LMFDB - Embedded newform 17.4.c.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 $ x^8 + 46x^6 + 561x^4 + 836*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.2
Root			$-0.648995i$ of defining polynomial
Character	$\chi$	$=$	17.4
Dual form			17.4.c.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.351005i q^{2} +(2.28193 - 2.28193i) q^{3} +7.87680 q^{4} +(-9.32676 + 9.32676i) q^{5} +(0.800971 + 0.800971i) q^{6} +(-23.5385 - 23.5385i) q^{7} +5.57284i q^{8} +16.5856i q^{9} +O(q^{10})$	\(q+0.351005i q^{2} +(2.28193 - 2.28193i) q^{3} +7.87680 q^{4} +(-9.32676 + 9.32676i) q^{5} +(0.800971 + 0.800971i) q^{6} +(-23.5385 - 23.5385i) q^{7} +5.57284i q^{8} +16.5856i q^{9} +(-3.27374 - 3.27374i) q^{10} +(9.63747 + 9.63747i) q^{11} +(17.9743 - 17.9743i) q^{12} -5.12996 q^{13} +(8.26214 - 8.26214i) q^{14} +42.5661i q^{15} +61.0583 q^{16} +(44.3321 - 54.2924i) q^{17} -5.82162 q^{18} -38.4093i q^{19} +(-73.4650 + 73.4650i) q^{20} -107.427 q^{21} +(-3.38280 + 3.38280i) q^{22} +(13.2465 + 13.2465i) q^{23} +(12.7169 + 12.7169i) q^{24} -48.9769i q^{25} -1.80065i q^{26} +(99.4593 + 99.4593i) q^{27} +(-185.408 - 185.408i) q^{28} +(-149.326 + 149.326i) q^{29} -14.9409 q^{30} +(165.754 - 165.754i) q^{31} +66.0145i q^{32} +43.9841 q^{33} +(19.0569 + 15.5608i) q^{34} +439.076 q^{35} +130.641i q^{36} +(1.96470 - 1.96470i) q^{37} +13.4819 q^{38} +(-11.7062 + 11.7062i) q^{39} +(-51.9766 - 51.9766i) q^{40} +(-214.806 - 214.806i) q^{41} -37.7073i q^{42} +149.494i q^{43} +(75.9123 + 75.9123i) q^{44} +(-154.690 - 154.690i) q^{45} +(-4.64959 + 4.64959i) q^{46} -366.525 q^{47} +(139.331 - 139.331i) q^{48} +765.122i q^{49} +17.1912 q^{50} +(-22.7288 - 225.054i) q^{51} -40.4077 q^{52} -499.269i q^{53} +(-34.9108 + 34.9108i) q^{54} -179.773 q^{55} +(131.176 - 131.176i) q^{56} +(-87.6475 - 87.6475i) q^{57} +(-52.4143 - 52.4143i) q^{58} +507.289i q^{59} +335.284i q^{60} +(-23.3801 - 23.3801i) q^{61} +(58.1805 + 58.1805i) q^{62} +(390.399 - 390.399i) q^{63} +465.295 q^{64} +(47.8459 - 47.8459i) q^{65} +15.4387i q^{66} +442.124 q^{67} +(349.195 - 427.650i) q^{68} +60.4552 q^{69} +154.118i q^{70} +(-336.486 + 336.486i) q^{71} -92.4287 q^{72} +(-520.414 + 520.414i) q^{73} +(0.689621 + 0.689621i) q^{74} +(-111.762 - 111.762i) q^{75} -302.543i q^{76} -453.703i q^{77} +(-4.10895 - 4.10895i) q^{78} +(-151.631 - 151.631i) q^{79} +(-569.476 + 569.476i) q^{80} +6.10881 q^{81} +(75.3981 - 75.3981i) q^{82} -1187.18i q^{83} -846.177 q^{84} +(92.8977 + 919.847i) q^{85} -52.4734 q^{86} +681.505i q^{87} +(-53.7081 + 53.7081i) q^{88} +325.436 q^{89} +(54.2969 - 54.2969i) q^{90} +(120.752 + 120.752i) q^{91} +(104.340 + 104.340i) q^{92} -756.478i q^{93} -128.652i q^{94} +(358.235 + 358.235i) q^{95} +(150.641 + 150.641i) q^{96} +(169.723 - 169.723i) q^{97} -268.562 q^{98} +(-159.843 + 159.843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) $ 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7	$ 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) $ 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7 + 78 * q^10 - 108 * q^11 - 174 * q^12 - 88 * q^13 + 108 * q^14 + 420 * q^16 - 10 * q^17 + 428 * q^18 - 306 * q^20 - 260 * q^21 + 30 * q^22 - 22 * q^23 - 862 * q^24 + 540 * q^27 - 764 * q^28 + 46 * q^29 - 120 * q^30 + 610 * q^31 + 816 * q^33 + 1002 * q^34 + 1172 * q^35 - 574 * q^37 - 768 * q^38 - 844 * q^39 - 342 * q^40 - 968 * q^41 + 550 * q^44 - 1154 * q^45 - 944 * q^46 - 368 * q^47 + 2494 * q^48 + 468 * q^50 + 296 * q^51 + 2564 * q^52 - 1592 * q^54 - 1996 * q^55 + 684 * q^56 - 300 * q^57 + 266 * q^58 + 1258 * q^61 - 2516 * q^62 + 122 * q^63 - 3044 * q^64 + 628 * q^65 + 764 * q^67 + 1914 * q^68 + 1812 * q^69 + 1266 * q^71 + 1404 * q^72 - 1732 * q^73 + 1538 * q^74 + 1292 * q^75 - 2836 * q^78 + 914 * q^79 + 498 * q^80 + 280 * q^81 - 280 * q^82 - 2952 * q^84 - 2498 * q^85 - 4244 * q^86 + 442 * q^88 - 2156 * q^89 + 2478 * q^90 - 1632 * q^91 - 1768 * q^92 + 1484 * q^95 + 3998 * q^96 + 1836 * q^97 + 6728 * q^98 - 2088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			0.351005i			0.124099i	0.998073	+	0.0620496i	$0.0197637\pi$
$2$			0.351005i			0.124099i	−0.998073	+	0.0620496i	$0.980236\pi$
$3$	2.28193	−	2.28193i	0.439158	−	0.439158i	−0.452570	−	0.891729i	$-0.649493\pi$
$3$	2.28193	−	2.28193i	0.439158	−	0.439158i	0.891729	+	0.452570i	$0.149493\pi$
$4$	7.87680			0.984599
$5$	−9.32676	+	9.32676i	−0.834211	+	0.834211i	−0.988090	−	0.153879i	$-0.950823\pi$
$5$	−9.32676	+	9.32676i	−0.834211	+	0.834211i	0.153879	+	0.988090i	$0.450823\pi$
$6$	0.800971	+	0.800971i	0.0544992	+	0.0544992i
$7$	−23.5385	−	23.5385i	−1.27096	−	1.27096i	−0.945585	−	0.325375i	$-0.894510\pi$
$7$	−23.5385	−	23.5385i	−1.27096	−	1.27096i	−0.325375	−	0.945585i	$-0.605490\pi$
$8$			5.57284i			0.246287i
$9$			16.5856i			0.614280i
$10$	−3.27374	−	3.27374i	−0.103525	−	0.103525i
$11$	9.63747	+	9.63747i	0.264164	+	0.264164i	0.826743	−	0.562579i	$-0.190191\pi$
$11$	9.63747	+	9.63747i	0.264164	+	0.264164i	−0.562579	+	0.826743i	$0.690191\pi$
$12$	17.9743	−	17.9743i	0.432395	−	0.432395i
$13$	−5.12996			−0.109446			−0.0547229	−	0.998502i	$-0.517428\pi$
$13$	−5.12996			−0.109446			−0.0547229	+	0.998502i	$0.517428\pi$
$14$	8.26214	−	8.26214i	0.157725	−	0.157725i
$15$			42.5661i			0.732701i
$16$	61.0583			0.954035
$17$	44.3321	−	54.2924i	0.632477	−	0.774579i
$17$	44.3321	−	54.2924i	0.632477	−	0.774579i
$18$	−5.82162			−0.0762317
$19$		−	38.4093i		−	0.463774i	−0.972743	−	0.231887i	$-0.925510\pi$
$19$		−	38.4093i		−	0.463774i	0.972743	−	0.231887i	$-0.0744900\pi$
$20$	−73.4650	+	73.4650i	−0.821363	+	0.821363i
$21$	−107.427			−1.11630
$22$	−3.38280	+	3.38280i	−0.0327825	+	0.0327825i
$23$	13.2465	+	13.2465i	0.120091	+	0.120091i	0.764598	−	0.644507i	$-0.222938\pi$
$23$	13.2465	+	13.2465i	0.120091	+	0.120091i	−0.644507	+	0.764598i	$0.722938\pi$
$24$	12.7169	+	12.7169i	0.108159	+	0.108159i
$25$		−	48.9769i		−	0.391815i
$26$		−	1.80065i		−	0.0135821i
$27$	99.4593	+	99.4593i	0.708924	+	0.708924i
$28$	−185.408	−	185.408i	−1.25139	−	1.25139i
$29$	−149.326	+	149.326i	−0.956179	+	0.956179i	−0.999079	−	0.0429005i	$-0.986340\pi$
$29$	−149.326	+	149.326i	−0.956179	+	0.956179i	0.0429005	+	0.999079i	$0.486340\pi$
$30$	−14.9409			−0.0909276
$31$	165.754	−	165.754i	0.960331	−	0.960331i	−0.0389120	−	0.999243i	$-0.512389\pi$
$31$	165.754	−	165.754i	0.960331	−	0.960331i	0.999243	+	0.0389120i	$0.0123892\pi$
$32$			66.0145i			0.364682i
$33$	43.9841			0.232020
$34$	19.0569	+	15.5608i	0.0961246	+	0.0784899i
$35$	439.076			2.12050
$36$			130.641i			0.604820i
$37$	1.96470	−	1.96470i	0.00872959	−	0.00872959i	−0.702729	−	0.711458i	$-0.748035\pi$
$37$	1.96470	−	1.96470i	0.00872959	−	0.00872959i	0.711458	+	0.702729i	$0.248035\pi$
$38$	13.4819			0.0575540
$39$	−11.7062	+	11.7062i	−0.0480640	+	0.0480640i
$40$	−51.9766	−	51.9766i	−0.205455	−	0.205455i
$41$	−214.806	−	214.806i	−0.818221	−	0.818221i	0.167629	−	0.985850i	$-0.446389\pi$
$41$	−214.806	−	214.806i	−0.818221	−	0.818221i	−0.985850	+	0.167629i	$0.946389\pi$
$42$		−	37.7073i		−	0.138533i
$43$			149.494i			0.530179i	0.964224	+	0.265089i	$0.0854015\pi$
$43$			149.494i			0.530179i	−0.964224	+	0.265089i	$0.914599\pi$
$44$	75.9123	+	75.9123i	0.260096	+	0.260096i
$45$	−154.690	−	154.690i	−0.512439	−	0.512439i
$46$	−4.64959	+	4.64959i	−0.0149031	+	0.0149031i
$47$	−366.525			−1.13751			−0.568757	−	0.822506i	$-0.692576\pi$
$47$	−366.525			−1.13751			−0.568757	+	0.822506i	$0.692576\pi$
$48$	139.331	−	139.331i	0.418972	−	0.418972i
$49$			765.122i			2.23068i
$50$	17.1912			0.0486240
$51$	−22.7288	−	225.054i	−0.0624053	−	0.617920i
$52$	−40.4077			−0.107760
$53$		−	499.269i		−	1.29396i	−0.762507	−	0.646981i	$-0.776031\pi$
$53$		−	499.269i		−	1.29396i	0.762507	−	0.646981i	$-0.223969\pi$
$54$	−34.9108	+	34.9108i	−0.0879769	+	0.0879769i
$55$	−179.773			−0.440737
$56$	131.176	−	131.176i	0.313021	−	0.313021i
$57$	−87.6475	−	87.6475i	−0.203670	−	0.203670i
$58$	−52.4143	−	52.4143i	−0.118661	−	0.118661i
$59$			507.289i			1.11938i	0.828702	+	0.559690i	$0.189080\pi$
$59$			507.289i			1.11938i	−0.828702	+	0.559690i	$0.810920\pi$
$60$			335.284i			0.721417i
$61$	−23.3801	−	23.3801i	−0.0490741	−	0.0490741i	0.682144	−	0.731218i	$-0.261048\pi$
$61$	−23.3801	−	23.3801i	−0.0490741	−	0.0490741i	−0.731218	+	0.682144i	$0.761048\pi$
$62$	58.1805	+	58.1805i	0.119176	+	0.119176i
$63$	390.399	−	390.399i	0.780725	−	0.780725i
$64$	465.295			0.908779
$65$	47.8459	−	47.8459i	0.0913009	−	0.0913009i
$66$			15.4387i			0.0287934i
$67$	442.124			0.806180			0.403090	−	0.915160i	$-0.367936\pi$
$67$	442.124			0.806180			0.403090	+	0.915160i	$0.367936\pi$
$68$	349.195	−	427.650i	0.622736	−	0.762650i
$69$	60.4552			0.105477
$70$			154.118i			0.263152i
$71$	−336.486	+	336.486i	−0.562444	+	0.562444i	−0.930001	−	0.367557i	$-0.880194\pi$
$71$	−336.486	+	336.486i	−0.562444	+	0.562444i	0.367557	+	0.930001i	$0.380194\pi$
$72$	−92.4287			−0.151289
$73$	−520.414	+	520.414i	−0.834382	+	0.834382i	−0.988113	−	0.153731i	$-0.950871\pi$
$73$	−520.414	+	520.414i	−0.834382	+	0.834382i	0.153731	+	0.988113i	$0.450871\pi$
$74$	0.689621	+	0.689621i	0.00108334	+	0.00108334i
$75$	−111.762	−	111.762i	−0.172069	−	0.172069i
$76$		−	302.543i		−	0.456632i
$77$		−	453.703i		−	0.671484i
$78$	−4.10895	−	4.10895i	−0.00596471	−	0.00596471i
$79$	−151.631	−	151.631i	−0.215947	−	0.215947i	0.590841	−	0.806788i	$-0.298796\pi$
$79$	−151.631	−	151.631i	−0.215947	−	0.215947i	−0.806788	+	0.590841i	$0.798796\pi$
$80$	−569.476	+	569.476i	−0.795867	+	0.795867i
$81$	6.10881			0.00837971
$82$	75.3981	−	75.3981i	0.101541	−	0.101541i
$83$		−	1187.18i		−	1.57000i	−0.619497	−	0.784999i	$-0.712664\pi$
$83$		−	1187.18i		−	1.57000i	0.619497	−	0.784999i	$-0.287336\pi$
$84$	−846.177			−1.09911
$85$	92.8977	+	919.847i	0.118543	+	1.17378i
$86$	−52.4734			−0.0657948
$87$			681.505i			0.839828i
$88$	−53.7081	+	53.7081i	−0.0650602	+	0.0650602i
$89$	325.436			0.387598			0.193799	−	0.981041i	$-0.437919\pi$
$89$	325.436			0.387598			0.193799	+	0.981041i	$0.437919\pi$
$90$	54.2969	−	54.2969i	0.0635933	−	0.0635933i
$91$	120.752	+	120.752i	0.139101	+	0.139101i
$92$	104.340	+	104.340i	0.118241	+	0.118241i
$93$		−	756.478i		−	0.843474i
$94$		−	128.652i		−	0.141165i
$95$	358.235	+	358.235i	0.386885	+	0.386885i
$96$	150.641	+	150.641i	0.160153	+	0.160153i
$97$	169.723	−	169.723i	0.177657	−	0.177657i	−0.612676	−	0.790334i	$-0.709907\pi$
$97$	169.723	−	169.723i	0.177657	−	0.177657i	0.790334	+	0.612676i	$0.209907\pi$
$98$	−268.562			−0.276825
$99$	−159.843	+	159.843i	−0.162271	+	0.162271i
$100$		−	385.781i		−	0.385781i
$101$	718.617			0.707971			0.353986	−	0.935251i	$-0.384826\pi$
$101$	718.617			0.707971			0.353986	+	0.935251i	$0.384826\pi$
$102$	78.9954	−	7.97794i	0.0766834	−	0.00774445i
$103$	−797.855			−0.763252			−0.381626	−	0.924317i	$-0.624636\pi$
$103$	−797.855			−0.763252			−0.381626	+	0.924317i	$0.624636\pi$
$104$		−	28.5885i		−	0.0269551i
$105$	1001.94	−	1001.94i	0.931234	−	0.931234i
$106$	175.246			0.160580
$107$	325.977	−	325.977i	0.294518	−	0.294518i	−0.544344	−	0.838862i	$-0.683221\pi$
$107$	325.977	−	325.977i	0.294518	−	0.294518i	0.838862	+	0.544344i	$0.183221\pi$
$108$	783.421	+	783.421i	0.698006	+	0.698006i
$109$	1107.84	+	1107.84i	0.973499	+	0.973499i	0.999658	−	0.0261591i	$-0.00832764\pi$
$109$	1107.84	+	1107.84i	0.973499	+	0.973499i	−0.0261591	+	0.999658i	$0.508328\pi$
$110$		−	63.1012i		−	0.0546951i
$111$		−	8.96663i		−	0.00766734i
$112$	−1437.22	−	1437.22i	−1.21254	−	1.21254i
$113$	1129.02	+	1129.02i	0.939902	+	0.939902i	0.998294	−	0.0583914i	$-0.0185972\pi$
$113$	1129.02	+	1129.02i	0.939902	+	0.939902i	−0.0583914	+	0.998294i	$0.518597\pi$
$114$	30.7648	−	30.7648i	0.0252753	−	0.0252753i
$115$	−247.093			−0.200362
$116$	−1176.21	+	1176.21i	−0.941453	+	0.941453i
$117$		−	85.0833i		−	0.0672304i
$118$	−178.061			−0.138914
$119$	−2321.47	+	234.451i	−1.78831	+	0.180606i
$120$	−237.214			−0.180455
$121$		−	1145.24i		−	0.860435i
$122$	8.20656	−	8.20656i	0.00609006	−	0.00609006i
$123$	−980.346			−0.718657
$124$	1305.61	−	1305.61i	0.945541	−	0.945541i
$125$	−709.049	−	709.049i	−0.507354	−	0.507354i
$126$	137.032	+	137.032i	0.0968874	+	0.0968874i
$127$			834.122i			0.582806i	0.956600	+	0.291403i	$0.0941221\pi$
$127$			834.122i			0.582806i	−0.956600	+	0.291403i	$0.905878\pi$
$128$			691.437i			0.477461i
$129$	341.136	+	341.136i	0.232832	+	0.232832i
$130$	16.7942	+	16.7942i	0.0113304	+	0.0113304i
$131$	859.796	−	859.796i	0.573440	−	0.573440i	−0.359648	−	0.933088i	$-0.617103\pi$
$131$	859.796	−	859.796i	0.573440	−	0.573440i	0.933088	+	0.359648i	$0.117103\pi$
$132$	346.454			0.228446
$133$	−904.099	+	904.099i	−0.589438	+	0.589438i
$134$			155.188i			0.100046i
$135$	−1855.27			−1.18278
$136$	302.563	+	247.056i	0.190769	+	0.155771i
$137$	−1665.56			−1.03867			−0.519337	−	0.854569i	$-0.673821\pi$
$137$	−1665.56			−1.03867			−0.519337	+	0.854569i	$0.673821\pi$
$138$			21.2201i			0.0130897i
$139$	972.948	−	972.948i	0.593700	−	0.593700i	−0.344929	−	0.938629i	$-0.612097\pi$
$139$	972.948	−	972.948i	0.593700	−	0.593700i	0.938629	+	0.344929i	$0.112097\pi$
$140$	3458.51			2.08784
$141$	−836.386	+	836.386i	−0.499549	+	0.499549i
$142$	−118.108	−	118.108i	−0.0697988	−	0.0697988i
$143$	−49.4398	−	49.4398i	−0.0289117	−	0.0289117i
$144$			1012.69i			0.586045i
$145$		−	2785.46i		−	1.59531i
$146$	−182.668	−	182.668i	−0.103546	−	0.103546i
$147$	1745.96	+	1745.96i	0.979620	+	0.979620i
$148$	15.4755	−	15.4755i	0.00859515	−	0.00859515i
$149$	1917.84			1.05447			0.527234	−	0.849720i	$-0.323229\pi$
$149$	1917.84			1.05447			0.527234	+	0.849720i	$0.323229\pi$
$150$	39.2291	−	39.2291i	0.0213536	−	0.0213536i
$151$		−	1878.30i		−	1.01228i	−0.862452	−	0.506138i	$-0.831073\pi$
$151$		−	1878.30i		−	1.01228i	0.862452	−	0.506138i	$-0.168927\pi$
$152$	214.049			0.114222
$153$	900.470	+	735.273i	0.475809	+	0.388518i
$154$	159.252			0.0833306
$155$			3091.89i			1.60224i
$156$	−92.2076	+	92.2076i	−0.0473238	+	0.0473238i
$157$	98.6939			0.0501696			0.0250848	−	0.999685i	$-0.492014\pi$
$157$	98.6939			0.0501696			0.0250848	+	0.999685i	$0.492014\pi$
$158$	53.2232	−	53.2232i	0.0267988	−	0.0267988i
$159$	−1139.30	−	1139.30i	−0.568254	−	0.568254i
$160$	−615.702	−	615.702i	−0.304222	−	0.304222i
$161$		−	623.605i		−	0.305260i
$162$			2.14423i			0.00103992i
$163$	445.289	+	445.289i	0.213974	+	0.213974i	0.805953	−	0.591979i	$-0.201653\pi$
$163$	445.289	+	445.289i	0.213974	+	0.213974i	−0.591979	+	0.805953i	$0.701653\pi$
$164$	−1691.98	−	1691.98i	−0.805620	−	0.805620i
$165$	−410.229	+	410.229i	−0.193553	+	0.193553i
$166$	416.706			0.194835
$167$	128.907	−	128.907i	0.0597313	−	0.0597313i	−0.676610	−	0.736341i	$-0.736552\pi$
$167$	128.907	−	128.907i	0.0597313	−	0.0597313i	0.736341	+	0.676610i	$0.236552\pi$
$168$		−	598.671i		−	0.274932i
$169$	−2170.68			−0.988022
$170$	−322.871	+	32.6076i	−0.145665	+	0.0147111i
$171$	637.041			0.284887
$172$			1177.54i			0.522014i
$173$	−1124.24	+	1124.24i	−0.494070	+	0.494070i	−0.909586	−	0.415516i	$-0.863601\pi$
$173$	−1124.24	+	1124.24i	−0.494070	+	0.494070i	0.415516	+	0.909586i	$0.363601\pi$
$174$	−239.212			−0.104222
$175$	−1152.84	+	1152.84i	−0.497982	+	0.497982i
$176$	588.447	+	588.447i	0.252022	+	0.252022i
$177$	1157.60	+	1157.60i	0.491585	+	0.491585i
$178$			114.230i			0.0481006i
$179$		−	2471.01i		−	1.03180i	−0.856650	−	0.515898i	$-0.827458\pi$
$179$		−	2471.01i		−	1.03180i	0.856650	−	0.515898i	$-0.172542\pi$
$180$	−1218.46	−	1218.46i	−0.504547	−	0.504547i
$181$	789.143	+	789.143i	0.324069	+	0.324069i	0.850326	−	0.526257i	$-0.176405\pi$
$181$	789.143	+	789.143i	0.324069	+	0.324069i	−0.526257	+	0.850326i	$0.676405\pi$
$182$	−42.3845	+	42.3845i	−0.0172624	+	0.0172624i
$183$	−106.704			−0.0431026
$184$	−73.8205	+	73.8205i	−0.0295768	+	0.0295768i
$185$			36.6486i			0.0145646i
$186$	265.528			0.104674
$187$	950.490	−	95.9924i	0.371694	−	0.0375383i
$188$	−2887.04			−1.12000
$189$		−	4682.25i		−	1.80203i
$190$	−125.742	+	125.742i	−0.0480122	+	0.0480122i
$191$	−3850.07			−1.45854			−0.729271	−	0.684225i	$-0.760141\pi$
$191$	−3850.07			−1.45854			−0.729271	+	0.684225i	$0.760141\pi$
$192$	1061.77	−	1061.77i	0.399098	−	0.399098i
$193$	1572.91	+	1572.91i	0.586634	+	0.586634i	0.936718	−	0.350084i	$-0.113847\pi$
$193$	1572.91	+	1572.91i	0.586634	+	0.586634i	−0.350084	+	0.936718i	$0.613847\pi$
$194$	59.5737	+	59.5737i	0.0220471	+	0.0220471i
$195$		−	218.362i		−	0.0801911i
$196$			6026.71i			2.19632i
$197$	1322.76	+	1322.76i	0.478390	+	0.478390i	0.904616	−	0.426227i	$-0.140157\pi$
$197$	1322.76	+	1322.76i	0.478390	+	0.478390i	−0.426227	+	0.904616i	$0.640157\pi$
$198$	−56.1057	−	56.1057i	−0.0201377	−	0.0201377i
$199$	617.640	−	617.640i	0.220017	−	0.220017i	−0.588489	−	0.808505i	$-0.700277\pi$
$199$	617.640	−	617.640i	0.220017	−	0.220017i	0.808505	+	0.588489i	$0.200277\pi$
$200$	272.941			0.0964991
$201$	1008.90	−	1008.90i	0.354041	−	0.354041i
$202$			252.239i			0.0878586i
$203$	7029.83			2.43053
$204$	−179.030	−	1772.71i	−0.0614442	−	0.608404i
$205$	4006.89			1.36514
$206$		−	280.052i		−	0.0947190i
$207$	−219.700	+	219.700i	−0.0737692	+	0.0737692i
$208$	−313.227			−0.104415
$209$	370.169	−	370.169i	0.122512	−	0.122512i
$210$	351.687	+	351.687i	0.115565	+	0.115565i
$211$	585.761	+	585.761i	0.191116	+	0.191116i	0.796178	−	0.605062i	$-0.206852\pi$
$211$	585.761	+	585.761i	0.191116	+	0.191116i	−0.605062	+	0.796178i	$0.706852\pi$
$212$		−	3932.64i		−	1.27403i
$213$			1535.68i			0.494004i
$214$	114.420	+	114.420i	0.0365494	+	0.0365494i
$215$	−1394.30	−	1394.30i	−0.442281	−	0.442281i
$216$	−554.271	+	554.271i	−0.174599	+	0.174599i
$217$	−7803.19			−2.44108
$218$	−388.856	+	388.856i	−0.120810	+	0.120810i
$219$			2375.10i			0.732851i
$220$	−1416.03			−0.433949
$221$	−227.422	+	278.518i	−0.0692220	+	0.0847745i
$222$	3.14734			0.000951511
$223$		−	1381.60i		−	0.414882i	−0.978248	−	0.207441i	$-0.933487\pi$
$223$		−	1381.60i		−	0.414882i	0.978248	−	0.207441i	$-0.0665134\pi$
$224$	1553.88	−	1553.88i	0.463496	−	0.463496i
$225$	812.310			0.240684
$226$	−396.291	+	396.291i	−0.116641	+	0.116641i
$227$	119.838	+	119.838i	0.0350394	+	0.0350394i	0.724409	−	0.689370i	$-0.242113\pi$
$227$	119.838	+	119.838i	0.0350394	+	0.0350394i	−0.689370	+	0.724409i	$0.742113\pi$
$228$	−690.382	−	690.382i	−0.200534	−	0.200534i
$229$			2463.08i			0.710764i	0.934721	+	0.355382i	$0.115649\pi$
$229$			2463.08i			0.710764i	−0.934721	+	0.355382i	$0.884351\pi$
$230$		−	86.7312i		−	0.0248647i
$231$	−1035.32	−	1035.32i	−0.294888	−	0.294888i
$232$	−832.172	−	832.172i	−0.235495	−	0.235495i
$233$	−1777.93	+	1777.93i	−0.499896	+	0.499896i	−0.911406	−	0.411509i	$-0.865002\pi$
$233$	−1777.93	+	1777.93i	−0.499896	+	0.499896i	0.411509	+	0.911406i	$0.365002\pi$
$234$	29.8647			0.00834324
$235$	3418.49	−	3418.49i	0.948927	−	0.948927i
$236$			3995.81i			1.10214i
$237$	−692.022			−0.189669
$238$	−82.2937	−	814.850i	−0.0224131	−	0.221928i
$239$	3438.63			0.930656			0.465328	−	0.885138i	$-0.345936\pi$
$239$	3438.63			0.930656			0.465328	+	0.885138i	$0.345936\pi$
$240$			2599.01i			0.699023i
$241$	−2894.48	+	2894.48i	−0.773651	+	0.773651i	−0.978743	−	0.205092i	$-0.934251\pi$
$241$	−2894.48	+	2894.48i	−0.773651	+	0.773651i	0.205092	+	0.978743i	$0.434251\pi$
$242$	401.985			0.106779
$243$	−2671.46	+	2671.46i	−0.705244	+	0.705244i
$244$	−184.161	−	184.161i	−0.0483183	−	0.0483183i
$245$	−7136.11	−	7136.11i	−1.86086	−	1.86086i
$246$		−	344.107i		−	0.0891848i
$247$			197.039i			0.0507581i
$248$	923.719	+	923.719i	0.236517	+	0.236517i
$249$	−2709.06	−	2709.06i	−0.689477	−	0.689477i
$250$	248.880	−	248.880i	0.0629622	−	0.0629622i
$251$	2927.86			0.736274			0.368137	−	0.929772i	$-0.379996\pi$
$251$	2927.86			0.736274			0.368137	+	0.929772i	$0.379996\pi$
$252$	3075.10	−	3075.10i	0.768702	−	0.768702i
$253$			255.325i			0.0634472i
$254$	−292.781			−0.0723258
$255$	2311.02	+	1887.04i	0.567535	+	0.463417i
$256$	3479.66			0.849526
$257$			1139.92i			0.276677i	0.990385	+	0.138338i	$0.0441762\pi$
$257$			1139.92i			0.276677i	−0.990385	+	0.138338i	$0.955824\pi$
$258$	−119.741	+	119.741i	−0.0288943	+	0.0288943i
$259$	−92.4923			−0.0221899
$260$	376.873	−	376.873i	0.0898948	−	0.0898948i
$261$	−2476.66	−	2476.66i	−0.587362	−	0.587362i
$262$	301.793	+	301.793i	0.0711635	+	0.0711635i
$263$			1853.52i			0.434573i	0.976108	+	0.217287i	$0.0697207\pi$
$263$			1853.52i			0.434573i	−0.976108	+	0.217287i	$0.930279\pi$
$264$			245.116i			0.0571435i
$265$	4656.57	+	4656.57i	1.07944	+	1.07944i
$266$	−317.344	−	317.344i	−0.0731488	−	0.0731488i
$267$	742.624	−	742.624i	0.170217	−	0.170217i
$268$	3482.52			0.793765
$269$	−1573.29	+	1573.29i	−0.356599	+	0.356599i	−0.862558	−	0.505959i	$-0.831139\pi$
$269$	−1573.29	+	1573.29i	−0.356599	+	0.356599i	0.505959	+	0.862558i	$0.331139\pi$
$270$		−	651.209i		−	0.146783i
$271$	737.207			0.165248			0.0826238	−	0.996581i	$-0.473670\pi$
$271$	737.207			0.165248			0.0826238	+	0.996581i	$0.473670\pi$
$272$	2706.84	−	3315.00i	0.603405	−	0.738976i
$273$	551.094			0.122175
$274$		−	584.621i		−	0.128899i
$275$	472.013	−	472.013i	0.103504	−	0.103504i
$276$	476.193			0.103853
$277$	1060.83	−	1060.83i	0.230105	−	0.230105i	−0.582631	−	0.812737i	$-0.697977\pi$
$277$	1060.83	−	1060.83i	0.230105	−	0.230105i	0.812737	+	0.582631i	$0.197977\pi$
$278$	341.510	+	341.510i	0.0736777	+	0.0736777i
$279$	2749.12	+	2749.12i	0.589912	+	0.589912i
$280$			2446.90i			0.522251i
$281$		−	5367.39i		−	1.13947i	−0.821828	−	0.569736i	$-0.807046\pi$
$281$		−	5367.39i		−	1.13947i	0.821828	−	0.569736i	$-0.192954\pi$
$282$	−293.576	−	293.576i	−0.0619936	−	0.0619936i
$283$	−3512.89	−	3512.89i	−0.737879	−	0.737879i	0.234289	−	0.972167i	$-0.424724\pi$
$283$	−3512.89	−	3512.89i	−0.737879	−	0.737879i	−0.972167	+	0.234289i	$0.924724\pi$
$284$	−2650.43	+	2650.43i	−0.553782	+	0.553782i
$285$	1634.94			0.339808
$286$	17.3537	−	17.3537i	0.00358791	−	0.00358791i
$287$			10112.4i			2.07985i
$288$	−1094.89			−0.224017
$289$	−982.333	−	4813.79i	−0.199946	−	0.979807i
$290$	977.712			0.197977
$291$		−	774.593i		−	0.156039i
$292$	−4099.20	+	4099.20i	−0.821532	+	0.821532i
$293$	−6477.52			−1.29154			−0.645769	−	0.763533i	$-0.723463\pi$
$293$	−6477.52			−1.29154			−0.645769	+	0.763533i	$0.723463\pi$
$294$	−612.841	+	612.841i	−0.121570	+	0.121570i
$295$	−4731.36	−	4731.36i	−0.933799	−	0.933799i
$296$	10.9490	+	10.9490i	0.00214999	+	0.00214999i
$297$			1917.07i			0.374545i
$298$			673.172i			0.130858i
$299$	−67.9540	−	67.9540i	−0.0131434	−	0.0131434i
$300$	−880.327	−	880.327i	−0.169419	−	0.169419i
$301$	3518.88	−	3518.88i	0.673836	−	0.673836i
$302$	659.293			0.125623
$303$	1639.84	−	1639.84i	0.310911	−	0.310911i
$304$		−	2345.21i		−	0.442457i
$305$	436.122			0.0818763
$306$	−258.085	+	316.070i	−0.0482148	+	0.0590475i
$307$	−5348.77			−0.994366			−0.497183	−	0.867646i	$-0.665632\pi$
$307$	−5348.77			−0.994366			−0.497183	+	0.867646i	$0.665632\pi$
$308$		−	3573.73i		−	0.661143i
$309$	−1820.65	+	1820.65i	−0.335189	+	0.335189i
$310$	−1085.27			−0.198836
$311$	2560.02	−	2560.02i	0.466771	−	0.466771i	−0.434096	−	0.900867i	$-0.642932\pi$
$311$	2560.02	−	2560.02i	0.466771	−	0.466771i	0.900867	+	0.434096i	$0.142932\pi$
$312$	−65.2370	−	65.2370i	−0.0118376	−	0.0118376i
$313$	1465.83	+	1465.83i	0.264709	+	0.264709i	0.826964	−	0.562255i	$-0.190066\pi$
$313$	1465.83	+	1465.83i	0.264709	+	0.264709i	−0.562255	+	0.826964i	$0.690066\pi$
$314$			34.6421i			0.00622601i
$315$			7282.32i			1.30258i
$316$	−1194.36	−	1194.36i	−0.212621	−	0.212621i
$317$	5632.69	+	5632.69i	0.997992	+	0.997992i	0.999998	−	0.00200599i	$-0.000638525\pi$
$317$	5632.69	+	5632.69i	0.997992	+	0.997992i	−0.00200599	+	0.999998i	$0.500639\pi$
$318$	399.900	−	399.900i	0.0705198	−	0.0705198i
$319$	−2878.25			−0.505176
$320$	−4339.69	+	4339.69i	−0.758113	+	0.758113i
$321$		−	1487.72i		−	0.258680i
$322$	218.889			0.0378826
$323$	−2085.34	−	1702.77i	−0.359230	−	0.293326i
$324$	48.1178			0.00825066
$325$			251.250i			0.0428826i
$326$	−156.299	+	156.299i	−0.0265539	+	0.0265539i
$327$	5056.01			0.855040
$328$	1197.08	−	1197.08i	0.201517	−	0.201517i
$329$	8627.45	+	8627.45i	1.44573	+	1.44573i
$330$	−143.993	−	143.993i	−0.0240198	−	0.0240198i
$331$		−	8062.01i		−	1.33875i	−0.742922	−	0.669377i	$-0.766561\pi$
$331$		−	8062.01i		−	1.33875i	0.742922	−	0.669377i	$-0.233439\pi$
$332$		−	9351.16i		−	1.54582i
$333$	32.5857	+	32.5857i	0.00536242	+	0.00536242i
$334$	45.2471	+	45.2471i	0.00741261	+	0.00741261i
$335$	−4123.59	+	4123.59i	−0.672524	+	0.672524i
$336$	−6559.28			−1.06499
$337$	5542.17	−	5542.17i	0.895850	−	0.895850i	−0.0992163	−	0.995066i	$-0.531634\pi$
$337$	5542.17	−	5542.17i	0.895850	−	0.895850i	0.995066	+	0.0992163i	$0.0316336\pi$
$338$		−	761.922i		−	0.122613i
$339$	5152.68			0.825532
$340$	731.736	+	7245.45i	0.116717	+	1.15570i
$341$	3194.89			0.507370
$342$			223.605i			0.0353543i
$343$	9936.13	−	9936.13i	1.56414	−	1.56414i
$344$	−833.109			−0.130576
$345$	−563.851	+	563.851i	−0.0879905	+	0.0879905i
$346$	−394.613	−	394.613i	−0.0613136	−	0.0613136i
$347$	−3298.32	−	3298.32i	−0.510268	−	0.510268i	0.404340	−	0.914609i	$-0.367501\pi$
$347$	−3298.32	−	3298.32i	−0.510268	−	0.510268i	−0.914609	+	0.404340i	$0.867501\pi$
$348$			5368.07i			0.826894i
$349$			9868.72i			1.51364i	0.653623	+	0.756820i	$0.273248\pi$
$349$			9868.72i			1.51364i	−0.653623	+	0.756820i	$0.726752\pi$
$350$	−404.654	−	404.654i	−0.0617991	−	0.0617991i
$351$	−510.223	−	510.223i	−0.0775888	−	0.0775888i
$352$	−636.213	+	636.213i	−0.0963359	+	0.0963359i
$353$	955.958			0.144137			0.0720687	−	0.997400i	$-0.477040\pi$
$353$	955.958			0.144137			0.0720687	+	0.997400i	$0.477040\pi$
$354$	−406.324	+	406.324i	−0.0610053	+	0.0610053i
$355$		−	6276.64i		−	0.938393i
$356$	2563.40			0.381628
$357$	−4762.44	+	5832.45i	−0.706037	+	0.864666i
$358$	867.337			0.128045
$359$			8341.26i			1.22628i	0.789974	+	0.613141i	$0.210094\pi$
$359$			8341.26i			1.22628i	−0.789974	+	0.613141i	$0.789906\pi$
$360$	862.061	−	862.061i	0.126207	−	0.126207i
$361$	5383.72			0.784914
$362$	−276.993	+	276.993i	−0.0402167	+	0.0402167i
$363$	−2613.36	−	2613.36i	−0.377867	−	0.377867i
$364$	951.136	+	951.136i	0.136959	+	0.136959i
$365$		−	9707.56i		−	1.39210i
$366$		−	37.4536i		−	0.00534900i
$367$	−5893.86	−	5893.86i	−0.838303	−	0.838303i	0.150333	−	0.988635i	$-0.451965\pi$
$367$	−5893.86	−	5893.86i	−0.838303	−	0.838303i	−0.988635	+	0.150333i	$0.951965\pi$
$368$	808.807	+	808.807i	0.114571	+	0.114571i
$369$	3562.68	−	3562.68i	0.502617	−	0.502617i
$370$	−12.8639			−0.00180746
$371$	−11752.1	+	11752.1i	−1.64457	+	1.64457i
$372$		−	5958.62i		−	0.830484i
$373$	−11406.4			−1.58338			−0.791689	−	0.610924i	$-0.790798\pi$
$373$	−11406.4			−1.58338			−0.791689	+	0.610924i	$0.790798\pi$
$374$	33.6939	+	333.627i	0.00465847	+	0.0461269i
$375$	−3236.00			−0.445617
$376$		−	2042.59i		−	0.280155i
$377$	766.038	−	766.038i	0.104650	−	0.104650i
$378$	1643.49			0.223630
$379$	−8247.07	+	8247.07i	−1.11774	+	1.11774i	−0.125668	+	0.992072i	$0.540107\pi$
$379$	−8247.07	+	8247.07i	−1.11774	+	1.11774i	−0.992072	+	0.125668i	$0.959893\pi$
$380$	2821.74	+	2821.74i	0.380927	+	0.380927i
$381$	1903.41	+	1903.41i	0.255944	+	0.255944i
$382$		−	1351.40i		−	0.181004i
$383$		−	4091.40i		−	0.545851i	−0.962035	−	0.272925i	$-0.912009\pi$
$383$		−	4091.40i		−	0.545851i	0.962035	−	0.272925i	$-0.0879912\pi$
$384$	1577.81	+	1577.81i	0.209681	+	0.209681i
$385$	4231.58	+	4231.58i	0.560159	+	0.560159i
$386$	−552.099	+	552.099i	−0.0728008	+	0.0728008i
$387$	−2479.45			−0.325678
$388$	1336.87	−	1336.87i	0.174921	−	0.174921i
$389$		−	9245.70i		−	1.20508i	−0.798089	−	0.602539i	$-0.794156\pi$
$389$		−	9245.70i		−	1.20508i	0.798089	−	0.602539i	$-0.205844\pi$
$390$	76.6464			0.00995165
$391$	1306.43	−	131.939i	0.168974	−	0.0170651i
$392$	−4263.91			−0.549387
$393$		−	3923.99i		−	0.503662i
$394$	−464.296	+	464.296i	−0.0593678	+	0.0593678i
$395$	2828.45			0.360290
$396$	−1259.05	+	1259.05i	−0.159772	+	0.159772i
$397$	4551.13	+	4551.13i	0.575352	+	0.575352i	0.933619	−	0.358267i	$-0.116632\pi$
$397$	4551.13	+	4551.13i	0.575352	+	0.575352i	−0.358267	+	0.933619i	$0.616632\pi$
$398$	216.795	+	216.795i	0.0273039	+	0.0273039i
$399$			4126.18i			0.517713i
$400$		−	2990.45i		−	0.373806i
$401$	−975.481	−	975.481i	−0.121479	−	0.121479i	0.643754	−	0.765233i	$-0.277376\pi$
$401$	−975.481	−	975.481i	−0.121479	−	0.121479i	−0.765233	+	0.643754i	$0.777376\pi$
$402$	354.129	+	354.129i	0.0439362	+	0.0439362i
$403$	−850.311	+	850.311i	−0.105104	+	0.105104i
$404$	5660.40			0.697068
$405$	−56.9754	+	56.9754i	−0.00699045	+	0.00699045i
$406$			2467.51i			0.301627i
$407$	37.8695			0.00461209
$408$	1254.19	−	126.664i	0.152186	−	0.0153696i
$409$	−13063.3			−1.57931			−0.789654	−	0.613552i	$-0.789740\pi$
$409$	−13063.3			−1.57931			−0.789654	+	0.613552i	$0.789740\pi$
$410$			1406.44i			0.169412i
$411$	−3800.70	+	3800.70i	−0.456142	+	0.456142i
$412$	−6284.54			−0.751498
$413$	11940.8	−	11940.8i	1.42269	−	1.42269i
$414$	−77.1160	−	77.1160i	−0.00915470	−	0.00915470i
$415$	11072.5	+	11072.5i	1.30971	+	1.30971i
$416$		−	338.652i		−	0.0399129i
$417$		−	4440.40i		−	0.521457i
$418$	129.931	+	129.931i	0.0152037	+	0.0152037i
$419$	5410.35	+	5410.35i	0.630818	+	0.630818i	0.948273	−	0.317455i	$-0.102828\pi$
$419$	5410.35	+	5410.35i	0.630818	+	0.630818i	−0.317455	+	0.948273i	$0.602828\pi$
$420$	7892.09	−	7892.09i	0.916892	−	0.916892i
$421$	15634.9			1.80997			0.904985	−	0.425443i	$-0.139882\pi$
$421$	15634.9			1.80997			0.904985	+	0.425443i	$0.139882\pi$
$422$	−205.605	+	205.605i	−0.0237173	+	0.0237173i
$423$		−	6079.02i		−	0.698752i
$424$	2782.35			0.318686
$425$	−2659.08	−	2171.25i	−0.303492	−	0.247814i
$426$	−539.031			−0.0613054
$427$			1100.67i			0.124742i
$428$	2567.66	−	2567.66i	0.289982	−	0.289982i
$429$	−225.637			−0.0253936
$430$	489.407	−	489.407i	0.0548867	−	0.0548867i
$431$	−7848.20	−	7848.20i	−0.877111	−	0.877111i	0.116124	−	0.993235i	$-0.462953\pi$
$431$	−7848.20	−	7848.20i	−0.877111	−	0.877111i	−0.993235	+	0.116124i	$0.962953\pi$
$432$	6072.81	+	6072.81i	0.676339	+	0.676339i
$433$			14696.8i			1.63114i	0.578660	+	0.815569i	$0.303576\pi$
$433$			14696.8i			1.63114i	−0.578660	+	0.815569i	$0.696424\pi$
$434$		−	2738.96i		−	0.302936i
$435$	−6356.23	−	6356.23i	−0.700593	−	0.700593i
$436$	8726.19	+	8726.19i	0.958506	+	0.958506i
$437$	508.789	−	508.789i	0.0556949	−	0.0556949i
$438$	−833.673			−0.0909463
$439$	−6648.30	+	6648.30i	−0.722793	+	0.722793i	−0.969173	−	0.246381i	$-0.920759\pi$
$439$	−6648.30	+	6648.30i	−0.722793	+	0.722793i	0.246381	+	0.969173i	$0.420759\pi$
$440$		−	1001.84i		−	0.108548i
$441$	−12690.0			−1.37026
$442$	−97.7614	−	79.8264i	−0.0105204	−	0.00859039i
$443$	−7550.22			−0.809756			−0.404878	−	0.914371i	$-0.632686\pi$
$443$	−7550.22			−0.809756			−0.404878	+	0.914371i	$0.632686\pi$
$444$		−	70.6283i		−	0.00754926i
$445$	−3035.27	+	3035.27i	−0.323338	+	0.323338i
$446$	484.948			0.0514865
$447$	4376.38	−	4376.38i	0.463078	−	0.463078i
$448$	−10952.3	−	10952.3i	−1.15502	−	1.15502i
$449$	−5110.98	−	5110.98i	−0.537199	−	0.537199i	0.385506	−	0.922705i	$-0.374027\pi$
$449$	−5110.98	−	5110.98i	−0.537199	−	0.537199i	−0.922705	+	0.385506i	$0.874027\pi$
$450$			285.125i			0.0298687i
$451$		−	4140.37i		−	0.432289i
$452$	8893.03	+	8893.03i	0.925427	+	0.925427i
$453$	−4286.15	−	4286.15i	−0.444550	−	0.444550i
$454$	−42.0638	+	42.0638i	−0.00434836	+	0.00434836i
$455$	−2252.44			−0.232080
$456$	488.446	−	488.446i	0.0501614	−	0.0501614i
$457$			6030.84i			0.617311i	0.951174	+	0.308655i	$0.0998790\pi$
$457$			6030.84i			0.617311i	−0.951174	+	0.308655i	$0.900121\pi$
$458$	−864.555			−0.0882053
$459$	9809.13	−	990.648i	0.997496	−	0.100740i
$460$	−1946.30			−0.197276
$461$			3790.02i			0.382904i	0.981502	+	0.191452i	$0.0613197\pi$
$461$			3790.02i			0.382904i	−0.981502	+	0.191452i	$0.938680\pi$
$462$	363.403	−	363.403i	0.0365953	−	0.0365953i
$463$	9287.18			0.932207			0.466103	−	0.884730i	$-0.345657\pi$
$463$	9287.18			0.932207			0.466103	+	0.884730i	$0.345657\pi$
$464$	−9117.60	+	9117.60i	−0.912228	+	0.912228i
$465$	7055.49	+	7055.49i	0.703635	+	0.703635i
$466$	−624.062	−	624.062i	−0.0620367	−	0.0620367i
$467$		−	596.896i		−	0.0591458i	−0.999563	−	0.0295729i	$-0.990585\pi$
$467$		−	596.896i		−	0.0591458i	0.999563	−	0.0295729i	$-0.00941471\pi$
$468$		−	670.184i		−	0.0661950i
$469$	−10406.9	−	10406.9i	−1.02462	−	1.02462i
$470$	1199.91	+	1199.91i	0.117761	+	0.117761i
$471$	225.213	−	225.213i	0.0220324	−	0.0220324i
$472$	−2827.04			−0.275689
$473$	−1440.75	+	1440.75i	−0.140054	+	0.140054i
$474$		−	242.903i		−	0.0235378i
$475$	−1881.17			−0.181714
$476$	−18285.8	+	1846.73i	−1.76077	+	0.177825i
$477$	8280.67			0.794855
$478$			1206.98i			0.115494i
$479$	3137.24	−	3137.24i	0.299257	−	0.299257i	−0.541466	−	0.840723i	$-0.682130\pi$
$479$	3137.24	−	3137.24i	0.299257	−	0.299257i	0.840723	+	0.541466i	$0.182130\pi$
$480$	−2809.98			−0.267203
$481$	−10.0788	+	10.0788i	−0.000955417	+	0.000955417i
$482$	−1015.98	−	1015.98i	−0.0960095	−	0.0960095i
$483$	−1423.02	−	1423.02i	−0.134058	−	0.134058i
$484$		−	9020.81i		−	0.847183i
$485$			3165.93i			0.296407i
$486$	−937.698	−	937.698i	−0.0875202	−	0.0875202i
$487$	−6119.48	−	6119.48i	−0.569405	−	0.569405i	0.362557	−	0.931962i	$-0.381904\pi$
$487$	−6119.48	−	6119.48i	−0.569405	−	0.569405i	−0.931962	+	0.362557i	$0.881904\pi$
$488$	130.294	−	130.294i	0.0120863	−	0.0120863i
$489$	2032.24			0.187937
$490$	2504.82	−	2504.82i	0.230931	−	0.230931i
$491$		−	5160.59i		−	0.474326i	−0.971470	−	0.237163i	$-0.923782\pi$
$491$		−	5160.59i		−	0.474326i	0.971470	−	0.237163i	$-0.0762176\pi$
$492$	−7721.98			−0.707589
$493$	1487.34	+	14727.2i	0.135875	+	1.34540i
$494$	−69.1616			−0.00629904
$495$		−	2981.63i		−	0.270736i
$496$	10120.6	−	10120.6i	0.916189	−	0.916189i
$497$	15840.7			1.42969
$498$	950.896	−	950.896i	0.0855636	−	0.0855636i
$499$	6169.10	+	6169.10i	0.553440	+	0.553440i	0.927432	−	0.373992i	$-0.122011\pi$
$499$	6169.10	+	6169.10i	0.553440	+	0.553440i	−0.373992	+	0.927432i	$0.622011\pi$
$500$	−5585.03	−	5585.03i	−0.499541	−	0.499541i
$501$		−	588.315i		−	0.0524630i
$502$			1027.69i			0.0913710i
$503$	11955.8	+	11955.8i	1.05980	+	1.05980i	0.998094	+	0.0617098i	$0.0196553\pi$
$503$	11955.8	+	11955.8i	1.05980	+	1.05980i	0.0617098	+	0.998094i	$0.480345\pi$
$504$	2175.63	+	2175.63i	0.192283	+	0.192283i
$505$	−6702.37	+	6702.37i	−0.590597	+	0.590597i
$506$	−89.6205			−0.00787375
$507$	−4953.35	+	4953.35i	−0.433898	+	0.433898i
$508$			6570.21i			0.573831i
$509$	11762.9			1.02433			0.512163	−	0.858888i	$-0.328844\pi$
$509$	11762.9			1.02433			0.512163	+	0.858888i	$0.328844\pi$
$510$	−662.362	+	811.179i	−0.0575096	+	0.0704306i
$511$	24499.5			2.12093
$512$			6752.88i			0.582886i
$513$	3820.17	−	3820.17i	0.328781	−	0.328781i
$514$	−400.117			−0.0343354
$515$	7441.40	−	7441.40i	0.636713	−	0.636713i
$516$	2687.06	+	2687.06i	0.229247	+	0.229247i
$517$	−3532.37	−	3532.37i	−0.300490	−	0.300490i
$518$		−	32.4653i		−	0.00275375i
$519$			5130.86i			0.433949i
$520$	266.638	+	266.638i	0.0224862	+	0.0224862i
$521$	−8023.47	−	8023.47i	−0.674692	−	0.674692i	0.284102	−	0.958794i	$-0.408305\pi$
$521$	−8023.47	−	8023.47i	−0.674692	−	0.674692i	−0.958794	+	0.284102i	$0.908305\pi$
$522$	869.321	−	869.321i	0.0728911	−	0.0728911i
$523$	−11430.3			−0.955661			−0.477831	−	0.878452i	$-0.658577\pi$
$523$	−11430.3			−0.955661			−0.477831	+	0.878452i	$0.658577\pi$
$524$	6772.43	−	6772.43i	0.564609	−	0.564609i
$525$			5261.42i			0.437385i
$526$	−650.595			−0.0539302
$527$	−1650.96	−	16347.4i	−0.136465	−	1.35124i
$528$	2685.59			0.221355
$529$		−	11816.1i		−	0.971157i
$530$	−1634.48	+	1634.48i	−0.133957	+	0.133957i
$531$	−8413.68			−0.687613
$532$	−7121.40	+	7121.40i	−0.580361	+	0.580361i
$533$	1101.95	+	1101.95i	0.0895509	+	0.0895509i
$534$	260.665	+	260.665i	0.0211238	+	0.0211238i
$535$			6080.62i			0.491380i
$536$			2463.89i			0.198552i
$537$	−5638.67	−	5638.67i	−0.453122	−	0.453122i
$538$	−552.233	−	552.233i	−0.0442536	−	0.0442536i
$539$	−7373.84	+	7373.84i	−0.589265	+	0.589265i
$540$	−14613.6			−1.16457
$541$	8857.23	−	8857.23i	0.703886	−	0.703886i	−0.261356	−	0.965242i	$-0.584170\pi$
$541$	8857.23	−	8857.23i	0.703886	−	0.703886i	0.965242	+	0.261356i	$0.0841698\pi$
$542$			258.764i			0.0205071i
$543$	3601.54			0.284635
$544$	3584.09	+	2926.56i	0.282475	+	0.230653i
$545$	−20665.0			−1.62421
$546$			193.437i			0.0151618i
$547$	−3624.69	+	3624.69i	−0.283329	+	0.283329i	−0.834435	−	0.551106i	$-0.814206\pi$
$547$	−3624.69	+	3624.69i	−0.283329	+	0.283329i	0.551106	+	0.834435i	$0.314206\pi$
$548$	−13119.3			−1.02268
$549$	387.773	−	387.773i	0.0301453	−	0.0301453i
$550$	165.679	+	165.679i	0.0128447	+	0.0128447i
$551$	5735.52	+	5735.52i	0.443451	+	0.443451i
$552$			336.907i			0.0259777i
$553$			7138.32i			0.548919i
$554$	372.357	+	372.357i	0.0285559	+	0.0285559i
$555$	83.6296	+	83.6296i	0.00639618	+	0.00639618i
$556$	7663.71	−	7663.71i	0.584557	−	0.584557i
$557$	7368.19			0.560503			0.280251	−	0.959927i	$-0.409582\pi$
$557$	7368.19			0.560503			0.280251	+	0.959927i	$0.409582\pi$
$558$	−964.956	+	964.956i	−0.0732076	+	0.0732076i
$559$		−	766.901i		−	0.0580259i
$560$	26809.2			2.02303
$561$	1949.91	−	2388.00i	0.146747	−	0.179718i
$562$	1883.98			0.141408
$563$			11247.6i			0.841969i	0.907068	+	0.420984i	$0.138315\pi$
$563$			11247.6i			0.841969i	−0.907068	+	0.420984i	$0.861685\pi$
$564$	−6588.04	+	6588.04i	−0.491855	+	0.491855i
$565$	−21060.1			−1.56815
$566$	1233.04	−	1233.04i	0.0915701	−	0.0915701i
$567$	−143.792	−	143.792i	−0.0106503	−	0.0106503i
$568$	−1875.18	−	1875.18i	−0.138523	−	0.138523i
$569$		−	25878.6i		−	1.90666i	−0.301935	−	0.953329i	$-0.597632\pi$
$569$		−	25878.6i		−	1.90666i	0.301935	−	0.953329i	$-0.402368\pi$
$570$			573.871i			0.0421699i
$571$	−3784.49	−	3784.49i	−0.277366	−	0.277366i	0.554691	−	0.832057i	$-0.312837\pi$
$571$	−3784.49	−	3784.49i	−0.277366	−	0.277366i	−0.832057	+	0.554691i	$0.812837\pi$
$572$	−389.428	−	389.428i	−0.0284664	−	0.0284664i
$573$	−8785.61	+	8785.61i	−0.640530	+	0.640530i
$574$	−3549.52			−0.258108
$575$	648.772	−	648.772i	0.0470533	−	0.0470533i
$576$			7717.17i			0.558245i
$577$	−3052.95			−0.220270			−0.110135	−	0.993917i	$-0.535128\pi$
$577$	−3052.95			−0.220270			−0.110135	+	0.993917i	$0.535128\pi$
$578$	1689.67	−	344.804i	0.121593	−	0.0248131i
$579$	7178.54			0.515250
$580$		−	21940.5i		−	1.57074i
$581$	−27944.4	+	27944.4i	−1.99540	+	1.99540i
$582$	271.886			0.0193644
$583$	4811.69	−	4811.69i	0.341818	−	0.341818i
$584$	−2900.19	−	2900.19i	−0.205498	−	0.205498i
$585$	793.552	+	793.552i	0.0560843	+	0.0560843i
$586$		−	2273.65i		−	0.160279i
$587$			6669.73i			0.468977i	0.972119	+	0.234488i	$0.0753414\pi$
$587$			6669.73i			0.468977i	−0.972119	+	0.234488i	$0.924659\pi$
$588$	13752.6	+	13752.6i	0.964534	+	0.964534i
$589$	−6366.49	−	6366.49i	−0.445376	−	0.445376i
$590$	1660.73	−	1660.73i	0.115884	−	0.115884i
$591$	6036.90			0.420178
$592$	119.961	−	119.961i	0.00832834	−	0.00832834i
$593$			13962.7i			0.966914i	0.875368	+	0.483457i	$0.160619\pi$
$593$			13962.7i			0.966914i	−0.875368	+	0.483457i	$0.839381\pi$
$594$	−672.903			−0.0464807
$595$	19465.2	−	23838.5i	1.34117	−	1.64249i
$596$	15106.4			1.03823
$597$		−	2818.83i		−	0.193244i
$598$	23.8522	−	23.8522i	0.00163109	−	0.00163109i
$599$	3286.64			0.224188			0.112094	−	0.993698i	$-0.464244\pi$
$599$	3286.64			0.224188			0.112094	+	0.993698i	$0.464244\pi$
$600$	622.832	−	622.832i	0.0423784	−	0.0423784i
$601$	1067.78	+	1067.78i	0.0724723	+	0.0724723i	0.742414	−	0.669942i	$-0.233681\pi$
$601$	1067.78	+	1067.78i	0.0724723	+	0.0724723i	−0.669942	+	0.742414i	$0.733681\pi$
$602$	1235.14	+	1235.14i	0.0836225	+	0.0836225i
$603$			7332.88i			0.495221i
$604$		−	14795.0i		−	0.996687i
$605$	10681.4	+	10681.4i	0.717784	+	0.717784i
$606$	575.591	+	575.591i	0.0385838	+	0.0385838i
$607$	4006.44	−	4006.44i	0.267902	−	0.267902i	−0.560352	−	0.828254i	$-0.689334\pi$
$607$	4006.44	−	4006.44i	0.267902	−	0.267902i	0.828254	+	0.560352i	$0.189334\pi$
$608$	2535.57			0.169130
$609$	16041.6	−	16041.6i	1.06739	−	1.06739i
$610$			153.081i			0.0101608i
$611$	1880.26			0.124496
$612$	7092.82	+	5791.59i	0.468481	+	0.382535i
$613$	−11074.1			−0.729653			−0.364827	−	0.931076i	$-0.618872\pi$
$613$	−11074.1			−0.729653			−0.364827	+	0.931076i	$0.618872\pi$
$614$		−	1877.45i		−	0.123400i
$615$	9143.45	−	9143.45i	0.599511	−	0.599511i
$616$	2528.42			0.165378
$617$	−15598.4	+	15598.4i	−1.01778	+	1.01778i	−0.0179387	+	0.999839i	$0.505710\pi$
$617$	−15598.4	+	15598.4i	−1.01778	+	1.01778i	−0.999839	+	0.0179387i	$0.994290\pi$
$618$	−639.059	−	639.059i	−0.0415966	−	0.0415966i
$619$	−13657.3	−	13657.3i	−0.886808	−	0.886808i	0.107407	−	0.994215i	$-0.465745\pi$
$619$	−13657.3	−	13657.3i	−0.886808	−	0.886808i	−0.994215	+	0.107407i	$0.965745\pi$
$620$			24354.2i			1.57756i
$621$			2634.97i			0.170270i
$622$	898.583	+	898.583i	0.0579259	+	0.0579259i
$623$	−7660.29	−	7660.29i	−0.492621	−	0.492621i
$624$	−714.762	+	714.762i	−0.0458548	+	0.0458548i
$625$	19348.4			1.23830
$626$	−514.516	+	514.516i	−0.0328501	+	0.0328501i
$627$		−	1689.40i		−	0.107605i
$628$	777.391			0.0493970
$629$	−19.5691	−	193.768i	−0.00124049	−	0.0122830i
$630$	−2556.14			−0.161649
$631$			29548.0i			1.86417i	0.362245	+	0.932083i	$0.382010\pi$
$631$			29548.0i			1.86417i	−0.362245	+	0.932083i	$0.617990\pi$
$632$	845.014	−	845.014i	0.0531849	−	0.0531849i
$633$	2673.34			0.167860
$634$	−1977.11	+	1977.11i	−0.123850	+	0.123850i
$635$	−7779.66	−	7779.66i	−0.486183	−	0.486183i
$636$	−8974.03	−	8974.03i	−0.559502	−	0.559502i
$637$		−	3925.05i		−	0.244138i
$638$		−	1010.28i		−	0.0626920i
$639$	−5580.81	−	5580.81i	−0.345498	−	0.345498i
$640$	−6448.87	−	6448.87i	−0.398303	−	0.398303i
$641$	−1355.67	+	1355.67i	−0.0835347	+	0.0835347i	−0.747639	−	0.664105i	$-0.768813\pi$
$641$	−1355.67	+	1355.67i	−0.0835347	+	0.0835347i	0.664105	+	0.747639i	$0.268813\pi$
$642$	522.197			0.0321020
$643$	3368.91	−	3368.91i	0.206620	−	0.206620i	−0.596209	−	0.802829i	$-0.703327\pi$
$643$	3368.91	−	3368.91i	0.206620	−	0.206620i	0.802829	+	0.596209i	$0.203327\pi$
$644$		−	4912.01i		−	0.300559i
$645$	−6363.39			−0.388463
$646$	597.680	−	731.964i	0.0364016	−	0.0445801i
$647$	26374.3			1.60260			0.801299	−	0.598264i	$-0.204143\pi$
$647$	26374.3			1.60260			0.801299	+	0.598264i	$0.204143\pi$
$648$			34.0434i			0.00206382i
$649$	−4888.98	+	4888.98i	−0.295700	+	0.295700i
$650$	−88.1901			−0.00532169
$651$	−17806.4	+	17806.4i	−1.07202	+	1.07202i
$652$	3507.45	+	3507.45i	0.210678	+	0.210678i
$653$	−17760.7	−	17760.7i	−1.06437	−	1.06437i	−0.997781	−	0.0665852i	$-0.978790\pi$
$653$	−17760.7	−	17760.7i	−1.06437	−	1.06437i	−0.0665852	−	0.997781i	$-0.521210\pi$
$654$			1774.69i			0.106110i
$655$			16038.2i			0.956741i
$656$	−13115.7	−	13115.7i	−0.780612	−	0.780612i
$657$	−8631.36	−	8631.36i	−0.512544	−	0.512544i
$658$	−3028.28	+	3028.28i	−0.179415	+	0.179415i
$659$	−16035.4			−0.947878			−0.473939	−	0.880558i	$-0.657168\pi$
$659$	−16035.4			−0.947878			−0.473939	+	0.880558i	$0.657168\pi$
$660$	−3231.29	+	3231.29i	−0.190572	+	0.190572i
$661$			15871.5i			0.933932i	0.884275	+	0.466966i	$0.154653\pi$
$661$			15871.5i			0.933932i	−0.884275	+	0.466966i	$0.845347\pi$
$662$	2829.81			0.166138
$663$	116.598	+	1154.52i	0.00683000	+	0.0676288i
$664$	6615.96			0.386670
$665$		−	16864.6i		−	0.983432i
$666$	−11.4378	+	11.4378i	−0.000665471	+	0.000665471i
$667$	−3956.09			−0.229656
$668$	1015.37	−	1015.37i	0.0588114	−	0.0588114i
$669$	−3152.71	−	3152.71i	−0.182199	−	0.182199i
$670$	−1447.40	−	1447.40i	−0.0834597	−	0.0834597i
$671$		−	450.651i		−	0.0259272i
$672$		−	7091.71i		−	0.407096i
$673$	20099.9	+	20099.9i	1.15126	+	1.15126i	0.986301	+	0.164956i	$0.0527482\pi$
$673$	20099.9	+	20099.9i	1.15126	+	1.15126i	0.164956	+	0.986301i	$0.447252\pi$
$674$	1945.33	+	1945.33i	0.111174	+	0.111174i
$675$	4871.21	−	4871.21i	0.277767	−	0.277767i
$676$	−17098.0			−0.972805
$677$	4357.73	−	4357.73i	0.247387	−	0.247387i	−0.572510	−	0.819898i	$-0.694030\pi$
$677$	4357.73	−	4357.73i	0.247387	−	0.247387i	0.819898	+	0.572510i	$0.194030\pi$
$678$			1808.62i			0.102448i
$679$	−7990.05			−0.451591
$680$	−5126.16	+	517.704i	−0.289087	+	0.0291957i
$681$	546.925			0.0307756
$682$			1121.42i			0.0629642i
$683$	16546.1	−	16546.1i	0.926965	−	0.926965i	−0.0705433	−	0.997509i	$-0.522473\pi$
$683$	16546.1	−	16546.1i	0.926965	−	0.926965i	0.997509	+	0.0705433i	$0.0224733\pi$
$684$	5017.84			0.280500
$685$	15534.3	−	15534.3i	0.866474	−	0.866474i
$686$	3487.64	+	3487.64i	0.194109	+	0.194109i
$687$	5620.59	+	5620.59i	0.312138	+	0.312138i
$688$			9127.87i			0.505809i
$689$			2561.23i			0.141619i
$690$	−197.915	−	197.915i	−0.0109195	−	0.0109195i
$691$	1897.89	+	1897.89i	0.104485	+	0.104485i	0.757417	−	0.652932i	$-0.226461\pi$
$691$	1897.89	+	1897.89i	0.104485	+	0.104485i	−0.652932	+	0.757417i	$0.726461\pi$
$692$	−8855.37	+	8855.37i	−0.486461	+	0.486461i
$693$	7524.92			0.412479
$694$	1157.73	−	1157.73i	0.0633239	−	0.0633239i
$695$			18148.9i			0.990542i
$696$	−3797.92			−0.206839
$697$	−21185.1	+	2139.54i	−1.15128	+	0.116271i
$698$	−3463.98			−0.187842
$699$			8114.22i			0.439067i
$700$	−9080.71	+	9080.71i	−0.490312	+	0.490312i
$701$	29195.5			1.57304			0.786519	−	0.617566i	$-0.211881\pi$
$701$	29195.5			1.57304			0.786519	+	0.617566i	$0.211881\pi$
$702$	179.091	−	179.091i	0.00962871	−	0.00962871i
$703$	−75.4629	−	75.4629i	−0.00404856	−	0.00404856i
$704$	4484.26	+	4484.26i	0.240067	+	0.240067i
$705$		−	15601.5i		−	0.833458i
$706$			335.546i			0.0178873i
$707$	−16915.2	−	16915.2i	−0.899803	−	0.899803i
$708$	9118.18	+	9118.18i	0.484014	+	0.484014i
$709$	18025.7	−	18025.7i	0.954823	−	0.954823i	−0.0442002	−	0.999023i	$-0.514074\pi$
$709$	18025.7	−	18025.7i	0.954823	−	0.954823i	0.999023	+	0.0442002i	$0.0140739\pi$
$710$	2203.14			0.116454
$711$	2514.88	−	2514.88i	0.132652	−	0.132652i
$712$			1813.61i			0.0954603i
$713$	4391.31			0.230653
$714$	−2047.22	−	1671.64i	−0.107304	−	0.0876186i
$715$	922.227			0.0482368
$716$		−	19463.6i		−	1.01591i
$717$	7846.73	−	7846.73i	0.408705	−	0.408705i
$718$	−2927.83			−0.152181
$719$	25950.3	−	25950.3i	1.34601	−	1.34601i	0.456071	−	0.889943i	$-0.349256\pi$
$719$	25950.3	−	25950.3i	1.34601	−	1.34601i	0.889943	−	0.456071i	$-0.150744\pi$
$720$	−9445.08	−	9445.08i	−0.488885	−	0.488885i
$721$	18780.3	+	18780.3i	0.970063	+	0.970063i
$722$			1889.72i			0.0974071i
$723$			13210.0i			0.679510i
$724$	6215.91	+	6215.91i	0.319078	+	0.319078i
$725$	7313.54	+	7313.54i	0.374646	+	0.374646i
$726$	917.303	−	917.303i	0.0468930	−	0.0468930i
$727$	−12123.1			−0.618462			−0.309231	−	0.950987i	$-0.600072\pi$
$727$	−12123.1			−0.618462			−0.309231	+	0.950987i	$0.600072\pi$
$728$	−672.930	+	672.930i	−0.0342589	+	0.0342589i
$729$			12357.1i			0.627807i
$730$	3407.41			0.172759
$731$	8116.42	+	6627.40i	0.410665	+	0.335326i
$732$	−840.484			−0.0424388
$733$		−	14071.9i		−	0.709080i	−0.935041	−	0.354540i	$-0.884637\pi$
$733$		−	14071.9i		−	0.709080i	0.935041	−	0.354540i	$-0.115363\pi$
$734$	2068.78	−	2068.78i	0.104033	−	0.104033i
$735$	−32568.3			−1.63442
$736$	−874.460	+	874.460i	−0.0437949	+	0.0437949i
$737$	4260.96	+	4260.96i	0.212964	+	0.212964i
$738$	1250.52	+	1250.52i	0.0623744	+	0.0623744i
$739$			19170.8i			0.954276i	0.878828	+	0.477138i	$0.158326\pi$
$739$			19170.8i			0.954276i	−0.878828	+	0.477138i	$0.841674\pi$
$740$			288.673i			0.0143403i
$741$	449.629	+	449.629i	0.0222909	+	0.0222909i
$742$	−4125.04	−	4125.04i	−0.204090	−	0.204090i
$743$	−16384.5	+	16384.5i	−0.809001	+	0.809001i	−0.984483	−	0.175482i	$-0.943852\pi$
$743$	−16384.5	+	16384.5i	−0.809001	+	0.809001i	0.175482	+	0.984483i	$0.443852\pi$
$744$	4215.73			0.207737
$745$	−17887.2	+	17887.2i	−0.879648	+	0.879648i
$746$		−	4003.70i		−	0.196496i
$747$	19690.0			0.964418
$748$	7486.82	−	756.112i	0.365969	−	0.0369602i
$749$	−15346.0			−0.748641
$750$		−	1135.86i		−	0.0553008i
$751$	−5458.47	+	5458.47i	−0.265223	+	0.265223i	−0.827172	−	0.561949i	$-0.810052\pi$
$751$	−5458.47	+	5458.47i	−0.265223	+	0.265223i	0.561949	+	0.827172i	$0.310052\pi$
$752$	−22379.4			−1.08523
$753$	6681.17	−	6681.17i	0.323341	−	0.323341i
$754$	268.884	+	268.884i	0.0129870	+	0.0129870i
$755$	17518.4	+	17518.4i	0.844452	+	0.844452i
$756$		−	36881.1i		−	1.77428i
$757$			200.163i			0.00961038i	0.999988	+	0.00480519i	$0.00152955\pi$
$757$			200.163i			0.00961038i	−0.999988	+	0.00480519i	$0.998470\pi$
$758$	−2894.77	−	2894.77i	−0.138711	−	0.138711i
$759$	582.634	+	582.634i	0.0278634	+	0.0278634i
$760$	−1996.39	+	1996.39i	−0.0952849	+	0.0952849i
$761$	−21047.7			−1.00260			−0.501300	−	0.865274i	$-0.667145\pi$
$761$	−21047.7			−1.00260			−0.501300	+	0.865274i	$0.667145\pi$
$762$	−668.108	+	668.108i	−0.0317625	+	0.0317625i
$763$		−	52153.6i		−	2.47456i
$764$	−30326.2			−1.43608
$765$	−15256.2	+	1540.76i	−0.721031	+	0.0728187i
$766$	1436.10			0.0677396
$767$		−	2602.37i		−	0.122511i
$768$	7940.35	−	7940.35i	0.373076	−	0.373076i
$769$	21670.0			1.01618			0.508089	−	0.861305i	$-0.330352\pi$
$769$	21670.0			1.01618			0.508089	+	0.861305i	$0.330352\pi$
$770$	−1485.31	+	1485.31i	−0.0695153	+	0.0695153i
$771$	2601.21	+	2601.21i	0.121505	+	0.121505i
$772$	12389.5	+	12389.5i	0.577599	+	0.577599i
$773$			9286.93i			0.432118i	0.976380	+	0.216059i	$0.0693204\pi$
$773$			9286.93i			0.432118i	−0.976380	+	0.216059i	$0.930680\pi$
$774$		−	870.301i		−	0.0404164i
$775$	−8118.11	−	8118.11i	−0.376272	−	0.376272i
$776$	945.840	+	945.840i	0.0437547	+	0.0437547i
$777$	−211.061	+	211.061i	−0.00974489	+	0.00974489i
$778$	3245.29			0.149549
$779$	−8250.56	+	8250.56i	−0.379470	+	0.379470i
$780$		−	1720.00i		−	0.0789561i
$781$	−6485.74			−0.297155
$782$	46.3114	+	458.563i	0.00211777	+	0.0209695i
$783$	−29703.8			−1.35572
$784$			46717.0i			2.12815i
$785$	−920.494	+	920.494i	−0.0418520	+	0.0418520i
$786$	1377.34			0.0625041
$787$	−16605.7	+	16605.7i	−0.752132	+	0.752132i	−0.974877	−	0.222745i	$-0.928498\pi$
$787$	−16605.7	+	16605.7i	−0.752132	+	0.752132i	0.222745	+	0.974877i	$0.428498\pi$
$788$	10419.1	+	10419.1i	0.471022	+	0.471022i
$789$	4229.60	+	4229.60i	0.190847	+	0.190847i
$790$			992.800i			0.0447117i
$791$		−	53150.7i		−	2.38916i
$792$	−890.779	−	890.779i	−0.0399652	−	0.0399652i
$793$	119.939	+	119.939i	0.00537096	+	0.00537096i
$794$	−1597.47	+	1597.47i	−0.0714008	+	0.0714008i
$795$	21251.9			0.948087
$796$	4865.02	−	4865.02i	0.216628	−	0.216628i
$797$		−	28764.0i		−	1.27839i	−0.769046	−	0.639193i	$-0.779269\pi$
$797$		−	28764.0i		−	1.27839i	0.769046	−	0.639193i	$-0.220731\pi$
$798$	−1448.31			−0.0642478
$799$	−16248.8	+	19899.5i	−0.719452	+	0.881095i
$800$	3233.19			0.142888
$801$			5397.55i			0.238094i
$802$	342.399	−	342.399i	0.0150755	−	0.0150755i
$803$	−10030.9			−0.440828
$804$	7946.88	−	7946.88i	0.348588	−	0.348588i
$805$	5816.21	+	5816.21i	0.254652	+	0.254652i
$806$	−298.464	−	298.464i	−0.0130433	−	0.0130433i
$807$			7180.28i			0.313207i
$808$			4004.74i			0.174364i
$809$	6469.15	+	6469.15i	0.281141	+	0.281141i	0.833564	−	0.552423i	$-0.186297\pi$
$809$	6469.15	+	6469.15i	0.281141	+	0.281141i	−0.552423	+	0.833564i	$0.686297\pi$
$810$	−19.9987	−	19.9987i	−0.000867509	−	0.000867509i
$811$	6524.52	−	6524.52i	0.282499	−	0.282499i	−0.551606	−	0.834105i	$-0.685985\pi$
$811$	6524.52	−	6524.52i	0.282499	−	0.282499i	0.834105	+	0.551606i	$0.185985\pi$
$812$	55372.6			2.39310
$813$	1682.26	−	1682.26i	0.0725699	−	0.0725699i
$814$			13.2924i			0.000572357i
$815$	−8306.20			−0.356998
$816$	−1387.78	−	13741.4i	−0.0595369	−	0.589518i
$817$	5741.98			0.245883
$818$		−	4585.28i		−	0.195991i
$819$	−2002.73	+	2002.73i	−0.0854471	+	0.0854471i
$820$	31561.4			1.34411
$821$	−18974.9	+	18974.9i	−0.806611	+	0.806611i	−0.984119	−	0.177508i	$-0.943196\pi$
$821$	−18974.9	+	18974.9i	−0.806611	+	0.806611i	0.177508	+	0.984119i	$0.443196\pi$
$822$	−1334.07	−	1334.07i	−0.0566069	−	0.0566069i
$823$	−23397.5	−	23397.5i	−0.990989	−	0.990989i	0.00897047	−	0.999960i	$-0.497145\pi$
$823$	−23397.5	−	23397.5i	−0.990989	−	0.990989i	−0.999960	+	0.00897047i	$0.997145\pi$
$824$		−	4446.32i		−	0.187979i
$825$		−	2154.21i		−	0.0909089i
$826$	4191.30	+	4191.30i	0.176554	+	0.176554i
$827$	18376.0	+	18376.0i	0.772669	+	0.772669i	0.978572	−	0.205903i	$-0.0660132\pi$
$827$	18376.0	+	18376.0i	0.772669	+	0.772669i	−0.205903	+	0.978572i	$0.566013\pi$
$828$	−1730.53	+	1730.53i	−0.0726331	+	0.0726331i
$829$	−4089.38			−0.171327			−0.0856635	−	0.996324i	$-0.527301\pi$
$829$	−4089.38			−0.171327			−0.0856635	+	0.996324i	$0.527301\pi$
$830$	−3886.52	+	3886.52i	−0.162534	+	0.162534i
$831$		−	4841.49i		−	0.202105i
$832$	−2386.94			−0.0994620
$833$	41540.3	+	33919.5i	1.72784	+	1.41085i
$834$	1558.61			0.0647124
$835$			2404.57i			0.0996570i
$836$	2915.74	−	2915.74i	0.120626	−	0.120626i
$837$	32971.5			1.36160
$838$	−1899.06	+	1899.06i	−0.0782840	+	0.0782840i
$839$	−10051.6	−	10051.6i	−0.413609	−	0.413609i	0.469384	−	0.882994i	$-0.344476\pi$
$839$	−10051.6	−	10051.6i	−0.413609	−	0.413609i	−0.882994	+	0.469384i	$0.844476\pi$
$840$	5583.66	+	5583.66i	0.229351	+	0.229351i
$841$		−	20207.7i		−	0.828556i
$842$			5487.93i			0.224616i
$843$	−12248.0	−	12248.0i	−0.500408	−	0.500408i
$844$	4613.92	+	4613.92i	0.188173	+	0.188173i
$845$	20245.4	−	20245.4i	0.824218	−	0.824218i
$846$	2133.77			0.0867146
$847$	−26957.2	+	26957.2i	−1.09358	+	1.09358i
$848$		−	30484.5i		−	1.23448i
$849$	−16032.4			−0.648091
$850$	762.120	−	933.350i	0.0307535	−	0.0376631i
$851$	52.0508			0.00209668
$852$			12096.2i			0.486396i
$853$	6528.75	−	6528.75i	0.262064	−	0.262064i	−0.563828	−	0.825892i	$-0.690672\pi$
$853$	6528.75	−	6528.75i	0.262064	−	0.262064i	0.825892	+	0.563828i	$0.190672\pi$
$854$	−386.340			−0.0154804
$855$	−5941.53	+	5941.53i	−0.237656	+	0.237656i
$856$	1816.62	+	1816.62i	0.0725359	+	0.0725359i
$857$	−5875.90	−	5875.90i	−0.234209	−	0.234209i	0.580238	−	0.814447i	$-0.302960\pi$
$857$	−5875.90	−	5875.90i	−0.234209	−	0.234209i	−0.814447	+	0.580238i	$0.802960\pi$
$858$		−	79.1998i		−	0.00315132i
$859$		−	19105.7i		−	0.758880i	−0.925216	−	0.379440i	$-0.876117\pi$
$859$		−	19105.7i		−	0.758880i	0.925216	−	0.379440i	$-0.123883\pi$
$860$	−10982.6	−	10982.6i	−0.435470	−	0.435470i
$861$	23075.9	+	23075.9i	0.913384	+	0.913384i
$862$	2754.76	−	2754.76i	0.108849	−	0.108849i
$863$	−24172.0			−0.953447			−0.476724	−	0.879053i	$-0.658176\pi$
$863$	−24172.0			−0.953447			−0.476724	+	0.879053i	$0.658176\pi$
$864$	−6565.76	+	6565.76i	−0.258532	+	0.258532i
$865$		−	20970.9i		−	0.824316i
$866$	−5158.65			−0.202423
$867$	−13226.4	−	8743.13i	−0.518098	−	0.342482i
$868$	−61464.1			−2.40349
$869$		−	2922.67i		−	0.114091i
$870$	2231.07	−	2231.07i	0.0869430	−	0.0869430i
$871$	−2268.08			−0.0882331
$872$	−6173.79	+	6173.79i	−0.239760	+	0.239760i
$873$	2814.95	+	2814.95i	0.109131	+	0.109131i
$874$	178.588	+	178.588i	0.00691169	+	0.00691169i
$875$			33379.9i			1.28965i
$876$			18708.2i			0.721565i
$877$	1967.47	+	1967.47i	0.0757546	+	0.0757546i	0.743969	−	0.668214i	$-0.232941\pi$
$877$	1967.47	+	1967.47i	0.0757546	+	0.0757546i	−0.668214	+	0.743969i	$0.732941\pi$
$878$	−2333.59	−	2333.59i	−0.0896980	−	0.0896980i
$879$	−14781.3	+	14781.3i	−0.567190	+	0.567190i
$880$	−10976.6			−0.420479
$881$	−7736.01	+	7736.01i	−0.295838	+	0.295838i	−0.839381	−	0.543543i	$-0.817082\pi$
$881$	−7736.01	+	7736.01i	−0.295838	+	0.295838i	0.543543	+	0.839381i	$0.317082\pi$
$882$		−	4454.26i		−	0.170048i
$883$	47442.1			1.80810			0.904052	−	0.427423i	$-0.140579\pi$
$883$	47442.1			1.80810			0.904052	+	0.427423i	$0.140579\pi$
$884$	−1791.36	+	2193.83i	−0.0681559	+	0.0834689i
$885$	−21593.3			−0.820171
$886$		−	2650.17i		−	0.100490i
$887$	13888.4	−	13888.4i	0.525735	−	0.525735i	−0.393563	−	0.919298i	$-0.628758\pi$
$887$	13888.4	−	13888.4i	0.525735	−	0.525735i	0.919298	+	0.393563i	$0.128758\pi$
$888$	49.9696			0.00188837
$889$	19634.0	−	19634.0i	0.740723	−	0.740723i
$890$	−1065.40	−	1065.40i	−0.0401260	−	0.0401260i
$891$	58.8734	+	58.8734i	0.00221362	+	0.00221362i
$892$		−	10882.6i		−	0.408492i
$893$			14078.0i			0.527550i
$894$	1536.13	+	1536.13i	0.0574676	+	0.0574676i
$895$	23046.5	+	23046.5i	0.860736	+	0.860736i
$896$	16275.4	−	16275.4i	0.606834	−	0.606834i
$897$	−310.133			−0.0115441
$898$	1793.98	−	1793.98i	0.0666659	−	0.0666659i
$899$			49502.8i			1.83650i
$900$	6398.40			0.236978
$901$	−27106.5	−	22133.7i	−1.00228	−	0.818401i
$902$	1453.29			0.0536467
$903$		−	16059.7i		−	0.591841i
$904$	−6291.83	+	6291.83i	−0.231486	+	0.231486i
$905$	−14720.3			−0.540684
$906$	1504.46	−	1504.46i	0.0551682	−	0.0551682i
$907$	−11678.9	−	11678.9i	−0.427554	−	0.427554i	0.460240	−	0.887794i	$-0.347763\pi$
$907$	−11678.9	−	11678.9i	−0.427554	−	0.427554i	−0.887794	+	0.460240i	$0.847763\pi$
$908$	943.940	+	943.940i	0.0344997	+	0.0344997i
$909$			11918.7i			0.434893i
$910$		−	790.620i		−	0.0288009i
$911$	−34290.0	−	34290.0i	−1.24707	−	1.24707i	−0.957009	−	0.290058i	$-0.906325\pi$
$911$	−34290.0	−	34290.0i	−1.24707	−	1.24707i	−0.290058	−	0.957009i	$-0.593675\pi$
$912$	−5351.61	−	5351.61i	−0.194309	−	0.194309i
$913$	11441.4	−	11441.4i	0.414737	−	0.414737i
$914$	−2116.86			−0.0766078
$915$	995.201	−	995.201i	0.0359567	−	0.0359567i
$916$			19401.2i			0.699818i
$917$	−40476.6			−1.45764
$918$	347.723	+	3443.06i	0.0125017	+	0.123788i
$919$	24953.8			0.895703			0.447851	−	0.894108i	$-0.352189\pi$
$919$	24953.8			0.895703			0.447851	+	0.894108i	$0.352189\pi$
$920$		−	1377.01i		−	0.0493465i
$921$	−12205.5	+	12205.5i	−0.436684	+	0.436684i
$922$	−1330.32			−0.0475181
$923$	1726.16	−	1726.16i	0.0615571	−	0.0615571i
$924$	−8155.00	−	8155.00i	−0.290346	−	0.290346i
$925$	−96.2250	−	96.2250i	−0.00342039	−	0.00342039i
$926$			3259.85i			0.115686i
$927$		−	13232.9i		−	0.468851i
$928$	−9857.70	−	9857.70i	−0.348701	−	0.348701i
$929$	13712.7	+	13712.7i	0.484282	+	0.484282i	0.906496	−	0.422214i	$-0.138747\pi$
$929$	13712.7	+	13712.7i	0.484282	+	0.484282i	−0.422214	+	0.906496i	$0.638747\pi$
$930$	−2476.51	+	2476.51i	−0.0873206	+	0.0873206i
$931$	29387.9			1.03453
$932$	−14004.4	+	14004.4i	−0.492198	+	0.492198i
$933$		−	11683.6i		−	0.409972i
$934$	209.514			0.00733994
$935$	−7969.70	+	9760.29i	−0.278756	+	0.341386i
$936$	474.156			0.0165580
$937$		−	41919.9i		−	1.46154i	−0.682624	−	0.730770i	$-0.739161\pi$
$937$		−	41919.9i		−	1.46154i	0.682624	−	0.730770i	$-0.260839\pi$
$938$	3652.89	−	3652.89i	0.127155	−	0.127155i
$939$	6689.87			0.232498
$940$	26926.8	−	26926.8i	0.934313	−	0.934313i
$941$	33981.5	+	33981.5i	1.17722	+	1.17722i	0.980449	+	0.196774i	$0.0630464\pi$
$941$	33981.5	+	33981.5i	1.17722	+	1.17722i	0.196774	+	0.980449i	$0.436954\pi$
$942$	79.0509	+	79.0509i	0.00273420	+	0.00273420i
$943$		−	5690.85i		−	0.196521i
$944$			30974.2i			1.06793i
$945$	43670.2	+	43670.2i	1.50327	+	1.50327i
$946$	−505.710	−	505.710i	−0.0173806	−	0.0173806i
$947$	27499.8	−	27499.8i	0.943638	−	0.943638i	−0.0548567	−	0.998494i	$-0.517470\pi$
$947$	27499.8	−	27499.8i	0.943638	−	0.943638i	0.998494	+	0.0548567i	$0.0174702\pi$
$948$	−5450.91			−0.186748
$949$	2669.71	−	2669.71i	0.0913196	−	0.0913196i
$950$		−	660.302i		−	0.0225505i
$951$	25706.8			0.876553
$952$	−1306.56	−	12937.2i	−0.0444810	−	0.440438i
$953$	−6364.48			−0.216333			−0.108167	−	0.994133i	$-0.534498\pi$
$953$	−6364.48			−0.216333			−0.108167	+	0.994133i	$0.534498\pi$
$954$			2906.56i			0.0986408i
$955$	35908.7	−	35908.7i	1.21673	−	1.21673i
$956$	27085.4			0.916323
$957$	−6567.98	+	6567.98i	−0.221852	+	0.221852i
$958$	1101.19	+	1101.19i	0.0371376	+	0.0371376i
$959$	39204.8	+	39204.8i	1.32011	+	1.32011i
$960$			19805.8i			0.665863i
$961$		−	25157.6i		−	0.844470i
$962$	−3.53773	−	3.53773i	−0.000118567	−	0.000118567i
$963$	5406.52	+	5406.52i	0.180916	+	0.180916i
$964$	−22799.2	+	22799.2i	−0.761736	+	0.761736i
$965$	−29340.3			−0.978753
$966$	499.489	−	499.489i	0.0166364	−	0.0166364i
$967$		−	1031.78i		−	0.0343121i	−0.999853	−	0.0171560i	$-0.994539\pi$
$967$		−	1031.78i		−	0.0343121i	0.999853	−	0.0171560i	$-0.00546120\pi$
$968$	6382.23			0.211914
$969$	−8644.20	+	872.999i	−0.286575	+	0.0289420i
$970$	−1111.26			−0.0367839
$971$			30980.7i			1.02391i	0.859012	+	0.511956i	$0.171079\pi$
$971$			30980.7i			1.02391i	−0.859012	+	0.511956i	$0.828921\pi$
$972$	−21042.6	+	21042.6i	−0.694383	+	0.694383i
$973$	−45803.5			−1.50914
$974$	2147.97	−	2147.97i	0.0706626	−	0.0706626i
$975$	573.335	+	573.335i	0.0188322	+	0.0188322i
$976$	−1427.55	−	1427.55i	−0.0468184	−	0.0468184i
$977$		−	37987.7i		−	1.24394i	−0.783040	−	0.621972i	$-0.786332\pi$
$977$		−	37987.7i		−	1.24394i	0.783040	−	0.621972i	$-0.213668\pi$
$978$			713.327i			0.0233228i
$979$	3136.38	+	3136.38i	0.102389	+	0.102389i
$980$	−56209.7	−	56209.7i	−1.83220	−	1.83220i
$981$	−18374.1	+	18374.1i	−0.598001	+	0.598001i
$982$	1811.40			0.0588635
$983$	38774.8	−	38774.8i	1.25811	−	1.25811i	0.306119	−	0.951993i	$-0.400970\pi$
$983$	38774.8	−	38774.8i	1.25811	−	1.25811i	0.951993	−	0.306119i	$-0.0990305\pi$
$984$		−	5463.31i		−	0.176996i
$985$	−24674.1			−0.798156
$986$	−5169.34	+	522.064i	−0.166963	+	0.0168620i
$987$	39374.5			1.26981
$988$			1552.03i			0.0499764i
$989$	−1980.28	+	1980.28i	−0.0636695	+	0.0636695i
$990$	1046.57			0.0335981
$991$	−27847.0	+	27847.0i	−0.892623	+	0.892623i	−0.994769	−	0.102146i	$-0.967429\pi$
$991$	−27847.0	+	27847.0i	−0.892623	+	0.892623i	0.102146	+	0.994769i	$0.467429\pi$
$992$	10942.2	+	10942.2i	0.350215	+	0.350215i
$993$	−18397.0	−	18397.0i	−0.587925	−	0.587925i
$994$			5560.19i			0.177423i
$995$			11521.2i			0.367081i
$996$	−21338.7	−	21338.7i	−0.678859	−	0.678859i
$997$	−15916.3	−	15916.3i	−0.505591	−	0.505591i	0.407579	−	0.913170i	$-0.366373\pi$
$997$	−15916.3	−	15916.3i	−0.505591	−	0.505591i	−0.913170	+	0.407579i	$0.866373\pi$
$998$	−2165.39	+	2165.39i	−0.0686815	+	0.0686815i
$999$	390.816			0.0123772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.c.a.4.2	✓	8
3.2	odd	2		153.4.f.a.55.3		8
4.3	odd	2		272.4.o.e.225.2		8
17.2	even	8		289.4.b.c.288.5		8
17.8	even	8		289.4.a.f.1.3		8
17.9	even	8		289.4.a.f.1.4		8
17.13	even	4	inner	17.4.c.a.13.3	yes	8
17.15	even	8		289.4.b.c.288.6		8
51.47	odd	4		153.4.f.a.64.2		8
68.47	odd	4		272.4.o.e.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.2	✓	8	1.1	even	1	trivial
17.4.c.a.13.3	yes	8	17.13	even	4	inner
153.4.f.a.55.3		8	3.2	odd	2
153.4.f.a.64.2		8	51.47	odd	4
272.4.o.e.81.2		8	68.47	odd	4
272.4.o.e.225.2		8	4.3	odd	2
289.4.a.f.1.3		8	17.8	even	8
289.4.a.f.1.4		8	17.9	even	8
289.4.b.c.288.5		8	17.2	even	8
289.4.b.c.288.6		8	17.15	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.351005i q^{2} +(2.28193 - 2.28193i) q^{3} +7.87680 q^{4} +(-9.32676 + 9.32676i) q^{5} +(0.800971 + 0.800971i) q^{6} +(-23.5385 - 23.5385i) q^{7} +5.57284i q^{8} +16.5856i q^{9} +O(q^{10})\)	\(q+0.351005i q^{2} +(2.28193 - 2.28193i) q^{3} +7.87680 q^{4} +(-9.32676 + 9.32676i) q^{5} +(0.800971 + 0.800971i) q^{6} +(-23.5385 - 23.5385i) q^{7} +5.57284i q^{8} +16.5856i q^{9} +(-3.27374 - 3.27374i) q^{10} +(9.63747 + 9.63747i) q^{11} +(17.9743 - 17.9743i) q^{12} -5.12996 q^{13} +(8.26214 - 8.26214i) q^{14} +42.5661i q^{15} +61.0583 q^{16} +(44.3321 - 54.2924i) q^{17} -5.82162 q^{18} -38.4093i q^{19} +(-73.4650 + 73.4650i) q^{20} -107.427 q^{21} +(-3.38280 + 3.38280i) q^{22} +(13.2465 + 13.2465i) q^{23} +(12.7169 + 12.7169i) q^{24} -48.9769i q^{25} -1.80065i q^{26} +(99.4593 + 99.4593i) q^{27} +(-185.408 - 185.408i) q^{28} +(-149.326 + 149.326i) q^{29} -14.9409 q^{30} +(165.754 - 165.754i) q^{31} +66.0145i q^{32} +43.9841 q^{33} +(19.0569 + 15.5608i) q^{34} +439.076 q^{35} +130.641i q^{36} +(1.96470 - 1.96470i) q^{37} +13.4819 q^{38} +(-11.7062 + 11.7062i) q^{39} +(-51.9766 - 51.9766i) q^{40} +(-214.806 - 214.806i) q^{41} -37.7073i q^{42} +149.494i q^{43} +(75.9123 + 75.9123i) q^{44} +(-154.690 - 154.690i) q^{45} +(-4.64959 + 4.64959i) q^{46} -366.525 q^{47} +(139.331 - 139.331i) q^{48} +765.122i q^{49} +17.1912 q^{50} +(-22.7288 - 225.054i) q^{51} -40.4077 q^{52} -499.269i q^{53} +(-34.9108 + 34.9108i) q^{54} -179.773 q^{55} +(131.176 - 131.176i) q^{56} +(-87.6475 - 87.6475i) q^{57} +(-52.4143 - 52.4143i) q^{58} +507.289i q^{59} +335.284i q^{60} +(-23.3801 - 23.3801i) q^{61} +(58.1805 + 58.1805i) q^{62} +(390.399 - 390.399i) q^{63} +465.295 q^{64} +(47.8459 - 47.8459i) q^{65} +15.4387i q^{66} +442.124 q^{67} +(349.195 - 427.650i) q^{68} +60.4552 q^{69} +154.118i q^{70} +(-336.486 + 336.486i) q^{71} -92.4287 q^{72} +(-520.414 + 520.414i) q^{73} +(0.689621 + 0.689621i) q^{74} +(-111.762 - 111.762i) q^{75} -302.543i q^{76} -453.703i q^{77} +(-4.10895 - 4.10895i) q^{78} +(-151.631 - 151.631i) q^{79} +(-569.476 + 569.476i) q^{80} +6.10881 q^{81} +(75.3981 - 75.3981i) q^{82} -1187.18i q^{83} -846.177 q^{84} +(92.8977 + 919.847i) q^{85} -52.4734 q^{86} +681.505i q^{87} +(-53.7081 + 53.7081i) q^{88} +325.436 q^{89} +(54.2969 - 54.2969i) q^{90} +(120.752 + 120.752i) q^{91} +(104.340 + 104.340i) q^{92} -756.478i q^{93} -128.652i q^{94} +(358.235 + 358.235i) q^{95} +(150.641 + 150.641i) q^{96} +(169.723 - 169.723i) q^{97} -268.562 q^{98} +(-159.843 + 159.843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) \) 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7	\( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) \) 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7 + 78 * q^10 - 108 * q^11 - 174 * q^12 - 88 * q^13 + 108 * q^14 + 420 * q^16 - 10 * q^17 + 428 * q^18 - 306 * q^20 - 260 * q^21 + 30 * q^22 - 22 * q^23 - 862 * q^24 + 540 * q^27 - 764 * q^28 + 46 * q^29 - 120 * q^30 + 610 * q^31 + 816 * q^33 + 1002 * q^34 + 1172 * q^35 - 574 * q^37 - 768 * q^38 - 844 * q^39 - 342 * q^40 - 968 * q^41 + 550 * q^44 - 1154 * q^45 - 944 * q^46 - 368 * q^47 + 2494 * q^48 + 468 * q^50 + 296 * q^51 + 2564 * q^52 - 1592 * q^54 - 1996 * q^55 + 684 * q^56 - 300 * q^57 + 266 * q^58 + 1258 * q^61 - 2516 * q^62 + 122 * q^63 - 3044 * q^64 + 628 * q^65 + 764 * q^67 + 1914 * q^68 + 1812 * q^69 + 1266 * q^71 + 1404 * q^72 - 1732 * q^73 + 1538 * q^74 + 1292 * q^75 - 2836 * q^78 + 914 * q^79 + 498 * q^80 + 280 * q^81 - 280 * q^82 - 2952 * q^84 - 2498 * q^85 - 4244 * q^86 + 442 * q^88 - 2156 * q^89 + 2478 * q^90 - 1632 * q^91 - 1768 * q^92 + 1484 * q^95 + 3998 * q^96 + 1836 * q^97 + 6728 * q^98 - 2088 * q^99

Introduction

L-functions

Modular forms

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