0.488701	+	0.872451i	$0.337471\pi$
$108$	−0.683293	+	5.15103i	−0.0657499	+	0.495658i
$109$			6.66506i			0.638397i	0.947688	+	0.319198i	$0.103414\pi$
$109$			6.66506i			0.638397i	−0.947688	+	0.319198i	$0.896586\pi$
$110$		0			0
$111$	−0.758796	+	2.40385i	−0.0720217	+	0.228163i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	4.33754	+	4.33754i	0.408042	+	0.408042i	0.881055	−	0.473014i	$-0.156834\pi$
$113$	4.33754	+	4.33754i	0.408042	+	0.408042i	−0.473014	+	0.881055i	$0.656834\pi$
$114$	−3.09945	+	9.81900i	−0.290290	+	0.919633i
$115$		0			0
$116$		−	5.19708i		−	0.482536i
$117$	−0.676494	−	3.85133i	−0.0625419	−	0.356056i
$118$	0.485314	−	0.485314i	0.0446767	−	0.0446767i
$119$	−6.73795			−0.617667
$120$		0			0
$121$	8.09334			0.735758
$122$	1.23739	−	1.23739i	0.112028	−	0.112028i
$123$	−16.8641	+	8.77187i	−1.52058	+	0.790933i
$124$			3.40667i			0.305928i
$125$		0			0
$126$	1.72234	−	2.45633i	0.153438	−	0.218827i
$127$	11.2191	+	11.2191i	0.995531	+	0.995531i	0.999990	−	0.00445951i	$-0.00141951\pi$
$127$	11.2191	+	11.2191i	0.995531	+	0.995531i	−0.00445951	+	0.999990i	$0.501420\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−19.0846	−	6.02422i	−1.68031	−	0.530403i
$130$		0			0
$131$			4.60740i			0.402550i	0.979535	+	0.201275i	$0.0645085\pi$
$131$			4.60740i			0.402550i	−0.979535	+	0.201275i	$0.935491\pi$
$132$	1.36267	+	2.61976i	0.118605	+	0.228020i
$133$	4.20356	−	4.20356i	0.364495	−	0.364495i
$134$	1.46798			0.126814
$135$		0			0
$136$	−6.73795			−0.577775
$137$	−2.21669	+	2.21669i	−0.189384	+	0.189384i	−0.795430	−	0.606046i	$-0.792755\pi$
$137$	−2.21669	+	2.21669i	−0.189384	+	0.189384i	0.606046	+	0.795430i	$0.292755\pi$
$138$	−2.82157	−	5.42452i	−0.240188	−	0.461766i
$139$			0.322961i			0.0273932i	0.999906	+	0.0136966i	$0.00435990\pi$
$139$			0.322961i			0.0273932i	−0.999906	+	0.0136966i	$0.995640\pi$
$140$		0			0
$141$	−1.01999	−	0.321968i	−0.0858984	−	0.0271146i
$142$	−8.66993	−	8.66993i	−0.727564	−	0.727564i
$143$	−1.57134	−	1.57134i	−0.131402	−	0.131402i
$144$	1.72234	−	2.45633i	0.143528	−	0.204694i
$145$		0			0
$146$			6.50104i			0.538030i
$147$	−1.53661	+	0.799269i	−0.126737	+	0.0659226i
$148$	1.02910	−	1.02910i	0.0845913	−	0.0845913i
$149$	−3.82532			−0.313382			−0.156691	−	0.987648i	$-0.550083\pi$
$149$	−3.82532			−0.313382			−0.156691	+	0.987648i	$0.550083\pi$
$150$		0			0
$151$	4.75057			0.386596			0.193298	−	0.981140i	$-0.438082\pi$
$151$	4.75057			0.386596			0.193298	+	0.981140i	$0.438082\pi$
$152$	4.20356	−	4.20356i	0.340953	−	0.340953i
$153$	−3.49707	−	19.9091i	−0.282721	−	1.60955i
$154$		−	1.70489i		−	0.137384i
$155$		0			0
$156$	−0.679581	+	2.15290i	−0.0544100	+	0.172370i
$157$	10.3066	+	10.3066i	0.822559	+	0.822559i	0.986474	−	0.163915i	$-0.0524123\pi$
$157$	10.3066	+	10.3066i	0.822559	+	0.822559i	−0.163915	+	0.986474i	$0.552412\pi$
$158$	5.08774	+	5.08774i	0.404759	+	0.404759i
$159$	5.06698	−	16.0521i	0.401837	−	1.27301i
$160$		0			0
$161$			3.53019i			0.278218i
$162$	8.15178	+	3.81424i	0.640465	+	0.299675i
$163$	−4.45269	+	4.45269i	−0.348762	+	0.348762i	−0.859648	−	0.510887i	$-0.829317\pi$
$163$	−4.45269	+	4.45269i	−0.348762	+	0.348762i	0.510887	+	0.859648i	$0.329317\pi$
$164$	10.9749			0.856993
$165$		0			0
$166$	−9.40009			−0.729589
$167$	−8.92259	+	8.92259i	−0.690451	+	0.690451i	−0.962331	−	0.271880i	$-0.912354\pi$
$167$	−8.92259	+	8.92259i	−0.690451	+	0.690451i	0.271880	+	0.962331i	$0.412354\pi$
$168$	−1.53661	+	0.799269i	−0.118552	+	0.0616649i
$169$			11.3011i			0.869313i
$170$		0			0
$171$	14.6022	+	10.2388i	1.11666	+	0.782983i
$172$	8.17020	+	8.17020i	0.622972	+	0.622972i
$173$	−4.45093	−	4.45093i	−0.338398	−	0.338398i	0.517366	−	0.855764i	$-0.326913\pi$
$173$	−4.45093	−	4.45093i	−0.338398	−	0.338398i	−0.855764	+	0.517366i	$0.826913\pi$
$174$	−8.58409	−	2.70964i	−0.650758	−	0.205418i
$175$		0			0
$176$		−	1.70489i		−	0.128511i
$177$	−0.548568	−	1.05463i	−0.0412329	−	0.0792710i
$178$	−1.59465	+	1.59465i	−0.119524	+	0.119524i
$179$	10.6798			0.798243			0.399121	−	0.916898i	$-0.369315\pi$
$179$	10.6798			0.798243			0.399121	+	0.916898i	$0.369315\pi$
$180$		0			0
$181$	12.8215			0.953012			0.476506	−	0.879171i	$-0.341903\pi$
$181$	12.8215			0.953012			0.476506	+	0.879171i	$0.341903\pi$
$182$	0.921665	−	0.921665i	0.0683184	−	0.0683184i
$183$	−1.39867	−	2.68897i	−0.103393	−	0.198774i
$184$			3.53019i			0.260249i
$185$		0			0
$186$	5.62685	+	1.77616i	0.412581	+	0.130235i
$187$	−8.12288	−	8.12288i	−0.594004	−	0.594004i
$188$	0.436661	+	0.436661i	0.0318468	+	0.0318468i
$189$	−3.15917	−	4.12549i	−0.229796	−	0.300085i
$190$		0			0
$191$			8.28637i			0.599580i	0.954005	+	0.299790i	$0.0969167\pi$
$191$			8.28637i			0.599580i	−0.954005	+	0.299790i	$0.903083\pi$
$192$	−1.53661	+	0.799269i	−0.110895	+	0.0576823i
$193$	3.59731	−	3.59731i	0.258940	−	0.258940i	−0.565683	−	0.824623i	$-0.691387\pi$
$193$	3.59731	−	3.59731i	0.258940	−	0.258940i	0.824623	+	0.565683i	$0.191387\pi$
$194$	18.6933			1.34210
$195$		0			0
$196$	1.00000			0.0714286
$197$	−5.50386	+	5.50386i	−0.392134	+	0.392134i	−0.875447	−	0.483314i	$-0.839433\pi$
$197$	−5.50386	+	5.50386i	−0.392134	+	0.392134i	0.483314	+	0.875447i	$0.339433\pi$
$198$	5.03756	−	0.884857i	0.358004	−	0.0628840i
$199$			20.7662i			1.47208i	0.676940	+	0.736038i	$0.263306\pi$
$199$			20.7662i			1.47208i	−0.676940	+	0.736038i	$0.736694\pi$
$200$		0			0
$201$	0.765374	−	2.42469i	0.0539853	−	0.171024i
$202$	12.6169	+	12.6169i	0.887719	+	0.887719i
$203$	3.67489	+	3.67489i	0.257927	+	0.257927i
$204$	−3.51302	+	11.1292i	−0.245961	+	0.779199i
$205$		0			0
$206$			16.8300i			1.17260i
$207$	−10.4309	+	1.83220i	−0.724996	+	0.127347i
$208$	0.921665	−	0.921665i	0.0639060	−	0.0639060i
$209$	10.1351			0.701061
$210$		0			0
$211$	26.0519			1.79349			0.896743	−	0.442551i	$-0.145927\pi$
$211$	26.0519			1.79349			0.896743	+	0.442551i	$0.145927\pi$
$212$	−6.87196	+	6.87196i	−0.471968	+	0.471968i
$213$	−18.8406	+	9.79994i	−1.29093	+	0.671481i
$214$		−	5.61377i		−	0.383750i
$215$		0			0
$216$	−3.15917	−	4.12549i	−0.214954	−	0.280704i
$217$	−2.40888	−	2.40888i	−0.163525	−	0.163525i
$218$	−4.71291	−	4.71291i	−0.319198	−	0.319198i
$219$	10.7379	+	3.38950i	0.725598	+	0.229041i
$220$		0			0
$221$		−	8.78246i		−	0.590772i
$222$	−1.16323	−	2.23633i	−0.0780707	−	0.150092i
$223$	1.49400	−	1.49400i	0.100045	−	0.100045i	−0.655312	−	0.755358i	$-0.727463\pi$
$223$	1.49400	−	1.49400i	0.100045	−	0.100045i	0.755358	+	0.655312i	$0.227463\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−6.13421			−0.408042
$227$	7.38425	−	7.38425i	0.490110	−	0.490110i	−0.418231	−	0.908341i	$-0.637350\pi$
$227$	7.38425	−	7.38425i	0.490110	−	0.490110i	0.908341	+	0.418231i	$0.137350\pi$
$228$	−4.75144	−	9.13472i	−0.314672	−	0.604962i
$229$			13.4219i			0.886944i	0.896288	+	0.443472i	$0.146254\pi$
$229$			13.4219i			0.886944i	−0.896288	+	0.443472i	$0.853746\pi$
$230$		0			0
$231$	−2.81600	−	0.888895i	−0.185279	−	0.0584850i
$232$	3.67489	+	3.67489i	0.241268	+	0.241268i
$233$	−8.32952	−	8.32952i	−0.545685	−	0.545685i	0.379505	−	0.925190i	$-0.376094\pi$
$233$	−8.32952	−	8.32952i	−0.545685	−	0.545685i	−0.925190	+	0.379505i	$0.876094\pi$
$234$	3.20166	+	2.24495i	0.209299	+	0.146757i
$235$		0			0
$236$			0.686337i			0.0446767i
$237$	11.0561	−	5.75086i	0.718173	−	0.373558i
$238$	4.76445	−	4.76445i	0.308834	−	0.308834i
$239$	0.372694			0.0241076			0.0120538	−	0.999927i	$-0.496163\pi$
$239$	0.372694			0.0241076			0.0120538	+	0.999927i	$0.496163\pi$
$240$		0			0
$241$	29.4165			1.89489			0.947443	−	0.319924i	$-0.103657\pi$
$241$	29.4165			1.89489			0.947443	+	0.319924i	$0.103657\pi$
$242$	−5.72286	+	5.72286i	−0.367879	+	0.367879i
$243$	10.5502	−	11.4758i	0.676796	−	0.736171i
$244$			1.74994i			0.112028i
$245$		0			0
$246$	5.72206	−	18.1274i	0.364825	−	1.15576i
$247$	5.47905	+	5.47905i	0.348623	+	0.348623i
$248$	−2.40888	−	2.40888i	−0.152964	−	0.152964i
$249$	−4.90100	+	15.5263i	−0.310589	+	0.983938i
$250$		0			0
$251$		−	2.86106i		−	0.180589i	−0.995915	−	0.0902943i	$-0.971219\pi$
$251$		−	2.86106i		−	0.180589i	0.995915	−	0.0902943i	$-0.0287808\pi$
$252$	0.519010	+	2.95476i	0.0326946	+	0.186133i
$253$	−4.25579	+	4.25579i	−0.267559	+	0.267559i
$254$	−15.8661			−0.995531
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.93961	−	2.93961i	0.183368	−	0.183368i	−0.609454	−	0.792822i	$-0.708611\pi$
$257$	2.93961	−	2.93961i	0.183368	−	0.183368i	0.792822	+	0.609454i	$0.208611\pi$
$258$	17.7546	−	9.23508i	1.10535	−	0.574951i
$259$			1.45536i			0.0904319i
$260$		0			0
$261$	−8.95112	+	12.7657i	−0.554061	+	0.790179i
$262$	−3.25792	−	3.25792i	−0.201275	−	0.201275i
$263$	16.7008	+	16.7008i	1.02982	+	1.02982i	0.999542	+	0.0302760i	$0.00963862\pi$
$263$	16.7008	+	16.7008i	1.02982	+	1.02982i	0.0302760	+	0.999542i	$0.490361\pi$
$264$	−2.81600	−	0.888895i	−0.173313	−	0.0547077i
$265$		0			0
$266$			5.94473i			0.364495i
$267$	1.80249	+	3.46532i	0.110311	+	0.212074i
$268$	−1.03802	+	1.03802i	−0.0634072	+	0.0634072i
$269$	−1.10509			−0.0673783			−0.0336891	−	0.999432i	$-0.510726\pi$
$269$	−1.10509			−0.0673783			−0.0336891	+	0.999432i	$0.510726\pi$
$270$		0			0
$271$	−23.9149			−1.45272			−0.726362	−	0.687312i	$-0.758790\pi$
$271$	−23.9149			−1.45272			−0.726362	+	0.687312i	$0.758790\pi$
$272$	4.76445	−	4.76445i	0.288887	−	0.288887i
$273$	−1.04179	−	2.00286i	−0.0630521	−	0.121219i
$274$		−	3.13487i		−	0.189384i
$275$		0			0
$276$	5.83087	+	1.84056i	0.350977	+	0.110789i
$277$	10.5902	+	10.5902i	0.636304	+	0.636304i	0.949642	−	0.313338i	$-0.101447\pi$
$277$	10.5902	+	10.5902i	0.636304	+	0.636304i	−0.313338	+	0.949642i	$0.601447\pi$
$278$	−0.228368	−	0.228368i	−0.0136966	−	0.0136966i
$279$	5.86744	−	8.36790i	0.351274	−	0.500973i
$280$		0			0
$281$		−	19.4466i		−	1.16009i	−0.814585	−	0.580044i	$-0.803036\pi$
$281$		−	19.4466i		−	1.16009i	0.814585	−	0.580044i	$-0.196964\pi$
$282$	0.948905	−	0.493574i	0.0565065	−	0.0293919i
$283$	17.2984	−	17.2984i	1.02829	−	1.02829i	0.0286974	−	0.999588i	$-0.490864\pi$
$283$	17.2984	−	17.2984i	1.02829	−	1.02829i	0.999588	−	0.0286974i	$-0.00913592\pi$
$284$	12.2611			0.727564
$285$		0			0
$286$	2.22221			0.131402
$287$	−7.76040	+	7.76040i	−0.458082	+	0.458082i
$288$	0.519010	+	2.95476i	0.0305830	+	0.174111i
$289$		−	28.4000i		−	1.67059i
$290$		0			0
$291$	9.74628	−	30.8760i	0.571337	−	1.80998i
$292$	−4.59693	−	4.59693i	−0.269015	−	0.269015i
$293$	17.8992	+	17.8992i	1.04568	+	1.04568i	0.998905	+	0.0467777i	$0.0148953\pi$
$293$	17.8992	+	17.8992i	1.04568	+	1.04568i	0.0467777	+	0.998905i	$0.485105\pi$
$294$	0.521378	−	1.65172i	0.0304074	−	0.0963300i
$295$		0			0
$296$			1.45536i			0.0845913i
$297$	1.16494	−	8.78196i	0.0675968	−	0.509581i
$298$	2.70491	−	2.70491i	0.156691	−	0.156691i
$299$	−4.60136			−0.266103
$300$		0			0
$301$	−11.5544			−0.665985
$302$	−3.35916	+	3.35916i	−0.193298	+	0.193298i
$303$	27.4176	−	14.2613i	1.57510	−	0.819291i
$304$			5.94473i			0.340953i
$305$		0			0
$306$	16.5506	+	11.6050i	0.946137	+	0.663416i
$307$	−7.54591	−	7.54591i	−0.430668	−	0.430668i	0.458187	−	0.888856i	$-0.348499\pi$
$307$	−7.54591	−	7.54591i	−0.430668	−	0.430668i	−0.888856	+	0.458187i	$0.848499\pi$
$308$	1.20554	+	1.20554i	0.0686921	+	0.0686921i
$309$	27.7984	+	8.77479i	1.58139	+	0.499181i
$310$		0			0
$311$			7.09388i			0.402257i	0.979565	+	0.201129i	$0.0644609\pi$
$311$			7.09388i			0.402257i	−0.979565	+	0.201129i	$0.935539\pi$
$312$	−1.04179	−	2.00286i	−0.0589799	−	0.113390i
$313$	−13.7044	+	13.7044i	−0.774616	+	0.774616i	−0.978910	−	0.204293i	$-0.934510\pi$
$313$	−13.7044	+	13.7044i	−0.774616	+	0.774616i	0.204293	+	0.978910i	$0.434510\pi$
$314$	−14.5758			−0.822559
$315$		0			0
$316$	−7.19515			−0.404759
$317$	20.1184	−	20.1184i	1.12996	−	1.12996i	0.139778	−	0.990183i	$-0.455361\pi$
$317$	20.1184	−	20.1184i	1.12996	−	1.12996i	0.990183	−	0.139778i	$-0.0446389\pi$
$318$	7.76764	+	14.9334i	0.435587	+	0.837425i
$319$			8.86046i			0.496090i
$320$		0			0
$321$	−9.27236	−	2.92690i	−0.517533	−	0.163364i
$322$	−2.49622	−	2.49622i	−0.139109	−	0.139109i
$323$	28.3234	+	28.3234i	1.57595	+	1.57595i
$324$	−8.46126	+	3.06710i	−0.470070	+	0.170395i
$325$		0			0
$326$		−	6.29706i		−	0.348762i
$327$	−10.2416	+	5.32718i	−0.566361	+	0.294593i
$328$	−7.76040	+	7.76040i	−0.428497	+	0.428497i
$329$	−0.617532			−0.0340456
$330$		0			0
$331$	7.35408			0.404217			0.202108	−	0.979363i	$-0.435221\pi$
$331$	7.35408			0.404217			0.202108	+	0.979363i	$0.435221\pi$
$332$	6.64687	−	6.64687i	0.364794	−	0.364794i
$333$	−4.30026	+	0.755349i	−0.235653	+	0.0413929i
$334$		−	12.6184i		−	0.690451i
$335$		0			0
$336$	0.521378	−	1.65172i	0.0284435	−	0.0901085i
$337$	22.3830	+	22.3830i	1.21928	+	1.21928i	0.967884	+	0.251397i	$0.0808898\pi$
$337$	22.3830	+	22.3830i	1.21928	+	1.21928i	0.251397	+	0.967884i	$0.419110\pi$
$338$	−7.99106	−	7.99106i	−0.434656	−	0.434656i
$339$	−3.19824	+	10.1320i	−0.173705	+	0.550293i
$340$		0			0
$341$		−	5.80801i		−	0.314521i
$342$	−17.5653	+	3.08537i	−0.949821	+	0.166838i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−11.5544			−0.622972
$345$		0			0
$346$	6.29457			0.338398
$347$	13.9437	−	13.9437i	0.748536	−	0.748536i	−0.225668	−	0.974204i	$-0.572457\pi$
$347$	13.9437	−	13.9437i	0.748536	−	0.748536i	0.974204	+	0.225668i	$0.0724566\pi$
$348$	7.98588	−	4.15386i	0.428088	−	0.222670i
$349$		−	4.36703i		−	0.233762i	−0.993146	−	0.116881i	$-0.962710\pi$
$349$		−	4.36703i		−	0.233762i	0.993146	−	0.116881i	$-0.0372896\pi$
$350$		0			0
$351$	5.37729	−	4.11776i	0.287019	−	0.219790i
$352$	1.20554	+	1.20554i	0.0642556	+	0.0642556i
$353$	−9.91003	−	9.91003i	−0.527458	−	0.527458i	0.392356	−	0.919814i	$-0.371660\pi$
$353$	−9.91003	−	9.91003i	−0.527458	−	0.527458i	−0.919814	+	0.392356i	$0.871660\pi$
$354$	1.13363	+	0.357841i	0.0602520	+	0.0190191i
$355$		0			0
$356$		−	2.25517i		−	0.119524i
$357$	−5.38544	−	10.3536i	−0.285028	−	0.547971i
$358$	−7.55173	+	7.55173i	−0.399121	+	0.399121i
$359$	31.8147			1.67912			0.839559	−	0.543269i	$-0.182814\pi$
$359$	31.8147			1.67912			0.839559	+	0.543269i	$0.182814\pi$
$360$		0			0
$361$	−16.3398			−0.859988
$362$	−9.06614	+	9.06614i	−0.476506	+	0.476506i
$363$	6.46876	+	12.4363i	0.339522	+	0.652737i
$364$			1.30343i			0.0683184i
$365$		0			0
$366$	2.89040	+	0.912379i	0.151083	+	0.0476908i
$367$	14.4435	+	14.4435i	0.753945	+	0.753945i	0.975213	−	0.221268i	$-0.0710196\pi$
$367$	14.4435	+	14.4435i	0.753945	+	0.753945i	−0.221268	+	0.975213i	$0.571020\pi$
$368$	−2.49622	−	2.49622i	−0.130125	−	0.130125i
$369$	−26.9579	−	18.9024i	−1.40337	−	0.984021i
$370$		0			0
$371$		−	9.71842i		−	0.504555i
$372$	−5.23472	+	2.72285i	−0.271408	+	0.141173i
$373$	13.5553	−	13.5553i	0.701867	−	0.701867i	−0.262944	−	0.964811i	$-0.584693\pi$
$373$	13.5553	−	13.5553i	0.701867	−	0.701867i	0.964811	+	0.262944i	$0.0846935\pi$
$374$	11.4875			0.594004
$375$		0			0
$376$	−0.617532			−0.0318468
$377$	−4.78996	+	4.78996i	−0.246696	+	0.246696i
$378$	5.15103	+	0.683293i	0.264940	+	0.0351448i
$379$			15.1496i			0.778182i	0.921199	+	0.389091i	$0.127211\pi$
$379$			15.1496i			0.778182i	−0.921199	+	0.389091i	$0.872789\pi$
$380$		0			0
$381$	−8.27227	+	26.2064i	−0.423801	+	1.34259i
$382$	−5.85935	−	5.85935i	−0.299790	−	0.299790i
$383$	−16.7428	−	16.7428i	−0.855519	−	0.855519i	0.135287	−	0.990806i	$-0.456804\pi$
$383$	−16.7428	−	16.7428i	−0.855519	−	0.855519i	−0.990806	+	0.135287i	$0.956804\pi$
$384$	0.521378	−	1.65172i	0.0266065	−	0.0842888i
$385$		0			0
$386$			5.08736i			0.258940i
$387$	−5.99686	−	34.1406i	−0.304837	−	1.73546i
$388$	−13.2182	+	13.2182i	−0.671050	+	0.671050i
$389$	−10.3633			−0.525439			−0.262719	−	0.964872i	$-0.584619\pi$
$389$	−10.3633			−0.525439			−0.262719	+	0.964872i	$0.584619\pi$
$390$		0			0
$391$	−23.7863			−1.20292
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−7.07977	+	3.68255i	−0.357127	+	0.185760i
$394$		−	7.78363i		−	0.392134i
$395$		0			0
$396$	−2.93640	+	4.18778i	−0.147560	+	0.210444i
$397$	−10.6075	−	10.6075i	−0.532373	−	0.532373i	0.388905	−	0.921278i	$-0.372853\pi$
$397$	−10.6075	−	10.6075i	−0.532373	−	0.532373i	−0.921278	+	0.388905i	$0.872853\pi$
$398$	−14.6839	−	14.6839i	−0.736038	−	0.736038i
$399$	9.81900	+	3.09945i	0.491565	+	0.155167i
$400$		0			0
$401$		−	9.37124i		−	0.467977i	−0.972239	−	0.233989i	$-0.924822\pi$
$401$		−	9.37124i		−	0.467977i	0.972239	−	0.233989i	$-0.0751779\pi$
$402$	1.17331	+	2.25572i	0.0585195	+	0.112505i
$403$	3.13981	−	3.13981i	0.156405	−	0.156405i
$404$	−17.8429			−0.887719
$405$		0			0
$406$	−5.19708			−0.257927
$407$	−1.75450	+	1.75450i	−0.0869674	+	0.0869674i
$408$	−5.38544	−	10.3536i	−0.266619	−	0.512580i
$409$		−	23.1943i		−	1.14689i	−0.819245	−	0.573443i	$-0.805607\pi$
$409$		−	23.1943i		−	1.14689i	0.819245	−	0.573443i	$-0.194393\pi$
$410$		0			0
$411$	−5.17791	−	1.63445i	−0.255408	−	0.0806216i
$412$	−11.9006	−	11.9006i	−0.586300	−	0.586300i
$413$	−0.485314	−	0.485314i	−0.0238807	−	0.0238807i
$414$	6.08018	−	8.67131i	0.298825	−	0.426171i
$415$		0			0
$416$			1.30343i			0.0639060i
$417$	−0.496265	+	0.258133i	−0.0243022	+	0.0126408i
$418$	−7.16661	+	7.16661i	−0.350531	+	0.350531i
$419$	1.64096			0.0801662			0.0400831	−	0.999196i	$-0.487238\pi$
$419$	1.64096			0.0801662			0.0400831	+	0.999196i	$0.487238\pi$
$420$		0			0
$421$	3.92047			0.191072			0.0955359	−	0.995426i	$-0.469544\pi$
$421$	3.92047			0.191072			0.0955359	+	0.995426i	$0.469544\pi$
$422$	−18.4215	+	18.4215i	−0.896743	+	0.896743i
$423$	−0.320505	−	1.82466i	−0.0155835	−	0.0887180i
$424$		−	9.71842i		−	0.471968i
$425$		0			0
$426$	6.39269	−	20.2519i	0.309727	−	0.981208i
$427$	−1.23739	−	1.23739i	−0.0598815	−	0.0598815i
$428$	3.96954	+	3.96954i	0.191875	+	0.191875i
$429$	1.15861	−	3.67046i	0.0559384	−	0.177212i
$430$		0			0
$431$			28.0498i			1.35111i	0.737308	+	0.675557i	$0.236097\pi$
$431$			28.0498i			1.35111i	−0.737308	+	0.675557i	$0.763903\pi$
$432$	5.15103	+	0.683293i	0.247829	+	0.0328750i
$433$	7.42460	−	7.42460i	0.356804	−	0.356804i	−0.505830	−	0.862633i	$-0.668814\pi$
$433$	7.42460	−	7.42460i	0.356804	−	0.356804i	0.862633	+	0.505830i	$0.168814\pi$
$434$	3.40667			0.163525
$435$		0			0
$436$	6.66506			0.319198
$437$	14.8394	−	14.8394i	0.709862	−	0.709862i
$438$	−9.98957	+	5.19608i	−0.477320	+	0.248278i
$439$			23.4410i			1.11878i	0.828905	+	0.559389i	$0.188964\pi$
$439$			23.4410i			1.11878i	−0.828905	+	0.559389i	$0.811036\pi$
$440$		0			0
$441$	−2.45633	−	1.72234i	−0.116968	−	0.0820161i
$442$	6.21014	+	6.21014i	0.295386	+	0.295386i
$443$	−10.0545	−	10.0545i	−0.477706	−	0.477706i	0.426692	−	0.904397i	$-0.359679\pi$
$443$	−10.0545	−	10.0545i	−0.477706	−	0.477706i	−0.904397	+	0.426692i	$0.859679\pi$
$444$	2.40385	+	0.758796i	0.114082	+	0.0360108i
$445$		0			0
$446$			2.11283i			0.100045i
$447$	−3.05746	−	5.87802i	−0.144613	−	0.278021i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−29.2933			−1.38244			−0.691218	−	0.722646i	$-0.742926\pi$
$449$	−29.2933			−1.38244			−0.691218	+	0.722646i	$0.742926\pi$
$450$		0			0
$451$	−18.7110			−0.881065
$452$	4.33754	−	4.33754i	0.204021	−	0.204021i
$453$	3.79699	+	7.29977i	0.178398	+	0.342973i
$454$			10.4429i			0.490110i
$455$		0			0
$456$	9.81900	+	3.09945i	0.459817	+	0.145145i
$457$	−21.3134	−	21.3134i	−0.996997	−	0.996997i	0.00299860	−	0.999996i	$-0.499046\pi$
$457$	−21.3134	−	21.3134i	−0.996997	−	0.996997i	−0.999996	+	0.00299860i	$0.999046\pi$
$458$	−9.49072	−	9.49072i	−0.443472	−	0.443472i
$459$	27.7974	−	21.2863i	1.29747	−	0.993561i
$460$		0			0
$461$			9.53108i			0.443907i	0.975057	+	0.221953i	$0.0712433\pi$
$461$			9.53108i			0.443907i	−0.975057	+	0.221953i	$0.928757\pi$
$462$	2.61976	−	1.36267i	0.121882	−	0.0633971i
$463$	−19.8492	+	19.8492i	−0.922471	+	0.922471i	−0.997204	−	0.0747323i	$-0.976190\pi$
$463$	−19.8492	+	19.8492i	−0.922471	+	0.922471i	0.0747323	+	0.997204i	$0.476190\pi$
$464$	−5.19708			−0.241268
$465$		0			0
$466$	11.7797			0.545685
$467$	−16.9197	+	16.9197i	−0.782949	+	0.782949i	−0.980327	−	0.197379i	$-0.936757\pi$
$467$	−16.9197	+	16.9197i	−0.782949	+	0.782949i	0.197379	+	0.980327i	$0.436757\pi$
$468$	−3.85133	+	0.676494i	−0.178028	+	0.0312709i
$469$		−	1.46798i		−	0.0677851i
$470$		0			0
$471$	−7.59950	+	24.0751i	−0.350167	+	1.10932i
$472$	−0.485314	−	0.485314i	−0.0223384	−	0.0223384i
$473$	−13.9293	−	13.9293i	−0.640471	−	0.640471i
$474$	−3.75139	+	11.8843i	−0.172307	+	0.545866i
$475$		0			0
$476$			6.73795i			0.308834i
$477$	28.7156	−	5.04396i	1.31480	−	0.230947i
$478$	−0.263534	+	0.263534i	−0.0120538	+	0.0120538i
$479$	5.16727			0.236099			0.118049	−	0.993008i	$-0.462336\pi$
$479$	5.16727			0.236099			0.118049	+	0.993008i	$0.462336\pi$
$480$		0			0
$481$	−1.89697			−0.0864943
$482$	−20.8006	+	20.8006i	−0.947443	+	0.947443i
$483$	−5.42452	+	2.82157i	−0.246824	+	0.128386i
$484$		−	8.09334i		−	0.367879i
$485$		0			0
$486$	0.654467	+	15.5747i	0.0296872	+	0.706483i
$487$	16.2445	+	16.2445i	0.736107	+	0.736107i	0.971822	−	0.235715i	$-0.0757433\pi$
$487$	16.2445	+	16.2445i	0.736107	+	0.736107i	−0.235715	+	0.971822i	$0.575743\pi$
$488$	−1.23739	−	1.23739i	−0.0560141	−	0.0560141i
$489$	−10.4009	−	3.28315i	−0.470347	−	0.148469i
$490$		0			0
$491$			9.61274i			0.433817i	0.976192	+	0.216908i	$0.0695973\pi$
$491$			9.61274i			0.433817i	−0.976192	+	0.216908i	$0.930403\pi$
$492$	8.77187	+	16.8641i	0.395466	+	0.760292i
$493$	−24.7612	+	24.7612i	−1.11519	+	1.11519i
$494$	−7.74854			−0.348623
$495$		0			0
$496$	3.40667			0.152964
$497$	−8.66993	+	8.66993i	−0.388899	+	0.388899i
$498$	−7.51320	−	14.4443i	−0.336675	−	0.647263i
$499$			6.60885i			0.295853i	0.988998	+	0.147926i	$0.0472599\pi$
$499$			6.60885i			0.295853i	−0.988998	+	0.147926i	$0.952740\pi$
$500$		0			0
$501$	−20.8421	−	6.57899i	−0.931156	−	0.293927i
$502$	2.02308	+	2.02308i	0.0902943	+	0.0902943i
$503$	−14.3231	−	14.3231i	−0.638634	−	0.638634i	0.311584	−	0.950219i	$-0.399140\pi$
$503$	−14.3231	−	14.3231i	−0.638634	−	0.638634i	−0.950219	+	0.311584i	$0.899140\pi$
$504$	−2.45633	−	1.72234i	−0.109414	−	0.0767190i
$505$		0			0
$506$		−	6.01860i		−	0.267559i
$507$	−17.3653	+	9.03259i	−0.771221	+	0.401152i
$508$	11.2191	−	11.2191i	0.497765	−	0.497765i
$509$	−21.9532			−0.973058			−0.486529	−	0.873664i	$-0.661737\pi$
$509$	−21.9532			−0.973058			−0.486529	+	0.873664i	$0.661737\pi$
$510$		0			0
$511$	6.50104			0.287589
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.06199	+	30.6215i	−0.179341	+	1.35197i
$514$			4.15724i			0.183368i
$515$		0			0
$516$	−6.02422	+	19.0846i	−0.265202	+	0.840153i
$517$	−0.744460	−	0.744460i	−0.0327413	−	0.0327413i
$518$	−1.02910	−	1.02910i	−0.0452160	−	0.0452160i
$519$	3.28185	−	10.3968i	0.144057	−	0.456371i
$520$		0			0
$521$		−	33.6715i		−	1.47518i	−0.675251	−	0.737588i	$-0.735965\pi$
$521$		−	33.6715i		−	1.47518i	0.675251	−	0.737588i	$-0.264035\pi$
$522$	−2.69734	−	15.3561i	−0.118059	−	0.672120i
$523$	−6.88874	+	6.88874i	−0.301223	+	0.301223i	−0.841492	−	0.540269i	$-0.818323\pi$
$523$	−6.88874	+	6.88874i	−0.301223	+	0.301223i	0.540269	+	0.841492i	$0.318323\pi$
$524$	4.60740			0.201275
$525$		0			0
$526$	−23.6185			−1.02982
$527$	16.2309	−	16.2309i	0.707030	−	0.707030i
$528$	2.61976	−	1.36267i	0.114010	−	0.0593025i
$529$		−	10.5378i		−	0.458164i
$530$		0			0
$531$	1.18210	−	1.68587i	0.0512990	−	0.0731605i
$532$	−4.20356	−	4.20356i	−0.182247	−	0.182247i
$533$	−10.1152	−	10.1152i	−0.438136	−	0.438136i
$534$	−3.72490	−	1.17580i	−0.161192	−	0.0508817i
$535$		0			0
$536$		−	1.46798i		−	0.0634072i
$537$	8.53600	+	16.4106i	0.368356	+	0.708170i
$538$	0.781414	−	0.781414i	0.0336891	−	0.0336891i
$539$	−1.70489			−0.0734349
$540$		0			0
$541$	1.57604			0.0677593			0.0338797	−	0.999426i	$-0.489214\pi$
$541$	1.57604			0.0677593			0.0338797	+	0.999426i	$0.489214\pi$
$542$	16.9104	−	16.9104i	0.726362	−	0.726362i
$543$	10.2478	+	19.7016i	0.439775	+	0.845476i
$544$			6.73795i			0.288887i
$545$		0			0
$546$	2.15290	+	0.679581i	0.0921355	+	0.0290834i
$547$	−5.30755	−	5.30755i	−0.226934	−	0.226934i	0.584476	−	0.811411i	$-0.301300\pi$
$547$	−5.30755	−	5.30755i	−0.226934	−	0.226934i	−0.811411	+	0.584476i	$0.801300\pi$
$548$	2.21669	+	2.21669i	0.0946922	+	0.0946922i
$549$	3.01398	−	4.29842i	0.128634	−	0.183452i
$550$		0			0
$551$		−	30.8952i		−	1.31618i
$552$	−5.42452	+	2.82157i	−0.230883	+	0.120094i
$553$	5.08774	−	5.08774i	0.216353	−	0.216353i
$554$	−14.9768			−0.636304
$555$		0			0
$556$	0.322961			0.0136966
$557$	−5.78892	+	5.78892i	−0.245284	+	0.245284i	−0.819032	−	0.573748i	$-0.805489\pi$
$557$	−5.78892	+	5.78892i	−0.245284	+	0.245284i	0.573748	+	0.819032i	$0.305489\pi$
$558$	1.76810	+	10.0659i	0.0748495	+	0.426124i
$559$		−	15.0604i		−	0.636986i
$560$		0			0
$561$	5.98933	−	18.9741i	0.252870	−	0.801086i
$562$	13.7508	+	13.7508i	0.580044	+	0.580044i
$563$	1.00705	+	1.00705i	0.0424423	+	0.0424423i	0.728009	−	0.685567i	$-0.240446\pi$
$563$	1.00705	+	1.00705i	0.0424423	+	0.0424423i	−0.685567	+	0.728009i	$0.740446\pi$
$564$	−0.321968	+	1.01999i	−0.0135573	+	0.0429492i
$565$		0			0
$566$			24.4637i			1.02829i
$567$	3.81424	−	8.15178i	0.160183	−	0.342343i
$568$	−8.66993	+	8.66993i	−0.363782	+	0.363782i
$569$	13.9047			0.582917			0.291459	−	0.956583i	$-0.405859\pi$
$569$	13.9047			0.582917			0.291459	+	0.956583i	$0.405859\pi$
$570$		0			0
$571$	34.8923			1.46020			0.730098	−	0.683343i	$-0.239475\pi$
$571$	34.8923			1.46020			0.730098	+	0.683343i	$0.239475\pi$
$572$	−1.57134	+	1.57134i	−0.0657010	+	0.0657010i
$573$	−12.7329	+	6.62304i	−0.531925	+	0.276681i
$574$		−	10.9749i		−	0.458082i
$575$		0			0
$576$	−2.45633	−	1.72234i	−0.102347	−	0.0717641i
$577$	−11.6857	−	11.6857i	−0.486482	−	0.486482i	0.420712	−	0.907194i	$-0.361780\pi$
$577$	−11.6857	−	11.6857i	−0.486482	−	0.486482i	−0.907194	+	0.420712i	$0.861780\pi$
$578$	20.0819	+	20.0819i	0.835295	+	0.835295i
$579$	8.40287	+	2.65244i	0.349212	+	0.110232i
$580$		0			0
$581$			9.40009i			0.389981i
$582$	14.9410	+	28.7243i	0.619323	+	1.19066i
$583$	11.7160	−	11.7160i	0.485226	−	0.485226i
$584$	6.50104			0.269015
$585$		0			0
$586$	−25.3133			−1.04568
$587$	19.5496	−	19.5496i	0.806898	−	0.806898i	−0.177265	−	0.984163i	$-0.556725\pi$
$587$	19.5496	−	19.5496i	0.806898	−	0.806898i	0.984163	+	0.177265i	$0.0567249\pi$
$588$	0.799269	+	1.53661i	0.0329613	+	0.0633687i
$589$			20.2517i			0.834457i
$590$		0			0
$591$	−12.8563	−	4.05822i	−0.528840	−	0.166933i
$592$	−1.02910	−	1.02910i	−0.0422957	−	0.0422957i
$593$	−11.8939	−	11.8939i	−0.488424	−	0.488424i	0.419385	−	0.907809i	$-0.362246\pi$
$593$	−11.8939	−	11.8939i	−0.488424	−	0.488424i	−0.907809	+	0.419385i	$0.862246\pi$
$594$	5.38604	+	7.03352i	0.220992	+	0.288589i
$595$		0			0
$596$			3.82532i			0.156691i
$597$	−31.9095	+	16.5978i	−1.30597	+	0.679302i
$598$	3.25365	−	3.25365i	0.133052	−	0.133052i
$599$	−33.0557			−1.35062			−0.675309	−	0.737535i	$-0.735990\pi$
$599$	−33.0557			−1.35062			−0.675309	+	0.737535i	$0.735990\pi$
$600$		0			0
$601$	−39.7500			−1.62144			−0.810718	−	0.585436i	$-0.800923\pi$
$601$	−39.7500			−1.62144			−0.810718	+	0.585436i	$0.800923\pi$
$602$	8.17020	−	8.17020i	0.332993	−	0.332993i
$603$	4.33754	−	0.761898i	0.176638	−	0.0310269i
$604$		−	4.75057i		−	0.193298i
$605$		0			0
$606$	−9.30292	+	29.4715i	−0.377905	+	1.19720i
$607$	−22.5491	−	22.5491i	−0.915238	−	0.915238i	0.0814398	−	0.996678i	$-0.474048\pi$
$607$	−22.5491	−	22.5491i	−0.915238	−	0.915238i	−0.996678	+	0.0814398i	$0.974048\pi$
$608$	−4.20356	−	4.20356i	−0.170477	−	0.170477i
$609$	−2.70964	+	8.58409i	−0.109800	+	0.347845i
$610$		0			0
$611$		−	0.804910i		−	0.0325632i
$612$	−19.9091	+	3.49707i	−0.804776	+	0.141361i
$613$	0.341141	−	0.341141i	0.0137786	−	0.0137786i	−0.700184	−	0.713962i	$-0.746899\pi$
$613$	0.341141	−	0.341141i	0.0137786	−	0.0137786i	0.713962	+	0.700184i	$0.246899\pi$
$614$	10.6715			0.430668
$615$		0			0
$616$	−1.70489			−0.0686921
$617$	24.0144	−	24.0144i	0.966784	−	0.966784i	−0.0326817	−	0.999466i	$-0.510405\pi$
$617$	24.0144	−	24.0144i	0.966784	−	0.966784i	0.999466	+	0.0326817i	$0.0104048\pi$
$618$	−25.8611	+	13.4517i	−1.04029	+	0.541106i
$619$			15.8572i			0.637355i	0.947863	+	0.318677i	$0.103239\pi$
$619$			15.8572i			0.637355i	−0.947863	+	0.318677i	$0.896761\pi$
$620$		0			0
$621$	−11.1525	−	14.5638i	−0.447533	−	0.584424i
$622$	−5.01613	−	5.01613i	−0.201129	−	0.201129i
$623$	1.59465	+	1.59465i	0.0638882	+	0.0638882i
$624$	2.15290	+	0.679581i	0.0861849	+	0.0272050i
$625$		0			0
$626$		−	19.3809i		−	0.774616i
$627$	8.10069	+	15.5737i	0.323510	+	0.621955i
$628$	10.3066	−	10.3066i	0.411280	−	0.411280i
$629$	−9.80618			−0.390998
$630$		0			0
$631$	9.22404			0.367203			0.183602	−	0.983001i	$-0.441224\pi$
$631$	9.22404			0.367203			0.183602	+	0.983001i	$0.441224\pi$
$632$	5.08774	−	5.08774i	0.202379	−	0.202379i
$633$	20.8225	+	40.0316i	0.827619	+	1.59111i
$634$			28.4517i			1.12996i
$635$		0			0
$636$	−16.0521	−	5.06698i	−0.636506	−	0.200919i
$637$	−0.921665	−	0.921665i	−0.0365177	−	0.0365177i
$638$	−6.26529	−	6.26529i	−0.248045	−	0.248045i
$639$	−30.1174	−	21.1178i	−1.19142	−	0.835408i
$640$		0			0
$641$			46.8024i			1.84858i	0.381688	+	0.924291i	$0.375343\pi$
$641$			46.8024i			1.84858i	−0.381688	+	0.924291i	$0.624657\pi$
$642$	8.62618	−	4.48692i	0.340448	−	0.177084i
$643$	15.5179	−	15.5179i	0.611968	−	0.611968i	−0.331491	−	0.943458i	$-0.607552\pi$
$643$	15.5179	−	15.5179i	0.611968	−	0.611968i	0.943458	+	0.331491i	$0.107552\pi$
$644$	3.53019			0.139109
$645$		0			0
$646$	−40.0553			−1.57595
$647$	−13.4045	+	13.4045i	−0.526986	+	0.526986i	−0.919672	−	0.392687i	$-0.871546\pi$
$647$	−13.4045	+	13.4045i	−0.526986	+	0.526986i	0.392687	+	0.919672i	$0.371546\pi$
$648$	3.81424	−	8.15178i	0.149838	−	0.320232i
$649$		−	1.17013i		−	0.0459317i
$650$		0			0
$651$	1.77616	−	5.62685i	0.0696134	−	0.220534i
$652$	4.45269	+	4.45269i	0.174381	+	0.174381i
$653$	22.3383	+	22.3383i	0.874165	+	0.874165i	0.992923	−	0.118758i	$-0.0378914\pi$
$653$	22.3383	+	22.3383i	0.874165	+	0.874165i	−0.118758	+	0.992923i	$0.537891\pi$
$654$	3.47502	−	11.0088i	0.135884	−	0.430477i
$655$		0			0
$656$		−	10.9749i		−	0.428497i
$657$	3.37411	+	19.2090i	0.131636	+	0.749416i
$658$	0.436661	−	0.436661i	0.0170228	−	0.0170228i
$659$	9.99021			0.389163			0.194582	−	0.980886i	$-0.437665\pi$
$659$	9.99021			0.389163			0.194582	+	0.980886i	$0.437665\pi$
$660$		0			0
$661$	−0.298368			−0.0116052			−0.00580259	−	0.999983i	$-0.501847\pi$
$661$	−0.298368			−0.0116052			−0.00580259	+	0.999983i	$0.501847\pi$
$662$	−5.20012	+	5.20012i	−0.202108	+	0.202108i
$663$	13.4952	−	7.01955i	0.524111	−	0.272617i
$664$			9.40009i			0.364794i
$665$		0			0
$666$	2.50663	−	3.57485i	0.0971299	−	0.138523i
$667$	12.9731	+	12.9731i	0.502319	+	0.502319i
$668$	8.92259	+	8.92259i	0.345225	+	0.345225i
$669$	3.48980	+	1.10158i	0.134923	+	0.0425897i
$670$		0			0
$671$		−	2.98345i		−	0.115175i
$672$	0.799269	+	1.53661i	0.0308325	+	0.0592760i
$673$	−3.14231	+	3.14231i	−0.121127	+	0.121127i	−0.765072	−	0.643945i	$-0.777297\pi$
$673$	−3.14231	+	3.14231i	−0.121127	+	0.121127i	0.643945	+	0.765072i	$0.277297\pi$
$674$	−31.6544			−1.21928
$675$		0			0
$676$	11.3011			0.434656
$677$	−4.61132	+	4.61132i	−0.177227	+	0.177227i	−0.790146	−	0.612919i	$-0.789995\pi$
$677$	−4.61132	+	4.61132i	−0.177227	+	0.177227i	0.612919	+	0.790146i	$0.289995\pi$
$678$	−4.90288	−	9.42588i	−0.188294	−	0.361999i
$679$		−	18.6933i		−	0.717383i
$680$		0			0
$681$	17.2487	+	5.44471i	0.660972	+	0.208642i
$682$	4.10688	+	4.10688i	0.157261	+	0.157261i
$683$	8.26190	+	8.26190i	0.316133	+	0.316133i	0.847280	−	0.531147i	$-0.178239\pi$
$683$	8.26190	+	8.26190i	0.316133	+	0.316133i	−0.531147	+	0.847280i	$0.678239\pi$
$684$	10.2388	−	14.6022i	0.391491	−	0.558329i
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$	−20.6242	+	10.7277i	−0.786863	+	0.409288i
$688$	8.17020	−	8.17020i	0.311486	−	0.311486i
$689$	12.6673			0.482586
$690$		0			0
$691$	−21.6167			−0.822338			−0.411169	−	0.911559i	$-0.634879\pi$
$691$	−21.6167			−0.822338			−0.411169	+	0.911559i	$0.634879\pi$
$692$	−4.45093	+	4.45093i	−0.169199	+	0.169199i
$693$	−0.884857	−	5.03756i	−0.0336129	−	0.191361i
$694$			19.7193i			0.748536i
$695$		0			0
$696$	−2.70964	+	8.58409i	−0.102709	+	0.325379i
$697$	−52.2892	−	52.2892i	−1.98060	−	1.98060i
$698$	3.08796	+	3.08796i	0.116881	+	0.116881i
$699$	6.14169	−	19.4567i	0.232300	−	0.735922i
$700$		0			0
$701$		−	1.45001i		−	0.0547660i	−0.999625	−	0.0273830i	$-0.991283\pi$
$701$		−	1.45001i		−	0.0547660i	0.999625	−	0.0273830i	$-0.00871737\pi$
$702$	−0.890626	+	6.71401i	−0.0336145	+	0.253404i
$703$	6.11771	−	6.11771i	0.230734	−	0.230734i
$704$	−1.70489			−0.0642556
$705$		0			0
$706$	14.0149			0.527458
$707$	12.6169	−	12.6169i	0.474506	−	0.474506i
$708$	−1.05463	+	0.548568i	−0.0396355	+	0.0206165i
$709$		−	0.737376i		−	0.0276927i	−0.999904	−	0.0138464i	$-0.995592\pi$
$709$		−	0.737376i		−	0.0276927i	0.999904	−	0.0138464i	$-0.00440758\pi$
$710$		0			0
$711$	17.6736	+	12.3925i	0.662814	+	0.464754i
$712$	1.59465	+	1.59465i	0.0597619	+	0.0597619i
$713$	−8.50380	−	8.50380i	−0.318470	−	0.318470i
$714$	11.1292	+	3.51302i	0.416499	+	0.131472i
$715$		0			0
$716$		−	10.6798i		−	0.399121i
$717$	0.297883	+	0.572685i	0.0111246	+	0.0213873i
$718$	−22.4964	+	22.4964i	−0.839559	+	0.839559i
$719$	−24.2873			−0.905762			−0.452881	−	0.891571i	$-0.649604\pi$
$719$	−24.2873			−0.905762			−0.452881	+	0.891571i	$0.649604\pi$
$720$		0			0
$721$	16.8300			0.626781
$722$	11.5540	−	11.5540i	0.429994	−	0.429994i
$723$	23.5117	+	45.2017i	0.874411	+	1.68107i
$724$		−	12.8215i		−	0.476506i
$725$		0			0
$726$	−13.3679	−	4.21969i	−0.496129	−	0.156607i
$727$	−0.423061	−	0.423061i	−0.0156905	−	0.0156905i	0.699218	−	0.714908i	$-0.253532\pi$
$727$	−0.423061	−	0.423061i	−0.0156905	−	0.0156905i	−0.714908	+	0.699218i	$0.753532\pi$
$728$	−0.921665	−	0.921665i	−0.0341592	−	0.0341592i
$729$	26.0662	+	7.03933i	0.965416	+	0.260716i
$730$		0			0
$731$		−	77.8531i		−	2.87950i
$732$	−2.68897	+	1.39867i	−0.0993871	+	0.0516963i
$733$	0.238162	−	0.238162i	0.00879670	−	0.00879670i	−0.702695	−	0.711491i	$-0.748020\pi$
$733$	0.238162	−	0.238162i	0.00879670	−	0.00879670i	0.711491	+	0.702695i	$0.248020\pi$
$734$	−20.4262			−0.753945
$735$		0			0
$736$	3.53019			0.130125
$737$	1.76971	−	1.76971i	0.0651882	−	0.0651882i
$738$	32.4281	−	5.69607i	1.19370	−	0.209675i
$739$		−	41.6831i		−	1.53334i	−0.642042	−	0.766669i	$-0.721913\pi$
$739$		−	41.6831i		−	1.53334i	0.642042	−	0.766669i	$-0.278087\pi$
$740$		0			0
$741$	−4.03992	+	12.7984i	−0.148410	+	0.470161i
$742$	6.87196	+	6.87196i	0.252278	+	0.252278i
$743$	−1.84534	−	1.84534i	−0.0676990	−	0.0676990i	0.672447	−	0.740146i	$-0.265243\pi$
$743$	−1.84534	−	1.84534i	−0.0676990	−	0.0676990i	−0.740146	+	0.672447i	$0.765243\pi$
$744$	1.77616	−	5.62685i	0.0651173	−	0.206290i
$745$		0			0
$746$			19.1701i			0.701867i
$747$	−27.7750	+	4.87874i	−1.01624	+	0.178504i
$748$	−8.12288	+	8.12288i	−0.297002	+	0.297002i
$749$	−5.61377			−0.205123
$750$		0			0
$751$	27.4131			1.00032			0.500160	−	0.865933i	$-0.333275\pi$
$751$	27.4131			1.00032			0.500160	+	0.865933i	$0.333275\pi$
$752$	0.436661	−	0.436661i	0.0159234	−	0.0159234i
$753$	4.39633	−	2.28676i	0.160211	−	0.0833341i
$754$		−	6.77403i		−	0.246696i
$755$		0			0
$756$	−4.12549	+	3.15917i	−0.150043	+	0.114898i
$757$	−28.1863	−	28.1863i	−1.02445	−	1.02445i	−0.999694	−	0.0247547i	$-0.992120\pi$
$757$	−28.1863	−	28.1863i	−1.02445	−	1.02445i	−0.0247547	−	0.999694i	$-0.507880\pi$
$758$	−10.7124	−	10.7124i	−0.389091	−	0.389091i
$759$	−9.94101	−	3.13797i	−0.360836	−	0.113901i
$760$		0			0
$761$			17.7595i			0.643782i	0.946777	+	0.321891i	$0.104318\pi$
$761$			17.7595i			0.643782i	−0.946777	+	0.321891i	$0.895682\pi$
$762$	−12.6813	−	24.3801i	−0.459396	−	0.883197i
$763$	−4.71291	+	4.71291i	−0.170619	+	0.170619i
$764$	8.28637			0.299790
$765$		0			0
$766$	23.6779			0.855519
$767$	0.632573	−	0.632573i	0.0228409	−	0.0228409i
$768$	0.799269	+	1.53661i	0.0288411	+	0.0554476i
$769$		−	31.6783i		−	1.14235i	−0.820828	−	0.571175i	$-0.806488\pi$
$769$		−	31.6783i		−	1.14235i	0.820828	−	0.571175i	$-0.193512\pi$
$770$		0			0
$771$	6.86658	+	2.16750i	0.247294	+	0.0780605i
$772$	−3.59731	−	3.59731i	−0.129470	−	0.129470i
$773$	−24.0703	−	24.0703i	−0.865748	−	0.865748i	0.126250	−	0.991998i	$-0.459706\pi$
$773$	−24.0703	−	24.0703i	−0.865748	−	0.865748i	−0.991998	+	0.126250i	$0.959706\pi$
$774$	28.3814	+	19.9006i	1.02015	+	0.715312i
$775$		0			0
$776$		−	18.6933i		−	0.671050i
$777$	−2.23633	+	1.16323i	−0.0802278	+	0.0417306i
$778$	7.32794	−	7.32794i	0.262719	−	0.262719i
$779$	65.2426			2.33756
$780$		0			0
$781$	−20.9039			−0.748001
$782$	16.8194	−	16.8194i	0.601461	−	0.601461i
$783$	−26.7703	−	3.55113i	−0.956692	−	0.126907i
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$	2.40220	−	7.61011i	0.0856836	−	0.271444i
$787$	19.3092	+	19.3092i	0.688297	+	0.688297i	0.961855	−	0.273558i	$-0.0882007\pi$
$787$	19.3092	+	19.3092i	0.688297	+	0.688297i	−0.273558	+	0.961855i	$0.588201\pi$
$788$	5.50386	+	5.50386i	0.196067	+	0.196067i
$789$	−12.3142	+	39.0111i	−0.438397	+	1.38883i
$790$		0			0
$791$			6.13421i			0.218107i
$792$	−0.884857	−	5.03756i	−0.0314420	−	0.179002i
$793$	1.61285	−	1.61285i	0.0572741	−	0.0572741i
$794$	15.0012			0.532373
$795$		0			0
$796$	20.7662			0.736038
$797$	16.7052	−	16.7052i	0.591727	−	0.591727i	−0.346371	−	0.938098i	$-0.612586\pi$
$797$	16.7052	−	16.7052i	0.591727	−	0.591727i	0.938098	+	0.346371i	$0.112586\pi$
$798$	−9.13472	+	4.75144i	−0.323366	+	0.168199i
$799$		−	4.16090i		−	0.147202i
$800$		0			0
$801$	−3.88417	+	5.53944i	−0.137240	+	0.195727i
$802$	6.62647	+	6.62647i	0.233989	+	0.233989i
$803$	7.83728	+	7.83728i	0.276572	+	0.276572i
$804$	−2.42469	−	0.765374i	−0.0855122	−	0.0269927i
$805$		0			0
$806$			4.44036i			0.156405i
$807$	−0.883261	−	1.69809i	−0.0310923	−	0.0597754i
$808$	12.6169	−	12.6169i	0.443860	−	0.443860i
$809$	−12.8721			−0.452560			−0.226280	−	0.974062i	$-0.572657\pi$
$809$	−12.8721			−0.452560			−0.226280	+	0.974062i	$0.572657\pi$
$810$		0			0
$811$	−1.25946			−0.0442256			−0.0221128	−	0.999755i	$-0.507039\pi$
$811$	−1.25946			−0.0442256			−0.0221128	+	0.999755i	$0.507039\pi$
$812$	3.67489	−	3.67489i	0.128963	−	0.128963i
$813$	−19.1144	−	36.7478i	−0.670372	−	1.28880i
$814$		−	2.48124i		−	0.0869674i
$815$		0			0
$816$	11.1292	+	3.51302i	0.389599	+	0.122980i
$817$	48.5696	+	48.5696i	1.69924	+	1.69924i
$818$	16.4009	+	16.4009i	0.573443	+	0.573443i
$819$	2.24495	−	3.20166i	0.0784449	−	0.111875i
$820$		0			0
$821$			26.4873i			0.924415i	0.886772	+	0.462207i	$0.152942\pi$
$821$			26.4873i			0.924415i	−0.886772	+	0.462207i	$0.847058\pi$
$822$	4.81707	−	2.50560i	0.168015	−	0.0873930i
$823$	−2.53245	+	2.53245i	−0.0882758	+	0.0882758i	−0.749866	−	0.661590i	$-0.769882\pi$
$823$	−2.53245	+	2.53245i	−0.0882758	+	0.0882758i	0.661590	+	0.749866i	$0.269882\pi$
$824$	16.8300			0.586300
$825$		0			0
$826$	0.686337			0.0238807
$827$	−9.56258	+	9.56258i	−0.332524	+	0.332524i	−0.853544	−	0.521021i	$-0.825551\pi$
$827$	−9.56258	+	9.56258i	−0.332524	+	0.332524i	0.521021	+	0.853544i	$0.325551\pi$
$828$	1.83220	+	10.4309i	0.0636735	+	0.362498i
$829$		−	38.5455i		−	1.33874i	−0.742928	−	0.669371i	$-0.766564\pi$
$829$		−	38.5455i		−	1.33874i	0.742928	−	0.669371i	$-0.233436\pi$
$830$		0			0
$831$	−7.80859	+	24.7374i	−0.270877	+	0.858132i
$832$	−0.921665	−	0.921665i	−0.0319530	−	0.0319530i
$833$	−4.76445	−	4.76445i	−0.165079	−	0.165079i
$834$	0.168385	−	0.533439i	0.00583069	−	0.0184715i
$835$		0			0
$836$		−	10.1351i		−	0.350531i
$837$	17.5479	+	2.32775i	0.606543	+	0.0804589i
$838$	−1.16034	+	1.16034i	−0.0400831	+	0.0400831i
$839$	18.9721			0.654989			0.327495	−	0.944853i	$-0.393796\pi$
$839$	18.9721			0.654989			0.327495	+	0.944853i	$0.393796\pi$
$840$		0			0
$841$	−1.99040			−0.0686344
$842$	−2.77219	+	2.77219i	−0.0955359	+	0.0955359i
$843$	29.8818	−	15.5431i	1.02919	−	0.535332i
$844$		−	26.0519i		−	0.896743i
$845$		0			0
$846$	1.51686	+	1.06360i	0.0521507	+	0.0365673i
$847$	5.72286	+	5.72286i	0.196640	+	0.196640i
$848$	6.87196	+	6.87196i	0.235984	+	0.235984i
$849$	40.4071	+	12.7548i	1.38677	+	0.437745i
$850$		0			0
$851$			5.13771i			0.176119i
$852$	9.79994	+	18.8406i	0.335741	+	0.645467i
$853$	25.7974	−	25.7974i	0.883284	−	0.883284i	−0.110582	−	0.993867i	$-0.535272\pi$
$853$	25.7974	−	25.7974i	0.883284	−	0.883284i	0.993867	+	0.110582i	$0.0352716\pi$
$854$	1.74994			0.0598815
$855$		0			0
$856$	−5.61377			−0.191875
$857$	−13.3333	+	13.3333i	−0.455458	+	0.455458i	−0.897161	−	0.441703i	$-0.854374\pi$
$857$	−13.3333	+	13.3333i	−0.455458	+	0.455458i	0.441703	+	0.897161i	$0.354374\pi$
$858$	1.77614	+	3.41467i	0.0606366	+	0.116575i
$859$			7.46319i			0.254641i	0.991862	+	0.127320i	$0.0406377\pi$
$859$			7.46319i			0.254641i	−0.991862	+	0.127320i	$0.959362\pi$
$860$		0			0
$861$	−18.1274	−	5.72206i	−0.617779	−	0.195007i
$862$	−19.8342	−	19.8342i	−0.675557	−	0.675557i
$863$	−14.6455	−	14.6455i	−0.498539	−	0.498539i	0.412444	−	0.910983i	$-0.364675\pi$
$863$	−14.6455	−	14.6455i	−0.498539	−	0.498539i	−0.910983	+	0.412444i	$0.864675\pi$
$864$	−4.12549	+	3.15917i	−0.140352	+	0.107477i
$865$		0			0
$866$			10.5000i			0.356804i
$867$	43.6398	−	22.6993i	1.48208	−	0.770908i
$868$	−2.40888	+	2.40888i	−0.0817627	+	0.0817627i
$869$	12.2670			0.416128
$870$		0			0
$871$	1.91341			0.0648336
$872$	−4.71291	+	4.71291i	−0.159599	+	0.159599i
$873$	55.2343	−	9.70201i	1.86940	−	0.328363i
$874$			20.9860i			0.709862i
$875$		0			0
$876$	3.38950	−	10.7379i	0.114521	−	0.362799i
$877$	−3.06648	−	3.06648i	−0.103548	−	0.103548i	0.653435	−	0.756983i	$-0.273327\pi$
$877$	−3.06648	−	3.06648i	−0.103548	−	0.103548i	−0.756983	+	0.653435i	$0.773327\pi$
$878$	−16.5753	−	16.5753i	−0.559389	−	0.559389i
$879$	−13.1978	+	41.8104i	−0.445151	+	1.41023i
$880$		0			0
$881$		−	4.11283i		−	0.138565i	−0.997597	−	0.0692824i	$-0.977929\pi$
$881$		−	4.11283i		−	0.138565i	0.997597	−	0.0692824i	$-0.0220710\pi$
$882$	2.95476	−	0.519010i	0.0994921	−	0.0174760i
$883$	8.74068	−	8.74068i	0.294147	−	0.294147i	−0.544569	−	0.838716i	$-0.683307\pi$
$883$	8.74068	−	8.74068i	0.294147	−	0.294147i	0.838716	+	0.544569i	$0.183307\pi$
$884$	−8.78246			−0.295386
$885$		0			0
$886$	14.2193			0.477706
$887$	2.49148	−	2.49148i	0.0836558	−	0.0836558i	−0.664041	−	0.747696i	$-0.731160\pi$
$887$	2.49148	−	2.49148i	0.0836558	−	0.0836558i	0.747696	+	0.664041i	$0.231160\pi$
$888$	−2.23633	+	1.16323i	−0.0750462	+	0.0390354i
$889$			15.8661i			0.532133i
$890$		0			0
$891$	14.4255	−	5.22909i	0.483274	−	0.175181i
$892$	−1.49400	−	1.49400i	−0.0500227	−	0.0500227i
$893$	2.59583	+	2.59583i	0.0868661	+	0.0868661i
$894$	6.31833	+	1.99444i	0.211317	+	0.0667040i
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$	−3.67772	−	7.07049i	−0.122796	−	0.236077i
$898$	20.7135	−	20.7135i	0.691218	−	0.691218i
$899$	−17.7047			−0.590485
$900$		0			0
$901$	65.4823			2.18153
$902$	13.2307	−	13.2307i	0.440533	−	0.440533i
$903$	−9.23508	−	17.7546i	−0.307324	−	0.590837i
$904$			6.13421i			0.204021i
$905$		0			0
$906$	−7.84659	−	2.47685i	−0.260686	−	0.0822877i
$907$	28.0384	+	28.0384i	0.931001	+	0.931001i	0.997769	−	0.0667678i	$-0.0212687\pi$
$907$	28.0384	+	28.0384i	0.931001	+	0.931001i	−0.0667678	+	0.997769i	$0.521269\pi$
$908$	−7.38425	−	7.38425i	−0.245055	−	0.245055i
$909$	43.8281	+	30.7316i	1.45369	+	1.01930i
$910$		0			0
$911$			35.7595i			1.18476i	0.805657	+	0.592382i	$0.201812\pi$
$911$			35.7595i			1.18476i	−0.805657	+	0.592382i	$0.798188\pi$
$912$	−9.13472	+	4.75144i	−0.302481	+	0.157336i
$913$	−11.3322	+	11.3322i	−0.375041	+	0.375041i
$914$	30.1416			0.996997
$915$		0			0
$916$	13.4219			0.443472
$917$	−3.25792	+	3.25792i	−0.107586	+	0.107586i
$918$	−4.60400	+	34.7074i	−0.151955	+	1.14552i
$919$			55.1175i			1.81816i	0.416623	+	0.909079i	$0.363214\pi$
$919$			55.1175i			1.81816i	−0.416623	+	0.909079i	$0.636786\pi$
$920$		0			0
$921$	5.56391	−	17.6263i	0.183337	−	0.580808i
$922$	−6.73949	−	6.73949i	−0.221953	−	0.221953i
$923$	−11.3007	−	11.3007i	−0.371966	−	0.371966i
$924$	−0.888895	+	2.81600i	−0.0292425	+	0.0926396i
$925$		0			0
$926$		−	28.0710i		−	0.922471i
$927$	8.73493	+	49.7286i	0.286893	+	1.63330i
$928$	3.67489	−	3.67489i	0.120634	−	0.120634i
$929$	6.70076			0.219845			0.109922	−	0.993940i	$-0.464940\pi$
$929$	6.70076			0.219845			0.109922	+	0.993940i	$0.464940\pi$
$930$		0			0
$931$	5.94473			0.194831
$932$	−8.32952	+	8.32952i	−0.272842	+	0.272842i
$933$	−10.9005	+	5.66992i	−0.356867	+	0.185625i
$934$		−	23.9280i		−	0.782949i
$935$		0			0
$936$	2.24495	−	3.20166i	0.0733785	−	0.104649i
$937$	−9.53939	−	9.53939i	−0.311638	−	0.311638i	0.533906	−	0.845544i	$-0.320724\pi$
$937$	−9.53939	−	9.53939i	−0.311638	−	0.311638i	−0.845544	+	0.533906i	$0.820724\pi$
$938$	1.03802	+	1.03802i	0.0338926	+	0.0338926i
$939$	−32.0117	−	10.1048i	−1.04466	−	0.329757i
$940$		0			0
$941$		−	44.9315i		−	1.46472i	−0.680915	−	0.732362i	$-0.738418\pi$
$941$		−	44.9315i		−	1.46472i	0.680915	−	0.732362i	$-0.261582\pi$
$942$	−11.6500	−	22.3973i	−0.379577	−	0.729743i
$943$	−27.3957	+	27.3957i	−0.892126	+	0.892126i
$944$	0.686337			0.0223384
$945$		0			0
$946$	19.6990			0.640471
$947$	−1.70096	+	1.70096i	−0.0552738	+	0.0552738i	−0.734203	−	0.678930i	$-0.762444\pi$
$947$	−1.70096	+	1.70096i	−0.0552738	+	0.0552738i	0.678930	+	0.734203i	$0.262444\pi$
$948$	−5.75086	−	11.0561i	−0.186779	−	0.359086i
$949$			8.47366i			0.275067i
$950$		0			0
$951$	46.9941	+	14.8341i	1.52389	+	0.481029i
$952$	−4.76445	−	4.76445i	−0.154417	−	0.154417i
$953$	−31.9131	−	31.9131i	−1.03377	−	1.03377i	−0.999410	−	0.0343567i	$-0.989062\pi$
$953$	−31.9131	−	31.9131i	−1.03377	−	1.03377i	−0.0343567	−	0.999410i	$-0.510938\pi$
$954$	−16.7384	+	23.8716i	−0.541926	+	0.772873i
$955$		0			0
$956$		−	0.372694i		−	0.0120538i
$957$	−13.6151	+	7.08189i	−0.440113	+	0.228925i
$958$	−3.65381	+	3.65381i	−0.118049	+	0.118049i
$959$	−3.13487			−0.101230
$960$		0			0
$961$	−19.3946			−0.625632
$962$	1.34136	−	1.34136i	0.0432471	−	0.0432471i
$963$	−2.91361	−	16.5874i	−0.0938896	−	0.534521i
$964$		−	29.4165i		−	0.947443i
$965$		0			0
$966$	1.84056	−	5.83087i	0.0592192	−	0.187605i
$967$	24.6132	+	24.6132i	0.791508	+	0.791508i	0.981739	−	0.190232i	$-0.0609239\pi$
$967$	24.6132	+	24.6132i	0.791508	+	0.791508i	−0.190232	+	0.981739i	$0.560924\pi$
$968$	5.72286	+	5.72286i	0.183940	+	0.183940i
$969$	−20.8840	+	66.1600i	−0.670890	+	2.12536i
$970$		0			0
$971$			17.9560i			0.576235i	0.957595	+	0.288117i	$0.0930293\pi$
$971$			17.9560i			0.576235i	−0.957595	+	0.288117i	$0.906971\pi$
$972$	−11.4758	−	10.5502i	−0.368085	−	0.338398i
$973$	−0.228368	+	0.228368i	−0.00732113	+	0.00732113i
$974$	−22.9731			−0.736107
$975$		0			0
$976$	1.74994			0.0560141
$977$	−14.6134	+	14.6134i	−0.467526	+	0.467526i	−0.901112	−	0.433586i	$-0.857248\pi$
$977$	−14.6134	+	14.6134i	−0.467526	+	0.467526i	0.433586	+	0.901112i	$0.357248\pi$
$978$	9.67612	−	5.03304i	0.309408	−	0.160939i
$979$			3.84483i			0.122881i
$980$		0			0
$981$	−16.3716	−	11.4795i	−0.522704	−	0.366512i
$982$	−6.79723	−	6.79723i	−0.216908	−	0.216908i
$983$	−1.53415	−	1.53415i	−0.0489318	−	0.0489318i	0.682217	−	0.731149i	$-0.261016\pi$
$983$	−1.53415	−	1.53415i	−0.0489318	−	0.0489318i	−0.731149	+	0.682217i	$0.761016\pi$
$984$	−18.1274	−	5.72206i	−0.577879	−	0.182413i
$985$		0			0
$986$		−	35.0177i		−	1.11519i
$987$	−0.493574	−	0.948905i	−0.0157106	−	0.0302040i
$988$	5.47905	−	5.47905i	0.174312	−	0.174312i
$989$	−40.7893			−1.29702
$990$		0			0
$991$	−6.06527			−0.192670			−0.0963348	−	0.995349i	$-0.530712\pi$
$991$	−6.06527			−0.192670			−0.0963348	+	0.995349i	$0.530712\pi$
$992$	−2.40888	+	2.40888i	−0.0764820	+	0.0764820i
$993$	5.87789	+	11.3003i	0.186529	+	0.358606i
$994$		−	12.2611i		−	0.388899i
$995$		0			0
$996$	15.5263	+	4.90100i	0.491969	+	0.155294i
$997$	−12.6897	−	12.6897i	−0.401887	−	0.401887i	0.477011	−	0.878897i	$-0.341720\pi$
$997$	−12.6897	−	12.6897i	−0.401887	−	0.401887i	−0.878897	+	0.477011i	$0.841720\pi$
$998$	−4.67316	−	4.67316i	−0.147926	−	0.147926i
$999$	−4.59774	−	6.00409i	−0.145466	−	0.189961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.c.407.3		12
3.2	odd	2		1050.2.j.d.407.4		12
5.2	odd	4		210.2.j.b.113.3	yes	12
5.3	odd	4		1050.2.j.d.743.4		12
5.4	even	2		210.2.j.a.197.4	yes	12
15.2	even	4		210.2.j.a.113.4	✓	12
15.8	even	4	inner	1050.2.j.c.743.3		12
15.14	odd	2		210.2.j.b.197.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.4	✓	12	15.2	even	4
210.2.j.a.197.4	yes	12	5.4	even	2
210.2.j.b.113.3	yes	12	5.2	odd	4
210.2.j.b.197.3	yes	12	15.14	odd	2
1050.2.j.c.407.3		12	1.1	even	1	trivial
1050.2.j.c.743.3		12	15.8	even	4	inner
1050.2.j.d.407.4		12	3.2	odd	2
1050.2.j.d.743.4		12	5.3	odd	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.799269 + 1.53661i) q^{3} -1.00000i q^{4} +(-1.65172 - 0.521378i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.72234 + 2.45633i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.799269 + 1.53661i) q^{3} -1.00000i q^{4} +(-1.65172 - 0.521378i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.72234 + 2.45633i) q^{9} +1.70489i q^{11} +(1.53661 - 0.799269i) q^{12} +(-0.921665 + 0.921665i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.76445 + 4.76445i) q^{17} +(-0.519010 - 2.95476i) q^{18} -5.94473i q^{19} +(-0.521378 + 1.65172i) q^{21} +(-1.20554 - 1.20554i) q^{22} +(2.49622 + 2.49622i) q^{23} +(-0.521378 + 1.65172i) q^{24} -1.30343i q^{26} +(-5.15103 - 0.683293i) q^{27} +(0.707107 - 0.707107i) q^{28} +5.19708 q^{29} -3.40667 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.61976 + 1.36267i) q^{33} -6.73795i q^{34} +(2.45633 + 1.72234i) q^{36} +(1.02910 + 1.02910i) q^{37} +(4.20356 + 4.20356i) q^{38} +(-2.15290 - 0.679581i) q^{39} +10.9749i q^{41} +(-0.799269 - 1.53661i) q^{42} +(-8.17020 + 8.17020i) q^{43} +1.70489 q^{44} -3.53019 q^{46} +(-0.436661 + 0.436661i) q^{47} +(-0.799269 - 1.53661i) q^{48} +1.00000i q^{49} +(-11.1292 - 3.51302i) q^{51} +(0.921665 + 0.921665i) q^{52} +(-6.87196 - 6.87196i) q^{53} +(4.12549 - 3.15917i) q^{54} +1.00000i q^{56} +(9.13472 - 4.75144i) q^{57} +(-3.67489 + 3.67489i) q^{58} -0.686337 q^{59} -1.74994 q^{61} +(2.40888 - 2.40888i) q^{62} +(-2.95476 + 0.519010i) q^{63} +1.00000i q^{64} +(0.888895 - 2.81600i) q^{66} +(-1.03802 - 1.03802i) q^{67} +(4.76445 + 4.76445i) q^{68} +(-1.84056 + 5.83087i) q^{69} +12.2611i q^{71} +(-2.95476 + 0.519010i) q^{72} +(4.59693 - 4.59693i) q^{73} -1.45536 q^{74} -5.94473 q^{76} +(-1.20554 + 1.20554i) q^{77} +(2.00286 - 1.04179i) q^{78} -7.19515i q^{79} +(-3.06710 - 8.46126i) q^{81} +(-7.76040 - 7.76040i) q^{82} +(6.64687 + 6.64687i) q^{83} +(1.65172 + 0.521378i) q^{84} -11.5544i q^{86} +(4.15386 + 7.98588i) q^{87} +(-1.20554 + 1.20554i) q^{88} +2.25517 q^{89} -1.30343 q^{91} +(2.49622 - 2.49622i) q^{92} +(-2.72285 - 5.23472i) q^{93} -0.617532i q^{94} +(1.65172 + 0.521378i) q^{96} +(-13.2182 - 13.2182i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.18778 - 2.93640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3}+O(q^{10}) \) 12 * q - 4 * q^3	\( 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

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