LMFDB - Embedded newform 1155.2.q.j.331.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (of order $3$, degree $2$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.8
Root			$1.28184 + 2.22022i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28184 - 2.22022i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.28624 - 3.95989i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.56369 q^{6} +(-2.09509 + 1.61573i) q^{7} -6.59506 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.28184 - 2.22022i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.28624 - 3.95989i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.56369 q^{6} +(-2.09509 + 1.61573i) q^{7} -6.59506 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.28184 - 2.22022i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.28624 + 3.95989i) q^{12} -1.89800 q^{13} +(0.901685 + 6.72268i) q^{14} -1.00000 q^{15} +(-3.88134 + 6.72268i) q^{16} +(-3.57249 - 6.18773i) q^{17} +(1.28184 + 2.22022i) q^{18} +(-2.89410 + 5.01273i) q^{19} -4.57249 q^{20} +(2.44681 + 1.00654i) q^{21} +2.56369 q^{22} +(-0.794226 + 1.37564i) q^{23} +(3.29753 + 5.71149i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.43294 + 4.21397i) q^{26} +1.00000 q^{27} +(11.1880 + 4.60240i) q^{28} -5.41638 q^{29} +(-1.28184 + 2.22022i) q^{30} +(-1.35072 - 2.33951i) q^{31} +(3.35548 + 5.81187i) q^{32} +(0.500000 - 0.866025i) q^{33} -18.3175 q^{34} +(0.351714 + 2.62227i) q^{35} +4.57249 q^{36} +(-5.24247 + 9.08023i) q^{37} +(7.41956 + 12.8511i) q^{38} +(0.949000 + 1.64372i) q^{39} +(-3.29753 + 5.71149i) q^{40} +8.49189 q^{41} +(5.37117 - 4.14222i) q^{42} +7.05730 q^{43} +(2.28624 - 3.95989i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.03615 + 3.52671i) q^{46} +(6.81472 - 11.8034i) q^{47} +7.76268 q^{48} +(1.77885 - 6.77021i) q^{49} -2.56369 q^{50} +(-3.57249 + 6.18773i) q^{51} +(4.33929 + 7.51587i) q^{52} +(-4.29912 - 7.44629i) q^{53} +(1.28184 - 2.22022i) q^{54} +1.00000 q^{55} +(13.8173 - 10.6558i) q^{56} +5.78820 q^{57} +(-6.94295 + 12.0255i) q^{58} +(-2.38965 - 4.13899i) q^{59} +(2.28624 + 3.95989i) q^{60} +(3.68109 - 6.37584i) q^{61} -6.92564 q^{62} +(-0.351714 - 2.62227i) q^{63} +1.67945 q^{64} +(-0.949000 + 1.64372i) q^{65} +(-1.28184 - 2.22022i) q^{66} +(-1.60624 - 2.78209i) q^{67} +(-16.3352 + 28.2933i) q^{68} +1.58845 q^{69} +(6.27285 + 2.58046i) q^{70} -6.06777 q^{71} +(3.29753 - 5.71149i) q^{72} +(-5.54699 - 9.60767i) q^{73} +(13.4401 + 23.2789i) q^{74} +(-0.500000 + 0.866025i) q^{75} +26.4665 q^{76} +(-2.44681 - 1.00654i) q^{77} +4.86588 q^{78} +(-4.31493 + 7.47368i) q^{79} +(3.88134 + 6.72268i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.8853 - 18.8538i) q^{82} -6.27078 q^{83} +(-1.60821 - 11.9903i) q^{84} -7.14498 q^{85} +(9.04635 - 15.6687i) q^{86} +(2.70819 + 4.69072i) q^{87} +(-3.29753 - 5.71149i) q^{88} +(6.80373 - 11.7844i) q^{89} +2.56369 q^{90} +(3.97649 - 3.06665i) q^{91} +7.26318 q^{92} +(-1.35072 + 2.33951i) q^{93} +(-17.4708 - 30.2603i) q^{94} +(2.89410 + 5.01273i) q^{95} +(3.35548 - 5.81187i) q^{96} -15.5039 q^{97} +(-12.7511 - 12.6278i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.28184	−	2.22022i	0.906400	−	1.56993i	0.0873734	−	0.996176i	$-0.472153\pi$
$2$	1.28184	−	2.22022i	0.906400	−	1.56993i	0.819027	−	0.573755i	$-0.194514\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.28624	−	3.95989i	−1.14312	−	1.97995i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.56369			−1.04662
$7$	−2.09509	+	1.61573i	−0.791871	+	0.610688i
$7$	−2.09509	+	1.61573i	−0.791871	+	0.610688i
$8$	−6.59506			−2.33170
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.28184	−	2.22022i	−0.405354	−	0.702095i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−2.28624	+	3.95989i	−0.659982	+	1.14312i
$13$	−1.89800			−0.526411			−0.263205	−	0.964740i	$-0.584780\pi$
$13$	−1.89800			−0.526411			−0.263205	+	0.964740i	$0.584780\pi$
$14$	0.901685	+	6.72268i	0.240985	+	1.79671i
$15$	−1.00000			−0.258199
$16$	−3.88134	+	6.72268i	−0.970335	+	1.68067i
$17$	−3.57249	−	6.18773i	−0.866456	−	1.50075i	−0.865594	−	0.500746i	$-0.833059\pi$
$17$	−3.57249	−	6.18773i	−0.866456	−	1.50075i	−0.000861630	−	1.00000i	$-0.500274\pi$
$18$	1.28184	+	2.22022i	0.302133	+	0.523310i
$19$	−2.89410	+	5.01273i	−0.663952	+	1.15000i	0.315617	+	0.948887i	$0.397789\pi$
$19$	−2.89410	+	5.01273i	−0.663952	+	1.15000i	−0.979568	+	0.201112i	$0.935545\pi$
$20$	−4.57249			−1.02244
$21$	2.44681	+	1.00654i	0.533938	+	0.219645i
$22$	2.56369			0.546580
$23$	−0.794226	+	1.37564i	−0.165608	+	0.286841i	−0.936871	−	0.349675i	$-0.886292\pi$
$23$	−0.794226	+	1.37564i	−0.165608	+	0.286841i	0.771263	+	0.636516i	$0.219625\pi$
$24$	3.29753	+	5.71149i	0.673105	+	1.16585i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.43294	+	4.21397i	−0.477139	+	0.826428i
$27$	1.00000			0.192450
$28$	11.1880	+	4.60240i	2.11433	+	0.869772i
$29$	−5.41638			−1.00580			−0.502898	−	0.864346i	$-0.667733\pi$
$29$	−5.41638			−1.00580			−0.502898	+	0.864346i	$0.667733\pi$
$30$	−1.28184	+	2.22022i	−0.234032	+	0.405354i
$31$	−1.35072	−	2.33951i	−0.242596	−	0.420189i	0.718857	−	0.695158i	$-0.244666\pi$
$31$	−1.35072	−	2.33951i	−0.242596	−	0.420189i	−0.961453	+	0.274969i	$0.911332\pi$
$32$	3.35548	+	5.81187i	0.593171	+	1.02740i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−18.3175			−3.14142
$35$	0.351714	+	2.62227i	0.0594505	+	0.443244i
$36$	4.57249			0.762082
$37$	−5.24247	+	9.08023i	−0.861857	+	1.49278i	0.00827709	+	0.999966i	$0.497365\pi$
$37$	−5.24247	+	9.08023i	−0.861857	+	1.49278i	−0.870134	+	0.492815i	$0.835968\pi$
$38$	7.41956	+	12.8511i	1.20361	+	2.08472i
$39$	0.949000	+	1.64372i	0.151962	+	0.263205i
$40$	−3.29753	+	5.71149i	−0.521385	+	0.903065i
$41$	8.49189			1.32621			0.663105	−	0.748526i	$-0.269238\pi$
$41$	8.49189			1.32621			0.663105	+	0.748526i	$0.269238\pi$
$42$	5.37117	−	4.14222i	0.828789	−	0.639159i
$43$	7.05730			1.07623			0.538114	−	0.842872i	$-0.319137\pi$
$43$	7.05730			1.07623			0.538114	+	0.842872i	$0.319137\pi$
$44$	2.28624	−	3.95989i	0.344664	−	0.596976i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	2.03615	+	3.52671i	0.300214	+	0.519985i
$47$	6.81472	−	11.8034i	0.994029	−	1.72171i	0.402518	−	0.915412i	$-0.368135\pi$
$47$	6.81472	−	11.8034i	0.994029	−	1.72171i	0.591511	−	0.806297i	$-0.298532\pi$
$48$	7.76268			1.12045
$49$	1.77885	−	6.77021i	0.254121	−	0.967172i
$50$	−2.56369			−0.362560
$51$	−3.57249	+	6.18773i	−0.500249	+	0.866456i
$52$	4.33929	+	7.51587i	0.601752	+	1.04226i
$53$	−4.29912	−	7.44629i	−0.590530	−	1.02283i	−0.994161	−	0.107906i	$-0.965586\pi$
$53$	−4.29912	−	7.44629i	−0.590530	−	1.02283i	0.403632	−	0.914922i	$-0.367748\pi$
$54$	1.28184	−	2.22022i	0.174437	−	0.302133i
$55$	1.00000			0.134840
$56$	13.8173	−	10.6558i	1.84641	−	1.42394i
$57$	5.78820			0.766666
$58$	−6.94295	+	12.0255i	−0.911654	+	1.57903i
$59$	−2.38965	−	4.13899i	−0.311106	−	0.538851i	0.667496	−	0.744613i	$-0.267366\pi$
$59$	−2.38965	−	4.13899i	−0.311106	−	0.538851i	−0.978602	+	0.205762i	$0.934033\pi$
$60$	2.28624	+	3.95989i	0.295153	+	0.511220i
$61$	3.68109	−	6.37584i	0.471316	−	0.816343i	−0.528146	−	0.849154i	$-0.677113\pi$
$61$	3.68109	−	6.37584i	0.471316	−	0.816343i	0.999462	+	0.0328110i	$0.0104459\pi$
$62$	−6.92564			−0.879557
$63$	−0.351714	−	2.62227i	−0.0443118	−	0.330375i
$64$	1.67945			0.209931
$65$	−0.949000	+	1.64372i	−0.117709	+	0.203878i
$66$	−1.28184	−	2.22022i	−0.157784	−	0.273290i
$67$	−1.60624	−	2.78209i	−0.196234	−	0.339887i	0.751070	−	0.660222i	$-0.229538\pi$
$67$	−1.60624	−	2.78209i	−0.196234	−	0.339887i	−0.947304	+	0.320335i	$0.896204\pi$
$68$	−16.3352	+	28.2933i	−1.98093	+	3.43107i
$69$	1.58845			0.191227
$70$	6.27285	+	2.58046i	0.749749	+	0.308424i
$71$	−6.06777			−0.720112			−0.360056	−	0.932931i	$-0.617242\pi$
$71$	−6.06777			−0.720112			−0.360056	+	0.932931i	$0.617242\pi$
$72$	3.29753	−	5.71149i	0.388617	−	0.673105i
$73$	−5.54699	−	9.60767i	−0.649226	−	1.12449i	−0.983308	−	0.181949i	$-0.941759\pi$
$73$	−5.54699	−	9.60767i	−0.649226	−	1.12449i	0.334082	−	0.942544i	$-0.391574\pi$
$74$	13.4401	+	23.2789i	1.56237	+	2.70611i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	26.4665			3.03591
$77$	−2.44681	−	1.00654i	−0.278840	−	0.114706i
$78$	4.86588			0.550952
$79$	−4.31493	+	7.47368i	−0.485467	+	0.840854i	−0.999861	−	0.0167003i	$-0.994684\pi$
$79$	−4.31493	+	7.47368i	−0.485467	+	0.840854i	0.514393	+	0.857554i	$0.328017\pi$
$80$	3.88134	+	6.72268i	0.433947	+	0.751618i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.8853	−	18.8538i	1.20208	−	2.08206i
$83$	−6.27078			−0.688307			−0.344154	−	0.938913i	$-0.611834\pi$
$83$	−6.27078			−0.688307			−0.344154	+	0.938913i	$0.611834\pi$
$84$	−1.60821	−	11.9903i	−0.175470	−	1.30825i
$85$	−7.14498			−0.774982
$86$	9.04635	−	15.6687i	0.975493	−	1.68960i
$87$	2.70819	+	4.69072i	0.290348	+	0.502898i
$88$	−3.29753	−	5.71149i	−0.351518	−	0.608846i
$89$	6.80373	−	11.7844i	0.721194	−	1.24914i	−0.239328	−	0.970939i	$-0.576927\pi$
$89$	6.80373	−	11.7844i	0.721194	−	1.24914i	0.960522	−	0.278205i	$-0.0897395\pi$
$90$	2.56369			0.270236
$91$	3.97649	−	3.06665i	0.416849	−	0.321472i
$92$	7.26318			0.757239
$93$	−1.35072	+	2.33951i	−0.140063	+	0.242596i
$94$	−17.4708	−	30.2603i	−1.80198	−	3.12111i
$95$	2.89410	+	5.01273i	0.296928	+	0.514295i
$96$	3.35548	−	5.81187i	0.342467	−	0.593171i
$97$	−15.5039			−1.57419			−0.787094	−	0.616834i	$-0.788415\pi$
$97$	−15.5039			−1.57419			−0.787094	+	0.616834i	$0.788415\pi$
$98$	−12.7511	−	12.6278i	−1.28806	−	1.27560i
$99$	−1.00000			−0.100504
$100$	−2.28624	+	3.95989i	−0.228624	+	0.395989i
$101$	5.80106	+	10.0477i	0.577227	+	0.999786i	0.995796	+	0.0916010i	$0.0291984\pi$
$101$	5.80106	+	10.0477i	0.577227	+	0.999786i	−0.418569	+	0.908185i	$0.637468\pi$
$102$	9.15874	+	15.8634i	0.906851	+	1.57071i
$103$	−1.00397	+	1.73893i	−0.0989240	+	0.171341i	−0.911240	−	0.411877i	$-0.864873\pi$
$103$	−1.00397	+	1.73893i	−0.0989240	+	0.171341i	0.812316	+	0.583218i	$0.198207\pi$
$104$	12.5174			1.22743
$105$	2.09509	−	1.61573i	0.204460	−	0.157679i
$106$	−22.0432			−2.14102
$107$	3.84707	−	6.66333i	0.371911	−	0.644168i	−0.617949	−	0.786218i	$-0.712036\pi$
$107$	3.84707	−	6.66333i	0.371911	−	0.644168i	0.989859	+	0.142050i	$0.0453694\pi$
$108$	−2.28624	−	3.95989i	−0.219994	−	0.381041i
$109$	2.50767	+	4.34342i	0.240192	+	0.416024i	0.960769	−	0.277351i	$-0.0894564\pi$
$109$	2.50767	+	4.34342i	0.240192	+	0.416024i	−0.720577	+	0.693375i	$0.756123\pi$
$110$	1.28184	−	2.22022i	0.122219	−	0.211689i
$111$	10.4849			0.995187
$112$	−2.73024	−	20.3558i	−0.257984	−	1.92345i
$113$	−3.23524			−0.304345			−0.152173	−	0.988354i	$-0.548627\pi$
$113$	−3.23524			−0.304345			−0.152173	+	0.988354i	$0.548627\pi$
$114$	7.41956	−	12.8511i	0.694906	−	1.20361i
$115$	0.794226	+	1.37564i	0.0740620	+	0.128279i
$116$	12.3832	+	21.4483i	1.14975	+	1.99142i
$117$	0.949000	−	1.64372i	0.0877351	−	0.151962i
$118$	−12.2526			−1.12794
$119$	17.4824	+	7.19172i	1.60261	+	0.659264i
$120$	6.59506			0.602044
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−9.43717	−	16.3457i	−0.854401	−	1.47987i
$123$	−4.24595	−	7.35419i	−0.382844	−	0.663105i
$124$	−6.17615	+	10.6974i	−0.554634	+	0.960655i
$125$	−1.00000			−0.0894427
$126$	−6.27285	−	2.58046i	−0.558830	−	0.229885i
$127$	16.4611			1.46069			0.730345	−	0.683079i	$-0.239360\pi$
$127$	16.4611			1.46069			0.730345	+	0.683079i	$0.239360\pi$
$128$	−4.55817	+	7.89498i	−0.402889	+	0.697825i
$129$	−3.52865	−	6.11180i	−0.310680	−	0.538114i
$130$	2.43294	+	4.21397i	0.213383	+	0.369590i
$131$	−4.51972	+	7.82839i	−0.394890	+	0.683970i	−0.993087	−	0.117379i	$-0.962551\pi$
$131$	−4.51972	+	7.82839i	−0.394890	+	0.683970i	0.598197	+	0.801349i	$0.295884\pi$
$132$	−4.57249			−0.397984
$133$	−2.03579	−	15.1782i	−0.176525	−	1.31612i
$134$	−8.23581			−0.711465
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	23.5608	+	40.8084i	2.02032	+	3.49930i
$137$	5.56106	+	9.63204i	0.475114	+	0.822921i	0.999594	−	0.0285019i	$-0.00907366\pi$
$137$	5.56106	+	9.63204i	0.475114	+	0.822921i	−0.524480	+	0.851423i	$0.675740\pi$
$138$	2.03615	−	3.52671i	0.173328	−	0.300214i
$139$	−9.55890			−0.810775			−0.405388	−	0.914145i	$-0.632863\pi$
$139$	−9.55890			−0.810775			−0.405388	+	0.914145i	$0.632863\pi$
$140$	9.57980	−	7.38790i	0.809641	−	0.624391i
$141$	−13.6294			−1.14781
$142$	−7.77794	+	13.4718i	−0.652710	+	1.13053i
$143$	−0.949000	−	1.64372i	−0.0793594	−	0.137454i
$144$	−3.88134	−	6.72268i	−0.323445	−	0.560223i
$145$	−2.70819	+	4.69072i	−0.224903	+	0.389543i
$146$	−28.4415			−2.35384
$147$	−6.75259	+	1.84458i	−0.556945	+	0.152138i
$148$	47.9423			3.94083
$149$	−4.09568	+	7.09392i	−0.335531	+	0.581157i	−0.983587	−	0.180436i	$-0.942249\pi$
$149$	−4.09568	+	7.09392i	−0.335531	+	0.581157i	0.648056	+	0.761593i	$0.275582\pi$
$150$	1.28184	+	2.22022i	0.104662	+	0.181280i
$151$	4.40519	+	7.63002i	0.358490	+	0.620922i	0.987709	−	0.156306i	$-0.0499585\pi$
$151$	4.40519	+	7.63002i	0.358490	+	0.620922i	−0.629219	+	0.777228i	$0.716625\pi$
$152$	19.0867	−	33.0592i	1.54814	−	2.68146i
$153$	7.14498			0.577637
$154$	−5.37117	+	4.14222i	−0.432821	+	0.333790i
$155$	−2.70144			−0.216985
$156$	4.33929	−	7.51587i	0.347421	−	0.601752i
$157$	−8.00183	−	13.8596i	−0.638615	−	1.10611i	−0.985737	−	0.168294i	$-0.946174\pi$
$157$	−8.00183	−	13.8596i	−0.638615	−	1.10611i	0.347122	−	0.937820i	$-0.387159\pi$
$158$	11.0621	+	19.1602i	0.880055	+	1.52430i
$159$	−4.29912	+	7.44629i	−0.340942	+	0.590530i
$160$	6.71096			0.530548
$161$	−0.558681	−	4.16535i	−0.0440303	−	0.328276i
$162$	−2.56369			−0.201422
$163$	5.11821	−	8.86501i	0.400889	−	0.694361i	−0.592944	−	0.805244i	$-0.702034\pi$
$163$	5.11821	−	8.86501i	0.400889	−	0.694361i	0.993833	+	0.110883i	$0.0353678\pi$
$164$	−19.4145	−	33.6270i	−1.51602	−	2.62583i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	−8.03816	+	13.9225i	−0.623882	+	1.08060i
$167$	1.57975			0.122245			0.0611224	−	0.998130i	$-0.480532\pi$
$167$	1.57975			0.122245			0.0611224	+	0.998130i	$0.480532\pi$
$168$	−16.1368	−	6.63820i	−1.24498	−	0.512148i
$169$	−9.39760			−0.722892
$170$	−9.15874	+	15.8634i	−0.702444	+	1.21667i
$171$	−2.89410	−	5.01273i	−0.221317	−	0.383333i
$172$	−16.1347	−	27.9461i	−1.23026	−	2.13087i
$173$	−10.1892	+	17.6481i	−0.774667	+	1.34176i	0.160314	+	0.987066i	$0.448749\pi$
$173$	−10.1892	+	17.6481i	−0.774667	+	1.34176i	−0.934981	+	0.354697i	$0.884584\pi$
$174$	13.8859			1.05269
$175$	2.44681	+	1.00654i	0.184961	+	0.0760874i
$176$	−7.76268			−0.585134
$177$	−2.38965	+	4.13899i	−0.179617	+	0.311106i
$178$	−17.4426	−	30.2115i	−1.30738	−	2.26445i
$179$	7.47349	+	12.9445i	0.558595	+	0.967514i	0.997614	+	0.0690366i	$0.0219925\pi$
$179$	7.47349	+	12.9445i	0.558595	+	0.967514i	−0.439020	+	0.898477i	$0.644674\pi$
$180$	2.28624	−	3.95989i	0.170407	−	0.295153i
$181$	−7.19546			−0.534834			−0.267417	−	0.963581i	$-0.586170\pi$
$181$	−7.19546			−0.534834			−0.267417	+	0.963581i	$0.586170\pi$
$182$	−1.71140	−	12.7596i	−0.126857	−	0.945808i
$183$	−7.36219			−0.544228
$184$	5.23797	−	9.07242i	0.386148	−	0.668828i
$185$	5.24247	+	9.08023i	0.385434	+	0.667592i
$186$	3.46282	+	5.99778i	0.253906	+	0.439779i
$187$	3.57249	−	6.18773i	0.261246	−	0.452492i
$188$	−62.3205			−4.54519
$189$	−2.09509	+	1.61573i	−0.152396	+	0.117527i
$190$	14.8391			1.07654
$191$	6.93798	−	12.0169i	0.502015	−	0.869515i	−0.497982	−	0.867187i	$-0.665926\pi$
$191$	6.93798	−	12.0169i	0.502015	−	0.869515i	0.999997	−	0.00232823i	$-0.000741100\pi$
$192$	−0.839725	−	1.45445i	−0.0606020	−	0.104966i
$193$	−5.88011	−	10.1846i	−0.423260	−	0.733107i	0.572997	−	0.819558i	$-0.305781\pi$
$193$	−5.88011	−	10.1846i	−0.423260	−	0.733107i	−0.996256	+	0.0864507i	$0.972447\pi$
$194$	−19.8736	+	34.4221i	−1.42684	+	2.47137i
$195$	1.89800			0.135919
$196$	−30.8762	+	8.43432i	−2.20544	+	0.602451i
$197$	−1.28355			−0.0914492			−0.0457246	−	0.998954i	$-0.514560\pi$
$197$	−1.28355			−0.0914492			−0.0457246	+	0.998954i	$0.514560\pi$
$198$	−1.28184	+	2.22022i	−0.0910966	+	0.157784i
$199$	−9.41172	−	16.3016i	−0.667179	−	1.15559i	−0.978690	−	0.205345i	$-0.934168\pi$
$199$	−9.41172	−	16.3016i	−0.667179	−	1.15559i	0.311511	−	0.950243i	$-0.399165\pi$
$200$	3.29753	+	5.71149i	0.233170	+	0.403863i
$201$	−1.60624	+	2.78209i	−0.113296	+	0.196234i
$202$	29.7442			2.09279
$203$	11.3478	−	8.75140i	0.796461	−	0.614228i
$204$	32.6703			2.28738
$205$	4.24595	−	7.35419i	0.296550	−	0.513639i
$206$	2.57386	+	4.45806i	0.179330	+	0.310608i
$207$	−0.794226	−	1.37564i	−0.0552025	−	0.0956136i
$208$	7.36678	−	12.7596i	0.510794	−	0.884722i
$209$	−5.78820			−0.400378
$210$	−0.901685	−	6.72268i	−0.0622222	−	0.463909i
$211$	15.6903			1.08017			0.540084	−	0.841611i	$-0.318393\pi$
$211$	15.6903			1.08017			0.540084	+	0.841611i	$0.318393\pi$
$212$	−19.6577	+	34.0481i	−1.35009	+	2.33843i
$213$	3.03389	+	5.25485i	0.207879	+	0.360056i
$214$	−9.86269	−	17.0827i	−0.674200	−	1.16775i
$215$	3.52865	−	6.11180i	0.240652	−	0.416821i
$216$	−6.59506			−0.448737
$217$	6.60990	+	2.71911i	0.448709	+	0.184585i
$218$	12.8578			0.870839
$219$	−5.54699	+	9.60767i	−0.374831	+	0.649226i
$220$	−2.28624	−	3.95989i	−0.154139	−	0.266976i
$221$	6.78058	+	11.7443i	0.456111	+	0.790008i
$222$	13.4401	−	23.2789i	0.902038	−	1.56237i
$223$	17.0892			1.14438			0.572188	−	0.820123i	$-0.306095\pi$
$223$	17.0892			1.14438			0.572188	+	0.820123i	$0.306095\pi$
$224$	−16.4204	−	6.75486i	−1.09714	−	0.451328i
$225$	1.00000			0.0666667
$226$	−4.14707	+	7.18293i	−0.275859	+	0.477801i
$227$	−5.20539	−	9.01601i	−0.345494	−	0.598413i	0.639949	−	0.768417i	$-0.278955\pi$
$227$	−5.20539	−	9.01601i	−0.345494	−	0.598413i	−0.985443	+	0.170004i	$0.945622\pi$
$228$	−13.2332	−	22.9206i	−0.876392	−	1.51796i
$229$	3.56397	−	6.17297i	0.235514	−	0.407921i	−0.723908	−	0.689896i	$-0.757656\pi$
$229$	3.56397	−	6.17297i	0.235514	−	0.407921i	0.959422	+	0.281975i	$0.0909895\pi$
$230$	4.07229			0.268519
$231$	0.351714	+	2.62227i	0.0231411	+	0.172533i
$232$	35.7213			2.34522
$233$	8.62938	−	14.9465i	0.565329	−	0.979179i	−0.431690	−	0.902022i	$-0.642082\pi$
$233$	8.62938	−	14.9465i	0.565329	−	0.979179i	0.997019	−	0.0771570i	$-0.0245843\pi$
$234$	−2.43294	−	4.21397i	−0.159046	−	0.275476i
$235$	−6.81472	−	11.8034i	−0.444543	−	0.769972i
$236$	−10.9266	+	18.9255i	−0.711264	+	1.23194i
$237$	8.62986			0.560569
$238$	38.3769	−	29.5961i	2.48760	−	1.91843i
$239$	−12.8102			−0.828624			−0.414312	−	0.910135i	$-0.635978\pi$
$239$	−12.8102			−0.828624			−0.414312	+	0.910135i	$0.635978\pi$
$240$	3.88134	−	6.72268i	0.250539	−	0.433947i
$241$	−6.18664	−	10.7156i	−0.398517	−	0.690251i	0.595026	−	0.803706i	$-0.297142\pi$
$241$	−6.18664	−	10.7156i	−0.398517	−	0.690251i	−0.993543	+	0.113455i	$0.963808\pi$
$242$	1.28184	+	2.22022i	0.0824000	+	0.142721i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−33.6635			−2.15509
$245$	−4.97375	−	4.92563i	−0.317761	−	0.314687i
$246$	−21.7705			−1.38804
$247$	5.49300	−	9.51416i	0.349511	−	0.605371i
$248$	8.90807	+	15.4292i	0.565663	+	0.979757i
$249$	3.13539	+	5.43065i	0.198697	+	0.344154i
$250$	−1.28184	+	2.22022i	−0.0810709	+	0.140419i
$251$	25.3091			1.59750			0.798748	−	0.601665i	$-0.205496\pi$
$251$	25.3091			1.59750			0.798748	+	0.601665i	$0.205496\pi$
$252$	−9.57980	+	7.38790i	−0.603471	+	0.465394i
$253$	−1.58845			−0.0998652
$254$	21.1006	−	36.5473i	1.32397	−	2.29318i
$255$	3.57249	+	6.18773i	0.223718	+	0.387491i
$256$	13.3652	+	23.1492i	0.835323	+	1.44682i
$257$	−12.7550	+	22.0922i	−0.795633	+	1.37808i	0.126804	+	0.991928i	$0.459528\pi$
$257$	−12.7550	+	22.0922i	−0.795633	+	1.37808i	−0.922437	+	0.386149i	$0.873805\pi$
$258$	−18.0927			−1.12640
$259$	−3.68770	−	27.4944i	−0.229143	−	1.70842i
$260$	8.67858			0.538223
$261$	2.70819	−	4.69072i	0.167633	−	0.290348i
$262$	11.5872	+	20.0695i	0.715857	+	1.23990i
$263$	−6.08665	−	10.5424i	−0.375319	−	0.650071i	0.615056	−	0.788484i	$-0.289133\pi$
$263$	−6.08665	−	10.5424i	−0.375319	−	0.650071i	−0.990375	+	0.138412i	$0.955800\pi$
$264$	−3.29753	+	5.71149i	−0.202949	+	0.351518i
$265$	−8.59824			−0.528186
$266$	−36.3085	−	14.9362i	−2.22622	−	0.915797i
$267$	−13.6075			−0.832763
$268$	−7.34453	+	12.7211i	−0.448638	+	0.777065i
$269$	5.85203	+	10.1360i	0.356805	+	0.618004i	0.987425	−	0.158087i	$-0.0505328\pi$
$269$	5.85203	+	10.1360i	0.356805	+	0.618004i	−0.630620	+	0.776092i	$0.717199\pi$
$270$	−1.28184	−	2.22022i	−0.0780105	−	0.135118i
$271$	1.95692	−	3.38949i	0.118875	−	0.205897i	−0.800447	−	0.599403i	$-0.795405\pi$
$271$	1.95692	−	3.38949i	0.118875	−	0.205897i	0.919322	+	0.393506i	$0.128738\pi$
$272$	55.4642			3.36301
$273$	−4.64404	−	1.91042i	−0.281070	−	0.115624i
$274$	28.5136			1.72257
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−3.63159	−	6.29010i	−0.218596	−	0.378620i
$277$	0.392126	+	0.679182i	0.0235605	+	0.0408081i	0.877565	−	0.479457i	$-0.159166\pi$
$277$	0.392126	+	0.679182i	0.0235605	+	0.0408081i	−0.854005	+	0.520265i	$0.825833\pi$
$278$	−12.2530	+	21.2228i	−0.734887	+	1.27286i
$279$	2.70144			0.161731
$280$	−2.31957	−	17.2940i	−0.138621	−	1.03352i
$281$	6.75257			0.402825			0.201412	−	0.979507i	$-0.435447\pi$
$281$	6.75257			0.402825			0.201412	+	0.979507i	$0.435447\pi$
$282$	−17.4708	+	30.2603i	−1.04037	+	1.80198i
$283$	−3.06379	−	5.30665i	−0.182124	−	0.315447i	0.760480	−	0.649362i	$-0.224964\pi$
$283$	−3.06379	−	5.30665i	−0.182124	−	0.315447i	−0.942604	+	0.333914i	$0.891630\pi$
$284$	13.8724	+	24.0277i	0.823176	+	1.42578i
$285$	2.89410	−	5.01273i	0.171432	−	0.296928i
$286$	−4.86588			−0.287725
$287$	−17.7913	+	13.7206i	−1.05019	+	0.809901i
$288$	−6.71096			−0.395447
$289$	−17.0254	+	29.4888i	−1.00149	+	1.73463i
$290$	6.94295	+	12.0255i	0.407704	+	0.706164i
$291$	7.75197	+	13.4268i	0.454429	+	0.787094i
$292$	−25.3636	+	43.9310i	−1.48429	+	2.57087i
$293$	13.2684			0.775145			0.387573	−	0.921839i	$-0.373314\pi$
$293$	13.2684			0.775145			0.387573	+	0.921839i	$0.373314\pi$
$294$	−4.56040	+	17.3567i	−0.265968	+	1.01226i
$295$	−4.77930			−0.278261
$296$	34.5744	−	59.8846i	2.00960	−	3.48072i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	10.5000	+	18.1866i	0.608251	+	1.05352i
$299$	1.50744	−	2.61097i	0.0871776	−	0.150996i
$300$	4.57249			0.263993
$301$	−14.7857	+	11.4027i	−0.852234	+	0.657239i
$302$	22.5871			1.29974
$303$	5.80106	−	10.0477i	0.333262	−	0.577227i
$304$	−22.4660	−	38.9122i	−1.28851	−	2.23177i
$305$	−3.68109	−	6.37584i	−0.210779	−	0.365080i
$306$	9.15874	−	15.8634i	0.523570	−	0.906851i
$307$	8.30013			0.473713			0.236857	−	0.971545i	$-0.423883\pi$
$307$	8.30013			0.473713			0.236857	+	0.971545i	$0.423883\pi$
$308$	1.60821	+	11.9903i	0.0916362	+	0.683211i
$309$	2.00794			0.114228
$310$	−3.46282	+	5.99778i	−0.196675	+	0.340651i
$311$	−1.75869	−	3.04615i	−0.0997263	−	0.172731i	0.811845	−	0.583873i	$-0.198463\pi$
$311$	−1.75869	−	3.04615i	−0.0997263	−	0.172731i	−0.911571	+	0.411142i	$0.865130\pi$
$312$	−6.25871	−	10.8404i	−0.354330	−	0.613717i
$313$	14.6571	−	25.3869i	0.828470	−	1.43495i	−0.0707682	−	0.997493i	$-0.522545\pi$
$313$	14.6571	−	25.3869i	0.828470	−	1.43495i	0.899238	−	0.437459i	$-0.144122\pi$
$314$	−41.0283			−2.31536
$315$	−2.44681	−	1.00654i	−0.137862	−	0.0567122i
$316$	39.4599			2.21979
$317$	−5.82303	+	10.0858i	−0.327054	+	0.566474i	−0.981926	−	0.189266i	$-0.939389\pi$
$317$	−5.82303	+	10.0858i	−0.327054	+	0.566474i	0.654872	+	0.755740i	$0.272723\pi$
$318$	11.0216	+	19.0900i	0.618060	+	1.07051i
$319$	−2.70819	−	4.69072i	−0.151630	−	0.262630i
$320$	0.839725	−	1.45445i	0.0469421	−	0.0813061i
$321$	−7.69415			−0.429445
$322$	−9.96413	−	4.09893i	−0.555279	−	0.228425i
$323$	41.3565			2.30114
$324$	−2.28624	+	3.95989i	−0.127014	+	0.219994i
$325$	0.949000	+	1.64372i	0.0526411	+	0.0911770i
$326$	−13.1215	−	22.7271i	−0.726732	−	1.25874i
$327$	2.50767	−	4.34342i	0.138675	−	0.240192i
$328$	−56.0045			−3.09233
$329$	4.79367	+	35.7401i	0.264283	+	1.97041i
$330$	−2.56369			−0.141126
$331$	−2.38623	+	4.13307i	−0.131159	+	0.227174i	−0.924124	−	0.382094i	$-0.875203\pi$
$331$	−2.38623	+	4.13307i	−0.131159	+	0.227174i	0.792965	+	0.609268i	$0.208537\pi$
$332$	14.3365	+	24.8316i	0.786819	+	1.36281i
$333$	−5.24247	−	9.08023i	−0.287286	−	0.497593i
$334$	2.02499	−	3.50739i	0.110803	−	0.191916i
$335$	−3.21249			−0.175517
$336$	−16.2635	+	12.5424i	−0.887249	+	0.684243i
$337$	10.0268			0.546192			0.273096	−	0.961987i	$-0.411952\pi$
$337$	10.0268			0.546192			0.273096	+	0.961987i	$0.411952\pi$
$338$	−12.0462	+	20.8647i	−0.655229	+	1.13489i
$339$	1.61762	+	2.80180i	0.0878569	+	0.152173i
$340$	16.3352	+	28.2933i	0.885899	+	1.53442i
$341$	1.35072	−	2.33951i	0.0731455	−	0.126692i
$342$	−14.8391			−0.802408
$343$	7.21197	+	17.0584i	0.389410	+	0.921065i
$344$	−46.5433			−2.50945
$345$	0.794226	−	1.37564i	0.0427597	−	0.0740620i
$346$	26.1218	+	45.2443i	1.40432	+	2.43235i
$347$	−5.65307	−	9.79141i	−0.303473	−	0.525630i	0.673447	−	0.739235i	$-0.264813\pi$
$347$	−5.65307	−	9.79141i	−0.303473	−	0.525630i	−0.976920	+	0.213605i	$0.931479\pi$
$348$	12.3832	−	21.4483i	0.663808	−	1.14975i
$349$	−8.89490			−0.476133			−0.238066	−	0.971249i	$-0.576514\pi$
$349$	−8.89490			−0.476133			−0.238066	+	0.971249i	$0.576514\pi$
$350$	5.37117	−	4.14222i	0.287101	−	0.221411i
$351$	−1.89800			−0.101308
$352$	−3.35548	+	5.81187i	−0.178848	+	0.309773i
$353$	−13.3118	−	23.0567i	−0.708516	−	1.22719i	−0.965408	−	0.260745i	$-0.916032\pi$
$353$	−13.3118	−	23.0567i	−0.708516	−	1.22719i	0.256892	−	0.966440i	$-0.417302\pi$
$354$	6.12631	+	10.6111i	0.325610	+	0.563972i
$355$	−3.03389	+	5.25485i	−0.161022	+	0.278898i
$356$	−62.2199			−3.29765
$357$	−2.51299	−	18.7361i	−0.133002	−	0.991617i
$358$	38.3193			2.02524
$359$	−7.54383	+	13.0663i	−0.398148	+	0.689613i	−0.993497	−	0.113854i	$-0.963680\pi$
$359$	−7.54383	+	13.0663i	−0.398148	+	0.689613i	0.595349	+	0.803467i	$0.297014\pi$
$360$	−3.29753	−	5.71149i	−0.173795	−	0.301022i
$361$	−7.25162	−	12.5602i	−0.381664	−	0.661062i
$362$	−9.22345	+	15.9755i	−0.484774	+	0.839653i
$363$	1.00000			0.0524864
$364$	−21.2348	−	8.73535i	−1.11301	−	0.457857i
$365$	−11.0940			−0.580686
$366$	−9.43717	+	16.3457i	−0.493289	+	0.854401i
$367$	−11.7005	−	20.2658i	−0.610759	−	1.05787i	−0.991113	−	0.133025i	$-0.957531\pi$
$367$	−11.7005	−	20.2658i	−0.610759	−	1.05787i	0.380353	−	0.924841i	$-0.375802\pi$
$368$	−6.16532	−	10.6787i	−0.321390	−	0.556663i
$369$	−4.24595	+	7.35419i	−0.221035	+	0.382844i
$370$	26.8801			1.39743
$371$	21.0383	+	8.65448i	1.09225	+	0.449318i
$372$	12.3523			0.640437
$373$	9.81582	−	17.0015i	0.508244	−	0.880304i	−0.491711	−	0.870759i	$-0.663628\pi$
$373$	9.81582	−	17.0015i	0.508244	−	0.880304i	0.999954	−	0.00954541i	$-0.00303844\pi$
$374$	−9.15874	−	15.8634i	−0.473587	−	0.820277i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−44.9435	+	77.8444i	−2.31778	+	4.01452i
$377$	10.2803			0.529462
$378$	0.901685	+	6.72268i	0.0463777	+	0.345777i
$379$	29.1037			1.49496			0.747478	−	0.664286i	$-0.231264\pi$
$379$	29.1037			1.49496			0.747478	+	0.664286i	$0.231264\pi$
$380$	13.2332	−	22.9206i	0.678851	−	1.17580i
$381$	−8.23056	−	14.2558i	−0.421665	−	0.730345i
$382$	−17.7868	−	30.8077i	−0.910053	−	1.57626i
$383$	10.8331	−	18.7636i	0.553548	−	0.958773i	−0.444467	−	0.895795i	$-0.646607\pi$
$383$	10.8331	−	18.7636i	0.553548	−	0.958773i	0.998015	−	0.0629781i	$-0.0200598\pi$
$384$	9.11634			0.465216
$385$	−2.09509	+	1.61573i	−0.106776	+	0.0823451i
$386$	−30.1495			−1.53457
$387$	−3.52865	+	6.11180i	−0.179371	+	0.310680i
$388$	35.4458	+	61.3940i	1.79949	+	3.11681i
$389$	−16.8798	−	29.2367i	−0.855841	−	1.48236i	−0.875863	−	0.482560i	$-0.839707\pi$
$389$	−16.8798	−	29.2367i	−0.855841	−	1.48236i	0.0200219	−	0.999800i	$-0.493626\pi$
$390$	2.43294	−	4.21397i	0.123197	−	0.213383i
$391$	11.3495			0.573967
$392$	−11.7316	+	44.6499i	−0.592534	+	2.25516i
$393$	9.03945			0.455980
$394$	−1.64531	+	2.84976i	−0.0828896	+	0.143569i
$395$	4.31493	+	7.47368i	0.217108	+	0.376041i
$396$	2.28624	+	3.95989i	0.114888	+	0.198992i
$397$	3.17200	−	5.49407i	0.159198	−	0.275740i	−0.775382	−	0.631493i	$-0.782442\pi$
$397$	3.17200	−	5.49407i	0.159198	−	0.275740i	0.934580	+	0.355754i	$0.115776\pi$
$398$	−48.2574			−2.41892
$399$	−12.1268	+	9.35215i	−0.607101	+	0.468193i
$400$	7.76268			0.388134
$401$	−4.33615	+	7.51042i	−0.216537	+	0.375053i	−0.953747	−	0.300611i	$-0.902809\pi$
$401$	−4.33615	+	7.51042i	−0.216537	+	0.375053i	0.737210	+	0.675664i	$0.236143\pi$
$402$	4.11790	+	7.13242i	0.205382	+	0.355733i
$403$	2.56366	+	4.44040i	0.127705	+	0.221192i
$404$	26.5253	−	45.9431i	1.31968	−	2.28576i
$405$	−1.00000			−0.0496904
$406$	−4.88387	−	36.4126i	−0.242382	−	1.80713i
$407$	−10.4849			−0.519719
$408$	23.5608	−	40.8084i	1.16643	−	2.02032i
$409$	6.80294	+	11.7830i	0.336384	+	0.582633i	0.983750	−	0.179546i	$-0.0574628\pi$
$409$	6.80294	+	11.7830i	0.336384	+	0.582633i	−0.647366	+	0.762179i	$0.724129\pi$
$410$	−10.8853	−	18.8538i	−0.537585	−	0.931125i
$411$	5.56106	−	9.63204i	0.274307	−	0.475114i
$412$	9.18128			0.452329
$413$	11.6940	+	4.81056i	0.575425	+	0.236712i
$414$	−4.07229			−0.200142
$415$	−3.13539	+	5.43065i	−0.153910	+	0.266580i
$416$	−6.36871	−	11.0309i	−0.312251	−	0.540835i
$417$	4.77945	+	8.27825i	0.234051	+	0.405388i
$418$	−7.41956	+	12.8511i	−0.362903	+	0.628566i
$419$	3.73618			0.182524			0.0912622	−	0.995827i	$-0.470910\pi$
$419$	3.73618			0.182524			0.0912622	+	0.995827i	$0.470910\pi$
$420$	−11.1880	−	4.60240i	−0.545919	−	0.224574i
$421$	−31.4235			−1.53149			−0.765745	−	0.643145i	$-0.777629\pi$
$421$	−31.4235			−1.53149			−0.765745	+	0.643145i	$0.777629\pi$
$422$	20.1126	−	34.8360i	0.979064	−	1.69579i
$423$	6.81472	+	11.8034i	0.331343	+	0.573903i
$424$	28.3529	+	49.1087i	1.37694	+	2.38493i
$425$	−3.57249	+	6.18773i	−0.173291	+	0.300149i
$426$	15.5559			0.753684
$427$	2.58938	+	19.3056i	0.125309	+	0.934265i
$428$	−35.1814			−1.70056
$429$	−0.949000	+	1.64372i	−0.0458182	+	0.0793594i
$430$	−9.04635	−	15.6687i	−0.436254	−	0.755614i
$431$	18.9013	+	32.7381i	0.910445	+	1.57694i	0.813436	+	0.581654i	$0.197594\pi$
$431$	18.9013	+	32.7381i	0.910445	+	1.57694i	0.0970089	+	0.995284i	$0.469072\pi$
$432$	−3.88134	+	6.72268i	−0.186741	+	0.323445i
$433$	17.9561			0.862917			0.431458	−	0.902133i	$-0.357999\pi$
$433$	17.9561			0.862917			0.431458	+	0.902133i	$0.357999\pi$
$434$	14.5099	−	11.1900i	0.696496	−	0.537135i
$435$	5.41638			0.259696
$436$	11.4663	−	19.8602i	0.549137	−	0.951133i
$437$	−4.59714	−	7.96248i	−0.219911	−	0.380897i
$438$	14.2207	+	24.6311i	0.679494	+	1.17692i
$439$	−10.0133	+	17.3435i	−0.477908	+	0.827761i	−0.999679	−	0.0253246i	$-0.991938\pi$
$439$	−10.0133	+	17.3435i	−0.477908	+	0.827761i	0.521771	+	0.853085i	$0.325271\pi$
$440$	−6.59506			−0.314407
$441$	4.97375	+	4.92563i	0.236845	+	0.234554i
$442$	34.7666			1.65368
$443$	19.9836	−	34.6127i	0.949451	−	1.64450i	0.202866	−	0.979207i	$-0.434974\pi$
$443$	19.9836	−	34.6127i	0.949451	−	1.64450i	0.746585	−	0.665290i	$-0.231692\pi$
$444$	−23.9711	−	41.5192i	−1.13762	−	1.97042i
$445$	−6.80373	−	11.7844i	−0.322528	−	0.558634i
$446$	21.9056	−	37.9417i	1.03726	−	1.79659i
$447$	8.19135			0.387438
$448$	−3.51861	+	2.71354i	−0.166239	+	0.128203i
$449$	−19.3186			−0.911703			−0.455852	−	0.890056i	$-0.650665\pi$
$449$	−19.3186			−0.911703			−0.455852	+	0.890056i	$0.650665\pi$
$450$	1.28184	−	2.22022i	0.0604267	−	0.104662i
$451$	4.24595	+	7.35419i	0.199934	+	0.346295i
$452$	7.39654	+	12.8112i	0.347904	+	0.602587i
$453$	4.40519	−	7.63002i	0.206974	−	0.358490i
$454$	−26.6900			−1.25262
$455$	−0.667553	−	4.97707i	−0.0312954	−	0.233329i
$456$	−38.1735			−1.78764
$457$	−14.5234	+	25.1553i	−0.679377	+	1.17672i	0.295792	+	0.955252i	$0.404417\pi$
$457$	−14.5234	+	25.1553i	−0.679377	+	1.17672i	−0.975169	+	0.221463i	$0.928917\pi$
$458$	−9.13689	−	15.8256i	−0.426939	−	0.739480i
$459$	−3.57249	−	6.18773i	−0.166750	−	0.288819i
$460$	3.63159	−	6.29010i	0.169324	−	0.293277i
$461$	21.9266			1.02122			0.510611	−	0.859812i	$-0.329419\pi$
$461$	21.9266			1.02122			0.510611	+	0.859812i	$0.329419\pi$
$462$	6.27285	+	2.58046i	0.291839	+	0.120054i
$463$	−21.2759			−0.988773			−0.494387	−	0.869242i	$-0.664607\pi$
$463$	−21.2759			−0.988773			−0.494387	+	0.869242i	$0.664607\pi$
$464$	21.0228	−	36.4126i	0.975959	−	1.69041i
$465$	1.35072	+	2.33951i	0.0626381	+	0.108492i
$466$	−22.1230	−	38.3182i	−1.02483	−	1.77506i
$467$	11.6761	−	20.2235i	0.540303	−	0.935833i	−0.458583	−	0.888652i	$-0.651643\pi$
$467$	11.6761	−	20.2235i	0.540303	−	0.935833i	0.998886	−	0.0471812i	$-0.0150238\pi$
$468$	−8.67858			−0.401168
$469$	7.86034	+	3.23350i	0.362957	+	0.149309i
$470$	−34.9416			−1.61174
$471$	−8.00183	+	13.8596i	−0.368705	+	0.638615i
$472$	15.7599	+	27.2969i	0.725406	+	1.25644i
$473$	3.52865	+	6.11180i	0.162248	+	0.281021i
$474$	11.0621	−	19.1602i	0.508100	−	0.880055i
$475$	5.78820			0.265581
$476$	−11.4906	−	85.6704i	−0.526672	−	3.92670i
$477$	8.59824			0.393686
$478$	−16.4207	+	28.4415i	−0.751065	+	1.30088i
$479$	−7.78188	−	13.4786i	−0.355563	−	0.615853i	0.631651	−	0.775253i	$-0.282378\pi$
$479$	−7.78188	−	13.4786i	−0.355563	−	0.615853i	−0.987214	+	0.159400i	$0.949044\pi$
$480$	−3.35548	−	5.81187i	−0.153156	−	0.265274i
$481$	9.95021	−	17.2343i	0.453691	−	0.785815i
$482$	−31.7212			−1.44486
$483$	−3.32796	+	2.56651i	−0.151427	+	0.116780i
$484$	4.57249			0.207840
$485$	−7.75197	+	13.4268i	−0.351999	+	0.609680i
$486$	1.28184	+	2.22022i	0.0581456	+	0.100711i
$487$	8.24302	+	14.2773i	0.373527	+	0.646967i	0.990105	−	0.140326i	$-0.0448151\pi$
$487$	8.24302	+	14.2773i	0.373527	+	0.646967i	−0.616579	+	0.787293i	$0.711482\pi$
$488$	−24.2770	+	42.0490i	−1.09897	+	1.90347i
$489$	−10.2364			−0.462907
$490$	−17.3115	+	4.72892i	−0.782055	+	0.213631i
$491$	22.3868			1.01030			0.505150	−	0.863032i	$-0.331437\pi$
$491$	22.3868			1.01030			0.505150	+	0.863032i	$0.331437\pi$
$492$	−19.4145	+	33.6270i	−0.875275	+	1.51602i
$493$	19.3500	+	33.5151i	0.871478	+	1.50944i
$494$	−14.0823	−	24.3913i	−0.633594	−	1.09742i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	20.9704			0.941599
$497$	12.7126	−	9.80387i	0.570236	−	0.439764i
$498$	16.0763			0.720397
$499$	5.88281	−	10.1893i	0.263351	−	0.456137i	−0.703779	−	0.710419i	$-0.748506\pi$
$499$	5.88281	−	10.1893i	0.263351	−	0.456137i	0.967130	+	0.254282i	$0.0818390\pi$
$500$	2.28624	+	3.95989i	0.102244	+	0.177092i
$501$	−0.789875	−	1.36810i	−0.0352890	−	0.0611224i
$502$	32.4423	−	56.1917i	1.44797	−	2.50796i
$503$	15.8132			0.705075			0.352538	−	0.935798i	$-0.385319\pi$
$503$	15.8132			0.705075			0.352538	+	0.935798i	$0.385319\pi$
$504$	2.31957	+	17.2940i	0.103322	+	0.770337i
$505$	11.6021			0.516287
$506$	−2.03615	+	3.52671i	−0.0905178	+	0.156781i
$507$	4.69880	+	8.13856i	0.208681	+	0.361446i
$508$	−37.6342	−	65.1843i	−1.66975	−	2.89209i
$509$	12.7788	−	22.1336i	0.566411	−	0.981053i	−0.430506	−	0.902588i	$-0.641665\pi$
$509$	12.7788	−	22.1336i	0.566411	−	0.981053i	0.996917	−	0.0784649i	$-0.0250019\pi$
$510$	18.3175			0.811112
$511$	27.1449	+	11.1666i	1.20082	+	0.493979i
$512$	50.2955			2.22277
$513$	−2.89410	+	5.01273i	−0.127778	+	0.221317i
$514$	32.6997	+	56.6376i	1.44232	+	2.49818i
$515$	1.00397	+	1.73893i	0.0442402	+	0.0766262i
$516$	−16.1347	+	27.9461i	−0.710291	+	1.23026i
$517$	13.6294			0.599422
$518$	−65.7705	−	27.0559i	−2.88979	−	1.18877i
$519$	20.3783			0.894509
$520$	6.25871	−	10.8404i	0.274463	−	0.475383i
$521$	−1.71584	−	2.97192i	−0.0751722	−	0.130202i	0.825989	−	0.563686i	$-0.190617\pi$
$521$	−1.71584	−	2.97192i	−0.0751722	−	0.130202i	−0.901161	+	0.433484i	$0.857284\pi$
$522$	−6.94295	−	12.0255i	−0.303885	−	0.526344i
$523$	−6.06468	+	10.5043i	−0.265190	+	0.459323i	−0.967613	−	0.252437i	$-0.918768\pi$
$523$	−6.06468	+	10.5043i	−0.265190	+	0.459323i	0.702423	+	0.711759i	$0.252101\pi$
$524$	41.3328			1.80563
$525$	−0.351714	−	2.62227i	−0.0153501	−	0.114445i
$526$	−31.2085			−1.36076
$527$	−9.65086	+	16.7158i	−0.420398	+	0.728151i
$528$	3.88134	+	6.72268i	0.168914	+	0.292567i
$529$	10.2384	+	17.7334i	0.445148	+	0.771019i
$530$	−11.0216	+	19.0900i	−0.478748	+	0.829215i
$531$	4.77930			0.207404
$532$	−55.4498	+	42.7626i	−2.40405	+	1.85399i
$533$	−16.1176			−0.698131
$534$	−17.4426	+	30.2115i	−0.754816	+	1.30738i
$535$	−3.84707	−	6.66333i	−0.166324	−	0.288081i
$536$	10.5933	+	18.3481i	0.457559	+	0.792516i
$537$	7.47349	−	12.9445i	0.322505	−	0.558595i
$538$	30.0056			1.29363
$539$	6.75259	−	1.84458i	0.290855	−	0.0794516i
$540$	−4.57249			−0.196769
$541$	14.6531	−	25.3800i	0.629988	−	1.09117i	−0.357566	−	0.933888i	$-0.616393\pi$
$541$	14.6531	−	25.3800i	0.629988	−	1.09117i	0.987554	−	0.157283i	$-0.0502734\pi$
$542$	−5.01694	−	8.68959i	−0.215496	−	0.373250i
$543$	3.59773	+	6.23145i	0.154393	+	0.267417i
$544$	23.9748	−	41.5257i	1.02791	−	1.78040i
$545$	5.01535			0.214834
$546$	−10.1945	+	7.86194i	−0.436283	+	0.336460i
$547$	−13.7688			−0.588712			−0.294356	−	0.955696i	$-0.595105\pi$
$547$	−13.7688			−0.588712			−0.294356	+	0.955696i	$0.595105\pi$
$548$	25.4279	−	44.0424i	1.08623	−	1.88140i
$549$	3.68109	+	6.37584i	0.157105	+	0.272114i
$550$	−1.28184	−	2.22022i	−0.0546580	−	0.0946704i
$551$	15.6755	−	27.1508i	0.667800	−	1.15666i
$552$	−10.4759			−0.445885
$553$	−3.03524	−	22.6298i	−0.129072	−	0.962317i
$554$	2.01057			0.0854211
$555$	5.24247	−	9.08023i	0.222531	−	0.385434i
$556$	21.8540	+	37.8522i	0.926816	+	1.60529i
$557$	13.1449	+	22.7677i	0.556969	+	0.964699i	0.997747	+	0.0670830i	$0.0213692\pi$
$557$	13.1449	+	22.7677i	0.556969	+	0.964699i	−0.440778	+	0.897616i	$0.645297\pi$
$558$	3.46282	−	5.99778i	0.146593	−	0.253906i
$559$	−13.3948			−0.566538
$560$	−18.9938	−	7.81346i	−0.802634	−	0.330179i
$561$	−7.14498			−0.301661
$562$	8.65574	−	14.9922i	0.365120	−	0.632407i
$563$	−4.83190	−	8.36910i	−0.203640	−	0.352715i	0.746058	−	0.665881i	$-0.231944\pi$
$563$	−4.83190	−	8.36910i	−0.203640	−	0.352715i	−0.949699	+	0.313165i	$0.898611\pi$
$564$	31.1602	+	53.9711i	1.31208	+	2.27259i
$565$	−1.61762	+	2.80180i	−0.0680537	+	0.117872i
$566$	−15.7092			−0.660308
$567$	2.44681	+	1.00654i	0.102756	+	0.0422708i
$568$	40.0173			1.67909
$569$	−8.64148	+	14.9675i	−0.362270	+	0.627470i	−0.988334	−	0.152302i	$-0.951331\pi$
$569$	−8.64148	+	14.9675i	−0.362270	+	0.627470i	0.626064	+	0.779771i	$0.284665\pi$
$570$	−7.41956	−	12.8511i	−0.310771	−	0.538272i
$571$	−2.74803	−	4.75973i	−0.115002	−	0.199189i	0.802779	−	0.596277i	$-0.203354\pi$
$571$	−2.74803	−	4.75973i	−0.115002	−	0.199189i	−0.917780	+	0.397088i	$0.870021\pi$
$572$	−4.33929	+	7.51587i	−0.181435	+	0.314255i
$573$	−13.8760			−0.579677
$574$	7.65701	+	57.0882i	0.319597	+	2.38282i
$575$	1.58845			0.0662431
$576$	−0.839725	+	1.45445i	−0.0349886	+	0.0606020i
$577$	−15.0966	−	26.1481i	−0.628481	−	1.08856i	−0.987857	−	0.155367i	$-0.950344\pi$
$577$	−15.0966	−	26.1481i	−0.628481	−	1.08856i	0.359376	−	0.933193i	$-0.382990\pi$
$578$	43.6477	+	75.6000i	1.81550	+	3.14455i
$579$	−5.88011	+	10.1846i	−0.244369	+	0.423260i
$580$	24.7663			1.02837
$581$	13.1379	−	10.1319i	0.545051	−	0.420341i
$582$	39.7473			1.64758
$583$	4.29912	−	7.44629i	0.178051	−	0.308394i
$584$	36.5827	+	63.3631i	1.51380	+	2.62199i
$585$	−0.949000	−	1.64372i	−0.0392363	−	0.0679593i
$586$	17.0079	−	29.4586i	0.702592	−	1.21692i
$587$	−0.946272			−0.0390568			−0.0195284	−	0.999809i	$-0.506216\pi$
$587$	−0.946272			−0.0390568			−0.0195284	+	0.999809i	$0.506216\pi$
$588$	22.7424	+	22.5224i	0.937881	+	0.928808i
$589$	15.6365			0.644289
$590$	−6.12631	+	10.6111i	−0.252216	+	0.436851i
$591$	0.641776	+	1.11159i	0.0263991	+	0.0457246i
$592$	−40.6956	−	70.4869i	−1.67258	−	2.89699i
$593$	−11.9505	+	20.6989i	−0.490750	+	0.850004i	−0.999943	−	0.0106485i	$-0.996610\pi$
$593$	−11.9505	+	20.6989i	−0.490750	+	0.850004i	0.509194	+	0.860652i	$0.329944\pi$
$594$	2.56369			0.105189
$595$	14.9694	−	11.5443i	0.613686	−	0.473272i
$596$	37.4549			1.53421
$597$	−9.41172	+	16.3016i	−0.385196	+	0.667179i
$598$	−3.86461	−	6.69370i	−0.158036	−	0.273726i
$599$	12.4214	+	21.5145i	0.507526	+	0.879060i	0.999962	+	0.00871192i	$0.00277312\pi$
$599$	12.4214	+	21.5145i	0.507526	+	0.879060i	−0.492436	+	0.870348i	$0.663894\pi$
$600$	3.29753	−	5.71149i	0.134621	−	0.233170i
$601$	−32.2357			−1.31492			−0.657462	−	0.753488i	$-0.728370\pi$
$601$	−32.2357			−1.31492			−0.657462	+	0.753488i	$0.728370\pi$
$602$	6.36346	+	47.4440i	0.259355	+	1.93367i
$603$	3.21249			0.130823
$604$	20.1427	−	34.8882i	0.819595	−	1.41958i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−14.8721	−	25.7592i	−0.604137	−	1.04640i
$607$	−7.09186	+	12.2835i	−0.287850	+	0.498570i	−0.973296	−	0.229553i	$-0.926274\pi$
$607$	−7.09186	+	12.2835i	−0.287850	+	0.498570i	0.685447	+	0.728123i	$0.259607\pi$
$608$	−38.8444			−1.57535
$609$	−13.2528	−	5.45181i	−0.537032	−	0.220918i
$610$	−18.8743			−0.764200
$611$	−12.9343	+	22.4029i	−0.523267	+	0.906326i
$612$	−16.3352	−	28.2933i	−0.660310	−	1.14369i
$613$	−15.1512	−	26.2426i	−0.611950	−	1.05993i	−0.990911	−	0.134516i	$-0.957052\pi$
$613$	−15.1512	−	26.2426i	−0.611950	−	1.05993i	0.378961	−	0.925413i	$-0.376281\pi$
$614$	10.6395	−	18.4281i	0.429374	−	0.743697i
$615$	−8.49189			−0.342426
$616$	16.1368	+	6.63820i	0.650172	+	0.267461i
$617$	41.4017			1.66677			0.833384	−	0.552694i	$-0.186400\pi$
$617$	41.4017			1.66677			0.833384	+	0.552694i	$0.186400\pi$
$618$	2.57386	−	4.45806i	0.103536	−	0.179330i
$619$	−9.00179	−	15.5916i	−0.361813	−	0.626678i	0.626447	−	0.779464i	$-0.284509\pi$
$619$	−9.00179	−	15.5916i	−0.361813	−	0.626678i	−0.988259	+	0.152786i	$0.951175\pi$
$620$	6.17615	+	10.6974i	0.248040	+	0.429618i
$621$	−0.794226	+	1.37564i	−0.0318712	+	0.0552025i
$622$	−9.01748			−0.361568
$623$	4.78593	+	35.6824i	0.191744	+	1.42959i
$624$	−14.7336			−0.589815
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−37.5763	−	65.0840i	−1.50185	−	2.60128i
$627$	2.89410	+	5.01273i	0.115579	+	0.200189i
$628$	−36.5883	+	63.3727i	−1.46003	+	2.52885i
$629$	74.9147			2.98704
$630$	−5.37117	+	4.14222i	−0.213992	+	0.165030i
$631$	−24.2616			−0.965838			−0.482919	−	0.875665i	$-0.660424\pi$
$631$	−24.2616			−0.965838			−0.482919	+	0.875665i	$0.660424\pi$
$632$	28.4572	−	49.2893i	1.13197	−	1.96062i
$633$	−7.84517	−	13.5882i	−0.311818	−	0.540084i
$634$	14.9284	+	25.8568i	0.592884	+	1.02690i
$635$	8.23056	−	14.2558i	0.326620	−	0.565722i
$636$	39.3154			1.55896
$637$	−3.37625	+	12.8499i	−0.133772	+	0.509130i
$638$	−13.8859			−0.549748
$639$	3.03389	−	5.25485i	0.120019	−	0.207879i
$640$	4.55817	+	7.89498i	0.180178	+	0.312077i
$641$	−17.5897	−	30.4662i	−0.694750	−	1.20334i	−0.970265	−	0.242046i	$-0.922181\pi$
$641$	−17.5897	−	30.4662i	−0.694750	−	1.20334i	0.275514	−	0.961297i	$-0.411152\pi$
$642$	−9.86269	+	17.0827i	−0.389249	+	0.674200i
$643$	−2.91111			−0.114803			−0.0574015	−	0.998351i	$-0.518282\pi$
$643$	−2.91111			−0.114803			−0.0574015	+	0.998351i	$0.518282\pi$
$644$	−15.2171	+	11.7353i	−0.599636	+	0.462437i
$645$	−7.05730			−0.277881
$646$	53.0126	−	91.8205i	2.08575	−	3.61263i
$647$	14.9179	+	25.8385i	0.586482	+	1.01582i	0.994689	+	0.102927i	$0.0328207\pi$
$647$	14.9179	+	25.8385i	0.586482	+	1.01582i	−0.408207	+	0.912889i	$0.633846\pi$
$648$	3.29753	+	5.71149i	0.129539	+	0.224368i
$649$	2.38965	−	4.13899i	0.0938019	−	0.162470i
$650$	4.86588			0.190855
$651$	−0.950134	−	7.08390i	−0.0372387	−	0.277640i
$652$	−46.8060			−1.83306
$653$	1.04930	−	1.81744i	0.0410622	−	0.0711219i	−0.844764	−	0.535139i	$-0.820259\pi$
$653$	1.04930	−	1.81744i	0.0410622	−	0.0711219i	0.885826	+	0.464017i	$0.153592\pi$
$654$	−6.42889	−	11.1352i	−0.251390	−	0.435420i
$655$	4.51972	+	7.82839i	0.176600	+	0.305881i
$656$	−32.9599	+	57.0882i	−1.28687	+	2.22892i
$657$	11.0940			0.432818
$658$	85.4955	+	35.1702i	3.33296	+	1.37108i
$659$	25.9807			1.01206			0.506032	−	0.862515i	$-0.331112\pi$
$659$	25.9807			1.01206			0.506032	+	0.862515i	$0.331112\pi$
$660$	−2.28624	+	3.95989i	−0.0889920	+	0.154139i
$661$	21.9004	+	37.9327i	0.851829	+	1.47541i	0.879556	+	0.475795i	$0.157840\pi$
$661$	21.9004	+	37.9327i	0.851829	+	1.47541i	−0.0277278	+	0.999616i	$0.508827\pi$
$662$	6.11755	+	10.5959i	0.237765	+	0.411822i
$663$	6.78058	−	11.7443i	0.263336	−	0.456111i
$664$	41.3561			1.60493
$665$	−14.1626	−	5.82606i	−0.549203	−	0.225925i
$666$	−26.8801			−1.04158
$667$	4.30183	−	7.45099i	0.166568	−	0.288503i
$668$	−3.61170	−	6.25564i	−0.139741	−	0.242038i
$669$	−8.54459	−	14.7997i	−0.330353	−	0.572188i
$670$	−4.11790	+	7.13242i	−0.159088	+	0.275549i
$671$	7.36219			0.284214
$672$	2.36034	+	17.5980i	0.0910521	+	0.678856i
$673$	−17.9117			−0.690444			−0.345222	−	0.938521i	$-0.612196\pi$
$673$	−17.9117			−0.690444			−0.345222	+	0.938521i	$0.612196\pi$
$674$	12.8527	−	22.2616i	0.495069	−	0.857484i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	21.4852	+	37.2135i	0.826354	+	1.43129i
$677$	−15.0893	+	26.1355i	−0.579931	+	1.00447i	0.415556	+	0.909568i	$0.363587\pi$
$677$	−15.0893	+	26.1355i	−0.579931	+	1.00447i	−0.995487	+	0.0949017i	$0.969746\pi$
$678$	8.29413			0.318534
$679$	32.4822	−	25.0502i	1.24655	−	0.961337i
$680$	47.1215			1.80703
$681$	−5.20539	+	9.01601i	−0.199471	+	0.345494i
$682$	−3.46282	−	5.99778i	−0.132598	−	0.229667i
$683$	−0.00119622	−	0.00207191i	−4.57719e−5	−	7.92793e-5i	0.866003	−	0.500040i	$-0.166681\pi$
$683$	−0.00119622	−	0.00207191i	−4.57719e−5	−	7.92793e-5i	−0.866048	+	0.499960i	$0.833348\pi$
$684$	−13.2332	+	22.9206i	−0.505985	+	0.876392i
$685$	11.1221			0.424954
$686$	47.1179	+	5.85401i	1.79897	+	0.223507i
$687$	−7.12793			−0.271948
$688$	−27.3918	+	47.4440i	−1.04430	+	1.80878i
$689$	8.15973	+	14.1331i	0.310861	+	0.538427i
$690$	−2.03615	−	3.52671i	−0.0775148	−	0.134260i
$691$	−15.0596	+	26.0840i	−0.572893	+	0.992280i	0.423374	+	0.905955i	$0.360846\pi$
$691$	−15.0596	+	26.0840i	−0.572893	+	0.992280i	−0.996267	+	0.0863251i	$0.972488\pi$
$692$	93.1796			3.54216
$693$	2.09509	−	1.61573i	0.0795861	−	0.0613764i
$694$	−28.9854			−1.10027
$695$	−4.77945	+	8.27825i	−0.181295	+	0.314012i
$696$	−17.8607	−	30.9356i	−0.677007	−	1.17261i
$697$	−30.3372	−	52.5456i	−1.14910	−	1.99030i
$698$	−11.4019	+	19.7486i	−0.431567	+	0.747496i
$699$	−17.2588			−0.652786
$700$	−1.60821	−	11.9903i	−0.0607846	−	0.453191i
$701$	−11.3960			−0.430419			−0.215210	−	0.976568i	$-0.569043\pi$
$701$	−11.3960			−0.430419			−0.215210	+	0.976568i	$0.569043\pi$
$702$	−2.43294	+	4.21397i	−0.0918254	+	0.159046i
$703$	−30.3445	−	52.5582i	−1.14446	−	1.98227i
$704$	0.839725	+	1.45445i	0.0316483	+	0.0548165i
$705$	−6.81472	+	11.8034i	−0.256657	+	0.444543i
$706$	−68.2546			−2.56879
$707$	−28.3882	−	11.6780i	−1.06765	−	0.439197i
$708$	21.8533			0.821296
$709$	14.5273	−	25.1620i	0.545584	−	0.944979i	−0.452986	−	0.891518i	$-0.649641\pi$
$709$	14.5273	−	25.1620i	0.545584	−	0.944979i	0.998570	−	0.0534613i	$-0.0170254\pi$
$710$	7.77794	+	13.4718i	0.291901	+	0.505587i
$711$	−4.31493	−	7.47368i	−0.161822	−	0.280285i
$712$	−44.8710	+	77.7188i	−1.68161	+	2.91263i
$713$	4.29111			0.160703
$714$	−44.8194	−	18.4373i	−1.67732	−	0.689999i
$715$	−1.89800			−0.0709812
$716$	34.1724	−	59.1884i	1.27708	−	2.21197i
$717$	6.40511	+	11.0940i	0.239203	+	0.414312i
$718$	19.3400	+	33.4979i	0.721763	+	1.25013i
$719$	−3.53361	+	6.12040i	−0.131781	+	0.228252i	−0.924363	−	0.381513i	$-0.875403\pi$
$719$	−3.53361	+	6.12040i	−0.131781	+	0.228252i	0.792582	+	0.609766i	$0.208736\pi$
$720$	−7.76268			−0.289298
$721$	−0.706220	−	5.26536i	−0.0263010	−	0.196092i
$722$	−37.1818			−1.38376
$723$	−6.18664	+	10.7156i	−0.230084	+	0.398517i
$724$	16.4506	+	28.4932i	0.611381	+	1.05894i
$725$	2.70819	+	4.69072i	0.100580	+	0.174209i
$726$	1.28184	−	2.22022i	0.0475737	−	0.0824000i
$727$	20.4353			0.757903			0.378951	−	0.925417i	$-0.376285\pi$
$727$	20.4353			0.757903			0.378951	+	0.925417i	$0.376285\pi$
$728$	−26.2252	+	20.2247i	−0.971970	+	0.749579i
$729$	1.00000			0.0370370
$730$	−14.2207	+	24.6311i	−0.526334	+	0.911636i
$731$	−25.2121	−	43.6687i	−0.932504	−	1.61514i
$732$	16.8318	+	29.1535i	0.622120	+	1.07754i
$733$	−10.7276	+	18.5807i	−0.396232	+	0.686295i	−0.993258	−	0.115928i	$-0.963016\pi$
$733$	−10.7276	+	18.5807i	−0.396232	+	0.686295i	0.597025	+	0.802222i	$0.296349\pi$
$734$	−59.9927			−2.21437
$735$	−1.77885	+	6.77021i	−0.0656137	+	0.249723i
$736$	−10.6600			−0.392935
$737$	1.60624	−	2.78209i	0.0591667	−	0.102480i
$738$	10.8853	+	18.8538i	0.400692	+	0.694020i
$739$	9.78936	+	16.9557i	0.360108	+	0.623725i	0.987978	−	0.154593i	$-0.0494067\pi$
$739$	9.78936	+	16.9557i	0.360108	+	0.623725i	−0.627871	+	0.778318i	$0.716073\pi$
$740$	23.9711	−	41.5192i	0.881197	−	1.52628i
$741$	−10.9860			−0.403581
$742$	46.1826	−	35.6158i	1.69542	−	1.30750i
$743$	−32.5938			−1.19575			−0.597875	−	0.801589i	$-0.703988\pi$
$743$	−32.5938			−1.19575			−0.597875	+	0.801589i	$0.703988\pi$
$744$	8.90807	−	15.4292i	0.326586	−	0.565663i
$745$	4.09568	+	7.09392i	0.150054	+	0.259901i
$746$	−25.1647	−	43.5865i	−0.921344	−	1.59582i
$747$	3.13539	−	5.43065i	0.114718	−	0.198697i
$748$	−32.6703			−1.19455
$749$	2.70614	+	20.1761i	0.0988802	+	0.737220i
$750$	2.56369			0.0936126
$751$	26.0945	−	45.1970i	0.952202	−	1.64926i	0.211557	−	0.977366i	$-0.432147\pi$
$751$	26.0945	−	45.1970i	0.952202	−	1.64926i	0.740645	−	0.671896i	$-0.234520\pi$
$752$	52.9005	+	91.6263i	1.92908	+	3.34127i
$753$	−12.6546	−	21.9183i	−0.461158	−	0.798748i
$754$	13.1777	−	22.8245i	0.479904	−	0.831219i
$755$	8.81039			0.320643
$756$	11.1880	+	4.60240i	0.406904	+	0.167388i
$757$	32.6845			1.18794			0.593969	−	0.804488i	$-0.297560\pi$
$757$	32.6845			1.18794			0.593969	+	0.804488i	$0.297560\pi$
$758$	37.3064	−	64.6166i	1.35503	−	2.34698i
$759$	0.794226	+	1.37564i	0.0288286	+	0.0499326i
$760$	−19.0867	−	33.0592i	−0.692349	−	1.19918i
$761$	−10.3568	+	17.9385i	−0.375434	+	0.650271i	−0.990392	−	0.138289i	$-0.955840\pi$
$761$	−10.3568	+	17.9385i	−0.375434	+	0.650271i	0.614958	+	0.788560i	$0.289173\pi$
$762$	−42.2012			−1.52879
$763$	−12.2716	−	5.04816i	−0.444262	−	0.182756i
$764$	−63.4477			−2.29546
$765$	3.57249	−	6.18773i	0.129164	−	0.223718i
$766$	−27.7728	−	48.1039i	−1.00347	−	1.73806i
$767$	4.53555	+	7.85581i	0.163769	+	0.283657i
$768$	13.3652	−	23.1492i	0.482274	−	0.835323i
$769$	6.07692			0.219139			0.109570	−	0.993979i	$-0.465053\pi$
$769$	6.07692			0.219139			0.109570	+	0.993979i	$0.465053\pi$
$770$	0.901685	+	6.72268i	0.0324945	+	0.242268i
$771$	25.5099			0.918718
$772$	−26.8867	+	46.5692i	−0.967675	+	1.67606i
$773$	24.1554	+	41.8384i	0.868809	+	1.50482i	0.863214	+	0.504838i	$0.168448\pi$
$773$	24.1554	+	41.8384i	0.868809	+	1.50482i	0.00559523	+	0.999984i	$0.498219\pi$
$774$	9.04635	+	15.6687i	0.325164	+	0.563201i
$775$	−1.35072	+	2.33951i	−0.0485193	+	0.0840378i
$776$	102.249			3.67054
$777$	−21.9670	+	16.9408i	−0.788060	+	0.607749i
$778$	−86.5491			−3.10294
$779$	−24.5764	+	42.5675i	−0.880540	+	1.52514i
$780$	−4.33929	−	7.51587i	−0.155372	−	0.269111i
$781$	−3.03389	−	5.25485i	−0.108561	−	0.188033i
$782$	14.5482	−	25.1983i	0.520244	−	0.901088i
$783$	−5.41638			−0.193566
$784$	38.6096	+	38.2361i	1.37891	+	1.36557i
$785$	−16.0037			−0.571195
$786$	11.5872	−	20.0695i	0.413300	−	0.715857i
$787$	16.0571	+	27.8117i	0.572374	+	0.991380i	0.996322	+	0.0856938i	$0.0273107\pi$
$787$	16.0571	+	27.8117i	0.572374	+	0.991380i	−0.423948	+	0.905687i	$0.639356\pi$
$788$	2.93451	+	5.08272i	0.104538	+	0.181065i
$789$	−6.08665	+	10.5424i	−0.216690	+	0.375319i
$790$	22.1243			0.787146
$791$	6.77813	−	5.22726i	0.241002	−	0.185860i
$792$	6.59506			0.234345
$793$	−6.98671	+	12.1013i	−0.248105	+	0.429731i
$794$	−8.13202	−	14.0851i	−0.288595	−	0.499861i
$795$	4.29912	+	7.44629i	0.152474	+	0.264093i
$796$	−43.0350	+	74.5388i	−1.52533	+	2.64196i
$797$	27.9461			0.989903			0.494952	−	0.868921i	$-0.335186\pi$
$797$	27.9461			0.989903			0.494952	+	0.868921i	$0.335186\pi$
$798$	5.21913	+	38.9122i	0.184755	+	1.37748i
$799$	−97.3821			−3.44513
$800$	3.35548	−	5.81187i	0.118634	−	0.205480i
$801$	6.80373	+	11.7844i	0.240398	+	0.416381i
$802$	11.1165	+	19.2544i	0.392538	+	0.679896i
$803$	5.54699	−	9.60767i	0.195749	−	0.339047i
$804$	14.6891			0.518043
$805$	−3.88664	−	1.59884i	−0.136986	−	0.0563518i
$806$	13.1449			0.463008
$807$	5.85203	−	10.1360i	0.206001	−	0.356805i
$808$	−38.2583	−	66.2653i	−1.34592	−	2.33121i
$809$	−4.18624	−	7.25079i	−0.147181	−	0.254924i	0.783004	−	0.622017i	$-0.213686\pi$
$809$	−4.18624	−	7.25079i	−0.147181	−	0.254924i	−0.930184	+	0.367093i	$0.880353\pi$
$810$	−1.28184	+	2.22022i	−0.0450394	+	0.0780105i
$811$	37.6282			1.32130			0.660652	−	0.750693i	$-0.270280\pi$
$811$	37.6282			1.32130			0.660652	+	0.750693i	$0.270280\pi$
$812$	−60.5985	−	24.9283i	−2.12659	−	0.874813i
$813$	−3.91385			−0.137265
$814$	−13.4401	+	23.2789i	−0.471074	+	0.815924i
$815$	−5.11821	−	8.86501i	−0.179283	−	0.310528i
$816$	−27.7321	−	48.0334i	−0.970817	−	1.68150i
$817$	−20.4245	+	35.3763i	−0.714564	+	1.23766i
$818$	34.8812			1.21959
$819$	0.667553	+	4.97707i	0.0233262	+	0.173913i
$820$	−38.8291			−1.35597
$821$	−7.09863	+	12.2952i	−0.247744	+	0.429105i	−0.962900	−	0.269860i	$-0.913023\pi$
$821$	−7.09863	+	12.2952i	−0.247744	+	0.429105i	0.715156	+	0.698965i	$0.246356\pi$
$822$	−14.2568	−	24.6935i	−0.497264	−	0.861286i
$823$	1.38126	+	2.39242i	0.0481478	+	0.0833945i	0.889095	−	0.457723i	$-0.151335\pi$
$823$	1.38126	+	2.39242i	0.0481478	+	0.0833945i	−0.840947	+	0.541117i	$0.818001\pi$
$824$	6.62123	−	11.4683i	0.230662	−	0.399518i
$825$	−1.00000			−0.0348155
$826$	25.6704	−	19.7969i	0.893187	−	0.688822i
$827$	4.46450			0.155246			0.0776230	−	0.996983i	$-0.475267\pi$
$827$	4.46450			0.155246			0.0776230	+	0.996983i	$0.475267\pi$
$828$	−3.63159	+	6.29010i	−0.126207	+	0.218596i
$829$	−4.07290	−	7.05447i	−0.141458	−	0.245012i	0.786588	−	0.617478i	$-0.211846\pi$
$829$	−4.07290	−	7.05447i	−0.141458	−	0.245012i	−0.928046	+	0.372466i	$0.878512\pi$
$830$	8.03816	+	13.9225i	0.279008	+	0.483257i
$831$	0.392126	−	0.679182i	0.0136027	−	0.0235605i
$832$	−3.18760			−0.110510
$833$	−48.2471	+	13.1795i	−1.67166	+	0.456642i
$834$	24.5060			0.848574
$835$	0.789875	−	1.36810i	0.0273348	−	0.0473452i
$836$	13.2332	+	22.9206i	0.457681	+	0.792727i
$837$	−1.35072	−	2.33951i	−0.0466877	−	0.0808654i
$838$	4.78920	−	8.29514i	0.165440	−	0.286551i
$839$	−7.52439			−0.259771			−0.129885	−	0.991529i	$-0.541461\pi$
$839$	−7.52439			−0.259771			−0.129885	+	0.991529i	$0.541461\pi$
$840$	−13.8173	+	10.6558i	−0.476741	+	0.367661i
$841$	0.337168			0.0116265
$842$	−40.2800	+	69.7671i	−1.38814	+	2.40433i
$843$	−3.37629	−	5.84790i	−0.116285	−	0.201412i
$844$	−35.8720	−	62.1321i	−1.23476	−	2.13867i
$845$	−4.69880	+	8.13856i	−0.161644	+	0.279975i
$846$	34.9416			1.20132
$847$	−0.351714	−	2.62227i	−0.0120850	−	0.0901022i
$848$	66.7454			2.29205
$849$	−3.06379	+	5.30665i	−0.105149	+	0.182124i
$850$	9.15874	+	15.8634i	0.314142	+	0.544110i
$851$	−8.32742	−	14.4235i	−0.285460	−	0.494432i
$852$	13.8724	−	24.0277i	0.475261	−	0.823176i
$853$	−38.2038			−1.30807			−0.654037	−	0.756462i	$-0.726926\pi$
$853$	−38.2038			−1.30807			−0.654037	+	0.756462i	$0.726926\pi$
$854$	46.1819	+	18.9978i	1.58031	+	0.650091i
$855$	−5.78820			−0.197952
$856$	−25.3717	+	43.9450i	−0.867186	+	1.50201i
$857$	−19.6911	−	34.1059i	−0.672634	−	1.16504i	−0.977155	−	0.212530i	$-0.931830\pi$
$857$	−19.6911	−	34.1059i	−0.672634	−	1.16504i	0.304521	−	0.952506i	$-0.401504\pi$
$858$	2.43294	+	4.21397i	0.0830592	+	0.143863i
$859$	−23.4263	+	40.5756i	−0.799296	+	1.38442i	0.120779	+	0.992679i	$0.461461\pi$
$859$	−23.4263	+	40.5756i	−0.799296	+	1.38442i	−0.920075	+	0.391742i	$0.871873\pi$
$860$	−32.2694			−1.10038
$861$	20.7780	+	8.54744i	0.708114	+	0.291296i
$862$	96.9142			3.30091
$863$	−22.0454	+	38.1837i	−0.750433	+	1.29979i	0.197179	+	0.980367i	$0.436822\pi$
$863$	−22.0454	+	38.1837i	−0.750433	+	1.29979i	−0.947613	+	0.319421i	$0.896511\pi$
$864$	3.35548	+	5.81187i	0.114156	+	0.197724i
$865$	10.1892	+	17.6481i	0.346442	+	0.600055i
$866$	23.0170	−	39.8665i	0.782148	−	1.35472i
$867$	34.0507			1.15642
$868$	−4.34448	−	32.3910i	−0.147461	−	1.09942i
$869$	−8.62986			−0.292748
$870$	6.94295	−	12.0255i	0.235388	−	0.407704i
$871$	3.04865	+	5.28042i	0.103300	+	0.178920i
$872$	−16.5383	−	28.6451i	−0.560056	−	0.970045i
$873$	7.75197	−	13.4268i	0.262365	−	0.454429i
$874$	−23.5712			−0.797309
$875$	2.09509	−	1.61573i	0.0708271	−	0.0546216i
$876$	50.7271			1.71391
$877$	−14.3969	+	24.9361i	−0.486148	+	0.842034i	−0.999873	−	0.0159212i	$-0.994932\pi$
$877$	−14.3969	+	24.9361i	−0.486148	+	0.842034i	0.513725	+	0.857955i	$0.328265\pi$
$878$	25.6709	+	44.4633i	0.866351	+	1.50056i
$879$	−6.63418	−	11.4907i	−0.223765	−	0.387573i
$880$	−3.88134	+	6.72268i	−0.130840	+	0.226621i
$881$	9.53677			0.321302			0.160651	−	0.987011i	$-0.448641\pi$
$881$	9.53677			0.321302			0.160651	+	0.987011i	$0.448641\pi$
$882$	17.3115	−	4.72892i	0.582910	−	0.159231i
$883$	−29.2161			−0.983200			−0.491600	−	0.870821i	$-0.663588\pi$
$883$	−29.2161			−0.983200			−0.491600	+	0.870821i	$0.663588\pi$
$884$	31.0042	−	53.7008i	1.04278	−	1.80615i
$885$	2.38965	+	4.13899i	0.0803271	+	0.139131i
$886$	−51.2318	−	88.7360i	−1.72116	−	2.98114i
$887$	−14.3169	+	24.7977i	−0.480716	+	0.832624i	−0.999755	−	0.0221262i	$-0.992956\pi$
$887$	−14.3169	+	24.7977i	−0.480716	+	0.832624i	0.519039	+	0.854750i	$0.326290\pi$
$888$	−69.1488			−2.32048
$889$	−34.4876	+	26.5967i	−1.15668	+	0.892025i
$890$	−34.8852			−1.16936
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−39.0700	−	67.6713i	−1.30816	−	2.26580i
$893$	39.4450	+	68.3207i	1.31997	+	2.28626i
$894$	10.5000	−	18.1866i	0.351174	−	0.608251i
$895$	14.9470			0.499622
$896$	−3.20635	−	23.9055i	−0.107117	−	0.798627i
$897$	−3.01488			−0.100664
$898$	−24.7635	+	42.8916i	−0.826368	+	1.43131i
$899$	7.31601	+	12.6717i	0.244002	+	0.422625i
$900$	−2.28624	−	3.95989i	−0.0762082	−	0.131996i
$901$	−30.7171	+	53.2036i	−1.02334	+	1.77247i
$902$	21.7705			0.724880
$903$	17.2679	+	7.10346i	0.574639	+	0.236388i
$904$	21.3366			0.709644
$905$	−3.59773	+	6.23145i	−0.119593	+	0.207140i
$906$	−11.2935	−	19.5610i	−0.375203	−	0.649870i
$907$	−2.19662	−	3.80466i	−0.0729376	−	0.126332i	0.827250	−	0.561834i	$-0.189904\pi$
$907$	−2.19662	−	3.80466i	−0.0729376	−	0.126332i	−0.900188	+	0.435502i	$0.856571\pi$
$908$	−23.8016	+	41.2256i	−0.789884	+	1.36812i
$909$	−11.6021			−0.384818
$910$	−11.9059	−	4.89771i	−0.394676	−	0.162357i
$911$	−14.2517			−0.472181			−0.236090	−	0.971731i	$-0.575866\pi$
$911$	−14.2517			−0.472181			−0.236090	+	0.971731i	$0.575866\pi$
$912$	−22.4660	+	38.9122i	−0.743922	+	1.28851i
$913$	−3.13539	−	5.43065i	−0.103766	−	0.179728i
$914$	37.2335	+	64.4903i	1.23157	+	2.13315i
$915$	−3.68109	+	6.37584i	−0.121693	+	0.210779i
$916$	−32.5924			−1.07688
$917$	−3.17930	−	23.7039i	−0.104990	−	0.782771i
$918$	−18.3175			−0.604567
$919$	12.3744	−	21.4331i	0.408194	−	0.707013i	−0.586494	−	0.809954i	$-0.699492\pi$
$919$	12.3744	−	21.4331i	0.408194	−	0.707013i	0.994687	+	0.102941i	$0.0328254\pi$
$920$	−5.23797	−	9.07242i	−0.172691	−	0.299109i
$921$	−4.15007	−	7.18812i	−0.136749	−	0.236857i
$922$	28.1064	−	48.6817i	0.925635	−	1.60325i
$923$	11.5166			0.379075
$924$	9.57980	−	7.38790i	0.315152	−	0.243044i
$925$	10.4849			0.344743
$926$	−27.2723	+	47.2370i	−0.896224	+	1.55231i
$927$	−1.00397	−	1.73893i	−0.0329747	−	0.0571138i
$928$	−18.1746	−	31.4793i	−0.596609	−	1.03336i
$929$	−27.8311	+	48.2048i	−0.913108	+	1.58155i	−0.103459	+	0.994634i	$0.532991\pi$
$929$	−27.8311	+	48.2048i	−0.913108	+	1.58155i	−0.809648	+	0.586915i	$0.800342\pi$
$930$	6.92564			0.227101
$931$	28.7890	+	28.5105i	0.943523	+	0.934394i
$932$	−78.9155			−2.58496
$933$	−1.75869	+	3.04615i	−0.0575770	+	0.0997263i
$934$	−29.9337	−	51.8468i	−0.979462	−	1.69648i
$935$	−3.57249	−	6.18773i	−0.116833	−	0.202361i
$936$	−6.25871	+	10.8404i	−0.204572	+	0.354330i
$937$	−28.1402			−0.919300			−0.459650	−	0.888100i	$-0.652025\pi$
$937$	−28.1402			−0.919300			−0.459650	+	0.888100i	$0.652025\pi$
$938$	17.2548	−	13.3068i	0.563389	−	0.434483i
$939$	−29.3143			−0.956635
$940$	−31.1602	+	53.9711i	−1.01633	+	1.76034i
$941$	−12.6728	−	21.9499i	−0.413121	−	0.715547i	0.582108	−	0.813111i	$-0.302228\pi$
$941$	−12.6728	−	21.9499i	−0.413121	−	0.715547i	−0.995229	+	0.0975646i	$0.968895\pi$
$942$	20.5142	+	35.5316i	0.668388	+	1.15768i
$943$	−6.74448	+	11.6818i	−0.219631	+	0.380411i
$944$	37.1001			1.20751
$945$	0.351714	+	2.62227i	0.0114413	+	0.0853024i
$946$	18.0927			0.588245
$947$	0.968191	−	1.67696i	0.0314620	−	0.0544937i	−0.849866	−	0.526999i	$-0.823317\pi$
$947$	0.968191	−	1.67696i	0.0314620	−	0.0544937i	0.881328	+	0.472506i	$0.156650\pi$
$948$	−19.7300	−	34.1733i	−0.640799	−	1.10990i
$949$	10.5282	+	18.2354i	0.341760	+	0.591945i
$950$	7.41956	−	12.8511i	0.240722	−	0.416943i
$951$	11.6461			0.377649
$952$	−115.297	−	47.4298i	−3.73681	−	1.53721i
$953$	34.5110			1.11792			0.558960	−	0.829194i	$-0.311200\pi$
$953$	34.5110			1.11792			0.558960	+	0.829194i	$0.311200\pi$
$954$	11.0216	−	19.0900i	0.356837	−	0.618060i
$955$	−6.93798	−	12.0169i	−0.224508	−	0.388859i
$956$	29.2873	+	50.7271i	0.947218	+	1.64063i
$957$	−2.70819	+	4.69072i	−0.0875433	+	0.151630i
$958$	−39.9006			−1.28913
$959$	−27.2137	−	11.1949i	−0.878776	−	0.361501i
$960$	−1.67945			−0.0542040
$961$	11.8511	−	20.5267i	0.382294	−	0.662153i
$962$	−25.5092	−	44.1833i	−0.822451	−	1.42453i
$963$	3.84707	+	6.66333i	0.123970	+	0.214723i
$964$	−28.2884	+	48.9969i	−0.911107	+	1.57808i
$965$	−11.7602			−0.378575
$966$	1.43228	+	10.6787i	0.0460830	+	0.343580i
$967$	26.9952			0.868109			0.434054	−	0.900887i	$-0.357083\pi$
$967$	26.9952			0.868109			0.434054	+	0.900887i	$0.357083\pi$
$968$	3.29753	−	5.71149i	0.105987	−	0.183574i
$969$	−20.6783	−	35.8158i	−0.664282	−	1.15057i
$970$	19.8736	+	34.4221i	0.638104	+	1.10523i
$971$	−14.2406	+	24.6654i	−0.457002	+	0.791550i	−0.998801	−	0.0489579i	$-0.984410\pi$
$971$	−14.2406	+	24.6654i	−0.457002	+	0.791550i	0.541799	+	0.840508i	$0.317743\pi$
$972$	4.57249			0.146663
$973$	20.0268	−	15.4446i	0.642030	−	0.495131i
$974$	42.2650			1.35426
$975$	0.949000	−	1.64372i	0.0303923	−	0.0526411i
$976$	28.5751	+	49.4936i	0.914668	+	1.58425i
$977$	−29.1327	−	50.4594i	−0.932039	−	1.61434i	−0.779831	−	0.625990i	$-0.784695\pi$
$977$	−29.1327	−	50.4594i	−0.932039	−	1.61434i	−0.152208	−	0.988349i	$-0.548638\pi$
$978$	−13.1215	+	22.7271i	−0.419579	+	0.726732i
$979$	13.6075			0.434896
$980$	−8.13375	+	30.9567i	−0.259823	+	0.988876i
$981$	−5.01535			−0.160128
$982$	28.6963	−	49.7035i	0.915736	−	1.58610i
$983$	−9.86331	−	17.0838i	−0.314591	−	0.544887i	0.664760	−	0.747057i	$-0.268534\pi$
$983$	−9.86331	−	17.0838i	−0.314591	−	0.544887i	−0.979350	+	0.202170i	$0.935201\pi$
$984$	28.0023	+	48.5013i	0.892679	+	1.54617i
$985$	−0.641776	+	1.11159i	−0.0204487	+	0.0354181i
$986$	99.2145			3.15963
$987$	28.5550	−	22.0215i	0.908915	−	0.700951i
$988$	−50.2334			−1.59814
$989$	−5.60509	+	9.70831i	−0.178232	+	0.308706i
$990$	1.28184	+	2.22022i	0.0407397	+	0.0705632i
$991$	−9.89753	−	17.1430i	−0.314405	−	0.544566i	0.664905	−	0.746928i	$-0.268472\pi$
$991$	−9.89753	−	17.1430i	−0.314405	−	0.544566i	−0.979311	+	0.202361i	$0.935138\pi$
$992$	9.06463	−	15.7004i	0.287802	−	0.498488i
$993$	4.77246			0.151450
$994$	−5.47122	−	40.7917i	−0.173537	−	1.29383i
$995$	−18.8234			−0.596743
$996$	14.3365	−	24.8316i	0.454270	−	0.786819i
$997$	3.07570	+	5.32727i	0.0974084	+	0.168716i	0.910611	−	0.413264i	$-0.135611\pi$
$997$	3.07570	+	5.32727i	0.0974084	+	0.168716i	−0.813203	+	0.581980i	$0.802278\pi$
$998$	−15.0817	−	26.1222i	−0.477402	−	0.826885i
$999$	−5.24247	+	9.08023i	−0.165864	+	0.287286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.8	✓	16
7.2	even	3		8085.2.a.cf.1.1		8
7.4	even	3	inner	1155.2.q.j.991.8	yes	16
7.5	odd	6		8085.2.a.ce.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.8	✓	16	1.1	even	1	trivial
1155.2.q.j.991.8	yes	16	7.4	even	3	inner
8085.2.a.ce.1.1		8	7.5	odd	6
8085.2.a.cf.1.1		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28184 - 2.22022i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.28624 - 3.95989i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.56369 q^{6} +(-2.09509 + 1.61573i) q^{7} -6.59506 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.28184 - 2.22022i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.28624 - 3.95989i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.56369 q^{6} +(-2.09509 + 1.61573i) q^{7} -6.59506 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.28184 - 2.22022i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.28624 + 3.95989i) q^{12} -1.89800 q^{13} +(0.901685 + 6.72268i) q^{14} -1.00000 q^{15} +(-3.88134 + 6.72268i) q^{16} +(-3.57249 - 6.18773i) q^{17} +(1.28184 + 2.22022i) q^{18} +(-2.89410 + 5.01273i) q^{19} -4.57249 q^{20} +(2.44681 + 1.00654i) q^{21} +2.56369 q^{22} +(-0.794226 + 1.37564i) q^{23} +(3.29753 + 5.71149i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.43294 + 4.21397i) q^{26} +1.00000 q^{27} +(11.1880 + 4.60240i) q^{28} -5.41638 q^{29} +(-1.28184 + 2.22022i) q^{30} +(-1.35072 - 2.33951i) q^{31} +(3.35548 + 5.81187i) q^{32} +(0.500000 - 0.866025i) q^{33} -18.3175 q^{34} +(0.351714 + 2.62227i) q^{35} +4.57249 q^{36} +(-5.24247 + 9.08023i) q^{37} +(7.41956 + 12.8511i) q^{38} +(0.949000 + 1.64372i) q^{39} +(-3.29753 + 5.71149i) q^{40} +8.49189 q^{41} +(5.37117 - 4.14222i) q^{42} +7.05730 q^{43} +(2.28624 - 3.95989i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.03615 + 3.52671i) q^{46} +(6.81472 - 11.8034i) q^{47} +7.76268 q^{48} +(1.77885 - 6.77021i) q^{49} -2.56369 q^{50} +(-3.57249 + 6.18773i) q^{51} +(4.33929 + 7.51587i) q^{52} +(-4.29912 - 7.44629i) q^{53} +(1.28184 - 2.22022i) q^{54} +1.00000 q^{55} +(13.8173 - 10.6558i) q^{56} +5.78820 q^{57} +(-6.94295 + 12.0255i) q^{58} +(-2.38965 - 4.13899i) q^{59} +(2.28624 + 3.95989i) q^{60} +(3.68109 - 6.37584i) q^{61} -6.92564 q^{62} +(-0.351714 - 2.62227i) q^{63} +1.67945 q^{64} +(-0.949000 + 1.64372i) q^{65} +(-1.28184 - 2.22022i) q^{66} +(-1.60624 - 2.78209i) q^{67} +(-16.3352 + 28.2933i) q^{68} +1.58845 q^{69} +(6.27285 + 2.58046i) q^{70} -6.06777 q^{71} +(3.29753 - 5.71149i) q^{72} +(-5.54699 - 9.60767i) q^{73} +(13.4401 + 23.2789i) q^{74} +(-0.500000 + 0.866025i) q^{75} +26.4665 q^{76} +(-2.44681 - 1.00654i) q^{77} +4.86588 q^{78} +(-4.31493 + 7.47368i) q^{79} +(3.88134 + 6.72268i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.8853 - 18.8538i) q^{82} -6.27078 q^{83} +(-1.60821 - 11.9903i) q^{84} -7.14498 q^{85} +(9.04635 - 15.6687i) q^{86} +(2.70819 + 4.69072i) q^{87} +(-3.29753 - 5.71149i) q^{88} +(6.80373 - 11.7844i) q^{89} +2.56369 q^{90} +(3.97649 - 3.06665i) q^{91} +7.26318 q^{92} +(-1.35072 + 2.33951i) q^{93} +(-17.4708 - 30.2603i) q^{94} +(2.89410 + 5.01273i) q^{95} +(3.35548 - 5.81187i) q^{96} -15.5039 q^{97} +(-12.7511 - 12.6278i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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