LMFDB - Embedded newform 294.3.b.e.197.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(197,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("294.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.b (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:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 11x^{2} - 10x + 3 $ x^4 - 2x^3 + 11x^2 - 10*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.4
Root			$0.500000 + 3.07253i$ of defining polynomial
Character	$\chi$	$=$	294.197
Dual form			294.3.b.e.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(1.84521 - 2.36542i) q^{3} -2.00000 q^{4} +0.488198i q^{5} +(3.34521 + 2.60952i) q^{6} -2.82843i q^{8} +(-2.19042 - 8.72938i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(1.84521 - 2.36542i) q^{3} -2.00000 q^{4} +0.488198i q^{5} +(3.34521 + 2.60952i) q^{6} -2.82843i q^{8} +(-2.19042 - 8.72938i) q^{9} -0.690416 q^{10} -15.1689i q^{11} +(-3.69042 + 4.73084i) q^{12} +17.3808 q^{13} +(1.15479 + 0.900826i) q^{15} +4.00000 q^{16} -0.488198i q^{17} +(12.3452 - 3.09772i) q^{18} -13.0712 q^{19} -0.976395i q^{20} +21.4521 q^{22} -6.68363i q^{23} +(-6.69042 - 5.21904i) q^{24} +24.7617 q^{25} +24.5802i q^{26} +(-24.6904 - 10.9263i) q^{27} -47.3084i q^{29} +(-1.27396 + 1.63312i) q^{30} +28.4521 q^{31} +5.65685i q^{32} +(-35.8808 - 27.9898i) q^{33} +0.690416 q^{34} +(4.38083 + 17.4588i) q^{36} -1.00000 q^{37} -18.4855i q^{38} +(32.0712 - 41.1130i) q^{39} +1.38083 q^{40} -28.3850i q^{41} -2.14249 q^{43} +30.3378i q^{44} +(4.26166 - 1.06936i) q^{45} +9.45208 q^{46} +73.5895i q^{47} +(7.38083 - 9.46168i) q^{48} +35.0183i q^{50} +(-1.15479 - 0.900826i) q^{51} -34.7617 q^{52} +60.8616i q^{53} +(15.4521 - 34.9175i) q^{54} +7.40543 q^{55} +(-24.1192 + 30.9190i) q^{57} +66.9042 q^{58} +100.998i q^{59} +(-2.30958 - 1.80165i) q^{60} +34.2383 q^{61} +40.2373i q^{62} -8.00000 q^{64} +8.48528i q^{65} +(39.5835 - 50.7432i) q^{66} -99.9754 q^{67} +0.976395i q^{68} +(-15.8096 - 12.3327i) q^{69} -82.9000i q^{71} +(-24.6904 + 6.19543i) q^{72} +51.7617 q^{73} -1.41421i q^{74} +(45.6904 - 58.5717i) q^{75} +26.1425 q^{76} +(58.1425 + 45.3556i) q^{78} -66.7371 q^{79} +1.95279i q^{80} +(-71.4042 + 38.2419i) q^{81} +40.1425 q^{82} +88.7584i q^{83} +0.238337 q^{85} -3.02994i q^{86} +(-111.904 - 87.2938i) q^{87} -42.9042 q^{88} -58.5369i q^{89} +(1.51230 + 6.02690i) q^{90} +13.3673i q^{92} +(52.5000 - 67.3011i) q^{93} -104.071 q^{94} -6.38135i q^{95} +(13.3808 + 10.4381i) q^{96} -25.0958 q^{97} +(-132.415 + 33.2262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9	$ 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9} + 16 q^{10} + 4 q^{12} + 32 q^{13} + 14 q^{15} + 16 q^{16} + 40 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} + 24 q^{25} - 80 q^{27} - 52 q^{30} + 20 q^{31} - 106 q^{33} - 16 q^{34} - 20 q^{36} - 4 q^{37} + 72 q^{39} - 32 q^{40} + 104 q^{43} - 58 q^{45} - 56 q^{46} - 8 q^{48} - 14 q^{51} - 64 q^{52} - 32 q^{54} + 236 q^{55} - 134 q^{57} + 80 q^{58} - 28 q^{60} + 212 q^{61} - 32 q^{64} + 224 q^{66} - 156 q^{67} - 82 q^{69} - 80 q^{72} + 132 q^{73} + 164 q^{75} - 8 q^{76} + 120 q^{78} + 52 q^{79} - 98 q^{81} + 48 q^{82} + 76 q^{85} - 260 q^{87} + 16 q^{88} + 128 q^{90} + 210 q^{93} - 360 q^{94} + 16 q^{96} - 288 q^{97} - 70 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9 + 16 * q^10 + 4 * q^12 + 32 * q^13 + 14 * q^15 + 16 * q^16 + 40 * q^18 + 4 * q^19 - 8 * q^22 - 8 * q^24 + 24 * q^25 - 80 * q^27 - 52 * q^30 + 20 * q^31 - 106 * q^33 - 16 * q^34 - 20 * q^36 - 4 * q^37 + 72 * q^39 - 32 * q^40 + 104 * q^43 - 58 * q^45 - 56 * q^46 - 8 * q^48 - 14 * q^51 - 64 * q^52 - 32 * q^54 + 236 * q^55 - 134 * q^57 + 80 * q^58 - 28 * q^60 + 212 * q^61 - 32 * q^64 + 224 * q^66 - 156 * q^67 - 82 * q^69 - 80 * q^72 + 132 * q^73 + 164 * q^75 - 8 * q^76 + 120 * q^78 + 52 * q^79 - 98 * q^81 + 48 * q^82 + 76 * q^85 - 260 * q^87 + 16 * q^88 + 128 * q^90 + 210 * q^93 - 360 * q^94 + 16 * q^96 - 288 * q^97 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$1$

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
$3$	1.84521	−	2.36542i	0.615069	−	0.788473i
$3$	1.84521	−	2.36542i	0.615069	−	0.788473i
$4$	−2.00000			−0.500000
$5$			0.488198i			0.0976395i	0.998808	+	0.0488198i	$0.0155460\pi$
$5$			0.488198i			0.0976395i	−0.998808	+	0.0488198i	$0.984454\pi$
$6$	3.34521	+	2.60952i	0.557535	+	0.434920i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	−2.19042	−	8.72938i	−0.243380	−	0.969931i
$10$	−0.690416			−0.0690416
$11$		−	15.1689i		−	1.37899i	−0.724290	−	0.689496i	$-0.757832\pi$
$11$		−	15.1689i		−	1.37899i	0.724290	−	0.689496i	$-0.242168\pi$
$12$	−3.69042	+	4.73084i	−0.307535	+	0.394237i
$13$	17.3808			1.33699			0.668494	−	0.743718i	$-0.266939\pi$
$13$	17.3808			1.33699			0.668494	+	0.743718i	$0.266939\pi$
$14$		0			0
$15$	1.15479	+	0.900826i	0.0769861	+	0.0600551i
$16$	4.00000			0.250000
$17$		−	0.488198i		−	0.0287175i	−0.999897	−	0.0143588i	$-0.995429\pi$
$17$		−	0.488198i		−	0.0287175i	0.999897	−	0.0143588i	$-0.00457069\pi$
$18$	12.3452	−	3.09772i	0.685845	−	0.172095i
$19$	−13.0712			−0.687960			−0.343980	−	0.938977i	$-0.611775\pi$
$19$	−13.0712			−0.687960			−0.343980	+	0.938977i	$0.611775\pi$
$20$		−	0.976395i		−	0.0488198i
$21$		0			0
$22$	21.4521			0.975094
$23$		−	6.68363i		−	0.290593i	−0.989388	−	0.145296i	$-0.953586\pi$
$23$		−	6.68363i		−	0.290593i	0.989388	−	0.145296i	$-0.0464135\pi$
$24$	−6.69042	−	5.21904i	−0.278767	−	0.217460i
$25$	24.7617			0.990467
$26$			24.5802i			0.945393i
$27$	−24.6904	−	10.9263i	−0.914460	−	0.404677i
$28$		0			0
$29$		−	47.3084i		−	1.63132i	−0.578529	−	0.815662i	$-0.696373\pi$
$29$		−	47.3084i		−	1.63132i	0.578529	−	0.815662i	$-0.303627\pi$
$30$	−1.27396	+	1.63312i	−0.0424654	+	0.0544374i
$31$	28.4521			0.917809			0.458904	−	0.888486i	$-0.348242\pi$
$31$	28.4521			0.917809			0.458904	+	0.888486i	$0.348242\pi$
$32$			5.65685i			0.176777i
$33$	−35.8808	−	27.9898i	−1.08730	−	0.848176i
$34$	0.690416			0.0203063
$35$		0			0
$36$	4.38083	+	17.4588i	0.121690	+	0.484966i
$37$	−1.00000			−0.0270270			−0.0135135	−	0.999909i	$-0.504302\pi$
$37$	−1.00000			−0.0270270			−0.0135135	+	0.999909i	$0.504302\pi$
$38$		−	18.4855i		−	0.486461i
$39$	32.0712	−	41.1130i	0.822340	−	1.05418i
$40$	1.38083			0.0345208
$41$		−	28.3850i		−	0.692318i	−0.938176	−	0.346159i	$-0.887486\pi$
$41$		−	28.3850i		−	0.692318i	0.938176	−	0.346159i	$-0.112514\pi$
$42$		0			0
$43$	−2.14249			−0.0498255			−0.0249127	−	0.999690i	$-0.507931\pi$
$43$	−2.14249			−0.0498255			−0.0249127	+	0.999690i	$0.507931\pi$
$44$			30.3378i			0.689496i
$45$	4.26166	−	1.06936i	0.0947036	−	0.0237635i
$46$	9.45208			0.205480
$47$			73.5895i			1.56573i	0.622189	+	0.782867i	$0.286243\pi$
$47$			73.5895i			1.56573i	−0.622189	+	0.782867i	$0.713757\pi$
$48$	7.38083	−	9.46168i	0.153767	−	0.197118i
$49$		0			0
$50$			35.0183i			0.700366i
$51$	−1.15479	−	0.900826i	−0.0226430	−	0.0176633i
$52$	−34.7617			−0.668494
$53$			60.8616i			1.14833i	0.818739	+	0.574166i	$0.194673\pi$
$53$			60.8616i			1.14833i	−0.818739	+	0.574166i	$0.805327\pi$
$54$	15.4521	−	34.9175i	0.286150	−	0.646621i
$55$	7.40543			0.134644
$56$		0			0
$57$	−24.1192	+	30.9190i	−0.423143	+	0.542438i
$58$	66.9042			1.15352
$59$			100.998i			1.71183i	0.517114	+	0.855916i	$0.327006\pi$
$59$			100.998i			1.71183i	−0.517114	+	0.855916i	$0.672994\pi$
$60$	−2.30958	−	1.80165i	−0.0384931	−	0.0300275i
$61$	34.2383			0.561284			0.280642	−	0.959812i	$-0.409453\pi$
$61$	34.2383			0.561284			0.280642	+	0.959812i	$0.409453\pi$
$62$			40.2373i			0.648989i
$63$		0			0
$64$	−8.00000			−0.125000
$65$			8.48528i			0.130543i
$66$	39.5835	−	50.7432i	0.599751	−	0.768836i
$67$	−99.9754			−1.49217			−0.746085	−	0.665851i	$-0.768069\pi$
$67$	−99.9754			−1.49217			−0.746085	+	0.665851i	$0.768069\pi$
$68$			0.976395i			0.0143588i
$69$	−15.8096	−	12.3327i	−0.229124	−	0.178735i
$70$		0			0
$71$		−	82.9000i		−	1.16761i	−0.811895	−	0.583803i	$-0.801564\pi$
$71$		−	82.9000i		−	1.16761i	0.811895	−	0.583803i	$-0.198436\pi$
$72$	−24.6904	+	6.19543i	−0.342922	+	0.0860477i
$73$	51.7617			0.709064			0.354532	−	0.935044i	$-0.384640\pi$
$73$	51.7617			0.709064			0.354532	+	0.935044i	$0.384640\pi$
$74$		−	1.41421i		−	0.0191110i
$75$	45.6904	−	58.5717i	0.609206	−	0.780956i
$76$	26.1425			0.343980
$77$		0			0
$78$	58.1425	+	45.3556i	0.745417	+	0.581482i
$79$	−66.7371			−0.844773			−0.422387	−	0.906416i	$-0.638807\pi$
$79$	−66.7371			−0.844773			−0.422387	+	0.906416i	$0.638807\pi$
$80$			1.95279i			0.0244099i
$81$	−71.4042	+	38.2419i	−0.881533	+	0.472123i
$82$	40.1425			0.489543
$83$			88.7584i			1.06938i	0.845049	+	0.534689i	$0.179571\pi$
$83$			88.7584i			1.06938i	−0.845049	+	0.534689i	$0.820429\pi$
$84$		0			0
$85$	0.238337			0.00280396
$86$		−	3.02994i		−	0.0352319i
$87$	−111.904	−	87.2938i	−1.28625	−	1.00338i
$88$	−42.9042			−0.487547
$89$		−	58.5369i		−	0.657718i	−0.944379	−	0.328859i	$-0.893336\pi$
$89$		−	58.5369i		−	0.657718i	0.944379	−	0.328859i	$-0.106664\pi$
$90$	1.51230	+	6.02690i	0.0168033	+	0.0669656i
$91$		0			0
$92$			13.3673i			0.145296i
$93$	52.5000	−	67.3011i	0.564516	−	0.723668i
$94$	−104.071			−1.10714
$95$		−	6.38135i		−	0.0671721i
$96$	13.3808	+	10.4381i	0.139384	+	0.108730i
$97$	−25.0958			−0.258720			−0.129360	−	0.991598i	$-0.541292\pi$
$97$	−25.0958			−0.258720			−0.129360	+	0.991598i	$0.541292\pi$
$98$		0			0
$99$	−132.415	+	33.2262i	−1.33753	+	0.335618i
$100$	−49.5233			−0.495233
$101$			94.1286i			0.931966i	0.884794	+	0.465983i	$0.154299\pi$
$101$			94.1286i			0.931966i	−0.884794	+	0.465983i	$0.845701\pi$
$102$	1.27396	−	1.63312i	0.0124898	−	0.0160110i
$103$	9.49873			0.0922207			0.0461103	−	0.998936i	$-0.485317\pi$
$103$	9.49873			0.0922207			0.0461103	+	0.998936i	$0.485317\pi$
$104$		−	49.1604i		−	0.472696i
$105$		0			0
$106$	−86.0712			−0.811993
$107$			34.0923i			0.318619i	0.987229	+	0.159310i	$0.0509268\pi$
$107$			34.0923i			0.318619i	−0.987229	+	0.159310i	$0.949073\pi$
$108$	49.3808	+	21.8525i	0.457230	+	0.202338i
$109$	66.3808			0.608998			0.304499	−	0.952513i	$-0.401511\pi$
$109$	66.3808			0.608998			0.304499	+	0.952513i	$0.401511\pi$
$110$			10.4729i			0.0952078i
$111$	−1.84521	+	2.36542i	−0.0166235	+	0.0213101i
$112$		0			0
$113$			72.0901i			0.637966i	0.947761	+	0.318983i	$0.103341\pi$
$113$			72.0901i			0.637966i	−0.947761	+	0.318983i	$0.896659\pi$
$114$	−43.7260	−	34.1097i	−0.383562	−	0.299208i
$115$	3.26293			0.0283733
$116$			94.6168i			0.815662i
$117$	−38.0712	−	151.724i	−0.325395	−	1.29679i
$118$	−142.833			−1.21045
$119$		0			0
$120$	2.54792	−	3.26625i	0.0212327	−	0.0272187i
$121$	−109.096			−0.901619
$122$			48.4203i			0.396888i
$123$	−67.1425	−	52.3763i	−0.545874	−	0.425823i
$124$	−56.9042			−0.458904
$125$			24.2935i			0.194348i
$126$		0			0
$127$	−59.3808			−0.467566			−0.233783	−	0.972289i	$-0.575110\pi$
$127$	−59.3808			−0.467566			−0.233783	+	0.972289i	$0.575110\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−3.95335	+	5.06790i	−0.0306461	+	0.0392860i
$130$	−12.0000			−0.0923077
$131$			101.300i			0.773285i	0.922230	+	0.386643i	$0.126365\pi$
$131$			101.300i			0.773285i	−0.922230	+	0.386643i	$0.873635\pi$
$132$	71.7617	+	55.9796i	0.543649	+	0.424088i
$133$		0			0
$134$		−	141.387i		−	1.05512i
$135$	5.33418	−	12.0538i	0.0395124	−	0.0892874i
$136$	−1.38083			−0.0101532
$137$			132.952i			0.970450i	0.874389	+	0.485225i	$0.161262\pi$
$137$			132.952i			0.970450i	−0.874389	+	0.485225i	$0.838738\pi$
$138$	17.4411	−	22.3581i	0.126384	−	0.162015i
$139$	−71.6658			−0.515581			−0.257791	−	0.966201i	$-0.582995\pi$
$139$	−71.6658			−0.515581			−0.257791	+	0.966201i	$0.582995\pi$
$140$		0			0
$141$	174.070	+	135.788i	1.23454	+	0.963035i
$142$	117.238			0.825622
$143$		−	263.648i		−	1.84369i
$144$	−8.76166	−	34.9175i	−0.0608449	−	0.242483i
$145$	23.0958			0.159282
$146$			73.2020i			0.501384i
$147$		0			0
$148$	2.00000			0.0135135
$149$			18.4352i			0.123726i	0.998085	+	0.0618629i	$0.0197042\pi$
$149$			18.4352i			0.123726i	−0.998085	+	0.0618629i	$0.980296\pi$
$150$	82.8329	+	64.6160i	0.552219	+	0.430773i
$151$	50.0246			0.331289			0.165644	−	0.986186i	$-0.447030\pi$
$151$	50.0246			0.331289			0.165644	+	0.986186i	$0.447030\pi$
$152$			36.9711i			0.243231i
$153$	−4.26166	+	1.06936i	−0.0278540	+	0.00698925i
$154$		0			0
$155$			13.8902i			0.0896144i
$156$	−64.1425	+	82.2259i	−0.411170	+	0.527089i
$157$	1.00000			0.00636943			0.00318471	−	0.999995i	$-0.498986\pi$
$157$	1.00000			0.00636943			0.00318471	+	0.999995i	$0.498986\pi$
$158$		−	94.3805i		−	0.597345i
$159$	143.963	+	112.302i	0.905428	+	0.706303i
$160$	−2.76166			−0.0172604
$161$		0			0
$162$	−54.0823	−	100.981i	−0.333841	−	0.623338i
$163$	115.926			0.711204			0.355602	−	0.934638i	$-0.384276\pi$
$163$	115.926			0.711204			0.355602	+	0.934638i	$0.384276\pi$
$164$			56.7701i			0.346159i
$165$	13.6646	−	17.5169i	0.0828155	−	0.106163i
$166$	−125.523			−0.756165
$167$		−	199.369i		−	1.19383i	−0.802305	−	0.596914i	$-0.796393\pi$
$167$		−	199.369i		−	1.19383i	0.802305	−	0.596914i	$-0.203607\pi$
$168$		0			0
$169$	133.093			0.787534
$170$			0.337059i			0.00198270i
$171$	28.6315	+	114.104i	0.167435	+	0.667274i
$172$	4.28499			0.0249127
$173$			34.7316i			0.200761i	0.994949	+	0.100380i	$0.0320060\pi$
$173$			34.7316i			0.200761i	−0.994949	+	0.100380i	$0.967994\pi$
$174$	123.452	−	158.256i	0.709495	−	0.909519i
$175$		0			0
$176$		−	60.6756i		−	0.344748i
$177$	238.903	+	186.363i	1.34973	+	1.05290i
$178$	82.7837			0.465077
$179$		−	216.119i		−	1.20737i	−0.797223	−	0.603685i	$-0.793699\pi$
$179$		−	216.119i		−	1.20737i	0.797223	−	0.603685i	$-0.206301\pi$
$180$	−8.52333	+	2.13871i	−0.0473518	+	0.0118817i
$181$	320.093			1.76847			0.884236	−	0.467041i	$-0.154680\pi$
$181$	320.093			1.76847			0.884236	+	0.467041i	$0.154680\pi$
$182$		0			0
$183$	63.1768	−	80.9880i	0.345229	−	0.442557i
$184$	−18.9042			−0.102740
$185$		−	0.488198i		−	0.00263891i
$186$	95.1781	+	74.2462i	0.511710	+	0.399173i
$187$	−7.40543			−0.0396012
$188$		−	147.179i		−	0.782867i
$189$		0			0
$190$	9.02460			0.0474979
$191$			39.9506i			0.209166i	0.994516	+	0.104583i	$0.0333507\pi$
$191$			39.9506i			0.209166i	−0.994516	+	0.104583i	$0.966649\pi$
$192$	−14.7617	+	18.9234i	−0.0768837	+	0.0985591i
$193$	346.852			1.79716			0.898581	−	0.438807i	$-0.144599\pi$
$193$	346.852			1.79716			0.898581	+	0.438807i	$0.144599\pi$
$194$		−	35.4909i		−	0.182943i
$195$	20.0712	+	15.6571i	0.102929	+	0.0802929i
$196$		0			0
$197$			92.3617i			0.468841i	0.972135	+	0.234421i	$0.0753193\pi$
$197$			92.3617i			0.468841i	−0.972135	+	0.234421i	$0.924681\pi$
$198$	−46.9890	−	187.263i	−0.237318	−	0.945775i
$199$	43.2137			0.217154			0.108577	−	0.994088i	$-0.465371\pi$
$199$	43.2137			0.217154			0.108577	+	0.994088i	$0.465371\pi$
$200$		−	70.0366i		−	0.350183i
$201$	−184.475	+	236.484i	−0.917788	+	1.17654i
$202$	−133.118			−0.659000
$203$		0			0
$204$	2.30958	+	1.80165i	0.0113215	+	0.00883163i
$205$	13.8575			0.0675976
$206$			13.4332i			0.0652099i
$207$	−58.3439	+	14.6399i	−0.281855	+	0.0707243i
$208$	69.5233			0.334247
$209$			198.277i			0.948692i
$210$		0			0
$211$	306.142			1.45091			0.725456	−	0.688268i	$-0.241629\pi$
$211$	306.142			1.45091			0.725456	+	0.688268i	$0.241629\pi$
$212$		−	121.723i		−	0.574166i
$213$	−196.093	−	152.968i	−0.920626	−	0.718159i
$214$	−48.2137			−0.225298
$215$		−	1.04596i		−	0.00486493i
$216$	−30.9042	+	69.8350i	−0.143075	+	0.323310i
$217$		0			0
$218$			93.8767i			0.430627i
$219$	95.5110	−	122.438i	0.436123	−	0.559078i
$220$	−14.8109			−0.0673221
$221$		−	8.48528i		−	0.0383949i
$222$	−3.34521	−	2.60952i	−0.0150685	−	0.0117546i
$223$	−1.57252			−0.00705164			−0.00352582	−	0.999994i	$-0.501122\pi$
$223$	−1.57252			−0.00705164			−0.00352582	+	0.999994i	$0.501122\pi$
$224$		0			0
$225$	−54.2383	−	216.154i	−0.241059	−	0.960684i
$226$	−101.951			−0.451110
$227$			4.80040i			0.0211472i	0.999944	+	0.0105736i	$0.00336574\pi$
$227$			4.80040i			0.0211472i	−0.999944	+	0.0105736i	$0.996634\pi$
$228$	48.2383	−	61.8380i	0.211572	−	0.271219i
$229$	−311.806			−1.36160			−0.680799	−	0.732471i	$-0.738367\pi$
$229$	−311.806			−1.36160			−0.680799	+	0.732471i	$0.738367\pi$
$230$			4.61448i			0.0200630i
$231$		0			0
$232$	−133.808			−0.576760
$233$			121.607i			0.521917i	0.965350	+	0.260959i	$0.0840387\pi$
$233$			121.607i			0.521917i	−0.965350	+	0.260959i	$0.915961\pi$
$234$	214.570	−	53.8409i	0.916966	−	0.230089i
$235$	−35.9262			−0.152878
$236$		−	201.996i		−	0.855916i
$237$	−123.144	+	157.861i	−0.519594	+	0.666081i
$238$		0			0
$239$		−	59.6992i		−	0.249788i	−0.992170	−	0.124894i	$-0.960141\pi$
$239$		−	59.6992i		−	0.249788i	0.992170	−	0.124894i	$-0.0398590\pi$
$240$	4.61917	+	3.60330i	0.0192465	+	0.0150138i
$241$	196.715			0.816245			0.408122	−	0.912927i	$-0.366184\pi$
$241$	196.715			0.816245			0.408122	+	0.912927i	$0.366184\pi$
$242$		−	154.285i		−	0.637541i
$243$	−41.2973	+	239.465i	−0.169948	+	0.985453i
$244$	−68.4767			−0.280642
$245$		0			0
$246$	74.0712	−	94.9538i	0.301103	−	0.385991i
$247$	−227.189			−0.919794
$248$		−	80.4746i		−	0.324494i
$249$	209.951	+	163.778i	0.843176	+	0.657742i
$250$	−34.3562			−0.137425
$251$		−	269.204i		−	1.07253i	−0.844051	−	0.536264i	$-0.819835\pi$
$251$		−	269.204i		−	1.07253i	0.844051	−	0.536264i	$-0.180165\pi$
$252$		0			0
$253$	−101.383			−0.400725
$254$		−	83.9772i		−	0.330619i
$255$	0.439781	−	0.563767i	0.00172463	−	0.00221085i
$256$	16.0000			0.0625000
$257$		−	188.745i		−	0.734418i	−0.930139	−	0.367209i	$-0.880313\pi$
$257$		−	188.745i		−	0.734418i	0.930139	−	0.367209i	$-0.119687\pi$
$258$	−7.16709	−	5.59088i	−0.0277794	−	0.0216701i
$259$		0			0
$260$		−	16.9706i		−	0.0652714i
$261$	−412.973	+	103.625i	−1.58227	+	0.397031i
$262$	−143.260			−0.546795
$263$		−	207.332i		−	0.788333i	−0.919039	−	0.394167i	$-0.871033\pi$
$263$		−	207.332i		−	0.788333i	0.919039	−	0.394167i	$-0.128967\pi$
$264$	−79.1671	+	101.486i	−0.299875	+	0.384418i
$265$	−29.7125			−0.112123
$266$		0			0
$267$	−138.464	−	108.013i	−0.518593	−	0.404542i
$268$	199.951			0.746085
$269$		−	182.957i		−	0.680136i	−0.940401	−	0.340068i	$-0.889550\pi$
$269$		−	182.957i		−	0.680136i	0.940401	−	0.340068i	$-0.110450\pi$
$270$	17.0467	+	7.54367i	0.0631357	+	0.0279395i
$271$	195.022			0.719639			0.359819	−	0.933022i	$-0.382838\pi$
$271$	195.022			0.719639			0.359819	+	0.933022i	$0.382838\pi$
$272$		−	1.95279i		−	0.00717938i
$273$		0			0
$274$	−188.022			−0.686212
$275$		−	375.607i		−	1.36585i
$276$	31.6192	+	24.6654i	0.114562	+	0.0893673i
$277$	−105.285			−0.380090			−0.190045	−	0.981775i	$-0.560863\pi$
$277$	−105.285			−0.380090			−0.190045	+	0.981775i	$0.560863\pi$
$278$		−	101.351i		−	0.364571i
$279$	−62.3219	−	248.369i	−0.223376	−	0.890212i
$280$		0			0
$281$			472.177i			1.68035i	0.542319	+	0.840173i	$0.317546\pi$
$281$			472.177i			1.68035i	−0.542319	+	0.840173i	$0.682454\pi$
$282$	−192.033	+	246.172i	−0.680968	+	0.872951i
$283$	−319.450			−1.12880			−0.564398	−	0.825502i	$-0.690892\pi$
$283$	−319.450			−1.12880			−0.564398	+	0.825502i	$0.690892\pi$
$284$			165.800i			0.583803i
$285$	−15.0946	−	11.7749i	−0.0529634	−	0.0413155i
$286$	372.855			1.30369
$287$		0			0
$288$	49.3808	−	12.3909i	0.171461	−	0.0430238i
$289$	288.762			0.999175
$290$			32.6625i			0.112629i
$291$	−46.3070	+	59.3622i	−0.159131	+	0.203994i
$292$	−103.523			−0.354532
$293$			477.594i			1.63001i	0.579451	+	0.815007i	$0.303267\pi$
$293$			477.594i			1.63001i	−0.579451	+	0.815007i	$0.696733\pi$
$294$		0			0
$295$	−49.3070			−0.167143
$296$			2.82843i			0.00955550i
$297$	−165.740	+	374.527i	−0.558046	+	1.26103i
$298$	−26.0712			−0.0874874
$299$		−	116.167i		−	0.388518i
$300$	−91.3808	+	117.143i	−0.304603	+	0.390478i
$301$		0			0
$302$			70.7455i			0.234256i
$303$	222.654	+	173.687i	0.734830	+	0.573224i
$304$	−52.2850			−0.171990
$305$			16.7151i			0.0548035i
$306$	−1.51230	−	6.02690i	−0.00494215	−	0.0196958i
$307$	104.619			0.340779			0.170390	−	0.985377i	$-0.445497\pi$
$307$	104.619			0.340779			0.170390	+	0.985377i	$0.445497\pi$
$308$		0			0
$309$	17.5271	−	22.4685i	0.0567221	−	0.0727135i
$310$	−19.6438			−0.0633670
$311$		−	192.755i		−	0.619792i	−0.950770	−	0.309896i	$-0.899706\pi$
$311$		−	192.755i		−	0.619792i	0.950770	−	0.309896i	$-0.100294\pi$
$312$	−116.285	−	90.7112i	−0.372708	−	0.290741i
$313$	540.902			1.72812			0.864060	−	0.503389i	$-0.167914\pi$
$313$	540.902			1.72812			0.864060	+	0.503389i	$0.167914\pi$
$314$			1.41421i			0.00450386i
$315$		0			0
$316$	133.474			0.422387
$317$		−	309.562i		−	0.976535i	−0.872694	−	0.488268i	$-0.837629\pi$
$317$		−	309.562i		−	0.976535i	0.872694	−	0.488268i	$-0.162371\pi$
$318$	−158.819	+	203.595i	−0.499432	+	0.640235i
$319$	−717.617			−2.24958
$320$		−	3.90558i		−	0.0122049i
$321$	80.6425	+	62.9073i	0.251223	+	0.195973i
$322$		0			0
$323$			6.38135i			0.0197565i
$324$	142.808	−	76.4839i	0.440766	−	0.236061i
$325$	430.378			1.32424
$326$			163.944i			0.502897i
$327$	122.486	−	157.018i	0.374576	−	0.480179i
$328$	−80.2850			−0.244771
$329$		0			0
$330$	24.7727	+	19.3246i	0.0750688	+	0.0585594i
$331$	−333.499			−1.00755			−0.503775	−	0.863835i	$-0.668056\pi$
$331$	−333.499			−1.00755			−0.503775	+	0.863835i	$0.668056\pi$
$332$		−	177.517i		−	0.534689i
$333$	2.19042	+	8.72938i	0.00657783	+	0.0262144i
$334$	281.951			0.844164
$335$		−	48.8078i		−	0.145695i
$336$		0			0
$337$	138.619			0.411333			0.205666	−	0.978622i	$-0.434064\pi$
$337$	138.619			0.411333			0.205666	+	0.978622i	$0.434064\pi$
$338$			188.222i			0.556871i
$339$	170.523	+	133.021i	0.503019	+	0.392393i
$340$	−0.476674			−0.00140198
$341$		−	431.587i		−	1.26565i
$342$	−161.367	+	40.4910i	−0.471834	+	0.118395i
$343$		0			0
$344$			6.05989i			0.0176160i
$345$	6.02079	−	7.71820i	0.0174516	−	0.0223716i
$346$	−49.1179			−0.141959
$347$			428.856i			1.23590i	0.786219	+	0.617948i	$0.212036\pi$
$347$			428.856i			1.23590i	−0.786219	+	0.617948i	$0.787964\pi$
$348$	223.808	+	174.588i	0.643127	+	0.501689i
$349$	−166.236			−0.476320			−0.238160	−	0.971226i	$-0.576544\pi$
$349$	−166.236			−0.476320			−0.238160	+	0.971226i	$0.576544\pi$
$350$		0			0
$351$	−429.140	−	189.908i	−1.22262	−	0.541047i
$352$	85.8083			0.243774
$353$			284.710i			0.806545i	0.915080	+	0.403272i	$0.132127\pi$
$353$			284.710i			0.806545i	−0.915080	+	0.403272i	$0.867873\pi$
$354$	−263.556	+	337.860i	−0.744510	+	0.954406i
$355$	40.4716			0.114005
$356$			117.074i			0.328859i
$357$		0			0
$358$	305.639			0.853739
$359$			422.462i			1.17678i	0.808579	+	0.588388i	$0.200237\pi$
$359$			422.462i			1.17678i	−0.808579	+	0.588388i	$0.799763\pi$
$360$	−3.02460	−	12.0538i	−0.00840165	−	0.0334828i
$361$	−190.142			−0.526711
$362$			452.680i			1.25050i
$363$	−201.305	+	258.057i	−0.554558	+	0.710902i
$364$		0			0
$365$			25.2699i			0.0692327i
$366$	114.534	+	89.3456i	0.312935	+	0.244114i
$367$	−170.501			−0.464581			−0.232291	−	0.972646i	$-0.574622\pi$
$367$	−170.501			−0.464581			−0.232291	+	0.972646i	$0.574622\pi$
$368$		−	26.7345i		−	0.0726481i
$369$	−247.784	+	62.1750i	−0.671501	+	0.168496i
$370$	0.690416			0.00186599
$371$		0			0
$372$	−105.000	+	134.602i	−0.282258	+	0.361834i
$373$	304.523			0.816416			0.408208	−	0.912889i	$-0.366154\pi$
$373$	304.523			0.816416			0.408208	+	0.912889i	$0.366154\pi$
$374$		−	10.4729i		−	0.0280023i
$375$	57.4644	+	44.8266i	0.153238	+	0.119538i
$376$	208.142			0.553570
$377$		−	822.259i		−	2.18106i
$378$		0			0
$379$	−512.899			−1.35330			−0.676648	−	0.736307i	$-0.736568\pi$
$379$	−512.899			−1.35330			−0.676648	+	0.736307i	$0.736568\pi$
$380$			12.7627i			0.0335861i
$381$	−109.570	+	140.461i	−0.287585	+	0.368663i
$382$	−56.4987			−0.147902
$383$		−	428.786i		−	1.11955i	−0.828646	−	0.559773i	$-0.810888\pi$
$383$		−	428.786i		−	1.11955i	0.828646	−	0.559773i	$-0.189112\pi$
$384$	−26.7617	−	20.8761i	−0.0696918	−	0.0543650i
$385$		0			0
$386$			490.523i			1.27079i
$387$	4.69295	+	18.7026i	0.0121265	+	0.0483273i
$388$	50.1917			0.129360
$389$		−	70.6951i		−	0.181735i	−0.995863	−	0.0908677i	$-0.971036\pi$
$389$		−	70.6951i		−	0.181735i	0.995863	−	0.0908677i	$-0.0289640\pi$
$390$	−22.1425	+	28.3850i	−0.0567756	+	0.0727821i
$391$	−3.26293			−0.00834509
$392$		0			0
$393$	239.618	+	186.920i	0.609715	+	0.475624i
$394$	−130.619			−0.331521
$395$		−	32.5809i		−	0.0824832i
$396$	264.830	−	66.4524i	0.668764	−	0.167809i
$397$	−53.3291			−0.134330			−0.0671651	−	0.997742i	$-0.521395\pi$
$397$	−53.3291			−0.134330			−0.0671651	+	0.997742i	$0.521395\pi$
$398$			61.1135i			0.153551i
$399$		0			0
$400$	99.0467			0.247617
$401$			292.382i			0.729133i	0.931177	+	0.364567i	$0.118783\pi$
$401$			292.382i			0.729133i	−0.931177	+	0.364567i	$0.881217\pi$
$402$	−334.439	−	260.888i	−0.831937	−	0.648974i
$403$	494.521			1.22710
$404$		−	188.257i		−	0.465983i
$405$	−18.6696	−	34.8593i	−0.0460978	−	0.0860725i
$406$		0			0
$407$			15.1689i			0.0372701i
$408$	−2.54792	+	3.26625i	−0.00624490	+	0.00800550i
$409$	4.56744			0.0111673			0.00558367	−	0.999984i	$-0.498223\pi$
$409$	4.56744			0.0111673			0.00558367	+	0.999984i	$0.498223\pi$
$410$			19.5975i			0.0477987i
$411$	314.486	+	245.323i	0.765174	+	0.596894i
$412$	−18.9975			−0.0461103
$413$		0			0
$414$	−20.7040	−	82.5108i	−0.0500096	−	0.199301i
$415$	−43.3316			−0.104414
$416$			98.3208i			0.236348i
$417$	−132.238	+	169.520i	−0.317118	+	0.406522i
$418$	−280.405			−0.670826
$419$			378.002i			0.902152i	0.892486	+	0.451076i	$0.148960\pi$
$419$			378.002i			0.902152i	−0.892486	+	0.451076i	$0.851040\pi$
$420$		0			0
$421$	−742.806			−1.76438			−0.882192	−	0.470890i	$-0.843933\pi$
$421$	−742.806			−1.76438			−0.882192	+	0.470890i	$0.843933\pi$
$422$			432.951i			1.02595i
$423$	642.391	−	161.192i	1.51865	−	0.381068i
$424$	172.142			0.405996
$425$		−	12.0886i		−	0.0284437i
$426$	216.329	−	277.318i	0.507815	−	0.650981i
$427$		0			0
$428$		−	68.1845i		−	0.159310i
$429$	−623.639	−	486.486i	−1.45370	−	1.13400i
$430$	1.47921			0.00344003
$431$		−	378.757i		−	0.878787i	−0.898295	−	0.439394i	$-0.855193\pi$
$431$		−	378.757i		−	0.878787i	0.898295	−	0.439394i	$-0.144807\pi$
$432$	−98.7617	−	43.7051i	−0.228615	−	0.101169i
$433$	−521.567			−1.20454			−0.602272	−	0.798291i	$-0.705738\pi$
$433$	−521.567			−1.20454			−0.602272	+	0.798291i	$0.705738\pi$
$434$		0			0
$435$	42.6166	−	54.6313i	0.0979693	−	0.125589i
$436$	−132.762			−0.304499
$437$			87.3634i			0.199916i
$438$	173.154	+	135.073i	0.395328	+	0.308386i
$439$	−730.113			−1.66313			−0.831564	−	0.555430i	$-0.812554\pi$
$439$	−730.113			−1.66313			−0.831564	+	0.555430i	$0.812554\pi$
$440$		−	20.9457i		−	0.0476039i
$441$		0			0
$442$	12.0000			0.0271493
$443$		−	645.800i		−	1.45779i	−0.684626	−	0.728894i	$-0.740035\pi$
$443$		−	645.800i		−	1.45779i	0.684626	−	0.728894i	$-0.259965\pi$
$444$	3.69042	−	4.73084i	0.00831175	−	0.0106550i
$445$	28.5776			0.0642193
$446$		−	2.22387i		−	0.00498626i
$447$	43.6069	+	34.0167i	0.0975545	+	0.0761000i
$448$		0			0
$449$		−	681.682i		−	1.51822i	−0.650961	−	0.759112i	$-0.725634\pi$
$449$		−	681.682i		−	1.51822i	0.650961	−	0.759112i	$-0.274366\pi$
$450$	305.688	−	76.7046i	0.679306	−	0.170455i
$451$	−430.570			−0.954701
$452$		−	144.180i		−	0.318983i
$453$	92.3058	−	118.329i	0.203766	−	0.261212i
$454$	−6.78880			−0.0149533
$455$		0			0
$456$	87.4521	+	68.2193i	0.191781	+	0.149604i
$457$	−62.9067			−0.137651			−0.0688257	−	0.997629i	$-0.521925\pi$
$457$	−62.9067			−0.137651			−0.0688257	+	0.997629i	$0.521925\pi$
$458$		−	440.960i		−	0.962795i
$459$	−5.33418	+	12.0538i	−0.0116213	+	0.0262610i
$460$	−6.52586			−0.0141867
$461$		−	113.099i		−	0.245333i	−0.992448	−	0.122667i	$-0.960855\pi$
$461$		−	113.099i		−	0.245333i	0.992448	−	0.122667i	$-0.0391446\pi$
$462$		0			0
$463$	595.951			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$463$	595.951			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$464$		−	189.234i		−	0.407831i
$465$	32.8562	+	25.6304i	0.0706586	+	0.0551191i
$466$	−171.978			−0.369051
$467$			522.124i			1.11804i	0.829154	+	0.559020i	$0.188822\pi$
$467$			522.124i			1.11804i	−0.829154	+	0.559020i	$0.811178\pi$
$468$	76.1425	+	303.448i	0.162698	+	0.648393i
$469$		0			0
$470$		−	50.8073i		−	0.108101i
$471$	1.84521	−	2.36542i	0.00391764	−	0.00502212i
$472$	285.666			0.605224
$473$			32.4993i			0.0687089i
$474$	−223.249	−	174.152i	−0.470990	−	0.367408i
$475$	−323.666			−0.681402
$476$		0			0
$477$	531.284	−	133.312i	1.11380	−	0.279480i
$478$	84.4275			0.176627
$479$			709.242i			1.48067i	0.672237	+	0.740336i	$0.265334\pi$
$479$			709.242i			1.48067i	−0.672237	+	0.740336i	$0.734666\pi$
$480$	−5.09584	+	6.53249i	−0.0106163	+	0.0136094i
$481$	−17.3808			−0.0361348
$482$			278.197i			0.577172i
$483$		0			0
$484$	218.192			0.450809
$485$		−	12.2517i		−	0.0252613i
$486$	−338.655	−	58.4032i	−0.696821	−	0.120171i
$487$	404.781			0.831173			0.415586	−	0.909554i	$-0.363576\pi$
$487$	404.781			0.831173			0.415586	+	0.909554i	$0.363576\pi$
$488$		−	96.8406i		−	0.198444i
$489$	213.908	−	274.214i	0.437440	−	0.560765i
$490$		0			0
$491$		−	202.531i		−	0.412487i	−0.978501	−	0.206244i	$-0.933876\pi$
$491$		−	202.531i		−	0.412487i	0.978501	−	0.206244i	$-0.0661239\pi$
$492$	134.285	+	104.753i	0.272937	+	0.212912i
$493$	−23.0958			−0.0468476
$494$		−	321.294i		−	0.650393i
$495$	−16.2210	−	64.6448i	−0.0327696	−	0.130596i
$496$	113.808			0.229452
$497$		0			0
$498$	−231.617	+	296.915i	−0.465094	+	0.596215i
$499$	19.1696			0.0384161			0.0192080	−	0.999816i	$-0.493886\pi$
$499$	19.1696			0.0384161			0.0192080	+	0.999816i	$0.493886\pi$
$500$		−	48.5871i		−	0.0971741i
$501$	−471.592	−	367.878i	−0.941301	−	0.734287i
$502$	380.712			0.758391
$503$			234.752i			0.466704i	0.972392	+	0.233352i	$0.0749695\pi$
$503$			234.752i			0.466704i	−0.972392	+	0.233352i	$0.925031\pi$
$504$		0			0
$505$	−45.9533			−0.0909967
$506$		−	143.378i		−	0.283355i
$507$	245.585	−	314.821i	0.484388	−	0.620950i
$508$	118.762			0.233783
$509$			717.762i			1.41014i	0.709137	+	0.705071i	$0.249085\pi$
$509$			717.762i			1.41014i	−0.709137	+	0.705071i	$0.750915\pi$
$510$	0.797287	+	0.621945i	0.00156331	+	0.00121950i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	322.735	+	142.820i	0.629112	+	0.278402i
$514$	266.926			0.519312
$515$			4.63726i			0.00900439i
$516$	7.90670	−	10.1358i	0.0153231	−	0.0196430i
$517$	1116.27			2.15913
$518$		0			0
$519$	82.1548	+	64.0870i	0.158294	+	0.123482i
$520$	24.0000			0.0461538
$521$		−	610.987i		−	1.17272i	−0.810051	−	0.586360i	$-0.800560\pi$
$521$		−	610.987i		−	1.17272i	0.810051	−	0.586360i	$-0.199440\pi$
$522$	−146.548	−	584.032i	−0.280743	−	1.11883i
$523$	−427.351			−0.817115			−0.408558	−	0.912733i	$-0.633968\pi$
$523$	−427.351			−0.817115			−0.408558	+	0.912733i	$0.633968\pi$
$524$		−	202.601i		−	0.386643i
$525$		0			0
$526$	293.211			0.557436
$527$		−	13.8902i		−	0.0263572i
$528$	−143.523	−	111.959i	−0.271824	−	0.212044i
$529$	484.329			0.915556
$530$		−	42.0198i		−	0.0792826i
$531$	881.651	−	221.228i	1.66036	−	0.416625i
$532$		0			0
$533$		−	493.355i		−	0.925620i
$534$	152.753	−	195.818i	0.286055	−	0.366701i
$535$	−16.6438			−0.0311098
$536$			282.773i			0.527562i
$537$	−511.212	−	398.785i	−0.951979	−	0.742616i
$538$	258.740			0.480929
$539$		0			0
$540$	−10.6684	+	24.1076i	−0.0197562	+	0.0446437i
$541$	−327.516			−0.605389			−0.302695	−	0.953088i	$-0.597886\pi$
$541$	−327.516			−0.605389			−0.302695	+	0.953088i	$0.597886\pi$
$542$			275.803i			0.508861i
$543$	590.639	−	757.155i	1.08773	−	1.39439i
$544$	2.76166			0.00507659
$545$			32.4070i			0.0594623i
$546$		0			0
$547$	313.754			0.573591			0.286795	−	0.957992i	$-0.407410\pi$
$547$	313.754			0.573591			0.286795	+	0.957992i	$0.407410\pi$
$548$		−	265.903i		−	0.485225i
$549$	−74.9962	−	298.879i	−0.136605	−	0.544407i
$550$	531.189			0.965798
$551$			618.380i			1.12229i
$552$	−34.8821	+	44.7163i	−0.0631922	+	0.0810077i
$553$		0			0
$554$		−	148.895i		−	0.268764i
$555$	−1.15479	−	0.900826i	−0.00208071	−	0.00162311i
$556$	143.332			0.257791
$557$		−	180.190i		−	0.323502i	−0.986832	−	0.161751i	$-0.948286\pi$
$557$		−	180.190i		−	0.323502i	0.986832	−	0.161751i	$-0.0517141\pi$
$558$	351.247	−	88.1365i	0.629475	−	0.157951i
$559$	−37.2383			−0.0666160
$560$		0			0
$561$	−13.6646	+	17.5169i	−0.0243575	+	0.0312245i
$562$	−667.759			−1.18818
$563$			401.958i			0.713958i	0.934112	+	0.356979i	$0.116193\pi$
$563$			401.958i			0.713958i	−0.934112	+	0.356979i	$0.883807\pi$
$564$	−348.140	−	271.576i	−0.617269	−	0.481517i
$565$	−35.1942			−0.0622907
$566$		−	451.770i		−	0.798180i
$567$		0			0
$568$	−234.477			−0.412811
$569$			42.7755i			0.0751766i	0.999293	+	0.0375883i	$0.0119675\pi$
$569$			42.7755i			0.0751766i	−0.999293	+	0.0375883i	$0.988032\pi$
$570$	16.6523	−	21.3470i	0.0292145	−	0.0374508i
$571$	−512.167			−0.896965			−0.448483	−	0.893792i	$-0.648035\pi$
$571$	−512.167			−0.896965			−0.448483	+	0.893792i	$0.648035\pi$
$572$			527.297i			0.921847i
$573$	94.5000	+	73.7172i	0.164921	+	0.128651i
$574$		0			0
$575$		−	165.498i		−	0.287822i
$576$	17.5233	+	69.8350i	0.0304224	+	0.121241i
$577$	69.4818			0.120419			0.0602095	−	0.998186i	$-0.480823\pi$
$577$	69.4818			0.120419			0.0602095	+	0.998186i	$0.480823\pi$
$578$			408.371i			0.706524i
$579$	640.015	−	820.451i	1.10538	−	1.41701i
$580$	−46.1917			−0.0796408
$581$		0			0
$582$	−83.9508	−	65.4881i	−0.144245	−	0.112522i
$583$	923.204			1.58354
$584$		−	146.404i		−	0.250692i
$585$	74.0712	−	18.5863i	0.126618	−	0.0317714i
$586$	−675.420			−1.15259
$587$			462.715i			0.788271i	0.919052	+	0.394136i	$0.128956\pi$
$587$			462.715i			0.788271i	−0.919052	+	0.394136i	$0.871044\pi$
$588$		0			0
$589$	−371.904			−0.631416
$590$		−	69.7307i		−	0.118188i
$591$	218.474	+	170.427i	0.369669	+	0.288370i
$592$	−4.00000			−0.00675676
$593$			543.407i			0.916369i	0.888857	+	0.458185i	$0.151500\pi$
$593$			543.407i			0.916369i	−0.888857	+	0.458185i	$0.848500\pi$
$594$	−529.661	−	234.391i	−0.891685	−	0.394598i
$595$		0			0
$596$		−	36.8703i		−	0.0618629i
$597$	79.7383	−	102.219i	0.133565	−	0.171220i
$598$	164.285			0.274724
$599$			135.102i			0.225547i	0.993621	+	0.112773i	$0.0359734\pi$
$599$			135.102i			0.225547i	−0.993621	+	0.112773i	$0.964027\pi$
$600$	−165.666	−	129.232i	−0.276110	−	0.215387i
$601$	−846.422			−1.40836			−0.704178	−	0.710023i	$-0.748684\pi$
$601$	−846.422			−1.40836			−0.704178	+	0.710023i	$0.748684\pi$
$602$		0			0
$603$	218.988	+	872.723i	0.363164	+	1.44730i
$604$	−100.049			−0.165644
$605$		−	53.2603i		−	0.0880336i
$606$	−245.630	+	314.880i	−0.405330	+	0.519603i
$607$	−423.833			−0.698242			−0.349121	−	0.937078i	$-0.613520\pi$
$607$	−423.833			−0.698242			−0.349121	+	0.937078i	$0.613520\pi$
$608$		−	73.9421i		−	0.121615i
$609$		0			0
$610$	−23.6387			−0.0387519
$611$			1279.05i			2.09337i
$612$	8.52333	−	2.13871i	0.0139270	−	0.00349463i
$613$	−84.9508			−0.138582			−0.0692910	−	0.997596i	$-0.522074\pi$
$613$	−84.9508			−0.138582			−0.0692910	+	0.997596i	$0.522074\pi$
$614$			147.954i			0.240967i
$615$	25.5700	−	32.7788i	0.0415772	−	0.0532989i
$616$		0			0
$617$			241.052i			0.390684i	0.980735	+	0.195342i	$0.0625817\pi$
$617$			241.052i			0.390684i	−0.980735	+	0.195342i	$0.937418\pi$
$618$	31.7752	+	24.7871i	0.0514162	+	0.0401086i
$619$	−1.74468			−0.00281855			−0.00140927	−	0.999999i	$-0.500449\pi$
$619$	−1.74468			−0.00281855			−0.00140927	+	0.999999i	$0.500449\pi$
$620$		−	27.7805i		−	0.0448072i
$621$	−73.0271	+	165.022i	−0.117596	+	0.265735i
$622$	272.597			0.438259
$623$		0			0
$624$	128.285	−	164.452i	0.205585	−	0.263545i
$625$	607.182			0.971490
$626$			764.950i			1.22197i
$627$	469.007	+	365.862i	0.748018	+	0.583511i
$628$	−2.00000			−0.00318471
$629$			0.488198i			0.000776149i
$630$		0			0
$631$	655.852			1.03939			0.519693	−	0.854353i	$-0.326046\pi$
$631$	655.852			1.03939			0.519693	+	0.854353i	$0.326046\pi$
$632$			188.761i			0.298672i
$633$	564.897	−	724.155i	0.892412	−	1.14401i
$634$	437.786			0.690515
$635$		−	28.9896i		−	0.0456529i
$636$	−287.926	−	224.604i	−0.452714	−	0.353152i
$637$		0			0
$638$		−	1014.86i		−	1.59069i
$639$	−723.666	+	181.586i	−1.13250	+	0.284171i
$640$	5.52333			0.00863020
$641$			958.814i			1.49581i	0.663806	+	0.747905i	$0.268940\pi$
$641$			958.814i			1.49581i	−0.663806	+	0.747905i	$0.731060\pi$
$642$	−88.9644	+	114.046i	−0.138574	+	0.177641i
$643$	−1189.28			−1.84958			−0.924788	−	0.380483i	$-0.875758\pi$
$643$	−1189.28			−1.84958			−0.924788	+	0.380483i	$0.875758\pi$
$644$		0			0
$645$	−2.47414	−	1.93002i	−0.00383587	−	0.00299227i
$646$	−9.02460			−0.0139700
$647$		−	442.804i		−	0.684395i	−0.939628	−	0.342198i	$-0.888829\pi$
$647$		−	442.804i		−	0.684395i	0.939628	−	0.342198i	$-0.111171\pi$
$648$	108.165	+	201.961i	0.166921	+	0.311669i
$649$	1532.03			2.36060
$650$			608.647i			0.936380i
$651$		0			0
$652$	−231.852			−0.355602
$653$		−	869.173i		−	1.33105i	−0.746377	−	0.665523i	$-0.768209\pi$
$653$		−	869.173i		−	1.33105i	0.746377	−	0.665523i	$-0.231791\pi$
$654$	222.058	+	173.222i	0.339538	+	0.264865i
$655$	−49.4546			−0.0755032
$656$		−	113.540i		−	0.173079i
$657$	−113.380	−	451.847i	−0.172572	−	0.687743i
$658$		0			0
$659$			892.094i			1.35371i	0.736117	+	0.676854i	$0.236657\pi$
$659$			892.094i			1.35371i	−0.736117	+	0.676854i	$0.763343\pi$
$660$	−27.3291	+	35.0339i	−0.0414077	+	0.0530816i
$661$	−1220.80			−1.84690			−0.923448	−	0.383724i	$-0.874641\pi$
$661$	−1220.80			−1.84690			−0.923448	+	0.383724i	$0.874641\pi$
$662$		−	471.638i		−	0.712445i
$663$	−20.0712	−	15.6571i	−0.0302734	−	0.0236155i
$664$	251.047			0.378082
$665$		0			0
$666$	−12.3452	+	3.09772i	−0.0185363	+	0.00465122i
$667$	−316.192			−0.474051
$668$			398.739i			0.596914i
$669$	−2.90162	+	3.71966i	−0.00433725	+	0.00556003i
$670$	69.0246			0.103022
$671$		−	519.358i		−	0.774006i
$672$		0			0
$673$	−476.142			−0.707493			−0.353746	−	0.935341i	$-0.615092\pi$
$673$	−476.142			−0.707493			−0.353746	+	0.935341i	$0.615092\pi$
$674$			196.037i			0.290856i
$675$	−611.376	−	270.553i	−0.905742	−	0.400819i
$676$	−266.187			−0.393767
$677$		−	683.914i		−	1.01021i	−0.863057	−	0.505107i	$-0.831453\pi$
$677$		−	683.914i		−	1.01021i	0.863057	−	0.505107i	$-0.168547\pi$
$678$	−188.120	+	241.156i	−0.277464	+	0.355688i
$679$		0			0
$680$		−	0.674119i		−	0.000991351i
$681$	11.3550	+	8.85774i	0.0166740	+	0.0130070i
$682$	610.356			0.894950
$683$			210.563i			0.308291i	0.988048	+	0.154146i	$0.0492625\pi$
$683$			210.563i			0.308291i	−0.988048	+	0.154146i	$0.950737\pi$
$684$	−57.2629	−	228.208i	−0.0837177	−	0.333637i
$685$	−64.9067			−0.0947543
$686$		0			0
$687$	−575.346	+	737.551i	−0.837477	+	1.07358i
$688$	−8.56998			−0.0124564
$689$			1057.82i			1.53530i
$690$	10.9152	+	8.51468i	0.0158191	+	0.0123401i
$691$	−931.071			−1.34743			−0.673713	−	0.738993i	$-0.735302\pi$
$691$	−931.071			−1.34743			−0.673713	+	0.738993i	$0.735302\pi$
$692$		−	69.4632i		−	0.100380i
$693$		0			0
$694$	−606.494			−0.873910
$695$		−	34.9871i		−	0.0503411i
$696$	−246.904	+	316.513i	−0.354747	+	0.454760i
$697$	−13.8575			−0.0198816
$698$		−	235.093i		−	0.336809i
$699$	287.651	+	224.390i	0.411518	+	0.321015i
$700$		0			0
$701$		−	459.553i		−	0.655568i	−0.944753	−	0.327784i	$-0.893698\pi$
$701$		−	459.553i		−	0.655568i	0.944753	−	0.327784i	$-0.106302\pi$
$702$	268.570	−	606.896i	0.382578	−	0.864524i
$703$	13.0712			0.0185935
$704$			121.351i			0.172374i
$705$	−66.2913	+	84.9806i	−0.0940303	+	0.120540i
$706$	−402.641			−0.570313
$707$		0			0
$708$	−477.806	−	372.725i	−0.674867	−	0.526448i
$709$	−163.280			−0.230296			−0.115148	−	0.993348i	$-0.536734\pi$
$709$	−163.280			−0.230296			−0.115148	+	0.993348i	$0.536734\pi$
$710$			57.2355i			0.0806134i
$711$	146.182	+	582.573i	0.205600	+	0.819372i
$712$	−165.567			−0.232539
$713$		−	190.163i		−	0.266708i
$714$		0			0
$715$	128.712			0.180017
$716$			432.238i			0.603685i
$717$	−141.214	−	110.158i	−0.196951	−	0.153637i
$718$	−597.452			−0.832106
$719$		−	618.252i		−	0.859878i	−0.902858	−	0.429939i	$-0.858535\pi$
$719$		−	618.252i		−	0.859878i	0.902858	−	0.429939i	$-0.141465\pi$
$720$	17.0467	−	4.27742i	0.0236759	−	0.00594087i
$721$		0			0
$722$		−	268.902i		−	0.372441i
$723$	362.980	−	465.313i	0.502047	−	0.643587i
$724$	−640.187			−0.884236
$725$		−	1171.43i		−	1.61577i
$726$	−364.948	−	284.688i	−0.502684	−	0.392132i
$727$	870.614			1.19754			0.598772	−	0.800920i	$-0.295656\pi$
$727$	870.614			1.19754			0.598772	+	0.800920i	$0.295656\pi$
$728$		0			0
$729$	490.233	+	539.548i	0.672474	+	0.740121i
$730$	−35.7371			−0.0489549
$731$			1.04596i			0.00143086i
$732$	−126.354	+	161.976i	−0.172614	+	0.221279i
$733$	1157.67			1.57936			0.789678	−	0.613521i	$-0.210247\pi$
$733$	1157.67			1.57936			0.789678	+	0.613521i	$0.210247\pi$
$734$		−	241.125i		−	0.328508i
$735$		0			0
$736$	37.8083			0.0513700
$737$			1516.52i			2.05769i
$738$	−87.9288	−	350.419i	−0.119145	−	0.474823i
$739$	−467.882			−0.633129			−0.316564	−	0.948571i	$-0.602529\pi$
$739$	−467.882			−0.633129			−0.316564	+	0.948571i	$0.602529\pi$
$740$			0.976395i			0.00131945i
$741$	−419.211	+	537.398i	−0.565737	+	0.725233i
$742$		0			0
$743$			659.621i			0.887780i	0.896081	+	0.443890i	$0.146402\pi$
$743$			659.621i			0.887780i	−0.896081	+	0.443890i	$0.853598\pi$
$744$	−190.356	−	148.492i	−0.255855	−	0.199587i
$745$	−9.00000			−0.0120805
$746$			430.661i			0.577294i
$747$	774.806	−	194.418i	1.03722	−	0.260265i
$748$	14.8109			0.0198006
$749$		0			0
$750$	−63.3944	+	81.2669i	−0.0845259	+	0.108356i
$751$	152.698			0.203326			0.101663	−	0.994819i	$-0.467584\pi$
$751$	152.698			0.203326			0.101663	+	0.994819i	$0.467584\pi$
$752$			294.358i			0.391433i
$753$	−636.781	−	496.738i	−0.845659	−	0.659679i
$754$	1162.85			1.54224
$755$			24.4219i			0.0323469i
$756$		0			0
$757$	304.909			0.402786			0.201393	−	0.979510i	$-0.435453\pi$
$757$	304.909			0.402786			0.201393	+	0.979510i	$0.435453\pi$
$758$		−	725.349i		−	0.956925i
$759$	−187.073	+	239.814i	−0.246474	+	0.315961i
$760$	−18.0492			−0.0237489
$761$			1168.34i			1.53527i	0.640885	+	0.767637i	$0.278567\pi$
$761$			1168.34i			1.53527i	−0.640885	+	0.767637i	$0.721433\pi$
$762$	−198.641	−	154.955i	−0.260684	−	0.203353i
$763$		0			0
$764$		−	79.9013i		−	0.104583i
$765$	−0.522057	−	2.08053i	−0.000682427	−	0.00271965i
$766$	606.395			0.791639
$767$			1755.43i			2.28870i
$768$	29.5233	−	37.8467i	0.0384418	−	0.0492796i
$769$	684.909			0.890649			0.445325	−	0.895369i	$-0.353088\pi$
$769$	684.909			0.890649			0.445325	+	0.895369i	$0.353088\pi$
$770$		0			0
$771$	−446.462	−	348.274i	−0.579069	−	0.451718i
$772$	−693.705			−0.898581
$773$		−	1501.71i		−	1.94270i	−0.237649	−	0.971351i	$-0.576377\pi$
$773$		−	1501.71i		−	1.94270i	0.237649	−	0.971351i	$-0.423623\pi$
$774$	−26.4495	+	6.63684i	−0.0341725	+	0.00857473i
$775$	704.521			0.909059
$776$			70.9818i			0.0914713i
$777$		0			0
$778$	99.9779			0.128506
$779$			371.028i			0.476287i
$780$	−40.1425	−	31.3142i	−0.0514647	−	0.0401464i
$781$	−1257.50			−1.61012
$782$		−	4.61448i		−	0.00590087i
$783$	−516.904	+	1168.06i	−0.660159	+	1.49178i
$784$		0			0
$785$			0.488198i			0.000621908i
$786$	−264.345	+	338.871i	−0.336317	+	0.431133i
$787$	788.447			1.00184			0.500919	−	0.865494i	$-0.332995\pi$
$787$	788.447			1.00184			0.500919	+	0.865494i	$0.332995\pi$
$788$		−	184.723i		−	0.234421i
$789$	−490.426	−	382.570i	−0.621579	−	0.484880i
$790$	46.0763			0.0583245
$791$		0			0
$792$	93.9779	+	374.527i	0.118659	+	0.472887i
$793$	595.091			0.750430
$794$		−	75.4187i		−	0.0949858i
$795$	−54.8257	+	70.2825i	−0.0689631	+	0.0884056i
$796$	−86.4275			−0.108577
$797$			1050.25i			1.31775i	0.752253	+	0.658875i	$0.228967\pi$
$797$			1050.25i			1.31775i	−0.752253	+	0.658875i	$0.771033\pi$
$798$		0			0
$799$	35.9262			0.0449640
$800$			140.073i			0.175091i
$801$	−510.991	+	128.220i	−0.637941	+	0.160075i
$802$	−413.491			−0.515575
$803$		−	785.168i		−	0.977793i
$804$	368.951	−	472.967i	0.458894	−	0.588268i
$805$		0			0
$806$			699.358i			0.867690i
$807$	−432.769	−	337.593i	−0.536269	−	0.418331i
$808$	266.236			0.329500
$809$		−	295.055i		−	0.364715i	−0.983232	−	0.182358i	$-0.941627\pi$
$809$		−	295.055i		−	0.364715i	0.983232	−	0.182358i	$-0.0583729\pi$
$810$	49.2986	−	26.4028i	0.0608624	−	0.0325961i
$811$	1122.32			1.38387			0.691935	−	0.721960i	$-0.256758\pi$
$811$	1122.32			1.38387			0.691935	+	0.721960i	$0.256758\pi$
$812$		0			0
$813$	359.856	−	461.309i	0.442628	−	0.567416i
$814$	−21.4521			−0.0263539
$815$			56.5949i			0.0694416i
$816$	−4.61917	−	3.60330i	−0.00566075	−	0.00441581i
$817$	28.0051			0.0342779
$818$			6.45934i			0.00789650i
$819$		0			0
$820$	−27.7150			−0.0337988
$821$		−	1178.66i		−	1.43564i	−0.696227	−	0.717822i	$-0.745139\pi$
$821$		−	1178.66i		−	1.43564i	0.696227	−	0.717822i	$-0.254861\pi$
$822$	−346.940	+	444.751i	−0.422068	+	0.541060i
$823$	−365.980			−0.444691			−0.222345	−	0.974968i	$-0.571371\pi$
$823$	−365.980			−0.444691			−0.222345	+	0.974968i	$0.571371\pi$
$824$		−	26.8665i		−	0.0326049i
$825$	−888.469	−	693.074i	−1.07693	−	0.840089i
$826$		0			0
$827$		−	791.154i		−	0.956655i	−0.878182	−	0.478327i	$-0.841243\pi$
$827$		−	791.154i		−	0.956655i	0.878182	−	0.478327i	$-0.158757\pi$
$828$	116.688	−	29.2799i	0.140927	−	0.0353621i
$829$	−413.231			−0.498469			−0.249234	−	0.968443i	$-0.580179\pi$
$829$	−413.231			−0.498469			−0.249234	+	0.968443i	$0.580179\pi$
$830$		−	61.2802i		−	0.0738316i
$831$	−194.273	+	249.043i	−0.233782	+	0.299691i
$832$	−139.047			−0.167123
$833$		0			0
$834$	−239.737	−	187.013i	−0.287455	−	0.224237i
$835$	97.3316			0.116565
$836$		−	396.553i		−	0.474346i
$837$	−702.494	−	310.875i	−0.839299	−	0.371416i
$838$	−534.575			−0.637918
$839$			1406.19i			1.67603i	0.545650	+	0.838013i	$0.316283\pi$
$839$			1406.19i			1.67603i	−0.545650	+	0.838013i	$0.683717\pi$
$840$		0			0
$841$	−1397.08			−1.66122
$842$		−	1050.49i		−	1.24761i
$843$	1116.90	+	871.265i	1.32491	+	1.03353i
$844$	−612.285			−0.725456
$845$			64.9758i			0.0768945i
$846$	227.959	+	908.477i	0.269455	+	1.07385i
$847$		0			0
$848$			243.446i			0.287083i
$849$	−589.451	+	755.632i	−0.694288	+	0.890026i
$850$	17.0958			0.0201128
$851$			6.68363i			0.00785385i
$852$	392.187	+	305.936i	0.460313	+	0.359079i
$853$	−451.573			−0.529393			−0.264697	−	0.964332i	$-0.585272\pi$
$853$	−451.573			−0.529393			−0.264697	+	0.964332i	$0.585272\pi$
$854$		0			0
$855$	−55.7053	+	13.9778i	−0.0651523	+	0.0163483i
$856$	96.4275			0.112649
$857$			1133.12i			1.32220i	0.750299	+	0.661099i	$0.229910\pi$
$857$			1133.12i			1.32220i	−0.750299	+	0.661099i	$0.770090\pi$
$858$	687.995	−	881.958i	0.801859	−	1.02792i
$859$	−1088.21			−1.26683			−0.633415	−	0.773813i	$-0.718347\pi$
$859$	−1088.21			−1.26683			−0.633415	+	0.773813i	$0.718347\pi$
$860$			2.09192i			0.00243247i
$861$		0			0
$862$	535.644			0.621396
$863$		−	911.843i		−	1.05660i	−0.849059	−	0.528298i	$-0.822830\pi$
$863$		−	911.843i		−	1.05660i	0.849059	−	0.528298i	$-0.177170\pi$
$864$	61.8083	−	139.670i	0.0715374	−	0.161655i
$865$	−16.9559			−0.0196022
$866$		−	737.608i		−	0.851741i
$867$	532.825	−	683.042i	0.614562	−	0.787823i
$868$		0			0
$869$			1012.33i			1.16494i
$870$	77.2604	+	60.2690i	0.0888051	+	0.0692747i
$871$	−1737.66			−1.99501
$872$		−	187.753i		−	0.215313i
$873$	54.9703	+	219.071i	0.0629672	+	0.250941i
$874$	−123.550			−0.141362
$875$		0			0
$876$	−191.022	+	244.876i	−0.218062	+	0.279539i
$877$	−992.184			−1.13134			−0.565669	−	0.824632i	$-0.691382\pi$
$877$	−992.184			−1.13134			−0.565669	+	0.824632i	$0.691382\pi$
$878$		−	1032.54i		−	1.17601i
$879$	1129.71	+	881.260i	1.28522	+	1.00257i
$880$	29.6217			0.0336610
$881$		−	1072.77i		−	1.21768i	−0.793294	−	0.608838i	$-0.791636\pi$
$881$		−	1072.77i		−	1.21768i	0.793294	−	0.608838i	$-0.208364\pi$
$882$		0			0
$883$	615.282			0.696809			0.348405	−	0.937344i	$-0.386724\pi$
$883$	615.282			0.696809			0.348405	+	0.937344i	$0.386724\pi$
$884$			16.9706i			0.0191975i
$885$	−90.9818	+	116.632i	−0.102804	+	0.131787i
$886$	913.299			1.03081
$887$		−	167.439i		−	0.188770i	−0.995536	−	0.0943848i	$-0.969912\pi$
$887$		−	167.439i		−	0.188770i	0.995536	−	0.0943848i	$-0.0300884\pi$
$888$	6.69042	+	5.21904i	0.00753425	+	0.00587729i
$889$		0			0
$890$			40.4148i			0.0454099i
$891$	580.089	+	1083.12i	0.651053	+	1.21563i
$892$	3.14503			0.00352582
$893$		−	961.906i		−	1.07716i
$894$	−48.1069	+	61.6694i	−0.0538108	+	0.0689815i
$895$	105.509			0.117887
$896$		0			0
$897$	−274.784	−	214.352i	−0.306336	−	0.238966i
$898$	964.044			1.07355
$899$		−	1346.02i		−	1.49724i
$900$	108.477	+	432.308i	0.120530	+	0.480342i
$901$	29.7125			0.0329772
$902$		−	608.918i		−	0.675075i
$903$		0			0
$904$	203.902			0.225555
$905$			156.269i			0.172673i
$906$	167.343	+	130.540i	0.184705	+	0.144084i
$907$	1583.54			1.74591			0.872956	−	0.487798i	$-0.162200\pi$
$907$	1583.54			1.74591			0.872956	+	0.487798i	$0.162200\pi$
$908$		−	9.60081i		−	0.0105736i
$909$	821.684	−	206.181i	0.903943	−	0.226821i
$910$		0			0
$911$		−	375.771i		−	0.412481i	−0.978501	−	0.206241i	$-0.933877\pi$
$911$		−	375.771i		−	0.412481i	0.978501	−	0.206241i	$-0.0661230\pi$
$912$	−96.4767	+	123.676i	−0.105786	+	0.135610i
$913$	1346.37			1.47466
$914$		−	88.9635i		−	0.0973342i
$915$	39.5382	+	30.8428i	0.0432111	+	0.0337080i
$916$	623.612			0.680799
$917$		0			0
$918$	−17.0467	−	7.54367i	−0.0185693	−	0.00821750i
$919$	181.729			0.197747			0.0988735	−	0.995100i	$-0.468476\pi$
$919$	181.729			0.197747			0.0988735	+	0.995100i	$0.468476\pi$
$920$		−	9.22897i		−	0.0100315i
$921$	193.044	−	247.468i	0.209603	−	0.268695i
$922$	159.946			0.173477
$923$		−	1440.87i		−	1.56107i
$924$		0			0
$925$	−24.7617			−0.0267694
$926$			842.802i			0.910153i
$927$	−20.8062	−	82.9180i	−0.0224446	−	0.0894477i
$928$	267.617			0.288380
$929$			1617.09i			1.74067i	0.492456	+	0.870337i	$0.336099\pi$
$929$			1617.09i			1.74067i	−0.492456	+	0.870337i	$0.663901\pi$
$930$	−36.2468	+	46.4657i	−0.0389751	+	0.0499632i
$931$		0			0
$932$		−	243.214i		−	0.260959i
$933$	−455.947	−	355.674i	−0.488689	−	0.381215i
$934$	−738.395			−0.790573
$935$		−	3.61531i		−	0.00386664i
$936$	−429.140	+	107.682i	−0.458483	+	0.115045i
$937$	−911.700			−0.972999			−0.486499	−	0.873681i	$-0.661726\pi$
$937$	−911.700			−0.972999			−0.486499	+	0.873681i	$0.661726\pi$
$938$		0			0
$939$	998.076	−	1279.46i	1.06291	−	1.36258i
$940$	71.8524			0.0764388
$941$			353.639i			0.375811i	0.982187	+	0.187906i	$0.0601699\pi$
$941$			353.639i			0.375811i	−0.982187	+	0.187906i	$0.939830\pi$
$942$	3.34521	+	2.60952i	0.00355118	+	0.00277019i
$943$	−189.715			−0.201182
$944$			403.992i			0.427958i
$945$		0			0
$946$	−45.9610			−0.0485845
$947$			70.8234i			0.0747872i	0.999301	+	0.0373936i	$0.0119055\pi$
$947$			70.8234i			0.0747872i	−0.999301	+	0.0373936i	$0.988094\pi$
$948$	246.288	−	315.722i	0.259797	−	0.333040i
$949$	899.661			0.948009
$950$		−	457.733i		−	0.481824i
$951$	−732.243	−	571.206i	−0.769972	−	0.600637i
$952$		0			0
$953$		−	302.798i		−	0.317731i	−0.987300	−	0.158866i	$-0.949216\pi$
$953$		−	302.798i		−	0.317731i	0.987300	−	0.158866i	$-0.0507836\pi$
$954$	188.532	+	751.349i	0.197622	+	0.787577i
$955$	−19.5038			−0.0204228
$956$			119.398i			0.124894i
$957$	−1324.15	+	1697.46i	−1.38365	+	1.77373i
$958$	−1003.02			−1.04699
$959$		0			0
$960$	−9.23834	−	7.20661i	−0.00962327	−	0.00750688i
$961$	−151.479			−0.157627
$962$		−	24.5802i		−	0.0255512i
$963$	297.604	−	74.6762i	0.309039	−	0.0775454i
$964$	−393.430			−0.408122
$965$			169.333i			0.175474i
$966$		0			0
$967$	693.562			0.717231			0.358615	−	0.933485i	$-0.383249\pi$
$967$	693.562			0.717231			0.358615	+	0.933485i	$0.383249\pi$
$968$			308.570i			0.318770i
$969$	15.0946	+	11.7749i	0.0155775	+	0.0121516i
$970$	17.3266			0.0178624
$971$		−	1333.25i		−	1.37307i	−0.727099	−	0.686533i	$-0.759132\pi$
$971$		−	1333.25i		−	1.37307i	0.727099	−	0.686533i	$-0.240868\pi$
$972$	82.5946	−	478.930i	0.0849738	−	0.492727i
$973$		0			0
$974$			572.447i			0.587728i
$975$	794.137	−	1018.03i	0.814500	−	1.04413i
$976$	136.953			0.140321
$977$		−	172.984i		−	0.177056i	−0.996074	−	0.0885281i	$-0.971784\pi$
$977$		−	172.984i		−	0.177056i	0.996074	−	0.0885281i	$-0.0282163\pi$
$978$	387.797	+	302.512i	0.396521	+	0.309317i
$979$	−887.941			−0.906988
$980$		0			0
$981$	−145.402	−	579.464i	−0.148218	−	0.590687i
$982$	286.422			0.291673
$983$			1075.76i			1.09436i	0.837014	+	0.547182i	$0.184299\pi$
$983$			1075.76i			1.09436i	−0.837014	+	0.547182i	$0.815701\pi$
$984$	−148.142	+	189.908i	−0.150551	+	0.192996i
$985$	−45.0908			−0.0457774
$986$		−	32.6625i		−	0.0331262i
$987$		0			0
$988$	454.378			0.459897
$989$			14.3196i			0.0144789i
$990$	91.4215	−	22.9399i	0.0923450	−	0.0231716i
$991$	−169.214			−0.170750			−0.0853752	−	0.996349i	$-0.527209\pi$
$991$	−169.214			−0.170750			−0.0853752	+	0.996349i	$0.527209\pi$
$992$			160.949i			0.162247i
$993$	−615.374	+	788.864i	−0.619712	+	0.794425i
$994$		0			0
$995$			21.0968i			0.0212029i
$996$	−419.902	−	327.555i	−0.421588	−	0.328871i
$997$	1586.71			1.59148			0.795742	−	0.605636i	$-0.207081\pi$
$997$	1586.71			1.59148			0.795742	+	0.605636i	$0.207081\pi$
$998$			27.1099i			0.0271643i
$999$	24.6904	+	10.9263i	0.0247151	+	0.0109372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.b.e.197.4		4
3.2	odd	2	inner	294.3.b.e.197.2		4
7.2	even	3		294.3.h.h.263.4		8
7.3	odd	6		42.3.h.b.23.2	yes	8
7.4	even	3		294.3.h.h.275.1		8
7.5	odd	6		42.3.h.b.11.3	yes	8
7.6	odd	2		294.3.b.i.197.3		4
21.2	odd	6		294.3.h.h.263.1		8
21.5	even	6		42.3.h.b.11.2	✓	8
21.11	odd	6		294.3.h.h.275.4		8
21.17	even	6		42.3.h.b.23.3	yes	8
21.20	even	2		294.3.b.i.197.1		4
28.3	even	6		336.3.bn.g.65.1		8
28.19	even	6		336.3.bn.g.305.3		8
84.47	odd	6		336.3.bn.g.305.1		8
84.59	odd	6		336.3.bn.g.65.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.2	✓	8	21.5	even	6
42.3.h.b.11.3	yes	8	7.5	odd	6
42.3.h.b.23.2	yes	8	7.3	odd	6
42.3.h.b.23.3	yes	8	21.17	even	6
294.3.b.e.197.2		4	3.2	odd	2	inner
294.3.b.e.197.4		4	1.1	even	1	trivial
294.3.b.i.197.1		4	21.20	even	2
294.3.b.i.197.3		4	7.6	odd	2
294.3.h.h.263.1		8	21.2	odd	6
294.3.h.h.263.4		8	7.2	even	3
294.3.h.h.275.1		8	7.4	even	3
294.3.h.h.275.4		8	21.11	odd	6
336.3.bn.g.65.1		8	28.3	even	6
336.3.bn.g.65.3		8	84.59	odd	6
336.3.bn.g.305.1		8	84.47	odd	6
336.3.bn.g.305.3		8	28.19	even	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(1.84521 - 2.36542i) q^{3} -2.00000 q^{4} +0.488198i q^{5} +(3.34521 + 2.60952i) q^{6} -2.82843i q^{8} +(-2.19042 - 8.72938i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(1.84521 - 2.36542i) q^{3} -2.00000 q^{4} +0.488198i q^{5} +(3.34521 + 2.60952i) q^{6} -2.82843i q^{8} +(-2.19042 - 8.72938i) q^{9} -0.690416 q^{10} -15.1689i q^{11} +(-3.69042 + 4.73084i) q^{12} +17.3808 q^{13} +(1.15479 + 0.900826i) q^{15} +4.00000 q^{16} -0.488198i q^{17} +(12.3452 - 3.09772i) q^{18} -13.0712 q^{19} -0.976395i q^{20} +21.4521 q^{22} -6.68363i q^{23} +(-6.69042 - 5.21904i) q^{24} +24.7617 q^{25} +24.5802i q^{26} +(-24.6904 - 10.9263i) q^{27} -47.3084i q^{29} +(-1.27396 + 1.63312i) q^{30} +28.4521 q^{31} +5.65685i q^{32} +(-35.8808 - 27.9898i) q^{33} +0.690416 q^{34} +(4.38083 + 17.4588i) q^{36} -1.00000 q^{37} -18.4855i q^{38} +(32.0712 - 41.1130i) q^{39} +1.38083 q^{40} -28.3850i q^{41} -2.14249 q^{43} +30.3378i q^{44} +(4.26166 - 1.06936i) q^{45} +9.45208 q^{46} +73.5895i q^{47} +(7.38083 - 9.46168i) q^{48} +35.0183i q^{50} +(-1.15479 - 0.900826i) q^{51} -34.7617 q^{52} +60.8616i q^{53} +(15.4521 - 34.9175i) q^{54} +7.40543 q^{55} +(-24.1192 + 30.9190i) q^{57} +66.9042 q^{58} +100.998i q^{59} +(-2.30958 - 1.80165i) q^{60} +34.2383 q^{61} +40.2373i q^{62} -8.00000 q^{64} +8.48528i q^{65} +(39.5835 - 50.7432i) q^{66} -99.9754 q^{67} +0.976395i q^{68} +(-15.8096 - 12.3327i) q^{69} -82.9000i q^{71} +(-24.6904 + 6.19543i) q^{72} +51.7617 q^{73} -1.41421i q^{74} +(45.6904 - 58.5717i) q^{75} +26.1425 q^{76} +(58.1425 + 45.3556i) q^{78} -66.7371 q^{79} +1.95279i q^{80} +(-71.4042 + 38.2419i) q^{81} +40.1425 q^{82} +88.7584i q^{83} +0.238337 q^{85} -3.02994i q^{86} +(-111.904 - 87.2938i) q^{87} -42.9042 q^{88} -58.5369i q^{89} +(1.51230 + 6.02690i) q^{90} +13.3673i q^{92} +(52.5000 - 67.3011i) q^{93} -104.071 q^{94} -6.38135i q^{95} +(13.3808 + 10.4381i) q^{96} -25.0958 q^{97} +(-132.415 + 33.2262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9	\( 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9} + 16 q^{10} + 4 q^{12} + 32 q^{13} + 14 q^{15} + 16 q^{16} + 40 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} + 24 q^{25} - 80 q^{27} - 52 q^{30} + 20 q^{31} - 106 q^{33} - 16 q^{34} - 20 q^{36} - 4 q^{37} + 72 q^{39} - 32 q^{40} + 104 q^{43} - 58 q^{45} - 56 q^{46} - 8 q^{48} - 14 q^{51} - 64 q^{52} - 32 q^{54} + 236 q^{55} - 134 q^{57} + 80 q^{58} - 28 q^{60} + 212 q^{61} - 32 q^{64} + 224 q^{66} - 156 q^{67} - 82 q^{69} - 80 q^{72} + 132 q^{73} + 164 q^{75} - 8 q^{76} + 120 q^{78} + 52 q^{79} - 98 q^{81} + 48 q^{82} + 76 q^{85} - 260 q^{87} + 16 q^{88} + 128 q^{90} + 210 q^{93} - 360 q^{94} + 16 q^{96} - 288 q^{97} - 70 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9 + 16 * q^10 + 4 * q^12 + 32 * q^13 + 14 * q^15 + 16 * q^16 + 40 * q^18 + 4 * q^19 - 8 * q^22 - 8 * q^24 + 24 * q^25 - 80 * q^27 - 52 * q^30 + 20 * q^31 - 106 * q^33 - 16 * q^34 - 20 * q^36 - 4 * q^37 + 72 * q^39 - 32 * q^40 + 104 * q^43 - 58 * q^45 - 56 * q^46 - 8 * q^48 - 14 * q^51 - 64 * q^52 - 32 * q^54 + 236 * q^55 - 134 * q^57 + 80 * q^58 - 28 * q^60 + 212 * q^61 - 32 * q^64 + 224 * q^66 - 156 * q^67 - 82 * q^69 - 80 * q^72 + 132 * q^73 + 164 * q^75 - 8 * q^76 + 120 * q^78 + 52 * q^79 - 98 * q^81 + 48 * q^82 + 76 * q^85 - 260 * q^87 + 16 * q^88 + 128 * q^90 + 210 * q^93 - 360 * q^94 + 16 * q^96 - 288 * q^97 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more