LMFDB - Embedded newform 325.2.o.b.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(74,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("325.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.2
Root			$-1.12824 - 0.651388i$ of defining polynomial
Character	$\chi$	$=$	325.74
Dual form			325.2.o.b.224.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12824 - 0.651388i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.151388 - 0.262211i) q^{4} +(-0.651388 - 1.12824i) q^{6} +(-0.866025 + 0.500000i) q^{7} +3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.80278 - 4.85455i) q^{11} -0.302776i q^{12} -3.60555i q^{13} +1.30278 q^{14} +(1.65139 - 2.86029i) q^{16} +(0.341603 - 0.197224i) q^{17} +2.60555i q^{18} +(0.802776 + 1.39045i) q^{19} -1.00000 q^{21} +(-6.32439 + 3.65139i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-2.34861 + 4.06792i) q^{26} -5.00000i q^{27} +(0.262211 + 0.151388i) q^{28} +(4.10555 - 7.11102i) q^{29} -4.00000 q^{31} +(1.46984 - 0.848612i) q^{32} +(4.85455 - 2.80278i) q^{33} -0.513878 q^{34} +(-0.302776 + 0.524423i) q^{36} +(3.12250 + 1.80278i) q^{37} -2.09167i q^{38} +(1.80278 - 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(1.12824 + 0.651388i) q^{42} +(-3.64692 + 2.10555i) q^{43} -1.69722 q^{44} +(1.95416 + 3.38471i) q^{46} -5.21110i q^{47} +(2.86029 - 1.65139i) q^{48} +(-3.00000 + 5.19615i) q^{49} +0.394449 q^{51} +(-0.945417 + 0.545837i) q^{52} -11.2111i q^{53} +(-3.25694 + 5.64118i) q^{54} +(-1.50000 - 2.59808i) q^{56} +1.60555i q^{57} +(-9.26407 + 5.34861i) q^{58} +(5.40833 + 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(4.51295 + 2.60555i) q^{62} +(1.73205 + 1.00000i) q^{63} -8.81665 q^{64} -7.30278 q^{66} +(6.06218 + 3.50000i) q^{67} +(-0.103429 - 0.0597147i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(8.40833 + 14.5636i) q^{71} +(5.19615 - 3.00000i) q^{72} +15.2111i q^{73} +(-2.34861 - 4.06792i) q^{74} +(0.243061 - 0.420994i) q^{76} +5.60555i q^{77} +(-4.06792 + 2.34861i) q^{78} +9.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.38471 - 1.95416i) q^{82} -5.21110i q^{83} +(0.151388 + 0.262211i) q^{84} +5.48612 q^{86} +(7.11102 - 4.10555i) q^{87} +(14.5636 + 8.40833i) q^{88} +(4.10555 - 7.11102i) q^{89} +(1.80278 + 3.12250i) q^{91} +0.908327i q^{92} +(-3.46410 - 2.00000i) q^{93} +(-3.39445 + 5.87936i) q^{94} +1.69722 q^{96} +(-13.5148 + 7.80278i) q^{97} +(6.76942 - 3.90833i) q^{98} -11.2111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{4} + 2 q^{6} - 8 q^{9} + 8 q^{11} - 4 q^{14} + 6 q^{16} - 8 q^{19} - 8 q^{21} - 12 q^{24} - 26 q^{26} + 4 q^{29} - 32 q^{31} + 68 q^{34} + 12 q^{36} - 12 q^{41} - 28 q^{44} - 6 q^{46} - 24 q^{49}+ \cdots - 32 q^{99}+O(q^{100}) $ 8 * q + 6 * q^4 + 2 * q^6 - 8 * q^9 + 8 * q^11 - 4 * q^14 + 6 * q^16 - 8 * q^19 - 8 * q^21 - 12 * q^24 - 26 * q^26 + 4 * q^29 - 32 * q^31 + 68 * q^34 + 12 * q^36 - 12 * q^41 - 28 * q^44 - 6 * q^46 - 24 * q^49 + 32 * q^51 + 10 * q^54 - 12 * q^56 + 4 * q^61 + 16 * q^64 - 44 * q^66 - 12 * q^69 + 24 * q^71 - 26 * q^74 + 38 * q^76 + 16 * q^79 - 4 * q^81 - 6 * q^84 + 116 * q^86 + 4 * q^89 - 56 * q^94 + 28 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.12824	−	0.651388i	−0.797784	−	0.460601i	0.0449118	−	0.998991i	$-0.485699\pi$
$2$	−1.12824	−	0.651388i	−0.797784	−	0.460601i	−0.842696	+	0.538390i	$0.819033\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	−0.151388	−	0.262211i	−0.0756939	−	0.131106i
$5$		0			0
$5$		0			0
$6$	−0.651388	−	1.12824i	−0.265928	−	0.460601i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$			3.00000i			1.06066i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	2.80278	−	4.85455i	0.845069	−	1.46370i	−0.0404929	−	0.999180i	$-0.512893\pi$
$11$	2.80278	−	4.85455i	0.845069	−	1.46370i	0.885562	−	0.464522i	$-0.153774\pi$
$12$		−	0.302776i		−	0.0874038i
$13$		−	3.60555i		−	1.00000i
$13$		−	3.60555i		−	1.00000i
$14$	1.30278			0.348181
$15$		0			0
$16$	1.65139	−	2.86029i	0.412847	−	0.715072i
$17$	0.341603	−	0.197224i	0.0828508	−	0.0478339i	−0.458002	−	0.888951i	$-0.651435\pi$
$17$	0.341603	−	0.197224i	0.0828508	−	0.0478339i	0.540853	+	0.841117i	$0.318102\pi$
$18$			2.60555i			0.614134i
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	0.943296	−	0.331952i	$-0.107707\pi$
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	−0.759127	+	0.650943i	$0.774374\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$	−6.32439	+	3.65139i	−1.34836	+	0.778478i
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$		0			0
$26$	−2.34861	+	4.06792i	−0.460601	+	0.797784i
$27$		−	5.00000i		−	0.962250i
$28$	0.262211	+	0.151388i	0.0495533	+	0.0286096i
$29$	4.10555	−	7.11102i	0.762382	−	1.32048i	−0.179238	−	0.983806i	$-0.557363\pi$
$29$	4.10555	−	7.11102i	0.762382	−	1.32048i	0.941620	−	0.336678i	$-0.109303\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.46984	−	0.848612i	0.259833	−	0.150015i
$33$	4.85455	−	2.80278i	0.845069	−	0.487901i
$34$	−0.513878			−0.0881294
$35$		0			0
$36$	−0.302776	+	0.524423i	−0.0504626	+	0.0874038i
$37$	3.12250	+	1.80278i	0.513336	+	0.296374i	0.734204	−	0.678929i	$-0.237556\pi$
$37$	3.12250	+	1.80278i	0.513336	+	0.296374i	−0.220868	+	0.975304i	$0.570889\pi$
$38$		−	2.09167i		−	0.339314i
$39$	1.80278	−	3.12250i	0.288675	−	0.500000i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	1.12824	+	0.651388i	0.174091	+	0.100511i
$43$	−3.64692	+	2.10555i	−0.556150	+	0.321094i	−0.751599	−	0.659620i	$-0.770717\pi$
$43$	−3.64692	+	2.10555i	−0.556150	+	0.321094i	0.195449	+	0.980714i	$0.437384\pi$
$44$	−1.69722			−0.255866
$45$		0			0
$46$	1.95416	+	3.38471i	0.288126	+	0.499048i
$47$		−	5.21110i		−	0.760117i	−0.924962	−	0.380059i	$-0.875904\pi$
$47$		−	5.21110i		−	0.760117i	0.924962	−	0.380059i	$-0.124096\pi$
$48$	2.86029	−	1.65139i	0.412847	−	0.238357i
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	0.394449			0.0552339
$52$	−0.945417	+	0.545837i	−0.131106	+	0.0756939i
$53$		−	11.2111i		−	1.53996i	−0.638066	−	0.769982i	$-0.720265\pi$
$53$		−	11.2111i		−	1.53996i	0.638066	−	0.769982i	$-0.279735\pi$
$54$	−3.25694	+	5.64118i	−0.443213	+	0.767668i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$			1.60555i			0.212660i
$58$	−9.26407	+	5.34861i	−1.21643	+	0.702307i
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	0.967014	+	0.254724i	$0.0819845\pi$
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	−0.262910	+	0.964820i	$0.584682\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	4.51295	+	2.60555i	0.573145	+	0.330905i
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$	−8.81665			−1.10208
$65$		0			0
$66$	−7.30278			−0.898910
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	0.822292	−	0.569066i	$-0.192695\pi$
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	−0.0816792	+	0.996659i	$0.526028\pi$
$68$	−0.103429	−	0.0597147i	−0.0125426	−	0.00724147i
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	8.40833	+	14.5636i	0.997885	+	1.72839i	0.555240	+	0.831690i	$0.312626\pi$
$71$	8.40833	+	14.5636i	0.997885	+	1.72839i	0.442645	+	0.896697i	$0.354040\pi$
$72$	5.19615	−	3.00000i	0.612372	−	0.353553i
$73$			15.2111i			1.78032i	0.455643	+	0.890162i	$0.349409\pi$
$73$			15.2111i			1.78032i	−0.455643	+	0.890162i	$0.650591\pi$
$74$	−2.34861	−	4.06792i	−0.273021	−	0.472886i
$75$		0			0
$76$	0.243061	−	0.420994i	0.0278810	−	0.0482913i
$77$			5.60555i			0.638812i
$78$	−4.06792	+	2.34861i	−0.460601	+	0.265928i
$79$	9.21110			1.03633			0.518165	−	0.855281i	$-0.326615\pi$
$79$	9.21110			1.03633			0.518165	+	0.855281i	$0.326615\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.38471	−	1.95416i	0.373779	−	0.215801i
$83$		−	5.21110i		−	0.571993i	−0.958231	−	0.285996i	$-0.907675\pi$
$83$		−	5.21110i		−	0.571993i	0.958231	−	0.285996i	$-0.0923245\pi$
$84$	0.151388	+	0.262211i	0.0165178	+	0.0286096i
$85$		0			0
$86$	5.48612			0.591584
$87$	7.11102	−	4.10555i	0.762382	−	0.440161i
$88$	14.5636	+	8.40833i	1.55249	+	0.896331i
$89$	4.10555	−	7.11102i	0.435188	−	0.753767i	−0.562123	−	0.827053i	$-0.690015\pi$
$89$	4.10555	−	7.11102i	0.435188	−	0.753767i	0.997311	+	0.0732864i	$0.0233487\pi$
$90$		0			0
$91$	1.80278	+	3.12250i	0.188982	+	0.327327i
$92$			0.908327i			0.0946996i
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$	−3.39445	+	5.87936i	−0.350111	+	0.606409i
$95$		0			0
$96$	1.69722			0.173222
$97$	−13.5148	+	7.80278i	−1.37222	+	0.792252i	−0.991207	−	0.132318i	$-0.957758\pi$
$97$	−13.5148	+	7.80278i	−1.37222	+	0.792252i	−0.381013	+	0.924570i	$0.624425\pi$
$98$	6.76942	−	3.90833i	0.683815	−	0.394801i
$99$	−11.2111			−1.12676
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−0.445032	−	0.256939i	−0.0440647	−	0.0254408i
$103$			4.00000i			0.394132i	0.980390	+	0.197066i	$0.0631413\pi$
$103$			4.00000i			0.394132i	−0.980390	+	0.197066i	$0.936859\pi$
$104$	10.8167			1.06066
$105$		0			0
$106$	−7.30278	+	12.6488i	−0.709308	+	1.22856i
$107$	7.11102	+	4.10555i	0.687449	+	0.396899i	0.802656	−	0.596443i	$-0.203420\pi$
$107$	7.11102	+	4.10555i	0.687449	+	0.396899i	−0.115207	+	0.993342i	$0.536753\pi$
$108$	−1.31106	+	0.756939i	−0.126157	+	0.0728365i
$109$	4.78890			0.458693			0.229347	−	0.973345i	$-0.426341\pi$
$109$	4.78890			0.458693			0.229347	+	0.973345i	$0.426341\pi$
$110$		0			0
$111$	1.80278	+	3.12250i	0.171112	+	0.296374i
$112$			3.30278i			0.312083i
$113$	−4.85455	+	2.80278i	−0.456678	+	0.263663i	−0.710646	−	0.703550i	$-0.751597\pi$
$113$	−4.85455	+	2.80278i	−0.456678	+	0.263663i	0.253969	+	0.967212i	$0.418264\pi$
$114$	1.04584	−	1.81144i	0.0979516	−	0.169657i
$115$		0			0
$116$	−2.48612			−0.230831
$117$	−6.24500	+	3.60555i	−0.577350	+	0.333333i
$118$		−	14.0917i		−	1.29724i
$119$	−0.197224	+	0.341603i	−0.0180795	+	0.0313147i
$120$		0			0
$121$	−10.2111	−	17.6861i	−0.928282	−	1.60783i
$122$		−	1.30278i		−	0.117948i
$123$	−2.59808	+	1.50000i	−0.234261	+	0.135250i
$124$	0.605551	+	1.04885i	0.0543801	+	0.0941891i
$125$		0			0
$126$	−1.30278	−	2.25647i	−0.116060	−	0.201023i
$127$	−8.84307	−	5.10555i	−0.784696	−	0.453044i	0.0533960	−	0.998573i	$-0.482995\pi$
$127$	−8.84307	−	5.10555i	−0.784696	−	0.453044i	−0.838092	+	0.545529i	$0.816329\pi$
$128$	7.00759	+	4.04584i	0.619390	+	0.357605i
$129$	−4.21110			−0.370767
$130$		0			0
$131$	−6.78890			−0.593149			−0.296574	−	0.955010i	$-0.595844\pi$
$131$	−6.78890			−0.593149			−0.296574	+	0.955010i	$0.595844\pi$
$132$	−1.46984	−	0.848612i	−0.127933	−	0.0738622i
$133$	−1.39045	−	0.802776i	−0.120567	−	0.0696095i
$134$	−4.55971	−	7.89766i	−0.393899	−	0.682254i
$135$		0			0
$136$	0.591673	+	1.02481i	0.0507355	+	0.0878765i
$137$	4.85455	−	2.80278i	0.414752	−	0.239457i	−0.278077	−	0.960559i	$-0.589697\pi$
$137$	4.85455	−	2.80278i	0.414752	−	0.239457i	0.692830	+	0.721101i	$0.256364\pi$
$138$			3.90833i			0.332699i
$139$	6.80278	+	11.7828i	0.577004	+	0.999400i	0.995821	+	0.0913293i	$0.0291116\pi$
$139$	6.80278	+	11.7828i	0.577004	+	0.999400i	−0.418817	+	0.908071i	$0.637555\pi$
$140$		0			0
$141$	2.60555	−	4.51295i	0.219427	−	0.380059i
$142$		−	21.9083i		−	1.83851i
$143$	−17.5033	−	10.1056i	−1.46370	−	0.845069i
$144$	−6.60555			−0.550463
$145$		0			0
$146$	9.90833	−	17.1617i	0.820019	−	1.42031i
$147$	−5.19615	+	3.00000i	−0.428571	+	0.247436i
$148$		−	1.09167i		−	0.0897350i
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	13.2111			1.07510			0.537552	−	0.843231i	$-0.319349\pi$
$151$	13.2111			1.07510			0.537552	+	0.843231i	$0.319349\pi$
$152$	−4.17134	+	2.40833i	−0.338341	+	0.195341i
$153$	−0.683205	−	0.394449i	−0.0552339	−	0.0318893i
$154$	3.65139	−	6.32439i	0.294237	−	0.509634i
$155$		0			0
$156$	−1.09167			−0.0874038
$157$		−	3.21110i		−	0.256274i	−0.991756	−	0.128137i	$-0.959100\pi$
$157$		−	3.21110i		−	0.256274i	0.991756	−	0.128137i	$-0.0408997\pi$
$158$	−10.3923	−	6.00000i	−0.826767	−	0.477334i
$159$	5.60555	−	9.70910i	0.444549	−	0.769982i
$160$		0			0
$161$	3.00000			0.236433
$162$	1.12824	−	0.651388i	0.0886427	−	0.0511779i
$163$	15.7713	−	9.10555i	1.23530	−	0.713202i	0.267172	−	0.963649i	$-0.413911\pi$
$163$	15.7713	−	9.10555i	1.23530	−	0.713202i	0.968130	+	0.250447i	$0.0805776\pi$
$164$	0.908327			0.0709284
$165$		0			0
$166$	−3.39445	+	5.87936i	−0.263460	+	0.456327i
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	0.167139	−	0.985933i	$-0.446547\pi$
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	−0.770274	+	0.637713i	$0.779881\pi$
$168$		−	3.00000i		−	0.231455i
$169$	−13.0000			−1.00000
$170$		0			0
$171$	1.60555	−	2.78090i	0.122780	−	0.212660i
$172$	1.10420	+	0.637510i	0.0841944	+	0.0486097i
$173$	14.5636	−	8.40833i	1.10725	−	0.639273i	0.169137	−	0.985593i	$-0.445902\pi$
$173$	14.5636	−	8.40833i	1.10725	−	0.639273i	0.938117	+	0.346319i	$0.112569\pi$
$174$	−10.6972			−0.810954
$175$		0			0
$176$	−9.25694	−	16.0335i	−0.697768	−	1.20857i
$177$			10.8167i			0.813029i
$178$	−9.26407	+	5.34861i	−0.694371	+	0.400895i
$179$	0.591673	−	1.02481i	0.0442237	−	0.0765977i	−0.843066	−	0.537810i	$-0.819252\pi$
$179$	0.591673	−	1.02481i	0.0442237	−	0.0765977i	0.887290	+	0.461212i	$0.152585\pi$
$180$		0			0
$181$	−25.6333			−1.90531			−0.952654	−	0.304055i	$-0.901659\pi$
$181$	−25.6333			−1.90531			−0.952654	+	0.304055i	$0.901659\pi$
$182$		−	4.69722i		−	0.348181i
$183$			1.00000i			0.0739221i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$	2.60555	+	4.51295i	0.191048	+	0.330905i
$187$		−	2.21110i		−	0.161692i
$188$	−1.36641	+	0.788897i	−0.0996557	+	0.0575363i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	0.939905	−	0.341436i	$-0.110913\pi$
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	−0.765645	+	0.643264i	$0.777580\pi$
$192$	−7.63545	−	4.40833i	−0.551041	−	0.318144i
$193$	7.26981	+	4.19722i	0.523292	+	0.302123i	0.738281	−	0.674494i	$-0.235638\pi$
$193$	7.26981	+	4.19722i	0.523292	+	0.302123i	−0.214988	+	0.976617i	$0.568971\pi$
$194$	20.3305			1.45965
$195$		0			0
$196$	1.81665			0.129761
$197$	−19.7598	−	11.4083i	−1.40783	−	0.812810i	−0.412649	−	0.910890i	$-0.635396\pi$
$197$	−19.7598	−	11.4083i	−1.40783	−	0.812810i	−0.995178	+	0.0980804i	$0.968730\pi$
$198$	12.6488	+	7.30278i	0.898910	+	0.518986i
$199$	−4.40833	−	7.63545i	−0.312498	−	0.541262i	0.666404	−	0.745590i	$-0.267832\pi$
$199$	−4.40833	−	7.63545i	−0.312498	−	0.541262i	−0.978902	+	0.204328i	$0.934499\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$	−10.1541	+	5.86249i	−0.714442	+	0.412483i
$203$			8.21110i			0.576306i
$204$	−0.0597147	−	0.103429i	−0.00418087	−	0.00724147i
$205$		0			0
$206$	2.60555	−	4.51295i	0.181537	−	0.314432i
$207$			6.00000i			0.417029i
$208$	−10.3129	−	5.95416i	−0.715072	−	0.412847i
$209$	9.00000			0.622543
$210$		0			0
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	−0.432792	−	0.901494i	$-0.642472\pi$
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	0.997113	−	0.0759376i	$-0.0241950\pi$
$212$	−2.93968	+	1.69722i	−0.201898	+	0.116566i
$213$			16.8167i			1.15226i
$214$	−5.34861	−	9.26407i	−0.365624	−	0.633279i
$215$		0			0
$216$	15.0000			1.02062
$217$	3.46410	−	2.00000i	0.235159	−	0.135769i
$218$	−5.40301	−	3.11943i	−0.365938	−	0.211274i
$219$	−7.60555	+	13.1732i	−0.513936	+	0.890162i
$220$		0			0
$221$	−0.711103	−	1.23167i	−0.0478339	−	0.0828508i
$222$		−	4.69722i		−	0.315257i
$223$	8.84307	+	5.10555i	0.592176	+	0.341893i	0.765957	−	0.642891i	$-0.222265\pi$
$223$	8.84307	+	5.10555i	0.592176	+	0.341893i	−0.173781	+	0.984784i	$0.555599\pi$
$224$	−0.848612	+	1.46984i	−0.0567003	+	0.0982078i
$225$		0			0
$226$	7.30278			0.485773
$227$	1.23167	−	0.711103i	0.0817485	−	0.0471975i	−0.458569	−	0.888659i	$-0.651638\pi$
$227$	1.23167	−	0.711103i	0.0817485	−	0.0471975i	0.540317	+	0.841462i	$0.318304\pi$
$228$	0.420994	−	0.243061i	0.0278810	−	0.0160971i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$	−2.80278	+	4.85455i	−0.184409	+	0.319406i
$232$	21.3331	+	12.3167i	1.40058	+	0.808628i
$233$		−	0.788897i		−	0.0516824i	−0.999666	−	0.0258412i	$-0.991774\pi$
$233$		−	0.788897i		−	0.0516824i	0.999666	−	0.0258412i	$-0.00822642\pi$
$234$	9.39445			0.614134
$235$		0			0
$236$	1.63751	−	2.83625i	0.106593	−	0.184624i
$237$	7.97705	+	4.60555i	0.518165	+	0.299163i
$238$	0.445032	−	0.256939i	0.0288471	−	0.0166549i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	−0.999669	−	0.0257384i	$-0.991806\pi$
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	0.477544	−	0.878608i	$-0.341527\pi$
$242$			26.6056i			1.71027i
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	0.151388	−	0.262211i	0.00969161	−	0.0167864i
$245$		0			0
$246$	3.90833			0.249186
$247$	5.01333	−	2.89445i	0.318991	−	0.184169i
$248$		−	12.0000i		−	0.762001i
$249$	2.60555	−	4.51295i	0.165120	−	0.285996i
$250$		0			0
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.814836	+	0.579691i	$0.196827\pi$
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.0946094	+	0.995514i	$0.469840\pi$
$252$		−	0.605551i		−	0.0381461i
$253$	−14.5636	+	8.40833i	−0.915609	+	0.528627i
$254$	6.65139	+	11.5205i	0.417345	+	0.722863i
$255$		0			0
$256$	3.54584	+	6.14157i	0.221615	+	0.383848i
$257$	20.4430	+	11.8028i	1.27520	+	0.736237i	0.975962	−	0.217942i	$-0.0699342\pi$
$257$	20.4430	+	11.8028i	1.27520	+	0.736237i	0.299238	+	0.954179i	$0.403268\pi$
$258$	4.75112	+	2.74306i	0.295792	+	0.170776i
$259$	−3.60555			−0.224038
$260$		0			0
$261$	−16.4222			−1.01651
$262$	7.65948	+	4.42221i	0.473204	+	0.273205i
$263$	22.6995	+	13.1056i	1.39971	+	0.808123i	0.994362	−	0.106040i	$-0.0338170\pi$
$263$	22.6995	+	13.1056i	1.39971	+	0.808123i	0.405348	+	0.914162i	$0.367150\pi$
$264$	8.40833	+	14.5636i	0.517497	+	0.896331i
$265$		0			0
$266$	1.04584	+	1.81144i	0.0641244	+	0.111067i
$267$	7.11102	−	4.10555i	0.435188	−	0.251256i
$268$		−	2.11943i		−	0.129465i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	−0.408327	+	0.707243i	−0.0248041	+	0.0429620i	−0.878161	−	0.478365i	$-0.841230\pi$
$271$	−0.408327	+	0.707243i	−0.0248041	+	0.0429620i	0.853357	+	0.521327i	$0.174563\pi$
$272$		−	1.30278i		−	0.0789924i
$273$			3.60555i			0.218218i
$274$	−7.30278			−0.441177
$275$		0			0
$276$	−0.454163	+	0.786634i	−0.0273374	+	0.0473498i
$277$	17.6621	−	10.1972i	1.06121	−	0.612692i	0.135446	−	0.990785i	$-0.456753\pi$
$277$	17.6621	−	10.1972i	1.06121	−	0.612692i	0.925768	+	0.378093i	$0.123420\pi$
$278$		−	17.7250i		−	1.06307i
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−5.87936	+	3.39445i	−0.350111	+	0.202136i
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	0.623148	−	0.782104i	$-0.285854\pi$
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	−0.365748	+	0.930714i	$0.619187\pi$
$284$	2.54584	−	4.40952i	0.151068	−	0.261657i
$285$		0			0
$286$	13.1653	+	22.8029i	0.778478	+	1.34836i
$287$		−	3.00000i		−	0.177084i
$288$	−2.93968	−	1.69722i	−0.173222	−	0.100010i
$289$	−8.42221	+	14.5877i	−0.495424	+	0.858099i
$290$		0			0
$291$	−15.6056			−0.914814
$292$	3.98852	−	2.30278i	0.233411	−	0.134760i
$293$	−15.2469	+	8.80278i	−0.890731	+	0.514264i	−0.874181	−	0.485599i	$-0.838601\pi$
$293$	−15.2469	+	8.80278i	−0.890731	+	0.514264i	−0.0165493	+	0.999863i	$0.505268\pi$
$294$	7.81665			0.455877
$295$		0			0
$296$	−5.40833	+	9.36750i	−0.314353	+	0.544475i
$297$	−24.2727	−	14.0139i	−1.40845	−	0.813168i
$298$		−	3.90833i		−	0.226403i
$299$	−5.40833	+	9.36750i	−0.312772	+	0.541736i
$300$		0			0
$301$	2.10555	−	3.64692i	0.121362	−	0.210205i
$302$	−14.9053	−	8.60555i	−0.857701	−	0.495194i
$303$	7.79423	−	4.50000i	0.447767	−	0.258518i
$304$	5.30278			0.304135
$305$		0			0
$306$	0.513878	+	0.890063i	0.0293765	+	0.0508815i
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$	1.46984	−	0.848612i	0.0837519	−	0.0483542i
$309$	−2.00000	+	3.46410i	−0.113776	+	0.197066i
$310$		0			0
$311$	5.21110			0.295495			0.147747	−	0.989025i	$-0.452798\pi$
$311$	5.21110			0.295495			0.147747	+	0.989025i	$0.452798\pi$
$312$	9.36750	+	5.40833i	0.530330	+	0.306186i
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	−2.09167	+	3.62288i	−0.118040	+	0.204451i
$315$		0			0
$316$	−1.39445	−	2.41526i	−0.0784439	−	0.135869i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−12.6488	+	7.30278i	−0.709308	+	0.409519i
$319$	−23.0139	−	39.8612i	−1.28853	−	2.23180i
$320$		0			0
$321$	4.10555	+	7.11102i	0.229150	+	0.396899i
$322$	−3.38471	−	1.95416i	−0.188623	−	0.108901i
$323$	0.548461	+	0.316654i	0.0305172	+	0.0176191i
$324$	0.302776			0.0168209
$325$		0			0
$326$	−23.7250			−1.31401
$327$	4.14731	+	2.39445i	0.229347	+	0.132413i
$328$	−7.79423	−	4.50000i	−0.430364	−	0.248471i
$329$	2.60555	+	4.51295i	0.143649	+	0.248807i
$330$		0			0
$331$	13.0139	+	22.5407i	0.715307	+	1.23895i	0.962841	+	0.270069i	$0.0870467\pi$
$331$	13.0139	+	22.5407i	0.715307	+	1.23895i	−0.247533	+	0.968879i	$0.579620\pi$
$332$	−1.36641	+	0.788897i	−0.0749915	+	0.0432964i
$333$		−	7.21110i		−	0.395166i
$334$	5.86249	+	10.1541i	0.320781	+	0.555609i
$335$		0			0
$336$	−1.65139	+	2.86029i	−0.0900906	+	0.156041i
$337$			17.6333i			0.960547i	0.877119	+	0.480274i	$0.159463\pi$
$337$			17.6333i			0.960547i	−0.877119	+	0.480274i	$0.840537\pi$
$338$	14.6671	+	8.46804i	0.797784	+	0.460601i
$339$	−5.60555			−0.304452
$340$		0			0
$341$	−11.2111	+	19.4182i	−0.607115	+	1.05155i
$342$	−3.62288	+	2.09167i	−0.195903	+	0.113105i
$343$		−	13.0000i		−	0.701934i
$344$	−6.31665	−	10.9408i	−0.340571	−	0.589887i
$345$		0			0
$346$	−21.9083			−1.17780
$347$	17.5033	−	10.1056i	0.939628	−	0.542494i	0.0497842	−	0.998760i	$-0.484147\pi$
$347$	17.5033	−	10.1056i	0.939628	−	0.542494i	0.889844	+	0.456266i	$0.150813\pi$
$348$	−2.15304	−	1.24306i	−0.115415	−	0.0666351i
$349$	−9.10555	+	15.7713i	−0.487409	+	0.844217i	−0.999895	−	0.0144783i	$-0.995391\pi$
$349$	−9.10555	+	15.7713i	−0.487409	+	0.844217i	0.512486	+	0.858695i	$0.328725\pi$
$350$		0			0
$351$	−18.0278			−0.962250
$352$		−	9.51388i		−	0.507091i
$353$	−4.17134	−	2.40833i	−0.222018	−	0.128182i	0.384866	−	0.922972i	$-0.374248\pi$
$353$	−4.17134	−	2.40833i	−0.222018	−	0.128182i	−0.606884	+	0.794790i	$0.707581\pi$
$354$	7.04584	−	12.2037i	0.374482	−	0.648622i
$355$		0			0
$356$	−2.48612			−0.131764
$357$	−0.341603	+	0.197224i	−0.0180795	+	0.0104382i
$358$	−1.33509	+	0.770817i	−0.0705619	+	0.0407390i
$359$	10.4222			0.550063			0.275031	−	0.961435i	$-0.411312\pi$
$359$	10.4222			0.550063			0.275031	+	0.961435i	$0.411312\pi$
$360$		0			0
$361$	8.21110	−	14.2220i	0.432163	−	0.748529i
$362$	28.9204	+	16.6972i	1.52002	+	0.877587i
$363$		−	20.4222i		−	1.07189i
$364$	0.545837	−	0.945417i	0.0286096	−	0.0495533i
$365$		0			0
$366$	0.651388	−	1.12824i	0.0340486	−	0.0589739i
$367$	15.0881	+	8.71110i	0.787591	+	0.454716i	0.839114	−	0.543956i	$-0.183074\pi$
$367$	15.0881	+	8.71110i	0.787591	+	0.454716i	−0.0515228	+	0.998672i	$0.516407\pi$
$368$	−8.58086	+	4.95416i	−0.447308	+	0.258254i
$369$	6.00000			0.312348
$370$		0			0
$371$	5.60555	+	9.70910i	0.291026	+	0.504071i
$372$			1.21110i			0.0627927i
$373$	23.9071	−	13.8028i	1.23786	−	0.714681i	0.269206	−	0.963083i	$-0.413239\pi$
$373$	23.9071	−	13.8028i	1.23786	−	0.714681i	0.968657	+	0.248402i	$0.0799054\pi$
$374$	−1.44029	+	2.49465i	−0.0744754	+	0.128995i
$375$		0			0
$376$	15.6333			0.806226
$377$	−25.6392	−	14.8028i	−1.32048	−	0.762382i
$378$		−	6.51388i		−	0.335038i
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	−0.833638	−	0.552312i	$-0.813746\pi$
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	0.895135	+	0.445795i	$0.147079\pi$
$380$		0			0
$381$	−5.10555	−	8.84307i	−0.261565	−	0.453044i
$382$		−	6.27502i		−	0.321058i
$383$	−16.1369	+	9.31665i	−0.824558	+	0.476059i	−0.851986	−	0.523565i	$-0.824602\pi$
$383$	−16.1369	+	9.31665i	−0.824558	+	0.476059i	0.0274277	+	0.999624i	$0.491268\pi$
$384$	4.04584	+	7.00759i	0.206463	+	0.357605i
$385$		0			0
$386$	−5.46804	−	9.47093i	−0.278316	−	0.482057i
$387$	7.29384	+	4.21110i	0.370767	+	0.214062i
$388$	4.09195	+	2.36249i	0.207737	+	0.119937i
$389$	0.788897			0.0399987			0.0199993	−	0.999800i	$-0.493634\pi$
$389$	0.788897			0.0399987			0.0199993	+	0.999800i	$0.493634\pi$
$390$		0			0
$391$	−1.18335			−0.0598444
$392$	−15.5885	−	9.00000i	−0.787336	−	0.454569i
$393$	−5.87936	−	3.39445i	−0.296574	−	0.171227i
$394$	14.8625	+	25.7426i	0.748761	+	1.29689i
$395$		0			0
$396$	1.69722	+	2.93968i	0.0852887	+	0.147724i
$397$	−12.1484	+	7.01388i	−0.609710	+	0.352016i	−0.772852	−	0.634586i	$-0.781171\pi$
$397$	−12.1484	+	7.01388i	−0.609710	+	0.352016i	0.163142	+	0.986603i	$0.447837\pi$
$398$			11.4861i			0.575747i
$399$	−0.802776	−	1.39045i	−0.0401890	−	0.0696095i
$400$		0			0
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	−0.837100	−	0.547049i	$-0.815751\pi$
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	0.892309	+	0.451425i	$0.149084\pi$
$402$		−	9.11943i		−	0.454836i
$403$			14.4222i			0.718421i
$404$	−2.72498			−0.135573
$405$		0			0
$406$	5.34861	−	9.26407i	0.265447	−	0.459768i
$407$	17.5033	−	10.1056i	0.867608	−	0.500914i
$408$			1.18335i			0.0585844i
$409$	−3.10555	−	5.37897i	−0.153560	−	0.265973i	0.778974	−	0.627056i	$-0.215740\pi$
$409$	−3.10555	−	5.37897i	−0.153560	−	0.265973i	−0.932534	+	0.361083i	$0.882407\pi$
$410$		0			0
$411$	5.60555			0.276501
$412$	1.04885	−	0.605551i	0.0516729	−	0.0298334i
$413$	−9.36750	−	5.40833i	−0.460944	−	0.266126i
$414$	3.90833	−	6.76942i	0.192084	−	0.332699i
$415$		0			0
$416$	−3.05971	−	5.29958i	−0.150015	−	0.259833i
$417$			13.6056i			0.666267i
$418$	−10.1541	−	5.86249i	−0.496655	−	0.286744i
$419$	−16.6194	+	28.7857i	−0.811912	+	1.40627i	0.0996117	+	0.995026i	$0.468240\pi$
$419$	−16.6194	+	28.7857i	−0.811912	+	1.40627i	−0.911524	+	0.411247i	$0.865093\pi$
$420$		0			0
$421$	3.57779			0.174371			0.0871855	−	0.996192i	$-0.472213\pi$
$421$	3.57779			0.174371			0.0871855	+	0.996192i	$0.472213\pi$
$422$	−18.4968	+	10.6791i	−0.900411	+	0.519853i
$423$	−9.02589	+	5.21110i	−0.438854	+	0.253372i
$424$	33.6333			1.63338
$425$		0			0
$426$	10.9542	−	18.9732i	0.530731	−	0.919253i
$427$	−0.866025	−	0.500000i	−0.0419099	−	0.0241967i
$428$		−	2.48612i		−	0.120171i
$429$	−10.1056	−	17.5033i	−0.487901	−	0.845069i
$430$		0			0
$431$	10.6194	−	18.3934i	0.511520	−	0.885978i	−0.488391	−	0.872625i	$-0.662416\pi$
$431$	10.6194	−	18.3934i	0.511520	−	0.885978i	0.999911	−	0.0133535i	$-0.00425069\pi$
$432$	−14.3014	−	8.25694i	−0.688078	−	0.397262i
$433$	3.12250	−	1.80278i	0.150058	−	0.0866359i	−0.423091	−	0.906087i	$-0.639055\pi$
$433$	3.12250	−	1.80278i	0.150058	−	0.0866359i	0.573149	+	0.819451i	$0.305722\pi$
$434$	−5.21110			−0.250141
$435$		0			0
$436$	−0.724981	−	1.25570i	−0.0347203	−	0.0601373i
$437$		−	4.81665i		−	0.230412i
$438$	17.1617	−	9.90833i	0.820019	−	0.473438i
$439$	11.6194	−	20.1254i	0.554565	−	0.960535i	−0.443372	−	0.896338i	$-0.646218\pi$
$439$	11.6194	−	20.1254i	0.554565	−	0.960535i	0.997937	−	0.0641973i	$-0.0204487\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$			1.85281i			0.0881294i
$443$			22.4222i			1.06531i	0.846332	+	0.532656i	$0.178806\pi$
$443$			22.4222i			1.06531i	−0.846332	+	0.532656i	$0.821194\pi$
$444$	0.545837	−	0.945417i	0.0259043	−	0.0448675i
$445$		0			0
$446$	−6.65139	−	11.5205i	−0.314952	−	0.545513i
$447$			3.00000i			0.141895i
$448$	7.63545	−	4.40833i	0.360741	−	0.208274i
$449$	−6.31665	−	10.9408i	−0.298101	−	0.516327i	0.677600	−	0.735430i	$-0.263020\pi$
$449$	−6.31665	−	10.9408i	−0.298101	−	0.516327i	−0.975702	+	0.219104i	$0.929687\pi$
$450$		0			0
$451$	8.40833	+	14.5636i	0.395933	+	0.685775i
$452$	1.46984	+	0.848612i	0.0691354	+	0.0399154i
$453$	11.4412	+	6.60555i	0.537552	+	0.310356i
$454$	−1.85281			−0.0869569
$455$		0			0
$456$	−4.81665			−0.225560
$457$	4.48891	+	2.59167i	0.209982	+	0.121233i	0.601303	−	0.799021i	$-0.294648\pi$
$457$	4.48891	+	2.59167i	0.209982	+	0.121233i	−0.391321	+	0.920254i	$0.627982\pi$
$458$	15.7953	+	9.11943i	0.738067	+	0.426123i
$459$	−0.986122	−	1.70801i	−0.0460282	−	0.0797232i
$460$		0			0
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	−0.999963	−	0.00857184i	$-0.997271\pi$
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	0.492558	−	0.870280i	$-0.336062\pi$
$462$	6.32439	−	3.65139i	0.294237	−	0.169878i
$463$			5.57779i			0.259222i	0.991565	+	0.129611i	$0.0413729\pi$
$463$			5.57779i			0.259222i	−0.991565	+	0.129611i	$0.958627\pi$
$464$	−13.5597	−	23.4861i	−0.629494	−	1.09032i
$465$		0			0
$466$	−0.513878	+	0.890063i	−0.0238049	+	0.0412314i
$467$			17.2111i			0.796435i	0.917291	+	0.398217i	$0.130371\pi$
$467$			17.2111i			0.796435i	−0.917291	+	0.398217i	$0.869629\pi$
$468$	1.89083	+	1.09167i	0.0874038	+	0.0504626i
$469$	−7.00000			−0.323230
$470$		0			0
$471$	1.60555	−	2.78090i	0.0739799	−	0.128137i
$472$	−28.1025	+	16.2250i	−1.29352	+	0.746815i
$473$			23.6056i			1.08538i
$474$	−6.00000	−	10.3923i	−0.275589	−	0.477334i
$475$		0			0
$476$	0.119429			0.00547404
$477$	−19.4182	+	11.2111i	−0.889098	+	0.513321i
$478$		0			0
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	−0.936338	−	0.351100i	$-0.885808\pi$
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	0.772230	+	0.635343i	$0.219141\pi$
$480$		0			0
$481$	6.50000	−	11.2583i	0.296374	−	0.513336i
$482$			21.1194i			0.961964i
$483$	2.59808	+	1.50000i	0.118217	+	0.0682524i
$484$	−3.09167	+	5.35493i	−0.140531	+	0.243406i
$485$		0			0
$486$	20.8444			0.945522
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	−0.519493	−	0.854475i	$-0.673879\pi$
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	0.480250	+	0.877132i	$0.340546\pi$
$488$	−2.59808	+	1.50000i	−0.117609	+	0.0679018i
$489$	18.2111			0.823535
$490$		0			0
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	−0.915238	−	0.402913i	$-0.867998\pi$
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	0.806552	+	0.591163i	$0.201331\pi$
$492$	0.786634	+	0.454163i	0.0354642	+	0.0204753i
$493$		−	3.23886i		−	0.145871i
$494$	−7.54163			−0.339314
$495$		0			0
$496$	−6.60555	+	11.4412i	−0.296598	+	0.513723i
$497$	−14.5636	−	8.40833i	−0.653269	−	0.377165i
$498$	−5.87936	+	3.39445i	−0.263460	+	0.152109i
$499$	26.4222			1.18282			0.591410	−	0.806371i	$-0.298571\pi$
$499$	26.4222			1.18282			0.591410	+	0.806371i	$0.298571\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$		−	37.5416i		−	1.67557i
$503$	−2.59808	+	1.50000i	−0.115842	+	0.0668817i	−0.556802	−	0.830645i	$-0.687972\pi$
$503$	−2.59808	+	1.50000i	−0.115842	+	0.0668817i	0.440959	+	0.897527i	$0.354638\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$		0			0
$506$	21.9083			0.973944
$507$	−11.2583	−	6.50000i	−0.500000	−	0.288675i
$508$			3.09167i			0.137171i
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	−7.60555	−	13.1732i	−0.336450	−	0.582748i
$512$		−	25.4222i		−	1.12351i
$513$	6.95224	−	4.01388i	0.306949	−	0.177217i
$514$	−15.3764	−	26.6327i	−0.678223	−	1.17472i
$515$		0			0
$516$	0.637510	+	1.10420i	0.0280648	+	0.0486097i
$517$	−25.2976	−	14.6056i	−1.11259	−	0.642351i
$518$	4.06792	+	2.34861i	0.178734	+	0.103192i
$519$	16.8167			0.738169
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	18.5281	+	10.6972i	0.810954	+	0.468205i
$523$	23.7483	+	13.7111i	1.03844	+	0.599545i	0.919392	−	0.393344i	$-0.128682\pi$
$523$	23.7483	+	13.7111i	1.03844	+	0.599545i	0.119050	+	0.992888i	$0.462015\pi$
$524$	1.02776	+	1.78013i	0.0448977	+	0.0777652i
$525$		0			0
$526$	−17.0736	−	29.5723i	−0.744444	−	1.28941i
$527$	−1.36641	+	0.788897i	−0.0595218	+	0.0343649i
$528$		−	18.5139i		−	0.805713i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	10.8167	−	18.7350i	0.469403	−	0.813029i
$532$			0.486122i			0.0210761i
$533$	9.36750	+	5.40833i	0.405751	+	0.234261i
$534$	−10.6972			−0.462914
$535$		0			0
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$	1.02481	−	0.591673i	0.0442237	−	0.0255326i
$538$			11.7250i			0.505500i
$539$	16.8167	+	29.1273i	0.724345	+	1.25460i
$540$		0			0
$541$	17.6333			0.758115			0.379058	−	0.925373i	$-0.376248\pi$
$541$	17.6333			0.758115			0.379058	+	0.925373i	$0.376248\pi$
$542$	0.921379	−	0.531958i	0.0395766	−	0.0228496i
$543$	−22.1991	−	12.8167i	−0.952654	−	0.550015i
$544$	0.334734	−	0.579776i	0.0143516	−	0.0248577i
$545$		0			0
$546$	2.34861	−	4.06792i	0.100511	−	0.174091i
$547$		−	24.8444i		−	1.06227i	−0.847287	−	0.531135i	$-0.821766\pi$
$547$		−	24.8444i		−	1.06227i	0.847287	−	0.531135i	$-0.178234\pi$
$548$	−1.46984	−	0.848612i	−0.0627884	−	0.0362509i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	13.1833			0.561629
$552$	7.79423	−	4.50000i	0.331744	−	0.191533i
$553$	−7.97705	+	4.60555i	−0.339219	+	0.195848i
$554$	−26.5694			−1.12883
$555$		0			0
$556$	2.05971	−	3.56753i	0.0873514	−	0.151297i
$557$	−4.85455	−	2.80278i	−0.205694	−	0.118757i	0.393615	−	0.919276i	$-0.371224\pi$
$557$	−4.85455	−	2.80278i	−0.205694	−	0.118757i	−0.599309	+	0.800518i	$0.704558\pi$
$558$		−	10.4222i		−	0.441207i
$559$	7.59167	+	13.1492i	0.321094	+	0.556150i
$560$		0			0
$561$	1.10555	−	1.91487i	0.0466764	−	0.0808459i
$562$	6.76942	+	3.90833i	0.285551	+	0.164863i
$563$	16.8201	−	9.71110i	0.708884	−	0.409274i	−0.101764	−	0.994809i	$-0.532449\pi$
$563$	16.8201	−	9.71110i	0.708884	−	0.409274i	0.810648	+	0.585534i	$0.199115\pi$
$564$	−1.57779			−0.0664372
$565$		0			0
$566$	−3.25694	−	5.64118i	−0.136899	−	0.237117i
$567$		−	1.00000i		−	0.0419961i
$568$	−43.6909	+	25.2250i	−1.83323	+	1.05842i
$569$	0.711103	−	1.23167i	0.0298110	−	0.0516341i	−0.850735	−	0.525595i	$-0.823843\pi$
$569$	0.711103	−	1.23167i	0.0298110	−	0.0516341i	0.880546	+	0.473961i	$0.157176\pi$
$570$		0			0
$571$	−36.8444			−1.54189			−0.770945	−	0.636901i	$-0.780216\pi$
$571$	−36.8444			−1.54189			−0.770945	+	0.636901i	$0.780216\pi$
$572$			6.11943i			0.255866i
$573$			4.81665i			0.201219i
$574$	−1.95416	+	3.38471i	−0.0815652	+	0.141275i
$575$		0			0
$576$	8.81665	+	15.2709i	0.367361	+	0.636287i
$577$			29.6333i			1.23365i	0.787100	+	0.616825i	$0.211582\pi$
$577$			29.6333i			1.23365i	−0.787100	+	0.616825i	$0.788418\pi$
$578$	19.0045	−	10.9722i	0.790482	−	0.456385i
$579$	4.19722	+	7.26981i	0.174431	+	0.302123i
$580$		0			0
$581$	2.60555	+	4.51295i	0.108096	+	0.187229i
$582$	17.6068	+	10.1653i	0.729824	+	0.421364i
$583$	−54.4249	−	31.4222i	−2.25405	−	1.30137i
$584$	−45.6333			−1.88832
$585$		0			0
$586$	22.9361			0.947481
$587$	3.96449	+	2.28890i	0.163632	+	0.0944729i	0.579580	−	0.814916i	$-0.303217\pi$
$587$	3.96449	+	2.28890i	0.163632	+	0.0944729i	−0.415948	+	0.909389i	$0.636550\pi$
$588$	1.57327	+	0.908327i	0.0648805	+	0.0374588i
$589$	−3.21110	−	5.56179i	−0.132311	−	0.229170i
$590$		0			0
$591$	−11.4083	−	19.7598i	−0.469276	−	0.812810i
$592$	10.3129	−	5.95416i	0.423858	−	0.244715i
$593$		−	35.2111i		−	1.44595i	−0.690876	−	0.722973i	$-0.742775\pi$
$593$		−	35.2111i		−	1.44595i	0.690876	−	0.722973i	$-0.257225\pi$
$594$	18.2569	+	31.6219i	0.749091	+	1.29746i
$595$		0			0
$596$	0.454163	−	0.786634i	0.0186033	−	0.0322218i
$597$		−	8.81665i		−	0.360842i
$598$	12.2037	−	7.04584i	0.499048	−	0.288126i
$599$	6.78890			0.277387			0.138693	−	0.990335i	$-0.455710\pi$
$599$	6.78890			0.277387			0.138693	+	0.990335i	$0.455710\pi$
$600$		0			0
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	0.420623	+	0.907235i	$0.361811\pi$
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	−0.996001	+	0.0893475i	$0.971522\pi$
$602$	−4.75112	+	2.74306i	−0.193641	+	0.111799i
$603$		−	14.0000i		−	0.570124i
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$		0			0
$606$	−11.7250			−0.476295
$607$	−17.1377	+	9.89445i	−0.695597	+	0.401603i	−0.805706	−	0.592316i	$-0.798214\pi$
$607$	−17.1377	+	9.89445i	−0.695597	+	0.401603i	0.110108	+	0.993920i	$0.464880\pi$
$608$	2.35990	+	1.36249i	0.0957067	+	0.0552563i
$609$	−4.10555	+	7.11102i	−0.166365	+	0.288153i
$610$		0			0
$611$	−18.7889			−0.760117
$612$			0.238859i			0.00965530i
$613$	1.39045	+	0.802776i	0.0561597	+	0.0324238i	0.527817	−	0.849358i	$-0.323011\pi$
$613$	1.39045	+	0.802776i	0.0561597	+	0.0324238i	−0.471657	+	0.881782i	$0.656344\pi$
$614$	−10.4222	+	18.0518i	−0.420606	+	0.728511i
$615$		0			0
$616$	−16.8167			−0.677562
$617$	22.9063	−	13.2250i	0.922174	−	0.532418i	0.0378463	−	0.999284i	$-0.487950\pi$
$617$	22.9063	−	13.2250i	0.922174	−	0.532418i	0.884328	+	0.466866i	$0.154617\pi$
$618$	4.51295	−	2.60555i	0.181537	−	0.104811i
$619$	14.4222			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$619$	14.4222			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$620$		0			0
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$	−5.87936	−	3.39445i	−0.235741	−	0.136105i
$623$			8.21110i			0.328971i
$624$	−5.95416	−	10.3129i	−0.238357	−	0.412847i
$625$		0			0
$626$	−9.11943	+	15.7953i	−0.364486	+	0.631308i
$627$	7.79423	+	4.50000i	0.311272	+	0.179713i
$628$	−0.841988	+	0.486122i	−0.0335990	+	0.0193984i
$629$	1.42221			0.0567070
$630$		0			0
$631$	−0.0138782	−	0.0240377i	−0.000552482	−	0.000956927i	0.865749	−	0.500478i	$-0.166843\pi$
$631$	−0.0138782	−	0.0240377i	−0.000552482	−	0.000956927i	−0.866302	+	0.499521i	$0.833509\pi$
$632$			27.6333i			1.09919i
$633$	14.1980	−	8.19722i	0.564320	−	0.325810i
$634$	3.90833	−	6.76942i	0.155219	−	0.268848i
$635$		0			0
$636$	−3.39445			−0.134599
$637$	18.7350	+	10.8167i	0.742307	+	0.428571i
$638$			59.9638i			2.37399i
$639$	16.8167	−	29.1273i	0.665257	−	1.15226i
$640$		0			0
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	0.991569	−	0.129579i	$-0.0413627\pi$
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	−0.608004	+	0.793934i	$0.708029\pi$
$642$		−	10.6972i		−	0.422186i
$643$	35.1895	−	20.3167i	1.38774	−	0.801211i	0.394678	−	0.918820i	$-0.370856\pi$
$643$	35.1895	−	20.3167i	1.38774	−	0.801211i	0.993060	+	0.117609i	$0.0375230\pi$
$644$	−0.454163	−	0.786634i	−0.0178965	−	0.0309977i
$645$		0			0
$646$	−0.412529	−	0.714521i	−0.0162307	−	0.0281125i
$647$	−9.16064	−	5.28890i	−0.360142	−	0.207928i	0.309001	−	0.951062i	$-0.400005\pi$
$647$	−9.16064	−	5.28890i	−0.360142	−	0.207928i	−0.669143	+	0.743134i	$0.733339\pi$
$648$	−2.59808	−	1.50000i	−0.102062	−	0.0589256i
$649$	60.6333			2.38007
$650$		0			0
$651$	4.00000			0.156772
$652$	−4.77516	−	2.75694i	−0.187010	−	0.107970i
$653$	−24.9560	−	14.4083i	−0.976602	−	0.563841i	−0.0753594	−	0.997156i	$-0.524010\pi$
$653$	−24.9560	−	14.4083i	−0.976602	−	0.563841i	−0.901243	+	0.433315i	$0.857344\pi$
$654$	−3.11943	−	5.40301i	−0.121979	−	0.211274i
$655$		0			0
$656$	4.95416	+	8.58086i	0.193428	+	0.335026i
$657$	26.3464	−	15.2111i	1.02787	−	0.593442i
$658$		−	6.78890i		−	0.264659i
$659$	−6.59167	−	11.4171i	−0.256775	−	0.444748i	0.708601	−	0.705609i	$-0.249327\pi$
$659$	−6.59167	−	11.4171i	−0.256775	−	0.444748i	−0.965376	+	0.260862i	$0.915993\pi$
$660$		0			0
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	0.195847	+	0.980634i	$0.437254\pi$
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	−0.947178	+	0.320709i	$0.896079\pi$
$662$		−	33.9083i		−	1.31788i
$663$		−	1.42221i		−	0.0552339i
$664$	15.6333			0.606690
$665$		0			0
$666$	−4.69722	+	8.13583i	−0.182014	+	0.315257i
$667$	−21.3331	+	12.3167i	−0.826020	+	0.476903i
$668$			2.72498i			0.105433i
$669$	5.10555	+	8.84307i	0.197392	+	0.341893i
$670$		0			0
$671$	5.60555			0.216400
$672$	−1.46984	+	0.848612i	−0.0567003	+	0.0327359i
$673$	−9.00186	−	5.19722i	−0.346996	−	0.200338i	0.316365	−	0.948637i	$-0.397537\pi$
$673$	−9.00186	−	5.19722i	−0.346996	−	0.200338i	−0.663361	+	0.748299i	$0.730871\pi$
$674$	11.4861	−	19.8945i	0.442429	−	0.766309i
$675$		0			0
$676$	1.96804	+	3.40875i	0.0756939	+	0.131106i
$677$			33.6333i			1.29263i	0.763069	+	0.646317i	$0.223691\pi$
$677$			33.6333i			1.29263i	−0.763069	+	0.646317i	$0.776309\pi$
$678$	6.32439	+	3.65139i	0.242887	+	0.140231i
$679$	7.80278	−	13.5148i	0.299443	−	0.518651i
$680$		0			0
$681$	1.42221			0.0544990
$682$	25.2976	−	14.6056i	0.968694	−	0.559275i
$683$	−18.8697	+	10.8944i	−0.722030	+	0.416864i	−0.815500	−	0.578758i	$-0.803538\pi$
$683$	−18.8697	+	10.8944i	−0.722030	+	0.416864i	0.0934691	+	0.995622i	$0.470204\pi$
$684$	−0.972244			−0.0371747
$685$		0			0
$686$	−8.46804	+	14.6671i	−0.323311	+	0.559992i
$687$	−12.1244	−	7.00000i	−0.462573	−	0.267067i
$688$			13.9083i			0.530250i
$689$	−40.4222			−1.53996
$690$		0			0
$691$	−3.01388	+	5.22019i	−0.114653	+	0.198585i	−0.917641	−	0.397410i	$-0.869909\pi$
$691$	−3.01388	+	5.22019i	−0.114653	+	0.198585i	0.802988	+	0.595995i	$0.203242\pi$
$692$	−4.40952	−	2.54584i	−0.167625	−	0.0967782i
$693$	9.70910	−	5.60555i	0.368818	−	0.212937i
$694$	−26.3305			−0.999493
$695$		0			0
$696$	12.3167	+	21.3331i	0.466862	+	0.808628i
$697$			1.18335i			0.0448224i
$698$	20.5464	−	11.8625i	0.777694	−	0.449002i
$699$	0.394449	−	0.683205i	0.0149194	−	0.0258412i
$700$		0			0
$701$	−7.57779			−0.286209			−0.143105	−	0.989708i	$-0.545709\pi$
$701$	−7.57779			−0.286209			−0.143105	+	0.989708i	$0.545709\pi$
$702$	20.3396	+	11.7431i	0.767668	+	0.443213i
$703$			5.78890i			0.218332i
$704$	−24.7111	+	42.8009i	−0.931335	+	1.61312i
$705$		0			0
$706$	3.13751	+	5.43433i	0.118082	+	0.204524i
$707$			9.00000i			0.338480i
$708$	2.83625	−	1.63751i	0.106593	−	0.0615414i
$709$	21.9222	+	37.9704i	0.823306	+	1.42601i	0.903207	+	0.429205i	$0.141206\pi$
$709$	21.9222	+	37.9704i	0.823306	+	1.42601i	−0.0799016	+	0.996803i	$0.525461\pi$
$710$		0			0
$711$	−9.21110	−	15.9541i	−0.345443	−	0.598325i
$712$	21.3331	+	12.3167i	0.799491	+	0.461586i
$713$	10.3923	+	6.00000i	0.389195	+	0.224702i
$714$	0.513878			0.0192314
$715$		0			0
$716$	−0.358288			−0.0133899
$717$		0			0
$718$	−11.7587	−	6.78890i	−0.438831	−	0.253359i
$719$	−9.19722	−	15.9301i	−0.342999	−	0.594091i	0.641989	−	0.766713i	$-0.278109\pi$
$719$	−9.19722	−	15.9301i	−0.342999	−	0.594091i	−0.984988	+	0.172622i	$0.944776\pi$
$720$		0			0
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$	−18.5281	+	10.6972i	−0.689546	+	0.398109i
$723$		−	16.2111i		−	0.602897i
$724$	3.88057	+	6.72135i	0.144220	+	0.249797i
$725$		0			0
$726$	−13.3028	+	23.0411i	−0.493712	+	0.855135i
$727$			42.4222i			1.57335i	0.617366	+	0.786676i	$0.288200\pi$
$727$			42.4222i			1.57335i	−0.617366	+	0.786676i	$0.711800\pi$
$728$	−9.36750	+	5.40833i	−0.347183	+	0.200446i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−0.830532	+	1.43852i	−0.0307183	+	0.0532057i
$732$	0.262211	−	0.151388i	0.00969161	−	0.00559545i
$733$		−	10.8444i		−	0.400547i	−0.979740	−	0.200274i	$-0.935817\pi$
$733$		−	10.8444i		−	0.400547i	0.979740	−	0.200274i	$-0.0641831\pi$
$734$	−11.3486	−	19.6564i	−0.418885	−	0.725530i
$735$		0			0
$736$	−5.09167			−0.187682
$737$	33.9818	−	19.6194i	1.25174	−	0.722691i
$738$	−6.76942	−	3.90833i	−0.249186	−	0.143868i
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	0.477411	+	0.878680i	$0.341575\pi$
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	−0.999665	+	0.0258895i	$0.991758\pi$
$740$		0			0
$741$	5.78890			0.212660
$742$		−	14.6056i		−	0.536187i
$743$	−5.74461	−	3.31665i	−0.210749	−	0.121676i	0.390910	−	0.920429i	$-0.372160\pi$
$743$	−5.74461	−	3.31665i	−0.210749	−	0.121676i	−0.601660	+	0.798753i	$0.705494\pi$
$744$	6.00000	−	10.3923i	0.219971	−	0.381000i
$745$		0			0
$746$	−35.9638			−1.31673
$747$	−9.02589	+	5.21110i	−0.330240	+	0.190664i
$748$	−0.579776	+	0.334734i	−0.0211987	+	0.0122391i
$749$	−8.21110			−0.300027
$750$		0			0
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	−0.647171	−	0.762345i	$-0.724048\pi$
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	0.983795	+	0.179294i	$0.0573814\pi$
$752$	−14.9053	−	8.60555i	−0.543539	−	0.313812i
$753$			28.8167i			1.05014i
$754$	19.2847	+	33.4021i	0.702307	+	1.21643i
$755$		0			0
$756$	0.756939	−	1.31106i	0.0275296	−	0.0476827i
$757$	18.0278	+	10.4083i	0.655230	+	0.378297i	0.790457	−	0.612518i	$-0.209843\pi$
$757$	18.0278	+	10.4083i	0.655230	+	0.378297i	−0.135227	+	0.990815i	$0.543176\pi$
$758$	−2.70151	+	1.55971i	−0.0981231	+	0.0566514i
$759$	−16.8167			−0.610406
$760$		0			0
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	0.998154	−	0.0607356i	$-0.0193447\pi$
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	−0.551676	+	0.834059i	$0.686011\pi$
$762$			13.3028i			0.481909i
$763$	−4.14731	+	2.39445i	−0.150143	+	0.0866849i
$764$	0.729183	−	1.26298i	0.0263809	−	0.0456931i
$765$		0			0
$766$	24.2750			0.877092
$767$	33.7750	−	19.5000i	1.21954	−	0.704104i
$768$			7.09167i			0.255899i
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	−0.749654	−	0.661830i	$-0.769780\pi$
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	0.947989	+	0.318304i	$0.103113\pi$
$770$		0			0
$771$	11.8028	+	20.4430i	0.425067	+	0.736237i
$772$		−	2.54163i		−	0.0914754i
$773$	−25.6392	+	14.8028i	−0.922176	+	0.532419i	−0.884329	−	0.466865i	$-0.845384\pi$
$773$	−25.6392	+	14.8028i	−0.922176	+	0.532419i	−0.0378477	+	0.999284i	$0.512050\pi$
$774$	−5.48612	−	9.50224i	−0.197195	−	0.341551i
$775$		0			0
$776$	−23.4083	−	40.5444i	−0.840310	−	1.45546i
$777$	−3.12250	−	1.80278i	−0.112019	−	0.0646742i
$778$	−0.890063	−	0.513878i	−0.0319103	−	0.0184234i
$779$	−4.81665			−0.172575
$780$		0			0
$781$	94.2666			3.37312
$782$	1.33509	+	0.770817i	0.0477429	+	0.0275644i
$783$	−35.5551	−	20.5278i	−1.27064	−	0.733602i
$784$	9.90833	+	17.1617i	0.353869	+	0.612919i
$785$		0			0
$786$	4.42221	+	7.65948i	0.157735	+	0.273205i
$787$	−24.7972	+	14.3167i	−0.883924	+	0.510334i	−0.871950	−	0.489595i	$-0.837145\pi$
$787$	−24.7972	+	14.3167i	−0.883924	+	0.510334i	−0.0119736	+	0.999928i	$0.503811\pi$
$788$			6.90833i			0.246099i
$789$	13.1056	+	22.6995i	0.466570	+	0.808123i
$790$		0			0
$791$	2.80278	−	4.85455i	0.0996552	−	0.172608i
$792$		−	33.6333i		−	1.19511i
$793$	3.12250	−	1.80278i	0.110883	−	0.0640184i
$794$	18.2750			0.648556
$795$		0			0
$796$	−1.33473	+	2.31183i	−0.0473084	+	0.0819405i
$797$	43.6909	−	25.2250i	1.54761	−	0.893515i	0.549289	−	0.835632i	$-0.314898\pi$
$797$	43.6909	−	25.2250i	1.54761	−	0.893515i	0.998323	−	0.0578825i	$-0.0184349\pi$
$798$			2.09167i			0.0740444i
$799$	−1.02776	−	1.78013i	−0.0363594	−	0.0629763i
$800$		0			0
$801$	−16.4222			−0.580250
$802$	−2.49465	+	1.44029i	−0.0880891	+	0.0508582i
$803$	73.8431	+	42.6333i	2.60586	+	1.50450i
$804$	1.05971	−	1.83548i	0.0373733	−	0.0647324i
$805$		0			0
$806$	9.39445	−	16.2717i	0.330905	−	0.573145i
$807$		−	9.00000i		−	0.316815i
$808$	23.3827	+	13.5000i	0.822600	+	0.474928i
$809$	8.52776	−	14.7705i	0.299820	−	0.519303i	−0.676275	−	0.736650i	$-0.736407\pi$
$809$	8.52776	−	14.7705i	0.299820	−	0.519303i	0.976095	+	0.217346i	$0.0697401\pi$
$810$		0			0
$811$	−17.5778			−0.617240			−0.308620	−	0.951185i	$-0.599867\pi$
$811$	−17.5778			−0.617240			−0.308620	+	0.951185i	$0.599867\pi$
$812$	2.15304	−	1.24306i	0.0755571	−	0.0436229i
$813$	−0.707243	+	0.408327i	−0.0248041	+	0.0143207i
$814$	−26.3305			−0.922885
$815$		0			0
$816$	0.651388	−	1.12824i	0.0228031	−	0.0394962i
$817$	−5.85532	−	3.38057i	−0.204852	−	0.118271i
$818$			8.09167i			0.282919i
$819$	3.60555	−	6.24500i	0.125988	−	0.218218i
$820$		0			0
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	−0.793972	−	0.607955i	$-0.791990\pi$
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	0.923490	+	0.383622i	$0.125324\pi$
$822$	−6.32439	−	3.65139i	−0.220588	−	0.127357i
$823$	−23.0651	+	13.3167i	−0.804000	+	0.464189i	−0.844868	−	0.534975i	$-0.820321\pi$
$823$	−23.0651	+	13.3167i	−0.804000	+	0.464189i	0.0408682	+	0.999165i	$0.486988\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	7.04584	+	12.2037i	0.245156	+	0.424623i
$827$		−	13.5778i		−	0.472146i	−0.971735	−	0.236073i	$-0.924140\pi$
$827$		−	13.5778i		−	0.472146i	0.971735	−	0.236073i	$-0.0758605\pi$
$828$	1.57327	−	0.908327i	0.0546749	−	0.0315665i
$829$	0.288897	−	0.500385i	0.0100338	−	0.0173791i	−0.860965	−	0.508664i	$-0.830139\pi$
$829$	0.288897	−	0.500385i	0.0100338	−	0.0173791i	0.870999	+	0.491285i	$0.163473\pi$
$830$		0			0
$831$	20.3944			0.707476
$832$			31.7889i			1.10208i
$833$			2.36669i			0.0820010i
$834$	8.86249	−	15.3503i	0.306883	−	0.531537i
$835$		0			0
$836$	−1.36249	−	2.35990i	−0.0471227	−	0.0816189i
$837$			20.0000i			0.691301i
$838$	37.5013	−	21.6514i	1.29546	−	0.747935i
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	0.970555	−	0.240879i	$-0.0774358\pi$
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	−0.693885	+	0.720086i	$0.744103\pi$
$840$		0			0
$841$	−19.2111	−	33.2746i	−0.662452	−	1.14740i
$842$	−4.03660	−	2.33053i	−0.139110	−	0.0803154i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	−4.96384			−0.170862
$845$		0			0
$846$	13.5778			0.466814
$847$	17.6861	+	10.2111i	0.607703	+	0.350858i
$848$	−32.0670	−	18.5139i	−1.10118	−	0.635769i
$849$	2.50000	+	4.33013i	0.0857998	+	0.148610i
$850$		0			0
$851$	−5.40833	−	9.36750i	−0.185395	−	0.321114i
$852$	4.40952	−	2.54584i	0.151068	−	0.0872189i
$853$		−	32.7889i		−	1.12267i	−0.827589	−	0.561335i	$-0.810288\pi$
$853$		−	32.7889i		−	1.12267i	0.827589	−	0.561335i	$-0.189712\pi$
$854$	0.651388	+	1.12824i	0.0222900	+	0.0386075i
$855$		0			0
$856$	−12.3167	+	21.3331i	−0.420975	+	0.729149i
$857$			6.00000i			0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$			6.00000i			0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$			26.3305i			0.898910i
$859$	−25.2111			−0.860192			−0.430096	−	0.902783i	$-0.641520\pi$
$859$	−25.2111			−0.860192			−0.430096	+	0.902783i	$0.641520\pi$
$860$		0			0
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	−23.9625	+	13.8347i	−0.816165	+	0.471213i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−4.24306	−	7.34920i	−0.144352	−	0.250025i
$865$		0			0
$866$	−4.69722			−0.159618
$867$	−14.5877	+	8.42221i	−0.495424	+	0.286033i
$868$	−1.04885	−	0.605551i	−0.0356001	−	0.0205537i
$869$	25.8167	−	44.7158i	0.875770	−	1.51688i
$870$		0			0
$871$	12.6194	−	21.8575i	0.427593	−	0.740613i
$872$			14.3667i			0.486518i
$873$	27.0296	+	15.6056i	0.914814	+	0.528168i
$874$	−3.13751	+	5.43433i	−0.106128	+	0.183819i
$875$		0			0
$876$	4.60555			0.155607
$877$	−32.9330	+	19.0139i	−1.11207	+	0.642053i	−0.939364	−	0.342921i	$-0.888584\pi$
$877$	−32.9330	+	19.0139i	−1.11207	+	0.642053i	−0.172704	+	0.984974i	$0.555250\pi$
$878$	−26.2189	+	15.1375i	−0.884846	+	0.510866i
$879$	−17.6056			−0.593821
$880$		0			0
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	0.388423	+	0.921481i	$0.373020\pi$
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	−0.992238	+	0.124356i	$0.960313\pi$
$882$	−13.5388	−	7.81665i	−0.455877	−	0.263200i
$883$			31.6333i			1.06455i	0.846573	+	0.532273i	$0.178662\pi$
$883$			31.6333i			1.06455i	−0.846573	+	0.532273i	$0.821338\pi$
$884$	−0.215305	+	0.372918i	−0.00724147	+	0.0125426i
$885$		0			0
$886$	14.6056	−	25.2976i	0.490683	−	0.849888i
$887$	−30.3590	−	17.5278i	−1.01935	−	0.588524i	−0.105437	−	0.994426i	$-0.533624\pi$
$887$	−30.3590	−	17.5278i	−1.01935	−	0.588524i	−0.913917	+	0.405901i	$0.866958\pi$
$888$	−9.36750	+	5.40833i	−0.314353	+	0.181492i
$889$	10.2111			0.342469
$890$		0			0
$891$	2.80278	+	4.85455i	0.0938965	+	0.162634i
$892$		−	3.09167i		−	0.103517i
$893$	7.24577	−	4.18335i	0.242470	−	0.139990i
$894$	1.95416	−	3.38471i	0.0653570	−	0.113202i
$895$		0			0
$896$	−8.09167			−0.270324
$897$	−9.36750	+	5.40833i	−0.312772	+	0.180579i
$898$			16.4584i			0.549223i
$899$	−16.4222	+	28.4441i	−0.547711	+	0.948664i
$900$		0			0
$901$	−2.21110	−	3.82974i	−0.0736625	−	0.127587i
$902$		−	21.9083i		−	0.729467i
$903$	3.64692	−	2.10555i	0.121362	−	0.0700684i
$904$	−8.40833	−	14.5636i	−0.279657	−	0.484380i
$905$		0			0
$906$	−8.60555	−	14.9053i	−0.285900	−	0.495194i
$907$	−41.8001	−	24.1333i	−1.38795	−	0.801333i	−0.394866	−	0.918739i	$-0.629209\pi$
$907$	−41.8001	−	24.1333i	−1.38795	−	0.801333i	−0.993084	+	0.117405i	$0.962542\pi$
$908$	−0.372918	−	0.215305i	−0.0123757	−	0.00714513i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	4.59234	+	2.65139i	0.152068	+	0.0877962i
$913$	−25.2976	−	14.6056i	−0.837227	−	0.483373i
$914$	−3.37637	−	5.84804i	−0.111680	−	0.193436i
$915$		0			0
$916$	2.11943	+	3.67096i	0.0700279	+	0.121292i
$917$	5.87936	−	3.39445i	0.194153	−	0.112095i
$918$			2.56939i			0.0848025i
$919$	−8.59167	−	14.8812i	−0.283413	−	0.490886i	0.688810	−	0.724942i	$-0.258133\pi$
$919$	−8.59167	−	14.8812i	−0.283413	−	0.490886i	−0.972223	+	0.234056i	$0.924800\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$			28.3860i			0.934845i
$923$	52.5100	−	30.3167i	1.72839	−	0.997885i
$924$	1.69722			0.0558346
$925$		0			0
$926$	3.63331	−	6.29307i	0.119398	−	0.206803i
$927$	6.92820	−	4.00000i	0.227552	−	0.131377i
$928$		−	13.9361i		−	0.457474i
$929$	6.71110	+	11.6240i	0.220184	+	0.381370i	0.954864	−	0.297044i	$-0.0960008\pi$
$929$	6.71110	+	11.6240i	0.220184	+	0.381370i	−0.734680	+	0.678414i	$0.762668\pi$
$930$		0			0
$931$	−9.63331			−0.315719
$932$	−0.206858	+	0.119429i	−0.00677586	+	0.00391204i
$933$	4.51295	+	2.60555i	0.147747	+	0.0853019i
$934$	11.2111	−	19.4182i	0.366838	−	0.635383i
$935$		0			0
$936$	−10.8167	−	18.7350i	−0.353553	−	0.612372i
$937$		−	46.4777i		−	1.51836i	−0.650880	−	0.759180i	$-0.725600\pi$
$937$		−	46.4777i		−	1.51836i	0.650880	−	0.759180i	$-0.274400\pi$
$938$	7.89766	+	4.55971i	0.257868	+	0.148880i
$939$	7.00000	−	12.1244i	0.228436	−	0.395663i
$940$		0			0
$941$	33.6333			1.09641			0.548207	−	0.836343i	$-0.315311\pi$
$941$	33.6333			1.09641			0.548207	+	0.836343i	$0.315311\pi$
$942$	−3.62288	+	2.09167i	−0.118040	+	0.0681504i
$943$	7.79423	−	4.50000i	0.253815	−	0.146540i
$944$	35.7250			1.16275
$945$		0			0
$946$	15.3764	−	26.6327i	0.499929	−	0.865902i
$947$	−21.3331	−	12.3167i	−0.693232	−	0.400237i	0.111590	−	0.993754i	$-0.464406\pi$
$947$	−21.3331	−	12.3167i	−0.693232	−	0.400237i	−0.804822	+	0.593517i	$0.797739\pi$
$948$		−	2.78890i		−	0.0905792i
$949$	54.8444			1.78032
$950$		0			0
$951$	−3.00000	+	5.19615i	−0.0972817	+	0.168497i
$952$	−1.02481	−	0.591673i	−0.0332142	−	0.0191762i
$953$	−43.6909	+	25.2250i	−1.41529	+	0.817117i	−0.995880	−	0.0906803i	$-0.971096\pi$
$953$	−43.6909	+	25.2250i	−1.41529	+	0.817117i	−0.419409	+	0.907798i	$0.637763\pi$
$954$	29.2111			0.945744
$955$		0			0
$956$		0			0
$957$		−	46.0278i		−	1.48787i
$958$	8.10452	−	4.67914i	0.261845	−	0.151176i
$959$	−2.80278	+	4.85455i	−0.0905063	+	0.156762i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−14.6671	+	8.46804i	−0.472886	+	0.273021i
$963$		−	16.4222i		−	0.529198i
$964$	−2.45416	+	4.25074i	−0.0790433	+	0.136907i
$965$		0			0
$966$	−1.95416	−	3.38471i	−0.0628742	−	0.108901i
$967$			56.4777i			1.81620i	0.418752	+	0.908100i	$0.362468\pi$
$967$			56.4777i			1.81620i	−0.418752	+	0.908100i	$0.637532\pi$
$968$	53.0584	−	30.6333i	1.70536	−	0.984592i
$969$	0.316654	+	0.548461i	0.0101724	+	0.0176191i
$970$		0			0
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	0.922871	−	0.385110i	$-0.125836\pi$
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	−0.794950	+	0.606675i	$0.792503\pi$
$972$	4.19538	+	2.42221i	0.134567	+	0.0776923i
$973$	−11.7828	−	6.80278i	−0.377738	−	0.218087i
$974$	1.30278			0.0417436
$975$		0			0
$976$	3.30278			0.105719
$977$	−6.22096	−	3.59167i	−0.199026	−	0.114908i	0.397175	−	0.917743i	$-0.369991\pi$
$977$	−6.22096	−	3.59167i	−0.199026	−	0.114908i	−0.596201	+	0.802835i	$0.703324\pi$
$978$	−20.5464	−	11.8625i	−0.657003	−	0.379321i
$979$	−23.0139	−	39.8612i	−0.735527	−	1.27397i
$980$		0			0
$981$	−4.78890	−	8.29461i	−0.152898	−	0.264827i
$982$	5.43433	−	3.13751i	0.173416	−	0.100122i
$983$			10.4222i			0.332417i	0.986091	+	0.166208i	$0.0531524\pi$
$983$			10.4222i			0.332417i	−0.986091	+	0.166208i	$0.946848\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$		0			0
$986$	−2.10975	+	3.65420i	−0.0671882	+	0.116373i
$987$			5.21110i			0.165871i
$988$	−1.51791	−	0.876369i	−0.0482913	−	0.0278810i
$989$	12.6333			0.401716
$990$		0			0
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	−0.895846	−	0.444365i	$-0.853429\pi$
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	0.832754	+	0.553642i	$0.186763\pi$
$992$	−5.87936	+	3.39445i	−0.186670	+	0.107774i
$993$			26.0278i			0.825966i
$994$	10.9542	+	18.9732i	0.347445	+	0.601792i
$995$		0			0
$996$	−1.57779			−0.0499943
$997$	40.2268	−	23.2250i	1.27400	−	0.735543i	0.298259	−	0.954485i	$-0.403594\pi$
$997$	40.2268	−	23.2250i	1.27400	−	0.735543i	0.975738	+	0.218942i	$0.0702607\pi$
$998$	−29.8105	−	17.2111i	−0.943635	−	0.544808i
$999$	9.01388	−	15.6125i	0.285186	−	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.o.b.74.2		8
5.2	odd	4		325.2.e.a.126.2		4
5.3	odd	4		65.2.e.b.61.1	yes	4
5.4	even	2	inner	325.2.o.b.74.3		8
13.3	even	3	inner	325.2.o.b.224.3		8
15.8	even	4		585.2.j.d.451.2		4
20.3	even	4		1040.2.q.o.321.1		4
65.3	odd	12		65.2.e.b.16.1	✓	4
65.8	even	4		845.2.m.d.316.2		8
65.17	odd	12		4225.2.a.t.1.2		2
65.18	even	4		845.2.m.d.316.3		8
65.22	odd	12		4225.2.a.x.1.1		2
65.23	odd	12		845.2.e.d.146.2		4
65.28	even	12		845.2.m.d.361.2		8
65.29	even	6	inner	325.2.o.b.224.2		8
65.33	even	12		845.2.c.d.506.3		4
65.38	odd	4		845.2.e.d.191.2		4
65.42	odd	12		325.2.e.a.276.2		4
65.43	odd	12		845.2.a.f.1.1		2
65.48	odd	12		845.2.a.c.1.2		2
65.58	even	12		845.2.c.d.506.2		4
65.63	even	12		845.2.m.d.361.3		8
195.68	even	12		585.2.j.d.406.2		4
195.113	even	12		7605.2.a.bg.1.1		2
195.173	even	12		7605.2.a.bb.1.2		2
260.3	even	12		1040.2.q.o.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	65.3	odd	12
65.2.e.b.61.1	yes	4	5.3	odd	4
325.2.e.a.126.2		4	5.2	odd	4
325.2.e.a.276.2		4	65.42	odd	12
325.2.o.b.74.2		8	1.1	even	1	trivial
325.2.o.b.74.3		8	5.4	even	2	inner
325.2.o.b.224.2		8	65.29	even	6	inner
325.2.o.b.224.3		8	13.3	even	3	inner
585.2.j.d.406.2		4	195.68	even	12
585.2.j.d.451.2		4	15.8	even	4
845.2.a.c.1.2		2	65.48	odd	12
845.2.a.f.1.1		2	65.43	odd	12
845.2.c.d.506.2		4	65.58	even	12
845.2.c.d.506.3		4	65.33	even	12
845.2.e.d.146.2		4	65.23	odd	12
845.2.e.d.191.2		4	65.38	odd	4
845.2.m.d.316.2		8	65.8	even	4
845.2.m.d.316.3		8	65.18	even	4
845.2.m.d.361.2		8	65.28	even	12
845.2.m.d.361.3		8	65.63	even	12
1040.2.q.o.81.1		4	260.3	even	12
1040.2.q.o.321.1		4	20.3	even	4
4225.2.a.t.1.2		2	65.17	odd	12
4225.2.a.x.1.1		2	65.22	odd	12
7605.2.a.bb.1.2		2	195.173	even	12
7605.2.a.bg.1.1		2	195.113	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12824 - 0.651388i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.151388 - 0.262211i) q^{4} +(-0.651388 - 1.12824i) q^{6} +(-0.866025 + 0.500000i) q^{7} +3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.80278 - 4.85455i) q^{11} -0.302776i q^{12} -3.60555i q^{13} +1.30278 q^{14} +(1.65139 - 2.86029i) q^{16} +(0.341603 - 0.197224i) q^{17} +2.60555i q^{18} +(0.802776 + 1.39045i) q^{19} -1.00000 q^{21} +(-6.32439 + 3.65139i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-2.34861 + 4.06792i) q^{26} -5.00000i q^{27} +(0.262211 + 0.151388i) q^{28} +(4.10555 - 7.11102i) q^{29} -4.00000 q^{31} +(1.46984 - 0.848612i) q^{32} +(4.85455 - 2.80278i) q^{33} -0.513878 q^{34} +(-0.302776 + 0.524423i) q^{36} +(3.12250 + 1.80278i) q^{37} -2.09167i q^{38} +(1.80278 - 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(1.12824 + 0.651388i) q^{42} +(-3.64692 + 2.10555i) q^{43} -1.69722 q^{44} +(1.95416 + 3.38471i) q^{46} -5.21110i q^{47} +(2.86029 - 1.65139i) q^{48} +(-3.00000 + 5.19615i) q^{49} +0.394449 q^{51} +(-0.945417 + 0.545837i) q^{52} -11.2111i q^{53} +(-3.25694 + 5.64118i) q^{54} +(-1.50000 - 2.59808i) q^{56} +1.60555i q^{57} +(-9.26407 + 5.34861i) q^{58} +(5.40833 + 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(4.51295 + 2.60555i) q^{62} +(1.73205 + 1.00000i) q^{63} -8.81665 q^{64} -7.30278 q^{66} +(6.06218 + 3.50000i) q^{67} +(-0.103429 - 0.0597147i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(8.40833 + 14.5636i) q^{71} +(5.19615 - 3.00000i) q^{72} +15.2111i q^{73} +(-2.34861 - 4.06792i) q^{74} +(0.243061 - 0.420994i) q^{76} +5.60555i q^{77} +(-4.06792 + 2.34861i) q^{78} +9.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.38471 - 1.95416i) q^{82} -5.21110i q^{83} +(0.151388 + 0.262211i) q^{84} +5.48612 q^{86} +(7.11102 - 4.10555i) q^{87} +(14.5636 + 8.40833i) q^{88} +(4.10555 - 7.11102i) q^{89} +(1.80278 + 3.12250i) q^{91} +0.908327i q^{92} +(-3.46410 - 2.00000i) q^{93} +(-3.39445 + 5.87936i) q^{94} +1.69722 q^{96} +(-13.5148 + 7.80278i) q^{97} +(6.76942 - 3.90833i) q^{98} -11.2111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{4} + 2 q^{6} - 8 q^{9} + 8 q^{11} - 4 q^{14} + 6 q^{16} - 8 q^{19} - 8 q^{21} - 12 q^{24} - 26 q^{26} + 4 q^{29} - 32 q^{31} + 68 q^{34} + 12 q^{36} - 12 q^{41} - 28 q^{44} - 6 q^{46} - 24 q^{49}+ \cdots - 32 q^{99}+O(q^{100}) \) 8 * q + 6 * q^4 + 2 * q^6 - 8 * q^9 + 8 * q^11 - 4 * q^14 + 6 * q^16 - 8 * q^19 - 8 * q^21 - 12 * q^24 - 26 * q^26 + 4 * q^29 - 32 * q^31 + 68 * q^34 + 12 * q^36 - 12 * q^41 - 28 * q^44 - 6 * q^46 - 24 * q^49 + 32 * q^51 + 10 * q^54 - 12 * q^56 + 4 * q^61 + 16 * q^64 - 44 * q^66 - 12 * q^69 + 24 * q^71 - 26 * q^74 + 38 * q^76 + 16 * q^79 - 4 * q^81 - 6 * q^84 + 116 * q^86 + 4 * q^89 - 56 * q^94 + 28 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

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