LMFDB - Embedded newform 525.2.i.g.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(151,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$525 = 3 \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	525.i (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 2x^{2} + 4$ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.g.151.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{3} +1.41421 q^{6} +(2.62132 + 0.358719i) q^{7} -2.82843 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.292893 - 0.507306i) q^{11} +4.41421 q^{13} +(-2.29289 + 2.95680i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.12132 + 1.94218i) q^{17} +(-0.707107 - 1.22474i) q^{18} +(-2.32843 + 4.03295i) q^{19} +(-1.00000 - 2.44949i) q^{21} +0.828427 q^{22} +(1.12132 - 1.94218i) q^{23} +(1.41421 + 2.44949i) q^{24} +(-3.12132 + 5.40629i) q^{26} +1.00000 q^{27} +8.24264 q^{29} +(2.91421 + 5.04757i) q^{31} +(-0.292893 + 0.507306i) q^{33} -3.17157 q^{34} +(-4.20711 + 7.28692i) q^{37} +(-3.29289 - 5.70346i) q^{38} +(-2.20711 - 3.82282i) q^{39} -6.24264 q^{41} +(3.70711 + 0.507306i) q^{42} +7.58579 q^{43} +(1.58579 + 2.74666i) q^{46} +(-6.65685 + 11.5300i) q^{47} -4.00000 q^{48} +(6.74264 + 1.88064i) q^{49} +(1.12132 - 1.94218i) q^{51} +(3.41421 + 5.91359i) q^{53} +(-0.707107 + 1.22474i) q^{54} +(-7.41421 - 1.01461i) q^{56} +4.65685 q^{57} +(-5.82843 + 10.0951i) q^{58} +(0.707107 + 1.22474i) q^{59} +(2.24264 - 3.88437i) q^{61} -8.24264 q^{62} +(-1.62132 + 2.09077i) q^{63} +8.00000 q^{64} +(-0.414214 - 0.717439i) q^{66} +(-6.86396 - 11.8887i) q^{67} -2.24264 q^{69} -0.585786 q^{71} +(1.41421 - 2.44949i) q^{72} +(-6.03553 - 10.4539i) q^{73} +(-5.94975 - 10.3053i) q^{74} +(-0.585786 - 1.43488i) q^{77} +6.24264 q^{78} +(-3.32843 + 5.76500i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.41421 - 7.64564i) q^{82} -2.58579 q^{83} +(-5.36396 + 9.29065i) q^{86} +(-4.12132 - 7.13834i) q^{87} +(0.828427 + 1.43488i) q^{88} +(6.12132 - 10.6024i) q^{89} +(11.5711 + 1.58346i) q^{91} +(2.91421 - 5.04757i) q^{93} +(-9.41421 - 16.3059i) q^{94} +5.17157 q^{97} +(-7.07107 + 6.92820i) q^{98} +0.585786 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{3} + 2 q^{7} - 2 q^{9} - 4 q^{11} + 12 q^{13} - 12 q^{14} + 8 q^{16} - 4 q^{17} + 2 q^{19} - 4 q^{21} - 8 q^{22} - 4 q^{23} - 4 q^{26} + 4 q^{27} + 16 q^{29} + 6 q^{31} - 4 q^{33} - 24 q^{34}+ \cdots + 8 q^{99}+O(q^{100})$ 4 * q - 2 * q^3 + 2 * q^7 - 2 * q^9 - 4 * q^11 + 12 * q^13 - 12 * q^14 + 8 * q^16 - 4 * q^17 + 2 * q^19 - 4 * q^21 - 8 * q^22 - 4 * q^23 - 4 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^31 - 4 * q^33 - 24 * q^34 - 14 * q^37 - 16 * q^38 - 6 * q^39 - 8 * q^41 + 12 * q^42 + 36 * q^43 + 12 * q^46 - 4 * q^47 - 16 * q^48 + 10 * q^49 - 4 * q^51 + 8 * q^53 - 24 * q^56 - 4 * q^57 - 12 * q^58 - 8 * q^61 - 16 * q^62 + 2 * q^63 + 32 * q^64 + 4 * q^66 - 2 * q^67 + 8 * q^69 - 8 * q^71 - 10 * q^73 - 4 * q^74 - 8 * q^77 + 8 * q^78 - 2 * q^79 - 2 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^86 - 8 * q^87 - 8 * q^88 + 16 * q^89 + 18 * q^91 + 6 * q^93 - 32 * q^94 + 32 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$ .

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	−1.00000			$\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	1.41421			0.577350
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$8$	−2.82843			−1.00000
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	0.818487	−	0.574526i	$-0.194813\pi$
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	−0.906797	+	0.421567i	$0.861480\pi$
$12$		0			0
$13$	4.41421			1.22428			0.612141	−	0.790748i	$-0.290308\pi$
$13$	4.41421			1.22428			0.612141	+	0.790748i	$0.290308\pi$
$14$	−2.29289	+	2.95680i	−0.612801	+	0.790237i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.12132	+	1.94218i	0.271960	+	0.471049i	0.969364	−	0.245630i	$-0.0789948\pi$
$17$	1.12132	+	1.94218i	0.271960	+	0.471049i	−0.697404	+	0.716679i	$0.745661\pi$
$18$	−0.707107	−	1.22474i	−0.166667	−	0.288675i
$19$	−2.32843	+	4.03295i	−0.534178	+	0.925223i	0.465025	+	0.885298i	$0.346045\pi$
$19$	−2.32843	+	4.03295i	−0.534178	+	0.925223i	−0.999203	+	0.0399255i	$0.987288\pi$
$20$		0			0
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$	0.828427			0.176621
$23$	1.12132	−	1.94218i	0.233811	−	0.404973i	−0.725115	−	0.688628i	$-0.758213\pi$
$23$	1.12132	−	1.94218i	0.233811	−	0.404973i	0.958927	+	0.283654i	$0.0915468\pi$
$24$	1.41421	+	2.44949i	0.288675	+	0.500000i
$25$		0			0
$26$	−3.12132	+	5.40629i	−0.612141	+	1.06026i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.24264			1.53062			0.765310	−	0.643662i	$-0.222586\pi$
$29$	8.24264			1.53062			0.765310	+	0.643662i	$0.222586\pi$
$30$		0			0
$31$	2.91421	+	5.04757i	0.523408	+	0.906570i	0.999629	+	0.0272438i	$0.00867303\pi$
$31$	2.91421	+	5.04757i	0.523408	+	0.906570i	−0.476221	+	0.879326i	$0.657994\pi$
$32$		0			0
$33$	−0.292893	+	0.507306i	−0.0509862	+	0.0883106i
$34$	−3.17157			−0.543920
$35$		0			0
$36$		0			0
$37$	−4.20711	+	7.28692i	−0.691644	+	1.19796i	0.279655	+	0.960101i	$0.409780\pi$
$37$	−4.20711	+	7.28692i	−0.691644	+	1.19796i	−0.971299	+	0.237862i	$0.923553\pi$
$38$	−3.29289	−	5.70346i	−0.534178	−	0.925223i
$39$	−2.20711	−	3.82282i	−0.353420	−	0.612141i
$40$		0			0
$41$	−6.24264			−0.974937			−0.487468	−	0.873141i	$-0.662080\pi$
$41$	−6.24264			−0.974937			−0.487468	+	0.873141i	$0.662080\pi$
$42$	3.70711	+	0.507306i	0.572019	+	0.0782790i
$43$	7.58579			1.15682			0.578411	−	0.815746i	$-0.303673\pi$
$43$	7.58579			1.15682			0.578411	+	0.815746i	$0.303673\pi$
$44$		0			0
$45$		0			0
$46$	1.58579	+	2.74666i	0.233811	+	0.404973i
$47$	−6.65685	+	11.5300i	−0.971002	+	1.68182i	−0.278459	+	0.960448i	$0.589824\pi$
$47$	−6.65685	+	11.5300i	−0.971002	+	1.68182i	−0.692543	+	0.721377i	$0.743510\pi$
$48$	−4.00000			−0.577350
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$	1.12132	−	1.94218i	0.157016	−	0.271960i
$52$		0			0
$53$	3.41421	+	5.91359i	0.468978	+	0.812294i	0.999371	−	0.0354577i	$-0.0112889\pi$
$53$	3.41421	+	5.91359i	0.468978	+	0.812294i	−0.530393	+	0.847752i	$0.677956\pi$
$54$	−0.707107	+	1.22474i	−0.0962250	+	0.166667i
$55$		0			0
$56$	−7.41421	−	1.01461i	−0.990766	−	0.135583i
$57$	4.65685			0.616815
$58$	−5.82843	+	10.0951i	−0.765310	+	1.32556i
$59$	0.707107	+	1.22474i	0.0920575	+	0.159448i	0.908377	−	0.418153i	$-0.137322\pi$
$59$	0.707107	+	1.22474i	0.0920575	+	0.159448i	−0.816319	+	0.577601i	$0.803989\pi$
$60$		0			0
$61$	2.24264	−	3.88437i	0.287141	−	0.497342i	−0.685985	−	0.727615i	$-0.740629\pi$
$61$	2.24264	−	3.88437i	0.287141	−	0.497342i	0.973126	+	0.230273i	$0.0739619\pi$
$62$	−8.24264			−1.04682
$63$	−1.62132	+	2.09077i	−0.204267	+	0.263412i
$64$	8.00000			1.00000
$65$		0			0
$66$	−0.414214	−	0.717439i	−0.0509862	−	0.0883106i
$67$	−6.86396	−	11.8887i	−0.838566	−	1.45244i	−0.891093	−	0.453820i	$-0.850061\pi$
$67$	−6.86396	−	11.8887i	−0.838566	−	1.45244i	0.0525271	−	0.998619i	$-0.483272\pi$
$68$		0			0
$69$	−2.24264			−0.269982
$70$		0			0
$71$	−0.585786			−0.0695201			−0.0347600	−	0.999396i	$-0.511067\pi$
$71$	−0.585786			−0.0695201			−0.0347600	+	0.999396i	$0.511067\pi$
$72$	1.41421	−	2.44949i	0.166667	−	0.288675i
$73$	−6.03553	−	10.4539i	−0.706406	−	1.22353i	−0.966182	−	0.257862i	$-0.916982\pi$
$73$	−6.03553	−	10.4539i	−0.706406	−	1.22353i	0.259776	−	0.965669i	$-0.416351\pi$
$74$	−5.94975	−	10.3053i	−0.691644	−	1.19796i
$75$		0			0
$76$		0			0
$77$	−0.585786	−	1.43488i	−0.0667566	−	0.163520i
$78$	6.24264			0.706840
$79$	−3.32843	+	5.76500i	−0.374477	+	0.648614i	−0.990249	−	0.139311i	$-0.955511\pi$
$79$	−3.32843	+	5.76500i	−0.374477	+	0.648614i	0.615771	+	0.787925i	$0.288845\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.41421	−	7.64564i	0.487468	−	0.844320i
$83$	−2.58579			−0.283827			−0.141913	−	0.989879i	$-0.545325\pi$
$83$	−2.58579			−0.283827			−0.141913	+	0.989879i	$0.545325\pi$
$84$		0			0
$85$		0			0
$86$	−5.36396	+	9.29065i	−0.578411	+	1.00184i
$87$	−4.12132	−	7.13834i	−0.441852	−	0.765310i
$88$	0.828427	+	1.43488i	0.0883106	+	0.152958i
$89$	6.12132	−	10.6024i	0.648859	−	1.12386i	−0.334537	−	0.942383i	$-0.608580\pi$
$89$	6.12132	−	10.6024i	0.648859	−	1.12386i	0.983396	−	0.181474i	$-0.0580867\pi$
$90$		0			0
$91$	11.5711	+	1.58346i	1.21298	+	0.165992i
$92$		0			0
$93$	2.91421	−	5.04757i	0.302190	−	0.523408i
$94$	−9.41421	−	16.3059i	−0.971002	−	1.68182i
$95$		0			0
$96$		0			0
$97$	5.17157			0.525094			0.262547	−	0.964919i	$-0.415438\pi$
$97$	5.17157			0.525094			0.262547	+	0.964919i	$0.415438\pi$
$98$	−7.07107	+	6.92820i	−0.714286	+	0.699854i
$99$	0.585786			0.0588738
$100$		0			0
$101$	−1.12132	−	1.94218i	−0.111576	−	0.193255i	0.804830	−	0.593505i	$-0.202256\pi$
$101$	−1.12132	−	1.94218i	−0.111576	−	0.193255i	−0.916406	+	0.400251i	$0.868923\pi$
$102$	1.58579	+	2.74666i	0.157016	+	0.271960i
$103$	3.62132	−	6.27231i	0.356819	−	0.618029i	−0.630608	−	0.776101i	$-0.717195\pi$
$103$	3.62132	−	6.27231i	0.356819	−	0.618029i	0.987428	+	0.158072i	$0.0505279\pi$
$104$	−12.4853			−1.22428
$105$		0			0
$106$	−9.65685			−0.937957
$107$	6.29289	−	10.8996i	0.608357	−	1.05371i	−0.383154	−	0.923684i	$-0.625162\pi$
$107$	6.29289	−	10.8996i	0.608357	−	1.05371i	0.991511	−	0.130021i	$-0.0415044\pi$
$108$		0			0
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	0.770419	−	0.637538i	$-0.220047\pi$
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	−0.937334	+	0.348433i	$0.886714\pi$
$110$		0			0
$111$	8.41421			0.798642
$112$	6.48528	−	8.36308i	0.612801	−	0.790237i
$113$	15.6569			1.47287			0.736436	−	0.676507i	$-0.236507\pi$
$113$	15.6569			1.47287			0.736436	+	0.676507i	$0.236507\pi$
$114$	−3.29289	+	5.70346i	−0.308408	+	0.534178i
$115$		0			0
$116$		0			0
$117$	−2.20711	+	3.82282i	−0.204047	+	0.353420i
$118$	−2.00000			−0.184115
$119$	2.24264	+	5.49333i	0.205583	+	0.503572i
$120$		0			0
$121$	5.32843	−	9.22911i	0.484402	−	0.839010i
$122$	3.17157	+	5.49333i	0.287141	+	0.497342i
$123$	3.12132	+	5.40629i	0.281440	+	0.487468i
$124$		0			0
$125$		0			0
$126$	−1.41421	−	3.46410i	−0.125988	−	0.308607i
$127$	3.92893			0.348636			0.174318	−	0.984689i	$-0.444228\pi$
$127$	3.92893			0.348636			0.174318	+	0.984689i	$0.444228\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$	−3.79289	−	6.56948i	−0.333946	−	0.578411i
$130$		0			0
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	−0.972198	−	0.234160i	$-0.924766\pi$
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	0.688887	+	0.724868i	$0.258099\pi$
$132$		0			0
$133$	−7.55025	+	9.73641i	−0.654690	+	0.844254i
$134$	19.4142			1.67713
$135$		0			0
$136$	−3.17157	−	5.49333i	−0.271960	−	0.471049i
$137$	−8.53553	−	14.7840i	−0.729240	−	1.26308i	−0.957205	−	0.289411i	$-0.906541\pi$
$137$	−8.53553	−	14.7840i	−0.729240	−	1.26308i	0.227965	−	0.973669i	$-0.426793\pi$
$138$	1.58579	−	2.74666i	0.134991	−	0.233811i
$139$	−5.48528			−0.465255			−0.232628	−	0.972566i	$-0.574732\pi$
$139$	−5.48528			−0.465255			−0.232628	+	0.972566i	$0.574732\pi$
$140$		0			0
$141$	13.3137			1.12122
$142$	0.414214	−	0.717439i	0.0347600	−	0.0602061i
$143$	−1.29289	−	2.23936i	−0.108117	−	0.187264i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$		0			0
$146$	17.0711			1.41281
$147$	−1.74264	−	6.77962i	−0.143731	−	0.559173i
$148$		0			0
$149$	−3.17157	+	5.49333i	−0.259825	+	0.450031i	−0.966195	−	0.257812i	$-0.916998\pi$
$149$	−3.17157	+	5.49333i	−0.259825	+	0.450031i	0.706370	+	0.707843i	$0.250332\pi$
$150$		0			0
$151$	−5.24264	−	9.08052i	−0.426640	−	0.738962i	0.569932	−	0.821692i	$-0.306970\pi$
$151$	−5.24264	−	9.08052i	−0.426640	−	0.738962i	−0.996572	+	0.0827296i	$0.973636\pi$
$152$	6.58579	−	11.4069i	0.534178	−	0.925223i
$153$	−2.24264			−0.181307
$154$	2.17157	+	0.297173i	0.174990	+	0.0239469i
$155$		0			0
$156$		0			0
$157$	6.07107	+	10.5154i	0.484524	+	0.839220i	0.999842	−	0.0177789i	$-0.00565951\pi$
$157$	6.07107	+	10.5154i	0.484524	+	0.839220i	−0.515318	+	0.856999i	$0.672326\pi$
$158$	−4.70711	−	8.15295i	−0.374477	−	0.648614i
$159$	3.41421	−	5.91359i	0.270765	−	0.468978i
$160$		0			0
$161$	3.63604	−	4.68885i	0.286560	−	0.369533i
$162$	1.41421			0.111111
$163$	1.65685	−	2.86976i	0.129775	−	0.224777i	−0.793814	−	0.608160i	$-0.791908\pi$
$163$	1.65685	−	2.86976i	0.129775	−	0.224777i	0.923589	+	0.383383i	$0.125241\pi$
$164$		0			0
$165$		0			0
$166$	1.82843	−	3.16693i	0.141913	−	0.245801i
$167$	−20.2426			−1.56642			−0.783211	−	0.621756i	$-0.786420\pi$
$167$	−20.2426			−1.56642			−0.783211	+	0.621756i	$0.786420\pi$
$168$	2.82843	+	6.92820i	0.218218	+	0.534522i
$169$	6.48528			0.498868
$170$		0			0
$171$	−2.32843	−	4.03295i	−0.178059	−	0.308408i
$172$		0			0
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	−0.807245	−	0.590217i	$-0.799042\pi$
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	0.914765	+	0.403986i	$0.132375\pi$
$174$	11.6569			0.883704
$175$		0			0
$176$	−2.34315			−0.176621
$177$	0.707107	−	1.22474i	0.0531494	−	0.0920575i
$178$	8.65685	+	14.9941i	0.648859	+	1.12386i
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	0.666954	−	0.745099i	$-0.267598\pi$
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	−0.978752	+	0.205049i	$0.934265\pi$
$180$		0			0
$181$	−10.6569			−0.792118			−0.396059	−	0.918225i	$-0.629622\pi$
$181$	−10.6569			−0.792118			−0.396059	+	0.918225i	$0.629622\pi$
$182$	−10.1213	+	13.0519i	−0.750242	+	0.967473i
$183$	−4.48528			−0.331562
$184$	−3.17157	+	5.49333i	−0.233811	+	0.404973i
$185$		0			0
$186$	4.12132	+	7.13834i	0.302190	+	0.523408i
$187$	0.656854	−	1.13770i	0.0480339	−	0.0831972i
$188$		0			0
$189$	2.62132	+	0.358719i	0.190673	+	0.0260930i
$190$		0			0
$191$	7.48528	−	12.9649i	0.541616	−	0.938106i	−0.457196	−	0.889366i	$-0.651146\pi$
$191$	7.48528	−	12.9649i	0.541616	−	0.938106i	0.998811	−	0.0487401i	$-0.0155206\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	−7.62132	−	13.2005i	−0.548595	−	0.950194i	−0.998371	−	0.0570527i	$-0.981830\pi$
$193$	−7.62132	−	13.2005i	−0.548595	−	0.950194i	0.449777	−	0.893141i	$-0.351504\pi$
$194$	−3.65685	+	6.33386i	−0.262547	+	0.454744i
$195$		0			0
$196$		0			0
$197$	25.5563			1.82081			0.910407	−	0.413713i	$-0.135768\pi$
$197$	25.5563			1.82081			0.910407	+	0.413713i	$0.135768\pi$
$198$	−0.414214	+	0.717439i	−0.0294369	+	0.0509862i
$199$	−11.2426	−	19.4728i	−0.796970	−	1.38039i	−0.921581	−	0.388186i	$-0.873102\pi$
$199$	−11.2426	−	19.4728i	−0.796970	−	1.38039i	0.124611	−	0.992206i	$-0.460232\pi$
$200$		0			0
$201$	−6.86396	+	11.8887i	−0.484146	+	0.838566i
$202$	3.17157			0.223151
$203$	21.6066	+	2.95680i	1.51649	+	0.207526i
$204$		0			0
$205$		0			0
$206$	5.12132	+	8.87039i	0.356819	+	0.618029i
$207$	1.12132	+	1.94218i	0.0779372	+	0.134991i
$208$	8.82843	−	15.2913i	0.612141	−	1.06026i
$209$	2.72792			0.188694
$210$		0			0
$211$	−28.1421			−1.93738			−0.968692	−	0.248265i	$-0.920140\pi$
$211$	−28.1421			−1.93738			−0.968692	+	0.248265i	$0.920140\pi$
$212$		0			0
$213$	0.292893	+	0.507306i	0.0200687	+	0.0347600i
$214$	8.89949	+	15.4144i	0.608357	+	1.05371i
$215$		0			0
$216$	−2.82843			−0.192450
$217$	5.82843	+	14.2767i	0.395659	+	0.969164i
$218$	4.92893			0.333829
$219$	−6.03553	+	10.4539i	−0.407844	+	0.706406i
$220$		0			0
$221$	4.94975	+	8.57321i	0.332956	+	0.576697i
$222$	−5.94975	+	10.3053i	−0.399321	+	0.691644i
$223$	−22.8284			−1.52870			−0.764352	−	0.644799i	$-0.776941\pi$
$223$	−22.8284			−1.52870			−0.764352	+	0.644799i	$0.776941\pi$
$224$		0			0
$225$		0			0
$226$	−11.0711	+	19.1757i	−0.736436	+	1.27555i
$227$	4.46447	+	7.73268i	0.296317	+	0.513236i	0.975290	−	0.220927i	$-0.0709082\pi$
$227$	4.46447	+	7.73268i	0.296317	+	0.513236i	−0.678973	+	0.734163i	$0.737575\pi$
$228$		0			0
$229$	−4.15685	+	7.19988i	−0.274693	+	0.475782i	−0.970058	−	0.242875i	$-0.921909\pi$
$229$	−4.15685	+	7.19988i	−0.274693	+	0.475782i	0.695365	+	0.718657i	$0.255243\pi$
$230$		0			0
$231$	−0.949747	+	1.22474i	−0.0624888	+	0.0805823i
$232$	−23.3137			−1.53062
$233$	−2.75736	+	4.77589i	−0.180641	+	0.312879i	−0.942099	−	0.335335i	$-0.891150\pi$
$233$	−2.75736	+	4.77589i	−0.180641	+	0.312879i	0.761458	+	0.648214i	$0.224484\pi$
$234$	−3.12132	−	5.40629i	−0.204047	−	0.353420i
$235$		0			0
$236$		0			0
$237$	6.65685			0.432409
$238$	−8.31371	−	1.13770i	−0.538898	−	0.0737465i
$239$	−5.31371			−0.343715			−0.171858	−	0.985122i	$-0.554977\pi$
$239$	−5.31371			−0.343715			−0.171858	+	0.985122i	$0.554977\pi$
$240$		0			0
$241$	10.8284	+	18.7554i	0.697520	+	1.20814i	0.969324	+	0.245788i	$0.0790466\pi$
$241$	10.8284	+	18.7554i	0.697520	+	1.20814i	−0.271803	+	0.962353i	$0.587620\pi$
$242$	7.53553	+	13.0519i	0.484402	+	0.839010i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$	−8.82843			−0.562880
$247$	−10.2782	+	17.8023i	−0.653985	+	1.13273i
$248$	−8.24264	−	14.2767i	−0.523408	−	0.906570i
$249$	1.29289	+	2.23936i	0.0819338	+	0.141913i
$250$		0			0
$251$	−2.58579			−0.163213			−0.0816067	−	0.996665i	$-0.526005\pi$
$251$	−2.58579			−0.163213			−0.0816067	+	0.996665i	$0.526005\pi$
$252$		0			0
$253$	−1.31371			−0.0825921
$254$	−2.77817	+	4.81194i	−0.174318	+	0.301928i
$255$		0			0
$256$		0			0
$257$	−5.05025	+	8.74729i	−0.315026	+	0.545641i	−0.979443	−	0.201721i	$-0.935347\pi$
$257$	−5.05025	+	8.74729i	−0.315026	+	0.545641i	0.664417	+	0.747362i	$0.268680\pi$
$258$	10.7279			0.667891
$259$	−13.6421	+	17.5922i	−0.847681	+	1.09313i
$260$		0			0
$261$	−4.12132	+	7.13834i	−0.255103	+	0.441852i
$262$	−4.58579	−	7.94282i	−0.283311	−	0.490709i
$263$	3.41421	+	5.91359i	0.210529	+	0.364648i	0.951880	−	0.306470i	$-0.0991479\pi$
$263$	3.41421	+	5.91359i	0.210529	+	0.364648i	−0.741351	+	0.671118i	$0.765815\pi$
$264$	0.828427	−	1.43488i	0.0509862	−	0.0883106i
$265$		0			0
$266$	−6.58579	−	16.1318i	−0.403800	−	0.989105i
$267$	−12.2426			−0.749237
$268$		0			0
$269$	10.0711	+	17.4436i	0.614044	+	1.06356i	0.990551	+	0.137142i	$0.0437915\pi$
$269$	10.0711	+	17.4436i	0.614044	+	1.06356i	−0.376508	+	0.926414i	$0.622875\pi$
$270$		0			0
$271$	4.07107	−	7.05130i	0.247300	−	0.428336i	−0.715476	−	0.698637i	$-0.753790\pi$
$271$	4.07107	−	7.05130i	0.247300	−	0.428336i	0.962776	+	0.270302i	$0.0871234\pi$
$272$	8.97056			0.543920
$273$	−4.41421	−	10.8126i	−0.267160	−	0.654407i
$274$	24.1421			1.45848
$275$		0			0
$276$		0			0
$277$	6.69239	+	11.5916i	0.402107	+	0.696469i	0.993980	−	0.109562i	$-0.0349448\pi$
$277$	6.69239	+	11.5916i	0.402107	+	0.696469i	−0.591873	+	0.806031i	$0.701611\pi$
$278$	3.87868	−	6.71807i	0.232628	−	0.402923i
$279$	−5.82843			−0.348939
$280$		0			0
$281$	−1.65685			−0.0988396			−0.0494198	−	0.998778i	$-0.515737\pi$
$281$	−1.65685			−0.0988396			−0.0494198	+	0.998778i	$0.515737\pi$
$282$	−9.41421	+	16.3059i	−0.560608	+	0.971002i
$283$	−2.37868	−	4.11999i	−0.141398	−	0.244908i	0.786625	−	0.617431i	$-0.211826\pi$
$283$	−2.37868	−	4.11999i	−0.141398	−	0.244908i	−0.928023	+	0.372522i	$0.878493\pi$
$284$		0			0
$285$		0			0
$286$	3.65685			0.216234
$287$	−16.3640	−	2.23936i	−0.965934	−	0.132185i
$288$		0			0
$289$	5.98528	−	10.3668i	0.352075	−	0.609812i
$290$		0			0
$291$	−2.58579	−	4.47871i	−0.151581	−	0.262547i
$292$		0			0
$293$	−7.31371			−0.427271			−0.213636	−	0.976913i	$-0.568531\pi$
$293$	−7.31371			−0.427271			−0.213636	+	0.976913i	$0.568531\pi$
$294$	9.53553	+	2.65962i	0.556124	+	0.155112i
$295$		0			0
$296$	11.8995	−	20.6105i	0.691644	−	1.19796i
$297$	−0.292893	−	0.507306i	−0.0169954	−	0.0294369i
$298$	−4.48528	−	7.76874i	−0.259825	−	0.450031i
$299$	4.94975	−	8.57321i	0.286251	−	0.495802i
$300$		0			0
$301$	19.8848	+	2.72117i	1.14614	+	0.156846i
$302$	14.8284			0.853280
$303$	−1.12132	+	1.94218i	−0.0644182	+	0.111576i
$304$	9.31371	+	16.1318i	0.534178	+	0.925223i
$305$		0			0
$306$	1.58579	−	2.74666i	0.0906534	−	0.157016i
$307$	−4.41421			−0.251932			−0.125966	−	0.992035i	$-0.540203\pi$
$307$	−4.41421			−0.251932			−0.125966	+	0.992035i	$0.540203\pi$
$308$		0			0
$309$	−7.24264			−0.412019
$310$		0			0
$311$	1.46447	+	2.53653i	0.0830423	+	0.143833i	0.904555	−	0.426356i	$-0.140203\pi$
$311$	1.46447	+	2.53653i	0.0830423	+	0.143833i	−0.821513	+	0.570190i	$0.806870\pi$
$312$	6.24264	+	10.8126i	0.353420	+	0.612141i
$313$	−8.10660	+	14.0410i	−0.458212	+	0.793647i	−0.998867	−	0.0475980i	$-0.984843\pi$
$313$	−8.10660	+	14.0410i	−0.458212	+	0.793647i	0.540654	+	0.841245i	$0.318177\pi$
$314$	−17.1716			−0.969048
$315$		0			0
$316$		0			0
$317$	9.94975	−	17.2335i	0.558833	−	0.967928i	−0.438761	−	0.898604i	$-0.644582\pi$
$317$	9.94975	−	17.2335i	0.558833	−	0.967928i	0.997594	−	0.0693241i	$-0.0220842\pi$
$318$	4.82843	+	8.36308i	0.270765	+	0.468978i
$319$	−2.41421	−	4.18154i	−0.135170	−	0.234121i
$320$		0			0
$321$	−12.5858			−0.702470
$322$	3.17157	+	7.76874i	0.176745	+	0.432935i
$323$	−10.4437			−0.581100
$324$		0			0
$325$		0			0
$326$	2.34315	+	4.05845i	0.129775	+	0.224777i
$327$	−1.74264	+	3.01834i	−0.0963683	+	0.166915i
$328$	17.6569			0.974937
$329$	−21.5858	+	27.8359i	−1.19006	+	1.53464i
$330$		0			0
$331$	−8.81371	+	15.2658i	−0.484445	+	0.839084i	−0.999840	−	0.0178689i	$-0.994312\pi$
$331$	−8.81371	+	15.2658i	−0.484445	+	0.839084i	0.515395	+	0.856953i	$0.327645\pi$
$332$		0			0
$333$	−4.20711	−	7.28692i	−0.230548	−	0.399321i
$334$	14.3137	−	24.7921i	0.783211	−	1.35656i
$335$		0			0
$336$	−10.4853	−	1.43488i	−0.572019	−	0.0782790i
$337$	−18.8995			−1.02952			−0.514761	−	0.857334i	$-0.672119\pi$
$337$	−18.8995			−1.02952			−0.514761	+	0.857334i	$0.672119\pi$
$338$	−4.58579	+	7.94282i	−0.249434	+	0.432032i
$339$	−7.82843	−	13.5592i	−0.425182	−	0.736436i
$340$		0			0
$341$	1.70711	−	2.95680i	0.0924450	−	0.160119i
$342$	6.58579			0.356119
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−21.4558			−1.15682
$345$		0			0
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	4.48528	+	7.76874i	0.240783	+	0.417048i	0.960937	−	0.276766i	$-0.0892626\pi$
$347$	4.48528	+	7.76874i	0.240783	+	0.417048i	−0.720155	+	0.693813i	$0.755929\pi$
$348$		0			0
$349$	28.6274			1.53239			0.766195	−	0.642608i	$-0.222148\pi$
$349$	28.6274			1.53239			0.766195	+	0.642608i	$0.222148\pi$
$350$		0			0
$351$	4.41421			0.235613
$352$		0			0
$353$	−6.94975	−	12.0373i	−0.369898	−	0.640682i	0.619651	−	0.784877i	$-0.287274\pi$
$353$	−6.94975	−	12.0373i	−0.369898	−	0.640682i	−0.989549	+	0.144195i	$0.953941\pi$
$354$	1.00000	+	1.73205i	0.0531494	+	0.0920575i
$355$		0			0
$356$		0			0
$357$	3.63604	−	4.68885i	0.192440	−	0.248160i
$358$	11.7990			0.623596
$359$	14.7071	−	25.4735i	0.776211	−	1.34444i	−0.157900	−	0.987455i	$-0.550472\pi$
$359$	14.7071	−	25.4735i	0.776211	−	1.34444i	0.934111	−	0.356982i	$-0.116194\pi$
$360$		0			0
$361$	−1.34315	−	2.32640i	−0.0706919	−	0.122442i
$362$	7.53553	−	13.0519i	0.396059	−	0.685994i
$363$	−10.6569			−0.559340
$364$		0			0
$365$		0			0
$366$	3.17157	−	5.49333i	0.165781	−	0.287141i
$367$	−11.2071	−	19.4113i	−0.585006	−	1.01326i	−0.994875	−	0.101116i	$-0.967759\pi$
$367$	−11.2071	−	19.4113i	−0.585006	−	1.01326i	0.409868	−	0.912145i	$-0.365575\pi$
$368$	−4.48528	−	7.76874i	−0.233811	−	0.404973i
$369$	3.12132	−	5.40629i	0.162489	−	0.281440i
$370$		0			0
$371$	6.82843	+	16.7262i	0.354514	+	0.868379i
$372$		0			0
$373$	5.37868	−	9.31615i	0.278497	−	0.482372i	−0.692514	−	0.721404i	$-0.743497\pi$
$373$	5.37868	−	9.31615i	0.278497	−	0.482372i	0.971012	+	0.239033i	$0.0768303\pi$
$374$	0.928932	+	1.60896i	0.0480339	+	0.0831972i
$375$		0			0
$376$	18.8284	−	32.6118i	0.971002	−	1.68182i
$377$	36.3848			1.87391
$378$	−2.29289	+	2.95680i	−0.117934	+	0.152081i
$379$	−24.7990			−1.27384			−0.636919	−	0.770931i	$-0.719792\pi$
$379$	−24.7990			−1.27384			−0.636919	+	0.770931i	$0.719792\pi$
$380$		0			0
$381$	−1.96447	−	3.40256i	−0.100643	−	0.174318i
$382$	10.5858	+	18.3351i	0.541616	+	0.938106i
$383$	−2.24264	+	3.88437i	−0.114594	+	0.198482i	−0.917617	−	0.397465i	$-0.869890\pi$
$383$	−2.24264	+	3.88437i	−0.114594	+	0.198482i	0.803024	+	0.595947i	$0.203223\pi$
$384$	11.3137			0.577350
$385$		0			0
$386$	21.5563			1.09719
$387$	−3.79289	+	6.56948i	−0.192804	+	0.333946i
$388$		0			0
$389$	18.4350	+	31.9304i	0.934693	+	1.61894i	0.775180	+	0.631740i	$0.217659\pi$
$389$	18.4350	+	31.9304i	0.934693	+	1.61894i	0.159513	+	0.987196i	$0.449008\pi$
$390$		0			0
$391$	5.02944			0.254350
$392$	−19.0711	−	5.31925i	−0.963234	−	0.268662i
$393$	6.48528			0.327139
$394$	−18.0711	+	31.3000i	−0.910407	+	1.57687i
$395$		0			0
$396$		0			0
$397$	9.10660	−	15.7731i	0.457047	−	0.791629i	−0.541756	−	0.840536i	$-0.682240\pi$
$397$	9.10660	−	15.7731i	0.457047	−	0.791629i	0.998803	+	0.0489067i	$0.0155737\pi$
$398$	31.7990			1.59394
$399$	12.2071	+	1.67050i	0.611120	+	0.0836298i
$400$		0			0
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	−0.583449	−	0.812150i	$-0.698297\pi$
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	0.995067	+	0.0992068i	$0.0316305\pi$
$402$	−9.70711	−	16.8132i	−0.484146	−	0.838566i
$403$	12.8640	+	22.2810i	0.640800	+	1.10990i
$404$		0			0
$405$		0			0
$406$	−18.8995	+	24.3718i	−0.937966	+	1.20955i
$407$	4.92893			0.244318
$408$	−3.17157	+	5.49333i	−0.157016	+	0.271960i
$409$	1.84315	+	3.19242i	0.0911377	+	0.157855i	0.907990	−	0.418992i	$-0.137616\pi$
$409$	1.84315	+	3.19242i	0.0911377	+	0.157855i	−0.816852	+	0.576847i	$0.804283\pi$
$410$		0			0
$411$	−8.53553	+	14.7840i	−0.421027	+	0.729240i
$412$		0			0
$413$	1.41421	+	3.46410i	0.0695889	+	0.170457i
$414$	−3.17157			−0.155874
$415$		0			0
$416$		0			0
$417$	2.74264	+	4.75039i	0.134308	+	0.232628i
$418$	−1.92893	+	3.34101i	−0.0943472	+	0.163414i
$419$	−8.82843			−0.431297			−0.215648	−	0.976471i	$-0.569187\pi$
$419$	−8.82843			−0.431297			−0.215648	+	0.976471i	$0.569187\pi$
$420$		0			0
$421$	10.5147			0.512456			0.256228	−	0.966616i	$-0.417520\pi$
$421$	10.5147			0.512456			0.256228	+	0.966616i	$0.417520\pi$
$422$	19.8995	−	34.4669i	0.968692	−	1.67782i
$423$	−6.65685	−	11.5300i	−0.323667	−	0.560608i
$424$	−9.65685	−	16.7262i	−0.468978	−	0.812294i
$425$		0			0
$426$	−0.828427			−0.0401374
$427$	7.27208	−	9.37769i	0.351921	−	0.453818i
$428$		0			0
$429$	−1.29289	+	2.23936i	−0.0624215	+	0.108117i
$430$		0			0
$431$	−15.5858	−	26.9954i	−0.750741	−	1.30032i	−0.947464	−	0.319862i	$-0.896363\pi$
$431$	−15.5858	−	26.9954i	−0.750741	−	1.30032i	0.196723	−	0.980459i	$-0.436970\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−6.55635			−0.315078			−0.157539	−	0.987513i	$-0.550356\pi$
$433$	−6.55635			−0.315078			−0.157539	+	0.987513i	$0.550356\pi$
$434$	−21.6066	−	2.95680i	−1.03715	−	0.141931i
$435$		0			0
$436$		0			0
$437$	5.22183	+	9.04447i	0.249794	+	0.432656i
$438$	−8.53553	−	14.7840i	−0.407844	−	0.706406i
$439$	−5.82843	+	10.0951i	−0.278176	+	0.481814i	−0.970931	−	0.239358i	$-0.923063\pi$
$439$	−5.82843	+	10.0951i	−0.278176	+	0.481814i	0.692756	+	0.721172i	$0.256396\pi$
$440$		0			0
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$	−14.0000			−0.665912
$443$	−8.24264	+	14.2767i	−0.391620	+	0.678305i	−0.992663	−	0.120911i	$-0.961418\pi$
$443$	−8.24264	+	14.2767i	−0.391620	+	0.678305i	0.601044	+	0.799216i	$0.294752\pi$
$444$		0			0
$445$		0			0
$446$	16.1421	−	27.9590i	0.764352	−	1.32390i
$447$	6.34315			0.300020
$448$	20.9706	+	2.86976i	0.990766	+	0.135583i
$449$	26.9706			1.27282			0.636410	−	0.771351i	$-0.280419\pi$
$449$	26.9706			1.27282			0.636410	+	0.771351i	$0.280419\pi$
$450$		0			0
$451$	1.82843	+	3.16693i	0.0860973	+	0.149125i
$452$		0			0
$453$	−5.24264	+	9.08052i	−0.246321	+	0.426640i
$454$	−12.6274			−0.592634
$455$		0			0
$456$	−13.1716			−0.616815
$457$	−0.550253	+	0.953065i	−0.0257397	+	0.0445825i	−0.878608	−	0.477543i	$-0.841527\pi$
$457$	−0.550253	+	0.953065i	−0.0257397	+	0.0445825i	0.852869	+	0.522126i	$0.174861\pi$
$458$	−5.87868	−	10.1822i	−0.274693	−	0.475782i
$459$	1.12132	+	1.94218i	0.0523388	+	0.0906534i
$460$		0			0
$461$	−12.9289			−0.602160			−0.301080	−	0.953599i	$-0.597347\pi$
$461$	−12.9289			−0.602160			−0.301080	+	0.953599i	$0.597347\pi$
$462$	−0.828427	−	2.02922i	−0.0385419	−	0.0944080i
$463$	7.58579			0.352541			0.176271	−	0.984342i	$-0.443597\pi$
$463$	7.58579			0.352541			0.176271	+	0.984342i	$0.443597\pi$
$464$	16.4853	−	28.5533i	0.765310	−	1.32556i
$465$		0			0
$466$	−3.89949	−	6.75412i	−0.180641	−	0.312879i
$467$	14.6569	−	25.3864i	0.678238	−	1.17474i	−0.297273	−	0.954793i	$-0.596077\pi$
$467$	14.6569	−	25.3864i	0.678238	−	1.17474i	0.975511	−	0.219951i	$-0.0705896\pi$
$468$		0			0
$469$	−13.7279	−	33.6264i	−0.633897	−	1.55272i
$470$		0			0
$471$	6.07107	−	10.5154i	0.279740	−	0.484524i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	−2.22183	−	3.84831i	−0.102160	−	0.176946i
$474$	−4.70711	+	8.15295i	−0.216205	+	0.374477i
$475$		0			0
$476$		0			0
$477$	−6.82843			−0.312652
$478$	3.75736	−	6.50794i	0.171858	−	0.297666i
$479$	−5.31371	−	9.20361i	−0.242790	−	0.420524i	0.718718	−	0.695301i	$-0.244729\pi$
$479$	−5.31371	−	9.20361i	−0.242790	−	0.420524i	−0.961508	+	0.274778i	$0.911396\pi$
$480$		0			0
$481$	−18.5711	+	32.1660i	−0.846768	+	1.46664i
$482$	−30.6274			−1.39504
$483$	−5.87868	−	0.804479i	−0.267489	−	0.0366051i
$484$		0			0
$485$		0			0
$486$	−0.707107	−	1.22474i	−0.0320750	−	0.0555556i
$487$	−9.44975	−	16.3674i	−0.428209	−	0.741680i	0.568505	−	0.822680i	$-0.307522\pi$
$487$	−9.44975	−	16.3674i	−0.428209	−	0.741680i	−0.996714	+	0.0810001i	$0.974189\pi$
$488$	−6.34315	+	10.9867i	−0.287141	+	0.497342i
$489$	−3.31371			−0.149851
$490$		0			0
$491$	18.1421			0.818743			0.409372	−	0.912368i	$-0.365748\pi$
$491$	18.1421			0.818743			0.409372	+	0.912368i	$0.365748\pi$
$492$		0			0
$493$	9.24264	+	16.0087i	0.416268	+	0.720997i
$494$	−14.5355	−	25.1763i	−0.653985	−	1.13273i
$495$		0			0
$496$	23.3137			1.04682
$497$	−1.53553	−	0.210133i	−0.0688781	−	0.00942575i
$498$	−3.65685			−0.163868
$499$	15.3995	−	26.6727i	0.689376	−	1.19403i	−0.282664	−	0.959219i	$-0.591218\pi$
$499$	15.3995	−	26.6727i	0.689376	−	1.19403i	0.972040	−	0.234815i	$-0.0754486\pi$
$500$		0			0
$501$	10.1213	+	17.5306i	0.452187	+	0.783211i
$502$	1.82843	−	3.16693i	0.0816067	−	0.141347i
$503$	1.51472			0.0675380			0.0337690	−	0.999430i	$-0.489249\pi$
$503$	1.51472			0.0675380			0.0337690	+	0.999430i	$0.489249\pi$
$504$	4.58579	−	5.91359i	0.204267	−	0.263412i
$505$		0			0
$506$	0.928932	−	1.60896i	0.0412961	−	0.0715269i
$507$	−3.24264	−	5.61642i	−0.144011	−	0.249434i
$508$		0			0
$509$	12.8995	−	22.3426i	0.571760	−	0.990317i	−0.424625	−	0.905369i	$-0.639594\pi$
$509$	12.8995	−	22.3426i	0.571760	−	0.990317i	0.996385	−	0.0849483i	$-0.0270725\pi$
$510$		0			0
$511$	−12.0711	−	29.5680i	−0.533993	−	1.30801i
$512$	−22.6274			−1.00000
$513$	−2.32843	+	4.03295i	−0.102803	+	0.178059i
$514$	−7.14214	−	12.3705i	−0.315026	−	0.545641i
$515$		0			0
$516$		0			0
$517$	7.79899			0.342999
$518$	−11.8995	−	29.1477i	−0.522834	−	1.28068i
$519$	−2.82843			−0.124154
$520$		0			0
$521$	−11.5563	−	20.0162i	−0.506293	−	0.876925i	−0.999973	−	0.00728166i	$-0.997682\pi$
$521$	−11.5563	−	20.0162i	−0.506293	−	0.876925i	0.493681	−	0.869643i	$-0.335651\pi$
$522$	−5.82843	−	10.0951i	−0.255103	−	0.441852i
$523$	−5.20711	+	9.01897i	−0.227691	+	0.394372i	−0.957123	−	0.289681i	$-0.906451\pi$
$523$	−5.20711	+	9.01897i	−0.227691	+	0.394372i	0.729432	+	0.684053i	$0.239784\pi$
$524$		0			0
$525$		0			0
$526$	−9.65685			−0.421059
$527$	−6.53553	+	11.3199i	−0.284692	+	0.493102i
$528$	1.17157	+	2.02922i	0.0509862	+	0.0883106i
$529$	8.98528	+	15.5630i	0.390664	+	0.676651i
$530$		0			0
$531$	−1.41421			−0.0613716
$532$		0			0
$533$	−27.5563			−1.19360
$534$	8.65685	−	14.9941i	0.374619	−	0.648859i
$535$		0			0
$536$	19.4142	+	33.6264i	0.838566	+	1.45244i
$537$	−4.17157	+	7.22538i	−0.180017	+	0.311798i
$538$	−28.4853			−1.22809
$539$	−1.02082	−	3.97141i	−0.0439696	−	0.171061i
$540$		0			0
$541$	−4.84315	+	8.38857i	−0.208223	+	0.360653i	−0.951155	−	0.308714i	$-0.900101\pi$
$541$	−4.84315	+	8.38857i	−0.208223	+	0.360653i	0.742932	+	0.669367i	$0.233435\pi$
$542$	5.75736	+	9.97204i	0.247300	+	0.428336i
$543$	5.32843	+	9.22911i	0.228665	+	0.396059i
$544$		0			0
$545$		0			0
$546$	16.3640	+	2.23936i	0.700313	+	0.0958356i
$547$	−7.79899			−0.333461			−0.166730	−	0.986003i	$-0.553321\pi$
$547$	−7.79899			−0.333461			−0.166730	+	0.986003i	$0.553321\pi$
$548$		0			0
$549$	2.24264	+	3.88437i	0.0957136	+	0.165781i
$550$		0			0
$551$	−19.1924	+	33.2422i	−0.817623	+	1.41616i
$552$	6.34315			0.269982
$553$	−10.7929	+	13.9180i	−0.458961	+	0.591852i
$554$	−18.9289			−0.804213
$555$		0			0
$556$		0			0
$557$	−9.82843	−	17.0233i	−0.416444	−	0.721302i	0.579135	−	0.815232i	$-0.303390\pi$
$557$	−9.82843	−	17.0233i	−0.416444	−	0.721302i	−0.995579	+	0.0939298i	$0.970057\pi$
$558$	4.12132	−	7.13834i	0.174469	−	0.302190i
$559$	33.4853			1.41628
$560$		0			0
$561$	−1.31371			−0.0554648
$562$	1.17157	−	2.02922i	0.0494198	−	0.0855976i
$563$	21.1421	+	36.6193i	0.891035	+	1.54332i	0.838637	+	0.544691i	$0.183353\pi$
$563$	21.1421	+	36.6193i	0.891035	+	1.54332i	0.0523981	+	0.998626i	$0.483314\pi$
$564$		0			0
$565$		0			0
$566$	6.72792			0.282796
$567$	−1.00000	−	2.44949i	−0.0419961	−	0.102869i
$568$	1.65685			0.0695201
$569$	−8.43503	+	14.6099i	−0.353615	+	0.612479i	−0.986880	−	0.161456i	$-0.948381\pi$
$569$	−8.43503	+	14.6099i	−0.353615	+	0.612479i	0.633265	+	0.773935i	$0.281714\pi$
$570$		0			0
$571$	2.98528	+	5.17066i	0.124930	+	0.216385i	0.921706	−	0.387890i	$-0.126796\pi$
$571$	2.98528	+	5.17066i	0.124930	+	0.216385i	−0.796775	+	0.604275i	$0.793463\pi$
$572$		0			0
$573$	−14.9706			−0.625404
$574$	14.3137	−	18.4582i	0.597443	−	0.770431i
$575$		0			0
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	−12.2782	−	21.2664i	−0.511147	−	0.885333i	−0.999917	−	0.0129197i	$-0.995887\pi$
$577$	−12.2782	−	21.2664i	−0.511147	−	0.885333i	0.488769	−	0.872413i	$-0.337446\pi$
$578$	8.46447	+	14.6609i	0.352075	+	0.609812i
$579$	−7.62132	+	13.2005i	−0.316731	+	0.548595i
$580$		0			0
$581$	−6.77817	−	0.927572i	−0.281206	−	0.0384822i
$582$	7.31371			0.303163
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	17.0711	+	29.5680i	0.706406	+	1.22353i
$585$		0			0
$586$	5.17157	−	8.95743i	0.213636	−	0.370028i
$587$	−21.7574			−0.898022			−0.449011	−	0.893526i	$-0.648224\pi$
$587$	−21.7574			−0.898022			−0.449011	+	0.893526i	$0.648224\pi$
$588$		0			0
$589$	−27.1421			−1.11837
$590$		0			0
$591$	−12.7782	−	22.1324i	−0.525624	−	0.910407i
$592$	16.8284	+	29.1477i	0.691644	+	1.19796i
$593$	5.29289	−	9.16756i	0.217353	−	0.376467i	−0.736645	−	0.676280i	$-0.763591\pi$
$593$	5.29289	−	9.16756i	0.217353	−	0.376467i	0.953998	+	0.299813i	$0.0969244\pi$
$594$	0.828427			0.0339908
$595$		0			0
$596$		0			0
$597$	−11.2426	+	19.4728i	−0.460131	+	0.796970i
$598$	7.00000	+	12.1244i	0.286251	+	0.495802i
$599$	6.92893	+	12.0013i	0.283108	+	0.490358i	0.972149	−	0.234365i	$-0.0753010\pi$
$599$	6.92893	+	12.0013i	0.283108	+	0.490358i	−0.689040	+	0.724723i	$0.741968\pi$
$600$		0			0
$601$	−29.8284			−1.21673			−0.608363	−	0.793659i	$-0.708174\pi$
$601$	−29.8284			−1.21673			−0.608363	+	0.793659i	$0.708174\pi$
$602$	−17.3934	+	22.4296i	−0.708902	+	0.914163i
$603$	13.7279			0.559044
$604$		0			0
$605$		0			0
$606$	−1.58579	−	2.74666i	−0.0644182	−	0.111576i
$607$	3.62132	−	6.27231i	0.146985	−	0.254585i	−0.783127	−	0.621862i	$-0.786376\pi$
$607$	3.62132	−	6.27231i	0.146985	−	0.254585i	0.930112	+	0.367277i	$0.119710\pi$
$608$		0			0
$609$	−8.24264	−	20.1903i	−0.334009	−	0.818151i
$610$		0			0
$611$	−29.3848	+	50.8959i	−1.18878	+	2.05903i
$612$		0			0
$613$	−9.07107	−	15.7116i	−0.366377	−	0.634584i	0.622619	−	0.782525i	$-0.286069\pi$
$613$	−9.07107	−	15.7116i	−0.366377	−	0.634584i	−0.988996	+	0.147941i	$0.952735\pi$
$614$	3.12132	−	5.40629i	0.125966	−	0.218180i
$615$		0			0
$616$	1.65685	+	4.05845i	0.0667566	+	0.163520i
$617$	3.17157			0.127683			0.0638414	−	0.997960i	$-0.479665\pi$
$617$	3.17157			0.127683			0.0638414	+	0.997960i	$0.479665\pi$
$618$	5.12132	−	8.87039i	0.206010	−	0.356819i
$619$	−3.01472	−	5.22165i	−0.121172	−	0.209876i	0.799058	−	0.601254i	$-0.205332\pi$
$619$	−3.01472	−	5.22165i	−0.121172	−	0.209876i	−0.920230	+	0.391378i	$0.871999\pi$
$620$		0			0
$621$	1.12132	−	1.94218i	0.0449970	−	0.0779372i
$622$	−4.14214			−0.166085
$623$	19.8492	−	25.5965i	0.795243	−	1.02550i
$624$	−17.6569			−0.706840
$625$		0			0
$626$	−11.4645	−	19.8570i	−0.458212	−	0.793647i
$627$	−1.36396	−	2.36245i	−0.0544714	−	0.0943472i
$628$		0			0
$629$	−18.8701			−0.752398
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	9.41421	−	16.3059i	0.374477	−	0.648614i
$633$	14.0711	+	24.3718i	0.559275	+	0.968692i
$634$	14.0711	+	24.3718i	0.558833	+	0.967928i
$635$		0			0
$636$		0			0
$637$	29.7635	+	8.30153i	1.17927	+	0.328919i
$638$	6.82843			0.270340
$639$	0.292893	−	0.507306i	0.0115867	−	0.0200687i
$640$		0			0
$641$	−14.6066	−	25.2994i	−0.576926	−	0.999265i	−0.995829	−	0.0912345i	$-0.970919\pi$
$641$	−14.6066	−	25.2994i	−0.576926	−	0.999265i	0.418903	−	0.908031i	$-0.362415\pi$
$642$	8.89949	−	15.4144i	0.351235	−	0.608357i
$643$	6.55635			0.258557			0.129279	−	0.991608i	$-0.458734\pi$
$643$	6.55635			0.258557			0.129279	+	0.991608i	$0.458734\pi$
$644$		0			0
$645$		0			0
$646$	7.38478	−	12.7908i	0.290550	−	0.503248i
$647$	23.1924	+	40.1704i	0.911787	+	1.57926i	0.811539	+	0.584299i	$0.198630\pi$
$647$	23.1924	+	40.1704i	0.911787	+	1.57926i	0.100248	+	0.994962i	$0.468036\pi$
$648$	1.41421	+	2.44949i	0.0555556	+	0.0962250i
$649$	0.414214	−	0.717439i	0.0162593	−	0.0281619i
$650$		0			0
$651$	9.44975	−	12.1859i	0.370365	−	0.477603i
$652$		0			0
$653$	8.12132	−	14.0665i	0.317812	−	0.550466i	−0.662219	−	0.749310i	$-0.730385\pi$
$653$	8.12132	−	14.0665i	0.317812	−	0.550466i	0.980031	+	0.198844i	$0.0637186\pi$
$654$	−2.46447	−	4.26858i	−0.0963683	−	0.166915i
$655$		0			0
$656$	−12.4853	+	21.6251i	−0.487468	+	0.844320i
$657$	12.0711			0.470937
$658$	−18.8284	−	46.1200i	−0.734009	−	1.79795i
$659$	−4.68629			−0.182552			−0.0912760	−	0.995826i	$-0.529095\pi$
$659$	−4.68629			−0.182552			−0.0912760	+	0.995826i	$0.529095\pi$
$660$		0			0
$661$	−4.84315	−	8.38857i	−0.188377	−	0.326278i	0.756333	−	0.654187i	$-0.226989\pi$
$661$	−4.84315	−	8.38857i	−0.188377	−	0.326278i	−0.944709	+	0.327910i	$0.893656\pi$
$662$	−12.4645	−	21.5891i	−0.484445	−	0.839084i
$663$	4.94975	−	8.57321i	0.192232	−	0.332956i
$664$	7.31371			0.283827
$665$		0			0
$666$	11.8995			0.461096
$667$	9.24264	−	16.0087i	0.357876	−	0.619860i
$668$		0			0
$669$	11.4142	+	19.7700i	0.441299	+	0.764352i
$670$		0			0
$671$	−2.62742			−0.101430
$672$		0			0
$673$	−27.7279			−1.06883			−0.534416	−	0.845221i	$-0.679469\pi$
$673$	−27.7279			−1.06883			−0.534416	+	0.845221i	$0.679469\pi$
$674$	13.3640	−	23.1471i	0.514761	−	0.891591i
$675$		0			0
$676$		0			0
$677$	−7.94975	+	13.7694i	−0.305534	+	0.529200i	−0.977380	−	0.211491i	$-0.932168\pi$
$677$	−7.94975	+	13.7694i	−0.305534	+	0.529200i	0.671846	+	0.740691i	$0.265502\pi$
$678$	22.1421			0.850364
$679$	13.5563	+	1.85514i	0.520245	+	0.0711939i
$680$		0			0
$681$	4.46447	−	7.73268i	0.171079	−	0.296317i
$682$	2.41421	+	4.18154i	0.0924450	+	0.160119i
$683$	11.7071	+	20.2773i	0.447960	+	0.775889i	0.998253	−	0.0590821i	$-0.0188174\pi$
$683$	11.7071	+	20.2773i	0.447960	+	0.775889i	−0.550293	+	0.834972i	$0.685484\pi$
$684$		0			0
$685$		0			0
$686$	−21.0208	+	15.6245i	−0.802578	+	0.596547i
$687$	8.31371			0.317188
$688$	15.1716	−	26.2779i	0.578411	−	1.00184i
$689$	15.0711	+	26.1039i	0.574162	+	0.994478i
$690$		0			0
$691$	−3.84315	+	6.65652i	−0.146200	+	0.253226i	−0.929820	−	0.368014i	$-0.880038\pi$
$691$	−3.84315	+	6.65652i	−0.146200	+	0.253226i	0.783620	+	0.621241i	$0.213371\pi$
$692$		0			0
$693$	1.53553	+	0.210133i	0.0583301	+	0.00798229i
$694$	−12.6863			−0.481565
$695$		0			0
$696$	11.6569	+	20.1903i	0.441852	+	0.765310i
$697$	−7.00000	−	12.1244i	−0.265144	−	0.459243i
$698$	−20.2426	+	35.0613i	−0.766195	+	1.32709i
$699$	5.51472			0.208586
$700$		0			0
$701$	−1.21320			−0.0458221			−0.0229110	−	0.999738i	$-0.507293\pi$
$701$	−1.21320			−0.0458221			−0.0229110	+	0.999738i	$0.507293\pi$
$702$	−3.12132	+	5.40629i	−0.117807	+	0.204047i
$703$	−19.5919	−	33.9341i	−0.738922	−	1.27985i
$704$	−2.34315	−	4.05845i	−0.0883106	−	0.152958i
$705$		0			0
$706$	19.6569			0.739795
$707$	−2.24264	−	5.49333i	−0.0843432	−	0.206598i
$708$		0			0
$709$	−25.5563	+	44.2649i	−0.959789	+	1.66240i	−0.236781	+	0.971563i	$0.576092\pi$
$709$	−25.5563	+	44.2649i	−0.959789	+	1.66240i	−0.723008	+	0.690840i	$0.757241\pi$
$710$		0			0
$711$	−3.32843	−	5.76500i	−0.124826	−	0.216205i
$712$	−17.3137	+	29.9882i	−0.648859	+	1.12386i
$713$	13.0711			0.489515
$714$	3.17157	+	7.76874i	0.118693	+	0.290738i
$715$		0			0
$716$		0			0
$717$	2.65685	+	4.60181i	0.0992220	+	0.171858i
$718$	20.7990	+	36.0249i	0.776211	+	1.34444i
$719$	−17.2426	+	29.8651i	−0.643042	+	1.11378i	0.341708	+	0.939806i	$0.388995\pi$
$719$	−17.2426	+	29.8651i	−0.643042	+	1.11378i	−0.984750	+	0.173975i	$0.944339\pi$
$720$		0			0
$721$	11.7426	−	15.1427i	0.437319	−	0.563944i
$722$	3.79899			0.141384
$723$	10.8284	−	18.7554i	0.402714	−	0.697520i
$724$		0			0
$725$		0			0
$726$	7.53553	−	13.0519i	0.279670	−	0.484402i
$727$	−13.2426			−0.491142			−0.245571	−	0.969379i	$-0.578976\pi$
$727$	−13.2426			−0.491142			−0.245571	+	0.969379i	$0.578976\pi$
$728$	−32.7279	−	4.47871i	−1.21298	−	0.165992i
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.50610	+	14.7330i	0.314609	+	0.544919i
$732$		0			0
$733$	−9.62132	+	16.6646i	−0.355372	+	0.615522i	−0.987181	−	0.159602i	$-0.948979\pi$
$733$	−9.62132	+	16.6646i	−0.355372	+	0.615522i	0.631810	+	0.775123i	$0.282312\pi$
$734$	31.6985			1.17001
$735$		0			0
$736$		0			0
$737$	−4.02082	+	6.96426i	−0.148109	+	0.256532i
$738$	4.41421	+	7.64564i	0.162489	+	0.281440i
$739$	3.42893	+	5.93908i	0.126135	+	0.218473i	0.922176	−	0.386770i	$-0.126409\pi$
$739$	3.42893	+	5.93908i	0.126135	+	0.218473i	−0.796041	+	0.605243i	$0.793076\pi$
$740$		0			0
$741$	20.5563			0.755156
$742$	−25.3137	−	3.46410i	−0.929295	−	0.127171i
$743$	−20.7279			−0.760434			−0.380217	−	0.924897i	$-0.624151\pi$
$743$	−20.7279			−0.760434			−0.380217	+	0.924897i	$0.624151\pi$
$744$	−8.24264	+	14.2767i	−0.302190	+	0.523408i
$745$		0			0
$746$	7.60660	+	13.1750i	0.278497	+	0.482372i
$747$	1.29289	−	2.23936i	0.0473045	−	0.0819338i
$748$		0			0
$749$	20.4056	−	26.3140i	0.745604	−	0.961492i
$750$		0			0
$751$	12.8137	−	22.1940i	0.467579	−	0.809870i	−0.531735	−	0.846911i	$-0.678460\pi$
$751$	12.8137	−	22.1940i	0.467579	−	0.809870i	0.999314	+	0.0370405i	$0.0117931\pi$
$752$	26.6274	+	46.1200i	0.971002	+	1.68182i
$753$	1.29289	+	2.23936i	0.0471156	+	0.0816067i
$754$	−25.7279	+	44.5621i	−0.936956	+	1.62285i
$755$		0			0
$756$		0			0
$757$	37.5980			1.36652			0.683261	−	0.730174i	$-0.260561\pi$
$757$	37.5980			1.36652			0.683261	+	0.730174i	$0.260561\pi$
$758$	17.5355	−	30.3724i	0.636919	−	1.10318i
$759$	0.656854	+	1.13770i	0.0238423	+	0.0412961i
$760$		0			0
$761$	17.5355	−	30.3724i	0.635663	−	1.10100i	−0.350712	−	0.936483i	$-0.614060\pi$
$761$	17.5355	−	30.3724i	0.635663	−	1.10100i	0.986374	−	0.164516i	$-0.0526064\pi$
$762$	5.55635			0.201285
$763$	−3.48528	−	8.53716i	−0.126176	−	0.309066i
$764$		0			0
$765$		0			0
$766$	−3.17157	−	5.49333i	−0.114594	−	0.198482i
$767$	3.12132	+	5.40629i	0.112704	+	0.195210i
$768$		0			0
$769$	17.9706			0.648035			0.324018	−	0.946051i	$-0.394966\pi$
$769$	17.9706			0.648035			0.324018	+	0.946051i	$0.394966\pi$
$770$		0			0
$771$	10.1005			0.363761
$772$		0			0
$773$	19.5355	+	33.8365i	0.702644	+	1.21702i	0.967535	+	0.252737i	$0.0813308\pi$
$773$	19.5355	+	33.8365i	0.702644	+	1.21702i	−0.264891	+	0.964278i	$0.585336\pi$
$774$	−5.36396	−	9.29065i	−0.192804	−	0.333946i
$775$		0			0
$776$	−14.6274			−0.525094
$777$	22.0563	+	3.01834i	0.791267	+	0.108282i
$778$	−52.1421			−1.86939
$779$	14.5355	−	25.1763i	0.520790	−	0.902034i
$780$		0			0
$781$	0.171573	+	0.297173i	0.00613936	+	0.0106337i
$782$	−3.55635	+	6.15978i	−0.127175	+	0.220273i
$783$	8.24264			0.294568
$784$	20.0000	−	19.5959i	0.714286	−	0.699854i
$785$		0			0
$786$	−4.58579	+	7.94282i	−0.163570	+	0.283311i
$787$	9.41421	+	16.3059i	0.335580	+	0.581242i	0.983596	−	0.180385i	$-0.0577342\pi$
$787$	9.41421	+	16.3059i	0.335580	+	0.581242i	−0.648016	+	0.761627i	$0.724401\pi$
$788$		0			0
$789$	3.41421	−	5.91359i	0.121549	−	0.210529i
$790$		0			0
$791$	41.0416	+	5.61642i	1.45927	+	0.199697i
$792$	−1.65685			−0.0588738
$793$	9.89949	−	17.1464i	0.351541	−	0.608888i
$794$	12.8787	+	22.3065i	0.457047	+	0.791629i
$795$		0			0
$796$		0			0
$797$	−41.5563			−1.47200			−0.736001	−	0.676981i	$-0.763288\pi$
$797$	−41.5563			−1.47200			−0.736001	+	0.676981i	$0.763288\pi$
$798$	−10.6777	+	13.7694i	−0.377985	+	0.487430i
$799$	−29.8579			−1.05630
$800$		0			0
$801$	6.12132	+	10.6024i	0.216286	+	0.374619i
$802$	11.6569	+	20.1903i	0.411618	+	0.712943i
$803$	−3.53553	+	6.12372i	−0.124766	+	0.216102i
$804$		0			0
$805$		0			0
$806$	−36.3848			−1.28160
$807$	10.0711	−	17.4436i	0.354518	−	0.614044i
$808$	3.17157	+	5.49333i	0.111576	+	0.193255i
$809$	−20.3137	−	35.1844i	−0.714192	−	1.23702i	−0.963270	−	0.268533i	$-0.913461\pi$
$809$	−20.3137	−	35.1844i	−0.714192	−	1.23702i	0.249078	−	0.968483i	$-0.419872\pi$
$810$		0			0
$811$	10.9706			0.385229			0.192614	−	0.981275i	$-0.438303\pi$
$811$	10.9706			0.385229			0.192614	+	0.981275i	$0.438303\pi$
$812$		0			0
$813$	−8.14214			−0.285557
$814$	−3.48528	+	6.03668i	−0.122159	+	0.211586i
$815$		0			0
$816$	−4.48528	−	7.76874i	−0.157016	−	0.271960i
$817$	−17.6630	+	30.5931i	−0.617948	+	1.07032i
$818$	−5.21320			−0.182275
$819$	−7.15685	+	9.22911i	−0.250081	+	0.322491i
$820$		0			0
$821$	8.77817	−	15.2042i	0.306360	−	0.530632i	−0.671203	−	0.741274i	$-0.734222\pi$
$821$	8.77817	−	15.2042i	0.306360	−	0.530632i	0.977563	+	0.210642i	$0.0675554\pi$
$822$	−12.0711	−	20.9077i	−0.421027	−	0.729240i
$823$	−17.1421	−	29.6910i	−0.597537	−	1.03496i	−0.993183	−	0.116562i	$-0.962813\pi$
$823$	−17.1421	−	29.6910i	−0.597537	−	1.03496i	0.395646	−	0.918403i	$-0.370521\pi$
$824$	−10.2426	+	17.7408i	−0.356819	+	0.618029i
$825$		0			0
$826$	−5.24264	−	0.717439i	−0.182415	−	0.0249629i
$827$	−7.17157			−0.249380			−0.124690	−	0.992196i	$-0.539794\pi$
$827$	−7.17157			−0.249380			−0.124690	+	0.992196i	$0.539794\pi$
$828$		0			0
$829$	3.67157	+	6.35935i	0.127519	+	0.220869i	0.922715	−	0.385483i	$-0.125965\pi$
$829$	3.67157	+	6.35935i	0.127519	+	0.220869i	−0.795196	+	0.606353i	$0.792632\pi$
$830$		0			0
$831$	6.69239	−	11.5916i	0.232156	−	0.402107i
$832$	35.3137			1.22428
$833$	3.90812	+	15.2042i	0.135408	+	0.526796i
$834$	−7.75736			−0.268615
$835$		0			0
$836$		0			0
$837$	2.91421	+	5.04757i	0.100730	+	0.174469i
$838$	6.24264	−	10.8126i	0.215648	−	0.373514i
$839$	−32.7279			−1.12989			−0.564947	−	0.825127i	$-0.691103\pi$
$839$	−32.7279			−1.12989			−0.564947	+	0.825127i	$0.691103\pi$
$840$		0			0
$841$	38.9411			1.34280
$842$	−7.43503	+	12.8778i	−0.256228	+	0.443800i
$843$	0.828427	+	1.43488i	0.0285325	+	0.0494198i
$844$		0			0
$845$		0			0
$846$	18.8284			0.647335
$847$	17.2782	−	22.2810i	0.593685	−	0.765585i
$848$	27.3137			0.937957
$849$	−2.37868	+	4.11999i	−0.0816361	+	0.141398i
$850$		0			0
$851$	9.43503	+	16.3419i	0.323429	+	0.560195i
$852$		0			0
$853$	44.0122			1.50695			0.753474	−	0.657477i	$-0.228376\pi$
$853$	44.0122			1.50695			0.753474	+	0.657477i	$0.228376\pi$
$854$	6.34315	+	15.5375i	0.217058	+	0.531681i
$855$		0			0
$856$	−17.7990	+	30.8288i	−0.608357	+	1.05371i
$857$	1.12132	+	1.94218i	0.0383036	+	0.0663437i	0.884542	−	0.466461i	$-0.154471\pi$
$857$	1.12132	+	1.94218i	0.0383036	+	0.0663437i	−0.846238	+	0.532805i	$0.821138\pi$
$858$	−1.82843	−	3.16693i	−0.0624215	−	0.108117i
$859$	−2.17157	+	3.76127i	−0.0740931	+	0.128333i	−0.900692	−	0.434459i	$-0.856940\pi$
$859$	−2.17157	+	3.76127i	−0.0740931	+	0.128333i	0.826598	+	0.562792i	$0.190273\pi$
$860$		0			0
$861$	6.24264	+	15.2913i	0.212749	+	0.521126i
$862$	44.0833			1.50148
$863$	14.8995	−	25.8067i	0.507185	−	0.878470i	−0.492781	−	0.870154i	$-0.664020\pi$
$863$	14.8995	−	25.8067i	0.507185	−	0.878470i	0.999965	−	0.00831615i	$-0.00264714\pi$
$864$		0			0
$865$		0			0
$866$	4.63604	−	8.02986i	0.157539	−	0.272866i
$867$	−11.9706			−0.406542
$868$		0			0
$869$	3.89949			0.132281
$870$		0			0
$871$	−30.2990	−	52.4794i	−1.02664	−	1.77820i
$872$	4.92893	+	8.53716i	0.166915	+	0.289105i
$873$	−2.58579	+	4.47871i	−0.0875156	+	0.151581i
$874$	−14.7696			−0.499588
$875$		0			0
$876$		0			0
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	−0.977018	−	0.213158i	$-0.931625\pi$
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	0.673109	+	0.739543i	$0.264958\pi$
$878$	−8.24264	−	14.2767i	−0.278176	−	0.481814i
$879$	3.65685	+	6.33386i	0.123343	+	0.213636i
$880$		0			0
$881$	−10.3431			−0.348469			−0.174235	−	0.984704i	$-0.555745\pi$
$881$	−10.3431			−0.348469			−0.174235	+	0.984704i	$0.555745\pi$
$882$	−2.46447	−	9.58783i	−0.0829829	−	0.322839i
$883$	6.07107			0.204308			0.102154	−	0.994769i	$-0.467427\pi$
$883$	6.07107			0.204308			0.102154	+	0.994769i	$0.467427\pi$
$884$		0			0
$885$		0			0
$886$	−11.6569	−	20.1903i	−0.391620	−	0.678305i
$887$	−18.6066	+	32.2276i	−0.624749	+	1.08210i	0.363841	+	0.931461i	$0.381465\pi$
$887$	−18.6066	+	32.2276i	−0.624749	+	1.08210i	−0.988589	+	0.150635i	$0.951868\pi$
$888$	−23.7990			−0.798642
$889$	10.2990	+	1.40938i	0.345417	+	0.0472692i
$890$		0			0
$891$	−0.292893	+	0.507306i	−0.00981229	+	0.0169954i
$892$		0			0
$893$	−31.0000	−	53.6936i	−1.03738	−	1.79679i
$894$	−4.48528	+	7.76874i	−0.150010	+	0.259825i
$895$		0			0
$896$	−18.3431	+	23.6544i	−0.612801	+	0.790237i
$897$	−9.89949			−0.330535
$898$	−19.0711	+	33.0321i	−0.636410	+	1.10229i
$899$	24.0208	+	41.6053i	0.801139	+	1.38761i
$900$		0			0
$901$	−7.65685	+	13.2621i	−0.255087	+	0.441823i
$902$	−5.17157			−0.172195
$903$	−7.58579	−	18.5813i	−0.252439	−	0.618347i
$904$	−44.2843			−1.47287
$905$		0			0
$906$	−7.41421	−	12.8418i	−0.246321	−	0.426640i
$907$	−22.6924	−	39.3044i	−0.753488	−	1.30508i	−0.946122	−	0.323809i	$-0.895036\pi$
$907$	−22.6924	−	39.3044i	−0.753488	−	1.30508i	0.192634	−	0.981271i	$-0.438297\pi$
$908$		0			0
$909$	2.24264			0.0743837
$910$		0			0
$911$	−4.24264			−0.140565			−0.0702825	−	0.997527i	$-0.522390\pi$
$911$	−4.24264			−0.140565			−0.0702825	+	0.997527i	$0.522390\pi$
$912$	9.31371	−	16.1318i	0.308408	−	0.534178i
$913$	0.757359	+	1.31178i	0.0250649	+	0.0434137i
$914$	−0.778175	−	1.34784i	−0.0257397	−	0.0445825i
$915$		0			0
$916$		0			0
$917$	−10.5147	+	13.5592i	−0.347227	+	0.447765i
$918$	−3.17157			−0.104678
$919$	17.6716	−	30.6081i	0.582931	−	1.00967i	−0.412198	−	0.911094i	$-0.635239\pi$
$919$	17.6716	−	30.6081i	0.582931	−	1.00967i	0.995130	−	0.0985727i	$-0.0314277\pi$
$920$		0			0
$921$	2.20711	+	3.82282i	0.0727266	+	0.125966i
$922$	9.14214	−	15.8346i	0.301080	−	0.521486i
$923$	−2.58579			−0.0851122
$924$		0			0
$925$		0			0
$926$	−5.36396	+	9.29065i	−0.176271	+	0.305310i
$927$	3.62132	+	6.27231i	0.118940	+	0.206010i
$928$		0			0
$929$	−15.5061	+	26.8573i	−0.508739	+	0.881161i	0.491210	+	0.871041i	$0.336555\pi$
$929$	−15.5061	+	26.8573i	−0.508739	+	0.881161i	−0.999949	+	0.0101199i	$0.996779\pi$
$930$		0			0
$931$	−23.2843	+	22.8138i	−0.763111	+	0.747693i
$932$		0			0
$933$	1.46447	−	2.53653i	0.0479445	−	0.0830423i
$934$	20.7279	+	35.9018i	0.678238	+	1.17474i
$935$		0			0
$936$	6.24264	−	10.8126i	0.204047	−	0.353420i
$937$	22.0711			0.721030			0.360515	−	0.932753i	$-0.382601\pi$
$937$	22.0711			0.721030			0.360515	+	0.932753i	$0.382601\pi$
$938$	50.8909	+	6.96426i	1.66165	+	0.227391i
$939$	16.2132			0.529098
$940$		0			0
$941$	18.3640	+	31.8073i	0.598648	+	1.03689i	0.993021	+	0.117938i	$0.0376285\pi$
$941$	18.3640	+	31.8073i	0.598648	+	1.03689i	−0.394373	+	0.918950i	$0.629038\pi$
$942$	8.58579	+	14.8710i	0.279740	+	0.484524i
$943$	−7.00000	+	12.1244i	−0.227951	+	0.394823i
$944$	5.65685			0.184115
$945$		0			0
$946$	6.28427			0.204319
$947$	−9.53553	+	16.5160i	−0.309863	+	0.536699i	−0.978332	−	0.207041i	$-0.933617\pi$
$947$	−9.53553	+	16.5160i	−0.309863	+	0.536699i	0.668469	+	0.743740i	$0.266950\pi$
$948$		0			0
$949$	−26.6421	−	46.1455i	−0.864840	−	1.49795i
$950$		0			0
$951$	−19.8995			−0.645285
$952$	−6.34315	−	15.5375i	−0.205583	−	0.503572i
$953$	−31.5147			−1.02086			−0.510431	−	0.859919i	$-0.670514\pi$
$953$	−31.5147			−1.02086			−0.510431	+	0.859919i	$0.670514\pi$
$954$	4.82843	−	8.36308i	0.156326	−	0.270765i
$955$		0			0
$956$		0			0
$957$	−2.41421	+	4.18154i	−0.0780404	+	0.135170i
$958$	15.0294			0.485579
$959$	−17.0711	−	41.8154i	−0.551254	−	1.35029i
$960$		0			0
$961$	−1.48528	+	2.57258i	−0.0479123	+	0.0829865i
$962$	−26.2635	−	45.4896i	−0.846768	−	1.46664i
$963$	6.29289	+	10.8996i	0.202786	+	0.351235i
$964$		0			0
$965$		0			0
$966$	5.14214	−	6.63103i	0.165446	−	0.213350i
$967$	13.3848			0.430425			0.215213	−	0.976567i	$-0.430956\pi$
$967$	13.3848			0.430425			0.215213	+	0.976567i	$0.430956\pi$
$968$	−15.0711	+	26.1039i	−0.484402	+	0.839010i
$969$	5.22183	+	9.04447i	0.167749	+	0.290550i
$970$		0			0
$971$	−12.8284	+	22.2195i	−0.411684	+	0.713057i	−0.995074	−	0.0991347i	$-0.968393\pi$
$971$	−12.8284	+	22.2195i	−0.411684	+	0.713057i	0.583390	+	0.812192i	$0.301726\pi$
$972$		0			0
$973$	−14.3787	−	1.96768i	−0.460959	−	0.0630808i
$974$	26.7279			0.856418
$975$		0			0
$976$	−8.97056	−	15.5375i	−0.287141	−	0.497342i
$977$	−22.8492	−	39.5760i	−0.731012	−	1.26615i	−0.956451	−	0.291893i	$-0.905715\pi$
$977$	−22.8492	−	39.5760i	−0.731012	−	1.26615i	0.225439	−	0.974257i	$-0.427618\pi$
$978$	2.34315	−	4.05845i	0.0749255	−	0.129775i
$979$	−7.17157			−0.229204
$980$		0			0
$981$	3.48528			0.111276
$982$	−12.8284	+	22.2195i	−0.409372	+	0.709052i
$983$	−28.5772	−	49.4971i	−0.911470	−	1.57871i	−0.811989	−	0.583673i	$-0.801615\pi$
$983$	−28.5772	−	49.4971i	−0.911470	−	1.57871i	−0.0994811	−	0.995039i	$-0.531718\pi$
$984$	−8.82843	−	15.2913i	−0.281440	−	0.487468i
$985$		0			0
$986$	−26.1421			−0.832535
$987$	34.8995	+	4.77589i	1.11086	+	0.152018i
$988$		0			0
$989$	8.50610	−	14.7330i	0.270478	−	0.468482i
$990$		0			0
$991$	9.67157	+	16.7517i	0.307228	+	0.532134i	0.977755	−	0.209751i	$-0.0672654\pi$
$991$	9.67157	+	16.7517i	0.307228	+	0.532134i	−0.670527	+	0.741885i	$0.733932\pi$
$992$		0			0
$993$	17.6274			0.559389
$994$	1.34315	−	1.73205i	0.0426020	−	0.0549373i
$995$		0			0
$996$		0			0
$997$	4.62132	+	8.00436i	0.146359	+	0.253501i	0.929879	−	0.367865i	$-0.119911\pi$
$997$	4.62132	+	8.00436i	0.146359	+	0.253501i	−0.783520	+	0.621366i	$0.786578\pi$
$998$	21.7782	+	37.7209i	0.689376	+	1.19403i
$999$	−4.20711	+	7.28692i	−0.133107	+	0.230548i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.g.226.1		4
5.2	odd	4		525.2.r.g.499.1		8
5.3	odd	4		525.2.r.g.499.4		8
5.4	even	2		105.2.i.c.16.2	✓	4
7.2	even	3		3675.2.a.z.1.2		2
7.4	even	3	inner	525.2.i.g.151.1		4
7.5	odd	6		3675.2.a.x.1.2		2
15.14	odd	2		315.2.j.d.226.1		4
20.19	odd	2		1680.2.bg.p.961.2		4
35.4	even	6		105.2.i.c.46.2	yes	4
35.9	even	6		735.2.a.i.1.1		2
35.18	odd	12		525.2.r.g.424.1		8
35.19	odd	6		735.2.a.j.1.1		2
35.24	odd	6		735.2.i.j.361.2		4
35.32	odd	12		525.2.r.g.424.4		8
35.34	odd	2		735.2.i.j.226.2		4
105.44	odd	6		2205.2.a.u.1.2		2
105.74	odd	6		315.2.j.d.46.1		4
105.89	even	6		2205.2.a.s.1.2		2
140.39	odd	6		1680.2.bg.p.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.c.16.2	✓	4	5.4	even	2
105.2.i.c.46.2	yes	4	35.4	even	6
315.2.j.d.46.1		4	105.74	odd	6
315.2.j.d.226.1		4	15.14	odd	2
525.2.i.g.151.1		4	7.4	even	3	inner
525.2.i.g.226.1		4	1.1	even	1	trivial
525.2.r.g.424.1		8	35.18	odd	12
525.2.r.g.424.4		8	35.32	odd	12
525.2.r.g.499.1		8	5.2	odd	4
525.2.r.g.499.4		8	5.3	odd	4
735.2.a.i.1.1		2	35.9	even	6
735.2.a.j.1.1		2	35.19	odd	6
735.2.i.j.226.2		4	35.34	odd	2
735.2.i.j.361.2		4	35.24	odd	6
1680.2.bg.p.961.2		4	20.19	odd	2
1680.2.bg.p.1201.2		4	140.39	odd	6
2205.2.a.s.1.2		2	105.89	even	6
2205.2.a.u.1.2		2	105.44	odd	6
3675.2.a.x.1.2		2	7.5	odd	6
3675.2.a.z.1.2		2	7.2	even	3

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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

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	525.2.i.g.226.1

Level	$525$
Weight	$2$
Character	525.226
Analytic conductor	$4.192$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$