LMFDB - Embedded newform 1050.3.e.e.701.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(701,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.e (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.10
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.e.701.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 - 3.48683i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(3.15796 + 8.42777i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 - 3.48683i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(3.15796 + 8.42777i) q^{9} +2.66621i q^{11} +(-4.93112 - 3.41820i) q^{12} -5.56242 q^{13} -3.74166i q^{14} +4.00000 q^{16} +18.5525i q^{17} +(11.9187 - 4.46603i) q^{18} -0.634999 q^{19} +(6.52326 + 4.52185i) q^{21} +3.77058 q^{22} -15.6144i q^{23} +(-4.83406 + 6.97365i) q^{24} +7.86645i q^{26} +(-6.61774 + 26.1764i) q^{27} -5.29150 q^{28} +43.3517i q^{29} +13.5411 q^{31} -5.65685i q^{32} +(-4.55681 + 6.57369i) q^{33} +26.2372 q^{34} +(-6.31593 - 16.8555i) q^{36} +35.0014 q^{37} +0.898024i q^{38} +(-13.7145 - 9.50672i) q^{39} +15.6116i q^{41} +(6.39486 - 9.22528i) q^{42} -64.4699 q^{43} -5.33241i q^{44} -22.0820 q^{46} +52.5576i q^{47} +(9.86224 + 6.83639i) q^{48} +7.00000 q^{49} +(-31.7081 + 45.7423i) q^{51} +11.1248 q^{52} +51.6056i q^{53} +(37.0191 + 9.35890i) q^{54} +7.48331i q^{56} +(-1.56563 - 1.08528i) q^{57} +61.3086 q^{58} -32.9384i q^{59} -104.197 q^{61} -19.1501i q^{62} +(8.35519 + 22.2978i) q^{63} -8.00000 q^{64} +(9.29660 + 6.44430i) q^{66} +113.588 q^{67} -37.1050i q^{68} +(26.6865 - 38.4981i) q^{69} -36.8746i q^{71} +(-23.8373 + 8.93207i) q^{72} +144.926 q^{73} -49.4995i q^{74} +1.27000 q^{76} +7.05412i q^{77} +(-13.4445 + 19.3952i) q^{78} -57.9487 q^{79} +(-61.0545 + 53.2292i) q^{81} +22.0781 q^{82} +45.0936i q^{83} +(-13.0465 - 9.04370i) q^{84} +91.1742i q^{86} +(-74.0924 + 106.886i) q^{87} -7.54117 q^{88} +80.9733i q^{89} -14.7168 q^{91} +31.2287i q^{92} +(33.3865 + 23.1432i) q^{93} +74.3277 q^{94} +(9.66812 - 13.9473i) q^{96} +96.2255 q^{97} -9.89949i q^{98} +(-22.4702 + 8.41978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 - 44 * q^9	$ 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	2.46556	+	1.70910i	0.821853	+	0.569700i
$3$	2.46556	+	1.70910i	0.821853	+	0.569700i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	2.41703	−	3.48683i	0.402838	−	0.581138i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			2.82843i			0.353553i
$9$	3.15796	+	8.42777i	0.350885	+	0.936419i
$10$		0			0
$11$			2.66621i			0.242382i	0.992629	+	0.121191i	$0.0386714\pi$
$11$			2.66621i			0.242382i	−0.992629	+	0.121191i	$0.961329\pi$
$12$	−4.93112	−	3.41820i	−0.410927	−	0.284850i
$13$	−5.56242			−0.427878			−0.213939	−	0.976847i	$-0.568629\pi$
$13$	−5.56242			−0.427878			−0.213939	+	0.976847i	$0.568629\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$			18.5525i			1.09132i	0.838005	+	0.545662i	$0.183722\pi$
$17$			18.5525i			1.09132i	−0.838005	+	0.545662i	$0.816278\pi$
$18$	11.9187	−	4.46603i	0.662148	−	0.248113i
$19$	−0.634999			−0.0334210			−0.0167105	−	0.999860i	$-0.505319\pi$
$19$	−0.634999			−0.0334210			−0.0167105	+	0.999860i	$0.505319\pi$
$20$		0			0
$21$	6.52326	+	4.52185i	0.310631	+	0.215326i
$22$	3.77058			0.171390
$23$		−	15.6144i		−	0.678885i	−0.940627	−	0.339442i	$-0.889762\pi$
$23$		−	15.6144i		−	0.678885i	0.940627	−	0.339442i	$-0.110238\pi$
$24$	−4.83406	+	6.97365i	−0.201419	+	0.290569i
$25$		0			0
$26$			7.86645i			0.302556i
$27$	−6.61774	+	26.1764i	−0.245101	+	0.969497i
$28$	−5.29150			−0.188982
$29$			43.3517i			1.49489i	0.664325	+	0.747444i	$0.268719\pi$
$29$			43.3517i			1.49489i	−0.664325	+	0.747444i	$0.731281\pi$
$30$		0			0
$31$	13.5411			0.436811			0.218406	−	0.975858i	$-0.429914\pi$
$31$	13.5411			0.436811			0.218406	+	0.975858i	$0.429914\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−4.55681	+	6.57369i	−0.138085	+	0.199203i
$34$	26.2372			0.771683
$35$		0			0
$36$	−6.31593	−	16.8555i	−0.175442	−	0.468209i
$37$	35.0014			0.945984			0.472992	−	0.881067i	$-0.343174\pi$
$37$	35.0014			0.945984			0.472992	+	0.881067i	$0.343174\pi$
$38$			0.898024i			0.0236322i
$39$	−13.7145	−	9.50672i	−0.351653	−	0.243762i
$40$		0			0
$41$			15.6116i			0.380770i	0.981710	+	0.190385i	$0.0609736\pi$
$41$			15.6116i			0.380770i	−0.981710	+	0.190385i	$0.939026\pi$
$42$	6.39486	−	9.22528i	0.152259	−	0.219649i
$43$	−64.4699			−1.49930			−0.749650	−	0.661835i	$-0.769778\pi$
$43$	−64.4699			−1.49930			−0.749650	+	0.661835i	$0.769778\pi$
$44$		−	5.33241i		−	0.121191i
$45$		0			0
$46$	−22.0820			−0.480044
$47$			52.5576i			1.11825i	0.829084	+	0.559124i	$0.188862\pi$
$47$			52.5576i			1.11825i	−0.829084	+	0.559124i	$0.811138\pi$
$48$	9.86224	+	6.83639i	0.205463	+	0.142425i
$49$	7.00000			0.142857
$50$		0			0
$51$	−31.7081	+	45.7423i	−0.621727	+	0.896908i
$52$	11.1248			0.213939
$53$			51.6056i			0.973691i	0.873488	+	0.486846i	$0.161853\pi$
$53$			51.6056i			0.973691i	−0.873488	+	0.486846i	$0.838147\pi$
$54$	37.0191	+	9.35890i	0.685538	+	0.173313i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−1.56563	−	1.08528i	−0.0274672	−	0.0190399i
$58$	61.3086			1.05705
$59$		−	32.9384i		−	0.558277i	−0.960251	−	0.279139i	$-0.909951\pi$
$59$		−	32.9384i		−	0.558277i	0.960251	−	0.279139i	$-0.0900489\pi$
$60$		0			0
$61$	−104.197			−1.70815			−0.854077	−	0.520147i	$-0.825877\pi$
$61$	−104.197			−1.70815			−0.854077	+	0.520147i	$0.825877\pi$
$62$		−	19.1501i		−	0.308872i
$63$	8.35519	+	22.2978i	0.132622	+	0.353933i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	9.29660	+	6.44430i	0.140858	+	0.0976409i
$67$	113.588			1.69535			0.847673	−	0.530519i	$-0.178003\pi$
$67$	113.588			1.69535			0.847673	+	0.530519i	$0.178003\pi$
$68$		−	37.1050i		−	0.545662i
$69$	26.6865	−	38.4981i	0.386760	−	0.557944i
$70$		0			0
$71$		−	36.8746i		−	0.519361i	−0.965695	−	0.259680i	$-0.916383\pi$
$71$		−	36.8746i		−	0.519361i	0.965695	−	0.259680i	$-0.0836172\pi$
$72$	−23.8373	+	8.93207i	−0.331074	+	0.124057i
$73$	144.926			1.98529			0.992645	−	0.121058i	$-0.0386288\pi$
$73$	144.926			1.98529			0.992645	+	0.121058i	$0.0386288\pi$
$74$		−	49.4995i		−	0.668912i
$75$		0			0
$76$	1.27000			0.0167105
$77$			7.05412i			0.0916119i
$78$	−13.4445	+	19.3952i	−0.172366	+	0.248656i
$79$	−57.9487			−0.733528			−0.366764	−	0.930314i	$-0.619534\pi$
$79$	−57.9487			−0.733528			−0.366764	+	0.930314i	$0.619534\pi$
$80$		0			0
$81$	−61.0545	+	53.2292i	−0.753760	+	0.657150i
$82$	22.0781			0.269245
$83$			45.0936i			0.543296i	0.962397	+	0.271648i	$0.0875686\pi$
$83$			45.0936i			0.543296i	−0.962397	+	0.271648i	$0.912431\pi$
$84$	−13.0465	−	9.04370i	−0.155316	−	0.107663i
$85$		0			0
$86$			91.1742i			1.06016i
$87$	−74.0924	+	106.886i	−0.851637	+	1.22858i
$88$	−7.54117			−0.0856951
$89$			80.9733i			0.909813i	0.890539	+	0.454906i	$0.150327\pi$
$89$			80.9733i			0.909813i	−0.890539	+	0.454906i	$0.849673\pi$
$90$		0			0
$91$	−14.7168			−0.161723
$92$			31.2287i			0.339442i
$93$	33.3865	+	23.1432i	0.358995	+	0.248851i
$94$	74.3277			0.790720
$95$		0			0
$96$	9.66812	−	13.9473i	0.100710	−	0.145284i
$97$	96.2255			0.992016			0.496008	−	0.868318i	$-0.334799\pi$
$97$	96.2255			0.992016			0.496008	+	0.868318i	$0.334799\pi$
$98$		−	9.89949i		−	0.101015i
$99$	−22.4702	+	8.41978i	−0.226971	+	0.0850483i
$100$		0			0
$101$		−	91.9696i		−	0.910590i	−0.890341	−	0.455295i	$-0.849534\pi$
$101$		−	91.9696i		−	0.910590i	0.890341	−	0.455295i	$-0.150466\pi$
$102$	64.6894	+	44.8420i	0.634210	+	0.439627i
$103$	−30.6043			−0.297129			−0.148565	−	0.988903i	$-0.547465\pi$
$103$	−30.6043			−0.297129			−0.148565	+	0.988903i	$0.547465\pi$
$104$		−	15.7329i		−	0.151278i
$105$		0			0
$106$	72.9814			0.688504
$107$			190.645i			1.78173i	0.454270	+	0.890864i	$0.349900\pi$
$107$			190.645i			1.78173i	−0.454270	+	0.890864i	$0.650100\pi$
$108$	13.2355	−	52.3529i	0.122551	−	0.484749i
$109$	−73.9965			−0.678867			−0.339433	−	0.940630i	$-0.610235\pi$
$109$	−73.9965			−0.678867			−0.339433	+	0.940630i	$0.610235\pi$
$110$		0			0
$111$	86.2980	+	59.8208i	0.777460	+	0.538927i
$112$	10.5830			0.0944911
$113$			128.861i			1.14037i	0.821518	+	0.570183i	$0.193128\pi$
$113$			128.861i			1.14037i	−0.821518	+	0.570183i	$0.806872\pi$
$114$	−1.53481	+	2.21413i	−0.0134633	+	0.0194222i
$115$		0			0
$116$		−	86.7035i		−	0.747444i
$117$	−17.5659	−	46.8788i	−0.150136	−	0.400673i
$118$	−46.5819			−0.394762
$119$			49.0853i			0.412482i
$120$		0			0
$121$	113.891			0.941251
$122$			147.357i			1.20785i
$123$	−26.6817	+	38.4912i	−0.216924	+	0.312937i
$124$	−27.0823			−0.218406
$125$		0			0
$126$	31.5338	−	11.8160i	0.250268	−	0.0937779i
$127$	95.8035			0.754358			0.377179	−	0.926140i	$-0.376894\pi$
$127$	95.8035			0.754358			0.377179	+	0.926140i	$0.376894\pi$
$128$			11.3137i			0.0883883i
$129$	−158.954	−	110.185i	−1.23220	−	0.854150i
$130$		0			0
$131$		−	148.465i		−	1.13332i	−0.823952	−	0.566660i	$-0.808235\pi$
$131$		−	148.465i		−	1.13332i	0.823952	−	0.566660i	$-0.191765\pi$
$132$	9.11361	−	13.1474i	0.0690425	−	0.0996013i
$133$	−1.68005			−0.0126320
$134$		−	160.638i		−	1.19879i
$135$		0			0
$136$	−52.4744			−0.385842
$137$		−	115.295i		−	0.841572i	−0.907160	−	0.420786i	$-0.861754\pi$
$137$		−	115.295i		−	0.841572i	0.907160	−	0.420786i	$-0.138246\pi$
$138$	−54.4445	−	37.7404i	−0.394526	−	0.273481i
$139$	−95.1005			−0.684176			−0.342088	−	0.939668i	$-0.611134\pi$
$139$	−95.1005			−0.684176			−0.342088	+	0.939668i	$0.611134\pi$
$140$		0			0
$141$	−89.8262	+	129.584i	−0.637065	+	0.919035i
$142$	−52.1486			−0.367244
$143$		−	14.8305i		−	0.103710i
$144$	12.6319	+	33.7111i	0.0877212	+	0.234105i
$145$		0			0
$146$		−	204.957i		−	1.40381i
$147$	17.2589	+	11.9637i	0.117408	+	0.0813857i
$148$	−70.0028			−0.472992
$149$			179.342i			1.20364i	0.798632	+	0.601820i	$0.205558\pi$
$149$			179.342i			1.20364i	−0.798632	+	0.601820i	$0.794442\pi$
$150$		0			0
$151$	45.6621			0.302398			0.151199	−	0.988503i	$-0.451687\pi$
$151$	45.6621			0.302398			0.151199	+	0.988503i	$0.451687\pi$
$152$		−	1.79605i		−	0.0118161i
$153$	−156.356	+	58.5882i	−1.02194	+	0.382929i
$154$	9.97603			0.0647794
$155$		0			0
$156$	27.4289	+	19.0134i	0.175827	+	0.121881i
$157$	−223.977			−1.42661			−0.713303	−	0.700856i	$-0.752802\pi$
$157$	−223.977			−1.42661			−0.713303	+	0.700856i	$0.752802\pi$
$158$			81.9518i			0.518683i
$159$	−88.1991	+	127.237i	−0.554711	+	0.800231i
$160$		0			0
$161$		−	41.3117i		−	0.256594i
$162$	75.2774	+	86.3441i	0.464675	+	0.532989i
$163$	300.309			1.84239			0.921195	−	0.389102i	$-0.127215\pi$
$163$	300.309			1.84239			0.921195	+	0.389102i	$0.127215\pi$
$164$		−	31.2231i		−	0.190385i
$165$		0			0
$166$	63.7719			0.384168
$167$			125.443i			0.751158i	0.926790	+	0.375579i	$0.122556\pi$
$167$			125.443i			0.751158i	−0.926790	+	0.375579i	$0.877444\pi$
$168$	−12.7897	+	18.4506i	−0.0761293	+	0.109825i
$169$	−138.060			−0.816920
$170$		0			0
$171$	−2.00530	−	5.35163i	−0.0117269	−	0.0312961i
$172$	128.940			0.749650
$173$		−	195.635i		−	1.13084i	−0.824804	−	0.565419i	$-0.808714\pi$
$173$		−	195.635i		−	1.13084i	0.824804	−	0.565419i	$-0.191286\pi$
$174$	151.160	+	104.782i	0.868736	+	0.602198i
$175$		0			0
$176$			10.6648i			0.0605956i
$177$	56.2949	−	81.2115i	0.318050	−	0.458822i
$178$	114.514			0.643335
$179$		−	164.110i		−	0.916815i	−0.888742	−	0.458408i	$-0.848420\pi$
$179$		−	164.110i		−	0.916815i	0.888742	−	0.458408i	$-0.151580\pi$
$180$		0			0
$181$	113.029			0.624468			0.312234	−	0.950005i	$-0.398923\pi$
$181$	113.029			0.624468			0.312234	+	0.950005i	$0.398923\pi$
$182$			20.8127i			0.114355i
$183$	−256.905	−	178.084i	−1.40385	−	0.973135i
$184$	44.1641			0.240022
$185$		0			0
$186$	32.7294	−	47.2156i	0.175964	−	0.253847i
$187$	−49.4648			−0.264518
$188$		−	105.115i		−	0.559124i
$189$	−17.5089	+	69.2563i	−0.0926397	+	0.366436i
$190$		0			0
$191$		−	196.398i		−	1.02826i	−0.857711	−	0.514132i	$-0.828114\pi$
$191$		−	196.398i		−	1.02826i	0.857711	−	0.514132i	$-0.171886\pi$
$192$	−19.7245	−	13.6728i	−0.102732	−	0.0712124i
$193$	282.304			1.46272			0.731358	−	0.681994i	$-0.238887\pi$
$193$	282.304			1.46272			0.731358	+	0.681994i	$0.238887\pi$
$194$		−	136.083i		−	0.701461i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$		−	286.761i		−	1.45564i	−0.685767	−	0.727821i	$-0.740533\pi$
$197$		−	286.761i		−	1.45564i	0.685767	−	0.727821i	$-0.259467\pi$
$198$	11.9074	+	31.7776i	0.0601382	+	0.160493i
$199$	74.9133			0.376449			0.188224	−	0.982126i	$-0.439727\pi$
$199$	74.9133			0.376449			0.188224	+	0.982126i	$0.439727\pi$
$200$		0			0
$201$	280.058	+	194.133i	1.39333	+	0.965838i
$202$	−130.065			−0.643884
$203$			114.698i			0.565014i
$204$	63.4162	−	91.4847i	0.310864	−	0.448454i
$205$		0			0
$206$			43.2810i			0.210102i
$207$	131.594	−	49.3096i	0.635720	−	0.238210i
$208$	−22.2497			−0.106970
$209$		−	1.69304i		−	0.00810066i
$210$		0			0
$211$	−136.746			−0.648083			−0.324042	−	0.946043i	$-0.605042\pi$
$211$	−136.746			−0.648083			−0.324042	+	0.946043i	$0.605042\pi$
$212$		−	103.211i		−	0.486846i
$213$	63.0224	−	90.9166i	0.295880	−	0.426838i
$214$	269.613			1.25987
$215$		0			0
$216$	−74.0381	−	18.7178i	−0.342769	−	0.0866565i
$217$	35.8265			0.165099
$218$			104.647i			0.480031i
$219$	357.324	+	247.693i	1.63162	+	1.13102i
$220$		0			0
$221$		−	103.197i		−	0.466954i
$222$	84.5994	−	122.044i	0.381079	−	0.549747i
$223$	−25.8662			−0.115992			−0.0579959	−	0.998317i	$-0.518471\pi$
$223$	−25.8662			−0.115992			−0.0579959	+	0.998317i	$0.518471\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	182.238			0.806361
$227$			24.3393i			0.107222i	0.998562	+	0.0536109i	$0.0170730\pi$
$227$			24.3393i			0.107222i	−0.998562	+	0.0536109i	$0.982927\pi$
$228$	3.13126	+	2.17055i	0.0137336	+	0.00951997i
$229$	241.018			1.05248			0.526239	−	0.850336i	$-0.323602\pi$
$229$	241.018			1.05248			0.526239	+	0.850336i	$0.323602\pi$
$230$		0			0
$231$	−12.0562	+	17.3923i	−0.0521913	+	0.0752915i
$232$	−122.617			−0.528523
$233$		−	24.9582i		−	0.107117i	−0.998565	−	0.0535584i	$-0.982944\pi$
$233$		−	24.9582i		−	0.107117i	0.998565	−	0.0535584i	$-0.0170563\pi$
$234$	−66.2966	+	24.8420i	−0.283319	+	0.106162i
$235$		0			0
$236$			65.8767i			0.279139i
$237$	−142.876	−	99.0401i	−0.602852	−	0.417891i
$238$	69.4172			0.291669
$239$		−	240.780i		−	1.00745i	−0.863864	−	0.503725i	$-0.831963\pi$
$239$		−	240.780i		−	1.00745i	0.863864	−	0.503725i	$-0.168037\pi$
$240$		0			0
$241$	−147.382			−0.611543			−0.305771	−	0.952105i	$-0.598914\pi$
$241$	−147.382			−0.611543			−0.305771	+	0.952105i	$0.598914\pi$
$242$		−	161.067i		−	0.665565i
$243$	−241.507	+	26.8914i	−0.993858	+	0.110664i
$244$	208.395			0.854077
$245$		0			0
$246$	54.4348	+	37.7336i	0.221280	+	0.153389i
$247$	3.53213			0.0143001
$248$			38.3001i			0.154436i
$249$	−77.0693	+	111.181i	−0.309515	+	0.446509i
$250$		0			0
$251$			387.525i			1.54393i	0.635668	+	0.771963i	$0.280725\pi$
$251$			387.525i			1.54393i	−0.635668	+	0.771963i	$0.719275\pi$
$252$	−16.7104	−	44.5956i	−0.0663110	−	0.176966i
$253$	41.6311			0.164550
$254$		−	135.487i		−	0.533412i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	11.2525i		−	0.0437839i	−0.999760	−	0.0218919i	$-0.993031\pi$
$257$		−	11.2525i		−	0.0437839i	0.999760	−	0.0218919i	$-0.00696897\pi$
$258$	−155.826	+	224.795i	−0.603975	+	0.871300i
$259$	92.6050			0.357548
$260$		0			0
$261$	−365.358	+	136.903i	−1.39984	+	0.524533i
$262$	−209.961			−0.801378
$263$		−	308.658i		−	1.17361i	−0.809730	−	0.586803i	$-0.800386\pi$
$263$		−	308.658i		−	1.17361i	0.809730	−	0.586803i	$-0.199614\pi$
$264$	−18.5932	−	12.8886i	−0.0704288	−	0.0488204i
$265$		0			0
$266$			2.37595i			0.00893214i
$267$	−138.391	+	199.644i	−0.518320	+	0.747732i
$268$	−227.176			−0.847673
$269$		−	198.926i		−	0.739503i	−0.929131	−	0.369751i	$-0.879443\pi$
$269$		−	198.926i		−	0.739503i	0.929131	−	0.369751i	$-0.120557\pi$
$270$		0			0
$271$	−176.341			−0.650706			−0.325353	−	0.945593i	$-0.605483\pi$
$271$	−176.341			−0.650706			−0.325353	+	0.945593i	$0.605483\pi$
$272$			74.2101i			0.272831i
$273$	−36.2851	−	25.1524i	−0.132912	−	0.0921334i
$274$	−163.052			−0.595082
$275$		0			0
$276$	−53.3729	+	76.9962i	−0.193380	+	0.278972i
$277$	433.093			1.56351			0.781757	−	0.623583i	$-0.214324\pi$
$277$	433.093			1.56351			0.781757	+	0.623583i	$0.214324\pi$
$278$			134.492i			0.483786i
$279$	42.7624	+	114.122i	0.153270	+	0.409038i
$280$		0			0
$281$		−	281.134i		−	1.00048i	−0.865887	−	0.500239i	$-0.833246\pi$
$281$		−	281.134i		−	1.00048i	0.865887	−	0.500239i	$-0.166754\pi$
$282$	183.259	+	127.033i	0.649856	+	0.450473i
$283$	−113.795			−0.402101			−0.201050	−	0.979581i	$-0.564435\pi$
$283$	−113.795			−0.402101			−0.201050	+	0.979581i	$0.564435\pi$
$284$			73.7492i			0.259680i
$285$		0			0
$286$	−20.9736			−0.0733341
$287$			41.3043i			0.143917i
$288$	47.6747	−	17.8641i	0.165537	−	0.0620283i
$289$	−55.1959			−0.190989
$290$		0			0
$291$	237.250	+	164.459i	0.815291	+	0.565151i
$292$	−289.852			−0.992645
$293$		−	355.330i		−	1.21273i	−0.795187	−	0.606365i	$-0.792627\pi$
$293$		−	355.330i		−	1.21273i	0.795187	−	0.606365i	$-0.207373\pi$
$294$	16.9192	−	24.4078i	0.0575483	−	0.0830197i
$295$		0			0
$296$			98.9989i			0.334456i
$297$	−69.7917	−	17.6443i	−0.234989	−	0.0594083i
$298$	253.628			0.851102
$299$			86.8535i			0.290480i
$300$		0			0
$301$	−170.571			−0.566682
$302$		−	64.5759i		−	0.213828i
$303$	157.185	−	226.756i	0.518763	−	0.748371i
$304$	−2.54000			−0.00835525
$305$		0			0
$306$	82.8562	+	221.121i	0.270772	+	0.722618i
$307$	−404.490			−1.31756			−0.658778	−	0.752337i	$-0.728926\pi$
$307$	−404.490			−1.31756			−0.658778	+	0.752337i	$0.728926\pi$
$308$		−	14.1082i		−	0.0458059i
$309$	−75.4567	−	52.3058i	−0.244196	−	0.169274i
$310$		0			0
$311$		−	530.330i		−	1.70524i	−0.522530	−	0.852621i	$-0.675012\pi$
$311$		−	530.330i		−	1.70524i	0.522530	−	0.852621i	$-0.324988\pi$
$312$	26.8891	−	38.7904i	0.0861829	−	0.124328i
$313$	−561.172			−1.79288			−0.896440	−	0.443165i	$-0.853856\pi$
$313$	−561.172			−1.79288			−0.896440	+	0.443165i	$0.853856\pi$
$314$			316.751i			1.00876i
$315$		0			0
$316$	115.897			0.366764
$317$		−	264.560i		−	0.834574i	−0.908775	−	0.417287i	$-0.862981\pi$
$317$		−	264.560i		−	0.834574i	0.908775	−	0.417287i	$-0.137019\pi$
$318$	179.940	+	124.732i	0.565849	+	0.392240i
$319$	−115.585			−0.362334
$320$		0			0
$321$	−325.831	+	470.046i	−1.01505	+	1.46432i
$322$	−58.4236			−0.181440
$323$		−	11.7808i		−	0.0364732i
$324$	122.109	−	106.458i	0.376880	−	0.328575i
$325$		0			0
$326$		−	424.702i		−	1.30277i
$327$	−182.443	−	126.467i	−0.557929	−	0.386750i
$328$	−44.1561			−0.134622
$329$			139.054i			0.422658i
$330$		0			0
$331$	540.436			1.63274			0.816369	−	0.577530i	$-0.195984\pi$
$331$	540.436			1.63274			0.816369	+	0.577530i	$0.195984\pi$
$332$		−	90.1871i		−	0.271648i
$333$	110.533	+	294.984i	0.331931	+	0.885837i
$334$	177.404			0.531149
$335$		0			0
$336$	26.0930	+	18.0874i	0.0776578	+	0.0538315i
$337$	−444.323			−1.31847			−0.659233	−	0.751939i	$-0.729119\pi$
$337$	−444.323			−1.31847			−0.659233	+	0.751939i	$0.729119\pi$
$338$			195.246i			0.577650i
$339$	−220.237	+	317.715i	−0.649666	+	0.937214i
$340$		0			0
$341$			36.1035i			0.105875i
$342$	−7.56834	+	2.83593i	−0.0221297	+	0.00829219i
$343$	18.5203			0.0539949
$344$		−	182.348i		−	0.530082i
$345$		0			0
$346$	−276.670			−0.799624
$347$		−	253.956i		−	0.731861i	−0.930642	−	0.365931i	$-0.880751\pi$
$347$		−	253.956i		−	0.731861i	0.930642	−	0.365931i	$-0.119249\pi$
$348$	148.185	−	213.773i	0.425818	−	0.614289i
$349$	−415.627			−1.19091			−0.595454	−	0.803389i	$-0.703028\pi$
$349$	−415.627			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$350$		0			0
$351$	36.8106	−	145.604i	0.104874	−	0.414827i
$352$	15.0823			0.0428475
$353$			278.041i			0.787652i	0.919185	+	0.393826i	$0.128849\pi$
$353$			278.041i			0.787652i	−0.919185	+	0.393826i	$0.871151\pi$
$354$	−114.850	−	79.6130i	−0.324436	−	0.224895i
$355$		0			0
$356$		−	161.947i		−	0.454906i
$357$	−83.8917	+	121.023i	−0.234991	+	0.339000i
$358$	−232.086			−0.648286
$359$		−	81.6150i		−	0.227340i	−0.993519	−	0.113670i	$-0.963739\pi$
$359$		−	81.6150i		−	0.227340i	0.993519	−	0.113670i	$-0.0362606\pi$
$360$		0			0
$361$	−360.597			−0.998883
$362$		−	159.847i		−	0.441565i
$363$	280.806	+	194.652i	0.773570	+	0.536230i
$364$	29.4335			0.0808614
$365$		0			0
$366$	−251.848	+	363.318i	−0.688110	+	0.992673i
$367$	514.501			1.40191			0.700955	−	0.713206i	$-0.252758\pi$
$367$	514.501			1.40191			0.700955	+	0.713206i	$0.252758\pi$
$368$		−	62.4574i		−	0.169721i
$369$	−131.571	+	49.3007i	−0.356560	+	0.133606i
$370$		0			0
$371$			136.536i			0.368021i
$372$	−66.7730	−	46.2863i	−0.179497	−	0.124426i
$373$	80.1359			0.214842			0.107421	−	0.994214i	$-0.465741\pi$
$373$	80.1359			0.214842			0.107421	+	0.994214i	$0.465741\pi$
$374$			69.9538i			0.187042i
$375$		0			0
$376$	−148.655			−0.395360
$377$		−	241.140i		−	0.639630i
$378$	97.9432	+	24.7613i	0.259109	+	0.0655061i
$379$	−706.877			−1.86511			−0.932556	−	0.361026i	$-0.882427\pi$
$379$	−706.877			−1.86511			−0.932556	+	0.361026i	$0.882427\pi$
$380$		0			0
$381$	236.209	+	163.738i	0.619972	+	0.429758i
$382$	−277.749			−0.727092
$383$		−	49.2802i		−	0.128669i	−0.997928	−	0.0643345i	$-0.979508\pi$
$383$		−	49.2802i		−	0.128669i	0.997928	−	0.0643345i	$-0.0204924\pi$
$384$	−19.3362	+	27.8946i	−0.0503548	+	0.0726422i
$385$		0			0
$386$		−	399.238i		−	1.03430i
$387$	−203.594	−	543.337i	−0.526081	−	1.40397i
$388$	−192.451			−0.496008
$389$			2.68340i			0.00689821i	0.999994	+	0.00344911i	$0.00109789\pi$
$389$			2.68340i			0.00689821i	−0.999994	+	0.00344911i	$0.998902\pi$
$390$		0			0
$391$	289.686			0.740884
$392$			19.7990i			0.0505076i
$393$	253.741	−	366.049i	0.645652	−	0.931423i
$394$	−405.542			−1.02929
$395$		0			0
$396$	44.9403	−	16.8396i	0.113486	−	0.0425241i
$397$	372.015			0.937065			0.468532	−	0.883446i	$-0.344783\pi$
$397$	372.015			0.937065			0.468532	+	0.883446i	$0.344783\pi$
$398$		−	105.943i		−	0.266190i
$399$	−4.14226	−	2.87137i	−0.0103816	−	0.00719642i
$400$		0			0
$401$		−	119.122i		−	0.297062i	−0.988908	−	0.148531i	$-0.952545\pi$
$401$		−	119.122i		−	0.297062i	0.988908	−	0.148531i	$-0.0474545\pi$
$402$	274.546	−	396.062i	0.682950	−	0.985230i
$403$	−75.3215			−0.186902
$404$			183.939i			0.455295i
$405$		0			0
$406$	162.207			0.399525
$407$			93.3209i			0.229290i
$408$	−129.379	−	89.6840i	−0.317105	−	0.219814i
$409$	−198.033			−0.484189			−0.242095	−	0.970253i	$-0.577834\pi$
$409$	−198.033			−0.484189			−0.242095	+	0.970253i	$0.577834\pi$
$410$		0			0
$411$	197.051	−	284.268i	0.479443	−	0.691649i
$412$	61.2086			0.148565
$413$		−	87.1467i		−	0.211009i
$414$	−69.7342	−	186.102i	−0.168440	−	0.449522i
$415$		0			0
$416$			31.4658i			0.0756389i
$417$	−234.476	−	162.536i	−0.562292	−	0.389775i
$418$	−2.39432			−0.00572803
$419$			229.736i			0.548295i	0.961688	+	0.274148i	$0.0883957\pi$
$419$			229.736i			0.548295i	−0.961688	+	0.274148i	$0.911604\pi$
$420$		0			0
$421$	−590.500			−1.40261			−0.701306	−	0.712860i	$-0.747399\pi$
$421$	−590.500			−1.40261			−0.701306	+	0.712860i	$0.747399\pi$
$422$			193.387i			0.458264i
$423$	−442.944	+	165.975i	−1.04715	+	0.392376i
$424$	−145.963			−0.344252
$425$		0			0
$426$	−128.575	−	89.1271i	−0.301820	−	0.209219i
$427$	−275.680			−0.645622
$428$		−	381.290i		−	0.890864i
$429$	25.3469	−	36.5656i	0.0590836	−	0.0852345i
$430$		0			0
$431$			414.879i			0.962597i	0.876557	+	0.481298i	$0.159835\pi$
$431$			414.879i			0.962597i	−0.876557	+	0.481298i	$0.840165\pi$
$432$	−26.4710	+	104.706i	−0.0612754	+	0.242374i
$433$	−219.764			−0.507538			−0.253769	−	0.967265i	$-0.581670\pi$
$433$	−219.764			−0.507538			−0.253769	+	0.967265i	$0.581670\pi$
$434$		−	50.6663i		−	0.116743i
$435$		0			0
$436$	147.993			0.339433
$437$			9.91510i			0.0226890i
$438$	350.291	−	505.333i	0.799751	−	1.15373i
$439$	638.375			1.45416			0.727079	−	0.686554i	$-0.240877\pi$
$439$	638.375			1.45416			0.727079	+	0.686554i	$0.240877\pi$
$440$		0			0
$441$	22.1057	+	58.9944i	0.0501264	+	0.133774i
$442$	−145.942			−0.330186
$443$			299.160i			0.675305i	0.941271	+	0.337652i	$0.109633\pi$
$443$			299.160i			0.675305i	−0.941271	+	0.337652i	$0.890367\pi$
$444$	−172.596	−	119.642i	−0.388730	−	0.269463i
$445$		0			0
$446$			36.5803i			0.0820185i
$447$	−306.514	+	442.179i	−0.685713	+	0.989216i
$448$	−21.1660			−0.0472456
$449$		−	580.653i		−	1.29321i	−0.762823	−	0.646607i	$-0.776187\pi$
$449$		−	580.653i		−	1.29321i	0.762823	−	0.646607i	$-0.223813\pi$
$450$		0			0
$451$	−41.6236			−0.0922918
$452$		−	257.723i		−	0.570183i
$453$	112.583	+	78.0410i	0.248527	+	0.172276i
$454$	34.4210			0.0758172
$455$		0			0
$456$	3.06962	−	4.42826i	0.00673163	−	0.00971111i
$457$	563.314			1.23264			0.616318	−	0.787498i	$-0.288624\pi$
$457$	563.314			1.23264			0.616318	+	0.787498i	$0.288624\pi$
$458$		−	340.850i		−	0.744215i
$459$	−485.639	−	122.776i	−1.05804	−	0.267485i
$460$		0			0
$461$		−	138.227i		−	0.299842i	−0.988698	−	0.149921i	$-0.952098\pi$
$461$		−	138.227i		−	0.299842i	0.988698	−	0.149921i	$-0.0479020\pi$
$462$	24.5965	+	17.0500i	0.0532391	+	0.0369048i
$463$	154.802			0.334346			0.167173	−	0.985928i	$-0.446536\pi$
$463$	154.802			0.334346			0.167173	+	0.985928i	$0.446536\pi$
$464$			173.407i			0.373722i
$465$		0			0
$466$	−35.2963			−0.0757431
$467$		−	462.873i		−	0.991162i	−0.868562	−	0.495581i	$-0.834955\pi$
$467$		−	462.873i		−	0.991162i	0.868562	−	0.495581i	$-0.165045\pi$
$468$	35.1318	+	93.7575i	0.0750680	+	0.200337i
$469$	300.526			0.640781
$470$		0			0
$471$	−552.229	−	382.799i	−1.17246	−	0.812737i
$472$	93.1637			0.197381
$473$		−	171.890i		−	0.363404i
$474$	−140.064	+	202.057i	−0.295493	+	0.426281i
$475$		0			0
$476$		−	98.1707i		−	0.206241i
$477$	−434.920	+	162.969i	−0.911782	+	0.341653i
$478$	−340.515			−0.712374
$479$		−	836.942i		−	1.74727i	−0.486582	−	0.873635i	$-0.661757\pi$
$479$		−	836.942i		−	1.74727i	0.486582	−	0.873635i	$-0.338243\pi$
$480$		0			0
$481$	−194.692			−0.404766
$482$			208.429i			0.432426i
$483$	70.6058	−	101.856i	0.146182	−	0.210883i
$484$	−227.783			−0.470625
$485$		0			0
$486$	38.0302	+	341.543i	0.0782515	+	0.702764i
$487$	−212.042			−0.435405			−0.217703	−	0.976015i	$-0.569856\pi$
$487$	−212.042			−0.435405			−0.217703	+	0.976015i	$0.569856\pi$
$488$		−	294.715i		−	0.603924i
$489$	740.431	+	513.258i	1.51417	+	1.04961i
$490$		0			0
$491$			79.1998i			0.161303i	0.996742	+	0.0806516i	$0.0257001\pi$
$491$			79.1998i			0.161303i	−0.996742	+	0.0806516i	$0.974300\pi$
$492$	53.3634	−	76.9824i	0.108462	−	0.156468i
$493$	−804.284			−1.63141
$494$		−	4.99519i		−	0.0101117i
$495$		0			0
$496$	54.1646			0.109203
$497$		−	97.5611i		−	0.196300i
$498$	157.233	+	108.992i	0.315730	+	0.218860i
$499$	259.432			0.519905			0.259952	−	0.965621i	$-0.416293\pi$
$499$	259.432			0.519905			0.259952	+	0.965621i	$0.416293\pi$
$500$		0			0
$501$	−214.395	+	309.288i	−0.427934	+	0.617341i
$502$	548.044			1.09172
$503$			175.890i			0.349683i	0.984597	+	0.174841i	$0.0559412\pi$
$503$			175.890i			0.349683i	−0.984597	+	0.174841i	$0.944059\pi$
$504$	−63.0676	+	23.6320i	−0.125134	+	0.0468890i
$505$		0			0
$506$		−	58.8752i		−	0.116354i
$507$	−340.394	−	235.957i	−0.671388	−	0.465399i
$508$	−191.607			−0.377179
$509$			577.094i			1.13378i	0.823794	+	0.566890i	$0.191853\pi$
$509$			577.094i			1.13378i	−0.823794	+	0.566890i	$0.808147\pi$
$510$		0			0
$511$	383.439			0.750369
$512$		−	22.6274i		−	0.0441942i
$513$	4.20226	−	16.6220i	0.00819154	−	0.0324016i
$514$	−15.9134			−0.0309599
$515$		0			0
$516$	317.909	+	220.371i	0.616102	+	0.427075i
$517$	−140.129			−0.271043
$518$		−	130.963i		−	0.252825i
$519$	334.360	−	482.350i	0.644238	−	0.929383i
$520$		0			0
$521$			198.309i			0.380631i	0.981723	+	0.190316i	$0.0609512\pi$
$521$			198.309i			0.380631i	−0.981723	+	0.190316i	$0.939049\pi$
$522$	193.610	+	516.695i	0.370901	+	0.989837i
$523$	307.722			0.588378			0.294189	−	0.955747i	$-0.404951\pi$
$523$	307.722			0.588378			0.294189	+	0.955747i	$0.404951\pi$
$524$			296.930i			0.566660i
$525$		0			0
$526$	−436.509			−0.829864
$527$			251.222i			0.476703i
$528$	−18.2272	+	26.2947i	−0.0345213	+	0.0498007i
$529$	285.192			0.539115
$530$		0			0
$531$	277.597	−	104.018i	0.522781	−	0.195891i
$532$	3.36010			0.00631598
$533$		−	86.8380i		−	0.162923i
$534$	282.340	+	195.715i	0.528726	+	0.366507i
$535$		0			0
$536$			321.276i			0.599395i
$537$	280.480	−	404.623i	0.522309	−	0.753487i
$538$	−281.324			−0.522907
$539$			18.6634i			0.0346260i
$540$		0			0
$541$	229.692			0.424569			0.212284	−	0.977208i	$-0.431910\pi$
$541$	229.692			0.424569			0.212284	+	0.977208i	$0.431910\pi$
$542$			249.384i			0.460118i
$543$	278.679	+	193.177i	0.513221	+	0.355759i
$544$	104.949			0.192921
$545$		0			0
$546$	−35.5709	+	51.3148i	−0.0651482	+	0.0939832i
$547$	296.031			0.541191			0.270596	−	0.962693i	$-0.412779\pi$
$547$	296.031			0.541191			0.270596	+	0.962693i	$0.412779\pi$
$548$			230.591i			0.420786i
$549$	−329.052	−	878.151i	−0.599365	−	1.59955i
$550$		0			0
$551$		−	27.5283i		−	0.0499606i
$552$	108.889	+	75.4807i	0.197263	+	0.136740i
$553$	−153.318			−0.277247
$554$		−	612.487i		−	1.10557i
$555$		0			0
$556$	190.201			0.342088
$557$			659.047i			1.18321i	0.806228	+	0.591604i	$0.201505\pi$
$557$			659.047i			1.18321i	−0.806228	+	0.591604i	$0.798495\pi$
$558$	161.392	−	60.4752i	0.289234	−	0.108379i
$559$	358.608			0.641518
$560$		0			0
$561$	−121.958	−	84.5403i	−0.217395	−	0.150696i
$562$	−397.584			−0.707444
$563$			1041.64i			1.85016i	0.379774	+	0.925079i	$0.376002\pi$
$563$			1041.64i			1.85016i	−0.379774	+	0.925079i	$0.623998\pi$
$564$	179.652	−	259.168i	0.318533	−	0.459518i
$565$		0			0
$566$			160.930i			0.284328i
$567$	−161.535	+	140.831i	−0.284894	+	0.248379i
$568$	104.297			0.183622
$569$			143.782i			0.252692i	0.991986	+	0.126346i	$0.0403250\pi$
$569$			143.782i			0.252692i	−0.991986	+	0.126346i	$0.959675\pi$
$570$		0			0
$571$	198.901			0.348337			0.174169	−	0.984716i	$-0.444276\pi$
$571$	198.901			0.348337			0.174169	+	0.984716i	$0.444276\pi$
$572$			29.6611i			0.0518551i
$573$	335.664	−	484.232i	0.585801	−	0.845082i
$574$	58.4131			0.101765
$575$		0			0
$576$	−25.2637	−	67.4221i	−0.0438606	−	0.117052i
$577$	55.7825			0.0966767			0.0483384	−	0.998831i	$-0.484607\pi$
$577$	55.7825			0.0966767			0.0483384	+	0.998831i	$0.484607\pi$
$578$			78.0588i			0.135050i
$579$	696.037	+	482.486i	1.20214	+	0.833308i
$580$		0			0
$581$			119.306i			0.205347i
$582$	232.580	−	335.522i	0.399622	−	0.576498i
$583$	−137.591			−0.236005
$584$			409.913i			0.701906i
$585$		0			0
$586$	−502.512			−0.857529
$587$		−	679.045i		−	1.15681i	−0.815751	−	0.578403i	$-0.803676\pi$
$587$		−	679.045i		−	1.15681i	0.815751	−	0.578403i	$-0.196324\pi$
$588$	−34.5178	−	23.9274i	−0.0587038	−	0.0406928i
$589$	−8.59862			−0.0145987
$590$		0			0
$591$	490.104	−	707.027i	0.829278	−	1.19632i
$592$	140.006			0.236496
$593$			794.933i			1.34053i	0.742123	+	0.670264i	$0.233819\pi$
$593$			794.933i			1.34053i	−0.742123	+	0.670264i	$0.766181\pi$
$594$	−24.9527	+	98.7004i	−0.0420080	+	0.166162i
$595$		0			0
$596$		−	358.685i		−	0.601820i
$597$	184.703	+	128.034i	0.309386	+	0.214463i
$598$	122.829			0.205400
$599$		−	525.925i		−	0.878004i	−0.898486	−	0.439002i	$-0.855332\pi$
$599$		−	525.925i		−	0.878004i	0.898486	−	0.439002i	$-0.144668\pi$
$600$		0			0
$601$	169.552			0.282116			0.141058	−	0.990001i	$-0.454950\pi$
$601$	169.552			0.282116			0.141058	+	0.990001i	$0.454950\pi$
$602$			241.224i			0.400705i
$603$	358.707	+	957.295i	0.594871	+	1.58755i
$604$	−91.3242			−0.151199
$605$		0			0
$606$	−320.682	−	222.293i	−0.529178	−	0.366821i
$607$	29.1399			0.0480064			0.0240032	−	0.999712i	$-0.492359\pi$
$607$	29.1399			0.0480064			0.0240032	+	0.999712i	$0.492359\pi$
$608$			3.59210i			0.00590806i
$609$	−196.030	+	282.794i	−0.321888	+	0.464359i
$610$		0			0
$611$		−	292.348i		−	0.478474i
$612$	312.713	−	117.176i	0.510968	−	0.191465i
$613$	−167.118			−0.272623			−0.136311	−	0.990666i	$-0.543525\pi$
$613$	−167.118			−0.272623			−0.136311	+	0.990666i	$0.543525\pi$
$614$			572.035i			0.931653i
$615$		0			0
$616$	−19.9521			−0.0323897
$617$			872.471i			1.41405i	0.707187	+	0.707027i	$0.249964\pi$
$617$			872.471i			1.41405i	−0.707187	+	0.707027i	$0.750036\pi$
$618$	−73.9715	+	106.712i	−0.119695	+	0.172673i
$619$	852.170			1.37669			0.688344	−	0.725384i	$-0.258338\pi$
$619$	852.170			1.37669			0.688344	+	0.725384i	$0.258338\pi$
$620$		0			0
$621$	408.728	+	103.332i	0.658177	+	0.166396i
$622$	−750.000			−1.20579
$623$			214.235i			0.343877i
$624$	−54.8579	−	38.0269i	−0.0879133	−	0.0609405i
$625$		0			0
$626$			793.616i			1.26776i
$627$	2.89357	−	4.17429i	0.00461494	−	0.00665755i
$628$	447.954			0.713303
$629$			649.364i			1.03238i
$630$		0			0
$631$	550.448			0.872343			0.436171	−	0.899864i	$-0.356334\pi$
$631$	550.448			0.872343			0.436171	+	0.899864i	$0.356334\pi$
$632$		−	163.904i		−	0.259341i
$633$	−337.154	−	233.712i	−0.532629	−	0.369213i
$634$	−374.144			−0.590133
$635$		0			0
$636$	176.398	−	254.473i	0.277356	−	0.400115i
$637$	−38.9369			−0.0611255
$638$			163.461i			0.256209i
$639$	310.771	−	116.449i	0.486339	−	0.182236i
$640$		0			0
$641$		−	56.3780i		−	0.0879532i	−0.999033	−	0.0439766i	$-0.985997\pi$
$641$		−	56.3780i		−	0.0879532i	0.999033	−	0.0439766i	$-0.0140027\pi$
$642$	664.746	+	460.795i	1.03543	+	0.717749i
$643$	934.856			1.45390			0.726948	−	0.686692i	$-0.240938\pi$
$643$	934.856			1.45390			0.726948	+	0.686692i	$0.240938\pi$
$644$			82.6234i			0.128297i
$645$		0			0
$646$	−16.6606			−0.0257904
$647$			523.120i			0.808532i	0.914641	+	0.404266i	$0.132473\pi$
$647$			523.120i			0.808532i	−0.914641	+	0.404266i	$0.867527\pi$
$648$	−150.555	−	172.688i	−0.232338	−	0.266494i
$649$	87.8204			0.135316
$650$		0			0
$651$	88.3324	+	61.2310i	0.135687	+	0.0940569i
$652$	−600.619			−0.921195
$653$		−	629.201i		−	0.963554i	−0.876294	−	0.481777i	$-0.839992\pi$
$653$		−	629.201i		−	0.963554i	0.876294	−	0.481777i	$-0.160008\pi$
$654$	−178.852	+	258.013i	−0.273474	+	0.394515i
$655$		0			0
$656$			62.4462i			0.0951924i
$657$	457.672	+	1221.40i	0.696608	+	1.85906i
$658$	196.653			0.298864
$659$		−	1205.86i		−	1.82983i	−0.403644	−	0.914916i	$-0.632257\pi$
$659$		−	1205.86i		−	1.82983i	0.403644	−	0.914916i	$-0.367743\pi$
$660$		0			0
$661$	421.451			0.637596			0.318798	−	0.947823i	$-0.396721\pi$
$661$	421.451			0.637596			0.318798	+	0.947823i	$0.396721\pi$
$662$		−	764.292i		−	1.15452i
$663$	176.374	−	254.438i	0.266024	−	0.383768i
$664$	−127.544			−0.192084
$665$		0			0
$666$	417.170	−	156.317i	0.626381	−	0.234711i
$667$	676.909			1.01486
$668$		−	250.887i		−	0.375579i
$669$	−63.7745	−	44.2078i	−0.0953281	−	0.0660804i
$670$		0			0
$671$		−	277.812i		−	0.414026i
$672$	25.5794	−	36.9011i	0.0380647	−	0.0549124i
$673$	208.482			0.309779			0.154890	−	0.987932i	$-0.450498\pi$
$673$	208.482			0.309779			0.154890	+	0.987932i	$0.450498\pi$
$674$			628.368i			0.932297i
$675$		0			0
$676$	276.119			0.408460
$677$			1253.11i			1.85097i	0.378784	+	0.925485i	$0.376342\pi$
$677$			1253.11i			1.85097i	−0.378784	+	0.925485i	$0.623658\pi$
$678$	449.317	+	311.462i	0.662710	+	0.459383i
$679$	254.589			0.374947
$680$		0			0
$681$	−41.5983	+	60.0101i	−0.0610842	+	0.0881205i
$682$	51.0580			0.0748651
$683$		−	982.114i		−	1.43794i	−0.695041	−	0.718971i	$-0.744614\pi$
$683$		−	982.114i		−	1.43794i	0.695041	−	0.718971i	$-0.255386\pi$
$684$	4.01061	+	10.7033i	0.00586346	+	0.0156480i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	594.243	+	411.923i	0.864983	+	0.599597i
$688$	−257.880			−0.374825
$689$		−	287.052i		−	0.416621i
$690$		0			0
$691$	204.605			0.296099			0.148050	−	0.988980i	$-0.452700\pi$
$691$	204.605			0.296099			0.148050	+	0.988980i	$0.452700\pi$
$692$			391.270i			0.565419i
$693$	−59.4504	+	22.2766i	−0.0857871	+	0.0321452i
$694$	−359.148			−0.517504
$695$		0			0
$696$	−302.320	−	209.565i	−0.434368	−	0.301099i
$697$	−289.634			−0.415543
$698$			587.785i			0.842099i
$699$	42.6561	−	61.5360i	0.0610244	−	0.0880343i
$700$		0			0
$701$		−	330.503i		−	0.471473i	−0.971817	−	0.235736i	$-0.924250\pi$
$701$		−	330.503i		−	0.471473i	0.971817	−	0.235736i	$-0.0757502\pi$
$702$	−205.915	−	52.0581i	−0.293327	−	0.0741568i
$703$	−22.2259			−0.0316157
$704$		−	21.3296i		−	0.0302978i
$705$		0			0
$706$	393.210			0.556954
$707$		−	243.329i		−	0.344171i
$708$	−112.590	+	162.423i	−0.159025	+	0.229411i
$709$	−265.328			−0.374229			−0.187114	−	0.982338i	$-0.559914\pi$
$709$	−265.328			−0.374229			−0.187114	+	0.982338i	$0.559914\pi$
$710$		0			0
$711$	−183.000	−	488.378i	−0.257384	−	0.686889i
$712$	−229.027			−0.321667
$713$		−	211.436i		−	0.296544i
$714$	171.152	+	118.641i	0.239709	+	0.166164i
$715$		0			0
$716$			328.220i			0.458408i
$717$	411.517	−	593.658i	0.573943	−	0.827975i
$718$	−115.421			−0.160754
$719$			994.084i			1.38259i	0.722572	+	0.691296i	$0.242960\pi$
$719$			994.084i			1.38259i	−0.722572	+	0.691296i	$0.757040\pi$
$720$		0			0
$721$	−80.9713			−0.112304
$722$			509.961i			0.706317i
$723$	−363.379	−	251.890i	−0.502598	−	0.348396i
$724$	−226.057			−0.312234
$725$		0			0
$726$	275.279	−	397.119i	0.379172	−	0.546996i
$727$	1244.89			1.71236			0.856182	−	0.516674i	$-0.172830\pi$
$727$	1244.89			1.71236			0.856182	+	0.516674i	$0.172830\pi$
$728$		−	41.6253i		−	0.0571776i
$729$	−641.411	−	346.458i	−0.879851	−	0.475251i
$730$		0			0
$731$		−	1196.08i		−	1.63622i
$732$	513.810	+	356.167i	0.701926	+	0.486567i
$733$	822.707			1.12238			0.561192	−	0.827686i	$-0.310343\pi$
$733$	822.707			1.12238			0.561192	+	0.827686i	$0.310343\pi$
$734$		−	727.614i		−	0.991300i
$735$		0			0
$736$	−88.3281			−0.120011
$737$			302.849i			0.410922i
$738$	69.7217	+	186.069i	0.0944739	+	0.252126i
$739$	550.154			0.744458			0.372229	−	0.928141i	$-0.378594\pi$
$739$	550.154			0.744458			0.372229	+	0.928141i	$0.378594\pi$
$740$		0			0
$741$	8.70868	+	6.03676i	0.0117526	+	0.00814677i
$742$	193.091			0.260230
$743$		−	356.858i		−	0.480293i	−0.970737	−	0.240147i	$-0.922805\pi$
$743$		−	356.858i		−	0.480293i	0.970737	−	0.240147i	$-0.0771955\pi$
$744$	−65.4587	+	94.4313i	−0.0879821	+	0.126924i
$745$		0			0
$746$		−	113.329i		−	0.151916i
$747$	−380.038	+	142.404i	−0.508752	+	0.190634i
$748$	98.9296			0.132259
$749$			504.399i			0.673430i
$750$		0			0
$751$	1027.14			1.36770			0.683850	−	0.729623i	$-0.260304\pi$
$751$	1027.14			1.36770			0.683850	+	0.729623i	$0.260304\pi$
$752$			210.231i			0.279562i
$753$	−662.319	+	955.467i	−0.879574	+	1.26888i
$754$	−341.024			−0.452287
$755$		0			0
$756$	35.0178	−	138.513i	0.0463198	−	0.183218i
$757$	799.336			1.05593			0.527963	−	0.849267i	$-0.322956\pi$
$757$	799.336			1.05593			0.527963	+	0.849267i	$0.322956\pi$
$758$			999.675i			1.31883i
$759$	102.644	+	71.1516i	0.135236	+	0.0937439i
$760$		0			0
$761$			799.993i			1.05124i	0.850720	+	0.525619i	$0.176166\pi$
$761$			799.993i			1.05124i	−0.850720	+	0.525619i	$0.823834\pi$
$762$	231.560	−	334.050i	0.303884	−	0.438386i
$763$	−195.776			−0.256588
$764$			392.797i			0.514132i
$765$		0			0
$766$	−69.6927			−0.0909827
$767$			183.217i			0.238875i
$768$	39.4489	+	27.3456i	0.0513658	+	0.0356062i
$769$	1066.44			1.38679			0.693393	−	0.720560i	$-0.256115\pi$
$769$	1066.44			1.38679			0.693393	+	0.720560i	$0.256115\pi$
$770$		0			0
$771$	19.2315	−	27.7436i	0.0249436	−	0.0359839i
$772$	−564.608			−0.731358
$773$			10.9234i			0.0141311i	0.999975	+	0.00706557i	$0.00224906\pi$
$773$			10.9234i			0.0141311i	−0.999975	+	0.00706557i	$0.997751\pi$
$774$	−768.395	+	287.925i	−0.992758	+	0.371996i
$775$		0			0
$776$			272.167i			0.350731i
$777$	228.323	+	158.271i	0.293852	+	0.203695i
$778$	3.79491			0.00487777
$779$		−	9.91332i		−	0.0127257i
$780$		0			0
$781$	98.3153			0.125884
$782$		−	409.677i		−	0.523884i
$783$	−1134.79	−	286.891i	−1.44929	−	0.366399i
$784$	28.0000			0.0357143
$785$		0			0
$786$	−517.672	−	358.844i	−0.658615	−	0.456545i
$787$	−741.962			−0.942772			−0.471386	−	0.881927i	$-0.656246\pi$
$787$	−741.962			−0.942772			−0.471386	+	0.881927i	$0.656246\pi$
$788$			573.523i			0.727821i
$789$	527.527	−	761.015i	0.668602	−	0.964531i
$790$		0			0
$791$			340.935i			0.431018i
$792$	−23.8147	−	63.5552i	−0.0300691	−	0.0802465i
$793$	579.589			0.730882
$794$		−	526.108i		−	0.662605i
$795$		0			0
$796$	−149.827			−0.188224
$797$		−	805.498i		−	1.01066i	−0.862925	−	0.505331i	$-0.831370\pi$
$797$		−	805.498i		−	1.01066i	0.862925	−	0.505331i	$-0.168630\pi$
$798$	−4.06073	+	5.85804i	−0.00508864	+	0.00734091i
$799$	−975.077			−1.22037
$800$		0			0
$801$	−682.424	+	255.711i	−0.851965	+	0.319239i
$802$	−168.464			−0.210055
$803$			386.403i			0.481199i
$804$	−560.117	−	388.267i	−0.696663	−	0.482919i
$805$		0			0
$806$			106.521i			0.132160i
$807$	339.985	−	490.464i	0.421294	−	0.607762i
$808$	260.129			0.321942
$809$			968.340i			1.19696i	0.801138	+	0.598480i	$0.204228\pi$
$809$			968.340i			1.19696i	−0.801138	+	0.598480i	$0.795772\pi$
$810$		0			0
$811$	−542.257			−0.668627			−0.334314	−	0.942462i	$-0.608504\pi$
$811$	−542.257			−0.668627			−0.334314	+	0.942462i	$0.608504\pi$
$812$		−	229.396i		−	0.282507i
$813$	−434.780	−	301.385i	−0.534784	−	0.370707i
$814$	131.976			0.162132
$815$		0			0
$816$	−126.832	+	182.969i	−0.155432	+	0.224227i
$817$	40.9383			0.0501081
$818$			280.062i			0.342374i
$819$	−46.4750	−	124.030i	−0.0567461	−	0.151440i
$820$		0			0
$821$			1034.06i			1.25951i	0.776793	+	0.629756i	$0.216845\pi$
$821$			1034.06i			1.25951i	−0.776793	+	0.629756i	$0.783155\pi$
$822$	−402.015	−	278.673i	−0.489070	−	0.339018i
$823$	−352.261			−0.428021			−0.214010	−	0.976831i	$-0.568653\pi$
$823$	−352.261			−0.428021			−0.214010	+	0.976831i	$0.568653\pi$
$824$		−	86.5620i		−	0.105051i
$825$		0			0
$826$	−123.244			−0.149206
$827$		−	1125.16i		−	1.36054i	−0.732964	−	0.680268i	$-0.761864\pi$
$827$		−	1125.16i		−	1.36054i	0.732964	−	0.680268i	$-0.238136\pi$
$828$	−263.188	+	98.6191i	−0.317860	+	0.119105i
$829$	−1107.76			−1.33626			−0.668128	−	0.744046i	$-0.732904\pi$
$829$	−1107.76			−1.33626			−0.668128	+	0.744046i	$0.732904\pi$
$830$		0			0
$831$	1067.82	+	740.200i	1.28498	+	0.890733i
$832$	44.4993			0.0534848
$833$			129.868i			0.155904i
$834$	−229.861	+	331.599i	−0.275612	+	0.397601i
$835$		0			0
$836$			3.38608i			0.00405033i
$837$	−89.6118	+	354.459i	−0.107063	+	0.423487i
$838$	324.895			0.387703
$839$		−	13.3680i		−	0.0159333i	−0.999968	−	0.00796664i	$-0.997464\pi$
$839$		−	13.3680i		−	0.0159333i	0.999968	−	0.00796664i	$-0.00253589\pi$
$840$		0			0
$841$	−1038.37			−1.23469
$842$			835.093i			0.991797i
$843$	480.486	−	693.153i	0.569972	−	0.822246i
$844$	273.491			0.324042
$845$		0			0
$846$	234.724	+	626.417i	0.277452	+	0.740445i
$847$	301.328			0.355759
$848$			206.423i			0.243423i
$849$	−280.567	−	194.486i	−0.330468	−	0.229077i
$850$		0			0
$851$		−	546.524i		−	0.642214i
$852$	−126.045	+	181.833i	−0.147940	+	0.213419i
$853$	498.127			0.583971			0.291985	−	0.956423i	$-0.405684\pi$
$853$	498.127			0.583971			0.291985	+	0.956423i	$0.405684\pi$
$854$			389.871i			0.456523i
$855$		0			0
$856$	−539.225			−0.629936
$857$			1519.40i			1.77293i	0.462799	+	0.886463i	$0.346845\pi$
$857$			1519.40i			1.77293i	−0.462799	+	0.886463i	$0.653155\pi$
$858$	−51.7115	−	35.8459i	−0.0602699	−	0.0417784i
$859$	−964.144			−1.12240			−0.561201	−	0.827679i	$-0.689661\pi$
$859$	−964.144			−1.12240			−0.561201	+	0.827679i	$0.689661\pi$
$860$		0			0
$861$	−70.5931	+	101.838i	−0.0819897	+	0.118279i
$862$	586.728			0.680659
$863$		−	1169.35i		−	1.35498i	−0.735532	−	0.677490i	$-0.763068\pi$
$863$		−	1169.35i		−	1.35498i	0.735532	−	0.677490i	$-0.236932\pi$
$864$	148.076	+	37.4356i	0.171385	+	0.0433282i
$865$		0			0
$866$			310.793i			0.358884i
$867$	−136.089	−	94.3353i	−0.156965	−	0.108807i
$868$	−71.6530			−0.0825495
$869$		−	154.503i		−	0.177794i
$870$		0			0
$871$	−631.825			−0.725402
$872$		−	209.294i		−	0.240016i
$873$	303.877	+	810.966i	0.348083	+	0.928942i
$874$	14.0221			0.0160436
$875$		0			0
$876$	−714.648	−	495.386i	−0.815809	−	0.565510i
$877$	−937.994			−1.06955			−0.534774	−	0.844995i	$-0.679603\pi$
$877$	−937.994			−1.06955			−0.534774	+	0.844995i	$0.679603\pi$
$878$		−	902.799i		−	1.02824i
$879$	607.294	−	876.087i	0.690892	−	0.996686i
$880$		0			0
$881$			274.915i			0.312049i	0.987753	+	0.156024i	$0.0498679\pi$
$881$			274.915i			0.312049i	−0.987753	+	0.156024i	$0.950132\pi$
$882$	83.4306	−	31.2622i	0.0945926	−	0.0354447i
$883$	1155.73			1.30886			0.654432	−	0.756121i	$-0.272908\pi$
$883$	1155.73			1.30886			0.654432	+	0.756121i	$0.272908\pi$
$884$			206.394i			0.233477i
$885$		0			0
$886$	423.076			0.477512
$887$			887.696i			1.00079i	0.865799	+	0.500393i	$0.166811\pi$
$887$			887.696i			1.00079i	−0.865799	+	0.500393i	$0.833189\pi$
$888$	−169.199	+	244.088i	−0.190539	+	0.274873i
$889$	253.472			0.285121
$890$		0			0
$891$	−141.920	−	162.784i	−0.159282	−	0.182698i
$892$	51.7323			0.0579959
$893$		−	33.3741i		−	0.0373730i
$894$	625.336	+	433.476i	0.699481	+	0.484873i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	−148.441	+	214.143i	−0.165486	+	0.238732i
$898$	−821.168			−0.914441
$899$			587.032i			0.652983i
$900$		0			0
$901$	−957.414			−1.06261
$902$			58.8647i			0.0652601i
$903$	−420.554	−	291.523i	−0.465729	−	0.322838i
$904$	−364.475			−0.403180
$905$		0			0
$906$	110.367	−	159.216i	0.121818	−	0.175735i
$907$	326.166			0.359610			0.179805	−	0.983702i	$-0.442453\pi$
$907$	326.166			0.359610			0.179805	+	0.983702i	$0.442453\pi$
$908$		−	48.6787i		−	0.0536109i
$909$	775.098	−	290.437i	0.852693	−	0.319512i
$910$		0			0
$911$			455.102i			0.499563i	0.968302	+	0.249782i	$0.0803588\pi$
$911$			455.102i			0.499563i	−0.968302	+	0.249782i	$0.919641\pi$
$912$	−6.26251	−	4.34110i	−0.00686679	−	0.00475998i
$913$	−120.229			−0.131685
$914$		−	796.647i		−	0.871605i
$915$		0			0
$916$	−482.035			−0.526239
$917$		−	392.801i		−	0.428355i
$918$	−173.631	+	686.797i	−0.189141	+	0.748145i
$919$	1354.04			1.47338			0.736690	−	0.676230i	$-0.236388\pi$
$919$	1354.04			1.47338			0.736690	+	0.676230i	$0.236388\pi$
$920$		0			0
$921$	−997.294	−	691.313i	−1.08284	−	0.750611i
$922$	−195.483			−0.212021
$923$			205.112i			0.222223i
$924$	24.1124	−	34.7847i	0.0260956	−	0.0376458i
$925$		0			0
$926$		−	218.923i		−	0.236418i
$927$	−96.6472	−	257.926i	−0.104258	−	0.278237i
$928$	245.234			0.264261
$929$		−	1705.50i		−	1.83585i	−0.396759	−	0.917923i	$-0.629865\pi$
$929$		−	1705.50i		−	1.83585i	0.396759	−	0.917923i	$-0.370135\pi$
$930$		0			0
$931$	−4.44499			−0.00477443
$932$			49.9165i			0.0535584i
$933$	906.386	−	1307.56i	0.971475	−	1.40146i
$934$	−654.601			−0.700857
$935$		0			0
$936$	132.593	−	49.6839i	0.141659	−	0.0530811i
$937$	445.015			0.474936			0.237468	−	0.971395i	$-0.423683\pi$
$937$	445.015			0.474936			0.237468	+	0.971395i	$0.423683\pi$
$938$		−	425.008i		−	0.453100i
$939$	−1383.60	−	959.098i	−1.47348	−	1.02140i
$940$		0			0
$941$			1110.66i			1.18030i	0.807294	+	0.590150i	$0.200931\pi$
$941$			1110.66i			1.18030i	−0.807294	+	0.590150i	$0.799069\pi$
$942$	−541.359	+	780.969i	−0.574692	+	0.829054i
$943$	243.764			0.258499
$944$		−	131.753i		−	0.139569i
$945$		0			0
$946$	−243.089			−0.256965
$947$		−	32.4631i		−	0.0342799i	−0.999853	−	0.0171400i	$-0.994544\pi$
$947$		−	32.4631i		−	0.0342799i	0.999853	−	0.0171400i	$-0.00545609\pi$
$948$	285.752	+	198.080i	0.301426	+	0.208945i
$949$	−806.140			−0.849463
$950$		0			0
$951$	452.159	−	652.288i	0.475456	−	0.685897i
$952$	−138.834			−0.145834
$953$			458.990i			0.481626i	0.970572	+	0.240813i	$0.0774141\pi$
$953$			458.990i			0.481626i	−0.970572	+	0.240813i	$0.922586\pi$
$954$	230.473	+	615.070i	0.241585	+	0.644728i
$955$		0			0
$956$			481.561i			0.503725i
$957$	−284.981	−	197.546i	−0.297785	−	0.206422i
$958$	−1183.61			−1.23551
$959$		−	305.043i		−	0.318084i
$960$		0			0
$961$	−777.637			−0.809196
$962$			275.337i			0.286213i
$963$	−1606.71	+	602.050i	−1.66844	+	0.625182i
$964$	294.764			0.305771
$965$		0			0
$966$	−144.047	−	99.8516i	−0.149117	−	0.103366i
$967$	899.118			0.929802			0.464901	−	0.885363i	$-0.346090\pi$
$967$	899.118			0.929802			0.464901	+	0.885363i	$0.346090\pi$
$968$			322.133i			0.332782i
$969$	20.1346	−	29.0463i	0.0207787	−	0.0299756i
$970$		0			0
$971$			1201.62i			1.23750i	0.785587	+	0.618752i	$0.212361\pi$
$971$			1201.62i			1.23750i	−0.785587	+	0.618752i	$0.787639\pi$
$972$	483.015	−	53.7829i	0.496929	−	0.0553322i
$973$	−251.612			−0.258594
$974$			299.873i			0.307878i
$975$		0			0
$976$	−416.790			−0.427039
$977$		−	227.188i		−	0.232536i	−0.993218	−	0.116268i	$-0.962907\pi$
$977$		−	227.188i		−	0.232536i	0.993218	−	0.116268i	$-0.0370932\pi$
$978$	725.857	−	1047.13i	0.742185	−	1.07068i
$979$	−215.891			−0.220522
$980$		0			0
$981$	−233.678	−	623.625i	−0.238204	−	0.635704i
$982$	112.005			0.114059
$983$		−	510.695i		−	0.519527i	−0.965672	−	0.259763i	$-0.916355\pi$
$983$		−	510.695i		−	0.519527i	0.965672	−	0.259763i	$-0.0836446\pi$
$984$	−108.870	−	75.4672i	−0.110640	−	0.0766943i
$985$		0			0
$986$			1137.43i			1.15358i
$987$	−237.658	+	342.847i	−0.240788	+	0.347363i
$988$	−7.06426			−0.00715006
$989$			1006.66i			1.01785i
$990$		0			0
$991$	1161.49			1.17204			0.586019	−	0.810297i	$-0.300694\pi$
$991$	1161.49			1.17204			0.586019	+	0.810297i	$0.300694\pi$
$992$		−	76.6003i		−	0.0772180i
$993$	1332.48	+	923.659i	1.34187	+	0.930170i
$994$	−137.972			−0.138805
$995$		0			0
$996$	154.139	−	222.362i	0.154758	−	0.223255i
$997$	−506.932			−0.508457			−0.254229	−	0.967144i	$-0.581822\pi$
$997$	−506.932			−0.508457			−0.254229	+	0.967144i	$0.581822\pi$
$998$		−	366.893i		−	0.367628i
$999$	−231.630	+	916.212i	−0.231862	+	0.917129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.e.e.701.10		24
3.2	odd	2	inner	1050.3.e.e.701.12		24
5.2	odd	4		210.3.c.a.29.19	yes	24
5.3	odd	4		210.3.c.a.29.6	yes	24
5.4	even	2	inner	1050.3.e.e.701.11		24
15.2	even	4		210.3.c.a.29.5	✓	24
15.8	even	4		210.3.c.a.29.20	yes	24
15.14	odd	2	inner	1050.3.e.e.701.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.5	✓	24	15.2	even	4
210.3.c.a.29.6	yes	24	5.3	odd	4
210.3.c.a.29.19	yes	24	5.2	odd	4
210.3.c.a.29.20	yes	24	15.8	even	4
1050.3.e.e.701.9		24	15.14	odd	2	inner
1050.3.e.e.701.10		24	1.1	even	1	trivial
1050.3.e.e.701.11		24	5.4	even	2	inner
1050.3.e.e.701.12		24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 - 3.48683i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(3.15796 + 8.42777i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 - 3.48683i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(3.15796 + 8.42777i) q^{9} +2.66621i q^{11} +(-4.93112 - 3.41820i) q^{12} -5.56242 q^{13} -3.74166i q^{14} +4.00000 q^{16} +18.5525i q^{17} +(11.9187 - 4.46603i) q^{18} -0.634999 q^{19} +(6.52326 + 4.52185i) q^{21} +3.77058 q^{22} -15.6144i q^{23} +(-4.83406 + 6.97365i) q^{24} +7.86645i q^{26} +(-6.61774 + 26.1764i) q^{27} -5.29150 q^{28} +43.3517i q^{29} +13.5411 q^{31} -5.65685i q^{32} +(-4.55681 + 6.57369i) q^{33} +26.2372 q^{34} +(-6.31593 - 16.8555i) q^{36} +35.0014 q^{37} +0.898024i q^{38} +(-13.7145 - 9.50672i) q^{39} +15.6116i q^{41} +(6.39486 - 9.22528i) q^{42} -64.4699 q^{43} -5.33241i q^{44} -22.0820 q^{46} +52.5576i q^{47} +(9.86224 + 6.83639i) q^{48} +7.00000 q^{49} +(-31.7081 + 45.7423i) q^{51} +11.1248 q^{52} +51.6056i q^{53} +(37.0191 + 9.35890i) q^{54} +7.48331i q^{56} +(-1.56563 - 1.08528i) q^{57} +61.3086 q^{58} -32.9384i q^{59} -104.197 q^{61} -19.1501i q^{62} +(8.35519 + 22.2978i) q^{63} -8.00000 q^{64} +(9.29660 + 6.44430i) q^{66} +113.588 q^{67} -37.1050i q^{68} +(26.6865 - 38.4981i) q^{69} -36.8746i q^{71} +(-23.8373 + 8.93207i) q^{72} +144.926 q^{73} -49.4995i q^{74} +1.27000 q^{76} +7.05412i q^{77} +(-13.4445 + 19.3952i) q^{78} -57.9487 q^{79} +(-61.0545 + 53.2292i) q^{81} +22.0781 q^{82} +45.0936i q^{83} +(-13.0465 - 9.04370i) q^{84} +91.1742i q^{86} +(-74.0924 + 106.886i) q^{87} -7.54117 q^{88} +80.9733i q^{89} -14.7168 q^{91} +31.2287i q^{92} +(33.3865 + 23.1432i) q^{93} +74.3277 q^{94} +(9.66812 - 13.9473i) q^{96} +96.2255 q^{97} -9.89949i q^{98} +(-22.4702 + 8.41978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 - 44 * q^9	\( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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