LMFDB - Embedded newform 700.2.k.b.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(43,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("700.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.k (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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	700.43
Dual form			700.2.k.b.407.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.649412 - 1.25629i) q^{2} +(2.28163 - 2.28163i) q^{3} +(-1.15653 - 1.63170i) q^{4} +(-1.38467 - 4.34811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.80095 + 0.393286i) q^{8} -7.41170i q^{9} +O(q^{10})$	\(q+(0.649412 - 1.25629i) q^{2} +(2.28163 - 2.28163i) q^{3} +(-1.15653 - 1.63170i) q^{4} +(-1.38467 - 4.34811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.80095 + 0.393286i) q^{8} -7.41170i q^{9} +1.40679i q^{11} +(-6.36171 - 1.08417i) q^{12} +(0.699298 + 0.699298i) q^{13} +(1.34753 - 0.429127i) q^{14} +(-1.32489 + 3.77421i) q^{16} +(3.26865 - 3.26865i) q^{17} +(-9.31125 - 4.81325i) q^{18} -2.80674 q^{19} +3.22672 q^{21} +(1.76734 + 0.913587i) q^{22} +(-1.48618 + 1.48618i) q^{23} +(-5.49341 + 7.28808i) q^{24} +(1.33265 - 0.424388i) q^{26} +(-10.0659 - 10.0659i) q^{27} +(0.335998 - 1.97157i) q^{28} +4.85706i q^{29} +3.67738i q^{31} +(3.88110 + 4.11547i) q^{32} +(3.20978 + 3.20978i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(5.85431 - 5.85431i) q^{37} +(-1.82273 + 3.52608i) q^{38} +3.19108 q^{39} +3.53368 q^{41} +(2.09547 - 4.05369i) q^{42} +(-2.49869 + 2.49869i) q^{43} +(2.29546 - 1.62699i) q^{44} +(0.901930 + 2.83222i) q^{46} +(1.86901 + 1.86901i) q^{47} +(5.58845 + 11.6343i) q^{48} +1.00000i q^{49} -14.9157i q^{51} +(0.332288 - 1.94980i) q^{52} +(0.696542 + 0.696542i) q^{53} +(-19.1826 + 6.10876i) q^{54} +(-2.25867 - 1.70248i) q^{56} +(-6.40395 + 6.40395i) q^{57} +(6.10187 + 3.15424i) q^{58} +7.06573 q^{59} +2.19831 q^{61} +(4.61985 + 2.38814i) q^{62} +(5.24087 - 5.24087i) q^{63} +(7.69065 - 2.20315i) q^{64} +(6.11688 - 1.94794i) q^{66} +(2.25963 + 2.25963i) q^{67} +(-9.11374 - 1.55317i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(2.91492 + 20.7598i) q^{72} +(-4.68856 - 4.68856i) q^{73} +(-3.55285 - 11.1566i) q^{74} +(3.24607 + 4.57976i) q^{76} +(-0.994751 + 0.994751i) q^{77} +(2.07233 - 4.00892i) q^{78} +0.599288 q^{79} -23.6982 q^{81} +(2.29482 - 4.43932i) q^{82} +(4.53764 - 4.53764i) q^{83} +(-3.73179 - 5.26504i) q^{84} +(1.51640 + 4.76176i) q^{86} +(11.0820 + 11.0820i) q^{87} +(-0.553271 - 3.94035i) q^{88} +0.463673i q^{89} +0.988956i q^{91} +(4.14381 + 0.706194i) q^{92} +(8.39043 + 8.39043i) q^{93} +(3.56178 - 1.13426i) q^{94} +(18.2452 + 0.534737i) q^{96} +(-8.00558 + 8.00558i) q^{97} +(1.25629 + 0.649412i) q^{98} +10.4267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.649412	−	1.25629i	0.459204	−	0.888331i
$2$	0.649412	−	1.25629i	0.459204	−	0.888331i
$3$	2.28163	−	2.28163i	1.31730	−	1.31730i	0.401398	−	0.915904i	$-0.368524\pi$
$3$	2.28163	−	2.28163i	1.31730	−	1.31730i	0.915904	−	0.401398i	$-0.131476\pi$
$4$	−1.15653	−	1.63170i	−0.578263	−	0.815850i
$5$		0			0
$5$		0			0
$6$	−1.38467	−	4.34811i	−0.565290	−	1.77511i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−2.80095	+	0.393286i	−0.990286	+	0.139048i
$9$		−	7.41170i		−	2.47057i
$10$		0			0
$11$			1.40679i			0.424163i	0.977252	+	0.212082i	$0.0680243\pi$
$11$			1.40679i			0.424163i	−0.977252	+	0.212082i	$0.931976\pi$
$12$	−6.36171	−	1.08417i	−1.83647	−	0.312973i
$13$	0.699298	+	0.699298i	0.193950	+	0.193950i	0.797401	−	0.603450i	$-0.206208\pi$
$13$	0.699298	+	0.699298i	0.193950	+	0.193950i	−0.603450	+	0.797401i	$0.706208\pi$
$14$	1.34753	−	0.429127i	0.360144	−	0.114689i
$15$		0			0
$16$	−1.32489	+	3.77421i	−0.331223	+	0.943553i
$17$	3.26865	−	3.26865i	0.792764	−	0.792764i	−0.189179	−	0.981943i	$-0.560583\pi$
$17$	3.26865	−	3.26865i	0.792764	−	0.792764i	0.981943	+	0.189179i	$0.0605826\pi$
$18$	−9.31125	−	4.81325i	−2.19468	−	1.13449i
$19$	−2.80674			−0.643910			−0.321955	−	0.946755i	$-0.604340\pi$
$19$	−2.80674			−0.643910			−0.321955	+	0.946755i	$0.604340\pi$
$20$		0			0
$21$	3.22672			0.704127
$22$	1.76734	+	0.913587i	0.376797	+	0.194777i
$23$	−1.48618	+	1.48618i	−0.309890	+	0.309890i	−0.844867	−	0.534977i	$-0.820320\pi$
$23$	−1.48618	+	1.48618i	−0.309890	+	0.309890i	0.534977	+	0.844867i	$0.320320\pi$
$24$	−5.49341	+	7.28808i	−1.12134	+	1.48767i
$25$		0			0
$26$	1.33265	−	0.424388i	0.261355	−	0.0832293i
$27$	−10.0659	−	10.0659i	−1.93718	−	1.93718i
$28$	0.335998	−	1.97157i	0.0634977	−	0.372593i
$29$			4.85706i			0.901933i	0.892541	+	0.450967i	$0.148921\pi$
$29$			4.85706i			0.901933i	−0.892541	+	0.450967i	$0.851079\pi$
$30$		0			0
$31$			3.67738i			0.660477i	0.943898	+	0.330238i	$0.107129\pi$
$31$			3.67738i			0.660477i	−0.943898	+	0.330238i	$0.892871\pi$
$32$	3.88110	+	4.11547i	0.686088	+	0.727518i
$33$	3.20978	+	3.20978i	0.558751	+	0.558751i
$34$	−1.98367	−	6.22907i	−0.340196	−	1.06828i
$35$		0			0
$36$	−12.0937	+	8.57184i	−2.01561	+	1.42864i
$37$	5.85431	−	5.85431i	0.962443	−	0.962443i	−0.0368766	−	0.999320i	$-0.511741\pi$
$37$	5.85431	−	5.85431i	0.962443	−	0.962443i	0.999320	+	0.0368766i	$0.0117409\pi$
$38$	−1.82273	+	3.52608i	−0.295686	+	0.572005i
$39$	3.19108			0.510982
$40$		0			0
$41$	3.53368			0.551868			0.275934	−	0.961177i	$-0.411013\pi$
$41$	3.53368			0.551868			0.275934	+	0.961177i	$0.411013\pi$
$42$	2.09547	−	4.05369i	0.323338	−	0.625498i
$43$	−2.49869	+	2.49869i	−0.381046	+	0.381046i	−0.871479	−	0.490433i	$-0.836839\pi$
$43$	−2.49869	+	2.49869i	−0.381046	+	0.381046i	0.490433	+	0.871479i	$0.336839\pi$
$44$	2.29546	−	1.62699i	0.346054	−	0.245278i
$45$		0			0
$46$	0.901930	+	2.83222i	0.132982	+	0.417588i
$47$	1.86901	+	1.86901i	0.272624	+	0.272624i	0.830156	−	0.557532i	$-0.188252\pi$
$47$	1.86901	+	1.86901i	0.272624	+	0.272624i	−0.557532	+	0.830156i	$0.688252\pi$
$48$	5.58845	+	11.6343i	0.806623	+	1.67926i
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	14.9157i		−	2.08862i
$52$	0.332288	−	1.94980i	0.0460800	−	0.270389i
$53$	0.696542	+	0.696542i	0.0956775	+	0.0956775i	0.753325	−	0.657648i	$-0.228449\pi$
$53$	0.696542	+	0.696542i	0.0956775	+	0.0956775i	−0.657648	+	0.753325i	$0.728449\pi$
$54$	−19.1826	+	6.10876i	−2.61042	+	0.831297i
$55$		0			0
$56$	−2.25867	−	1.70248i	−0.301827	−	0.227503i
$57$	−6.40395	+	6.40395i	−0.848224	+	0.848224i
$58$	6.10187	+	3.15424i	0.801215	+	0.414171i
$59$	7.06573			0.919879			0.459940	−	0.887950i	$-0.347871\pi$
$59$	7.06573			0.919879			0.459940	+	0.887950i	$0.347871\pi$
$60$		0			0
$61$	2.19831			0.281465			0.140732	−	0.990048i	$-0.455054\pi$
$61$	2.19831			0.281465			0.140732	+	0.990048i	$0.455054\pi$
$62$	4.61985	+	2.38814i	0.586722	+	0.303294i
$63$	5.24087	−	5.24087i	0.660287	−	0.660287i
$64$	7.69065	−	2.20315i	0.961331	−	0.275394i
$65$		0			0
$66$	6.11688	−	1.94794i	0.752936	−	0.239775i
$67$	2.25963	+	2.25963i	0.276057	+	0.276057i	0.831533	−	0.555476i	$-0.187464\pi$
$67$	2.25963	+	2.25963i	0.276057	+	0.276057i	−0.555476	+	0.831533i	$0.687464\pi$
$68$	−9.11374	−	1.55317i	−1.10520	−	0.188350i
$69$			6.78184i			0.816438i
$70$		0			0
$71$			12.1891i			1.44658i	0.690546	+	0.723289i	$0.257370\pi$
$71$			12.1891i			1.44658i	−0.690546	+	0.723289i	$0.742630\pi$
$72$	2.91492	+	20.7598i	0.343527	+	2.44657i
$73$	−4.68856	−	4.68856i	−0.548754	−	0.548754i	0.377326	−	0.926080i	$-0.376843\pi$
$73$	−4.68856	−	4.68856i	−0.548754	−	0.548754i	−0.926080	+	0.377326i	$0.876843\pi$
$74$	−3.55285	−	11.1566i	−0.413010	−	1.29693i
$75$		0			0
$76$	3.24607	+	4.57976i	0.372350	+	0.525334i
$77$	−0.994751	+	0.994751i	−0.113362	+	0.113362i
$78$	2.07233	−	4.00892i	0.234645	−	0.453921i
$79$	0.599288			0.0674252			0.0337126	−	0.999432i	$-0.489267\pi$
$79$	0.599288			0.0674252			0.0337126	+	0.999432i	$0.489267\pi$
$80$		0			0
$81$	−23.6982			−2.63314
$82$	2.29482	−	4.43932i	0.253420	−	0.490241i
$83$	4.53764	−	4.53764i	0.498071	−	0.498071i	−0.412766	−	0.910837i	$-0.635437\pi$
$83$	4.53764	−	4.53764i	0.498071	−	0.498071i	0.910837	+	0.412766i	$0.135437\pi$
$84$	−3.73179	−	5.26504i	−0.407171	−	0.574462i
$85$		0			0
$86$	1.51640	+	4.76176i	0.163517	+	0.513473i
$87$	11.0820	+	11.0820i	1.18812	+	1.18812i
$88$	−0.553271	−	3.94035i	−0.0589789	−	0.420043i
$89$			0.463673i			0.0491493i	0.999698	+	0.0245746i	$0.00782314\pi$
$89$			0.463673i			0.0491493i	−0.999698	+	0.0245746i	$0.992177\pi$
$90$		0			0
$91$			0.988956i			0.103671i
$92$	4.14381	+	0.706194i	0.432022	+	0.0736258i
$93$	8.39043	+	8.39043i	0.870047	+	0.870047i
$94$	3.56178	−	1.13426i	0.367370	−	0.116990i
$95$		0			0
$96$	18.2452	+	0.534737i	1.86215	+	0.0545763i
$97$	−8.00558	+	8.00558i	−0.812843	+	0.812843i	−0.985059	−	0.172216i	$-0.944907\pi$
$97$	−8.00558	+	8.00558i	−0.812843	+	0.812843i	0.172216	+	0.985059i	$0.444907\pi$
$98$	1.25629	+	0.649412i	0.126904	+	0.0656006i
$99$	10.4267			1.04792
$100$		0			0
$101$	−6.03099			−0.600106			−0.300053	−	0.953923i	$-0.597004\pi$
$101$	−6.03099			−0.600106			−0.300053	+	0.953923i	$0.597004\pi$
$102$	−18.7385	−	9.68645i	−1.85538	−	0.959102i
$103$	9.95088	−	9.95088i	0.980489	−	0.980489i	−0.0193242	−	0.999813i	$-0.506151\pi$
$103$	9.95088	−	9.95088i	0.980489	−	0.980489i	0.999813	+	0.0193242i	$0.00615146\pi$
$104$	−2.23372	−	1.68367i	−0.219035	−	0.165098i
$105$		0			0
$106$	1.32740	−	0.422716i	0.128929	−	0.0410578i
$107$	−14.1841	−	14.1841i	−1.37123	−	1.37123i	−0.858626	−	0.512603i	$-0.828681\pi$
$107$	−14.1841	−	14.1841i	−1.37123	−	1.37123i	−0.512603	−	0.858626i	$-0.671319\pi$
$108$	−4.78304	+	28.0660i	−0.460249	+	2.70065i
$109$			1.01514i			0.0972330i	0.998818	+	0.0486165i	$0.0154812\pi$
$109$			1.01514i			0.0972330i	−0.998818	+	0.0486165i	$0.984519\pi$
$110$		0			0
$111$		−	26.7148i		−	2.53566i
$112$	−3.60561	+	1.73193i	−0.340698	+	0.163652i
$113$	−7.39345	−	7.39345i	−0.695518	−	0.695518i	0.267923	−	0.963440i	$-0.413663\pi$
$113$	−7.39345	−	7.39345i	−0.695518	−	0.695518i	−0.963440	+	0.267923i	$0.913663\pi$
$114$	3.88641	+	12.2040i	0.363996	+	1.14301i
$115$		0			0
$116$	7.92527	−	5.61732i	0.735842	−	0.521555i
$117$	5.18299	−	5.18299i	0.479167	−	0.479167i
$118$	4.58857	−	8.87660i	0.422412	−	0.817157i
$119$	4.62257			0.423750
$120$		0			0
$121$	9.02094			0.820086
$122$	1.42761	−	2.76172i	0.129250	−	0.250034i
$123$	8.06256	−	8.06256i	0.726977	−	0.726977i
$124$	6.00038	−	4.25299i	0.538850	−	0.381930i
$125$		0			0
$126$	−3.18056	−	9.98753i	−0.283347	−	0.889760i
$127$	−8.87092	−	8.87092i	−0.787167	−	0.787167i	0.193862	−	0.981029i	$-0.437899\pi$
$127$	−8.87092	−	8.87092i	−0.787167	−	0.787167i	−0.981029	+	0.193862i	$0.937899\pi$
$128$	2.22661	−	11.0924i	0.196806	−	0.980442i
$129$			11.4022i			1.00391i
$130$		0			0
$131$			13.1487i			1.14881i	0.818572	+	0.574404i	$0.194766\pi$
$131$			13.1487i			1.14881i	−0.818572	+	0.574404i	$0.805234\pi$
$132$	1.52520	−	8.94960i	0.132752	−	0.778962i
$133$	−1.98466	−	1.98466i	−0.172092	−	0.172092i
$134$	4.30618	−	1.37132i	0.371997	−	0.118464i
$135$		0			0
$136$	−7.86981	+	10.4408i	−0.674831	+	0.895295i
$137$	−4.94200	+	4.94200i	−0.422224	+	0.422224i	−0.885969	−	0.463745i	$-0.846505\pi$
$137$	−4.94200	+	4.94200i	−0.422224	+	0.422224i	0.463745	+	0.885969i	$0.346505\pi$
$138$	8.51996	+	4.40421i	0.725267	+	0.374912i
$139$	−21.2377			−1.80136			−0.900679	−	0.434485i	$-0.856931\pi$
$139$	−21.2377			−1.80136			−0.900679	+	0.434485i	$0.856931\pi$
$140$		0			0
$141$	8.52881			0.718255
$142$	15.3130	+	7.91574i	1.28504	+	0.664274i
$143$	−0.983765	+	0.983765i	−0.0822666	+	0.0822666i
$144$	27.9733	+	9.81970i	2.33111	+	0.818308i
$145$		0			0
$146$	−8.93499	+	2.84538i	−0.739465	+	0.235485i
$147$	2.28163	+	2.28163i	0.188186	+	0.188186i
$148$	−16.3232	−	2.78181i	−1.34176	−	0.228664i
$149$			6.64454i			0.544342i	0.962249	+	0.272171i	$0.0877416\pi$
$149$			6.64454i			0.544342i	−0.962249	+	0.272171i	$0.912258\pi$
$150$		0			0
$151$		−	20.3868i		−	1.65906i	−0.558464	−	0.829529i	$-0.688609\pi$
$151$		−	20.3868i		−	1.65906i	0.558464	−	0.829529i	$-0.311391\pi$
$152$	7.86154	−	1.10385i	0.637655	−	0.0895342i
$153$	−24.2263	−	24.2263i	−1.95858	−	1.95858i
$154$	0.603692	+	1.89570i	0.0486469	+	0.152760i
$155$		0			0
$156$	−3.69057	−	5.20689i	−0.295482	−	0.416885i
$157$	−12.5648	+	12.5648i	−1.00278	+	1.00278i	−0.00278769	+	0.999996i	$0.500887\pi$
$157$	−12.5648	+	12.5648i	−1.00278	+	1.00278i	−0.999996	+	0.00278769i	$0.999113\pi$
$158$	0.389185	−	0.752879i	0.0309619	−	0.0598959i
$159$	3.17851			0.252072
$160$		0			0
$161$	−2.10178			−0.165643
$162$	−15.3899	+	29.7719i	−1.20915	+	2.33910i
$163$	−12.2953	+	12.2953i	−0.963042	+	0.963042i	−0.999341	−	0.0362991i	$-0.988443\pi$
$163$	−12.2953	+	12.2953i	−0.963042	+	0.963042i	0.0362991	+	0.999341i	$0.488443\pi$
$164$	−4.08680	−	5.76591i	−0.319125	−	0.450242i
$165$		0			0
$166$	−2.75379	−	8.64739i	−0.213736	−	0.671168i
$167$	6.88960	+	6.88960i	0.533133	+	0.533133i	0.921503	−	0.388370i	$-0.126962\pi$
$167$	6.88960	+	6.88960i	0.533133	+	0.533133i	−0.388370	+	0.921503i	$0.626962\pi$
$168$	−9.03788	+	1.26902i	−0.697287	+	0.0979073i
$169$		−	12.0220i		−	0.924767i
$170$		0			0
$171$			20.8027i			1.59082i
$172$	6.96691	+	1.18731i	0.531222	+	0.0905315i
$173$	17.4943	+	17.4943i	1.33007	+	1.33007i	0.905303	+	0.424767i	$0.139644\pi$
$173$	17.4943	+	17.4943i	1.33007	+	1.33007i	0.424767	+	0.905303i	$0.360356\pi$
$174$	21.1190	−	6.72543i	1.60103	−	0.509854i
$175$		0			0
$176$	−5.30952	−	1.86384i	−0.400220	−	0.140493i
$177$	16.1214	−	16.1214i	1.21176	−	1.21176i
$178$	0.582508	+	0.301115i	0.0436608	+	0.0225695i
$179$	20.5554			1.53638			0.768192	−	0.640219i	$-0.221156\pi$
$179$	20.5554			1.53638			0.768192	+	0.640219i	$0.221156\pi$
$180$		0			0
$181$	−7.85989			−0.584221			−0.292110	−	0.956385i	$-0.594357\pi$
$181$	−7.85989			−0.584221			−0.292110	+	0.956385i	$0.594357\pi$
$182$	1.24242	+	0.642240i	0.0920940	+	0.0476060i
$183$	5.01574	−	5.01574i	0.370774	−	0.370774i
$184$	3.57823	−	4.74722i	0.263790	−	0.349969i
$185$		0			0
$186$	15.9897	−	5.09196i	1.17242	−	0.373361i
$187$	4.59830	+	4.59830i	0.336261	+	0.336261i
$188$	0.888105	−	5.21123i	0.0647717	−	0.380068i
$189$		−	14.2353i		−	1.03547i
$190$		0			0
$191$			8.67251i			0.627520i	0.949502	+	0.313760i	$0.101589\pi$
$191$			8.67251i			0.627520i	−0.949502	+	0.313760i	$0.898411\pi$
$192$	12.5205	−	22.5740i	0.903587	−	1.62914i
$193$	3.75160	+	3.75160i	0.270046	+	0.270046i	0.829119	−	0.559073i	$-0.188843\pi$
$193$	3.75160	+	3.75160i	0.270046	+	0.270046i	−0.559073	+	0.829119i	$0.688843\pi$
$194$	4.85840	+	15.2562i	0.348813	+	1.09533i
$195$		0			0
$196$	1.63170	−	1.15653i	0.116550	−	0.0826091i
$197$	12.3437	−	12.3437i	0.879452	−	0.879452i	−0.114026	−	0.993478i	$-0.536375\pi$
$197$	12.3437	−	12.3437i	0.879452	−	0.879452i	0.993478	+	0.114026i	$0.0363747\pi$
$198$	6.77124	−	13.0990i	0.481211	−	0.930903i
$199$	−4.29882			−0.304735			−0.152368	−	0.988324i	$-0.548690\pi$
$199$	−4.29882			−0.304735			−0.152368	+	0.988324i	$0.548690\pi$
$200$		0			0
$201$	10.3113			0.727302
$202$	−3.91660	+	7.57667i	−0.275571	+	0.533092i
$203$	−3.43446	+	3.43446i	−0.241052	+	0.241052i
$204$	−24.3380	+	17.2504i	−1.70400	+	1.20777i
$205$		0			0
$206$	−6.03896	−	18.9634i	−0.420754	−	1.32124i
$207$	11.0151	+	11.0151i	0.765605	+	0.765605i
$208$	−3.56579	+	1.71280i	−0.247243	+	0.118762i
$209$		−	3.94849i		−	0.273123i
$210$		0			0
$211$		−	19.5494i		−	1.34583i	−0.739718	−	0.672917i	$-0.765041\pi$
$211$		−	19.5494i		−	1.34583i	0.739718	−	0.672917i	$-0.234959\pi$
$212$	0.330978	−	1.94212i	0.0227317	−	0.133385i
$213$	27.8110	+	27.8110i	1.90558	+	1.90558i
$214$	−27.0307	+	8.60801i	−1.84778	+	0.588431i
$215$		0			0
$216$	32.1528	+	24.2353i	2.18772	+	1.64900i
$217$	−2.60030	+	2.60030i	−0.176520	+	0.176520i
$218$	1.27531	+	0.659246i	0.0863751	+	0.0446498i
$219$	−21.3951			−1.44575
$220$		0			0
$221$	4.57152			0.307514
$222$	−33.5615	−	17.3489i	−2.25250	−	1.16438i
$223$	−9.54503	+	9.54503i	−0.639183	+	0.639183i	−0.950354	−	0.311171i	$-0.899279\pi$
$223$	−9.54503	+	9.54503i	−0.639183	+	0.639183i	0.311171	+	0.950354i	$0.399279\pi$
$224$	−0.165722	+	5.65443i	−0.0110727	+	0.377802i
$225$		0			0
$226$	−14.0897	+	4.48692i	−0.937234	+	0.298465i
$227$	13.0467	+	13.0467i	0.865938	+	0.865938i	0.992020	−	0.126082i	$-0.0402403\pi$
$227$	13.0467	+	13.0467i	0.865938	+	0.865938i	−0.126082	+	0.992020i	$0.540240\pi$
$228$	17.8557	+	3.04299i	1.18252	+	0.201527i
$229$			15.6173i			1.03202i	0.856583	+	0.516010i	$0.172583\pi$
$229$			15.6173i			1.03202i	−0.856583	+	0.516010i	$0.827417\pi$
$230$		0			0
$231$			4.53931i			0.298665i
$232$	−1.91021	−	13.6044i	−0.125412	−	0.893172i
$233$	−2.70319	−	2.70319i	−0.177092	−	0.177092i	0.612995	−	0.790087i	$-0.289965\pi$
$233$	−2.70319	−	2.70319i	−0.177092	−	0.177092i	−0.790087	+	0.612995i	$0.789965\pi$
$234$	−3.14544	−	9.87723i	−0.205624	−	0.645695i
$235$		0			0
$236$	−8.17170	−	11.5291i	−0.531932	−	0.750484i
$237$	1.36736	−	1.36736i	0.0888193	−	0.0888193i
$238$	3.00195	−	5.80728i	0.194588	−	0.376430i
$239$	−15.4752			−1.00101			−0.500505	−	0.865734i	$-0.666852\pi$
$239$	−15.4752			−1.00101			−0.500505	+	0.865734i	$0.666852\pi$
$240$		0			0
$241$	28.7620			1.85272			0.926361	−	0.376636i	$-0.122919\pi$
$241$	28.7620			1.85272			0.926361	+	0.376636i	$0.122919\pi$
$242$	5.85831	−	11.3329i	0.376587	−	0.728507i
$243$	−23.8730	+	23.8730i	−1.53146	+	1.53146i
$244$	−2.54241	−	3.58699i	−0.162761	−	0.229633i
$245$		0			0
$246$	−4.89298	−	15.3648i	−0.311965	−	0.979626i
$247$	−1.96275	−	1.96275i	−0.124887	−	0.124887i
$248$	−1.44626	−	10.3002i	−0.0918378	−	0.654061i
$249$		−	20.7065i		−	1.31222i
$250$		0			0
$251$			26.0285i			1.64291i	0.570277	+	0.821453i	$0.306836\pi$
$251$			26.0285i			1.64291i	−0.570277	+	0.821453i	$0.693164\pi$
$252$	−14.6127	−	2.49032i	−0.920515	−	0.156875i
$253$	−2.09075	−	2.09075i	−0.131444	−	0.131444i
$254$	−16.9053	+	5.38356i	−1.06073	+	0.337795i
$255$		0			0
$256$	−12.4893	−	10.0008i	−0.780583	−	0.625052i
$257$	−16.3200	+	16.3200i	−1.01801	+	1.01801i	−0.0181764	+	0.999835i	$0.505786\pi$
$257$	−16.3200	+	16.3200i	−1.01801	+	1.01801i	−0.999835	+	0.0181764i	$0.994214\pi$
$258$	14.3244	+	7.40472i	0.891801	+	0.460998i
$259$	8.27925			0.514448
$260$		0			0
$261$	35.9991			2.22829
$262$	16.5186	+	8.53894i	1.02052	+	0.527538i
$263$	8.02566	−	8.02566i	0.494883	−	0.494883i	−0.414958	−	0.909841i	$-0.636204\pi$
$263$	8.02566	−	8.02566i	0.494883	−	0.494883i	0.909841	+	0.414958i	$0.136204\pi$
$264$	−10.2528	−	7.72807i	−0.631016	−	0.475630i
$265$		0			0
$266$	−3.78218	+	1.20445i	−0.231900	+	0.0738494i
$267$	1.05793	+	1.05793i	0.0647444	+	0.0647444i
$268$	1.07371	−	6.30035i	0.0655875	−	0.384855i
$269$			27.2178i			1.65950i	0.558136	+	0.829749i	$0.311517\pi$
$269$			27.2178i			1.65950i	−0.558136	+	0.829749i	$0.688483\pi$
$270$		0			0
$271$		−	0.155837i		−	0.00946643i	−0.999989	−	0.00473321i	$-0.998493\pi$
$271$		−	0.155837i		−	0.00946643i	0.999989	−	0.00473321i	$-0.00150663\pi$
$272$	8.00597	+	16.6672i	0.485433	+	1.01060i
$273$	2.25644	+	2.25644i	0.136566	+	0.136566i
$274$	2.99919	+	9.41799i	0.181188	+	0.568961i
$275$		0			0
$276$	11.0659	−	7.84339i	0.666091	−	0.472116i
$277$	14.8018	−	14.8018i	0.889353	−	0.889353i	−0.105108	−	0.994461i	$-0.533519\pi$
$277$	14.8018	−	14.8018i	0.889353	−	0.889353i	0.994461	+	0.105108i	$0.0335187\pi$
$278$	−13.7920	+	26.6807i	−0.827191	+	1.60020i
$279$	27.2556			1.63175
$280$		0			0
$281$	−2.56355			−0.152929			−0.0764644	−	0.997072i	$-0.524363\pi$
$281$	−2.56355			−0.152929			−0.0764644	+	0.997072i	$0.524363\pi$
$282$	5.53871	−	10.7147i	0.329826	−	0.638048i
$283$	−14.5487	+	14.5487i	−0.864828	+	0.864828i	−0.991894	−	0.127066i	$-0.959444\pi$
$283$	−14.5487	+	14.5487i	−0.864828	+	0.864828i	0.127066	+	0.991894i	$0.459444\pi$
$284$	19.8889	−	14.0970i	1.18019	−	0.836503i
$285$		0			0
$286$	0.597025	+	1.87476i	0.0353028	+	0.110857i
$287$	2.49869	+	2.49869i	0.147493	+	0.147493i
$288$	30.5026	−	28.7656i	1.79738	−	1.69503i
$289$		−	4.36814i		−	0.256949i
$290$		0			0
$291$			36.5316i			2.14152i
$292$	−2.22788	+	13.0728i	−0.130377	+	0.765025i
$293$	−4.71102	−	4.71102i	−0.275221	−	0.275221i	0.555977	−	0.831198i	$-0.312344\pi$
$293$	−4.71102	−	4.71102i	−0.275221	−	0.275221i	−0.831198	+	0.555977i	$0.812344\pi$
$294$	4.34811	−	1.38467i	0.253587	−	0.0807557i
$295$		0			0
$296$	−14.0952	+	18.7001i	−0.819268	+	1.08692i
$297$	14.1606	−	14.1606i	0.821681	−	0.821681i
$298$	8.34746	+	4.31505i	0.483556	+	0.249964i
$299$	−2.07857			−0.120207
$300$		0			0
$301$	−3.53368			−0.203678
$302$	−25.6118	−	13.2395i	−1.47379	−	0.761846i
$303$	−13.7605	+	13.7605i	−0.790520	+	0.790520i
$304$	3.71862	−	10.5932i	0.213278	−	0.607563i
$305$		0			0
$306$	−46.1680	+	14.7024i	−2.63925	+	0.840478i
$307$	−16.8508	−	16.8508i	−0.961723	−	0.961723i	0.0375706	−	0.999294i	$-0.488038\pi$
$307$	−16.8508	−	16.8508i	−0.961723	−	0.961723i	−0.999294	+	0.0375706i	$0.988038\pi$
$308$	2.77359	+	0.472679i	0.158040	+	0.0269334i
$309$		−	45.4085i		−	2.58320i
$310$		0			0
$311$		−	18.1620i		−	1.02987i	−0.857229	−	0.514936i	$-0.827816\pi$
$311$		−	18.1620i		−	1.02987i	0.857229	−	0.514936i	$-0.172184\pi$
$312$	−8.93806	+	1.25501i	−0.506018	+	0.0710509i
$313$	1.10904	+	1.10904i	0.0626869	+	0.0626869i	0.737755	−	0.675068i	$-0.235886\pi$
$313$	1.10904	+	1.10904i	0.0626869	+	0.0626869i	−0.675068	+	0.737755i	$0.735886\pi$
$314$	7.62532	+	23.9449i	0.430322	+	1.35129i
$315$		0			0
$316$	−0.693093	−	0.977859i	−0.0389895	−	0.0550088i
$317$	−20.8879	+	20.8879i	−1.17318	+	1.17318i	−0.191733	+	0.981447i	$0.561411\pi$
$317$	−20.8879	+	20.8879i	−1.17318	+	1.17318i	−0.981447	+	0.191733i	$0.938589\pi$
$318$	2.06416	−	3.99313i	0.115753	−	0.223923i
$319$	−6.83286			−0.382567
$320$		0			0
$321$	−64.7258			−3.61264
$322$	−1.36492	+	2.64044i	−0.0760641	+	0.147146i
$323$	−9.17425	+	9.17425i	−0.510469	+	0.510469i
$324$	27.4077	+	38.6684i	1.52265	+	2.14825i
$325$		0			0
$326$	7.46173	+	23.4312i	0.413267	+	1.29773i
$327$	2.31618	+	2.31618i	0.128085	+	0.128085i
$328$	−9.89766	+	1.38975i	−0.546507	+	0.0767360i
$329$			2.64318i			0.145723i
$330$		0			0
$331$		−	12.6325i		−	0.694343i	−0.937802	−	0.347172i	$-0.887142\pi$
$331$		−	12.6325i		−	0.694343i	0.937802	−	0.347172i	$-0.112858\pi$
$332$	−12.6520	−	2.15617i	−0.694367	−	0.118335i
$333$	−43.3904	−	43.3904i	−2.37778	−	2.37778i
$334$	13.1295	−	4.18114i	0.718416	−	0.228782i
$335$		0			0
$336$	−4.27505	+	12.1783i	−0.233223	+	0.664381i
$337$	−4.10542	+	4.10542i	−0.223636	+	0.223636i	−0.810028	−	0.586391i	$-0.800548\pi$
$337$	−4.10542	+	4.10542i	−0.223636	+	0.223636i	0.586391	+	0.810028i	$0.300548\pi$
$338$	−15.1031	−	7.80721i	−0.821499	−	0.424656i
$339$	−33.7383			−1.83241
$340$		0			0
$341$	−5.17330			−0.280150
$342$	26.1342	+	13.5095i	1.41318	+	0.730513i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	6.01600	−	7.98140i	0.324361	−	0.430328i
$345$		0			0
$346$	33.3390	−	10.6169i	1.79232	−	0.570769i
$347$	−10.4434	−	10.4434i	−0.560631	−	0.560631i	0.368855	−	0.929487i	$-0.379750\pi$
$347$	−10.4434	−	10.4434i	−0.560631	−	0.560631i	−0.929487	+	0.368855i	$0.879750\pi$
$348$	5.26589	−	30.8992i	0.282281	−	1.65637i
$349$			5.05181i			0.270417i	0.990817	+	0.135209i	$0.0431705\pi$
$349$			5.05181i			0.270417i	−0.990817	+	0.135209i	$0.956830\pi$
$350$		0			0
$351$		−	14.0781i		−	0.751434i
$352$	−5.78960	+	5.45989i	−0.308587	+	0.291013i
$353$	−7.68947	−	7.68947i	−0.409269	−	0.409269i	0.472215	−	0.881484i	$-0.343455\pi$
$353$	−7.68947	−	7.68947i	−0.409269	−	0.409269i	−0.881484	+	0.472215i	$0.843455\pi$
$354$	−9.78371	−	30.7226i	−0.519998	−	1.63289i
$355$		0			0
$356$	0.756576	−	0.536251i	0.0400984	−	0.0284212i
$357$	10.5470	−	10.5470i	0.558207	−	0.558207i
$358$	13.3489	−	25.8236i	0.705514	−	1.36482i
$359$	4.98657			0.263181			0.131591	−	0.991304i	$-0.457992\pi$
$359$	4.98657			0.263181			0.131591	+	0.991304i	$0.457992\pi$
$360$		0			0
$361$	−11.1222			−0.585379
$362$	−5.10431	+	9.87429i	−0.268276	+	0.518981i
$363$	20.5825	−	20.5825i	1.08030	−	1.08030i
$364$	1.61368	−	1.14375i	0.0845798	−	0.0599490i
$365$		0			0
$366$	−3.04394	−	9.55851i	−0.159109	−	0.499631i
$367$	−11.2675	−	11.2675i	−0.588160	−	0.588160i	0.348973	−	0.937133i	$-0.386531\pi$
$367$	−11.2675	−	11.2675i	−0.588160	−	0.588160i	−0.937133	+	0.348973i	$0.886531\pi$
$368$	−3.64013	−	7.57819i	−0.189755	−	0.395041i
$369$		−	26.1906i		−	1.36343i
$370$		0			0
$371$			0.985060i			0.0511418i
$372$	3.98691	−	23.3944i	0.206712	−	1.21294i
$373$	0.416629	+	0.416629i	0.0215722	+	0.0215722i	0.717811	−	0.696238i	$-0.245144\pi$
$373$	0.416629	+	0.416629i	0.0215722	+	0.0215722i	−0.696238	+	0.717811i	$0.745144\pi$
$374$	8.76300	−	2.79061i	0.453124	−	0.144299i
$375$		0			0
$376$	−5.97007	−	4.49996i	−0.307883	−	0.232068i
$377$	−3.39653	+	3.39653i	−0.174930	+	0.174930i
$378$	−17.8837	−	9.24460i	−0.919838	−	0.475491i
$379$	−23.7583			−1.22038			−0.610191	−	0.792254i	$-0.708907\pi$
$379$	−23.7583			−1.22038			−0.610191	+	0.792254i	$0.708907\pi$
$380$		0			0
$381$	−40.4804			−2.07387
$382$	10.8952	+	5.63203i	0.557446	+	0.288160i
$383$	3.03775	−	3.03775i	0.155222	−	0.155222i	−0.625224	−	0.780446i	$-0.714992\pi$
$383$	3.03775	−	3.03775i	0.155222	−	0.155222i	0.780446	+	0.625224i	$0.214992\pi$
$384$	−20.2286	−	30.3892i	−1.03229	−	1.55079i
$385$		0			0
$386$	7.14943	−	2.27676i	0.363896	−	0.115884i
$387$	18.5195	+	18.5195i	0.941401	+	0.941401i
$388$	22.3214	+	3.80404i	1.13320	+	0.193121i
$389$			25.1901i			1.27719i	0.769544	+	0.638593i	$0.220483\pi$
$389$			25.1901i			1.27719i	−0.769544	+	0.638593i	$0.779517\pi$
$390$		0			0
$391$			9.71561i			0.491340i
$392$	−0.393286	−	2.80095i	−0.0198640	−	0.141469i
$393$	30.0006	+	30.0006i	1.51333	+	1.51333i
$394$	−7.49111	−	23.5234i	−0.377396	−	1.18509i
$395$		0			0
$396$	−12.0588	−	17.0133i	−0.605976	−	0.854949i
$397$	2.73642	−	2.73642i	0.137337	−	0.137337i	−0.635096	−	0.772433i	$-0.719040\pi$
$397$	2.73642	−	2.73642i	0.137337	−	0.137337i	0.772433	+	0.635096i	$0.219040\pi$
$398$	−2.79171	+	5.40057i	−0.139936	+	0.270706i
$399$	−9.05656			−0.453395
$400$		0			0
$401$	−5.48728			−0.274022			−0.137011	−	0.990570i	$-0.543750\pi$
$401$	−5.48728			−0.274022			−0.137011	+	0.990570i	$0.543750\pi$
$402$	6.69627	−	12.9540i	0.333980	−	0.646085i
$403$	−2.57158	+	2.57158i	−0.128100	+	0.128100i
$404$	6.97500	+	9.84076i	0.347019	+	0.489596i
$405$		0			0
$406$	2.08430	+	6.54506i	0.103442	+	0.324826i
$407$	8.23579	+	8.23579i	0.408233	+	0.408233i
$408$	5.86615	+	41.7782i	0.290418	+	2.06833i
$409$		−	16.9930i		−	0.840250i	−0.907466	−	0.420125i	$-0.861986\pi$
$409$		−	16.9930i		−	0.840250i	0.907466	−	0.420125i	$-0.138014\pi$
$410$		0			0
$411$			22.5517i			1.11239i
$412$	−27.7453	−	4.72839i	−1.36691	−	0.232951i
$413$	4.99622	+	4.99622i	0.245848	+	0.245848i
$414$	20.9916	−	6.68484i	1.03168	−	0.328542i
$415$		0			0
$416$	−0.163891	+	5.59198i	−0.00803544	+	0.274169i
$417$	−48.4567	+	48.4567i	−2.37293	+	2.37293i
$418$	−4.96045	−	2.56420i	−0.242624	−	0.125419i
$419$	−3.87556			−0.189334			−0.0946668	−	0.995509i	$-0.530179\pi$
$419$	−3.87556			−0.189334			−0.0946668	+	0.995509i	$0.530179\pi$
$420$		0			0
$421$	20.7160			1.00964			0.504818	−	0.863226i	$-0.331560\pi$
$421$	20.7160			1.00964			0.504818	+	0.863226i	$0.331560\pi$
$422$	−24.5597	−	12.6956i	−1.19555	−	0.618012i
$423$	13.8526	−	13.8526i	0.673535	−	0.673535i
$424$	−2.22492	−	1.67704i	−0.108052	−	0.0814443i
$425$		0			0
$426$	52.9995	−	16.8779i	2.56783	−	0.817735i
$427$	1.55444	+	1.55444i	0.0752247	+	0.0752247i
$428$	−6.73991	+	39.5485i	−0.325786	+	1.91165i
$429$			4.48918i			0.216740i
$430$		0			0
$431$		−	9.76894i		−	0.470553i	−0.971928	−	0.235277i	$-0.924400\pi$
$431$		−	9.76894i		−	0.470553i	0.971928	−	0.235277i	$-0.0755996\pi$
$432$	51.3270	−	24.6546i	2.46947	−	1.18619i
$433$	−7.00877	−	7.00877i	−0.336820	−	0.336820i	0.518349	−	0.855169i	$-0.326547\pi$
$433$	−7.00877	−	7.00877i	−0.336820	−	0.336820i	−0.855169	+	0.518349i	$0.826547\pi$
$434$	1.57806	+	4.95540i	0.0757494	+	0.237867i
$435$		0			0
$436$	1.65641	−	1.17404i	0.0793276	−	0.0562263i
$437$	4.17133	−	4.17133i	0.199542	−	0.199542i
$438$	−13.8943	+	26.8785i	−0.663894	+	1.28430i
$439$	4.42580			0.211232			0.105616	−	0.994407i	$-0.466319\pi$
$439$	4.42580			0.211232			0.105616	+	0.994407i	$0.466319\pi$
$440$		0			0
$441$	7.41170			0.352938
$442$	2.96880	−	5.74315i	0.141211	−	0.273174i
$443$	3.11256	−	3.11256i	0.147882	−	0.147882i	−0.629289	−	0.777171i	$-0.716654\pi$
$443$	3.11256	−	3.11256i	0.147882	−	0.147882i	0.777171	+	0.629289i	$0.216654\pi$
$444$	−43.5905	+	30.8964i	−2.06872	+	1.46628i
$445$		0			0
$446$	5.79266	+	18.1900i	0.274291	+	0.861321i
$447$	15.1604	+	15.1604i	0.717062	+	0.717062i
$448$	6.99597	+	3.88025i	0.330529	+	0.183325i
$449$			21.8355i			1.03048i	0.857046	+	0.515240i	$0.172297\pi$
$449$			21.8355i			1.03048i	−0.857046	+	0.515240i	$0.827703\pi$
$450$		0			0
$451$			4.97115i			0.234082i
$452$	−3.51317	+	20.6146i	−0.165246	+	0.969631i
$453$	−46.5153	−	46.5153i	−2.18548	−	2.18548i
$454$	24.8631	−	7.91772i	1.16688	−	0.371597i
$455$		0			0
$456$	15.4186	−	20.4557i	0.722041	−	0.957928i
$457$	15.5775	−	15.5775i	0.728683	−	0.728683i	−0.241674	−	0.970357i	$-0.577696\pi$
$457$	15.5775	−	15.5775i	0.728683	−	0.728683i	0.970357	+	0.241674i	$0.0776965\pi$
$458$	19.6198	+	10.1421i	0.916775	+	0.473908i
$459$	−65.8037			−3.07146
$460$		0			0
$461$	−19.7670			−0.920641			−0.460321	−	0.887753i	$-0.652266\pi$
$461$	−19.7670			−0.920641			−0.460321	+	0.887753i	$0.652266\pi$
$462$	5.70269	+	2.94789i	0.265313	+	0.137148i
$463$	14.5239	−	14.5239i	0.674983	−	0.674983i	−0.283877	−	0.958861i	$-0.591621\pi$
$463$	14.5239	−	14.5239i	0.674983	−	0.674983i	0.958861	+	0.283877i	$0.0916209\pi$
$464$	−18.3316	−	6.43507i	−0.851022	−	0.298741i
$465$		0			0
$466$	−5.15147	+	1.64050i	−0.238637	+	0.0759949i
$467$	19.9348	+	19.9348i	0.922473	+	0.922473i	0.997204	−	0.0747303i	$-0.0238096\pi$
$467$	19.9348	+	19.9348i	0.922473	+	0.922473i	−0.0747303	+	0.997204i	$0.523810\pi$
$468$	−14.4513	−	2.46282i	−0.668014	−	0.113844i
$469$			3.19559i			0.147559i
$470$		0			0
$471$			57.3367i			2.64194i
$472$	−19.7908	+	2.77885i	−0.910943	+	0.127907i
$473$	−3.51513	−	3.51513i	−0.161626	−	0.161626i
$474$	−0.829817	−	2.60577i	−0.0381148	−	0.119687i
$475$		0			0
$476$	−5.34612	−	7.54265i	−0.245039	−	0.345717i
$477$	5.16257	−	5.16257i	0.236378	−	0.236378i
$478$	−10.0498	+	19.4414i	−0.459668	+	0.889228i
$479$	1.41875			0.0648244			0.0324122	−	0.999475i	$-0.489681\pi$
$479$	1.41875			0.0648244			0.0324122	+	0.999475i	$0.489681\pi$
$480$		0			0
$481$	8.18782			0.373332
$482$	18.6784	−	36.1334i	0.850777	−	1.64583i
$483$	−4.79549	+	4.79549i	−0.218202	+	0.218202i
$484$	−10.4330	−	14.7195i	−0.474225	−	0.669067i
$485$		0			0
$486$	14.4880	+	45.4949i	0.657189	+	2.06369i
$487$	−23.8013	−	23.8013i	−1.07854	−	1.07854i	−0.996641	−	0.0818995i	$-0.973901\pi$
$487$	−23.8013	−	23.8013i	−1.07854	−	1.07854i	−0.0818995	−	0.996641i	$-0.526099\pi$
$488$	−6.15736	+	0.864566i	−0.278731	+	0.0391370i
$489$			56.1067i			2.53723i
$490$		0			0
$491$		−	3.16673i		−	0.142913i	−0.997444	−	0.0714563i	$-0.977235\pi$
$491$		−	3.16673i		−	0.142913i	0.997444	−	0.0714563i	$-0.0227647\pi$
$492$	−22.4803	−	3.83111i	−1.01349	−	0.172720i
$493$	15.8760	+	15.8760i	0.715020	+	0.715020i
$494$	−3.74041	+	1.19115i	−0.168289	+	0.0535922i
$495$		0			0
$496$	−13.8792	−	4.87213i	−0.623195	−	0.218765i
$497$	−8.61898	+	8.61898i	−0.386614	+	0.386614i
$498$	−26.0133	−	13.4470i	−1.16568	−	0.602576i
$499$	−7.44903			−0.333464			−0.166732	−	0.986002i	$-0.553322\pi$
$499$	−7.44903			−0.333464			−0.166732	+	0.986002i	$0.553322\pi$
$500$		0			0
$501$	31.4391			1.40459
$502$	32.6994	+	16.9032i	1.45944	+	0.754429i
$503$	−19.3043	+	19.3043i	−0.860736	+	0.860736i	−0.991424	−	0.130687i	$-0.958282\pi$
$503$	−19.3043	+	19.3043i	−0.860736	+	0.860736i	0.130687	+	0.991424i	$0.458282\pi$
$504$	−12.6182	+	16.7406i	−0.562061	+	0.745684i
$505$		0			0
$506$	−3.98434	+	1.26883i	−0.177125	+	0.0564062i
$507$	−27.4297	−	27.4297i	−1.21820	−	1.21820i
$508$	−4.21523	+	24.7341i	−0.187020	+	1.09740i
$509$		−	11.3832i		−	0.504553i	−0.967655	−	0.252276i	$-0.918821\pi$
$509$		−	11.3832i		−	0.504553i	0.967655	−	0.252276i	$-0.0811792\pi$
$510$		0			0
$511$		−	6.63062i		−	0.293321i
$512$	−20.6747	+	9.19554i	−0.913700	+	0.406390i
$513$	28.2523	+	28.2523i	1.24737	+	1.24737i
$514$	9.90421	+	31.1010i	0.436856	+	1.37181i
$515$		0			0
$516$	18.6049	−	13.1869i	0.819037	−	0.580522i
$517$	−2.62931	+	2.62931i	−0.115637	+	0.115637i
$518$	5.37665	−	10.4011i	0.236236	−	0.457000i
$519$	79.8313			3.50421
$520$		0			0
$521$	−1.23560			−0.0541325			−0.0270662	−	0.999634i	$-0.508617\pi$
$521$	−1.23560			−0.0541325			−0.0270662	+	0.999634i	$0.508617\pi$
$522$	23.3783	−	45.2253i	1.02324	−	1.97946i
$523$	4.46402	−	4.46402i	0.195198	−	0.195198i	−0.602740	−	0.797938i	$-0.705924\pi$
$523$	4.46402	−	4.46402i	0.195198	−	0.195198i	0.797938	+	0.602740i	$0.205924\pi$
$524$	21.4548	−	15.2068i	0.937256	−	0.664314i
$525$		0			0
$526$	−4.87059	−	15.2945i	−0.212368	−	0.666872i
$527$	12.0201	+	12.0201i	0.523602	+	0.523602i
$528$	−16.3670	+	7.86178i	−0.712282	+	0.342140i
$529$			18.5825i			0.807936i
$530$		0			0
$531$		−	52.3691i		−	2.27262i
$532$	−0.943060	+	5.53370i	−0.0408868	+	0.239916i
$533$	2.47109	+	2.47109i	0.107035	+	0.107035i
$534$	2.01610	−	0.642035i	0.0872454	−	0.0277836i
$535$		0			0
$536$	−7.21778	−	5.44042i	−0.311761	−	0.234991i
$537$	46.8999	−	46.8999i	2.02388	−	2.02388i
$538$	34.1934	+	17.6756i	1.47418	+	0.762048i
$539$	−1.40679			−0.0605948
$540$		0			0
$541$	−32.2710			−1.38744			−0.693719	−	0.720246i	$-0.744029\pi$
$541$	−32.2710			−1.38744			−0.693719	+	0.720246i	$0.744029\pi$
$542$	−0.195776	−	0.101203i	−0.00840932	−	0.00434702i
$543$	−17.9334	+	17.9334i	−0.769595	+	0.769595i
$544$	26.1380	+	0.766059i	1.12066	+	0.0328445i
$545$		0			0
$546$	4.30009	−	1.36938i	0.184027	−	0.0586040i
$547$	−17.6256	−	17.6256i	−0.753617	−	0.753617i	0.221536	−	0.975152i	$-0.428893\pi$
$547$	−17.6256	−	17.6256i	−0.753617	−	0.753617i	−0.975152	+	0.221536i	$0.928893\pi$
$548$	13.7794	+	2.34831i	0.588628	+	0.100315i
$549$		−	16.2932i		−	0.695378i
$550$		0			0
$551$		−	13.6325i		−	0.580764i
$552$	−2.66721	−	18.9956i	−0.113524	−	0.808507i
$553$	0.423761	+	0.423761i	0.0180201	+	0.0180201i
$554$	−8.98286	−	28.2078i	−0.381645	−	1.19843i
$555$		0			0
$556$	24.5620	+	34.6536i	1.04166	+	1.46964i
$557$	−4.37875	+	4.37875i	−0.185534	+	0.185534i	−0.793762	−	0.608228i	$-0.791880\pi$
$557$	−4.37875	+	4.37875i	−0.185534	+	0.185534i	0.608228	+	0.793762i	$0.291880\pi$
$558$	17.7002	−	34.2410i	0.749307	−	1.44954i
$559$	−3.49465			−0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	−1.66480	+	3.22057i	−0.0702255	+	0.135851i
$563$	−3.63223	+	3.63223i	−0.153080	+	0.153080i	−0.779492	−	0.626412i	$-0.784523\pi$
$563$	−3.63223	+	3.63223i	−0.153080	+	0.153080i	0.626412	+	0.779492i	$0.284523\pi$
$564$	−9.86379	−	13.9165i	−0.415341	−	0.585989i
$565$		0			0
$566$	8.82925	+	27.7254i	0.371121	+	1.16539i
$567$	−16.7572	−	16.7572i	−0.703736	−	0.703736i
$568$	−4.79380	−	34.1410i	−0.201143	−	1.43253i
$569$		−	34.6567i		−	1.45288i	−0.687227	−	0.726442i	$-0.741172\pi$
$569$		−	34.6567i		−	1.45288i	0.687227	−	0.726442i	$-0.258828\pi$
$570$		0			0
$571$		−	33.3982i		−	1.39767i	−0.715282	−	0.698836i	$-0.753702\pi$
$571$		−	33.3982i		−	1.39767i	0.715282	−	0.698836i	$-0.246298\pi$
$572$	2.74296	+	0.467459i	0.114689	+	0.0195454i
$573$	19.7875	+	19.7875i	0.826634	+	0.826634i
$574$	4.76176	−	1.51640i	0.198752	−	0.0632932i
$575$		0			0
$576$	−16.3291	−	57.0008i	−0.680379	−	2.37503i
$577$	24.3607	−	24.3607i	1.01415	−	1.01415i	0.0142510	−	0.999898i	$-0.495464\pi$
$577$	24.3607	−	24.3607i	1.01415	−	1.01415i	0.999898	−	0.0142510i	$-0.00453637\pi$
$578$	−5.48765	−	2.83672i	−0.228256	−	0.117992i
$579$	17.1196			0.711464
$580$		0			0
$581$	6.41719			0.266230
$582$	45.8942	+	23.7241i	1.90238	+	0.983394i
$583$	−0.979889	+	0.979889i	−0.0405829	+	0.0405829i
$584$	14.9764	+	11.2885i	0.619726	+	0.467120i
$585$		0			0
$586$	−8.97779	+	2.85901i	−0.370869	+	0.118105i
$587$	23.3690	+	23.3690i	0.964544	+	0.964544i	0.999393	−	0.0348489i	$-0.0110950\pi$
$587$	23.3690	+	23.3690i	0.964544	+	0.964544i	−0.0348489	+	0.999393i	$0.511095\pi$
$588$	1.08417	−	6.36171i	0.0447105	−	0.262353i
$589$		−	10.3214i		−	0.425288i
$590$		0			0
$591$		−	56.3276i		−	2.31701i
$592$	14.3391	+	29.8517i	0.589333	+	1.22690i
$593$	4.58805	+	4.58805i	0.188409	+	0.188409i	0.795008	−	0.606599i	$-0.207467\pi$
$593$	4.58805	+	4.58805i	0.188409	+	0.188409i	−0.606599	+	0.795008i	$0.707467\pi$
$594$	−8.59374	−	26.9859i	−0.352606	−	1.10724i
$595$		0			0
$596$	10.8419	−	7.68459i	0.444101	−	0.314773i
$597$	−9.80834	+	9.80834i	−0.401429	+	0.401429i
$598$	−1.34985	+	2.61128i	−0.0551994	+	0.106783i
$599$	17.5172			0.715733			0.357867	−	0.933773i	$-0.383504\pi$
$599$	17.5172			0.715733			0.357867	+	0.933773i	$0.383504\pi$
$600$		0			0
$601$	2.55297			0.104138			0.0520689	−	0.998643i	$-0.483418\pi$
$601$	2.55297			0.104138			0.0520689	+	0.998643i	$0.483418\pi$
$602$	−2.29482	+	4.43932i	−0.0935297	+	0.180933i
$603$	16.7477	−	16.7477i	0.682018	−	0.682018i
$604$	−33.2652	+	23.5779i	−1.35354	+	0.959372i
$605$		0			0
$606$	8.35093	+	26.2234i	0.339233	+	1.06525i
$607$	−15.6500	−	15.6500i	−0.635214	−	0.635214i	0.314157	−	0.949371i	$-0.398278\pi$
$607$	−15.6500	−	15.6500i	−0.635214	−	0.635214i	−0.949371	+	0.314157i	$0.898278\pi$
$608$	−10.8932	−	11.5510i	−0.441779	−	0.468457i
$609$			15.6724i			0.635076i
$610$		0			0
$611$			2.61399i			0.105751i
$612$	−11.5117	+	67.5483i	−0.465332	+	2.73048i
$613$	−5.70344	−	5.70344i	−0.230360	−	0.230360i	0.582483	−	0.812843i	$-0.302081\pi$
$613$	−5.70344	−	5.70344i	−0.230360	−	0.230360i	−0.812843	+	0.582483i	$0.802081\pi$
$614$	−32.1125	+	10.2263i	−1.29596	+	0.412701i
$615$		0			0
$616$	2.39503	−	3.17747i	0.0964984	−	0.128024i
$617$	20.7105	−	20.7105i	0.833772	−	0.833772i	−0.154258	−	0.988031i	$-0.549299\pi$
$617$	20.7105	−	20.7105i	0.833772	−	0.833772i	0.988031	+	0.154258i	$0.0492987\pi$
$618$	−57.0462	−	29.4889i	−2.29474	−	1.18622i
$619$	30.5003			1.22591			0.612956	−	0.790117i	$-0.289980\pi$
$619$	30.5003			1.22591			0.612956	+	0.790117i	$0.289980\pi$
$620$		0			0
$621$	29.9195			1.20063
$622$	−22.8167	−	11.7946i	−0.914866	−	0.472921i
$623$	−0.327867	+	0.327867i	−0.0131357	+	0.0131357i
$624$	−4.22784	+	12.0438i	−0.169249	+	0.482138i
$625$		0			0
$626$	2.11351	−	0.673054i	0.0844728	−	0.0269006i
$627$	−9.00902	−	9.00902i	−0.359786	−	0.359786i
$628$	35.0336	+	5.97048i	1.39799	+	0.238248i
$629$		−	38.2714i		−	1.52598i
$630$		0			0
$631$			24.2931i			0.967092i	0.875319	+	0.483546i	$0.160651\pi$
$631$			24.2931i			0.967092i	−0.875319	+	0.483546i	$0.839349\pi$
$632$	−1.67858	+	0.235692i	−0.0667702	+	0.00937532i
$633$	−44.6045	−	44.6045i	−1.77287	−	1.77287i
$634$	12.6764	+	39.8061i	0.503443	+	1.58090i
$635$		0			0
$636$	−3.67603	−	5.18637i	−0.145764	−	0.205653i
$637$	−0.699298	+	0.699298i	−0.0277072	+	0.0277072i
$638$	−4.43735	+	8.58406i	−0.175676	+	0.339846i
$639$	90.3419			3.57387
$640$		0			0
$641$	22.4171			0.885424			0.442712	−	0.896664i	$-0.354016\pi$
$641$	22.4171			0.885424			0.442712	+	0.896664i	$0.354016\pi$
$642$	−42.0338	+	81.3144i	−1.65894	+	3.20922i
$643$	3.56268	−	3.56268i	0.140498	−	0.140498i	−0.633359	−	0.773858i	$-0.718325\pi$
$643$	3.56268	−	3.56268i	0.140498	−	0.140498i	0.773858	+	0.633359i	$0.218325\pi$
$644$	2.43076	+	3.42947i	0.0957855	+	0.135140i
$645$		0			0
$646$	5.56764	+	17.4834i	0.219056	+	0.687875i
$647$	11.7294	+	11.7294i	0.461132	+	0.461132i	0.899026	−	0.437895i	$-0.144276\pi$
$647$	11.7294	+	11.7294i	0.461132	+	0.461132i	−0.437895	+	0.899026i	$0.644276\pi$
$648$	66.3776	−	9.32019i	2.60756	−	0.366132i
$649$			9.94000i			0.390179i
$650$		0			0
$651$			11.8659i			0.465060i
$652$	34.2821	+	5.84240i	1.34259	+	0.228806i
$653$	8.87321	+	8.87321i	0.347235	+	0.347235i	0.859079	−	0.511843i	$-0.171037\pi$
$653$	8.87321	+	8.87321i	0.347235	+	0.347235i	−0.511843	+	0.859079i	$0.671037\pi$
$654$	4.41395	−	1.40564i	0.172599	−	0.0549648i
$655$		0			0
$656$	−4.68174	+	13.3368i	−0.182791	+	0.520716i
$657$	−34.7502	+	34.7502i	−1.35573	+	1.35573i
$658$	3.32060	+	1.71652i	0.129451	+	0.0669168i
$659$	−33.3787			−1.30025			−0.650126	−	0.759827i	$-0.725284\pi$
$659$	−33.3787			−1.30025			−0.650126	+	0.759827i	$0.725284\pi$
$660$		0			0
$661$	−6.95780			−0.270627			−0.135313	−	0.990803i	$-0.543204\pi$
$661$	−6.95780			−0.270627			−0.135313	+	0.990803i	$0.543204\pi$
$662$	−15.8700	−	8.20368i	−0.616806	−	0.318845i
$663$	10.4305	−	10.4305i	0.405088	−	0.405088i
$664$	−10.9251	+	14.4943i	−0.423977	+	0.562488i
$665$		0			0
$666$	−82.6892	+	26.3327i	−3.20414	+	1.02037i
$667$	−7.21847	−	7.21847i	−0.279500	−	0.279500i
$668$	3.27375	−	19.2098i	0.126665	−	0.743248i
$669$			43.5565i			1.68399i
$670$		0			0
$671$			3.09256i			0.119387i
$672$	12.5232	+	13.2794i	0.483093	+	0.512266i
$673$	5.34897	+	5.34897i	0.206188	+	0.206188i	0.802645	−	0.596457i	$-0.203425\pi$
$673$	5.34897	+	5.34897i	0.206188	+	0.206188i	−0.596457	+	0.802645i	$0.703425\pi$
$674$	2.49149	+	7.82371i	0.0959684	+	0.301358i
$675$		0			0
$676$	−19.6162	+	13.9037i	−0.754471	+	0.534759i
$677$	−21.2244	+	21.2244i	−0.815721	+	0.815721i	−0.985485	−	0.169764i	$-0.945700\pi$
$677$	−21.2244	+	21.2244i	−0.815721	+	0.815721i	0.169764	+	0.985485i	$0.445700\pi$
$678$	−21.9101	+	42.3851i	−0.841451	+	1.62779i
$679$	−11.3216			−0.434483
$680$		0			0
$681$	59.5354			2.28140
$682$	−3.35961	+	6.49917i	−0.128646	+	0.248866i
$683$	13.4673	−	13.4673i	0.515313	−	0.515313i	−0.400837	−	0.916150i	$-0.631281\pi$
$683$	13.4673	−	13.4673i	0.515313	−	0.515313i	0.916150	+	0.400837i	$0.131281\pi$
$684$	33.9438	−	24.0589i	1.29787	−	0.919916i
$685$		0			0
$686$	0.429127	+	1.34753i	0.0163841	+	0.0514491i
$687$	35.6329	+	35.6329i	1.35948	+	1.35948i
$688$	−6.12009	−	12.7411i	−0.233326	−	0.485749i
$689$			0.974181i			0.0371133i
$690$		0			0
$691$		−	28.2561i		−	1.07491i	−0.843291	−	0.537457i	$-0.819385\pi$
$691$		−	28.2561i		−	1.07491i	0.843291	−	0.537457i	$-0.180615\pi$
$692$	8.31284	−	48.7782i	0.316007	−	1.85427i
$693$	7.37280	+	7.37280i	0.280070	+	0.280070i
$694$	−19.9020	+	6.33786i	−0.755470	+	0.240582i
$695$		0			0
$696$	−35.3986	−	26.6818i	−1.34178	−	1.01137i
$697$	11.5504	−	11.5504i	0.437501	−	0.437501i
$698$	6.34654	+	3.28071i	0.240220	+	0.124177i
$699$	−12.3354			−0.466567
$700$		0			0
$701$	−26.0149			−0.982568			−0.491284	−	0.871000i	$-0.663472\pi$
$701$	−26.0149			−0.982568			−0.491284	+	0.871000i	$0.663472\pi$
$702$	−17.6862	−	9.14250i	−0.667522	−	0.345061i
$703$	−16.4315	+	16.4315i	−0.619727	+	0.619727i
$704$	3.09937	+	10.8191i	0.116812	+	0.407762i
$705$		0			0
$706$	−14.6538	+	4.66656i	−0.551504	+	0.175628i
$707$	−4.26455	−	4.26455i	−0.160385	−	0.160385i
$708$	−44.9501	−	7.66046i	−1.68933	−	0.287898i
$709$		−	17.6058i		−	0.661200i	−0.943771	−	0.330600i	$-0.892749\pi$
$709$		−	17.6058i		−	0.661200i	0.943771	−	0.330600i	$-0.107251\pi$
$710$		0			0
$711$		−	4.44175i		−	0.166579i
$712$	−0.182356	−	1.29873i	−0.00683409	−	0.0486718i
$713$	−5.46525	−	5.46525i	−0.204675	−	0.204675i
$714$	−6.40074	−	20.0995i	−0.239542	−	0.752203i
$715$		0			0
$716$	−23.7729	−	33.5403i	−0.888435	−	1.25346i
$717$	−35.3088	+	35.3088i	−1.31863	+	1.31863i
$718$	3.23834	−	6.26458i	0.120854	−	0.233792i
$719$	23.1731			0.864212			0.432106	−	0.901823i	$-0.357771\pi$
$719$	23.1731			0.864212			0.432106	+	0.901823i	$0.357771\pi$
$720$		0			0
$721$	14.0727			0.524093
$722$	−7.22290	+	13.9727i	−0.268809	+	0.520011i
$723$	65.6243	−	65.6243i	2.44059	−	2.44059i
$724$	9.09017	+	12.8250i	0.337834	+	0.476637i
$725$		0			0
$726$	−12.4910	−	39.2241i	−0.463586	−	1.45574i
$727$	−15.3777	−	15.3777i	−0.570326	−	0.570326i	0.361893	−	0.932220i	$-0.382131\pi$
$727$	−15.3777	−	15.3777i	−0.570326	−	0.570326i	−0.932220	+	0.361893i	$0.882131\pi$
$728$	−0.388943	−	2.77002i	−0.0144152	−	0.102664i
$729$			37.8443i			1.40164i
$730$		0			0
$731$			16.3347i			0.604160i
$732$	−13.9850	−	2.38335i	−0.516901	−	0.0880910i
$733$	29.5375	+	29.5375i	1.09099	+	1.09099i	0.995423	+	0.0955709i	$0.0304677\pi$
$733$	29.5375	+	29.5375i	1.09099	+	1.09099i	0.0955709	+	0.995423i	$0.469532\pi$
$734$	−21.4725	+	6.83800i	−0.792566	+	0.252395i
$735$		0			0
$736$	−11.8844	−	0.348310i	−0.438063	−	0.0128389i
$737$	−3.17882	+	3.17882i	−0.117093	+	0.117093i
$738$	−32.9030	−	17.0085i	−1.21117	−	0.626091i
$739$	28.9475			1.06485			0.532426	−	0.846476i	$-0.321280\pi$
$739$	28.9475			1.06485			0.532426	+	0.846476i	$0.321280\pi$
$740$		0			0
$741$	−8.95654			−0.329027
$742$	1.23752	+	0.639710i	0.0454308	+	0.0234845i
$743$	−23.4115	+	23.4115i	−0.858885	+	0.858885i	−0.991207	−	0.132322i	$-0.957757\pi$
$743$	−23.4115	+	23.4115i	−0.858885	+	0.858885i	0.132322	+	0.991207i	$0.457757\pi$
$744$	−26.8010	−	20.2013i	−0.982574	−	0.740617i
$745$		0			0
$746$	0.793971	−	0.252843i	0.0290694	−	0.00925723i
$747$	−33.6316	−	33.6316i	−1.23052	−	1.23052i
$748$	2.18499	−	12.8211i	0.0798912	−	0.468786i
$749$		−	20.0593i		−	0.732953i
$750$		0			0
$751$			44.0147i			1.60612i	0.595899	+	0.803059i	$0.296796\pi$
$751$			44.0147i			1.60612i	−0.595899	+	0.803059i	$0.703204\pi$
$752$	−9.53029	+	4.57781i	−0.347534	+	0.166936i
$753$	59.3875	+	59.3875i	2.16420	+	2.16420i
$754$	2.06128	+	6.47277i	0.0750673	+	0.235725i
$755$		0			0
$756$	−23.2278	+	16.4635i	−0.844786	+	0.598773i
$757$	−24.7062	+	24.7062i	−0.897961	+	0.897961i	−0.995256	−	0.0972943i	$-0.968981\pi$
$757$	−24.7062	+	24.7062i	−0.897961	+	0.897961i	0.0972943	+	0.995256i	$0.468981\pi$
$758$	−15.4289	+	29.8473i	−0.560405	+	1.08410i
$759$	−9.54063			−0.346303
$760$		0			0
$761$	−4.49696			−0.163015			−0.0815073	−	0.996673i	$-0.525973\pi$
$761$	−4.49696			−0.163015			−0.0815073	+	0.996673i	$0.525973\pi$
$762$	−26.2885	+	50.8551i	−0.952331	+	1.84229i
$763$	−0.717814	+	0.717814i	−0.0259866	+	0.0259866i
$764$	14.1509	−	10.0300i	0.511963	−	0.362872i
$765$		0			0
$766$	−1.84354	−	5.78904i	−0.0666098	−	0.209167i
$767$	4.94105	+	4.94105i	0.178411	+	0.178411i
$768$	−51.3143	+	5.67783i	−1.85165	+	0.204881i
$769$			14.9079i			0.537593i	0.963197	+	0.268797i	$0.0866259\pi$
$769$			14.9079i			0.537593i	−0.963197	+	0.268797i	$0.913374\pi$
$770$		0			0
$771$			74.4723i			2.68206i
$772$	1.78266	−	10.4603i	0.0641593	−	0.376475i
$773$	−19.5855	−	19.5855i	−0.704443	−	0.704443i	0.260918	−	0.965361i	$-0.415975\pi$
$773$	−19.5855	−	19.5855i	−0.704443	−	0.704443i	−0.965361	+	0.260918i	$0.915975\pi$
$774$	35.2927	−	11.2391i	1.26857	−	0.403981i
$775$		0			0
$776$	19.2747	−	25.5717i	0.691923	−	0.917971i
$777$	18.8902	−	18.8902i	0.677683	−	0.677683i
$778$	31.6460	+	16.3587i	1.13456	+	0.586489i
$779$	−9.91812			−0.355354
$780$		0			0
$781$	−17.1475			−0.613585
$782$	12.2056	+	6.30944i	0.436472	+	0.225625i
$783$	48.8906	−	48.8906i	1.74721	−	1.74721i
$784$	−3.77421	−	1.32489i	−0.134793	−	0.0473175i
$785$		0			0
$786$	57.1721	−	18.2067i	2.03926	−	0.649410i
$787$	3.97509	+	3.97509i	0.141697	+	0.141697i	0.774397	−	0.632700i	$-0.218053\pi$
$787$	3.97509	+	3.97509i	0.141697	+	0.141697i	−0.632700	+	0.774397i	$0.718053\pi$
$788$	−34.4170	−	5.86539i	−1.22606	−	0.208946i
$789$		−	36.6232i		−	1.30382i
$790$		0			0
$791$		−	10.4559i		−	0.371770i
$792$	−29.2047	+	4.10068i	−1.03774	+	0.145711i
$793$	1.53727	+	1.53727i	0.0545902	+	0.0545902i
$794$	−1.66067	−	5.21481i	−0.0589350	−	0.185067i
$795$		0			0
$796$	4.97170	+	7.01439i	0.176217	+	0.248618i
$797$	10.9874	−	10.9874i	0.389195	−	0.389195i	−0.485205	−	0.874400i	$-0.661255\pi$
$797$	10.9874	−	10.9874i	0.389195	−	0.389195i	0.874400	+	0.485205i	$0.161255\pi$
$798$	−5.88144	+	11.3777i	−0.208201	+	0.402765i
$799$	12.2183			0.432252
$800$		0			0
$801$	3.43661			0.121427
$802$	−3.56351	+	6.89362i	−0.125832	+	0.243422i
$803$	6.59582	−	6.59582i	0.232761	−	0.232761i
$804$	−11.9253	−	16.8249i	−0.420572	−	0.593369i
$805$		0			0
$806$	1.56063	+	4.90067i	0.0549710	+	0.172619i
$807$	62.1011	+	62.1011i	2.18606	+	2.18606i
$808$	16.8925	−	2.37190i	0.594276	−	0.0834433i
$809$		−	16.6619i		−	0.585802i	−0.956143	−	0.292901i	$-0.905379\pi$
$809$		−	16.6619i		−	0.585802i	0.956143	−	0.292901i	$-0.0946207\pi$
$810$		0			0
$811$		−	30.5372i		−	1.07231i	−0.844120	−	0.536154i	$-0.819877\pi$
$811$		−	30.5372i		−	1.07231i	0.844120	−	0.536154i	$-0.180123\pi$
$812$	9.57605	+	1.63196i	0.336054	+	0.0572707i
$813$	−0.355563	−	0.355563i	−0.0124701	−	0.0124701i
$814$	15.6950	−	4.99811i	0.550108	−	0.175184i
$815$		0			0
$816$	56.2951	+	19.7617i	1.97072	+	0.691798i
$817$	7.01317	−	7.01317i	0.245360	−	0.245360i
$818$	−21.3481	−	11.0355i	−0.746420	−	0.385846i
$819$	7.32985			0.256126
$820$		0			0
$821$	−18.4845			−0.645114			−0.322557	−	0.946550i	$-0.604542\pi$
$821$	−18.4845			−0.645114			−0.322557	+	0.946550i	$0.604542\pi$
$822$	28.3314	+	14.6453i	0.988173	+	0.510815i
$823$	30.2574	−	30.2574i	1.05471	−	1.05471i	0.0562914	−	0.998414i	$-0.482072\pi$
$823$	30.2574	−	30.2574i	1.05471	−	1.05471i	0.998414	−	0.0562914i	$-0.0179276\pi$
$824$	−23.9584	+	31.7855i	−0.834630	+	1.10730i
$825$		0			0
$826$	9.52131	−	3.03209i	0.331289	−	0.105500i
$827$	22.7990	+	22.7990i	0.792801	+	0.792801i	0.981949	−	0.189148i	$-0.0605726\pi$
$827$	22.7990	+	22.7990i	0.792801	+	0.792801i	−0.189148	+	0.981949i	$0.560573\pi$
$828$	5.23410	−	30.7127i	0.181898	−	1.06734i
$829$		−	33.4892i		−	1.16313i	−0.813501	−	0.581563i	$-0.802441\pi$
$829$		−	33.4892i		−	1.16313i	0.813501	−	0.581563i	$-0.197559\pi$
$830$		0			0
$831$		−	67.5445i		−	2.34309i
$832$	6.91871	+	3.83740i	0.239863	+	0.133038i
$833$	3.26865	+	3.26865i	0.113252	+	0.113252i
$834$	29.4072	+	92.3440i	1.01829	+	3.19761i
$835$		0			0
$836$	−6.44276	+	4.56654i	−0.222828	+	0.157937i
$837$	37.0161	−	37.0161i	1.27946	−	1.27946i
$838$	−2.51684	+	4.86883i	−0.0869428	+	0.168191i
$839$	6.43773			0.222255			0.111127	−	0.993806i	$-0.464554\pi$
$839$	6.43773			0.222255			0.111127	+	0.993806i	$0.464554\pi$
$840$		0			0
$841$	5.40897			0.186516
$842$	13.4532	−	26.0253i	0.463629	−	0.896890i
$843$	−5.84909	+	5.84909i	−0.201453	+	0.201453i
$844$	−31.8987	+	22.6094i	−1.09800	+	0.778247i
$845$		0			0
$846$	−8.40681	−	26.3989i	−0.289032	−	0.907612i
$847$	6.37877	+	6.37877i	0.219177	+	0.219177i
$848$	−3.55174	+	1.70605i	−0.121967	+	0.0585862i
$849$			66.3894i			2.27848i
$850$		0			0
$851$			17.4011i			0.596504i
$852$	13.2151	−	77.5434i	0.452740	−	2.65659i
$853$	−10.0581	−	10.0581i	−0.344383	−	0.344383i	0.513629	−	0.858012i	$-0.328301\pi$
$853$	−10.0581	−	10.0581i	−0.344383	−	0.344383i	−0.858012	+	0.513629i	$0.828301\pi$
$854$	2.96230	−	0.943355i	0.101368	−	0.0322809i
$855$		0			0
$856$	45.3074	+	34.1506i	1.54857	+	1.16724i
$857$	0.368344	−	0.368344i	0.0125824	−	0.0125824i	−0.700788	−	0.713370i	$-0.747168\pi$
$857$	0.368344	−	0.368344i	0.0125824	−	0.0125824i	0.713370	+	0.700788i	$0.247168\pi$
$858$	5.63971	+	2.91533i	0.192537	+	0.0995278i
$859$	4.00947			0.136801			0.0684006	−	0.997658i	$-0.478210\pi$
$859$	4.00947			0.136801			0.0684006	+	0.997658i	$0.478210\pi$
$860$		0			0
$861$	11.4022			0.388585
$862$	−12.2726	−	6.34407i	−0.418007	−	0.216080i
$863$	10.4856	−	10.4856i	0.356934	−	0.356934i	−0.505747	−	0.862682i	$-0.668783\pi$
$863$	10.4856	−	10.4856i	0.356934	−	0.356934i	0.862682	+	0.505747i	$0.168783\pi$
$864$	2.35910	−	80.4926i	0.0802582	−	2.73841i
$865$		0			0
$866$	−13.3566	+	4.25346i	−0.453877	+	0.144539i
$867$	−9.96649	−	9.96649i	−0.338480	−	0.338480i
$868$	7.25023	+	1.23559i	0.246089	+	0.0419388i
$869$			0.843073i			0.0285993i
$870$		0			0
$871$			3.16030i			0.107083i
$872$	−0.399241	−	2.84336i	−0.0135200	−	0.0962884i
$873$	59.3350	+	59.3350i	2.00818	+	2.00818i
$874$	−2.53148	−	7.94930i	−0.0856287	−	0.268889i
$875$		0			0
$876$	24.7440	+	34.9104i	0.836024	+	1.17951i
$877$	21.9287	−	21.9287i	0.740479	−	0.740479i	−0.232191	−	0.972670i	$-0.574589\pi$
$877$	21.9287	−	21.9287i	0.740479	−	0.740479i	0.972670	+	0.232191i	$0.0745894\pi$
$878$	2.87417	−	5.56008i	0.0969984	−	0.187644i
$879$	−21.4976			−0.725097
$880$		0			0
$881$	26.6186			0.896802			0.448401	−	0.893833i	$-0.351994\pi$
$881$	26.6186			0.896802			0.448401	+	0.893833i	$0.351994\pi$
$882$	4.81325	−	9.31125i	0.162071	−	0.313526i
$883$	−20.2772	+	20.2772i	−0.682383	+	0.682383i	−0.960537	−	0.278154i	$-0.910278\pi$
$883$	−20.2772	+	20.2772i	−0.682383	+	0.682383i	0.278154	+	0.960537i	$0.410278\pi$
$884$	−5.28708	−	7.45935i	−0.177824	−	0.250885i
$885$		0			0
$886$	−1.88894	−	5.93161i	−0.0634602	−	0.199276i
$887$	−30.2167	−	30.2167i	−1.01458	−	1.01458i	−0.999892	−	0.0146841i	$-0.995326\pi$
$887$	−30.2167	−	30.2167i	−1.01458	−	1.01458i	−0.0146841	−	0.999892i	$-0.504674\pi$
$888$	10.5066	+	74.8268i	0.352577	+	2.51102i
$889$		−	12.5454i		−	0.420758i
$890$		0			0
$891$		−	33.3385i		−	1.11688i
$892$	26.6137	+	4.53555i	0.891093	+	0.151861i
$893$	−5.24583	−	5.24583i	−0.175545	−	0.175545i
$894$	28.8912	−	9.20050i	0.966267	−	0.307711i
$895$		0			0
$896$	9.41799	−	6.26909i	0.314633	−	0.209436i
$897$	−4.74253	+	4.74253i	−0.158348	+	0.158348i
$898$	27.4317	+	14.1802i	0.915408	+	0.473201i
$899$	−17.8613			−0.595706
$900$		0			0
$901$	4.55351			0.151699
$902$	6.24520	+	3.22832i	0.207942	+	0.107491i
$903$	−8.06256	+	8.06256i	−0.268305	+	0.268305i
$904$	23.6164	+	17.8010i	0.785471	+	0.592051i
$905$		0			0
$906$	−88.6443	+	28.2291i	−2.94501	+	0.937848i
$907$	−0.867234	−	0.867234i	−0.0287960	−	0.0287960i	0.692562	−	0.721358i	$-0.256482\pi$
$907$	−0.867234	−	0.867234i	−0.0287960	−	0.0287960i	−0.721358	+	0.692562i	$0.756482\pi$
$908$	6.19943	−	36.3771i	0.205735	−	1.20722i
$909$			44.6999i			1.48260i
$910$		0			0
$911$		−	13.4236i		−	0.444743i	−0.974962	−	0.222372i	$-0.928620\pi$
$911$		−	13.4236i		−	0.444743i	0.974962	−	0.222372i	$-0.0713799\pi$
$912$	−15.6853	−	32.6544i	−0.519393	−	1.08130i
$913$	6.38351	+	6.38351i	0.211263	+	0.211263i
$914$	−9.45361	−	29.6860i	−0.312698	−	0.981926i
$915$		0			0
$916$	25.4827	−	18.0618i	0.841974	−	0.596779i
$917$	−9.29755	+	9.29755i	−0.307032	+	0.307032i
$918$	−42.7338	+	82.6686i	−1.41042	+	2.72847i
$919$	−26.2486			−0.865862			−0.432931	−	0.901427i	$-0.642521\pi$
$919$	−26.2486			−0.865862			−0.432931	+	0.901427i	$0.642521\pi$
$920$		0			0
$921$	−76.8945			−2.53376
$922$	−12.8369	+	24.8331i	−0.422762	+	0.817834i
$923$	−8.52380	+	8.52380i	−0.280564	+	0.280564i
$924$	7.40680	−	5.24984i	0.243666	−	0.172707i
$925$		0			0
$926$	−8.81423	−	27.6782i	−0.289653	−	0.909563i
$927$	−73.7530	−	73.7530i	−2.42236	−	2.42236i
$928$	−19.9891	+	18.8507i	−0.656173	+	0.618806i
$929$		−	19.9084i		−	0.653175i	−0.945167	−	0.326587i	$-0.894101\pi$
$929$		−	19.9084i		−	0.653175i	0.945167	−	0.326587i	$-0.105899\pi$
$930$		0			0
$931$		−	2.80674i		−	0.0919872i
$932$	−1.28448	+	7.53711i	−0.0420747	+	0.246886i
$933$	−41.4390	−	41.4390i	−1.35665	−	1.35665i
$934$	37.9898	−	12.0980i	1.24307	−	0.395858i
$935$		0			0
$936$	−12.4789	+	16.5557i	−0.407885	+	0.541140i
$937$	3.76752	−	3.76752i	0.123080	−	0.123080i	−0.642884	−	0.765964i	$-0.722262\pi$
$937$	3.76752	−	3.76752i	0.123080	−	0.123080i	0.765964	+	0.642884i	$0.222262\pi$
$938$	4.01459	+	2.07526i	0.131081	+	0.0677596i
$939$	5.06087			0.165155
$940$		0			0
$941$	4.83923			0.157754			0.0788772	−	0.996884i	$-0.474866\pi$
$941$	4.83923			0.157754			0.0788772	+	0.996884i	$0.474866\pi$
$942$	72.0316	+	37.2352i	2.34691	+	1.21319i
$943$	−5.25169	+	5.25169i	−0.171019	+	0.171019i
$944$	−9.36132	+	26.6675i	−0.304685	+	0.867954i
$945$		0			0
$946$	−6.69879	+	2.13325i	−0.217797	+	0.0693580i
$947$	−21.9318	−	21.9318i	−0.712689	−	0.712689i	0.254408	−	0.967097i	$-0.418119\pi$
$947$	−21.9318	−	21.9318i	−0.712689	−	0.712689i	−0.967097	+	0.254408i	$0.918119\pi$
$948$	−3.81250	−	0.649731i	−0.123824	−	0.0211023i
$949$		−	6.55739i		−	0.212862i
$950$		0			0
$951$			95.3170i			3.09086i
$952$	−12.9476	+	1.81799i	−0.419634	+	0.0589215i
$953$	−22.3422	−	22.3422i	−0.723734	−	0.723734i	0.245630	−	0.969364i	$-0.421005\pi$
$953$	−22.3422	−	22.3422i	−0.723734	−	0.723734i	−0.969364	+	0.245630i	$0.921005\pi$
$954$	−3.13304	−	9.83831i	−0.101436	−	0.318527i
$955$		0			0
$956$	17.8975	+	25.2509i	0.578847	+	0.816674i
$957$	−15.5901	+	15.5901i	−0.503956	+	0.503956i
$958$	0.921354	−	1.78236i	0.0297676	−	0.0575855i
$959$	−6.98905			−0.225688
$960$		0			0
$961$	17.4769			0.563770
$962$	5.31727	−	10.2863i	0.171436	−	0.331643i
$963$	−105.128	+	105.128i	−3.38771	+	3.38771i
$964$	−33.2640	−	46.9309i	−1.07136	−	1.51154i
$965$		0			0
$966$	2.91027	+	9.13877i	0.0936365	+	0.294035i
$967$	8.85634	+	8.85634i	0.284801	+	0.284801i	0.835020	−	0.550219i	$-0.185456\pi$
$967$	8.85634	+	8.85634i	0.284801	+	0.284801i	−0.550219	+	0.835020i	$0.685456\pi$
$968$	−25.2672	+	3.54781i	−0.812119	+	0.114031i
$969$			41.8646i			1.34488i
$970$		0			0
$971$		−	9.45772i		−	0.303513i	−0.988418	−	0.151756i	$-0.951507\pi$
$971$		−	9.45772i		−	0.303513i	0.988418	−	0.151756i	$-0.0484929\pi$
$972$	66.5634	+	11.3438i	2.13502	+	0.363854i
$973$	−15.0173	−	15.0173i	−0.481433	−	0.481433i
$974$	−45.3582	+	14.4445i	−1.45337	+	0.462831i
$975$		0			0
$976$	−2.91252	+	8.29689i	−0.0932276	+	0.265577i
$977$	43.6781	−	43.6781i	1.39739	−	1.39739i	0.589935	−	0.807451i	$-0.299153\pi$
$977$	43.6781	−	43.6781i	1.39739	−	1.39739i	0.807451	−	0.589935i	$-0.200847\pi$
$978$	70.4863	+	36.4364i	2.25390	+	1.16511i
$979$	−0.652291			−0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	−3.97833	−	2.05652i	−0.126954	−	0.0656260i
$983$	41.9474	−	41.9474i	1.33791	−	1.33791i	0.439835	−	0.898079i	$-0.355037\pi$
$983$	41.9474	−	41.9474i	1.33791	−	1.33791i	0.898079	−	0.439835i	$-0.144963\pi$
$984$	−19.4119	+	25.7537i	−0.618830	+	0.820999i
$985$		0			0
$986$	30.2550	−	9.63480i	0.963515	−	0.306834i
$987$	6.03078	+	6.03078i	0.191962	+	0.191962i
$988$	−0.932645	+	5.47258i	−0.0296714	+	0.174106i
$989$		−	7.42701i		−	0.236165i
$990$		0			0
$991$		−	17.3438i		−	0.550944i	−0.961309	−	0.275472i	$-0.911166\pi$
$991$		−	17.3438i		−	0.550944i	0.961309	−	0.275472i	$-0.0888341\pi$
$992$	−15.1341	+	14.2723i	−0.480509	+	0.453145i
$993$	−28.8227	−	28.8227i	−0.914660	−	0.914660i
$994$	5.23066	+	16.4252i	0.165907	+	0.520976i
$995$		0			0
$996$	−33.7867	+	23.9476i	−1.07057	+	0.758808i
$997$	−10.9093	+	10.9093i	−0.345501	+	0.345501i	−0.858431	−	0.512929i	$-0.828560\pi$
$997$	−10.9093	+	10.9093i	−0.345501	+	0.345501i	0.512929	+	0.858431i	$0.328560\pi$
$998$	−4.83749	+	9.35813i	−0.153128	+	0.296227i
$999$	−117.858			−3.72886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.k.b.43.13		36
4.3	odd	2	inner	700.2.k.b.43.16		36
5.2	odd	4	inner	700.2.k.b.407.16		36
5.3	odd	4		140.2.k.a.127.3	yes	36
5.4	even	2		140.2.k.a.43.6	yes	36
20.3	even	4		140.2.k.a.127.6	yes	36
20.7	even	4	inner	700.2.k.b.407.13		36
20.19	odd	2		140.2.k.a.43.3	✓	36
35.3	even	12		980.2.x.l.667.16		72
35.4	even	6		980.2.x.k.863.7		72
35.9	even	6		980.2.x.k.263.18		72
35.13	even	4		980.2.k.l.687.3		36
35.18	odd	12		980.2.x.k.667.16		72
35.19	odd	6		980.2.x.l.263.18		72
35.23	odd	12		980.2.x.k.67.10		72
35.24	odd	6		980.2.x.l.863.7		72
35.33	even	12		980.2.x.l.67.10		72
35.34	odd	2		980.2.k.l.883.6		36
140.3	odd	12		980.2.x.l.667.18		72
140.19	even	6		980.2.x.l.263.16		72
140.23	even	12		980.2.x.k.67.7		72
140.39	odd	6		980.2.x.k.863.10		72
140.59	even	6		980.2.x.l.863.10		72
140.79	odd	6		980.2.x.k.263.16		72
140.83	odd	4		980.2.k.l.687.6		36
140.103	odd	12		980.2.x.l.67.7		72
140.123	even	12		980.2.x.k.667.18		72
140.139	even	2		980.2.k.l.883.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	20.19	odd	2
140.2.k.a.43.6	yes	36	5.4	even	2
140.2.k.a.127.3	yes	36	5.3	odd	4
140.2.k.a.127.6	yes	36	20.3	even	4
700.2.k.b.43.13		36	1.1	even	1	trivial
700.2.k.b.43.16		36	4.3	odd	2	inner
700.2.k.b.407.13		36	20.7	even	4	inner
700.2.k.b.407.16		36	5.2	odd	4	inner
980.2.k.l.687.3		36	35.13	even	4
980.2.k.l.687.6		36	140.83	odd	4
980.2.k.l.883.3		36	140.139	even	2
980.2.k.l.883.6		36	35.34	odd	2
980.2.x.k.67.7		72	140.23	even	12
980.2.x.k.67.10		72	35.23	odd	12
980.2.x.k.263.16		72	140.79	odd	6
980.2.x.k.263.18		72	35.9	even	6
980.2.x.k.667.16		72	35.18	odd	12
980.2.x.k.667.18		72	140.123	even	12
980.2.x.k.863.7		72	35.4	even	6
980.2.x.k.863.10		72	140.39	odd	6
980.2.x.l.67.7		72	140.103	odd	12
980.2.x.l.67.10		72	35.33	even	12
980.2.x.l.263.16		72	140.19	even	6
980.2.x.l.263.18		72	35.19	odd	6
980.2.x.l.667.16		72	35.3	even	12
980.2.x.l.667.18		72	140.3	odd	12
980.2.x.l.863.7		72	35.24	odd	6
980.2.x.l.863.10		72	140.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.649412 - 1.25629i) q^{2} +(2.28163 - 2.28163i) q^{3} +(-1.15653 - 1.63170i) q^{4} +(-1.38467 - 4.34811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.80095 + 0.393286i) q^{8} -7.41170i q^{9} +O(q^{10})\)	\(q+(0.649412 - 1.25629i) q^{2} +(2.28163 - 2.28163i) q^{3} +(-1.15653 - 1.63170i) q^{4} +(-1.38467 - 4.34811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.80095 + 0.393286i) q^{8} -7.41170i q^{9} +1.40679i q^{11} +(-6.36171 - 1.08417i) q^{12} +(0.699298 + 0.699298i) q^{13} +(1.34753 - 0.429127i) q^{14} +(-1.32489 + 3.77421i) q^{16} +(3.26865 - 3.26865i) q^{17} +(-9.31125 - 4.81325i) q^{18} -2.80674 q^{19} +3.22672 q^{21} +(1.76734 + 0.913587i) q^{22} +(-1.48618 + 1.48618i) q^{23} +(-5.49341 + 7.28808i) q^{24} +(1.33265 - 0.424388i) q^{26} +(-10.0659 - 10.0659i) q^{27} +(0.335998 - 1.97157i) q^{28} +4.85706i q^{29} +3.67738i q^{31} +(3.88110 + 4.11547i) q^{32} +(3.20978 + 3.20978i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(5.85431 - 5.85431i) q^{37} +(-1.82273 + 3.52608i) q^{38} +3.19108 q^{39} +3.53368 q^{41} +(2.09547 - 4.05369i) q^{42} +(-2.49869 + 2.49869i) q^{43} +(2.29546 - 1.62699i) q^{44} +(0.901930 + 2.83222i) q^{46} +(1.86901 + 1.86901i) q^{47} +(5.58845 + 11.6343i) q^{48} +1.00000i q^{49} -14.9157i q^{51} +(0.332288 - 1.94980i) q^{52} +(0.696542 + 0.696542i) q^{53} +(-19.1826 + 6.10876i) q^{54} +(-2.25867 - 1.70248i) q^{56} +(-6.40395 + 6.40395i) q^{57} +(6.10187 + 3.15424i) q^{58} +7.06573 q^{59} +2.19831 q^{61} +(4.61985 + 2.38814i) q^{62} +(5.24087 - 5.24087i) q^{63} +(7.69065 - 2.20315i) q^{64} +(6.11688 - 1.94794i) q^{66} +(2.25963 + 2.25963i) q^{67} +(-9.11374 - 1.55317i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(2.91492 + 20.7598i) q^{72} +(-4.68856 - 4.68856i) q^{73} +(-3.55285 - 11.1566i) q^{74} +(3.24607 + 4.57976i) q^{76} +(-0.994751 + 0.994751i) q^{77} +(2.07233 - 4.00892i) q^{78} +0.599288 q^{79} -23.6982 q^{81} +(2.29482 - 4.43932i) q^{82} +(4.53764 - 4.53764i) q^{83} +(-3.73179 - 5.26504i) q^{84} +(1.51640 + 4.76176i) q^{86} +(11.0820 + 11.0820i) q^{87} +(-0.553271 - 3.94035i) q^{88} +0.463673i q^{89} +0.988956i q^{91} +(4.14381 + 0.706194i) q^{92} +(8.39043 + 8.39043i) q^{93} +(3.56178 - 1.13426i) q^{94} +(18.2452 + 0.534737i) q^{96} +(-8.00558 + 8.00558i) q^{97} +(1.25629 + 0.649412i) q^{98} +10.4267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

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