LMFDB - Embedded newform 392.3.k.o.67.3

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			67.3
Root			$0.944308 - 1.76303i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.o.275.3

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.422652	−	0.906292i	$-0.638901\pi$
$3$	1.72064	−	2.98023i	0.573546	−	0.993411i	0.996198	−	0.0871191i	$-0.0277661\pi$
$4$	−2.21656	−	3.32969i	−0.554141	−	0.832423i
$5$	4.22869	−	2.44143i	0.845737	−	0.488287i	−0.0134729	−	0.999909i	$-0.504289\pi$
$5$	4.22869	−	2.44143i	0.845737	−	0.488287i	0.859210	+	0.511623i	$0.170955\pi$
$6$	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	0.300518	−	0.953776i	$-0.402840\pi$
$11$	10.7388	−	18.6001i	0.976253	−	1.69092i	0.675735	−	0.737144i	$-0.263826\pi$
$12$	−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	$-0.831134\pi$
$17$	0.117445	−	0.203420i	0.00690851	−	0.0119659i	0.869459	+	0.494005i	$0.164468\pi$
$18$	5.68190	−	0.181120i	0.315661	−	0.0100622i
$19$	−2.27936	−	3.94797i	−0.119966	−	0.207788i	0.799788	−	0.600283i	$-0.204945\pi$
$19$	−2.27936	−	3.94797i	−0.119966	−	0.207788i	−0.919754	+	0.392495i	$0.871612\pi$
$20$	−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	−0.691816	−	0.722074i	$-0.743189\pi$
$23$	−9.48497	+	5.47615i	−0.412390	+	0.238094i	0.279426	+	0.960167i	$0.409856\pi$
$24$	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	$-0.796239\pi$
$29$		−	34.6435i		−	1.19460i	0.802016	−	0.597302i	$-0.203761\pi$
$30$	29.6248	+	15.8675i	0.987492	+	0.528917i
$31$	−29.5383	−	17.0539i	−0.952848	−	0.550127i	−0.0588837	−	0.998265i	$-0.518754\pi$
$31$	−29.5383	−	17.0539i	−0.952848	−	0.550127i	−0.893965	+	0.448138i	$0.852087\pi$
$32$	−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	0.294587	−	0.955625i	$-0.404818\pi$
$37$	46.9706	−	27.1185i	1.26948	−	0.732932i	0.974889	+	0.222693i	$0.0714847\pi$
$38$	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	$-0.652632\pi$
$41$	−37.8300			−0.922682			−0.461341	+	0.887223i	$0.652632\pi$
$42$		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	$-0.387152\pi$
$47$	62.6455	−	36.1684i	1.33288	−	0.769541i	0.985741	+	0.168271i	$0.0538185\pi$
$48$	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	0.666490	−	0.745514i	$-0.267796\pi$
$53$	18.7674	+	10.8353i	0.354101	+	0.204440i	−0.312389	+	0.949954i	$0.601129\pi$
$54$	−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	$-0.928909\pi$
$59$	−17.4503	+	30.2249i	−0.295768	+	0.512286i	0.679395	+	0.733773i	$0.262242\pi$
$60$	−55.9498	+	37.2456i	−0.932497	+	0.620760i
$61$	−55.0803	+	31.8006i	−0.902955	+	0.521321i	−0.878158	−	0.478371i	$-0.841227\pi$
$61$	−55.0803	+	31.8006i	−0.902955	+	0.521321i	−0.0247973	+	0.999693i	$0.507894\pi$
$62$	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	−0.926576	−	0.376107i	$-0.877263\pi$
$67$	−9.21718	+	15.9646i	−0.137570	+	0.238278i	0.789006	+	0.614385i	$0.210596\pi$
$68$	−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	$0.108628\pi$
$71$			47.5244i			0.669358i	−0.942332	+	0.334679i	$0.891372\pi$
$72$	−13.1974	−	18.5175i	−0.183297	−	0.257188i
$73$	−27.9551	+	48.4197i	−0.382947	+	0.663284i	−0.991482	−	0.130243i	$-0.958424\pi$
$73$	−27.9551	+	48.4197i	−0.382947	+	0.663284i	0.608535	+	0.793527i	$0.291758\pi$
$74$	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	0.121293	−	0.992617i	$-0.461296\pi$
$79$	82.2841	−	47.5067i	1.04157	−	0.601351i	0.920278	+	0.391266i	$0.127963\pi$
$80$	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	$-0.358225\pi$
$83$	71.5156			0.861634			0.430817	+	0.902439i	$0.358225\pi$
$84$		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	0.830675	+	0.556758i	$0.187955\pi$
$89$	79.8779	+	138.353i	0.897504	+	1.55452i	0.0668296	+	0.997764i	$0.478712\pi$
$90$	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	$-0.654445\pi$
$97$	−90.4794			−0.932777			−0.466389	+	0.884580i	$0.654445\pi$
$98$		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	−0.997875	−	0.0651645i	$-0.979243\pi$
$101$	−156.878	−	90.5735i	−1.55325	−	0.896767i	−0.555371	−	0.831602i	$-0.687424\pi$
$102$	1.61582	−	0.0515070i	0.0158413	−	0.000504970i
$103$	−34.0350	+	19.6501i	−0.330437	+	0.190778i	−0.656035	−	0.754730i	$-0.727768\pi$
$103$	−34.0350	+	19.6501i	−0.330437	+	0.190778i	0.325598	+	0.945508i	$0.394434\pi$
$104$	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	0.762096	−	0.647464i	$-0.224170\pi$
$107$	−19.2249	−	33.2985i	−0.179672	−	0.311201i	−0.941768	+	0.336263i	$0.890837\pi$
$108$	−46.9691	−	70.5563i	−0.434899	−	0.653299i
$109$	24.1436	+	13.9393i	0.221501	+	0.127883i	0.606645	−	0.794973i	$-0.292515\pi$
$109$	24.1436	+	13.9393i	0.221501	+	0.127883i	−0.385144	+	0.922856i	$0.625848\pi$
$110$	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	$-0.968442\pi$
$127$		−	25.1408i		−	0.197959i	0.995089	−	0.0989796i	$-0.0315579\pi$
$128$	−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	$-0.00641881\pi$
$131$	63.1991	+	109.464i	0.482436	+	0.835603i	−0.517361	+	0.855767i	$0.673085\pi$
$132$	−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	−0.922723	−	0.385465i	$-0.874041\pi$
$137$	−17.4728	+	30.2638i	−0.127539	+	0.220904i	0.795184	+	0.606369i	$0.207374\pi$
$138$	−66.4485	−	35.5909i	−0.481511	−	0.257905i
$139$	−119.148			−0.857177			−0.428589	−	0.903500i	$-0.640989\pi$
$139$	−119.148			−0.857177			−0.428589	+	0.903500i	$0.640989\pi$
$140$		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	−0.810579	−	0.585630i	$-0.800847\pi$
$149$	−105.596	+	60.9659i	−0.708698	+	0.409167i	0.101881	+	0.994797i	$0.467514\pi$
$150$	−7.96326	+	0.253843i	−0.0530884	+	0.00169228i
$151$	190.876	+	110.202i	1.26408	+	0.729815i	0.973861	−	0.227146i	$-0.0729396\pi$
$151$	190.876	+	110.202i	1.26408	+	0.729815i	0.290216	+	0.956961i	$0.406273\pi$
$152$	−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	$-0.326470\pi$
$157$	5.86312	+	3.38507i	0.0373447	+	0.0215610i	−0.481211	+	0.876605i	$0.659803\pi$
$158$	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	0.986363	+	0.164583i	$0.0526278\pi$
$163$	103.621	+	179.478i	0.635715	+	1.10109i	−0.350649	+	0.936507i	$0.614039\pi$
$164$	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	$-0.749335\pi$
$173$	−76.9489	+	44.4265i	−0.444791	+	0.256800i	0.260836	+	0.965383i	$0.416002\pi$
$174$	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	−0.956176	−	0.292792i	$-0.905416\pi$
$179$	−40.1896	+	69.6104i	−0.224523	+	0.388885i	0.731653	+	0.681677i	$0.238749\pi$
$180$	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	0.0367067	−	0.999326i	$-0.488313\pi$
$191$	175.816	−	101.507i	0.920502	−	0.531452i	0.883795	+	0.467874i	$0.154980\pi$
$192$	71.8683	−	208.186i	0.374314	−	1.08430i
$193$	−43.6664	+	75.6325i	−0.226251	+	0.391878i	−0.956694	−	0.291096i	$-0.905980\pi$
$193$	−43.6664	+	75.6325i	−0.226251	+	0.391878i	0.730443	+	0.682974i	$0.239314\pi$
$194$	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	$0.0175109\pi$
$197$			21.6639i			0.109969i	−0.998487	+	0.0549845i	$0.982489\pi$
$198$	57.6478	−	107.629i	0.291151	−	0.543581i
$199$	157.558	+	90.9664i	0.791751	+	0.457118i	0.840579	−	0.541690i	$-0.182215\pi$
$199$	157.558	+	90.9664i	0.791751	+	0.457118i	−0.0488277	+	0.998807i	$0.515549\pi$
$200$	−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	$-0.814206\pi$
$227$	13.6326	−	23.6123i	0.0600554	−	0.104019i	0.894490	+	0.447088i	$0.147539\pi$
$228$	34.7731	+	52.2356i	0.152513	+	0.229104i
$229$	152.721	−	88.1737i	0.666906	−	0.385038i	−0.127998	−	0.991774i	$-0.540855\pi$
$229$	152.721	−	88.1737i	0.666906	−	0.385038i	0.794903	+	0.606736i	$0.207522\pi$
$230$	−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	0.778596	−	0.627526i	$-0.215932\pi$
$233$	−35.9183	−	62.2123i	−0.154156	−	0.267006i	−0.932751	+	0.360520i	$0.882599\pi$
$234$	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	$0.0475183\pi$
$239$			71.0926i			0.297459i	−0.988878	+	0.148729i	$0.952482\pi$
$240$	248.033	+	103.738i	1.03347	+	0.432243i
$241$	−28.0556	+	48.5938i	−0.116413	+	0.201634i	−0.918344	−	0.395783i	$-0.870473\pi$
$241$	−28.0556	+	48.5938i	−0.116413	+	0.201634i	0.801930	+	0.597417i	$0.203806\pi$
$242$	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	$-0.237198\pi$
$251$	368.953			1.46993			0.734966	+	0.678104i	$0.237198\pi$
$252$		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	$-0.181375\pi$
$257$	−11.8714	−	20.5619i	−0.0461923	−	0.0800073i	−0.888197	+	0.459463i	$0.848042\pi$
$258$	−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	0.373243	−	0.927734i	$-0.378246\pi$
$263$	−64.0605	−	36.9853i	−0.243576	−	0.140629i	−0.616819	+	0.787105i	$0.711579\pi$
$264$	−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	$-0.118930\pi$
$269$	290.632	+	167.797i	1.08042	+	0.623779i	0.149408	+	0.988776i	$0.452263\pi$
$270$	6.59311	+	206.831i	0.0244189	+	0.766042i
$271$	−162.186	+	93.6379i	−0.598471	+	0.345527i	−0.768440	−	0.639922i	$-0.778967\pi$
$271$	−162.186	+	93.6379i	−0.598471	+	0.345527i	0.169969	+	0.985449i	$0.445633\pi$
$272$	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	0.692739	−	0.721189i	$-0.256404\pi$
$277$	114.828	+	66.2958i	0.414541	+	0.239335i	−0.278198	+	0.960524i	$0.589737\pi$
$278$	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	$-0.795726\pi$
$283$	33.3579	−	57.7776i	0.117873	−	0.204161i	0.918924	+	0.394434i	$0.129059\pi$
$284$	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	$-0.499641\pi$
$307$	0.693177			0.00225790			0.00112895	+	0.999999i	$0.499641\pi$
$308$		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	$-0.365196\pi$
$311$	−53.8307	−	31.0792i	−0.173089	−	0.0999330i	−0.584042	+	0.811724i	$0.698530\pi$
$312$	327.514	+	149.413i	1.04972	+	0.478888i
$313$	−106.797	−	184.978i	−0.341204	−	0.590983i	0.643452	−	0.765486i	$-0.277501\pi$
$313$	−106.797	−	184.978i	−0.341204	−	0.590983i	−0.984657	+	0.174503i	$0.944168\pi$
$314$	−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	−0.467615	−	0.883932i	$-0.654887\pi$
$317$	20.3150	−	11.7288i	0.0640850	−	0.0369995i	0.531700	+	0.846933i	$0.321553\pi$
$318$	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	−0.939464	−	0.342648i	$-0.888676\pi$
$331$	−253.703	−	439.426i	−0.766474	−	1.32757i	0.172990	−	0.984924i	$-0.444657\pi$
$332$	−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	−0.947567	−	0.319557i	$-0.896466\pi$
$347$	−68.3727	+	118.425i	−0.197039	+	0.341282i	0.750528	+	0.660839i	$0.229799\pi$
$348$	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	0.242884	+	0.970055i	$0.421907\pi$
$353$	−253.684	+	439.393i	−0.718651	+	1.24474i	−0.961535	+	0.274684i	$0.911427\pi$
$354$	−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	−0.988648	−	0.150248i	$-0.951993\pi$
$359$	−485.675	+	280.404i	−1.35285	+	0.781071i	−0.364206	+	0.931318i	$0.618660\pi$
$360$	−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	$-0.321646\pi$
$367$	23.3334	+	13.4716i	0.0635788	+	0.0367072i	−0.467874	+	0.883795i	$0.654980\pi$
$368$	−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	0.278249	−	0.960509i	$-0.410246\pi$
$373$	465.951	−	269.017i	1.24920	−	0.721225i	0.970950	+	0.239284i	$0.0769126\pi$
$374$	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	$-0.523387\pi$
$383$	288.621	−	166.636i	0.753580	−	0.435080i	0.826986	+	0.562222i	$0.190053\pi$
$384$	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	0.617054	−	0.786921i	$-0.288326\pi$
$389$	94.9498	+	54.8193i	0.244087	+	0.140924i	−0.372967	+	0.927845i	$0.621659\pi$
$390$	−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	$-0.538585\pi$
$397$	269.280	−	155.469i	0.678288	−	0.391610i	0.799210	+	0.601052i	$0.205252\pi$
$398$	−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	0.999446	+	0.0332953i	$0.0106002\pi$
$401$	211.952	+	367.111i	0.528557	+	0.915488i	−0.470888	+	0.882193i	$0.656066\pi$
$402$	−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	0.455251	+	0.890363i	$0.349549\pi$
$409$	−222.272	+	384.986i	−0.543451	+	0.941285i	−0.998703	+	0.0509223i	$0.983784\pi$
$410$	−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	$-0.316340\pi$
$419$	457.129			1.09100			0.545500	+	0.838111i	$0.316340\pi$
$420$		0			0
$421$		−	25.4812i		−	0.0605255i	−0.999542	−	0.0302628i	$-0.990366\pi$
$421$		−	25.4812i		−	0.0605255i	0.999542	−	0.0302628i	$-0.00963441\pi$
$422$	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	0.369572	−	0.929202i	$-0.379504\pi$
$431$	−107.903	−	62.2976i	−0.250354	−	0.144542i	−0.619926	+	0.784660i	$0.712838\pi$
$432$	−130.821	+	312.785i	−0.302826	+	0.724039i
$433$	−272.271			−0.628802			−0.314401	−	0.949290i	$-0.601804\pi$
$433$	−272.271			−0.628802			−0.314401	+	0.949290i	$0.601804\pi$
$434$		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	$-0.760492\pi$
$439$	−220.896	+	127.535i	−0.503181	+	0.290512i	0.226845	+	0.973931i	$0.427159\pi$
$440$	−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	0.782384	−	0.622796i	$-0.214003\pi$
$443$	−65.6370	−	113.687i	−0.148165	−	0.256629i	−0.930549	+	0.366167i	$0.880670\pi$
$444$	−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	−0.943716	−	0.330758i	$-0.892696\pi$
$457$	−346.544	−	600.232i	−0.758302	−	1.31342i	0.185413	−	0.982661i	$-0.440638\pi$
$458$	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	$-0.758423\pi$
$463$		−	637.226i		−	1.37630i	0.725569	−	0.688150i	$-0.241577\pi$
$464$	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	$-0.0981544\pi$
$467$	99.7417	+	172.758i	0.213580	+	0.369931i	−0.739253	+	0.673428i	$0.764821\pi$
$468$	−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	$-0.581811\pi$
$479$	−583.840	−	337.080i	−1.21887	−	0.703716i	−0.964677	+	0.263436i	$0.915144\pi$
$480$	−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	0.0983072	−	0.995156i	$-0.468657\pi$
$487$	−347.898	−	200.859i	−0.714370	−	0.412442i	−0.812677	+	0.582715i	$0.801991\pi$
$488$	−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	0.759911	−	0.650028i	$-0.225243\pi$
$499$	−91.3096	−	158.153i	−0.182985	−	0.316940i	−0.942896	+	0.333088i	$0.891909\pi$
$500$	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	$-0.574866\pi$
$509$	250.747	−	144.769i	0.492627	−	0.284418i	0.725664	+	0.688050i	$0.241533\pi$
$510$	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	−0.256070	−	0.966658i	$-0.582428\pi$
$521$	369.449	−	639.905i	0.709116	−	1.22822i	0.965185	−	0.261566i	$-0.0842390\pi$
$522$	−6.27465	−	196.841i	−0.0120204	−	0.377090i
$523$	−323.563	−	560.428i	−0.618668	−	1.07156i	−0.989729	−	0.142956i	$-0.954339\pi$
$523$	−323.563	−	560.428i	−0.618668	−	1.07156i	0.371061	−	0.928608i	$-0.378994\pi$
$524$	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	−0.636180	−	0.771541i	$-0.719486\pi$
$541$	−154.778	+	89.3612i	−0.286096	+	0.165178i	0.350084	+	0.936718i	$0.386153\pi$
$542$	−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	−0.342985	−	0.939341i	$-0.611438\pi$
$557$	−739.679	−	427.054i	−1.32797	−	0.766704i	−0.984986	+	0.172637i	$0.944771\pi$
$558$	−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	$-0.904500\pi$
$563$	−124.827	+	216.207i	−0.221718	+	0.384026i	0.733612	+	0.679569i	$0.237833\pi$
$564$	−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	0.816528	−	0.577306i	$-0.195896\pi$
$569$	−52.1763	−	90.3719i	−0.0916982	−	0.158826i	−0.908226	+	0.418480i	$0.862563\pi$
$570$	−4.88114	−	153.125i	−0.00856340	−	0.268641i
$571$	324.853	−	562.661i	0.568919	−	0.985396i	−0.427755	−	0.903895i	$-0.640695\pi$
$571$	324.853	−	562.661i	0.568919	−	0.985396i	0.996673	−	0.0815010i	$-0.0259714\pi$
$572$	−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	$-0.736398\pi$
$577$	173.011	−	299.664i	0.299846	−	0.519349i	0.976101	+	0.217320i	$0.0697314\pi$
$578$	−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	$-0.940485\pi$
$587$	−1153.54			−1.96514			−0.982572	+	0.185885i	$0.940485\pi$
$588$		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	−0.951536	−	0.307538i	$-0.900495\pi$
$593$	−440.068	−	762.219i	−0.742104	−	1.28536i	0.209432	−	0.977823i	$-0.432839\pi$
$594$	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	0.0419604	−	0.999119i	$-0.486640\pi$
$599$	−480.591	−	277.469i	−0.802322	−	0.463221i	−0.844282	+	0.535898i	$0.819973\pi$
$600$	18.4963	+	25.9525i	0.0308271	+	0.0432542i
$601$	−666.057			−1.10825			−0.554124	−	0.832434i	$-0.686946\pi$
$601$	−666.057			−1.10825			−0.554124	+	0.832434i	$0.686946\pi$
$602$		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	$-0.615866\pi$
$607$	167.079	−	96.4633i	0.275254	−	0.158918i	0.631273	+	0.775561i	$0.282533\pi$
$608$	−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	0.863775	−	0.503877i	$-0.168094\pi$
$613$	526.747	+	304.117i	0.859293	+	0.496113i	−0.00448257	+	0.999990i	$0.501427\pi$
$614$	−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	$-0.926856\pi$
$619$	−179.262	+	310.491i	−0.289600	+	0.501602i	0.684114	+	0.729375i	$0.260189\pi$
$620$	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	$0.100142\pi$
$631$			390.515i			0.618883i	−0.950918	+	0.309442i	$0.899858\pi$
$632$	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	−0.646929	−	0.762551i	$-0.723947\pi$
$641$	215.968	−	374.068i	0.336924	−	0.583569i	0.983852	+	0.178981i	$0.0572802\pi$
$642$	124.948	−	233.278i	0.194622	−	0.363362i
$643$	49.9370			0.0776625			0.0388313	−	0.999246i	$-0.487637\pi$
$643$	49.9370			0.0776625			0.0388313	+	0.999246i	$0.487637\pi$
$644$		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	$-0.388749\pi$
$647$	−194.112	−	112.070i	−0.300018	−	0.173216i	−0.642451	+	0.766327i	$0.722082\pi$
$648$	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	−0.552598	−	0.833448i	$-0.686364\pi$
$653$	−69.9434	+	40.3818i	−0.107111	+	0.0618405i	0.445488	+	0.895288i	$0.353030\pi$
$654$	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	$-0.304417\pi$
$661$	103.862	+	59.9649i	0.157129	+	0.0907184i	−0.419374	+	0.907814i	$0.637750\pi$
$662$	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	$-0.914176\pi$
$677$	−822.639	+	474.951i	−1.21512	+	0.701552i	−0.251253	+	0.967922i	$0.580842\pi$
$678$	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	−0.327758	−	0.944762i	$-0.606293\pi$
$683$	446.893	−	774.041i	0.654308	−	1.13330i	0.982067	−	0.188534i	$-0.0603735\pi$
$684$	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	−0.857291	−	0.514833i	$-0.827854\pi$
$691$	−604.282	−	1046.65i	−0.874504	−	1.51468i	−0.0172129	−	0.999852i	$-0.505479\pi$
$692$	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	$-0.949964\pi$
$701$		−	219.477i		−	0.313091i	0.987671	−	0.156546i	$-0.0500358\pi$
$702$	−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	−0.546838	+	0.837239i	$0.684169\pi$
$709$	−1095.64	+	632.566i	−1.54533	+	0.892195i	−0.998489	+	0.0549560i	$0.982498\pi$
$710$	−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	$-0.966705\pi$
$719$	−1007.59	+	581.735i	−1.40138	+	0.809089i	−0.406848	+	0.913496i	$0.633372\pi$
$720$	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	$-0.339093\pi$
$733$	1087.83	−	628.061i	1.48408	−	0.856836i	0.999836	+	0.0180947i	$0.00576004\pi$
$734$	−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	−0.999198	−	0.0400312i	$-0.987254\pi$
$739$	−343.584	+	595.105i	−0.464931	+	0.805284i	0.534267	+	0.845316i	$0.320588\pi$
$740$	−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	$0.0784694\pi$
$743$			362.628i			0.488059i	−0.969768	+	0.244030i	$0.921531\pi$
$744$	−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	−0.643071	−	0.765807i	$-0.722340\pi$
$751$	−226.350	+	130.683i	−0.301398	+	0.174012i	0.341673	+	0.939819i	$0.389006\pi$
$752$	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	$0.373138\pi$
$757$			1395.34i			1.84325i	−0.388081	+	0.921625i	$0.626862\pi$
$758$	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	$-0.0993459\pi$
$761$	159.750	+	276.695i	0.209921	+	0.363594i	−0.741768	+	0.670656i	$0.766013\pi$
$762$	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	$-0.364540\pi$
$769$	634.936			0.825664			0.412832	+	0.910807i	$0.364540\pi$
$770$		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	$-0.313521\pi$
$773$	83.2825	+	48.0832i	0.107739	+	0.0622033i	−0.445162	+	0.895450i	$0.646854\pi$
$774$	−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	−0.0532926	−	0.998579i	$-0.516972\pi$
$787$	659.623	−	1142.50i	0.838148	−	1.45172i	0.891441	−	0.453137i	$-0.149695\pi$
$788$	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	0.179998	+	0.983667i	$0.442391\pi$
$809$	−616.362	+	1067.57i	−0.761881	+	1.31962i	−0.941880	+	0.335950i	$0.890943\pi$
$810$	847.972	+	454.188i	1.04688	+	0.560725i
$811$	−1009.05			−1.24421			−0.622103	−	0.782935i	$-0.713722\pi$
$811$	−1009.05			−1.24421			−0.622103	+	0.782935i	$0.713722\pi$
$812$		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	0.0851429	−	0.996369i	$-0.472865\pi$
$821$	813.278	−	469.547i	0.990595	−	0.571920i	0.905452	+	0.424448i	$0.139532\pi$
$822$	−240.393	+	7.66295i	−0.292449	+	0.00932233i
$823$	−789.036	−	455.550i	−0.958731	−	0.553524i	−0.0629491	−	0.998017i	$-0.520051\pi$
$823$	−789.036	−	455.550i	−0.958731	−	0.553524i	−0.895782	+	0.444493i	$0.853384\pi$
$824$	−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	0.994321	+	0.106421i	$0.0339391\pi$
$829$	1312.84	+	757.970i	1.58365	+	0.914318i	0.589324	+	0.807897i	$0.299394\pi$
$830$	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	$-0.886708\pi$
$857$	−143.029	+	247.734i	−0.166895	+	0.289071i	0.770431	+	0.637523i	$0.220041\pi$
$858$	61.5834	+	1931.92i	0.0717756	+	2.25166i
$859$	−359.891	−	623.350i	−0.418965	−	0.725669i	0.576870	−	0.816836i	$-0.304274\pi$
$859$	−359.891	−	623.350i	−0.418965	−	0.725669i	−0.995836	+	0.0911667i	$0.970940\pi$
$860$	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	−0.942521	−	0.334147i	$-0.891552\pi$
$863$	−970.358	+	560.236i	−1.12440	+	0.649173i	−0.181880	+	0.983321i	$0.558218\pi$
$864$	−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	−0.570069	−	0.821597i	$-0.693084\pi$
$877$	−125.920	+	72.6998i	−0.143580	+	0.0828960i	0.426489	+	0.904493i	$0.359750\pi$
$878$	−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	$-0.412913\pi$
$881$	476.080			0.540386			0.270193	+	0.962806i	$0.412913\pi$
$882$		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	$-0.348782\pi$
$887$	1291.67	−	745.743i	1.45622	−	0.840748i	0.998822	+	0.0485153i	$0.0154490\pi$
$888$	−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	0.349125	+	0.937076i	$0.386479\pi$
$907$	−577.731	+	1000.66i	−0.636969	+	1.10326i	−0.986094	+	0.166187i	$0.946855\pi$
$908$	−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	$0.173506\pi$
$911$			944.690i			1.03698i	−0.855083	+	0.518491i	$0.826494\pi$
$912$	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	−0.568627	−	0.822595i	$-0.692525\pi$
$919$	−129.167	+	74.5748i	−0.140552	+	0.0811478i	0.428075	+	0.903743i	$0.359192\pi$
$920$	−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	$-0.156585\pi$
$929$	29.4199	+	50.9568i	0.0316684	+	0.0548513i	−0.849757	+	0.527175i	$0.823251\pi$
$930$	−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	$-0.861819\pi$
$937$	−1700.18			−1.81449			−0.907246	+	0.420601i	$0.861819\pi$
$938$		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	$-0.342910\pi$
$941$	−49.0270	−	28.3058i	−0.0521010	−	0.0300805i	−0.525824	+	0.850593i	$0.676243\pi$
$942$	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	0.794869	−	0.606781i	$-0.207540\pi$
$947$	−121.267	−	210.040i	−0.128053	−	0.221795i	−0.922922	+	0.384986i	$0.874206\pi$
$948$	−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	$-0.782297\pi$
$967$		−	1221.99i		−	1.26369i	0.775093	−	0.631847i	$-0.217703\pi$
$968$	−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	0.997451	+	0.0713553i	$0.0227324\pi$
$971$	544.266	+	942.696i	0.560521	+	0.970851i	−0.436930	+	0.899496i	$0.643934\pi$
$972$	−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	−0.455463	−	0.890255i	$-0.650526\pi$
$977$	530.757	−	919.299i	0.543252	−	0.940940i	0.998715	−	0.0506853i	$-0.0161405\pi$
$978$	−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	$-0.0984495\pi$
$983$	1145.42	+	661.306i	1.16522	+	0.672743i	0.212674	+	0.977123i	$0.431783\pi$
$984$	−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	0.174746	−	0.984613i	$-0.444089\pi$
$991$	−585.266	−	337.903i	−0.590581	−	0.340972i	−0.765327	+	0.643642i	$0.777423\pi$
$992$	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	$-0.399126\pi$
$997$	−354.395	−	204.610i	−0.355462	−	0.205226i	−0.667088	+	0.744979i	$0.732460\pi$
$998$	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.o.67.3		16
7.2	even	3	inner	392.3.k.o.275.8		16
7.3	odd	6		392.3.g.m.99.3		8
7.4	even	3		56.3.g.b.43.3	✓	8
7.5	odd	6		392.3.k.n.275.8		16
7.6	odd	2		392.3.k.n.67.3		16
8.3	odd	2	inner	392.3.k.o.67.8		16
21.11	odd	6		504.3.g.b.379.6		8
28.3	even	6		1568.3.g.m.687.3		8
28.11	odd	6		224.3.g.b.15.6		8
56.3	even	6		392.3.g.m.99.4		8
56.11	odd	6		56.3.g.b.43.4	yes	8
56.19	even	6		392.3.k.n.275.3		16
56.27	even	2		392.3.k.n.67.8		16
56.45	odd	6		1568.3.g.m.687.4		8
56.51	odd	6	inner	392.3.k.o.275.3		16
56.53	even	6		224.3.g.b.15.5		8
84.11	even	6		2016.3.g.b.1135.3		8
112.11	odd	12		1792.3.d.j.1023.5		16
112.53	even	12		1792.3.d.j.1023.11		16
112.67	odd	12		1792.3.d.j.1023.12		16
112.109	even	12		1792.3.d.j.1023.6		16
168.11	even	6		504.3.g.b.379.5		8
168.53	odd	6		2016.3.g.b.1135.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	7.4	even	3
56.3.g.b.43.4	yes	8	56.11	odd	6
224.3.g.b.15.5		8	56.53	even	6
224.3.g.b.15.6		8	28.11	odd	6
392.3.g.m.99.3		8	7.3	odd	6
392.3.g.m.99.4		8	56.3	even	6
392.3.k.n.67.3		16	7.6	odd	2
392.3.k.n.67.8		16	56.27	even	2
392.3.k.n.275.3		16	56.19	even	6
392.3.k.n.275.8		16	7.5	odd	6
392.3.k.o.67.3		16	1.1	even	1	trivial
392.3.k.o.67.8		16	8.3	odd	2	inner
392.3.k.o.275.3		16	56.51	odd	6	inner
392.3.k.o.275.8		16	7.2	even	3	inner
504.3.g.b.379.5		8	168.11	even	6
504.3.g.b.379.6		8	21.11	odd	6
1568.3.g.m.687.3		8	28.3	even	6
1568.3.g.m.687.4		8	56.45	odd	6
1792.3.d.j.1023.5		16	112.11	odd	12
1792.3.d.j.1023.6		16	112.109	even	12
1792.3.d.j.1023.11		16	112.53	even	12
1792.3.d.j.1023.12		16	112.67	odd	12
2016.3.g.b.1135.3		8	84.11	even	6
2016.3.g.b.1135.6		8	168.53	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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