LMFDB - Embedded newform 132.4.i.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,4,Mod(25,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("132.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	132.i (of order $5$, degree $4$, 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:	$7.78825212076$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
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} - x^{7} + 58x^{6} - 115x^{5} + 2421x^{4} + 3435x^{3} + 83262x^{2} + 124773x + 4791721 $ x^8 - x^7 + 58x^6 - 115x^5 + 2421x^4 + 3435x^3 + 83262x^2 + 124773x + 4791721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.2
Root			$2.06788 + 6.36429i$ of defining polynomial
Character	$\chi$	$=$	132.37
Dual form			132.4.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.927051 + 2.85317i) q^{3} +(1.60477 - 1.16593i) q^{5} +(3.78898 + 11.6613i) q^{7} +(-7.28115 - 5.29007i) q^{9} +(-8.21788 + 35.5453i) q^{11} +(5.26513 + 3.82534i) q^{13} +(1.83890 + 5.65957i) q^{15} +(-62.9784 + 45.7565i) q^{17} +(-28.2631 + 86.9850i) q^{19} -36.7842 q^{21} -20.2371 q^{23} +(-37.4112 + 115.140i) q^{25} +(21.8435 - 15.8702i) q^{27} +(-23.5838 - 72.5834i) q^{29} +(92.8764 + 67.4787i) q^{31} +(-93.7983 - 56.3993i) q^{33} +(19.6767 + 14.2960i) q^{35} +(27.6238 + 85.0174i) q^{37} +(-15.7954 + 11.4760i) q^{39} +(30.4658 - 93.7641i) q^{41} +488.233 q^{43} -17.8525 q^{45} +(33.0191 - 101.622i) q^{47} +(155.864 - 113.242i) q^{49} +(-72.1668 - 222.106i) q^{51} +(-447.009 - 324.771i) q^{53} +(28.2556 + 66.6235i) q^{55} +(-221.982 - 161.279i) q^{57} +(-52.3705 - 161.180i) q^{59} +(235.345 - 170.988i) q^{61} +(34.1008 - 104.952i) q^{63} +12.9094 q^{65} +107.351 q^{67} +(18.7608 - 57.7398i) q^{69} +(589.515 - 428.308i) q^{71} +(110.836 + 341.119i) q^{73} +(-293.832 - 213.481i) q^{75} +(-445.641 + 38.8493i) q^{77} +(413.815 + 300.654i) q^{79} +(25.0304 + 77.0356i) q^{81} +(515.712 - 374.687i) q^{83} +(-47.7168 + 146.857i) q^{85} +228.956 q^{87} -830.847 q^{89} +(-24.6589 + 75.8924i) q^{91} +(-278.629 + 202.436i) q^{93} +(56.0629 + 172.544i) q^{95} +(-642.830 - 467.043i) q^{97} +(247.873 - 215.337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 27 q^{5} + 13 q^{7} - 18 q^{9} - 45 q^{11} - 89 q^{13} - 99 q^{15} - 24 q^{17} - 28 q^{19} + 66 q^{21} - 348 q^{23} - 9 q^{25} + 54 q^{27} - 249 q^{29} - 217 q^{31} - 540 q^{33} + 630 q^{35}+ \cdots - 1215 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - 27 * q^5 + 13 * q^7 - 18 * q^9 - 45 * q^11 - 89 * q^13 - 99 * q^15 - 24 * q^17 - 28 * q^19 + 66 * q^21 - 348 * q^23 - 9 * q^25 + 54 * q^27 - 249 * q^29 - 217 * q^31 - 540 * q^33 + 630 * q^35 + 585 * q^37 + 267 * q^39 - 177 * q^41 + 684 * q^43 - 108 * q^45 - 93 * q^47 + 1377 * q^49 - 423 * q^51 - 693 * q^53 - 472 * q^55 - 501 * q^57 + 1086 * q^59 + 1069 * q^61 + 117 * q^63 - 114 * q^65 + 470 * q^67 + 369 * q^69 + 1479 * q^71 + 947 * q^73 - 393 * q^75 - 3693 * q^77 + 1251 * q^79 - 162 * q^81 + 1185 * q^83 - 2585 * q^85 + 1062 * q^87 - 1716 * q^89 + 4191 * q^91 + 651 * q^93 - 141 * q^95 - 3783 * q^97 - 1215 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$4$		0			0
$5$	1.60477	−	1.16593i	0.143535	−	0.104284i	−0.513700	−	0.857970i	$-0.671726\pi$
$5$	1.60477	−	1.16593i	0.143535	−	0.104284i	0.657235	+	0.753685i	$0.271726\pi$
$6$		0			0
$7$	3.78898	+	11.6613i	0.204586	+	0.629650i	0.999730	+	0.0232301i	$0.00739502\pi$
$7$	3.78898	+	11.6613i	0.204586	+	0.629650i	−0.795144	+	0.606420i	$0.792605\pi$
$8$		0			0
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$		0			0
$11$	−8.21788	+	35.5453i	−0.225253	+	0.974300i
$11$	−8.21788	+	35.5453i	−0.225253	+	0.974300i
$12$		0			0
$13$	5.26513	+	3.82534i	0.112330	+	0.0816123i	0.642532	−	0.766259i	$-0.277884\pi$
$13$	5.26513	+	3.82534i	0.112330	+	0.0816123i	−0.530202	+	0.847871i	$0.677884\pi$
$14$		0			0
$15$	1.83890	+	5.65957i	0.0316535	+	0.0974196i
$16$		0			0
$17$	−62.9784	+	45.7565i	−0.898500	+	0.652798i	−0.938080	−	0.346418i	$-0.887398\pi$
$17$	−62.9784	+	45.7565i	−0.898500	+	0.652798i	0.0395805	+	0.999216i	$0.487398\pi$
$18$		0			0
$19$	−28.2631	+	86.9850i	−0.341264	+	1.05030i	0.622290	+	0.782787i	$0.286202\pi$
$19$	−28.2631	+	86.9850i	−0.341264	+	1.05030i	−0.963554	+	0.267515i	$0.913798\pi$
$20$		0			0
$21$	−36.7842			−0.382237
$22$		0			0
$23$	−20.2371			−0.183466			−0.0917331	−	0.995784i	$-0.529241\pi$
$23$	−20.2371			−0.183466			−0.0917331	+	0.995784i	$0.529241\pi$
$24$		0			0
$25$	−37.4112	+	115.140i	−0.299290	+	0.921120i
$26$		0			0
$27$	21.8435	−	15.8702i	0.155695	−	0.113119i
$28$		0			0
$29$	−23.5838	−	72.5834i	−0.151014	−	0.464773i	0.846721	−	0.532036i	$-0.178573\pi$
$29$	−23.5838	−	72.5834i	−0.151014	−	0.464773i	−0.997735	+	0.0672639i	$0.978573\pi$
$30$		0			0
$31$	92.8764	+	67.4787i	0.538100	+	0.390953i	0.823379	−	0.567492i	$-0.192086\pi$
$31$	92.8764	+	67.4787i	0.538100	+	0.390953i	−0.285279	+	0.958445i	$0.592086\pi$
$32$		0			0
$33$	−93.7983	−	56.3993i	−0.494794	−	0.297511i
$34$		0			0
$35$	19.6767	+	14.2960i	0.0950279	+	0.0690418i
$36$		0			0
$37$	27.6238	+	85.0174i	0.122739	+	0.377751i	0.993482	−	0.113987i	$-0.0363621\pi$
$37$	27.6238	+	85.0174i	0.122739	+	0.377751i	−0.870744	+	0.491737i	$0.836362\pi$
$38$		0			0
$39$	−15.7954	+	11.4760i	−0.0648535	+	0.0471189i
$40$		0			0
$41$	30.4658	−	93.7641i	0.116048	−	0.357159i	−0.876116	−	0.482100i	$-0.839874\pi$
$41$	30.4658	−	93.7641i	0.116048	−	0.357159i	0.992164	+	0.124941i	$0.0398743\pi$
$42$		0			0
$43$	488.233			1.73151			0.865753	−	0.500471i	$-0.166840\pi$
$43$	488.233			1.73151			0.865753	+	0.500471i	$0.166840\pi$
$44$		0			0
$45$	−17.8525			−0.0591397
$46$		0			0
$47$	33.0191	−	101.622i	0.102475	−	0.315386i	−0.886654	−	0.462433i	$-0.846977\pi$
$47$	33.0191	−	101.622i	0.102475	−	0.315386i	0.989130	+	0.147046i	$0.0469766\pi$
$48$		0			0
$49$	155.864	−	113.242i	0.454413	−	0.330150i
$50$		0			0
$51$	−72.1668	−	222.106i	−0.198144	−	0.609826i
$52$		0			0
$53$	−447.009	−	324.771i	−1.15852	−	0.841712i	−0.168928	−	0.985628i	$-0.554030\pi$
$53$	−447.009	−	324.771i	−1.15852	−	0.841712i	−0.989590	+	0.143916i	$0.954030\pi$
$54$		0			0
$55$	28.2556	+	66.6235i	0.0692725	+	0.163337i
$56$		0			0
$57$	−221.982	−	161.279i	−0.515828	−	0.374771i
$58$		0			0
$59$	−52.3705	−	161.180i	−0.115560	−	0.355658i	0.876503	−	0.481396i	$-0.159870\pi$
$59$	−52.3705	−	161.180i	−0.115560	−	0.355658i	−0.992063	+	0.125738i	$0.959870\pi$
$60$		0			0
$61$	235.345	−	170.988i	0.493982	−	0.358899i	−0.312732	−	0.949841i	$-0.601244\pi$
$61$	235.345	−	170.988i	0.493982	−	0.358899i	0.806713	+	0.590943i	$0.201244\pi$
$62$		0			0
$63$	34.1008	−	104.952i	0.0681953	−	0.209883i
$64$		0			0
$65$	12.9094			0.0246341
$66$		0			0
$67$	107.351			0.195747			0.0978736	−	0.995199i	$-0.468796\pi$
$67$	107.351			0.195747			0.0978736	+	0.995199i	$0.468796\pi$
$68$		0			0
$69$	18.7608	−	57.7398i	0.0327324	−	0.100740i
$70$		0			0
$71$	589.515	−	428.308i	0.985389	−	0.715927i	0.0264824	−	0.999649i	$-0.491569\pi$
$71$	589.515	−	428.308i	0.985389	−	0.715927i	0.958906	+	0.283722i	$0.0915694\pi$
$72$		0			0
$73$	110.836	+	341.119i	0.177704	+	0.546917i	0.999747	−	0.0225091i	$-0.00716546\pi$
$73$	110.836	+	341.119i	0.177704	+	0.546917i	−0.822043	+	0.569426i	$0.807165\pi$
$74$		0			0
$75$	−293.832	−	213.481i	−0.452383	−	0.328676i
$76$		0			0
$77$	−445.641	+	38.8493i	−0.659552	+	0.0574973i
$78$		0			0
$79$	413.815	+	300.654i	0.589339	+	0.428180i	0.842079	−	0.539354i	$-0.181332\pi$
$79$	413.815	+	300.654i	0.589339	+	0.428180i	−0.252740	+	0.967534i	$0.581332\pi$
$80$		0			0
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$		0			0
$83$	515.712	−	374.687i	0.682010	−	0.495509i	−0.192014	−	0.981392i	$-0.561502\pi$
$83$	515.712	−	374.687i	0.682010	−	0.495509i	0.874024	+	0.485883i	$0.161502\pi$
$84$		0			0
$85$	−47.7168	+	146.857i	−0.0608896	+	0.187399i
$86$		0			0
$87$	228.956			0.282146
$88$		0			0
$89$	−830.847			−0.989547			−0.494773	−	0.869022i	$-0.664749\pi$
$89$	−830.847			−0.989547			−0.494773	+	0.869022i	$0.664749\pi$
$90$		0			0
$91$	−24.6589	+	75.8924i	−0.0284061	+	0.0874251i
$92$		0			0
$93$	−278.629	+	202.436i	−0.310672	+	0.225717i
$94$		0			0
$95$	56.0629	+	172.544i	0.0605467	+	0.186344i
$96$		0			0
$97$	−642.830	−	467.043i	−0.672882	−	0.488877i	0.198107	−	0.980180i	$-0.436521\pi$
$97$	−642.830	−	467.043i	−0.672882	−	0.488877i	−0.870989	+	0.491303i	$0.836521\pi$
$98$		0			0
$99$	247.873	−	215.337i	0.251638	−	0.218608i
$100$		0			0
$101$	381.819	+	277.407i	0.376162	+	0.273298i	0.759762	−	0.650202i	$-0.225316\pi$
$101$	381.819	+	277.407i	0.376162	+	0.273298i	−0.383599	+	0.923500i	$0.625316\pi$
$102$		0			0
$103$	571.034	+	1757.46i	0.546268	+	1.68124i	0.717955	+	0.696090i	$0.245078\pi$
$103$	571.034	+	1757.46i	0.546268	+	1.68124i	−0.171686	+	0.985152i	$0.554922\pi$
$104$		0			0
$105$	−59.0302	+	42.8880i	−0.0548644	+	0.0398613i
$106$		0			0
$107$	−287.507	+	884.855i	−0.259760	+	0.799460i	0.733094	+	0.680127i	$0.238075\pi$
$107$	−287.507	+	884.855i	−0.259760	+	0.799460i	−0.992854	+	0.119332i	$0.961925\pi$
$108$		0			0
$109$	433.332			0.380786			0.190393	−	0.981708i	$-0.439024\pi$
$109$	433.332			0.380786			0.190393	+	0.981708i	$0.439024\pi$
$110$		0			0
$111$	−268.178			−0.229318
$112$		0			0
$113$	−520.776	+	1602.78i	−0.433544	+	1.33431i	0.461026	+	0.887386i	$0.347481\pi$
$113$	−520.776	+	1602.78i	−0.433544	+	1.33431i	−0.894571	+	0.446926i	$0.852519\pi$
$114$		0			0
$115$	−32.4759	+	23.5951i	−0.0263338	+	0.0191327i
$116$		0			0
$117$	−18.0999	−	55.7058i	−0.0143020	−	0.0440171i
$118$		0			0
$119$	−772.203	−	561.038i	−0.594855	−	0.432187i
$120$		0			0
$121$	−1195.93	−	584.214i	−0.898522	−	0.438928i
$122$		0			0
$123$	239.282	+	173.848i	0.175409	+	0.127442i
$124$		0			0
$125$	150.830	+	464.208i	0.107925	+	0.332160i
$126$		0			0
$127$	−100.382	+	72.9320i	−0.0701377	+	0.0509580i	−0.622302	−	0.782778i	$-0.713802\pi$
$127$	−100.382	+	72.9320i	−0.0701377	+	0.0509580i	0.552164	+	0.833736i	$0.313802\pi$
$128$		0			0
$129$	−452.617	+	1393.01i	−0.308920	+	0.950758i
$130$		0			0
$131$	−140.240			−0.0935328			−0.0467664	−	0.998906i	$-0.514892\pi$
$131$	−140.240			−0.0935328			−0.0467664	+	0.998906i	$0.514892\pi$
$132$		0			0
$133$	−1121.45			−0.731140
$134$		0			0
$135$	16.5501	−	50.9361i	0.0105512	−	0.0324732i
$136$		0			0
$137$	610.321	−	443.424i	0.380608	−	0.276528i	−0.380988	−	0.924580i	$-0.624416\pi$
$137$	610.321	−	443.424i	0.380608	−	0.276528i	0.761596	+	0.648052i	$0.224416\pi$
$138$		0			0
$139$	−367.333	−	1130.53i	−0.224149	−	0.689861i	−0.998377	−	0.0569534i	$-0.981861\pi$
$139$	−367.333	−	1130.53i	−0.224149	−	0.689861i	0.774227	−	0.632907i	$-0.218139\pi$
$140$		0			0
$141$	259.336	+	188.418i	0.154894	+	0.112537i
$142$		0			0
$143$	−179.241	+	155.714i	−0.104817	+	0.0910594i
$144$		0			0
$145$	−122.474	−	88.9827i	−0.0701443	−	0.0509628i
$146$		0			0
$147$	178.604	+	549.686i	0.100211	+	0.308417i
$148$		0			0
$149$	1173.73	−	852.763i	0.645339	−	0.468866i	−0.216341	−	0.976318i	$-0.569412\pi$
$149$	1173.73	−	852.763i	0.645339	−	0.468866i	0.861680	+	0.507452i	$0.169412\pi$
$150$		0			0
$151$	−870.060	+	2677.77i	−0.468904	+	1.44314i	0.385102	+	0.922874i	$0.374166\pi$
$151$	−870.060	+	2677.77i	−0.468904	+	1.44314i	−0.854006	+	0.520263i	$0.825834\pi$
$152$		0			0
$153$	700.610			0.370202
$154$		0			0
$155$	227.721			0.118006
$156$		0			0
$157$	742.481	−	2285.12i	0.377429	−	1.16161i	−0.564396	−	0.825504i	$-0.690891\pi$
$157$	742.481	−	2285.12i	0.377429	−	1.16161i	0.941825	−	0.336104i	$-0.109109\pi$
$158$		0			0
$159$	1341.03	−	974.314i	0.668871	−	0.485963i
$160$		0			0
$161$	−76.6779	−	235.990i	−0.0375346	−	0.115520i
$162$		0			0
$163$	−1694.23	−	1230.93i	−0.814123	−	0.591495i	0.100900	−	0.994897i	$-0.467828\pi$
$163$	−1694.23	−	1230.93i	−0.814123	−	0.591495i	−0.915023	+	0.403402i	$0.867828\pi$
$164$		0			0
$165$	−216.283	+	18.8547i	−0.102046	+	0.00889598i
$166$		0			0
$167$	3089.83	+	2244.90i	1.43173	+	1.04021i	0.989692	+	0.143214i	$0.0457437\pi$
$167$	3089.83	+	2244.90i	1.43173	+	1.04021i	0.442036	+	0.896997i	$0.354256\pi$
$168$		0			0
$169$	−665.822	−	2049.19i	−0.303060	−	0.932722i
$170$		0			0
$171$	665.945	−	483.837i	0.297813	−	0.216374i
$172$		0			0
$173$	−611.373	+	1881.61i	−0.268681	+	0.826916i	0.722141	+	0.691746i	$0.243158\pi$
$173$	−611.373	+	1881.61i	−0.268681	+	0.826916i	−0.990822	+	0.135170i	$0.956842\pi$
$174$		0			0
$175$	−1484.43			−0.641214
$176$		0			0
$177$	508.424			0.215907
$178$		0			0
$179$	818.393	−	2518.76i	0.341729	−	1.05174i	−0.621582	−	0.783349i	$-0.713510\pi$
$179$	818.393	−	2518.76i	0.341729	−	1.05174i	0.963311	−	0.268386i	$-0.0864903\pi$
$180$		0			0
$181$	3446.85	−	2504.29i	1.41548	−	1.02841i	0.422988	−	0.906135i	$-0.360981\pi$
$181$	3446.85	−	2504.29i	1.41548	−	1.02841i	0.992496	−	0.122274i	$-0.0390188\pi$
$182$		0			0
$183$	269.682	+	829.995i	0.108937	+	0.335273i
$184$		0			0
$185$	143.455	+	104.226i	0.0570108	+	0.0414208i
$186$		0			0
$187$	−1108.88	−	2614.60i	−0.433632	−	1.02245i
$188$		0			0
$189$	267.831	+	194.591i	0.103079	+	0.0748910i
$190$		0			0
$191$	−407.397	−	1253.84i	−0.154336	−	0.474998i	0.843757	−	0.536726i	$-0.180339\pi$
$191$	−407.397	−	1253.84i	−0.154336	−	0.474998i	−0.998093	+	0.0617276i	$0.980339\pi$
$192$		0			0
$193$	2230.05	−	1620.23i	0.831724	−	0.604283i	−0.0883223	−	0.996092i	$-0.528151\pi$
$193$	2230.05	−	1620.23i	0.831724	−	0.604283i	0.920047	+	0.391809i	$0.128151\pi$
$194$		0			0
$195$	−11.9677	+	36.8328i	−0.00439500	+	0.0135264i
$196$		0			0
$197$	1901.61			0.687738			0.343869	−	0.939018i	$-0.388262\pi$
$197$	1901.61			0.687738			0.343869	+	0.939018i	$0.388262\pi$
$198$		0			0
$199$	−3994.66			−1.42299			−0.711493	−	0.702693i	$-0.751981\pi$
$199$	−3994.66			−1.42299			−0.711493	+	0.702693i	$0.751981\pi$
$200$		0			0
$201$	−99.5203	+	306.292i	−0.0349235	+	0.107483i
$202$		0			0
$203$	757.058	−	550.034i	0.261749	−	0.190172i
$204$		0			0
$205$	−60.4322	−	185.991i	−0.0205891	−	0.0633668i
$206$		0			0
$207$	147.349	+	107.056i	0.0494758	+	0.0359462i
$208$		0			0
$209$	−2859.64	−	1719.45i	−0.946438	−	0.569077i
$210$		0			0
$211$	−417.464	−	303.305i	−0.136206	−	0.0989592i	0.517596	−	0.855625i	$-0.326827\pi$
$211$	−417.464	−	303.305i	−0.136206	−	0.0989592i	−0.653802	+	0.756666i	$0.726827\pi$
$212$		0			0
$213$	675.525	+	2079.05i	0.217306	+	0.668799i
$214$		0			0
$215$	783.502	−	569.247i	0.248532	−	0.180569i
$216$		0			0
$217$	−434.981	+	1338.73i	−0.136076	+	0.418798i
$218$		0			0
$219$	−1076.02			−0.332013
$220$		0			0
$221$	−506.624			−0.154204
$222$		0			0
$223$	−271.131	+	834.455i	−0.0814182	+	0.250579i	−0.983477	−	0.181034i	$-0.942056\pi$
$223$	−271.131	+	834.455i	−0.0814182	+	0.250579i	0.902059	+	0.431614i	$0.142056\pi$
$224$		0			0
$225$	881.495	−	640.444i	0.261184	−	0.189761i
$226$		0			0
$227$	−1238.72	−	3812.39i	−0.362189	−	1.11470i	−0.951723	−	0.306959i	$-0.900689\pi$
$227$	−1238.72	−	3812.39i	−0.362189	−	1.11470i	0.589534	−	0.807743i	$-0.299311\pi$
$228$		0			0
$229$	−1386.93	−	1007.66i	−0.400222	−	0.290779i	0.369409	−	0.929267i	$-0.379560\pi$
$229$	−1386.93	−	1007.66i	−0.400222	−	0.290779i	−0.769632	+	0.638488i	$0.779560\pi$
$230$		0			0
$231$	302.288	−	1307.50i	0.0861000	−	0.372413i
$232$		0			0
$233$	5121.82	+	3721.22i	1.44009	+	1.04629i	0.988023	+	0.154305i	$0.0493137\pi$
$233$	5121.82	+	3721.22i	1.44009	+	1.04629i	0.452068	+	0.891983i	$0.350686\pi$
$234$		0			0
$235$	−65.4970	−	201.579i	−0.0181811	−	0.0559556i
$236$		0			0
$237$	−1241.44	+	901.962i	−0.340255	+	0.247210i
$238$		0			0
$239$	−1863.05	+	5733.87i	−0.504228	+	1.55185i	0.297837	+	0.954617i	$0.403735\pi$
$239$	−1863.05	+	5733.87i	−0.504228	+	1.55185i	−0.802065	+	0.597237i	$0.796265\pi$
$240$		0			0
$241$	2528.58			0.675852			0.337926	−	0.941173i	$-0.390275\pi$
$241$	2528.58			0.675852			0.337926	+	0.941173i	$0.390275\pi$
$242$		0			0
$243$	−243.000			−0.0641500
$244$		0			0
$245$	118.093	−	363.454i	0.0307947	−	0.0947763i
$246$		0			0
$247$	−481.557	+	349.871i	−0.124051	+	0.0901287i
$248$		0			0
$249$	590.954	+	1818.77i	0.150402	+	0.462891i
$250$		0			0
$251$	−2313.85	−	1681.11i	−0.581867	−	0.422751i	0.257530	−	0.966270i	$-0.417092\pi$
$251$	−2313.85	−	1681.11i	−0.581867	−	0.422751i	−0.839397	+	0.543519i	$0.817092\pi$
$252$		0			0
$253$	166.306	−	719.333i	0.0413263	−	0.178751i
$254$		0			0
$255$	−374.773	−	272.288i	−0.0920360	−	0.0668681i
$256$		0			0
$257$	1454.89	+	4477.69i	0.353127	+	1.08681i	0.957088	+	0.289798i	$0.0935882\pi$
$257$	1454.89	+	4477.69i	0.353127	+	1.08681i	−0.603961	+	0.797014i	$0.706412\pi$
$258$		0			0
$259$	−886.746	+	644.259i	−0.212740	+	0.154565i
$260$		0			0
$261$	−212.254	+	653.251i	−0.0503379	+	0.154924i
$262$		0			0
$263$	−1322.27			−0.310018			−0.155009	−	0.987913i	$-0.549541\pi$
$263$	−1322.27			−0.310018			−0.155009	+	0.987913i	$0.549541\pi$
$264$		0			0
$265$	−1096.01			−0.254065
$266$		0			0
$267$	770.238	−	2370.55i	0.176546	−	0.543353i
$268$		0			0
$269$	−4208.37	+	3057.56i	−0.953863	+	0.693022i	−0.951717	−	0.306976i	$-0.900683\pi$
$269$	−4208.37	+	3057.56i	−0.953863	+	0.693022i	−0.00214547	+	0.999998i	$0.500683\pi$
$270$		0			0
$271$	1664.83	+	5123.81i	0.373177	+	1.14852i	0.944700	+	0.327935i	$0.106353\pi$
$271$	1664.83	+	5123.81i	0.373177	+	1.14852i	−0.571523	+	0.820586i	$0.693647\pi$
$272$		0			0
$273$	−193.674	−	140.712i	−0.0429365	−	0.0311952i
$274$		0			0
$275$	−3785.24	−	2276.00i	−0.830031	−	0.499083i
$276$		0			0
$277$	2523.21	+	1833.22i	0.547310	+	0.397644i	0.826793	−	0.562507i	$-0.190163\pi$
$277$	2523.21	+	1833.22i	0.547310	+	0.397644i	−0.279483	+	0.960151i	$0.590163\pi$
$278$		0			0
$279$	−319.281	−	982.645i	−0.0685120	−	0.210858i
$280$		0			0
$281$	5524.63	−	4013.88i	1.17285	−	0.852127i	0.181505	−	0.983390i	$-0.441903\pi$
$281$	5524.63	−	4013.88i	1.17285	−	0.852127i	0.991348	+	0.131263i	$0.0419031\pi$
$282$		0			0
$283$	−2827.14	+	8701.05i	−0.593838	+	1.82765i	−0.0334114	+	0.999442i	$0.510637\pi$
$283$	−2827.14	+	8701.05i	−0.593838	+	1.82765i	−0.560427	+	0.828204i	$0.689363\pi$
$284$		0			0
$285$	−544.271			−0.113122
$286$		0			0
$287$	1208.84			0.248627
$288$		0			0
$289$	354.420	−	1090.79i	0.0721391	−	0.222021i
$290$		0			0
$291$	1928.49	−	1401.13i	0.388488	−	0.282253i
$292$		0			0
$293$	1000.77	+	3080.04i	0.199541	+	0.614123i	0.999894	+	0.0145935i	$0.00464542\pi$
$293$	1000.77	+	3080.04i	0.199541	+	0.614123i	−0.800353	+	0.599529i	$0.795355\pi$
$294$		0			0
$295$	−271.968	−	197.596i	−0.0536766	−	0.0389983i
$296$		0			0
$297$	384.604	+	906.851i	0.0751413	+	0.177175i
$298$		0			0
$299$	−106.551	−	77.4138i	−0.0206087	−	0.0149731i
$300$		0			0
$301$	1849.90	+	5693.42i	0.354242	+	1.09024i
$302$		0			0
$303$	−1145.46	+	832.222i	−0.217177	+	0.157789i
$304$		0			0
$305$	178.314	−	548.794i	0.0334762	−	0.103029i
$306$		0			0
$307$	−3909.16			−0.726735			−0.363367	−	0.931646i	$-0.618373\pi$
$307$	−3909.16			−0.726735			−0.363367	+	0.931646i	$0.618373\pi$
$308$		0			0
$309$	−5543.71			−1.02062
$310$		0			0
$311$	−2705.87	+	8327.83i	−0.493364	+	1.51842i	0.326128	+	0.945326i	$0.394256\pi$
$311$	−2705.87	+	8327.83i	−0.493364	+	1.51842i	−0.819491	+	0.573091i	$0.805744\pi$
$312$		0			0
$313$	4483.78	−	3257.66i	0.809707	−	0.588286i	−0.104039	−	0.994573i	$-0.533177\pi$
$313$	4483.78	−	3257.66i	0.809707	−	0.588286i	0.913746	+	0.406287i	$0.133177\pi$
$314$		0			0
$315$	−67.6426	−	208.183i	−0.0120991	−	0.0372373i
$316$		0			0
$317$	−6558.45	−	4765.00i	−1.16202	−	0.844255i	−0.171985	−	0.985099i	$-0.555018\pi$
$317$	−6558.45	−	4765.00i	−1.16202	−	0.844255i	−0.990032	+	0.140845i	$0.955018\pi$
$318$		0			0
$319$	2773.81	−	241.810i	0.486844	−	0.0424413i
$320$		0			0
$321$	−2258.11	−	1640.61i	−0.392633	−	0.285265i
$322$		0			0
$323$	−2200.16	−	6771.39i	−0.379010	−	1.16647i
$324$		0			0
$325$	−637.425	+	463.116i	−0.108794	+	0.0790433i
$326$		0			0
$327$	−401.721	+	1236.37i	−0.0679365	+	0.209087i
$328$		0			0
$329$	1310.16			0.219548
$330$		0			0
$331$	2603.54			0.432336			0.216168	−	0.976356i	$-0.430644\pi$
$331$	2603.54			0.432336			0.216168	+	0.976356i	$0.430644\pi$
$332$		0			0
$333$	248.614	−	765.156i	0.0409129	−	0.125917i
$334$		0			0
$335$	172.274	−	125.165i	0.0280966	−	0.0204134i
$336$		0			0
$337$	−238.684	−	734.594i	−0.0385814	−	0.118741i	0.929911	−	0.367785i	$-0.119884\pi$
$337$	−238.684	−	734.594i	−0.0385814	−	0.118741i	−0.968492	+	0.249044i	$0.919884\pi$
$338$		0			0
$339$	−4090.23	−	2971.73i	−0.655312	−	0.476112i
$340$		0			0
$341$	−3161.80	+	2746.79i	−0.502114	+	0.436208i
$342$		0			0
$343$	5313.56	+	3860.53i	0.836458	+	0.607722i
$344$		0			0
$345$	−37.2141	−	114.533i	−0.00580735	−	0.0178732i
$346$		0			0
$347$	3408.56	−	2476.46i	0.527323	−	0.383123i	−0.292032	−	0.956408i	$-0.594332\pi$
$347$	3408.56	−	2476.46i	0.527323	−	0.383123i	0.819355	+	0.573286i	$0.194332\pi$
$348$		0			0
$349$	1483.19	−	4564.79i	0.227488	−	0.700137i	−0.770541	−	0.637390i	$-0.780014\pi$
$349$	1483.19	−	4564.79i	0.227488	−	0.700137i	0.998029	−	0.0627467i	$-0.0199860\pi$
$350$		0			0
$351$	175.718			0.0267211
$352$		0			0
$353$	−448.615			−0.0676412			−0.0338206	−	0.999428i	$-0.510767\pi$
$353$	−448.615			−0.0676412			−0.0338206	+	0.999428i	$0.510767\pi$
$354$		0			0
$355$	446.658	−	1374.67i	0.0667779	−	0.205521i
$356$		0			0
$357$	2316.61	−	1683.11i	0.343440	−	0.249523i
$358$		0			0
$359$	−3435.35	−	10572.9i	−0.505045	−	1.55437i	−0.800695	−	0.599072i	$-0.795536\pi$
$359$	−3435.35	−	10572.9i	−0.505045	−	1.55437i	0.295651	−	0.955296i	$-0.404464\pi$
$360$		0			0
$361$	−1218.54	−	885.320i	−0.177655	−	0.129074i
$362$		0			0
$363$	2775.55	−	2870.60i	0.401319	−	0.415062i
$364$		0			0
$365$	575.589	+	418.190i	0.0825417	+	0.0599700i
$366$		0			0
$367$	3149.15	+	9692.08i	0.447913	+	1.37854i	0.879257	+	0.476348i	$0.158040\pi$
$367$	3149.15	+	9692.08i	0.447913	+	1.37854i	−0.431344	+	0.902188i	$0.641960\pi$
$368$		0			0
$369$	−717.845	+	521.545i	−0.101272	+	0.0735787i
$370$		0			0
$371$	2093.54	−	6443.25i	0.292968	−	0.901663i
$372$		0			0
$373$	11174.0			1.55112			0.775560	−	0.631274i	$-0.217468\pi$
$373$	11174.0			1.55112			0.775560	+	0.631274i	$0.217468\pi$
$374$		0			0
$375$	−1464.29			−0.201642
$376$		0			0
$377$	153.485	−	472.377i	0.0209678	−	0.0645323i
$378$		0			0
$379$	7717.65	−	5607.20i	1.04599	−	0.759954i	0.0745413	−	0.997218i	$-0.476251\pi$
$379$	7717.65	−	5607.20i	1.04599	−	0.759954i	0.971445	+	0.237264i	$0.0762507\pi$
$380$		0			0
$381$	−115.028	−	354.019i	−0.0154673	−	0.0476036i
$382$		0			0
$383$	9441.77	+	6859.85i	1.25967	+	0.915201i	0.998741	−	0.0501584i	$-0.0159726\pi$
$383$	9441.77	+	6859.85i	1.25967	+	0.915201i	0.260925	+	0.965359i	$0.415973\pi$
$384$		0			0
$385$	−669.856	+	581.932i	−0.0886728	+	0.0770338i
$386$		0			0
$387$	−3554.90	−	2582.78i	−0.466939	−	0.339251i
$388$		0			0
$389$	−3268.87	−	10060.6i	−0.426063	−	1.31129i	−0.901973	−	0.431793i	$-0.857881\pi$
$389$	−3268.87	−	10060.6i	−0.426063	−	1.31129i	0.475910	−	0.879494i	$-0.342119\pi$
$390$		0			0
$391$	1274.50	−	925.977i	0.164844	−	0.119766i
$392$		0			0
$393$	130.009	−	400.128i	0.0166873	−	0.0513582i
$394$		0			0
$395$	1014.62			0.129243
$396$		0			0
$397$	−337.577			−0.0426763			−0.0213381	−	0.999772i	$-0.506793\pi$
$397$	−337.577			−0.0426763			−0.0213381	+	0.999772i	$0.506793\pi$
$398$		0			0
$399$	1039.64	−	3199.67i	0.130443	−	0.401464i
$400$		0			0
$401$	−4762.00	+	3459.79i	−0.593024	+	0.430857i	−0.843396	−	0.537292i	$-0.819447\pi$
$401$	−4762.00	+	3459.79i	−0.593024	+	0.430857i	0.250372	+	0.968150i	$0.419447\pi$
$402$		0			0
$403$	230.878	+	710.569i	0.0285381	+	0.0878311i
$404$		0			0
$405$	129.986	+	94.4407i	0.0159483	+	0.0115872i
$406$		0			0
$407$	−3248.98	+	283.233i	−0.395690	+	0.0344947i
$408$		0			0
$409$	−10318.7	−	7496.99i	−1.24750	−	0.906363i	−0.249427	−	0.968394i	$-0.580242\pi$
$409$	−10318.7	−	7496.99i	−1.24750	−	0.906363i	−0.998074	+	0.0620309i	$0.980242\pi$
$410$		0			0
$411$	699.366	+	2152.43i	0.0839347	+	0.258325i
$412$		0			0
$413$	1681.13	−	1221.41i	0.200298	−	0.145525i
$414$		0			0
$415$	390.740	−	1202.57i	0.0462185	−	0.142246i
$416$		0			0
$417$	3566.14			0.418788
$418$		0			0
$419$	4686.15			0.546380			0.273190	−	0.961960i	$-0.411921\pi$
$419$	4686.15			0.546380			0.273190	+	0.961960i	$0.411921\pi$
$420$		0			0
$421$	−479.525	+	1475.83i	−0.0555121	+	0.170849i	−0.974968	−	0.222344i	$-0.928629\pi$
$421$	−479.525	+	1475.83i	−0.0555121	+	0.170849i	0.919456	+	0.393192i	$0.128629\pi$
$422$		0			0
$423$	−778.007	+	565.255i	−0.0894279	+	0.0649732i
$424$		0			0
$425$	−2912.30	−	8963.13i	−0.332393	−	1.02300i
$426$		0			0
$427$	2885.66	+	2096.56i	0.327042	+	0.237610i
$428$		0			0
$429$	−278.114	−	655.760i	−0.0312994	−	0.0738005i
$430$		0			0
$431$	9433.01	+	6853.48i	1.05423	+	0.765941i	0.973012	−	0.230756i	$-0.0741198\pi$
$431$	9433.01	+	6853.48i	1.05423	+	0.765941i	0.0812156	+	0.996697i	$0.474120\pi$
$432$		0			0
$433$	785.662	+	2418.02i	0.0871975	+	0.268366i	0.985142	−	0.171743i	$-0.0549398\pi$
$433$	785.662	+	2418.02i	0.0871975	+	0.268366i	−0.897944	+	0.440109i	$0.854940\pi$
$434$		0			0
$435$	367.422	−	266.948i	0.0404978	−	0.0294234i
$436$		0			0
$437$	571.963	−	1760.32i	0.0626103	−	0.192695i
$438$		0			0
$439$	−5101.99			−0.554681			−0.277340	−	0.960772i	$-0.589453\pi$
$439$	−5101.99			−0.554681			−0.277340	+	0.960772i	$0.589453\pi$
$440$		0			0
$441$	−1733.92			−0.187228
$442$		0			0
$443$	846.872	−	2606.40i	0.0908264	−	0.279535i	−0.895317	−	0.445429i	$-0.853051\pi$
$443$	846.872	−	2606.40i	0.0908264	−	0.279535i	0.986144	+	0.165894i	$0.0530511\pi$
$444$		0			0
$445$	−1333.32	+	968.714i	−0.142035	+	0.103194i
$446$		0			0
$447$	1344.97	+	4139.40i	0.142315	+	0.438002i
$448$		0			0
$449$	−8818.11	−	6406.73i	−0.926843	−	0.673391i	0.0183750	−	0.999831i	$-0.494151\pi$
$449$	−8818.11	−	6406.73i	−0.926843	−	0.673391i	−0.945218	+	0.326440i	$0.894151\pi$
$450$		0			0
$451$	3082.51	+	1853.46i	0.321840	+	0.193517i
$452$		0			0
$453$	−6833.54	−	4964.86i	−0.708758	−	0.514943i
$454$		0			0
$455$	48.9136	+	150.541i	0.00503979	+	0.0155109i
$456$		0			0
$457$	−11106.2	+	8069.11i	−1.13682	+	0.825946i	−0.986673	−	0.162718i	$-0.947974\pi$
$457$	−11106.2	+	8069.11i	−1.13682	+	0.825946i	−0.150144	+	0.988664i	$0.547974\pi$
$458$		0			0
$459$	−649.501	+	1998.96i	−0.0660482	+	0.203275i
$460$		0			0
$461$	3104.40			0.313636			0.156818	−	0.987628i	$-0.449876\pi$
$461$	3104.40			0.313636			0.156818	+	0.987628i	$0.449876\pi$
$462$		0			0
$463$	3771.28			0.378545			0.189272	−	0.981925i	$-0.439387\pi$
$463$	3771.28			0.378545			0.189272	+	0.981925i	$0.439387\pi$
$464$		0			0
$465$	−211.109	+	649.727i	−0.0210537	+	0.0647965i
$466$		0			0
$467$	−9914.73	+	7203.47i	−0.982439	+	0.713784i	−0.958252	−	0.285924i	$-0.907700\pi$
$467$	−9914.73	+	7203.47i	−0.982439	+	0.713784i	−0.0241865	+	0.999707i	$0.507700\pi$
$468$		0			0
$469$	406.753	+	1251.86i	0.0400471	+	0.123252i
$470$		0			0
$471$	5831.52	+	4236.85i	0.570493	+	0.414487i
$472$		0			0
$473$	−4012.24	+	17354.4i	−0.390027	+	1.68701i
$474$		0			0
$475$	−8958.09	−	6508.43i	−0.865316	−	0.628689i
$476$		0			0
$477$	1536.68	+	4729.42i	0.147505	+	0.453973i
$478$		0			0
$479$	843.488	−	612.830i	0.0804592	−	0.0584570i	−0.546828	−	0.837245i	$-0.684165\pi$
$479$	843.488	−	612.830i	0.0804592	−	0.0584570i	0.627288	+	0.778788i	$0.284165\pi$
$480$		0			0
$481$	−179.778	+	553.298i	−0.0170419	+	0.0524496i
$482$		0			0
$483$	744.405			0.0701275
$484$		0			0
$485$	−1576.14			−0.147564
$486$		0			0
$487$	536.464	−	1651.07i	0.0499169	−	0.153628i	−0.922991	−	0.384822i	$-0.874263\pi$
$487$	536.464	−	1651.07i	0.0499169	−	0.153628i	0.972908	+	0.231193i	$0.0742630\pi$
$488$		0			0
$489$	5082.68	−	3692.78i	0.470034	−	0.341500i
$490$		0			0
$491$	3489.83	+	10740.6i	0.320761	+	0.987202i	0.973318	+	0.229462i	$0.0736966\pi$
$491$	3489.83	+	10740.6i	0.320761	+	0.987202i	−0.652556	+	0.757740i	$0.726303\pi$
$492$		0			0
$493$	4806.43	+	3492.07i	0.439089	+	0.319016i
$494$		0			0
$495$	146.709	−	634.570i	0.0133214	−	0.0576198i
$496$		0			0
$497$	7228.28	+	5251.66i	0.652380	+	0.473982i
$498$		0			0
$499$	−4140.83	−	12744.2i	−0.371481	−	1.14330i	−0.945822	−	0.324686i	$-0.894741\pi$
$499$	−4140.83	−	12744.2i	−0.371481	−	1.14330i	0.574341	−	0.818616i	$-0.305259\pi$
$500$		0			0
$501$	−9269.50	+	6734.69i	−0.826608	+	0.600566i
$502$		0			0
$503$	2410.37	−	7418.36i	0.213664	−	0.657591i	−0.785582	−	0.618758i	$-0.787636\pi$
$503$	2410.37	−	7418.36i	0.213664	−	0.657591i	0.999246	−	0.0388326i	$-0.0123639\pi$
$504$		0			0
$505$	936.171			0.0824932
$506$		0			0
$507$	6463.94			0.566220
$508$		0			0
$509$	−6733.56	+	20723.8i	−0.586365	+	1.80465i	0.00735129	+	0.999973i	$0.497660\pi$
$509$	−6733.56	+	20723.8i	−0.586365	+	1.80465i	−0.593717	+	0.804674i	$0.702340\pi$
$510$		0			0
$511$	−3557.93	+	2584.99i	−0.308011	+	0.223783i
$512$		0			0
$513$	763.105	+	2348.60i	0.0656762	+	0.202131i
$514$		0			0
$515$	2965.46	+	2154.54i	0.253736	+	0.184350i
$516$		0			0
$517$	3340.85	+	2008.80i	0.284198	+	0.170883i
$518$		0			0
$519$	−4801.79	−	3488.70i	−0.406118	−	0.295062i
$520$		0			0
$521$	−258.126	−	794.431i	−0.0217058	−	0.0668036i	0.939617	−	0.342228i	$-0.111182\pi$
$521$	−258.126	−	794.431i	−0.0217058	−	0.0668036i	−0.961323	+	0.275425i	$0.911182\pi$
$522$		0			0
$523$	−664.886	+	483.068i	−0.0555898	+	0.0403883i	−0.615233	−	0.788345i	$-0.710938\pi$
$523$	−664.886	+	483.068i	−0.0555898	+	0.0403883i	0.559643	+	0.828734i	$0.310938\pi$
$524$		0			0
$525$	1376.14	−	4235.33i	0.114400	−	0.352086i
$526$		0			0
$527$	−8936.79			−0.738696
$528$		0			0
$529$	−11757.5			−0.966340
$530$		0			0
$531$	−471.335	+	1450.62i	−0.0385201	+	0.118553i
$532$		0			0
$533$	519.087	−	377.138i	0.0421841	−	0.0306486i
$534$		0			0
$535$	570.300	+	1755.20i	0.0460864	+	0.141839i
$536$		0			0
$537$	6427.74	+	4670.03i	0.516532	+	0.375282i
$538$		0			0
$539$	2744.33	+	6470.82i	0.219308	+	0.517102i
$540$		0			0
$541$	−16604.9	−	12064.2i	−1.31960	−	0.958744i	−0.999937	−	0.0112114i	$-0.996431\pi$
$541$	−16604.9	−	12064.2i	−1.31960	−	0.958744i	−0.319660	−	0.947532i	$-0.603569\pi$
$542$		0			0
$543$	3949.74	+	12156.1i	0.312154	+	0.960712i
$544$		0			0
$545$	695.399	−	505.237i	0.0546562	−	0.0397101i
$546$		0			0
$547$	1843.40	−	5673.41i	0.144092	−	0.443469i	−0.852801	−	0.522236i	$-0.825098\pi$
$547$	1843.40	−	5673.41i	0.144092	−	0.443469i	0.996893	+	0.0787666i	$0.0250982\pi$
$548$		0			0
$549$	−2618.12			−0.203532
$550$		0			0
$551$	6980.22			0.539687
$552$		0			0
$553$	−1938.08	+	5964.79i	−0.149033	+	0.458677i
$554$		0			0
$555$	−430.364	+	312.678i	−0.0329152	+	0.0239143i
$556$		0			0
$557$	−451.401	−	1389.27i	−0.0343383	−	0.105683i	0.932418	−	0.361381i	$-0.117695\pi$
$557$	−451.401	−	1389.27i	−0.0343383	−	0.105683i	−0.966757	+	0.255698i	$0.917695\pi$
$558$		0			0
$559$	2570.61	+	1867.66i	0.194499	+	0.141312i
$560$		0			0
$561$	8487.89	−	739.943i	0.638786	−	0.0556870i
$562$		0			0
$563$	20000.9	+	14531.5i	1.49723	+	1.08780i	0.971469	+	0.237167i	$0.0762187\pi$
$563$	20000.9	+	14531.5i	1.49723	+	1.08780i	0.525759	+	0.850633i	$0.323781\pi$
$564$		0			0
$565$	1033.02	+	3179.29i	0.0769191	+	0.236733i
$566$		0			0
$567$	−803.494	+	583.773i	−0.0595125	+	0.0432384i
$568$		0			0
$569$	7905.61	−	24331.0i	0.582461	−	1.79263i	−0.0267756	−	0.999641i	$-0.508524\pi$
$569$	7905.61	−	24331.0i	0.582461	−	1.79263i	0.609236	−	0.792989i	$-0.291476\pi$
$570$		0			0
$571$	−8840.84			−0.647947			−0.323973	−	0.946066i	$-0.605019\pi$
$571$	−8840.84			−0.647947			−0.323973	+	0.946066i	$0.605019\pi$
$572$		0			0
$573$	3955.09			0.288353
$574$		0			0
$575$	757.094	−	2330.10i	0.0549096	−	0.168994i
$576$		0			0
$577$	−14479.3	+	10519.8i	−1.04468	+	0.759003i	−0.971193	−	0.238293i	$-0.923412\pi$
$577$	−14479.3	+	10519.8i	−1.04468	+	0.759003i	−0.0734847	+	0.997296i	$0.523412\pi$
$578$		0			0
$579$	2555.41	+	7864.76i	0.183419	+	0.564505i
$580$		0			0
$581$	6323.36	+	4594.19i	0.451527	+	0.328053i
$582$		0			0
$583$	15217.6	−	13220.1i	1.08104	−	0.939146i
$584$		0			0
$585$	−93.9956	−	68.2918i	−0.00664314	−	0.00482653i
$586$		0			0
$587$	−8445.52	−	25992.6i	−0.593840	−	1.82765i	−0.560419	−	0.828209i	$-0.689360\pi$
$587$	−8445.52	−	25992.6i	−0.593840	−	1.82765i	−0.0334206	−	0.999441i	$-0.510640\pi$
$588$		0			0
$589$	−8494.61	+	6171.70i	−0.594252	+	0.431749i
$590$		0			0
$591$	−1762.89	+	5425.63i	−0.122700	+	0.377632i
$592$		0			0
$593$	−389.353			−0.0269626			−0.0134813	−	0.999909i	$-0.504291\pi$
$593$	−389.353			−0.0269626			−0.0134813	+	0.999909i	$0.504291\pi$
$594$		0			0
$595$	−1893.34			−0.130453
$596$		0			0
$597$	3703.26	−	11397.5i	0.253876	−	0.781351i
$598$		0			0
$599$	−20429.9	+	14843.2i	−1.39356	+	1.01248i	−0.398096	+	0.917344i	$0.630329\pi$
$599$	−20429.9	+	14843.2i	−1.39356	+	1.01248i	−0.995464	+	0.0951368i	$0.969671\pi$
$600$		0			0
$601$	−2181.63	−	6714.37i	−0.148071	−	0.455715i	0.849322	−	0.527875i	$-0.177011\pi$
$601$	−2181.63	−	6714.37i	−0.148071	−	0.455715i	−0.997393	+	0.0721596i	$0.977011\pi$
$602$		0			0
$603$	−781.642	−	567.896i	−0.0527876	−	0.0383524i
$604$		0			0
$605$	−2600.35	+	456.850i	−0.174743	+	0.0307002i
$606$		0			0
$607$	−12283.3	−	8924.34i	−0.821357	−	0.596751i	0.0957435	−	0.995406i	$-0.469477\pi$
$607$	−12283.3	−	8924.34i	−0.821357	−	0.596751i	−0.917101	+	0.398655i	$0.869477\pi$
$608$		0			0
$609$	867.511	+	2669.92i	0.0577230	+	0.177653i
$610$		0			0
$611$	562.591	−	408.746i	0.0372504	−	0.0270640i
$612$		0			0
$613$	4796.66	−	14762.6i	0.316044	−	0.972685i	−0.659278	−	0.751899i	$-0.729138\pi$
$613$	4796.66	−	14762.6i	0.316044	−	0.972685i	0.975322	−	0.220785i	$-0.0708620\pi$
$614$		0			0
$615$	586.688			0.0384676
$616$		0			0
$617$	27430.4			1.78980			0.894899	−	0.446269i	$-0.147248\pi$
$617$	27430.4			1.78980			0.894899	+	0.446269i	$0.147248\pi$
$618$		0			0
$619$	6668.83	−	20524.5i	0.433025	−	1.33272i	−0.462071	−	0.886843i	$-0.652894\pi$
$619$	6668.83	−	20524.5i	0.433025	−	1.33272i	0.895097	−	0.445872i	$-0.147106\pi$
$620$		0			0
$621$	−442.048	+	321.167i	−0.0285648	+	0.0207536i
$622$		0			0
$623$	−3148.07	−	9688.75i	−0.202447	−	0.623068i
$624$		0			0
$625$	−11459.7	−	8325.96i	−0.733421	−	0.532862i
$626$		0			0
$627$	7556.93	−	6565.02i	0.481331	−	0.418153i
$628$		0			0
$629$	−5629.80	−	4090.29i	−0.356875	−	0.259285i
$630$		0			0
$631$	−2320.52	−	7141.83i	−0.146400	−	0.450573i	0.850788	−	0.525509i	$-0.176125\pi$
$631$	−2320.52	−	7141.83i	−0.146400	−	0.450573i	−0.997188	+	0.0749353i	$0.976125\pi$
$632$		0			0
$633$	1252.39	−	909.916i	0.0786384	−	0.0571341i
$634$		0			0
$635$	−76.0566	+	234.078i	−0.00475310	+	0.0146285i
$636$		0			0
$637$	1253.83			0.0779883
$638$		0			0
$639$	−6558.13			−0.406003
$640$		0			0
$641$	−2424.82	+	7462.83i	−0.149414	+	0.459850i	−0.997552	−	0.0699253i	$-0.977724\pi$
$641$	−2424.82	+	7462.83i	−0.149414	+	0.459850i	0.848138	+	0.529776i	$0.177724\pi$
$642$		0			0
$643$	706.659	−	513.418i	0.0433404	−	0.0314887i	−0.565904	−	0.824471i	$-0.691473\pi$
$643$	706.659	−	513.418i	0.0433404	−	0.0314887i	0.609245	+	0.792982i	$0.291473\pi$
$644$		0			0
$645$	897.813	+	2763.18i	0.0548083	+	0.168683i
$646$		0			0
$647$	20663.0	+	15012.6i	1.25556	+	0.912217i	0.998531	−	0.0541866i	$-0.0172566\pi$
$647$	20663.0	+	15012.6i	1.25556	+	0.912217i	0.257028	+	0.966404i	$0.417257\pi$
$648$		0			0
$649$	6159.56	−	536.967i	0.372548	−	0.0324774i
$650$		0			0
$651$	−3416.39	−	2482.15i	−0.205682	−	0.149436i
$652$		0			0
$653$	−3190.62	−	9819.73i	−0.191208	−	0.588477i	−1.00000		0.000382475i	$-0.999878\pi$
$653$	−3190.62	−	9819.73i	−0.191208	−	0.588477i	0.808792	−	0.588095i	$-0.200122\pi$
$654$		0			0
$655$	−225.053	+	163.510i	−0.0134252	+	0.00975401i
$656$		0			0
$657$	997.526	−	3070.07i	0.0592347	−	0.182306i
$658$		0			0
$659$	−28905.7			−1.70866			−0.854329	−	0.519733i	$-0.826031\pi$
$659$	−28905.7			−1.70866			−0.854329	+	0.519733i	$0.826031\pi$
$660$		0			0
$661$	28041.5			1.65006			0.825028	−	0.565092i	$-0.191159\pi$
$661$	28041.5			1.65006			0.825028	+	0.565092i	$0.191159\pi$
$662$		0			0
$663$	469.666	−	1445.48i	0.0275118	−	0.0846726i
$664$		0			0
$665$	−1799.66	+	1307.53i	−0.104944	+	0.0762465i
$666$		0			0
$667$	477.267	+	1468.88i	0.0277059	+	0.0852701i
$668$		0			0
$669$	−2129.49	−	1547.16i	−0.123065	−	0.0894123i
$670$		0			0
$671$	4143.79	+	9770.57i	0.238404	+	0.562129i
$672$		0			0
$673$	−7569.87	−	5499.83i	−0.433576	−	0.315012i	0.349501	−	0.936936i	$-0.386351\pi$
$673$	−7569.87	−	5499.83i	−0.433576	−	0.315012i	−0.783077	+	0.621924i	$0.786351\pi$
$674$		0			0
$675$	1010.10	+	3108.78i	0.0575984	+	0.177270i
$676$		0			0
$677$	18651.9	−	13551.4i	1.05886	−	0.769309i	0.0849856	−	0.996382i	$-0.472916\pi$
$677$	18651.9	−	13551.4i	1.05886	−	0.769309i	0.973878	+	0.227073i	$0.0729156\pi$
$678$		0			0
$679$	3010.66	−	9265.84i	0.170160	−	0.523697i
$680$		0			0
$681$	12025.8			0.676693
$682$		0			0
$683$	18443.9			1.03329			0.516645	−	0.856200i	$-0.327181\pi$
$683$	18443.9			1.03329			0.516645	+	0.856200i	$0.327181\pi$
$684$		0			0
$685$	462.422	−	1423.19i	0.0257931	−	0.0793829i
$686$		0			0
$687$	4160.79	−	3022.99i	0.231068	−	0.167881i
$688$		0			0
$689$	−1111.20	−	3419.93i	−0.0614418	−	0.189098i
$690$		0			0
$691$	20208.4	+	14682.3i	1.11254	+	0.808306i	0.983061	−	0.183276i	$-0.0586703\pi$
$691$	20208.4	+	14682.3i	1.11254	+	0.808306i	0.129476	+	0.991582i	$0.458670\pi$
$692$		0			0
$693$	3450.30	+	2074.60i	0.189128	+	0.113720i
$694$		0			0
$695$	−1907.61	−	1385.96i	−0.104115	−	0.0756440i
$696$		0			0
$697$	2371.63	+	7299.12i	0.128884	+	0.396663i
$698$		0			0
$699$	−15365.5	+	11163.7i	−0.831437	+	0.604075i
$700$		0			0
$701$	7753.13	−	23861.7i	0.417734	−	1.28565i	−0.492048	−	0.870568i	$-0.663751\pi$
$701$	7753.13	−	23861.7i	0.417734	−	1.28565i	0.909782	−	0.415086i	$-0.136249\pi$
$702$		0			0
$703$	−8175.97			−0.438638
$704$		0			0
$705$	635.858			0.0339685
$706$		0			0
$707$	−1788.22	+	5503.59i	−0.0951246	+	0.292763i
$708$		0			0
$709$	12414.6	−	9019.76i	0.657604	−	0.477777i	−0.208249	−	0.978076i	$-0.566776\pi$
$709$	12414.6	−	9019.76i	0.657604	−	0.477777i	0.865853	+	0.500298i	$0.166776\pi$
$710$		0			0
$711$	−1422.57	−	4378.22i	−0.0750359	−	0.230937i
$712$		0			0
$713$	−1879.55	−	1365.57i	−0.0987232	−	0.0717266i
$714$		0			0
$715$	−106.088	+	458.869i	−0.00554891	+	0.0240010i
$716$		0			0
$717$	−14632.6	−	10631.2i	−0.762152	−	0.553736i
$718$		0			0
$719$	−9216.75	−	28366.3i	−0.478063	−	1.47133i	−0.841783	−	0.539817i	$-0.818494\pi$
$719$	−9216.75	−	28366.3i	−0.478063	−	1.47133i	0.363720	−	0.931508i	$-0.381506\pi$
$720$		0			0
$721$	−18330.6	+	13318.0i	−0.946835	+	0.687916i
$722$		0			0
$723$	−2344.13	+	7214.48i	−0.120580	+	0.371106i
$724$		0			0
$725$	9239.55			0.473308
$726$		0			0
$727$	−19398.7			−0.989626			−0.494813	−	0.869000i	$-0.664763\pi$
$727$	−19398.7			−0.989626			−0.494813	+	0.869000i	$0.664763\pi$
$728$		0			0
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−30748.1	+	22339.8i	−1.55576	+	1.13032i
$732$		0			0
$733$	10180.5	+	31332.4i	0.512996	+	1.57884i	0.786900	+	0.617081i	$0.211685\pi$
$733$	10180.5	+	31332.4i	0.512996	+	1.57884i	−0.273904	+	0.961757i	$0.588315\pi$
$734$		0			0
$735$	927.516	+	673.880i	0.0465469	+	0.0338183i
$736$		0			0
$737$	−882.201	+	3815.84i	−0.0440927	+	0.190717i
$738$		0			0
$739$	5707.17	+	4146.50i	0.284089	+	0.206403i	0.720699	−	0.693248i	$-0.243821\pi$
$739$	5707.17	+	4146.50i	0.284089	+	0.206403i	−0.436610	+	0.899651i	$0.643821\pi$
$740$		0			0
$741$	−551.815	−	1698.31i	−0.0273568	−	0.0841957i
$742$		0			0
$743$	−4025.05	+	2924.37i	−0.198741	+	0.144394i	−0.682705	−	0.730694i	$-0.739197\pi$
$743$	−4025.05	+	2924.37i	−0.198741	+	0.144394i	0.483964	+	0.875088i	$0.339197\pi$
$744$		0			0
$745$	889.298	−	2736.98i	0.0437334	−	0.134598i
$746$		0			0
$747$	−5737.10			−0.281003
$748$		0			0
$749$	−11407.9			−0.556523
$750$		0			0
$751$	10127.4	−	31168.8i	0.492081	−	1.51447i	−0.329376	−	0.944199i	$-0.606838\pi$
$751$	10127.4	−	31168.8i	0.492081	−	1.51447i	0.821457	−	0.570270i	$-0.193162\pi$
$752$		0			0
$753$	6941.54	−	5043.32i	0.335941	−	0.244076i
$754$		0			0
$755$	1725.86	+	5311.64i	0.0831925	+	0.256040i
$756$		0			0
$757$	25632.9	+	18623.4i	1.23070	+	0.894158i	0.996943	−	0.0781357i	$-0.0248968\pi$
$757$	25632.9	+	18623.4i	1.23070	+	0.894158i	0.233761	+	0.972294i	$0.424897\pi$
$758$		0			0
$759$	1898.20	+	1141.36i	0.0907779	+	0.0545832i
$760$		0			0
$761$	16845.6	+	12239.0i	0.802432	+	0.583001i	0.911627	−	0.411019i	$-0.134827\pi$
$761$	16845.6	+	12239.0i	0.802432	+	0.583001i	−0.109195	+	0.994020i	$0.534827\pi$
$762$		0			0
$763$	1641.89	+	5053.21i	0.0779035	+	0.239762i
$764$		0			0
$765$	1124.32	−	816.865i	0.0531370	−	0.0386063i
$766$		0			0
$767$	340.831	−	1048.97i	0.0160452	−	0.0493821i
$768$		0			0
$769$	−15356.6			−0.720123			−0.360062	−	0.932929i	$-0.617244\pi$
$769$	−15356.6			−0.720123			−0.360062	+	0.932929i	$0.617244\pi$
$770$		0			0
$771$	−14124.4			−0.659762
$772$		0			0
$773$	−7407.09	+	22796.7i	−0.344650	+	1.06072i	0.617121	+	0.786868i	$0.288299\pi$
$773$	−7407.09	+	22796.7i	−0.344650	+	1.06072i	−0.961771	+	0.273855i	$0.911701\pi$
$774$		0			0
$775$	−11244.1	+	8169.33i	−0.521162	+	0.378646i
$776$		0			0
$777$	−1016.12	−	3127.30i	−0.0469152	−	0.144390i
$778$		0			0
$779$	7295.01	+	5300.14i	0.335521	+	0.243770i
$780$		0			0
$781$	10379.8	+	24474.3i	0.475566	+	1.12133i
$782$		0			0
$783$	−1667.07	−	1211.19i	−0.0760869	−	0.0552804i
$784$		0			0
$785$	−1472.79	−	4532.78i	−0.0669632	−	0.206092i
$786$		0			0
$787$	−20832.6	+	15135.7i	−0.943584	+	0.685554i	−0.949281	−	0.314430i	$-0.898187\pi$
$787$	−20832.6	+	15135.7i	−0.943584	+	0.685554i	0.00569705	+	0.999984i	$0.498187\pi$
$788$		0			0
$789$	1225.81	−	3772.67i	0.0553107	−	0.170229i
$790$		0			0
$791$	−20663.7			−0.928847
$792$		0			0
$793$	1893.21			0.0847793
$794$		0			0
$795$	1016.06	−	3127.10i	0.0453281	−	0.139505i
$796$		0			0
$797$	−18104.8	+	13153.9i	−0.804651	+	0.584613i	−0.912275	−	0.409579i	$-0.865676\pi$
$797$	−18104.8	+	13153.9i	−0.804651	+	0.584613i	0.107624	+	0.994192i	$0.465676\pi$
$798$		0			0
$799$	2570.39	+	7910.86i	0.113810	+	0.350270i
$800$		0			0
$801$	6049.53	+	4395.24i	0.266853	+	0.193880i
$802$		0			0
$803$	−13036.0	+	1136.43i	−0.572890	+	0.0499424i
$804$		0			0
$805$	−398.200	−	289.309i	−0.0174344	−	0.0126668i
$806$		0			0
$807$	−4822.37	−	14841.7i	−0.210354	−	0.647402i
$808$		0			0
$809$	327.625	−	238.034i	0.0142382	−	0.0103446i	−0.580643	−	0.814158i	$-0.697199\pi$
$809$	327.625	−	238.034i	0.0142382	−	0.0103446i	0.594882	+	0.803813i	$0.297199\pi$
$810$		0			0
$811$	−1964.56	+	6046.29i	−0.0850616	+	0.261793i	−0.984536	−	0.175180i	$-0.943949\pi$
$811$	−1964.56	+	6046.29i	−0.0850616	+	0.261793i	0.899475	+	0.436973i	$0.143949\pi$
$812$		0			0
$813$	−16162.5			−0.697224
$814$		0			0
$815$	−4154.03			−0.178539
$816$		0			0
$817$	−13799.0	+	42468.9i	−0.590900	+	1.81860i
$818$		0			0
$819$	581.021	−	422.137i	0.0247894	−	0.0180106i
$820$		0			0
$821$	−13029.9	−	40102.0i	−0.553895	−	1.70471i	−0.698844	−	0.715274i	$-0.746302\pi$
$821$	−13029.9	−	40102.0i	−0.553895	−	1.70471i	0.144949	−	0.989439i	$-0.453698\pi$
$822$		0			0
$823$	12019.8	+	8732.87i	0.509092	+	0.369877i	0.812479	−	0.582991i	$-0.198118\pi$
$823$	12019.8	+	8732.87i	0.509092	+	0.369877i	−0.303387	+	0.952867i	$0.598118\pi$
$824$		0			0
$825$	10002.9	−	8689.96i	0.422130	−	0.366722i
$826$		0			0
$827$	296.623	+	215.509i	0.0124723	+	0.00906167i	0.594004	−	0.804462i	$-0.297546\pi$
$827$	296.623	+	215.509i	0.0124723	+	0.00906167i	−0.581532	+	0.813524i	$0.697546\pi$
$828$		0			0
$829$	9464.11	+	29127.5i	0.396504	+	1.22032i	0.927784	+	0.373118i	$0.121711\pi$
$829$	9464.11	+	29127.5i	0.396504	+	1.22032i	−0.531279	+	0.847197i	$0.678289\pi$
$830$		0			0
$831$	−7569.62	+	5499.65i	−0.315989	+	0.229580i
$832$		0			0
$833$	−4634.50	+	14263.5i	−0.192768	+	0.593280i
$834$		0			0
$835$	7575.88			0.313981
$836$		0			0
$837$	3099.64			0.128004
$838$		0			0
$839$	6047.10	−	18611.1i	0.248831	−	0.765822i	−0.746152	−	0.665776i	$-0.768101\pi$
$839$	6047.10	−	18611.1i	0.248831	−	0.765822i	0.994983	−	0.100047i	$-0.0318992\pi$
$840$		0			0
$841$	15019.0	−	10911.9i	0.615809	−	0.447411i
$842$		0			0
$843$	6330.66	+	19483.8i	0.258647	+	0.796034i
$844$		0			0
$845$	−3457.71	−	2512.18i	−0.140768	−	0.102274i
$846$		0			0
$847$	2281.32	−	16159.7i	0.0925466	−	0.655553i
$848$		0			0
$849$	−22204.7	−	16132.6i	−0.897600	−	0.652144i
$850$		0			0
$851$	−559.025	−	1720.50i	−0.0225184	−	0.0693045i
$852$		0			0
$853$	6707.36	−	4873.18i	0.269233	−	0.195609i	−0.444975	−	0.895543i	$-0.646787\pi$
$853$	6707.36	−	4873.18i	0.269233	−	0.195609i	0.714207	+	0.699934i	$0.246787\pi$
$854$		0			0
$855$	504.567	−	1552.90i	0.0201822	−	0.0621145i
$856$		0			0
$857$	36841.7			1.46848			0.734240	−	0.678890i	$-0.237539\pi$
$857$	36841.7			1.46848			0.734240	+	0.678890i	$0.237539\pi$
$858$		0			0
$859$	24003.0			0.953400			0.476700	−	0.879066i	$-0.341833\pi$
$859$	24003.0			0.953400			0.476700	+	0.879066i	$0.341833\pi$
$860$		0			0
$861$	−1120.66	+	3449.04i	−0.0443577	+	0.136519i
$862$		0			0
$863$	−15761.4	+	11451.3i	−0.621697	+	0.451689i	−0.853514	−	0.521070i	$-0.825533\pi$
$863$	−15761.4	+	11451.3i	−0.621697	+	0.451689i	0.231817	+	0.972759i	$0.425533\pi$
$864$		0			0
$865$	1212.72	+	3732.38i	0.0476692	+	0.146711i
$866$		0			0
$867$	2783.65	+	2022.44i	0.109040	+	0.0792222i
$868$		0			0
$869$	−14087.5	+	12238.4i	−0.549927	+	0.477745i
$870$		0			0
$871$	565.220	+	410.656i	0.0219882	+	0.0159754i
$872$		0			0
$873$	2209.85	+	6801.23i	0.0856726	+	0.263673i
$874$		0			0
$875$	−4841.76	+	3517.75i	−0.187065	+	0.135910i
$876$		0			0
$877$	761.474	−	2343.58i	0.0293194	−	0.0902360i	−0.935326	−	0.353787i	$-0.884894\pi$
$877$	761.474	−	2343.58i	0.0293194	−	0.0902360i	0.964645	+	0.263551i	$0.0848938\pi$
$878$		0			0
$879$	−9715.64			−0.372810
$880$		0			0
$881$	12953.1			0.495349			0.247675	−	0.968843i	$-0.420334\pi$
$881$	12953.1			0.495349			0.247675	+	0.968843i	$0.420334\pi$
$882$		0			0
$883$	3138.31	−	9658.74i	0.119607	−	0.368111i	−0.873273	−	0.487231i	$-0.838007\pi$
$883$	3138.31	−	9658.74i	0.119607	−	0.368111i	0.992880	+	0.119119i	$0.0380071\pi$
$884$		0			0
$885$	815.904	−	592.789i	0.0309902	−	0.0225157i
$886$		0			0
$887$	−3710.82	−	11420.7i	−0.140470	−	0.432323i	0.855930	−	0.517091i	$-0.172985\pi$
$887$	−3710.82	−	11420.7i	−0.140470	−	0.432323i	−0.996401	+	0.0847679i	$0.972985\pi$
$888$		0			0
$889$	−1230.83	−	894.248i	−0.0464349	−	0.0337369i
$890$		0			0
$891$	−2943.95	+	256.642i	−0.110691	+	0.00964965i
$892$		0			0
$893$	7906.41	+	5744.34i	0.296280	+	0.215260i
$894$		0			0
$895$	−1623.37	−	4996.22i	−0.0606294	−	0.186598i
$896$		0			0
$897$	319.653	−	232.241i	0.0118984	−	0.00864472i
$898$		0			0
$899$	2707.46	−	8332.69i	0.100444	−	0.309133i
$900$		0			0
$901$	43012.3			1.59040
$902$		0			0
$903$	−17959.2			−0.661845
$904$		0			0
$905$	2611.58	−	8037.61i	0.0959247	−	0.295226i
$906$		0			0
$907$	−5268.47	+	3827.77i	−0.192874	+	0.140131i	−0.680031	−	0.733183i	$-0.738034\pi$
$907$	−5268.47	+	3827.77i	−0.192874	+	0.140131i	0.487157	+	0.873314i	$0.338034\pi$
$908$		0			0
$909$	−1312.58	−	4039.69i	−0.0478937	−	0.147402i
$910$		0			0
$911$	−13675.2	−	9935.64i	−0.497345	−	0.361342i	0.310657	−	0.950522i	$-0.399451\pi$
$911$	−13675.2	−	9935.64i	−0.497345	−	0.361342i	−0.808002	+	0.589180i	$0.799451\pi$
$912$		0			0
$913$	9080.29	+	21410.3i	0.329150	+	0.776097i
$914$		0			0
$915$	1400.50	+	1017.52i	0.0506000	+	0.0367631i
$916$		0			0
$917$	−531.366	−	1635.38i	−0.0191355	−	0.0588930i
$918$		0			0
$919$	27195.5	−	19758.7i	0.976166	−	0.709226i	0.0193174	−	0.999813i	$-0.493851\pi$
$919$	27195.5	−	19758.7i	0.976166	−	0.709226i	0.956848	+	0.290587i	$0.0938507\pi$
$920$		0			0
$921$	3623.99	−	11153.5i	0.129658	−	0.399045i
$922$		0			0
$923$	4742.30			0.169117
$924$		0			0
$925$	−10822.3			−0.384688
$926$		0			0
$927$	5139.31	−	15817.2i	0.182089	−	0.560414i
$928$		0			0
$929$	14105.6	−	10248.3i	0.498160	−	0.361934i	−0.310154	−	0.950686i	$-0.600381\pi$
$929$	14105.6	−	10248.3i	0.498160	−	0.361934i	0.808314	+	0.588752i	$0.200381\pi$
$930$		0			0
$931$	5445.12	+	16758.4i	0.191683	+	0.589939i
$932$		0			0
$933$	−21252.2	−	15440.6i	−0.745730	−	0.541805i
$934$		0			0
$935$	−4827.95	−	2902.96i	−0.168867	−	0.101537i
$936$		0			0
$937$	−32056.6	−	23290.5i	−1.11766	−	0.812024i	−0.133804	−	0.991008i	$-0.542719\pi$
$937$	−32056.6	−	23290.5i	−1.11766	−	0.812024i	−0.983852	+	0.178983i	$0.942719\pi$
$938$		0			0
$939$	5137.95	+	15813.0i	0.178563	+	0.549561i
$940$		0			0
$941$	1854.88	−	1347.65i	0.0642586	−	0.0466866i	−0.555192	−	0.831722i	$-0.687355\pi$
$941$	1854.88	−	1347.65i	0.0642586	−	0.0466866i	0.619451	+	0.785035i	$0.287355\pi$
$942$		0			0
$943$	−616.539	+	1897.51i	−0.0212909	+	0.0655265i
$944$		0			0
$945$	656.688			0.0226054
$946$		0			0
$947$	22750.9			0.780680			0.390340	−	0.920671i	$-0.372357\pi$
$947$	22750.9			0.780680			0.390340	+	0.920671i	$0.372357\pi$
$948$		0			0
$949$	−721.329	+	2220.02i	−0.0246737	+	0.0759378i
$950$		0			0
$951$	19675.4	−	14295.0i	0.670891	−	0.487431i
$952$		0			0
$953$	−12914.9	−	39747.8i	−0.438985	−	1.35106i	−0.888947	−	0.458010i	$-0.848562\pi$
$953$	−12914.9	−	39747.8i	−0.438985	−	1.35106i	0.449961	−	0.893048i	$-0.351438\pi$
$954$		0			0
$955$	−2115.67	−	1537.13i	−0.0716875	−	0.0520840i
$956$		0			0
$957$	−1881.54	+	8138.31i	−0.0635542	+	0.274895i
$958$		0			0
$959$	7483.39	+	5437.00i	0.251983	+	0.183076i
$960$		0			0
$961$	−5133.26	−	15798.6i	−0.172309	−	0.530313i
$962$		0			0
$963$	6774.32	−	4921.84i	0.226687	−	0.164698i
$964$		0			0
$965$	1689.65	−	5200.19i	0.0563644	−	0.173472i
$966$		0			0
$967$	−17075.1			−0.567836			−0.283918	−	0.958849i	$-0.591634\pi$
$967$	−17075.1			−0.567836			−0.283918	+	0.958849i	$0.591634\pi$
$968$		0			0
$969$	21359.6			0.708121
$970$		0			0
$971$	−5934.01	+	18263.0i	−0.196119	+	0.603592i	0.803843	+	0.594842i	$0.202785\pi$
$971$	−5934.01	+	18263.0i	−0.196119	+	0.603592i	−0.999962	+	0.00875008i	$0.997215\pi$
$972$		0			0
$973$	11791.7	−	8567.15i	0.388513	−	0.282271i
$974$		0			0
$975$	−730.424	−	2248.01i	−0.0239921	−	0.0738401i
$976$		0			0
$977$	−27764.0	−	20171.8i	−0.909161	−	0.660544i	0.0316416	−	0.999499i	$-0.489926\pi$
$977$	−27764.0	−	20171.8i	−0.909161	−	0.660544i	−0.940803	+	0.338955i	$0.889926\pi$
$978$		0			0
$979$	6827.81	−	29532.7i	0.222899	−	0.964116i
$980$		0			0
$981$	−3155.16	−	2292.36i	−0.102688	−	0.0746069i
$982$		0			0
$983$	1435.17	+	4416.99i	0.0465664	+	0.143317i	0.971636	−	0.236480i	$-0.0759939\pi$
$983$	1435.17	+	4416.99i	0.0465664	+	0.143317i	−0.925070	+	0.379797i	$0.875994\pi$
$984$		0			0
$985$	3051.66	−	2217.16i	0.0987146	−	0.0717203i
$986$		0			0
$987$	−1214.58	+	3738.10i	−0.0391698	+	0.120552i
$988$		0			0
$989$	−9880.40			−0.317673
$990$		0			0
$991$	−14255.1			−0.456941			−0.228471	−	0.973551i	$-0.573372\pi$
$991$	−14255.1			−0.456941			−0.228471	+	0.973551i	$0.573372\pi$
$992$		0			0
$993$	−2413.61	+	7428.33i	−0.0771335	+	0.237393i
$994$		0			0
$995$	−6410.52	+	4657.52i	−0.204248	+	0.148395i
$996$		0			0
$997$	−4467.91	−	13750.8i	−0.141926	−	0.436803i	0.854677	−	0.519160i	$-0.173755\pi$
$997$	−4467.91	−	13750.8i	−0.141926	−	0.436803i	−0.996603	+	0.0823571i	$0.973755\pi$
$998$		0			0
$999$	1952.64	+	1418.68i	0.0618407	+	0.0449299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.4.i.b.37.2	yes	8
3.2	odd	2		396.4.j.b.37.1		8
11.3	even	5	inner	132.4.i.b.25.2	✓	8
11.5	even	5		1452.4.a.o.1.2		4
11.6	odd	10		1452.4.a.p.1.2		4
33.14	odd	10		396.4.j.b.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.4.i.b.25.2	✓	8	11.3	even	5	inner
132.4.i.b.37.2	yes	8	1.1	even	1	trivial
396.4.j.b.37.1		8	3.2	odd	2
396.4.j.b.289.1		8	33.14	odd	10
1452.4.a.o.1.2		4	11.5	even	5
1452.4.a.p.1.2		4	11.6	odd	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	132.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927051 + 2.85317i) q^{3} +(1.60477 - 1.16593i) q^{5} +(3.78898 + 11.6613i) q^{7} +(-7.28115 - 5.29007i) q^{9} +(-8.21788 + 35.5453i) q^{11} +(5.26513 + 3.82534i) q^{13} +(1.83890 + 5.65957i) q^{15} +(-62.9784 + 45.7565i) q^{17} +(-28.2631 + 86.9850i) q^{19} -36.7842 q^{21} -20.2371 q^{23} +(-37.4112 + 115.140i) q^{25} +(21.8435 - 15.8702i) q^{27} +(-23.5838 - 72.5834i) q^{29} +(92.8764 + 67.4787i) q^{31} +(-93.7983 - 56.3993i) q^{33} +(19.6767 + 14.2960i) q^{35} +(27.6238 + 85.0174i) q^{37} +(-15.7954 + 11.4760i) q^{39} +(30.4658 - 93.7641i) q^{41} +488.233 q^{43} -17.8525 q^{45} +(33.0191 - 101.622i) q^{47} +(155.864 - 113.242i) q^{49} +(-72.1668 - 222.106i) q^{51} +(-447.009 - 324.771i) q^{53} +(28.2556 + 66.6235i) q^{55} +(-221.982 - 161.279i) q^{57} +(-52.3705 - 161.180i) q^{59} +(235.345 - 170.988i) q^{61} +(34.1008 - 104.952i) q^{63} +12.9094 q^{65} +107.351 q^{67} +(18.7608 - 57.7398i) q^{69} +(589.515 - 428.308i) q^{71} +(110.836 + 341.119i) q^{73} +(-293.832 - 213.481i) q^{75} +(-445.641 + 38.8493i) q^{77} +(413.815 + 300.654i) q^{79} +(25.0304 + 77.0356i) q^{81} +(515.712 - 374.687i) q^{83} +(-47.7168 + 146.857i) q^{85} +228.956 q^{87} -830.847 q^{89} +(-24.6589 + 75.8924i) q^{91} +(-278.629 + 202.436i) q^{93} +(56.0629 + 172.544i) q^{95} +(-642.830 - 467.043i) q^{97} +(247.873 - 215.337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 27 q^{5} + 13 q^{7} - 18 q^{9} - 45 q^{11} - 89 q^{13} - 99 q^{15} - 24 q^{17} - 28 q^{19} + 66 q^{21} - 348 q^{23} - 9 q^{25} + 54 q^{27} - 249 q^{29} - 217 q^{31} - 540 q^{33} + 630 q^{35}+ \cdots - 1215 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - 27 * q^5 + 13 * q^7 - 18 * q^9 - 45 * q^11 - 89 * q^13 - 99 * q^15 - 24 * q^17 - 28 * q^19 + 66 * q^21 - 348 * q^23 - 9 * q^25 + 54 * q^27 - 249 * q^29 - 217 * q^31 - 540 * q^33 + 630 * q^35 + 585 * q^37 + 267 * q^39 - 177 * q^41 + 684 * q^43 - 108 * q^45 - 93 * q^47 + 1377 * q^49 - 423 * q^51 - 693 * q^53 - 472 * q^55 - 501 * q^57 + 1086 * q^59 + 1069 * q^61 + 117 * q^63 - 114 * q^65 + 470 * q^67 + 369 * q^69 + 1479 * q^71 + 947 * q^73 - 393 * q^75 - 3693 * q^77 + 1251 * q^79 - 162 * q^81 + 1185 * q^83 - 2585 * q^85 + 1062 * q^87 - 1716 * q^89 + 4191 * q^91 + 651 * q^93 - 141 * q^95 - 3783 * q^97 - 1215 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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