LMFDB - Embedded newform 392.3.k.n.275.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.3
Root			$-1.99898 + 0.0637211i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.944308 - 1.76303i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(-2.21656 + 3.32969i) q^{4} +(-4.22869 - 2.44143i) q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +O(q^{10})$	\(q+(-0.944308 - 1.76303i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(-2.21656 + 3.32969i) q^{4} +(-4.22869 - 2.44143i) q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +(-0.311142 + 9.76078i) q^{10} +(10.7388 + 18.6001i) q^{11} +(13.7372 + 0.876683i) q^{12} +13.0760i q^{13} +16.8033i q^{15} +(-6.17369 - 14.7609i) q^{16} +(-0.117445 - 0.203420i) q^{17} +(5.68190 + 0.181120i) q^{18} +(2.27936 - 3.94797i) q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} +(-9.48497 - 5.47615i) q^{23} +(-11.4265 - 25.0469i) q^{24} +(-0.578804 - 1.00252i) q^{25} +(23.0534 - 12.3478i) q^{26} -21.1900 q^{27} +34.6435i q^{29} +(29.6248 - 15.8675i) q^{30} +(29.5383 - 17.0539i) q^{31} +(-20.1942 + 24.8233i) q^{32} +(36.9551 - 64.0082i) q^{33} +(-0.247732 + 0.399150i) q^{34} +(-5.04614 - 10.1884i) q^{36} +(46.9706 + 27.1185i) q^{37} +(-9.11282 - 0.290487i) q^{38} +(38.9696 - 22.4991i) q^{39} +(-31.8107 - 22.6714i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(-85.7359 - 5.47152i) q^{44} +(12.0196 - 6.93951i) q^{45} +(-0.697893 + 21.8935i) q^{46} +(-62.6455 - 36.1684i) q^{47} +(-33.3684 + 43.7973i) q^{48} +(-1.22090 + 1.96714i) q^{50} +(-0.404160 + 0.700025i) q^{51} +(-43.5391 - 28.9838i) q^{52} +(18.7674 - 10.8353i) q^{53} +(20.0099 + 37.3587i) q^{54} -104.872i q^{55} -15.6878 q^{57} +(61.0777 - 32.7142i) q^{58} +(17.4503 + 30.2249i) q^{59} +(-55.9498 - 37.2456i) q^{60} +(55.0803 + 31.8006i) q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} +(31.9242 - 55.2944i) q^{65} +(-147.746 - 4.70965i) q^{66} +(-9.21718 - 15.9646i) q^{67} +(0.937649 + 0.0598392i) q^{68} +37.6899i q^{69} -47.5244i q^{71} +(-13.1974 + 18.5175i) q^{72} +(27.9551 + 48.4197i) q^{73} +(3.45604 - 108.419i) q^{74} +(-1.99182 + 3.44994i) q^{75} +(8.09317 + 16.3405i) q^{76} +(-76.4660 - 47.4586i) q^{78} +(82.2841 + 47.5067i) q^{79} +(-9.93128 + 77.4921i) q^{80} +(49.2512 + 85.3055i) q^{81} +(-35.7232 - 66.6955i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(4.57720 + 8.54567i) q^{86} +(103.246 - 59.6090i) q^{87} +(71.3146 + 156.322i) q^{88} +(-79.8779 + 138.353i) q^{89} +(-23.5848 - 14.6379i) q^{90} +(39.2579 - 19.4438i) q^{92} +(-101.649 - 58.6874i) q^{93} +(-4.60938 + 144.600i) q^{94} +(-19.2774 + 11.1298i) q^{95} +(108.726 + 17.4714i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.944308	−	1.76303i	−0.472154	−	0.881516i
$2$	−0.944308	−	1.76303i	−0.472154	−	0.881516i
$3$	−1.72064	−	2.98023i	−0.573546	−	0.993411i	−0.996198	−	0.0871191i	$-0.972234\pi$
$3$	−1.72064	−	2.98023i	−0.573546	−	0.993411i	0.422652	−	0.906292i	$-0.361099\pi$
$4$	−2.21656	+	3.32969i	−0.554141	+	0.832423i
$5$	−4.22869	−	2.44143i	−0.845737	−	0.488287i	0.0134729	−	0.999909i	$-0.495711\pi$
$5$	−4.22869	−	2.44143i	−0.845737	−	0.488287i	−0.859210	+	0.511623i	$0.829045\pi$
$6$	−3.62943	+	5.84780i	−0.604906	+	0.974633i
$7$		0			0
$7$		0			0
$8$	7.96347	+	0.763618i	0.995434	+	0.0954523i
$9$	−1.42120	+	2.46158i	−0.157911	+	0.273509i
$10$	−0.311142	+	9.76078i	−0.0311142	+	0.976078i
$11$	10.7388	+	18.6001i	0.976253	+	1.69092i	0.675735	+	0.737144i	$0.263826\pi$
$11$	10.7388	+	18.6001i	0.976253	+	1.69092i	0.300518	+	0.953776i	$0.402840\pi$
$12$	13.7372	+	0.876683i	1.14476	+	0.0730569i
$13$			13.0760i			1.00585i	0.864331	+	0.502924i	$0.167742\pi$
$13$			13.0760i			1.00585i	−0.864331	+	0.502924i	$0.832258\pi$
$14$		0			0
$15$			16.8033i			1.12022i
$16$	−6.17369	−	14.7609i	−0.385856	−	0.922559i
$17$	−0.117445	−	0.203420i	−0.00690851	−	0.0119659i	0.862550	−	0.505971i	$-0.168866\pi$
$17$	−0.117445	−	0.203420i	−0.00690851	−	0.0119659i	−0.869459	+	0.494005i	$0.835532\pi$
$18$	5.68190	+	0.181120i	0.315661	+	0.0100622i
$19$	2.27936	−	3.94797i	0.119966	−	0.207788i	−0.799788	−	0.600283i	$-0.795055\pi$
$19$	2.27936	−	3.94797i	0.119966	−	0.207788i	0.919754	+	0.392495i	$0.128388\pi$
$20$	17.5024	−	8.66863i	0.875119	−	0.433431i
$21$		0			0
$22$	22.6519	−	36.4971i	1.02963	−	1.65896i
$23$	−9.48497	−	5.47615i	−0.412390	−	0.238094i	0.279426	−	0.960167i	$-0.409856\pi$
$23$	−9.48497	−	5.47615i	−0.412390	−	0.238094i	−0.691816	+	0.722074i	$0.743189\pi$
$24$	−11.4265	−	25.0469i	−0.476104	−	1.04362i
$25$	−0.578804	−	1.00252i	−0.0231522	−	0.0401007i
$26$	23.0534	−	12.3478i	0.886671	−	0.474915i
$27$	−21.1900			−0.784816
$28$		0			0
$29$			34.6435i			1.19460i	0.802016	+	0.597302i	$0.203761\pi$
$29$			34.6435i			1.19460i	−0.802016	+	0.597302i	$0.796239\pi$
$30$	29.6248	−	15.8675i	0.987492	−	0.528917i
$31$	29.5383	−	17.0539i	0.952848	−	0.550127i	0.0588837	−	0.998265i	$-0.481246\pi$
$31$	29.5383	−	17.0539i	0.952848	−	0.550127i	0.893965	+	0.448138i	$0.147913\pi$
$32$	−20.1942	+	24.8233i	−0.631067	+	0.775728i
$33$	36.9551	−	64.0082i	1.11985	−	1.93964i
$34$	−0.247732	+	0.399150i	−0.00728624	+	0.0117397i
$35$		0			0
$36$	−5.04614	−	10.1884i	−0.140171	−	0.283011i
$37$	46.9706	+	27.1185i	1.26948	+	0.732932i	0.974889	−	0.222693i	$-0.0714847\pi$
$37$	46.9706	+	27.1185i	1.26948	+	0.732932i	0.294587	+	0.955625i	$0.404818\pi$
$38$	−9.11282	−	0.290487i	−0.239811	−	0.00764439i
$39$	38.9696	−	22.4991i	0.999221	−	0.576900i
$40$	−31.8107	−	22.6714i	−0.795268	−	0.566785i
$41$	37.8300			0.922682			0.461341	−	0.887223i	$-0.347368\pi$
$41$	37.8300			0.922682			0.461341	+	0.887223i	$0.347368\pi$
$42$		0			0
$43$	−4.84714			−0.112724			−0.0563621	−	0.998410i	$-0.517950\pi$
$43$	−4.84714			−0.112724			−0.0563621	+	0.998410i	$0.517950\pi$
$44$	−85.7359	−	5.47152i	−1.94854	−	0.124353i
$45$	12.0196	−	6.93951i	0.267102	−	0.154211i
$46$	−0.697893	+	21.8935i	−0.0151716	+	0.475945i
$47$	−62.6455	−	36.1684i	−1.33288	−	0.769541i	−0.347143	−	0.937812i	$-0.612848\pi$
$47$	−62.6455	−	36.1684i	−1.33288	−	0.769541i	−0.985741	+	0.168271i	$0.946182\pi$
$48$	−33.3684	+	43.7973i	−0.695175	+	0.912444i
$49$		0			0
$50$	−1.22090	+	1.96714i	−0.0244180	+	0.0393427i
$51$	−0.404160	+	0.700025i	−0.00792470	+	0.0137260i
$52$	−43.5391	−	28.9838i	−0.837291	−	0.557382i
$53$	18.7674	−	10.8353i	0.354101	−	0.204440i	−0.312389	−	0.949954i	$-0.601129\pi$
$53$	18.7674	−	10.8353i	0.354101	−	0.204440i	0.666490	+	0.745514i	$0.267796\pi$
$54$	20.0099	+	37.3587i	0.370554	+	0.691828i
$55$		−	104.872i		−	1.90677i
$56$		0			0
$57$	−15.6878			−0.275225
$58$	61.0777	−	32.7142i	1.05306	−	0.564037i
$59$	17.4503	+	30.2249i	0.295768	+	0.512286i	0.975163	−	0.221487i	$-0.0710910\pi$
$59$	17.4503	+	30.2249i	0.295768	+	0.512286i	−0.679395	+	0.733773i	$0.737758\pi$
$60$	−55.9498	−	37.2456i	−0.932497	−	0.620760i
$61$	55.0803	+	31.8006i	0.902955	+	0.521321i	0.878158	−	0.478371i	$-0.158773\pi$
$61$	55.0803	+	31.8006i	0.902955	+	0.521321i	0.0247973	+	0.999693i	$0.492106\pi$
$62$	−57.9599	−	35.9728i	−0.934837	−	0.580206i
$63$		0			0
$64$	62.8338	+	12.1621i	0.981778	+	0.190033i
$65$	31.9242	−	55.2944i	0.491142	−	0.850683i
$66$	−147.746	−	4.70965i	−2.23857	−	0.0713583i
$67$	−9.21718	−	15.9646i	−0.137570	−	0.238278i	0.789006	−	0.614385i	$-0.210596\pi$
$67$	−9.21718	−	15.9646i	−0.137570	−	0.238278i	−0.926576	+	0.376107i	$0.877263\pi$
$68$	0.937649	+	0.0598392i	0.0137890	+	0.000879988i
$69$			37.6899i			0.546231i
$70$		0			0
$71$		−	47.5244i		−	0.669358i	−0.942332	−	0.334679i	$-0.891372\pi$
$71$		−	47.5244i		−	0.669358i	0.942332	−	0.334679i	$-0.108628\pi$
$72$	−13.1974	+	18.5175i	−0.183297	+	0.257188i
$73$	27.9551	+	48.4197i	0.382947	+	0.663284i	0.991482	−	0.130243i	$-0.0415758\pi$
$73$	27.9551	+	48.4197i	0.382947	+	0.663284i	−0.608535	+	0.793527i	$0.708242\pi$
$74$	3.45604	−	108.419i	0.0467032	−	1.46512i
$75$	−1.99182	+	3.44994i	−0.0265577	+	0.0459992i
$76$	8.09317	+	16.3405i	0.106489	+	0.215007i
$77$		0			0
$78$	−76.4660	−	47.4586i	−0.980333	−	0.608443i
$79$	82.2841	+	47.5067i	1.04157	+	0.601351i	0.920278	−	0.391266i	$-0.127963\pi$
$79$	82.2841	+	47.5067i	1.04157	+	0.601351i	0.121293	+	0.992617i	$0.461296\pi$
$80$	−9.93128	+	77.4921i	−0.124141	+	0.968651i
$81$	49.2512	+	85.3055i	0.608039	+	1.05315i
$82$	−35.7232	−	66.6955i	−0.435648	−	0.813359i
$83$	−71.5156			−0.861634			−0.430817	−	0.902439i	$-0.641775\pi$
$83$	−71.5156			−0.861634			−0.430817	+	0.902439i	$0.641775\pi$
$84$		0			0
$85$			1.14693i			0.0134933i
$86$	4.57720	+	8.54567i	0.0532232	+	0.0993682i
$87$	103.246	−	59.6090i	1.18673	−	0.685161i
$88$	71.3146	+	156.322i	0.810394	+	1.77639i
$89$	−79.8779	+	138.353i	−0.897504	+	1.55452i	−0.0668296	+	0.997764i	$0.521288\pi$
$89$	−79.8779	+	138.353i	−0.897504	+	1.55452i	−0.830675	+	0.556758i	$0.812045\pi$
$90$	−23.5848	−	14.6379i	−0.262053	−	0.162643i
$91$		0			0
$92$	39.2579	−	19.4438i	0.426717	−	0.211346i
$93$	−101.649	−	58.6874i	−1.09301	−	0.631047i
$94$	−4.60938	+	144.600i	−0.0490360	+	1.53830i
$95$	−19.2774	+	11.1298i	−0.202920	+	0.117156i
$96$	108.726	+	17.4714i	1.13256	+	0.181994i
$97$	90.4794			0.932777			0.466389	−	0.884580i	$-0.345555\pi$
$97$	90.4794			0.932777			0.466389	+	0.884580i	$0.345555\pi$
$98$		0			0
$99$	−61.0477			−0.616643
$100$	4.62103	+	0.294906i	0.0462103	+	0.00294906i
$101$	156.878	−	90.5735i	1.55325	−	0.896767i	0.555371	−	0.831602i	$-0.312576\pi$
$101$	156.878	−	90.5735i	1.55325	−	0.896767i	0.997875	−	0.0651645i	$-0.0207572\pi$
$102$	1.61582	+	0.0515070i	0.0158413	+	0.000504970i
$103$	34.0350	+	19.6501i	0.330437	+	0.190778i	0.656035	−	0.754730i	$-0.272232\pi$
$103$	34.0350	+	19.6501i	0.330437	+	0.190778i	−0.325598	+	0.945508i	$0.605566\pi$
$104$	−9.98509	+	104.131i	−0.0960105	+	1.00126i
$105$		0			0
$106$	−36.8252	−	22.8556i	−0.347408	−	0.215618i
$107$	−19.2249	+	33.2985i	−0.179672	+	0.311201i	−0.941768	−	0.336263i	$-0.890837\pi$
$107$	−19.2249	+	33.2985i	−0.179672	+	0.311201i	0.762096	+	0.647464i	$0.224170\pi$
$108$	46.9691	−	70.5563i	0.434899	−	0.653299i
$109$	24.1436	−	13.9393i	0.221501	−	0.127883i	−0.385144	−	0.922856i	$-0.625848\pi$
$109$	24.1436	−	13.9393i	0.221501	−	0.127883i	0.606645	+	0.794973i	$0.292515\pi$
$110$	−184.893	+	99.0316i	−1.68085	+	0.900288i
$111$		−	186.644i		−	1.68148i
$112$		0			0
$113$	82.4419			0.729574			0.364787	−	0.931091i	$-0.381142\pi$
$113$	82.4419			0.729574			0.364787	+	0.931091i	$0.381142\pi$
$114$	14.8141	+	27.6581i	0.129949	+	0.242615i
$115$	26.7393	+	46.3139i	0.232516	+	0.402729i
$116$	−115.352	−	76.7896i	−0.994416	−	0.661979i
$117$	−32.1877	−	18.5836i	−0.275109	−	0.158834i
$118$	36.8089	−	59.3071i	0.311940	−	0.502603i
$119$		0			0
$120$	−12.8313	+	133.813i	−0.106928	+	1.11511i
$121$	−170.143	+	294.697i	−1.40614	+	2.43551i
$122$	4.05274	−	127.138i	0.0332192	−	1.04211i
$123$	−65.0917	−	112.742i	−0.529201	−	0.916603i
$124$	−8.68916	+	136.155i	−0.0700738	+	1.09802i
$125$			127.724i			1.02179i
$126$		0			0
$127$			25.1408i			0.197959i	0.995089	+	0.0989796i	$0.0315579\pi$
$127$			25.1408i			0.197959i	−0.995089	+	0.0989796i	$0.968442\pi$
$128$	−37.8923	−	122.263i	−0.296033	−	0.955178i
$129$	8.34018	+	14.4456i	0.0646526	+	0.111982i
$130$	−127.632	−	4.06850i	−0.981786	−	0.0312961i
$131$	−63.1991	+	109.464i	−0.482436	+	0.835603i	−0.999797	−	0.0201639i	$-0.993581\pi$
$131$	−63.1991	+	109.464i	−0.482436	+	0.835603i	0.517361	+	0.855767i	$0.326915\pi$
$132$	131.214	+	264.928i	0.994046	+	2.00703i
$133$		0			0
$134$	−19.4423	+	31.3257i	−0.145092	+	0.233774i
$135$	89.6060	+	51.7341i	0.663748	+	0.383215i
$136$	−0.779932	−	1.70961i	−0.00573479	−	0.0125707i
$137$	−17.4728	−	30.2638i	−0.127539	−	0.220904i	0.795184	−	0.606369i	$-0.207374\pi$
$137$	−17.4728	−	30.2638i	−0.127539	−	0.220904i	−0.922723	+	0.385465i	$0.874041\pi$
$138$	66.4485	−	35.5909i	0.481511	−	0.257905i
$139$	119.148			0.857177			0.428589	−	0.903500i	$-0.359011\pi$
$139$	119.148			0.857177			0.428589	+	0.903500i	$0.359011\pi$
$140$		0			0
$141$			248.931i			1.76547i
$142$	−83.7870	+	44.8777i	−0.590049	+	0.316040i
$143$	−243.216	+	140.421i	−1.70081	+	0.981962i
$144$	45.1093	+	5.78115i	0.313259	+	0.0401469i
$145$	84.5799	−	146.497i	0.583310	−	1.01032i
$146$	58.9673	−	95.0090i	0.403885	−	0.650746i
$147$		0			0
$148$	−194.409	+	96.2877i	−1.31358	+	0.650593i
$149$	−105.596	−	60.9659i	−0.708698	−	0.409167i	0.101881	−	0.994797i	$-0.467514\pi$
$149$	−105.596	−	60.9659i	−0.708698	−	0.409167i	−0.810579	+	0.585630i	$0.800847\pi$
$150$	7.96326	+	0.253843i	0.0530884	+	0.00169228i
$151$	190.876	−	110.202i	1.26408	−	0.729815i	0.290216	−	0.956961i	$-0.406273\pi$
$151$	190.876	−	110.202i	1.26408	−	0.729815i	0.973861	+	0.227146i	$0.0729396\pi$
$152$	21.1664	−	29.6990i	0.139252	−	0.195388i
$153$	0.667647			0.00436371
$154$		0			0
$155$	−166.544			−1.07448
$156$	−11.4635	+	179.627i	−0.0734841	+	1.15146i
$157$	−5.86312	+	3.38507i	−0.0373447	+	0.0215610i	−0.518556	−	0.855044i	$-0.673530\pi$
$157$	−5.86312	+	3.38507i	−0.0373447	+	0.0215610i	0.481211	+	0.876605i	$0.340197\pi$
$158$	6.05436	−	189.930i	0.0383188	−	1.20209i
$159$	−64.5837	−	37.2874i	−0.406187	−	0.234512i
$160$	145.999	−	55.6672i	0.912495	−	0.347920i
$161$		0			0
$162$	103.888	−	167.386i	0.641285	−	1.03325i
$163$	103.621	−	179.478i	0.635715	−	1.10109i	−0.350649	−	0.936507i	$-0.614039\pi$
$163$	103.621	−	179.478i	0.635715	−	1.10109i	0.986363	−	0.164583i	$-0.0526278\pi$
$164$	−83.8526	+	125.962i	−0.511296	+	0.768062i
$165$	−312.544	+	180.447i	−1.89420	+	1.09362i
$166$	67.5328	+	126.084i	0.406824	+	0.759544i
$167$			165.529i			0.991193i	0.868553	+	0.495596i	$0.165050\pi$
$167$			165.529i			0.991193i	−0.868553	+	0.495596i	$0.834950\pi$
$168$		0			0
$169$	−1.98237			−0.0117300
$170$	2.02208	−	1.08306i	0.0118946	−	0.00637093i
$171$	6.47884	+	11.2217i	0.0378879	+	0.0656238i
$172$	10.7440	−	16.1395i	0.0624651	−	0.0938342i
$173$	76.9489	+	44.4265i	0.444791	+	0.256800i	0.705628	−	0.708583i	$-0.250665\pi$
$173$	76.9489	+	44.4265i	0.444791	+	0.256800i	−0.260836	+	0.965383i	$0.583998\pi$
$174$	−202.588	−	125.736i	−1.16430	−	0.722623i
$175$		0			0
$176$	208.258	−	273.346i	1.18328	−	1.55310i
$177$	60.0515	−	104.012i	0.339274	−	0.587639i
$178$	319.349	+	10.1798i	1.79410	+	0.0571900i
$179$	−40.1896	−	69.6104i	−0.224523	−	0.388885i	0.731653	−	0.681677i	$-0.238749\pi$
$179$	−40.1896	−	69.6104i	−0.224523	−	0.388885i	−0.956176	+	0.292792i	$0.905416\pi$
$180$	−3.53575	+	55.4034i	−0.0196431	+	0.307797i
$181$			276.353i			1.52681i	0.645919	+	0.763406i	$0.276474\pi$
$181$			276.353i			1.52681i	−0.645919	+	0.763406i	$0.723526\pi$
$182$		0			0
$183$		−	218.869i		−	1.19601i
$184$	−71.3516	−	50.8521i	−0.387781	−	0.276370i
$185$	−132.416	−	229.351i	−0.715762	−	1.23974i
$186$	−7.47925	+	234.630i	−0.0402110	+	1.26145i
$187$	2.52243	−	4.36897i	0.0134889	−	0.0233635i
$188$	259.288	−	128.421i	1.37919	−	0.683089i
$189$		0			0
$190$	37.8260	+	23.4767i	0.199084	+	0.123562i
$191$	175.816	+	101.507i	0.920502	+	0.531452i	0.883795	−	0.467874i	$-0.154980\pi$
$191$	175.816	+	101.507i	0.920502	+	0.531452i	0.0367067	+	0.999326i	$0.488313\pi$
$192$	−71.8683	−	208.186i	−0.374314	−	1.08430i
$193$	−43.6664	−	75.6325i	−0.226251	−	0.391878i	0.730443	−	0.682974i	$-0.239314\pi$
$193$	−43.6664	−	75.6325i	−0.226251	−	0.391878i	−0.956694	+	0.291096i	$0.905980\pi$
$194$	−85.4404	−	159.518i	−0.440415	−	0.822258i
$195$	−219.720			−1.12677
$196$		0			0
$197$		−	21.6639i		−	0.109969i	−0.998487	−	0.0549845i	$-0.982489\pi$
$197$		−	21.6639i		−	0.109969i	0.998487	−	0.0549845i	$-0.0175109\pi$
$198$	57.6478	+	107.629i	0.291151	+	0.543581i
$199$	−157.558	+	90.9664i	−0.791751	+	0.457118i	−0.840579	−	0.541690i	$-0.817785\pi$
$199$	−157.558	+	90.9664i	−0.791751	+	0.457118i	0.0488277	+	0.998807i	$0.484451\pi$
$200$	−3.84375	−	8.42551i	−0.0192187	−	0.0421275i
$201$	−31.7189	+	54.9387i	−0.157805	+	0.273327i
$202$	−307.825	−	191.051i	−1.52389	−	0.945799i
$203$		0			0
$204$	−1.43502	−	2.89738i	−0.00703442	−	0.0142028i
$205$	−159.971	−	92.3594i	−0.780347	−	0.450533i
$206$	2.50426	−	78.5606i	0.0121566	−	0.381362i
$207$	26.9600	−	15.5654i	0.130242	−	0.0751950i
$208$	193.014	−	80.7273i	0.927954	−	0.388112i
$209$	97.9103			0.468470
$210$		0			0
$211$	−21.4204			−0.101519			−0.0507594	−	0.998711i	$-0.516164\pi$
$211$	−21.4204			−0.101519			−0.0507594	+	0.998711i	$0.516164\pi$
$212$	−5.52071	+	86.5067i	−0.0260411	+	0.408051i
$213$	−141.634	+	81.7723i	−0.664947	+	0.383908i
$214$	76.8606	+	2.45007i	0.359162	+	0.0114489i
$215$	20.4971	+	11.8340i	0.0953351	+	0.0550418i
$216$	−168.746	−	16.1811i	−0.781233	−	0.0749125i
$217$		0			0
$218$	−47.3744	−	29.4029i	−0.217314	−	0.134876i
$219$	96.2014	−	166.626i	0.439276	−	0.760848i
$220$	349.192	+	232.456i	1.58724	+	1.05662i
$221$	2.65992	−	1.53571i	0.0120359	−	0.00694891i
$222$	−329.060	+	176.250i	−1.48225	+	0.793918i
$223$		−	195.958i		−	0.878735i	−0.898307	−	0.439367i	$-0.855203\pi$
$223$		−	195.958i		−	0.878735i	0.898307	−	0.439367i	$-0.144797\pi$
$224$		0			0
$225$	3.29038			0.0146239
$226$	−77.8506	−	145.348i	−0.344471	−	0.643131i
$227$	−13.6326	−	23.6123i	−0.0600554	−	0.104019i	0.834435	−	0.551107i	$-0.185794\pi$
$227$	−13.6326	−	23.6123i	−0.0600554	−	0.104019i	−0.894490	+	0.447088i	$0.852461\pi$
$228$	34.7731	−	52.2356i	0.152513	−	0.229104i
$229$	−152.721	−	88.1737i	−0.666906	−	0.385038i	0.127998	−	0.991774i	$-0.459145\pi$
$229$	−152.721	−	88.1737i	−0.666906	−	0.385038i	−0.794903	+	0.606736i	$0.792478\pi$
$230$	56.4027	−	90.8768i	0.245229	−	0.395117i
$231$		0			0
$232$	−26.4544	+	275.883i	−0.114028	+	1.18915i
$233$	−35.9183	+	62.2123i	−0.154156	+	0.267006i	−0.932751	−	0.360520i	$-0.882599\pi$
$233$	−35.9183	+	62.2123i	−0.154156	+	0.267006i	0.778596	+	0.627526i	$0.215932\pi$
$234$	−2.36833	+	74.2966i	−0.0101211	+	0.317507i
$235$	176.606	+	305.890i	0.751513	+	1.30166i
$236$	−139.319	−	8.89112i	−0.590336	−	0.0376743i
$237$		−	326.968i		−	1.37961i
$238$		0			0
$239$		−	71.0926i		−	0.297459i	−0.988878	−	0.148729i	$-0.952482\pi$
$239$		−	71.0926i		−	0.297459i	0.988878	−	0.148729i	$-0.0475183\pi$
$240$	248.033	−	103.738i	1.03347	−	0.432243i
$241$	28.0556	+	48.5938i	0.116413	+	0.201634i	0.918344	−	0.395783i	$-0.129527\pi$
$241$	28.0556	+	48.5938i	0.116413	+	0.201634i	−0.801930	+	0.597417i	$0.796194\pi$
$242$	680.227	+	21.6834i	2.81086	+	0.0896009i
$243$	74.1318	−	128.400i	0.305069	−	0.528395i
$244$	−227.975	+	112.912i	−0.934324	+	0.462755i
$245$		0			0
$246$	−137.301	+	221.222i	−0.558136	+	0.899277i
$247$	51.6237	+	29.8050i	0.209003	+	0.120668i
$248$	248.250	−	113.253i	1.00101	−	0.456664i
$249$	123.053	+	213.133i	0.494187	+	0.855957i
$250$	225.182	−	120.611i	0.900727	−	0.482444i
$251$	−368.953			−1.46993			−0.734966	−	0.678104i	$-0.762802\pi$
$251$	−368.953			−1.46993			−0.734966	+	0.678104i	$0.762802\pi$
$252$		0			0
$253$		−	235.229i		−	0.929759i
$254$	44.3241	−	23.7407i	0.174504	−	0.0934673i
$255$	3.41813	−	1.97346i	0.0134044	−	0.00773905i
$256$	−179.771	+	182.259i	−0.702231	+	0.711949i
$257$	11.8714	−	20.5619i	0.0461923	−	0.0800073i	−0.842005	−	0.539470i	$-0.818625\pi$
$257$	11.8714	−	20.5619i	0.0461923	−	0.0800073i	0.888197	+	0.459463i	$0.151958\pi$
$258$	17.5924	−	28.3451i	0.0681876	−	0.109865i
$259$		0			0
$260$	113.351	+	228.861i	0.435966	+	0.880236i
$261$	−85.2780	−	49.2353i	−0.326735	−	0.188641i
$262$	252.668	+	8.05423i	0.964382	+	0.0307414i
$263$	−64.0605	+	36.9853i	−0.243576	+	0.140629i	−0.616819	−	0.787105i	$-0.711579\pi$
$263$	−64.0605	+	36.9853i	−0.243576	+	0.140629i	0.373243	+	0.927734i	$0.378246\pi$
$264$	343.169	−	481.508i	1.29988	−	1.82389i
$265$	−105.815			−0.399302
$266$		0			0
$267$	549.764			2.05904
$268$	73.5878	+	4.69625i	0.274581	+	0.0175233i
$269$	−290.632	+	167.797i	−1.08042	+	0.623779i	−0.931009	−	0.364997i	$-0.881070\pi$
$269$	−290.632	+	167.797i	−1.08042	+	0.623779i	−0.149408	+	0.988776i	$0.547737\pi$
$270$	6.59311	−	206.831i	0.0244189	−	0.766042i
$271$	162.186	+	93.6379i	0.598471	+	0.345527i	0.768440	−	0.639922i	$-0.221033\pi$
$271$	162.186	+	93.6379i	0.598471	+	0.345527i	−0.169969	+	0.985449i	$0.554367\pi$
$272$	−2.27761	+	2.98945i	−0.00837355	+	0.0109906i
$273$		0			0
$274$	−36.8564	+	59.3835i	−0.134512	+	0.216728i
$275$	12.4313	−	21.5317i	0.0452047	−	0.0782969i
$276$	−125.496	−	83.5421i	−0.454695	−	0.302689i
$277$	114.828	−	66.2958i	0.414541	−	0.239335i	−0.278198	−	0.960524i	$-0.589737\pi$
$277$	114.828	−	66.2958i	0.414541	−	0.239335i	0.692739	+	0.721189i	$0.256404\pi$
$278$	−112.512	−	210.061i	−0.404720	−	0.755615i
$279$			96.9480i			0.347484i
$280$		0			0
$281$	331.520			1.17979			0.589894	−	0.807481i	$-0.299170\pi$
$281$	331.520			1.17979			0.589894	+	0.807481i	$0.299170\pi$
$282$	438.874	−	235.068i	1.55629	−	0.833574i
$283$	−33.3579	−	57.7776i	−0.117873	−	0.204161i	0.801052	−	0.598595i	$-0.204274\pi$
$283$	−33.3579	−	57.7776i	−0.117873	−	0.204161i	−0.918924	+	0.394434i	$0.870941\pi$
$284$	158.242	+	105.341i	0.557189	+	0.370918i
$285$	66.3389	+	38.3008i	0.232768	+	0.134389i
$286$	477.237	+	296.197i	1.66866	+	1.03565i
$287$		0			0
$288$	−32.4048	−	84.9884i	−0.112517	−	0.295099i
$289$	144.472	−	250.234i	0.499905	−	0.865860i
$290$	−338.148	−	10.7790i	−1.16603	−	0.0371691i
$291$	−155.682	−	269.650i	−0.534991	−	0.926632i
$292$	−223.187	−	14.2434i	−0.764340	−	0.0487789i
$293$			289.215i			0.987082i	0.869723	+	0.493541i	$0.164298\pi$
$293$			289.215i			0.987082i	−0.869723	+	0.493541i	$0.835702\pi$
$294$		0			0
$295$		−	170.415i		−	0.577679i
$296$	353.341	+	251.825i	1.19372	+	0.850760i
$297$	−227.555	−	394.137i	−0.766180	−	1.32706i
$298$	−7.76962	+	243.740i	−0.0260726	+	0.817918i
$299$	71.6063	−	124.026i	0.239486	−	0.414802i
$300$	−7.07223	−	14.2792i	−0.0235741	−	0.0475973i
$301$		0			0
$302$	−374.535	−	232.455i	−1.24018	−	0.769719i
$303$	−539.860	−	311.688i	−1.78172	−	1.02867i
$304$	−72.3478	−	9.27200i	−0.237986	−	0.0305000i
$305$	−155.278	−	268.950i	−0.509109	−	0.881802i
$306$	−0.630465	−	1.17708i	−0.00206034	−	0.00384668i
$307$	−0.693177			−0.00225790			−0.00112895	−	0.999999i	$-0.500359\pi$
$307$	−0.693177			−0.00225790			−0.00112895	+	0.999999i	$0.500359\pi$
$308$		0			0
$309$		−	135.243i		−	0.437680i
$310$	157.269	+	293.623i	0.507320	+	0.947171i
$311$	53.8307	−	31.0792i	0.173089	−	0.0999330i	−0.410953	−	0.911657i	$-0.634804\pi$
$311$	53.8307	−	31.0792i	0.173089	−	0.0999330i	0.584042	+	0.811724i	$0.301470\pi$
$312$	327.514	−	149.413i	1.04972	−	0.478888i
$313$	106.797	−	184.978i	0.341204	−	0.590983i	−0.643452	−	0.765486i	$-0.722499\pi$
$313$	106.797	−	184.978i	0.341204	−	0.590983i	0.984657	+	0.174503i	$0.0558319\pi$
$314$	11.5046	+	7.14031i	0.0366388	+	0.0227398i
$315$		0			0
$316$	−340.571	+	168.679i	−1.07776	+	0.533794i
$317$	20.3150	+	11.7288i	0.0640850	+	0.0369995i	0.531700	−	0.846933i	$-0.321553\pi$
$317$	20.3150	+	11.7288i	0.0640850	+	0.0369995i	−0.467615	+	0.883932i	$0.654887\pi$
$318$	−4.75199	+	149.074i	−0.0149434	+	0.468786i
$319$	−644.374	+	372.030i	−2.01998	+	1.16624i
$320$	−236.011	−	204.834i	−0.737536	−	0.640107i
$321$	132.317			0.412201
$322$		0			0
$323$	−1.07079			−0.00331515
$324$	−393.209	−	25.0940i	−1.21361	−	0.0774505i
$325$	13.1089	−	7.56845i	0.0403352	−	0.0232875i
$326$	−414.275	−	13.2058i	−1.27078	−	0.0405084i
$327$	−83.0847	−	47.9690i	−0.254082	−	0.146694i
$328$	301.258	+	28.8877i	0.918469	+	0.0880721i
$329$		0			0
$330$	613.271	+	380.627i	1.85840	+	1.15341i
$331$	−253.703	+	439.426i	−0.766474	+	1.32757i	0.172990	+	0.984924i	$0.444657\pi$
$331$	−253.703	+	439.426i	−0.766474	+	1.32757i	−0.939464	+	0.342648i	$0.888676\pi$
$332$	158.519	−	238.125i	0.477467	−	0.717244i
$333$	−133.509	+	77.0814i	−0.400927	+	0.231476i
$334$	291.833	−	156.311i	0.873752	−	0.467996i
$335$			90.0126i			0.268694i
$336$		0			0
$337$	−342.726			−1.01699			−0.508495	−	0.861065i	$-0.669798\pi$
$337$	−342.726			−1.01699			−0.508495	+	0.861065i	$0.669798\pi$
$338$	1.87197	+	3.49498i	0.00553836	+	0.0103402i
$339$	−141.853	−	245.696i	−0.418445	−	0.724767i
$340$	−3.81893	−	2.54225i	−0.0112322	−	0.00747721i
$341$	634.411	+	366.277i	1.86044	+	1.07413i
$342$	13.6662	−	22.0191i	0.0399595	−	0.0643834i
$343$		0			0
$344$	−38.6001	−	3.70137i	−0.112210	−	0.0107598i
$345$	92.0174	−	159.379i	0.266717	−	0.461968i
$346$	5.66181	−	177.616i	0.0163636	−	0.513340i
$347$	−68.3727	−	118.425i	−0.197039	−	0.341282i	0.750528	−	0.660839i	$-0.229799\pi$
$347$	−68.3727	−	118.425i	−0.197039	−	0.341282i	−0.947567	+	0.319557i	$0.896466\pi$
$348$	−30.3714	+	475.904i	−0.0872741	+	1.36754i
$349$			82.0565i			0.235119i	0.993066	+	0.117559i	$0.0375071\pi$
$349$			82.0565i			0.235119i	−0.993066	+	0.117559i	$0.962493\pi$
$350$		0			0
$351$		−	277.081i		−	0.789406i
$352$	−678.577	−	109.042i	−1.92778	−	0.309778i
$353$	253.684	+	439.393i	0.718651	+	1.24474i	0.961535	+	0.274684i	$0.0885732\pi$
$353$	253.684	+	439.393i	0.718651	+	1.24474i	−0.242884	+	0.970055i	$0.578093\pi$
$354$	−240.084	−	7.65309i	−0.678203	−	0.0216189i
$355$	−116.028	+	200.966i	−0.326838	+	0.566101i
$356$	−283.617	−	572.636i	−0.796676	−	1.60853i
$357$		0			0
$358$	−84.7740	+	136.589i	−0.236799	+	0.381534i
$359$	−485.675	−	280.404i	−1.35285	−	0.781071i	−0.364206	−	0.931318i	$-0.618660\pi$
$359$	−485.675	−	280.404i	−1.35285	−	0.781071i	−0.988648	+	0.150248i	$0.951993\pi$
$360$	101.017	−	46.0842i	0.280602	−	0.128012i
$361$	170.109	+	294.637i	0.471216	+	0.816170i
$362$	487.219	−	260.962i	1.34591	−	0.720891i
$363$	1171.02			3.22595
$364$		0			0
$365$		−	273.003i		−	0.747952i
$366$	−385.874	+	206.680i	−1.05430	+	0.564700i
$367$	−23.3334	+	13.4716i	−0.0635788	+	0.0367072i	−0.531452	−	0.847088i	$-0.678354\pi$
$367$	−23.3334	+	13.4716i	−0.0635788	+	0.0367072i	0.467874	+	0.883795i	$0.345020\pi$
$368$	−22.2759	+	173.815i	−0.0605324	+	0.472324i
$369$	−53.7638	+	93.1216i	−0.145701	+	0.252362i
$370$	−279.312	+	450.032i	−0.754897	+	1.21630i
$371$		0			0
$372$	420.723	−	208.377i	1.13098	−	0.560153i
$373$	465.951	+	269.017i	1.24920	+	0.721225i	0.970950	−	0.239284i	$-0.0769126\pi$
$373$	465.951	+	269.017i	1.24920	+	0.721225i	0.278249	+	0.960509i	$0.410246\pi$
$374$	−10.0846	−	0.321464i	−0.0269641	−	0.000859528i
$375$	380.648	−	219.767i	1.01506	−	0.586046i
$376$	−471.257	−	335.863i	−1.25334	−	0.893254i
$377$	−453.000			−1.20159
$378$		0			0
$379$	−182.132			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$379$	−182.132			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$380$	5.67075	−	88.8578i	0.0149230	−	0.233836i
$381$	74.9256	−	43.2583i	0.196655	−	0.113539i
$382$	12.9363	−	405.823i	0.0338647	−	1.06236i
$383$	−288.621	−	166.636i	−0.753580	−	0.435080i	0.0734058	−	0.997302i	$-0.476613\pi$
$383$	−288.621	−	166.636i	−0.753580	−	0.435080i	−0.826986	+	0.562222i	$0.809947\pi$
$384$	−299.173	+	323.298i	−0.779095	+	0.841921i
$385$		0			0
$386$	−92.1079	+	148.406i	−0.238621	+	0.384471i
$387$	6.88874	−	11.9316i	0.0178004	−	0.0308311i
$388$	−200.553	+	301.268i	−0.516890	+	0.776465i
$389$	94.9498	−	54.8193i	0.244087	−	0.140924i	−0.372967	−	0.927845i	$-0.621659\pi$
$389$	94.9498	−	54.8193i	0.244087	−	0.140924i	0.617054	+	0.786921i	$0.288326\pi$
$390$	207.484	+	387.374i	0.532010	+	0.993267i
$391$			2.57258i			0.00657948i
$392$		0			0
$393$	434.971			1.10680
$394$	−38.1942	+	20.4574i	−0.0969395	+	0.0519223i
$395$	−231.969	−	401.782i	−0.587263	−	1.01717i
$396$	135.316	−	203.270i	0.341707	−	0.513308i
$397$	−269.280	−	155.469i	−0.678288	−	0.391610i	0.120922	−	0.992662i	$-0.461415\pi$
$397$	−269.280	−	155.469i	−0.678288	−	0.391610i	−0.799210	+	0.601052i	$0.794748\pi$
$398$	309.160	+	191.880i	0.776785	+	0.482111i
$399$		0			0
$400$	−11.2248	+	14.7329i	−0.0280619	+	0.0368323i
$401$	211.952	−	367.111i	0.528557	−	0.915488i	−0.470888	−	0.882193i	$-0.656066\pi$
$401$	211.952	−	367.111i	0.528557	−	0.915488i	0.999446	−	0.0332953i	$-0.0106002\pi$
$402$	126.811	+	4.04233i	0.315451	+	0.0100555i
$403$	222.998	+	386.243i	0.553344	+	0.958420i
$404$	−46.1481	+	723.117i	−0.114228	+	1.78989i
$405$		−	480.974i		−	1.18759i
$406$		0			0
$407$			1164.88i			2.86211i
$408$	−3.75306	+	5.26600i	−0.00919869	+	0.0129069i
$409$	222.272	+	384.986i	0.543451	+	0.941285i	0.998703	+	0.0509223i	$0.0162161\pi$
$409$	222.272	+	384.986i	0.543451	+	0.941285i	−0.455251	+	0.890363i	$0.650451\pi$
$410$	−11.7705	+	369.250i	−0.0287085	+	0.900610i
$411$	−60.1288	+	104.146i	−0.146299	+	0.253397i
$412$	−140.870	+	69.7703i	−0.341917	+	0.169345i
$413$		0			0
$414$	−52.9008	−	32.8329i	−0.127780	−	0.0793064i
$415$	302.417	+	174.601i	0.728716	+	0.420725i
$416$	−324.590	−	264.059i	−0.780264	−	0.634758i
$417$	−205.010	−	355.088i	−0.491631	−	0.851529i
$418$	−92.4575	−	172.619i	−0.221190	−	0.412964i
$419$	−457.129			−1.09100			−0.545500	−	0.838111i	$-0.683660\pi$
$419$	−457.129			−1.09100			−0.545500	+	0.838111i	$0.683660\pi$
$420$		0			0
$421$			25.4812i			0.0605255i	0.999542	+	0.0302628i	$0.00963441\pi$
$421$			25.4812i			0.0605255i	−0.999542	+	0.0302628i	$0.990366\pi$
$422$	20.2275	+	37.7649i	0.0479325	+	0.0894904i
$423$	178.063	−	102.805i	0.420953	−	0.243037i
$424$	157.727	−	71.9558i	0.371999	−	0.169707i
$425$	−0.135955	+	0.235481i	−0.000319894	+	0.000554072i
$426$	277.913	+	172.487i	0.652378	+	0.404898i
$427$		0			0
$428$	−68.2606	−	137.821i	−0.159487	−	0.322013i
$429$	836.973	+	483.226i	1.95099	+	1.12640i
$430$	1.50815	−	47.3119i	0.00350732	−	0.110028i
$431$	−107.903	+	62.2976i	−0.250354	+	0.144542i	−0.619926	−	0.784660i	$-0.712838\pi$
$431$	−107.903	+	62.2976i	−0.250354	+	0.144542i	0.369572	+	0.929202i	$0.379504\pi$
$432$	130.821	+	312.785i	0.302826	+	0.724039i
$433$	272.271			0.628802			0.314401	−	0.949290i	$-0.398196\pi$
$433$	272.271			0.628802			0.314401	+	0.949290i	$0.398196\pi$
$434$		0			0
$435$	−582.126			−1.33822
$436$	−7.10221	+	111.288i	−0.0162895	+	0.255248i
$437$	−43.2394	+	24.9643i	−0.0989459	+	0.0571264i
$438$	−384.610	−	12.2601i	−0.878106	−	0.0279912i
$439$	220.896	+	127.535i	0.503181	+	0.290512i	0.730026	−	0.683419i	$-0.239508\pi$
$439$	220.896	+	127.535i	0.503181	+	0.290512i	−0.226845	+	0.973931i	$0.572841\pi$
$440$	80.0823	−	835.146i	0.182005	−	1.89806i
$441$		0			0
$442$	−5.21929	−	3.23935i	−0.0118084	−	0.00732885i
$443$	−65.6370	+	113.687i	−0.148165	+	0.256629i	−0.930549	−	0.366167i	$-0.880670\pi$
$443$	−65.6370	+	113.687i	−0.148165	+	0.256629i	0.782384	+	0.622796i	$0.214003\pi$
$444$	621.468	+	413.709i	1.39970	+	0.931778i
$445$	675.557	−	390.033i	1.51811	−	0.876479i
$446$	−345.480	+	185.045i	−0.774619	+	0.414898i
$447$			419.601i			0.938704i
$448$		0			0
$449$	−642.824			−1.43168			−0.715839	−	0.698265i	$-0.753956\pi$
$449$	−642.824			−1.43168			−0.715839	+	0.698265i	$0.753956\pi$
$450$	−3.10713	−	5.80104i	−0.00690473	−	0.0128912i
$451$	406.248	+	703.642i	0.900772	+	1.56018i
$452$	−182.738	+	274.506i	−0.404287	+	0.607314i
$453$	−656.856	−	379.236i	−1.45001	−	0.837165i
$454$	−28.7559	+	46.3320i	−0.0633390	+	0.102053i
$455$		0			0
$456$	−124.930	−	11.9795i	−0.273968	−	0.0262709i
$457$	−346.544	+	600.232i	−0.758302	+	1.31342i	0.185413	+	0.982661i	$0.440638\pi$
$457$	−346.544	+	600.232i	−0.758302	+	1.31342i	−0.943716	+	0.330758i	$0.892696\pi$
$458$	−11.2371	+	352.516i	−0.0245351	+	0.769685i
$459$	2.48866	+	4.31048i	0.00542191	+	0.00939102i
$460$	−213.480	−	13.6240i	−0.464088	−	0.0296173i
$461$			258.699i			0.561170i	0.959829	+	0.280585i	$0.0905285\pi$
$461$			258.699i			0.561170i	−0.959829	+	0.280585i	$0.909472\pi$
$462$		0			0
$463$			637.226i			1.37630i	0.725569	+	0.688150i	$0.241577\pi$
$463$			637.226i			1.37630i	−0.725569	+	0.688150i	$0.758423\pi$
$464$	511.371	−	213.878i	1.10209	−	0.460945i
$465$	286.563	+	496.341i	0.616264	+	1.06740i
$466$	143.600	+	4.57751i	0.308155	+	0.00982298i
$467$	−99.7417	+	172.758i	−0.213580	+	0.369931i	−0.952832	−	0.303498i	$-0.901846\pi$
$467$	−99.7417	+	172.758i	−0.213580	+	0.369931i	0.739253	+	0.673428i	$0.235179\pi$
$468$	133.224	−	65.9835i	0.284666	−	0.140990i
$469$		0			0
$470$	372.524	−	600.216i	0.792603	−	1.27705i
$471$	20.1766	+	11.6490i	0.0428378	+	0.0247324i
$472$	115.885	+	254.020i	0.245519	+	0.538179i
$473$	−52.0524	−	90.1575i	−0.110047	−	0.190608i
$474$	−576.455	+	308.758i	−1.21615	+	0.651389i
$475$	−5.27721			−0.0111099
$476$		0			0
$477$			61.5966i			0.129133i
$478$	−125.339	+	67.1334i	−0.262215	+	0.140446i
$479$	583.840	−	337.080i	1.21887	−	0.703716i	0.254196	−	0.967153i	$-0.418189\pi$
$479$	583.840	−	337.080i	1.21887	−	0.703716i	0.964677	+	0.263436i	$0.0848559\pi$
$480$	−417.113	−	339.329i	−0.868986	−	0.706934i
$481$	−354.602	+	614.188i	−0.737218	+	1.27690i
$482$	59.1792	−	95.3505i	0.122778	−	0.197823i
$483$		0			0
$484$	−604.115	−	1219.74i	−1.24817	−	2.52012i
$485$	−382.609	−	220.899i	−0.788885	−	0.455463i
$486$	−296.377	−	9.44752i	−0.609828	−	0.0194393i
$487$	−347.898	+	200.859i	−0.714370	+	0.412442i	−0.812677	−	0.582715i	$-0.801991\pi$
$487$	−347.898	+	200.859i	−0.714370	+	0.412442i	0.0983072	+	0.995156i	$0.468657\pi$
$488$	414.347	+	295.303i	0.849071	+	0.605130i
$489$	−713.181			−1.45845
$490$		0			0
$491$	428.880			0.873482			0.436741	−	0.899587i	$-0.356133\pi$
$491$	428.880			0.873482			0.436741	+	0.899587i	$0.356133\pi$
$492$	519.677	+	33.1649i	1.05625	+	0.0674083i
$493$	7.04719	−	4.06870i	0.0142945	−	0.00825293i
$494$	3.79841	−	119.159i	0.00768909	−	0.241213i
$495$	258.152	+	149.044i	0.521518	+	0.301099i
$496$	−434.093	−	330.727i	−0.875187	−	0.666789i
$497$		0			0
$498$	259.561	−	418.209i	0.521207	−	0.839778i
$499$	−91.3096	+	158.153i	−0.182985	+	0.316940i	−0.942896	−	0.333088i	$-0.891909\pi$
$499$	−91.3096	+	158.153i	−0.182985	+	0.316940i	0.759911	+	0.650028i	$0.225243\pi$
$500$	−425.282	−	283.109i	−0.850564	−	0.566217i
$501$	493.316	−	284.816i	0.984662	−	0.568495i
$502$	348.405	+	650.476i	0.694035	+	1.29577i
$503$			380.158i			0.755781i	0.925850	+	0.377891i	$0.123350\pi$
$503$			380.158i			0.755781i	−0.925850	+	0.377891i	$0.876650\pi$
$504$		0			0
$505$	−884.516			−1.75152
$506$	−414.716	+	222.129i	−0.819597	+	0.438989i
$507$	3.41094	+	5.90792i	0.00672769	+	0.0116527i
$508$	−83.7112	−	55.7263i	−0.164786	−	0.109697i
$509$	−250.747	−	144.769i	−0.492627	−	0.284418i	0.233037	−	0.972468i	$-0.425134\pi$
$509$	−250.747	−	144.769i	−0.492627	−	0.284418i	−0.725664	+	0.688050i	$0.758467\pi$
$510$	−6.70703	−	4.16272i	−0.0131510	−	0.00816219i
$511$		0			0
$512$	491.088	+	144.834i	0.959156	+	0.282878i
$513$	−48.2998	+	83.6576i	−0.0941516	+	0.163075i
$514$	−47.4615	−	1.51292i	−0.0923376	−	0.00294342i
$515$	−95.9490	−	166.188i	−0.186309	−	0.322696i
$516$	−66.5860	−	4.24941i	−0.129043	−	0.00823529i
$517$		−	1553.62i		−	3.00507i
$518$		0			0
$519$		−	305.768i		−	0.589148i
$520$	296.452	−	415.958i	0.570099	−	0.799918i
$521$	−369.449	−	639.905i	−0.709116	−	1.22822i	−0.965185	−	0.261566i	$-0.915761\pi$
$521$	−369.449	−	639.905i	−0.709116	−	1.22822i	0.256070	−	0.966658i	$-0.417572\pi$
$522$	−6.27465	+	196.841i	−0.0120204	+	0.377090i
$523$	323.563	−	560.428i	0.618668	−	1.07156i	−0.371061	−	0.928608i	$-0.621006\pi$
$523$	323.563	−	560.428i	0.618668	−	1.07156i	0.989729	−	0.142956i	$-0.0456606\pi$
$524$	−224.397	−	453.068i	−0.428238	−	0.864633i
$525$		0			0
$526$	125.699	+	78.0151i	0.238972	+	0.148318i
$527$	−6.93823	−	4.00579i	−0.0131655	−	0.00760111i
$528$	−1172.97	−	150.326i	−2.22154	−	0.284709i
$529$	−204.524	−	354.245i	−0.386623	−	0.669651i
$530$	99.9220	+	186.555i	0.188532	+	0.351991i
$531$	−99.2014			−0.186820
$532$		0			0
$533$			494.666i			0.928078i
$534$	−519.147	−	969.251i	−0.972185	−	1.81508i
$535$	162.592	−	93.8727i	0.303911	−	0.175463i
$536$	−61.2099	−	134.172i	−0.114198	−	0.250321i
$537$	−138.303	+	239.549i	−0.257548	+	0.446087i
$538$	570.277	+	353.942i	1.05999	+	0.657885i
$539$		0			0
$540$	−370.876	+	183.689i	−0.686807	+	0.340164i
$541$	−154.778	−	89.3612i	−0.286096	−	0.165178i	0.350084	−	0.936718i	$-0.386153\pi$
$541$	−154.778	−	89.3612i	−0.286096	−	0.165178i	−0.636180	+	0.771541i	$0.719486\pi$
$542$	11.9334	−	374.361i	0.0220174	−	0.690704i
$543$	823.597	−	475.504i	1.51675	−	0.875698i
$544$	7.42125	+	1.19253i	0.0136420	+	0.00219216i
$545$	−136.127			−0.249775
$546$		0			0
$547$	452.236			0.826758			0.413379	−	0.910559i	$-0.364349\pi$
$547$	452.236			0.826758			0.413379	+	0.910559i	$0.364349\pi$
$548$	139.499	+	8.90258i	0.254560	+	0.0162456i
$549$	−156.560	+	90.3898i	−0.285172	+	0.164644i
$550$	−49.7000	−	1.58427i	−0.0903636	−	0.00288050i
$551$	136.772	+	78.9651i	0.248224	+	0.143312i
$552$	−28.7807	+	300.143i	−0.0521390	+	0.543737i
$553$		0			0
$554$	−225.314	−	139.841i	−0.406705	−	0.252421i
$555$	−455.680	+	789.261i	−0.821045	+	1.42209i
$556$	−264.098	+	396.725i	−0.474997	+	0.713534i
$557$	−739.679	+	427.054i	−1.32797	+	0.766704i	−0.984986	−	0.172637i	$-0.944771\pi$
$557$	−739.679	+	427.054i	−1.32797	+	0.766704i	−0.342985	+	0.939341i	$0.611438\pi$
$558$	170.922	−	91.5488i	0.306313	−	0.164066i
$559$		−	63.3814i		−	0.113383i
$560$		0			0
$561$	−17.3607			−0.0309460
$562$	−313.057	−	584.481i	−0.557042	−	1.04000i
$563$	124.827	+	216.207i	0.221718	+	0.384026i	0.955330	−	0.295542i	$-0.0955003\pi$
$563$	124.827	+	216.207i	0.221718	+	0.384026i	−0.733612	+	0.679569i	$0.762167\pi$
$564$	−828.864	−	551.772i	−1.46962	−	0.978319i
$565$	−348.621	−	201.276i	−0.617028	−	0.356241i
$566$	−70.3636	+	113.371i	−0.124317	+	0.200302i
$567$		0			0
$568$	36.2905	−	378.459i	0.0638917	−	0.666301i
$569$	−52.1763	+	90.3719i	−0.0916982	+	0.158826i	−0.908226	−	0.418480i	$-0.862563\pi$
$569$	−52.1763	+	90.3719i	−0.0916982	+	0.158826i	0.816528	+	0.577306i	$0.195896\pi$
$570$	4.88114	−	153.125i	0.00856340	−	0.268641i
$571$	324.853	+	562.661i	0.568919	+	0.985396i	0.996673	+	0.0815010i	$0.0259714\pi$
$571$	324.853	+	562.661i	0.568919	+	0.985396i	−0.427755	+	0.903895i	$0.640695\pi$
$572$	71.5457	−	1121.08i	0.125080	−	1.95994i
$573$		−	698.630i		−	1.21925i
$574$		0			0
$575$			12.6785i			0.0220495i
$576$	−119.237	+	137.386i	−0.207009	+	0.238517i
$577$	−173.011	−	299.664i	−0.299846	−	0.519349i	0.676255	−	0.736668i	$-0.263602\pi$
$577$	−173.011	−	299.664i	−0.299846	−	0.519349i	−0.976101	+	0.217320i	$0.930269\pi$
$578$	−577.596	−	18.4119i	−0.999302	−	0.0318545i
$579$	−150.268	+	260.272i	−0.259531	+	0.449520i
$580$	300.312	+	606.344i	0.517779	+	1.04542i
$581$		0			0
$582$	−328.389	+	529.106i	−0.564242	+	0.909116i
$583$	403.077	+	232.717i	0.691385	+	0.399171i
$584$	185.646	+	406.936i	0.317887	+	0.696809i
$585$	90.7412	+	157.168i	0.155113	+	0.268664i
$586$	509.895	−	273.108i	0.870128	−	0.466055i
$587$	1153.54			1.96514			0.982572	−	0.185885i	$-0.0595150\pi$
$587$	1153.54			1.96514			0.982572	+	0.185885i	$0.0595150\pi$
$588$		0			0
$589$		−	155.488i		−	0.263987i
$590$	−300.448	+	160.925i	−0.509233	+	0.272754i
$591$	−64.5635	+	37.2758i	−0.109244	+	0.0630723i
$592$	110.313	−	860.751i	0.186339	−	1.45397i
$593$	440.068	−	762.219i	0.742104	−	1.28536i	−0.209432	−	0.977823i	$-0.567161\pi$
$593$	440.068	−	762.219i	0.742104	−	1.28536i	0.951536	−	0.307538i	$-0.0995052\pi$
$594$	−479.994	+	773.374i	−0.808071	+	1.30198i
$595$		0			0
$596$	437.058	−	216.467i	0.733318	−	0.363200i
$597$	542.202	+	313.041i	0.908212	+	0.524356i
$598$	−286.280	−	9.12566i	−0.478729	−	0.0152603i
$599$	−480.591	+	277.469i	−0.802322	+	0.463221i	−0.844282	−	0.535898i	$-0.819973\pi$
$599$	−480.591	+	277.469i	−0.802322	+	0.463221i	0.0419604	+	0.999119i	$0.486640\pi$
$600$	−18.4963	+	25.9525i	−0.0308271	+	0.0432542i
$601$	666.057			1.10825			0.554124	−	0.832434i	$-0.313054\pi$
$601$	666.057			1.10825			0.554124	+	0.832434i	$0.313054\pi$
$602$		0			0
$603$	52.3977			0.0868950
$604$	−56.1491	+	879.827i	−0.0929620	+	1.45667i
$605$	1438.96	−	830.786i	2.37845	−	1.37320i
$606$	−39.7223	+	1246.12i	−0.0655483	+	2.05630i
$607$	−167.079	−	96.4633i	−0.275254	−	0.158918i	0.356019	−	0.934479i	$-0.384134\pi$
$607$	−167.079	−	96.4633i	−0.275254	−	0.158918i	−0.631273	+	0.775561i	$0.717467\pi$
$608$	51.9718	+	136.307i	0.0854800	+	0.224189i
$609$		0			0
$610$	−327.536	+	527.732i	−0.536945	+	0.865134i
$611$	472.939	−	819.155i	0.774041	−	1.34068i
$612$	−1.47988	+	2.22306i	−0.00241811	+	0.00363245i
$613$	526.747	−	304.117i	0.859293	−	0.496113i	−0.00448257	−	0.999990i	$-0.501427\pi$
$613$	526.747	−	304.117i	0.859293	−	0.496113i	0.863775	+	0.503877i	$0.168094\pi$
$614$	0.654573	+	1.22209i	0.00106608	+	0.00199038i
$615$			635.668i			1.03361i
$616$		0			0
$617$	0.884056			0.00143283			0.000716415	−	1.00000i	$-0.499772\pi$
$617$	0.884056			0.00143283			0.000716415		1.00000i	$0.499772\pi$
$618$	−238.438	+	127.711i	−0.385822	+	0.206652i
$619$	179.262	+	310.491i	0.289600	+	0.501602i	0.973714	−	0.227773i	$-0.0731445\pi$
$619$	179.262	+	310.491i	0.289600	+	0.501602i	−0.684114	+	0.729375i	$0.739811\pi$
$620$	369.156	−	554.541i	0.595413	−	0.894421i
$621$	200.987	+	116.040i	0.323650	+	0.186860i
$622$	−105.626	−	65.5569i	−0.169817	−	0.105397i
$623$		0			0
$624$	−572.694	−	436.326i	−0.917780	−	0.699240i
$625$	297.360	−	515.042i	0.475776	−	0.824068i
$626$	−426.971	−	13.6104i	−0.682062	−	0.0217419i
$627$	−168.468	−	291.796i	−0.268689	−	0.465384i
$628$	1.72473	−	27.0256i	0.00274638	−	0.0430344i
$629$		−	12.7397i		−	0.0202539i
$630$		0			0
$631$		−	390.515i		−	0.618883i	−0.950918	−	0.309442i	$-0.899858\pi$
$631$		−	390.515i		−	0.618883i	0.950918	−	0.309442i	$-0.100142\pi$
$632$	618.990	+	441.152i	0.979414	+	0.698026i
$633$	36.8569	+	63.8379i	0.0582257	+	0.100850i
$634$	1.49475	−	46.8916i	0.00235765	−	0.0739614i
$635$	61.3797	−	106.313i	0.0966609	−	0.167422i
$636$	267.309	−	132.394i	0.420298	−	0.208166i
$637$		0			0
$638$	1264.39	+	784.742i	1.98180	+	1.23000i
$639$	116.985	+	67.5415i	0.183076	+	0.105699i
$640$	−138.262	+	609.522i	−0.216034	+	0.952379i
$641$	215.968	+	374.068i	0.336924	+	0.583569i	0.983852	−	0.178981i	$-0.0572802\pi$
$641$	215.968	+	374.068i	0.336924	+	0.583569i	−0.646929	+	0.762551i	$0.723947\pi$
$642$	−124.948	−	233.278i	−0.194622	−	0.363362i
$643$	−49.9370			−0.0776625			−0.0388313	−	0.999246i	$-0.512363\pi$
$643$	−49.9370			−0.0776625			−0.0388313	+	0.999246i	$0.512363\pi$
$644$		0			0
$645$		−	81.4480i		−	0.126276i
$646$	1.01116	+	1.88785i	0.00156526	+	0.00292236i
$647$	194.112	−	112.070i	0.300018	−	0.173216i	−0.342433	−	0.939542i	$-0.611251\pi$
$647$	194.112	−	112.070i	0.300018	−	0.173216i	0.642451	+	0.766327i	$0.277918\pi$
$648$	327.069	+	716.937i	0.504737	+	1.10638i
$649$	−374.791	+	649.157i	−0.577490	+	1.00024i
$650$	−25.7223	−	15.9645i	−0.0395728	−	0.0245608i
$651$		0			0
$652$	367.922	+	742.851i	0.564297	+	1.13934i
$653$	−69.9434	−	40.3818i	−0.107111	−	0.0618405i	0.445488	−	0.895288i	$-0.353030\pi$
$653$	−69.9434	−	40.3818i	−0.107111	−	0.0618405i	−0.552598	+	0.833448i	$0.686364\pi$
$654$	−6.11327	+	191.778i	−0.00934751	+	0.293239i
$655$	534.498	−	308.593i	0.816028	−	0.471134i
$656$	−233.550	−	558.406i	−0.356022	−	0.851229i
$657$	−158.919			−0.241886
$658$		0			0
$659$	−940.466			−1.42711			−0.713555	−	0.700599i	$-0.752916\pi$
$659$	−940.466			−1.42711			−0.713555	+	0.700599i	$0.752916\pi$
$660$	91.9396	−	1440.65i	0.139302	−	2.18280i
$661$	−103.862	+	59.9649i	−0.157129	+	0.0907184i	−0.576503	−	0.817095i	$-0.695583\pi$
$661$	−103.862	+	59.9649i	−0.157129	+	0.0907184i	0.419374	+	0.907814i	$0.362250\pi$
$662$	1014.30	+	32.3325i	1.53217	+	0.0488406i
$663$	−9.15354	−	5.28480i	−0.0138062	−	0.00797104i
$664$	−569.513	−	54.6107i	−0.857700	−	0.0822450i
$665$		0			0
$666$	261.970	+	162.592i	0.393349	+	0.244132i
$667$	189.713	−	328.593i	0.284428	−	0.492643i
$668$	−551.161	−	366.906i	−0.825091	−	0.549261i
$669$	−584.000	+	337.173i	−0.872945	+	0.503995i
$670$	158.695	−	84.9996i	0.236858	−	0.126865i
$671$			1366.00i			2.03577i
$672$		0			0
$673$	1085.06			1.61227			0.806136	−	0.591731i	$-0.201555\pi$
$673$	1085.06			1.61227			0.806136	+	0.591731i	$0.201555\pi$
$674$	323.639	+	604.236i	0.480176	+	0.896493i
$675$	12.2649	+	21.2434i	0.0181702	+	0.0314717i
$676$	4.39405	−	6.60068i	0.00650007	−	0.00976431i
$677$	822.639	+	474.951i	1.21512	+	0.701552i	0.963871	−	0.266370i	$-0.0858242\pi$
$677$	822.639	+	474.951i	1.21512	+	0.701552i	0.251253	+	0.967922i	$0.419158\pi$
$678$	−299.217	+	482.104i	−0.441324	+	0.711068i
$679$		0			0
$680$	−0.875819	+	9.13357i	−0.00128797	+	0.0134317i
$681$	−46.9135	+	81.2566i	−0.0688891	+	0.119319i
$682$	46.6792	−	1464.37i	0.0684446	−	2.14716i
$683$	446.893	+	774.041i	0.654308	+	1.13330i	0.982067	+	0.188534i	$0.0603735\pi$
$683$	446.893	+	774.041i	0.654308	+	1.13330i	−0.327758	+	0.944762i	$0.606293\pi$
$684$	−51.7255	−	3.30103i	−0.0756220	−	0.00482607i
$685$			170.635i			0.249102i
$686$		0			0
$687$			606.861i			0.883349i
$688$	29.9248	+	71.5484i	0.0434953	+	0.103995i
$689$	141.683	+	245.402i	0.205636	+	0.356172i
$690$	−367.883	−	11.7269i	−0.533164	−	0.0169955i
$691$	604.282	−	1046.65i	0.874504	−	1.51468i	0.0172129	−	0.999852i	$-0.494521\pi$
$691$	604.282	−	1046.65i	0.874504	−	1.51468i	0.857291	−	0.514833i	$-0.172146\pi$
$692$	−318.489	+	157.742i	−0.460244	+	0.227951i
$693$		0			0
$694$	−144.222	+	232.373i	−0.207813	+	0.334831i
$695$	−503.838	−	290.891i	−0.724947	−	0.418548i
$696$	867.714	−	395.854i	1.24672	−	0.568756i
$697$	−4.44293	−	7.69537i	−0.00637436	−	0.0110407i
$698$	144.668	−	77.4866i	0.207261	−	0.111012i
$699$	247.210			0.353662
$700$		0			0
$701$			219.477i			0.313091i	0.987671	+	0.156546i	$0.0500358\pi$
$701$			219.477i			0.313091i	−0.987671	+	0.156546i	$0.949964\pi$
$702$	−488.503	+	261.650i	−0.695874	+	0.372721i
$703$	214.126	−	123.626i	0.304589	−	0.175854i
$704$	448.542	+	1299.32i	0.637133	+	1.84563i
$705$	607.749	−	1052.65i	0.862055	−	1.49312i
$706$	535.108	−	862.175i	0.757944	−	1.22121i
$707$		0			0
$708$	213.221	+	430.502i	0.301159	+	0.608054i
$709$	−1095.64	−	632.566i	−1.54533	−	0.892195i	−0.998489	−	0.0549560i	$-0.982498\pi$
$709$	−1095.64	−	632.566i	−1.54533	−	0.892195i	−0.546838	−	0.837239i	$-0.684169\pi$
$710$	463.875	+	14.7868i	0.653345	+	0.0208265i
$711$	−233.884	+	135.033i	−0.328950	+	0.189920i
$712$	−741.754	+	1040.77i	−1.04179	+	1.46176i
$713$	−373.560			−0.523927
$714$		0			0
$715$	1371.31			1.91792
$716$	320.864	+	20.4770i	0.448134	+	0.0285991i
$717$	−211.873	+	122.325i	−0.295499	+	0.170606i
$718$	−35.7354	+	1121.05i	−0.0497707	+	1.56135i
$719$	1007.59	+	581.735i	1.40138	+	0.809089i	0.994535	−	0.104407i	$-0.0332946\pi$
$719$	1007.59	+	581.735i	1.40138	+	0.809089i	0.406848	+	0.913496i	$0.366628\pi$
$720$	−176.639	−	134.578i	−0.245332	−	0.186914i
$721$		0			0
$722$	358.820	−	578.136i	0.496981	−	0.800743i
$723$	96.5472	−	167.225i	0.133537	−	0.231293i
$724$	−920.170	−	612.554i	−1.27095	−	0.846069i
$725$	34.7308	−	20.0518i	0.0479045	−	0.0276577i
$726$	−1105.80	−	2064.54i	−1.52314	−	2.84373i
$727$		−	1303.68i		−	1.79324i	−0.442803	−	0.896619i	$-0.646016\pi$
$727$		−	1303.68i		−	1.79324i	0.442803	−	0.896619i	$-0.353984\pi$
$728$		0			0
$729$	376.305			0.516193
$730$	−481.312	+	257.799i	−0.659332	+	0.353149i
$731$	0.569271	+	0.986006i	0.000778756	+	0.00134885i
$732$	728.767	+	485.138i	0.995584	+	0.662757i
$733$	−1087.83	−	628.061i	−1.48408	−	0.856836i	−0.484248	−	0.874931i	$-0.660907\pi$
$733$	−1087.83	−	628.061i	−1.48408	−	0.856836i	−0.999836	+	0.0180947i	$0.994240\pi$
$734$	45.7847	+	28.4163i	0.0623770	+	0.0387143i
$735$		0			0
$736$	327.477	−	124.862i	0.444942	−	0.169649i
$737$	197.963	−	342.882i	0.268606	−	0.465240i
$738$	214.946	+	6.85178i	0.291255	+	0.00928425i
$739$	−343.584	−	595.105i	−0.464931	−	0.805284i	0.534267	−	0.845316i	$-0.320588\pi$
$739$	−343.584	−	595.105i	−0.464931	−	0.805284i	−0.999198	+	0.0400312i	$0.987254\pi$
$740$	1057.18	+	67.4673i	1.42862	+	0.0911720i
$741$		−	205.134i		−	0.276835i
$742$		0			0
$743$		−	362.628i		−	0.488059i	−0.969768	−	0.244030i	$-0.921531\pi$
$743$		−	362.628i		−	0.488059i	0.969768	−	0.244030i	$-0.0784694\pi$
$744$	−764.668	−	544.976i	−1.02778	−	0.732495i
$745$	297.688	+	515.611i	0.399581	+	0.692095i
$746$	34.2841	−	1075.52i	0.0459573	−	1.44172i
$747$	101.638	−	176.042i	0.136061	−	0.235665i
$748$	8.95620	+	18.0830i	0.0119735	+	0.0241751i
$749$		0			0
$750$	−746.905	−	463.566i	−0.995874	−	0.618088i
$751$	−226.350	−	130.683i	−0.301398	−	0.174012i	0.341673	−	0.939819i	$-0.389006\pi$
$751$	−226.350	−	130.683i	−0.301398	−	0.174012i	−0.643071	+	0.765807i	$0.722340\pi$
$752$	−147.126	+	1148.00i	−0.195646	+	1.52660i
$753$	634.835	+	1099.57i	0.843074	+	1.46025i
$754$	427.771	+	798.653i	0.567336	+	1.05922i
$755$	−1076.20			−1.42544
$756$		0			0
$757$		−	1395.34i		−	1.84325i	−0.388081	−	0.921625i	$-0.626862\pi$
$757$		−	1395.34i		−	1.84325i	0.388081	−	0.921625i	$-0.373138\pi$
$758$	171.989	+	321.105i	0.226899	+	0.423622i
$759$	−701.037	+	404.744i	−0.923633	+	0.533260i
$760$	−162.014	+	73.9114i	−0.213176	+	0.0972519i
$761$	−159.750	+	276.695i	−0.209921	+	0.363594i	−0.951690	−	0.307062i	$-0.900654\pi$
$761$	−159.750	+	276.695i	−0.209921	+	0.363594i	0.741768	+	0.670656i	$0.233987\pi$
$762$	−147.019	−	91.2470i	−0.192938	−	0.119747i
$763$		0			0
$764$	−727.695	+	360.415i	−0.952481	+	0.471747i
$765$	−2.82327	−	1.63002i	−0.00369055	−	0.00213074i
$766$	−21.2364	+	666.204i	−0.0277238	+	0.869718i
$767$	−395.221	+	228.181i	−0.515282	+	0.297498i
$768$	852.496	+	222.158i	1.11002	+	0.289268i
$769$	−634.936			−0.825664			−0.412832	−	0.910807i	$-0.635460\pi$
$769$	−634.936			−0.825664			−0.412832	+	0.910807i	$0.635460\pi$
$770$		0			0
$771$	−81.7056			−0.105974
$772$	348.622	+	22.2485i	0.451583	+	0.0288193i
$773$	−83.2825	+	48.0832i	−0.107739	+	0.0622033i	−0.552901	−	0.833247i	$-0.686479\pi$
$773$	−83.2825	+	48.0832i	−0.107739	+	0.0622033i	0.445162	+	0.895450i	$0.353146\pi$
$774$	−27.5410	−	0.877916i	−0.0355827	−	0.00113426i
$775$	−34.1938	−	19.7418i	−0.0441210	−	0.0254733i
$776$	720.530	+	69.0917i	0.928518	+	0.0890358i
$777$		0			0
$778$	−186.310	−	115.633i	−0.239473	−	0.148629i
$779$	86.2282	−	149.352i	0.110691	−	0.191722i
$780$	487.024	−	731.601i	0.624390	−	0.937950i
$781$	883.960	−	510.354i	1.13183	−	0.653463i
$782$	4.53554	−	2.42931i	0.00579992	−	0.00310653i
$783$		−	734.098i		−	0.937545i
$784$		0			0
$785$	33.0577			0.0421117
$786$	−410.747	−	766.868i	−0.522579	−	0.975659i
$787$	−659.623	−	1142.50i	−0.838148	−	1.45172i	−0.891441	−	0.453137i	$-0.850305\pi$
$787$	−659.623	−	1142.50i	−0.838148	−	1.45172i	0.0532926	−	0.998579i	$-0.483028\pi$
$788$	72.1341	+	48.0194i	0.0915407	+	0.0609384i
$789$	220.450	+	127.277i	0.279404	+	0.161314i
$790$	−489.305	+	788.375i	−0.619373	+	0.997943i
$791$		0			0
$792$	−486.152	−	46.6171i	−0.613828	−	0.0588600i
$793$	−415.825	+	720.231i	−0.524370	+	0.908235i
$794$	−19.8133	+	621.560i	−0.0249538	+	0.782822i
$795$	182.069	+	315.354i	0.229018	+	0.396671i
$796$	46.3483	−	726.254i	0.0582265	−	0.912379i
$797$			818.575i			1.02707i	0.858068	+	0.513535i	$0.171664\pi$
$797$			818.575i			1.02707i	−0.858068	+	0.513535i	$0.828336\pi$
$798$		0			0
$799$			16.9911i			0.0212655i
$800$	36.5743	+	5.87718i	0.0457178	+	0.00734648i
$801$	−227.044	−	393.252i	−0.283451	−	0.490951i
$802$	−847.376	−	27.0116i	−1.05658	−	0.0336803i
$803$	−600.409	+	1039.94i	−0.747707	+	1.29507i
$804$	−112.622	−	227.389i	−0.140077	−	0.282823i
$805$		0			0
$806$	470.381	−	757.885i	0.583599	−	0.940304i
$807$	1000.15	+	577.435i	1.23934	+	0.715532i
$808$	1318.46	−	601.484i	1.63175	−	0.744411i
$809$	−616.362	−	1067.57i	−0.761881	−	1.31962i	−0.941880	−	0.335950i	$-0.890943\pi$
$809$	−616.362	−	1067.57i	−0.761881	−	1.31962i	0.179998	−	0.983667i	$-0.442391\pi$
$810$	−847.972	+	454.188i	−1.04688	+	0.560725i
$811$	1009.05			1.24421			0.622103	−	0.782935i	$-0.286278\pi$
$811$	1009.05			1.24421			0.622103	+	0.782935i	$0.286278\pi$
$812$		0			0
$813$		−	644.468i		−	0.792703i
$814$	2053.72	−	1100.00i	2.52300	−	1.35136i
$815$	−876.366	+	505.970i	−1.07530	+	0.620822i
$816$	12.8282	+	1.64404i	0.0157208	+	0.00201476i
$817$	−11.0484	+	19.1364i	−0.0135231	+	0.0234227i
$818$	468.849	−	755.417i	0.573165	−	0.923493i
$819$		0			0
$820$	662.114	−	327.934i	0.807457	−	0.399919i
$821$	813.278	+	469.547i	0.990595	+	0.571920i	0.905452	−	0.424448i	$-0.139532\pi$
$821$	813.278	+	469.547i	0.990595	+	0.571920i	0.0851429	+	0.996369i	$0.472865\pi$
$822$	240.393	+	7.66295i	0.292449	+	0.00932233i
$823$	−789.036	+	455.550i	−0.958731	+	0.553524i	−0.895782	−	0.444493i	$-0.853384\pi$
$823$	−789.036	+	455.550i	−0.958731	+	0.553524i	−0.0629491	+	0.998017i	$0.520051\pi$
$824$	256.032	+	182.473i	0.310718	+	0.221448i
$825$	−85.5591			−0.103708
$826$		0			0
$827$	−65.6564			−0.0793910			−0.0396955	−	0.999212i	$-0.512639\pi$
$827$	−65.6564			−0.0793910			−0.0396955	+	0.999212i	$0.512639\pi$
$828$	−7.93071	+	124.270i	−0.00957816	+	0.150085i
$829$	−1312.84	+	757.970i	−1.58365	+	0.914318i	−0.589324	+	0.807897i	$0.700606\pi$
$829$	−1312.84	+	757.970i	−1.58365	+	0.914318i	−0.994321	+	0.106421i	$0.966061\pi$
$830$	22.2515	−	698.048i	0.0268090	−	0.841022i
$831$	−395.154	−	228.142i	−0.475516	−	0.274539i
$832$	−159.032	+	821.616i	−0.191144	+	0.987519i
$833$		0			0
$834$	−432.438	+	696.752i	−0.518511	+	0.835433i
$835$	404.129	−	699.971i	0.483986	−	0.838289i
$836$	−217.024	+	326.011i	−0.259599	+	0.389965i
$837$	−625.918	+	361.374i	−0.747811	+	0.431749i
$838$	431.671	+	805.933i	0.515120	+	0.961734i
$839$		−	869.972i		−	1.03692i	−0.855103	−	0.518458i	$-0.826506\pi$
$839$		−	869.972i		−	1.03692i	0.855103	−	0.518458i	$-0.173494\pi$
$840$		0			0
$841$	−359.174			−0.427080
$842$	44.9242	−	24.0621i	0.0533542	−	0.0285774i
$843$	−570.427	−	988.008i	−0.676663	−	1.17201i
$844$	47.4798	−	71.3235i	0.0562557	−	0.0845065i
$845$	8.38282	+	4.83982i	0.00992049	+	0.00572760i
$846$	−349.395	−	216.852i	−0.412996	−	0.256326i
$847$		0			0
$848$	−275.804	−	210.130i	−0.325240	−	0.247795i
$849$	−114.794	+	198.829i	−0.135211	+	0.234192i
$850$	0.543543	+	0.0173264i	0.000639462	+	2.03840e-5i
$851$	−297.010	−	514.436i	−0.349013	−	0.604508i
$852$	41.6638	−	652.850i	0.0489012	−	0.766256i
$853$			1643.91i			1.92721i	0.267322	+	0.963607i	$0.413861\pi$
$853$			1643.91i			1.92721i	−0.267322	+	0.963607i	$0.586139\pi$
$854$		0			0
$855$		−	63.2706i		−	0.0740007i
$856$	−178.524	+	250.491i	−0.208557	+	0.292630i
$857$	143.029	+	247.734i	0.166895	+	0.289071i	0.937327	−	0.348452i	$-0.113292\pi$
$857$	143.029	+	247.734i	0.166895	+	0.289071i	−0.770431	+	0.637523i	$0.779959\pi$
$858$	61.5834	−	1931.92i	0.0717756	−	2.25166i
$859$	359.891	−	623.350i	0.418965	−	0.725669i	−0.576870	−	0.816836i	$-0.695726\pi$
$859$	359.891	−	623.350i	0.418965	−	0.725669i	0.995836	+	0.0911667i	$0.0290596\pi$
$860$	−84.8365	+	42.0181i	−0.0986471	+	0.0488582i
$861$		0			0
$862$	211.726	+	131.408i	0.245622	+	0.152445i
$863$	−970.358	−	560.236i	−1.12440	−	0.649173i	−0.181880	−	0.983321i	$-0.558218\pi$
$863$	−970.358	−	560.236i	−1.12440	−	0.649173i	−0.942521	+	0.334147i	$0.891552\pi$
$864$	427.915	−	526.007i	0.495272	−	0.608804i
$865$	−216.929	−	375.731i	−0.250785	−	0.434372i
$866$	−257.108	−	480.023i	−0.296892	−	0.554299i
$867$	−994.339			−1.14687
$868$		0			0
$869$			2040.66i			2.34828i
$870$	549.706	+	1026.31i	0.631846	+	1.17966i
$871$	208.754	−	120.524i	0.239671	−	0.138374i
$872$	202.911	−	92.5687i	0.232696	−	0.106157i
$873$	−128.589	+	222.723i	−0.147296	+	0.255123i
$874$	84.8441	+	52.6584i	0.0970756	+	0.0602499i
$875$		0			0
$876$	341.576	+	689.658i	0.389927	+	0.787281i
$877$	−125.920	−	72.6998i	−0.143580	−	0.0828960i	0.426489	−	0.904493i	$-0.359750\pi$
$877$	−125.920	−	72.6998i	−0.143580	−	0.0828960i	−0.570069	+	0.821597i	$0.693084\pi$
$878$	16.2533	−	509.880i	0.0185117	−	0.580728i
$879$	861.928	−	497.634i	0.980578	−	0.566137i
$880$	−1548.01	+	647.448i	−1.75910	+	0.735736i
$881$	−476.080			−0.540386			−0.270193	−	0.962806i	$-0.587087\pi$
$881$	−476.080			−0.540386			−0.270193	+	0.962806i	$0.587087\pi$
$882$		0			0
$883$	−1101.22			−1.24714			−0.623568	−	0.781769i	$-0.714318\pi$
$883$	−1101.22			−1.24714			−0.623568	+	0.781769i	$0.714318\pi$
$884$	−0.782459	+	12.2607i	−0.000885135	+	0.0138696i
$885$	−507.878	+	293.223i	−0.573873	+	0.331326i
$886$	262.415	+	8.36493i	0.296179	+	0.00944123i
$887$	−1291.67	−	745.743i	−1.45622	−	0.840748i	−0.457396	−	0.889263i	$-0.651218\pi$
$887$	−1291.67	−	745.743i	−1.45622	−	0.840748i	−0.998822	+	0.0485153i	$0.984551\pi$
$888$	142.525	−	1486.34i	0.160501	−	1.67380i
$889$		0			0
$890$	−1325.57	−	822.717i	−1.48941	−	0.924401i
$891$	−1057.80	+	1832.16i	−1.18720	+	2.05629i
$892$	652.479	+	434.353i	0.731479	+	0.486943i
$893$	−285.584	+	164.882i	−0.319802	+	0.184638i
$894$	739.770	−	396.233i	0.827483	−	0.443213i
$895$			392.481i			0.438526i
$896$		0			0
$897$	−492.834			−0.549425
$898$	607.024	+	1133.32i	0.675973	+	1.26205i
$899$	590.809	+	1023.31i	0.657184	+	1.13828i
$900$	−7.29333	+	10.9559i	−0.00810370	+	0.0121733i
$901$	−4.40825	−	2.54510i	−0.00489262	−	0.00282476i
$902$	856.920	−	1380.68i	0.950023	−	1.53069i
$903$		0			0
$904$	656.524	+	62.9541i	0.726243	+	0.0696395i
$905$	674.698	−	1168.61i	0.745522	−	1.29128i
$906$	−48.3307	+	1516.17i	−0.0533451	+	1.67348i
$907$	−577.731	−	1000.66i	−0.636969	−	1.10326i	−0.986094	−	0.166187i	$-0.946855\pi$
$907$	−577.731	−	1000.66i	−0.636969	−	1.10326i	0.349125	−	0.937076i	$-0.386479\pi$
$908$	108.839	+	6.94594i	0.119867	+	0.00764971i
$909$			514.891i			0.566436i
$910$		0			0
$911$		−	944.690i		−	1.03698i	−0.855083	−	0.518491i	$-0.826494\pi$
$911$		−	944.690i		−	1.03698i	0.855083	−	0.518491i	$-0.173506\pi$
$912$	96.8518	+	231.567i	0.106197	+	0.253911i
$913$	−767.991	−	1330.20i	−0.841173	−	1.45695i
$914$	1385.47	+	44.1644i	1.51583	+	0.0483199i
$915$	−534.355	+	925.530i	−0.583995	+	1.01151i
$916$	632.108	−	313.072i	0.690074	−	0.341782i
$917$		0			0
$918$	5.24945	−	8.45800i	0.00571836	−	0.00921351i
$919$	−129.167	−	74.5748i	−0.140552	−	0.0811478i	0.428075	−	0.903743i	$-0.359192\pi$
$919$	−129.167	−	74.5748i	−0.140552	−	0.0811478i	−0.568627	+	0.822595i	$0.692525\pi$
$920$	177.572	+	389.238i	0.193013	+	0.423085i
$921$	1.19271	+	2.06583i	0.00129501	+	0.00224303i
$922$	456.095	−	244.292i	0.494680	−	0.264959i
$923$	621.430			0.673272
$924$		0			0
$925$		−	62.7851i		−	0.0678758i
$926$	1123.45	−	601.738i	1.21323	−	0.649825i
$927$	−96.7409	+	55.8534i	−0.104359	+	0.0602517i
$928$	−859.967	−	699.597i	−0.926688	−	0.753876i
$929$	−29.4199	+	50.9568i	−0.0316684	+	0.0548513i	−0.881425	−	0.472324i	$-0.843415\pi$
$929$	−29.4199	+	50.9568i	−0.0316684	+	0.0548513i	0.849757	+	0.527175i	$0.176749\pi$
$930$	604.462	−	973.918i	0.649959	−	1.04722i
$931$		0			0
$932$	−127.533	−	257.494i	−0.136838	−	0.276282i
$933$	−185.246	−	106.952i	−0.198549	−	0.114632i
$934$	398.764	+	12.7113i	0.426942	+	0.0136095i
$935$	−21.3331	+	12.3167i	−0.0228161	+	0.0131729i
$936$	−242.135	−	172.569i	−0.258692	−	0.184369i
$937$	1700.18			1.81449			0.907246	−	0.420601i	$-0.138181\pi$
$937$	1700.18			1.81449			0.907246	+	0.420601i	$0.138181\pi$
$938$		0			0
$939$	−735.036			−0.782786
$940$	−1409.98	−	89.9823i	−1.49997	−	0.0957259i
$941$	49.0270	−	28.3058i	0.0521010	−	0.0300805i	−0.473723	−	0.880674i	$-0.657090\pi$
$941$	49.0270	−	28.3058i	0.0521010	−	0.0300805i	0.525824	+	0.850593i	$0.323757\pi$
$942$	1.48457	−	46.5722i	0.00157598	−	0.0494397i
$943$	−358.816	−	207.163i	−0.380505	−	0.219685i
$944$	338.415	−	444.182i	0.358490	−	0.470532i
$945$		0			0
$946$	−109.797	+	176.907i	−0.116064	+	0.187005i
$947$	−121.267	+	210.040i	−0.128053	+	0.221795i	−0.922922	−	0.384986i	$-0.874206\pi$
$947$	−121.267	+	210.040i	−0.128053	+	0.221795i	0.794869	+	0.606781i	$0.207540\pi$
$948$	1088.70	+	724.745i	1.14842	+	0.764499i
$949$	−633.138	+	365.542i	−0.667163	+	0.385187i
$950$	4.98332	+	9.30389i	0.00524560	+	0.00979357i
$951$		−	80.7244i		−	0.0848837i
$952$		0			0
$953$	−364.070			−0.382025			−0.191013	−	0.981588i	$-0.561177\pi$
$953$	−364.070			−0.382025			−0.191013	+	0.981588i	$0.561177\pi$
$954$	108.597	−	58.1661i	0.113833	−	0.0609708i
$955$	−495.647	−	858.485i	−0.519002	−	0.898938i
$956$	236.717	+	157.581i	0.247611	+	0.164834i
$957$	2217.47	+	1280.26i	2.31711	+	1.33778i
$958$	−1145.61	−	711.021i	−1.19583	−	0.742193i
$959$		0			0
$960$	−204.364	+	1055.81i	−0.212879	+	1.09981i
$961$	101.174	−	175.238i	0.105280	−	0.182350i
$962$	1417.69	+	45.1913i	1.47369	+	0.0469764i
$963$	−54.6448	−	94.6475i	−0.0567443	−	0.0982840i
$964$	−223.989	−	14.2946i	−0.232354	−	0.0148285i
$965$			426.435i			0.441901i
$966$		0			0
$967$			1221.99i			1.26369i	0.775093	+	0.631847i	$0.217703\pi$
$967$			1221.99i			1.26369i	−0.775093	+	0.631847i	$0.782297\pi$
$968$	−1579.97	+	2216.88i	−1.63220	+	2.29017i
$969$	1.84245	+	3.19122i	0.00190139	+	0.00329331i
$970$	−28.1519	+	883.149i	−0.0290226	+	0.910463i
$971$	−544.266	+	942.696i	−0.560521	+	0.970851i	0.436930	+	0.899496i	$0.356066\pi$
$971$	−544.266	+	942.696i	−0.560521	+	0.970851i	−0.997451	+	0.0713553i	$0.977268\pi$
$972$	263.215	+	531.443i	0.270797	+	0.546752i
$973$		0			0
$974$	682.644	+	423.683i	0.700866	+	0.434992i
$975$	−45.1115	−	26.0451i	−0.0462682	−	0.0267130i
$976$	129.359	−	1009.36i	0.132540	−	1.03418i
$977$	530.757	+	919.299i	0.543252	+	0.940940i	0.998715	+	0.0506853i	$0.0161405\pi$
$977$	530.757	+	919.299i	0.543252	+	0.940940i	−0.455463	+	0.890255i	$0.650526\pi$
$978$	673.462	+	1257.36i	0.688612	+	1.28564i
$979$	−3431.17			−3.50477
$980$		0			0
$981$			79.2419i			0.0807766i
$982$	−404.995	−	756.129i	−0.412418	−	0.769989i
$983$	−1145.42	+	661.306i	−1.16522	+	0.672743i	−0.952551	−	0.304381i	$-0.901551\pi$
$983$	−1145.42	+	661.306i	−1.16522	+	0.672743i	−0.212674	+	0.977123i	$0.568217\pi$
$984$	−432.264	−	947.524i	−0.439293	−	0.962931i
$985$	−52.8910	+	91.6099i	−0.0536964	+	0.0930049i
$986$	−13.8280	−	8.58232i	−0.0140243	−	0.00870417i
$987$		0			0
$988$	−213.669	+	105.826i	−0.216264	+	0.107112i
$989$	45.9750	+	26.5437i	0.0464864	+	0.0268389i
$990$	18.9945	−	595.873i	0.0191863	−	0.601892i
$991$	−585.266	+	337.903i	−0.590581	+	0.340972i	−0.765327	−	0.643642i	$-0.777423\pi$
$991$	−585.266	+	337.903i	−0.590581	+	0.340972i	0.174746	+	0.984613i	$0.444089\pi$
$992$	−173.166	+	1077.63i	−0.174562	+	1.08632i
$993$	1746.12			1.75843
$994$		0			0
$995$	888.354			0.892818
$996$	−982.422	−	62.6965i	−0.986368	−	0.0629483i
$997$	354.395	−	204.610i	0.355462	−	0.205226i	−0.311627	−	0.950205i	$-0.600874\pi$
$997$	354.395	−	204.610i	0.355462	−	0.205226i	0.667088	+	0.744979i	$0.267540\pi$
$998$	365.053	+	11.6367i	0.365784	+	0.0116600i
$999$	−995.309	−	574.642i	−0.996305	−	0.575217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.3		16
7.2	even	3		392.3.g.m.99.4		8
7.3	odd	6		392.3.k.o.67.8		16
7.4	even	3	inner	392.3.k.n.67.8		16
7.5	odd	6		56.3.g.b.43.4	yes	8
7.6	odd	2		392.3.k.o.275.3		16
8.3	odd	2	inner	392.3.k.n.275.8		16
21.5	even	6		504.3.g.b.379.5		8
28.19	even	6		224.3.g.b.15.5		8
28.23	odd	6		1568.3.g.m.687.4		8
56.3	even	6		392.3.k.o.67.3		16
56.5	odd	6		224.3.g.b.15.6		8
56.11	odd	6	inner	392.3.k.n.67.3		16
56.19	even	6		56.3.g.b.43.3	✓	8
56.27	even	2		392.3.k.o.275.8		16
56.37	even	6		1568.3.g.m.687.3		8
56.51	odd	6		392.3.g.m.99.3		8
84.47	odd	6		2016.3.g.b.1135.6		8
112.5	odd	12		1792.3.d.j.1023.12		16
112.19	even	12		1792.3.d.j.1023.11		16
112.61	odd	12		1792.3.d.j.1023.5		16
112.75	even	12		1792.3.d.j.1023.6		16
168.5	even	6		2016.3.g.b.1135.3		8
168.131	odd	6		504.3.g.b.379.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	56.19	even	6
56.3.g.b.43.4	yes	8	7.5	odd	6
224.3.g.b.15.5		8	28.19	even	6
224.3.g.b.15.6		8	56.5	odd	6
392.3.g.m.99.3		8	56.51	odd	6
392.3.g.m.99.4		8	7.2	even	3
392.3.k.n.67.3		16	56.11	odd	6	inner
392.3.k.n.67.8		16	7.4	even	3	inner
392.3.k.n.275.3		16	1.1	even	1	trivial
392.3.k.n.275.8		16	8.3	odd	2	inner
392.3.k.o.67.3		16	56.3	even	6
392.3.k.o.67.8		16	7.3	odd	6
392.3.k.o.275.3		16	7.6	odd	2
392.3.k.o.275.8		16	56.27	even	2
504.3.g.b.379.5		8	21.5	even	6
504.3.g.b.379.6		8	168.131	odd	6
1568.3.g.m.687.3		8	56.37	even	6
1568.3.g.m.687.4		8	28.23	odd	6
1792.3.d.j.1023.5		16	112.61	odd	12
1792.3.d.j.1023.6		16	112.75	even	12
1792.3.d.j.1023.11		16	112.19	even	12
1792.3.d.j.1023.12		16	112.5	odd	12
2016.3.g.b.1135.3		8	168.5	even	6
2016.3.g.b.1135.6		8	84.47	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.944308 - 1.76303i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(-2.21656 + 3.32969i) q^{4} +(-4.22869 - 2.44143i) q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +O(q^{10})\)	\(q+(-0.944308 - 1.76303i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(-2.21656 + 3.32969i) q^{4} +(-4.22869 - 2.44143i) q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +(-0.311142 + 9.76078i) q^{10} +(10.7388 + 18.6001i) q^{11} +(13.7372 + 0.876683i) q^{12} +13.0760i q^{13} +16.8033i q^{15} +(-6.17369 - 14.7609i) q^{16} +(-0.117445 - 0.203420i) q^{17} +(5.68190 + 0.181120i) q^{18} +(2.27936 - 3.94797i) q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} +(-9.48497 - 5.47615i) q^{23} +(-11.4265 - 25.0469i) q^{24} +(-0.578804 - 1.00252i) q^{25} +(23.0534 - 12.3478i) q^{26} -21.1900 q^{27} +34.6435i q^{29} +(29.6248 - 15.8675i) q^{30} +(29.5383 - 17.0539i) q^{31} +(-20.1942 + 24.8233i) q^{32} +(36.9551 - 64.0082i) q^{33} +(-0.247732 + 0.399150i) q^{34} +(-5.04614 - 10.1884i) q^{36} +(46.9706 + 27.1185i) q^{37} +(-9.11282 - 0.290487i) q^{38} +(38.9696 - 22.4991i) q^{39} +(-31.8107 - 22.6714i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(-85.7359 - 5.47152i) q^{44} +(12.0196 - 6.93951i) q^{45} +(-0.697893 + 21.8935i) q^{46} +(-62.6455 - 36.1684i) q^{47} +(-33.3684 + 43.7973i) q^{48} +(-1.22090 + 1.96714i) q^{50} +(-0.404160 + 0.700025i) q^{51} +(-43.5391 - 28.9838i) q^{52} +(18.7674 - 10.8353i) q^{53} +(20.0099 + 37.3587i) q^{54} -104.872i q^{55} -15.6878 q^{57} +(61.0777 - 32.7142i) q^{58} +(17.4503 + 30.2249i) q^{59} +(-55.9498 - 37.2456i) q^{60} +(55.0803 + 31.8006i) q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} +(31.9242 - 55.2944i) q^{65} +(-147.746 - 4.70965i) q^{66} +(-9.21718 - 15.9646i) q^{67} +(0.937649 + 0.0598392i) q^{68} +37.6899i q^{69} -47.5244i q^{71} +(-13.1974 + 18.5175i) q^{72} +(27.9551 + 48.4197i) q^{73} +(3.45604 - 108.419i) q^{74} +(-1.99182 + 3.44994i) q^{75} +(8.09317 + 16.3405i) q^{76} +(-76.4660 - 47.4586i) q^{78} +(82.2841 + 47.5067i) q^{79} +(-9.93128 + 77.4921i) q^{80} +(49.2512 + 85.3055i) q^{81} +(-35.7232 - 66.6955i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(4.57720 + 8.54567i) q^{86} +(103.246 - 59.6090i) q^{87} +(71.3146 + 156.322i) q^{88} +(-79.8779 + 138.353i) q^{89} +(-23.5848 - 14.6379i) q^{90} +(39.2579 - 19.4438i) q^{92} +(-101.649 - 58.6874i) q^{93} +(-4.60938 + 144.600i) q^{94} +(-19.2774 + 11.1298i) q^{95} +(108.726 + 17.4714i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

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