LMFDB - Embedded newform 196.3.c.e.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,3,Mod(99,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, 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("196.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.c (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:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	196.99
Dual form			196.3.c.e.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} -2.44949i q^{3} +(-2.00000 - 3.46410i) q^{4} -5.65685 q^{5} +(4.24264 + 2.44949i) q^{6} +8.00000 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} -2.44949i q^{3} +(-2.00000 - 3.46410i) q^{4} -5.65685 q^{5} +(4.24264 + 2.44949i) q^{6} +8.00000 q^{8} +3.00000 q^{9} +(5.65685 - 9.79796i) q^{10} +17.3205i q^{11} +(-8.48528 + 4.89898i) q^{12} -14.1421 q^{13} +13.8564i q^{15} +(-8.00000 + 13.8564i) q^{16} +18.3848 q^{17} +(-3.00000 + 5.19615i) q^{18} +26.9444i q^{19} +(11.3137 + 19.5959i) q^{20} +(-30.0000 - 17.3205i) q^{22} +27.7128i q^{23} -19.5959i q^{24} +7.00000 q^{25} +(14.1421 - 24.4949i) q^{26} -29.3939i q^{27} +2.00000 q^{29} +(-24.0000 - 13.8564i) q^{30} +14.6969i q^{31} +(-16.0000 - 27.7128i) q^{32} +42.4264 q^{33} +(-18.3848 + 31.8434i) q^{34} +(-6.00000 - 10.3923i) q^{36} -30.0000 q^{37} +(-46.6690 - 26.9444i) q^{38} +34.6410i q^{39} -45.2548 q^{40} -24.0416 q^{41} +24.2487i q^{43} +(60.0000 - 34.6410i) q^{44} -16.9706 q^{45} +(-48.0000 - 27.7128i) q^{46} -24.4949i q^{47} +(33.9411 + 19.5959i) q^{48} +(-7.00000 + 12.1244i) q^{50} -45.0333i q^{51} +(28.2843 + 48.9898i) q^{52} +66.0000 q^{53} +(50.9117 + 29.3939i) q^{54} -97.9796i q^{55} +66.0000 q^{57} +(-2.00000 + 3.46410i) q^{58} +66.1362i q^{59} +(48.0000 - 27.7128i) q^{60} -45.2548 q^{61} +(-25.4558 - 14.6969i) q^{62} +64.0000 q^{64} +80.0000 q^{65} +(-42.4264 + 73.4847i) q^{66} -6.92820i q^{67} +(-36.7696 - 63.6867i) q^{68} +67.8823 q^{69} -48.4974i q^{71} +24.0000 q^{72} +18.3848 q^{73} +(30.0000 - 51.9615i) q^{74} -17.1464i q^{75} +(93.3381 - 53.8888i) q^{76} +(-60.0000 - 34.6410i) q^{78} -20.7846i q^{79} +(45.2548 - 78.3837i) q^{80} -45.0000 q^{81} +(24.0416 - 41.6413i) q^{82} +154.318i q^{83} -104.000 q^{85} +(-42.0000 - 24.2487i) q^{86} -4.89898i q^{87} +138.564i q^{88} +24.0416 q^{89} +(16.9706 - 29.3939i) q^{90} +(96.0000 - 55.4256i) q^{92} +36.0000 q^{93} +(42.4264 + 24.4949i) q^{94} -152.420i q^{95} +(-67.8823 + 39.1918i) q^{96} -83.4386 q^{97} +51.9615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 + 12 * q^9	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} + 12 q^{9} - 32 q^{16} - 12 q^{18} - 120 q^{22} + 28 q^{25} + 8 q^{29} - 96 q^{30} - 64 q^{32} - 24 q^{36} - 120 q^{37} + 240 q^{44} - 192 q^{46} - 28 q^{50} + 264 q^{53} + 264 q^{57} - 8 q^{58} + 192 q^{60} + 256 q^{64} + 320 q^{65} + 96 q^{72} + 120 q^{74} - 240 q^{78} - 180 q^{81} - 416 q^{85} - 168 q^{86} + 384 q^{92} + 144 q^{93}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 + 12 * q^9 - 32 * q^16 - 12 * q^18 - 120 * q^22 + 28 * q^25 + 8 * q^29 - 96 * q^30 - 64 * q^32 - 24 * q^36 - 120 * q^37 + 240 * q^44 - 192 * q^46 - 28 * q^50 + 264 * q^53 + 264 * q^57 - 8 * q^58 + 192 * q^60 + 256 * q^64 + 320 * q^65 + 96 * q^72 + 120 * q^74 - 240 * q^78 - 180 * q^81 - 416 * q^85 - 168 * q^86 + 384 * q^92 + 144 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$3$		−	2.44949i		−	0.816497i	−0.912871	−	0.408248i	$-0.866140\pi$
$3$		−	2.44949i		−	0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−5.65685			−1.13137			−0.565685	−	0.824621i	$-0.691388\pi$
$5$	−5.65685			−1.13137			−0.565685	+	0.824621i	$0.691388\pi$
$6$	4.24264	+	2.44949i	0.707107	+	0.408248i
$7$		0			0
$7$		0			0
$8$	8.00000			1.00000
$9$	3.00000			0.333333
$10$	5.65685	−	9.79796i	0.565685	−	0.979796i
$11$			17.3205i			1.57459i	0.616575	+	0.787296i	$0.288520\pi$
$11$			17.3205i			1.57459i	−0.616575	+	0.787296i	$0.711480\pi$
$12$	−8.48528	+	4.89898i	−0.707107	+	0.408248i
$13$	−14.1421			−1.08786			−0.543928	−	0.839132i	$-0.683064\pi$
$13$	−14.1421			−1.08786			−0.543928	+	0.839132i	$0.683064\pi$
$14$		0			0
$15$			13.8564i			0.923760i
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	18.3848			1.08146			0.540729	−	0.841197i	$-0.318149\pi$
$17$	18.3848			1.08146			0.540729	+	0.841197i	$0.318149\pi$
$18$	−3.00000	+	5.19615i	−0.166667	+	0.288675i
$19$			26.9444i			1.41813i	0.705145	+	0.709063i	$0.250882\pi$
$19$			26.9444i			1.41813i	−0.705145	+	0.709063i	$0.749118\pi$
$20$	11.3137	+	19.5959i	0.565685	+	0.979796i
$21$		0			0
$22$	−30.0000	−	17.3205i	−1.36364	−	0.787296i
$23$			27.7128i			1.20490i	0.798155	+	0.602452i	$0.205810\pi$
$23$			27.7128i			1.20490i	−0.798155	+	0.602452i	$0.794190\pi$
$24$		−	19.5959i		−	0.816497i
$25$	7.00000			0.280000
$26$	14.1421	−	24.4949i	0.543928	−	0.942111i
$27$		−	29.3939i		−	1.08866i
$28$		0			0
$29$	2.00000			0.0689655			0.0344828	−	0.999405i	$-0.489022\pi$
$29$	2.00000			0.0689655			0.0344828	+	0.999405i	$0.489022\pi$
$30$	−24.0000	−	13.8564i	−0.800000	−	0.461880i
$31$			14.6969i			0.474095i	0.971498	+	0.237047i	$0.0761797\pi$
$31$			14.6969i			0.474095i	−0.971498	+	0.237047i	$0.923820\pi$
$32$	−16.0000	−	27.7128i	−0.500000	−	0.866025i
$33$	42.4264			1.28565
$34$	−18.3848	+	31.8434i	−0.540729	+	0.936570i
$35$		0			0
$36$	−6.00000	−	10.3923i	−0.166667	−	0.288675i
$37$	−30.0000			−0.810811			−0.405405	−	0.914137i	$-0.632870\pi$
$37$	−30.0000			−0.810811			−0.405405	+	0.914137i	$0.632870\pi$
$38$	−46.6690	−	26.9444i	−1.22813	−	0.709063i
$39$			34.6410i			0.888231i
$40$	−45.2548			−1.13137
$41$	−24.0416			−0.586381			−0.293191	−	0.956054i	$-0.594717\pi$
$41$	−24.0416			−0.586381			−0.293191	+	0.956054i	$0.594717\pi$
$42$		0			0
$43$			24.2487i			0.563924i	0.959426	+	0.281962i	$0.0909851\pi$
$43$			24.2487i			0.563924i	−0.959426	+	0.281962i	$0.909015\pi$
$44$	60.0000	−	34.6410i	1.36364	−	0.787296i
$45$	−16.9706			−0.377124
$46$	−48.0000	−	27.7128i	−1.04348	−	0.602452i
$47$		−	24.4949i		−	0.521168i	−0.965451	−	0.260584i	$-0.916085\pi$
$47$		−	24.4949i		−	0.521168i	0.965451	−	0.260584i	$-0.0839151\pi$
$48$	33.9411	+	19.5959i	0.707107	+	0.408248i
$49$		0			0
$50$	−7.00000	+	12.1244i	−0.140000	+	0.242487i
$51$		−	45.0333i		−	0.883006i
$52$	28.2843	+	48.9898i	0.543928	+	0.942111i
$53$	66.0000			1.24528			0.622642	−	0.782507i	$-0.286060\pi$
$53$	66.0000			1.24528			0.622642	+	0.782507i	$0.286060\pi$
$54$	50.9117	+	29.3939i	0.942809	+	0.544331i
$55$		−	97.9796i		−	1.78145i
$56$		0			0
$57$	66.0000			1.15789
$58$	−2.00000	+	3.46410i	−0.0344828	+	0.0597259i
$59$			66.1362i			1.12095i	0.828170	+	0.560476i	$0.189382\pi$
$59$			66.1362i			1.12095i	−0.828170	+	0.560476i	$0.810618\pi$
$60$	48.0000	−	27.7128i	0.800000	−	0.461880i
$61$	−45.2548			−0.741883			−0.370941	−	0.928656i	$-0.620965\pi$
$61$	−45.2548			−0.741883			−0.370941	+	0.928656i	$0.620965\pi$
$62$	−25.4558	−	14.6969i	−0.410578	−	0.237047i
$63$		0			0
$64$	64.0000			1.00000
$65$	80.0000			1.23077
$66$	−42.4264	+	73.4847i	−0.642824	+	1.11340i
$67$		−	6.92820i		−	0.103406i	−0.998663	−	0.0517030i	$-0.983535\pi$
$67$		−	6.92820i		−	0.103406i	0.998663	−	0.0517030i	$-0.0164649\pi$
$68$	−36.7696	−	63.6867i	−0.540729	−	0.936570i
$69$	67.8823			0.983801
$70$		0			0
$71$		−	48.4974i		−	0.683062i	−0.939870	−	0.341531i	$-0.889055\pi$
$71$		−	48.4974i		−	0.683062i	0.939870	−	0.341531i	$-0.110945\pi$
$72$	24.0000			0.333333
$73$	18.3848			0.251846			0.125923	−	0.992040i	$-0.459811\pi$
$73$	18.3848			0.251846			0.125923	+	0.992040i	$0.459811\pi$
$74$	30.0000	−	51.9615i	0.405405	−	0.702183i
$75$		−	17.1464i		−	0.228619i
$76$	93.3381	−	53.8888i	1.22813	−	0.709063i
$77$		0			0
$78$	−60.0000	−	34.6410i	−0.769231	−	0.444116i
$79$		−	20.7846i		−	0.263096i	−0.991310	−	0.131548i	$-0.958005\pi$
$79$		−	20.7846i		−	0.263096i	0.991310	−	0.131548i	$-0.0419948\pi$
$80$	45.2548	−	78.3837i	0.565685	−	0.979796i
$81$	−45.0000			−0.555556
$82$	24.0416	−	41.6413i	0.293191	−	0.507821i
$83$			154.318i			1.85925i	0.368505	+	0.929626i	$0.379870\pi$
$83$			154.318i			1.85925i	−0.368505	+	0.929626i	$0.620130\pi$
$84$		0			0
$85$	−104.000			−1.22353
$86$	−42.0000	−	24.2487i	−0.488372	−	0.281962i
$87$		−	4.89898i		−	0.0563101i
$88$			138.564i			1.57459i
$89$	24.0416			0.270131			0.135065	−	0.990837i	$-0.456876\pi$
$89$	24.0416			0.270131			0.135065	+	0.990837i	$0.456876\pi$
$90$	16.9706	−	29.3939i	0.188562	−	0.326599i
$91$		0			0
$92$	96.0000	−	55.4256i	1.04348	−	0.602452i
$93$	36.0000			0.387097
$94$	42.4264	+	24.4949i	0.451345	+	0.260584i
$95$		−	152.420i		−	1.60443i
$96$	−67.8823	+	39.1918i	−0.707107	+	0.408248i
$97$	−83.4386			−0.860192			−0.430096	−	0.902783i	$-0.641520\pi$
$97$	−83.4386			−0.860192			−0.430096	+	0.902783i	$0.641520\pi$
$98$		0			0
$99$			51.9615i			0.524864i
$100$	−14.0000	−	24.2487i	−0.140000	−	0.242487i
$101$	−90.5097			−0.896135			−0.448068	−	0.894000i	$-0.647888\pi$
$101$	−90.5097			−0.896135			−0.448068	+	0.894000i	$0.647888\pi$
$102$	78.0000	+	45.0333i	0.764706	+	0.441503i
$103$			44.0908i			0.428066i	0.976826	+	0.214033i	$0.0686600\pi$
$103$			44.0908i			0.428066i	−0.976826	+	0.214033i	$0.931340\pi$
$104$	−113.137			−1.08786
$105$		0			0
$106$	−66.0000	+	114.315i	−0.622642	+	1.07845i
$107$		−	20.7846i		−	0.194249i	−0.995272	−	0.0971243i	$-0.969036\pi$
$107$		−	20.7846i		−	0.194249i	0.995272	−	0.0971243i	$-0.0309645\pi$
$108$	−101.823	+	58.7878i	−0.942809	+	0.544331i
$109$	−186.000			−1.70642			−0.853211	−	0.521566i	$-0.825348\pi$
$109$	−186.000			−1.70642			−0.853211	+	0.521566i	$0.825348\pi$
$110$	169.706	+	97.9796i	1.54278	+	0.890724i
$111$			73.4847i			0.662024i
$112$		0			0
$113$	−12.0000			−0.106195			−0.0530973	−	0.998589i	$-0.516909\pi$
$113$	−12.0000			−0.106195			−0.0530973	+	0.998589i	$0.516909\pi$
$114$	−66.0000	+	114.315i	−0.578947	+	1.00277i
$115$		−	156.767i		−	1.36319i
$116$	−4.00000	−	6.92820i	−0.0344828	−	0.0597259i
$117$	−42.4264			−0.362619
$118$	−114.551	−	66.1362i	−0.970774	−	0.560476i
$119$		0			0
$120$			110.851i			0.923760i
$121$	−179.000			−1.47934
$122$	45.2548	−	78.3837i	0.370941	−	0.642489i
$123$			58.8897i			0.478778i
$124$	50.9117	−	29.3939i	0.410578	−	0.237047i
$125$	101.823			0.814587
$126$		0			0
$127$		−	145.492i		−	1.14561i	−0.819692	−	0.572804i	$-0.805856\pi$
$127$		−	145.492i		−	1.14561i	0.819692	−	0.572804i	$-0.194144\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$	59.3970			0.460442
$130$	−80.0000	+	138.564i	−0.615385	+	1.06588i
$131$		−	75.9342i		−	0.579650i	−0.957080	−	0.289825i	$-0.906403\pi$
$131$		−	75.9342i		−	0.579650i	0.957080	−	0.289825i	$-0.0935971\pi$
$132$	−84.8528	−	146.969i	−0.642824	−	1.11340i
$133$		0			0
$134$	12.0000	+	6.92820i	0.0895522	+	0.0517030i
$135$			166.277i			1.23168i
$136$	147.078			1.08146
$137$	164.000			1.19708			0.598540	−	0.801093i	$-0.295748\pi$
$137$	164.000			1.19708			0.598540	+	0.801093i	$0.295748\pi$
$138$	−67.8823	+	117.576i	−0.491900	+	0.851996i
$139$			85.7321i			0.616778i	0.951260	+	0.308389i	$0.0997898\pi$
$139$			85.7321i			0.616778i	−0.951260	+	0.308389i	$0.900210\pi$
$140$		0			0
$141$	−60.0000			−0.425532
$142$	84.0000	+	48.4974i	0.591549	+	0.341531i
$143$		−	244.949i		−	1.71293i
$144$	−24.0000	+	41.5692i	−0.166667	+	0.288675i
$145$	−11.3137			−0.0780256
$146$	−18.3848	+	31.8434i	−0.125923	+	0.218105i
$147$		0			0
$148$	60.0000	+	103.923i	0.405405	+	0.702183i
$149$	−114.000			−0.765101			−0.382550	−	0.923935i	$-0.624954\pi$
$149$	−114.000			−0.765101			−0.382550	+	0.923935i	$0.624954\pi$
$150$	29.6985	+	17.1464i	0.197990	+	0.114310i
$151$		−	6.92820i		−	0.0458821i	−0.999737	−	0.0229411i	$-0.992697\pi$
$151$		−	6.92820i		−	0.0458821i	0.999737	−	0.0229411i	$-0.00730301\pi$
$152$			215.555i			1.41813i
$153$	55.1543			0.360486
$154$		0			0
$155$		−	83.1384i		−	0.536377i
$156$	120.000	−	69.2820i	0.769231	−	0.444116i
$157$	−31.1127			−0.198170			−0.0990850	−	0.995079i	$-0.531592\pi$
$157$	−31.1127			−0.198170			−0.0990850	+	0.995079i	$0.531592\pi$
$158$	36.0000	+	20.7846i	0.227848	+	0.131548i
$159$		−	161.666i		−	1.01677i
$160$	90.5097	+	156.767i	0.565685	+	0.979796i
$161$		0			0
$162$	45.0000	−	77.9423i	0.277778	−	0.481125i
$163$		−	45.0333i		−	0.276278i	−0.990413	−	0.138139i	$-0.955888\pi$
$163$		−	45.0333i		−	0.276278i	0.990413	−	0.138139i	$-0.0441121\pi$
$164$	48.0833	+	83.2827i	0.293191	+	0.507821i
$165$	−240.000			−1.45455
$166$	−267.286	−	154.318i	−1.61016	−	0.929626i
$167$			171.464i			1.02673i	0.858170	+	0.513366i	$0.171602\pi$
$167$			171.464i			1.02673i	−0.858170	+	0.513366i	$0.828398\pi$
$168$		0			0
$169$	31.0000			0.183432
$170$	104.000	−	180.133i	0.611765	−	1.05961i
$171$			80.8332i			0.472709i
$172$	84.0000	−	48.4974i	0.488372	−	0.281962i
$173$	−104.652			−0.604924			−0.302462	−	0.953161i	$-0.597808\pi$
$173$	−104.652			−0.604924			−0.302462	+	0.953161i	$0.597808\pi$
$174$	8.48528	+	4.89898i	0.0487660	+	0.0281551i
$175$		0			0
$176$	−240.000	−	138.564i	−1.36364	−	0.787296i
$177$	162.000			0.915254
$178$	−24.0416	+	41.6413i	−0.135065	+	0.233940i
$179$		−	200.918i		−	1.12245i	−0.827665	−	0.561223i	$-0.810331\pi$
$179$		−	200.918i		−	1.12245i	0.827665	−	0.561223i	$-0.189669\pi$
$180$	33.9411	+	58.7878i	0.188562	+	0.326599i
$181$	302.642			1.67205			0.836027	−	0.548689i	$-0.184873\pi$
$181$	302.642			1.67205			0.836027	+	0.548689i	$0.184873\pi$
$182$		0			0
$183$			110.851i			0.605745i
$184$			221.703i			1.20490i
$185$	169.706			0.917328
$186$	−36.0000	+	62.3538i	−0.193548	+	0.335236i
$187$			318.434i			1.70285i
$188$	−84.8528	+	48.9898i	−0.451345	+	0.260584i
$189$		0			0
$190$	264.000	+	152.420i	1.38947	+	0.802213i
$191$		−	20.7846i		−	0.108820i	−0.998519	−	0.0544100i	$-0.982672\pi$
$191$		−	20.7846i		−	0.108820i	0.998519	−	0.0544100i	$-0.0173278\pi$
$192$		−	156.767i		−	0.816497i
$193$	304.000			1.57513			0.787565	−	0.616232i	$-0.211342\pi$
$193$	304.000			1.57513			0.787565	+	0.616232i	$0.211342\pi$
$194$	83.4386	−	144.520i	0.430096	−	0.744948i
$195$		−	195.959i		−	1.00492i
$196$		0			0
$197$	198.000			1.00508			0.502538	−	0.864555i	$-0.332400\pi$
$197$	198.000			1.00508			0.502538	+	0.864555i	$0.332400\pi$
$198$	−90.0000	−	51.9615i	−0.454545	−	0.262432i
$199$			289.040i			1.45246i	0.687451	+	0.726231i	$0.258730\pi$
$199$			289.040i			1.45246i	−0.687451	+	0.726231i	$0.741270\pi$
$200$	56.0000			0.280000
$201$	−16.9706			−0.0844307
$202$	90.5097	−	156.767i	0.448068	−	0.776076i
$203$		0			0
$204$	−156.000	+	90.0666i	−0.764706	+	0.441503i
$205$	136.000			0.663415
$206$	−76.3675	−	44.0908i	−0.370716	−	0.214033i
$207$			83.1384i			0.401635i
$208$	113.137	−	195.959i	0.543928	−	0.942111i
$209$	−466.690			−2.23297
$210$		0			0
$211$		−	48.4974i		−	0.229846i	−0.993374	−	0.114923i	$-0.963338\pi$
$211$		−	48.4974i		−	0.229846i	0.993374	−	0.114923i	$-0.0366621\pi$
$212$	−132.000	−	228.631i	−0.622642	−	1.07845i
$213$	−118.794			−0.557718
$214$	36.0000	+	20.7846i	0.168224	+	0.0971243i
$215$		−	137.171i		−	0.638007i
$216$		−	235.151i		−	1.08866i
$217$		0			0
$218$	186.000	−	322.161i	0.853211	−	1.47780i
$219$		−	45.0333i		−	0.205632i
$220$	−339.411	+	195.959i	−1.54278	+	0.890724i
$221$	−260.000			−1.17647
$222$	−127.279	−	73.4847i	−0.573330	−	0.331012i
$223$		−	342.929i		−	1.53780i	−0.639371	−	0.768898i	$-0.720805\pi$
$223$		−	342.929i		−	1.53780i	0.639371	−	0.768898i	$-0.279195\pi$
$224$		0			0
$225$	21.0000			0.0933333
$226$	12.0000	−	20.7846i	0.0530973	−	0.0919673i
$227$			100.429i			0.442419i	0.975226	+	0.221209i	$0.0710004\pi$
$227$			100.429i			0.442419i	−0.975226	+	0.221209i	$0.929000\pi$
$228$	−132.000	−	228.631i	−0.578947	−	1.00277i
$229$	370.524			1.61801			0.809004	−	0.587803i	$-0.200007\pi$
$229$	370.524			1.61801			0.809004	+	0.587803i	$0.200007\pi$
$230$	271.529	+	156.767i	1.18056	+	0.681597i
$231$		0			0
$232$	16.0000			0.0689655
$233$	40.0000			0.171674			0.0858369	−	0.996309i	$-0.472644\pi$
$233$	40.0000			0.171674			0.0858369	+	0.996309i	$0.472644\pi$
$234$	42.4264	−	73.4847i	0.181309	−	0.314037i
$235$			138.564i			0.589634i
$236$	229.103	−	132.272i	0.970774	−	0.560476i
$237$	−50.9117			−0.214817
$238$		0			0
$239$			387.979i			1.62334i	0.584113	+	0.811672i	$0.301442\pi$
$239$			387.979i			1.62334i	−0.584113	+	0.811672i	$0.698558\pi$
$240$	−192.000	−	110.851i	−0.800000	−	0.461880i
$241$	−357.796			−1.48463			−0.742315	−	0.670051i	$-0.766272\pi$
$241$	−357.796			−1.48463			−0.742315	+	0.670051i	$0.766272\pi$
$242$	179.000	−	310.037i	0.739669	−	1.28115i
$243$		−	154.318i		−	0.635053i
$244$	90.5097	+	156.767i	0.370941	+	0.642489i
$245$		0			0
$246$	−102.000	−	58.8897i	−0.414634	−	0.239389i
$247$		−	381.051i		−	1.54272i
$248$			117.576i			0.474095i
$249$	378.000			1.51807
$250$	−101.823	+	176.363i	−0.407294	+	0.705453i
$251$		−	51.4393i		−	0.204937i	−0.994736	−	0.102469i	$-0.967326\pi$
$251$		−	51.4393i		−	0.204937i	0.994736	−	0.102469i	$-0.0326741\pi$
$252$		0			0
$253$	−480.000			−1.89723
$254$	252.000	+	145.492i	0.992126	+	0.572804i
$255$			254.747i			0.999008i
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	43.8406			0.170586			0.0852930	−	0.996356i	$-0.472817\pi$
$257$	43.8406			0.170586			0.0852930	+	0.996356i	$0.472817\pi$
$258$	−59.3970	+	102.879i	−0.230221	+	0.398754i
$259$		0			0
$260$	−160.000	−	277.128i	−0.615385	−	1.06588i
$261$	6.00000			0.0229885
$262$	131.522	+	75.9342i	0.501992	+	0.289825i
$263$			284.056i			1.08006i	0.841645	+	0.540031i	$0.181588\pi$
$263$			284.056i			1.08006i	−0.841645	+	0.540031i	$0.818412\pi$
$264$	339.411			1.28565
$265$	−373.352			−1.40888
$266$		0			0
$267$		−	58.8897i		−	0.220561i
$268$	−24.0000	+	13.8564i	−0.0895522	+	0.0517030i
$269$	166.877			0.620361			0.310181	−	0.950678i	$-0.399610\pi$
$269$	166.877			0.620361			0.310181	+	0.950678i	$0.399610\pi$
$270$	−288.000	−	166.277i	−1.06667	−	0.615840i
$271$			421.312i			1.55466i	0.629094	+	0.777329i	$0.283426\pi$
$271$			421.312i			1.55466i	−0.629094	+	0.777329i	$0.716574\pi$
$272$	−147.078	+	254.747i	−0.540729	+	0.936570i
$273$		0			0
$274$	−164.000	+	284.056i	−0.598540	+	1.03670i
$275$			121.244i			0.440886i
$276$	−135.765	−	235.151i	−0.491900	−	0.851996i
$277$	10.0000			0.0361011			0.0180505	−	0.999837i	$-0.494254\pi$
$277$	10.0000			0.0361011			0.0180505	+	0.999837i	$0.494254\pi$
$278$	−148.492	−	85.7321i	−0.534145	−	0.308389i
$279$			44.0908i			0.158032i
$280$		0			0
$281$	352.000			1.25267			0.626335	−	0.779554i	$-0.284554\pi$
$281$	352.000			1.25267			0.626335	+	0.779554i	$0.284554\pi$
$282$	60.0000	−	103.923i	0.212766	−	0.368521i
$283$		−	71.0352i		−	0.251008i	−0.992093	−	0.125504i	$-0.959945\pi$
$283$		−	71.0352i		−	0.251008i	0.992093	−	0.125504i	$-0.0400548\pi$
$284$	−168.000	+	96.9948i	−0.591549	+	0.341531i
$285$	−373.352			−1.31001
$286$	424.264	+	244.949i	1.48344	+	0.856465i
$287$		0			0
$288$	−48.0000	−	83.1384i	−0.166667	−	0.288675i
$289$	49.0000			0.169550
$290$	11.3137	−	19.5959i	0.0390128	−	0.0675721i
$291$			204.382i			0.702344i
$292$	−36.7696	−	63.6867i	−0.125923	−	0.218105i
$293$	401.637			1.37077			0.685387	−	0.728179i	$-0.259633\pi$
$293$	401.637			1.37077			0.685387	+	0.728179i	$0.259633\pi$
$294$		0			0
$295$		−	374.123i		−	1.26821i
$296$	−240.000			−0.810811
$297$	509.117			1.71420
$298$	114.000	−	197.454i	0.382550	−	0.662597i
$299$		−	391.918i		−	1.31076i
$300$	−59.3970	+	34.2929i	−0.197990	+	0.114310i
$301$		0			0
$302$	12.0000	+	6.92820i	0.0397351	+	0.0229411i
$303$			221.703i			0.731691i
$304$	−373.352	−	215.555i	−1.22813	−	0.709063i
$305$	256.000			0.839344
$306$	−55.1543	+	95.5301i	−0.180243	+	0.312190i
$307$		−	565.832i		−	1.84310i	−0.388258	−	0.921551i	$-0.626923\pi$
$307$		−	565.832i		−	1.84310i	0.388258	−	0.921551i	$-0.373077\pi$
$308$		0			0
$309$	108.000			0.349515
$310$	144.000	+	83.1384i	0.464516	+	0.268189i
$311$		−	19.5959i		−	0.0630094i	−0.999504	−	0.0315047i	$-0.989970\pi$
$311$		−	19.5959i		−	0.0630094i	0.999504	−	0.0315047i	$-0.0100299\pi$
$312$			277.128i			0.888231i
$313$	439.820			1.40518			0.702589	−	0.711596i	$-0.252027\pi$
$313$	439.820			1.40518			0.702589	+	0.711596i	$0.252027\pi$
$314$	31.1127	−	53.8888i	0.0990850	−	0.171620i
$315$		0			0
$316$	−72.0000	+	41.5692i	−0.227848	+	0.131548i
$317$	−114.000			−0.359621			−0.179811	−	0.983701i	$-0.557549\pi$
$317$	−114.000			−0.359621			−0.179811	+	0.983701i	$0.557549\pi$
$318$	280.014	+	161.666i	0.880548	+	0.508385i
$319$			34.6410i			0.108593i
$320$	−362.039			−1.13137
$321$	−50.9117			−0.158603
$322$		0			0
$323$			495.367i			1.53364i
$324$	90.0000	+	155.885i	0.277778	+	0.481125i
$325$	−98.9949			−0.304600
$326$	78.0000	+	45.0333i	0.239264	+	0.138139i
$327$			455.605i			1.39329i
$328$	−192.333			−0.586381
$329$		0			0
$330$	240.000	−	415.692i	0.727273	−	1.25967i
$331$			536.936i			1.62216i	0.584934	+	0.811081i	$0.301121\pi$
$331$			536.936i			1.62216i	−0.584934	+	0.811081i	$0.698879\pi$
$332$	534.573	−	308.636i	1.61016	−	0.929626i
$333$	−90.0000			−0.270270
$334$	−296.985	−	171.464i	−0.889176	−	0.513366i
$335$			39.1918i			0.116991i
$336$		0			0
$337$	450.000			1.33531			0.667656	−	0.744470i	$-0.267298\pi$
$337$	450.000			1.33531			0.667656	+	0.744470i	$0.267298\pi$
$338$	−31.0000	+	53.6936i	−0.0917160	+	0.158857i
$339$			29.3939i			0.0867076i
$340$	208.000	+	360.267i	0.611765	+	1.05961i
$341$	−254.558			−0.746506
$342$	−140.007	−	80.8332i	−0.409378	−	0.236354i
$343$		0			0
$344$			193.990i			0.563924i
$345$	−384.000			−1.11304
$346$	104.652	−	181.262i	0.302462	−	0.523879i
$347$		−	31.1769i		−	0.0898470i	−0.998990	−	0.0449235i	$-0.985696\pi$
$347$		−	31.1769i		−	0.0898470i	0.998990	−	0.0449235i	$-0.0143044\pi$
$348$	−16.9706	+	9.79796i	−0.0487660	+	0.0281551i
$349$	−14.1421			−0.0405219			−0.0202609	−	0.999795i	$-0.506450\pi$
$349$	−14.1421			−0.0405219			−0.0202609	+	0.999795i	$0.506450\pi$
$350$		0			0
$351$			415.692i			1.18431i
$352$	480.000	−	277.128i	1.36364	−	0.787296i
$353$	295.571			0.837311			0.418655	−	0.908145i	$-0.362502\pi$
$353$	295.571			0.837311			0.418655	+	0.908145i	$0.362502\pi$
$354$	−162.000	+	280.592i	−0.457627	+	0.792633i
$355$			274.343i			0.772797i
$356$	−48.0833	−	83.2827i	−0.135065	−	0.233940i
$357$		0			0
$358$	348.000	+	200.918i	0.972067	+	0.561223i
$359$			76.2102i			0.212285i	0.994351	+	0.106142i	$0.0338499\pi$
$359$			76.2102i			0.212285i	−0.994351	+	0.106142i	$0.966150\pi$
$360$	−135.765			−0.377124
$361$	−365.000			−1.01108
$362$	−302.642	+	524.191i	−0.836027	+	1.44804i
$363$			438.459i			1.20788i
$364$		0			0
$365$	−104.000			−0.284932
$366$	−192.000	−	110.851i	−0.524590	−	0.302872i
$367$		−	705.453i		−	1.92222i	−0.276174	−	0.961108i	$-0.589067\pi$
$367$		−	705.453i		−	1.92222i	0.276174	−	0.961108i	$-0.410933\pi$
$368$	−384.000	−	221.703i	−1.04348	−	0.602452i
$369$	−72.1249			−0.195460
$370$	−169.706	+	293.939i	−0.458664	+	0.794429i
$371$		0			0
$372$	−72.0000	−	124.708i	−0.193548	−	0.335236i
$373$	−2.00000			−0.00536193			−0.00268097	−	0.999996i	$-0.500853\pi$
$373$	−2.00000			−0.00536193			−0.00268097	+	0.999996i	$0.500853\pi$
$374$	−551.543	−	318.434i	−1.47471	−	0.851427i
$375$		−	249.415i		−	0.665108i
$376$		−	195.959i		−	0.521168i
$377$	−28.2843			−0.0750246
$378$		0			0
$379$		−	509.223i		−	1.34360i	−0.740734	−	0.671798i	$-0.765522\pi$
$379$		−	509.223i		−	1.34360i	0.740734	−	0.671798i	$-0.234478\pi$
$380$	−528.000	+	304.841i	−1.38947	+	0.802213i
$381$	−356.382			−0.935385
$382$	36.0000	+	20.7846i	0.0942408	+	0.0544100i
$383$		−	93.0806i		−	0.243030i	−0.992590	−	0.121515i	$-0.961225\pi$
$383$		−	93.0806i		−	0.243030i	0.992590	−	0.121515i	$-0.0387753\pi$
$384$	271.529	+	156.767i	0.707107	+	0.408248i
$385$		0			0
$386$	−304.000	+	526.543i	−0.787565	+	1.36410i
$387$			72.7461i			0.187975i
$388$	166.877	+	289.040i	0.430096	+	0.744948i
$389$	−214.000			−0.550129			−0.275064	−	0.961426i	$-0.588699\pi$
$389$	−214.000			−0.550129			−0.275064	+	0.961426i	$0.588699\pi$
$390$	339.411	+	195.959i	0.870285	+	0.502459i
$391$			509.494i			1.30305i
$392$		0			0
$393$	−186.000			−0.473282
$394$	−198.000	+	342.946i	−0.502538	+	0.870421i
$395$			117.576i			0.297660i
$396$	180.000	−	103.923i	0.454545	−	0.262432i
$397$	−223.446			−0.562836			−0.281418	−	0.959585i	$-0.590805\pi$
$397$	−223.446			−0.562836			−0.281418	+	0.959585i	$0.590805\pi$
$398$	−500.632	−	289.040i	−1.25787	−	0.726231i
$399$		0			0
$400$	−56.0000	+	96.9948i	−0.140000	+	0.242487i
$401$	502.000			1.25187			0.625935	−	0.779875i	$-0.284717\pi$
$401$	502.000			1.25187			0.625935	+	0.779875i	$0.284717\pi$
$402$	16.9706	−	29.3939i	0.0422153	−	0.0731191i
$403$		−	207.846i		−	0.515747i
$404$	181.019	+	313.535i	0.448068	+	0.776076i
$405$	254.558			0.628539
$406$		0			0
$407$		−	519.615i		−	1.27670i
$408$		−	360.267i		−	0.883006i
$409$	255.973			0.625850			0.312925	−	0.949778i	$-0.398691\pi$
$409$	255.973			0.625850			0.312925	+	0.949778i	$0.398691\pi$
$410$	−136.000	+	235.559i	−0.331707	+	0.574534i
$411$		−	401.716i		−	0.977412i
$412$	152.735	−	88.1816i	0.370716	−	0.214033i
$413$		0			0
$414$	−144.000	−	83.1384i	−0.347826	−	0.200817i
$415$		−	872.954i		−	2.10350i
$416$	226.274	+	391.918i	0.543928	+	0.942111i
$417$	210.000			0.503597
$418$	466.690	−	808.332i	1.11648	−	1.93381i
$419$		−	17.1464i		−	0.0409223i	−0.999791	−	0.0204611i	$-0.993487\pi$
$419$		−	17.1464i		−	0.0409223i	0.999791	−	0.0204611i	$-0.00651343\pi$
$420$		0			0
$421$	−614.000			−1.45843			−0.729216	−	0.684283i	$-0.760115\pi$
$421$	−614.000			−1.45843			−0.729216	+	0.684283i	$0.760115\pi$
$422$	84.0000	+	48.4974i	0.199052	+	0.114923i
$423$		−	73.4847i		−	0.173723i
$424$	528.000			1.24528
$425$	128.693			0.302808
$426$	118.794	−	205.757i	0.278859	−	0.482998i
$427$		0			0
$428$	−72.0000	+	41.5692i	−0.168224	+	0.0971243i
$429$	−600.000			−1.39860
$430$	237.588	+	137.171i	0.552530	+	0.319003i
$431$			332.554i			0.771586i	0.922585	+	0.385793i	$0.126072\pi$
$431$			332.554i			0.771586i	−0.922585	+	0.385793i	$0.873928\pi$
$432$	407.294	+	235.151i	0.942809	+	0.544331i
$433$	−202.233			−0.467050			−0.233525	−	0.972351i	$-0.575026\pi$
$433$	−202.233			−0.467050			−0.233525	+	0.972351i	$0.575026\pi$
$434$		0			0
$435$			27.7128i			0.0637076i
$436$	372.000	+	644.323i	0.853211	+	1.47780i
$437$	−746.705			−1.70871
$438$	78.0000	+	45.0333i	0.178082	+	0.102816i
$439$		−	607.473i		−	1.38377i	−0.722009	−	0.691883i	$-0.756781\pi$
$439$		−	607.473i		−	1.38377i	0.722009	−	0.691883i	$-0.243219\pi$
$440$		−	783.837i		−	1.78145i
$441$		0			0
$442$	260.000	−	450.333i	0.588235	−	1.01885i
$443$			76.2102i			0.172032i	0.996294	+	0.0860161i	$0.0274136\pi$
$443$			76.2102i			0.172032i	−0.996294	+	0.0860161i	$0.972586\pi$
$444$	254.558	−	146.969i	0.573330	−	0.331012i
$445$	−136.000			−0.305618
$446$	593.970	+	342.929i	1.33177	+	0.768898i
$447$			279.242i			0.624702i
$448$		0			0
$449$	−642.000			−1.42984			−0.714922	−	0.699204i	$-0.753538\pi$
$449$	−642.000			−1.42984			−0.714922	+	0.699204i	$0.753538\pi$
$450$	−21.0000	+	36.3731i	−0.0466667	+	0.0808290i
$451$		−	416.413i		−	0.923311i
$452$	24.0000	+	41.5692i	0.0530973	+	0.0919673i
$453$	−16.9706			−0.0374626
$454$	−173.948	−	100.429i	−0.383146	−	0.221209i
$455$		0			0
$456$	528.000			1.15789
$457$	152.000			0.332604			0.166302	−	0.986075i	$-0.446817\pi$
$457$	152.000			0.332604			0.166302	+	0.986075i	$0.446817\pi$
$458$	−370.524	+	641.766i	−0.809004	+	1.40124i
$459$		−	540.400i		−	1.17734i
$460$	−543.058	+	313.535i	−1.18056	+	0.681597i
$461$	183.848			0.398802			0.199401	−	0.979918i	$-0.436100\pi$
$461$	183.848			0.398802			0.199401	+	0.979918i	$0.436100\pi$
$462$		0			0
$463$			96.9948i			0.209492i	0.994499	+	0.104746i	$0.0334030\pi$
$463$			96.9948i			0.209492i	−0.994499	+	0.104746i	$0.966597\pi$
$464$	−16.0000	+	27.7128i	−0.0344828	+	0.0597259i
$465$	−203.647			−0.437950
$466$	−40.0000	+	69.2820i	−0.0858369	+	0.148674i
$467$			232.702i			0.498290i	0.968466	+	0.249145i	$0.0801496\pi$
$467$			232.702i			0.498290i	−0.968466	+	0.249145i	$0.919850\pi$
$468$	84.8528	+	146.969i	0.181309	+	0.314037i
$469$		0			0
$470$	−240.000	−	138.564i	−0.510638	−	0.294817i
$471$			76.2102i			0.161805i
$472$			529.090i			1.12095i
$473$	−420.000			−0.887949
$474$	50.9117	−	88.1816i	0.107409	−	0.186037i
$475$			188.611i			0.397075i
$476$		0			0
$477$	198.000			0.415094
$478$	−672.000	−	387.979i	−1.40586	−	0.811672i
$479$			906.311i			1.89209i	0.324035	+	0.946045i	$0.394960\pi$
$479$			906.311i			1.89209i	−0.324035	+	0.946045i	$0.605040\pi$
$480$	384.000	−	221.703i	0.800000	−	0.461880i
$481$	424.264			0.882046
$482$	357.796	−	619.721i	0.742315	−	1.28573i
$483$		0			0
$484$	358.000	+	620.074i	0.739669	+	1.28115i
$485$	472.000			0.973196
$486$	267.286	+	154.318i	0.549972	+	0.317526i
$487$		−	540.400i		−	1.10965i	−0.831967	−	0.554825i	$-0.812785\pi$
$487$		−	540.400i		−	1.10965i	0.831967	−	0.554825i	$-0.187215\pi$
$488$	−362.039			−0.741883
$489$	−110.309			−0.225580
$490$		0			0
$491$		−	436.477i		−	0.888955i	−0.895790	−	0.444477i	$-0.853389\pi$
$491$		−	436.477i		−	0.888955i	0.895790	−	0.444477i	$-0.146611\pi$
$492$	204.000	−	117.779i	0.414634	−	0.239389i
$493$	36.7696			0.0745833
$494$	660.000	+	381.051i	1.33603	+	0.771359i
$495$		−	293.939i		−	0.593816i
$496$	−203.647	−	117.576i	−0.410578	−	0.237047i
$497$		0			0
$498$	−378.000	+	654.715i	−0.759036	+	1.31469i
$499$		−	796.743i		−	1.59668i	−0.602207	−	0.798340i	$-0.705712\pi$
$499$		−	796.743i		−	1.59668i	0.602207	−	0.798340i	$-0.294288\pi$
$500$	−203.647	−	352.727i	−0.407294	−	0.705453i
$501$	420.000			0.838323
$502$	89.0955	+	51.4393i	0.177481	+	0.102469i
$503$			137.171i			0.272707i	0.990660	+	0.136353i	$0.0435382\pi$
$503$			137.171i			0.272707i	−0.990660	+	0.136353i	$0.956462\pi$
$504$		0			0
$505$	512.000			1.01386
$506$	480.000	−	831.384i	0.948617	−	1.64305i
$507$		−	75.9342i		−	0.149772i
$508$	−504.000	+	290.985i	−0.992126	+	0.572804i
$509$	−461.034			−0.905763			−0.452882	−	0.891571i	$-0.649604\pi$
$509$	−461.034			−0.905763			−0.452882	+	0.891571i	$0.649604\pi$
$510$	−441.235	−	254.747i	−0.865166	−	0.499504i
$511$		0			0
$512$	512.000			1.00000
$513$	792.000			1.54386
$514$	−43.8406	+	75.9342i	−0.0852930	+	0.147732i
$515$		−	249.415i		−	0.484302i
$516$	−118.794	−	205.757i	−0.230221	−	0.398754i
$517$	424.264			0.820627
$518$		0			0
$519$			256.344i			0.493918i
$520$	640.000			1.23077
$521$	57.9828			0.111291			0.0556456	−	0.998451i	$-0.482278\pi$
$521$	57.9828			0.111291			0.0556456	+	0.998451i	$0.482278\pi$
$522$	−6.00000	+	10.3923i	−0.0114943	+	0.0199086i
$523$			266.994i			0.510506i	0.966874	+	0.255253i	$0.0821587\pi$
$523$			266.994i			0.510506i	−0.966874	+	0.255253i	$0.917841\pi$
$524$	−263.044	+	151.868i	−0.501992	+	0.289825i
$525$		0			0
$526$	−492.000	−	284.056i	−0.935361	−	0.540031i
$527$			270.200i			0.512713i
$528$	−339.411	+	587.878i	−0.642824	+	1.11340i
$529$	−239.000			−0.451796
$530$	373.352	−	646.665i	0.704438	−	1.22012i
$531$			198.409i			0.373651i
$532$		0			0
$533$	340.000			0.637899
$534$	102.000	+	58.8897i	0.191011	+	0.110280i
$535$			117.576i			0.219767i
$536$		−	55.4256i		−	0.103406i
$537$	−492.146			−0.916474
$538$	−166.877	+	289.040i	−0.310181	+	0.537249i
$539$		0			0
$540$	576.000	−	332.554i	1.06667	−	0.615840i
$541$	−562.000			−1.03882			−0.519409	−	0.854526i	$-0.673848\pi$
$541$	−562.000			−1.03882			−0.519409	+	0.854526i	$0.673848\pi$
$542$	−729.734	−	421.312i	−1.34637	−	0.777329i
$543$		−	741.318i		−	1.36523i
$544$	−294.156	−	509.494i	−0.540729	−	0.936570i
$545$	1052.17			1.93060
$546$		0			0
$547$		−	315.233i		−	0.576295i	−0.957586	−	0.288147i	$-0.906961\pi$
$547$		−	315.233i		−	0.576295i	0.957586	−	0.288147i	$-0.0930393\pi$
$548$	−328.000	−	568.113i	−0.598540	−	1.03670i
$549$	−135.765			−0.247294
$550$	−210.000	−	121.244i	−0.381818	−	0.220443i
$551$			53.8888i			0.0978018i
$552$	543.058			0.983801
$553$		0			0
$554$	−10.0000	+	17.3205i	−0.0180505	+	0.0312645i
$555$		−	415.692i		−	0.748995i
$556$	296.985	−	171.464i	0.534145	−	0.308389i
$557$	−354.000			−0.635548			−0.317774	−	0.948167i	$-0.602935\pi$
$557$	−354.000			−0.635548			−0.317774	+	0.948167i	$0.602935\pi$
$558$	−76.3675	−	44.0908i	−0.136859	−	0.0790158i
$559$		−	342.929i		−	0.613468i
$560$		0			0
$561$	780.000			1.39037
$562$	−352.000	+	609.682i	−0.626335	+	1.08484i
$563$		−	276.792i		−	0.491638i	−0.969316	−	0.245819i	$-0.920943\pi$
$563$		−	276.792i		−	0.491638i	0.969316	−	0.245819i	$-0.0790569\pi$
$564$	120.000	+	207.846i	0.212766	+	0.368521i
$565$	67.8823			0.120146
$566$	123.037	+	71.0352i	0.217379	+	0.125504i
$567$		0			0
$568$		−	387.979i		−	0.683062i
$569$	−982.000			−1.72583			−0.862917	−	0.505345i	$-0.831365\pi$
$569$	−982.000			−1.72583			−0.862917	+	0.505345i	$0.831365\pi$
$570$	373.352	−	646.665i	0.655004	−	1.13450i
$571$		−	79.6743i		−	0.139535i	−0.997563	−	0.0697674i	$-0.977774\pi$
$571$		−	79.6743i		−	0.139535i	0.997563	−	0.0697674i	$-0.0222257\pi$
$572$	−848.528	+	489.898i	−1.48344	+	0.856465i
$573$	−50.9117			−0.0888511
$574$		0			0
$575$			193.990i			0.337373i
$576$	192.000			0.333333
$577$	−159.806			−0.276960			−0.138480	−	0.990365i	$-0.544222\pi$
$577$	−159.806			−0.276960			−0.138480	+	0.990365i	$0.544222\pi$
$578$	−49.0000	+	84.8705i	−0.0847751	+	0.146835i
$579$		−	744.645i		−	1.28609i
$580$	22.6274	+	39.1918i	0.0390128	+	0.0675721i
$581$		0			0
$582$	−354.000	−	204.382i	−0.608247	−	0.351172i
$583$			1143.15i			1.96081i
$584$	147.078			0.251846
$585$	240.000			0.410256
$586$	−401.637	+	695.655i	−0.685387	+	1.18712i
$587$		−	531.539i		−	0.905518i	−0.891633	−	0.452759i	$-0.850440\pi$
$587$		−	531.539i		−	0.905518i	0.891633	−	0.452759i	$-0.149560\pi$
$588$		0			0
$589$	−396.000			−0.672326
$590$	648.000	+	374.123i	1.09831	+	0.634107i
$591$		−	484.999i		−	0.820641i
$592$	240.000	−	415.692i	0.405405	−	0.702183i
$593$	697.207			1.17573			0.587864	−	0.808959i	$-0.299969\pi$
$593$	697.207			1.17573			0.587864	+	0.808959i	$0.299969\pi$
$594$	−509.117	+	881.816i	−0.857099	+	1.48454i
$595$		0			0
$596$	228.000	+	394.908i	0.382550	+	0.662597i
$597$	708.000			1.18593
$598$	678.823	+	391.918i	1.13515	+	0.655382i
$599$			1011.52i			1.68868i	0.535810	+	0.844339i	$0.320006\pi$
$599$			1011.52i			1.68868i	−0.535810	+	0.844339i	$0.679994\pi$
$600$		−	137.171i		−	0.228619i
$601$	−816.001			−1.35774			−0.678870	−	0.734259i	$-0.737530\pi$
$601$	−816.001			−1.35774			−0.678870	+	0.734259i	$0.737530\pi$
$602$		0			0
$603$		−	20.7846i		−	0.0344687i
$604$	−24.0000	+	13.8564i	−0.0397351	+	0.0229411i
$605$	1012.58			1.67368
$606$	−384.000	−	221.703i	−0.633663	−	0.365846i
$607$			146.969i			0.242124i	0.992645	+	0.121062i	$0.0386300\pi$
$607$			146.969i			0.242124i	−0.992645	+	0.121062i	$0.961370\pi$
$608$	746.705	−	431.110i	1.22813	−	0.709063i
$609$		0			0
$610$	−256.000	+	443.405i	−0.419672	+	0.726893i
$611$			346.410i			0.566956i
$612$	−110.309	−	191.060i	−0.180243	−	0.312190i
$613$	738.000			1.20392			0.601958	−	0.798528i	$-0.294388\pi$
$613$	738.000			1.20392			0.601958	+	0.798528i	$0.294388\pi$
$614$	980.050	+	565.832i	1.59617	+	0.921551i
$615$		−	333.131i		−	0.541676i
$616$		0			0
$617$	−754.000			−1.22204			−0.611021	−	0.791614i	$-0.709241\pi$
$617$	−754.000			−1.22204			−0.611021	+	0.791614i	$0.709241\pi$
$618$	−108.000	+	187.061i	−0.174757	+	0.302688i
$619$			786.286i			1.27025i	0.772408	+	0.635126i	$0.219052\pi$
$619$			786.286i			1.27025i	−0.772408	+	0.635126i	$0.780948\pi$
$620$	−288.000	+	166.277i	−0.464516	+	0.268189i
$621$	814.587			1.31173
$622$	33.9411	+	19.5959i	0.0545677	+	0.0315047i
$623$		0			0
$624$	−480.000	−	277.128i	−0.769231	−	0.444116i
$625$	−751.000			−1.20160
$626$	−439.820	+	761.791i	−0.702589	+	1.21692i
$627$			1143.15i			1.82321i
$628$	62.2254	+	107.778i	0.0990850	+	0.171620i
$629$	−551.543			−0.876857
$630$		0			0
$631$		−	48.4974i		−	0.0768580i	−0.999261	−	0.0384290i	$-0.987765\pi$
$631$		−	48.4974i		−	0.0768580i	0.999261	−	0.0384290i	$-0.0122353\pi$
$632$		−	166.277i		−	0.263096i
$633$	−118.794			−0.187668
$634$	114.000	−	197.454i	0.179811	−	0.311441i
$635$			823.029i			1.29611i
$636$	−560.029	+	323.333i	−0.880548	+	0.508385i
$637$		0			0
$638$	−60.0000	−	34.6410i	−0.0940439	−	0.0542963i
$639$		−	145.492i		−	0.227687i
$640$	362.039	−	627.069i	0.565685	−	0.979796i
$641$	850.000			1.32605			0.663027	−	0.748596i	$-0.269272\pi$
$641$	850.000			1.32605			0.663027	+	0.748596i	$0.269272\pi$
$642$	50.9117	−	88.1816i	0.0793017	−	0.137355i
$643$			565.832i			0.879988i	0.898001	+	0.439994i	$0.145019\pi$
$643$			565.832i			0.879988i	−0.898001	+	0.439994i	$0.854981\pi$
$644$		0			0
$645$	−336.000			−0.520930
$646$	−858.000	−	495.367i	−1.32817	−	0.766821i
$647$		−	259.646i		−	0.401307i	−0.979662	−	0.200654i	$-0.935693\pi$
$647$		−	259.646i		−	0.401307i	0.979662	−	0.200654i	$-0.0643066\pi$
$648$	−360.000			−0.555556
$649$	−1145.51			−1.76504
$650$	98.9949	−	171.464i	0.152300	−	0.263791i
$651$		0			0
$652$	−156.000	+	90.0666i	−0.239264	+	0.138139i
$653$	−58.0000			−0.0888208			−0.0444104	−	0.999013i	$-0.514141\pi$
$653$	−58.0000			−0.0888208			−0.0444104	+	0.999013i	$0.514141\pi$
$654$	−789.131	−	455.605i	−1.20662	−	0.696644i
$655$			429.549i			0.655799i
$656$	192.333	−	333.131i	0.293191	−	0.507821i
$657$	55.1543			0.0839488
$658$		0			0
$659$			1139.69i			1.72942i	0.502269	+	0.864711i	$0.332499\pi$
$659$			1139.69i			1.72942i	−0.502269	+	0.864711i	$0.667501\pi$
$660$	480.000	+	831.384i	0.727273	+	1.25967i
$661$	503.460			0.761664			0.380832	−	0.924644i	$-0.375638\pi$
$661$	503.460			0.761664			0.380832	+	0.924644i	$0.375638\pi$
$662$	−930.000	−	536.936i	−1.40483	−	0.811081i
$663$			636.867i			0.960584i
$664$			1234.54i			1.85925i
$665$		0			0
$666$	90.0000	−	155.885i	0.135135	−	0.234061i
$667$			55.4256i			0.0830969i
$668$	593.970	−	342.929i	0.889176	−	0.513366i
$669$	−840.000			−1.25561
$670$	−67.8823	−	39.1918i	−0.101317	−	0.0584953i
$671$		−	783.837i		−	1.16816i
$672$		0			0
$673$	156.000			0.231798			0.115899	−	0.993261i	$-0.463025\pi$
$673$	156.000			0.231798			0.115899	+	0.993261i	$0.463025\pi$
$674$	−450.000	+	779.423i	−0.667656	+	1.15641i
$675$		−	205.757i		−	0.304825i
$676$	−62.0000	−	107.387i	−0.0917160	−	0.158857i
$677$	14.1421			0.0208894			0.0104447	−	0.999945i	$-0.496675\pi$
$677$	14.1421			0.0208894			0.0104447	+	0.999945i	$0.496675\pi$
$678$	−50.9117	−	29.3939i	−0.0750910	−	0.0433538i
$679$		0			0
$680$	−832.000			−1.22353
$681$	246.000			0.361233
$682$	254.558	−	440.908i	0.373253	−	0.646493i
$683$			1254.00i			1.83602i	0.396552	+	0.918012i	$0.370207\pi$
$683$			1254.00i			1.83602i	−0.396552	+	0.918012i	$0.629793\pi$
$684$	280.014	−	161.666i	0.409378	−	0.236354i
$685$	−927.724			−1.35434
$686$		0			0
$687$		−	907.595i		−	1.32110i
$688$	−336.000	−	193.990i	−0.488372	−	0.281962i
$689$	−933.381			−1.35469
$690$	384.000	−	665.108i	0.556522	−	0.963924i
$691$			335.580i			0.485644i	0.970071	+	0.242822i	$0.0780731\pi$
$691$			335.580i			0.485644i	−0.970071	+	0.242822i	$0.921927\pi$
$692$	209.304	+	362.524i	0.302462	+	0.523879i
$693$		0			0
$694$	54.0000	+	31.1769i	0.0778098	+	0.0449235i
$695$		−	484.974i		−	0.697805i
$696$		−	39.1918i		−	0.0563101i
$697$	−442.000			−0.634146
$698$	14.1421	−	24.4949i	0.0202609	−	0.0350930i
$699$		−	97.9796i		−	0.140171i
$700$		0			0
$701$	814.000			1.16120			0.580599	−	0.814190i	$-0.302818\pi$
$701$	814.000			1.16120			0.580599	+	0.814190i	$0.302818\pi$
$702$	−720.000	−	415.692i	−1.02564	−	0.592154i
$703$		−	808.332i		−	1.14983i
$704$			1108.51i			1.57459i
$705$	339.411			0.481434
$706$	−295.571	+	511.943i	−0.418655	+	0.725132i
$707$		0			0
$708$	−324.000	−	561.184i	−0.457627	−	0.792633i
$709$	306.000			0.431594			0.215797	−	0.976438i	$-0.430765\pi$
$709$	306.000			0.431594			0.215797	+	0.976438i	$0.430765\pi$
$710$	−475.176	−	274.343i	−0.669262	−	0.386398i
$711$		−	62.3538i		−	0.0876988i
$712$	192.333			0.270131
$713$	−407.294			−0.571239
$714$		0			0
$715$			1385.64i			1.93796i
$716$	−696.000	+	401.836i	−0.972067	+	0.561223i
$717$	950.352			1.32546
$718$	−132.000	−	76.2102i	−0.183844	−	0.106142i
$719$		−	298.838i		−	0.415630i	−0.978168	−	0.207815i	$-0.933365\pi$
$719$		−	298.838i		−	0.415630i	0.978168	−	0.207815i	$-0.0666352\pi$
$720$	135.765	−	235.151i	0.188562	−	0.326599i
$721$		0			0
$722$	365.000	−	632.199i	0.505540	−	0.875621i
$723$			876.418i			1.21220i
$724$	−605.283	−	1048.38i	−0.836027	−	1.44804i
$725$	14.0000			0.0193103
$726$	−759.433	−	438.459i	−1.04605	−	0.603938i
$727$		−	377.221i		−	0.518874i	−0.965760	−	0.259437i	$-0.916463\pi$
$727$		−	377.221i		−	0.518874i	0.965760	−	0.259437i	$-0.0835370\pi$
$728$		0			0
$729$	−783.000			−1.07407
$730$	104.000	−	180.133i	0.142466	−	0.246758i
$731$			445.807i			0.609859i
$732$	384.000	−	221.703i	0.524590	−	0.302872i
$733$	429.921			0.586522			0.293261	−	0.956032i	$-0.405259\pi$
$733$	429.921			0.586522			0.293261	+	0.956032i	$0.405259\pi$
$734$	1221.88	+	705.453i	1.66469	+	0.961108i
$735$		0			0
$736$	768.000	−	443.405i	1.04348	−	0.602452i
$737$	120.000			0.162822
$738$	72.1249	−	124.924i	0.0977302	−	0.169274i
$739$		−	1001.13i		−	1.35470i	−0.735660	−	0.677351i	$-0.763128\pi$
$739$		−	1001.13i		−	1.35470i	0.735660	−	0.677351i	$-0.236872\pi$
$740$	−339.411	−	587.878i	−0.458664	−	0.794429i
$741$	−933.381			−1.25962
$742$		0			0
$743$			436.477i			0.587452i	0.955890	+	0.293726i	$0.0948953\pi$
$743$			436.477i			0.587452i	−0.955890	+	0.293726i	$0.905105\pi$
$744$	288.000			0.387097
$745$	644.881			0.865613
$746$	2.00000	−	3.46410i	0.00268097	−	0.00464357i
$747$			462.954i			0.619750i
$748$	1103.09	−	636.867i	1.47471	−	0.851427i
$749$		0			0
$750$	432.000	+	249.415i	0.576000	+	0.332554i
$751$			609.682i			0.811827i	0.913912	+	0.405913i	$0.133047\pi$
$751$			609.682i			0.811827i	−0.913912	+	0.405913i	$0.866953\pi$
$752$	339.411	+	195.959i	0.451345	+	0.260584i
$753$	−126.000			−0.167331
$754$	28.2843	−	48.9898i	0.0375123	−	0.0649732i
$755$			39.1918i			0.0519097i
$756$		0			0
$757$	786.000			1.03831			0.519155	−	0.854680i	$-0.326247\pi$
$757$	786.000			1.03831			0.519155	+	0.854680i	$0.326247\pi$
$758$	882.000	+	509.223i	1.16359	+	0.671798i
$759$			1175.76i			1.54908i
$760$		−	1219.36i		−	1.60443i
$761$	−807.516			−1.06112			−0.530562	−	0.847646i	$-0.678019\pi$
$761$	−807.516			−1.06112			−0.530562	+	0.847646i	$0.678019\pi$
$762$	356.382	−	617.271i	0.467693	−	0.810067i
$763$		0			0
$764$	−72.0000	+	41.5692i	−0.0942408	+	0.0544100i
$765$	−312.000			−0.407843
$766$	161.220	+	93.0806i	0.210470	+	0.121515i
$767$		−	935.307i		−	1.21944i
$768$	−543.058	+	313.535i	−0.707107	+	0.408248i
$769$	926.310			1.20456			0.602282	−	0.798283i	$-0.294258\pi$
$769$	926.310			1.20456			0.602282	+	0.798283i	$0.294258\pi$
$770$		0			0
$771$		−	107.387i		−	0.139283i
$772$	−608.000	−	1053.09i	−0.787565	−	1.36410i
$773$	−1318.05			−1.70511			−0.852553	−	0.522641i	$-0.824947\pi$
$773$	−1318.05			−1.70511			−0.852553	+	0.522641i	$0.824947\pi$
$774$	−126.000	−	72.7461i	−0.162791	−	0.0939873i
$775$			102.879i			0.132747i
$776$	−667.509			−0.860192
$777$		0			0
$778$	214.000	−	370.659i	0.275064	−	0.476425i
$779$		−	647.787i		−	0.831562i
$780$	−678.823	+	391.918i	−0.870285	+	0.502459i
$781$	840.000			1.07554
$782$	−882.469	−	509.494i	−1.12848	−	0.651527i
$783$		−	58.7878i		−	0.0750801i
$784$		0			0
$785$	176.000			0.224204
$786$	186.000	−	322.161i	0.236641	−	0.409875i
$787$			820.579i			1.04267i	0.853353	+	0.521334i	$0.174565\pi$
$787$			820.579i			1.04267i	−0.853353	+	0.521334i	$0.825435\pi$
$788$	−396.000	−	685.892i	−0.502538	−	0.870421i
$789$	695.793			0.881867
$790$	−203.647	−	117.576i	−0.257781	−	0.148830i
$791$		0			0
$792$			415.692i			0.524864i
$793$	640.000			0.807062
$794$	223.446	−	387.019i	0.281418	−	0.487430i
$795$			914.523i			1.15034i
$796$	1001.26	−	578.080i	1.25787	−	0.726231i
$797$	461.034			0.578461			0.289231	−	0.957259i	$-0.406601\pi$
$797$	461.034			0.578461			0.289231	+	0.957259i	$0.406601\pi$
$798$		0			0
$799$		−	450.333i		−	0.563621i
$800$	−112.000	−	193.990i	−0.140000	−	0.242487i
$801$	72.1249			0.0900436
$802$	−502.000	+	869.490i	−0.625935	+	1.08415i
$803$			318.434i			0.396555i
$804$	33.9411	+	58.7878i	0.0422153	+	0.0731191i
$805$		0			0
$806$	360.000	+	207.846i	0.446650	+	0.257874i
$807$		−	408.764i		−	0.506523i
$808$	−724.077			−0.896135
$809$	−144.000			−0.177998			−0.0889988	−	0.996032i	$-0.528367\pi$
$809$	−144.000			−0.177998			−0.0889988	+	0.996032i	$0.528367\pi$
$810$	−254.558	+	440.908i	−0.314270	+	0.544331i
$811$			17.1464i			0.0211423i	0.999944	+	0.0105712i	$0.00336497\pi$
$811$			17.1464i			0.0211423i	−0.999944	+	0.0105712i	$0.996635\pi$
$812$		0			0
$813$	1032.00			1.26937
$814$	900.000	+	519.615i	1.10565	+	0.638348i
$815$			254.747i			0.312573i
$816$	624.000	+	360.267i	0.764706	+	0.441503i
$817$	−653.367			−0.799714
$818$	−255.973	+	443.358i	−0.312925	+	0.542002i
$819$		0			0
$820$	−272.000	−	471.118i	−0.331707	−	0.574534i
$821$	1314.00			1.60049			0.800244	−	0.599675i	$-0.204703\pi$
$821$	1314.00			1.60049			0.800244	+	0.599675i	$0.204703\pi$
$822$	695.793	+	401.716i	0.846464	+	0.488706i
$823$			1399.50i			1.70048i	0.526393	+	0.850241i	$0.323544\pi$
$823$			1399.50i			1.70048i	−0.526393	+	0.850241i	$0.676456\pi$
$824$			352.727i			0.428066i
$825$	296.985			0.359982
$826$		0			0
$827$			242.487i			0.293213i	0.989195	+	0.146606i	$0.0468351\pi$
$827$			242.487i			0.293213i	−0.989195	+	0.146606i	$0.953165\pi$
$828$	288.000	−	166.277i	0.347826	−	0.200817i
$829$	1335.02			1.61040			0.805198	−	0.593007i	$-0.202059\pi$
$829$	1335.02			1.61040			0.805198	+	0.593007i	$0.202059\pi$
$830$	1512.00	+	872.954i	1.82169	+	1.05175i
$831$		−	24.4949i		−	0.0294764i
$832$	−905.097			−1.08786
$833$		0			0
$834$	−210.000	+	363.731i	−0.251799	+	0.436128i
$835$		−	969.948i		−	1.16161i
$836$	933.381	+	1616.66i	1.11648	+	1.93381i
$837$	432.000			0.516129
$838$	29.6985	+	17.1464i	0.0354397	+	0.0204611i
$839$		−	1200.25i		−	1.43057i	−0.698832	−	0.715286i	$-0.746296\pi$
$839$		−	1200.25i		−	1.43057i	0.698832	−	0.715286i	$-0.253704\pi$
$840$		0			0
$841$	−837.000			−0.995244
$842$	614.000	−	1063.48i	0.729216	−	1.26304i
$843$		−	862.220i		−	1.02280i
$844$	−168.000	+	96.9948i	−0.199052	+	0.114923i
$845$	−175.362			−0.207530
$846$	127.279	+	73.4847i	0.150448	+	0.0868613i
$847$		0			0
$848$	−528.000	+	914.523i	−0.622642	+	1.07845i
$849$	−174.000			−0.204947
$850$	−128.693	+	222.904i	−0.151404	+	0.262239i
$851$		−	831.384i		−	0.976950i
$852$	237.588	+	411.514i	0.278859	+	0.482998i
$853$	342.240			0.401219			0.200609	−	0.979671i	$-0.435708\pi$
$853$	342.240			0.401219			0.200609	+	0.979671i	$0.435708\pi$
$854$		0			0
$855$		−	457.261i		−	0.534809i
$856$		−	166.277i		−	0.194249i
$857$	−120.208			−0.140266			−0.0701331	−	0.997538i	$-0.522342\pi$
$857$	−120.208			−0.140266			−0.0701331	+	0.997538i	$0.522342\pi$
$858$	600.000	−	1039.23i	0.699301	−	1.21122i
$859$		−	1584.82i		−	1.84496i	−0.386046	−	0.922480i	$-0.626159\pi$
$859$		−	1584.82i		−	1.84496i	0.386046	−	0.922480i	$-0.373841\pi$
$860$	−475.176	+	274.343i	−0.552530	+	0.319003i
$861$		0			0
$862$	−576.000	−	332.554i	−0.668213	−	0.385793i
$863$			464.190i			0.537879i	0.963157	+	0.268940i	$0.0866732\pi$
$863$			464.190i			0.537879i	−0.963157	+	0.268940i	$0.913327\pi$
$864$	−814.587	+	470.302i	−0.942809	+	0.544331i
$865$	592.000			0.684393
$866$	202.233	−	350.277i	0.233525	−	0.404477i
$867$		−	120.025i		−	0.138437i
$868$		0			0
$869$	360.000			0.414269
$870$	−48.0000	−	27.7128i	−0.0551724	−	0.0318538i
$871$			97.9796i			0.112491i
$872$	−1488.00			−1.70642
$873$	−250.316			−0.286731
$874$	746.705	−	1293.33i	0.854353	−	1.47978i
$875$		0			0
$876$	−156.000	+	90.0666i	−0.178082	+	0.102816i
$877$	−870.000			−0.992018			−0.496009	−	0.868317i	$-0.665202\pi$
$877$	−870.000			−0.992018			−0.496009	+	0.868317i	$0.665202\pi$
$878$	1052.17	+	607.473i	1.19838	+	0.691883i
$879$		−	983.805i		−	1.11923i
$880$	1357.65	+	783.837i	1.54278	+	0.890724i
$881$	807.516			0.916590			0.458295	−	0.888800i	$-0.348460\pi$
$881$	807.516			0.916590			0.458295	+	0.888800i	$0.348460\pi$
$882$		0			0
$883$		−	1406.43i		−	1.59278i	−0.604783	−	0.796390i	$-0.706740\pi$
$883$		−	1406.43i		−	1.59278i	0.604783	−	0.796390i	$-0.293260\pi$
$884$	520.000	+	900.666i	0.588235	+	1.01885i
$885$	−916.410			−1.03549
$886$	−132.000	−	76.2102i	−0.148984	−	0.0860161i
$887$		−	916.109i		−	1.03282i	−0.856342	−	0.516409i	$-0.827269\pi$
$887$		−	916.109i		−	1.03282i	0.856342	−	0.516409i	$-0.172731\pi$
$888$			587.878i			0.662024i
$889$		0			0
$890$	136.000	−	235.559i	0.152809	−	0.264673i
$891$		−	779.423i		−	0.874773i
$892$	−1187.94	+	685.857i	−1.33177	+	0.768898i
$893$	660.000			0.739082
$894$	−483.661	−	279.242i	−0.541008	−	0.312351i
$895$			1136.56i			1.26990i
$896$		0			0
$897$	−960.000			−1.07023
$898$	642.000	−	1111.98i	0.714922	−	1.23828i
$899$			29.3939i			0.0326962i
$900$	−42.0000	−	72.7461i	−0.0466667	−	0.0808290i
$901$	1213.40			1.34672
$902$	721.249	+	416.413i	0.799611	+	0.461655i
$903$		0			0
$904$	−96.0000			−0.106195
$905$	−1712.00			−1.89171
$906$	16.9706	−	29.3939i	0.0187313	−	0.0324436i
$907$		−	491.902i		−	0.542340i	−0.962531	−	0.271170i	$-0.912589\pi$
$907$		−	491.902i		−	0.542340i	0.962531	−	0.271170i	$-0.0874106\pi$
$908$	347.897	−	200.858i	0.383146	−	0.221209i
$909$	−271.529			−0.298712
$910$		0			0
$911$			48.4974i			0.0532354i	0.999646	+	0.0266177i	$0.00847367\pi$
$911$			48.4974i			0.0532354i	−0.999646	+	0.0266177i	$0.991526\pi$
$912$	−528.000	+	914.523i	−0.578947	+	1.00277i
$913$	−2672.86			−2.92756
$914$	−152.000	+	263.272i	−0.166302	+	0.288043i
$915$		−	627.069i		−	0.685322i
$916$	−741.048	−	1283.53i	−0.809004	−	1.40124i
$917$		0			0
$918$	936.000	+	540.400i	1.01961	+	0.588671i
$919$			221.703i			0.241243i	0.992699	+	0.120622i	$0.0384888\pi$
$919$			221.703i			0.241243i	−0.992699	+	0.120622i	$0.961511\pi$
$920$		−	1254.14i		−	1.36319i
$921$	−1386.00			−1.50489
$922$	−183.848	+	318.434i	−0.199401	+	0.345373i
$923$			685.857i			0.743074i
$924$		0			0
$925$	−210.000			−0.227027
$926$	−168.000	−	96.9948i	−0.181425	−	0.104746i
$927$			132.272i			0.142689i
$928$	−32.0000	−	55.4256i	−0.0344828	−	0.0597259i
$929$	1093.19			1.17674			0.588368	−	0.808594i	$-0.299771\pi$
$929$	1093.19			1.17674			0.588368	+	0.808594i	$0.299771\pi$
$930$	203.647	−	352.727i	0.218975	−	0.379276i
$931$		0			0
$932$	−80.0000	−	138.564i	−0.0858369	−	0.148674i
$933$	−48.0000			−0.0514469
$934$	−403.051	−	232.702i	−0.431532	−	0.249145i
$935$		−	1801.33i		−	1.92656i
$936$	−339.411			−0.362619
$937$	1262.89			1.34780			0.673902	−	0.738821i	$-0.264617\pi$
$937$	1262.89			1.34780			0.673902	+	0.738821i	$0.264617\pi$
$938$		0			0
$939$		−	1077.34i		−	1.14732i
$940$	480.000	−	277.128i	0.510638	−	0.294817i
$941$	820.244			0.871673			0.435836	−	0.900026i	$-0.356453\pi$
$941$	820.244			0.871673			0.435836	+	0.900026i	$0.356453\pi$
$942$	−132.000	−	76.2102i	−0.140127	−	0.0809026i
$943$		−	666.261i		−	0.706534i
$944$	−916.410	−	529.090i	−0.970774	−	0.560476i
$945$		0			0
$946$	420.000	−	727.461i	0.443975	−	0.768987i
$947$		−	190.526i		−	0.201189i	−0.994928	−	0.100594i	$-0.967926\pi$
$947$		−	190.526i		−	0.201189i	0.994928	−	0.100594i	$-0.0320744\pi$
$948$	101.823	+	176.363i	0.107409	+	0.186037i
$949$	−260.000			−0.273973
$950$	−326.683	−	188.611i	−0.343877	−	0.198538i
$951$			279.242i			0.293630i
$952$		0			0
$953$	−642.000			−0.673662			−0.336831	−	0.941565i	$-0.609355\pi$
$953$	−642.000			−0.673662			−0.336831	+	0.941565i	$0.609355\pi$
$954$	−198.000	+	342.946i	−0.207547	+	0.359482i
$955$			117.576i			0.123116i
$956$	1344.00	−	775.959i	1.40586	−	0.811672i
$957$	84.8528			0.0886654
$958$	−1569.78	−	906.311i	−1.63860	−	0.946045i
$959$		0			0
$960$			886.810i			0.923760i
$961$	745.000			0.775234
$962$	−424.264	+	734.847i	−0.441023	+	0.763874i
$963$		−	62.3538i		−	0.0647496i
$964$	715.592	+	1239.44i	0.742315	+	1.28573i
$965$	−1719.68			−1.78206
$966$		0			0
$967$			1842.90i			1.90579i	0.303295	+	0.952897i	$0.401913\pi$
$967$			1842.90i			1.90579i	−0.303295	+	0.952897i	$0.598087\pi$
$968$	−1432.00			−1.47934
$969$	1213.40			1.25221
$970$	−472.000	+	817.528i	−0.486598	+	0.842812i
$971$			1124.32i			1.15789i	0.815365	+	0.578947i	$0.196536\pi$
$971$			1124.32i			1.15789i	−0.815365	+	0.578947i	$0.803464\pi$
$972$	−534.573	+	308.636i	−0.549972	+	0.317526i
$973$		0			0
$974$	936.000	+	540.400i	0.960986	+	0.554825i
$975$			242.487i			0.248705i
$976$	362.039	−	627.069i	0.370941	−	0.642489i
$977$	−1516.00			−1.55169			−0.775844	−	0.630924i	$-0.782676\pi$
$977$	−1516.00			−1.55169			−0.775844	+	0.630924i	$0.782676\pi$
$978$	110.309	−	191.060i	0.112790	−	0.195358i
$979$			416.413i			0.425346i
$980$		0			0
$981$	−558.000			−0.568807
$982$	756.000	+	436.477i	0.769857	+	0.444477i
$983$		−	1699.95i		−	1.72934i	−0.502336	−	0.864672i	$-0.667526\pi$
$983$		−	1699.95i		−	1.72934i	0.502336	−	0.864672i	$-0.332474\pi$
$984$			471.118i			0.478778i
$985$	−1120.06			−1.13711
$986$	−36.7696	+	63.6867i	−0.0372916	+	0.0645910i
$987$		0			0
$988$	−1320.00	+	762.102i	−1.33603	+	0.771359i
$989$	−672.000			−0.679474
$990$	509.117	+	293.939i	0.514259	+	0.296908i
$991$			914.523i			0.922828i	0.887185	+	0.461414i	$0.152658\pi$
$991$			914.523i			0.922828i	−0.887185	+	0.461414i	$0.847342\pi$
$992$	407.294	−	235.151i	0.410578	−	0.237047i
$993$	1315.22			1.32449
$994$		0			0
$995$		−	1635.06i		−	1.64327i
$996$	−756.000	−	1309.43i	−0.759036	−	1.31469i
$997$	−922.067			−0.924842			−0.462421	−	0.886661i	$-0.653019\pi$
$997$	−922.067			−0.924842			−0.462421	+	0.886661i	$0.653019\pi$
$998$	1380.00	+	796.743i	1.38277	+	0.798340i
$999$			881.816i			0.882699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.c.e.99.3	yes	4
4.3	odd	2	inner	196.3.c.e.99.2	yes	4
7.2	even	3		196.3.g.f.67.2		4
7.3	odd	6		196.3.g.b.79.2		4
7.4	even	3		196.3.g.b.79.1		4
7.5	odd	6		196.3.g.f.67.1		4
7.6	odd	2	inner	196.3.c.e.99.4	yes	4
28.3	even	6		196.3.g.f.79.1		4
28.11	odd	6		196.3.g.f.79.2		4
28.19	even	6		196.3.g.b.67.2		4
28.23	odd	6		196.3.g.b.67.1		4
28.27	even	2	inner	196.3.c.e.99.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.c.e.99.1	✓	4	28.27	even	2	inner
196.3.c.e.99.2	yes	4	4.3	odd	2	inner
196.3.c.e.99.3	yes	4	1.1	even	1	trivial
196.3.c.e.99.4	yes	4	7.6	odd	2	inner
196.3.g.b.67.1		4	28.23	odd	6
196.3.g.b.67.2		4	28.19	even	6
196.3.g.b.79.1		4	7.4	even	3
196.3.g.b.79.2		4	7.3	odd	6
196.3.g.f.67.1		4	7.5	odd	6
196.3.g.f.67.2		4	7.2	even	3
196.3.g.f.79.1		4	28.3	even	6
196.3.g.f.79.2		4	28.11	odd	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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} -2.44949i q^{3} +(-2.00000 - 3.46410i) q^{4} -5.65685 q^{5} +(4.24264 + 2.44949i) q^{6} +8.00000 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} -2.44949i q^{3} +(-2.00000 - 3.46410i) q^{4} -5.65685 q^{5} +(4.24264 + 2.44949i) q^{6} +8.00000 q^{8} +3.00000 q^{9} +(5.65685 - 9.79796i) q^{10} +17.3205i q^{11} +(-8.48528 + 4.89898i) q^{12} -14.1421 q^{13} +13.8564i q^{15} +(-8.00000 + 13.8564i) q^{16} +18.3848 q^{17} +(-3.00000 + 5.19615i) q^{18} +26.9444i q^{19} +(11.3137 + 19.5959i) q^{20} +(-30.0000 - 17.3205i) q^{22} +27.7128i q^{23} -19.5959i q^{24} +7.00000 q^{25} +(14.1421 - 24.4949i) q^{26} -29.3939i q^{27} +2.00000 q^{29} +(-24.0000 - 13.8564i) q^{30} +14.6969i q^{31} +(-16.0000 - 27.7128i) q^{32} +42.4264 q^{33} +(-18.3848 + 31.8434i) q^{34} +(-6.00000 - 10.3923i) q^{36} -30.0000 q^{37} +(-46.6690 - 26.9444i) q^{38} +34.6410i q^{39} -45.2548 q^{40} -24.0416 q^{41} +24.2487i q^{43} +(60.0000 - 34.6410i) q^{44} -16.9706 q^{45} +(-48.0000 - 27.7128i) q^{46} -24.4949i q^{47} +(33.9411 + 19.5959i) q^{48} +(-7.00000 + 12.1244i) q^{50} -45.0333i q^{51} +(28.2843 + 48.9898i) q^{52} +66.0000 q^{53} +(50.9117 + 29.3939i) q^{54} -97.9796i q^{55} +66.0000 q^{57} +(-2.00000 + 3.46410i) q^{58} +66.1362i q^{59} +(48.0000 - 27.7128i) q^{60} -45.2548 q^{61} +(-25.4558 - 14.6969i) q^{62} +64.0000 q^{64} +80.0000 q^{65} +(-42.4264 + 73.4847i) q^{66} -6.92820i q^{67} +(-36.7696 - 63.6867i) q^{68} +67.8823 q^{69} -48.4974i q^{71} +24.0000 q^{72} +18.3848 q^{73} +(30.0000 - 51.9615i) q^{74} -17.1464i q^{75} +(93.3381 - 53.8888i) q^{76} +(-60.0000 - 34.6410i) q^{78} -20.7846i q^{79} +(45.2548 - 78.3837i) q^{80} -45.0000 q^{81} +(24.0416 - 41.6413i) q^{82} +154.318i q^{83} -104.000 q^{85} +(-42.0000 - 24.2487i) q^{86} -4.89898i q^{87} +138.564i q^{88} +24.0416 q^{89} +(16.9706 - 29.3939i) q^{90} +(96.0000 - 55.4256i) q^{92} +36.0000 q^{93} +(42.4264 + 24.4949i) q^{94} -152.420i q^{95} +(-67.8823 + 39.1918i) q^{96} -83.4386 q^{97} +51.9615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 + 12 * q^9	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} + 12 q^{9} - 32 q^{16} - 12 q^{18} - 120 q^{22} + 28 q^{25} + 8 q^{29} - 96 q^{30} - 64 q^{32} - 24 q^{36} - 120 q^{37} + 240 q^{44} - 192 q^{46} - 28 q^{50} + 264 q^{53} + 264 q^{57} - 8 q^{58} + 192 q^{60} + 256 q^{64} + 320 q^{65} + 96 q^{72} + 120 q^{74} - 240 q^{78} - 180 q^{81} - 416 q^{85} - 168 q^{86} + 384 q^{92} + 144 q^{93}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 + 12 * q^9 - 32 * q^16 - 12 * q^18 - 120 * q^22 + 28 * q^25 + 8 * q^29 - 96 * q^30 - 64 * q^32 - 24 * q^36 - 120 * q^37 + 240 * q^44 - 192 * q^46 - 28 * q^50 + 264 * q^53 + 264 * q^57 - 8 * q^58 + 192 * q^60 + 256 * q^64 + 320 * q^65 + 96 * q^72 + 120 * q^74 - 240 * q^78 - 180 * q^81 - 416 * q^85 - 168 * q^86 + 384 * q^92 + 144 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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