LMFDB - Embedded newform 810.3.j.e.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	810.269
Dual form			810.3.j.e.539.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.29410 + 4.82963i) q^{5} +(-4.33013 - 2.50000i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.29410 + 4.82963i) q^{5} +(-4.33013 - 2.50000i) q^{7} -2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(-1.22474 - 0.707107i) q^{11} +(7.79423 - 4.50000i) q^{13} +(-6.12372 + 3.53553i) q^{14} +(-2.00000 + 3.46410i) q^{16} +11.3137 q^{17} +21.0000 q^{19} +(9.65926 - 2.58819i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(-0.707107 - 1.22474i) q^{23} +(-21.6506 - 12.5000i) q^{25} -12.7279i q^{26} +10.0000i q^{28} +(-33.0681 - 19.0919i) q^{29} +(-20.0000 - 34.6410i) q^{31} +(2.82843 + 4.89898i) q^{32} +(8.00000 - 13.8564i) q^{34} +(17.6777 - 17.6777i) q^{35} -25.0000i q^{37} +(14.8492 - 25.7196i) q^{38} +(3.66025 - 13.6603i) q^{40} +(45.3156 - 26.1630i) q^{41} +(-55.4256 - 32.0000i) q^{43} +2.82843i q^{44} -2.00000 q^{46} +(-11.3137 + 19.5959i) q^{47} +(-12.0000 - 20.7846i) q^{49} +(-30.6186 + 17.6777i) q^{50} +(-15.5885 - 9.00000i) q^{52} +72.1249 q^{53} +(5.00000 - 5.00000i) q^{55} +(12.2474 + 7.07107i) q^{56} +(-46.7654 + 27.0000i) q^{58} +(78.3837 - 45.2548i) q^{59} +(48.5000 - 84.0045i) q^{61} -56.5685 q^{62} +8.00000 q^{64} +(11.6469 + 43.4667i) q^{65} +(-113.449 + 65.5000i) q^{67} +(-11.3137 - 19.5959i) q^{68} +(-9.15064 - 34.1506i) q^{70} -89.0955i q^{71} -17.0000i q^{73} +(-30.6186 - 17.6777i) q^{74} +(-21.0000 - 36.3731i) q^{76} +(3.53553 + 6.12372i) q^{77} +(58.5000 - 101.325i) q^{79} +(-14.1421 - 14.1421i) q^{80} -74.0000i q^{82} +(28.9914 - 50.2145i) q^{83} +(-14.6410 + 54.6410i) q^{85} +(-78.3837 + 45.2548i) q^{86} +(3.46410 + 2.00000i) q^{88} +147.078i q^{89} -45.0000 q^{91} +(-1.41421 + 2.44949i) q^{92} +(16.0000 + 27.7128i) q^{94} +(-27.1760 + 101.422i) q^{95} +(35.5070 + 20.5000i) q^{97} -33.9411 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} + 168 q^{19} - 160 q^{31} + 64 q^{34} - 40 q^{40} - 16 q^{46} - 96 q^{49} + 40 q^{55} + 388 q^{61} + 64 q^{64} + 100 q^{70} - 168 q^{76} + 468 q^{79} + 160 q^{85} - 360 q^{91} + 128 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 + 40 * q^10 - 16 * q^16 + 168 * q^19 - 160 * q^31 + 64 * q^34 - 40 * q^40 - 16 * q^46 - 96 * q^49 + 40 * q^55 + 388 * q^61 + 64 * q^64 + 100 * q^70 - 168 * q^76 + 468 * q^79 + 160 * q^85 - 360 * q^91 + 128 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−1.29410	+	4.82963i	−0.258819	+	0.965926i
$5$	−1.29410	+	4.82963i	−0.258819	+	0.965926i
$6$		0			0
$7$	−4.33013	−	2.50000i	−0.618590	−	0.357143i	0.157730	−	0.987482i	$-0.449582\pi$
$7$	−4.33013	−	2.50000i	−0.618590	−	0.357143i	−0.776320	+	0.630339i	$0.782916\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	5.00000	+	5.00000i	0.500000	+	0.500000i
$11$	−1.22474	−	0.707107i	−0.111340	−	0.0642824i	0.443296	−	0.896375i	$-0.353809\pi$
$11$	−1.22474	−	0.707107i	−0.111340	−	0.0642824i	−0.554636	+	0.832093i	$0.687143\pi$
$12$		0			0
$13$	7.79423	−	4.50000i	0.599556	−	0.346154i	−0.169311	−	0.985563i	$-0.554154\pi$
$13$	7.79423	−	4.50000i	0.599556	−	0.346154i	0.768867	+	0.639409i	$0.220821\pi$
$14$	−6.12372	+	3.53553i	−0.437409	+	0.252538i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	11.3137			0.665512			0.332756	−	0.943013i	$-0.392021\pi$
$17$	11.3137			0.665512			0.332756	+	0.943013i	$0.392021\pi$
$18$		0			0
$19$	21.0000			1.10526			0.552632	−	0.833426i	$-0.313624\pi$
$19$	21.0000			1.10526			0.552632	+	0.833426i	$0.313624\pi$
$20$	9.65926	−	2.58819i	0.482963	−	0.129410i
$21$		0			0
$22$	−1.73205	+	1.00000i	−0.0787296	+	0.0454545i
$23$	−0.707107	−	1.22474i	−0.0307438	−	0.0532498i	0.850244	−	0.526389i	$-0.176454\pi$
$23$	−0.707107	−	1.22474i	−0.0307438	−	0.0532498i	−0.880988	+	0.473139i	$0.843121\pi$
$24$		0			0
$25$	−21.6506	−	12.5000i	−0.866025	−	0.500000i
$26$		−	12.7279i		−	0.489535i
$27$		0			0
$28$			10.0000i			0.357143i
$29$	−33.0681	−	19.0919i	−1.14028	−	0.658341i	−0.193780	−	0.981045i	$-0.562075\pi$
$29$	−33.0681	−	19.0919i	−1.14028	−	0.658341i	−0.946500	+	0.322704i	$0.895408\pi$
$30$		0			0
$31$	−20.0000	−	34.6410i	−0.645161	−	1.11745i	−0.984264	−	0.176703i	$-0.943457\pi$
$31$	−20.0000	−	34.6410i	−0.645161	−	1.11745i	0.339103	−	0.940749i	$-0.389876\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$	8.00000	−	13.8564i	0.235294	−	0.407541i
$35$	17.6777	−	17.6777i	0.505076	−	0.505076i
$36$		0			0
$37$		−	25.0000i		−	0.675676i	−0.941204	−	0.337838i	$-0.890304\pi$
$37$		−	25.0000i		−	0.675676i	0.941204	−	0.337838i	$-0.109696\pi$
$38$	14.8492	−	25.7196i	0.390770	−	0.676833i
$39$		0			0
$40$	3.66025	−	13.6603i	0.0915064	−	0.341506i
$41$	45.3156	−	26.1630i	1.10526	−	0.638121i	0.167661	−	0.985845i	$-0.446379\pi$
$41$	45.3156	−	26.1630i	1.10526	−	0.638121i	0.937597	+	0.347724i	$0.113045\pi$
$42$		0			0
$43$	−55.4256	−	32.0000i	−1.28897	−	0.744186i	−0.310498	−	0.950574i	$-0.600496\pi$
$43$	−55.4256	−	32.0000i	−1.28897	−	0.744186i	−0.978470	+	0.206388i	$0.933829\pi$
$44$			2.82843i			0.0642824i
$45$		0			0
$46$	−2.00000			−0.0434783
$47$	−11.3137	+	19.5959i	−0.240717	+	0.416934i	−0.960919	−	0.276830i	$-0.910716\pi$
$47$	−11.3137	+	19.5959i	−0.240717	+	0.416934i	0.720202	+	0.693765i	$0.244049\pi$
$48$		0			0
$49$	−12.0000	−	20.7846i	−0.244898	−	0.424176i
$50$	−30.6186	+	17.6777i	−0.612372	+	0.353553i
$51$		0			0
$52$	−15.5885	−	9.00000i	−0.299778	−	0.173077i
$53$	72.1249			1.36085			0.680424	−	0.732819i	$-0.261796\pi$
$53$	72.1249			1.36085			0.680424	+	0.732819i	$0.261796\pi$
$54$		0			0
$55$	5.00000	−	5.00000i	0.0909091	−	0.0909091i
$56$	12.2474	+	7.07107i	0.218704	+	0.126269i
$57$		0			0
$58$	−46.7654	+	27.0000i	−0.806300	+	0.465517i
$59$	78.3837	−	45.2548i	1.32854	−	0.767031i	0.343463	−	0.939166i	$-0.388400\pi$
$59$	78.3837	−	45.2548i	1.32854	−	0.767031i	0.985073	+	0.172135i	$0.0550665\pi$
$60$		0			0
$61$	48.5000	−	84.0045i	0.795082	−	1.37712i	−0.127705	−	0.991812i	$-0.540761\pi$
$61$	48.5000	−	84.0045i	0.795082	−	1.37712i	0.922787	−	0.385310i	$-0.125906\pi$
$62$	−56.5685			−0.912396
$63$		0			0
$64$	8.00000			0.125000
$65$	11.6469	+	43.4667i	0.179182	+	0.668718i
$66$		0			0
$67$	−113.449	+	65.5000i	−1.69327	+	0.977612i	−0.741429	+	0.671032i	$0.765851\pi$
$67$	−113.449	+	65.5000i	−1.69327	+	0.977612i	−0.951845	+	0.306580i	$0.900815\pi$
$68$	−11.3137	−	19.5959i	−0.166378	−	0.288175i
$69$		0			0
$70$	−9.15064	−	34.1506i	−0.130723	−	0.487866i
$71$		−	89.0955i		−	1.25487i	−0.778671	−	0.627433i	$-0.784106\pi$
$71$		−	89.0955i		−	1.25487i	0.778671	−	0.627433i	$-0.215894\pi$
$72$		0			0
$73$		−	17.0000i		−	0.232877i	−0.993198	−	0.116438i	$-0.962852\pi$
$73$		−	17.0000i		−	0.232877i	0.993198	−	0.116438i	$-0.0371477\pi$
$74$	−30.6186	−	17.6777i	−0.413765	−	0.238887i
$75$		0			0
$76$	−21.0000	−	36.3731i	−0.276316	−	0.478593i
$77$	3.53553	+	6.12372i	0.0459160	+	0.0795289i
$78$		0			0
$79$	58.5000	−	101.325i	0.740506	−	1.28259i	−0.211759	−	0.977322i	$-0.567919\pi$
$79$	58.5000	−	101.325i	0.740506	−	1.28259i	0.952265	−	0.305273i	$-0.0987476\pi$
$80$	−14.1421	−	14.1421i	−0.176777	−	0.176777i
$81$		0			0
$82$		−	74.0000i		−	0.902439i
$83$	28.9914	−	50.2145i	0.349294	−	0.604994i	−0.636830	−	0.771004i	$-0.719755\pi$
$83$	28.9914	−	50.2145i	0.349294	−	0.604994i	0.986124	+	0.166009i	$0.0530882\pi$
$84$		0			0
$85$	−14.6410	+	54.6410i	−0.172247	+	0.642835i
$86$	−78.3837	+	45.2548i	−0.911438	+	0.526219i
$87$		0			0
$88$	3.46410	+	2.00000i	0.0393648	+	0.0227273i
$89$			147.078i			1.65256i	0.563257	+	0.826282i	$0.309548\pi$
$89$			147.078i			1.65256i	−0.563257	+	0.826282i	$0.690452\pi$
$90$		0			0
$91$	−45.0000			−0.494505
$92$	−1.41421	+	2.44949i	−0.0153719	+	0.0266249i
$93$		0			0
$94$	16.0000	+	27.7128i	0.170213	+	0.294817i
$95$	−27.1760	+	101.422i	−0.286063	+	1.06760i
$96$		0			0
$97$	35.5070	+	20.5000i	0.366052	+	0.211340i	0.671732	−	0.740794i	$-0.265551\pi$
$97$	35.5070	+	20.5000i	0.366052	+	0.211340i	−0.305680	+	0.952134i	$0.598884\pi$
$98$	−33.9411			−0.346338
$99$		0			0
$100$			50.0000i			0.500000i
$101$	78.3837	+	45.2548i	0.776076	+	0.448068i	0.835038	−	0.550193i	$-0.185446\pi$
$101$	78.3837	+	45.2548i	0.776076	+	0.448068i	−0.0589618	+	0.998260i	$0.518779\pi$
$102$		0			0
$103$	−11.2583	+	6.50000i	−0.109304	+	0.0631068i	−0.553655	−	0.832746i	$-0.686768\pi$
$103$	−11.2583	+	6.50000i	−0.109304	+	0.0631068i	0.444351	+	0.895853i	$0.353434\pi$
$104$	−22.0454	+	12.7279i	−0.211975	+	0.122384i
$105$		0			0
$106$	51.0000	−	88.3346i	0.481132	−	0.833345i
$107$	−123.037			−1.14987			−0.574937	−	0.818197i	$-0.694974\pi$
$107$	−123.037			−1.14987			−0.574937	+	0.818197i	$0.694974\pi$
$108$		0			0
$109$	8.00000			0.0733945			0.0366972	−	0.999326i	$-0.488316\pi$
$109$	8.00000			0.0733945			0.0366972	+	0.999326i	$0.488316\pi$
$110$	−2.58819	−	9.65926i	−0.0235290	−	0.0878114i
$111$		0			0
$112$	17.3205	−	10.0000i	0.154647	−	0.0892857i
$113$	19.0919	+	33.0681i	0.168955	+	0.292638i	0.938053	−	0.346493i	$-0.112628\pi$
$113$	19.0919	+	33.0681i	0.168955	+	0.292638i	−0.769098	+	0.639131i	$0.779294\pi$
$114$		0			0
$115$	6.83013	−	1.83013i	0.0593924	−	0.0159141i
$116$			76.3675i			0.658341i
$117$		0			0
$118$		−	128.000i		−	1.08475i
$119$	−48.9898	−	28.2843i	−0.411679	−	0.237683i
$120$		0			0
$121$	−59.5000	−	103.057i	−0.491736	−	0.851711i
$122$	−68.5894	−	118.800i	−0.562208	−	0.973773i
$123$		0			0
$124$	−40.0000	+	69.2820i	−0.322581	+	0.558726i
$125$	88.3883	−	88.3883i	0.707107	−	0.707107i
$126$		0			0
$127$			8.00000i			0.0629921i	0.999504	+	0.0314961i	$0.0100272\pi$
$127$			8.00000i			0.0629921i	−0.999504	+	0.0314961i	$0.989973\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	61.4711	+	16.4711i	0.472855	+	0.126701i
$131$	−117.576	+	67.8823i	−0.897523	+	0.518185i	−0.876396	−	0.481592i	$-0.840059\pi$
$131$	−117.576	+	67.8823i	−0.897523	+	0.518185i	−0.0211272	+	0.999777i	$0.506726\pi$
$132$		0			0
$133$	−90.9327	−	52.5000i	−0.683704	−	0.394737i
$134$			185.262i			1.38255i
$135$		0			0
$136$	−32.0000			−0.235294
$137$	−133.643	+	231.477i	−0.975498	+	1.68961i	−0.297215	+	0.954811i	$0.596058\pi$
$137$	−133.643	+	231.477i	−0.975498	+	1.68961i	−0.678283	+	0.734801i	$0.737276\pi$
$138$		0			0
$139$	18.5000	+	32.0429i	0.133094	+	0.230525i	0.924868	−	0.380289i	$-0.124176\pi$
$139$	18.5000	+	32.0429i	0.133094	+	0.230525i	−0.791774	+	0.610814i	$0.790842\pi$
$140$	−48.2963	−	12.9410i	−0.344974	−	0.0924354i
$141$		0			0
$142$	−109.119	−	63.0000i	−0.768445	−	0.443662i
$143$	−12.7279			−0.0890064
$144$		0			0
$145$	135.000	−	135.000i	0.931034	−	0.931034i
$146$	−20.8207	−	12.0208i	−0.142607	−	0.0823344i
$147$		0			0
$148$	−43.3013	+	25.0000i	−0.292576	+	0.168919i
$149$	225.353	−	130.108i	1.51244	−	0.873206i	0.512542	−	0.858662i	$-0.328704\pi$
$149$	225.353	−	130.108i	1.51244	−	0.873206i	0.999894	−	0.0145438i	$-0.00462959\pi$
$150$		0			0
$151$	−54.5000	+	94.3968i	−0.360927	+	0.625144i	−0.988114	−	0.153725i	$-0.950873\pi$
$151$	−54.5000	+	94.3968i	−0.360927	+	0.625144i	0.627187	+	0.778869i	$0.284206\pi$
$152$	−59.3970			−0.390770
$153$		0			0
$154$	10.0000			0.0649351
$155$	193.185	−	51.7638i	1.24636	−	0.333960i
$156$		0			0
$157$	102.191	−	59.0000i	0.650898	−	0.375796i	−0.137902	−	0.990446i	$-0.544036\pi$
$157$	102.191	−	59.0000i	0.650898	−	0.375796i	0.788800	+	0.614650i	$0.210703\pi$
$158$	−82.7315	−	143.295i	−0.523617	−	0.906931i
$159$		0			0
$160$	−27.3205	+	7.32051i	−0.170753	+	0.0457532i
$161$			7.07107i			0.0439197i
$162$		0			0
$163$			203.000i			1.24540i	0.782461	+	0.622699i	$0.213964\pi$
$163$			203.000i			1.24540i	−0.782461	+	0.622699i	$0.786036\pi$
$164$	−90.6311	−	52.3259i	−0.552629	−	0.319060i
$165$		0			0
$166$	−41.0000	−	71.0141i	−0.246988	−	0.427796i
$167$	50.9117	+	88.1816i	0.304860	+	0.528034i	0.977230	−	0.212182i	$-0.0680569\pi$
$167$	50.9117	+	88.1816i	0.304860	+	0.528034i	−0.672370	+	0.740215i	$0.734724\pi$
$168$		0			0
$169$	−44.0000	+	76.2102i	−0.260355	+	0.450948i
$170$	56.5685	+	56.5685i	0.332756	+	0.332756i
$171$		0			0
$172$			128.000i			0.744186i
$173$	−5.65685	+	9.79796i	−0.0326986	+	0.0566356i	−0.881912	−	0.471415i	$-0.843743\pi$
$173$	−5.65685	+	9.79796i	−0.0326986	+	0.0566356i	0.849213	+	0.528050i	$0.177077\pi$
$174$		0			0
$175$	62.5000	+	108.253i	0.357143	+	0.618590i
$176$	4.89898	−	2.82843i	0.0278351	−	0.0160706i
$177$		0			0
$178$	180.133	+	104.000i	1.01198	+	0.584270i
$179$		−	125.865i		−	0.703156i	−0.936159	−	0.351578i	$-0.885645\pi$
$179$		−	125.865i		−	0.703156i	0.936159	−	0.351578i	$-0.114355\pi$
$180$		0			0
$181$	−127.000			−0.701657			−0.350829	−	0.936440i	$-0.614100\pi$
$181$	−127.000			−0.701657			−0.350829	+	0.936440i	$0.614100\pi$
$182$	−31.8198	+	55.1135i	−0.174834	+	0.302822i
$183$		0			0
$184$	2.00000	+	3.46410i	0.0108696	+	0.0188266i
$185$	120.741	+	32.3524i	0.652653	+	0.174878i
$186$		0			0
$187$	−13.8564	−	8.00000i	−0.0740984	−	0.0427807i
$188$	45.2548			0.240717
$189$		0			0
$190$	105.000	+	105.000i	0.552632	+	0.552632i
$191$	88.1816	+	50.9117i	0.461684	+	0.266553i	0.712752	−	0.701416i	$-0.247448\pi$
$191$	88.1816	+	50.9117i	0.461684	+	0.266553i	−0.251068	+	0.967969i	$0.580782\pi$
$192$		0			0
$193$	234.693	−	135.500i	1.21603	−	0.702073i	0.251960	−	0.967738i	$-0.418925\pi$
$193$	234.693	−	135.500i	1.21603	−	0.702073i	0.964065	+	0.265665i	$0.0855915\pi$
$194$	50.2145	−	28.9914i	0.258838	−	0.149440i
$195$		0			0
$196$	−24.0000	+	41.5692i	−0.122449	+	0.212088i
$197$	−316.784			−1.60804			−0.804020	−	0.594602i	$-0.797309\pi$
$197$	−316.784			−1.60804			−0.804020	+	0.594602i	$0.797309\pi$
$198$		0			0
$199$	147.000			0.738693			0.369347	−	0.929292i	$-0.379581\pi$
$199$	147.000			0.738693			0.369347	+	0.929292i	$0.379581\pi$
$200$	61.2372	+	35.3553i	0.306186	+	0.176777i
$201$		0			0
$202$	110.851	−	64.0000i	0.548769	−	0.316832i
$203$	95.4594	+	165.341i	0.470243	+	0.814486i
$204$		0			0
$205$	67.7147	+	252.715i	0.330316	+	1.23275i
$206$			18.3848i			0.0892465i
$207$		0			0
$208$			36.0000i			0.173077i
$209$	−25.7196	−	14.8492i	−0.123060	−	0.0710490i
$210$		0			0
$211$	−70.5000	−	122.110i	−0.334123	−	0.578718i	0.649193	−	0.760624i	$-0.275107\pi$
$211$	−70.5000	−	122.110i	−0.334123	−	0.578718i	−0.983316	+	0.181906i	$0.941774\pi$
$212$	−72.1249	−	124.924i	−0.340212	−	0.589264i
$213$		0			0
$214$	−87.0000	+	150.688i	−0.406542	+	0.704151i
$215$	226.274	−	226.274i	1.05244	−	1.05244i
$216$		0			0
$217$			200.000i			0.921659i
$218$	5.65685	−	9.79796i	0.0259489	−	0.0449448i
$219$		0			0
$220$	−13.6603	−	3.66025i	−0.0620921	−	0.0166375i
$221$	88.1816	−	50.9117i	0.399012	−	0.230370i
$222$		0			0
$223$	6.92820	+	4.00000i	0.0310682	+	0.0179372i	0.515454	−	0.856917i	$-0.327623\pi$
$223$	6.92820	+	4.00000i	0.0310682	+	0.0179372i	−0.484385	+	0.874855i	$0.660957\pi$
$224$		−	28.2843i		−	0.126269i
$225$		0			0
$226$	54.0000			0.238938
$227$	34.6482	−	60.0125i	0.152635	−	0.264372i	−0.779560	−	0.626327i	$-0.784557\pi$
$227$	34.6482	−	60.0125i	0.152635	−	0.264372i	0.932196	+	0.361955i	$0.117891\pi$
$228$		0			0
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	0.874627	−	0.484797i	$-0.161106\pi$
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	−0.857160	+	0.515051i	$0.827773\pi$
$230$	2.58819	−	9.65926i	0.0112530	−	0.0419968i
$231$		0			0
$232$	93.5307	+	54.0000i	0.403150	+	0.232759i
$233$	316.784			1.35959			0.679794	−	0.733403i	$-0.262069\pi$
$233$	316.784			1.35959			0.679794	+	0.733403i	$0.262069\pi$
$234$		0			0
$235$	−80.0000	−	80.0000i	−0.340426	−	0.340426i
$236$	−156.767	−	90.5097i	−0.664268	−	0.383516i
$237$		0			0
$238$	−69.2820	+	40.0000i	−0.291101	+	0.168067i
$239$	−177.588	+	102.530i	−0.743046	+	0.428998i	−0.823176	−	0.567787i	$-0.807800\pi$
$239$	−177.588	+	102.530i	−0.743046	+	0.428998i	0.0801297	+	0.996784i	$0.474467\pi$
$240$		0			0
$241$	−39.5000	+	68.4160i	−0.163900	+	0.283884i	−0.936264	−	0.351297i	$-0.885741\pi$
$241$	−39.5000	+	68.4160i	−0.163900	+	0.283884i	0.772364	+	0.635180i	$0.219074\pi$
$242$	−168.291			−0.695419
$243$		0			0
$244$	−194.000			−0.795082
$245$	115.911	−	31.0583i	0.473107	−	0.126769i
$246$		0			0
$247$	163.679	−	94.5000i	0.662667	−	0.382591i
$248$	56.5685	+	97.9796i	0.228099	+	0.395079i
$249$		0			0
$250$	−45.7532	−	170.753i	−0.183013	−	0.683013i
$251$		−	46.6690i		−	0.185932i	−0.995669	−	0.0929662i	$-0.970365\pi$
$251$		−	46.6690i		−	0.185932i	0.995669	−	0.0929662i	$-0.0296349\pi$
$252$		0			0
$253$			2.00000i			0.00790514i
$254$	9.79796	+	5.65685i	0.0385746	+	0.0222711i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−84.8528	−	146.969i	−0.330167	−	0.571865i	0.652378	−	0.757894i	$-0.273772\pi$
$257$	−84.8528	−	146.969i	−0.330167	−	0.571865i	−0.982544	+	0.186029i	$0.940438\pi$
$258$		0			0
$259$	−62.5000	+	108.253i	−0.241313	+	0.417966i
$260$	63.6396	−	63.6396i	0.244768	−	0.244768i
$261$		0			0
$262$			192.000i			0.732824i
$263$	141.421	−	244.949i	0.537724	−	0.931365i	−0.461302	−	0.887243i	$-0.652618\pi$
$263$	141.421	−	244.949i	0.537724	−	0.931365i	0.999026	−	0.0441219i	$-0.0140490\pi$
$264$		0			0
$265$	−93.3365	+	348.336i	−0.352213	+	1.31448i
$266$	−128.598	+	74.2462i	−0.483452	+	0.279121i
$267$		0			0
$268$	226.899	+	131.000i	0.846637	+	0.488806i
$269$		−	101.823i		−	0.378526i	−0.981926	−	0.189263i	$-0.939390\pi$
$269$		−	101.823i		−	0.378526i	0.981926	−	0.189263i	$-0.0606098\pi$
$270$		0			0
$271$	−221.000			−0.815498			−0.407749	−	0.913094i	$-0.633686\pi$
$271$	−221.000			−0.815498			−0.407749	+	0.913094i	$0.633686\pi$
$272$	−22.6274	+	39.1918i	−0.0831890	+	0.144088i
$273$		0			0
$274$	189.000	+	327.358i	0.689781	+	1.19474i
$275$	17.6777	+	30.6186i	0.0642824	+	0.111340i
$276$		0			0
$277$	76.2102	+	44.0000i	0.275127	+	0.158845i	0.631215	−	0.775608i	$-0.282556\pi$
$277$	76.2102	+	44.0000i	0.275127	+	0.158845i	−0.356088	+	0.934452i	$0.615890\pi$
$278$	52.3259			0.188223
$279$		0			0
$280$	−50.0000	+	50.0000i	−0.178571	+	0.178571i
$281$	−176.363	−	101.823i	−0.627627	−	0.362361i	0.152205	−	0.988349i	$-0.451362\pi$
$281$	−176.363	−	101.823i	−0.627627	−	0.362361i	−0.779833	+	0.625988i	$0.784696\pi$
$282$		0			0
$283$	27.7128	−	16.0000i	0.0979251	−	0.0565371i	−0.450238	−	0.892909i	$-0.648661\pi$
$283$	27.7128	−	16.0000i	0.0979251	−	0.0565371i	0.548163	+	0.836372i	$0.315327\pi$
$284$	−154.318	+	89.0955i	−0.543373	+	0.313716i
$285$		0			0
$286$	−9.00000	+	15.5885i	−0.0314685	+	0.0545051i
$287$	−261.630			−0.911601
$288$		0			0
$289$	−161.000			−0.557093
$290$	−69.8811	−	260.800i	−0.240969	−	0.899310i
$291$		0			0
$292$	−29.4449	+	17.0000i	−0.100839	+	0.0582192i
$293$	86.9741	+	150.644i	0.296840	+	0.514142i	0.975411	−	0.220393i	$-0.0707338\pi$
$293$	86.9741	+	150.644i	0.296840	+	0.514142i	−0.678571	+	0.734535i	$0.737401\pi$
$294$		0			0
$295$	117.128	+	437.128i	0.397045	+	1.48179i
$296$			70.7107i			0.238887i
$297$		0			0
$298$		−	368.000i		−	1.23490i
$299$	−11.0227	−	6.36396i	−0.0368652	−	0.0212842i
$300$		0			0
$301$	160.000	+	277.128i	0.531561	+	0.920691i
$302$	77.0746	+	133.497i	0.255214	+	0.442044i
$303$		0			0
$304$	−42.0000	+	72.7461i	−0.138158	+	0.239296i
$305$	342.947	+	342.947i	1.12442	+	1.12442i
$306$		0			0
$307$		−	486.000i		−	1.58306i	−0.611129	−	0.791531i	$-0.709284\pi$
$307$		−	486.000i		−	1.58306i	0.611129	−	0.791531i	$-0.290716\pi$
$308$	7.07107	−	12.2474i	0.0229580	−	0.0397644i
$309$		0			0
$310$	73.2051	−	273.205i	0.236145	−	0.881307i
$311$	58.7878	−	33.9411i	0.189028	−	0.109135i	−0.402499	−	0.915420i	$-0.631858\pi$
$311$	58.7878	−	33.9411i	0.189028	−	0.109135i	0.591528	+	0.806285i	$0.298525\pi$
$312$		0			0
$313$	243.353	+	140.500i	0.777486	+	0.448882i	0.835539	−	0.549432i	$-0.185156\pi$
$313$	243.353	+	140.500i	0.777486	+	0.448882i	−0.0580525	+	0.998314i	$0.518489\pi$
$314$		−	166.877i		−	0.531456i
$315$		0			0
$316$	−234.000			−0.740506
$317$	−260.215	+	450.706i	−0.820868	+	1.42179i	0.0841679	+	0.996452i	$0.473177\pi$
$317$	−260.215	+	450.706i	−0.820868	+	1.42179i	−0.905036	+	0.425334i	$0.860157\pi$
$318$		0			0
$319$	27.0000	+	46.7654i	0.0846395	+	0.146600i
$320$	−10.3528	+	38.6370i	−0.0323524	+	0.120741i
$321$		0			0
$322$	8.66025	+	5.00000i	0.0268952	+	0.0155280i
$323$	237.588			0.735566
$324$		0			0
$325$	−225.000			−0.692308
$326$	248.623	+	143.543i	0.762648	+	0.440315i
$327$		0			0
$328$	−128.172	+	74.0000i	−0.390768	+	0.225610i
$329$	97.9796	−	56.5685i	0.297810	−	0.171941i
$330$		0			0
$331$	29.5000	−	51.0955i	0.0891239	−	0.154367i	−0.818017	−	0.575194i	$-0.804927\pi$
$331$	29.5000	−	51.0955i	0.0891239	−	0.154367i	0.907141	+	0.420827i	$0.138260\pi$
$332$	−115.966			−0.349294
$333$		0			0
$334$	144.000			0.431138
$335$	−169.526	−	632.681i	−0.506049	−	1.88860i
$336$		0			0
$337$	−47.6314	+	27.5000i	−0.141339	+	0.0816024i	−0.569002	−	0.822336i	$-0.692670\pi$
$337$	−47.6314	+	27.5000i	−0.141339	+	0.0816024i	0.427663	+	0.903938i	$0.359337\pi$
$338$	62.2254	+	107.778i	0.184099	+	0.318868i
$339$		0			0
$340$	109.282	−	29.2820i	0.321418	−	0.0861236i
$341$			56.5685i			0.165890i
$342$		0			0
$343$			365.000i			1.06414i
$344$	156.767	+	90.5097i	0.455719	+	0.263109i
$345$		0			0
$346$	8.00000	+	13.8564i	0.0231214	+	0.0400474i
$347$	−299.106	−	518.067i	−0.861977	−	1.49299i	−0.870017	−	0.493021i	$-0.835893\pi$
$347$	−299.106	−	518.067i	−0.861977	−	1.49299i	0.00803996	−	0.999968i	$-0.497441\pi$
$348$		0			0
$349$	219.500	−	380.185i	0.628940	−	1.08936i	−0.358825	−	0.933405i	$-0.616823\pi$
$349$	219.500	−	380.185i	0.628940	−	1.08936i	0.987765	−	0.155951i	$-0.0498442\pi$
$350$	176.777			0.505076
$351$		0			0
$352$		−	8.00000i		−	0.0227273i
$353$	−260.215	+	450.706i	−0.737154	+	1.27679i	0.216618	+	0.976256i	$0.430497\pi$
$353$	−260.215	+	450.706i	−0.737154	+	1.27679i	−0.953772	+	0.300531i	$0.902836\pi$
$354$		0			0
$355$	430.298	+	115.298i	1.21211	+	0.324783i
$356$	254.747	−	147.078i	0.715581	−	0.413141i
$357$		0			0
$358$	−154.153	−	89.0000i	−0.430594	−	0.248603i
$359$		−	55.1543i		−	0.153633i	−0.997045	−	0.0768166i	$-0.975524\pi$
$359$		−	55.1543i		−	0.153633i	0.997045	−	0.0768166i	$-0.0244756\pi$
$360$		0			0
$361$	80.0000			0.221607
$362$	−89.8026	+	155.543i	−0.248073	+	0.429676i
$363$		0			0
$364$	45.0000	+	77.9423i	0.123626	+	0.214127i
$365$	82.1037	+	21.9996i	0.224942	+	0.0602729i
$366$		0			0
$367$	510.089	+	294.500i	1.38989	+	0.802452i	0.993302	−	0.115545i	$-0.0368615\pi$
$367$	510.089	+	294.500i	1.38989	+	0.802452i	0.396586	+	0.917998i	$0.370195\pi$
$368$	5.65685			0.0153719
$369$		0			0
$370$	125.000	−	125.000i	0.337838	−	0.337838i
$371$	−312.310	−	180.312i	−0.841806	−	0.486017i
$372$		0			0
$373$	7.79423	−	4.50000i	0.0208961	−	0.0120643i	−0.489516	−	0.871995i	$-0.662826\pi$
$373$	7.79423	−	4.50000i	0.0208961	−	0.0120643i	0.510412	+	0.859930i	$0.329493\pi$
$374$	−19.5959	+	11.3137i	−0.0523955	+	0.0302506i
$375$		0			0
$376$	32.0000	−	55.4256i	0.0851064	−	0.147409i
$377$	−343.654			−0.911549
$378$		0			0
$379$	157.000			0.414248			0.207124	−	0.978315i	$-0.433590\pi$
$379$	157.000			0.414248			0.207124	+	0.978315i	$0.433590\pi$
$380$	202.844	−	54.3520i	0.533801	−	0.143032i
$381$		0			0
$382$	124.708	−	72.0000i	0.326460	−	0.188482i
$383$	−141.421	−	244.949i	−0.369246	−	0.639553i	0.620202	−	0.784443i	$-0.287051\pi$
$383$	−141.421	−	244.949i	−0.369246	−	0.639553i	−0.989448	+	0.144889i	$0.953717\pi$
$384$		0			0
$385$	−34.1506	+	9.15064i	−0.0887029	+	0.0237679i
$386$		−	383.252i		−	0.992881i
$387$		0			0
$388$		−	82.0000i		−	0.211340i
$389$	519.292	+	299.813i	1.33494	+	0.770728i	0.986052	−	0.166436i	$-0.0532260\pi$
$389$	519.292	+	299.813i	1.33494	+	0.770728i	0.348888	+	0.937164i	$0.386559\pi$
$390$		0			0
$391$	−8.00000	−	13.8564i	−0.0204604	−	0.0354384i
$392$	33.9411	+	58.7878i	0.0865845	+	0.149969i
$393$		0			0
$394$	−224.000	+	387.979i	−0.568528	+	0.984719i
$395$	413.657	+	413.657i	1.04723	+	1.04723i
$396$		0			0
$397$			296.000i			0.745592i	0.927913	+	0.372796i	$0.121601\pi$
$397$			296.000i			0.745592i	−0.927913	+	0.372796i	$0.878399\pi$
$398$	103.945	−	180.037i	0.261168	−	0.452356i
$399$		0			0
$400$	86.6025	−	50.0000i	0.216506	−	0.125000i
$401$	336.805	−	194.454i	0.839912	−	0.484924i	−0.0173221	−	0.999850i	$-0.505514\pi$
$401$	336.805	−	194.454i	0.839912	−	0.484924i	0.857234	+	0.514926i	$0.172181\pi$
$402$		0			0
$403$	−311.769	−	180.000i	−0.773621	−	0.446650i
$404$		−	181.019i		−	0.448068i
$405$		0			0
$406$	270.000			0.665025
$407$	−17.6777	+	30.6186i	−0.0434341	+	0.0752300i
$408$		0			0
$409$	−72.5000	−	125.574i	−0.177262	−	0.307026i	0.763680	−	0.645595i	$-0.223391\pi$
$409$	−72.5000	−	125.574i	−0.177262	−	0.307026i	−0.940942	+	0.338569i	$0.890057\pi$
$410$	357.393	+	95.7630i	0.871689	+	0.233568i
$411$		0			0
$412$	22.5167	+	13.0000i	0.0546521	+	0.0315534i
$413$	−452.548			−1.09576
$414$		0			0
$415$	205.000	+	205.000i	0.493976	+	0.493976i
$416$	44.0908	+	25.4558i	0.105988	+	0.0611919i
$417$		0			0
$418$	−36.3731	+	21.0000i	−0.0870169	+	0.0502392i
$419$	−607.473	+	350.725i	−1.44982	+	0.837052i	−0.998470	−	0.0552959i	$-0.982390\pi$
$419$	−607.473	+	350.725i	−1.44982	+	0.837052i	−0.451347	+	0.892348i	$0.649056\pi$
$420$		0			0
$421$	−252.500	+	437.343i	−0.599762	+	1.03882i	0.393093	+	0.919499i	$0.371405\pi$
$421$	−252.500	+	437.343i	−0.599762	+	1.03882i	−0.992856	+	0.119320i	$0.961928\pi$
$422$	−199.404			−0.472522
$423$		0			0
$424$	−204.000			−0.481132
$425$	−244.949	−	141.421i	−0.576351	−	0.332756i
$426$		0			0
$427$	−420.022	+	242.500i	−0.983659	+	0.567916i
$428$	123.037	+	213.106i	0.287469	+	0.497910i
$429$		0			0
$430$	−117.128	−	437.128i	−0.272391	−	1.01658i
$431$			43.8406i			0.101718i	0.998706	+	0.0508592i	$0.0161960\pi$
$431$			43.8406i			0.101718i	−0.998706	+	0.0508592i	$0.983804\pi$
$432$		0			0
$433$		−	32.0000i		−	0.0739030i	−0.999317	−	0.0369515i	$-0.988235\pi$
$433$		−	32.0000i		−	0.0739030i	0.999317	−	0.0369515i	$-0.0117647\pi$
$434$	244.949	+	141.421i	0.564399	+	0.325856i
$435$		0			0
$436$	−8.00000	−	13.8564i	−0.0183486	−	0.0317807i
$437$	−14.8492	−	25.7196i	−0.0339800	−	0.0588550i
$438$		0			0
$439$	252.000	−	436.477i	0.574032	−	0.994252i	−0.422114	−	0.906543i	$-0.638712\pi$
$439$	252.000	−	436.477i	0.574032	−	0.994252i	0.996146	−	0.0877097i	$-0.0279548\pi$
$440$	−14.1421	+	14.1421i	−0.0321412	+	0.0321412i
$441$		0			0
$442$		−	144.000i		−	0.325792i
$443$	118.794	−	205.757i	0.268158	−	0.464463i	−0.700228	−	0.713919i	$-0.746918\pi$
$443$	118.794	−	205.757i	0.268158	−	0.464463i	0.968386	+	0.249456i	$0.0802518\pi$
$444$		0			0
$445$	−710.333	−	190.333i	−1.59625	−	0.427715i
$446$	9.79796	−	5.65685i	0.0219685	−	0.0126835i
$447$		0			0
$448$	−34.6410	−	20.0000i	−0.0773237	−	0.0446429i
$449$		−	67.8823i		−	0.151185i	−0.997139	−	0.0755927i	$-0.975915\pi$
$449$		−	67.8823i		−	0.151185i	0.997139	−	0.0755927i	$-0.0240849\pi$
$450$		0			0
$451$	−74.0000			−0.164080
$452$	38.1838	−	66.1362i	0.0844774	−	0.146319i
$453$		0			0
$454$	−49.0000	−	84.8705i	−0.107930	−	0.186939i
$455$	58.2343	−	217.333i	0.127987	−	0.477656i
$456$		0			0
$457$	−651.251	−	376.000i	−1.42506	−	0.822757i	−0.428332	−	0.903621i	$-0.640899\pi$
$457$	−651.251	−	376.000i	−1.42506	−	0.822757i	−0.996725	+	0.0808643i	$0.974232\pi$
$458$	11.3137			0.0247024
$459$		0			0
$460$	−10.0000	−	10.0000i	−0.0217391	−	0.0217391i
$461$	529.090	+	305.470i	1.14770	+	0.662625i	0.948326	−	0.317298i	$-0.102776\pi$
$461$	529.090	+	305.470i	1.14770	+	0.662625i	0.199374	+	0.979923i	$0.436109\pi$
$462$		0			0
$463$	517.017	−	298.500i	1.11667	−	0.644708i	0.176120	−	0.984369i	$-0.443645\pi$
$463$	517.017	−	298.500i	1.11667	−	0.644708i	0.940548	+	0.339660i	$0.110312\pi$
$464$	132.272	−	76.3675i	0.285070	−	0.164585i
$465$		0			0
$466$	224.000	−	387.979i	0.480687	−	0.832574i
$467$	−848.528			−1.81698			−0.908488	−	0.417910i	$-0.862763\pi$
$467$	−848.528			−1.81698			−0.908488	+	0.417910i	$0.862763\pi$
$468$		0			0
$469$	655.000			1.39659
$470$	−154.548	+	41.4110i	−0.328826	+	0.0881086i
$471$		0			0
$472$	−221.703	+	128.000i	−0.469709	+	0.271186i
$473$	45.2548	+	78.3837i	0.0956762	+	0.165716i
$474$		0			0
$475$	−454.663	−	262.500i	−0.957186	−	0.552632i
$476$			113.137i			0.237683i
$477$		0			0
$478$			290.000i			0.606695i
$479$	−145.745	−	84.1457i	−0.304269	−	0.175670i	0.340090	−	0.940393i	$-0.389542\pi$
$479$	−145.745	−	84.1457i	−0.304269	−	0.175670i	−0.644359	+	0.764723i	$0.722876\pi$
$480$		0			0
$481$	−112.500	−	194.856i	−0.233888	−	0.405105i
$482$	55.8614	+	96.7548i	0.115895	+	0.200736i
$483$		0			0
$484$	−119.000	+	206.114i	−0.245868	+	0.425855i
$485$	−144.957	+	144.957i	−0.298880	+	0.298880i
$486$		0			0
$487$		−	507.000i		−	1.04107i	−0.853841	−	0.520534i	$-0.825733\pi$
$487$		−	507.000i		−	1.04107i	0.853841	−	0.520534i	$-0.174267\pi$
$488$	−137.179	+	237.601i	−0.281104	+	0.486886i
$489$		0			0
$490$	43.9230	−	163.923i	0.0896389	−	0.334537i
$491$	−371.098	+	214.253i	−0.755800	+	0.436361i	−0.827786	−	0.561044i	$-0.810400\pi$
$491$	−371.098	+	214.253i	−0.755800	+	0.436361i	0.0719859	+	0.997406i	$0.477066\pi$
$492$		0			0
$493$	−374.123	−	216.000i	−0.758870	−	0.438134i
$494$		−	267.286i		−	0.541066i
$495$		0			0
$496$	160.000			0.322581
$497$	−222.739	+	385.795i	−0.448166	+	0.776247i
$498$		0			0
$499$	−435.000	−	753.442i	−0.871743	−	1.50990i	−0.860192	−	0.509971i	$-0.829656\pi$
$499$	−435.000	−	753.442i	−0.871743	−	1.50990i	−0.0115517	−	0.999933i	$-0.503677\pi$
$500$	−241.481	−	64.7048i	−0.482963	−	0.129410i
$501$		0			0
$502$	−57.1577	−	33.0000i	−0.113860	−	0.0657371i
$503$	462.448			0.919379			0.459690	−	0.888080i	$-0.347961\pi$
$503$	462.448			0.919379			0.459690	+	0.888080i	$0.347961\pi$
$504$		0			0
$505$	−320.000	+	320.000i	−0.633663	+	0.633663i
$506$	2.44949	+	1.41421i	0.00484089	+	0.00279489i
$507$		0			0
$508$	13.8564	−	8.00000i	0.0272764	−	0.0157480i
$509$	−709.127	+	409.415i	−1.39318	+	0.804351i	−0.993666	−	0.112377i	$-0.964154\pi$
$509$	−709.127	+	409.415i	−1.39318	+	0.804351i	−0.399512	+	0.916728i	$0.630820\pi$
$510$		0			0
$511$	−42.5000	+	73.6122i	−0.0831703	+	0.144055i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−240.000			−0.466926
$515$	−16.8232	−	62.7852i	−0.0326665	−	0.121913i
$516$		0			0
$517$	27.7128	−	16.0000i	0.0536031	−	0.0309478i
$518$	88.3883	+	153.093i	0.170634	+	0.295547i
$519$		0			0
$520$	−32.9423	−	122.942i	−0.0633506	−	0.236427i
$521$			864.084i			1.65851i	0.558869	+	0.829256i	$0.311235\pi$
$521$			864.084i			1.65851i	−0.558869	+	0.829256i	$0.688765\pi$
$522$		0			0
$523$		−	163.000i		−	0.311663i	−0.987784	−	0.155832i	$-0.950194\pi$
$523$		−	163.000i		−	0.311663i	0.987784	−	0.155832i	$-0.0498058\pi$
$524$	235.151	+	135.765i	0.448761	+	0.259093i
$525$		0			0
$526$	−200.000	−	346.410i	−0.380228	−	0.658574i
$527$	−226.274	−	391.918i	−0.429363	−	0.743678i
$528$		0			0
$529$	263.500	−	456.395i	0.498110	−	0.862751i
$530$	360.624	+	360.624i	0.680424	+	0.680424i
$531$		0			0
$532$			210.000i			0.394737i
$533$	235.467	−	407.840i	0.441776	−	0.765178i
$534$		0			0
$535$	159.221	−	594.221i	0.297609	−	1.11069i
$536$	320.883	−	185.262i	0.598663	−	0.345638i
$537$		0			0
$538$	−124.708	−	72.0000i	−0.231799	−	0.133829i
$539$			33.9411i			0.0629705i
$540$		0			0
$541$	697.000			1.28835			0.644177	−	0.764876i	$-0.277200\pi$
$541$	697.000			1.28835			0.644177	+	0.764876i	$0.277200\pi$
$542$	−156.271	+	270.669i	−0.288322	+	0.499389i
$543$		0			0
$544$	32.0000	+	55.4256i	0.0588235	+	0.101885i
$545$	−10.3528	+	38.6370i	−0.0189959	+	0.0708936i
$546$		0			0
$547$	−336.884	−	194.500i	−0.615875	−	0.355576i	0.159386	−	0.987216i	$-0.449049\pi$
$547$	−336.884	−	194.500i	−0.615875	−	0.355576i	−0.775261	+	0.631640i	$0.782382\pi$
$548$	534.573			0.975498
$549$		0			0
$550$	50.0000			0.0909091
$551$	−694.430	−	400.930i	−1.26031	−	0.727640i
$552$		0			0
$553$	−506.625	+	292.500i	−0.916139	+	0.528933i
$554$	107.778	−	62.2254i	0.194544	−	0.112320i
$555$		0			0
$556$	37.0000	−	64.0859i	0.0665468	−	0.115262i
$557$	−1086.12			−1.94994			−0.974969	−	0.222339i	$-0.928631\pi$
$557$	−1086.12			−1.94994			−0.974969	+	0.222339i	$0.928631\pi$
$558$		0			0
$559$	−576.000			−1.03041
$560$	25.8819	+	96.5926i	0.0462177	+	0.172487i
$561$		0			0
$562$	−249.415	+	144.000i	−0.443799	+	0.256228i
$563$	−311.127	−	538.888i	−0.552623	−	0.957172i	−0.998084	−	0.0618704i	$-0.980293\pi$
$563$	−311.127	−	538.888i	−0.552623	−	0.957172i	0.445461	−	0.895301i	$-0.353040\pi$
$564$		0			0
$565$	−184.413	+	49.4134i	−0.326395	+	0.0874574i
$566$		−	45.2548i		−	0.0799555i
$567$		0			0
$568$			252.000i			0.443662i
$569$	401.716	+	231.931i	0.706004	+	0.407612i	0.809580	−	0.587010i	$-0.199695\pi$
$569$	401.716	+	231.931i	0.706004	+	0.407612i	−0.103576	+	0.994622i	$0.533028\pi$
$570$		0			0
$571$	461.500	+	799.341i	0.808231	+	1.39990i	0.914088	+	0.405516i	$0.132908\pi$
$571$	461.500	+	799.341i	0.808231	+	1.39990i	−0.105857	+	0.994381i	$0.533758\pi$
$572$	12.7279	+	22.0454i	0.0222516	+	0.0385409i
$573$		0			0
$574$	−185.000	+	320.429i	−0.322300	+	0.558239i
$575$			35.3553i			0.0614875i
$576$		0			0
$577$		−	247.000i		−	0.428076i	−0.976825	−	0.214038i	$-0.931338\pi$
$577$		−	247.000i		−	0.428076i	0.976825	−	0.214038i	$-0.0686617\pi$
$578$	−113.844	+	197.184i	−0.196962	+	0.341149i
$579$		0			0
$580$	−368.827	−	98.8269i	−0.635908	−	0.170391i
$581$	−251.073	+	144.957i	−0.432139	+	0.249496i
$582$		0			0
$583$	−88.3346	−	51.0000i	−0.151517	−	0.0874786i
$584$			48.0833i			0.0823344i
$585$		0			0
$586$	246.000			0.419795
$587$	−226.981	+	393.143i	−0.386680	+	0.669750i	−0.992001	−	0.126232i	$-0.959712\pi$
$587$	−226.981	+	393.143i	−0.386680	+	0.669750i	0.605321	+	0.795982i	$0.293045\pi$
$588$		0			0
$589$	−420.000	−	727.461i	−0.713073	−	1.23508i
$590$	618.193	+	165.644i	1.04778	+	0.280753i
$591$		0			0
$592$	86.6025	+	50.0000i	0.146288	+	0.0844595i
$593$	4.24264			0.00715454			0.00357727	−	0.999994i	$-0.498861\pi$
$593$	4.24264			0.00715454			0.00357727	+	0.999994i	$0.498861\pi$
$594$		0			0
$595$	200.000	−	200.000i	0.336134	−	0.336134i
$596$	−450.706	−	260.215i	−0.756218	−	0.436603i
$597$		0			0
$598$	−15.5885	+	9.00000i	−0.0260677	+	0.0150502i
$599$	−194.734	+	112.430i	−0.325099	+	0.187696i	−0.653663	−	0.756786i	$-0.726769\pi$
$599$	−194.734	+	112.430i	−0.325099	+	0.187696i	0.328564	+	0.944482i	$0.393435\pi$
$600$		0			0
$601$	368.000	−	637.395i	0.612313	−	1.06056i	−0.378537	−	0.925586i	$-0.623573\pi$
$601$	368.000	−	637.395i	0.612313	−	1.06056i	0.990850	−	0.134971i	$-0.0430940\pi$
$602$	452.548			0.751741
$603$		0			0
$604$	218.000			0.360927
$605$	574.726	−	153.997i	0.949960	−	0.254541i
$606$		0			0
$607$	−378.453	+	218.500i	−0.623481	+	0.359967i	−0.778223	−	0.627988i	$-0.783879\pi$
$607$	−378.453	+	218.500i	−0.623481	+	0.359967i	0.154742	+	0.987955i	$0.450545\pi$
$608$	59.3970	+	102.879i	0.0976924	+	0.169208i
$609$		0			0
$610$	662.522	−	177.522i	1.08610	−	0.291020i
$611$			203.647i			0.333301i
$612$		0			0
$613$		−	335.000i		−	0.546493i	−0.961944	−	0.273246i	$-0.911903\pi$
$613$		−	335.000i		−	0.546493i	0.961944	−	0.273246i	$-0.0880974\pi$
$614$	−595.226	−	343.654i	−0.969423	−	0.559697i
$615$		0			0
$616$	−10.0000	−	17.3205i	−0.0162338	−	0.0281177i
$617$	127.986	+	221.679i	0.207433	+	0.359285i	0.950905	−	0.309482i	$-0.100156\pi$
$617$	127.986	+	221.679i	0.207433	+	0.359285i	−0.743472	+	0.668767i	$0.766822\pi$
$618$		0			0
$619$	482.500	−	835.715i	0.779483	−	1.35010i	−0.152757	−	0.988264i	$-0.548815\pi$
$619$	482.500	−	835.715i	0.779483	−	1.35010i	0.932240	−	0.361840i	$-0.117851\pi$
$620$	−282.843	−	282.843i	−0.456198	−	0.456198i
$621$		0			0
$622$		−	96.0000i		−	0.154341i
$623$	367.696	−	636.867i	0.590201	−	1.02226i
$624$		0			0
$625$	312.500	+	541.266i	0.500000	+	0.866025i
$626$	344.153	−	198.697i	0.549766	−	0.317407i
$627$		0			0
$628$	−204.382	−	118.000i	−0.325449	−	0.187898i
$629$		−	282.843i		−	0.449670i
$630$		0			0
$631$	275.000			0.435816			0.217908	−	0.975969i	$-0.430077\pi$
$631$	275.000			0.435816			0.217908	+	0.975969i	$0.430077\pi$
$632$	−165.463	+	286.590i	−0.261809	+	0.453466i
$633$		0			0
$634$	368.000	+	637.395i	0.580442	+	1.00535i
$635$	−38.6370	−	10.3528i	−0.0608457	−	0.0163036i
$636$		0			0
$637$	−187.061	−	108.000i	−0.293660	−	0.169545i
$638$	76.3675			0.119698
$639$		0			0
$640$	40.0000	+	40.0000i	0.0625000	+	0.0625000i
$641$	421.312	+	243.245i	0.657273	+	0.379477i	0.791237	−	0.611509i	$-0.209437\pi$
$641$	421.312	+	243.245i	0.657273	+	0.379477i	−0.133964	+	0.990986i	$0.542771\pi$
$642$		0			0
$643$	−997.661	+	576.000i	−1.55157	+	0.895801i	−0.553559	+	0.832810i	$0.686731\pi$
$643$	−997.661	+	576.000i	−1.55157	+	0.895801i	−0.998014	+	0.0629907i	$0.979936\pi$
$644$	12.2474	−	7.07107i	0.0190178	−	0.0109799i
$645$		0			0
$646$	168.000	−	290.985i	0.260062	−	0.450440i
$647$	691.550			1.06886			0.534428	−	0.845214i	$-0.320527\pi$
$647$	691.550			1.06886			0.534428	+	0.845214i	$0.320527\pi$
$648$		0			0
$649$	−128.000			−0.197227
$650$	−159.099	+	275.568i	−0.244768	+	0.423950i
$651$		0			0
$652$	351.606	−	203.000i	0.539273	−	0.311350i
$653$	175.362	+	303.737i	0.268549	+	0.465140i	0.968487	−	0.249063i	$-0.0801226\pi$
$653$	175.362	+	303.737i	0.268549	+	0.465140i	−0.699938	+	0.714203i	$0.746789\pi$
$654$		0			0
$655$	−175.692	−	655.692i	−0.268232	−	1.00106i
$656$			209.304i			0.319060i
$657$		0			0
$658$		−	160.000i		−	0.243161i
$659$	−431.110	−	248.902i	−0.654188	−	0.377696i	0.135871	−	0.990727i	$-0.456617\pi$
$659$	−431.110	−	248.902i	−0.654188	−	0.377696i	−0.790059	+	0.613031i	$0.789950\pi$
$660$		0			0
$661$	288.500	+	499.697i	0.436460	+	0.755971i	0.997414	−	0.0718765i	$-0.0228987\pi$
$661$	288.500	+	499.697i	0.436460	+	0.755971i	−0.560954	+	0.827847i	$0.689565\pi$
$662$	−41.7193	−	72.2599i	−0.0630201	−	0.109154i
$663$		0			0
$664$	−82.0000	+	142.028i	−0.123494	+	0.213898i
$665$	371.231	−	371.231i	0.558242	−	0.558242i
$666$		0			0
$667$			54.0000i			0.0809595i
$668$	101.823	−	176.363i	0.152430	−	0.264017i
$669$		0			0
$670$	−894.747	−	239.747i	−1.33544	−	0.357831i
$671$	−118.800	+	68.5894i	−0.177050	+	0.102220i
$672$		0			0
$673$	423.486	+	244.500i	0.629252	+	0.363299i	0.780462	−	0.625203i	$-0.214984\pi$
$673$	423.486	+	244.500i	0.629252	+	0.363299i	−0.151210	+	0.988502i	$0.548317\pi$
$674$			77.7817i			0.115403i
$675$		0			0
$676$	176.000			0.260355
$677$	299.813	−	519.292i	0.442856	−	0.767048i	−0.555044	−	0.831821i	$-0.687299\pi$
$677$	299.813	−	519.292i	0.442856	−	0.767048i	0.997900	+	0.0647722i	$0.0206321\pi$
$678$		0			0
$679$	−102.500	−	177.535i	−0.150957	−	0.261466i
$680$	41.4110	−	154.548i	0.0608986	−	0.227277i
$681$		0			0
$682$	69.2820	+	40.0000i	0.101587	+	0.0586510i
$683$	−236.174			−0.345789			−0.172894	−	0.984940i	$-0.555312\pi$
$683$	−236.174			−0.345789			−0.172894	+	0.984940i	$0.555312\pi$
$684$		0			0
$685$	−945.000	−	945.000i	−1.37956	−	1.37956i
$686$	447.032	+	258.094i	0.651650	+	0.376230i
$687$		0			0
$688$	221.703	−	128.000i	0.322242	−	0.186047i
$689$	562.158	−	324.562i	0.815904	−	0.471062i
$690$		0			0
$691$	−320.000	+	554.256i	−0.463097	+	0.802107i	−0.999113	−	0.0421001i	$-0.986595\pi$
$691$	−320.000	+	554.256i	−0.463097	+	0.802107i	0.536016	+	0.844208i	$0.319928\pi$
$692$	22.6274			0.0326986
$693$		0			0
$694$	−846.000			−1.21902
$695$	−178.696	+	47.8815i	−0.257117	+	0.0688943i
$696$		0			0
$697$	512.687	−	296.000i	0.735562	−	0.424677i
$698$	−310.420	−	537.663i	−0.444728	−	0.770291i
$699$		0			0
$700$	125.000	−	216.506i	0.178571	−	0.309295i
$701$		−	1093.19i		−	1.55947i	−0.626111	−	0.779734i	$-0.715354\pi$
$701$		−	1093.19i		−	1.55947i	0.626111	−	0.779734i	$-0.284646\pi$
$702$		0			0
$703$		−	525.000i		−	0.746799i
$704$	−9.79796	−	5.65685i	−0.0139176	−	0.00803530i
$705$		0			0
$706$	368.000	+	637.395i	0.521246	+	0.902825i
$707$	−226.274	−	391.918i	−0.320048	−	0.554340i
$708$		0			0
$709$	244.500	−	423.486i	0.344852	−	0.597301i	−0.640475	−	0.767979i	$-0.721262\pi$
$709$	244.500	−	423.486i	0.344852	−	0.597301i	0.985327	+	0.170678i	$0.0545958\pi$
$710$	445.477	−	445.477i	0.627433	−	0.627433i
$711$		0			0
$712$		−	416.000i		−	0.584270i
$713$	−28.2843	+	48.9898i	−0.0396694	+	0.0687094i
$714$		0			0
$715$	16.4711	−	61.4711i	0.0230366	−	0.0859736i
$716$	−218.005	+	125.865i	−0.304476	+	0.175789i
$717$		0			0
$718$	−67.5500	−	39.0000i	−0.0940808	−	0.0543175i
$719$		−	620.840i		−	0.863477i	−0.901999	−	0.431738i	$-0.857900\pi$
$719$		−	620.840i		−	0.863477i	0.901999	−	0.431738i	$-0.142100\pi$
$720$		0			0
$721$	65.0000			0.0901526
$722$	56.5685	−	97.9796i	0.0783498	−	0.135706i
$723$		0			0
$724$	127.000	+	219.970i	0.175414	+	0.303827i
$725$	477.297	+	826.703i	0.658341	+	1.14028i
$726$		0			0
$727$	935.307	+	540.000i	1.28653	+	0.742779i	0.978034	−	0.208447i	$-0.0668409\pi$
$727$	935.307	+	540.000i	1.28653	+	0.742779i	0.308496	+	0.951225i	$0.400174\pi$
$728$	127.279			0.174834
$729$		0			0
$730$	85.0000	−	85.0000i	0.116438	−	0.116438i
$731$	−627.069	−	362.039i	−0.857824	−	0.495265i
$732$		0			0
$733$	214.774	−	124.000i	0.293007	−	0.169168i	−0.346290	−	0.938128i	$-0.612559\pi$
$733$	214.774	−	124.000i	0.293007	−	0.169168i	0.639297	+	0.768960i	$0.279225\pi$
$734$	721.375	−	416.486i	0.982799	−	0.567419i
$735$		0			0
$736$	4.00000	−	6.92820i	0.00543478	−	0.00941332i
$737$	185.262			0.251373
$738$		0			0
$739$	848.000			1.14750			0.573748	−	0.819032i	$-0.305489\pi$
$739$	848.000			1.14750			0.573748	+	0.819032i	$0.305489\pi$
$740$	−64.7048	−	241.481i	−0.0874389	−	0.326326i
$741$		0			0
$742$	−441.673	+	255.000i	−0.595247	+	0.343666i
$743$	16.9706	+	29.3939i	0.0228406	+	0.0395611i	0.877220	−	0.480089i	$-0.159396\pi$
$743$	16.9706	+	29.3939i	0.0228406	+	0.0395611i	−0.854379	+	0.519650i	$0.826062\pi$
$744$		0			0
$745$	336.743	+	1256.74i	0.452005	+	1.68690i
$746$		−	12.7279i		−	0.0170616i
$747$		0			0
$748$			32.0000i			0.0427807i
$749$	532.764	+	307.591i	0.711300	+	0.410669i
$750$		0			0
$751$	66.5000	+	115.181i	0.0885486	+	0.153371i	0.906898	−	0.421351i	$-0.138444\pi$
$751$	66.5000	+	115.181i	0.0885486	+	0.153371i	−0.818349	+	0.574721i	$0.805110\pi$
$752$	−45.2548	−	78.3837i	−0.0601793	−	0.104234i
$753$		0			0
$754$	−243.000	+	420.888i	−0.322281	+	0.558207i
$755$	−385.373	−	385.373i	−0.510428	−	0.510428i
$756$		0			0
$757$			1271.00i			1.67900i	0.543363	+	0.839498i	$0.317151\pi$
$757$			1271.00i			1.67900i	−0.543363	+	0.839498i	$0.682849\pi$
$758$	111.016	−	192.285i	0.146459	−	0.253674i
$759$		0			0
$760$	76.8653	−	286.865i	0.101139	−	0.377454i
$761$	−466.628	+	269.408i	−0.613177	+	0.354018i	−0.774208	−	0.632931i	$-0.781852\pi$
$761$	−466.628	+	269.408i	−0.613177	+	0.354018i	0.161031	+	0.986949i	$0.448518\pi$
$762$		0			0
$763$	−34.6410	−	20.0000i	−0.0454011	−	0.0262123i
$764$		−	203.647i		−	0.266553i
$765$		0			0
$766$	−400.000			−0.522193
$767$	407.294	−	705.453i	0.531022	−	0.919756i
$768$		0			0
$769$	40.5000	+	70.1481i	0.0526658	+	0.0912198i	0.891156	−	0.453696i	$-0.149895\pi$
$769$	40.5000	+	70.1481i	0.0526658	+	0.0912198i	−0.838491	+	0.544916i	$0.816562\pi$
$770$	−12.9410	+	48.2963i	−0.0168064	+	0.0627225i
$771$		0			0
$772$	−469.386	−	271.000i	−0.608013	−	0.351036i
$773$	−445.477			−0.576297			−0.288148	−	0.957586i	$-0.593040\pi$
$773$	−445.477			−0.576297			−0.288148	+	0.957586i	$0.593040\pi$
$774$		0			0
$775$			1000.00i			1.29032i
$776$	−100.429	−	57.9828i	−0.129419	−	0.0747200i
$777$		0			0
$778$	734.390	−	424.000i	0.943945	−	0.544987i
$779$	951.627	−	549.422i	1.22160	−	0.705291i
$780$		0			0
$781$	−63.0000	+	109.119i	−0.0806658	+	0.139717i
$782$	−22.6274			−0.0289353
$783$		0			0
$784$	96.0000			0.122449
$785$	152.703	+	569.896i	0.194526	+	0.725982i
$786$		0			0
$787$	342.080	−	197.500i	0.434663	−	0.250953i	−0.266668	−	0.963788i	$-0.585923\pi$
$787$	342.080	−	197.500i	0.434663	−	0.250953i	0.701331	+	0.712835i	$0.252589\pi$
$788$	316.784	+	548.686i	0.402010	+	0.696302i
$789$		0			0
$790$	799.125	−	214.125i	1.01155	−	0.271044i
$791$		−	190.919i		−	0.241364i
$792$		0			0
$793$		−	873.000i		−	1.10088i
$794$	362.524	+	209.304i	0.456580	+	0.263607i
$795$		0			0
$796$	−147.000	−	254.611i	−0.184673	−	0.319864i
$797$	537.401	+	930.806i	0.674280	+	1.16789i	0.976679	+	0.214706i	$0.0688792\pi$
$797$	537.401	+	930.806i	0.674280	+	1.16789i	−0.302399	+	0.953181i	$0.597787\pi$
$798$		0			0
$799$	−128.000	+	221.703i	−0.160200	+	0.277475i
$800$		−	141.421i		−	0.176777i
$801$		0			0
$802$		−	550.000i		−	0.685786i
$803$	−12.0208	+	20.8207i	−0.0149699	+	0.0259286i
$804$		0			0
$805$	−34.1506	−	9.15064i	−0.0424231	−	0.0113672i
$806$	−440.908	+	254.558i	−0.547032	+	0.315829i
$807$		0			0
$808$	−221.703	−	128.000i	−0.274384	−	0.158416i
$809$			1255.82i			1.55231i	0.630540	+	0.776157i	$0.282833\pi$
$809$			1255.82i			1.55231i	−0.630540	+	0.776157i	$0.717167\pi$
$810$		0			0
$811$	−752.000			−0.927250			−0.463625	−	0.886031i	$-0.653452\pi$
$811$	−752.000			−0.927250			−0.463625	+	0.886031i	$0.653452\pi$
$812$	190.919	−	330.681i	0.235122	−	0.407243i
$813$		0			0
$814$	25.0000	+	43.3013i	0.0307125	+	0.0531957i
$815$	−980.415	−	262.701i	−1.20296	−	0.322333i
$816$		0			0
$817$	−1163.94	−	672.000i	−1.42465	−	0.822521i
$818$	−205.061			−0.250686
$819$		0			0
$820$	370.000	−	370.000i	0.451220	−	0.451220i
$821$	431.110	+	248.902i	0.525104	+	0.303169i	0.739020	−	0.673683i	$-0.235289\pi$
$821$	431.110	+	248.902i	0.525104	+	0.303169i	−0.213917	+	0.976852i	$0.568622\pi$
$822$		0			0
$823$	−459.859	+	265.500i	−0.558760	+	0.322600i	−0.752648	−	0.658423i	$-0.771224\pi$
$823$	−459.859	+	265.500i	−0.558760	+	0.322600i	0.193888	+	0.981024i	$0.437890\pi$
$824$	31.8434	−	18.3848i	0.0386449	−	0.0223116i
$825$		0			0
$826$	−320.000	+	554.256i	−0.387409	+	0.671012i
$827$	350.725			0.424093			0.212047	−	0.977260i	$-0.431987\pi$
$827$	350.725			0.424093			0.212047	+	0.977260i	$0.431987\pi$
$828$		0			0
$829$	−705.000			−0.850422			−0.425211	−	0.905094i	$-0.639800\pi$
$829$	−705.000			−0.850422			−0.425211	+	0.905094i	$0.639800\pi$
$830$	396.030	−	106.116i	0.477144	−	0.127850i
$831$		0			0
$832$	62.3538	−	36.0000i	0.0749445	−	0.0432692i
$833$	−135.765	−	235.151i	−0.162983	−	0.282294i
$834$		0			0
$835$	−491.769	+	131.769i	−0.588945	+	0.157807i
$836$			59.3970i			0.0710490i
$837$		0			0
$838$			992.000i			1.18377i
$839$	−1401.11	−	808.930i	−1.66997	−	0.964160i	−0.967648	−	0.252304i	$-0.918812\pi$
$839$	−1401.11	−	808.930i	−1.66997	−	0.964160i	−0.702326	−	0.711855i	$-0.747855\pi$
$840$		0			0
$841$	308.500	+	534.338i	0.366825	+	0.635360i
$842$	357.089	+	618.496i	0.424096	+	0.734556i
$843$		0			0
$844$	−141.000	+	244.219i	−0.167062	+	0.289359i
$845$	−311.127	−	311.127i	−0.368198	−	0.368198i
$846$		0			0
$847$			595.000i			0.702479i
$848$	−144.250	+	249.848i	−0.170106	+	0.294632i
$849$		0			0
$850$	−346.410	+	200.000i	−0.407541	+	0.235294i
$851$	−30.6186	+	17.6777i	−0.0359796	+	0.0207728i
$852$		0			0
$853$	1419.42	+	819.500i	1.66403	+	0.960727i	0.970762	+	0.240045i	$0.0771622\pi$
$853$	1419.42	+	819.500i	1.66403	+	0.960727i	0.693266	+	0.720682i	$0.256171\pi$
$854$			685.894i			0.803154i
$855$		0			0
$856$	348.000			0.406542
$857$	−494.268	+	856.097i	−0.576742	+	0.998946i	0.419108	+	0.907936i	$0.362343\pi$
$857$	−494.268	+	856.097i	−0.576742	+	0.998946i	−0.995850	+	0.0910097i	$0.970991\pi$
$858$		0			0
$859$	−177.500	−	307.439i	−0.206636	−	0.357903i	0.744017	−	0.668161i	$-0.232918\pi$
$859$	−177.500	−	307.439i	−0.206636	−	0.357903i	−0.950653	+	0.310257i	$0.899585\pi$
$860$	−618.193	−	165.644i	−0.718829	−	0.192610i
$861$		0			0
$862$	53.6936	+	31.0000i	0.0622895	+	0.0359629i
$863$	1459.47			1.69116			0.845578	−	0.533851i	$-0.179256\pi$
$863$	1459.47			1.69116			0.845578	+	0.533851i	$0.179256\pi$
$864$		0			0
$865$	−40.0000	−	40.0000i	−0.0462428	−	0.0462428i
$866$	−39.1918	−	22.6274i	−0.0452562	−	0.0261287i
$867$		0			0
$868$	346.410	−	200.000i	0.399090	−	0.230415i
$869$	−143.295	+	82.7315i	−0.164897	+	0.0952031i
$870$		0			0
$871$	−589.500	+	1021.04i	−0.676808	+	1.17227i
$872$	−22.6274			−0.0259489
$873$		0			0
$874$	−42.0000			−0.0480549
$875$	−603.704	+	161.762i	−0.689947	+	0.184871i
$876$		0			0
$877$	977.743	−	564.500i	1.11487	−	0.643672i	0.174785	−	0.984607i	$-0.444077\pi$
$877$	977.743	−	564.500i	1.11487	−	0.643672i	0.940087	+	0.340935i	$0.110744\pi$
$878$	−356.382	−	617.271i	−0.405902	−	0.703043i
$879$		0			0
$880$	7.32051	+	27.3205i	0.00831876	+	0.0310460i
$881$		−	165.463i		−	0.187813i	−0.995581	−	0.0939063i	$-0.970065\pi$
$881$		−	165.463i		−	0.187813i	0.995581	−	0.0939063i	$-0.0299354\pi$
$882$		0			0
$883$			1227.00i			1.38958i	0.719212	+	0.694790i	$0.244503\pi$
$883$			1227.00i			1.38958i	−0.719212	+	0.694790i	$0.755497\pi$
$884$	−176.363	−	101.823i	−0.199506	−	0.115185i
$885$		0			0
$886$	−168.000	−	290.985i	−0.189616	−	0.328425i
$887$	118.794	+	205.757i	0.133928	+	0.231970i	0.925187	−	0.379511i	$-0.123908\pi$
$887$	118.794	+	205.757i	0.133928	+	0.231970i	−0.791260	+	0.611480i	$0.790574\pi$
$888$		0			0
$889$	20.0000	−	34.6410i	0.0224972	−	0.0389663i
$890$	−735.391	+	735.391i	−0.826282	+	0.826282i
$891$		0			0
$892$		−	16.0000i		−	0.0179372i
$893$	−237.588	+	411.514i	−0.266056	+	0.460822i
$894$		0			0
$895$	607.881	+	162.881i	0.679197	+	0.181990i
$896$	−48.9898	+	28.2843i	−0.0546761	+	0.0315673i
$897$		0			0
$898$	−83.1384	−	48.0000i	−0.0925818	−	0.0534521i
$899$			1527.35i			1.69894i
$900$		0			0
$901$	816.000			0.905660
$902$	−52.3259	+	90.6311i	−0.0580110	+	0.100478i
$903$		0			0
$904$	−54.0000	−	93.5307i	−0.0597345	−	0.103463i
$905$	164.350	−	613.363i	0.181602	−	0.677749i
$906$		0			0
$907$	870.356	+	502.500i	0.959598	+	0.554024i	0.896049	−	0.443954i	$-0.146425\pi$
$907$	870.356	+	502.500i	0.959598	+	0.554024i	0.0635488	+	0.997979i	$0.479758\pi$
$908$	−138.593			−0.152635
$909$		0			0
$910$	−225.000	−	225.000i	−0.247253	−	0.247253i
$911$	676.059	+	390.323i	0.742107	+	0.428455i	0.822835	−	0.568281i	$-0.192391\pi$
$911$	676.059	+	390.323i	0.742107	+	0.428455i	−0.0807281	+	0.996736i	$0.525725\pi$
$912$		0			0
$913$	−71.0141	+	41.0000i	−0.0777810	+	0.0449069i
$914$	−921.008	+	531.744i	−1.00767	+	0.581777i
$915$		0			0
$916$	8.00000	−	13.8564i	0.00873362	−	0.0151271i
$917$	678.823			0.740264
$918$		0			0
$919$	600.000			0.652884			0.326442	−	0.945217i	$-0.394150\pi$
$919$	600.000			0.652884			0.326442	+	0.945217i	$0.394150\pi$
$920$	−19.3185	+	5.17638i	−0.0209984	+	0.00562650i
$921$		0			0
$922$	748.246	−	432.000i	0.811547	−	0.468547i
$923$	−400.930	−	694.430i	−0.434377	−	0.752362i
$924$		0			0
$925$	−312.500	+	541.266i	−0.337838	+	0.585152i
$926$		−	844.285i		−	0.911755i
$927$		0			0
$928$		−	216.000i		−	0.232759i
$929$	−1091.25	−	630.032i	−1.17465	−	0.678183i	−0.219877	−	0.975528i	$-0.570566\pi$
$929$	−1091.25	−	630.032i	−1.17465	−	0.678183i	−0.954770	+	0.297344i	$0.903899\pi$
$930$		0			0
$931$	−252.000	−	436.477i	−0.270677	−	0.468826i
$932$	−316.784	−	548.686i	−0.339897	−	0.588719i
$933$		0			0
$934$	−600.000	+	1039.23i	−0.642398	+	1.11267i
$935$	56.5685	−	56.5685i	0.0605011	−	0.0605011i
$936$		0			0
$937$			1465.00i			1.56350i	0.623592	+	0.781750i	$0.285673\pi$
$937$			1465.00i			1.56350i	−0.623592	+	0.781750i	$0.714327\pi$
$938$	463.155	−	802.208i	0.493769	−	0.855232i
$939$		0			0
$940$	−58.5641	+	218.564i	−0.0623022	+	0.232515i
$941$	221.679	−	127.986i	0.235578	−	0.136011i	−0.377565	−	0.925983i	$-0.623238\pi$
$941$	221.679	−	127.986i	0.235578	−	0.136011i	0.613143	+	0.789972i	$0.289905\pi$
$942$		0			0
$943$	−64.0859	−	37.0000i	−0.0679596	−	0.0392365i
$944$			362.039i			0.383516i
$945$		0			0
$946$	128.000			0.135307
$947$	203.647	−	352.727i	0.215044	−	0.372467i	−0.738242	−	0.674536i	$-0.764344\pi$
$947$	203.647	−	352.727i	0.215044	−	0.372467i	0.953286	+	0.302069i	$0.0976771\pi$
$948$		0			0
$949$	−76.5000	−	132.502i	−0.0806112	−	0.139623i
$950$	−642.991	+	371.231i	−0.676833	+	0.390770i
$951$		0			0
$952$	138.564	+	80.0000i	0.145550	+	0.0840336i
$953$	−497.803			−0.522354			−0.261177	−	0.965291i	$-0.584111\pi$
$953$	−497.803			−0.522354			−0.261177	+	0.965291i	$0.584111\pi$
$954$		0			0
$955$	−360.000	+	360.000i	−0.376963	+	0.376963i
$956$	355.176	+	205.061i	0.371523	+	0.214499i
$957$		0			0
$958$	−206.114	+	119.000i	−0.215150	+	0.124217i
$959$	1157.38	−	668.216i	1.20687	−	0.696784i
$960$		0			0
$961$	−319.500	+	553.390i	−0.332466	+	0.575848i
$962$	−318.198			−0.330767
$963$		0			0
$964$	158.000			0.163900
$965$	350.700	+	1308.83i	0.363419	+	1.35630i
$966$		0			0
$967$	−425.218	+	245.500i	−0.439730	+	0.253878i	−0.703483	−	0.710712i	$-0.748373\pi$
$967$	−425.218	+	245.500i	−0.439730	+	0.253878i	0.263753	+	0.964590i	$0.415039\pi$
$968$	168.291	+	291.489i	0.173855	+	0.301125i
$969$		0			0
$970$	75.0352	+	280.035i	0.0773559	+	0.288696i
$971$			509.117i			0.524322i	0.965024	+	0.262161i	$0.0844352\pi$
$971$			509.117i			0.524322i	−0.965024	+	0.262161i	$0.915565\pi$
$972$		0			0
$973$		−	185.000i		−	0.190134i
$974$	−620.946	−	358.503i	−0.637521	−	0.368073i
$975$		0			0
$976$	194.000	+	336.018i	0.198770	+	0.344281i
$977$	−235.467	−	407.840i	−0.241010	−	0.417441i	0.719992	−	0.693982i	$-0.244145\pi$
$977$	−235.467	−	407.840i	−0.241010	−	0.417441i	−0.961002	+	0.276541i	$0.910812\pi$
$978$		0			0
$979$	104.000	−	180.133i	0.106231	−	0.183997i
$980$	−169.706	−	169.706i	−0.173169	−	0.173169i
$981$		0			0
$982$			606.000i			0.617108i
$983$	−300.520	+	520.517i	−0.305718	+	0.529518i	−0.977421	−	0.211302i	$-0.932230\pi$
$983$	−300.520	+	520.517i	−0.305718	+	0.529518i	0.671703	+	0.740820i	$0.265563\pi$
$984$		0			0
$985$	409.948	−	1529.95i	0.416191	−	1.55325i
$986$	−529.090	+	305.470i	−0.536602	+	0.309807i
$987$		0			0
$988$	−327.358	−	189.000i	−0.331334	−	0.191296i
$989$			90.5097i			0.0915163i
$990$		0			0
$991$	−755.000			−0.761857			−0.380928	−	0.924605i	$-0.624396\pi$
$991$	−755.000			−0.761857			−0.380928	+	0.924605i	$0.624396\pi$
$992$	113.137	−	195.959i	0.114049	−	0.197539i
$993$		0			0
$994$	315.000	+	545.596i	0.316901	+	0.548889i
$995$	−190.232	+	709.955i	−0.191188	+	0.713523i
$996$		0			0
$997$	−20.7846	−	12.0000i	−0.0208472	−	0.0120361i	0.489540	−	0.871981i	$-0.337165\pi$
$997$	−20.7846	−	12.0000i	−0.0208472	−	0.0120361i	−0.510387	+	0.859945i	$0.670498\pi$
$998$	−1230.37			−1.23283
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.e.269.3		8
3.2	odd	2	inner	810.3.j.e.269.2		8
5.4	even	2	inner	810.3.j.e.269.1		8
9.2	odd	6		270.3.b.c.269.4	yes	4
9.4	even	3	inner	810.3.j.e.539.4		8
9.5	odd	6	inner	810.3.j.e.539.1		8
9.7	even	3		270.3.b.c.269.1	✓	4
15.14	odd	2	inner	810.3.j.e.269.4		8
36.7	odd	6		2160.3.c.i.1889.1		4
36.11	even	6		2160.3.c.i.1889.4		4
45.2	even	12		1350.3.d.f.701.2		2
45.4	even	6	inner	810.3.j.e.539.2		8
45.7	odd	12		1350.3.d.f.701.1		2
45.14	odd	6	inner	810.3.j.e.539.3		8
45.29	odd	6		270.3.b.c.269.2	yes	4
45.34	even	6		270.3.b.c.269.3	yes	4
45.38	even	12		1350.3.d.g.701.1		2
45.43	odd	12		1350.3.d.g.701.2		2
180.79	odd	6		2160.3.c.i.1889.3		4
180.119	even	6		2160.3.c.i.1889.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.c.269.1	✓	4	9.7	even	3
270.3.b.c.269.2	yes	4	45.29	odd	6
270.3.b.c.269.3	yes	4	45.34	even	6
270.3.b.c.269.4	yes	4	9.2	odd	6
810.3.j.e.269.1		8	5.4	even	2	inner
810.3.j.e.269.2		8	3.2	odd	2	inner
810.3.j.e.269.3		8	1.1	even	1	trivial
810.3.j.e.269.4		8	15.14	odd	2	inner
810.3.j.e.539.1		8	9.5	odd	6	inner
810.3.j.e.539.2		8	45.4	even	6	inner
810.3.j.e.539.3		8	45.14	odd	6	inner
810.3.j.e.539.4		8	9.4	even	3	inner
1350.3.d.f.701.1		2	45.7	odd	12
1350.3.d.f.701.2		2	45.2	even	12
1350.3.d.g.701.1		2	45.38	even	12
1350.3.d.g.701.2		2	45.43	odd	12
2160.3.c.i.1889.1		4	36.7	odd	6
2160.3.c.i.1889.2		4	180.119	even	6
2160.3.c.i.1889.3		4	180.79	odd	6
2160.3.c.i.1889.4		4	36.11	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.29410 + 4.82963i) q^{5} +(-4.33013 - 2.50000i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.29410 + 4.82963i) q^{5} +(-4.33013 - 2.50000i) q^{7} -2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(-1.22474 - 0.707107i) q^{11} +(7.79423 - 4.50000i) q^{13} +(-6.12372 + 3.53553i) q^{14} +(-2.00000 + 3.46410i) q^{16} +11.3137 q^{17} +21.0000 q^{19} +(9.65926 - 2.58819i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(-0.707107 - 1.22474i) q^{23} +(-21.6506 - 12.5000i) q^{25} -12.7279i q^{26} +10.0000i q^{28} +(-33.0681 - 19.0919i) q^{29} +(-20.0000 - 34.6410i) q^{31} +(2.82843 + 4.89898i) q^{32} +(8.00000 - 13.8564i) q^{34} +(17.6777 - 17.6777i) q^{35} -25.0000i q^{37} +(14.8492 - 25.7196i) q^{38} +(3.66025 - 13.6603i) q^{40} +(45.3156 - 26.1630i) q^{41} +(-55.4256 - 32.0000i) q^{43} +2.82843i q^{44} -2.00000 q^{46} +(-11.3137 + 19.5959i) q^{47} +(-12.0000 - 20.7846i) q^{49} +(-30.6186 + 17.6777i) q^{50} +(-15.5885 - 9.00000i) q^{52} +72.1249 q^{53} +(5.00000 - 5.00000i) q^{55} +(12.2474 + 7.07107i) q^{56} +(-46.7654 + 27.0000i) q^{58} +(78.3837 - 45.2548i) q^{59} +(48.5000 - 84.0045i) q^{61} -56.5685 q^{62} +8.00000 q^{64} +(11.6469 + 43.4667i) q^{65} +(-113.449 + 65.5000i) q^{67} +(-11.3137 - 19.5959i) q^{68} +(-9.15064 - 34.1506i) q^{70} -89.0955i q^{71} -17.0000i q^{73} +(-30.6186 - 17.6777i) q^{74} +(-21.0000 - 36.3731i) q^{76} +(3.53553 + 6.12372i) q^{77} +(58.5000 - 101.325i) q^{79} +(-14.1421 - 14.1421i) q^{80} -74.0000i q^{82} +(28.9914 - 50.2145i) q^{83} +(-14.6410 + 54.6410i) q^{85} +(-78.3837 + 45.2548i) q^{86} +(3.46410 + 2.00000i) q^{88} +147.078i q^{89} -45.0000 q^{91} +(-1.41421 + 2.44949i) q^{92} +(16.0000 + 27.7128i) q^{94} +(-27.1760 + 101.422i) q^{95} +(35.5070 + 20.5000i) q^{97} -33.9411 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} + 168 q^{19} - 160 q^{31} + 64 q^{34} - 40 q^{40} - 16 q^{46} - 96 q^{49} + 40 q^{55} + 388 q^{61} + 64 q^{64} + 100 q^{70} - 168 q^{76} + 468 q^{79} + 160 q^{85} - 360 q^{91} + 128 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 + 40 * q^10 - 16 * q^16 + 168 * q^19 - 160 * q^31 + 64 * q^34 - 40 * q^40 - 16 * q^46 - 96 * q^49 + 40 * q^55 + 388 * q^61 + 64 * q^64 + 100 * q^70 - 168 * q^76 + 468 * q^79 + 160 * q^85 - 360 * q^91 + 128 * q^94

Introduction

L-functions

Modular forms

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Database

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