LMFDB - Embedded newform 225.4.k.d.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.63422 + 1.52087i) q^{2} +(3.29398 + 4.01867i) q^{3} +(0.626094 - 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(11.8751 - 6.85611i) q^{7} -20.5251i q^{8} +(-5.29939 + 26.4748i) q^{9} +O(q^{10})$	\(q+(-2.63422 + 1.52087i) q^{2} +(3.29398 + 4.01867i) q^{3} +(0.626094 - 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(11.8751 - 6.85611i) q^{7} -20.5251i q^{8} +(-5.29939 + 26.4748i) q^{9} +(-15.9034 - 27.5455i) q^{11} +(6.42029 - 1.05602i) q^{12} +(-50.4401 - 29.1216i) q^{13} +(-20.8545 + 36.1211i) q^{14} +(36.2248 + 62.7431i) q^{16} -109.055i q^{17} +(-26.3050 - 77.8003i) q^{18} -129.695 q^{19} +(66.6689 + 25.1383i) q^{21} +(83.7863 + 48.3740i) q^{22} +(-68.9949 - 39.8342i) q^{23} +(82.4836 - 67.6093i) q^{24} +177.161 q^{26} +(-123.850 + 65.9111i) q^{27} -17.1703i q^{28} +(4.51769 + 7.82486i) q^{29} +(16.6904 - 28.9087i) q^{31} +(-48.6463 - 28.0860i) q^{32} +(58.3108 - 154.645i) q^{33} +(165.858 + 287.275i) q^{34} +(25.3921 + 22.3225i) q^{36} +22.1645i q^{37} +(341.647 - 197.250i) q^{38} +(-49.1186 - 298.628i) q^{39} +(-60.8698 + 105.430i) q^{41} +(-213.853 + 35.1747i) q^{42} +(8.78298 - 5.07086i) q^{43} -39.8281 q^{44} +242.331 q^{46} +(382.343 - 220.746i) q^{47} +(-132.820 + 352.250i) q^{48} +(-77.4875 + 134.212i) q^{49} +(438.255 - 359.225i) q^{51} +(-63.1604 + 36.4657i) q^{52} -593.610i q^{53} +(226.006 - 361.984i) q^{54} +(-140.722 - 243.738i) q^{56} +(-427.214 - 521.202i) q^{57} +(-23.8012 - 13.7416i) q^{58} +(221.230 - 383.182i) q^{59} +(-72.2881 - 125.207i) q^{61} +101.536i q^{62} +(118.583 + 350.725i) q^{63} -408.736 q^{64} +(81.5912 + 496.052i) q^{66} +(747.138 + 431.360i) q^{67} +(-118.262 - 68.2786i) q^{68} +(-67.1873 - 408.481i) q^{69} -818.541 q^{71} +(543.398 + 108.771i) q^{72} +495.052i q^{73} +(-33.7093 - 58.3863i) q^{74} +(-81.2014 + 140.645i) q^{76} +(-377.710 - 218.071i) q^{77} +(583.563 + 711.950i) q^{78} +(585.263 + 1013.71i) q^{79} +(-672.833 - 280.601i) q^{81} -370.300i q^{82} +(-367.232 + 212.022i) q^{83} +(69.0017 - 56.5586i) q^{84} +(-15.4242 + 26.7156i) q^{86} +(-16.5644 + 43.9300i) q^{87} +(-565.374 + 326.419i) q^{88} -1031.37 q^{89} -798.643 q^{91} +(-86.3945 + 49.8799i) q^{92} +(171.152 - 28.1513i) q^{93} +(-671.452 + 1162.99i) q^{94} +(-47.3718 - 288.008i) q^{96} +(-1384.53 + 799.356i) q^{97} -471.394i q^{98} +(813.541 - 275.066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.63422	+	1.52087i	−0.931339	+	0.537709i	−0.887235	−	0.461318i	$-0.847377\pi$
$2$	−2.63422	+	1.52087i	−0.931339	+	0.537709i	−0.0441043	+	0.999027i	$0.514043\pi$
$3$	3.29398	+	4.01867i	0.633927	+	0.773393i
$3$	3.29398	+	4.01867i	0.633927	+	0.773393i
$4$	0.626094	−	1.08443i	0.0782617	−	0.135553i
$5$		0			0
$5$		0			0
$6$	−14.7890	−	5.57636i	−1.00626	−	0.379423i
$7$	11.8751	−	6.85611i	0.641197	−	0.370195i	−0.143879	−	0.989595i	$-0.545957\pi$
$7$	11.8751	−	6.85611i	0.641197	−	0.370195i	0.785075	+	0.619400i	$0.212624\pi$
$8$		−	20.5251i		−	0.907090i
$9$	−5.29939	+	26.4748i	−0.196274	+	0.980549i
$10$		0			0
$11$	−15.9034	−	27.5455i	−0.435914	−	0.755026i	0.561455	−	0.827507i	$-0.310242\pi$
$11$	−15.9034	−	27.5455i	−0.435914	−	0.755026i	−0.997370	+	0.0724812i	$0.976908\pi$
$12$	6.42029	−	1.05602i	0.154448	−	0.0254038i
$13$	−50.4401	−	29.1216i	−1.07612	−	0.621298i	−0.146272	−	0.989244i	$-0.546728\pi$
$13$	−50.4401	−	29.1216i	−1.07612	−	0.621298i	−0.929847	+	0.367946i	$0.880061\pi$
$14$	−20.8545	+	36.1211i	−0.398115	+	0.689555i
$15$		0			0
$16$	36.2248	+	62.7431i	0.566012	+	0.980361i
$17$		−	109.055i		−	1.55586i	−0.628348	−	0.777932i	$-0.716269\pi$
$17$		−	109.055i		−	1.55586i	0.628348	−	0.777932i	$-0.283731\pi$
$18$	−26.3050	−	77.8003i	−0.344453	−	1.01876i
$19$	−129.695			−1.56601			−0.783004	−	0.622017i	$-0.786313\pi$
$19$	−129.695			−1.56601			−0.783004	+	0.622017i	$0.786313\pi$
$20$		0			0
$21$	66.6689	+	25.1383i	0.692778	+	0.261221i
$22$	83.7863	+	48.3740i	0.811968	+	0.468790i
$23$	−68.9949	−	39.8342i	−0.625497	−	0.361131i	0.153509	−	0.988147i	$-0.450943\pi$
$23$	−68.9949	−	39.8342i	−0.625497	−	0.361131i	−0.779006	+	0.627017i	$0.784276\pi$
$24$	82.4836	−	67.6093i	0.701537	−	0.575028i
$25$		0			0
$26$	177.161			1.33631
$27$	−123.850	+	65.9111i	−0.882773	+	0.469800i
$28$		−	17.1703i		−	0.115888i
$29$	4.51769	+	7.82486i	0.0289280	+	0.0501048i	0.880127	−	0.474738i	$-0.157457\pi$
$29$	4.51769	+	7.82486i	0.0289280	+	0.0501048i	−0.851199	+	0.524843i	$0.824124\pi$
$30$		0			0
$31$	16.6904	−	28.9087i	0.0966998	−	0.167489i	−0.813617	−	0.581401i	$-0.802505\pi$
$31$	16.6904	−	28.9087i	0.0966998	−	0.167489i	0.910317	+	0.413912i	$0.135838\pi$
$32$	−48.6463	−	28.0860i	−0.268735	−	0.155154i
$33$	58.3108	−	154.645i	0.307594	−	0.815764i
$34$	165.858	+	287.275i	0.836602	+	1.44904i
$35$		0			0
$36$	25.3921	+	22.3225i	0.117556	+	0.103345i
$37$			22.1645i			0.0984817i	0.998787	+	0.0492408i	$0.0156802\pi$
$37$			22.1645i			0.0984817i	−0.998787	+	0.0492408i	$0.984320\pi$
$38$	341.647	−	197.250i	1.45848	−	0.842056i
$39$	−49.1186	−	298.628i	−0.201673	−	1.22612i
$40$		0			0
$41$	−60.8698	+	105.430i	−0.231860	+	0.401593i	−0.958356	−	0.285578i	$-0.907814\pi$
$41$	−60.8698	+	105.430i	−0.231860	+	0.401593i	0.726495	+	0.687171i	$0.241148\pi$
$42$	−213.853	+	35.1747i	−0.785672	+	0.129228i
$43$	8.78298	−	5.07086i	0.0311487	−	0.0179837i	−0.484345	−	0.874877i	$-0.660942\pi$
$43$	8.78298	−	5.07086i	0.0311487	−	0.0179837i	0.515493	+	0.856894i	$0.327609\pi$
$44$	−39.8281			−0.136462
$45$		0			0
$46$	242.331			0.776733
$47$	382.343	−	220.746i	1.18661	−	0.685088i	0.229073	−	0.973409i	$-0.426430\pi$
$47$	382.343	−	220.746i	1.18661	−	0.685088i	0.957534	+	0.288321i	$0.0930971\pi$
$48$	−132.820	+	352.250i	−0.399395	+	1.05923i
$49$	−77.4875	+	134.212i	−0.225911	+	0.391289i
$50$		0			0
$51$	438.255	−	359.225i	1.20329	−	0.986304i
$52$	−63.1604	+	36.4657i	−0.168438	+	0.0972477i
$53$		−	593.610i		−	1.53846i	−0.638969	−	0.769232i	$-0.720639\pi$
$53$		−	593.610i		−	1.53846i	0.638969	−	0.769232i	$-0.279361\pi$
$54$	226.006	−	361.984i	0.569546	−	0.912218i
$55$		0			0
$56$	−140.722	−	243.738i	−0.335800	−	0.581623i
$57$	−427.214	−	521.202i	−0.992734	−	1.21114i
$58$	−23.8012	−	13.7416i	−0.0538836	−	0.0311097i
$59$	221.230	−	383.182i	0.488164	−	0.845525i	−0.511743	−	0.859139i	$-0.671000\pi$
$59$	221.230	−	383.182i	0.488164	−	0.845525i	0.999907	+	0.0136133i	$0.00433337\pi$
$60$		0			0
$61$	−72.2881	−	125.207i	−0.151730	−	0.262804i	0.780133	−	0.625613i	$-0.215151\pi$
$61$	−72.2881	−	125.207i	−0.151730	−	0.262804i	−0.931864	+	0.362809i	$0.881818\pi$
$62$			101.536i			0.207985i
$63$	118.583	+	350.725i	0.237145	+	0.701385i
$64$	−408.736			−0.798312
$65$		0			0
$66$	81.5912	+	496.052i	0.152169	+	0.925149i
$67$	747.138	+	431.360i	1.36235	+	0.786553i	0.989936	−	0.141514i	$-0.0451969\pi$
$67$	747.138	+	431.360i	1.36235	+	0.786553i	0.372414	+	0.928067i	$0.378530\pi$
$68$	−118.262	−	68.2786i	−0.210902	−	0.121765i
$69$	−67.1873	−	408.481i	−0.117223	−	0.712685i
$70$		0			0
$71$	−818.541			−1.36821			−0.684105	−	0.729384i	$-0.739807\pi$
$71$	−818.541			−1.36821			−0.684105	+	0.729384i	$0.739807\pi$
$72$	543.398	+	108.771i	0.889446	+	0.178038i
$73$			495.052i			0.793719i	0.917879	+	0.396859i	$0.129900\pi$
$73$			495.052i			0.793719i	−0.917879	+	0.396859i	$0.870100\pi$
$74$	−33.7093	−	58.3863i	−0.0529545	−	0.0917198i
$75$		0			0
$76$	−81.2014	+	140.645i	−0.122558	+	0.212277i
$77$	−377.710	−	218.071i	−0.559014	−	0.322747i
$78$	583.563	+	711.950i	0.847122	+	1.03349i
$79$	585.263	+	1013.71i	0.833510	+	1.44368i	0.895238	+	0.445588i	$0.147005\pi$
$79$	585.263	+	1013.71i	0.833510	+	1.44368i	−0.0617284	+	0.998093i	$0.519661\pi$
$80$		0			0
$81$	−672.833	−	280.601i	−0.922953	−	0.384912i
$82$		−	370.300i		−	0.498693i
$83$	−367.232	+	212.022i	−0.485651	+	0.280390i	−0.722768	−	0.691090i	$-0.757131\pi$
$83$	−367.232	+	212.022i	−0.485651	+	0.280390i	0.237118	+	0.971481i	$0.423797\pi$
$84$	69.0017	−	56.5586i	0.0896273	−	0.0734648i
$85$		0			0
$86$	−15.4242	+	26.7156i	−0.0193400	+	0.0334978i
$87$	−16.5644	+	43.9300i	−0.0204125	+	0.0541355i
$88$	−565.374	+	326.419i	−0.684876	+	0.395413i
$89$	−1031.37			−1.22837			−0.614183	−	0.789163i	$-0.710514\pi$
$89$	−1031.37			−1.22837			−0.614183	+	0.789163i	$0.710514\pi$
$90$		0			0
$91$	−798.643			−0.920006
$92$	−86.3945	+	49.8799i	−0.0979049	+	0.0565254i
$93$	171.152	−	28.1513i	0.190835	−	0.0313888i
$94$	−671.452	+	1162.99i	−0.736756	+	1.27610i
$95$		0			0
$96$	−47.3718	−	288.008i	−0.0503632	−	0.306195i
$97$	−1384.53	+	799.356i	−1.44925	+	0.836725i	−0.998437	−	0.0558930i	$-0.982199\pi$
$97$	−1384.53	+	799.356i	−1.44925	+	0.836725i	−0.450814	+	0.892618i	$0.648866\pi$
$98$		−	471.394i		−	0.485897i
$99$	813.541	−	275.066i	0.825898	−	0.279244i
$100$		0			0
$101$	107.000	+	185.330i	0.105415	+	0.182584i	0.913908	−	0.405922i	$-0.133050\pi$
$101$	107.000	+	185.330i	0.105415	+	0.182584i	−0.808493	+	0.588506i	$0.799716\pi$
$102$	−608.129	+	1612.81i	−0.590331	+	1.56561i
$103$	−1448.27	−	836.160i	−1.38546	−	0.799897i	−0.392662	−	0.919683i	$-0.628446\pi$
$103$	−1448.27	−	836.160i	−1.38546	−	0.799897i	−0.992800	+	0.119786i	$0.961779\pi$
$104$	−597.723	+	1035.29i	−0.563573	+	0.976137i
$105$		0			0
$106$	902.804	+	1563.70i	0.827246	+	1.43283i
$107$			600.699i			0.542727i	0.962477	+	0.271363i	$0.0874745\pi$
$107$			600.699i			0.542727i	−0.962477	+	0.271363i	$0.912525\pi$
$108$	−6.06581	+	175.572i	−0.00540447	+	0.156430i
$109$	771.570			0.678009			0.339005	−	0.940785i	$-0.389910\pi$
$109$	771.570			0.678009			0.339005	+	0.940785i	$0.389910\pi$
$110$		0			0
$111$	−89.0718	+	73.0094i	−0.0761650	+	0.0624302i
$112$	860.348	+	496.722i	0.725850	+	0.419070i
$113$	1010.37	+	583.338i	0.841131	+	0.485627i	0.857648	−	0.514237i	$-0.171925\pi$
$113$	1010.37	+	583.338i	0.841131	+	0.485627i	−0.0165177	+	0.999864i	$0.505258\pi$
$114$	1918.06	+	723.228i	1.57581	+	0.594180i
$115$		0			0
$116$	11.3140			0.00905583
$117$	1038.29	−	1181.06i	0.820427	−	0.933244i
$118$			1345.85i			1.04996i
$119$	−747.692	−	1295.04i	−0.575973	−	0.997615i
$120$		0			0
$121$	159.663	−	276.545i	0.119957	−	0.207772i
$122$	380.846	+	219.882i	0.282624	+	0.163173i
$123$	−624.190	+	102.667i	−0.457572	+	0.0752618i
$124$	−20.8996	−	36.1991i	−0.0151358	−	0.0262159i
$125$		0			0
$126$	−845.783	−	743.539i	−0.598003	−	0.525712i
$127$		−	1630.10i		−	1.13896i	−0.822006	−	0.569479i	$-0.807145\pi$
$127$		−	1630.10i		−	1.13896i	0.822006	−	0.569479i	$-0.192855\pi$
$128$	1465.87	−	846.322i	1.01223	−	0.584414i
$129$	49.3091	+	18.5926i	0.0336544	+	0.0126898i
$130$		0			0
$131$	−129.412	+	224.149i	−0.0863115	+	0.149496i	−0.905949	−	0.423386i	$-0.860841\pi$
$131$	−129.412	+	224.149i	−0.0863115	+	0.149496i	0.819638	+	0.572882i	$0.194175\pi$
$132$	−131.193	−	160.056i	−0.0865067	−	0.105538i
$133$	−1540.15	+	889.206i	−1.00412	+	0.579729i
$134$	−2624.17			−1.69175
$135$		0			0
$136$	−2238.36			−1.41131
$137$	−911.726	+	526.385i	−0.568569	+	0.328264i	−0.756578	−	0.653904i	$-0.773130\pi$
$137$	−911.726	+	526.385i	−0.568569	+	0.328264i	0.188009	+	0.982167i	$0.439797\pi$
$138$	798.232	+	973.847i	0.492392	+	0.600720i
$139$	1192.25	−	2065.03i	0.727519	−	1.26010i	−0.230410	−	0.973094i	$-0.574007\pi$
$139$	1192.25	−	2065.03i	0.727519	−	1.26010i	0.957929	−	0.287006i	$-0.0926599\pi$
$140$		0			0
$141$	2146.54	+	809.378i	1.28206	+	0.483418i
$142$	2156.22	−	1244.89i	1.27427	−	0.735699i
$143$			1852.53i			1.08333i
$144$	−1853.08	+	626.544i	−1.07239	+	0.362583i
$145$		0			0
$146$	−752.910	−	1304.08i	−0.426790	−	0.739221i
$147$	−794.597	+	130.696i	−0.445831	+	0.0733308i
$148$	24.0358	+	13.8771i	0.0133495	+	0.00770735i
$149$	573.144	−	992.715i	0.315126	−	0.545815i	−0.664338	−	0.747432i	$-0.731286\pi$
$149$	573.144	−	992.715i	0.315126	−	0.545815i	0.979464	+	0.201617i	$0.0646198\pi$
$150$		0			0
$151$	583.058	+	1009.89i	0.314229	+	0.544261i	0.979273	−	0.202543i	$-0.0649207\pi$
$151$	583.058	+	1009.89i	0.314229	+	0.544261i	−0.665044	+	0.746804i	$0.731587\pi$
$152$			2662.01i			1.42051i
$153$	2887.21	+	577.924i	1.52560	+	0.305375i
$154$	1326.63			0.694175
$155$		0			0
$156$	−354.593	−	133.704i	−0.181988	−	0.0686208i
$157$	−3009.97	−	1737.81i	−1.53008	−	0.883390i	−0.999357	−	0.0358423i	$-0.988589\pi$
$157$	−3009.97	−	1737.81i	−1.53008	−	0.883390i	−0.530719	−	0.847548i	$-0.678078\pi$
$158$	−3083.43	−	1780.22i	−1.55256	−	0.896371i
$159$	2385.52	−	1955.34i	1.18984	−	0.975274i
$160$		0			0
$161$	−1092.43			−0.534755
$162$	2199.15	−	284.126i	1.06655	−	0.137796i
$163$		−	2223.32i		−	1.06837i	−0.845369	−	0.534183i	$-0.820619\pi$
$163$		−	2223.32i		−	1.06837i	0.845369	−	0.534183i	$-0.179381\pi$
$164$	76.2204	+	132.018i	0.0362915	+	0.0628588i
$165$		0			0
$166$	644.915	−	1117.03i	0.301537	−	0.522277i
$167$	−1375.23	−	793.991i	−0.637238	−	0.367909i	0.146312	−	0.989239i	$-0.453260\pi$
$167$	−1375.23	−	793.991i	−0.637238	−	0.367909i	−0.783550	+	0.621329i	$0.786593\pi$
$168$	515.967	−	1368.39i	0.236951	−	0.628412i
$169$	597.632	+	1035.13i	0.272022	+	0.471156i
$170$		0			0
$171$	687.306	−	3433.66i	0.307366	−	1.53555i
$172$		−	12.6993i		−	0.00562974i
$173$	1305.79	−	753.898i	0.573857	−	0.331317i	−0.184831	−	0.982770i	$-0.559174\pi$
$173$	1305.79	−	753.898i	0.573857	−	0.331317i	0.758689	+	0.651454i	$0.225840\pi$
$174$	−23.1776	−	140.914i	−0.0100982	−	0.0613945i
$175$		0			0
$176$	1152.19	−	1995.66i	0.493465	−	0.854707i
$177$	2268.61	−	373.143i	0.963384	−	0.158458i
$178$	2716.85	−	1568.58i	1.14403	−	0.660504i
$179$	−1572.66			−0.656683			−0.328341	−	0.944559i	$-0.606490\pi$
$179$	−1572.66			−0.656683			−0.328341	+	0.944559i	$0.606490\pi$
$180$		0			0
$181$	1984.41			0.814918			0.407459	−	0.913223i	$-0.366415\pi$
$181$	1984.41			0.814918			0.407459	+	0.913223i	$0.366415\pi$
$182$	2103.81	−	1214.63i	0.856838	−	0.494695i
$183$	265.048	−	702.930i	0.107065	−	0.283946i
$184$	−817.601	+	1416.13i	−0.327578	+	0.567382i
$185$		0			0
$186$	−408.040	+	334.458i	−0.160854	+	0.131847i
$187$	−3003.97	+	1734.34i	−1.17472	+	0.678223i
$188$		−	552.831i		−	0.214465i
$189$	−1018.84	+	1631.83i	−0.392114	+	0.628032i
$190$		0			0
$191$	1174.18	+	2033.73i	0.444819	+	0.770450i	0.998040	−	0.0625853i	$-0.0199345\pi$
$191$	1174.18	+	2033.73i	0.444819	+	0.770450i	−0.553220	+	0.833035i	$0.686601\pi$
$192$	−1346.37	−	1642.57i	−0.506071	−	0.617409i
$193$	202.797	+	117.085i	0.0756354	+	0.0436681i	0.537341	−	0.843365i	$-0.319429\pi$
$193$	202.797	+	117.085i	0.0756354	+	0.0436681i	−0.461705	+	0.887033i	$0.652762\pi$
$194$	2431.43	−	4211.37i	0.899829	−	1.55855i
$195$		0			0
$196$	97.0288	+	168.059i	0.0353604	+	0.0612460i
$197$			717.846i			0.259616i	0.991539	+	0.129808i	$0.0414362\pi$
$197$			717.846i			0.259616i	−0.991539	+	0.129808i	$0.958564\pi$
$198$	−1724.71	+	1961.87i	−0.619040	+	0.704163i
$199$	−1701.45			−0.606094			−0.303047	−	0.952976i	$-0.598004\pi$
$199$	−1701.45			−0.606094			−0.303047	+	0.952976i	$0.598004\pi$
$200$		0			0
$201$	727.564	+	4423.39i	0.255315	+	1.55225i
$202$	−563.725	−	325.467i	−0.196354	−	0.113365i
$203$	107.296	+	61.9475i	0.0370971	+	0.0214180i
$204$	−115.164	−	700.164i	−0.0395248	−	0.240300i
$205$		0			0
$206$	5086.77			1.72045
$207$	1420.23	−	1615.53i	0.476875	−	0.542450i
$208$		−	4219.69i		−	1.40665i
$209$	2062.60	+	3572.52i	0.682645	+	1.18238i
$210$		0			0
$211$	2469.33	−	4277.01i	0.805667	−	1.39546i	−0.110172	−	0.993912i	$-0.535140\pi$
$211$	2469.33	−	4277.01i	0.805667	−	1.39546i	0.915840	−	0.401544i	$-0.131526\pi$
$212$	−643.727	−	371.656i	−0.208544	−	0.120403i
$213$	−2696.26	−	3289.44i	−0.867345	−	1.05816i
$214$	−913.585	−	1582.38i	−0.291829	−	0.505463i
$215$		0			0
$216$	1352.83	+	2542.03i	0.426150	+	0.800754i
$217$		−	457.726i		−	0.143191i
$218$	−2032.49	+	1173.46i	−0.631456	+	0.364572i
$219$	−1989.45	+	1630.69i	−0.613857	+	0.503160i
$220$		0			0
$221$	−3175.85	+	5500.73i	−0.966655	+	1.67430i
$222$	123.597	−	327.790i	0.0373662	−	0.0990983i
$223$	−2644.10	+	1526.57i	−0.794001	+	0.458416i	−0.841369	−	0.540461i	$-0.818250\pi$
$223$	−2644.10	+	1526.57i	−0.794001	+	0.458416i	0.0473684	+	0.998877i	$0.484917\pi$
$224$	−770.242			−0.229750
$225$		0			0
$226$	−3548.73			−1.04450
$227$	727.420	−	419.976i	0.212690	−	0.122797i	−0.389871	−	0.920869i	$-0.627480\pi$
$227$	727.420	−	419.976i	0.212690	−	0.122797i	0.602561	+	0.798073i	$0.294147\pi$
$228$	−832.682	+	136.960i	−0.241867	+	0.0397825i
$229$	700.753	−	1213.74i	0.202214	−	0.350245i	−0.747027	−	0.664793i	$-0.768520\pi$
$229$	700.753	−	1213.74i	0.202214	−	0.350245i	0.949242	+	0.314548i	$0.101853\pi$
$230$		0			0
$231$	−367.814	−	2236.21i	−0.104764	−	0.636935i
$232$	160.606	−	92.7259i	0.0454496	−	0.0262403i
$233$		−	2856.99i		−	0.803295i	−0.915794	−	0.401647i	$-0.868438\pi$
$233$		−	2856.99i		−	0.803295i	0.915794	−	0.401647i	$-0.131562\pi$
$234$	−938.843	+	4690.30i	−0.262282	+	1.31032i
$235$		0			0
$236$	−277.021	−	479.815i	−0.0764092	−	0.132345i
$237$	−2145.90	+	5691.11i	−0.588149	+	1.55982i
$238$	3939.18	+	2274.29i	1.07285	+	0.619412i
$239$	−854.917	+	1480.76i	−0.231381	+	0.400763i	−0.958215	−	0.286050i	$-0.907658\pi$
$239$	−854.917	+	1480.76i	−0.231381	+	0.400763i	0.726834	+	0.686813i	$0.240991\pi$
$240$		0			0
$241$	2166.23	+	3752.02i	0.579000	+	1.00286i	0.995594	+	0.0937648i	$0.0298902\pi$
$241$	2166.23	+	3752.02i	0.579000	+	1.00286i	−0.416594	+	0.909092i	$0.636776\pi$
$242$			971.309i			0.258009i
$243$	−1088.66	−	3628.19i	−0.287396	−	0.957812i
$244$	−181.036			−0.0474987
$245$		0			0
$246$	1488.11	−	1219.76i	0.385686	−	0.316135i
$247$	6541.84	+	3776.93i	1.68521	+	0.972957i
$248$	−593.354	−	342.573i	−0.151927	−	0.0877154i
$249$	−2061.70	−	777.390i	−0.524719	−	0.197852i
$250$		0			0
$251$	−1724.73			−0.433722			−0.216861	−	0.976202i	$-0.569582\pi$
$251$	−1724.73			−0.433722			−0.216861	+	0.976202i	$0.569582\pi$
$252$	454.580	+	90.9920i	0.113634	+	0.0227459i
$253$			2534.00i			0.629688i
$254$	2479.16	+	4294.04i	0.612428	+	1.06076i
$255$		0			0
$256$	−939.349	+	1627.00i	−0.229333	+	0.397217i
$257$	−5069.07	−	2926.63i	−1.23035	−	0.710342i	−0.263246	−	0.964729i	$-0.584793\pi$
$257$	−5069.07	−	2926.63i	−1.23035	−	0.710342i	−0.967103	+	0.254386i	$0.918127\pi$
$258$	−158.168	+	26.0156i	−0.0381671	+	0.00627776i
$259$	151.962	+	263.206i	0.0364574	+	0.0631462i
$260$		0			0
$261$	−231.103	+	78.1380i	−0.0548081	+	0.0185311i
$262$		−	787.277i		−	0.185642i
$263$	339.794	−	196.180i	0.0796677	−	0.0459962i	−0.459637	−	0.888107i	$-0.652020\pi$
$263$	339.794	−	196.180i	0.0796677	−	0.0459962i	0.539305	+	0.842111i	$0.318687\pi$
$264$	−3174.10	−	1196.83i	−0.739971	−	0.279015i
$265$		0			0
$266$	2704.73	−	4684.73i	0.623450	−	1.07985i
$267$	−3397.30	−	4144.72i	−0.778695	−	0.950010i
$268$	935.557	−	540.144i	0.213240	−	0.123114i
$269$	4610.33			1.04497			0.522485	−	0.852648i	$-0.325005\pi$
$269$	4610.33			1.04497			0.522485	+	0.852648i	$0.325005\pi$
$270$		0			0
$271$	−1155.72			−0.259058			−0.129529	−	0.991576i	$-0.541347\pi$
$271$	−1155.72			−0.259058			−0.129529	+	0.991576i	$0.541347\pi$
$272$	6842.44	−	3950.49i	1.52531	−	0.880638i
$273$	−2630.71	−	3209.48i	−0.583216	−	0.711526i
$274$	1601.13	−	2773.23i	0.353020	−	0.611449i
$275$		0			0
$276$	−485.033	−	182.888i	−0.105781	−	0.0398860i
$277$	526.898	−	304.205i	0.114290	−	0.0659852i	−0.441765	−	0.897131i	$-0.645648\pi$
$277$	526.898	−	304.205i	0.114290	−	0.0659852i	0.556055	+	0.831145i	$0.312314\pi$
$278$			7253.02i			1.56477i
$279$	676.904	+	595.075i	0.145251	+	0.127693i
$280$		0			0
$281$	−1374.62	−	2380.91i	−0.291825	−	0.505456i	0.682416	−	0.730964i	$-0.260929\pi$
$281$	−1374.62	−	2380.91i	−0.291825	−	0.505456i	−0.974241	+	0.225508i	$0.927596\pi$
$282$	−6885.42	+	1132.52i	−1.45397	+	0.239151i
$283$	−884.697	−	510.780i	−0.185830	−	0.107289i	0.404199	−	0.914671i	$-0.367550\pi$
$283$	−884.697	−	510.780i	−0.185830	−	0.107289i	−0.590029	+	0.807382i	$0.700884\pi$
$284$	−512.483	+	887.647i	−0.107078	+	0.185465i
$285$		0			0
$286$	−2817.46	−	4879.98i	−0.582516	−	1.00895i
$287$			1669.32i			0.343334i
$288$	1001.37	−	1139.06i	0.204882	−	0.233056i
$289$	−6979.96			−1.42071
$290$		0			0
$291$	−7772.95	−	2930.89i	−1.56584	−	0.590418i
$292$	536.848	+	309.949i	0.107591	+	0.0621178i
$293$	4531.47	+	2616.25i	0.903521	+	0.521648i	0.878341	−	0.478035i	$-0.158651\pi$
$293$	4531.47	+	2616.25i	0.903521	+	0.521648i	0.0251800	+	0.999683i	$0.491984\pi$
$294$	1894.37	−	1552.76i	0.375790	−	0.308023i
$295$		0			0
$296$	454.929			0.0893317
$297$	3785.18	+	2363.29i	0.739524	+	0.461724i
$298$			3486.71i			0.677785i
$299$	2320.07	+	4018.48i	0.448739	+	0.777240i
$300$		0			0
$301$	69.5327	−	120.434i	0.0133149	−	0.0230622i
$302$	−3071.81	−	1773.51i	−0.585307	−	0.337927i
$303$	−392.322	+	1040.47i	−0.0743839	+	0.197272i
$304$	−4698.18	−	8137.49i	−0.886379	−	1.53525i
$305$		0			0
$306$	−8484.50	+	2868.69i	−1.58506	+	0.535921i
$307$			4912.68i			0.913296i	0.889648	+	0.456648i	$0.150950\pi$
$307$			4912.68i			0.913296i	−0.889648	+	0.456648i	$0.849050\pi$
$308$	−472.964	+	273.066i	−0.0874988	+	0.0505174i
$309$	−1410.33	−	8574.42i	−0.259647	−	1.57858i
$310$		0			0
$311$	414.430	−	717.813i	0.0755632	−	0.130879i	−0.825768	−	0.564010i	$-0.809258\pi$
$311$	414.430	−	717.813i	0.0755632	−	0.130879i	0.901331	+	0.433131i	$0.142591\pi$
$312$	−6129.36	+	1008.16i	−1.11220	+	0.182936i
$313$	7999.66	−	4618.60i	1.44462	−	0.834054i	0.446471	−	0.894798i	$-0.352681\pi$
$313$	7999.66	−	4618.60i	1.44462	−	0.834054i	0.998153	+	0.0607442i	$0.0193474\pi$
$314$	10571.9			1.90003
$315$		0			0
$316$	1465.72			0.260928
$317$	7879.45	−	4549.20i	1.39607	−	0.806021i	0.402091	−	0.915599i	$-0.368283\pi$
$317$	7879.45	−	4549.20i	1.39607	−	0.806021i	0.993978	+	0.109578i	$0.0349500\pi$
$318$	−3310.18	+	8778.88i	−0.583729	+	1.54810i
$319$	143.693	−	248.884i	0.0252203	−	0.0436828i
$320$		0			0
$321$	−2414.01	+	1978.69i	−0.419741	+	0.344049i
$322$	2877.71	−	1661.45i	0.498039	−	0.287543i
$323$			14143.9i			2.43649i
$324$	−725.548	+	553.955i	−0.124408	+	0.0949855i
$325$		0			0
$326$	3381.38	+	5856.72i	0.574470	+	0.995011i
$327$	2541.54	+	3100.68i	0.429808	+	0.524368i
$328$	2163.95	+	1249.36i	0.364281	+	0.210318i
$329$	3026.92	−	5242.78i	0.507233	−	0.878553i
$330$		0			0
$331$	−2981.73	−	5164.50i	−0.495137	−	0.857603i	0.504847	−	0.863209i	$-0.331549\pi$
$331$	−2981.73	−	5164.50i	−0.495137	−	0.857603i	−0.999984	+	0.00560570i	$0.998216\pi$
$332$			530.982i			0.0877754i
$333$	−586.801	−	117.458i	−0.0965661	−	0.0193294i
$334$	4830.23			0.791313
$335$		0			0
$336$	837.807	+	5093.65i	0.136030	+	0.827027i
$337$	516.890	+	298.427i	0.0835514	+	0.0482384i	0.541194	−	0.840898i	$-0.317973\pi$
$337$	516.890	+	298.427i	0.0835514	+	0.0482384i	−0.457642	+	0.889136i	$0.651306\pi$
$338$	−3148.60	−	1817.84i	−0.506690	−	0.292537i
$339$	983.901	+	5981.85i	0.157635	+	0.958377i
$340$		0			0
$341$	−1061.74			−0.168611
$342$	3411.63	+	10090.3i	0.539415	+	1.59539i
$343$			6828.34i			1.07492i
$344$	−104.080	−	180.272i	−0.0163128	−	0.0282546i
$345$		0			0
$346$	−2293.16	+	3971.87i	−0.356304	+	0.617137i
$347$	−3950.90	−	2281.05i	−0.611226	−	0.352891i	0.162219	−	0.986755i	$-0.448135\pi$
$347$	−3950.90	−	2281.05i	−0.611226	−	0.352891i	−0.773445	+	0.633863i	$0.781468\pi$
$348$	37.2680	+	45.4671i	0.00574074	+	0.00700372i
$349$	337.633	+	584.798i	0.0517854	+	0.0896949i	0.890756	−	0.454482i	$-0.150175\pi$
$349$	337.633	+	584.798i	0.0517854	+	0.0896949i	−0.838971	+	0.544177i	$0.816842\pi$
$350$		0			0
$351$	8166.42	+	282.140i	1.24185	+	0.0429046i
$352$			1786.65i			0.270536i
$353$	−2911.43	+	1680.91i	−0.438979	+	0.253445i	−0.703165	−	0.711027i	$-0.748230\pi$
$353$	−2911.43	+	1680.91i	−0.438979	+	0.253445i	0.264185	+	0.964472i	$0.414897\pi$
$354$	−5408.52	+	4433.20i	−0.812033	+	0.665598i
$355$		0			0
$356$	−645.732	+	1118.44i	−0.0961341	+	0.166509i
$357$	2741.46	−	7270.57i	0.406424	−	1.07787i
$358$	4142.74	−	2391.81i	0.611594	−	0.353104i
$359$	−7701.61			−1.13224			−0.566122	−	0.824322i	$-0.691557\pi$
$359$	−7701.61			−1.13224			−0.566122	+	0.824322i	$0.691557\pi$
$360$		0			0
$361$	9961.87			1.45238
$362$	−5227.39	+	3018.03i	−0.758965	+	0.438189i
$363$	1637.27	−	269.300i	0.236734	−	0.0389382i
$364$	−500.026	+	866.070i	−0.0720013	+	0.124710i
$365$		0			0
$366$	370.868	+	2254.78i	0.0529661	+	0.322020i
$367$	−5117.77	+	2954.75i	−0.727917	+	0.420263i	−0.817660	−	0.575702i	$-0.804729\pi$
$367$	−5117.77	+	2954.75i	−0.727917	+	0.420263i	0.0897425	+	0.995965i	$0.471396\pi$
$368$		−	5771.94i		−	0.817617i
$369$	−2468.66	−	2170.23i	−0.348274	−	0.306172i
$370$		0			0
$371$	−4069.86	−	7049.20i	−0.569532	−	0.986459i
$372$	76.6295	−	203.228i	0.0106803	−	0.0283249i
$373$	7295.73	+	4212.19i	1.01276	+	0.584716i	0.911998	−	0.410195i	$-0.134539\pi$
$373$	7295.73	+	4212.19i	1.01276	+	0.584716i	0.100760	+	0.994911i	$0.467873\pi$
$374$	5275.42	−	9137.30i	0.729374	−	1.26331i
$375$		0			0
$376$	−4530.84	−	7847.64i	−0.621436	−	1.07636i
$377$		−	526.249i		−	0.0718917i
$378$	202.046	−	5848.13i	0.0274923	−	0.795754i
$379$	3510.24			0.475749			0.237875	−	0.971296i	$-0.423549\pi$
$379$	3510.24			0.475749			0.237875	+	0.971296i	$0.423549\pi$
$380$		0			0
$381$	6550.81	−	5369.50i	0.880862	−	0.722016i
$382$	−6186.09	−	3571.54i	−0.828555	−	0.478367i
$383$	−4964.08	−	2866.01i	−0.662279	−	0.382367i	0.130866	−	0.991400i	$-0.458224\pi$
$383$	−4964.08	−	2866.01i	−0.662279	−	0.382367i	−0.793145	+	0.609033i	$0.791558\pi$
$384$	8229.64	+	3103.09i	1.09366	+	0.412380i
$385$		0			0
$386$	−712.283			−0.0939229
$387$	87.7056	+	259.400i	0.0115202	+	0.0340725i
$388$			2001.89i			0.261934i
$389$	7183.60	+	12442.4i	0.936306	+	1.62173i	0.772288	+	0.635273i	$0.219112\pi$
$389$	7183.60	+	12442.4i	0.936306	+	1.62173i	0.164019	+	0.986457i	$0.447554\pi$
$390$		0			0
$391$	−4344.11	+	7524.23i	−0.561870	+	0.973188i
$392$	2754.72	+	1590.44i	0.354934	+	0.204922i
$393$	−1327.06	+	218.276i	−0.170334	+	0.0280167i
$394$	−1091.75	−	1890.97i	−0.139598	−	0.241791i
$395$		0			0
$396$	211.065	−	1054.44i	0.0267838	−	0.133807i
$397$			9014.42i			1.13960i	0.821784	+	0.569800i	$0.192979\pi$
$397$			9014.42i			1.13960i	−0.821784	+	0.569800i	$0.807021\pi$
$398$	4482.01	−	2587.69i	0.564479	−	0.325902i
$399$	−8646.64	−	3260.32i	−1.08490	−	0.409073i
$400$		0			0
$401$	−5255.55	+	9102.87i	−0.654487	+	1.13361i	0.327535	+	0.944839i	$0.393782\pi$
$401$	−5255.55	+	9102.87i	−0.654487	+	1.13361i	−0.982022	+	0.188766i	$0.939551\pi$
$402$	−8643.97	−	10545.7i	−1.07244	−	1.30839i
$403$	−1683.73	+	972.104i	−0.208121	+	0.120159i
$404$	267.969			0.0329998
$405$		0			0
$406$	−376.857			−0.0460667
$407$	610.533	−	352.491i	0.0743562	−	0.0429296i
$408$	−7373.12	−	8995.23i	−0.894666	−	1.09150i
$409$	1659.10	−	2873.65i	0.200580	−	0.347415i	−0.748135	−	0.663546i	$-0.769051\pi$
$409$	1659.10	−	2873.65i	0.200580	−	0.347415i	0.948715	+	0.316131i	$0.102384\pi$
$410$		0			0
$411$	−5118.57	−	1930.02i	−0.614308	−	0.231632i
$412$	−1813.51	+	1047.03i	−0.216857	+	0.125203i
$413$		−	6067.11i		−	0.722864i
$414$	−1284.20	+	6415.66i	−0.152452	+	0.761625i
$415$		0			0
$416$	1635.81	+	2833.31i	0.192794	+	0.333929i
$417$	12225.9	−	2010.93i	1.43575	−	0.236153i
$418$	−10866.7	−	6273.89i	−1.27155	−	0.734129i
$419$	−243.069	+	421.008i	−0.0283406	+	0.0490873i	−0.879848	−	0.475255i	$-0.842356\pi$
$419$	−243.069	+	421.008i	−0.0283406	+	0.0490873i	0.851507	+	0.524343i	$0.175689\pi$
$420$		0			0
$421$	−2525.96	−	4375.10i	−0.292418	−	0.506482i	0.681963	−	0.731387i	$-0.261126\pi$
$421$	−2525.96	−	4375.10i	−0.292418	−	0.506482i	−0.974381	+	0.224904i	$0.927793\pi$
$422$			15022.1i			1.73286i
$423$	3818.03	+	11292.3i	0.438863	+	1.29799i
$424$	−12183.9			−1.39553
$425$		0			0
$426$	12105.4	+	4564.48i	1.37678	+	0.519130i
$427$	−1716.86	−	991.230i	−0.194578	−	0.112340i
$428$	651.414	+	376.094i	0.0735684	+	0.0424747i
$429$	−7444.70	+	6102.19i	−0.837840	+	0.686752i
$430$		0			0
$431$	6944.24			0.776084			0.388042	−	0.921642i	$-0.373152\pi$
$431$	6944.24			0.776084			0.388042	+	0.921642i	$0.373152\pi$
$432$	−8621.89	−	5383.10i	−0.960234	−	0.599525i
$433$		−	13738.3i		−	1.52476i	−0.647131	−	0.762378i	$-0.724032\pi$
$433$		−	13738.3i		−	1.52476i	0.647131	−	0.762378i	$-0.275968\pi$
$434$	696.142	+	1205.75i	0.0769952	+	0.133360i
$435$		0			0
$436$	483.075	−	836.711i	0.0530622	−	0.0919064i
$437$	8948.31	+	5166.31i	0.979533	+	0.565533i
$438$	2760.59	−	7321.31i	0.301155	−	0.798688i
$439$	4240.92	+	7345.48i	0.461066	+	0.798589i	0.999014	−	0.0443883i	$-0.0141339\pi$
$439$	4240.92	+	7345.48i	0.461066	+	0.798589i	−0.537949	+	0.842978i	$0.680801\pi$
$440$		0			0
$441$	−3142.61	−	2762.71i	−0.339338	−	0.298317i
$442$		−	19320.2i		−	2.07912i
$443$	−483.411	+	279.098i	−0.0518455	+	0.0299330i	−0.525699	−	0.850671i	$-0.676196\pi$
$443$	−483.411	+	279.098i	−0.0518455	+	0.0299330i	0.473853	+	0.880604i	$0.342863\pi$
$444$	23.4061	+	142.303i	0.00250181	+	0.0152103i
$445$		0			0
$446$	4643.44	−	8042.67i	0.492989	−	0.853882i
$447$	5877.32	−	966.707i	0.621896	−	0.102290i
$448$	−4853.79	+	2802.34i	−0.511875	+	0.295531i
$449$	−14775.0			−1.55295			−0.776476	−	0.630147i	$-0.782995\pi$
$449$	−14775.0			−1.55295			−0.776476	+	0.630147i	$0.782995\pi$
$450$		0			0
$451$	3872.15			0.404285
$452$	1265.17	−	730.449i	0.131657	−	0.0760120i
$453$	−2137.82	+	5669.66i	−0.221729	+	0.588044i
$454$	−1277.46	+	2212.62i	−0.132058	+	0.228730i
$455$		0			0
$456$	−10697.7	+	8768.60i	−1.09861	+	0.900499i
$457$	12304.4	−	7103.97i	1.25947	−	0.727154i	0.286497	−	0.958081i	$-0.407509\pi$
$457$	12304.4	−	7103.97i	1.25947	−	0.727154i	0.972971	+	0.230927i	$0.0741758\pi$
$458$			4263.02i			0.434930i
$459$	7187.92	+	13506.4i	0.730944	+	1.37347i
$460$		0			0
$461$	3851.26	+	6670.57i	0.389091	+	0.673925i	0.992328	−	0.123637i	$-0.0394558\pi$
$461$	3851.26	+	6670.57i	0.389091	+	0.673925i	−0.603237	+	0.797562i	$0.706123\pi$
$462$	4369.90	+	5331.29i	0.440056	+	0.536870i
$463$	−6849.45	−	3954.53i	−0.687518	−	0.396939i	0.115163	−	0.993347i	$-0.463261\pi$
$463$	−6849.45	−	3954.53i	−0.687518	−	0.396939i	−0.802682	+	0.596408i	$0.796594\pi$
$464$	−327.304	+	566.908i	−0.0327472	+	0.0567199i
$465$		0			0
$466$	4345.11	+	7525.96i	0.431939	+	0.748140i
$467$		−	11639.8i		−	1.15337i	−0.816967	−	0.576685i	$-0.804346\pi$
$467$		−	11639.8i		−	1.15337i	0.816967	−	0.576685i	$-0.195654\pi$
$468$	−630.711	−	1865.41i	−0.0622962	−	0.184249i
$469$	11829.8			1.16471
$470$		0			0
$471$	−2931.11	−	17820.4i	−0.286749	−	1.74336i
$472$	−7864.84	−	4540.77i	−0.766967	−	0.442809i
$473$	−279.359	−	161.288i	−0.0271563	−	0.0156787i
$474$	−3002.65	−	18255.3i	−0.290962	−	1.76897i
$475$		0			0
$476$	−1872.50			−0.180307
$477$	15715.7	+	3145.77i	1.50854	+	0.301960i
$478$		−	5200.87i		−	0.497662i
$479$	−9347.93	−	16191.1i	−0.891687	−	1.54445i	−0.837853	−	0.545897i	$-0.816189\pi$
$479$	−9347.93	−	16191.1i	−0.891687	−	1.54445i	−0.0538341	−	0.998550i	$-0.517144\pi$
$480$		0			0
$481$	645.465	−	1117.98i	0.0611865	−	0.105978i
$482$	−11412.7	−	6589.10i	−1.07849	−	0.622667i
$483$	−3598.45	−	4390.12i	−0.338996	−	0.413576i
$484$	−199.928	−	346.286i	−0.0187761	−	0.0325212i
$485$		0			0
$486$	8385.77	+	7901.75i	0.782687	+	0.737512i
$487$			2249.54i			0.209315i	0.994508	+	0.104658i	$0.0333747\pi$
$487$			2249.54i			0.209315i	−0.994508	+	0.104658i	$0.966625\pi$
$488$	−2569.88	+	1483.72i	−0.238387	+	0.137633i
$489$	8934.78	−	7323.57i	0.826267	−	0.677266i
$490$		0			0
$491$	−994.175	+	1721.96i	−0.0913778	+	0.158271i	−0.908091	−	0.418773i	$-0.862460\pi$
$491$	−994.175	+	1721.96i	−0.0913778	+	0.158271i	0.816713	+	0.577044i	$0.195794\pi$
$492$	−279.466	+	741.168i	−0.0256084	+	0.0679155i
$493$	853.339	−	492.676i	0.0779563	−	0.0450081i
$494$	−22976.9			−2.09267
$495$		0			0
$496$	2418.43			0.218933
$497$	−9720.28	+	5612.01i	−0.877292	+	0.506505i
$498$	6613.29	−	1087.76i	0.595078	−	0.0978790i
$499$	1206.95	−	2090.50i	0.108278	−	0.187543i	−0.806795	−	0.590832i	$-0.798800\pi$
$499$	1206.95	−	2090.50i	0.108278	−	0.187543i	0.915073	+	0.403289i	$0.132133\pi$
$500$		0			0
$501$	−1339.20	−	8142.00i	−0.119423	−	0.726063i
$502$	4543.34	−	2623.10i	0.403942	−	0.233216i
$503$		−	8758.56i		−	0.776391i	−0.921577	−	0.388196i	$-0.873098\pi$
$503$		−	8758.56i		−	0.776391i	0.921577	−	0.388196i	$-0.126902\pi$
$504$	7198.67	−	2433.94i	0.636219	−	0.215111i
$505$		0			0
$506$	−3853.88	−	6675.12i	−0.338589	−	0.586453i
$507$	−2191.25	+	5811.38i	−0.191947	+	0.509058i
$508$	−1767.72	−	1020.59i	−0.154389	−	0.0891368i
$509$	−5924.01	+	10260.7i	−0.515869	+	0.893511i	0.483961	+	0.875089i	$0.339198\pi$
$509$	−5924.01	+	10260.7i	−0.515869	+	0.893511i	−0.999830	+	0.0184220i	$0.994136\pi$
$510$		0			0
$511$	3394.13	+	5878.81i	0.293831	+	0.508930i
$512$			7826.64i			0.675570i
$513$	16062.7	−	8548.36i	1.38243	−	0.735710i
$514$	17804.1			1.52783
$515$		0			0
$516$	51.0344	−	41.8313i	0.00435400	−	0.00356884i
$517$	−12161.1	−	7021.23i	−1.03452	−	0.597279i
$518$	−800.606	−	462.230i	−0.0679085	−	0.0392070i
$519$	7330.91	+	2764.21i	0.620022	+	0.233787i
$520$		0			0
$521$	3816.55			0.320933			0.160466	−	0.987041i	$-0.448700\pi$
$521$	3816.55			0.320933			0.160466	+	0.987041i	$0.448700\pi$
$522$	489.939	−	557.310i	0.0410806	−	0.0467295i
$523$		−	12158.9i		−	1.01658i	−0.861187	−	0.508288i	$-0.830278\pi$
$523$		−	12158.9i		−	1.01658i	0.861187	−	0.508288i	$-0.169722\pi$
$524$	162.049	+	280.676i	0.0135098	+	0.0233996i
$525$		0			0
$526$	−596.729	+	1033.57i	−0.0494651	+	0.0856761i
$527$	−3152.63	−	1820.17i	−0.260590	−	0.150452i
$528$	11815.2	−	1943.37i	0.973846	−	0.160179i
$529$	−2909.97	−	5040.22i	−0.239169	−	0.414253i
$530$		0			0
$531$	8972.28	+	7887.65i	0.733265	+	0.644623i
$532$			2226.90i			0.181482i
$533$	6140.55	−	3545.25i	0.499018	−	0.288108i
$534$	15252.8	+	5751.27i	1.23606	+	0.466071i
$535$		0			0
$536$	8853.71	−	15335.1i	0.713474	−	1.23577i
$537$	−5180.31	−	6320.00i	−0.416289	−	0.507874i
$538$	−12144.7	+	7011.72i	−0.973222	+	0.561890i
$539$	4929.26			0.393911
$540$		0			0
$541$	14919.8			1.18568			0.592840	−	0.805321i	$-0.298007\pi$
$541$	14919.8			1.18568			0.592840	+	0.805321i	$0.298007\pi$
$542$	3044.42	−	1757.69i	0.241271	−	0.139298i
$543$	6536.61	+	7974.69i	0.516598	+	0.630252i
$544$	−3062.91	+	5305.12i	−0.241399	+	0.418116i
$545$		0			0
$546$	11811.1	+	4453.52i	0.925766	+	0.349072i
$547$	889.543	−	513.578i	0.0695322	−	0.0401444i	−0.464831	−	0.885400i	$-0.653885\pi$
$547$	889.543	−	513.578i	0.0695322	−	0.0401444i	0.534363	+	0.845255i	$0.320552\pi$
$548$			1318.27i			0.102762i
$549$	3697.91	−	1250.30i	0.287473	−	0.0971973i
$550$		0			0
$551$	−585.923	−	1014.85i	−0.0453015	−	0.0784646i
$552$	−8384.10	+	1379.02i	−0.646469	+	0.106332i
$553$	13900.2	+	8025.26i	1.06889	+	0.617123i
$554$	−925.313	+	1602.69i	−0.0709617	+	0.122909i
$555$		0			0
$556$	−1492.92	−	2585.81i	−0.113874	−	0.197235i
$557$			10590.8i			0.805648i	0.915277	+	0.402824i	$0.131971\pi$
$557$			10590.8i			0.805648i	−0.915277	+	0.402824i	$0.868029\pi$
$558$	−2688.15	−	538.079i	−0.203940	−	0.0408220i
$559$	−590.685			−0.0446929
$560$		0			0
$561$	−16864.8	−	6359.07i	−1.26922	−	0.478574i
$562$	7242.11	+	4181.23i	0.543576	+	0.313834i
$563$	1898.38	+	1096.03i	0.142109	+	0.0820467i	0.569369	−	0.822082i	$-0.307188\pi$
$563$	1898.38	+	1096.03i	0.142109	+	0.0820467i	−0.427260	+	0.904129i	$0.640521\pi$
$564$	2221.64	−	1821.01i	0.165865	−	0.135955i
$565$		0			0
$566$	3107.32			0.230761
$567$	−9913.81	+	1280.84i	−0.734287	+	0.0948684i
$568$			16800.6i			1.24109i
$569$	−8284.89	−	14349.8i	−0.610405	−	1.05725i	−0.991172	−	0.132582i	$-0.957673\pi$
$569$	−8284.89	−	14349.8i	−0.610405	−	1.05725i	0.380767	−	0.924671i	$-0.375660\pi$
$570$		0			0
$571$	−3639.66	+	6304.08i	−0.266752	+	0.462027i	−0.968021	−	0.250869i	$-0.919284\pi$
$571$	−3639.66	+	6304.08i	−0.266752	+	0.462027i	0.701269	+	0.712896i	$0.252617\pi$
$572$	2008.93	+	1159.86i	0.146849	+	0.0847833i
$573$	−4305.19	+	11417.7i	−0.313878	+	0.832429i
$574$	−2538.82	−	4397.36i	−0.184614	−	0.319760i
$575$		0			0
$576$	2166.05	−	10821.2i	0.156688	−	0.782784i
$577$			17938.0i			1.29422i	0.762395	+	0.647112i	$0.224024\pi$
$577$			17938.0i			1.29422i	−0.762395	+	0.647112i	$0.775976\pi$
$578$	18386.8	−	10615.6i	1.32317	−	0.763930i
$579$	197.484	+	1200.65i	0.0141747	+	0.0861782i
$580$		0			0
$581$	−2907.29	+	5035.57i	−0.207598	+	0.359571i
$582$	24933.2	−	4101.03i	1.77580	−	0.292085i
$583$	−16351.3	+	9440.42i	−1.16158	+	0.670639i
$584$	10161.0			0.719974
$585$		0			0
$586$	−15915.9			−1.12198
$587$	−9967.67	+	5754.83i	−0.700868	+	0.404646i	−0.807671	−	0.589634i	$-0.799272\pi$
$587$	−9967.67	+	5754.83i	−0.700868	+	0.404646i	0.106803	+	0.994280i	$0.465939\pi$
$588$	−355.762	+	943.509i	−0.0249513	+	0.0661729i
$589$	−2164.67	+	3749.32i	−0.151433	+	0.262289i
$590$		0			0
$591$	−2884.79	+	2364.57i	−0.200785	+	0.164578i
$592$	−1390.67	+	802.904i	−0.0965476	+	0.0557418i
$593$		−	9612.80i		−	0.665684i	−0.942983	−	0.332842i	$-0.891992\pi$
$593$		−	9612.80i		−	0.665684i	0.942983	−	0.332842i	$-0.108008\pi$
$594$	−13565.3	−	468.664i	−0.937021	−	0.0323729i
$595$		0			0
$596$	−717.684	−	1243.07i	−0.0493247	−	0.0854328i
$597$	−5604.55	−	6837.57i	−0.384219	−	0.468749i
$598$	−12223.2	−	7057.05i	−0.835857	−	0.482582i
$599$	3686.00	−	6384.33i	0.251429	−	0.435487i	−0.712491	−	0.701681i	$-0.752433\pi$
$599$	3686.00	−	6384.33i	0.251429	−	0.435487i	0.963919	+	0.266194i	$0.0857663\pi$
$600$		0			0
$601$	12095.3	+	20949.7i	0.820927	+	1.42189i	0.904993	+	0.425427i	$0.139876\pi$
$601$	12095.3	+	20949.7i	0.820927	+	1.42189i	−0.0840654	+	0.996460i	$0.526790\pi$
$602$			423.001i			0.0286383i
$603$	−15379.6	+	17494.4i	−1.03865	+	1.18147i
$604$	1460.20			0.0983684
$605$		0			0
$606$	−548.956	−	3337.50i	−0.0367984	−	0.223724i
$607$	−1141.19	−	658.866i	−0.0763088	−	0.0440569i	0.461360	−	0.887213i	$-0.347362\pi$
$607$	−1141.19	−	658.866i	−0.0763088	−	0.0440569i	−0.537669	+	0.843156i	$0.680695\pi$
$608$	6309.20	+	3642.62i	0.420842	+	0.242973i
$609$	104.485	+	635.242i	0.00695230	+	0.0422681i
$610$		0			0
$611$	−25713.9			−1.70257
$612$	2434.38	−	2769.13i	0.160791	−	0.182901i
$613$		−	4137.52i		−	0.272615i	−0.990667	−	0.136307i	$-0.956477\pi$
$613$		−	4137.52i		−	0.272615i	0.990667	−	0.136307i	$-0.0435235\pi$
$614$	−7471.56	−	12941.1i	−0.491087	−	0.850588i
$615$		0			0
$616$	−4475.93	+	7752.54i	−0.292760	+	0.507076i
$617$	−6747.74	−	3895.81i	−0.440281	−	0.254197i	0.263436	−	0.964677i	$-0.415144\pi$
$617$	−6747.74	−	3895.81i	−0.440281	−	0.254197i	−0.703717	+	0.710480i	$0.748478\pi$
$618$	16755.7	+	20442.0i	1.09064	+	1.33058i
$619$	10978.2	+	19014.8i	0.712844	+	1.23468i	0.963785	+	0.266680i	$0.0859268\pi$
$619$	10978.2	+	19014.8i	0.712844	+	1.23468i	−0.250941	+	0.968002i	$0.580740\pi$
$620$		0			0
$621$	11170.5	+	385.927i	0.721831	+	0.0249384i
$622$			2521.18i			0.162524i
$623$	−12247.6	+	7071.17i	−0.787625	+	0.454736i
$624$	16957.5	−	13899.6i	1.08789	−	0.891712i
$625$		0			0
$626$	−14048.6	+	24332.9i	−0.896957	+	1.55357i
$627$	−7562.63	+	20056.7i	−0.481694	+	1.27749i
$628$	−3769.05	+	2176.06i	−0.239493	+	0.138271i
$629$	2417.15			0.153224
$630$		0			0
$631$	−11152.7			−0.703618			−0.351809	−	0.936072i	$-0.614433\pi$
$631$	−11152.7			−0.703618			−0.351809	+	0.936072i	$0.614433\pi$
$632$	20806.4	−	12012.6i	1.30955	−	0.756068i
$633$	25321.8	−	4164.95i	1.58997	−	0.261520i
$634$	−13837.5	+	23967.2i	−0.866810	+	1.50136i
$635$		0			0
$636$	−626.861	−	3811.15i	−0.0390828	−	0.237613i
$637$	7816.94	−	4513.11i	0.486214	−	0.280716i
$638$			874.155i			0.0542447i
$639$	4337.77	−	21670.7i	0.268544	−	1.34160i
$640$		0			0
$641$	−2404.72	−	4165.10i	−0.148176	−	0.256648i	0.782377	−	0.622805i	$-0.214007\pi$
$641$	−2404.72	−	4165.10i	−0.148176	−	0.256648i	−0.930553	+	0.366156i	$0.880674\pi$
$642$	3349.71	−	8883.71i	0.205923	−	0.546125i
$643$	2210.98	+	1276.51i	0.135603	+	0.0782904i	0.566267	−	0.824222i	$-0.308387\pi$
$643$	2210.98	+	1276.51i	0.135603	+	0.0782904i	−0.430664	+	0.902512i	$0.641721\pi$
$644$	−683.964	+	1184.66i	−0.0418509	+	0.0724879i
$645$		0			0
$646$	−21511.0	−	37258.2i	−1.31013	−	2.26920i
$647$		−	8446.00i		−	0.513210i	−0.966516	−	0.256605i	$-0.917396\pi$
$647$		−	8446.00i		−	0.513210i	0.966516	−	0.256605i	$-0.0826039\pi$
$648$	−5759.36	+	13810.0i	−0.349150	+	0.837201i
$649$	−14073.2			−0.851191
$650$		0			0
$651$	1839.45	−	1507.74i	0.110743	−	0.0907727i
$652$	−2411.02	−	1392.01i	−0.144821	−	0.0836122i
$653$	−7010.37	−	4047.44i	−0.420118	−	0.242555i	0.275010	−	0.961441i	$-0.411319\pi$
$653$	−7010.37	−	4047.44i	−0.420118	−	0.242555i	−0.695128	+	0.718886i	$0.744652\pi$
$654$	−11410.7	−	4302.55i	−0.682254	−	0.257252i
$655$		0			0
$656$	−8819.97			−0.524942
$657$	−13106.4	−	2623.47i	−0.778280	−	0.155786i
$658$			18414.2i			1.09097i
$659$	1087.67	+	1883.89i	0.0642936	+	0.111360i	0.896380	−	0.443286i	$-0.146187\pi$
$659$	1087.67	+	1883.89i	0.0642936	+	0.111360i	−0.832087	+	0.554645i	$0.812854\pi$
$660$		0			0
$661$	4438.47	−	7687.66i	0.261175	−	0.452368i	−0.705379	−	0.708830i	$-0.749223\pi$
$661$	4438.47	−	7687.66i	0.261175	−	0.452368i	0.966554	+	0.256462i	$0.0825567\pi$
$662$	15709.1	+	9069.64i	0.922282	+	0.532480i
$663$	−32566.8	+	5356.62i	−1.90768	+	0.313776i
$664$	4351.77	+	7537.48i	0.254339	+	0.440529i
$665$		0			0
$666$	1724.41	−	583.037i	0.100329	−	0.0339223i
$667$		−	719.834i		−	0.0417872i
$668$	−1722.05	+	994.226i	−0.0997427	+	0.0575865i
$669$	−14844.4	−	5597.27i	−0.857874	−	0.323472i
$670$		0			0
$671$	−2299.25	+	3982.42i	−0.132283	+	0.229120i
$672$	−2537.16	−	3095.35i	−0.145645	−	0.177687i
$673$	−7939.65	+	4583.96i	−0.454757	+	0.262554i	−0.709837	−	0.704366i	$-0.751231\pi$
$673$	−7939.65	+	4583.96i	−0.454757	+	0.262554i	0.255080	+	0.966920i	$0.417898\pi$
$674$	−1815.47			−0.103753
$675$		0			0
$676$	1496.70			0.0851557
$677$	16348.7	−	9438.93i	0.928112	−	0.535846i	0.0418983	−	0.999122i	$-0.486659\pi$
$677$	16348.7	−	9438.93i	0.928112	−	0.535846i	0.886214	+	0.463276i	$0.153326\pi$
$678$	−11689.4	−	14261.2i	−0.662139	−	0.807812i
$679$	−10961.0	+	18984.9i	−0.619503	+	1.07301i
$680$		0			0
$681$	4083.85	+	1539.87i	0.229800	+	0.0866488i
$682$	2796.86	−	1614.77i	0.157034	−	0.0906638i
$683$		−	27207.5i		−	1.52426i	−0.647426	−	0.762128i	$-0.724155\pi$
$683$		−	27207.5i		−	1.52426i	0.647426	−	0.762128i	$-0.275845\pi$
$684$	−3293.23	−	2895.13i	−0.184094	−	0.161839i
$685$		0			0
$686$	−10385.0	−	17987.4i	−0.577991	−	1.00111i
$687$	7185.89	−	1181.94i	0.399067	−	0.0656388i
$688$	636.323	+	367.381i	0.0352610	+	0.0203580i
$689$	−17286.9	+	29941.7i	−0.955845	+	1.65557i
$690$		0			0
$691$	8703.62	+	15075.1i	0.479162	+	0.829934i	0.999714	−	0.0238963i	$-0.00760715\pi$
$691$	8703.62	+	15075.1i	0.479162	+	0.829934i	−0.520552	+	0.853830i	$0.674274\pi$
$692$		−	1888.04i		−	0.103718i
$693$	7775.03	−	8844.17i	0.426189	−	0.484794i
$694$	13876.7			0.759011
$695$		0			0
$696$	901.668	+	339.985i	0.0491058	+	0.0185159i
$697$	11497.6	+	6638.15i	0.624825	+	0.360743i
$698$	−1778.80	−	1026.99i	−0.0964595	−	0.0556909i
$699$	11481.3	−	9410.87i	0.621263	−	0.509230i
$700$		0			0
$701$	18543.0			0.999086			0.499543	−	0.866289i	$-0.333501\pi$
$701$	18543.0			0.999086			0.499543	+	0.866289i	$0.333501\pi$
$702$	−21941.3	+	11676.8i	−1.17966	+	0.627798i
$703$		−	2874.63i		−	0.154223i
$704$	6500.29	+	11258.8i	0.347996	+	0.602746i
$705$		0			0
$706$	5112.91	−	8855.81i	0.272559	−	0.472086i
$707$	2541.28	+	1467.21i	0.135184	+	0.0780482i
$708$	1015.72	−	2693.76i	0.0539165	−	0.142991i
$709$	13116.9	+	22719.1i	0.694803	+	1.20343i	0.970247	+	0.242117i	$0.0778417\pi$
$709$	13116.9	+	22719.1i	0.694803	+	1.20343i	−0.275444	+	0.961317i	$0.588825\pi$
$710$		0			0
$711$	−29939.2	+	10122.7i	−1.57920	+	0.533941i
$712$			21168.9i			1.11424i
$713$	−2303.11	+	1329.70i	−0.120971	+	0.0698425i
$714$	3835.98	+	23321.7i	0.201061	+	1.22240i
$715$		0			0
$716$	−984.633	+	1705.43i	−0.0513931	+	0.0890155i
$717$	−8766.76	+	1441.96i	−0.456626	+	0.0751062i
$718$	20287.8	−	11713.2i	1.05450	−	0.608817i
$719$	3043.06			0.157840			0.0789199	−	0.996881i	$-0.474853\pi$
$719$	3043.06			0.157840			0.0789199	+	0.996881i	$0.474853\pi$
$720$		0			0
$721$	−22931.2			−1.18447
$722$	−26241.8	+	15150.7i	−1.35266	+	0.780958i
$723$	−7942.60	+	21064.4i	−0.408559	+	1.08353i
$724$	1242.43	−	2151.95i	0.0637769	−	0.110465i
$725$		0			0
$726$	−3903.37	+	3199.47i	−0.199542	+	0.163559i
$727$	−19002.7	+	10971.2i	−0.969426	+	0.559698i	−0.899061	−	0.437823i	$-0.855750\pi$
$727$	−19002.7	+	10971.2i	−0.969426	+	0.559698i	−0.0703647	+	0.997521i	$0.522416\pi$
$728$			16392.2i			0.834528i
$729$	10994.5	−	16326.1i	0.558577	−	0.829453i
$730$		0			0
$731$	−553.002	−	957.827i	−0.0279802	−	0.0484631i
$732$	−596.330	−	727.525i	−0.0301107	−	0.0367351i
$733$	23016.2	+	13288.4i	1.15979	+	0.669604i	0.951253	−	0.308411i	$-0.0997972\pi$
$733$	23016.2	+	13288.4i	1.15979	+	0.669604i	0.208535	+	0.978015i	$0.433131\pi$
$734$	8987.58	−	15566.9i	0.451959	−	0.782815i
$735$		0			0
$736$	2237.56	+	3875.57i	0.112062	+	0.194097i
$737$		−	27440.4i		−	1.37148i
$738$	9803.63	+	1962.37i	0.488993	+	0.0978803i
$739$	−28787.7			−1.43298			−0.716489	−	0.697598i	$-0.754252\pi$
$739$	−28787.7			−1.43298			−0.716489	+	0.697598i	$0.754252\pi$
$740$		0			0
$741$	6370.45	+	38730.6i	0.315822	+	1.92011i
$742$	21441.8	+	12379.5i	1.06086	+	0.612485i
$743$	3899.73	+	2251.51i	0.192553	+	0.111171i	0.593177	−	0.805072i	$-0.297873\pi$
$743$	3899.73	+	2251.51i	0.192553	+	0.111171i	−0.400624	+	0.916243i	$0.631207\pi$
$744$	−577.808	−	3512.92i	−0.0284724	−	0.173105i
$745$		0			0
$746$	−25624.8			−1.25763
$747$	−3667.13	−	10846.0i	−0.179616	−	0.531238i
$748$			4343.45i			0.212316i
$749$	4118.46	+	7133.38i	0.200915	+	0.347995i
$750$		0			0
$751$	−2852.83	+	4941.24i	−0.138617	+	0.240091i	−0.926973	−	0.375128i	$-0.877599\pi$
$751$	−2852.83	+	4941.24i	−0.138617	+	0.240091i	0.788357	+	0.615219i	$0.210932\pi$
$752$	27700.6	+	15993.0i	1.34327	+	0.775536i
$753$	−5681.24	−	6931.13i	−0.274948	−	0.335438i
$754$	800.356	+	1386.26i	0.0386568	+	0.0669556i
$755$		0			0
$756$	1131.71	+	2126.53i	0.0544444	+	0.102303i
$757$		−	17397.6i		−	0.835305i	−0.908607	−	0.417652i	$-0.862853\pi$
$757$		−	17397.6i		−	0.835305i	0.908607	−	0.417652i	$-0.137147\pi$
$758$	−9246.77	+	5338.62i	−0.443084	+	0.255815i
$759$	−10183.3	+	8346.94i	−0.486996	+	0.399176i
$760$		0			0
$761$	17757.2	−	30756.3i	0.845857	−	1.46507i	−0.0390179	−	0.999239i	$-0.512423\pi$
$761$	17757.2	−	30756.3i	0.845857	−	1.46507i	0.884875	−	0.465829i	$-0.154244\pi$
$762$	−9090.00	+	24107.4i	−0.432147	+	1.14609i
$763$	9162.50	−	5289.97i	0.434737	−	0.250996i
$764$	2940.58			0.139249
$765$		0			0
$766$	17435.3			0.822408
$767$	−22317.7	+	12885.1i	−1.05065	+	0.606591i
$768$	−9632.57	+	1584.37i	−0.452585	+	0.0744416i
$769$	15631.8	−	27075.1i	0.733027	−	1.26964i	−0.222556	−	0.974920i	$-0.571440\pi$
$769$	15631.8	−	27075.1i	0.733027	−	1.26964i	0.955583	−	0.294721i	$-0.0952266\pi$
$770$		0			0
$771$	−4936.26	−	30011.2i	−0.230577	−	1.40185i
$772$	253.940	−	146.612i	0.0118387	−	0.00683508i
$773$		−	6676.47i		−	0.310654i	−0.987863	−	0.155327i	$-0.950357\pi$
$773$		−	6676.47i		−	0.310654i	0.987863	−	0.155327i	$-0.0496432\pi$
$774$	−625.551	−	549.930i	−0.0290503	−	0.0255385i
$775$		0			0
$776$	16406.9	+	28417.5i	0.758985	+	1.31460i
$777$	−557.179	+	1477.68i	−0.0257254	+	0.0682260i
$778$	−37846.5	−	21850.7i	−1.74404	−	1.00692i
$779$	7894.53	−	13673.7i	0.363095	−	0.628898i
$780$		0			0
$781$	13017.6	+	22547.1i	0.596422	+	1.03303i
$782$		−	26427.3i		−	1.20849i
$783$	−1075.26	−	671.341i	−0.0490761	−	0.0306408i
$784$	−11227.9			−0.511473
$785$		0			0
$786$	3163.81	−	2593.28i	0.143574	−	0.117683i
$787$	8169.93	+	4716.91i	0.370047	+	0.213646i	0.673479	−	0.739207i	$-0.264799\pi$
$787$	8169.93	+	4716.91i	0.370047	+	0.213646i	−0.303432	+	0.952853i	$0.598133\pi$
$788$	778.451	+	449.439i	0.0351919	+	0.0203180i
$789$	1907.66	+	719.306i	0.0860766	+	0.0324562i
$790$		0			0
$791$	15997.7			0.719107
$792$	−5645.75	−	16698.0i	−0.253299	−	0.749164i
$793$			8420.57i			0.377078i
$794$	−13709.8	−	23746.0i	−0.612773	−	1.06135i
$795$		0			0
$796$	−1065.27	+	1845.10i	−0.0474340	+	0.0821580i
$797$	−20331.1	−	11738.1i	−0.903592	−	0.521689i	−0.0252283	−	0.999682i	$-0.508031\pi$
$797$	−20331.1	−	11738.1i	−0.903592	−	0.521689i	−0.878364	+	0.477992i	$0.841365\pi$
$798$	27735.7	−	4562.00i	1.23037	−	0.202372i
$799$	−24073.4	−	41696.4i	−1.06590	−	1.84620i
$800$		0			0
$801$	5465.61	−	27305.3i	0.241096	−	1.20447i
$802$		−	31972.0i		−	1.40769i
$803$	13636.5	−	7873.02i	0.599278	−	0.345993i
$804$	5252.37	+	1980.47i	0.230394	+	0.0868729i
$805$		0			0
$806$	2956.89	−	5121.48i	0.129221	−	0.223817i
$807$	15186.3	+	18527.4i	0.662435	+	0.808173i
$808$	3803.91	−	2196.19i	0.165620	−	0.0956208i
$809$	33269.8			1.44586			0.722932	−	0.690919i	$-0.242794\pi$
$809$	33269.8			1.44586			0.722932	+	0.690919i	$0.242794\pi$
$810$		0			0
$811$	27892.8			1.20771			0.603853	−	0.797096i	$-0.293631\pi$
$811$	27892.8			1.20771			0.603853	+	0.797096i	$0.293631\pi$
$812$	134.355	−	77.5699i	0.00580657	−	0.00335243i
$813$	−3806.91	−	4644.44i	−0.164224	−	0.200354i
$814$	−1072.19	+	1857.08i	−0.0461672	+	0.0799640i
$815$		0			0
$816$	38414.6	+	14484.7i	1.64801	+	0.621404i
$817$	−1139.11	+	657.666i	−0.0487790	+	0.0281626i
$818$			10093.1i			0.431415i
$819$	4232.32	−	21143.9i	0.180573	−	0.902111i
$820$		0			0
$821$	1848.66	+	3201.98i	0.0785856	+	0.136114i	0.902640	−	0.430397i	$-0.141626\pi$
$821$	1848.66	+	3201.98i	0.0785856	+	0.136114i	−0.824054	+	0.566511i	$0.808293\pi$
$822$	16418.8	−	2700.58i	0.696680	−	0.114591i
$823$	−6187.32	−	3572.25i	−0.262061	−	0.151301i	0.363213	−	0.931706i	$-0.381680\pi$
$823$	−6187.32	−	3572.25i	−0.262061	−	0.151301i	−0.625275	+	0.780405i	$0.715013\pi$
$824$	−17162.3	+	29725.9i	−0.725578	+	1.25674i
$825$		0			0
$826$	9227.29	+	15982.1i	0.388691	+	0.673232i
$827$		−	19866.9i		−	0.835357i	−0.908595	−	0.417679i	$-0.862844\pi$
$827$		−	19866.9i		−	0.835357i	0.908595	−	0.417679i	$-0.137156\pi$
$828$	−862.723	−	2551.61i	−0.0362098	−	0.107095i
$829$	36736.5			1.53910			0.769548	−	0.638589i	$-0.220482\pi$
$829$	36736.5			1.53910			0.769548	+	0.638589i	$0.220482\pi$
$830$		0			0
$831$	2958.09	+	1115.39i	0.123484	+	0.0465611i
$832$	20616.7	+	11903.0i	0.859079	+	0.495990i
$833$	14636.5	+	8450.38i	0.608793	+	0.351487i
$834$	−29147.5	+	23891.3i	−1.21018	+	0.991952i
$835$		0			0
$836$	5165.52			0.213700
$837$	−161.703	+	4680.42i	−0.00667773	+	0.193284i
$838$		−	1478.71i		−	0.0609560i
$839$	15006.1	+	25991.4i	0.617485	+	1.06951i	0.989943	+	0.141466i	$0.0451816\pi$
$839$	15006.1	+	25991.4i	0.617485	+	1.06951i	−0.372458	+	0.928049i	$0.621485\pi$
$840$		0			0
$841$	12153.7	−	21050.8i	0.498326	−	0.863127i
$842$	13307.9	+	7683.32i	0.544680	+	0.314471i
$843$	5040.12	−	13366.8i	0.205920	−	0.546117i
$844$	−3092.07	−	5355.62i	−0.126106	−	0.218422i
$845$		0			0
$846$	−27231.7	−	23939.7i	−1.10667	−	0.972890i
$847$		−	4378.68i		−	0.177631i
$848$	37245.0	−	21503.4i	1.50825	−	0.870789i
$849$	−861.519	−	5237.80i	−0.0348260	−	0.211733i
$850$		0			0
$851$	882.905	−	1529.24i	0.0355648	−	0.0616000i
$852$	−5255.27	+	864.391i	−0.211318	+	0.0347577i
$853$	−4660.10	+	2690.51i	−0.187056	+	0.107997i	−0.590604	−	0.806962i	$-0.701110\pi$
$853$	−4660.10	+	2690.51i	−0.187056	+	0.107997i	0.403548	+	0.914959i	$0.367777\pi$
$854$	6030.13			0.241624
$855$		0			0
$856$	12329.4			0.492302
$857$	−12678.4	+	7319.88i	−0.505352	+	0.291765i	−0.730921	−	0.682462i	$-0.760909\pi$
$857$	−12678.4	+	7319.88i	−0.505352	+	0.291765i	0.225569	+	0.974227i	$0.427576\pi$
$858$	10330.4	−	27397.0i	0.411041	−	1.09011i
$859$	14770.0	−	25582.4i	0.586667	−	1.01614i	−0.407999	−	0.912983i	$-0.633773\pi$
$859$	14770.0	−	25582.4i	0.586667	−	1.01614i	0.994665	−	0.103154i	$-0.0328935\pi$
$860$		0			0
$861$	−6708.44	+	5498.71i	−0.265532	+	0.217649i
$862$	−18292.7	+	10561.3i	−0.722797	+	0.417307i
$863$			3387.63i			0.133622i	0.997766	+	0.0668112i	$0.0212825\pi$
$863$			3387.63i			0.133622i	−0.997766	+	0.0668112i	$0.978717\pi$
$864$	7876.00	+	272.106i	0.310124	+	0.0107144i
$865$		0			0
$866$	20894.1	+	36189.7i	0.819875	+	1.42007i
$867$	−22991.9	−	28050.2i	−0.900628	−	1.09877i
$868$	−496.370	−	286.580i	−0.0194100	−	0.0112064i
$869$	18615.4	−	32242.8i	0.726678	−	1.25864i
$870$		0			0
$871$	−25123.8	−	43515.7i	−0.977368	−	1.69285i
$872$		−	15836.5i		−	0.615015i
$873$	−13825.7	−	40891.2i	−0.536000	−	1.58529i
$874$	−31429.2			−1.21637
$875$		0			0
$876$	522.783	+	3178.38i	0.0201635	+	0.122588i
$877$	−211.400	−	122.052i	−0.00813967	−	0.00469944i	0.495925	−	0.868366i	$-0.334829\pi$
$877$	−211.400	−	122.052i	−0.00813967	−	0.00469944i	−0.504064	+	0.863666i	$0.668163\pi$
$878$	−22343.1	−	12899.8i	−0.858817	−	0.495838i
$879$	4412.75	+	26828.4i	0.169327	+	1.02946i
$880$		0			0
$881$	13910.2			0.531948			0.265974	−	0.963980i	$-0.414307\pi$
$881$	13910.2			0.531948			0.265974	+	0.963980i	$0.414307\pi$
$882$	12480.1	+	2498.10i	0.476446	+	0.0953689i
$883$		−	8805.87i		−	0.335607i	−0.985820	−	0.167803i	$-0.946333\pi$
$883$		−	8805.87i		−	0.335607i	0.985820	−	0.167803i	$-0.0536674\pi$
$884$	3976.76	+	6887.95i	0.151304	+	0.262067i
$885$		0			0
$886$	848.943	−	1470.41i	0.0321905	−	0.0557556i
$887$	11501.5	+	6640.41i	0.435381	+	0.251368i	0.701637	−	0.712535i	$-0.252453\pi$
$887$	11501.5	+	6640.41i	0.435381	+	0.251368i	−0.266255	+	0.963903i	$0.585786\pi$
$888$	1498.53	+	1828.21i	0.0566298	+	0.0690885i
$889$	−11176.1	−	19357.6i	−0.421637	−	0.730296i
$890$		0			0
$891$	2971.04	+	22996.0i	0.111710	+	0.864642i
$892$			3823.11i			0.143506i
$893$	−49588.2	+	28629.7i	−1.85824	+	1.07285i
$894$	−14011.9	+	11485.2i	−0.524194	+	0.429666i
$895$		0			0
$896$	11605.0	−	20100.4i	0.432695	−	0.749449i
$897$	−8506.67	+	22560.4i	−0.316644	+	0.839765i
$898$	38920.7	−	22470.9i	1.44633	−	0.835036i
$899$	301.609			0.0111893
$900$		0			0
$901$	−64736.1			−2.39364
$902$	−10200.1	+	5889.04i	−0.376526	+	0.217387i
$903$	713.025	−	117.279i	0.0262768	−	0.00432204i
$904$	11973.1	−	20738.0i	0.440507	−	0.762981i
$905$		0			0
$906$	−2991.33	−	18186.5i	−0.109691	−	0.666894i
$907$	938.982	−	542.122i	0.0343753	−	0.0198466i	−0.482714	−	0.875778i	$-0.660349\pi$
$907$	938.982	−	542.122i	0.0343753	−	0.0198466i	0.517089	+	0.855932i	$0.327016\pi$
$908$		−	1051.78i		−	0.0384411i
$909$	−5473.61	+	1850.68i	−0.199723	+	0.0675281i
$910$		0			0
$911$	−25094.4	−	43464.7i	−0.912638	−	1.58073i	−0.810324	−	0.585983i	$-0.800709\pi$
$911$	−25094.4	−	43464.7i	−0.912638	−	1.58073i	−0.102314	−	0.994752i	$-0.532625\pi$
$912$	17226.2	−	45685.2i	0.625455	−	1.65876i
$913$	11680.5	+	6743.74i	0.423404	+	0.244452i
$914$	−21608.4	+	37426.9i	−0.781995	+	1.35445i
$915$		0			0
$916$	−877.475	−	1519.83i	−0.0316513	−	0.0548216i
$917$			3549.06i			0.127808i
$918$	−39476.1	−	24647.0i	−1.41929	−	0.886136i
$919$	−30376.1			−1.09033			−0.545166	−	0.838328i	$-0.683533\pi$
$919$	−30376.1			−1.09033			−0.545166	+	0.838328i	$0.683533\pi$
$920$		0			0
$921$	−19742.5	+	16182.3i	−0.706336	+	0.578962i
$922$	−20290.2	−	11714.5i	−0.724751	−	0.418435i
$923$	41287.2	+	23837.2i	1.47236	+	0.850066i
$924$	−2655.30	−	1001.21i	−0.0945377	−	0.0356466i
$925$		0			0
$926$	24057.3			0.853750
$927$	29812.2	−	33911.6i	1.05627	−	1.20151i
$928$		−	507.534i		−	0.0179533i
$929$	−23098.8	−	40008.3i	−0.815766	−	1.41295i	−0.908776	−	0.417283i	$-0.862982\pi$
$929$	−23098.8	−	40008.3i	−0.815766	−	1.41295i	0.0930102	−	0.995665i	$-0.470351\pi$
$930$		0			0
$931$	10049.8	−	17406.7i	0.353778	−	0.612762i
$932$	−3098.20	−	1788.74i	−0.108889	−	0.0628672i
$933$	4249.78	−	699.007i	0.149123	−	0.0245278i
$934$	17702.6	+	30661.7i	0.620177	+	1.07418i
$935$		0			0
$936$	−24241.5	−	21311.0i	−0.846536	−	0.744201i
$937$		−	37004.7i		−	1.29017i	−0.764111	−	0.645085i	$-0.776822\pi$
$937$		−	37004.7i		−	1.29017i	0.764111	−	0.645085i	$-0.223178\pi$
$938$	−31162.4	+	17991.6i	−1.08474	+	0.626277i
$939$	44911.3	+	16934.4i	1.56084	+	0.588533i
$940$		0			0
$941$	−21907.2	+	37944.4i	−0.758932	+	1.31451i	0.184464	+	0.982839i	$0.440945\pi$
$941$	−21907.2	+	37944.4i	−0.758932	+	1.31451i	−0.943396	+	0.331669i	$0.892388\pi$
$942$	34823.7	+	42485.1i	1.20448	+	1.46947i
$943$	8399.41	−	4849.40i	0.290055	−	0.167464i
$944$	32056.0			1.10523
$945$		0			0
$946$	981.191			0.0337223
$947$	−3992.14	+	2304.86i	−0.136988	+	0.0790898i	−0.566928	−	0.823768i	$-0.691868\pi$
$947$	−3992.14	+	2304.86i	−0.136988	+	0.0790898i	0.429940	+	0.902857i	$0.358535\pi$
$948$	4828.05	+	5890.24i	0.165409	+	0.201800i
$949$	14416.7	−	24970.5i	0.493136	−	0.854136i
$950$		0			0
$951$	44236.5	+	16679.9i	1.50838	+	0.568752i
$952$	−26580.8	+	15346.5i	−0.904927	+	0.522460i
$953$			4281.80i			0.145542i	0.997349	+	0.0727708i	$0.0231841\pi$
$953$			4281.80i			0.145542i	−0.997349	+	0.0727708i	$0.976816\pi$
$954$	−46183.1	+	15614.9i	−1.56733	+	0.529928i
$955$		0			0
$956$	1070.52	+	1854.19i	0.0362165	+	0.0627288i
$957$	1473.50	−	242.363i	0.0497718	−	0.00818651i
$958$	49249.1	+	28434.0i	1.66093	+	0.958936i
$959$	−7217.91	+	12501.8i	−0.243043	+	0.420963i
$960$		0			0
$961$	14338.4	+	24834.8i	0.481298	+	0.833633i
$962$			3926.68i			0.131602i
$963$	−15903.4	−	3183.34i	−0.532170	−	0.106523i
$964$	5425.05			0.181254
$965$		0			0
$966$	16155.9	+	6091.79i	0.538104	+	0.202899i
$967$	−31375.9	−	18114.9i	−1.04341	−	0.602416i	−0.122616	−	0.992454i	$-0.539128\pi$
$967$	−31375.9	−	18114.9i	−1.04341	−	0.602416i	−0.920799	+	0.390038i	$0.872462\pi$
$968$	−5676.11	−	3277.10i	−0.188468	−	0.108812i
$969$	−56839.7	+	46589.7i	−1.88437	+	1.54456i
$970$		0			0
$971$	844.928			0.0279249			0.0139624	−	0.999903i	$-0.495555\pi$
$971$	844.928			0.0279249			0.0139624	+	0.999903i	$0.495555\pi$
$972$	−4616.10	−	1091.02i	−0.152327	−	0.0360025i
$973$		−	32696.7i		−	1.07730i
$974$	−3421.26	−	5925.80i	−0.112551	−	0.194943i
$975$		0			0
$976$	5237.24	−	9071.16i	0.171762	−	0.297501i
$977$	39702.9	+	22922.5i	1.30011	+	0.750619i	0.980423	−	0.196904i	$-0.0630887\pi$
$977$	39702.9	+	22922.5i	1.30011	+	0.750619i	0.319687	+	0.947523i	$0.396422\pi$
$978$	−12398.0	+	32880.6i	−0.405363	+	1.07506i
$979$	16402.2	+	28409.5i	0.535463	+	0.927449i
$980$		0			0
$981$	−4088.85	+	20427.2i	−0.133075	+	0.664821i
$982$		−	6048.05i		−	0.196539i
$983$	−34815.9	+	20101.0i	−1.12966	+	0.652210i	−0.943849	−	0.330376i	$-0.892824\pi$
$983$	−34815.9	+	20101.0i	−1.12966	+	0.652210i	−0.185811	+	0.982586i	$0.559491\pi$
$984$	2107.26	+	12811.6i	0.0682692	+	0.415059i
$985$		0			0
$986$	−1498.59	+	2595.64i	−0.0484025	+	0.0838356i
$987$	31039.6	−	5105.42i	1.00101	−	0.164648i
$988$	8191.61	−	4729.43i	0.263775	−	0.152291i
$989$	−807.974			−0.0259778
$990$		0			0
$991$	1797.91			0.0576313			0.0288157	−	0.999585i	$-0.490826\pi$
$991$	1797.91			0.0576313			0.0288157	+	0.999585i	$0.490826\pi$
$992$	−1623.86	+	937.534i	−0.0519733	+	0.0300068i
$993$	10932.7	−	28994.3i	0.349384	−	0.926594i
$994$	17070.3	−	29566.6i	0.544704	−	0.943455i
$995$		0			0
$996$	−2133.84	+	1749.04i	−0.0678849	+	0.0556432i
$997$	−7908.61	+	4566.04i	−0.251222	+	0.145043i	−0.620324	−	0.784346i	$-0.712999\pi$
$997$	−7908.61	+	4566.04i	−0.251222	+	0.145043i	0.369102	+	0.929389i	$0.379665\pi$
$998$			7342.47i			0.232888i
$999$	−1460.89	−	2745.07i	−0.0462667	−	0.0869370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.49.4		28
5.2	odd	4		45.4.e.c.31.2	yes	14
5.3	odd	4		225.4.e.d.76.6		14
5.4	even	2	inner	225.4.k.d.49.11		28
9.7	even	3	inner	225.4.k.d.124.11		28
15.2	even	4		135.4.e.c.91.6		14
45.2	even	12		135.4.e.c.46.6		14
45.7	odd	12		45.4.e.c.16.2	✓	14
45.13	odd	12		2025.4.a.bb.1.2		7
45.22	odd	12		405.4.a.m.1.6		7
45.23	even	12		2025.4.a.ba.1.6		7
45.32	even	12		405.4.a.n.1.2		7
45.34	even	6	inner	225.4.k.d.124.4		28
45.43	odd	12		225.4.e.d.151.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.2	✓	14	45.7	odd	12
45.4.e.c.31.2	yes	14	5.2	odd	4
135.4.e.c.46.6		14	45.2	even	12
135.4.e.c.91.6		14	15.2	even	4
225.4.e.d.76.6		14	5.3	odd	4
225.4.e.d.151.6		14	45.43	odd	12
225.4.k.d.49.4		28	1.1	even	1	trivial
225.4.k.d.49.11		28	5.4	even	2	inner
225.4.k.d.124.4		28	45.34	even	6	inner
225.4.k.d.124.11		28	9.7	even	3	inner
405.4.a.m.1.6		7	45.22	odd	12
405.4.a.n.1.2		7	45.32	even	12
2025.4.a.ba.1.6		7	45.23	even	12
2025.4.a.bb.1.2		7	45.13	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.63422 + 1.52087i) q^{2} +(3.29398 + 4.01867i) q^{3} +(0.626094 - 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(11.8751 - 6.85611i) q^{7} -20.5251i q^{8} +(-5.29939 + 26.4748i) q^{9} +O(q^{10})\)	\(q+(-2.63422 + 1.52087i) q^{2} +(3.29398 + 4.01867i) q^{3} +(0.626094 - 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(11.8751 - 6.85611i) q^{7} -20.5251i q^{8} +(-5.29939 + 26.4748i) q^{9} +(-15.9034 - 27.5455i) q^{11} +(6.42029 - 1.05602i) q^{12} +(-50.4401 - 29.1216i) q^{13} +(-20.8545 + 36.1211i) q^{14} +(36.2248 + 62.7431i) q^{16} -109.055i q^{17} +(-26.3050 - 77.8003i) q^{18} -129.695 q^{19} +(66.6689 + 25.1383i) q^{21} +(83.7863 + 48.3740i) q^{22} +(-68.9949 - 39.8342i) q^{23} +(82.4836 - 67.6093i) q^{24} +177.161 q^{26} +(-123.850 + 65.9111i) q^{27} -17.1703i q^{28} +(4.51769 + 7.82486i) q^{29} +(16.6904 - 28.9087i) q^{31} +(-48.6463 - 28.0860i) q^{32} +(58.3108 - 154.645i) q^{33} +(165.858 + 287.275i) q^{34} +(25.3921 + 22.3225i) q^{36} +22.1645i q^{37} +(341.647 - 197.250i) q^{38} +(-49.1186 - 298.628i) q^{39} +(-60.8698 + 105.430i) q^{41} +(-213.853 + 35.1747i) q^{42} +(8.78298 - 5.07086i) q^{43} -39.8281 q^{44} +242.331 q^{46} +(382.343 - 220.746i) q^{47} +(-132.820 + 352.250i) q^{48} +(-77.4875 + 134.212i) q^{49} +(438.255 - 359.225i) q^{51} +(-63.1604 + 36.4657i) q^{52} -593.610i q^{53} +(226.006 - 361.984i) q^{54} +(-140.722 - 243.738i) q^{56} +(-427.214 - 521.202i) q^{57} +(-23.8012 - 13.7416i) q^{58} +(221.230 - 383.182i) q^{59} +(-72.2881 - 125.207i) q^{61} +101.536i q^{62} +(118.583 + 350.725i) q^{63} -408.736 q^{64} +(81.5912 + 496.052i) q^{66} +(747.138 + 431.360i) q^{67} +(-118.262 - 68.2786i) q^{68} +(-67.1873 - 408.481i) q^{69} -818.541 q^{71} +(543.398 + 108.771i) q^{72} +495.052i q^{73} +(-33.7093 - 58.3863i) q^{74} +(-81.2014 + 140.645i) q^{76} +(-377.710 - 218.071i) q^{77} +(583.563 + 711.950i) q^{78} +(585.263 + 1013.71i) q^{79} +(-672.833 - 280.601i) q^{81} -370.300i q^{82} +(-367.232 + 212.022i) q^{83} +(69.0017 - 56.5586i) q^{84} +(-15.4242 + 26.7156i) q^{86} +(-16.5644 + 43.9300i) q^{87} +(-565.374 + 326.419i) q^{88} -1031.37 q^{89} -798.643 q^{91} +(-86.3945 + 49.8799i) q^{92} +(171.152 - 28.1513i) q^{93} +(-671.452 + 1162.99i) q^{94} +(-47.3718 - 288.008i) q^{96} +(-1384.53 + 799.356i) q^{97} -471.394i q^{98} +(813.541 - 275.066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Introduction

L-functions

Modular forms

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