LMFDB - Embedded newform 224.3.o.a.207.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			207.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	224.207
Dual form			224.3.o.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 6.92820i) q^{7} +(4.00000 + 6.92820i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 6.92820i) q^{7} +(4.00000 + 6.92820i) q^{9} +(8.50000 - 14.7224i) q^{11} -13.8564i q^{13} +5.19615i q^{15} +(12.5000 - 21.6506i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-5.50000 - 4.33013i) q^{21} +(-4.50000 + 2.59808i) q^{23} +(1.00000 - 1.73205i) q^{25} +17.0000 q^{27} +13.8564i q^{29} +(-28.5000 - 16.4545i) q^{31} +(-8.50000 - 14.7224i) q^{33} +(13.5000 + 33.7750i) q^{35} +(7.50000 - 4.33013i) q^{37} +(-12.0000 - 6.92820i) q^{39} +26.0000 q^{41} -14.0000 q^{43} +(-36.0000 - 20.7846i) q^{45} +(43.5000 - 25.1147i) q^{47} +(-47.0000 - 13.8564i) q^{49} +(-12.5000 - 21.6506i) q^{51} +(79.5000 + 45.8993i) q^{53} +88.3346i q^{55} -7.00000 q^{57} +(-27.5000 + 47.6314i) q^{59} +(19.5000 - 11.2583i) q^{61} +(52.0000 - 20.7846i) q^{63} +(36.0000 + 62.3538i) q^{65} +(8.50000 - 14.7224i) q^{67} +5.19615i q^{69} +(-59.5000 + 103.057i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-93.5000 - 73.6122i) q^{77} +(-64.5000 + 37.2391i) q^{79} +(-27.5000 + 47.6314i) q^{81} -110.000 q^{83} +129.904i q^{85} +(12.0000 + 6.92820i) q^{87} +(-35.5000 - 61.4878i) q^{89} +(-96.0000 - 13.8564i) q^{91} +(-28.5000 + 16.4545i) q^{93} +(31.5000 + 18.1865i) q^{95} -22.0000 q^{97} +136.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - 9 q^{5} + 2 q^{7} + 8 q^{9}+O(q^{10}) $ 2 * q + q^3 - 9 * q^5 + 2 * q^7 + 8 * q^9	$ 2 q + q^{3} - 9 q^{5} + 2 q^{7} + 8 q^{9} + 17 q^{11} + 25 q^{17} - 7 q^{19} - 11 q^{21} - 9 q^{23} + 2 q^{25} + 34 q^{27} - 57 q^{31} - 17 q^{33} + 27 q^{35} + 15 q^{37} - 24 q^{39} + 52 q^{41} - 28 q^{43} - 72 q^{45} + 87 q^{47} - 94 q^{49} - 25 q^{51} + 159 q^{53} - 14 q^{57} - 55 q^{59} + 39 q^{61} + 104 q^{63} + 72 q^{65} + 17 q^{67} - 119 q^{73} - 2 q^{75} - 187 q^{77} - 129 q^{79} - 55 q^{81} - 220 q^{83} + 24 q^{87} - 71 q^{89} - 192 q^{91} - 57 q^{93} + 63 q^{95} - 44 q^{97} + 272 q^{99}+O(q^{100}) $ 2 * q + q^3 - 9 * q^5 + 2 * q^7 + 8 * q^9 + 17 * q^11 + 25 * q^17 - 7 * q^19 - 11 * q^21 - 9 * q^23 + 2 * q^25 + 34 * q^27 - 57 * q^31 - 17 * q^33 + 27 * q^35 + 15 * q^37 - 24 * q^39 + 52 * q^41 - 28 * q^43 - 72 * q^45 + 87 * q^47 - 94 * q^49 - 25 * q^51 + 159 * q^53 - 14 * q^57 - 55 * q^59 + 39 * q^61 + 104 * q^63 + 72 * q^65 + 17 * q^67 - 119 * q^73 - 2 * q^75 - 187 * q^77 - 129 * q^79 - 55 * q^81 - 220 * q^83 + 24 * q^87 - 71 * q^89 - 192 * q^91 - 57 * q^93 + 63 * q^95 - 44 * q^97 + 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.166667	−	0.288675i	−0.770579	−	0.637344i	$-0.780033\pi$
$3$	0.500000	−	0.866025i	0.166667	−	0.288675i	0.937246	+	0.348669i	$0.113366\pi$
$4$		0			0
$5$	−4.50000	+	2.59808i	−0.900000	+	0.519615i	−0.877200	−	0.480125i	$-0.840591\pi$
$5$	−4.50000	+	2.59808i	−0.900000	+	0.519615i	−0.0227998	+	0.999740i	$0.507258\pi$
$6$		0			0
$7$	1.00000	−	6.92820i	0.142857	−	0.989743i
$7$	1.00000	−	6.92820i	0.142857	−	0.989743i
$8$		0			0
$9$	4.00000	+	6.92820i	0.444444	+	0.769800i
$10$		0			0
$11$	8.50000	−	14.7224i	0.772727	−	1.33840i	−0.163336	−	0.986571i	$-0.552225\pi$
$11$	8.50000	−	14.7224i	0.772727	−	1.33840i	0.936063	−	0.351832i	$-0.114441\pi$
$12$		0			0
$13$		−	13.8564i		−	1.06588i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$		−	13.8564i		−	1.06588i	0.846154	−	0.532939i	$-0.178912\pi$
$14$		0			0
$15$			5.19615i			0.346410i
$16$		0			0
$17$	12.5000	−	21.6506i	0.735294	−	1.27357i	−0.219300	−	0.975657i	$-0.570377\pi$
$17$	12.5000	−	21.6506i	0.735294	−	1.27357i	0.954594	−	0.297909i	$-0.0962893\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.184211	−	0.319062i	0.759100	−	0.650974i	$-0.225639\pi$
$19$	−3.50000	−	6.06218i	−0.184211	−	0.319062i	−0.943310	+	0.331912i	$0.892306\pi$
$20$		0			0
$21$	−5.50000	−	4.33013i	−0.261905	−	0.206197i
$22$		0			0
$23$	−4.50000	+	2.59808i	−0.195652	+	0.112960i	−0.594626	−	0.804003i	$-0.702700\pi$
$23$	−4.50000	+	2.59808i	−0.195652	+	0.112960i	0.398974	+	0.916962i	$0.369366\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.0400000	−	0.0692820i
$26$		0			0
$27$	17.0000			0.629630
$28$		0			0
$29$			13.8564i			0.477807i	0.971043	+	0.238904i	$0.0767880\pi$
$29$			13.8564i			0.477807i	−0.971043	+	0.238904i	$0.923212\pi$
$30$		0			0
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.0359257	−	0.999354i	$-0.511438\pi$
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.883429	+	0.468565i	$0.844771\pi$
$32$		0			0
$33$	−8.50000	−	14.7224i	−0.257576	−	0.446134i
$34$		0			0
$35$	13.5000	+	33.7750i	0.385714	+	0.965000i
$36$		0			0
$37$	7.50000	−	4.33013i	0.202703	−	0.117030i	−0.395213	−	0.918590i	$-0.629329\pi$
$37$	7.50000	−	4.33013i	0.202703	−	0.117030i	0.597916	+	0.801559i	$0.295996\pi$
$38$		0			0
$39$	−12.0000	−	6.92820i	−0.307692	−	0.177646i
$40$		0			0
$41$	26.0000			0.634146			0.317073	−	0.948401i	$-0.397300\pi$
$41$	26.0000			0.634146			0.317073	+	0.948401i	$0.397300\pi$
$42$		0			0
$43$	−14.0000			−0.325581			−0.162791	−	0.986661i	$-0.552050\pi$
$43$	−14.0000			−0.325581			−0.162791	+	0.986661i	$0.552050\pi$
$44$		0			0
$45$	−36.0000	−	20.7846i	−0.800000	−	0.461880i
$46$		0			0
$47$	43.5000	−	25.1147i	0.925532	−	0.534356i	0.0401362	−	0.999194i	$-0.487221\pi$
$47$	43.5000	−	25.1147i	0.925532	−	0.534356i	0.885396	+	0.464838i	$0.153887\pi$
$48$		0			0
$49$	−47.0000	−	13.8564i	−0.959184	−	0.282784i
$50$		0			0
$51$	−12.5000	−	21.6506i	−0.245098	−	0.424522i
$52$		0			0
$53$	79.5000	+	45.8993i	1.50000	+	0.866025i	1.00000			$0$
$53$	79.5000	+	45.8993i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$			88.3346i			1.60608i
$56$		0			0
$57$	−7.00000			−0.122807
$58$		0			0
$59$	−27.5000	+	47.6314i	−0.466102	+	0.807312i	−0.999250	−	0.0387097i	$-0.987675\pi$
$59$	−27.5000	+	47.6314i	−0.466102	+	0.807312i	0.533149	+	0.846021i	$0.321009\pi$
$60$		0			0
$61$	19.5000	−	11.2583i	0.319672	−	0.184563i	−0.331574	−	0.943429i	$-0.607580\pi$
$61$	19.5000	−	11.2583i	0.319672	−	0.184563i	0.651246	+	0.758866i	$0.274246\pi$
$62$		0			0
$63$	52.0000	−	20.7846i	0.825397	−	0.329914i
$64$		0			0
$65$	36.0000	+	62.3538i	0.553846	+	0.959290i
$66$		0			0
$67$	8.50000	−	14.7224i	0.126866	−	0.219738i	−0.795595	−	0.605829i	$-0.792842\pi$
$67$	8.50000	−	14.7224i	0.126866	−	0.219738i	0.922461	+	0.386091i	$0.126175\pi$
$68$		0			0
$69$			5.19615i			0.0753066i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−59.5000	+	103.057i	−0.815068	+	1.41174i	0.0942102	+	0.995552i	$0.469967\pi$
$73$	−59.5000	+	103.057i	−0.815068	+	1.41174i	−0.909279	+	0.416188i	$0.863366\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.0133333	−	0.0230940i
$76$		0			0
$77$	−93.5000	−	73.6122i	−1.21429	−	0.956002i
$78$		0			0
$79$	−64.5000	+	37.2391i	−0.816456	+	0.471381i	−0.849193	−	0.528083i	$-0.822911\pi$
$79$	−64.5000	+	37.2391i	−0.816456	+	0.471381i	0.0327370	+	0.999464i	$0.489578\pi$
$80$		0			0
$81$	−27.5000	+	47.6314i	−0.339506	+	0.588042i
$82$		0			0
$83$	−110.000			−1.32530			−0.662651	−	0.748929i	$-0.730569\pi$
$83$	−110.000			−1.32530			−0.662651	+	0.748929i	$0.730569\pi$
$84$		0			0
$85$			129.904i			1.52828i
$86$		0			0
$87$	12.0000	+	6.92820i	0.137931	+	0.0796345i
$88$		0			0
$89$	−35.5000	−	61.4878i	−0.398876	−	0.690874i	0.594711	−	0.803939i	$-0.297266\pi$
$89$	−35.5000	−	61.4878i	−0.398876	−	0.690874i	−0.993588	+	0.113065i	$0.963933\pi$
$90$		0			0
$91$	−96.0000	−	13.8564i	−1.05495	−	0.152268i
$92$		0			0
$93$	−28.5000	+	16.4545i	−0.306452	+	0.176930i
$94$		0			0
$95$	31.5000	+	18.1865i	0.331579	+	0.191437i
$96$		0			0
$97$	−22.0000			−0.226804			−0.113402	−	0.993549i	$-0.536175\pi$
$97$	−22.0000			−0.226804			−0.113402	+	0.993549i	$0.536175\pi$
$98$		0			0
$99$	136.000			1.37374
$100$		0			0
$101$	67.5000	+	38.9711i	0.668317	+	0.385853i	0.795439	−	0.606034i	$-0.207241\pi$
$101$	67.5000	+	38.9711i	0.668317	+	0.385853i	−0.127122	+	0.991887i	$0.540574\pi$
$102$		0			0
$103$	139.500	−	80.5404i	1.35437	−	0.781945i	0.365511	−	0.930807i	$-0.380894\pi$
$103$	139.500	−	80.5404i	1.35437	−	0.781945i	0.988858	+	0.148862i	$0.0475610\pi$
$104$		0			0
$105$	36.0000	+	5.19615i	0.342857	+	0.0494872i
$106$		0			0
$107$	32.5000	+	56.2917i	0.303738	+	0.526090i	0.976980	−	0.213333i	$-0.0684318\pi$
$107$	32.5000	+	56.2917i	0.303738	+	0.526090i	−0.673241	+	0.739423i	$0.735098\pi$
$108$		0			0
$109$	7.50000	+	4.33013i	0.0688073	+	0.0397259i	0.534009	−	0.845479i	$-0.320685\pi$
$109$	7.50000	+	4.33013i	0.0688073	+	0.0397259i	−0.465202	+	0.885205i	$0.654018\pi$
$110$		0			0
$111$		−	8.66025i		−	0.0780203i
$112$		0			0
$113$	122.000			1.07965			0.539823	−	0.841779i	$-0.318491\pi$
$113$	122.000			1.07965			0.539823	+	0.841779i	$0.318491\pi$
$114$		0			0
$115$	13.5000	−	23.3827i	0.117391	−	0.203328i
$116$		0			0
$117$	96.0000	−	55.4256i	0.820513	−	0.473723i
$118$		0			0
$119$	−137.500	−	108.253i	−1.15546	−	0.909691i
$120$		0			0
$121$	−84.0000	−	145.492i	−0.694215	−	1.20242i
$122$		0			0
$123$	13.0000	−	22.5167i	0.105691	−	0.183062i
$124$		0			0
$125$		−	119.512i		−	0.956092i
$126$		0			0
$127$			166.277i			1.30927i	0.755947	+	0.654633i	$0.227177\pi$
$127$			166.277i			1.30927i	−0.755947	+	0.654633i	$0.772823\pi$
$128$		0			0
$129$	−7.00000	+	12.1244i	−0.0542636	+	0.0939873i
$130$		0			0
$131$	8.50000	+	14.7224i	0.0648855	+	0.112385i	0.896643	−	0.442754i	$-0.145998\pi$
$131$	8.50000	+	14.7224i	0.0648855	+	0.112385i	−0.831758	+	0.555139i	$0.812665\pi$
$132$		0			0
$133$	−45.5000	+	18.1865i	−0.342105	+	0.136741i
$134$		0			0
$135$	−76.5000	+	44.1673i	−0.566667	+	0.327165i
$136$		0			0
$137$	72.5000	−	125.574i	0.529197	−	0.916596i	−0.470223	−	0.882548i	$-0.655827\pi$
$137$	72.5000	−	125.574i	0.529197	−	0.916596i	0.999420	−	0.0340486i	$-0.0108401\pi$
$138$		0			0
$139$	82.0000			0.589928			0.294964	−	0.955508i	$-0.404692\pi$
$139$	82.0000			0.589928			0.294964	+	0.955508i	$0.404692\pi$
$140$		0			0
$141$		−	50.2295i		−	0.356237i
$142$		0			0
$143$	−204.000	−	117.779i	−1.42657	−	0.823633i
$144$		0			0
$145$	−36.0000	−	62.3538i	−0.248276	−	0.430026i
$146$		0			0
$147$	−35.5000	+	33.7750i	−0.241497	+	0.229762i
$148$		0			0
$149$	−4.50000	+	2.59808i	−0.0302013	+	0.0174368i	−0.515025	−	0.857175i	$-0.672217\pi$
$149$	−4.50000	+	2.59808i	−0.0302013	+	0.0174368i	0.484823	+	0.874612i	$0.338884\pi$
$150$		0			0
$151$	31.5000	+	18.1865i	0.208609	+	0.120441i	0.600665	−	0.799501i	$-0.294903\pi$
$151$	31.5000	+	18.1865i	0.208609	+	0.120441i	−0.392056	+	0.919942i	$0.628236\pi$
$152$		0			0
$153$	200.000			1.30719
$154$		0			0
$155$	171.000			1.10323
$156$		0			0
$157$	−268.500	−	155.019i	−1.71019	−	0.987379i	−0.934282	−	0.356534i	$-0.883958\pi$
$157$	−268.500	−	155.019i	−1.71019	−	0.987379i	−0.775909	−	0.630845i	$-0.782708\pi$
$158$		0			0
$159$	79.5000	−	45.8993i	0.500000	−	0.288675i
$160$		0			0
$161$	13.5000	+	33.7750i	0.0838509	+	0.209783i
$162$		0			0
$163$	8.50000	+	14.7224i	0.0521472	+	0.0903217i	0.890921	−	0.454159i	$-0.150060\pi$
$163$	8.50000	+	14.7224i	0.0521472	+	0.0903217i	−0.838773	+	0.544481i	$0.816727\pi$
$164$		0			0
$165$	76.5000	+	44.1673i	0.463636	+	0.267681i
$166$		0			0
$167$			13.8564i			0.0829725i	0.999139	+	0.0414862i	$0.0132093\pi$
$167$			13.8564i			0.0829725i	−0.999139	+	0.0414862i	$0.986791\pi$
$168$		0			0
$169$	−23.0000			−0.136095
$170$		0			0
$171$	28.0000	−	48.4974i	0.163743	−	0.283611i
$172$		0			0
$173$	91.5000	−	52.8275i	0.528902	−	0.305362i	−0.211667	−	0.977342i	$-0.567889\pi$
$173$	91.5000	−	52.8275i	0.528902	−	0.305362i	0.740569	+	0.671980i	$0.234556\pi$
$174$		0			0
$175$	−11.0000	−	8.66025i	−0.0628571	−	0.0494872i
$176$		0			0
$177$	27.5000	+	47.6314i	0.155367	+	0.269104i
$178$		0			0
$179$	44.5000	−	77.0763i	0.248603	−	0.430594i	−0.714535	−	0.699600i	$-0.753362\pi$
$179$	44.5000	−	77.0763i	0.248603	−	0.430594i	0.963139	+	0.269006i	$0.0866951\pi$
$180$		0			0
$181$			249.415i			1.37799i	0.724768	+	0.688993i	$0.241947\pi$
$181$			249.415i			1.37799i	−0.724768	+	0.688993i	$0.758053\pi$
$182$		0			0
$183$		−	22.5167i		−	0.123042i
$184$		0			0
$185$	−22.5000	+	38.9711i	−0.121622	+	0.210655i
$186$		0			0
$187$	−212.500	−	368.061i	−1.13636	−	1.96824i
$188$		0			0
$189$	17.0000	−	117.779i	0.0899471	−	0.623172i
$190$		0			0
$191$	187.500	−	108.253i	0.981675	−	0.566771i	0.0788999	−	0.996883i	$-0.474859\pi$
$191$	187.500	−	108.253i	0.981675	−	0.566771i	0.902776	+	0.430112i	$0.141526\pi$
$192$		0			0
$193$	36.5000	−	63.2199i	0.189119	−	0.327564i	−0.755838	−	0.654759i	$-0.772770\pi$
$193$	36.5000	−	63.2199i	0.189119	−	0.327564i	0.944957	+	0.327195i	$0.106103\pi$
$194$		0			0
$195$	72.0000			0.369231
$196$		0			0
$197$			207.846i			1.05506i	0.849538	+	0.527528i	$0.176881\pi$
$197$			207.846i			1.05506i	−0.849538	+	0.527528i	$0.823119\pi$
$198$		0			0
$199$	55.5000	+	32.0429i	0.278894	+	0.161020i	0.632923	−	0.774215i	$-0.281855\pi$
$199$	55.5000	+	32.0429i	0.278894	+	0.161020i	−0.354028	+	0.935235i	$0.615188\pi$
$200$		0			0
$201$	−8.50000	−	14.7224i	−0.0422886	−	0.0732459i
$202$		0			0
$203$	96.0000	+	13.8564i	0.472906	+	0.0682582i
$204$		0			0
$205$	−117.000	+	67.5500i	−0.570732	+	0.329512i
$206$		0			0
$207$	−36.0000	−	20.7846i	−0.173913	−	0.100409i
$208$		0			0
$209$	−119.000			−0.569378
$210$		0			0
$211$	−302.000			−1.43128			−0.715640	−	0.698470i	$-0.753865\pi$
$211$	−302.000			−1.43128			−0.715640	+	0.698470i	$0.753865\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	63.0000	−	36.3731i	0.293023	−	0.169177i
$216$		0			0
$217$	−142.500	+	180.999i	−0.656682	+	0.834098i
$218$		0			0
$219$	59.5000	+	103.057i	0.271689	+	0.470580i
$220$		0			0
$221$	−300.000	−	173.205i	−1.35747	−	0.783733i
$222$		0			0
$223$		−	138.564i		−	0.621364i	−0.950514	−	0.310682i	$-0.899443\pi$
$223$		−	138.564i		−	0.621364i	0.950514	−	0.310682i	$-0.100557\pi$
$224$		0			0
$225$	16.0000			0.0711111
$226$		0			0
$227$	−27.5000	+	47.6314i	−0.121145	+	0.209830i	−0.920220	−	0.391402i	$-0.871990\pi$
$227$	−27.5000	+	47.6314i	−0.121145	+	0.209830i	0.799074	+	0.601232i	$0.205323\pi$
$228$		0			0
$229$	283.500	−	163.679i	1.23799	−	0.714755i	0.269308	−	0.963054i	$-0.413205\pi$
$229$	283.500	−	163.679i	1.23799	−	0.714755i	0.968683	+	0.248300i	$0.0798717\pi$
$230$		0			0
$231$	−110.500	+	44.1673i	−0.478355	+	0.191200i
$232$		0			0
$233$	192.500	+	333.420i	0.826180	+	1.43099i	0.901014	+	0.433790i	$0.142824\pi$
$233$	192.500	+	333.420i	0.826180	+	1.43099i	−0.0748337	+	0.997196i	$0.523843\pi$
$234$		0			0
$235$	−130.500	+	226.033i	−0.555319	+	0.961841i
$236$		0			0
$237$			74.4782i			0.314254i
$238$		0			0
$239$			429.549i			1.79727i	0.438693	+	0.898637i	$0.355442\pi$
$239$			429.549i			1.79727i	−0.438693	+	0.898637i	$0.644558\pi$
$240$		0			0
$241$	72.5000	−	125.574i	0.300830	−	0.521053i	−0.675494	−	0.737365i	$-0.736070\pi$
$241$	72.5000	−	125.574i	0.300830	−	0.521053i	0.976324	+	0.216313i	$0.0694030\pi$
$242$		0			0
$243$	104.000	+	180.133i	0.427984	+	0.741289i
$244$		0			0
$245$	247.500	−	59.7558i	1.01020	−	0.243901i
$246$		0			0
$247$	−84.0000	+	48.4974i	−0.340081	+	0.196346i
$248$		0			0
$249$	−55.0000	+	95.2628i	−0.220884	+	0.382582i
$250$		0			0
$251$	58.0000			0.231076			0.115538	−	0.993303i	$-0.463141\pi$
$251$	58.0000			0.231076			0.115538	+	0.993303i	$0.463141\pi$
$252$		0			0
$253$			88.3346i			0.349149i
$254$		0			0
$255$	112.500	+	64.9519i	0.441176	+	0.254713i
$256$		0			0
$257$	−59.5000	−	103.057i	−0.231518	−	0.401000i	0.726737	−	0.686915i	$-0.241036\pi$
$257$	−59.5000	−	103.057i	−0.231518	−	0.401000i	−0.958255	+	0.285915i	$0.907702\pi$
$258$		0			0
$259$	−22.5000	−	56.2917i	−0.0868726	−	0.217342i
$260$		0			0
$261$	−96.0000	+	55.4256i	−0.367816	+	0.212359i
$262$		0			0
$263$	283.500	+	163.679i	1.07795	+	0.622353i	0.930342	−	0.366694i	$-0.119510\pi$
$263$	283.500	+	163.679i	1.07795	+	0.622353i	0.147605	+	0.989046i	$0.452844\pi$
$264$		0			0
$265$	−477.000			−1.80000
$266$		0			0
$267$	−71.0000			−0.265918
$268$		0			0
$269$	115.500	+	66.6840i	0.429368	+	0.247896i	0.699077	−	0.715046i	$-0.253594\pi$
$269$	115.500	+	66.6840i	0.429368	+	0.247896i	−0.269709	+	0.962942i	$0.586928\pi$
$270$		0			0
$271$	−376.500	+	217.372i	−1.38930	+	0.802112i	−0.993236	−	0.116111i	$-0.962957\pi$
$271$	−376.500	+	217.372i	−1.38930	+	0.802112i	−0.396063	+	0.918223i	$0.629624\pi$
$272$		0			0
$273$	−60.0000	+	76.2102i	−0.219780	+	0.279158i
$274$		0			0
$275$	−17.0000	−	29.4449i	−0.0618182	−	0.107072i
$276$		0			0
$277$	175.500	+	101.325i	0.633574	+	0.365794i	0.782135	−	0.623109i	$-0.214131\pi$
$277$	175.500	+	101.325i	0.633574	+	0.365794i	−0.148561	+	0.988903i	$0.547464\pi$
$278$		0			0
$279$		−	263.272i		−	0.943626i
$280$		0			0
$281$	74.0000			0.263345			0.131673	−	0.991293i	$-0.457965\pi$
$281$	74.0000			0.263345			0.131673	+	0.991293i	$0.457965\pi$
$282$		0			0
$283$	−231.500	+	400.970i	−0.818021	+	1.41685i	0.0891169	+	0.996021i	$0.471596\pi$
$283$	−231.500	+	400.970i	−0.818021	+	1.41685i	−0.907138	+	0.420833i	$0.861738\pi$
$284$		0			0
$285$	31.5000	−	18.1865i	0.110526	−	0.0638124i
$286$		0			0
$287$	26.0000	−	180.133i	0.0905923	−	0.627642i
$288$		0			0
$289$	−168.000	−	290.985i	−0.581315	−	1.00687i
$290$		0			0
$291$	−11.0000	+	19.0526i	−0.0378007	+	0.0654727i
$292$		0			0
$293$			110.851i			0.378332i	0.981945	+	0.189166i	$0.0605784\pi$
$293$			110.851i			0.378332i	−0.981945	+	0.189166i	$0.939422\pi$
$294$		0			0
$295$		−	285.788i		−	0.968774i
$296$		0			0
$297$	144.500	−	250.281i	0.486532	−	0.842698i
$298$		0			0
$299$	36.0000	+	62.3538i	0.120401	+	0.208541i
$300$		0			0
$301$	−14.0000	+	96.9948i	−0.0465116	+	0.322242i
$302$		0			0
$303$	67.5000	−	38.9711i	0.222772	−	0.128618i
$304$		0			0
$305$	−58.5000	+	101.325i	−0.191803	+	0.332213i
$306$		0			0
$307$	274.000			0.892508			0.446254	−	0.894906i	$-0.352758\pi$
$307$	274.000			0.892508			0.446254	+	0.894906i	$0.352758\pi$
$308$		0			0
$309$		−	161.081i		−	0.521297i
$310$		0			0
$311$	43.5000	+	25.1147i	0.139871	+	0.0807548i	0.568303	−	0.822820i	$-0.307600\pi$
$311$	43.5000	+	25.1147i	0.139871	+	0.0807548i	−0.428431	+	0.903574i	$0.640934\pi$
$312$		0			0
$313$	204.500	+	354.204i	0.653355	+	1.13164i	0.982304	+	0.187296i	$0.0599723\pi$
$313$	204.500	+	354.204i	0.653355	+	1.13164i	−0.328949	+	0.944348i	$0.606694\pi$
$314$		0			0
$315$	−180.000	+	228.631i	−0.571429	+	0.725812i
$316$		0			0
$317$	163.500	−	94.3968i	0.515773	−	0.297782i	−0.219431	−	0.975628i	$-0.570420\pi$
$317$	163.500	−	94.3968i	0.515773	−	0.297782i	0.735203	+	0.677847i	$0.237087\pi$
$318$		0			0
$319$	204.000	+	117.779i	0.639498	+	0.369215i
$320$		0			0
$321$	65.0000			0.202492
$322$		0			0
$323$	−175.000			−0.541796
$324$		0			0
$325$	−24.0000	−	13.8564i	−0.0738462	−	0.0426351i
$326$		0			0
$327$	7.50000	−	4.33013i	0.0229358	−	0.0132420i
$328$		0			0
$329$	−130.500	−	326.492i	−0.396657	−	0.992376i
$330$		0			0
$331$	−147.500	−	255.477i	−0.445619	−	0.771835i	0.552476	−	0.833529i	$-0.313683\pi$
$331$	−147.500	−	255.477i	−0.445619	−	0.771835i	−0.998095	+	0.0616936i	$0.980350\pi$
$332$		0			0
$333$	60.0000	+	34.6410i	0.180180	+	0.104027i
$334$		0			0
$335$			88.3346i			0.263685i
$336$		0			0
$337$	26.0000			0.0771513			0.0385757	−	0.999256i	$-0.487718\pi$
$337$	26.0000			0.0771513			0.0385757	+	0.999256i	$0.487718\pi$
$338$		0			0
$339$	61.0000	−	105.655i	0.179941	−	0.311667i
$340$		0			0
$341$	−484.500	+	279.726i	−1.42082	+	0.820311i
$342$		0			0
$343$	−143.000	+	311.769i	−0.416910	+	0.908948i
$344$		0			0
$345$	−13.5000	−	23.3827i	−0.0391304	−	0.0677759i
$346$		0			0
$347$	188.500	−	326.492i	0.543228	−	0.940898i	−0.455488	−	0.890242i	$-0.650535\pi$
$347$	188.500	−	326.492i	0.543228	−	0.940898i	0.998716	−	0.0506562i	$-0.0161313\pi$
$348$		0			0
$349$			96.9948i			0.277922i	0.990298	+	0.138961i	$0.0443763\pi$
$349$			96.9948i			0.277922i	−0.990298	+	0.138961i	$0.955624\pi$
$350$		0			0
$351$		−	235.559i		−	0.671108i
$352$		0			0
$353$	−251.500	+	435.611i	−0.712465	+	1.23402i	0.251465	+	0.967866i	$0.419088\pi$
$353$	−251.500	+	435.611i	−0.712465	+	1.23402i	−0.963929	+	0.266158i	$0.914246\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−162.500	+	64.9519i	−0.455182	+	0.181938i
$358$		0			0
$359$	−160.500	+	92.6647i	−0.447075	+	0.258119i	−0.706594	−	0.707619i	$-0.749769\pi$
$359$	−160.500	+	92.6647i	−0.447075	+	0.258119i	0.259519	+	0.965738i	$0.416436\pi$
$360$		0			0
$361$	156.000	−	270.200i	0.432133	−	0.748476i
$362$		0			0
$363$	−168.000			−0.462810
$364$		0			0
$365$		−	618.342i		−	1.69409i
$366$		0			0
$367$	−256.500	−	148.090i	−0.698910	−	0.403516i	0.108031	−	0.994147i	$-0.465545\pi$
$367$	−256.500	−	148.090i	−0.698910	−	0.403516i	−0.806941	+	0.590632i	$0.798879\pi$
$368$		0			0
$369$	104.000	+	180.133i	0.281843	+	0.488166i
$370$		0			0
$371$	397.500	−	504.893i	1.07143	−	1.36090i
$372$		0			0
$373$	103.500	−	59.7558i	0.277480	−	0.160203i	−0.354802	−	0.934941i	$-0.615452\pi$
$373$	103.500	−	59.7558i	0.277480	−	0.160203i	0.632282	+	0.774738i	$0.282118\pi$
$374$		0			0
$375$	−103.500	−	59.7558i	−0.276000	−	0.159349i
$376$		0			0
$377$	192.000			0.509284
$378$		0			0
$379$	634.000			1.67282			0.836412	−	0.548102i	$-0.184649\pi$
$379$	634.000			1.67282			0.836412	+	0.548102i	$0.184649\pi$
$380$		0			0
$381$	144.000	+	83.1384i	0.377953	+	0.218211i
$382$		0			0
$383$	211.500	−	122.110i	0.552219	−	0.318824i	−0.197797	−	0.980243i	$-0.563379\pi$
$383$	211.500	−	122.110i	0.552219	−	0.318824i	0.750017	+	0.661419i	$0.230045\pi$
$384$		0			0
$385$	612.000	+	88.3346i	1.58961	+	0.229440i
$386$		0			0
$387$	−56.0000	−	96.9948i	−0.144703	−	0.250633i
$388$		0			0
$389$	−508.500	−	293.583i	−1.30720	−	0.754711i	−0.325570	−	0.945518i	$-0.605556\pi$
$389$	−508.500	−	293.583i	−1.30720	−	0.754711i	−0.981628	+	0.190807i	$0.938890\pi$
$390$		0			0
$391$			129.904i			0.332235i
$392$		0			0
$393$	17.0000			0.0432570
$394$		0			0
$395$	193.500	−	335.152i	0.489873	−	0.848486i
$396$		0			0
$397$	−208.500	+	120.378i	−0.525189	+	0.303218i	−0.739055	−	0.673645i	$-0.764728\pi$
$397$	−208.500	+	120.378i	−0.525189	+	0.303218i	0.213866	+	0.976863i	$0.431394\pi$
$398$		0			0
$399$	−7.00000	+	48.4974i	−0.0175439	+	0.121547i
$400$		0			0
$401$	−59.5000	−	103.057i	−0.148379	−	0.257000i	0.782249	−	0.622965i	$-0.214072\pi$
$401$	−59.5000	−	103.057i	−0.148379	−	0.257000i	−0.930629	+	0.365965i	$0.880739\pi$
$402$		0			0
$403$	−228.000	+	394.908i	−0.565757	+	0.979920i
$404$		0			0
$405$		−	285.788i		−	0.705650i
$406$		0			0
$407$		−	147.224i		−	0.361731i
$408$		0			0
$409$	72.5000	−	125.574i	0.177262	−	0.307026i	−0.763680	−	0.645595i	$-0.776609\pi$
$409$	72.5000	−	125.574i	0.177262	−	0.307026i	0.940942	+	0.338569i	$0.109943\pi$
$410$		0			0
$411$	−72.5000	−	125.574i	−0.176399	−	0.305532i
$412$		0			0
$413$	302.500	+	238.157i	0.732446	+	0.576651i
$414$		0			0
$415$	495.000	−	285.788i	1.19277	−	0.688647i
$416$		0			0
$417$	41.0000	−	71.0141i	0.0983213	−	0.170298i
$418$		0			0
$419$	−302.000			−0.720764			−0.360382	−	0.932805i	$-0.617354\pi$
$419$	−302.000			−0.720764			−0.360382	+	0.932805i	$0.617354\pi$
$420$		0			0
$421$		−	401.836i		−	0.954479i	−0.878773	−	0.477240i	$-0.841637\pi$
$421$		−	401.836i		−	0.954479i	0.878773	−	0.477240i	$-0.158363\pi$
$422$		0			0
$423$	348.000	+	200.918i	0.822695	+	0.474983i
$424$		0			0
$425$	−25.0000	−	43.3013i	−0.0588235	−	0.101885i
$426$		0			0
$427$	−58.5000	−	146.358i	−0.137002	−	0.342759i
$428$		0			0
$429$	−204.000	+	117.779i	−0.475524	+	0.274544i
$430$		0			0
$431$	−700.500	−	404.434i	−1.62529	−	0.938362i	−0.985473	−	0.169835i	$-0.945677\pi$
$431$	−700.500	−	404.434i	−1.62529	−	0.938362i	−0.639817	−	0.768527i	$-0.720990\pi$
$432$		0			0
$433$	410.000			0.946882			0.473441	−	0.880825i	$-0.343012\pi$
$433$	410.000			0.946882			0.473441	+	0.880825i	$0.343012\pi$
$434$		0			0
$435$	−72.0000			−0.165517
$436$		0			0
$437$	31.5000	+	18.1865i	0.0720824	+	0.0416168i
$438$		0			0
$439$	−424.500	+	245.085i	−0.966970	+	0.558281i	−0.898311	−	0.439360i	$-0.855205\pi$
$439$	−424.500	+	245.085i	−0.966970	+	0.558281i	−0.0686591	+	0.997640i	$0.521872\pi$
$440$		0			0
$441$	−92.0000	−	381.051i	−0.208617	−	0.864062i
$442$		0			0
$443$	200.500	+	347.276i	0.452596	+	0.783919i	0.998546	−	0.0538983i	$-0.0171647\pi$
$443$	200.500	+	347.276i	0.452596	+	0.783919i	−0.545950	+	0.837817i	$0.683831\pi$
$444$		0			0
$445$	319.500	+	184.463i	0.717978	+	0.414525i
$446$		0			0
$447$			5.19615i			0.0116245i
$448$		0			0
$449$	−310.000			−0.690423			−0.345212	−	0.938525i	$-0.612193\pi$
$449$	−310.000			−0.690423			−0.345212	+	0.938525i	$0.612193\pi$
$450$		0			0
$451$	221.000	−	382.783i	0.490022	−	0.848743i
$452$		0			0
$453$	31.5000	−	18.1865i	0.0695364	−	0.0401469i
$454$		0			0
$455$	468.000	−	187.061i	1.02857	−	0.411124i
$456$		0			0
$457$	−83.5000	−	144.626i	−0.182713	−	0.316469i	0.760090	−	0.649818i	$-0.225155\pi$
$457$	−83.5000	−	144.626i	−0.182713	−	0.316469i	−0.942804	+	0.333349i	$0.891821\pi$
$458$		0			0
$459$	212.500	−	368.061i	0.462963	−	0.801875i
$460$		0			0
$461$			13.8564i			0.0300573i	0.999887	+	0.0150286i	$0.00478394\pi$
$461$			13.8564i			0.0300573i	−0.999887	+	0.0150286i	$0.995216\pi$
$462$		0			0
$463$		−	609.682i		−	1.31681i	−0.752665	−	0.658404i	$-0.771232\pi$
$463$		−	609.682i		−	1.31681i	0.752665	−	0.658404i	$-0.228768\pi$
$464$		0			0
$465$	85.5000	−	148.090i	0.183871	−	0.318474i
$466$		0			0
$467$	392.500	+	679.830i	0.840471	+	1.45574i	0.889497	+	0.456941i	$0.151055\pi$
$467$	392.500	+	679.830i	0.840471	+	1.45574i	−0.0490258	+	0.998798i	$0.515612\pi$
$468$		0			0
$469$	−93.5000	−	73.6122i	−0.199360	−	0.156956i
$470$		0			0
$471$	−268.500	+	155.019i	−0.570064	+	0.329126i
$472$		0			0
$473$	−119.000	+	206.114i	−0.251586	+	0.435759i
$474$		0			0
$475$	−14.0000			−0.0294737
$476$		0			0
$477$			734.390i			1.53960i
$478$		0			0
$479$	535.500	+	309.171i	1.11795	+	0.645451i	0.940878	−	0.338746i	$-0.110003\pi$
$479$	535.500	+	309.171i	1.11795	+	0.645451i	0.177076	+	0.984197i	$0.443336\pi$
$480$		0			0
$481$	−60.0000	−	103.923i	−0.124740	−	0.216056i
$482$		0			0
$483$	36.0000	+	5.19615i	0.0745342	+	0.0107581i
$484$		0			0
$485$	99.0000	−	57.1577i	0.204124	−	0.117851i
$486$		0			0
$487$	−340.500	−	196.588i	−0.699179	−	0.403671i	0.107863	−	0.994166i	$-0.465599\pi$
$487$	−340.500	−	196.588i	−0.699179	−	0.403671i	−0.807041	+	0.590495i	$0.798933\pi$
$488$		0			0
$489$	17.0000			0.0347648
$490$		0			0
$491$	−422.000			−0.859470			−0.429735	−	0.902955i	$-0.641393\pi$
$491$	−422.000			−0.859470			−0.429735	+	0.902955i	$0.641393\pi$
$492$		0			0
$493$	300.000	+	173.205i	0.608519	+	0.351329i
$494$		0			0
$495$	−612.000	+	353.338i	−1.23636	+	0.713815i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	32.5000	+	56.2917i	0.0651303	+	0.112809i	0.896752	−	0.442534i	$-0.145920\pi$
$499$	32.5000	+	56.2917i	0.0651303	+	0.112809i	−0.831622	+	0.555343i	$0.812587\pi$
$500$		0			0
$501$	12.0000	+	6.92820i	0.0239521	+	0.0138287i
$502$		0			0
$503$			249.415i			0.495855i	0.968779	+	0.247928i	$0.0797496\pi$
$503$			249.415i			0.495855i	−0.968779	+	0.247928i	$0.920250\pi$
$504$		0			0
$505$	−405.000			−0.801980
$506$		0			0
$507$	−11.5000	+	19.9186i	−0.0226824	+	0.0392871i
$508$		0			0
$509$	−472.500	+	272.798i	−0.928291	+	0.535949i	−0.886271	−	0.463168i	$-0.846713\pi$
$509$	−472.500	+	272.798i	−0.928291	+	0.535949i	−0.0420202	+	0.999117i	$0.513379\pi$
$510$		0			0
$511$	654.500	+	515.285i	1.28082	+	1.00839i
$512$		0			0
$513$	−59.5000	−	103.057i	−0.115984	−	0.200891i
$514$		0			0
$515$	−418.500	+	724.863i	−0.812621	+	1.40750i
$516$		0			0
$517$		−	853.901i		−	1.65165i
$518$		0			0
$519$		−	105.655i		−	0.203574i
$520$		0			0
$521$	12.5000	−	21.6506i	0.0239923	−	0.0415559i	−0.853780	−	0.520634i	$-0.825696\pi$
$521$	12.5000	−	21.6506i	0.0239923	−	0.0415559i	0.877772	+	0.479078i	$0.159029\pi$
$522$		0			0
$523$	296.500	+	513.553i	0.566922	+	0.981937i	0.996868	+	0.0790826i	$0.0251991\pi$
$523$	296.500	+	513.553i	0.566922	+	0.981937i	−0.429946	+	0.902854i	$0.641468\pi$
$524$		0			0
$525$	−13.0000	+	5.19615i	−0.0247619	+	0.00989743i
$526$		0			0
$527$	−712.500	+	411.362i	−1.35199	+	0.780573i
$528$		0			0
$529$	−251.000	+	434.745i	−0.474480	+	0.821824i
$530$		0			0
$531$	−440.000			−0.828625
$532$		0			0
$533$		−	360.267i		−	0.675922i
$534$		0			0
$535$	−292.500	−	168.875i	−0.546729	−	0.315654i
$536$		0			0
$537$	−44.5000	−	77.0763i	−0.0828678	−	0.143531i
$538$		0			0
$539$	−603.500	+	574.175i	−1.11967	+	1.06526i
$540$		0			0
$541$	655.500	−	378.453i	1.21165	−	0.699544i	0.248528	−	0.968625i	$-0.420053\pi$
$541$	655.500	−	378.453i	1.21165	−	0.699544i	0.963117	+	0.269081i	$0.0867200\pi$
$542$		0			0
$543$	216.000	+	124.708i	0.397790	+	0.229664i
$544$		0			0
$545$	−45.0000			−0.0825688
$546$		0			0
$547$	−662.000			−1.21024			−0.605119	−	0.796135i	$-0.706874\pi$
$547$	−662.000			−1.21024			−0.605119	+	0.796135i	$0.706874\pi$
$548$		0			0
$549$	156.000	+	90.0666i	0.284153	+	0.164056i
$550$		0			0
$551$	84.0000	−	48.4974i	0.152450	−	0.0880171i
$552$		0			0
$553$	193.500	+	484.108i	0.349910	+	0.875422i
$554$		0			0
$555$	22.5000	+	38.9711i	0.0405405	+	0.0702183i
$556$		0			0
$557$	511.500	+	295.315i	0.918312	+	0.530188i	0.883096	−	0.469192i	$-0.155455\pi$
$557$	511.500	+	295.315i	0.918312	+	0.530188i	0.0352161	+	0.999380i	$0.488788\pi$
$558$		0			0
$559$			193.990i			0.347030i
$560$		0			0
$561$	−425.000			−0.757576
$562$		0			0
$563$	368.500	−	638.261i	0.654529	−	1.13368i	−0.327482	−	0.944857i	$-0.606200\pi$
$563$	368.500	−	638.261i	0.654529	−	1.13368i	0.982012	−	0.188821i	$-0.0604665\pi$
$564$		0			0
$565$	−549.000	+	316.965i	−0.971681	+	0.561001i
$566$		0			0
$567$	302.500	+	238.157i	0.533510	+	0.420030i
$568$		0			0
$569$	60.5000	+	104.789i	0.106327	+	0.184164i	0.914280	−	0.405084i	$-0.132758\pi$
$569$	60.5000	+	104.789i	0.106327	+	0.184164i	−0.807953	+	0.589247i	$0.799424\pi$
$570$		0			0
$571$	368.500	−	638.261i	0.645359	−	1.11779i	−0.338859	−	0.940837i	$-0.610041\pi$
$571$	368.500	−	638.261i	0.645359	−	1.11779i	0.984218	−	0.176958i	$-0.0566255\pi$
$572$		0			0
$573$		−	216.506i		−	0.377847i
$574$		0			0
$575$			10.3923i			0.0180736i
$576$		0			0
$577$	−23.5000	+	40.7032i	−0.0407279	+	0.0705428i	−0.885671	−	0.464314i	$-0.846301\pi$
$577$	−23.5000	+	40.7032i	−0.0407279	+	0.0705428i	0.844943	+	0.534857i	$0.179634\pi$
$578$		0			0
$579$	−36.5000	−	63.2199i	−0.0630397	−	0.109188i
$580$		0			0
$581$	−110.000	+	762.102i	−0.189329	+	1.31171i
$582$		0			0
$583$	1351.50	−	780.289i	2.31818	−	1.33840i
$584$		0			0
$585$	−288.000	+	498.831i	−0.492308	+	0.852702i
$586$		0			0
$587$	−446.000			−0.759796			−0.379898	−	0.925028i	$-0.624041\pi$
$587$	−446.000			−0.759796			−0.379898	+	0.925028i	$0.624041\pi$
$588$		0			0
$589$			230.363i			0.391108i
$590$		0			0
$591$	180.000	+	103.923i	0.304569	+	0.175843i
$592$		0			0
$593$	−107.500	−	186.195i	−0.181282	−	0.313989i	0.761036	−	0.648710i	$-0.224691\pi$
$593$	−107.500	−	186.195i	−0.181282	−	0.313989i	−0.942317	+	0.334721i	$0.891358\pi$
$594$		0			0
$595$	900.000	+	129.904i	1.51261	+	0.218326i
$596$		0			0
$597$	55.5000	−	32.0429i	0.0929648	−	0.0536733i
$598$		0			0
$599$	−244.500	−	141.162i	−0.408180	−	0.235663i	0.281827	−	0.959465i	$-0.409059\pi$
$599$	−244.500	−	141.162i	−0.408180	−	0.235663i	−0.690008	+	0.723802i	$0.742393\pi$
$600$		0			0
$601$	266.000			0.442596			0.221298	−	0.975206i	$-0.428971\pi$
$601$	266.000			0.442596			0.221298	+	0.975206i	$0.428971\pi$
$602$		0			0
$603$	136.000			0.225539
$604$		0			0
$605$	756.000	+	436.477i	1.24959	+	0.721449i
$606$		0			0
$607$	571.500	−	329.956i	0.941516	−	0.543584i	0.0510805	−	0.998695i	$-0.483733\pi$
$607$	571.500	−	329.956i	0.941516	−	0.543584i	0.890435	+	0.455110i	$0.150400\pi$
$608$		0			0
$609$	60.0000	−	76.2102i	0.0985222	−	0.125140i
$610$		0			0
$611$	−348.000	−	602.754i	−0.569558	−	0.986504i
$612$		0			0
$613$	−604.500	−	349.008i	−0.986134	−	0.569345i	−0.0820174	−	0.996631i	$-0.526136\pi$
$613$	−604.500	−	349.008i	−0.986134	−	0.569345i	−0.904116	+	0.427286i	$0.859470\pi$
$614$		0			0
$615$			135.100i			0.219675i
$616$		0			0
$617$	−118.000			−0.191248			−0.0956240	−	0.995418i	$-0.530485\pi$
$617$	−118.000			−0.191248			−0.0956240	+	0.995418i	$0.530485\pi$
$618$		0			0
$619$	−459.500	+	795.877i	−0.742326	+	1.28575i	0.209107	+	0.977893i	$0.432944\pi$
$619$	−459.500	+	795.877i	−0.742326	+	1.28575i	−0.951434	+	0.307854i	$0.900389\pi$
$620$		0			0
$621$	−76.5000	+	44.1673i	−0.123188	+	0.0711229i
$622$		0			0
$623$	−461.500	+	184.463i	−0.740770	+	0.296089i
$624$		0			0
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$		0			0
$627$	−59.5000	+	103.057i	−0.0948963	+	0.164365i
$628$		0			0
$629$		−	216.506i		−	0.344207i
$630$		0			0
$631$			166.277i			0.263513i	0.991282	+	0.131757i	$0.0420617\pi$
$631$			166.277i			0.263513i	−0.991282	+	0.131757i	$0.957938\pi$
$632$		0			0
$633$	−151.000	+	261.540i	−0.238547	+	0.413175i
$634$		0			0
$635$	−432.000	−	748.246i	−0.680315	−	1.17834i
$636$		0			0
$637$	−192.000	+	651.251i	−0.301413	+	1.02237i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.500000	−	0.866025i	0.000780031	−	0.00135105i	−0.865635	−	0.500675i	$-0.833085\pi$
$641$	0.500000	−	0.866025i	0.000780031	−	0.00135105i	0.866415	+	0.499324i	$0.166418\pi$
$642$		0			0
$643$	514.000			0.799378			0.399689	−	0.916651i	$-0.369118\pi$
$643$	514.000			0.799378			0.399689	+	0.916651i	$0.369118\pi$
$644$		0			0
$645$		−	72.7461i		−	0.112785i
$646$		0			0
$647$	−52.5000	−	30.3109i	−0.0811437	−	0.0468484i	0.458879	−	0.888499i	$-0.348251\pi$
$647$	−52.5000	−	30.3109i	−0.0811437	−	0.0468484i	−0.540023	+	0.841650i	$0.681584\pi$
$648$		0			0
$649$	467.500	+	809.734i	0.720339	+	1.24766i
$650$		0			0
$651$	85.5000	+	213.908i	0.131336	+	0.328584i
$652$		0			0
$653$	283.500	−	163.679i	0.434150	−	0.250657i	−0.266963	−	0.963707i	$-0.586020\pi$
$653$	283.500	−	163.679i	0.434150	−	0.250657i	0.701113	+	0.713050i	$0.252687\pi$
$654$		0			0
$655$	−76.5000	−	44.1673i	−0.116794	−	0.0674310i
$656$		0			0
$657$	−952.000			−1.44901
$658$		0			0
$659$	−542.000			−0.822458			−0.411229	−	0.911532i	$-0.634900\pi$
$659$	−542.000			−0.822458			−0.411229	+	0.911532i	$0.634900\pi$
$660$		0			0
$661$	−1024.50	−	591.495i	−1.54992	−	0.894849i	−0.998146	−	0.0608582i	$-0.980616\pi$
$661$	−1024.50	−	591.495i	−1.54992	−	0.894849i	−0.551778	−	0.833991i	$-0.686050\pi$
$662$		0			0
$663$	−300.000	+	173.205i	−0.452489	+	0.261244i
$664$		0			0
$665$	157.500	−	200.052i	0.236842	−	0.300830i
$666$		0			0
$667$	−36.0000	−	62.3538i	−0.0539730	−	0.0934840i
$668$		0			0
$669$	−120.000	−	69.2820i	−0.179372	−	0.103561i
$670$		0			0
$671$		−	382.783i		−	0.570467i
$672$		0			0
$673$	218.000			0.323923			0.161961	−	0.986797i	$-0.448218\pi$
$673$	218.000			0.323923			0.161961	+	0.986797i	$0.448218\pi$
$674$		0			0
$675$	17.0000	−	29.4449i	0.0251852	−	0.0436220i
$676$		0			0
$677$	−556.500	+	321.295i	−0.822009	+	0.474587i	−0.851109	−	0.524989i	$-0.824069\pi$
$677$	−556.500	+	321.295i	−0.822009	+	0.474587i	0.0290999	+	0.999577i	$0.490736\pi$
$678$		0			0
$679$	−22.0000	+	152.420i	−0.0324006	+	0.224478i
$680$		0			0
$681$	27.5000	+	47.6314i	0.0403818	+	0.0699433i
$682$		0			0
$683$	−183.500	+	317.831i	−0.268668	+	0.465346i	−0.968518	−	0.248943i	$-0.919917\pi$
$683$	−183.500	+	317.831i	−0.268668	+	0.465346i	0.699850	+	0.714289i	$0.253250\pi$
$684$		0			0
$685$			753.442i			1.09992i
$686$		0			0
$687$		−	327.358i		−	0.476503i
$688$		0			0
$689$	636.000	−	1101.58i	0.923077	−	1.59882i
$690$		0			0
$691$	248.500	+	430.415i	0.359624	+	0.622887i	0.987898	−	0.155105i	$-0.0495717\pi$
$691$	248.500	+	430.415i	0.359624	+	0.622887i	−0.628274	+	0.777992i	$0.716238\pi$
$692$		0			0
$693$	136.000	−	942.236i	0.196248	−	1.35965i
$694$		0			0
$695$	−369.000	+	213.042i	−0.530935	+	0.306536i
$696$		0			0
$697$	325.000	−	562.917i	0.466284	−	0.807628i
$698$		0			0
$699$	385.000			0.550787
$700$		0			0
$701$		−	332.554i		−	0.474399i	−0.971461	−	0.237200i	$-0.923770\pi$
$701$		−	332.554i		−	0.474399i	0.971461	−	0.237200i	$-0.0762295\pi$
$702$		0			0
$703$	−52.5000	−	30.3109i	−0.0746799	−	0.0431165i
$704$		0			0
$705$	130.500	+	226.033i	0.185106	+	0.320614i
$706$		0			0
$707$	337.500	−	428.683i	0.477369	−	0.606340i
$708$		0			0
$709$	343.500	−	198.320i	0.484485	−	0.279718i	−0.237799	−	0.971314i	$-0.576426\pi$
$709$	343.500	−	198.320i	0.484485	−	0.279718i	0.722284	+	0.691597i	$0.243092\pi$
$710$		0			0
$711$	−516.000	−	297.913i	−0.725738	−	0.419005i
$712$		0			0
$713$	171.000			0.239832
$714$		0			0
$715$	1224.00			1.71189
$716$		0			0
$717$	372.000	+	214.774i	0.518828	+	0.299546i
$718$		0			0
$719$	55.5000	−	32.0429i	0.0771905	−	0.0445660i	−0.460908	−	0.887448i	$-0.652476\pi$
$719$	55.5000	−	32.0429i	0.0771905	−	0.0445660i	0.538098	+	0.842882i	$0.319143\pi$
$720$		0			0
$721$	−418.500	−	1047.02i	−0.580444	−	1.45218i
$722$		0			0
$723$	−72.5000	−	125.574i	−0.100277	−	0.173684i
$724$		0			0
$725$	24.0000	+	13.8564i	0.0331034	+	0.0191123i
$726$		0			0
$727$		−	55.4256i		−	0.0762388i	−0.999273	−	0.0381194i	$-0.987863\pi$
$727$		−	55.4256i		−	0.0762388i	0.999273	−	0.0381194i	$-0.0121367\pi$
$728$		0			0
$729$	−287.000			−0.393690
$730$		0			0
$731$	−175.000	+	303.109i	−0.239398	+	0.414650i
$732$		0			0
$733$	715.500	−	413.094i	0.976126	−	0.563566i	0.0750273	−	0.997181i	$-0.476096\pi$
$733$	715.500	−	413.094i	0.976126	−	0.563566i	0.901098	+	0.433615i	$0.142762\pi$
$734$		0			0
$735$	72.0000	−	244.219i	0.0979592	−	0.332271i
$736$		0			0
$737$	−144.500	−	250.281i	−0.196065	−	0.339595i
$738$		0			0
$739$	356.500	−	617.476i	0.482409	−	0.835556i	−0.517387	−	0.855751i	$-0.673095\pi$
$739$	356.500	−	617.476i	0.482409	−	0.835556i	0.999796	+	0.0201950i	$0.00642870\pi$
$740$		0			0
$741$			96.9948i			0.130897i
$742$		0			0
$743$			637.395i			0.857866i	0.903336	+	0.428933i	$0.141110\pi$
$743$			637.395i			0.857866i	−0.903336	+	0.428933i	$0.858890\pi$
$744$		0			0
$745$	13.5000	−	23.3827i	0.0181208	−	0.0313862i
$746$		0			0
$747$	−440.000	−	762.102i	−0.589023	−	1.02022i
$748$		0			0
$749$	422.500	−	168.875i	0.564085	−	0.225467i
$750$		0			0
$751$	−1012.50	+	584.567i	−1.34820	+	0.778385i	−0.987995	−	0.154487i	$-0.950627\pi$
$751$	−1012.50	+	584.567i	−1.34820	+	0.778385i	−0.360208	+	0.932872i	$0.617294\pi$
$752$		0			0
$753$	29.0000	−	50.2295i	0.0385126	−	0.0667058i
$754$		0			0
$755$	−189.000			−0.250331
$756$		0			0
$757$		−	1039.23i		−	1.37283i	−0.727211	−	0.686414i	$-0.759184\pi$
$757$		−	1039.23i		−	1.37283i	0.727211	−	0.686414i	$-0.240816\pi$
$758$		0			0
$759$	76.5000	+	44.1673i	0.100791	+	0.0581914i
$760$		0			0
$761$	−431.500	−	747.380i	−0.567017	−	0.982102i	−0.996859	−	0.0791982i	$-0.974764\pi$
$761$	−431.500	−	747.380i	−0.567017	−	0.982102i	0.429842	−	0.902904i	$-0.358569\pi$
$762$		0			0
$763$	37.5000	−	47.6314i	0.0491481	−	0.0624265i
$764$		0			0
$765$	−900.000	+	519.615i	−1.17647	+	0.679236i
$766$		0			0
$767$	660.000	+	381.051i	0.860495	+	0.496807i
$768$		0			0
$769$	410.000			0.533160			0.266580	−	0.963813i	$-0.414106\pi$
$769$	410.000			0.533160			0.266580	+	0.963813i	$0.414106\pi$
$770$		0			0
$771$	−119.000			−0.154345
$772$		0			0
$773$	691.500	+	399.238i	0.894567	+	0.516478i	0.875433	−	0.483339i	$-0.160576\pi$
$773$	691.500	+	399.238i	0.894567	+	0.516478i	0.0191332	+	0.999817i	$0.493909\pi$
$774$		0			0
$775$	−57.0000	+	32.9090i	−0.0735484	+	0.0424632i
$776$		0			0
$777$	−60.0000	−	8.66025i	−0.0772201	−	0.0111458i
$778$		0			0
$779$	−91.0000	−	157.617i	−0.116816	−	0.202332i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			235.559i			0.300842i
$784$		0			0
$785$	1611.00			2.05223
$786$		0			0
$787$	−15.5000	+	26.8468i	−0.0196950	+	0.0341128i	−0.875705	−	0.482847i	$-0.839603\pi$
$787$	−15.5000	+	26.8468i	−0.0196950	+	0.0341128i	0.856010	+	0.516959i	$0.172936\pi$
$788$		0			0
$789$	283.500	−	163.679i	0.359316	−	0.207451i
$790$		0			0
$791$	122.000	−	845.241i	0.154235	−	1.06857i
$792$		0			0
$793$	−156.000	−	270.200i	−0.196721	−	0.340731i
$794$		0			0
$795$	−238.500	+	413.094i	−0.300000	+	0.519615i
$796$		0			0
$797$		−	595.825i		−	0.747585i	−0.927512	−	0.373793i	$-0.878057\pi$
$797$		−	595.825i		−	0.747585i	0.927512	−	0.373793i	$-0.121943\pi$
$798$		0			0
$799$		−	1255.74i		−	1.57164i
$800$		0			0
$801$	284.000	−	491.902i	0.354557	−	0.614110i
$802$		0			0
$803$	1011.50	+	1751.97i	1.25965	+	2.18178i
$804$		0			0
$805$	−148.500	−	116.913i	−0.184472	−	0.145234i
$806$		0			0
$807$	115.500	−	66.6840i	0.143123	−	0.0826319i
$808$		0			0
$809$	156.500	−	271.066i	0.193449	−	0.335063i	−0.752942	−	0.658087i	$-0.771366\pi$
$809$	156.500	−	271.066i	0.193449	−	0.335063i	0.946391	+	0.323024i	$0.104699\pi$
$810$		0			0
$811$	1138.00			1.40321			0.701603	−	0.712568i	$-0.252468\pi$
$811$	1138.00			1.40321			0.701603	+	0.712568i	$0.252468\pi$
$812$		0			0
$813$			434.745i			0.534741i
$814$		0			0
$815$	−76.5000	−	44.1673i	−0.0938650	−	0.0541930i
$816$		0			0
$817$	49.0000	+	84.8705i	0.0599755	+	0.103881i
$818$		0			0
$819$	−288.000	−	720.533i	−0.351648	−	0.879772i
$820$		0			0
$821$	−1060.50	+	612.280i	−1.29172	+	0.745773i	−0.978959	−	0.204059i	$-0.934587\pi$
$821$	−1060.50	+	612.280i	−1.29172	+	0.745773i	−0.312759	+	0.949833i	$0.601253\pi$
$822$		0			0
$823$	−100.500	−	58.0237i	−0.122114	−	0.0705027i	0.437699	−	0.899122i	$-0.355794\pi$
$823$	−100.500	−	58.0237i	−0.122114	−	0.0705027i	−0.559813	+	0.828619i	$0.689127\pi$
$824$		0			0
$825$	−34.0000			−0.0412121
$826$		0			0
$827$	754.000			0.911729			0.455865	−	0.890049i	$-0.349330\pi$
$827$	754.000			0.911729			0.455865	+	0.890049i	$0.349330\pi$
$828$		0			0
$829$	−784.500	−	452.931i	−0.946321	−	0.546359i	−0.0543848	−	0.998520i	$-0.517320\pi$
$829$	−784.500	−	452.931i	−0.946321	−	0.546359i	−0.891936	+	0.452161i	$0.850653\pi$
$830$		0			0
$831$	175.500	−	101.325i	0.211191	−	0.121931i
$832$		0			0
$833$	−887.500	+	844.375i	−1.06543	+	1.01366i
$834$		0			0
$835$	−36.0000	−	62.3538i	−0.0431138	−	0.0746752i
$836$		0			0
$837$	−484.500	−	279.726i	−0.578853	−	0.334201i
$838$		0			0
$839$		−	1053.09i		−	1.25517i	−0.778548	−	0.627585i	$-0.784044\pi$
$839$		−	1053.09i		−	1.25517i	0.778548	−	0.627585i	$-0.215956\pi$
$840$		0			0
$841$	649.000			0.771700
$842$		0			0
$843$	37.0000	−	64.0859i	0.0438909	−	0.0760212i
$844$		0			0
$845$	103.500	−	59.7558i	0.122485	−	0.0707169i
$846$		0			0
$847$	−1092.00	+	436.477i	−1.28926	+	0.515321i
$848$		0			0
$849$	231.500	+	400.970i	0.272674	+	0.472285i
$850$		0			0
$851$	−22.5000	+	38.9711i	−0.0264395	+	0.0457945i
$852$		0			0
$853$			845.241i			0.990904i	0.868635	+	0.495452i	$0.164997\pi$
$853$			845.241i			0.990904i	−0.868635	+	0.495452i	$0.835003\pi$
$854$		0			0
$855$			290.985i			0.340333i
$856$		0			0
$857$	−443.500	+	768.165i	−0.517503	+	0.896341i	0.482290	+	0.876011i	$0.339805\pi$
$857$	−443.500	+	768.165i	−0.517503	+	0.896341i	−0.999793	+	0.0203300i	$0.993528\pi$
$858$		0			0
$859$	−831.500	−	1440.20i	−0.967986	−	1.67660i	−0.701369	−	0.712798i	$-0.747427\pi$
$859$	−831.500	−	1440.20i	−0.967986	−	1.67660i	−0.266617	−	0.963803i	$-0.585906\pi$
$860$		0			0
$861$	−143.000	−	112.583i	−0.166086	−	0.130759i
$862$		0			0
$863$	487.500	−	281.458i	0.564890	−	0.326139i	−0.190216	−	0.981742i	$-0.560919\pi$
$863$	487.500	−	281.458i	0.564890	−	0.326139i	0.755106	+	0.655603i	$0.227585\pi$
$864$		0			0
$865$	−274.500	+	475.448i	−0.317341	+	0.549651i
$866$		0			0
$867$	−336.000			−0.387543
$868$		0			0
$869$			1266.13i			1.45700i
$870$		0			0
$871$	−204.000	−	117.779i	−0.234214	−	0.135223i
$872$		0			0
$873$	−88.0000	−	152.420i	−0.100802	−	0.174594i
$874$		0			0
$875$	−828.000	−	119.512i	−0.946286	−	0.136585i
$876$		0			0
$877$	103.500	−	59.7558i	0.118016	−	0.0681365i	−0.439830	−	0.898081i	$-0.644961\pi$
$877$	103.500	−	59.7558i	0.118016	−	0.0681365i	0.557846	+	0.829944i	$0.311628\pi$
$878$		0			0
$879$	96.0000	+	55.4256i	0.109215	+	0.0630553i
$880$		0			0
$881$	−574.000			−0.651532			−0.325766	−	0.945450i	$-0.605622\pi$
$881$	−574.000			−0.651532			−0.325766	+	0.945450i	$0.605622\pi$
$882$		0			0
$883$	−1166.00			−1.32050			−0.660249	−	0.751047i	$-0.729549\pi$
$883$	−1166.00			−1.32050			−0.660249	+	0.751047i	$0.729549\pi$
$884$		0			0
$885$	−247.500	−	142.894i	−0.279661	−	0.161462i
$886$		0			0
$887$	−472.500	+	272.798i	−0.532694	+	0.307551i	−0.742113	−	0.670275i	$-0.766176\pi$
$887$	−472.500	+	272.798i	−0.532694	+	0.307551i	0.209419	+	0.977826i	$0.432843\pi$
$888$		0			0
$889$	1152.00	+	166.277i	1.29584	+	0.187038i
$890$		0			0
$891$	467.500	+	809.734i	0.524691	+	0.908792i
$892$		0			0
$893$	−304.500	−	175.803i	−0.340985	−	0.196868i
$894$		0			0
$895$			462.458i			0.516712i
$896$		0			0
$897$	72.0000			0.0802676
$898$		0			0
$899$	228.000	−	394.908i	0.253615	−	0.439274i
$900$		0			0
$901$	1987.50	−	1147.48i	2.20588	−	1.27357i
$902$		0			0
$903$	77.0000	+	60.6218i	0.0852713	+	0.0671338i
$904$		0			0
$905$	−648.000	−	1122.37i	−0.716022	−	1.24019i
$906$		0			0
$907$	260.500	−	451.199i	0.287211	−	0.497463i	−0.685932	−	0.727665i	$-0.740605\pi$
$907$	260.500	−	451.199i	0.287211	−	0.497463i	0.973143	+	0.230202i	$0.0739387\pi$
$908$		0			0
$909$			623.538i			0.685961i
$910$		0			0
$911$			1191.65i			1.30807i	0.756465	+	0.654035i	$0.226925\pi$
$911$			1191.65i			1.30807i	−0.756465	+	0.654035i	$0.773075\pi$
$912$		0			0
$913$	−935.000	+	1619.47i	−1.02410	+	1.77379i
$914$		0			0
$915$	58.5000	+	101.325i	0.0639344	+	0.110738i
$916$		0			0
$917$	110.500	−	44.1673i	0.120502	−	0.0481650i
$918$		0			0
$919$	1207.50	−	697.150i	1.31393	−	0.758597i	0.331184	−	0.943566i	$-0.392552\pi$
$919$	1207.50	−	697.150i	1.31393	−	0.758597i	0.982744	+	0.184969i	$0.0592186\pi$
$920$		0			0
$921$	137.000	−	237.291i	0.148751	−	0.257645i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	17.3205i		−	0.0187249i
$926$		0			0
$927$	1116.00	+	644.323i	1.20388	+	0.695062i
$928$		0			0
$929$	480.500	+	832.250i	0.517223	+	0.895856i	0.999800	+	0.0200027i	$0.00636749\pi$
$929$	480.500	+	832.250i	0.517223	+	0.895856i	−0.482577	+	0.875853i	$0.660299\pi$
$930$		0			0
$931$	80.5000	+	333.420i	0.0864662	+	0.358131i
$932$		0			0
$933$	43.5000	−	25.1147i	0.0466238	−	0.0269183i
$934$		0			0
$935$	1912.50	+	1104.18i	2.04545	+	1.18094i
$936$		0			0
$937$	−142.000			−0.151547			−0.0757737	−	0.997125i	$-0.524143\pi$
$937$	−142.000			−0.151547			−0.0757737	+	0.997125i	$0.524143\pi$
$938$		0			0
$939$	409.000			0.435570
$940$		0			0
$941$	−1060.50	−	612.280i	−1.12699	−	0.650669i	−0.183816	−	0.982961i	$-0.558845\pi$
$941$	−1060.50	−	612.280i	−1.12699	−	0.650669i	−0.943177	+	0.332291i	$0.892178\pi$
$942$		0			0
$943$	−117.000	+	67.5500i	−0.124072	+	0.0716331i
$944$		0			0
$945$	229.500	+	574.175i	0.242857	+	0.607592i
$946$		0			0
$947$	−87.5000	−	151.554i	−0.0923970	−	0.160036i	0.816122	−	0.577879i	$-0.196120\pi$
$947$	−87.5000	−	151.554i	−0.0923970	−	0.160036i	−0.908519	+	0.417843i	$0.862786\pi$
$948$		0			0
$949$	1428.00	+	824.456i	1.50474	+	0.868763i
$950$		0			0
$951$		−	188.794i		−	0.198521i
$952$		0			0
$953$	−454.000			−0.476390			−0.238195	−	0.971217i	$-0.576556\pi$
$953$	−454.000			−0.476390			−0.238195	+	0.971217i	$0.576556\pi$
$954$		0			0
$955$	−562.500	+	974.279i	−0.589005	+	1.02019i
$956$		0			0
$957$	204.000	−	117.779i	0.213166	−	0.123072i
$958$		0			0
$959$	−797.500	−	627.868i	−0.831595	−	0.654712i
$960$		0			0
$961$	61.0000	+	105.655i	0.0634755	+	0.109943i
$962$		0			0
$963$	−260.000	+	450.333i	−0.269990	+	0.467636i
$964$		0			0
$965$			379.319i			0.393077i
$966$		0			0
$967$			720.533i			0.745122i	0.928008	+	0.372561i	$0.121520\pi$
$967$			720.533i			0.745122i	−0.928008	+	0.372561i	$0.878480\pi$
$968$		0			0
$969$	−87.5000	+	151.554i	−0.0902993	+	0.156403i
$970$		0			0
$971$	−819.500	−	1419.42i	−0.843975	−	1.46181i	−0.886508	−	0.462713i	$-0.846876\pi$
$971$	−819.500	−	1419.42i	−0.843975	−	1.46181i	0.0425329	−	0.999095i	$-0.486457\pi$
$972$		0			0
$973$	82.0000	−	568.113i	0.0842754	−	0.583877i
$974$		0			0
$975$	−24.0000	+	13.8564i	−0.0246154	+	0.0142117i
$976$		0			0
$977$	396.500	−	686.758i	0.405834	−	0.702925i	−0.588584	−	0.808436i	$-0.700314\pi$
$977$	396.500	−	686.758i	0.405834	−	0.702925i	0.994418	+	0.105511i	$0.0336477\pi$
$978$		0			0
$979$	−1207.00			−1.23289
$980$		0			0
$981$			69.2820i			0.0706239i
$982$		0			0
$983$	−1336.50	−	771.629i	−1.35961	−	0.784973i	−0.370042	−	0.929015i	$-0.620657\pi$
$983$	−1336.50	−	771.629i	−1.35961	−	0.784973i	−0.989572	+	0.144042i	$0.953990\pi$
$984$		0			0
$985$	−540.000	−	935.307i	−0.548223	−	0.949551i
$986$		0			0
$987$	−348.000	−	50.2295i	−0.352584	−	0.0508911i
$988$		0			0
$989$	63.0000	−	36.3731i	0.0637007	−	0.0367776i
$990$		0			0
$991$	775.500	+	447.735i	0.782543	+	0.451801i	0.837331	−	0.546697i	$-0.184115\pi$
$991$	775.500	+	447.735i	0.782543	+	0.451801i	−0.0547878	+	0.998498i	$0.517448\pi$
$992$		0			0
$993$	−295.000			−0.297080
$994$		0			0
$995$	−333.000			−0.334673
$996$		0			0
$997$	−688.500	−	397.506i	−0.690572	−	0.398702i	0.113254	−	0.993566i	$-0.463872\pi$
$997$	−688.500	−	397.506i	−0.690572	−	0.398702i	−0.803826	+	0.594864i	$0.797206\pi$
$998$		0			0
$999$	127.500	−	73.6122i	0.127628	−	0.0736858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.a.207.1		2
4.3	odd	2		56.3.k.a.11.1	✓	2
7.2	even	3		224.3.o.b.79.1		2
7.3	odd	6		1568.3.g.f.687.2		2
7.4	even	3		1568.3.g.c.687.1		2
8.3	odd	2		224.3.o.b.207.1		2
8.5	even	2		56.3.k.b.11.1	yes	2
28.3	even	6		392.3.g.d.99.1		2
28.11	odd	6		392.3.g.e.99.1		2
28.19	even	6		392.3.k.c.275.1		2
28.23	odd	6		56.3.k.b.51.1	yes	2
28.27	even	2		392.3.k.a.67.1		2
56.3	even	6		1568.3.g.f.687.1		2
56.5	odd	6		392.3.k.a.275.1		2
56.11	odd	6		1568.3.g.c.687.2		2
56.13	odd	2		392.3.k.c.67.1		2
56.37	even	6		56.3.k.a.51.1	yes	2
56.45	odd	6		392.3.g.d.99.2		2
56.51	odd	6	inner	224.3.o.a.79.1		2
56.53	even	6		392.3.g.e.99.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.a.11.1	✓	2	4.3	odd	2
56.3.k.a.51.1	yes	2	56.37	even	6
56.3.k.b.11.1	yes	2	8.5	even	2
56.3.k.b.51.1	yes	2	28.23	odd	6
224.3.o.a.79.1		2	56.51	odd	6	inner
224.3.o.a.207.1		2	1.1	even	1	trivial
224.3.o.b.79.1		2	7.2	even	3
224.3.o.b.207.1		2	8.3	odd	2
392.3.g.d.99.1		2	28.3	even	6
392.3.g.d.99.2		2	56.45	odd	6
392.3.g.e.99.1		2	28.11	odd	6
392.3.g.e.99.2		2	56.53	even	6
392.3.k.a.67.1		2	28.27	even	2
392.3.k.a.275.1		2	56.5	odd	6
392.3.k.c.67.1		2	56.13	odd	2
392.3.k.c.275.1		2	28.19	even	6
1568.3.g.c.687.1		2	7.4	even	3
1568.3.g.c.687.2		2	56.11	odd	6
1568.3.g.f.687.1		2	56.3	even	6
1568.3.g.f.687.2		2	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 6.92820i) q^{7} +(4.00000 + 6.92820i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 6.92820i) q^{7} +(4.00000 + 6.92820i) q^{9} +(8.50000 - 14.7224i) q^{11} -13.8564i q^{13} +5.19615i q^{15} +(12.5000 - 21.6506i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-5.50000 - 4.33013i) q^{21} +(-4.50000 + 2.59808i) q^{23} +(1.00000 - 1.73205i) q^{25} +17.0000 q^{27} +13.8564i q^{29} +(-28.5000 - 16.4545i) q^{31} +(-8.50000 - 14.7224i) q^{33} +(13.5000 + 33.7750i) q^{35} +(7.50000 - 4.33013i) q^{37} +(-12.0000 - 6.92820i) q^{39} +26.0000 q^{41} -14.0000 q^{43} +(-36.0000 - 20.7846i) q^{45} +(43.5000 - 25.1147i) q^{47} +(-47.0000 - 13.8564i) q^{49} +(-12.5000 - 21.6506i) q^{51} +(79.5000 + 45.8993i) q^{53} +88.3346i q^{55} -7.00000 q^{57} +(-27.5000 + 47.6314i) q^{59} +(19.5000 - 11.2583i) q^{61} +(52.0000 - 20.7846i) q^{63} +(36.0000 + 62.3538i) q^{65} +(8.50000 - 14.7224i) q^{67} +5.19615i q^{69} +(-59.5000 + 103.057i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-93.5000 - 73.6122i) q^{77} +(-64.5000 + 37.2391i) q^{79} +(-27.5000 + 47.6314i) q^{81} -110.000 q^{83} +129.904i q^{85} +(12.0000 + 6.92820i) q^{87} +(-35.5000 - 61.4878i) q^{89} +(-96.0000 - 13.8564i) q^{91} +(-28.5000 + 16.4545i) q^{93} +(31.5000 + 18.1865i) q^{95} -22.0000 q^{97} +136.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - 9 q^{5} + 2 q^{7} + 8 q^{9}+O(q^{10}) \) 2 * q + q^3 - 9 * q^5 + 2 * q^7 + 8 * q^9	\( 2 q + q^{3} - 9 q^{5} + 2 q^{7} + 8 q^{9} + 17 q^{11} + 25 q^{17} - 7 q^{19} - 11 q^{21} - 9 q^{23} + 2 q^{25} + 34 q^{27} - 57 q^{31} - 17 q^{33} + 27 q^{35} + 15 q^{37} - 24 q^{39} + 52 q^{41} - 28 q^{43} - 72 q^{45} + 87 q^{47} - 94 q^{49} - 25 q^{51} + 159 q^{53} - 14 q^{57} - 55 q^{59} + 39 q^{61} + 104 q^{63} + 72 q^{65} + 17 q^{67} - 119 q^{73} - 2 q^{75} - 187 q^{77} - 129 q^{79} - 55 q^{81} - 220 q^{83} + 24 q^{87} - 71 q^{89} - 192 q^{91} - 57 q^{93} + 63 q^{95} - 44 q^{97} + 272 q^{99}+O(q^{100}) \) 2 * q + q^3 - 9 * q^5 + 2 * q^7 + 8 * q^9 + 17 * q^11 + 25 * q^17 - 7 * q^19 - 11 * q^21 - 9 * q^23 + 2 * q^25 + 34 * q^27 - 57 * q^31 - 17 * q^33 + 27 * q^35 + 15 * q^37 - 24 * q^39 + 52 * q^41 - 28 * q^43 - 72 * q^45 + 87 * q^47 - 94 * q^49 - 25 * q^51 + 159 * q^53 - 14 * q^57 - 55 * q^59 + 39 * q^61 + 104 * q^63 + 72 * q^65 + 17 * q^67 - 119 * q^73 - 2 * q^75 - 187 * q^77 - 129 * q^79 - 55 * q^81 - 220 * q^83 + 24 * q^87 - 71 * q^89 - 192 * q^91 - 57 * q^93 + 63 * q^95 - 44 * q^97 + 272 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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