LMFDB - Embedded newform 1134.3.q.c.701.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,3,Mod(701,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("1134.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1134.q (of order $6$, degree $2$, not 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:	$30.8992619785$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			701.3
Root			$-1.00781 + 0.581861i$ of defining polynomial
Character	$\chi$	$=$	1134.701
Dual form			1134.3.q.c.1079.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -8.58301 q^{10} +(10.5120 - 6.06910i) q^{11} +(9.29150 - 16.0934i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +10.9015i q^{17} +20.0000 q^{19} +(-10.5120 + 6.06910i) q^{20} +(8.58301 - 14.8662i) q^{22} +(-10.5120 - 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} -26.2803i q^{26} +5.29150 q^{28} +(-36.2316 + 20.9183i) q^{29} +(-12.5830 + 21.7944i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(7.70850 + 13.3515i) q^{34} -16.0573i q^{35} +38.0000 q^{37} +(24.4949 - 14.1421i) q^{38} +(-8.58301 + 14.8662i) q^{40} +(-52.5103 - 30.3169i) q^{41} +(-41.7490 - 72.3114i) q^{43} -24.2764i q^{44} -17.1660 q^{46} +(14.6969 - 8.48528i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(14.4936 + 8.36789i) q^{50} +(-18.5830 - 32.1867i) q^{52} -94.0424i q^{53} -73.6680 q^{55} +(6.48074 - 3.74166i) q^{56} +(-29.5830 + 51.2393i) q^{58} +(-50.4179 - 29.1088i) q^{59} +(-7.83399 - 13.5689i) q^{61} +35.5901i q^{62} -8.00000 q^{64} +(-97.6722 + 56.3911i) q^{65} +(66.3320 - 114.890i) q^{67} +(18.8819 + 10.9015i) q^{68} +(-11.3542 - 19.6661i) q^{70} +12.1382i q^{71} -76.9150 q^{73} +(46.5403 - 26.8701i) q^{74} +(20.0000 - 34.6410i) q^{76} +(27.8121 + 16.0573i) q^{77} +(-16.8340 - 29.1573i) q^{79} +24.2764i q^{80} -85.7490 q^{82} +(52.4607 - 30.2882i) q^{83} +(33.0810 - 57.2980i) q^{85} +(-102.264 - 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +4.77506i q^{89} +49.1660 q^{91} +(-21.0240 + 12.1382i) q^{92} +(12.0000 - 20.7846i) q^{94} +(-105.120 - 60.6910i) q^{95} +(94.2065 + 163.170i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 + 16 * q^10 + 32 * q^13 - 16 * q^16 + 160 * q^19 - 16 * q^22 + 132 * q^25 - 16 * q^31 + 104 * q^34 + 304 * q^37 + 16 * q^40 - 80 * q^43 + 32 * q^46 - 28 * q^49 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 - 112 * q^70 - 192 * q^73 + 160 * q^76 - 304 * q^79 - 432 * q^82 - 328 * q^85 + 32 * q^88 + 224 * q^91 + 96 * q^94 + 288 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−5.25600	−	3.03455i	−1.05120	−	0.606910i	−0.128214	−	0.991746i	$-0.540925\pi$
$5$	−5.25600	−	3.03455i	−1.05120	−	0.606910i	−0.922985	+	0.384836i	$0.874258\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−8.58301			−0.858301
$11$	10.5120	−	6.06910i	0.955636	−	0.551736i	0.0608086	−	0.998149i	$-0.480632\pi$
$11$	10.5120	−	6.06910i	0.955636	−	0.551736i	0.894827	+	0.446413i	$0.147299\pi$
$12$		0			0
$13$	9.29150	−	16.0934i	0.714731	−	1.23795i	−0.248332	−	0.968675i	$-0.579882\pi$
$13$	9.29150	−	16.0934i	0.714731	−	1.23795i	0.963063	−	0.269275i	$-0.0867842\pi$
$14$	3.24037	+	1.87083i	0.231455	+	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			10.9015i			0.641262i	0.947204	+	0.320631i	$0.103895\pi$
$17$			10.9015i			0.641262i	−0.947204	+	0.320631i	$0.896105\pi$
$18$		0			0
$19$	20.0000			1.05263			0.526316	−	0.850289i	$-0.323573\pi$
$19$	20.0000			1.05263			0.526316	+	0.850289i	$0.323573\pi$
$20$	−10.5120	+	6.06910i	−0.525600	+	0.303455i
$21$		0			0
$22$	8.58301	−	14.8662i	0.390137	−	0.675736i
$23$	−10.5120	−	6.06910i	−0.457043	−	0.263874i	0.253757	−	0.967268i	$-0.418334\pi$
$23$	−10.5120	−	6.06910i	−0.457043	−	0.263874i	−0.710800	+	0.703394i	$0.751667\pi$
$24$		0			0
$25$	5.91699	+	10.2485i	0.236680	+	0.409941i
$26$		−	26.2803i		−	1.01078i
$27$		0			0
$28$	5.29150			0.188982
$29$	−36.2316	+	20.9183i	−1.24937	+	0.721322i	−0.970983	−	0.239148i	$-0.923132\pi$
$29$	−36.2316	+	20.9183i	−1.24937	+	0.721322i	−0.278384	+	0.960470i	$0.589799\pi$
$30$		0			0
$31$	−12.5830	+	21.7944i	−0.405903	+	0.703045i	−0.994426	−	0.105435i	$-0.966376\pi$
$31$	−12.5830	+	21.7944i	−0.405903	+	0.703045i	0.588523	+	0.808481i	$0.299710\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	7.70850	+	13.3515i	0.226721	+	0.392691i
$35$		−	16.0573i		−	0.458781i
$36$		0			0
$37$	38.0000			1.02703			0.513514	−	0.858082i	$-0.328344\pi$
$37$	38.0000			1.02703			0.513514	+	0.858082i	$0.328344\pi$
$38$	24.4949	−	14.1421i	0.644603	−	0.372161i
$39$		0			0
$40$	−8.58301	+	14.8662i	−0.214575	+	0.371655i
$41$	−52.5103	−	30.3169i	−1.28074	−	0.739435i	−0.303756	−	0.952750i	$-0.598241\pi$
$41$	−52.5103	−	30.3169i	−1.28074	−	0.739435i	−0.976984	+	0.213314i	$0.931574\pi$
$42$		0			0
$43$	−41.7490	−	72.3114i	−0.970907	−	1.68166i	−0.692828	−	0.721103i	$-0.743636\pi$
$43$	−41.7490	−	72.3114i	−0.970907	−	1.68166i	−0.278079	−	0.960558i	$-0.589698\pi$
$44$		−	24.2764i		−	0.551736i
$45$		0			0
$46$	−17.1660			−0.373174
$47$	14.6969	−	8.48528i	0.312701	−	0.180538i	−0.335434	−	0.942064i	$-0.608883\pi$
$47$	14.6969	−	8.48528i	0.312701	−	0.180538i	0.648134	+	0.761526i	$0.275549\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	14.4936	+	8.36789i	0.289872	+	0.167358i
$51$		0			0
$52$	−18.5830	−	32.1867i	−0.357365	−	0.618975i
$53$		−	94.0424i		−	1.77439i	−0.461399	−	0.887193i	$-0.652652\pi$
$53$		−	94.0424i		−	1.77439i	0.461399	−	0.887193i	$-0.347348\pi$
$54$		0			0
$55$	−73.6680			−1.33942
$56$	6.48074	−	3.74166i	0.115728	−	0.0668153i
$57$		0			0
$58$	−29.5830	+	51.2393i	−0.510052	+	0.883436i
$59$	−50.4179	−	29.1088i	−0.854540	−	0.493369i	0.00764008	−	0.999971i	$-0.497568\pi$
$59$	−50.4179	−	29.1088i	−0.854540	−	0.493369i	−0.862180	+	0.506602i	$0.830901\pi$
$60$		0			0
$61$	−7.83399	−	13.5689i	−0.128426	−	0.222440i	0.794641	−	0.607080i	$-0.207659\pi$
$61$	−7.83399	−	13.5689i	−0.128426	−	0.222440i	−0.923067	+	0.384639i	$0.874326\pi$
$62$			35.5901i			0.574034i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−97.6722	+	56.3911i	−1.50265	+	0.867555i
$66$		0			0
$67$	66.3320	−	114.890i	0.990030	−	1.71478i	0.373031	−	0.927819i	$-0.378319\pi$
$67$	66.3320	−	114.890i	0.990030	−	1.71478i	0.617000	−	0.786964i	$-0.288348\pi$
$68$	18.8819	+	10.9015i	0.277675	+	0.160316i
$69$		0			0
$70$	−11.3542	−	19.6661i	−0.162204	−	0.280945i
$71$			12.1382i			0.170961i	0.996340	+	0.0854803i	$0.0272425\pi$
$71$			12.1382i			0.170961i	−0.996340	+	0.0854803i	$0.972758\pi$
$72$		0			0
$73$	−76.9150			−1.05363			−0.526815	−	0.849980i	$-0.676614\pi$
$73$	−76.9150			−1.05363			−0.526815	+	0.849980i	$0.676614\pi$
$74$	46.5403	−	26.8701i	0.628923	−	0.363109i
$75$		0			0
$76$	20.0000	−	34.6410i	0.263158	−	0.455803i
$77$	27.8121	+	16.0573i	0.361196	+	0.208537i
$78$		0			0
$79$	−16.8340	−	29.1573i	−0.213088	−	0.369080i	0.739591	−	0.673056i	$-0.235019\pi$
$79$	−16.8340	−	29.1573i	−0.213088	−	0.369080i	−0.952680	+	0.303976i	$0.901686\pi$
$80$			24.2764i			0.303455i
$81$		0			0
$82$	−85.7490			−1.04572
$83$	52.4607	−	30.2882i	0.632057	−	0.364918i	−0.149491	−	0.988763i	$-0.547764\pi$
$83$	52.4607	−	30.2882i	0.632057	−	0.364918i	0.781548	+	0.623845i	$0.214430\pi$
$84$		0			0
$85$	33.0810	−	57.2980i	0.389189	−	0.674095i
$86$	−102.264	−	59.0420i	−1.18911	−	0.686535i
$87$		0			0
$88$	−17.1660	−	29.7324i	−0.195068	−	0.337868i
$89$			4.77506i			0.0536523i	0.999640	+	0.0268262i	$0.00854006\pi$
$89$			4.77506i			0.0536523i	−0.999640	+	0.0268262i	$0.991460\pi$
$90$		0			0
$91$	49.1660			0.540286
$92$	−21.0240	+	12.1382i	−0.228522	+	0.131937i
$93$		0			0
$94$	12.0000	−	20.7846i	0.127660	−	0.221113i
$95$	−105.120	−	60.6910i	−1.10653	−	0.638853i
$96$		0			0
$97$	94.2065	+	163.170i	0.971201	+	1.68217i	0.691940	+	0.721955i	$0.256756\pi$
$97$	94.2065	+	163.170i	0.971201	+	1.68217i	0.279261	+	0.960215i	$0.409910\pi$
$98$			9.89949i			0.101015i
$99$		0			0
$100$	23.6680			0.236680
$101$	−92.4162	+	53.3565i	−0.915012	+	0.528282i	−0.882040	−	0.471174i	$-0.843830\pi$
$101$	−92.4162	+	53.3565i	−0.915012	+	0.528282i	−0.0329716	+	0.999456i	$0.510497\pi$
$102$		0			0
$103$	−65.7490	+	113.881i	−0.638340	+	1.10564i	0.347457	+	0.937696i	$0.387045\pi$
$103$	−65.7490	+	113.881i	−0.638340	+	1.10564i	−0.985797	+	0.167941i	$0.946288\pi$
$104$	−45.5189	−	26.2803i	−0.437682	−	0.252696i
$105$		0			0
$106$	−66.4980	−	115.178i	−0.627340	−	1.08658i
$107$		−	82.3793i		−	0.769900i	−0.922937	−	0.384950i	$-0.874219\pi$
$107$		−	82.3793i		−	0.769900i	0.922937	−	0.384950i	$-0.125781\pi$
$108$		0			0
$109$	33.8301			0.310367			0.155184	−	0.987886i	$-0.450403\pi$
$109$	33.8301			0.310367			0.155184	+	0.987886i	$0.450403\pi$
$110$	−90.2245	+	52.0911i	−0.820223	+	0.473556i
$111$		0			0
$112$	5.29150	−	9.16515i	0.0472456	−	0.0818317i
$113$	−24.6982	−	14.2595i	−0.218568	−	0.126190i	0.386719	−	0.922198i	$-0.373608\pi$
$113$	−24.6982	−	14.2595i	−0.218568	−	0.126190i	−0.605287	+	0.796007i	$0.706942\pi$
$114$		0			0
$115$	36.8340	+	63.7983i	0.320296	+	0.554768i
$116$			83.6734i			0.721322i
$117$		0			0
$118$	−82.3320			−0.697729
$119$	−24.9784	+	14.4213i	−0.209902	+	0.121187i
$120$		0			0
$121$	13.1680	−	22.8076i	0.108826	−	0.188493i
$122$	−19.1893	−	11.0789i	−0.157289	−	0.0908109i
$123$		0			0
$124$	25.1660	+	43.5888i	0.202952	+	0.351523i
$125$			79.9059i			0.639247i
$126$		0			0
$127$	129.668			1.02101			0.510504	−	0.859875i	$-0.329459\pi$
$127$	129.668			1.02101			0.510504	+	0.859875i	$0.329459\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−79.7490	+	138.129i	−0.613454	+	1.06253i
$131$	−128.187	−	74.0087i	−0.978525	−	0.564952i	−0.0767004	−	0.997054i	$-0.524438\pi$
$131$	−128.187	−	74.0087i	−0.978525	−	0.564952i	−0.901824	+	0.432103i	$0.857772\pi$
$132$		0			0
$133$	26.4575	+	45.8258i	0.198929	+	0.344555i
$134$		−	187.615i		−	1.40011i
$135$		0			0
$136$	30.8340			0.226721
$137$	66.6469	−	38.4786i	0.486474	−	0.280866i	−0.236637	−	0.971598i	$-0.576045\pi$
$137$	66.6469	−	38.4786i	0.486474	−	0.280866i	0.723111	+	0.690732i	$0.242712\pi$
$138$		0			0
$139$	−108.664	+	188.212i	−0.781756	+	1.35404i	0.149162	+	0.988813i	$0.452342\pi$
$139$	−108.664	+	188.212i	−0.781756	+	1.35404i	−0.930918	+	0.365228i	$0.880991\pi$
$140$	−27.8121	−	16.0573i	−0.198658	−	0.114695i
$141$		0			0
$142$	8.58301	+	14.8662i	0.0604437	+	0.104692i
$143$		−	225.564i		−	1.57737i
$144$		0			0
$145$	253.911			1.75111
$146$	−94.2013	+	54.3871i	−0.645214	+	0.372515i
$147$		0			0
$148$	38.0000	−	65.8179i	0.256757	−	0.444716i
$149$	140.231	+	80.9623i	0.941147	+	0.543371i	0.890320	−	0.455336i	$-0.150481\pi$
$149$	140.231	+	80.9623i	0.941147	+	0.543371i	0.0508272	+	0.998707i	$0.483814\pi$
$150$		0			0
$151$	46.5830	+	80.6841i	0.308497	+	0.534332i	0.978034	−	0.208447i	$-0.0668408\pi$
$151$	46.5830	+	80.6841i	0.308497	+	0.534332i	−0.669537	+	0.742779i	$0.733507\pi$
$152$		−	56.5685i		−	0.372161i
$153$		0			0
$154$	45.4170			0.294916
$155$	132.272	−	76.3675i	0.853371	−	0.492694i
$156$		0			0
$157$	92.4980	−	160.211i	0.589159	−	1.02045i	−0.405183	−	0.914235i	$-0.632792\pi$
$157$	92.4980	−	160.211i	0.589159	−	1.02045i	0.994343	−	0.106219i	$-0.0338743\pi$
$158$	−41.2347	−	23.8069i	−0.260979	−	0.150676i
$159$		0			0
$160$	17.1660	+	29.7324i	0.107288	+	0.185828i
$161$		−	32.1147i		−	0.199470i
$162$		0			0
$163$	86.9961			0.533718			0.266859	−	0.963736i	$-0.414014\pi$
$163$	86.9961			0.533718			0.266859	+	0.963736i	$0.414014\pi$
$164$	−105.021	+	60.6337i	−0.640370	+	0.369718i
$165$		0			0
$166$	42.8340	−	74.1906i	0.258036	−	0.446932i
$167$	52.4607	+	30.2882i	0.314136	+	0.181366i	0.648776	−	0.760980i	$-0.275281\pi$
$167$	52.4607	+	30.2882i	0.314136	+	0.181366i	−0.334640	+	0.942346i	$0.608615\pi$
$168$		0			0
$169$	−88.1640	−	152.705i	−0.521681	−	0.903578i
$170$		−	93.5673i		−	0.550396i
$171$		0			0
$172$	−166.996			−0.970907
$173$	−140.791	+	81.2858i	−0.813822	+	0.469860i	−0.848281	−	0.529546i	$-0.822362\pi$
$173$	−140.791	+	81.2858i	−0.813822	+	0.469860i	0.0344594	+	0.999406i	$0.489029\pi$
$174$		0			0
$175$	−15.6549	+	27.1151i	−0.0894566	+	0.154943i
$176$	−42.0480	−	24.2764i	−0.238909	−	0.137934i
$177$		0			0
$178$	3.37648	+	5.84823i	0.0189690	+	0.0328552i
$179$		−	223.091i		−	1.24632i	−0.782095	−	0.623159i	$-0.785849\pi$
$179$		−	223.091i		−	1.24632i	0.782095	−	0.623159i	$-0.214151\pi$
$180$		0			0
$181$	188.915			1.04373			0.521865	−	0.853028i	$-0.325237\pi$
$181$	188.915			1.04373			0.521865	+	0.853028i	$0.325237\pi$
$182$	60.2158	−	34.7656i	0.330856	−	0.191020i
$183$		0			0
$184$	−17.1660	+	29.7324i	−0.0932935	+	0.161589i
$185$	−199.728	−	115.313i	−1.07961	−	0.623313i
$186$		0			0
$187$	66.1621	+	114.596i	0.353808	+	0.612813i
$188$		−	33.9411i		−	0.180538i
$189$		0			0
$190$	−171.660			−0.903474
$191$	197.486	−	114.019i	1.03396	−	0.596957i	0.115844	−	0.993267i	$-0.463043\pi$
$191$	197.486	−	114.019i	1.03396	−	0.596957i	0.918117	+	0.396310i	$0.129709\pi$
$192$		0			0
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	−0.985742	−	0.168264i	$-0.946184\pi$
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	0.638592	+	0.769546i	$0.279517\pi$
$194$	230.758	+	133.228i	1.18947	+	0.686743i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$			188.560i			0.957157i	0.878045	+	0.478579i	$0.158848\pi$
$197$			188.560i			0.957157i	−0.878045	+	0.478579i	$0.841152\pi$
$198$		0			0
$199$	102.494			0.515046			0.257523	−	0.966272i	$-0.417094\pi$
$199$	102.494			0.515046			0.257523	+	0.966272i	$0.417094\pi$
$200$	28.9872	−	16.7358i	0.144936	−	0.0836789i
$201$		0			0
$202$	−75.4575	+	130.696i	−0.373552	+	0.647011i
$203$	−95.8599	−	55.3447i	−0.472216	−	0.272634i
$204$		0			0
$205$	183.996	+	318.691i	0.897542	+	1.55459i
$206$			185.966i			0.902749i
$207$		0			0
$208$	−74.3320			−0.357365
$209$	210.240	−	121.382i	1.00593	−	0.580775i
$210$		0			0
$211$	42.2510	−	73.1809i	0.200242	−	0.346829i	−0.748365	−	0.663288i	$-0.769161\pi$
$211$	42.2510	−	73.1809i	0.200242	−	0.346829i	0.948606	+	0.316459i	$0.102494\pi$
$212$	−162.886	−	94.0424i	−0.768331	−	0.443596i
$213$		0			0
$214$	−58.2510	−	100.894i	−0.272201	−	0.471466i
$215$			506.758i			2.35701i
$216$		0			0
$217$	−66.5830			−0.306834
$218$	41.4332	−	23.9215i	0.190060	−	0.109731i
$219$		0			0
$220$	−73.6680	+	127.597i	−0.334854	+	0.579985i
$221$	175.441	+	101.291i	0.793851	+	0.458330i
$222$		0			0
$223$	79.2470	+	137.260i	0.355368	+	0.615515i	0.987181	−	0.159606i	$-0.0510222\pi$
$223$	79.2470	+	137.260i	0.355368	+	0.615515i	−0.631813	+	0.775121i	$0.717689\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−40.3320			−0.178460
$227$	−88.1816	+	50.9117i	−0.388465	+	0.224281i	−0.681495	−	0.731823i	$-0.738670\pi$
$227$	−88.1816	+	50.9117i	−0.388465	+	0.224281i	0.293030	+	0.956103i	$0.405337\pi$
$228$		0			0
$229$	134.458	−	232.887i	0.587151	−	1.01697i	−0.407453	−	0.913226i	$-0.633583\pi$
$229$	134.458	−	232.887i	0.587151	−	1.01697i	0.994604	−	0.103749i	$-0.0330837\pi$
$230$	90.2245	+	52.0911i	0.392280	+	0.226483i
$231$		0			0
$232$	59.1660	+	102.479i	0.255026	+	0.441718i
$233$			26.2748i			0.112767i	0.998409	+	0.0563836i	$0.0179570\pi$
$233$			26.2748i			0.112767i	−0.998409	+	0.0563836i	$0.982043\pi$
$234$		0			0
$235$	−102.996			−0.438281
$236$	−100.836	+	58.2175i	−0.427270	+	0.246684i
$237$		0			0
$238$	−20.3948	+	35.3248i	−0.0856923	+	0.148423i
$239$	79.9110	+	46.1366i	0.334356	+	0.193040i	0.657773	−	0.753216i	$-0.271499\pi$
$239$	79.9110	+	46.1366i	0.334356	+	0.193040i	−0.323418	+	0.946256i	$0.604832\pi$
$240$		0			0
$241$	−171.624	−	297.261i	−0.712131	−	1.23345i	−0.964056	−	0.265700i	$-0.914397\pi$
$241$	−171.624	−	297.261i	−0.712131	−	1.23345i	0.251925	−	0.967747i	$-0.418936\pi$
$242$		−	37.2447i		−	0.153904i
$243$		0			0
$244$	−31.3360			−0.128426
$245$	36.7920	−	21.2419i	0.150171	−	0.0867014i
$246$		0			0
$247$	185.830	−	321.867i	0.752348	−	1.30311i
$248$	61.6439	+	35.5901i	0.248564	+	0.143509i
$249$		0			0
$250$	56.5020	+	97.8643i	0.226008	+	0.391457i
$251$		−	356.382i		−	1.41985i	−0.704278	−	0.709924i	$-0.748729\pi$
$251$		−	356.382i		−	1.41985i	0.704278	−	0.709924i	$-0.251271\pi$
$252$		0			0
$253$	−147.336			−0.582356
$254$	158.810	−	91.6891i	0.625237	−	0.360981i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−220.603	−	127.365i	−0.858377	−	0.495584i	0.00509129	−	0.999987i	$-0.498379\pi$
$257$	−220.603	−	127.365i	−0.858377	−	0.495584i	−0.863469	+	0.504403i	$0.831713\pi$
$258$		0			0
$259$	50.2693	+	87.0689i	0.194090	+	0.336174i
$260$			225.564i			0.867555i
$261$		0			0
$262$	−209.328			−0.798962
$263$	−226.880	+	130.989i	−0.862663	+	0.498059i	−0.864903	−	0.501939i	$-0.832620\pi$
$263$	−226.880	+	130.989i	−0.862663	+	0.498059i	0.00224015	+	0.999997i	$0.499287\pi$
$264$		0			0
$265$	−285.376	+	494.287i	−1.07689	+	1.86523i
$266$	64.8074	+	37.4166i	0.243637	+	0.140664i
$267$		0			0
$268$	−132.664	−	229.781i	−0.495015	−	0.857391i
$269$		−	93.6246i		−	0.348047i	−0.984742	−	0.174023i	$-0.944323\pi$
$269$		−	93.6246i		−	0.348047i	0.984742	−	0.174023i	$-0.0556768\pi$
$270$		0			0
$271$	1.16601			0.00430262			0.00215131	−	0.999998i	$-0.499315\pi$
$271$	1.16601			0.00430262			0.00215131	+	0.999998i	$0.499315\pi$
$272$	37.7638	−	21.8029i	0.138837	−	0.0801578i
$273$		0			0
$274$	54.4170	−	94.2530i	0.198602	−	0.343989i
$275$	124.399	+	71.8217i	0.452359	+	0.261170i
$276$		0			0
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	0.835699	−	0.549188i	$-0.185063\pi$
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	−0.893460	+	0.449142i	$0.851730\pi$
$278$			307.348i			1.10557i
$279$		0			0
$280$	−45.4170			−0.162204
$281$	−144.416	+	83.3785i	−0.513935	+	0.296721i	−0.734450	−	0.678663i	$-0.762560\pi$
$281$	−144.416	+	83.3785i	−0.513935	+	0.296721i	0.220514	+	0.975384i	$0.429226\pi$
$282$		0			0
$283$	−8.16995	+	14.1508i	−0.0288691	+	0.0500027i	−0.880099	−	0.474790i	$-0.842524\pi$
$283$	−8.16995	+	14.1508i	−0.0288691	+	0.0500027i	0.851230	+	0.524793i	$0.175857\pi$
$284$	21.0240	+	12.1382i	0.0740281	+	0.0427401i
$285$		0			0
$286$	−159.498	−	276.259i	−0.557685	−	0.965939i
$287$		−	160.422i		−	0.558961i
$288$		0			0
$289$	170.158			0.588782
$290$	310.976	−	179.542i	1.07233	−	0.619111i
$291$		0			0
$292$	−76.9150	+	133.221i	−0.263408	+	0.456235i
$293$	319.495	+	184.461i	1.09043	+	0.629558i	0.933690	−	0.358082i	$-0.116569\pi$
$293$	319.495	+	184.461i	1.09043	+	0.629558i	0.156737	+	0.987640i	$0.449903\pi$
$294$		0			0
$295$	176.664	+	305.991i	0.598861	+	1.03726i
$296$		−	107.480i		−	0.363109i
$297$		0			0
$298$	228.996			0.768443
$299$	−195.344	+	112.782i	−0.653326	+	0.377198i
$300$		0			0
$301$	110.458	−	191.318i	0.366968	−	0.635608i
$302$	114.105	+	65.8783i	0.377830	+	0.218140i
$303$		0			0
$304$	−40.0000	−	69.2820i	−0.131579	−	0.227901i
$305$			95.0906i			0.311772i
$306$		0			0
$307$	−192.664			−0.627570			−0.313785	−	0.949494i	$-0.601597\pi$
$307$	−192.664			−0.627570			−0.313785	+	0.949494i	$0.601597\pi$
$308$	55.6242	−	32.1147i	0.180598	−	0.104268i
$309$		0			0
$310$	108.000	−	187.061i	0.348387	−	0.603424i
$311$	113.688	+	65.6380i	0.365557	+	0.211055i	0.671516	−	0.740990i	$-0.265644\pi$
$311$	113.688	+	65.6380i	0.365557	+	0.211055i	−0.305959	+	0.952045i	$0.598977\pi$
$312$		0			0
$313$	−21.6640	−	37.5232i	−0.0692142	−	0.119882i	0.829341	−	0.558742i	$-0.188716\pi$
$313$	−21.6640	−	37.5232i	−0.0692142	−	0.119882i	−0.898556	+	0.438860i	$0.855383\pi$
$314$		−	261.624i		−	0.833197i
$315$		0			0
$316$	−67.3360			−0.213088
$317$	218.000	−	125.862i	0.687696	−	0.397042i	−0.115052	−	0.993359i	$-0.536703\pi$
$317$	218.000	−	125.862i	0.687696	−	0.397042i	0.802748	+	0.596318i	$0.203370\pi$
$318$		0			0
$319$	−253.911	+	439.787i	−0.795960	+	1.37864i
$320$	42.0480	+	24.2764i	0.131400	+	0.0758638i
$321$		0			0
$322$	−22.7085	−	39.3323i	−0.0705233	−	0.122150i
$323$			218.029i			0.675013i
$324$		0			0
$325$	219.911			0.676650
$326$	106.548	−	61.5155i	0.326834	−	0.188698i
$327$		0			0
$328$	−85.7490	+	148.522i	−0.261430	+	0.452810i
$329$	38.8844	+	22.4499i	0.118190	+	0.0682369i
$330$		0			0
$331$	−180.745	−	313.060i	−0.546058	−	0.945800i	−0.998540	−	0.0540260i	$-0.982795\pi$
$331$	−180.745	−	313.060i	−0.546058	−	0.945800i	0.452482	−	0.891774i	$-0.350539\pi$
$332$		−	121.153i		−	0.364918i
$333$		0			0
$334$	85.6680			0.256491
$335$	−697.282	+	402.576i	−2.08144	+	1.20172i
$336$		0			0
$337$	149.417	−	258.798i	0.443374	−	0.767946i	−0.554563	−	0.832141i	$-0.687115\pi$
$337$	149.417	−	258.798i	0.443374	−	0.767946i	0.997937	+	0.0641954i	$0.0204481\pi$
$338$	−215.957	−	124.683i	−0.638926	−	0.368884i
$339$		0			0
$340$	−66.1621	−	114.596i	−0.194594	−	0.337047i
$341$			305.470i			0.895807i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$	−204.528	+	118.084i	−0.594557	+	0.343268i
$345$		0			0
$346$	−114.956	+	199.109i	−0.332241	+	0.575459i
$347$	178.505	+	103.060i	0.514425	+	0.297003i	0.734651	−	0.678446i	$-0.237346\pi$
$347$	178.505	+	103.060i	0.514425	+	0.297003i	−0.220226	+	0.975449i	$0.570679\pi$
$348$		0			0
$349$	−217.162	−	376.136i	−0.622241	−	1.07775i	−0.989067	−	0.147464i	$-0.952889\pi$
$349$	−217.162	−	376.136i	−0.622241	−	1.07775i	0.366827	−	0.930289i	$-0.380444\pi$
$350$			44.2787i			0.126511i
$351$		0			0
$352$	−68.6640			−0.195068
$353$	160.595	−	92.7197i	0.454944	−	0.262662i	−0.254972	−	0.966948i	$-0.582066\pi$
$353$	160.595	−	92.7197i	0.454944	−	0.262662i	0.709916	+	0.704286i	$0.248733\pi$
$354$		0			0
$355$	36.8340	−	63.7983i	0.103758	−	0.179714i
$356$	8.27064	+	4.77506i	0.0232321	+	0.0134131i
$357$		0			0
$358$	−157.749	−	273.229i	−0.440640	−	0.763210i
$359$			516.767i			1.43946i	0.694254	+	0.719731i	$0.255735\pi$
$359$			516.767i			1.43946i	−0.694254	+	0.719731i	$0.744265\pi$
$360$		0			0
$361$	39.0000			0.108033
$362$	231.373	−	133.583i	0.639151	−	0.369014i
$363$		0			0
$364$	49.1660	−	85.1580i	0.135071	−	0.233951i
$365$	404.265	+	233.403i	1.10758	+	0.639459i
$366$		0			0
$367$	58.7451	+	101.749i	0.160068	+	0.277246i	0.934893	−	0.354930i	$-0.115495\pi$
$367$	58.7451	+	101.749i	0.160068	+	0.277246i	−0.774825	+	0.632176i	$0.782162\pi$
$368$			48.5528i			0.131937i
$369$		0			0
$370$	−326.154			−0.881498
$371$	215.478	−	124.406i	0.580804	−	0.335327i
$372$		0			0
$373$	201.332	−	348.717i	0.539764	−	0.934899i	−0.459152	−	0.888358i	$-0.651847\pi$
$373$	201.332	−	348.717i	0.539764	−	0.934899i	0.998916	−	0.0465413i	$-0.0148199\pi$
$374$	162.063	+	93.5673i	0.433324	+	0.250180i
$375$		0			0
$376$	−24.0000	−	41.5692i	−0.0638298	−	0.110556i
$377$			777.451i			2.06221i
$378$		0			0
$379$	398.834			1.05233			0.526166	−	0.850382i	$-0.323629\pi$
$379$	398.834			1.05233			0.526166	+	0.850382i	$0.323629\pi$
$380$	−210.240	+	121.382i	−0.553263	+	0.319426i
$381$		0			0
$382$	161.247	−	279.288i	0.422113	−	0.731121i
$383$	645.019	+	372.402i	1.68412	+	0.972329i	0.958869	+	0.283849i	$0.0916114\pi$
$383$	645.019	+	372.402i	1.68412	+	0.972329i	0.725255	+	0.688481i	$0.241722\pi$
$384$		0			0
$385$	−97.4536	−	168.795i	−0.253126	−	0.438427i
$386$			189.505i			0.490945i
$387$		0			0
$388$	376.826			0.971201
$389$	463.464	−	267.581i	1.19142	−	0.687869i	0.232795	−	0.972526i	$-0.425213\pi$
$389$	463.464	−	267.581i	1.19142	−	0.687869i	0.958630	+	0.284656i	$0.0918795\pi$
$390$		0			0
$391$	66.1621	−	114.596i	0.169212	−	0.293085i
$392$	17.1464	+	9.89949i	0.0437409	+	0.0252538i
$393$		0			0
$394$	133.332	+	230.938i	0.338406	+	0.586137i
$395$			204.334i			0.517302i
$396$		0			0
$397$	−94.3241			−0.237592			−0.118796	−	0.992919i	$-0.537904\pi$
$397$	−94.3241			−0.237592			−0.118796	+	0.992919i	$0.537904\pi$
$398$	125.529	−	72.4743i	0.315400	−	0.182096i
$399$		0			0
$400$	23.6680	−	40.9941i	0.0591699	−	0.102485i
$401$	−89.7138	−	51.7963i	−0.223725	−	0.129168i	0.383949	−	0.923354i	$-0.374564\pi$
$401$	−89.7138	−	51.7963i	−0.223725	−	0.129168i	−0.607674	+	0.794187i	$0.707897\pi$
$402$		0			0
$403$	233.830	+	405.006i	0.580223	+	1.00498i
$404$			213.426i			0.528282i
$405$		0			0
$406$	−156.539			−0.385563
$407$	399.456	−	230.626i	0.981464	−	0.566648i
$408$		0			0
$409$	4.87844	−	8.44971i	0.0119277	−	0.0206594i	−0.860000	−	0.510294i	$-0.829537\pi$
$409$	4.87844	−	8.44971i	0.0119277	−	0.0206594i	0.871928	+	0.489635i	$0.162870\pi$
$410$	450.696	+	260.210i	1.09926	+	0.634658i
$411$		0			0
$412$	131.498	+	227.761i	0.319170	+	0.552819i
$413$		−	154.029i		−	0.372952i
$414$		0			0
$415$	−367.644			−0.885890
$416$	−91.0378	+	52.5607i	−0.218841	+	0.126348i
$417$		0			0
$418$	171.660	−	297.324i	0.410670	−	0.711301i
$419$	293.939	+	169.706i	0.701525	+	0.405025i	0.807915	−	0.589299i	$-0.200596\pi$
$419$	293.939	+	169.706i	0.701525	+	0.405025i	−0.106390	+	0.994324i	$0.533929\pi$
$420$		0			0
$421$	299.660	+	519.027i	0.711782	+	1.23284i	0.964188	+	0.265221i	$0.0854448\pi$
$421$	299.660	+	519.027i	0.711782	+	1.23284i	−0.252406	+	0.967621i	$0.581222\pi$
$422$		−	119.504i		−	0.283184i
$423$		0			0
$424$	−265.992			−0.627340
$425$	−111.724	+	64.5039i	−0.262880	+	0.151774i
$426$		0			0
$427$	20.7268	−	35.8998i	0.0485405	−	0.0840746i
$428$	−142.685	−	82.3793i	−0.333377	−	0.192475i
$429$		0			0
$430$	358.332	+	620.649i	0.833330	+	1.44337i
$431$		−	710.978i		−	1.64960i	−0.565424	−	0.824800i	$-0.691288\pi$
$431$		−	710.978i		−	1.64960i	0.565424	−	0.824800i	$-0.308712\pi$
$432$		0			0
$433$	377.984			0.872943			0.436471	−	0.899718i	$-0.356228\pi$
$433$	377.984			0.872943			0.436471	+	0.899718i	$0.356228\pi$
$434$	−81.5472	+	47.0813i	−0.187897	+	0.108482i
$435$		0			0
$436$	33.8301	−	58.5954i	0.0775919	−	0.134393i
$437$	−210.240	−	121.382i	−0.481098	−	0.277762i
$438$		0			0
$439$	−264.073	−	457.388i	−0.601533	−	1.04189i	−0.992589	−	0.121519i	$-0.961223\pi$
$439$	−264.073	−	457.388i	−0.601533	−	1.04189i	0.391056	−	0.920367i	$-0.372110\pi$
$440$			208.365i			0.473556i
$441$		0			0
$442$	286.494			0.648177
$443$	−31.7345	+	18.3219i	−0.0716354	+	0.0413587i	−0.535390	−	0.844605i	$-0.679835\pi$
$443$	−31.7345	+	18.3219i	−0.0716354	+	0.0413587i	0.463754	+	0.885964i	$0.346502\pi$
$444$		0			0
$445$	14.4902	−	25.0977i	0.0325622	−	0.0563993i
$446$	194.115	+	112.072i	0.435235	+	0.251283i
$447$		0			0
$448$	−10.5830	−	18.3303i	−0.0236228	−	0.0409159i
$449$			397.612i			0.885550i	0.896633	+	0.442775i	$0.146006\pi$
$449$			397.612i			0.885550i	−0.896633	+	0.442775i	$0.853994\pi$
$450$		0			0
$451$	−735.984			−1.63189
$452$	−49.3964	+	28.5190i	−0.109284	+	0.0630952i
$453$		0			0
$454$	−72.0000	+	124.708i	−0.158590	+	0.274686i
$455$	−258.416	−	149.197i	−0.567948	−	0.327905i
$456$		0			0
$457$	−172.162	−	298.193i	−0.376722	−	0.652502i	0.613861	−	0.789414i	$-0.289616\pi$
$457$	−172.162	−	298.193i	−0.376722	−	0.652502i	−0.990583	+	0.136912i	$0.956282\pi$
$458$		−	380.303i		−	0.830357i
$459$		0			0
$460$	147.336			0.320296
$461$	321.240	−	185.468i	0.696833	−	0.402317i	−0.109334	−	0.994005i	$-0.534872\pi$
$461$	321.240	−	185.468i	0.696833	−	0.402317i	0.806167	+	0.591688i	$0.201538\pi$
$462$		0			0
$463$	−39.1660	+	67.8375i	−0.0845918	+	0.146517i	−0.905217	−	0.424949i	$-0.860292\pi$
$463$	−39.1660	+	67.8375i	−0.0845918	+	0.146517i	0.820625	+	0.571467i	$0.193625\pi$
$464$	144.927	+	83.6734i	0.312342	+	0.180331i
$465$		0			0
$466$	18.5791	+	32.1799i	0.0398692	+	0.0690556i
$467$			399.758i			0.856014i	0.903775	+	0.428007i	$0.140784\pi$
$467$			399.758i			0.856014i	−0.903775	+	0.428007i	$0.859216\pi$
$468$		0			0
$469$	350.996			0.748392
$470$	−126.144	+	72.8292i	−0.268391	+	0.154956i
$471$		0			0
$472$	−82.3320	+	142.603i	−0.174432	+	0.302126i
$473$	−877.731	−	506.758i	−1.85567	−	1.07137i
$474$		0			0
$475$	118.340	+	204.971i	0.249137	+	0.431517i
$476$			57.6851i			0.121187i
$477$		0			0
$478$	130.494			0.273000
$479$	609.100	−	351.664i	1.27161	−	0.734163i	0.296317	−	0.955090i	$-0.404241\pi$
$479$	609.100	−	351.664i	1.27161	−	0.734163i	0.975290	+	0.220927i	$0.0709081\pi$
$480$		0			0
$481$	353.077	−	611.547i	0.734048	−	1.27141i
$482$	−420.390	−	242.712i	−0.872179	−	0.503553i
$483$		0			0
$484$	−26.3360	−	45.6152i	−0.0544131	−	0.0942463i
$485$		−	1143.50i		−	2.35773i
$486$		0			0
$487$	−82.5098			−0.169425			−0.0847124	−	0.996405i	$-0.526997\pi$
$487$	−82.5098			−0.169425			−0.0847124	+	0.996405i	$0.526997\pi$
$488$	−38.3786	+	22.1579i	−0.0786446	+	0.0454055i
$489$		0			0
$490$	30.0405	−	52.0317i	0.0613072	−	0.106187i
$491$	−159.524	−	92.1014i	−0.324897	−	0.187579i	0.328676	−	0.944443i	$-0.393397\pi$
$491$	−159.524	−	92.1014i	−0.324897	−	0.187579i	−0.653573	+	0.756863i	$0.726731\pi$
$492$		0			0
$493$	−228.041	−	394.978i	−0.462557	−	0.801172i
$494$		−	525.607i		−	1.06398i
$495$		0			0
$496$	100.664			0.202952
$497$	−27.8121	+	16.0573i	−0.0559600	+	0.0323085i
$498$		0			0
$499$	−376.405	+	651.953i	−0.754319	+	1.30652i	0.191393	+	0.981513i	$0.438699\pi$
$499$	−376.405	+	651.953i	−0.754319	+	1.30652i	−0.945712	+	0.325005i	$0.894634\pi$
$500$	138.401	+	79.9059i	0.276802	+	0.159812i
$501$		0			0
$502$	−252.000	−	436.477i	−0.501992	−	0.869476i
$503$			662.540i			1.31718i	0.752504	+	0.658588i	$0.228846\pi$
$503$			662.540i			1.31718i	−0.752504	+	0.658588i	$0.771154\pi$
$504$		0			0
$505$	647.652			1.28248
$506$	−180.449	+	104.182i	−0.356618	+	0.205894i
$507$		0			0
$508$	129.668	−	224.592i	0.255252	−	0.442109i
$509$	821.958	+	474.557i	1.61485	+	0.932333i	0.988225	+	0.153010i	$0.0488968\pi$
$509$	821.958	+	474.557i	1.61485	+	0.932333i	0.626623	+	0.779322i	$0.284437\pi$
$510$		0			0
$511$	−101.749	−	176.234i	−0.199117	−	0.344882i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−360.243			−0.700862
$515$	691.153	−	399.037i	1.34204	−	0.774830i
$516$		0			0
$517$	102.996	−	178.394i	0.199219	−	0.345057i
$518$	123.134	+	71.0915i	0.237711	+	0.137242i
$519$		0			0
$520$	159.498	+	276.259i	0.306727	+	0.531267i
$521$		−	714.344i		−	1.37110i	−0.728025	−	0.685551i	$-0.759561\pi$
$521$		−	714.344i		−	1.37110i	0.728025	−	0.685551i	$-0.240439\pi$
$522$		0			0
$523$	−232.000			−0.443595			−0.221797	−	0.975093i	$-0.571192\pi$
$523$	−232.000			−0.443595			−0.221797	+	0.975093i	$0.571192\pi$
$524$	−256.373	+	148.017i	−0.489262	+	0.282476i
$525$		0			0
$526$	−185.247	+	320.857i	−0.352181	+	0.609995i
$527$	−237.591	−	137.173i	−0.450837	−	0.260291i
$528$		0			0
$529$	−190.832	−	330.531i	−0.360741	−	0.624822i
$530$			807.167i			1.52296i
$531$		0			0
$532$	105.830			0.198929
$533$	−975.800	+	563.378i	−1.83077	+	1.05699i
$534$		0			0
$535$	−249.984	+	432.985i	−0.467260	+	0.809319i
$536$	−324.959	−	187.615i	−0.606267	−	0.350029i
$537$		0			0
$538$	−66.2026	−	114.666i	−0.123053	−	0.213134i
$539$			84.9674i			0.157639i
$540$		0			0
$541$	165.668			0.306225			0.153113	−	0.988209i	$-0.451070\pi$
$541$	165.668			0.306225			0.153113	+	0.988209i	$0.451070\pi$
$542$	1.42807	−	0.824494i	0.00263481	−	0.00152121i
$543$		0			0
$544$	30.8340	−	53.4060i	0.0566801	−	0.0981729i
$545$	−177.811	−	102.659i	−0.326258	−	0.188365i
$546$		0			0
$547$	−147.838	−	256.063i	−0.270270	−	0.468122i	0.698661	−	0.715453i	$-0.253780\pi$
$547$	−147.838	−	256.063i	−0.270270	−	0.468122i	−0.968931	+	0.247331i	$0.920446\pi$
$548$		−	153.915i		−	0.280866i
$549$		0			0
$550$	203.142			0.369350
$551$	−724.633	+	418.367i	−1.31512	+	0.759287i
$552$		0			0
$553$	44.5385	−	77.1430i	0.0805399	−	0.139499i
$554$	−39.1918	−	22.6274i	−0.0707434	−	0.0408437i
$555$		0			0
$556$	217.328	+	376.423i	0.390878	+	0.677020i
$557$		−	76.8426i		−	0.137958i	−0.997618	−	0.0689790i	$-0.978026\pi$
$557$		−	76.8426i		−	0.137958i	0.997618	−	0.0689790i	$-0.0219742\pi$
$558$		0			0
$559$	−1551.64			−2.77575
$560$	−55.6242	+	32.1147i	−0.0993290	+	0.0573476i
$561$		0			0
$562$	−117.915	+	204.235i	−0.209813	+	0.363407i
$563$	880.170	+	508.167i	1.56336	+	0.902605i	0.996914	+	0.0785049i	$0.0250146\pi$
$563$	880.170	+	508.167i	1.56336	+	0.902605i	0.566444	+	0.824100i	$0.308319\pi$
$564$		0			0
$565$	86.5425	+	149.896i	0.153173	+	0.265303i
$566$			23.1081i			0.0408270i
$567$		0			0
$568$	34.3320			0.0604437
$569$	507.952	−	293.266i	0.892710	−	0.515406i	0.0178822	−	0.999840i	$-0.494308\pi$
$569$	507.952	−	293.266i	0.892710	−	0.515406i	0.874828	+	0.484434i	$0.160974\pi$
$570$		0			0
$571$	−475.822	+	824.148i	−0.833314	+	1.44334i	0.0620822	+	0.998071i	$0.480226\pi$
$571$	−475.822	+	824.148i	−0.833314	+	1.44334i	−0.895396	+	0.445271i	$0.853107\pi$
$572$	−390.689	−	225.564i	−0.683022	−	0.394343i
$573$		0			0
$574$	−113.435	−	196.476i	−0.197622	−	0.342292i
$575$		−	143.643i		−	0.249815i
$576$		0			0
$577$	−148.672			−0.257664			−0.128832	−	0.991666i	$-0.541123\pi$
$577$	−148.672			−0.257664			−0.128832	+	0.991666i	$0.541123\pi$
$578$	208.400	−	120.320i	0.360554	−	0.208166i
$579$		0			0
$580$	253.911	−	439.787i	0.437778	−	0.758253i
$581$	138.798	+	80.1351i	0.238895	+	0.137926i
$582$		0			0
$583$	−570.753	−	988.573i	−0.978993	−	1.69567i
$584$			217.549i			0.372515i
$585$		0			0
$586$	521.733			0.890330
$587$	−288.009	+	166.282i	−0.490645	+	0.283274i	−0.724842	−	0.688915i	$-0.758087\pi$
$587$	−288.009	+	166.282i	−0.490645	+	0.283274i	0.234197	+	0.972189i	$0.424754\pi$
$588$		0			0
$589$	−251.660	+	435.888i	−0.427267	+	0.740048i
$590$	432.737	+	249.841i	0.733452	+	0.423459i
$591$		0			0
$592$	−76.0000	−	131.636i	−0.128378	−	0.222358i
$593$		−	217.251i		−	0.366359i	−0.983079	−	0.183180i	$-0.941361\pi$
$593$		−	217.251i		−	0.366359i	0.983079	−	0.183180i	$-0.0586390\pi$
$594$		0			0
$595$	175.048			0.294199
$596$	280.462	−	161.925i	0.470573	−	0.271686i
$597$		0			0
$598$	−159.498	+	276.259i	−0.266719	+	0.461971i
$599$	−149.111	−	86.0896i	−0.248934	−	0.143722i	0.370342	−	0.928895i	$-0.379240\pi$
$599$	−149.111	−	86.0896i	−0.248934	−	0.143722i	−0.619276	+	0.785173i	$0.712574\pi$
$600$		0			0
$601$	209.000	+	361.999i	0.347754	+	0.602327i	0.985850	−	0.167629i	$-0.0536112\pi$
$601$	209.000	+	361.999i	0.347754	+	0.602327i	−0.638096	+	0.769957i	$0.720278\pi$
$602$		−	312.421i		−	0.518972i
$603$		0			0
$604$	186.332			0.308497
$605$	−138.422	+	79.9178i	−0.228796	+	0.132096i
$606$		0			0
$607$	−313.579	+	543.135i	−0.516605	+	0.894786i	0.483209	+	0.875505i	$0.339471\pi$
$607$	−313.579	+	543.135i	−0.516605	+	0.894786i	−0.999814	+	0.0192808i	$0.993862\pi$
$608$	−97.9796	−	56.5685i	−0.161151	−	0.0930404i
$609$		0			0
$610$	67.2392	+	116.462i	0.110228	+	0.190921i
$611$		−	315.364i		−	0.516144i
$612$		0			0
$613$	−279.328			−0.455674			−0.227837	−	0.973699i	$-0.573165\pi$
$613$	−279.328			−0.455674			−0.227837	+	0.973699i	$0.573165\pi$
$614$	−235.964	+	136.234i	−0.384307	+	0.221880i
$615$		0			0
$616$	45.4170	−	78.6645i	0.0737289	−	0.127702i
$617$	310.366	+	179.190i	0.503025	+	0.290422i	0.729962	−	0.683488i	$-0.239538\pi$
$617$	310.366	+	179.190i	0.503025	+	0.290422i	−0.226937	+	0.973909i	$0.572871\pi$
$618$		0			0
$619$	491.822	+	851.861i	0.794543	+	1.37619i	0.923129	+	0.384491i	$0.125623\pi$
$619$	491.822	+	851.861i	0.794543	+	1.37619i	−0.128586	+	0.991698i	$0.541044\pi$
$620$		−	305.470i		−	0.492694i
$621$		0			0
$622$	185.652			0.298476
$623$	−10.9410	+	6.31681i	−0.0175619	+	0.0101393i
$624$		0			0
$625$	390.403	−	676.198i	0.624645	−	1.08192i
$626$	−53.0658	−	30.6376i	−0.0847697	−	0.0489418i
$627$		0			0
$628$	−184.996	−	320.423i	−0.294580	−	0.510227i
$629$			414.256i			0.658594i
$630$		0			0
$631$	−298.996			−0.473845			−0.236922	−	0.971529i	$-0.576139\pi$
$631$	−298.996			−0.473845			−0.236922	+	0.971529i	$0.576139\pi$
$632$	−82.4694	+	47.6137i	−0.130490	+	0.0753382i
$633$		0			0
$634$	177.996	−	308.298i	0.280751	−	0.486275i
$635$	−681.534	−	393.484i	−1.07328	−	0.619660i
$636$		0			0
$637$	65.0405	+	112.653i	0.102104	+	0.176850i
$638$			718.169i			1.12566i
$639$		0			0
$640$	68.6640			0.107288
$641$	270.163	−	155.979i	0.421471	−	0.243336i	−0.274236	−	0.961663i	$-0.588425\pi$
$641$	270.163	−	155.979i	0.421471	−	0.243336i	0.695706	+	0.718326i	$0.255091\pi$
$642$		0			0
$643$	302.000	−	523.079i	0.469673	−	0.813498i	−0.529725	−	0.848169i	$-0.677705\pi$
$643$	302.000	−	523.079i	0.469673	−	0.813498i	0.999399	+	0.0346710i	$0.0110383\pi$
$644$	−55.6242	−	32.1147i	−0.0863730	−	0.0498675i
$645$		0			0
$646$	154.170	+	267.030i	0.238653	+	0.413359i
$647$		−	179.600i		−	0.277588i	−0.990321	−	0.138794i	$-0.955677\pi$
$647$		−	179.600i		−	0.277588i	0.990321	−	0.138794i	$-0.0443226\pi$
$648$		0			0
$649$	−706.656			−1.08884
$650$	269.335	−	155.501i	0.414362	−	0.239232i
$651$		0			0
$652$	86.9961	−	150.682i	0.133430	−	0.231107i
$653$	417.331	+	240.946i	0.639097	+	0.368983i	0.784267	−	0.620424i	$-0.213039\pi$
$653$	417.331	+	240.946i	0.639097	+	0.368983i	−0.145169	+	0.989407i	$0.546373\pi$
$654$		0			0
$655$	449.166	+	777.978i	0.685750	+	1.18775i
$656$			242.535i			0.369718i
$657$		0			0
$658$	63.4980			0.0965016
$659$	−759.857	+	438.704i	−1.15305	+	0.665711i	−0.949628	−	0.313380i	$-0.898538\pi$
$659$	−759.857	+	438.704i	−1.15305	+	0.665711i	−0.203418	+	0.979092i	$0.565205\pi$
$660$		0			0
$661$	260.822	−	451.757i	0.394587	−	0.683445i	−0.598461	−	0.801152i	$-0.704221\pi$
$661$	260.822	−	451.757i	0.394587	−	0.683445i	0.993048	+	0.117707i	$0.0375543\pi$
$662$	−442.733	−	255.612i	−0.668781	−	0.386121i
$663$		0			0
$664$	−85.6680	−	148.381i	−0.129018	−	0.223466i
$665$		−	321.147i		−	0.482927i
$666$		0			0
$667$	507.822			0.761353
$668$	104.921	−	60.5764i	0.157068	−	0.0906832i
$669$		0			0
$670$	−569.328	+	986.105i	−0.849743	+	1.47180i
$671$	−164.702	−	95.0906i	−0.245457	−	0.141715i
$672$		0			0
$673$	329.996	+	571.570i	0.490336	+	0.849287i	0.999938	−	0.0111234i	$-0.00354077\pi$
$673$	329.996	+	571.570i	0.490336	+	0.849287i	−0.509602	+	0.860410i	$0.670207\pi$
$674$		−	422.615i		−	0.627025i
$675$		0			0
$676$	−352.656			−0.521681
$677$	−880.121	+	508.138i	−1.30003	+	0.750573i	−0.980409	−	0.196972i	$-0.936889\pi$
$677$	−880.121	+	508.138i	−1.30003	+	0.750573i	−0.319622	+	0.947545i	$0.603556\pi$
$678$		0			0
$679$	−249.247	+	431.709i	−0.367080	+	0.635801i
$680$	−162.063	−	93.5673i	−0.238328	−	0.137599i
$681$		0			0
$682$	216.000	+	374.123i	0.316716	+	0.548567i
$683$			235.114i			0.344238i	0.985076	+	0.172119i	$0.0550613\pi$
$683$			235.114i			0.344238i	−0.985076	+	0.172119i	$0.944939\pi$
$684$		0			0
$685$	−467.061			−0.681841
$686$	−22.6826	+	13.0958i	−0.0330650	+	0.0190901i
$687$		0			0
$688$	−166.996	+	289.246i	−0.242727	+	0.420415i
$689$	−1513.46	−	873.795i	−2.19660	−	1.26821i
$690$		0			0
$691$	25.4902	+	44.1502i	0.0368888	+	0.0638933i	0.883880	−	0.467713i	$-0.154922\pi$
$691$	25.4902	+	44.1502i	0.0368888	+	0.0638933i	−0.846992	+	0.531606i	$0.821589\pi$
$692$			325.143i			0.469860i
$693$		0			0
$694$	291.498			0.420026
$695$	1142.28	−	659.493i	1.64356	−	0.948911i
$696$		0			0
$697$	330.498	−	572.439i	0.474172	−	0.821290i
$698$	−531.936	−	307.114i	−0.762086	−	0.439991i
$699$		0			0
$700$	31.3098	+	54.2302i	0.0447283	+	0.0774716i
$701$		−	141.530i		−	0.201898i	−0.994892	−	0.100949i	$-0.967812\pi$
$701$		−	141.530i		−	0.201898i	0.994892	−	0.100949i	$-0.0321879\pi$
$702$		0			0
$703$	760.000			1.08108
$704$	−84.0959	+	48.5528i	−0.119454	+	0.0689671i
$705$		0			0
$706$	131.125	−	227.116i	0.185730	−	0.321694i
$707$	−244.510	−	141.168i	−0.345842	−	0.199672i
$708$		0			0
$709$	27.7490	+	48.0627i	0.0391382	+	0.0677894i	0.884931	−	0.465722i	$-0.154205\pi$
$709$	27.7490	+	48.0627i	0.0391382	+	0.0677894i	−0.845793	+	0.533512i	$0.820872\pi$
$710$		−	104.182i		−	0.146736i
$711$		0			0
$712$	13.5059			0.0189690
$713$	264.545	−	152.735i	0.371031	−	0.214215i
$714$		0			0
$715$	−684.486	+	1185.56i	−0.957323	+	1.65813i
$716$	−386.405	−	223.091i	−0.539671	−	0.311579i
$717$		0			0
$718$	365.409	+	632.907i	0.508926	+	0.881486i
$719$			1009.03i			1.40338i	0.712484	+	0.701688i	$0.247570\pi$
$719$			1009.03i			1.40338i	−0.712484	+	0.701688i	$0.752430\pi$
$720$		0			0
$721$	−347.911			−0.482540
$722$	47.7650	−	27.5772i	0.0661566	−	0.0381955i
$723$		0			0
$724$	188.915	−	327.210i	0.260932	−	0.451948i
$725$	−428.765	−	247.547i	−0.591400	−	0.341445i
$726$		0			0
$727$	182.591	+	316.257i	0.251157	+	0.435016i	0.963845	−	0.266465i	$-0.0858557\pi$
$727$	182.591	+	316.257i	0.251157	+	0.435016i	−0.712688	+	0.701481i	$0.752522\pi$
$728$		−	139.062i		−	0.191020i
$729$		0			0
$730$	660.162			0.904332
$731$	788.300	−	455.125i	1.07839	−	0.622606i
$732$		0			0
$733$	176.539	−	305.774i	0.240844	−	0.417154i	−0.720111	−	0.693859i	$-0.755909\pi$
$733$	176.539	−	305.774i	0.240844	−	0.417154i	0.960955	+	0.276705i	$0.0892425\pi$
$734$	143.895	+	83.0781i	0.196043	+	0.113185i
$735$		0			0
$736$	34.3320	+	59.4648i	0.0466468	+	0.0807946i
$737$		−	1610.30i		−	2.18494i
$738$		0			0
$739$	329.684			0.446121			0.223061	−	0.974805i	$-0.428395\pi$
$739$	329.684			0.446121			0.223061	+	0.974805i	$0.428395\pi$
$740$	−399.456	+	230.626i	−0.539805	+	0.311657i
$741$		0			0
$742$	175.937	−	304.732i	0.237112	−	0.410690i
$743$	−97.0478	−	56.0306i	−0.130616	−	0.0754112i	0.433268	−	0.901265i	$-0.357360\pi$
$743$	−97.0478	−	56.0306i	−0.130616	−	0.0754112i	−0.563884	+	0.825854i	$0.690694\pi$
$744$		0			0
$745$	−491.369	−	851.075i	−0.659555	−	1.14238i
$746$		−	569.453i		−	0.763342i
$747$		0			0
$748$	264.648			0.353808
$749$	188.755	−	108.978i	0.252009	−	0.145497i
$750$		0			0
$751$	72.4131	−	125.423i	0.0964222	−	0.167008i	−0.813779	−	0.581174i	$-0.802593\pi$
$751$	72.4131	−	125.423i	0.0964222	−	0.167008i	0.910201	+	0.414166i	$0.135927\pi$
$752$	−58.7878	−	33.9411i	−0.0781752	−	0.0451345i
$753$		0			0
$754$	549.741	+	952.180i	0.729100	+	1.26284i
$755$		−	565.434i		−	0.748919i
$756$		0			0
$757$	78.1699			0.103263			0.0516314	−	0.998666i	$-0.483558\pi$
$757$	78.1699			0.103263			0.0516314	+	0.998666i	$0.483558\pi$
$758$	488.470	−	282.018i	0.644419	−	0.372056i
$759$		0			0
$760$	−171.660	+	297.324i	−0.225869	+	0.391216i
$761$	1269.16	+	732.752i	1.66776	+	0.962880i	0.968843	+	0.247676i	$0.0796667\pi$
$761$	1269.16	+	732.752i	1.66776	+	0.962880i	0.698915	+	0.715205i	$0.253667\pi$
$762$		0			0
$763$	44.7530	+	77.5144i	0.0586539	+	0.101592i
$764$		−	456.076i		−	0.596957i
$765$		0			0
$766$	1053.31			1.37508
$767$	−936.915	+	540.928i	−1.22153	+	0.705252i
$768$		0			0
$769$	−364.660	+	631.610i	−0.474200	+	0.821339i	−0.999564	−	0.0295389i	$-0.990596\pi$
$769$	−364.660	+	631.610i	−0.474200	+	0.821339i	0.525363	+	0.850878i	$0.323929\pi$
$770$	−238.712	−	137.820i	−0.310015	−	0.178987i
$771$		0			0
$772$	134.000	+	232.095i	0.173575	+	0.300641i
$773$			434.559i			0.562172i	0.959683	+	0.281086i	$0.0906947\pi$
$773$			434.559i			0.562172i	−0.959683	+	0.281086i	$0.909305\pi$
$774$		0			0
$775$	−297.814			−0.384277
$776$	461.516	−	266.456i	0.594737	−	0.343372i
$777$		0			0
$778$	378.417	−	655.437i	0.486397	−	0.842465i
$779$	−1050.21	−	606.337i	−1.34815	−	0.778353i
$780$		0			0
$781$	73.6680	+	127.597i	0.0943252	+	0.163376i
$782$		−	187.135i		−	0.239303i
$783$		0			0
$784$	28.0000			0.0357143
$785$	−972.339	+	561.380i	−1.23865	+	0.715134i
$786$		0			0
$787$	7.67585	−	13.2950i	0.00975331	−	0.0168932i	−0.861108	−	0.508423i	$-0.830229\pi$
$787$	7.67585	−	13.2950i	0.00975331	−	0.0168932i	0.870861	+	0.491530i	$0.163562\pi$
$788$	326.595	+	188.560i	0.414461	+	0.239289i
$789$		0			0
$790$	144.486	+	250.257i	0.182894	+	0.316782i
$791$		−	75.4543i		−	0.0953910i
$792$		0			0
$793$	−291.158			−0.367160
$794$	−115.523	+	66.6972i	−0.145495	+	0.0840016i
$795$		0			0
$796$	102.494	−	177.525i	0.128761	−	0.223021i
$797$	−903.684	−	521.742i	−1.13386	−	0.654633i	−0.188955	−	0.981986i	$-0.560510\pi$
$797$	−903.684	−	521.742i	−1.13386	−	0.654633i	−0.944902	+	0.327353i	$0.893843\pi$
$798$		0			0
$799$	92.5020	+	160.218i	0.115772	+	0.200523i
$800$		−	66.9432i		−	0.0836789i
$801$		0			0
$802$	−146.502			−0.182671
$803$	−808.530	+	466.805i	−1.00689	+	0.581326i
$804$		0			0
$805$	−97.4536	+	168.795i	−0.121060	+	0.209683i
$806$	572.764	+	330.686i	0.710626	+	0.410280i
$807$		0			0
$808$	150.915	+	261.392i	0.186776	+	0.323506i
$809$		−	1041.31i		−	1.28716i	−0.765378	−	0.643581i	$-0.777448\pi$
$809$		−	1041.31i		−	1.28716i	0.765378	−	0.643581i	$-0.222552\pi$
$810$		0			0
$811$	502.316			0.619379			0.309689	−	0.950838i	$-0.399775\pi$
$811$	502.316			0.619379			0.309689	+	0.950838i	$0.399775\pi$
$812$	−191.720	+	110.689i	−0.236108	+	0.136317i
$813$		0			0
$814$	326.154	−	564.916i	0.400681	−	0.694000i
$815$	−457.251	−	263.994i	−0.561044	−	0.323919i
$816$		0			0
$817$	−834.980	−	1446.23i	−1.02201	−	1.77017i
$818$		−	13.7983i		−	0.0168684i
$819$		0			0
$820$	735.984			0.897542
$821$	20.0170	−	11.5568i	0.0243813	−	0.0140765i	−0.487760	−	0.872978i	$-0.662186\pi$
$821$	20.0170	−	11.5568i	0.0243813	−	0.0140765i	0.512141	+	0.858901i	$0.328852\pi$
$822$		0			0
$823$	300.332	−	520.190i	0.364923	−	0.632066i	−0.623840	−	0.781552i	$-0.714428\pi$
$823$	300.332	−	520.190i	0.364923	−	0.632066i	0.988764	+	0.149486i	$0.0477618\pi$
$824$	322.103	+	185.966i	0.390902	+	0.225687i
$825$		0			0
$826$	−108.915	−	188.646i	−0.131858	−	0.228385i
$827$			1309.21i			1.58308i	0.611118	+	0.791540i	$0.290720\pi$
$827$			1309.21i			1.58308i	−0.611118	+	0.791540i	$0.709280\pi$
$828$		0			0
$829$	−621.919			−0.750204			−0.375102	−	0.926984i	$-0.622392\pi$
$829$	−621.919			−0.750204			−0.375102	+	0.926984i	$0.622392\pi$
$830$	−450.271	+	259.964i	−0.542495	+	0.313209i
$831$		0			0
$832$	−74.3320	+	128.747i	−0.0893414	+	0.154744i
$833$	−66.0866	−	38.1551i	−0.0793357	−	0.0458045i
$834$		0			0
$835$	−183.822	−	318.389i	−0.220146	−	0.381305i
$836$		−	485.528i		−	0.580775i
$837$		0			0
$838$	480.000			0.572792
$839$	−1030.83	+	595.149i	−1.22864	+	0.709355i	−0.966745	−	0.255741i	$-0.917680\pi$
$839$	−1030.83	+	595.149i	−1.22864	+	0.709355i	−0.261894	+	0.965097i	$0.584347\pi$
$840$		0			0
$841$	454.654	−	787.484i	0.540611	−	0.936366i
$842$	734.014	+	423.783i	0.871751	+	0.503306i
$843$		0			0
$844$	−84.5020	−	146.362i	−0.100121	−	0.173414i
$845$			1070.15i			1.26645i
$846$		0			0
$847$	69.6784			0.0822649
$848$	−325.772	+	188.085i	−0.384166	+	0.221798i
$849$		0			0
$850$	−91.2223	+	158.002i	−0.107320	+	0.185884i
$851$	−399.456	−	230.626i	−0.469396	−	0.271006i
$852$		0			0
$853$	−68.5059	−	118.656i	−0.0803117	−	0.139104i	0.823072	−	0.567937i	$-0.192258\pi$
$853$	−68.5059	−	118.656i	−0.0803117	−	0.139104i	−0.903384	+	0.428833i	$0.858925\pi$
$854$		−	58.6242i		−	0.0686466i
$855$		0			0
$856$	−233.004			−0.272201
$857$	−403.690	+	233.071i	−0.471050	+	0.271961i	−0.716679	−	0.697403i	$-0.754339\pi$
$857$	−403.690	+	233.071i	−0.471050	+	0.271961i	0.245629	+	0.969364i	$0.421006\pi$
$858$		0			0
$859$	−11.9921	+	20.7710i	−0.0139606	+	0.0241804i	−0.872921	−	0.487861i	$-0.837777\pi$
$859$	−11.9921	+	20.7710i	−0.0139606	+	0.0241804i	0.858961	+	0.512041i	$0.171111\pi$
$860$	877.731	+	506.758i	1.02062	+	0.589253i
$861$		0			0
$862$	−502.737	−	870.766i	−0.583222	−	1.01017i
$863$		−	0.114603i		−	0.000132796i	−1.00000		6.63982e-5i	$-0.999979\pi$
$863$		−	0.114603i		−	0.000132796i	1.00000		6.63982e-5i	$-2.11352e-5\pi$
$864$		0			0
$865$	986.664			1.14065
$866$	462.934	−	267.275i	0.534566	−	0.308632i
$867$		0			0
$868$	−66.5830	+	115.325i	−0.0767085	+	0.132863i
$869$	−353.918	−	204.334i	−0.407270	−	0.235137i
$870$		0			0
$871$	−1232.65	−	2135.01i	−1.41521	−	2.45122i
$872$		−	95.6858i		−	0.109731i
$873$		0			0
$874$	−343.320			−0.392815
$875$	−183.087	+	105.706i	−0.209243	+	0.120806i
$876$		0			0
$877$	−498.652	+	863.691i	−0.568589	+	0.984824i	0.428117	+	0.903723i	$0.359177\pi$
$877$	−498.652	+	863.691i	−0.568589	+	0.984824i	−0.996706	+	0.0811012i	$0.974156\pi$
$878$	−646.845	−	373.456i	−0.736725	−	0.425348i
$879$		0			0
$880$	147.336	+	255.193i	0.167427	+	0.289992i
$881$		−	935.649i		−	1.06203i	−0.847362	−	0.531015i	$-0.821811\pi$
$881$		−	935.649i		−	1.06203i	0.847362	−	0.531015i	$-0.178189\pi$
$882$		0			0
$883$	−1549.47			−1.75478			−0.877392	−	0.479774i	$-0.840719\pi$
$883$	−1549.47			−1.75478			−0.877392	+	0.479774i	$0.840719\pi$
$884$	350.882	−	202.582i	0.396926	−	0.229165i
$885$		0			0
$886$	−25.9111	+	44.8793i	−0.0292450	+	0.0506539i
$887$	−774.654	−	447.246i	−0.873341	−	0.504224i	−0.00488401	−	0.999988i	$-0.501555\pi$
$887$	−774.654	−	447.246i	−0.873341	−	0.504224i	−0.868457	+	0.495764i	$0.834888\pi$
$888$		0			0
$889$	171.535	+	297.107i	0.192952	+	0.334203i
$890$		−	40.9844i		−	0.0460498i
$891$		0			0
$892$	316.988			0.355368
$893$	293.939	−	169.706i	0.329159	−	0.190040i
$894$		0			0
$895$	−676.980	+	1172.56i	−0.756403	+	1.31013i
$896$	−25.9230	−	14.9666i	−0.0289319	−	0.0167038i
$897$		0			0
$898$	281.154	+	486.973i	0.313089	+	0.542287i
$899$		−	1052.86i		−	1.17115i
$900$		0			0
$901$	1025.20			1.13785
$902$	−901.393	+	520.419i	−0.999327	+	0.576962i
$903$		0			0
$904$	−40.3320	+	69.8571i	−0.0446151	+	0.0772756i
$905$	−992.937	−	573.272i	−1.09717	−	0.633450i
$906$		0			0
$907$	67.9190	+	117.639i	0.0748831	+	0.129701i	0.901035	−	0.433746i	$-0.142808\pi$
$907$	67.9190	+	117.639i	0.0748831	+	0.129701i	−0.826152	+	0.563447i	$0.809475\pi$
$908$			203.647i			0.224281i
$909$		0			0
$910$	−421.992			−0.463728
$911$	1075.61	−	621.006i	1.18070	−	0.681675i	0.224521	−	0.974469i	$-0.427918\pi$
$911$	1075.61	−	621.006i	1.18070	−	0.681675i	0.956175	+	0.292794i	$0.0945851\pi$
$912$		0			0
$913$	367.644	−	636.779i	0.402677	−	0.697458i
$914$	−421.709	−	243.474i	−0.461389	−	0.266383i
$915$		0			0
$916$	−268.915	−	465.774i	−0.293575	−	0.508487i
$917$		−	391.617i		−	0.427063i
$918$		0			0
$919$	−388.162			−0.422374			−0.211187	−	0.977446i	$-0.567733\pi$
$919$	−388.162			−0.422374			−0.211187	+	0.977446i	$0.567733\pi$
$920$	180.449	−	104.182i	0.196140	−	0.113242i
$921$		0			0
$922$	262.292	−	454.302i	0.284481	−	0.492736i
$923$	195.344	+	112.782i	0.211641	+	0.122191i
$924$		0			0
$925$	224.846	+	389.444i	0.243077	+	0.421021i
$926$			110.778i			0.119631i
$927$		0			0
$928$	236.664			0.255026
$929$	538.403	−	310.847i	0.579551	−	0.334604i	−0.181404	−	0.983409i	$-0.558064\pi$
$929$	538.403	−	310.847i	0.579551	−	0.334604i	0.760955	+	0.648805i	$0.224731\pi$
$930$		0			0
$931$	−70.0000	+	121.244i	−0.0751880	+	0.130229i
$932$	45.5092	+	26.2748i	0.0488297	+	0.0281918i
$933$		0			0
$934$	282.672	+	489.602i	0.302647	+	0.524199i
$935$		−	803.089i		−	0.858918i
$936$		0			0
$937$	1262.00			1.34685			0.673426	−	0.739255i	$-0.264822\pi$
$937$	1262.00			1.34685			0.673426	+	0.739255i	$0.264822\pi$
$938$	429.881	−	248.192i	0.458295	−	0.264597i
$939$		0			0
$940$	−102.996	+	178.394i	−0.109570	+	0.189781i
$941$	582.324	+	336.205i	0.618835	+	0.357285i	0.776415	−	0.630222i	$-0.217036\pi$
$941$	582.324	+	336.205i	0.618835	+	0.357285i	−0.157580	+	0.987506i	$0.550369\pi$
$942$		0			0
$943$	367.992	+	637.381i	0.390236	+	0.675908i
$944$			232.870i			0.246684i
$945$		0			0
$946$	−1433.33			−1.51515
$947$	−1004.37	+	579.874i	−1.06058	+	0.612327i	−0.925593	−	0.378520i	$-0.876433\pi$
$947$	−1004.37	+	579.874i	−1.06058	+	0.612327i	−0.134989	+	0.990847i	$0.543100\pi$
$948$		0			0
$949$	−714.656	+	1237.82i	−0.753062	+	1.30434i
$950$	289.872	+	167.358i	0.305129	+	0.176166i
$951$		0			0
$952$	40.7895	+	70.6495i	0.0428461	+	0.0742117i
$953$			163.104i			0.171148i	0.996332	+	0.0855740i	$0.0272724\pi$
$953$			163.104i			0.171148i	−0.996332	+	0.0855740i	$0.972728\pi$
$954$		0			0
$955$	−1383.98			−1.44920
$956$	159.822	−	92.2733i	0.167178	−	0.0965201i
$957$		0			0
$958$	497.328	−	861.398i	0.519132	−	0.899162i
$959$	176.331	+	101.805i	0.183870	+	0.106157i
$960$		0			0
$961$	163.836	+	283.772i	0.170485	+	0.295288i
$962$		−	998.653i		−	1.03810i
$963$		0			0
$964$	−686.494			−0.712131
$965$	704.303	−	406.630i	0.729848	−	0.421378i
$966$		0			0
$967$	−443.506	+	768.175i	−0.458641	+	0.794390i	−0.998889	−	0.0471160i	$-0.984997\pi$
$967$	−443.506	+	768.175i	−0.458641	+	0.794390i	0.540248	+	0.841506i	$0.318330\pi$
$968$	−64.5097	−	37.2447i	−0.0666422	−	0.0384759i
$969$		0			0
$970$	−808.575	−	1400.49i	−0.833583	−	1.44381i
$971$			1416.32i			1.45862i	0.684183	+	0.729310i	$0.260159\pi$
$971$			1416.32i			1.45862i	−0.684183	+	0.729310i	$0.739841\pi$
$972$		0			0
$973$	−574.996			−0.590952
$974$	−101.054	+	58.3433i	−0.103751	+	0.0599007i
$975$		0			0
$976$	−31.3360	+	54.2755i	−0.0321065	+	0.0556101i
$977$	293.627	+	169.525i	0.300539	+	0.173516i	0.642685	−	0.766131i	$-0.277820\pi$
$977$	293.627	+	169.525i	0.300539	+	0.173516i	−0.342146	+	0.939647i	$0.611154\pi$
$978$		0			0
$979$	28.9803	+	50.1954i	0.0296020	+	0.0512721i
$980$		−	84.9674i		−	0.0867014i
$981$		0			0
$982$	−260.502			−0.265277
$983$	422.523	−	243.943i	0.429830	−	0.248162i	−0.269444	−	0.963016i	$-0.586840\pi$
$983$	422.523	−	243.943i	0.429830	−	0.248162i	0.699274	+	0.714854i	$0.253507\pi$
$984$		0			0
$985$	572.195	−	991.070i	0.580908	−	1.00616i
$986$	−558.583	−	322.498i	−0.566514	−	0.327077i
$987$		0			0
$988$	−371.660	−	643.734i	−0.376174	−	0.651553i
$989$			1013.52i			1.02479i
$990$		0			0
$991$	−937.474			−0.945988			−0.472994	−	0.881066i	$-0.656827\pi$
$991$	−937.474			−0.945988			−0.472994	+	0.881066i	$0.656827\pi$
$992$	123.288	−	71.1802i	0.124282	−	0.0717543i
$993$		0			0
$994$	−22.7085	+	39.3323i	−0.0228456	+	0.0395697i
$995$	−538.709	−	311.024i	−0.541416	−	0.312586i
$996$		0			0
$997$	−230.506	−	399.248i	−0.231200	−	0.400449i	0.726962	−	0.686678i	$-0.240932\pi$
$997$	−230.506	−	399.248i	−0.231200	−	0.400449i	−0.958161	+	0.286229i	$0.907598\pi$
$998$			1064.63i			1.06677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.3.q.c.701.3		8
3.2	odd	2	inner	1134.3.q.c.701.2		8
9.2	odd	6	inner	1134.3.q.c.1079.3		8
9.4	even	3		126.3.b.a.71.4	yes	4
9.5	odd	6		126.3.b.a.71.1	✓	4
9.7	even	3	inner	1134.3.q.c.1079.2		8
36.23	even	6		1008.3.d.a.449.2		4
36.31	odd	6		1008.3.d.a.449.3		4
45.4	even	6		3150.3.e.e.701.2		4
45.13	odd	12		3150.3.c.b.449.7		8
45.14	odd	6		3150.3.e.e.701.4		4
45.22	odd	12		3150.3.c.b.449.1		8
45.23	even	12		3150.3.c.b.449.4		8
45.32	even	12		3150.3.c.b.449.6		8
63.4	even	3		882.3.s.e.863.1		8
63.5	even	6		882.3.s.i.557.2		8
63.13	odd	6		882.3.b.f.197.3		4
63.23	odd	6		882.3.s.e.557.1		8
63.31	odd	6		882.3.s.i.863.2		8
63.32	odd	6		882.3.s.e.863.4		8
63.40	odd	6		882.3.s.i.557.3		8
63.41	even	6		882.3.b.f.197.2		4
63.58	even	3		882.3.s.e.557.4		8
63.59	even	6		882.3.s.i.863.3		8
72.5	odd	6		4032.3.d.i.449.3		4
72.13	even	6		4032.3.d.i.449.2		4
72.59	even	6		4032.3.d.j.449.3		4
72.67	odd	6		4032.3.d.j.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.b.a.71.1	✓	4	9.5	odd	6
126.3.b.a.71.4	yes	4	9.4	even	3
882.3.b.f.197.2		4	63.41	even	6
882.3.b.f.197.3		4	63.13	odd	6
882.3.s.e.557.1		8	63.23	odd	6
882.3.s.e.557.4		8	63.58	even	3
882.3.s.e.863.1		8	63.4	even	3
882.3.s.e.863.4		8	63.32	odd	6
882.3.s.i.557.2		8	63.5	even	6
882.3.s.i.557.3		8	63.40	odd	6
882.3.s.i.863.2		8	63.31	odd	6
882.3.s.i.863.3		8	63.59	even	6
1008.3.d.a.449.2		4	36.23	even	6
1008.3.d.a.449.3		4	36.31	odd	6
1134.3.q.c.701.2		8	3.2	odd	2	inner
1134.3.q.c.701.3		8	1.1	even	1	trivial
1134.3.q.c.1079.2		8	9.7	even	3	inner
1134.3.q.c.1079.3		8	9.2	odd	6	inner
3150.3.c.b.449.1		8	45.22	odd	12
3150.3.c.b.449.4		8	45.23	even	12
3150.3.c.b.449.6		8	45.32	even	12
3150.3.c.b.449.7		8	45.13	odd	12
3150.3.e.e.701.2		4	45.4	even	6
3150.3.e.e.701.4		4	45.14	odd	6
4032.3.d.i.449.2		4	72.13	even	6
4032.3.d.i.449.3		4	72.5	odd	6
4032.3.d.j.449.2		4	72.67	odd	6
4032.3.d.j.449.3		4	72.59	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1134.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -8.58301 q^{10} +(10.5120 - 6.06910i) q^{11} +(9.29150 - 16.0934i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +10.9015i q^{17} +20.0000 q^{19} +(-10.5120 + 6.06910i) q^{20} +(8.58301 - 14.8662i) q^{22} +(-10.5120 - 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} -26.2803i q^{26} +5.29150 q^{28} +(-36.2316 + 20.9183i) q^{29} +(-12.5830 + 21.7944i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(7.70850 + 13.3515i) q^{34} -16.0573i q^{35} +38.0000 q^{37} +(24.4949 - 14.1421i) q^{38} +(-8.58301 + 14.8662i) q^{40} +(-52.5103 - 30.3169i) q^{41} +(-41.7490 - 72.3114i) q^{43} -24.2764i q^{44} -17.1660 q^{46} +(14.6969 - 8.48528i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(14.4936 + 8.36789i) q^{50} +(-18.5830 - 32.1867i) q^{52} -94.0424i q^{53} -73.6680 q^{55} +(6.48074 - 3.74166i) q^{56} +(-29.5830 + 51.2393i) q^{58} +(-50.4179 - 29.1088i) q^{59} +(-7.83399 - 13.5689i) q^{61} +35.5901i q^{62} -8.00000 q^{64} +(-97.6722 + 56.3911i) q^{65} +(66.3320 - 114.890i) q^{67} +(18.8819 + 10.9015i) q^{68} +(-11.3542 - 19.6661i) q^{70} +12.1382i q^{71} -76.9150 q^{73} +(46.5403 - 26.8701i) q^{74} +(20.0000 - 34.6410i) q^{76} +(27.8121 + 16.0573i) q^{77} +(-16.8340 - 29.1573i) q^{79} +24.2764i q^{80} -85.7490 q^{82} +(52.4607 - 30.2882i) q^{83} +(33.0810 - 57.2980i) q^{85} +(-102.264 - 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +4.77506i q^{89} +49.1660 q^{91} +(-21.0240 + 12.1382i) q^{92} +(12.0000 - 20.7846i) q^{94} +(-105.120 - 60.6910i) q^{95} +(94.2065 + 163.170i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 + 16 * q^10 + 32 * q^13 - 16 * q^16 + 160 * q^19 - 16 * q^22 + 132 * q^25 - 16 * q^31 + 104 * q^34 + 304 * q^37 + 16 * q^40 - 80 * q^43 + 32 * q^46 - 28 * q^49 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 - 112 * q^70 - 192 * q^73 + 160 * q^76 - 304 * q^79 - 432 * q^82 - 328 * q^85 + 32 * q^88 + 224 * q^91 + 96 * q^94 + 288 * q^97

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