LMFDB - Embedded newform 1000.2.d.c.501.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (of order $2$, degree $1$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.29
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.800179 - 1.16607i) q^{2} +2.62662i q^{3} +(-0.719426 - 1.86613i) q^{4} +(3.06282 + 2.10177i) q^{6} +0.269237 q^{7} +(-2.75170 - 0.654336i) q^{8} -3.89913 q^{9} +O(q^{10})$	\(q+(0.800179 - 1.16607i) q^{2} +2.62662i q^{3} +(-0.719426 - 1.86613i) q^{4} +(3.06282 + 2.10177i) q^{6} +0.269237 q^{7} +(-2.75170 - 0.654336i) q^{8} -3.89913 q^{9} +4.58163i q^{11} +(4.90160 - 1.88966i) q^{12} -1.55366i q^{13} +(0.215438 - 0.313948i) q^{14} +(-2.96485 + 2.68508i) q^{16} +0.609109 q^{17} +(-3.12001 + 4.54665i) q^{18} +6.69309i q^{19} +0.707183i q^{21} +(5.34249 + 3.66612i) q^{22} +3.52675 q^{23} +(1.71869 - 7.22767i) q^{24} +(-1.81167 - 1.24321i) q^{26} -2.36168i q^{27} +(-0.193696 - 0.502430i) q^{28} +7.73304i q^{29} -3.34096 q^{31} +(0.758569 + 5.60576i) q^{32} -12.0342 q^{33} +(0.487396 - 0.710262i) q^{34} +(2.80514 + 7.27627i) q^{36} -5.32768i q^{37} +(7.80459 + 5.35567i) q^{38} +4.08087 q^{39} +4.38291 q^{41} +(0.824623 + 0.565873i) q^{42} +12.2644i q^{43} +(8.54989 - 3.29614i) q^{44} +(2.82203 - 4.11243i) q^{46} -9.54651 q^{47} +(-7.05268 - 7.78754i) q^{48} -6.92751 q^{49} +1.59990i q^{51} +(-2.89932 + 1.11774i) q^{52} -10.6574i q^{53} +(-2.75388 - 1.88977i) q^{54} +(-0.740859 - 0.176171i) q^{56} -17.5802 q^{57} +(9.01725 + 6.18782i) q^{58} -10.2256i q^{59} +13.2628i q^{61} +(-2.67337 + 3.89579i) q^{62} -1.04979 q^{63} +(7.14369 + 3.60107i) q^{64} +(-9.62951 + 14.0327i) q^{66} -3.93398i q^{67} +(-0.438209 - 1.13667i) q^{68} +9.26343i q^{69} +6.95638 q^{71} +(10.7292 + 2.55134i) q^{72} +5.93156 q^{73} +(-6.21243 - 4.26310i) q^{74} +(12.4901 - 4.81518i) q^{76} +1.23354i q^{77} +(3.26543 - 4.75857i) q^{78} +10.1382 q^{79} -5.49416 q^{81} +(3.50712 - 5.11077i) q^{82} -6.52313i q^{83} +(1.31969 - 0.508766i) q^{84} +(14.3012 + 9.81376i) q^{86} -20.3118 q^{87} +(2.99793 - 12.6073i) q^{88} +6.69564 q^{89} -0.418302i q^{91} +(-2.53724 - 6.58136i) q^{92} -8.77544i q^{93} +(-7.63892 + 11.1319i) q^{94} +(-14.7242 + 1.99247i) q^{96} -3.99182 q^{97} +(-5.54325 + 8.07794i) q^{98} -17.8644i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.800179	−	1.16607i	0.565812	−	0.824534i
$2$	0.800179	−	1.16607i	0.565812	−	0.824534i
$3$			2.62662i			1.51648i	0.651976	+	0.758240i	$0.273940\pi$
$3$			2.62662i			1.51648i	−0.651976	+	0.758240i	$0.726060\pi$
$4$	−0.719426	−	1.86613i	−0.359713	−	0.933063i
$5$		0			0
$5$		0			0
$6$	3.06282	+	2.10177i	1.25039	+	0.858043i
$7$	0.269237			0.101762			0.0508810	−	0.998705i	$-0.483797\pi$
$7$	0.269237			0.101762			0.0508810	+	0.998705i	$0.483797\pi$
$8$	−2.75170	−	0.654336i	−0.972872	−	0.231343i
$9$	−3.89913			−1.29971
$10$		0			0
$11$			4.58163i			1.38141i	0.723135	+	0.690706i	$0.242700\pi$
$11$			4.58163i			1.38141i	−0.723135	+	0.690706i	$0.757300\pi$
$12$	4.90160	−	1.88966i	1.41497	−	0.545497i
$13$		−	1.55366i		−	0.430908i	−0.976514	−	0.215454i	$-0.930877\pi$
$13$		−	1.55366i		−	0.430908i	0.976514	−	0.215454i	$-0.0691231\pi$
$14$	0.215438	−	0.313948i	0.0575782	−	0.0839062i
$15$		0			0
$16$	−2.96485	+	2.68508i	−0.741213	+	0.671270i
$17$	0.609109			0.147731			0.0738653	−	0.997268i	$-0.476467\pi$
$17$	0.609109			0.147731			0.0738653	+	0.997268i	$0.476467\pi$
$18$	−3.12001	+	4.54665i	−0.735392	+	1.07166i
$19$			6.69309i			1.53550i	0.640749	+	0.767750i	$0.278624\pi$
$19$			6.69309i			1.53550i	−0.640749	+	0.767750i	$0.721376\pi$
$20$		0			0
$21$			0.707183i			0.154320i
$22$	5.34249	+	3.66612i	1.13902	+	0.781620i
$23$	3.52675			0.735378			0.367689	−	0.929949i	$-0.380149\pi$
$23$	3.52675			0.735378			0.367689	+	0.929949i	$0.380149\pi$
$24$	1.71869	−	7.22767i	0.350827	−	1.47534i
$25$		0			0
$26$	−1.81167	−	1.24321i	−0.355298	−	0.243813i
$27$		−	2.36168i		−	0.454506i
$28$	−0.193696	−	0.502430i	−0.0366051	−	0.0949503i
$29$			7.73304i			1.43599i	0.696048	+	0.717995i	$0.254940\pi$
$29$			7.73304i			1.43599i	−0.696048	+	0.717995i	$0.745060\pi$
$30$		0			0
$31$	−3.34096			−0.600054			−0.300027	−	0.953931i	$-0.596996\pi$
$31$	−3.34096			−0.600054			−0.300027	+	0.953931i	$0.596996\pi$
$32$	0.758569	+	5.60576i	0.134097	+	0.990968i
$33$	−12.0342			−2.09488
$34$	0.487396	−	0.710262i	0.0835878	−	0.121809i
$35$		0			0
$36$	2.80514	+	7.27627i	0.467523	+	1.21271i
$37$		−	5.32768i		−	0.875865i	−0.899008	−	0.437933i	$-0.855711\pi$
$37$		−	5.32768i		−	0.875865i	0.899008	−	0.437933i	$-0.144289\pi$
$38$	7.80459	+	5.35567i	1.26607	+	0.868805i
$39$	4.08087			0.653463
$40$		0			0
$41$	4.38291			0.684496			0.342248	−	0.939610i	$-0.388812\pi$
$41$	4.38291			0.684496			0.342248	+	0.939610i	$0.388812\pi$
$42$	0.824623	+	0.565873i	0.127242	+	0.0873161i
$43$			12.2644i			1.87031i	0.354238	+	0.935155i	$0.384740\pi$
$43$			12.2644i			1.87031i	−0.354238	+	0.935155i	$0.615260\pi$
$44$	8.54989	−	3.29614i	1.28894	−	0.496912i
$45$		0			0
$46$	2.82203	−	4.11243i	0.416086	−	0.606345i
$47$	−9.54651			−1.39250			−0.696251	−	0.717798i	$-0.745150\pi$
$47$	−9.54651			−1.39250			−0.696251	+	0.717798i	$0.745150\pi$
$48$	−7.05268	−	7.78754i	−1.01797	−	1.12403i
$49$	−6.92751			−0.989645
$50$		0			0
$51$			1.59990i			0.224030i
$52$	−2.89932	+	1.11774i	−0.402064	+	0.155003i
$53$		−	10.6574i		−	1.46391i	−0.681353	−	0.731955i	$-0.738608\pi$
$53$		−	10.6574i		−	1.46391i	0.681353	−	0.731955i	$-0.261392\pi$
$54$	−2.75388	−	1.88977i	−0.374755	−	0.257165i
$55$		0			0
$56$	−0.740859	−	0.176171i	−0.0990014	−	0.0235419i
$57$	−17.5802			−2.32855
$58$	9.01725	+	6.18782i	1.18402	+	0.812501i
$59$		−	10.2256i		−	1.33126i	−0.746283	−	0.665629i	$-0.768163\pi$
$59$		−	10.2256i		−	1.33126i	0.746283	−	0.665629i	$-0.231837\pi$
$60$		0			0
$61$			13.2628i			1.69812i	0.528294	+	0.849062i	$0.322832\pi$
$61$			13.2628i			1.69812i	−0.528294	+	0.849062i	$0.677168\pi$
$62$	−2.67337	+	3.89579i	−0.339518	+	0.494765i
$63$	−1.04979			−0.132261
$64$	7.14369	+	3.60107i	0.892961	+	0.450134i
$65$		0			0
$66$	−9.62951	+	14.0327i	−1.18531	+	1.72730i
$67$		−	3.93398i		−	0.480613i	−0.970697	−	0.240306i	$-0.922752\pi$
$67$		−	3.93398i		−	0.480613i	0.970697	−	0.240306i	$-0.0772479\pi$
$68$	−0.438209	−	1.13667i	−0.0531406	−	0.137842i
$69$			9.26343i			1.11519i
$70$		0			0
$71$	6.95638			0.825571			0.412785	−	0.910828i	$-0.364556\pi$
$71$	6.95638			0.825571			0.412785	+	0.910828i	$0.364556\pi$
$72$	10.7292	+	2.55134i	1.26445	+	0.300679i
$73$	5.93156			0.694236			0.347118	−	0.937821i	$-0.387160\pi$
$73$	5.93156			0.694236			0.347118	+	0.937821i	$0.387160\pi$
$74$	−6.21243	−	4.26310i	−0.722181	−	0.495575i
$75$		0			0
$76$	12.4901	−	4.81518i	1.43272	−	0.552339i
$77$			1.23354i			0.140575i
$78$	3.26543	−	4.75857i	0.369737	−	0.538802i
$79$	10.1382			1.14064			0.570321	−	0.821422i	$-0.306819\pi$
$79$	10.1382			1.14064			0.570321	+	0.821422i	$0.306819\pi$
$80$		0			0
$81$	−5.49416			−0.610462
$82$	3.50712	−	5.11077i	0.387296	−	0.564390i
$83$		−	6.52313i		−	0.716007i	−0.933720	−	0.358003i	$-0.883458\pi$
$83$		−	6.52313i		−	0.716007i	0.933720	−	0.358003i	$-0.116542\pi$
$84$	1.31969	−	0.508766i	0.143990	−	0.0555109i
$85$		0			0
$86$	14.3012	+	9.81376i	1.54213	+	1.05824i
$87$	−20.3118			−2.17765
$88$	2.99793	−	12.6073i	0.319580	−	1.34394i
$89$	6.69564			0.709736			0.354868	−	0.934916i	$-0.384526\pi$
$89$	6.69564			0.709736			0.354868	+	0.934916i	$0.384526\pi$
$90$		0			0
$91$		−	0.418302i		−	0.0438500i
$92$	−2.53724	−	6.58136i	−0.264525	−	0.686154i
$93$		−	8.77544i		−	0.909970i
$94$	−7.63892	+	11.1319i	−0.787895	+	1.14817i
$95$		0			0
$96$	−14.7242	+	1.99247i	−1.50278	+	0.203356i
$97$	−3.99182			−0.405307			−0.202654	−	0.979250i	$-0.564957\pi$
$97$	−3.99182			−0.405307			−0.202654	+	0.979250i	$0.564957\pi$
$98$	−5.54325	+	8.07794i	−0.559953	+	0.815996i
$99$		−	17.8644i		−	1.79544i
$100$		0			0
$101$			0.361133i			0.0359340i	0.999839	+	0.0179670i	$0.00571939\pi$
$101$			0.361133i			0.0359340i	−0.999839	+	0.0179670i	$0.994281\pi$
$102$	1.86559	+	1.28020i	0.184721	+	0.126759i
$103$	19.0514			1.87719			0.938596	−	0.345019i	$-0.112128\pi$
$103$	19.0514			1.87719			0.938596	+	0.345019i	$0.112128\pi$
$104$	−1.01662	+	4.27520i	−0.0996874	+	0.419218i
$105$		0			0
$106$	−12.4273	−	8.52785i	−1.20704	−	0.828298i
$107$			7.68019i			0.742472i	0.928539	+	0.371236i	$0.121066\pi$
$107$			7.68019i			0.742472i	−0.928539	+	0.371236i	$0.878934\pi$
$108$	−4.40719	+	1.69905i	−0.424082	+	0.163492i
$109$			1.81184i			0.173543i	0.996228	+	0.0867716i	$0.0276550\pi$
$109$			1.81184i			0.173543i	−0.996228	+	0.0867716i	$0.972345\pi$
$110$		0			0
$111$	13.9938			1.32823
$112$	−0.798248	+	0.722922i	−0.0754273	+	0.0683097i
$113$	1.11278			0.104681			0.0523406	−	0.998629i	$-0.483332\pi$
$113$	1.11278			0.104681			0.0523406	+	0.998629i	$0.483332\pi$
$114$	−14.0673	+	20.4997i	−1.31752	+	1.91997i
$115$		0			0
$116$	14.4308	−	5.56335i	1.33987	−	0.516544i
$117$			6.05792i			0.560055i
$118$	−11.9237	−	8.18230i	−1.09767	−	0.753242i
$119$	0.163994			0.0150333
$120$		0			0
$121$	−9.99130			−0.908300
$122$	15.4653	+	10.6126i	1.40016	+	0.960819i
$123$			11.5122i			1.03802i
$124$	2.40357	+	6.23465i	0.215847	+	0.559889i
$125$		0			0
$126$	−0.840020	+	1.22413i	−0.0748350	+	0.109054i
$127$	9.81903			0.871298			0.435649	−	0.900117i	$-0.356519\pi$
$127$	9.81903			0.871298			0.435649	+	0.900117i	$0.356519\pi$
$128$	9.91533	−	5.44852i	0.876399	−	0.481585i
$129$	−32.2140			−2.83629
$130$		0			0
$131$			5.00551i			0.437333i	0.975800	+	0.218667i	$0.0701708\pi$
$131$			5.00551i			0.437333i	−0.975800	+	0.218667i	$0.929829\pi$
$132$	8.65771	+	22.4573i	0.753557	+	1.95466i
$133$			1.80203i			0.156255i
$134$	−4.58729	−	3.14789i	−0.396281	−	0.271936i
$135$		0			0
$136$	−1.67608	−	0.398562i	−0.143723	−	0.0341764i
$137$	−12.1561			−1.03856			−0.519282	−	0.854603i	$-0.673800\pi$
$137$	−12.1561			−1.03856			−0.519282	+	0.854603i	$0.673800\pi$
$138$	10.8018	+	7.41241i	0.919509	+	0.630986i
$139$		−	7.81838i		−	0.663147i	−0.943429	−	0.331573i	$-0.892421\pi$
$139$		−	7.81838i		−	0.663147i	0.943429	−	0.331573i	$-0.107579\pi$
$140$		0			0
$141$		−	25.0751i		−	2.11170i
$142$	5.56636	−	8.11161i	0.467118	−	0.680711i
$143$	7.11829			0.595261
$144$	11.5604	−	10.4695i	0.963363	−	0.872457i
$145$		0			0
$146$	4.74631	−	6.91659i	0.392807	−	0.572421i
$147$		−	18.1959i		−	1.50078i
$148$	−9.94212	+	3.83287i	−0.817237	+	0.315060i
$149$		−	17.0047i		−	1.39308i	−0.717520	−	0.696538i	$-0.754723\pi$
$149$		−	17.0047i		−	1.39308i	0.717520	−	0.696538i	$-0.245277\pi$
$150$		0			0
$151$	−13.2804			−1.08075			−0.540373	−	0.841425i	$-0.681717\pi$
$151$	−13.2804			−1.08075			−0.540373	+	0.841425i	$0.681717\pi$
$152$	4.37953	−	18.4174i	0.355227	−	1.49385i
$153$	−2.37500			−0.192007
$154$	1.43839	+	0.987055i	0.115909	+	0.0795392i
$155$		0			0
$156$	−2.93589	−	7.61542i	−0.235059	−	0.609722i
$157$		−	19.0554i		−	1.52078i	−0.649465	−	0.760391i	$-0.725007\pi$
$157$		−	19.0554i		−	1.52078i	0.649465	−	0.760391i	$-0.274993\pi$
$158$	8.11241	−	11.8219i	0.645389	−	0.940498i
$159$	27.9930			2.21999
$160$		0			0
$161$	0.949531			0.0748335
$162$	−4.39632	+	6.40656i	−0.345407	+	0.503347i
$163$		−	16.7152i		−	1.30923i	−0.755961	−	0.654617i	$-0.772830\pi$
$163$		−	16.7152i		−	1.30923i	0.755961	−	0.654617i	$-0.227170\pi$
$164$	−3.15318	−	8.17907i	−0.246222	−	0.638678i
$165$		0			0
$166$	−7.60641	−	5.21968i	−0.590372	−	0.405125i
$167$	12.2045			0.944409			0.472204	−	0.881489i	$-0.343458\pi$
$167$	12.2045			0.944409			0.472204	+	0.881489i	$0.343458\pi$
$168$	0.462736	−	1.94595i	0.0357008	−	0.150134i
$169$	10.5861			0.814319
$170$		0			0
$171$		−	26.0972i		−	1.99571i
$172$	22.8870	−	8.82336i	1.74512	−	0.672775i
$173$			2.55690i			0.194397i	0.995265	+	0.0971986i	$0.0309882\pi$
$173$			2.55690i			0.194397i	−0.995265	+	0.0971986i	$0.969012\pi$
$174$	−16.2531	+	23.6849i	−1.23214	+	1.79555i
$175$		0			0
$176$	−12.3020	−	13.5838i	−0.927300	−	1.02392i
$177$	26.8587			2.01883
$178$	5.35771	−	7.80756i	0.401577	−	0.585202i
$179$		−	18.3566i		−	1.37204i	−0.727584	−	0.686019i	$-0.759357\pi$
$179$		−	18.3566i		−	1.37204i	0.727584	−	0.686019i	$-0.240643\pi$
$180$		0			0
$181$			8.74009i			0.649646i	0.945775	+	0.324823i	$0.105305\pi$
$181$			8.74009i			0.649646i	−0.945775	+	0.324823i	$0.894695\pi$
$182$	−0.487769	−	0.334717i	−0.0361558	−	0.0248109i
$183$	−34.8362			−2.57517
$184$	−9.70455	−	2.30768i	−0.715429	−	0.170125i
$185$		0			0
$186$	−10.2327	−	7.02192i	−0.750302	−	0.514872i
$187$			2.79071i			0.204077i
$188$	6.86801	+	17.8150i	0.500901	+	1.29929i
$189$		−	0.635851i		−	0.0462514i
$190$		0			0
$191$	−21.5766			−1.56123			−0.780614	−	0.625013i	$-0.785094\pi$
$191$	−21.5766			−1.56123			−0.780614	+	0.625013i	$0.785094\pi$
$192$	−9.45865	+	18.7638i	−0.682619	+	1.35416i
$193$	9.90462			0.712950			0.356475	−	0.934305i	$-0.383978\pi$
$193$	9.90462			0.712950			0.356475	+	0.934305i	$0.383978\pi$
$194$	−3.19417	+	4.65473i	−0.229328	+	0.334190i
$195$		0			0
$196$	4.98383	+	12.9276i	0.355988	+	0.923401i
$197$		−	9.37856i		−	0.668195i	−0.942539	−	0.334097i	$-0.891569\pi$
$197$		−	9.37856i		−	0.668195i	0.942539	−	0.334097i	$-0.108431\pi$
$198$	−20.8311	−	14.2947i	−1.48040	−	1.01588i
$199$	16.8855			1.19698			0.598491	−	0.801130i	$-0.295767\pi$
$199$	16.8855			1.19698			0.598491	+	0.801130i	$0.295767\pi$
$200$		0			0
$201$	10.3331			0.728839
$202$	0.421105	+	0.288971i	0.0296288	+	0.0203319i
$203$			2.08202i			0.146129i
$204$	2.98561	−	1.15101i	0.209034	−	0.0805866i
$205$		0			0
$206$	15.2445	−	22.2152i	1.06214	−	1.54781i
$207$	−13.7513			−0.955779
$208$	4.17170	+	4.60637i	0.289255	+	0.319394i
$209$	−30.6652			−2.12116
$210$		0			0
$211$		−	14.0265i		−	0.965623i	−0.875724	−	0.482811i	$-0.839616\pi$
$211$		−	14.0265i		−	0.965623i	0.875724	−	0.482811i	$-0.160384\pi$
$212$	−19.8881	+	7.66723i	−1.36592	+	0.526587i
$213$			18.2718i			1.25196i
$214$	8.95561	+	6.14553i	0.612193	+	0.420100i
$215$		0			0
$216$	−1.54533	+	6.49863i	−0.105147	+	0.442176i
$217$	−0.899510			−0.0610627
$218$	2.11273	+	1.44980i	0.143092	+	0.0981928i
$219$			15.5799i			1.05280i
$220$		0			0
$221$		−	0.946347i		−	0.0636582i
$222$	11.1975	−	16.3177i	0.751530	−	1.09517i
$223$	−2.06137			−0.138039			−0.0690197	−	0.997615i	$-0.521987\pi$
$223$	−2.06137			−0.138039			−0.0690197	+	0.997615i	$0.521987\pi$
$224$	0.204235	+	1.50928i	0.0136460	+	0.100843i
$225$		0			0
$226$	0.890421	−	1.29757i	0.0592299	−	0.0863133i
$227$		−	3.13275i		−	0.207928i	−0.994581	−	0.103964i	$-0.966847\pi$
$227$		−	3.13275i		−	0.207928i	0.994581	−	0.103964i	$-0.0331526\pi$
$228$	12.6477	+	32.8069i	0.837611	+	2.17269i
$229$			17.0738i			1.12827i	0.825682	+	0.564136i	$0.190791\pi$
$229$			17.0738i			1.12827i	−0.825682	+	0.564136i	$0.809209\pi$
$230$		0			0
$231$	−3.24005			−0.213179
$232$	5.06001	−	21.2790i	0.332206	−	1.39704i
$233$	−7.63474			−0.500169			−0.250084	−	0.968224i	$-0.580458\pi$
$233$	−7.63474			−0.500169			−0.250084	+	0.968224i	$0.580458\pi$
$234$	7.06395	+	4.84743i	0.461785	+	0.316886i
$235$		0			0
$236$	−19.0822	+	7.35655i	−1.24215	+	0.478871i
$237$			26.6293i			1.72976i
$238$	0.131225	−	0.191229i	0.00850605	−	0.0123955i
$239$	4.92104			0.318315			0.159158	−	0.987253i	$-0.449122\pi$
$239$	4.92104			0.318315			0.159158	+	0.987253i	$0.449122\pi$
$240$		0			0
$241$	19.1214			1.23172			0.615860	−	0.787855i	$-0.288809\pi$
$241$	19.1214			1.23172			0.615860	+	0.787855i	$0.288809\pi$
$242$	−7.99484	+	11.6505i	−0.513927	+	0.748925i
$243$		−	21.5161i		−	1.38026i
$244$	24.7500	−	9.54158i	1.58446	−	0.610837i
$245$		0			0
$246$	13.4241	+	9.21186i	0.855887	+	0.587327i
$247$	10.3988			0.661659
$248$	9.19332	+	2.18611i	0.583776	+	0.138818i
$249$	17.1338			1.08581
$250$		0			0
$251$			29.7004i			1.87467i	0.348423	+	0.937337i	$0.386717\pi$
$251$			29.7004i			1.87467i	−0.348423	+	0.937337i	$0.613283\pi$
$252$	0.755246	+	1.95904i	0.0475760	+	0.123408i
$253$			16.1583i			1.01586i
$254$	7.85699	−	11.4497i	0.492991	−	0.718415i
$255$		0			0
$256$	1.58070	−	15.9217i	0.0987939	−	0.995108i
$257$	−13.1697			−0.821501			−0.410750	−	0.911748i	$-0.634733\pi$
$257$	−13.1697			−0.821501			−0.410750	+	0.911748i	$0.634733\pi$
$258$	−25.7770	+	37.5637i	−1.60481	+	2.33862i
$259$		−	1.43441i		−	0.0891297i
$260$		0			0
$261$		−	30.1522i		−	1.86637i
$262$	5.83676	+	4.00531i	0.360596	+	0.247449i
$263$	−17.7204			−1.09269			−0.546345	−	0.837560i	$-0.683981\pi$
$263$	−17.7204			−1.09269			−0.546345	+	0.837560i	$0.683981\pi$
$264$	33.1145	+	7.87441i	2.03805	+	0.484636i
$265$		0			0
$266$	2.10128	+	1.44194i	0.128838	+	0.0884113i
$267$			17.5869i			1.07630i
$268$	−7.34131	+	2.83021i	−0.448442	+	0.172883i
$269$		−	1.52445i		−	0.0929474i	−0.998920	−	0.0464737i	$-0.985202\pi$
$269$		−	1.52445i		−	0.0929474i	0.998920	−	0.0464737i	$-0.0147984\pi$
$270$		0			0
$271$	16.1497			0.981024			0.490512	−	0.871435i	$-0.336810\pi$
$271$	16.1497			0.981024			0.490512	+	0.871435i	$0.336810\pi$
$272$	−1.80592	+	1.63550i	−0.109500	+	0.0991670i
$273$	1.09872			0.0664976
$274$	−9.72704	+	14.1748i	−0.587632	+	0.856331i
$275$		0			0
$276$	17.2867	−	6.66436i	1.04054	−	0.401147i
$277$			12.3707i			0.743283i	0.928376	+	0.371642i	$0.121205\pi$
$277$			12.3707i			0.743283i	−0.928376	+	0.371642i	$0.878795\pi$
$278$	−9.11676	−	6.25611i	−0.546787	−	0.375217i
$279$	13.0269			0.779897
$280$		0			0
$281$	−4.03820			−0.240899			−0.120450	−	0.992719i	$-0.538434\pi$
$281$	−4.03820			−0.240899			−0.120450	+	0.992719i	$0.538434\pi$
$282$	−29.2392	−	20.0645i	−1.74117	−	1.19483i
$283$		−	4.13989i		−	0.246091i	−0.992401	−	0.123046i	$-0.960734\pi$
$283$		−	4.13989i		−	0.246091i	0.992401	−	0.123046i	$-0.0392661\pi$
$284$	−5.00460	−	12.9815i	−0.296969	−	0.770310i
$285$		0			0
$286$	5.69591	−	8.30040i	0.336806	−	0.490813i
$287$	1.18004			0.0696557
$288$	−2.95776	−	21.8576i	−0.174288	−	1.28797i
$289$	−16.6290			−0.978176
$290$		0			0
$291$		−	10.4850i		−	0.614641i
$292$	−4.26732	−	11.0690i	−0.249726	−	0.647766i
$293$			25.2638i			1.47593i	0.674840	+	0.737964i	$0.264213\pi$
$293$			25.2638i			1.47593i	−0.674840	+	0.737964i	$0.735787\pi$
$294$	−21.2177	−	14.5600i	−1.23744	−	0.849157i
$295$		0			0
$296$	−3.48609	+	14.6602i	−0.202625	+	0.852105i
$297$	10.8203			0.627860
$298$	−19.8286	−	13.6068i	−1.14864	−	0.788219i
$299$		−	5.47937i		−	0.316880i
$300$		0			0
$301$			3.30204i			0.190326i
$302$	−10.6267	+	15.4859i	−0.611500	+	0.891112i
$303$	−0.948558			−0.0544933
$304$	−17.9715	−	19.8440i	−1.03073	−	1.13813i
$305$		0			0
$306$	−1.90042	+	2.76940i	−0.108640	+	0.158316i
$307$			10.6692i			0.608922i	0.952525	+	0.304461i	$0.0984764\pi$
$307$			10.6692i			0.608922i	−0.952525	+	0.304461i	$0.901524\pi$
$308$	2.30195	−	0.887443i	0.131166	−	0.0505667i
$309$			50.0408i			2.84672i
$310$		0			0
$311$	1.78111			0.100998			0.0504988	−	0.998724i	$-0.483919\pi$
$311$	1.78111			0.100998			0.0504988	+	0.998724i	$0.483919\pi$
$312$	−11.2293	−	2.67026i	−0.635736	−	0.151174i
$313$	26.6250			1.50494			0.752468	−	0.658629i	$-0.228863\pi$
$313$	26.6250			1.50494			0.752468	+	0.658629i	$0.228863\pi$
$314$	−22.2198	−	15.2477i	−1.25394	−	0.860478i
$315$		0			0
$316$	−7.29371	−	18.9192i	−0.410303	−	1.06429i
$317$		−	9.16369i		−	0.514684i	−0.966320	−	0.257342i	$-0.917153\pi$
$317$		−	9.16369i		−	0.514684i	0.966320	−	0.257342i	$-0.0828467\pi$
$318$	22.3994	−	32.6417i	1.25610	−	1.83046i
$319$	−35.4299			−1.98369
$320$		0			0
$321$	−20.1729			−1.12594
$322$	0.759795	−	1.10722i	0.0423417	−	0.0617028i
$323$			4.07682i			0.226840i
$324$	3.95264	+	10.2528i	0.219591	+	0.569600i
$325$		0			0
$326$	−19.4910	−	13.3751i	−1.07951	−	0.740781i
$327$	−4.75903			−0.263175
$328$	−12.0605	−	2.86790i	−0.665927	−	0.158353i
$329$	−2.57027			−0.141704
$330$		0			0
$331$			7.83419i			0.430606i	0.976547	+	0.215303i	$0.0690739\pi$
$331$			7.83419i			0.430606i	−0.976547	+	0.215303i	$0.930926\pi$
$332$	−12.1730	+	4.69291i	−0.668079	+	0.257557i
$333$			20.7733i			1.13837i
$334$	9.76575	−	14.2312i	0.534358	−	0.778697i
$335$		0			0
$336$	−1.89884	−	2.09669i	−0.103590	−	0.114384i
$337$	−0.636306			−0.0346618			−0.0173309	−	0.999850i	$-0.505517\pi$
$337$	−0.636306			−0.0346618			−0.0173309	+	0.999850i	$0.505517\pi$
$338$	8.47081	−	12.3442i	0.460752	−	0.671434i
$339$			2.92284i			0.158747i
$340$		0			0
$341$		−	15.3070i		−	0.828923i
$342$	−30.4311	−	20.8825i	−1.64553	−	1.12920i
$343$	−3.74980			−0.202470
$344$	8.02508	−	33.7481i	0.432683	−	1.81957i
$345$		0			0
$346$	2.98151	+	2.04598i	0.160287	+	0.109992i
$347$			23.5999i			1.26691i	0.773780	+	0.633455i	$0.218364\pi$
$347$			23.5999i			1.26691i	−0.773780	+	0.633455i	$0.781636\pi$
$348$	14.6128	+	37.9043i	0.783329	+	2.03188i
$349$			19.1542i			1.02530i	0.858597	+	0.512651i	$0.171336\pi$
$349$			19.1542i			1.02530i	−0.858597	+	0.512651i	$0.828664\pi$
$350$		0			0
$351$	−3.66925			−0.195850
$352$	−25.6835	+	3.47548i	−1.36894	+	0.185244i
$353$	21.9765			1.16969			0.584845	−	0.811145i	$-0.301155\pi$
$353$	21.9765			1.16969			0.584845	+	0.811145i	$0.301155\pi$
$354$	21.4918	−	31.3191i	1.14228	−	1.66459i
$355$		0			0
$356$	−4.81702	−	12.4949i	−0.255301	−	0.662229i
$357$			0.430751i			0.0227978i
$358$	−21.4050	−	14.6886i	−1.13129	−	0.776316i
$359$	−5.63031			−0.297156			−0.148578	−	0.988901i	$-0.547470\pi$
$359$	−5.63031			−0.297156			−0.148578	+	0.988901i	$0.547470\pi$
$360$		0			0
$361$	−25.7974			−1.35776
$362$	10.1915	+	6.99364i	0.535655	+	0.367578i
$363$		−	26.2434i		−	1.37742i
$364$	−0.780605	+	0.300938i	−0.0409148	+	0.0157734i
$365$		0			0
$366$	−27.8752	+	40.6214i	−1.45706	+	2.12332i
$367$	5.21463			0.272201			0.136101	−	0.990695i	$-0.456543\pi$
$367$	5.21463			0.272201			0.136101	+	0.990695i	$0.456543\pi$
$368$	−10.4563	+	9.46960i	−0.545072	+	0.493637i
$369$	−17.0896			−0.889647
$370$		0			0
$371$		−	2.86937i		−	0.148970i
$372$	−16.3761	+	6.31328i	−0.849060	+	0.327328i
$373$		−	12.6000i		−	0.652405i	−0.945300	−	0.326202i	$-0.894231\pi$
$373$		−	12.6000i		−	0.652405i	0.945300	−	0.326202i	$-0.105769\pi$
$374$	3.25415	+	2.23307i	0.168268	+	0.115469i
$375$		0			0
$376$	26.2691	+	6.24663i	1.35473	+	0.322145i
$377$	12.0145			0.618779
$378$	−0.741445	−	0.508795i	−0.0381358	−	0.0261696i
$379$			1.28403i			0.0659562i	0.999456	+	0.0329781i	$0.0104992\pi$
$379$			1.28403i			0.0659562i	−0.999456	+	0.0329781i	$0.989501\pi$
$380$		0			0
$381$			25.7909i			1.32131i
$382$	−17.2652	+	25.1598i	−0.883362	+	1.28729i
$383$	−18.3642			−0.938369			−0.469185	−	0.883100i	$-0.655452\pi$
$383$	−18.3642			−0.938369			−0.469185	+	0.883100i	$0.655452\pi$
$384$	14.3112	+	26.0438i	0.730314	+	1.32904i
$385$		0			0
$386$	7.92547	−	11.5495i	0.403396	−	0.587852i
$387$		−	47.8207i		−	2.43086i
$388$	2.87182	+	7.44923i	0.145794	+	0.378177i
$389$		−	20.5311i		−	1.04097i	−0.853871	−	0.520485i	$-0.825751\pi$
$389$		−	20.5311i		−	1.04097i	0.853871	−	0.520485i	$-0.174249\pi$
$390$		0			0
$391$	2.14817			0.108638
$392$	19.0624	+	4.53292i	0.962798	+	0.228947i
$393$	−13.1476			−0.663207
$394$	−10.9360	−	7.50453i	−0.550949	−	0.378073i
$395$		0			0
$396$	−33.3372	+	12.8521i	−1.67526	+	0.645842i
$397$		−	17.0191i		−	0.854164i	−0.904213	−	0.427082i	$-0.859542\pi$
$397$		−	17.0191i		−	0.854164i	0.904213	−	0.427082i	$-0.140458\pi$
$398$	13.5114	−	19.6896i	0.677267	−	0.986952i
$399$	−4.73324			−0.236958
$400$		0			0
$401$	7.62575			0.380812			0.190406	−	0.981705i	$-0.439020\pi$
$401$	7.62575			0.380812			0.190406	+	0.981705i	$0.439020\pi$
$402$	8.26832	−	12.0491i	0.412386	−	0.600953i
$403$			5.19072i			0.258568i
$404$	0.673919	−	0.259808i	0.0335287	−	0.0129259i
$405$		0			0
$406$	2.42778	+	1.66599i	0.120488	+	0.0826817i
$407$	24.4094			1.20993
$408$	1.04687	−	4.40243i	0.0518278	−	0.217953i
$409$	7.37530			0.364685			0.182342	−	0.983235i	$-0.441632\pi$
$409$	7.37530			0.364685			0.182342	+	0.983235i	$0.441632\pi$
$410$		0			0
$411$		−	31.9294i		−	1.57496i
$412$	−13.7061	−	35.5523i	−0.675250	−	1.75154i
$413$		−	2.75310i		−	0.135471i
$414$	−11.0035	+	16.0349i	−0.540792	+	0.788073i
$415$		0			0
$416$	8.70944	−	1.17856i	0.427016	−	0.0577835i
$417$	20.5359			1.00565
$418$	−24.5377	+	35.7577i	−1.20018	+	1.74897i
$419$			22.0835i			1.07885i	0.842034	+	0.539425i	$0.181358\pi$
$419$			22.0835i			1.07885i	−0.842034	+	0.539425i	$0.818642\pi$
$420$		0			0
$421$			29.2485i			1.42549i	0.701425	+	0.712743i	$0.252547\pi$
$421$			29.2485i			1.42549i	−0.701425	+	0.712743i	$0.747453\pi$
$422$	−16.3558	−	11.2237i	−0.796189	−	0.546361i
$423$	37.2231			1.80985
$424$	−6.97354	+	29.3260i	−0.338665	+	1.42420i
$425$		0			0
$426$	21.3061	+	14.6207i	1.03229	+	0.708375i
$427$			3.57083i			0.172804i
$428$	14.3322	−	5.52532i	0.692773	−	0.267077i
$429$			18.6970i			0.902701i
$430$		0			0
$431$	−6.99018			−0.336705			−0.168353	−	0.985727i	$-0.553845\pi$
$431$	−6.99018			−0.336705			−0.168353	+	0.985727i	$0.553845\pi$
$432$	6.34130	+	7.00203i	0.305096	+	0.336885i
$433$	19.1288			0.919271			0.459636	−	0.888108i	$-0.347980\pi$
$433$	19.1288			0.919271			0.459636	+	0.888108i	$0.347980\pi$
$434$	−0.719769	+	1.04889i	−0.0345500	+	0.0503483i
$435$		0			0
$436$	3.38113	−	1.30349i	0.161927	−	0.0624257i
$437$			23.6049i			1.12917i
$438$	18.1673	+	12.4667i	0.868065	+	0.595684i
$439$	−2.78856			−0.133091			−0.0665453	−	0.997783i	$-0.521198\pi$
$439$	−2.78856			−0.133091			−0.0665453	+	0.997783i	$0.521198\pi$
$440$		0			0
$441$	27.0113			1.28625
$442$	−1.10350	−	0.757248i	−0.0524884	−	0.0360186i
$443$		−	16.8836i		−	0.802164i	−0.916042	−	0.401082i	$-0.868634\pi$
$443$		−	16.8836i		−	0.802164i	0.916042	−	0.401082i	$-0.131366\pi$
$444$	−10.0675	−	26.1142i	−0.477782	−	1.23932i
$445$		0			0
$446$	−1.64946	+	2.40369i	−0.0781043	+	0.113818i
$447$	44.6648			2.11257
$448$	1.92334	+	0.969542i	0.0908695	+	0.0458065i
$449$	−13.1404			−0.620135			−0.310068	−	0.950714i	$-0.600352\pi$
$449$	−13.1404			−0.620135			−0.310068	+	0.950714i	$0.600352\pi$
$450$		0			0
$451$			20.0809i			0.945571i
$452$	−0.800561	−	2.07658i	−0.0376552	−	0.0976742i
$453$		−	34.8827i		−	1.63893i
$454$	−3.65299	−	2.50676i	−0.171443	−	0.117648i
$455$		0			0
$456$	48.3754	+	11.5034i	2.26539	+	0.538695i
$457$	33.4760			1.56594			0.782971	−	0.622058i	$-0.213703\pi$
$457$	33.4760			1.56594			0.782971	+	0.622058i	$0.213703\pi$
$458$	19.9093	+	13.6621i	0.930298	+	0.638390i
$459$		−	1.43852i		−	0.0671444i
$460$		0			0
$461$			27.6037i			1.28563i	0.766021	+	0.642816i	$0.222234\pi$
$461$			27.6037i			1.28563i	−0.766021	+	0.642816i	$0.777766\pi$
$462$	−2.59262	+	3.77811i	−0.120620	+	0.175774i
$463$	14.9227			0.693517			0.346758	−	0.937955i	$-0.387282\pi$
$463$	14.9227			0.693517			0.346758	+	0.937955i	$0.387282\pi$
$464$	−20.7638	−	22.9273i	−0.963937	−	1.06437i
$465$		0			0
$466$	−6.10916	+	8.90262i	−0.283002	+	0.412406i
$467$			11.8685i			0.549210i	0.961557	+	0.274605i	$0.0885472\pi$
$467$			11.8685i			0.549210i	−0.961557	+	0.274605i	$0.911453\pi$
$468$	11.3048	−	4.35823i	0.522567	−	0.201459i
$469$		−	1.05917i		−	0.0489081i
$470$		0			0
$471$	50.0512			2.30624
$472$	−6.69097	+	28.1377i	−0.307977	+	1.29514i
$473$	−56.1911			−2.58367
$474$	31.0516	+	21.3082i	1.42625	+	0.978719i
$475$		0			0
$476$	−0.117982	−	0.306034i	−0.00540769	−	0.0140271i
$477$			41.5547i			1.90266i
$478$	3.93771	−	5.73826i	0.180107	−	0.262462i
$479$	15.4425			0.705586			0.352793	−	0.935701i	$-0.385232\pi$
$479$	15.4425			0.705586			0.352793	+	0.935701i	$0.385232\pi$
$480$		0			0
$481$	−8.27740			−0.377417
$482$	15.3006	−	22.2969i	0.696923	−	1.01560i
$483$			2.49406i			0.113484i
$484$	7.18800	+	18.6450i	0.326727	+	0.847501i
$485$		0			0
$486$	−25.0892	−	17.2168i	−1.13807	−	0.780968i
$487$	7.58171			0.343560			0.171780	−	0.985135i	$-0.445048\pi$
$487$	7.58171			0.343560			0.171780	+	0.985135i	$0.445048\pi$
$488$	8.67831	−	36.4951i	0.392849	−	1.65206i
$489$	43.9044			1.98543
$490$		0			0
$491$			5.55509i			0.250698i	0.992113	+	0.125349i	$0.0400050\pi$
$491$			5.55509i			0.250698i	−0.992113	+	0.125349i	$0.959995\pi$
$492$	21.4833	−	8.28221i	0.968542	−	0.373391i
$493$			4.71026i			0.212140i
$494$	8.32089	−	12.1257i	0.374375	−	0.545560i
$495$		0			0
$496$	9.90546	−	8.97074i	0.444768	−	0.402798i
$497$	1.87291			0.0840117
$498$	13.7101	−	19.9792i	0.614364	−	0.895287i
$499$			14.1201i			0.632102i	0.948742	+	0.316051i	$0.102357\pi$
$499$			14.1201i			0.632102i	−0.948742	+	0.316051i	$0.897643\pi$
$500$		0			0
$501$			32.0565i			1.43218i
$502$	34.6327	+	23.7657i	1.54573	+	1.06071i
$503$	−14.3503			−0.639847			−0.319924	−	0.947443i	$-0.603657\pi$
$503$	−14.3503			−0.639847			−0.319924	+	0.947443i	$0.603657\pi$
$504$	2.88871	+	0.686916i	0.128673	+	0.0305977i
$505$		0			0
$506$	18.8416	+	12.9295i	0.837612	+	0.574787i
$507$			27.8058i			1.23490i
$508$	−7.06407	−	18.3236i	−0.313417	−	0.812976i
$509$		−	42.9057i		−	1.90176i	−0.309557	−	0.950881i	$-0.600181\pi$
$509$		−	42.9057i		−	1.90176i	0.309557	−	0.950881i	$-0.399819\pi$
$510$		0			0
$511$	1.59699			0.0706468
$512$	−17.3010	−	14.5834i	−0.764602	−	0.644503i
$513$	15.8069			0.697893
$514$	−10.5381	+	15.3567i	−0.464815	+	0.677356i
$515$		0			0
$516$	23.1756	+	60.1155i	1.02025	+	2.64644i
$517$		−	43.7386i		−	1.92362i
$518$	−1.67262	−	1.14778i	−0.0734905	−	0.0504307i
$519$	−6.71600			−0.294800
$520$		0			0
$521$	11.4542			0.501817			0.250909	−	0.968011i	$-0.419271\pi$
$521$	11.4542			0.501817			0.250909	+	0.968011i	$0.419271\pi$
$522$	−35.1595	−	24.1271i	−1.53889	−	1.05602i
$523$			21.7522i			0.951156i	0.879674	+	0.475578i	$0.157761\pi$
$523$			21.7522i			0.951156i	−0.879674	+	0.475578i	$0.842239\pi$
$524$	9.34091	−	3.60109i	0.408060	−	0.157315i
$525$		0			0
$526$	−14.1795	+	20.6632i	−0.618257	+	0.900960i
$527$	−2.03501			−0.0886464
$528$	35.6796	−	32.3128i	1.55276	−	1.40623i
$529$	−10.5620			−0.459219
$530$		0			0
$531$			39.8709i			1.73025i
$532$	3.36281	−	1.29642i	0.145796	−	0.0562071i
$533$		−	6.80955i		−	0.294955i
$534$	20.5075	+	14.0727i	0.887446	+	0.608984i
$535$		0			0
$536$	−2.57415	+	10.8251i	−0.111186	+	0.467575i
$537$	48.2158			2.08067
$538$	−1.77761	−	1.21983i	−0.0766383	−	0.0525908i
$539$		−	31.7393i		−	1.36711i
$540$		0			0
$541$		−	36.5960i		−	1.57339i	−0.617344	−	0.786693i	$-0.711791\pi$
$541$		−	36.5960i		−	1.57339i	0.617344	−	0.786693i	$-0.288209\pi$
$542$	12.9226	−	18.8316i	0.555075	−	0.808887i
$543$	−22.9569			−0.985175
$544$	0.462051	+	3.41452i	0.0198103	+	0.146396i
$545$		0			0
$546$	0.879174	−	1.28118i	0.0376252	−	0.0548296i
$547$			15.8078i			0.675893i	0.941165	+	0.337946i	$0.109732\pi$
$547$			15.8078i			0.675893i	−0.941165	+	0.337946i	$0.890268\pi$
$548$	8.74539	+	22.6848i	0.373585	+	0.969045i
$549$		−	51.7133i		−	2.20707i
$550$		0			0
$551$	−51.7580			−2.20496
$552$	6.06140	−	25.4902i	0.257990	−	1.08493i
$553$	2.72959			0.116074
$554$	14.4251	+	9.89878i	0.612863	+	0.420559i
$555$		0			0
$556$	−14.5901	+	5.62475i	−0.618758	+	0.238542i
$557$		−	12.7121i		−	0.538629i	−0.963052	−	0.269315i	$-0.913203\pi$
$557$		−	12.7121i		−	0.538629i	0.963052	−	0.269315i	$-0.0867971\pi$
$558$	10.4238	−	15.1902i	0.441275	−	0.643052i
$559$	19.0548			0.805931
$560$		0			0
$561$	−7.33013			−0.309478
$562$	−3.23129	+	4.70882i	−0.136304	+	0.198630i
$563$			14.3700i			0.605624i	0.953050	+	0.302812i	$0.0979255\pi$
$563$			14.3700i			0.605624i	−0.953050	+	0.302812i	$0.902075\pi$
$564$	−46.7932	+	18.0396i	−1.97035	+	0.759606i
$565$		0			0
$566$	−4.82740	−	3.31266i	−0.202911	−	0.139241i
$567$	−1.47923			−0.0621219
$568$	−19.1419	−	4.55182i	−0.803175	−	0.190990i
$569$	32.5495			1.36455			0.682274	−	0.731097i	$-0.260991\pi$
$569$	32.5495			1.36455			0.682274	+	0.731097i	$0.260991\pi$
$570$		0			0
$571$			16.2274i			0.679097i	0.940589	+	0.339548i	$0.110274\pi$
$571$			16.2274i			0.679097i	−0.940589	+	0.339548i	$0.889726\pi$
$572$	−5.12108	−	13.2836i	−0.214123	−	0.555416i
$573$		−	56.6736i		−	2.36757i
$574$	0.944245	−	1.37601i	0.0394120	−	0.0574335i
$575$		0			0
$576$	−27.8542	−	14.0411i	−1.16059	−	0.585044i
$577$	−30.1137			−1.25365			−0.626825	−	0.779160i	$-0.715646\pi$
$577$	−30.1137			−1.25365			−0.626825	+	0.779160i	$0.715646\pi$
$578$	−13.3062	+	19.3905i	−0.553464	+	0.806539i
$579$			26.0157i			1.08117i
$580$		0			0
$581$		−	1.75627i		−	0.0728622i
$582$	−12.2262	−	8.38987i	−0.506792	−	0.347771i
$583$	48.8283			2.02226
$584$	−16.3219	−	3.88123i	−0.675403	−	0.160607i
$585$		0			0
$586$	29.4593	+	20.2156i	1.21695	+	0.835098i
$587$			14.1963i			0.585943i	0.956121	+	0.292971i	$0.0946440\pi$
$587$			14.1963i			0.585943i	−0.956121	+	0.292971i	$0.905356\pi$
$588$	−33.9559	+	13.0906i	−1.40032	+	0.539849i
$589$		−	22.3614i		−	0.921384i
$590$		0			0
$591$	24.6339			1.01330
$592$	14.3052	+	15.7958i	0.587942	+	0.649203i
$593$	−12.2025			−0.501098			−0.250549	−	0.968104i	$-0.580611\pi$
$593$	−12.2025			−0.501098			−0.250549	+	0.968104i	$0.580611\pi$
$594$	8.65821	−	12.6172i	0.355251	−	0.517692i
$595$		0			0
$596$	−31.7328	+	12.2336i	−1.29983	+	0.501107i
$597$			44.3518i			1.81520i
$598$	−6.38931	−	4.38448i	−0.261278	−	0.179295i
$599$	−2.44106			−0.0997391			−0.0498695	−	0.998756i	$-0.515881\pi$
$599$	−2.44106			−0.0997391			−0.0498695	+	0.998756i	$0.515881\pi$
$600$		0			0
$601$	−13.7234			−0.559789			−0.279895	−	0.960031i	$-0.590300\pi$
$601$	−13.7234			−0.559789			−0.279895	+	0.960031i	$0.590300\pi$
$602$	3.85040	+	2.64223i	0.156931	+	0.107689i
$603$			15.3391i			0.624657i
$604$	9.55429	+	24.7830i	0.388759	+	1.00840i
$605$		0			0
$606$	−0.759017	+	1.10608i	−0.0308330	+	0.0449315i
$607$	25.0502			1.01676			0.508378	−	0.861134i	$-0.330245\pi$
$607$	25.0502			1.01676			0.508378	+	0.861134i	$0.330245\pi$
$608$	−37.5199	+	5.07717i	−1.52163	+	0.205906i
$609$	−5.46868			−0.221602
$610$		0			0
$611$			14.8320i			0.600040i
$612$	1.70863	+	4.43204i	0.0690674	+	0.179155i
$613$			26.4690i			1.06907i	0.845146	+	0.534536i	$0.179514\pi$
$613$			26.4690i			1.06907i	−0.845146	+	0.534536i	$0.820486\pi$
$614$	12.4410	+	8.53726i	0.502077	+	0.344536i
$615$		0			0
$616$	0.807152	−	3.39434i	0.0325211	−	0.136762i
$617$	−20.2771			−0.816324			−0.408162	−	0.912909i	$-0.633830\pi$
$617$	−20.2771			−0.816324			−0.408162	+	0.912909i	$0.633830\pi$
$618$	58.3510	+	40.0416i	2.34722	+	1.61071i
$619$			13.1584i			0.528880i	0.964402	+	0.264440i	$0.0851871\pi$
$619$			13.1584i			0.528880i	−0.964402	+	0.264440i	$0.914813\pi$
$620$		0			0
$621$		−	8.32906i		−	0.334234i
$622$	1.42521	−	2.07690i	0.0571457	−	0.0832760i
$623$	1.80271			0.0722241
$624$	−12.0992	+	10.9575i	−0.484355	+	0.438650i
$625$		0			0
$626$	21.3048	−	31.0466i	0.851511	−	1.24087i
$627$		−	80.5459i		−	3.21669i
$628$	−35.5597	+	13.7089i	−1.41899	+	0.547045i
$629$		−	3.24514i		−	0.129392i
$630$		0			0
$631$	30.4366			1.21166			0.605830	−	0.795594i	$-0.292841\pi$
$631$	30.4366			1.21166			0.605830	+	0.795594i	$0.292841\pi$
$632$	−27.8974	−	6.63382i	−1.10970	−	0.263879i
$633$	36.8422			1.46435
$634$	−10.6855	−	7.33260i	−0.424375	−	0.291215i
$635$		0			0
$636$	−20.1389	−	52.2385i	−0.798559	−	2.07139i
$637$			10.7630i			0.426445i
$638$	−28.3503	+	41.3137i	−1.12240	+	1.63562i
$639$	−27.1239			−1.07300
$640$		0			0
$641$	22.4237			0.885683			0.442841	−	0.896600i	$-0.353971\pi$
$641$	22.4237			0.885683			0.442841	+	0.896600i	$0.353971\pi$
$642$	−16.1420	+	23.5230i	−0.637072	+	0.928379i
$643$			36.0640i			1.42222i	0.703078	+	0.711112i	$0.251808\pi$
$643$			36.0640i			1.42222i	−0.703078	+	0.711112i	$0.748192\pi$
$644$	−0.683117	−	1.77194i	−0.0269186	−	0.0698244i
$645$		0			0
$646$	4.75385	+	3.26219i	0.187038	+	0.128349i
$647$	2.35270			0.0924942			0.0462471	−	0.998930i	$-0.485274\pi$
$647$	2.35270			0.0924942			0.0462471	+	0.998930i	$0.485274\pi$
$648$	15.1183	+	3.59503i	0.593902	+	0.141226i
$649$	46.8498			1.83902
$650$		0			0
$651$		−	2.36267i		−	0.0926004i
$652$	−31.1926	+	12.0253i	−1.22160	+	0.470949i
$653$		−	13.9239i		−	0.544886i	−0.962172	−	0.272443i	$-0.912168\pi$
$653$		−	13.9239i		−	0.544886i	0.962172	−	0.272443i	$-0.0878317\pi$
$654$	−3.80807	+	5.54934i	−0.148907	+	0.216997i
$655$		0			0
$656$	−12.9947	+	11.7685i	−0.507357	+	0.459481i
$657$	−23.1279			−0.902306
$658$	−2.05668	+	2.99711i	−0.0801777	+	0.116840i
$659$		−	20.8197i		−	0.811022i	−0.914090	−	0.405511i	$-0.867094\pi$
$659$		−	20.8197i		−	0.811022i	0.914090	−	0.405511i	$-0.132906\pi$
$660$		0			0
$661$		−	9.83003i		−	0.382344i	−0.981557	−	0.191172i	$-0.938771\pi$
$661$		−	9.83003i		−	0.382344i	0.981557	−	0.191172i	$-0.0612288\pi$
$662$	9.13519	+	6.26876i	0.355049	+	0.243642i
$663$	2.48569			0.0965364
$664$	−4.26832	+	17.9497i	−0.165643	+	0.696583i
$665$		0			0
$666$	24.2231	+	16.6224i	0.938626	+	0.644105i
$667$			27.2725i			1.05600i
$668$	−8.78020	−	22.7750i	−0.339716	−	0.881193i
$669$		−	5.41443i		−	0.209334i
$670$		0			0
$671$	−60.7650			−2.34581
$672$	−3.96430	+	0.536447i	−0.152926	+	0.0206939i
$673$	−45.7820			−1.76476			−0.882382	−	0.470533i	$-0.844062\pi$
$673$	−45.7820			−1.76476			−0.882382	+	0.470533i	$0.844062\pi$
$674$	−0.509159	+	0.741975i	−0.0196121	+	0.0285798i
$675$		0			0
$676$	−7.61595	−	19.7551i	−0.292921	−	0.759811i
$677$		−	49.9162i		−	1.91844i	−0.282669	−	0.959218i	$-0.591220\pi$
$677$		−	49.9162i		−	1.91844i	0.282669	−	0.959218i	$-0.408780\pi$
$678$	3.40823	+	2.33880i	0.130892	+	0.0898210i
$679$	−1.07474			−0.0412449
$680$		0			0
$681$	8.22853			0.315318
$682$	−17.8490	−	12.2484i	−0.683475	−	0.469015i
$683$		−	14.4414i		−	0.552584i	−0.961074	−	0.276292i	$-0.910894\pi$
$683$		−	14.4414i		−	0.552584i	0.961074	−	0.276292i	$-0.0891056\pi$
$684$	−48.7007	+	18.7750i	−1.86212	+	0.717881i
$685$		0			0
$686$	−3.00051	+	4.37252i	−0.114560	+	0.166944i
$687$	−44.8465			−1.71100
$688$	−32.9310	−	36.3623i	−1.25548	−	1.38630i
$689$	−16.5580			−0.630810
$690$		0			0
$691$		−	20.6371i		−	0.785072i	−0.919737	−	0.392536i	$-0.871598\pi$
$691$		−	20.6371i		−	0.785072i	0.919737	−	0.392536i	$-0.128402\pi$
$692$	4.77149	−	1.83950i	0.181385	−	0.0699272i
$693$		−	4.80975i		−	0.182707i
$694$	27.5191	+	18.8842i	1.04461	+	0.716833i
$695$		0			0
$696$	55.8919	+	13.2907i	2.11858	+	0.503784i
$697$	2.66967			0.101121
$698$	22.3351	+	15.3268i	0.845396	+	0.580128i
$699$		−	20.0536i		−	0.758496i
$700$		0			0
$701$		−	30.0040i		−	1.13323i	−0.823981	−	0.566617i	$-0.808252\pi$
$701$		−	30.0040i		−	1.13323i	0.823981	−	0.566617i	$-0.191748\pi$
$702$	−2.93605	+	4.27859i	−0.110814	+	0.161485i
$703$	35.6586			1.34489
$704$	−16.4988	+	32.7297i	−0.621821	+	1.23355i
$705$		0			0
$706$	17.5851	−	25.6261i	0.661825	−	0.964450i
$707$			0.0972302i			0.00365672i
$708$	−19.3229	−	50.1218i	−0.726198	−	1.88369i
$709$		−	8.10493i		−	0.304387i	−0.988351	−	0.152194i	$-0.951366\pi$
$709$		−	8.10493i		−	0.304387i	0.988351	−	0.152194i	$-0.0486337\pi$
$710$		0			0
$711$	−39.5303			−1.48250
$712$	−18.4244	−	4.38120i	−0.690483	−	0.164192i
$713$	−11.7827			−0.441267
$714$	0.502285	+	0.344678i	0.0187975	+	0.0128993i
$715$		0			0
$716$	−34.2557	+	13.2062i	−1.28020	+	0.493540i
$717$			12.9257i			0.482719i
$718$	−4.50526	+	6.56532i	−0.168135	+	0.245015i
$719$	−38.0224			−1.41800			−0.708998	−	0.705210i	$-0.750852\pi$
$719$	−38.0224			−1.41800			−0.708998	+	0.705210i	$0.750852\pi$
$720$		0			0
$721$	5.12934			0.191027
$722$	−20.6426	+	30.0816i	−0.768237	+	1.11952i
$723$			50.2248i			1.86788i
$724$	16.3101	−	6.28785i	0.606161	−	0.233686i
$725$		0			0
$726$	−30.6015	−	20.9994i	−1.13573	−	0.779361i
$727$	−33.5323			−1.24364			−0.621821	−	0.783159i	$-0.713607\pi$
$727$	−33.5323			−1.24364			−0.621821	+	0.783159i	$0.713607\pi$
$728$	−0.273710	+	1.15104i	−0.0101444	+	0.0426604i
$729$	40.0322			1.48267
$730$		0			0
$731$			7.47038i			0.276302i
$732$	25.0621	+	65.0088i	0.926322	+	2.40280i
$733$			8.77824i			0.324232i	0.986772	+	0.162116i	$0.0518318\pi$
$733$			8.77824i			0.324232i	−0.986772	+	0.162116i	$0.948168\pi$
$734$	4.17264	−	6.08061i	0.154015	−	0.224439i
$735$		0			0
$736$	2.67528	+	19.7701i	0.0986123	+	0.728737i
$737$	18.0240			0.663924
$738$	−13.6747	+	19.9276i	−0.503373	+	0.733544i
$739$		−	10.4760i		−	0.385365i	−0.981261	−	0.192683i	$-0.938281\pi$
$739$		−	10.4760i		−	0.385365i	0.981261	−	0.192683i	$-0.0617187\pi$
$740$		0			0
$741$			27.3136i			1.00339i
$742$	−3.34588	−	2.29601i	−0.122831	−	0.0842892i
$743$	4.29242			0.157474			0.0787368	−	0.996895i	$-0.474911\pi$
$743$	4.29242			0.157474			0.0787368	+	0.996895i	$0.474911\pi$
$744$	−5.74209	+	24.1474i	−0.210515	+	0.885285i
$745$		0			0
$746$	−14.6925	−	10.0823i	−0.537930	−	0.369139i
$747$			25.4346i			0.930602i
$748$	5.20781	−	2.00771i	0.190417	−	0.0734091i
$749$			2.06779i			0.0755554i
$750$		0			0
$751$	54.2895			1.98105			0.990526	−	0.137324i	$-0.0438500\pi$
$751$	54.2895			1.98105			0.990526	+	0.137324i	$0.0438500\pi$
$752$	28.3040	−	25.6331i	1.03214	−	0.934744i
$753$	−78.0118			−2.84291
$754$	9.61377	−	14.0097i	0.350113	−	0.510204i
$755$		0			0
$756$	−1.18658	+	0.457448i	−0.0431554	+	0.0166372i
$757$			15.6468i			0.568691i	0.958722	+	0.284345i	$0.0917763\pi$
$757$			15.6468i			0.568691i	−0.958722	+	0.284345i	$0.908224\pi$
$758$	1.49727	+	1.02745i	0.0543832	+	0.0373188i
$759$	−42.4416			−1.54053
$760$		0			0
$761$	33.5439			1.21597			0.607983	−	0.793950i	$-0.291979\pi$
$761$	33.5439			1.21597			0.607983	+	0.793950i	$0.291979\pi$
$762$	30.0739	+	20.6373i	1.08946	+	0.747611i
$763$			0.487815i			0.0176601i
$764$	15.5228	+	40.2647i	0.561594	+	1.45673i
$765$		0			0
$766$	−14.6947	+	21.4139i	−0.530941	+	0.773717i
$767$	−15.8871			−0.573649
$768$	41.8203	+	4.15190i	1.50906	+	0.149819i
$769$	−12.1137			−0.436832			−0.218416	−	0.975856i	$-0.570089\pi$
$769$	−12.1137			−0.436832			−0.218416	+	0.975856i	$0.570089\pi$
$770$		0			0
$771$		−	34.5917i		−	1.24579i
$772$	−7.12564	−	18.4833i	−0.256457	−	0.665227i
$773$		−	29.0451i		−	1.04468i	−0.852737	−	0.522340i	$-0.825059\pi$
$773$		−	29.0451i		−	1.04468i	0.852737	−	0.522340i	$-0.174941\pi$
$774$	−55.7622	−	38.2651i	−2.00433	−	1.37541i
$775$		0			0
$776$	10.9843	+	2.61199i	0.394312	+	0.0937650i
$777$	3.76764			0.135163
$778$	−23.9407	−	16.4286i	−0.858315	−	0.588993i
$779$			29.3352i			1.05104i
$780$		0			0
$781$			31.8716i			1.14045i
$782$	1.71892	−	2.50492i	0.0614686	−	0.0895756i
$783$	18.2630			0.652665
$784$	20.5391	−	18.6009i	0.733538	−	0.664318i
$785$		0			0
$786$	−10.5204	+	15.3310i	−0.375251	+	0.546837i
$787$		−	29.0437i		−	1.03530i	−0.855593	−	0.517649i	$-0.826807\pi$
$787$		−	29.0437i		−	1.03530i	0.855593	−	0.517649i	$-0.173193\pi$
$788$	−17.5016	+	6.74718i	−0.623468	+	0.240358i
$789$		−	46.5449i		−	1.65704i
$790$		0			0
$791$	0.299601			0.0106526
$792$	−11.6893	+	49.1574i	−0.415362	+	1.74673i
$793$	20.6058			0.731734
$794$	−19.8454	−	13.6183i	−0.704287	−	0.483296i
$795$		0			0
$796$	−12.1479	−	31.5105i	−0.430570	−	1.11686i
$797$		−	40.5313i		−	1.43569i	−0.696201	−	0.717847i	$-0.745128\pi$
$797$		−	40.5313i		−	1.43569i	0.696201	−	0.717847i	$-0.254872\pi$
$798$	−3.78744	+	5.51927i	−0.134074	+	0.195380i
$799$	−5.81486			−0.205715
$800$		0			0
$801$	−26.1072			−0.922452
$802$	6.10197	−	8.89213i	0.215468	−	0.313992i
$803$			27.1762i			0.959026i
$804$	−7.43389	−	19.2828i	−0.262173	−	0.680053i
$805$		0			0
$806$	6.05272	+	4.15350i	0.213198	+	0.146301i
$807$	4.00415			0.140953
$808$	0.236302	−	0.993728i	0.00831309	−	0.0349592i
$809$	52.0674			1.83059			0.915297	−	0.402781i	$-0.131956\pi$
$809$	52.0674			1.83059			0.915297	+	0.402781i	$0.131956\pi$
$810$		0			0
$811$			27.5707i			0.968138i	0.875030	+	0.484069i	$0.160842\pi$
$811$			27.5707i			0.968138i	−0.875030	+	0.484069i	$0.839158\pi$
$812$	3.88531	−	1.49786i	0.136348	−	0.0525646i
$813$			42.4191i			1.48770i
$814$	19.5319	−	28.4630i	0.684594	−	0.997629i
$815$		0			0
$816$	−4.29585	−	4.74346i	−0.150385	−	0.166054i
$817$	−82.0870			−2.87186
$818$	5.90156	−	8.60009i	0.206343	−	0.300695i
$819$			1.63102i			0.0569923i
$820$		0			0
$821$		−	51.8915i		−	1.81103i	−0.424318	−	0.905513i	$-0.639486\pi$
$821$		−	51.8915i		−	1.81103i	0.424318	−	0.905513i	$-0.360514\pi$
$822$	−37.2318	−	25.5492i	−1.29861	−	0.891132i
$823$	−42.8229			−1.49271			−0.746356	−	0.665547i	$-0.768198\pi$
$823$	−42.8229			−1.49271			−0.746356	+	0.665547i	$0.768198\pi$
$824$	−52.4237	−	12.4660i	−1.82627	−	0.434275i
$825$		0			0
$826$	−3.21030	−	2.20298i	−0.111701	−	0.0766514i
$827$			24.7187i			0.859554i	0.902935	+	0.429777i	$0.141408\pi$
$827$			24.7187i			0.859554i	−0.902935	+	0.429777i	$0.858592\pi$
$828$	9.89302	+	25.6616i	0.343806	+	0.891802i
$829$			9.70912i			0.337212i	0.985684	+	0.168606i	$0.0539265\pi$
$829$			9.70912i			0.337212i	−0.985684	+	0.168606i	$0.946073\pi$
$830$		0			0
$831$	−32.4931			−1.12717
$832$	5.59484	−	11.0989i	0.193966	−	0.384784i
$833$	−4.21961			−0.146201
$834$	16.4324	−	23.9463i	0.569008	−	0.829192i
$835$		0			0
$836$	22.0614	+	57.2252i	0.763008	+	1.97917i
$837$			7.89028i			0.272728i
$838$	25.7509	+	17.6708i	0.889549	+	0.610427i
$839$	−15.1090			−0.521620			−0.260810	−	0.965390i	$-0.583990\pi$
$839$	−15.1090			−0.521620			−0.260810	+	0.965390i	$0.583990\pi$
$840$		0			0
$841$	−30.8000			−1.06207
$842$	34.1057	+	23.4041i	1.17536	+	0.806557i
$843$		−	10.6068i		−	0.365319i
$844$	−26.1752	+	10.0910i	−0.900987	+	0.347347i
$845$		0			0
$846$	29.7852	−	43.4047i	1.02404	−	1.49228i
$847$	−2.69003			−0.0924304
$848$	28.6160	+	31.5977i	0.982678	+	1.08507i
$849$	10.8739			0.373192
$850$		0			0
$851$		−	18.7894i		−	0.644092i
$852$	34.0974	−	13.1452i	1.16816	−	0.450347i
$853$		−	15.5755i		−	0.533295i	−0.963794	−	0.266647i	$-0.914084\pi$
$853$		−	15.5755i		−	0.533295i	0.963794	−	0.266647i	$-0.0859159\pi$
$854$	4.16382	+	2.85730i	0.142483	+	0.0977748i
$855$		0			0
$856$	5.02543	−	21.1336i	0.171766	−	0.722330i
$857$	−24.5547			−0.838773			−0.419386	−	0.907808i	$-0.637755\pi$
$857$	−24.5547			−0.838773			−0.419386	+	0.907808i	$0.637755\pi$
$858$	21.8020	+	14.9610i	0.744308	+	0.510759i
$859$			38.2985i			1.30673i	0.757044	+	0.653363i	$0.226643\pi$
$859$			38.2985i			1.30673i	−0.757044	+	0.653363i	$0.773357\pi$
$860$		0			0
$861$			3.09952i			0.105631i
$862$	−5.59340	+	8.15102i	−0.190512	+	0.277625i
$863$	−45.7916			−1.55876			−0.779382	−	0.626549i	$-0.784467\pi$
$863$	−45.7916			−1.55876			−0.779382	+	0.626549i	$0.784467\pi$
$864$	13.2390	−	1.79150i	0.450401	−	0.0609480i
$865$		0			0
$866$	15.3065	−	22.3055i	0.520135	−	0.757970i
$867$		−	43.6780i		−	1.48338i
$868$	0.647131	+	1.67860i	0.0219650	+	0.0569754i
$869$			46.4496i			1.57570i
$870$		0			0
$871$	−6.11207			−0.207100
$872$	1.18556	−	4.98565i	0.0401480	−	0.168835i
$873$	15.5646			0.526783
$874$	27.5249	+	18.8881i	0.931042	+	0.638900i
$875$		0			0
$876$	29.0741	−	11.2086i	0.982324	−	0.378704i
$877$			42.8419i			1.44667i	0.690499	+	0.723334i	$0.257391\pi$
$877$			42.8419i			1.44667i	−0.690499	+	0.723334i	$0.742609\pi$
$878$	−2.23135	+	3.25165i	−0.0753043	+	0.109738i
$879$	−66.3585			−2.23822
$880$		0			0
$881$	26.0361			0.877180			0.438590	−	0.898687i	$-0.355478\pi$
$881$	26.0361			0.877180			0.438590	+	0.898687i	$0.355478\pi$
$882$	21.6139	−	31.4970i	0.727777	−	1.06056i
$883$			19.3468i			0.651072i	0.945530	+	0.325536i	$0.105545\pi$
$883$			19.3468i			0.651072i	−0.945530	+	0.325536i	$0.894455\pi$
$884$	−1.76600	+	0.680827i	−0.0593971	+	0.0228987i
$885$		0			0
$886$	−19.6874	−	13.5099i	−0.661411	−	0.453874i
$887$	26.1028			0.876445			0.438222	−	0.898867i	$-0.355608\pi$
$887$	26.1028			0.876445			0.438222	+	0.898867i	$0.355608\pi$
$888$	−38.5067	−	9.15665i	−1.29220	−	0.307277i
$889$	2.64365			0.0886650
$890$		0			0
$891$		−	25.1722i		−	0.843300i
$892$	1.48300	+	3.84677i	0.0496545	+	0.128799i
$893$		−	63.8957i		−	2.13819i
$894$	35.7398	−	52.0821i	1.19532	−	1.74189i
$895$		0			0
$896$	2.66957	−	1.46694i	0.0891841	−	0.0490071i
$897$	14.3922			0.480542
$898$	−10.5147	+	15.3226i	−0.350880	+	0.511323i
$899$		−	25.8358i		−	0.861672i
$900$		0			0
$901$		−	6.49153i		−	0.216264i
$902$	23.4156	+	16.0683i	0.779656	+	0.535016i
$903$	−8.67321			−0.288626
$904$	−3.06203	−	0.728130i	−0.101841	−	0.0242173i
$905$		0			0
$906$	−40.6755	−	27.9124i	−1.35135	−	0.927327i
$907$			47.0568i			1.56249i	0.624222	+	0.781247i	$0.285416\pi$
$907$			47.0568i			1.56249i	−0.624222	+	0.781247i	$0.714584\pi$
$908$	−5.84610	+	2.25378i	−0.194010	+	0.0747943i
$909$		−	1.40810i		−	0.0467039i
$910$		0			0
$911$	57.6189			1.90900			0.954499	−	0.298214i	$-0.0963909\pi$
$911$	57.6189			1.90900			0.954499	+	0.298214i	$0.0963909\pi$
$912$	52.1227	−	47.2042i	1.72596	−	1.56309i
$913$	29.8866			0.989101
$914$	26.7868	−	39.0353i	0.886029	−	1.29117i
$915$		0			0
$916$	31.8620	−	12.2834i	1.05275	−	0.405854i
$917$			1.34767i			0.0445039i
$918$	−1.67741	−	1.15107i	−0.0553628	−	0.0379911i
$919$	22.6047			0.745661			0.372830	−	0.927900i	$-0.378387\pi$
$919$	22.6047			0.745661			0.372830	+	0.927900i	$0.378387\pi$
$920$		0			0
$921$	−28.0239			−0.923418
$922$	32.1878	+	22.0879i	1.06005	+	0.727426i
$923$		−	10.8079i		−	0.355745i
$924$	2.33097	+	6.04634i	0.0766834	+	0.198910i
$925$		0			0
$926$	11.9408	−	17.4009i	0.392400	−	0.571828i
$927$	−74.2840			−2.43981
$928$	−43.3496	+	5.86605i	−1.42302	+	0.192562i
$929$	22.2533			0.730108			0.365054	−	0.930986i	$-0.381050\pi$
$929$	22.2533			0.730108			0.365054	+	0.930986i	$0.381050\pi$
$930$		0			0
$931$		−	46.3665i		−	1.51960i
$932$	5.49263	+	14.2474i	0.179917	+	0.466689i
$933$			4.67831i			0.153161i
$934$	13.8395	+	9.49696i	0.452843	+	0.310750i
$935$		0			0
$936$	3.96392	−	16.6696i	0.129565	−	0.544862i
$937$	20.8873			0.682358			0.341179	−	0.939998i	$-0.389174\pi$
$937$	20.8873			0.682358			0.341179	+	0.939998i	$0.389174\pi$
$938$	−1.23507	−	0.847529i	−0.0403264	−	0.0276728i
$939$			69.9339i			2.28221i
$940$		0			0
$941$			13.7530i			0.448335i	0.974551	+	0.224168i	$0.0719664\pi$
$941$			13.7530i			0.448335i	−0.974551	+	0.224168i	$0.928034\pi$
$942$	40.0499	−	58.3630i	1.30490	−	1.90157i
$943$	15.4574			0.503364
$944$	27.4565	+	30.3174i	0.893633	+	0.986746i
$945$		0			0
$946$	−44.9630	+	65.5226i	−1.46187	+	2.13032i
$947$		−	31.2715i		−	1.01619i	−0.861302	−	0.508094i	$-0.830350\pi$
$947$		−	31.2715i		−	1.01619i	0.861302	−	0.508094i	$-0.169650\pi$
$948$	49.6936	−	19.1578i	1.61397	−	0.622217i
$949$		−	9.21562i		−	0.299152i
$950$		0			0
$951$	24.0695			0.780508
$952$	−0.451263	−	0.107308i	−0.0146255	−	0.00347786i
$953$	−26.2447			−0.850150			−0.425075	−	0.905158i	$-0.639752\pi$
$953$	−26.2447			−0.850150			−0.425075	+	0.905158i	$0.639752\pi$
$954$	48.4556	+	33.2512i	1.56881	+	1.07655i
$955$		0			0
$956$	−3.54032	−	9.18327i	−0.114502	−	0.297008i
$957$		−	93.0609i		−	3.00823i
$958$	12.3568	−	18.0070i	0.399229	−	0.581780i
$959$	−3.27286			−0.105686
$960$		0			0
$961$	−19.8380			−0.639935
$962$	−6.62340	+	9.65200i	−0.213547	+	0.311193i
$963$		−	29.9461i		−	0.964998i
$964$	−13.7565	−	35.6830i	−0.443066	−	1.14927i
$965$		0			0
$966$	2.90824	+	1.99569i	0.0935711	+	0.0642104i
$967$	−18.5089			−0.595208			−0.297604	−	0.954689i	$-0.596187\pi$
$967$	−18.5089			−0.595208			−0.297604	+	0.954689i	$0.596187\pi$
$968$	27.4931	+	6.53767i	0.883660	+	0.210129i
$969$	−10.7083			−0.343999
$970$		0			0
$971$		−	16.7762i		−	0.538373i	−0.963088	−	0.269187i	$-0.913245\pi$
$971$		−	16.7762i		−	0.538373i	0.963088	−	0.269187i	$-0.0867548\pi$
$972$	−40.1518	+	15.4793i	−1.28787	+	0.496497i
$973$		−	2.10500i		−	0.0674831i
$974$	6.06673	−	8.84078i	0.194390	−	0.283277i
$975$		0			0
$976$	−35.6116	−	39.3221i	−1.13990	−	1.25867i
$977$	11.2815			0.360926			0.180463	−	0.983582i	$-0.442240\pi$
$977$	11.2815			0.360926			0.180463	+	0.983582i	$0.442240\pi$
$978$	35.1314	−	51.1955i	1.12338	−	1.63705i
$979$			30.6769i			0.980438i
$980$		0			0
$981$		−	7.06462i		−	0.225556i
$982$	6.47761	+	4.44507i	0.206709	+	0.141848i
$983$	28.6404			0.913488			0.456744	−	0.889598i	$-0.349016\pi$
$983$	28.6404			0.913488			0.456744	+	0.889598i	$0.349016\pi$
$984$	7.53288	−	31.6782i	0.240140	−	1.00987i
$985$		0			0
$986$	5.49248	+	3.76906i	0.174916	+	0.120031i
$987$		−	6.75113i		−	0.214891i
$988$	−7.48115	−	19.4054i	−0.238007	−	0.617369i
$989$			43.2537i			1.37539i
$990$		0			0
$991$	−17.4805			−0.555287			−0.277643	−	0.960684i	$-0.589553\pi$
$991$	−17.4805			−0.555287			−0.277643	+	0.960684i	$0.589553\pi$
$992$	−2.53435	−	18.7286i	−0.0804657	−	0.594635i
$993$	−20.5774			−0.653005
$994$	1.49867	−	2.18394i	0.0475349	−	0.0692705i
$995$		0			0
$996$	−12.3265	−	31.9738i	−0.390580	−	1.01313i
$997$			17.6990i			0.560533i	0.959922	+	0.280266i	$0.0904228\pi$
$997$			17.6990i			0.560533i	−0.959922	+	0.280266i	$0.909577\pi$
$998$	16.4650	+	11.2986i	0.521190	+	0.357651i
$999$	−12.5823			−0.398086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.29	yes	40
4.3	odd	2		4000.2.d.c.2001.13		40
5.2	odd	4		1000.2.f.d.749.16		20
5.3	odd	4		1000.2.f.c.749.5		20
5.4	even	2	inner	1000.2.d.c.501.12	yes	40
8.3	odd	2		4000.2.d.c.2001.14		40
8.5	even	2	inner	1000.2.d.c.501.30	yes	40
20.3	even	4		4000.2.f.c.3249.20		20
20.7	even	4		4000.2.f.d.3249.1		20
20.19	odd	2		4000.2.d.c.2001.28		40
40.3	even	4		4000.2.f.d.3249.2		20
40.13	odd	4		1000.2.f.d.749.15		20
40.19	odd	2		4000.2.d.c.2001.27		40
40.27	even	4		4000.2.f.c.3249.19		20
40.29	even	2	inner	1000.2.d.c.501.11	✓	40
40.37	odd	4		1000.2.f.c.749.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.11	✓	40	40.29	even	2	inner
1000.2.d.c.501.12	yes	40	5.4	even	2	inner
1000.2.d.c.501.29	yes	40	1.1	even	1	trivial
1000.2.d.c.501.30	yes	40	8.5	even	2	inner
1000.2.f.c.749.5		20	5.3	odd	4
1000.2.f.c.749.6		20	40.37	odd	4
1000.2.f.d.749.15		20	40.13	odd	4
1000.2.f.d.749.16		20	5.2	odd	4
4000.2.d.c.2001.13		40	4.3	odd	2
4000.2.d.c.2001.14		40	8.3	odd	2
4000.2.d.c.2001.27		40	40.19	odd	2
4000.2.d.c.2001.28		40	20.19	odd	2
4000.2.f.c.3249.19		20	40.27	even	4
4000.2.f.c.3249.20		20	20.3	even	4
4000.2.f.d.3249.1		20	20.7	even	4
4000.2.f.d.3249.2		20	40.3	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800179 - 1.16607i) q^{2} +2.62662i q^{3} +(-0.719426 - 1.86613i) q^{4} +(3.06282 + 2.10177i) q^{6} +0.269237 q^{7} +(-2.75170 - 0.654336i) q^{8} -3.89913 q^{9} +O(q^{10})\)	\(q+(0.800179 - 1.16607i) q^{2} +2.62662i q^{3} +(-0.719426 - 1.86613i) q^{4} +(3.06282 + 2.10177i) q^{6} +0.269237 q^{7} +(-2.75170 - 0.654336i) q^{8} -3.89913 q^{9} +4.58163i q^{11} +(4.90160 - 1.88966i) q^{12} -1.55366i q^{13} +(0.215438 - 0.313948i) q^{14} +(-2.96485 + 2.68508i) q^{16} +0.609109 q^{17} +(-3.12001 + 4.54665i) q^{18} +6.69309i q^{19} +0.707183i q^{21} +(5.34249 + 3.66612i) q^{22} +3.52675 q^{23} +(1.71869 - 7.22767i) q^{24} +(-1.81167 - 1.24321i) q^{26} -2.36168i q^{27} +(-0.193696 - 0.502430i) q^{28} +7.73304i q^{29} -3.34096 q^{31} +(0.758569 + 5.60576i) q^{32} -12.0342 q^{33} +(0.487396 - 0.710262i) q^{34} +(2.80514 + 7.27627i) q^{36} -5.32768i q^{37} +(7.80459 + 5.35567i) q^{38} +4.08087 q^{39} +4.38291 q^{41} +(0.824623 + 0.565873i) q^{42} +12.2644i q^{43} +(8.54989 - 3.29614i) q^{44} +(2.82203 - 4.11243i) q^{46} -9.54651 q^{47} +(-7.05268 - 7.78754i) q^{48} -6.92751 q^{49} +1.59990i q^{51} +(-2.89932 + 1.11774i) q^{52} -10.6574i q^{53} +(-2.75388 - 1.88977i) q^{54} +(-0.740859 - 0.176171i) q^{56} -17.5802 q^{57} +(9.01725 + 6.18782i) q^{58} -10.2256i q^{59} +13.2628i q^{61} +(-2.67337 + 3.89579i) q^{62} -1.04979 q^{63} +(7.14369 + 3.60107i) q^{64} +(-9.62951 + 14.0327i) q^{66} -3.93398i q^{67} +(-0.438209 - 1.13667i) q^{68} +9.26343i q^{69} +6.95638 q^{71} +(10.7292 + 2.55134i) q^{72} +5.93156 q^{73} +(-6.21243 - 4.26310i) q^{74} +(12.4901 - 4.81518i) q^{76} +1.23354i q^{77} +(3.26543 - 4.75857i) q^{78} +10.1382 q^{79} -5.49416 q^{81} +(3.50712 - 5.11077i) q^{82} -6.52313i q^{83} +(1.31969 - 0.508766i) q^{84} +(14.3012 + 9.81376i) q^{86} -20.3118 q^{87} +(2.99793 - 12.6073i) q^{88} +6.69564 q^{89} -0.418302i q^{91} +(-2.53724 - 6.58136i) q^{92} -8.77544i q^{93} +(-7.63892 + 11.1319i) q^{94} +(-14.7242 + 1.99247i) q^{96} -3.99182 q^{97} +(-5.54325 + 8.07794i) q^{98} -17.8644i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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