LMFDB - Embedded newform 1530.2.m.h.647.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(647,1530)] 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("1530.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.17364600040304039428096.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 20 x^{14} - 40 x^{13} + 104 x^{12} - 180 x^{11} + 242 x^{10} - 132 x^{9} - 302 x^{8} + \cdots + 1 $ x^16 - 4x^15 + 20x^14 - 40x^13 + 104x^12 - 180x^11 + 242x^10 - 132x^9 - 302x^8 + 416x^7 + 296x^6 - 416x^5 + 2x^4 + 32x^3 + 46x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.3
Root			$0.776205 - 1.87392i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.h.953.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.64468 - 1.51493i) q^{5} +(0.552409 + 0.552409i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0917505 + 2.23418i) q^{10} +6.31923i q^{11} +(-2.87834 + 2.87834i) q^{13} -0.781225 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +0.819950i q^{19} +(-1.51493 - 1.64468i) q^{20} +(-4.46837 - 4.46837i) q^{22} +(1.74540 + 1.74540i) q^{23} +(0.409975 - 4.98316i) q^{25} -4.07059i q^{26} +(0.552409 - 0.552409i) q^{28} -4.59231 q^{29} -8.39314 q^{31} +(0.707107 - 0.707107i) q^{32} -1.00000i q^{34} +(1.74540 + 0.0716778i) q^{35} +(-5.24725 - 5.24725i) q^{37} +(-0.579792 - 0.579792i) q^{38} +(2.23418 + 0.0917505i) q^{40} +9.72745i q^{41} +(-6.34671 + 6.34671i) q^{43} +6.31923 q^{44} -2.46837 q^{46} +(0.839302 - 0.839302i) q^{47} -6.38969i q^{49} +(3.23373 + 3.81353i) q^{50} +(2.87834 + 2.87834i) q^{52} +(2.65638 + 2.65638i) q^{53} +(9.57319 + 10.3931i) q^{55} +0.781225i q^{56} +(3.24725 - 3.24725i) q^{58} +9.73233 q^{59} +12.1498 q^{61} +(5.93485 - 5.93485i) q^{62} +1.00000i q^{64} +(-0.373479 + 9.09446i) q^{65} +(-11.2680 - 11.2680i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-1.28487 + 1.18350i) q^{70} +10.9353i q^{71} +(-2.69484 + 2.69484i) q^{73} +7.42074 q^{74} +0.819950 q^{76} +(-3.49080 + 3.49080i) q^{77} +16.7948i q^{79} +(-1.64468 + 1.51493i) q^{80} +(-6.87834 - 6.87834i) q^{82} +(6.72697 + 6.72697i) q^{83} +(-0.0917505 + 2.23418i) q^{85} -8.97561i q^{86} +(-4.46837 + 4.46837i) q^{88} -7.62705 q^{89} -3.18005 q^{91} +(1.74540 - 1.74540i) q^{92} +1.18695i q^{94} +(1.24217 + 1.34856i) q^{95} +(3.34671 + 3.34671i) q^{97} +(4.51819 + 4.51819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70}+ \cdots - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.64468	−	1.51493i	0.735525	−	0.677497i
$5$	1.64468	−	1.51493i	0.735525	−	0.677497i
$6$		0			0
$7$	0.552409	+	0.552409i	0.208791	+	0.208791i	0.803754	−	0.594962i	$-0.202833\pi$
$7$	0.552409	+	0.552409i	0.208791	+	0.208791i	−0.594962	+	0.803754i	$0.702833\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.0917505	+	2.23418i	−0.0290141	+	0.706511i
$11$			6.31923i			1.90532i	0.304039	+	0.952660i	$0.401665\pi$
$11$			6.31923i			1.90532i	−0.304039	+	0.952660i	$0.598335\pi$
$12$		0			0
$13$	−2.87834	+	2.87834i	−0.798309	+	0.798309i	−0.982829	−	0.184520i	$-0.940927\pi$
$13$	−2.87834	+	2.87834i	−0.798309	+	0.798309i	0.184520	+	0.982829i	$0.440927\pi$
$14$	−0.781225			−0.208791
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$			0.819950i			0.188109i	0.995567	+	0.0940547i	$0.0299829\pi$
$19$			0.819950i			0.188109i	−0.995567	+	0.0940547i	$0.970017\pi$
$20$	−1.51493	−	1.64468i	−0.338749	−	0.367763i
$21$		0			0
$22$	−4.46837	−	4.46837i	−0.952660	−	0.952660i
$23$	1.74540	+	1.74540i	0.363941	+	0.363941i	0.865262	−	0.501320i	$-0.167152\pi$
$23$	1.74540	+	1.74540i	0.363941	+	0.363941i	−0.501320	+	0.865262i	$0.667152\pi$
$24$		0			0
$25$	0.409975	−	4.98316i	0.0819950	−	0.996633i
$26$		−	4.07059i		−	0.798309i
$27$		0			0
$28$	0.552409	−	0.552409i	0.104396	−	0.104396i
$29$	−4.59231			−0.852770			−0.426385	−	0.904542i	$-0.640213\pi$
$29$	−4.59231			−0.852770			−0.426385	+	0.904542i	$0.640213\pi$
$30$		0			0
$31$	−8.39314			−1.50745			−0.753726	−	0.657189i	$-0.771745\pi$
$31$	−8.39314			−1.50745			−0.753726	+	0.657189i	$0.771745\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	1.00000i		−	0.171499i
$35$	1.74540	+	0.0716778i	0.295027	+	0.0121158i
$36$		0			0
$37$	−5.24725	−	5.24725i	−0.862643	−	0.862643i	0.129001	−	0.991644i	$-0.458823\pi$
$37$	−5.24725	−	5.24725i	−0.862643	−	0.862643i	−0.991644	+	0.129001i	$0.958823\pi$
$38$	−0.579792	−	0.579792i	−0.0940547	−	0.0940547i
$39$		0			0
$40$	2.23418	+	0.0917505i	0.353256	+	0.0145070i
$41$			9.72745i			1.51917i	0.650407	+	0.759586i	$0.274598\pi$
$41$			9.72745i			1.51917i	−0.650407	+	0.759586i	$0.725402\pi$
$42$		0			0
$43$	−6.34671	+	6.34671i	−0.967865	+	0.967865i	−0.999500	−	0.0316346i	$-0.989929\pi$
$43$	−6.34671	+	6.34671i	−0.967865	+	0.967865i	0.0316346	+	0.999500i	$0.489929\pi$
$44$	6.31923			0.952660
$45$		0			0
$46$	−2.46837			−0.363941
$47$	0.839302	−	0.839302i	0.122425	−	0.122425i	−0.643240	−	0.765665i	$-0.722410\pi$
$47$	0.839302	−	0.839302i	0.122425	−	0.122425i	0.765665	+	0.643240i	$0.222410\pi$
$48$		0			0
$49$		−	6.38969i		−	0.912813i
$50$	3.23373	+	3.81353i	0.457319	+	0.539314i
$51$		0			0
$52$	2.87834	+	2.87834i	0.399155	+	0.399155i
$53$	2.65638	+	2.65638i	0.364882	+	0.364882i	0.865607	−	0.500725i	$-0.166933\pi$
$53$	2.65638	+	2.65638i	0.364882	+	0.364882i	−0.500725	+	0.865607i	$0.666933\pi$
$54$		0			0
$55$	9.57319	+	10.3931i	1.29085	+	1.40141i
$56$			0.781225i			0.104396i
$57$		0			0
$58$	3.24725	−	3.24725i	0.426385	−	0.426385i
$59$	9.73233			1.26704			0.633521	−	0.773726i	$-0.281609\pi$
$59$	9.73233			1.26704			0.633521	+	0.773726i	$0.281609\pi$
$60$		0			0
$61$	12.1498			1.55563			0.777813	−	0.628496i	$-0.216329\pi$
$61$	12.1498			1.55563			0.777813	+	0.628496i	$0.216329\pi$
$62$	5.93485	−	5.93485i	0.753726	−	0.753726i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.373479	+	9.09446i	−0.0463244	+	1.12803i
$66$		0			0
$67$	−11.2680	−	11.2680i	−1.37661	−	1.37661i	−0.850282	−	0.526327i	$-0.823569\pi$
$67$	−11.2680	−	11.2680i	−1.37661	−	1.37661i	−0.526327	−	0.850282i	$-0.676431\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$		0			0
$70$	−1.28487	+	1.18350i	−0.153571	+	0.141455i
$71$			10.9353i			1.29779i	0.760879	+	0.648894i	$0.224768\pi$
$71$			10.9353i			1.29779i	−0.760879	+	0.648894i	$0.775232\pi$
$72$		0			0
$73$	−2.69484	+	2.69484i	−0.315408	+	0.315408i	−0.847000	−	0.531593i	$-0.821594\pi$
$73$	−2.69484	+	2.69484i	−0.315408	+	0.315408i	0.531593	+	0.847000i	$0.321594\pi$
$74$	7.42074			0.862643
$75$		0			0
$76$	0.819950			0.0940547
$77$	−3.49080	+	3.49080i	−0.397814	+	0.397814i
$78$		0			0
$79$			16.7948i			1.88956i	0.327702	+	0.944781i	$0.393726\pi$
$79$			16.7948i			1.88956i	−0.327702	+	0.944781i	$0.606274\pi$
$80$	−1.64468	+	1.51493i	−0.183881	+	0.169374i
$81$		0			0
$82$	−6.87834	−	6.87834i	−0.759586	−	0.759586i
$83$	6.72697	+	6.72697i	0.738381	+	0.738381i	0.972265	−	0.233883i	$-0.0751434\pi$
$83$	6.72697	+	6.72697i	0.738381	+	0.738381i	−0.233883	+	0.972265i	$0.575143\pi$
$84$		0			0
$85$	−0.0917505	+	2.23418i	−0.00995174	+	0.242331i
$86$		−	8.97561i		−	0.967865i
$87$		0			0
$88$	−4.46837	+	4.46837i	−0.476330	+	0.476330i
$89$	−7.62705			−0.808466			−0.404233	−	0.914656i	$-0.632461\pi$
$89$	−7.62705			−0.808466			−0.404233	+	0.914656i	$0.632461\pi$
$90$		0			0
$91$	−3.18005			−0.333360
$92$	1.74540	−	1.74540i	0.181971	−	0.181971i
$93$		0			0
$94$			1.18695i			0.122425i
$95$	1.24217	+	1.34856i	0.127444	+	0.138359i
$96$		0			0
$97$	3.34671	+	3.34671i	0.339807	+	0.339807i	0.856295	−	0.516487i	$-0.172761\pi$
$97$	3.34671	+	3.34671i	0.339807	+	0.339807i	−0.516487	+	0.856295i	$0.672761\pi$
$98$	4.51819	+	4.51819i	0.456406	+	0.456406i
$99$		0			0
$100$	−4.98316	−	0.409975i	−0.498316	−	0.0409975i
$101$			11.6558i			1.15980i	0.814689	+	0.579898i	$0.196908\pi$
$101$			11.6558i			1.15980i	−0.814689	+	0.579898i	$0.803092\pi$
$102$		0			0
$103$	7.49796	−	7.49796i	0.738796	−	0.738796i	−0.233549	−	0.972345i	$-0.575034\pi$
$103$	7.49796	−	7.49796i	0.738796	−	0.738796i	0.972345	+	0.233549i	$0.0750340\pi$
$104$	−4.07059			−0.399155
$105$		0			0
$106$	−3.75669			−0.364882
$107$	5.33657	−	5.33657i	0.515906	−	0.515906i	−0.400424	−	0.916330i	$-0.631137\pi$
$107$	5.33657	−	5.33657i	0.515906	−	0.515906i	0.916330	+	0.400424i	$0.131137\pi$
$108$		0			0
$109$		−	2.92822i		−	0.280473i	−0.990118	−	0.140236i	$-0.955214\pi$
$109$		−	2.92822i		−	0.280473i	0.990118	−	0.140236i	$-0.0447862\pi$
$110$	−14.1183	−	0.579792i	−1.34613	−	0.0552810i
$111$		0			0
$112$	−0.552409	−	0.552409i	−0.0521978	−	0.0521978i
$113$	−9.72257	−	9.72257i	−0.914622	−	0.914622i	0.0820093	−	0.996632i	$-0.473866\pi$
$113$	−9.72257	−	9.72257i	−0.914622	−	0.914622i	−0.996632	+	0.0820093i	$0.973866\pi$
$114$		0			0
$115$	5.51479	+	0.226474i	0.514257	+	0.0211188i
$116$			4.59231i			0.426385i
$117$		0			0
$118$	−6.88180	+	6.88180i	−0.633521	+	0.633521i
$119$	−0.781225			−0.0716148
$120$		0			0
$121$	−28.9327			−2.63024
$122$	−8.59123	+	8.59123i	−0.777813	+	0.777813i
$123$		0			0
$124$			8.39314i			0.753726i
$125$	−6.87486	−	8.81682i	−0.614906	−	0.788600i
$126$		0			0
$127$	8.50993	+	8.50993i	0.755134	+	0.755134i	0.975433	−	0.220299i	$-0.0707031\pi$
$127$	8.50993	+	8.50993i	0.755134	+	0.755134i	−0.220299	+	0.975433i	$0.570703\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−6.16666	−	6.69484i	−0.540852	−	0.587177i
$131$		−	5.45612i		−	0.476703i	−0.971179	−	0.238352i	$-0.923393\pi$
$131$		−	5.45612i		−	0.476703i	0.971179	−	0.238352i	$-0.0766071\pi$
$132$		0			0
$133$	−0.452948	+	0.452948i	−0.0392756	+	0.0392756i
$134$	15.9354			1.37661
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	6.38000	−	6.38000i	0.545080	−	0.545080i	−0.379933	−	0.925014i	$-0.624053\pi$
$137$	6.38000	−	6.38000i	0.545080	−	0.545080i	0.925014	+	0.379933i	$0.124053\pi$
$138$		0			0
$139$			10.1237i			0.858680i	0.903143	+	0.429340i	$0.141254\pi$
$139$			10.1237i			0.858680i	−0.903143	+	0.429340i	$0.858746\pi$
$140$	0.0716778	−	1.74540i	0.00605788	−	0.147513i
$141$		0			0
$142$	−7.73246	−	7.73246i	−0.648894	−	0.648894i
$143$	−18.1889	−	18.1889i	−1.52103	−	1.52103i
$144$		0			0
$145$	−7.55290	+	6.95703i	−0.627234	+	0.577750i
$146$		−	3.81108i		−	0.315408i
$147$		0			0
$148$	−5.24725	+	5.24725i	−0.431322	+	0.431322i
$149$	8.42451			0.690163			0.345081	−	0.938573i	$-0.387851\pi$
$149$	8.42451			0.690163			0.345081	+	0.938573i	$0.387851\pi$
$150$		0			0
$151$	2.66259			0.216678			0.108339	−	0.994114i	$-0.465447\pi$
$151$	2.66259			0.216678			0.108339	+	0.994114i	$0.465447\pi$
$152$	−0.579792	+	0.579792i	−0.0470274	+	0.0470274i
$153$		0			0
$154$		−	4.93674i		−	0.397814i
$155$	−13.8041	+	12.7150i	−1.10877	+	1.02129i
$156$		0			0
$157$	9.98316	+	9.98316i	0.796743	+	0.796743i	0.982581	−	0.185837i	$-0.0594997\pi$
$157$	9.98316	+	9.98316i	0.796743	+	0.796743i	−0.185837	+	0.982581i	$0.559500\pi$
$158$	−11.8757	−	11.8757i	−0.944781	−	0.944781i
$159$		0			0
$160$	0.0917505	−	2.23418i	0.00725351	−	0.176628i
$161$			1.92835i			0.151975i
$162$		0			0
$163$	11.3037	−	11.3037i	0.885377	−	0.885377i	−0.108698	−	0.994075i	$-0.534668\pi$
$163$	11.3037	−	11.3037i	0.885377	−	0.885377i	0.994075	+	0.108698i	$0.0346680\pi$
$164$	9.72745			0.759586
$165$		0			0
$166$	−9.51338			−0.738381
$167$	−5.35505	+	5.35505i	−0.414386	+	0.414386i	−0.883263	−	0.468877i	$-0.844659\pi$
$167$	−5.35505	+	5.35505i	−0.414386	+	0.414386i	0.468877	+	0.883263i	$0.344659\pi$
$168$		0			0
$169$		−	3.56974i		−	0.274595i
$170$	−1.51493	−	1.64468i	−0.116190	−	0.126142i
$171$		0			0
$172$	6.34671	+	6.34671i	0.483932	+	0.483932i
$173$	−13.4088	−	13.4088i	−1.01945	−	1.01945i	−0.999807	−	0.0196435i	$-0.993747\pi$
$173$	−13.4088	−	13.4088i	−1.01945	−	1.01945i	−0.0196435	−	0.999807i	$-0.506253\pi$
$174$		0			0
$175$	2.97922	−	2.52627i	0.225208	−	0.190968i
$176$		−	6.31923i		−	0.476330i
$177$		0			0
$178$	5.39314	−	5.39314i	0.404233	−	0.404233i
$179$	11.5445			0.862878			0.431439	−	0.902142i	$-0.358006\pi$
$179$	11.5445			0.862878			0.431439	+	0.902142i	$0.358006\pi$
$180$		0			0
$181$	11.2952			0.839567			0.419784	−	0.907624i	$-0.362106\pi$
$181$	11.2952			0.839567			0.419784	+	0.907624i	$0.362106\pi$
$182$	2.24863	−	2.24863i	0.166680	−	0.166680i
$183$		0			0
$184$			2.46837i			0.181971i
$185$	−16.5793	−	0.680856i	−1.21893	−	0.0500575i
$186$		0			0
$187$	−4.46837	−	4.46837i	−0.326760	−	0.326760i
$188$	−0.839302	−	0.839302i	−0.0612124	−	0.0612124i
$189$		0			0
$190$	−1.83192	−	0.0752308i	−0.132901	−	0.00545782i
$191$			12.2356i			0.885336i	0.896685	+	0.442668i	$0.145968\pi$
$191$			12.2356i			0.885336i	−0.896685	+	0.442668i	$0.854032\pi$
$192$		0			0
$193$	−11.7137	+	11.7137i	−0.843172	+	0.843172i	−0.989270	−	0.146098i	$-0.953328\pi$
$193$	−11.7137	+	11.7137i	−0.843172	+	0.843172i	0.146098	+	0.989270i	$0.453328\pi$
$194$	−4.73297			−0.339807
$195$		0			0
$196$	−6.38969			−0.456406
$197$	−5.18301	+	5.18301i	−0.369274	+	0.369274i	−0.867212	−	0.497938i	$-0.834091\pi$
$197$	−5.18301	+	5.18301i	−0.369274	+	0.369274i	0.497938	+	0.867212i	$0.334091\pi$
$198$		0			0
$199$		−	4.76014i		−	0.337437i	−0.985664	−	0.168719i	$-0.946037\pi$
$199$		−	4.76014i		−	0.337437i	0.985664	−	0.168719i	$-0.0539629\pi$
$200$	3.81353	−	3.23373i	0.269657	−	0.228659i
$201$		0			0
$202$	−8.24190	−	8.24190i	−0.579898	−	0.579898i
$203$	−2.53684	−	2.53684i	−0.178051	−	0.178051i
$204$		0			0
$205$	14.7364	+	15.9986i	1.02923	+	1.11739i
$206$			10.6037i			0.738796i
$207$		0			0
$208$	2.87834	−	2.87834i	0.199577	−	0.199577i
$209$	−5.18145			−0.358409
$210$		0			0
$211$	16.0831			1.10721			0.553604	−	0.832780i	$-0.313252\pi$
$211$	16.0831			1.10721			0.553604	+	0.832780i	$0.313252\pi$
$212$	2.65638	−	2.65638i	0.182441	−	0.182441i
$213$		0			0
$214$			7.54705i			0.515906i
$215$	−0.823517	+	20.0532i	−0.0561634	+	1.36761i
$216$		0			0
$217$	−4.63645	−	4.63645i	−0.314743	−	0.314743i
$218$	2.07056	+	2.07056i	0.140236	+	0.140236i
$219$		0			0
$220$	10.3931	−	9.57319i	0.700705	−	0.645424i
$221$		−	4.07059i		−	0.273818i
$222$		0			0
$223$	16.5852	−	16.5852i	1.11062	−	1.11062i	0.117558	−	0.993066i	$-0.462493\pi$
$223$	16.5852	−	16.5852i	1.11062	−	1.11062i	0.993066	−	0.117558i	$-0.0375067\pi$
$224$	0.781225			0.0521978
$225$		0			0
$226$	13.7498			0.914622
$227$	8.56786	−	8.56786i	0.568669	−	0.568669i	−0.363086	−	0.931755i	$-0.618277\pi$
$227$	8.56786	−	8.56786i	0.568669	−	0.568669i	0.931755	+	0.363086i	$0.118277\pi$
$228$		0			0
$229$			1.63300i			0.107912i	0.998543	+	0.0539558i	$0.0171830\pi$
$229$			1.63300i			0.107912i	−0.998543	+	0.0539558i	$0.982817\pi$
$230$	−4.05969	+	3.73941i	−0.267688	+	0.246569i
$231$		0			0
$232$	−3.24725	−	3.24725i	−0.213193	−	0.213193i
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	0.436475	−	0.899716i	$-0.356227\pi$
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	−0.899716	+	0.436475i	$0.856227\pi$
$234$		0			0
$235$	0.108903	−	2.65187i	0.00710408	−	0.172989i
$236$		−	9.73233i		−	0.633521i
$237$		0			0
$238$	0.552409	−	0.552409i	0.0358074	−	0.0358074i
$239$	8.36913			0.541354			0.270677	−	0.962670i	$-0.412752\pi$
$239$	8.36913			0.541354			0.270677	+	0.962670i	$0.412752\pi$
$240$		0			0
$241$	3.87348			0.249513			0.124756	−	0.992187i	$-0.460185\pi$
$241$	3.87348			0.249513			0.124756	+	0.992187i	$0.460185\pi$
$242$	20.4585	−	20.4585i	1.31512	−	1.31512i
$243$		0			0
$244$		−	12.1498i		−	0.777813i
$245$	−9.67993	−	10.5090i	−0.618428	−	0.671397i
$246$		0			0
$247$	−2.36010	−	2.36010i	−0.150170	−	0.150170i
$248$	−5.93485	−	5.93485i	−0.376863	−	0.376863i
$249$		0			0
$250$	11.0957	+	1.37317i	0.701753	+	0.0868468i
$251$			10.5163i			0.663780i	0.943318	+	0.331890i	$0.107686\pi$
$251$			10.5163i			0.663780i	−0.943318	+	0.331890i	$0.892314\pi$
$252$		0			0
$253$	−11.0296	+	11.0296i	−0.693424	+	0.693424i
$254$	−12.0349			−0.755134
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.3295	+	13.3295i	−0.831473	+	0.831473i	−0.987718	−	0.156245i	$-0.950061\pi$
$257$	−13.3295	+	13.3295i	−0.831473	+	0.831473i	0.156245	+	0.987718i	$0.450061\pi$
$258$		0			0
$259$		−	5.79726i		−	0.360224i
$260$	9.09446	+	0.373479i	0.564014	+	0.0231622i
$261$		0			0
$262$	3.85806	+	3.85806i	0.238352	+	0.238352i
$263$	0.625412	+	0.625412i	0.0385645	+	0.0385645i	0.726126	−	0.687562i	$-0.241319\pi$
$263$	0.625412	+	0.625412i	0.0385645	+	0.0385645i	−0.687562	+	0.726126i	$0.741319\pi$
$264$		0			0
$265$	8.39314	+	0.344678i	0.515586	+	0.0211734i
$266$		−	0.640566i		−	0.0392756i
$267$		0			0
$268$	−11.2680	+	11.2680i	−0.688305	+	0.688305i
$269$	26.7692			1.63215			0.816075	−	0.577946i	$-0.196146\pi$
$269$	26.7692			1.63215			0.816075	+	0.577946i	$0.196146\pi$
$270$		0			0
$271$	4.11679			0.250077			0.125039	−	0.992152i	$-0.460095\pi$
$271$	4.11679			0.250077			0.125039	+	0.992152i	$0.460095\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$		0			0
$274$			9.02269i			0.545080i
$275$	31.4898	+	2.59073i	1.89890	+	0.156227i
$276$		0			0
$277$	−12.3744	−	12.3744i	−0.743505	−	0.743505i	0.229745	−	0.973251i	$-0.426211\pi$
$277$	−12.3744	−	12.3744i	−0.743505	−	0.743505i	−0.973251	+	0.229745i	$0.926211\pi$
$278$	−7.15853	−	7.15853i	−0.429340	−	0.429340i
$279$		0			0
$280$	1.18350	+	1.28487i	0.0707277	+	0.0767856i
$281$			21.7216i			1.29580i	0.761725	+	0.647900i	$0.224353\pi$
$281$			21.7216i			1.29580i	−0.761725	+	0.647900i	$0.775647\pi$
$282$		0			0
$283$	−11.1048	+	11.1048i	−0.660113	+	0.660113i	−0.955407	−	0.295294i	$-0.904583\pi$
$283$	−11.1048	+	11.1048i	−0.660113	+	0.660113i	0.295294	+	0.955407i	$0.404583\pi$
$284$	10.9353			0.648894
$285$		0			0
$286$	25.7230			1.52103
$287$	−5.37353	+	5.37353i	−0.317190	+	0.317190i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	0.421347	−	10.2601i	0.0247423	−	0.602492i
$291$		0			0
$292$	2.69484	+	2.69484i	0.157704	+	0.157704i
$293$	−13.4967	−	13.4967i	−0.788485	−	0.788485i	0.192761	−	0.981246i	$-0.438256\pi$
$293$	−13.4967	−	13.4967i	−0.788485	−	0.788485i	−0.981246	+	0.192761i	$0.938256\pi$
$294$		0			0
$295$	16.0066	−	14.7438i	0.931941	−	0.858417i
$296$		−	7.42074i		−	0.431322i
$297$		0			0
$298$	−5.95703	+	5.95703i	−0.345081	+	0.345081i
$299$	−10.0477			−0.581075
$300$		0			0
$301$	−7.01197			−0.404163
$302$	−1.88273	+	1.88273i	−0.108339	+	0.108339i
$303$		0			0
$304$		−	0.819950i		−	0.0470274i
$305$	19.9826	−	18.4061i	1.14420	−	1.05393i
$306$		0			0
$307$	−20.4704	−	20.4704i	−1.16831	−	1.16831i	−0.982606	−	0.185702i	$-0.940544\pi$
$307$	−20.4704	−	20.4704i	−1.16831	−	1.16831i	−0.185702	−	0.982606i	$-0.559456\pi$
$308$	3.49080	+	3.49080i	0.198907	+	0.198907i
$309$		0			0
$310$	0.770075	−	18.7518i	0.0437373	−	1.06503i
$311$		−	11.8572i		−	0.672362i	−0.941797	−	0.336181i	$-0.890865\pi$
$311$		−	11.8572i		−	0.672362i	0.941797	−	0.336181i	$-0.109135\pi$
$312$		0			0
$313$	8.53367	−	8.53367i	0.482351	−	0.482351i	−0.423530	−	0.905882i	$-0.639209\pi$
$313$	8.53367	−	8.53367i	0.482351	−	0.482351i	0.905882	+	0.423530i	$0.139209\pi$
$314$	−14.1183			−0.796743
$315$		0			0
$316$	16.7948			0.944781
$317$	−11.7037	+	11.7037i	−0.657343	+	0.657343i	−0.954751	−	0.297407i	$-0.903878\pi$
$317$	−11.7037	+	11.7037i	−0.657343	+	0.657343i	0.297407	+	0.954751i	$0.403878\pi$
$318$		0			0
$319$		−	29.0199i		−	1.62480i
$320$	1.51493	+	1.64468i	0.0846872	+	0.0919407i
$321$		0			0
$322$	−1.36355	−	1.36355i	−0.0759877	−	0.0759877i
$323$	−0.579792	−	0.579792i	−0.0322605	−	0.0322605i
$324$		0			0
$325$	13.1632	+	15.5233i	0.730164	+	0.861078i
$326$			15.9859i			0.885377i
$327$		0			0
$328$	−6.87834	+	6.87834i	−0.379793	+	0.379793i
$329$	0.927277			0.0511224
$330$		0			0
$331$	5.74979			0.316037			0.158018	−	0.987436i	$-0.449489\pi$
$331$	5.74979			0.316037			0.158018	+	0.987436i	$0.449489\pi$
$332$	6.72697	−	6.72697i	0.369191	−	0.369191i
$333$		0			0
$334$		−	7.57319i		−	0.414386i
$335$	−35.6026	−	1.46208i	−1.94518	−	0.0798820i
$336$		0			0
$337$	12.0845	+	12.0845i	0.658286	+	0.658286i	0.954974	−	0.296688i	$-0.0958822\pi$
$337$	12.0845	+	12.0845i	0.658286	+	0.658286i	−0.296688	+	0.954974i	$0.595882\pi$
$338$	2.52419	+	2.52419i	0.137298	+	0.137298i
$339$		0			0
$340$	2.23418	+	0.0917505i	0.121166	+	0.00497587i
$341$		−	53.0382i		−	2.87218i
$342$		0			0
$343$	7.39659	−	7.39659i	0.399378	−	0.399378i
$344$	−8.97561			−0.483932
$345$		0			0
$346$	18.9629			1.01945
$347$	18.5092	−	18.5092i	0.993626	−	0.993626i	−0.00635376	−	0.999980i	$-0.502022\pi$
$347$	18.5092	−	18.5092i	0.993626	−	0.993626i	0.999980	+	0.00635376i	$0.00202248\pi$
$348$		0			0
$349$		−	10.6034i		−	0.567588i	−0.958885	−	0.283794i	$-0.908407\pi$
$349$		−	10.6034i		−	0.567588i	0.958885	−	0.283794i	$-0.0915931\pi$
$350$	−0.320283	+	3.89297i	−0.0171198	+	0.208088i
$351$		0			0
$352$	4.46837	+	4.46837i	0.238165	+	0.238165i
$353$	13.1944	+	13.1944i	0.702269	+	0.702269i	0.964897	−	0.262628i	$-0.0845892\pi$
$353$	13.1944	+	13.1944i	0.702269	+	0.702269i	−0.262628	+	0.964897i	$0.584589\pi$
$354$		0			0
$355$	16.5663	+	17.9852i	0.879247	+	0.954555i
$356$			7.62705i			0.404233i
$357$		0			0
$358$	−8.16321	+	8.16321i	−0.431439	+	0.431439i
$359$	31.5841			1.66694			0.833472	−	0.552561i	$-0.186349\pi$
$359$	31.5841			1.66694			0.833472	+	0.552561i	$0.186349\pi$
$360$		0			0
$361$	18.3277			0.964615
$362$	−7.98693	+	7.98693i	−0.419784	+	0.419784i
$363$		0			0
$364$			3.18005i			0.166680i
$365$	−0.349669	+	8.51467i	−0.0183025	+	0.445678i
$366$		0			0
$367$	11.7671	+	11.7671i	0.614238	+	0.614238i	0.944048	−	0.329809i	$-0.106984\pi$
$367$	11.7671	+	11.7671i	0.614238	+	0.614238i	−0.329809	+	0.944048i	$0.606984\pi$
$368$	−1.74540	−	1.74540i	−0.0909853	−	0.0909853i
$369$		0			0
$370$	12.2048	−	11.2419i	0.634496	−	0.584438i
$371$			2.93482i			0.152368i
$372$		0			0
$373$	−16.1415	+	16.1415i	−0.835776	+	0.835776i	−0.988300	−	0.152524i	$-0.951260\pi$
$373$	−16.1415	+	16.1415i	−0.835776	+	0.835776i	0.152524	+	0.988300i	$0.451260\pi$
$374$	6.31923			0.326760
$375$		0			0
$376$	1.18695			0.0612124
$377$	13.2183	−	13.2183i	0.680775	−	0.680775i
$378$		0			0
$379$		−	3.54705i		−	0.182200i	−0.995842	−	0.0910999i	$-0.970962\pi$
$379$		−	3.54705i		−	0.182200i	0.995842	−	0.0910999i	$-0.0290383\pi$
$380$	1.34856	−	1.24217i	0.0691796	−	0.0637218i
$381$		0			0
$382$	−8.65187	−	8.65187i	−0.442668	−	0.442668i
$383$	−3.72850	−	3.72850i	−0.190518	−	0.190518i	0.605402	−	0.795920i	$-0.293012\pi$
$383$	−3.72850	−	3.72850i	−0.190518	−	0.190518i	−0.795920	+	0.605402i	$0.793012\pi$
$384$		0			0
$385$	−0.452948	+	11.0296i	−0.0230844	+	0.562120i
$386$		−	16.5657i		−	0.843172i
$387$		0			0
$388$	3.34671	−	3.34671i	0.169904	−	0.169904i
$389$	7.26492			0.368346			0.184173	−	0.982894i	$-0.441039\pi$
$389$	7.26492			0.368346			0.184173	+	0.982894i	$0.441039\pi$
$390$		0			0
$391$	−2.46837			−0.124831
$392$	4.51819	−	4.51819i	0.228203	−	0.228203i
$393$		0			0
$394$		−	7.32988i		−	0.369274i
$395$	25.4429	+	27.6221i	1.28017	+	1.38982i
$396$		0			0
$397$	18.5019	+	18.5019i	0.928584	+	0.928584i	0.997615	−	0.0690308i	$-0.0219907\pi$
$397$	18.5019	+	18.5019i	0.928584	+	0.928584i	−0.0690308	+	0.997615i	$0.521991\pi$
$398$	3.36593	+	3.36593i	0.168719	+	0.168719i
$399$		0			0
$400$	−0.409975	+	4.98316i	−0.0204988	+	0.249158i
$401$			30.8512i			1.54063i	0.637661	+	0.770317i	$0.279902\pi$
$401$			30.8512i			1.54063i	−0.637661	+	0.770317i	$0.720098\pi$
$402$		0			0
$403$	24.1583	−	24.1583i	1.20341	−	1.20341i
$404$	11.6558			0.579898
$405$		0			0
$406$	3.58763			0.178051
$407$	33.1586	−	33.1586i	1.64361	−	1.64361i
$408$		0			0
$409$		−	28.4769i		−	1.40809i	−0.710155	−	0.704046i	$-0.751375\pi$
$409$		−	28.4769i		−	1.40809i	0.710155	−	0.704046i	$-0.248625\pi$
$410$	−21.7329	−	0.892498i	−1.07331	−	0.0440773i
$411$		0			0
$412$	−7.49796	−	7.49796i	−0.369398	−	0.369398i
$413$	5.37623	+	5.37623i	0.264547	+	0.264547i
$414$		0			0
$415$	21.2546	+	0.872857i	1.04335	+	0.0428469i
$416$			4.07059i			0.199577i
$417$		0			0
$418$	3.66384	−	3.66384i	0.179204	−	0.179204i
$419$	−31.2672			−1.52750			−0.763751	−	0.645510i	$-0.776645\pi$
$419$	−31.2672			−1.52750			−0.763751	+	0.645510i	$0.776645\pi$
$420$		0			0
$421$	−14.8171			−0.722142			−0.361071	−	0.932538i	$-0.617589\pi$
$421$	−14.8171			−0.722142			−0.361071	+	0.932538i	$0.617589\pi$
$422$	−11.3725	+	11.3725i	−0.553604	+	0.553604i
$423$		0			0
$424$			3.75669i			0.182441i
$425$	3.23373	+	3.81353i	0.156859	+	0.184983i
$426$		0			0
$427$	6.71168	+	6.71168i	0.324801	+	0.324801i
$428$	−5.33657	−	5.33657i	−0.257953	−	0.257953i
$429$		0			0
$430$	−13.5974	−	14.7620i	−0.655726	−	0.711889i
$431$		−	2.74115i		−	0.132036i	−0.997818	−	0.0660182i	$-0.978970\pi$
$431$		−	2.74115i		−	0.132036i	0.997818	−	0.0660182i	$-0.0210295\pi$
$432$		0			0
$433$	−5.33396	+	5.33396i	−0.256334	+	0.256334i	−0.823561	−	0.567227i	$-0.808016\pi$
$433$	−5.33396	+	5.33396i	−0.256334	+	0.256334i	0.567227	+	0.823561i	$0.308016\pi$
$434$	6.55693			0.314743
$435$		0			0
$436$	−2.92822			−0.140236
$437$	−1.43114	+	1.43114i	−0.0684608	+	0.0684608i
$438$		0			0
$439$			16.9667i			0.809776i	0.914366	+	0.404888i	$0.132689\pi$
$439$			16.9667i			0.809776i	−0.914366	+	0.404888i	$0.867311\pi$
$440$	−0.579792	+	14.1183i	−0.0276405	+	0.673065i
$441$		0			0
$442$	2.87834	+	2.87834i	0.136909	+	0.136909i
$443$	−9.75414	−	9.75414i	−0.463433	−	0.463433i	0.436346	−	0.899779i	$-0.356272\pi$
$443$	−9.75414	−	9.75414i	−0.463433	−	0.463433i	−0.899779	+	0.436346i	$0.856272\pi$
$444$		0			0
$445$	−12.5441	+	11.5544i	−0.594647	+	0.547733i
$446$			23.4550i			1.11062i
$447$		0			0
$448$	−0.552409	+	0.552409i	−0.0260989	+	0.0260989i
$449$	−7.20526			−0.340037			−0.170019	−	0.985441i	$-0.554383\pi$
$449$	−7.20526			−0.340037			−0.170019	+	0.985441i	$0.554383\pi$
$450$		0			0
$451$	−61.4700			−2.89451
$452$	−9.72257	+	9.72257i	−0.457311	+	0.457311i
$453$		0			0
$454$			12.1168i			0.568669i
$455$	−5.23018	+	4.81755i	−0.245195	+	0.225850i
$456$		0			0
$457$	−8.32298	−	8.32298i	−0.389332	−	0.389332i	0.485117	−	0.874449i	$-0.338777\pi$
$457$	−8.32298	−	8.32298i	−0.389332	−	0.389332i	−0.874449	+	0.485117i	$0.838777\pi$
$458$	−1.15470	−	1.15470i	−0.0539558	−	0.0539558i
$459$		0			0
$460$	0.226474	−	5.51479i	0.0105594	−	0.257129i
$461$		−	36.8317i		−	1.71542i	−0.514130	−	0.857712i	$-0.671885\pi$
$461$		−	36.8317i		−	1.71542i	0.514130	−	0.857712i	$-0.328115\pi$
$462$		0			0
$463$	14.1914	−	14.1914i	0.659530	−	0.659530i	−0.295739	−	0.955269i	$-0.595566\pi$
$463$	14.1914	−	14.1914i	0.659530	−	0.659530i	0.955269	+	0.295739i	$0.0955659\pi$
$464$	4.59231			0.213193
$465$		0			0
$466$	10.0000			0.463241
$467$	−3.46899	+	3.46899i	−0.160526	+	0.160526i	−0.782800	−	0.622274i	$-0.786209\pi$
$467$	−3.46899	+	3.46899i	−0.160526	+	0.160526i	0.622274	+	0.782800i	$0.286209\pi$
$468$		0			0
$469$		−	12.4491i		−	0.574848i
$470$	1.79815	+	1.95216i	0.0829424	+	0.0900465i
$471$		0			0
$472$	6.88180	+	6.88180i	0.316760	+	0.316760i
$473$	−40.1063	−	40.1063i	−1.84409	−	1.84409i
$474$		0			0
$475$	4.08595	+	0.336159i	0.187476	+	0.0154240i
$476$			0.781225i			0.0358074i
$477$		0			0
$478$	−5.91787	+	5.91787i	−0.270677	+	0.270677i
$479$	−8.28724			−0.378654			−0.189327	−	0.981914i	$-0.560631\pi$
$479$	−8.28724			−0.378654			−0.189327	+	0.981914i	$0.560631\pi$
$480$		0			0
$481$	30.2068			1.37731
$482$	−2.73896	+	2.73896i	−0.124756	+	0.124756i
$483$		0			0
$484$			28.9327i			1.31512i
$485$	10.5743	+	0.434252i	0.480155	+	0.0197184i
$486$		0			0
$487$	−0.0771373	−	0.0771373i	−0.00349543	−	0.00349543i	0.705357	−	0.708852i	$-0.250787\pi$
$487$	−0.0771373	−	0.0771373i	−0.00349543	−	0.00349543i	−0.708852	+	0.705357i	$0.750787\pi$
$488$	8.59123	+	8.59123i	0.388907	+	0.388907i
$489$		0			0
$490$	14.2757	+	0.586257i	0.644912	+	0.0264844i
$491$			3.53465i			0.159516i	0.996814	+	0.0797582i	$0.0254148\pi$
$491$			3.53465i			0.159516i	−0.996814	+	0.0797582i	$0.974585\pi$
$492$		0			0
$493$	3.24725	−	3.24725i	0.146249	−	0.146249i
$494$	3.33768			0.150170
$495$		0			0
$496$	8.39314			0.376863
$497$	−6.04079	+	6.04079i	−0.270966	+	0.270966i
$498$		0			0
$499$		−	22.5628i		−	1.01005i	−0.863104	−	0.505026i	$-0.831483\pi$
$499$		−	22.5628i		−	1.01005i	0.863104	−	0.505026i	$-0.168517\pi$
$500$	−8.81682	+	6.87486i	−0.394300	+	0.307453i
$501$		0			0
$502$	−7.43611	−	7.43611i	−0.331890	−	0.331890i
$503$	10.4056	+	10.4056i	0.463963	+	0.463963i	0.899952	−	0.435989i	$-0.143601\pi$
$503$	10.4056	+	10.4056i	0.463963	+	0.463963i	−0.435989	+	0.899952i	$0.643601\pi$
$504$		0			0
$505$	17.6577	+	19.1701i	0.785758	+	0.853059i
$506$		−	15.5982i		−	0.693424i
$507$		0			0
$508$	8.50993	−	8.50993i	0.377567	−	0.377567i
$509$	0.570031			0.0252662			0.0126331	−	0.999920i	$-0.495979\pi$
$509$	0.570031			0.0252662			0.0126331	+	0.999920i	$0.495979\pi$
$510$		0			0
$511$	−2.97731			−0.131709
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	18.8508i		−	0.831473i
$515$	0.972896	−	23.6907i	0.0428709	−	1.04394i
$516$		0			0
$517$	5.30374	+	5.30374i	0.233258	+	0.233258i
$518$	4.09929	+	4.09929i	0.180112	+	0.180112i
$519$		0			0
$520$	−6.69484	+	6.16666i	−0.293588	+	0.270426i
$521$			37.8328i			1.65748i	0.559630	+	0.828742i	$0.310943\pi$
$521$			37.8328i			1.65748i	−0.559630	+	0.828742i	$0.689057\pi$
$522$		0			0
$523$	−19.0316	+	19.0316i	−0.832195	+	0.832195i	−0.987817	−	0.155622i	$-0.950262\pi$
$523$	−19.0316	+	19.0316i	−0.832195	+	0.832195i	0.155622	+	0.987817i	$0.450262\pi$
$524$	−5.45612			−0.238352
$525$		0			0
$526$	−0.884466			−0.0385645
$527$	5.93485	−	5.93485i	0.258526	−	0.258526i
$528$		0			0
$529$		−	16.9072i		−	0.735094i
$530$	−6.17857	+	5.69112i	−0.268380	+	0.247207i
$531$		0			0
$532$	0.452948	+	0.452948i	0.0196378	+	0.0196378i
$533$	−27.9990	−	27.9990i	−1.21277	−	1.21277i
$534$		0			0
$535$	0.692446	−	16.8615i	0.0299370	−	0.728987i
$536$		−	15.9354i		−	0.688305i
$537$		0			0
$538$	−18.9287	+	18.9287i	−0.816075	+	0.816075i
$539$	40.3779			1.73920
$540$		0			0
$541$	33.9710			1.46053			0.730264	−	0.683165i	$-0.239397\pi$
$541$	33.9710			1.46053			0.730264	+	0.683165i	$0.239397\pi$
$542$	−2.91101	+	2.91101i	−0.125039	+	0.125039i
$543$		0			0
$544$			1.00000i			0.0428746i
$545$	−4.43605	−	4.81600i	−0.190019	−	0.206295i
$546$		0			0
$547$	−22.5845	−	22.5845i	−0.965645	−	0.965645i	0.0337846	−	0.999429i	$-0.489244\pi$
$547$	−22.5845	−	22.5845i	−0.965645	−	0.965645i	−0.999429	+	0.0337846i	$0.989244\pi$
$548$	−6.38000	−	6.38000i	−0.272540	−	0.272540i
$549$		0			0
$550$	−24.0985	+	20.4347i	−1.02757	+	0.871338i
$551$		−	3.76547i		−	0.160414i
$552$		0			0
$553$	−9.27760	+	9.27760i	−0.394524	+	0.394524i
$554$	17.5000			0.743505
$555$		0			0
$556$	10.1237			0.429340
$557$	14.6694	−	14.6694i	0.621564	−	0.621564i	−0.324368	−	0.945931i	$-0.605151\pi$
$557$	14.6694	−	14.6694i	0.621564	−	0.621564i	0.945931	+	0.324368i	$0.105151\pi$
$558$		0			0
$559$		−	36.5361i		−	1.54531i
$560$	−1.74540	−	0.0716778i	−0.0737567	−	0.00302894i
$561$		0			0
$562$	−15.3595	−	15.3595i	−0.647900	−	0.647900i
$563$	−5.63016	−	5.63016i	−0.237283	−	0.237283i	0.578441	−	0.815724i	$-0.303661\pi$
$563$	−5.63016	−	5.63016i	−0.237283	−	0.237283i	−0.815724	+	0.578441i	$0.803661\pi$
$564$		0			0
$565$	−30.7196	−	1.26155i	−1.29238	−	0.0530738i
$566$		−	15.7046i		−	0.660113i
$567$		0			0
$568$	−7.73246	+	7.73246i	−0.324447	+	0.324447i
$569$	−26.7387			−1.12095			−0.560473	−	0.828172i	$-0.689381\pi$
$569$	−26.7387			−1.12095			−0.560473	+	0.828172i	$0.689381\pi$
$570$		0			0
$571$	−26.6934			−1.11709			−0.558543	−	0.829476i	$-0.688639\pi$
$571$	−26.6934			−1.11709			−0.558543	+	0.829476i	$0.688639\pi$
$572$	−18.1889	+	18.1889i	−0.760517	+	0.760517i
$573$		0			0
$574$		−	7.59933i		−	0.317190i
$575$	9.41319	−	7.98205i	0.392557	−	0.332874i
$576$		0			0
$577$	9.94364	+	9.94364i	0.413959	+	0.413959i	0.883115	−	0.469156i	$-0.155442\pi$
$577$	9.94364	+	9.94364i	0.413959	+	0.413959i	−0.469156	+	0.883115i	$0.655442\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$	6.95703	+	7.55290i	0.288875	+	0.313617i
$581$			7.43209i			0.308335i
$582$		0			0
$583$	−16.7863	+	16.7863i	−0.695217	+	0.695217i
$584$	−3.81108			−0.157704
$585$		0			0
$586$	19.0872			0.788485
$587$	−5.48481	+	5.48481i	−0.226382	+	0.226382i	−0.811179	−	0.584797i	$-0.801174\pi$
$587$	−5.48481	+	5.48481i	−0.226382	+	0.226382i	0.584797	+	0.811179i	$0.301174\pi$
$588$		0			0
$589$		−	6.88196i		−	0.283566i
$590$	−0.892946	+	21.7438i	−0.0367620	+	0.895179i
$591$		0			0
$592$	5.24725	+	5.24725i	0.215661	+	0.215661i
$593$	−20.4424	−	20.4424i	−0.839470	−	0.839470i	0.149319	−	0.988789i	$-0.452292\pi$
$593$	−20.4424	−	20.4424i	−0.839470	−	0.839470i	−0.988789	+	0.149319i	$0.952292\pi$
$594$		0			0
$595$	−1.28487	+	1.18350i	−0.0526745	+	0.0485188i
$596$		−	8.42451i		−	0.345081i
$597$		0			0
$598$	7.10482	−	7.10482i	0.290538	−	0.290538i
$599$	15.7731			0.644472			0.322236	−	0.946659i	$-0.395566\pi$
$599$	15.7731			0.644472			0.322236	+	0.946659i	$0.395566\pi$
$600$		0			0
$601$	−45.8776			−1.87138			−0.935692	−	0.352817i	$-0.885224\pi$
$601$	−45.8776			−1.87138			−0.935692	+	0.352817i	$0.885224\pi$
$602$	4.95821	−	4.95821i	0.202082	−	0.202082i
$603$		0			0
$604$		−	2.66259i		−	0.108339i
$605$	−47.5851	+	43.8309i	−1.93461	+	1.78198i
$606$		0			0
$607$	3.62419	+	3.62419i	0.147101	+	0.147101i	0.776822	−	0.629720i	$-0.216831\pi$
$607$	3.62419	+	3.62419i	0.147101	+	0.147101i	−0.629720	+	0.776822i	$0.716831\pi$
$608$	0.579792	+	0.579792i	0.0235137	+	0.0235137i
$609$		0			0
$610$	−1.11475	+	27.1450i	−0.0451350	+	1.09907i
$611$			4.83160i			0.195466i
$612$		0			0
$613$	4.78931	−	4.78931i	0.193438	−	0.193438i	−0.603742	−	0.797180i	$-0.706324\pi$
$613$	4.78931	−	4.78931i	0.193438	−	0.193438i	0.797180	+	0.603742i	$0.206324\pi$
$614$	28.9495			1.16831
$615$		0			0
$616$	−4.93674			−0.198907
$617$	20.9181	−	20.9181i	0.842132	−	0.842132i	−0.147004	−	0.989136i	$-0.546963\pi$
$617$	20.9181	−	20.9181i	0.842132	−	0.842132i	0.989136	+	0.147004i	$0.0469630\pi$
$618$		0			0
$619$			7.48254i			0.300749i	0.988629	+	0.150374i	$0.0480479\pi$
$619$			7.48254i			0.300749i	−0.988629	+	0.150374i	$0.951952\pi$
$620$	12.7150	+	13.8041i	0.510647	+	0.554385i
$621$		0			0
$622$	8.38433	+	8.38433i	0.336181	+	0.336181i
$623$	−4.21325	−	4.21325i	−0.168800	−	0.168800i
$624$		0			0
$625$	−24.6638	−	4.08595i	−0.986554	−	0.163438i
$626$			12.0684i			0.482351i
$627$		0			0
$628$	9.98316	−	9.98316i	0.398372	−	0.398372i
$629$	7.42074			0.295884
$630$		0			0
$631$	6.62891			0.263893			0.131946	−	0.991257i	$-0.457877\pi$
$631$	6.62891			0.263893			0.131946	+	0.991257i	$0.457877\pi$
$632$	−11.8757	+	11.8757i	−0.472391	+	0.472391i
$633$		0			0
$634$		−	16.5515i		−	0.657343i
$635$	26.8881	+	1.10420i	1.06702	+	0.0438190i
$636$		0			0
$637$	18.3917	+	18.3917i	0.728707	+	0.728707i
$638$	20.5201	+	20.5201i	0.812400	+	0.812400i
$639$		0			0
$640$	−2.23418	−	0.0917505i	−0.0883139	−	0.00362676i
$641$		−	16.5341i		−	0.653059i	−0.945187	−	0.326529i	$-0.894121\pi$
$641$		−	16.5341i		−	0.653059i	0.945187	−	0.326529i	$-0.105879\pi$
$642$		0			0
$643$	7.80896	−	7.80896i	0.307955	−	0.307955i	−0.536161	−	0.844116i	$-0.680126\pi$
$643$	7.80896	−	7.80896i	0.307955	−	0.307955i	0.844116	+	0.536161i	$0.180126\pi$
$644$	1.92835			0.0759877
$645$		0			0
$646$	0.819950			0.0322605
$647$	−6.10644	+	6.10644i	−0.240069	+	0.240069i	−0.816879	−	0.576810i	$-0.804297\pi$
$647$	−6.10644	+	6.10644i	−0.240069	+	0.240069i	0.576810	+	0.816879i	$0.304297\pi$
$648$		0			0
$649$			61.5008i			2.41412i
$650$	−20.2844	−	1.66884i	−0.795621	−	0.0654574i
$651$		0			0
$652$	−11.3037	−	11.3037i	−0.442689	−	0.442689i
$653$	22.6032	+	22.6032i	0.884530	+	0.884530i	0.993991	−	0.109461i	$-0.0349125\pi$
$653$	22.6032	+	22.6032i	0.884530	+	0.884530i	−0.109461	+	0.993991i	$0.534913\pi$
$654$		0			0
$655$	−8.26563	−	8.97359i	−0.322965	−	0.350627i
$656$		−	9.72745i		−	0.379793i
$657$		0			0
$658$	−0.655684	+	0.655684i	−0.0255612	+	0.0255612i
$659$	−9.04414			−0.352310			−0.176155	−	0.984362i	$-0.556366\pi$
$659$	−9.04414			−0.352310			−0.176155	+	0.984362i	$0.556366\pi$
$660$		0			0
$661$	−43.4205			−1.68886			−0.844431	−	0.535664i	$-0.820062\pi$
$661$	−43.4205			−1.68886			−0.844431	+	0.535664i	$0.820062\pi$
$662$	−4.06571	+	4.06571i	−0.158018	+	0.158018i
$663$		0			0
$664$			9.51338i			0.369191i
$665$	−0.0587722	+	1.43114i	−0.00227909	+	0.0554973i
$666$		0			0
$667$	−8.01542	−	8.01542i	−0.310358	−	0.310358i
$668$	5.35505	+	5.35505i	0.207193	+	0.207193i
$669$		0			0
$670$	26.2087	−	24.1410i	1.01253	−	0.932649i
$671$			76.7775i			2.96396i
$672$		0			0
$673$	19.5969	−	19.5969i	0.755406	−	0.755406i	−0.220077	−	0.975483i	$-0.570631\pi$
$673$	19.5969	−	19.5969i	0.755406	−	0.755406i	0.975483	+	0.220077i	$0.0706307\pi$
$674$	−17.0901			−0.658286
$675$		0			0
$676$	−3.56974			−0.137298
$677$	11.5755	−	11.5755i	0.444881	−	0.444881i	−0.448767	−	0.893649i	$-0.648137\pi$
$677$	11.5755	−	11.5755i	0.444881	−	0.444881i	0.893649	+	0.448767i	$0.148137\pi$
$678$		0			0
$679$			3.69751i			0.141898i
$680$	−1.64468	+	1.51493i	−0.0630708	+	0.0580949i
$681$		0			0
$682$	37.5036	+	37.5036i	1.43609	+	1.43609i
$683$	15.7415	+	15.7415i	0.602334	+	0.602334i	0.940931	−	0.338598i	$-0.109953\pi$
$683$	15.7415	+	15.7415i	0.602334	+	0.602334i	−0.338598	+	0.940931i	$0.609953\pi$
$684$		0			0
$685$	0.827836	−	20.1583i	0.0316300	−	0.770211i
$686$			10.4604i			0.399378i
$687$		0			0
$688$	6.34671	−	6.34671i	0.241966	−	0.241966i
$689$	−15.2920			−0.582577
$690$		0			0
$691$	3.94773			0.150179			0.0750893	−	0.997177i	$-0.476076\pi$
$691$	3.94773			0.150179			0.0750893	+	0.997177i	$0.476076\pi$
$692$	−13.4088	+	13.4088i	−0.509725	+	0.509725i
$693$		0			0
$694$			26.1760i			0.993626i
$695$	15.3367	+	16.6503i	0.581754	+	0.631581i
$696$		0			0
$697$	−6.87834	−	6.87834i	−0.260536	−	0.260536i
$698$	7.49774	+	7.49774i	0.283794	+	0.283794i
$699$		0			0
$700$	−2.52627	−	2.97922i	−0.0954841	−	0.112604i
$701$			9.46794i			0.357599i	0.983886	+	0.178800i	$0.0572214\pi$
$701$			9.46794i			0.357599i	−0.983886	+	0.178800i	$0.942779\pi$
$702$		0			0
$703$	4.30249	−	4.30249i	0.162271	−	0.162271i
$704$	−6.31923			−0.238165
$705$		0			0
$706$	−18.6598			−0.702269
$707$	−6.43877	+	6.43877i	−0.242155	+	0.242155i
$708$		0			0
$709$		−	46.9302i		−	1.76250i	−0.472650	−	0.881250i	$-0.656703\pi$
$709$		−	46.9302i		−	1.76250i	0.472650	−	0.881250i	$-0.343297\pi$
$710$	−24.4316	−	1.00332i	−0.916901	−	0.0376541i
$711$		0			0
$712$	−5.39314	−	5.39314i	−0.202116	−	0.202116i
$713$	−14.6494	−	14.6494i	−0.548624	−	0.548624i
$714$		0			0
$715$	−57.4700	−	2.36010i	−2.14926	−	0.0882627i
$716$		−	11.5445i		−	0.431439i
$717$		0			0
$718$	−22.3333	+	22.3333i	−0.833472	+	0.833472i
$719$	8.90289			0.332022			0.166011	−	0.986124i	$-0.446911\pi$
$719$	8.90289			0.332022			0.166011	+	0.986124i	$0.446911\pi$
$720$		0			0
$721$	8.28389			0.308508
$722$	−12.9596	+	12.9596i	−0.482307	+	0.482307i
$723$		0			0
$724$		−	11.2952i		−	0.419784i
$725$	−1.88273	+	22.8842i	−0.0699229	+	0.849899i
$726$		0			0
$727$	−5.11334	−	5.11334i	−0.189643	−	0.189643i	0.605899	−	0.795542i	$-0.292814\pi$
$727$	−5.11334	−	5.11334i	−0.189643	−	0.189643i	−0.795542	+	0.605899i	$0.792814\pi$
$728$	−2.24863	−	2.24863i	−0.0833399	−	0.0833399i
$729$		0			0
$730$	−5.77353	−	6.26803i	−0.213688	−	0.231990i
$731$		−	8.97561i		−	0.331975i
$732$		0			0
$733$	11.8220	−	11.8220i	0.436655	−	0.436655i	−0.454230	−	0.890885i	$-0.650085\pi$
$733$	11.8220	−	11.8220i	0.436655	−	0.436655i	0.890885	+	0.454230i	$0.150085\pi$
$734$	−16.6412			−0.614238
$735$		0			0
$736$	2.46837			0.0909853
$737$	71.2053	−	71.2053i	2.62288	−	2.62288i
$738$		0			0
$739$			27.1841i			0.999984i	0.866030	+	0.499992i	$0.166664\pi$
$739$			27.1841i			0.999984i	−0.866030	+	0.499992i	$0.833336\pi$
$740$	−0.680856	+	16.5793i	−0.0250288	+	0.609467i
$741$		0			0
$742$	−2.07523	−	2.07523i	−0.0761841	−	0.0761841i
$743$	26.0283	+	26.0283i	0.954886	+	0.954886i	0.999025	−	0.0441394i	$-0.0140546\pi$
$743$	26.0283	+	26.0283i	0.954886	+	0.954886i	−0.0441394	+	0.999025i	$0.514055\pi$
$744$		0			0
$745$	13.8557	−	12.7625i	0.507632	−	0.467583i
$746$		−	22.8275i		−	0.835776i
$747$		0			0
$748$	−4.46837	+	4.46837i	−0.163380	+	0.163380i
$749$	5.89595			0.215433
$750$		0			0
$751$	18.1123			0.660929			0.330464	−	0.943818i	$-0.392795\pi$
$751$	18.1123			0.660929			0.330464	+	0.943818i	$0.392795\pi$
$752$	−0.839302	+	0.839302i	−0.0306062	+	0.0306062i
$753$		0			0
$754$			18.6934i			0.680775i
$755$	4.37911	−	4.03363i	0.159372	−	0.146799i
$756$		0			0
$757$	−8.99895	−	8.99895i	−0.327072	−	0.327072i	0.524400	−	0.851472i	$-0.324290\pi$
$757$	−8.99895	−	8.99895i	−0.327072	−	0.327072i	−0.851472	+	0.524400i	$0.824290\pi$
$758$	2.50814	+	2.50814i	0.0910999	+	0.0910999i
$759$		0			0
$760$	−0.0752308	+	1.83192i	−0.00272891	+	0.0664507i
$761$		−	38.6454i		−	1.40089i	−0.713704	−	0.700447i	$-0.752984\pi$
$761$		−	38.6454i		−	1.40089i	0.713704	−	0.700447i	$-0.247016\pi$
$762$		0			0
$763$	1.61758	−	1.61758i	0.0585602	−	0.0585602i
$764$	12.2356			0.442668
$765$		0			0
$766$	5.27290			0.190518
$767$	−28.0130	+	28.0130i	−1.01149	+	1.01149i
$768$		0			0
$769$			16.3759i			0.590529i	0.955416	+	0.295265i	$0.0954078\pi$
$769$			16.3759i			0.590529i	−0.955416	+	0.295265i	$0.904592\pi$
$770$	−7.47881	−	8.11938i	−0.269518	−	0.292602i
$771$		0			0
$772$	11.7137	+	11.7137i	0.421586	+	0.421586i
$773$	7.37620	+	7.37620i	0.265303	+	0.265303i	0.827204	−	0.561901i	$-0.189930\pi$
$773$	7.37620	+	7.37620i	0.265303	+	0.265303i	−0.561901	+	0.827204i	$0.689930\pi$
$774$		0			0
$775$	−3.44098	+	41.8244i	−0.123604	+	1.50238i
$776$			4.73297i			0.169904i
$777$		0			0
$778$	−5.13708	+	5.13708i	−0.184173	+	0.184173i
$779$	−7.97602			−0.285771
$780$		0			0
$781$	−69.1030			−2.47270
$782$	1.74540	−	1.74540i	0.0624154	−	0.0624154i
$783$		0			0
$784$			6.38969i			0.228203i
$785$	31.5429	+	1.29536i	1.12582	+	0.0462335i
$786$		0			0
$787$	19.9625	+	19.9625i	0.711587	+	0.711587i	0.966867	−	0.255280i	$-0.0821677\pi$
$787$	19.9625	+	19.9625i	0.711587	+	0.711587i	−0.255280	+	0.966867i	$0.582168\pi$
$788$	5.18301	+	5.18301i	0.184637	+	0.184637i
$789$		0			0
$790$	−37.5227	−	1.54093i	−1.33500	−	0.0548239i
$791$		−	10.7417i		−	0.381930i
$792$		0			0
$793$	−34.9714	+	34.9714i	−1.24187	+	1.24187i
$794$	−26.1656			−0.928584
$795$		0			0
$796$	−4.76014			−0.168719
$797$	14.1373	−	14.1373i	0.500767	−	0.500767i	−0.410909	−	0.911676i	$-0.634789\pi$
$797$	14.1373	−	14.1373i	0.500767	−	0.500767i	0.911676	+	0.410909i	$0.134789\pi$
$798$		0			0
$799$			1.18695i			0.0419914i
$800$	−3.23373	−	3.81353i	−0.114330	−	0.134828i
$801$		0			0
$802$	−21.8151	−	21.8151i	−0.770317	−	0.770317i
$803$	−17.0293	−	17.0293i	−0.600952	−	0.600952i
$804$		0			0
$805$	2.92132	+	3.17153i	0.102963	+	0.111782i
$806$			34.1651i			1.20341i
$807$		0			0
$808$	−8.24190	+	8.24190i	−0.289949	+	0.289949i
$809$	−46.7263			−1.64281			−0.821405	−	0.570345i	$-0.806809\pi$
$809$	−46.7263			−1.64281			−0.821405	+	0.570345i	$0.806809\pi$
$810$		0			0
$811$	−15.2247			−0.534611			−0.267306	−	0.963612i	$-0.586133\pi$
$811$	−15.2247			−0.534611			−0.267306	+	0.963612i	$0.586133\pi$
$812$	−2.53684	+	2.53684i	−0.0890255	+	0.0890255i
$813$		0			0
$814$			46.8933i			1.64361i
$815$	1.46671	−	35.7155i	0.0513768	−	1.25106i
$816$		0			0
$817$	−5.20399	−	5.20399i	−0.182065	−	0.182065i
$818$	20.1362	+	20.1362i	0.704046	+	0.704046i
$819$		0			0
$820$	15.9986	−	14.7364i	0.558695	−	0.514617i
$821$			4.68804i			0.163614i	0.996648	+	0.0818069i	$0.0260691\pi$
$821$			4.68804i			0.163614i	−0.996648	+	0.0818069i	$0.973931\pi$
$822$		0			0
$823$	−28.9865	+	28.9865i	−1.01040	+	1.01040i	−0.0104596	+	0.999945i	$0.503329\pi$
$823$	−28.9865	+	28.9865i	−1.01040	+	1.01040i	−0.999945	+	0.0104596i	$0.996671\pi$
$824$	10.6037			0.369398
$825$		0			0
$826$	−7.60314			−0.264547
$827$	31.9500	−	31.9500i	1.11101	−	1.11101i	0.117996	−	0.993014i	$-0.462353\pi$
$827$	31.9500	−	31.9500i	1.11101	−	1.11101i	0.993014	−	0.117996i	$-0.0376471\pi$
$828$		0			0
$829$			39.5175i			1.37250i	0.727367	+	0.686249i	$0.240744\pi$
$829$			39.5175i			1.37250i	−0.727367	+	0.686249i	$0.759256\pi$
$830$	−15.6465	+	14.4121i	−0.543098	+	0.500251i
$831$		0			0
$832$	−2.87834	−	2.87834i	−0.0997887	−	0.0997887i
$833$	4.51819	+	4.51819i	0.156546	+	0.156546i
$834$		0			0
$835$	−0.694844	+	16.9199i	−0.0240461	+	0.585537i
$836$			5.18145i			0.179204i
$837$		0			0
$838$	22.1093	−	22.1093i	0.763751	−	0.763751i
$839$	−2.25909			−0.0779925			−0.0389962	−	0.999239i	$-0.512416\pi$
$839$	−2.25909			−0.0779925			−0.0389962	+	0.999239i	$0.512416\pi$
$840$		0			0
$841$	−7.91069			−0.272783
$842$	10.4773	−	10.4773i	0.361071	−	0.361071i
$843$		0			0
$844$		−	16.0831i		−	0.553604i
$845$	−5.40790	−	5.87109i	−0.186037	−	0.201972i
$846$		0			0
$847$	−15.9827	−	15.9827i	−0.549171	−	0.549171i
$848$	−2.65638	−	2.65638i	−0.0912205	−	0.0912205i
$849$		0			0
$850$	−4.98316	−	0.409975i	−0.170921	−	0.0140620i
$851$		−	18.3171i		−	0.627903i
$852$		0			0
$853$	−26.6517	+	26.6517i	−0.912538	+	0.912538i	−0.996471	−	0.0839335i	$-0.973252\pi$
$853$	−26.6517	+	26.6517i	−0.912538	+	0.912538i	0.0839335	+	0.996471i	$0.473252\pi$
$854$	−9.49175			−0.324801
$855$		0			0
$856$	7.54705			0.257953
$857$	−16.2775	+	16.2775i	−0.556029	+	0.556029i	−0.928174	−	0.372146i	$-0.878622\pi$
$857$	−16.2775	+	16.2775i	−0.556029	+	0.556029i	0.372146	+	0.928174i	$0.378622\pi$
$858$		0			0
$859$		−	27.9594i		−	0.953963i	−0.878913	−	0.476982i	$-0.841731\pi$
$859$		−	27.9594i		−	0.953963i	0.878913	−	0.476982i	$-0.158269\pi$
$860$	20.0532	+	0.823517i	0.683807	+	0.0280817i
$861$		0			0
$862$	1.93828	+	1.93828i	0.0660182	+	0.0660182i
$863$	3.25510	+	3.25510i	0.110805	+	0.110805i	0.760336	−	0.649531i	$-0.225035\pi$
$863$	3.25510	+	3.25510i	0.110805	+	0.110805i	−0.649531	+	0.760336i	$0.725035\pi$
$864$		0			0
$865$	−42.3666	−	1.73985i	−1.44051	−	0.0591568i
$866$		−	7.54336i		−	0.256334i
$867$		0			0
$868$	−4.63645	+	4.63645i	−0.157371	+	0.157371i
$869$	−106.130			−3.60022
$870$		0			0
$871$	64.8666			2.19792
$872$	2.07056	−	2.07056i	0.0701182	−	0.0701182i
$873$		0			0
$874$		−	2.02394i		−	0.0684608i
$875$	1.07275	−	8.66823i	0.0362657	−	0.293040i
$876$		0			0
$877$	35.0861	+	35.0861i	1.18477	+	1.18477i	0.978493	+	0.206279i	$0.0661356\pi$
$877$	35.0861	+	35.0861i	1.18477	+	1.18477i	0.206279	+	0.978493i	$0.433864\pi$
$878$	−11.9973	−	11.9973i	−0.404888	−	0.404888i
$879$		0			0
$880$	−9.57319	−	10.3931i	−0.322712	−	0.350353i
$881$			24.4474i			0.823653i	0.911262	+	0.411827i	$0.135109\pi$
$881$			24.4474i			0.823653i	−0.911262	+	0.411827i	$0.864891\pi$
$882$		0			0
$883$	3.42823	−	3.42823i	0.115369	−	0.115369i	−0.647065	−	0.762434i	$-0.724004\pi$
$883$	3.42823	−	3.42823i	0.115369	−	0.115369i	0.762434	+	0.647065i	$0.224004\pi$
$884$	−4.07059			−0.136909
$885$		0			0
$886$	13.7944			0.463433
$887$	−19.6281	+	19.6281i	−0.659047	+	0.659047i	−0.955155	−	0.296108i	$-0.904311\pi$
$887$	−19.6281	+	19.6281i	−0.659047	+	0.659047i	0.296108	+	0.955155i	$0.404311\pi$
$888$		0			0
$889$			9.40193i			0.315331i
$890$	0.699786	−	17.0402i	0.0234569	−	0.571190i
$891$		0			0
$892$	−16.5852	−	16.5852i	−0.555312	−	0.555312i
$893$	0.688186	+	0.688186i	0.0230293	+	0.0230293i
$894$		0			0
$895$	18.9871	−	17.4891i	0.634669	−	0.584598i
$896$		−	0.781225i		−	0.0260989i
$897$		0			0
$898$	5.09489	−	5.09489i	0.170019	−	0.170019i
$899$	38.5439			1.28551
$900$		0			0
$901$	−3.75669			−0.125153
$902$	43.4658	−	43.4658i	1.44725	−	1.44725i
$903$		0			0
$904$		−	13.7498i		−	0.457311i
$905$	18.5771	−	17.1115i	0.617523	−	0.568804i
$906$		0			0
$907$	−33.7577	−	33.7577i	−1.12091	−	1.12091i	−0.991606	−	0.129300i	$-0.958727\pi$
$907$	−33.7577	−	33.7577i	−1.12091	−	1.12091i	−0.129300	−	0.991606i	$-0.541273\pi$
$908$	−8.56786	−	8.56786i	−0.284335	−	0.284335i
$909$		0			0
$910$	0.291771	−	7.10482i	0.00967212	−	0.235522i
$911$			18.1016i			0.599734i	0.953981	+	0.299867i	$0.0969423\pi$
$911$			18.1016i			0.599734i	−0.953981	+	0.299867i	$0.903058\pi$
$912$		0			0
$913$	−42.5093	+	42.5093i	−1.40685	+	1.40685i
$914$	11.7705			0.389332
$915$		0			0
$916$	1.63300			0.0539558
$917$	3.01401	−	3.01401i	0.0995314	−	0.0995314i
$918$		0			0
$919$		−	12.3195i		−	0.406384i	−0.979139	−	0.203192i	$-0.934869\pi$
$919$		−	12.3195i		−	0.406384i	0.979139	−	0.203192i	$-0.0651315\pi$
$920$	3.73941	+	4.05969i	0.123285	+	0.133844i
$921$		0			0
$922$	26.0440	+	26.0440i	0.857712	+	0.857712i
$923$	−31.4757	−	31.4757i	−1.03604	−	1.03604i
$924$		0			0
$925$	−28.2992	+	23.9967i	−0.930471	+	0.789006i
$926$			20.0697i			0.659530i
$927$		0			0
$928$	−3.24725	+	3.24725i	−0.106596	+	0.106596i
$929$	50.3422			1.65167			0.825836	−	0.563910i	$-0.190704\pi$
$929$	50.3422			1.65167			0.825836	+	0.563910i	$0.190704\pi$
$930$		0			0
$931$	5.23923			0.171709
$932$	−7.07107	+	7.07107i	−0.231621	+	0.231621i
$933$		0			0
$934$		−	4.90590i		−	0.160526i
$935$	−14.1183	−	0.579792i	−0.461719	−	0.0189612i
$936$		0			0
$937$	−6.28451	−	6.28451i	−0.205306	−	0.205306i	0.596963	−	0.802269i	$-0.296374\pi$
$937$	−6.28451	−	6.28451i	−0.205306	−	0.205306i	−0.802269	+	0.596963i	$0.796374\pi$
$938$	8.80287	+	8.80287i	0.287424	+	0.287424i
$939$		0			0
$940$	−2.65187	−	0.108903i	−0.0864945	−	0.00355204i
$941$			5.84624i			0.190582i	0.995449	+	0.0952910i	$0.0303782\pi$
$941$			5.84624i			0.190582i	−0.995449	+	0.0952910i	$0.969622\pi$
$942$		0			0
$943$	−16.9783	+	16.9783i	−0.552889	+	0.552889i
$944$	−9.73233			−0.316760
$945$		0			0
$946$	56.7189			1.84409
$947$	−34.9447	+	34.9447i	−1.13555	+	1.13555i	−0.146311	+	0.989239i	$0.546740\pi$
$947$	−34.9447	+	34.9447i	−1.13555	+	1.13555i	−0.989239	+	0.146311i	$0.953260\pi$
$948$		0			0
$949$		−	15.5134i		−	0.503586i
$950$	−3.12690	+	2.65150i	−0.101450	+	0.0860260i
$951$		0			0
$952$	−0.552409	−	0.552409i	−0.0179037	−	0.0179037i
$953$	−11.1076	−	11.1076i	−0.359810	−	0.359810i	0.503933	−	0.863743i	$-0.331886\pi$
$953$	−11.1076	−	11.1076i	−0.359810	−	0.359810i	−0.863743	+	0.503933i	$0.831886\pi$
$954$		0			0
$955$	18.5361	+	20.1237i	0.599813	+	0.651187i
$956$		−	8.36913i		−	0.270677i
$957$		0			0
$958$	5.85996	−	5.85996i	0.189327	−	0.189327i
$959$	7.04875			0.227616
$960$		0			0
$961$	39.4448			1.27241
$962$	−21.3594	+	21.3594i	−0.688656	+	0.688656i
$963$		0			0
$964$		−	3.87348i		−	0.124756i
$965$	−1.51991	+	37.0108i	−0.0489277	+	1.19142i
$966$		0			0
$967$	17.9679	+	17.9679i	0.577810	+	0.577810i	0.934299	−	0.356489i	$-0.116026\pi$
$967$	17.9679	+	17.9679i	0.577810	+	0.577810i	−0.356489	+	0.934299i	$0.616026\pi$
$968$	−20.4585	−	20.4585i	−0.657560	−	0.657560i
$969$		0			0
$970$	−7.78424	+	7.17012i	−0.249937	+	0.230219i
$971$			27.8430i			0.893523i	0.894653	+	0.446761i	$0.147423\pi$
$971$			27.8430i			0.893523i	−0.894653	+	0.446761i	$0.852577\pi$
$972$		0			0
$973$	−5.59242	+	5.59242i	−0.179285	+	0.179285i
$974$	0.109089			0.00349543
$975$		0			0
$976$	−12.1498			−0.388907
$977$	−17.2183	+	17.2183i	−0.550863	+	0.550863i	−0.926690	−	0.375827i	$-0.877359\pi$
$977$	−17.2183	+	17.2183i	−0.550863	+	0.550863i	0.375827	+	0.926690i	$0.377359\pi$
$978$		0			0
$979$		−	48.1971i		−	1.54039i
$980$	−10.5090	+	9.67993i	−0.335698	+	0.309214i
$981$		0			0
$982$	−2.49937	−	2.49937i	−0.0797582	−	0.0797582i
$983$	19.6352	+	19.6352i	0.626264	+	0.626264i	0.947126	−	0.320862i	$-0.103973\pi$
$983$	19.6352	+	19.6352i	0.626264	+	0.626264i	−0.320862	+	0.947126i	$0.603973\pi$
$984$		0			0
$985$	−0.672520	+	16.3763i	−0.0214283	+	0.521792i
$986$			4.59231i			0.146249i
$987$		0			0
$988$	−2.36010	+	2.36010i	−0.0750848	+	0.0750848i
$989$	−22.1551			−0.704492
$990$		0			0
$991$	9.56912			0.303973			0.151986	−	0.988383i	$-0.451433\pi$
$991$	9.56912			0.303973			0.151986	+	0.988383i	$0.451433\pi$
$992$	−5.93485	+	5.93485i	−0.188432	+	0.188432i
$993$		0			0
$994$		−	8.54297i		−	0.270966i
$995$	−7.21128	−	7.82893i	−0.228613	−	0.248194i
$996$		0			0
$997$	5.78395	+	5.78395i	0.183180	+	0.183180i	0.792740	−	0.609560i	$-0.208654\pi$
$997$	5.78395	+	5.78395i	0.183180	+	0.183180i	−0.609560	+	0.792740i	$0.708654\pi$
$998$	15.9543	+	15.9543i	0.505026	+	0.505026i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.h.647.3	✓	16
3.2	odd	2	inner	1530.2.m.h.647.6	yes	16
5.3	odd	4	inner	1530.2.m.h.953.6	yes	16
15.8	even	4	inner	1530.2.m.h.953.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.h.647.3	✓	16	1.1	even	1	trivial
1530.2.m.h.647.6	yes	16	3.2	odd	2	inner
1530.2.m.h.953.3	yes	16	15.8	even	4	inner
1530.2.m.h.953.6	yes	16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.64468 - 1.51493i) q^{5} +(0.552409 + 0.552409i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0917505 + 2.23418i) q^{10} +6.31923i q^{11} +(-2.87834 + 2.87834i) q^{13} -0.781225 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +0.819950i q^{19} +(-1.51493 - 1.64468i) q^{20} +(-4.46837 - 4.46837i) q^{22} +(1.74540 + 1.74540i) q^{23} +(0.409975 - 4.98316i) q^{25} -4.07059i q^{26} +(0.552409 - 0.552409i) q^{28} -4.59231 q^{29} -8.39314 q^{31} +(0.707107 - 0.707107i) q^{32} -1.00000i q^{34} +(1.74540 + 0.0716778i) q^{35} +(-5.24725 - 5.24725i) q^{37} +(-0.579792 - 0.579792i) q^{38} +(2.23418 + 0.0917505i) q^{40} +9.72745i q^{41} +(-6.34671 + 6.34671i) q^{43} +6.31923 q^{44} -2.46837 q^{46} +(0.839302 - 0.839302i) q^{47} -6.38969i q^{49} +(3.23373 + 3.81353i) q^{50} +(2.87834 + 2.87834i) q^{52} +(2.65638 + 2.65638i) q^{53} +(9.57319 + 10.3931i) q^{55} +0.781225i q^{56} +(3.24725 - 3.24725i) q^{58} +9.73233 q^{59} +12.1498 q^{61} +(5.93485 - 5.93485i) q^{62} +1.00000i q^{64} +(-0.373479 + 9.09446i) q^{65} +(-11.2680 - 11.2680i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-1.28487 + 1.18350i) q^{70} +10.9353i q^{71} +(-2.69484 + 2.69484i) q^{73} +7.42074 q^{74} +0.819950 q^{76} +(-3.49080 + 3.49080i) q^{77} +16.7948i q^{79} +(-1.64468 + 1.51493i) q^{80} +(-6.87834 - 6.87834i) q^{82} +(6.72697 + 6.72697i) q^{83} +(-0.0917505 + 2.23418i) q^{85} -8.97561i q^{86} +(-4.46837 + 4.46837i) q^{88} -7.62705 q^{89} -3.18005 q^{91} +(1.74540 - 1.74540i) q^{92} +1.18695i q^{94} +(1.24217 + 1.34856i) q^{95} +(3.34671 + 3.34671i) q^{97} +(4.51819 + 4.51819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70}+ \cdots - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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