LMFDB - Embedded newform 1005.2.i.c.841.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1005,2,Mod(766,1005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1005, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1005.766");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1005 = 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1005.i (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:	$8.02496540314$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 8x^{10} - 2x^{9} + 22x^{8} - 6x^{7} + 35x^{6} + 6x^{5} + 22x^{4} + 2x^{3} + 8x^{2} + 2x + 1 $ x^12 - 2x^11 + 8x^10 - 2x^9 + 22x^8 - 6x^7 + 35x^6 + 6x^5 + 22x^4 + 2x^3 + 8x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.6
Root			$-0.739181 + 1.28030i$ of defining polynomial
Character	$\chi$	$=$	1005.841
Dual form			1005.2.i.c.766.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32271 + 2.29101i) q^{2} -1.00000 q^{3} +(-2.49914 + 4.32863i) q^{4} -1.00000 q^{5} +(-1.32271 - 2.29101i) q^{6} +(2.30194 - 3.98707i) q^{7} -7.93171 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.32271 + 2.29101i) q^{2} -1.00000 q^{3} +(-2.49914 + 4.32863i) q^{4} -1.00000 q^{5} +(-1.32271 - 2.29101i) q^{6} +(2.30194 - 3.98707i) q^{7} -7.93171 q^{8} +1.00000 q^{9} +(-1.32271 - 2.29101i) q^{10} +(2.12237 - 3.67605i) q^{11} +(2.49914 - 4.32863i) q^{12} +(-2.34349 - 4.05904i) q^{13} +12.1792 q^{14} +1.00000 q^{15} +(-5.49310 - 9.51432i) q^{16} +(-1.32043 - 2.28705i) q^{17} +(1.32271 + 2.29101i) q^{18} +(0.541550 + 0.937991i) q^{19} +(2.49914 - 4.32863i) q^{20} +(-2.30194 + 3.98707i) q^{21} +11.2291 q^{22} +(-4.31870 - 7.48021i) q^{23} +7.93171 q^{24} +1.00000 q^{25} +(6.19952 - 10.7379i) q^{26} -1.00000 q^{27} +(11.5057 + 19.9285i) q^{28} +(1.68289 - 2.91485i) q^{29} +(1.32271 + 2.29101i) q^{30} +(-5.03551 + 8.72176i) q^{31} +(6.59987 - 11.4313i) q^{32} +(-2.12237 + 3.67605i) q^{33} +(3.49310 - 6.05022i) q^{34} +(-2.30194 + 3.98707i) q^{35} +(-2.49914 + 4.32863i) q^{36} +(1.34349 + 2.32699i) q^{37} +(-1.43263 + 2.48139i) q^{38} +(2.34349 + 4.05904i) q^{39} +7.93171 q^{40} +(1.52306 - 2.63801i) q^{41} -12.1792 q^{42} -9.91345 q^{43} +(10.6082 + 18.3739i) q^{44} -1.00000 q^{45} +(11.4248 - 19.7883i) q^{46} +(-3.07577 + 5.32739i) q^{47} +(5.49310 + 9.51432i) q^{48} +(-7.09783 - 12.2938i) q^{49} +(1.32271 + 2.29101i) q^{50} +(1.32043 + 2.28705i) q^{51} +23.4268 q^{52} +11.2874 q^{53} +(-1.32271 - 2.29101i) q^{54} +(-2.12237 + 3.67605i) q^{55} +(-18.2583 + 31.6243i) q^{56} +(-0.541550 - 0.937991i) q^{57} +8.90393 q^{58} +11.6436 q^{59} +(-2.49914 + 4.32863i) q^{60} +(-0.749226 - 1.29770i) q^{61} -26.6421 q^{62} +(2.30194 - 3.98707i) q^{63} +12.9465 q^{64} +(2.34349 + 4.05904i) q^{65} -11.2291 q^{66} +(-7.76558 - 2.58761i) q^{67} +13.1997 q^{68} +(4.31870 + 7.48021i) q^{69} -12.1792 q^{70} +(3.23228 - 5.59848i) q^{71} -7.93171 q^{72} +(3.63150 + 6.28994i) q^{73} +(-3.55409 + 6.15587i) q^{74} -1.00000 q^{75} -5.41363 q^{76} +(-9.77111 - 16.9241i) q^{77} +(-6.19952 + 10.7379i) q^{78} +(-4.24905 + 7.35957i) q^{79} +(5.49310 + 9.51432i) q^{80} +1.00000 q^{81} +8.05827 q^{82} +(-0.100786 - 0.174567i) q^{83} +(-11.5057 - 19.9285i) q^{84} +(1.32043 + 2.28705i) q^{85} +(-13.1126 - 22.7118i) q^{86} +(-1.68289 + 2.91485i) q^{87} +(-16.8340 + 29.1573i) q^{88} -5.07447 q^{89} +(-1.32271 - 2.29101i) q^{90} -21.5782 q^{91} +43.1721 q^{92} +(5.03551 - 8.72176i) q^{93} -16.2734 q^{94} +(-0.541550 - 0.937991i) q^{95} +(-6.59987 + 11.4313i) q^{96} +(2.59271 + 4.49071i) q^{97} +(18.7768 - 32.5224i) q^{98} +(2.12237 - 3.67605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 12 q^{3} - 9 q^{4} - 12 q^{5} + q^{6} + 10 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - q^2 - 12 * q^3 - 9 * q^4 - 12 * q^5 + q^6 + 10 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - q^{2} - 12 q^{3} - 9 q^{4} - 12 q^{5} + q^{6} + 10 q^{7} - 12 q^{8} + 12 q^{9} + q^{10} + 9 q^{12} - 12 q^{13} + 34 q^{14} + 12 q^{15} - 7 q^{16} - 8 q^{17} - q^{18} + 8 q^{19} + 9 q^{20} - 10 q^{21} + 6 q^{22} - 2 q^{23} + 12 q^{24} + 12 q^{25} + 21 q^{26} - 12 q^{27} + 15 q^{28} - 2 q^{29} - q^{30} - 24 q^{31} + 11 q^{32} - 17 q^{34} - 10 q^{35} - 9 q^{36} - 3 q^{38} + 12 q^{39} + 12 q^{40} + 10 q^{41} - 34 q^{42} - 32 q^{43} - q^{44} - 12 q^{45} - 5 q^{46} + 2 q^{47} + 7 q^{48} - 12 q^{49} - q^{50} + 8 q^{51} + 58 q^{52} - 16 q^{53} + q^{54} - 38 q^{56} - 8 q^{57} - 38 q^{58} - 32 q^{59} - 9 q^{60} - 22 q^{61} - 38 q^{62} + 10 q^{63} - 8 q^{64} + 12 q^{65} - 6 q^{66} + 22 q^{68} + 2 q^{69} - 34 q^{70} + 16 q^{71} - 12 q^{72} + 20 q^{73} - 23 q^{74} - 12 q^{75} - 46 q^{76} - 28 q^{77} - 21 q^{78} + 4 q^{79} + 7 q^{80} + 12 q^{81} + 74 q^{82} - 2 q^{83} - 15 q^{84} + 8 q^{85} - 4 q^{86} + 2 q^{87} - 64 q^{88} - 72 q^{89} + q^{90} - 40 q^{91} + 146 q^{92} + 24 q^{93} - 90 q^{94} - 8 q^{95} - 11 q^{96} + 28 q^{97} + 54 q^{98}+O(q^{100}) \) 12 * q - q^2 - 12 * q^3 - 9 * q^4 - 12 * q^5 + q^6 + 10 * q^7 - 12 * q^8 + 12 * q^9 + q^10 + 9 * q^12 - 12 * q^13 + 34 * q^14 + 12 * q^15 - 7 * q^16 - 8 * q^17 - q^18 + 8 * q^19 + 9 * q^20 - 10 * q^21 + 6 * q^22 - 2 * q^23 + 12 * q^24 + 12 * q^25 + 21 * q^26 - 12 * q^27 + 15 * q^28 - 2 * q^29 - q^30 - 24 * q^31 + 11 * q^32 - 17 * q^34 - 10 * q^35 - 9 * q^36 - 3 * q^38 + 12 * q^39 + 12 * q^40 + 10 * q^41 - 34 * q^42 - 32 * q^43 - q^44 - 12 * q^45 - 5 * q^46 + 2 * q^47 + 7 * q^48 - 12 * q^49 - q^50 + 8 * q^51 + 58 * q^52 - 16 * q^53 + q^54 - 38 * q^56 - 8 * q^57 - 38 * q^58 - 32 * q^59 - 9 * q^60 - 22 * q^61 - 38 * q^62 + 10 * q^63 - 8 * q^64 + 12 * q^65 - 6 * q^66 + 22 * q^68 + 2 * q^69 - 34 * q^70 + 16 * q^71 - 12 * q^72 + 20 * q^73 - 23 * q^74 - 12 * q^75 - 46 * q^76 - 28 * q^77 - 21 * q^78 + 4 * q^79 + 7 * q^80 + 12 * q^81 + 74 * q^82 - 2 * q^83 - 15 * q^84 + 8 * q^85 - 4 * q^86 + 2 * q^87 - 64 * q^88 - 72 * q^89 + q^90 - 40 * q^91 + 146 * q^92 + 24 * q^93 - 90 * q^94 - 8 * q^95 - 11 * q^96 + 28 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1005\mathbb{Z}\right)^\times$.

$n$	$136$	$202$	$671$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.32271	+	2.29101i	0.935299	+	1.61999i	0.774100	+	0.633063i	$0.218203\pi$
$2$	1.32271	+	2.29101i	0.935299	+	1.61999i	0.161199	+	0.986922i	$0.448464\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−2.49914	+	4.32863i	−1.24957	+	2.16432i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.32271	−	2.29101i	−0.539995	−	0.935299i
$7$	2.30194	−	3.98707i	0.870051	−	1.50697i	0.00810748	−	0.999967i	$-0.497419\pi$
$7$	2.30194	−	3.98707i	0.870051	−	1.50697i	0.861943	−	0.507005i	$-0.169247\pi$
$8$	−7.93171			−2.80428
$9$	1.00000			0.333333
$10$	−1.32271	−	2.29101i	−0.418278	−	0.724479i
$11$	2.12237	−	3.67605i	0.639918	−	1.10837i	−0.345533	−	0.938407i	$-0.612302\pi$
$11$	2.12237	−	3.67605i	0.639918	−	1.10837i	0.985450	−	0.169963i	$-0.0543649\pi$
$12$	2.49914	−	4.32863i	0.721439	−	1.24957i
$13$	−2.34349	−	4.05904i	−0.649966	−	1.12577i	−0.983130	−	0.182906i	$-0.941450\pi$
$13$	−2.34349	−	4.05904i	−0.649966	−	1.12577i	0.333164	−	0.942869i	$-0.391884\pi$
$14$	12.1792			3.25503
$15$	1.00000			0.258199
$16$	−5.49310	−	9.51432i	−1.37327	−	2.37858i
$17$	−1.32043	−	2.28705i	−0.320251	−	0.554691i	0.660289	−	0.751012i	$-0.270434\pi$
$17$	−1.32043	−	2.28705i	−0.320251	−	0.554691i	−0.980540	+	0.196321i	$0.937101\pi$
$18$	1.32271	+	2.29101i	0.311766	+	0.539995i
$19$	0.541550	+	0.937991i	0.124240	+	0.215190i	0.921436	−	0.388531i	$-0.127017\pi$
$19$	0.541550	+	0.937991i	0.124240	+	0.215190i	−0.797196	+	0.603721i	$0.793684\pi$
$20$	2.49914	−	4.32863i	0.558824	−	0.967912i
$21$	−2.30194	+	3.98707i	−0.502324	+	0.870051i
$22$	11.2291			2.39406
$23$	−4.31870	−	7.48021i	−0.900512	−	1.55973i	−0.826831	−	0.562450i	$-0.809859\pi$
$23$	−4.31870	−	7.48021i	−0.900512	−	1.55973i	−0.0736806	−	0.997282i	$-0.523475\pi$
$24$	7.93171			1.61905
$25$	1.00000			0.200000
$26$	6.19952	−	10.7379i	1.21583	−	2.10587i
$27$	−1.00000			−0.192450
$28$	11.5057	+	19.9285i	2.17438	+	3.76613i
$29$	1.68289	−	2.91485i	0.312505	−	0.541275i	−0.666399	−	0.745595i	$-0.732165\pi$
$29$	1.68289	−	2.91485i	0.312505	−	0.541275i	0.978904	+	0.204321i	$0.0654985\pi$
$30$	1.32271	+	2.29101i	0.241493	+	0.418278i
$31$	−5.03551	+	8.72176i	−0.904404	+	1.56647i	−0.0826889	+	0.996575i	$0.526351\pi$
$31$	−5.03551	+	8.72176i	−0.904404	+	1.56647i	−0.821715	+	0.569898i	$0.806983\pi$
$32$	6.59987	−	11.4313i	1.16670	−	2.02079i
$33$	−2.12237	+	3.67605i	−0.369457	+	0.639918i
$34$	3.49310	−	6.05022i	0.599061	−	1.03760i
$35$	−2.30194	+	3.98707i	−0.389098	+	0.673938i
$36$	−2.49914	+	4.32863i	−0.416523	+	0.721439i
$37$	1.34349	+	2.32699i	0.220868	+	0.382555i	0.955072	−	0.296375i	$-0.0957777\pi$
$37$	1.34349	+	2.32699i	0.220868	+	0.382555i	−0.734204	+	0.678929i	$0.762444\pi$
$38$	−1.43263	+	2.48139i	−0.232403	+	0.402534i
$39$	2.34349	+	4.05904i	0.375258	+	0.649966i
$40$	7.93171			1.25411
$41$	1.52306	−	2.63801i	0.237862	−	0.411989i	−0.722239	−	0.691644i	$-0.756887\pi$
$41$	1.52306	−	2.63801i	0.237862	−	0.411989i	0.960100	+	0.279655i	$0.0902202\pi$
$42$	−12.1792			−1.87929
$43$	−9.91345			−1.51179			−0.755893	−	0.654695i	$-0.772797\pi$
$43$	−9.91345			−1.51179			−0.755893	+	0.654695i	$0.772797\pi$
$44$	10.6082	+	18.3739i	1.59924	+	2.76997i
$45$	−1.00000			−0.149071
$46$	11.4248	−	19.7883i	1.68450	−	2.91763i
$47$	−3.07577	+	5.32739i	−0.448647	+	0.777080i	−0.998298	−	0.0583146i	$-0.981427\pi$
$47$	−3.07577	+	5.32739i	−0.448647	+	0.777080i	0.549651	+	0.835394i	$0.314761\pi$
$48$	5.49310	+	9.51432i	0.792860	+	1.37327i
$49$	−7.09783	−	12.2938i	−1.01398	−	1.75626i
$50$	1.32271	+	2.29101i	0.187060	+	0.323997i
$51$	1.32043	+	2.28705i	0.184897	+	0.320251i
$52$	23.4268			3.24871
$53$	11.2874			1.55044			0.775222	−	0.631689i	$-0.217638\pi$
$53$	11.2874			1.55044			0.775222	+	0.631689i	$0.217638\pi$
$54$	−1.32271	−	2.29101i	−0.179998	−	0.311766i
$55$	−2.12237	+	3.67605i	−0.286180	+	0.495678i
$56$	−18.2583	+	31.6243i	−2.43987	+	4.22597i
$57$	−0.541550	−	0.937991i	−0.0717300	−	0.124240i
$58$	8.90393			1.16914
$59$	11.6436			1.51587			0.757933	−	0.652333i	$-0.226209\pi$
$59$	11.6436			1.51587			0.757933	+	0.652333i	$0.226209\pi$
$60$	−2.49914	+	4.32863i	−0.322637	+	0.558824i
$61$	−0.749226	−	1.29770i	−0.0959285	−	0.166153i	0.814067	−	0.580771i	$-0.197249\pi$
$61$	−0.749226	−	1.29770i	−0.0959285	−	0.166153i	−0.909996	+	0.414618i	$0.863915\pi$
$62$	−26.6421			−3.38355
$63$	2.30194	−	3.98707i	0.290017	−	0.502324i
$64$	12.9465			1.61831
$65$	2.34349	+	4.05904i	0.290674	+	0.503462i
$66$	−11.2291			−1.38221
$67$	−7.76558	−	2.58761i	−0.948717	−	0.316127i
$67$	−7.76558	−	2.58761i	−0.948717	−	0.316127i
$68$	13.1997			1.60070
$69$	4.31870	+	7.48021i	0.519911	+	0.900512i
$70$	−12.1792			−1.45569
$71$	3.23228	−	5.59848i	0.383601	−	0.664417i	−0.607973	−	0.793958i	$-0.708017\pi$
$71$	3.23228	−	5.59848i	0.383601	−	0.664417i	0.991574	+	0.129541i	$0.0413503\pi$
$72$	−7.93171			−0.934761
$73$	3.63150	+	6.28994i	0.425035	+	0.736181i	0.996424	−	0.0844978i	$-0.0269286\pi$
$73$	3.63150	+	6.28994i	0.425035	+	0.736181i	−0.571389	+	0.820679i	$0.693595\pi$
$74$	−3.55409	+	6.15587i	−0.413155	+	0.715606i
$75$	−1.00000			−0.115470
$76$	−5.41363			−0.620985
$77$	−9.77111	−	16.9241i	−1.11352	−	1.92868i
$78$	−6.19952	+	10.7379i	−0.701957	+	1.21583i
$79$	−4.24905	+	7.35957i	−0.478055	+	0.828016i	−0.999684	−	0.0251569i	$-0.991991\pi$
$79$	−4.24905	+	7.35957i	−0.478055	+	0.828016i	0.521628	+	0.853173i	$0.325325\pi$
$80$	5.49310	+	9.51432i	0.614147	+	1.06373i
$81$	1.00000			0.111111
$82$	8.05827			0.889887
$83$	−0.100786	−	0.174567i	−0.0110627	−	0.0191612i	0.860441	−	0.509550i	$-0.170188\pi$
$83$	−0.100786	−	0.174567i	−0.0110627	−	0.0191612i	−0.871504	+	0.490389i	$0.836855\pi$
$84$	−11.5057	−	19.9285i	−1.25538	−	2.17438i
$85$	1.32043	+	2.28705i	0.143221	+	0.248065i
$86$	−13.1126	−	22.7118i	−1.41397	−	2.44907i
$87$	−1.68289	+	2.91485i	−0.180425	+	0.312505i
$88$	−16.8340	+	29.1573i	−1.79451	+	3.10818i
$89$	−5.07447			−0.537893			−0.268946	−	0.963155i	$-0.586675\pi$
$89$	−5.07447			−0.537893			−0.268946	+	0.963155i	$0.586675\pi$
$90$	−1.32271	−	2.29101i	−0.139426	−	0.241493i
$91$	−21.5782			−2.26201
$92$	43.1721			4.50100
$93$	5.03551	−	8.72176i	0.522158	−	0.904404i
$94$	−16.2734			−1.67848
$95$	−0.541550	−	0.937991i	−0.0555618	−	0.0962359i
$96$	−6.59987	+	11.4313i	−0.673596	+	1.16670i
$97$	2.59271	+	4.49071i	0.263250	+	0.455963i	0.967104	−	0.254383i	$-0.0818722\pi$
$97$	2.59271	+	4.49071i	0.263250	+	0.455963i	−0.703854	+	0.710345i	$0.748539\pi$
$98$	18.7768	−	32.5224i	1.89674	−	3.28525i
$99$	2.12237	−	3.67605i	0.213306	−	0.369457i
$100$	−2.49914	+	4.32863i	−0.249914	+	0.432863i
$101$	−1.73660	+	3.00788i	−0.172798	+	0.299295i	−0.939397	−	0.342831i	$-0.888614\pi$
$101$	−1.73660	+	3.00788i	−0.172798	+	0.299295i	0.766599	+	0.642126i	$0.221947\pi$
$102$	−3.49310	+	6.05022i	−0.345868	+	0.599061i
$103$	5.76908	−	9.99234i	0.568444	−	0.984574i	−0.428276	−	0.903648i	$-0.640879\pi$
$103$	5.76908	−	9.99234i	0.568444	−	0.984574i	0.996720	−	0.0809264i	$-0.0257879\pi$
$104$	18.5879	+	32.1951i	1.82269	+	3.15699i
$105$	2.30194	−	3.98707i	0.224646	−	0.389098i
$106$	14.9300	+	25.8595i	1.45013	+	2.51170i
$107$	2.77192			0.267971			0.133986	−	0.990983i	$-0.457222\pi$
$107$	2.77192			0.267971			0.133986	+	0.990983i	$0.457222\pi$
$108$	2.49914	−	4.32863i	0.240480	−	0.416523i
$109$	7.47378			0.715859			0.357929	−	0.933749i	$-0.383483\pi$
$109$	7.47378			0.715859			0.357929	+	0.933749i	$0.383483\pi$
$110$	−11.2291			−1.07066
$111$	−1.34349	−	2.32699i	−0.127518	−	0.220868i
$112$	−50.5791			−4.77927
$113$	10.2800	−	17.8055i	0.967060	−	1.67500i	0.263086	−	0.964772i	$-0.415260\pi$
$113$	10.2800	−	17.8055i	0.967060	−	1.67500i	0.703974	−	0.710226i	$-0.251407\pi$
$114$	1.43263	−	2.48139i	0.134178	−	0.232403i
$115$	4.31870	+	7.48021i	0.402721	+	0.697533i
$116$	8.41155	+	14.5692i	0.780993	+	1.35272i
$117$	−2.34349	−	4.05904i	−0.216655	−	0.375258i
$118$	15.4011	+	26.6755i	1.41779	+	2.45568i
$119$	−12.1582			−1.11454
$120$	−7.93171			−0.724063
$121$	−3.50888	−	6.07756i	−0.318989	−	0.552506i
$122$	1.98202	−	3.43296i	0.179444	−	0.310806i
$123$	−1.52306	+	2.63801i	−0.137330	+	0.237862i
$124$	−25.1689	−	43.5937i	−2.26023	−	3.91483i
$125$	−1.00000			−0.0894427
$126$	12.1792			1.08501
$127$	5.31057	−	9.19817i	0.471237	−	0.816206i	−0.528222	−	0.849106i	$-0.677141\pi$
$127$	5.31057	−	9.19817i	0.471237	−	0.816206i	0.999459	+	0.0329006i	$0.0104745\pi$
$128$	3.92479	+	6.79793i	0.346905	+	0.600858i
$129$	9.91345			0.872830
$130$	−6.19952	+	10.7379i	−0.543734	+	0.941775i
$131$	11.3739			0.993747			0.496873	−	0.867823i	$-0.334481\pi$
$131$	11.3739			0.993747			0.496873	+	0.867823i	$0.334481\pi$
$132$	−10.6082	−	18.3739i	−0.923323	−	1.59924i
$133$	4.98645			0.432380
$134$	−4.34340	−	21.2137i	−0.375212	−	1.83258i
$135$	1.00000			0.0860663
$136$	10.4733	+	18.1402i	0.898074	+	1.55551i
$137$	16.2753			1.39049			0.695247	−	0.718771i	$-0.255295\pi$
$137$	16.2753			1.39049			0.695247	+	0.718771i	$0.255295\pi$
$138$	−11.4248	+	19.7883i	−0.972544	+	1.68450i
$139$	−1.34050			−0.113700			−0.0568500	−	0.998383i	$-0.518106\pi$
$139$	−1.34050			−0.113700			−0.0568500	+	0.998383i	$0.518106\pi$
$140$	−11.5057	−	19.9285i	−0.972410	−	1.68426i
$141$	3.07577	−	5.32739i	0.259027	−	0.448647i
$142$	17.1015			1.43513
$143$	−19.8950			−1.66370
$144$	−5.49310	−	9.51432i	−0.457758	−	0.792860i
$145$	−1.68289	+	2.91485i	−0.139757	+	0.242065i
$146$	−9.60685	+	16.6396i	−0.795069	+	1.37710i
$147$	7.09783	+	12.2938i	0.585420	+	1.01398i
$148$	−13.4302			−1.10396
$149$	−6.31967			−0.517727			−0.258864	−	0.965914i	$-0.583348\pi$
$149$	−6.31967			−0.517727			−0.258864	+	0.965914i	$0.583348\pi$
$150$	−1.32271	−	2.29101i	−0.107999	−	0.187060i
$151$	0.664400	+	1.15077i	0.0540681	+	0.0936487i	0.891793	−	0.452444i	$-0.149448\pi$
$151$	0.664400	+	1.15077i	0.0540681	+	0.0936487i	−0.837725	+	0.546093i	$0.816115\pi$
$152$	−4.29541	−	7.43987i	−0.348404	−	0.603453i
$153$	−1.32043	−	2.28705i	−0.106750	−	0.184897i
$154$	25.8487	−	44.7713i	2.08295	−	3.60778i
$155$	5.03551	−	8.72176i	0.404462	−	0.700548i
$156$	−23.4268			−1.87564
$157$	−3.64013	−	6.30488i	−0.290514	−	0.503184i	0.683418	−	0.730028i	$-0.260493\pi$
$157$	−3.64013	−	6.30488i	−0.290514	−	0.503184i	−0.973931	+	0.226843i	$0.927160\pi$
$158$	−22.4811			−1.78850
$159$	−11.2874			−0.895149
$160$	−6.59987	+	11.4313i	−0.521765	+	0.903724i
$161$	−39.7655			−3.13396
$162$	1.32271	+	2.29101i	0.103922	+	0.179998i
$163$	1.71100	−	2.96353i	0.134016	−	0.232122i	−0.791205	−	0.611551i	$-0.790546\pi$
$163$	1.71100	−	2.96353i	0.134016	−	0.232122i	0.925221	+	0.379429i	$0.123879\pi$
$164$	7.61266	+	13.1855i	0.594449	+	1.02962i
$165$	2.12237	−	3.67605i	0.165226	−	0.286180i
$166$	0.266622	−	0.461804i	0.0206939	−	0.0358429i
$167$	0.714827	−	1.23812i	0.0553150	−	0.0958084i	−0.837042	−	0.547139i	$-0.815717\pi$
$167$	0.714827	−	1.23812i	0.0553150	−	0.0958084i	0.892357	+	0.451330i	$0.149050\pi$
$168$	18.2583	−	31.6243i	1.40866	−	2.43987i
$169$	−4.48387	+	7.76628i	−0.344913	+	0.597406i
$170$	−3.49310	+	6.05022i	−0.267908	+	0.464031i
$171$	0.541550	+	0.937991i	0.0414133	+	0.0717300i
$172$	24.7751	−	42.9117i	1.88908	−	3.27198i
$173$	5.61128	+	9.71902i	0.426618	+	0.738923i	0.996570	−	0.0827543i	$-0.0263717\pi$
$173$	5.61128	+	9.71902i	0.426618	+	0.738923i	−0.569952	+	0.821678i	$0.693038\pi$
$174$	−8.90393			−0.675005
$175$	2.30194	−	3.98707i	0.174010	−	0.301394i
$176$	−46.6335			−3.51513
$177$	−11.6436			−0.875185
$178$	−6.71207	−	11.6256i	−0.503091	−	0.871378i
$179$	17.3998			1.30052			0.650262	−	0.759710i	$-0.274659\pi$
$179$	17.3998			1.30052			0.650262	+	0.759710i	$0.274659\pi$
$180$	2.49914	−	4.32863i	0.186275	−	0.322637i
$181$	−10.9526	+	18.9704i	−0.814097	+	1.41006i	0.0958773	+	0.995393i	$0.469434\pi$
$181$	−10.9526	+	18.9704i	−0.814097	+	1.41006i	−0.909974	+	0.414664i	$0.863899\pi$
$182$	−28.5418	−	49.4359i	−2.11566	−	3.66443i
$183$	0.749226	+	1.29770i	0.0553844	+	0.0959285i
$184$	34.2547	+	59.3309i	2.52529	+	4.37393i
$185$	−1.34349	−	2.32699i	−0.0987752	−	0.171084i
$186$	26.6421			1.95350
$187$	−11.2097			−0.819737
$188$	−15.3735	−	26.6278i	−1.12123	−	1.94203i
$189$	−2.30194	+	3.98707i	−0.167441	+	0.290017i
$190$	1.43263	−	2.48139i	0.103934	−	0.180019i
$191$	−9.24529	−	16.0133i	−0.668966	−	1.15868i	−0.978194	−	0.207695i	$-0.933404\pi$
$191$	−9.24529	−	16.0133i	−0.668966	−	1.15868i	0.309228	−	0.950988i	$-0.399929\pi$
$192$	−12.9465			−0.934334
$193$	−9.49104			−0.683180			−0.341590	−	0.939849i	$-0.610965\pi$
$193$	−9.49104			−0.683180			−0.341590	+	0.939849i	$0.610965\pi$
$194$	−6.85883	+	11.8798i	−0.492435	+	0.852923i
$195$	−2.34349	−	4.05904i	−0.167821	−	0.290674i
$196$	70.9538			5.06813
$197$	−8.67792	+	15.0306i	−0.618276	+	1.07089i	0.371524	+	0.928423i	$0.378835\pi$
$197$	−8.67792	+	15.0306i	−0.618276	+	1.07089i	−0.989800	+	0.142462i	$0.954498\pi$
$198$	11.2291			0.798019
$199$	2.66440	+	4.61488i	0.188874	+	0.327140i	0.944875	−	0.327431i	$-0.106183\pi$
$199$	2.66440	+	4.61488i	0.188874	+	0.327140i	−0.756001	+	0.654571i	$0.772849\pi$
$200$	−7.93171			−0.560856
$201$	7.76558	+	2.58761i	0.547742	+	0.182516i
$202$	−9.18808			−0.646471
$203$	−7.74782	−	13.4196i	−0.543791	−	0.941873i
$204$	−13.1997			−0.924166
$205$	−1.52306	+	2.63801i	−0.106375	+	0.184247i
$206$	30.5233			2.12666
$207$	−4.31870	−	7.48021i	−0.300171	−	0.519911i
$208$	−25.7460	+	44.5934i	−1.78516	+	3.09199i
$209$	4.59747			0.318013
$210$	12.1792			0.840445
$211$	3.51937	+	6.09574i	0.242284	+	0.419648i	0.961364	−	0.275279i	$-0.0887702\pi$
$211$	3.51937	+	6.09574i	0.242284	+	0.419648i	−0.719081	+	0.694927i	$0.755437\pi$
$212$	−28.2088	+	48.8590i	−1.93738	+	3.35565i
$213$	−3.23228	+	5.59848i	−0.221472	+	0.383601i
$214$	3.66645	+	6.35048i	0.250633	+	0.434110i
$215$	9.91345			0.676092
$216$	7.93171			0.539684
$217$	23.1829	+	40.1539i	1.57375	+	2.72582i
$218$	9.88567	+	17.1225i	0.669542	+	1.15968i
$219$	−3.63150	−	6.28994i	−0.245394	−	0.425035i
$220$	−10.6082	−	18.3739i	−0.715203	−	1.23877i
$221$	−6.18882	+	10.7193i	−0.416305	+	0.721061i
$222$	3.55409	−	6.15587i	0.238535	−	0.413155i
$223$	2.70570			0.181187			0.0905934	−	0.995888i	$-0.471124\pi$
$223$	2.70570			0.181187			0.0905934	+	0.995888i	$0.471124\pi$
$224$	−30.3850	−	52.6283i	−2.03018	−	3.51638i
$225$	1.00000			0.0666667
$226$	54.3899			3.61796
$227$	−2.62310	+	4.54334i	−0.174101	+	0.301552i	−0.939850	−	0.341588i	$-0.889035\pi$
$227$	−2.62310	+	4.54334i	−0.174101	+	0.301552i	0.765749	+	0.643140i	$0.222369\pi$
$228$	5.41363			0.358526
$229$	8.53971	+	14.7912i	0.564320	+	0.977431i	0.997113	+	0.0759372i	$0.0241948\pi$
$229$	8.53971	+	14.7912i	0.564320	+	0.977431i	−0.432793	+	0.901493i	$0.642472\pi$
$230$	−11.4248	+	19.7883i	−0.753329	+	1.30480i
$231$	9.77111	+	16.9241i	0.642892	+	1.11352i
$232$	−13.3482	+	23.1198i	−0.876353	+	1.51789i
$233$	6.64923	−	11.5168i	0.435605	−	0.754491i	−0.561739	−	0.827314i	$-0.689868\pi$
$233$	6.64923	−	11.5168i	0.435605	−	0.754491i	0.997345	+	0.0728234i	$0.0232009\pi$
$234$	6.19952	−	10.7379i	0.405275	−	0.701957i
$235$	3.07577	−	5.32739i	0.200641	−	0.347521i
$236$	−29.0989	+	50.4008i	−1.89418	+	3.28081i
$237$	4.24905	−	7.35957i	0.276005	−	0.478055i
$238$	−16.0818	−	27.8545i	−1.04243	−	1.80554i
$239$	−1.53772	+	2.66341i	−0.0994668	+	0.172282i	−0.911464	−	0.411380i	$-0.865047\pi$
$239$	−1.53772	+	2.66341i	−0.0994668	+	0.172282i	0.811997	+	0.583661i	$0.198380\pi$
$240$	−5.49310	−	9.51432i	−0.354578	−	0.614147i
$241$	10.6166			0.683872			0.341936	−	0.939723i	$-0.388917\pi$
$241$	10.6166			0.683872			0.341936	+	0.939723i	$0.388917\pi$
$242$	9.28248	−	16.0777i	0.596701	−	1.03352i
$243$	−1.00000			−0.0641500
$244$	7.48967			0.479477
$245$	7.09783	+	12.2938i	0.453464	+	0.785423i
$246$	−8.05827			−0.513777
$247$	2.53823	−	4.39634i	0.161504	−	0.279733i
$248$	39.9402	−	69.1784i	2.53620	−	4.39283i
$249$	0.100786	+	0.174567i	0.00638707	+	0.0110627i
$250$	−1.32271	−	2.29101i	−0.0836557	−	0.144896i
$251$	−12.1770	−	21.0912i	−0.768605	−	1.33126i	−0.938319	−	0.345770i	$-0.887618\pi$
$251$	−12.1770	−	21.0912i	−0.768605	−	1.33126i	0.169714	−	0.985493i	$-0.445716\pi$
$252$	11.5057	+	19.9285i	0.724792	+	1.25538i
$253$	−36.6635			−2.30501
$254$	28.0974			1.76299
$255$	−1.32043	−	2.28705i	−0.0826885	−	0.143221i
$256$	2.56379	−	4.44061i	0.160237	−	0.277538i
$257$	−0.363705	+	0.629955i	−0.0226873	+	0.0392955i	−0.877146	−	0.480224i	$-0.840556\pi$
$257$	−0.363705	+	0.629955i	−0.0226873	+	0.0392955i	0.854459	+	0.519519i	$0.173889\pi$
$258$	13.1126	+	22.7118i	0.816357	+	1.41397i
$259$	12.3705			0.768665
$260$	−23.4268			−1.45287
$261$	1.68289	−	2.91485i	0.104168	−	0.180425i
$262$	15.0445	+	26.0578i	0.929450	+	1.60985i
$263$	−8.11617			−0.500464			−0.250232	−	0.968186i	$-0.580507\pi$
$263$	−8.11617			−0.500464			−0.250232	+	0.968186i	$0.580507\pi$
$264$	16.8340	−	29.1573i	1.03606	−	1.79451i
$265$	−11.2874			−0.693379
$266$	6.59564	+	11.4240i	0.404405	+	0.700450i
$267$	5.07447			0.310553
$268$	30.6081	−	27.1475i	1.86969	−	1.65830i
$269$	8.67585			0.528976			0.264488	−	0.964389i	$-0.414797\pi$
$269$	8.67585			0.528976			0.264488	+	0.964389i	$0.414797\pi$
$270$	1.32271	+	2.29101i	0.0804977	+	0.139426i
$271$	−21.7510			−1.32128			−0.660639	−	0.750703i	$-0.729715\pi$
$271$	−21.7510			−1.32128			−0.660639	+	0.750703i	$0.729715\pi$
$272$	−14.5065	+	25.1260i	−0.879585	+	1.52349i
$273$	21.5782			1.30597
$274$	21.5276	+	37.2868i	1.30053	+	2.25258i
$275$	2.12237	−	3.67605i	0.127984	−	0.221674i
$276$	−43.1721			−2.59866
$277$	12.5690			0.755196			0.377598	−	0.925970i	$-0.376750\pi$
$277$	12.5690			0.755196			0.377598	+	0.925970i	$0.376750\pi$
$278$	−1.77310	−	3.07110i	−0.106343	−	0.184192i
$279$	−5.03551	+	8.72176i	−0.301468	+	0.522158i
$280$	18.2583	−	31.6243i	1.09114	−	1.88991i
$281$	7.46770	+	12.9344i	0.445486	+	0.771604i	0.998086	−	0.0618426i	$-0.0196977\pi$
$281$	7.46770	+	12.9344i	0.445486	+	0.771604i	−0.552600	+	0.833446i	$0.686364\pi$
$282$	16.2734			0.969069
$283$	15.8375			0.941444			0.470722	−	0.882281i	$-0.343993\pi$
$283$	15.8375			0.941444			0.470722	+	0.882281i	$0.343993\pi$
$284$	16.1558	+	27.9827i	0.958672	+	1.66047i
$285$	0.541550	+	0.937991i	0.0320786	+	0.0555618i
$286$	−26.3153	−	45.5795i	−1.55606	−	2.69517i
$287$	−7.01197	−	12.1451i	−0.413904	−	0.716902i
$288$	6.59987	−	11.4313i	0.388901	−	0.673596i
$289$	5.01293	−	8.68266i	0.294878	−	0.510745i
$290$	−8.90393			−0.522857
$291$	−2.59271	−	4.49071i	−0.151988	−	0.263250i
$292$	−36.3024			−2.12444
$293$	−20.3924			−1.19134			−0.595669	−	0.803230i	$-0.703113\pi$
$293$	−20.3924			−1.19134			−0.595669	+	0.803230i	$0.703113\pi$
$294$	−18.7768	+	32.5224i	−1.09508	+	1.89674i
$295$	−11.6436			−0.677916
$296$	−10.6561	−	18.4570i	−0.619376	−	1.07279i
$297$	−2.12237	+	3.67605i	−0.123152	+	0.213306i
$298$	−8.35910	−	14.4784i	−0.484230	−	0.838711i
$299$	−20.2416	+	35.0596i	−1.17060	+	2.02755i
$300$	2.49914	−	4.32863i	0.144288	−	0.249914i
$301$	−22.8201	+	39.5256i	−1.31533	+	2.27822i
$302$	−1.75762	+	3.04429i	−0.101140	+	0.175179i
$303$	1.73660	−	3.00788i	0.0997649	−	0.172798i
$304$	5.94957	−	10.3050i	0.341231	−	0.591030i
$305$	0.749226	+	1.29770i	0.0429005	+	0.0743059i
$306$	3.49310	−	6.05022i	0.199687	−	0.345868i
$307$	16.1828	+	28.0294i	0.923600	+	1.59972i	0.793797	+	0.608182i	$0.208101\pi$
$307$	16.1828	+	28.0294i	0.923600	+	1.59972i	0.129803	+	0.991540i	$0.458566\pi$
$308$	97.6774			5.56569
$309$	−5.76908	+	9.99234i	−0.328191	+	0.568444i
$310$	26.6421			1.51317
$311$	0.103810			0.00588650			0.00294325	−	0.999996i	$-0.499063\pi$
$311$	0.103810			0.00588650			0.00294325	+	0.999996i	$0.499063\pi$
$312$	−18.5879	−	32.1951i	−1.05233	−	1.82269i
$313$	−28.9638			−1.63713			−0.818564	−	0.574415i	$-0.805230\pi$
$313$	−28.9638			−1.63713			−0.818564	+	0.574415i	$0.805230\pi$
$314$	9.62968	−	16.6791i	0.543434	−	0.941256i
$315$	−2.30194	+	3.98707i	−0.129699	+	0.224646i
$316$	−21.2379	−	36.7851i	−1.19473	−	2.06933i
$317$	12.3956	+	21.4698i	0.696205	+	1.20586i	0.969773	+	0.244010i	$0.0784630\pi$
$317$	12.3956	+	21.4698i	0.696205	+	1.20586i	−0.273567	+	0.961853i	$0.588204\pi$
$318$	−14.9300	−	25.8595i	−0.837232	−	1.45013i
$319$	−7.14343	−	12.3728i	−0.399955	−	0.692742i
$320$	−12.9465			−0.723732
$321$	−2.77192			−0.154713
$322$	−52.5984	−	91.1031i	−2.93119	−	5.07697i
$323$	1.43016	−	2.47710i	0.0795760	−	0.137830i
$324$	−2.49914	+	4.32863i	−0.138841	+	0.240480i
$325$	−2.34349	−	4.05904i	−0.129993	−	0.225155i
$326$	9.05263			0.501379
$327$	−7.47378			−0.413301
$328$	−12.0805	+	20.9240i	−0.667031	+	1.15533i
$329$	14.1605	+	24.5266i	0.780692	+	1.35220i
$330$	11.2291			0.618143
$331$	15.6114	−	27.0397i	0.858079	−	1.48624i	−0.0156800	−	0.999877i	$-0.504991\pi$
$331$	15.6114	−	27.0397i	0.858079	−	1.48624i	0.873759	−	0.486359i	$-0.161675\pi$
$332$	1.00751			0.0552945
$333$	1.34349	+	2.32699i	0.0736227	+	0.127518i
$334$	3.78204			0.206944
$335$	7.76558	+	2.58761i	0.424279	+	0.141376i
$336$	50.5791			2.75931
$337$	−8.20226	−	14.2067i	−0.446806	−	0.773890i	0.551370	−	0.834261i	$-0.314105\pi$
$337$	−8.20226	−	14.2067i	−0.446806	−	0.773890i	−0.998176	+	0.0603705i	$0.980772\pi$
$338$	−23.7235			−1.29039
$339$	−10.2800	+	17.8055i	−0.558333	+	0.967060i
$340$	−13.1997			−0.715856
$341$	21.3744	+	37.0215i	1.15749	+	2.00483i
$342$	−1.43263	+	2.48139i	−0.0774677	+	0.134178i
$343$	−33.1280			−1.78874
$344$	78.6306			4.23948
$345$	−4.31870	−	7.48021i	−0.232511	−	0.402721i
$346$	−14.8442	+	25.7109i	−0.798030	+	1.38223i
$347$	14.9556	−	25.9038i	0.802857	−	1.39059i	−0.114871	−	0.993380i	$-0.536645\pi$
$347$	14.9556	−	25.9038i	0.802857	−	1.39059i	0.917728	−	0.397209i	$-0.130021\pi$
$348$	−8.41155	−	14.5692i	−0.450907	−	0.780993i
$349$	33.2509			1.77988			0.889939	−	0.456079i	$-0.150747\pi$
$349$	33.2509			1.77988			0.889939	+	0.456079i	$0.150747\pi$
$350$	12.1792			0.651006
$351$	2.34349	+	4.05904i	0.125086	+	0.216655i
$352$	−28.0147	−	48.5228i	−1.49319	−	2.58628i
$353$	−5.04716	−	8.74193i	−0.268633	−	0.465286i	0.699876	−	0.714264i	$-0.253239\pi$
$353$	−5.04716	−	8.74193i	−0.268633	−	0.465286i	−0.968509	+	0.248978i	$0.919905\pi$
$354$	−15.4011	−	26.6755i	−0.818560	−	1.41779i
$355$	−3.23228	+	5.59848i	−0.171552	+	0.297136i
$356$	12.6818	−	21.9655i	0.672134	−	1.16417i
$357$	12.1582			0.643479
$358$	23.0150	+	39.8631i	1.21638	+	2.10683i
$359$	−33.7346			−1.78044			−0.890222	−	0.455527i	$-0.849451\pi$
$359$	−33.7346			−1.78044			−0.890222	+	0.455527i	$0.849451\pi$
$360$	7.93171			0.418038
$361$	8.91345	−	15.4385i	0.469129	−	0.812555i
$362$	−57.9483			−3.04570
$363$	3.50888	+	6.07756i	0.184169	+	0.318989i
$364$	53.9270	−	93.4043i	2.82654	−	4.89572i
$365$	−3.63150	−	6.28994i	−0.190081	−	0.329230i
$366$	−1.98202	+	3.43296i	−0.103602	+	0.179444i
$367$	5.22513	−	9.05019i	0.272750	−	0.472416i	−0.696815	−	0.717251i	$-0.745400\pi$
$367$	5.22513	−	9.05019i	0.272750	−	0.472416i	0.969565	+	0.244834i	$0.0787336\pi$
$368$	−47.4461	+	82.1791i	−2.47330	+	4.28388i
$369$	1.52306	−	2.63801i	0.0792872	−	0.137330i
$370$	3.55409	−	6.15587i	0.184769	−	0.320029i
$371$	25.9829	−	45.0037i	1.34896	−	2.33647i
$372$	25.1689	+	43.5937i	1.30494	+	2.26023i
$373$	15.7028	−	27.1980i	0.813059	−	1.40826i	−0.0976542	−	0.995220i	$-0.531134\pi$
$373$	15.7028	−	27.1980i	0.813059	−	1.40826i	0.910713	−	0.413039i	$-0.135533\pi$
$374$	−14.8273	−	25.6816i	−0.766699	−	1.32796i
$375$	1.00000			0.0516398
$376$	24.3961	−	42.2553i	1.25813	−	2.17915i
$377$	−15.7753			−0.812471
$378$	−12.1792			−0.626431
$379$	4.04844	+	7.01211i	0.207955	+	0.360188i	0.951070	−	0.308975i	$-0.0999861\pi$
$379$	4.04844	+	7.01211i	0.207955	+	0.360188i	−0.743116	+	0.669163i	$0.766653\pi$
$380$	5.41363			0.277713
$381$	−5.31057	+	9.19817i	−0.272069	+	0.471237i
$382$	24.4577	−	42.3620i	1.25137	−	2.16743i
$383$	−14.7387	−	25.5282i	−0.753112	−	1.30443i	−0.946307	−	0.323268i	$-0.895218\pi$
$383$	−14.7387	−	25.5282i	−0.753112	−	1.30443i	0.193195	−	0.981160i	$-0.438115\pi$
$384$	−3.92479	−	6.79793i	−0.200286	−	0.346905i
$385$	9.77111	+	16.9241i	0.497982	+	0.862530i
$386$	−12.5539	−	21.7440i	−0.638978	−	1.10674i
$387$	−9.91345			−0.503929
$388$	−25.9182			−1.31580
$389$	11.9482	+	20.6949i	0.605799	+	1.04927i	0.991925	+	0.126828i	$0.0404797\pi$
$389$	11.9482	+	20.6949i	0.605799	+	1.04927i	−0.386126	+	0.922446i	$0.626187\pi$
$390$	6.19952	−	10.7379i	0.313925	−	0.543734i
$391$	−11.4051	+	19.7542i	−0.576780	+	0.999012i
$392$	56.2980	+	97.5109i	2.84348	+	4.92504i
$393$	−11.3739			−0.573740
$394$	−45.9136			−2.31309
$395$	4.24905	−	7.35957i	0.213793	−	0.370300i
$396$	10.6082	+	18.3739i	0.533081	+	0.923323i
$397$	−29.3372			−1.47239			−0.736196	−	0.676768i	$-0.763380\pi$
$397$	−29.3372			−1.47239			−0.736196	+	0.676768i	$0.763380\pi$
$398$	−7.04847	+	12.2083i	−0.353308	+	0.611947i
$399$	−4.98645			−0.249635
$400$	−5.49310	−	9.51432i	−0.274655	−	0.475716i
$401$	−16.1745			−0.807715			−0.403857	−	0.914822i	$-0.632331\pi$
$401$	−16.1745			−0.807715			−0.403857	+	0.914822i	$0.632331\pi$
$402$	4.34340	+	21.2137i	0.216629	+	1.05804i
$403$	47.2026			2.35133
$404$	−8.67999	−	15.0342i	−0.431846	−	0.747979i
$405$	−1.00000			−0.0496904
$406$	20.4963	−	35.5006i	1.01721	−	1.76187i
$407$	11.4055			0.565349
$408$	−10.4733	−	18.1402i	−0.518504	−	0.898074i
$409$	−9.52966	+	16.5059i	−0.471211	+	0.816162i	−0.999458	−	0.0329293i	$-0.989516\pi$
$409$	−9.52966	+	16.5059i	−0.471211	+	0.816162i	0.528246	+	0.849091i	$0.322850\pi$
$410$	−8.05827			−0.397970
$411$	−16.2753			−0.802802
$412$	28.8354	+	49.9444i	1.42062	+	2.46059i
$413$	26.8028	−	46.4238i	1.31888	−	2.28437i
$414$	11.4248	−	19.7883i	0.561498	−	0.972544i
$415$	0.100786	+	0.174567i	0.00494740	+	0.00856915i
$416$	−61.8668			−3.03327
$417$	1.34050			0.0656447
$418$	6.08113	+	10.5328i	0.297438	+	0.515177i
$419$	−0.728747	−	1.26223i	−0.0356016	−	0.0616638i	0.847676	−	0.530515i	$-0.178001\pi$
$419$	−0.728747	−	1.26223i	−0.0356016	−	0.0616638i	−0.883277	+	0.468851i	$0.844668\pi$
$420$	11.5057	+	19.9285i	0.561421	+	0.972410i
$421$	18.8088	+	32.5779i	0.916687	+	1.58775i	0.804412	+	0.594071i	$0.202480\pi$
$421$	18.8088	+	32.5779i	0.916687	+	1.58775i	0.112275	+	0.993677i	$0.464186\pi$
$422$	−9.31024	+	16.1258i	−0.453215	+	0.784992i
$423$	−3.07577	+	5.32739i	−0.149549	+	0.259027i
$424$	−89.5283			−4.34788
$425$	−1.32043	−	2.28705i	−0.0640502	−	0.110938i
$426$	−17.1015			−0.828572
$427$	−6.89868			−0.333851
$428$	−6.92740	+	11.9986i	−0.334849	+	0.579975i
$429$	19.8950			0.960538
$430$	13.1126	+	22.7118i	0.632348	+	1.09526i
$431$	−8.66045	+	15.0003i	−0.417159	+	0.722541i	−0.995652	−	0.0931460i	$-0.970308\pi$
$431$	−8.66045	+	15.0003i	−0.417159	+	0.722541i	0.578493	+	0.815687i	$0.303641\pi$
$432$	5.49310	+	9.51432i	0.264287	+	0.457758i
$433$	−0.318934	+	0.552410i	−0.0153270	+	0.0265471i	−0.873587	−	0.486668i	$-0.838212\pi$
$433$	−0.318934	+	0.552410i	−0.0153270	+	0.0265471i	0.858260	+	0.513215i	$0.171546\pi$
$434$	−61.3285	+	106.224i	−2.94386	+	5.09892i
$435$	1.68289	−	2.91485i	0.0806885	−	0.139757i
$436$	−18.6780	+	32.3513i	−0.894514	+	1.54934i
$437$	4.67758	−	8.10181i	0.223759	−	0.387562i
$438$	9.60685	−	16.6396i	0.459033	−	0.795069i
$439$	5.84249	+	10.1195i	0.278847	+	0.482977i	0.971098	−	0.238679i	$-0.0767144\pi$
$439$	5.84249	+	10.1195i	0.278847	+	0.482977i	−0.692251	+	0.721656i	$0.743381\pi$
$440$	16.8340	−	29.1573i	0.802529	−	1.39002i
$441$	−7.09783	−	12.2938i	−0.337992	−	0.585420i
$442$	−32.7441			−1.55748
$443$	0.444543	−	0.769972i	0.0211209	−	0.0365825i	−0.855272	−	0.518180i	$-0.826610\pi$
$443$	0.444543	−	0.769972i	0.0211209	−	0.0365825i	0.876393	+	0.481597i	$0.159943\pi$
$444$	13.4302			0.637371
$445$	5.07447			0.240553
$446$	3.57886	+	6.19877i	0.169464	+	0.293520i
$447$	6.31967			0.298910
$448$	29.8021	−	51.6187i	1.40802	−	2.43875i
$449$	−6.16822	+	10.6837i	−0.291096	+	0.504194i	−0.974069	−	0.226250i	$-0.927353\pi$
$449$	−6.16822	+	10.6837i	−0.291096	+	0.504194i	0.682973	+	0.730444i	$0.260687\pi$
$450$	1.32271	+	2.29101i	0.0623533	+	0.107999i
$451$	−6.46498	−	11.1977i	−0.304424	−	0.527278i
$452$	51.3822	+	88.9966i	2.41682	+	4.18605i
$453$	−0.664400	−	1.15077i	−0.0312162	−	0.0540681i
$454$	−13.8784			−0.651347
$455$	21.5782			1.01160
$456$	4.29541	+	7.43987i	0.201151	+	0.348404i
$457$	8.19106	−	14.1873i	0.383161	−	0.663655i	−0.608351	−	0.793668i	$-0.708169\pi$
$457$	8.19106	−	14.1873i	0.383161	−	0.663655i	0.991512	+	0.130013i	$0.0415019\pi$
$458$	−22.5912	+	39.1290i	−1.05562	+	1.82838i
$459$	1.32043	+	2.28705i	0.0616323	+	0.106750i
$460$	−43.1721			−2.01291
$461$	6.59429			0.307127			0.153563	−	0.988139i	$-0.450925\pi$
$461$	6.59429			0.307127			0.153563	+	0.988139i	$0.450925\pi$
$462$	−25.8487	+	44.7713i	−1.20259	+	2.08295i
$463$	3.04048	+	5.26627i	0.141303	+	0.244744i	0.927988	−	0.372611i	$-0.121537\pi$
$463$	3.04048	+	5.26627i	0.141303	+	0.244744i	−0.786684	+	0.617355i	$0.788204\pi$
$464$	−36.9771			−1.71662
$465$	−5.03551	+	8.72176i	−0.233516	+	0.404462i
$466$	35.1801			1.62969
$467$	8.92645	+	15.4611i	0.413067	+	0.715453i	0.995223	−	0.0976240i	$-0.0311242\pi$
$467$	8.92645	+	15.4611i	0.413067	+	0.715453i	−0.582157	+	0.813077i	$0.697791\pi$
$468$	23.4268			1.08290
$469$	−28.1929	+	25.0054i	−1.30183	+	1.15464i
$470$	16.2734			0.750638
$471$	3.64013	+	6.30488i	0.167728	+	0.290514i
$472$	−92.3535			−4.25091
$473$	−21.0400	+	36.4423i	−0.967419	+	1.67562i
$474$	22.4811			1.03259
$475$	0.541550	+	0.937991i	0.0248480	+	0.0430380i
$476$	30.3850	−	52.6283i	1.39269	−	2.41221i
$477$	11.2874			0.516814
$478$	−8.13584			−0.372125
$479$	−16.6753	−	28.8824i	−0.761912	−	1.31967i	−0.941864	−	0.335995i	$-0.890927\pi$
$479$	−16.6753	−	28.8824i	−0.761912	−	1.31967i	0.179952	−	0.983675i	$-0.442406\pi$
$480$	6.59987	−	11.4313i	0.301241	−	0.521765i
$481$	6.29689	−	10.9065i	0.287114	−	0.497295i
$482$	14.0426	+	24.3226i	0.639625	+	1.10786i
$483$	39.7655			1.80939
$484$	35.0767			1.59440
$485$	−2.59271	−	4.49071i	−0.117729	−	0.203913i
$486$	−1.32271	−	2.29101i	−0.0599995	−	0.103922i
$487$	3.35557	+	5.81202i	0.152055	+	0.263368i	0.931983	−	0.362502i	$-0.118077\pi$
$487$	3.35557	+	5.81202i	0.152055	+	0.263368i	−0.779927	+	0.625870i	$0.784744\pi$
$488$	5.94264	+	10.2930i	0.269011	+	0.465940i
$489$	−1.71100	+	2.96353i	−0.0773739	+	0.134016i
$490$	−18.7768	+	32.5224i	−0.848249	+	1.46921i
$491$	15.7063			0.708817			0.354409	−	0.935091i	$-0.384682\pi$
$491$	15.7063			0.708817			0.354409	+	0.935091i	$0.384682\pi$
$492$	−7.61266	−	13.1855i	−0.343205	−	0.594449i
$493$	−8.88856			−0.400320
$494$	13.4294			0.604217
$495$	−2.12237	+	3.67605i	−0.0953933	+	0.165226i
$496$	110.642			4.96798
$497$	−14.8810	−	25.7747i	−0.667505	−	1.15615i
$498$	−0.266622	+	0.461804i	−0.0119476	+	0.0206939i
$499$	−6.33929	−	10.9800i	−0.283786	−	0.491531i	0.688528	−	0.725210i	$-0.258257\pi$
$499$	−6.33929	−	10.9800i	−0.283786	−	0.491531i	−0.972314	+	0.233678i	$0.924924\pi$
$500$	2.49914	−	4.32863i	0.111765	−	0.193582i
$501$	−0.714827	+	1.23812i	−0.0319361	+	0.0553150i
$502$	32.2133	−	55.7951i	1.43775	−	2.49026i
$503$	−0.624139	+	1.08104i	−0.0278290	+	0.0482012i	−0.879604	−	0.475706i	$-0.842193\pi$
$503$	−0.624139	+	1.08104i	−0.0278290	+	0.0482012i	0.851776	+	0.523907i	$0.175526\pi$
$504$	−18.2583	+	31.6243i	−0.813289	+	1.40866i
$505$	1.73660	−	3.00788i	0.0772776	−	0.133849i
$506$	−48.4952	−	83.9962i	−2.15588	−	3.73409i
$507$	4.48387	−	7.76628i	0.199135	−	0.344913i
$508$	26.5437	+	45.9750i	1.17768	+	2.03981i
$509$	11.9977			0.531788			0.265894	−	0.964002i	$-0.414333\pi$
$509$	11.9977			0.531788			0.265894	+	0.964002i	$0.414333\pi$
$510$	3.49310	−	6.05022i	0.154677	−	0.267908i
$511$	33.4379			1.47921
$512$	29.2638			1.29329
$513$	−0.541550	−	0.937991i	−0.0239100	−	0.0414133i
$514$	−1.92431			−0.0848776
$515$	−5.76908	+	9.99234i	−0.254216	+	0.440315i
$516$	−24.7751	+	42.9117i	−1.09066	+	1.88908i
$517$	13.0558	+	22.6134i	0.574195	+	0.994534i
$518$	16.3626	+	28.3409i	0.718932	+	1.24523i
$519$	−5.61128	−	9.71902i	−0.246308	−	0.426618i
$520$	−18.5879	−	32.1951i	−0.815131	−	1.41185i
$521$	−6.03500			−0.264398			−0.132199	−	0.991223i	$-0.542204\pi$
$521$	−6.03500			−0.264398			−0.132199	+	0.991223i	$0.542204\pi$
$522$	8.90393			0.389714
$523$	−4.97169	−	8.61122i	−0.217397	−	0.376542i	0.736614	−	0.676313i	$-0.236423\pi$
$523$	−4.97169	−	8.61122i	−0.217397	−	0.376542i	−0.954011	+	0.299770i	$0.903090\pi$
$524$	−28.4251	+	49.2336i	−1.24175	+	2.15078i
$525$	−2.30194	+	3.98707i	−0.100465	+	0.174010i
$526$	−10.7354	−	18.5942i	−0.468084	−	0.810745i
$527$	26.5961			1.15855
$528$	46.6335			2.02946
$529$	−25.8024	+	44.6910i	−1.12184	+	1.94309i
$530$	−14.9300	−	25.8595i	−0.648517	−	1.12326i
$531$	11.6436			0.505288
$532$	−12.4618	+	21.5845i	−0.540289	+	0.935808i
$533$	−14.2771			−0.618409
$534$	6.71207	+	11.6256i	0.290459	+	0.503091i
$535$	−2.77192			−0.119840
$536$	61.5943	+	20.5242i	2.66047	+	0.886510i
$537$	−17.3998			−0.750858
$538$	11.4757	+	19.8764i	0.494751	+	0.856934i
$539$	−60.2568			−2.59545
$540$	−2.49914	+	4.32863i	−0.107546	+	0.186275i
$541$	−17.1364			−0.736750			−0.368375	−	0.929677i	$-0.620086\pi$
$541$	−17.1364			−0.736750			−0.368375	+	0.929677i	$0.620086\pi$
$542$	−28.7703	−	49.8316i	−1.23579	−	2.14045i
$543$	10.9526	−	18.9704i	0.470019	−	0.814097i
$544$	−34.8586			−1.49455
$545$	−7.47378			−0.320142
$546$	28.5418	+	49.4359i	1.22148	+	2.11566i
$547$	−5.21539	+	9.03331i	−0.222994	+	0.386237i	−0.955716	−	0.294292i	$-0.904916\pi$
$547$	−5.21539	+	9.03331i	−0.222994	+	0.386237i	0.732722	+	0.680528i	$0.238250\pi$
$548$	−40.6742	+	70.4499i	−1.73752	+	3.00947i
$549$	−0.749226	−	1.29770i	−0.0319762	−	0.0553844i
$550$	11.2291			0.478811
$551$	3.64548			0.155303
$552$	−34.2547	−	59.3309i	−1.45798	−	2.52529i
$553$	19.5621	+	33.8825i	0.831865	+	1.44083i
$554$	16.6251	+	28.7956i	0.706334	+	1.22341i
$555$	1.34349	+	2.32699i	0.0570279	+	0.0987752i
$556$	3.35010	−	5.80254i	0.142076	−	0.246083i
$557$	12.0020	−	20.7880i	0.508539	−	0.880815i	−0.491412	−	0.870927i	$-0.663519\pi$
$557$	12.0020	−	20.7880i	0.508539	−	0.880815i	0.999951	−	0.00988823i	$-0.00314757\pi$
$558$	−26.6421			−1.12785
$559$	23.2320	+	40.2391i	0.982611	+	1.70193i
$560$	50.5791			2.13736
$561$	11.2097			0.473276
$562$	−19.7552	+	34.2171i	−0.833325	+	1.44336i
$563$	14.8311			0.625058			0.312529	−	0.949908i	$-0.398824\pi$
$563$	14.8311			0.625058			0.312529	+	0.949908i	$0.398824\pi$
$564$	15.3735	+	26.6278i	0.647343	+	1.12123i
$565$	−10.2800	+	17.8055i	−0.432483	+	0.749082i
$566$	20.9485	+	36.2839i	0.880532	+	1.52513i
$567$	2.30194	−	3.98707i	0.0966723	−	0.167441i
$568$	−25.6375	+	44.4055i	−1.07573	+	1.86321i
$569$	17.4080	−	30.1516i	0.729783	−	1.26402i	−0.227192	−	0.973850i	$-0.572954\pi$
$569$	17.4080	−	30.1516i	0.729783	−	1.26402i	0.956975	−	0.290171i	$-0.0937122\pi$
$570$	−1.43263	+	2.48139i	−0.0600062	+	0.103934i
$571$	8.13726	−	14.0941i	0.340534	−	0.589822i	−0.643998	−	0.765027i	$-0.722726\pi$
$571$	8.13726	−	14.0941i	0.340534	−	0.589822i	0.984532	+	0.175205i	$0.0560589\pi$
$572$	49.7202	−	86.1180i	2.07891	−	3.60077i
$573$	9.24529	+	16.0133i	0.386227	+	0.668966i
$574$	18.5496	−	32.1289i	0.774247	−	1.34104i
$575$	−4.31870	−	7.48021i	−0.180102	−	0.311946i
$576$	12.9465			0.539438
$577$	4.20342	−	7.28053i	0.174991	−	0.303092i	−0.765167	−	0.643831i	$-0.777344\pi$
$577$	4.20342	−	7.28053i	0.174991	−	0.303092i	0.940158	+	0.340739i	$0.110677\pi$
$578$	26.5227			1.10320
$579$	9.49104			0.394434
$580$	−8.41155	−	14.5692i	−0.349271	−	0.604955i
$581$	−0.928015			−0.0385005
$582$	6.85883	−	11.8798i	0.284308	−	0.492435i
$583$	23.9560	−	41.4930i	0.992156	−	1.71846i
$584$	−28.8040	−	49.8899i	−1.19192	−	2.06446i
$585$	2.34349	+	4.05904i	0.0968913	+	0.167821i
$586$	−26.9733	−	46.7191i	−1.11426	−	1.92995i
$587$	2.01008	+	3.48156i	0.0829648	+	0.143699i	0.904522	−	0.426427i	$-0.140228\pi$
$587$	2.01008	+	3.48156i	0.0829648	+	0.143699i	−0.821557	+	0.570126i	$0.806894\pi$
$588$	−70.9538			−2.92609
$589$	−10.9079			−0.449453
$590$	−15.4011	−	26.6755i	−0.634054	−	1.09821i
$591$	8.67792	−	15.0306i	0.356962	−	0.618276i
$592$	14.7598	−	25.5647i	0.606624	−	1.05070i
$593$	18.8886	+	32.7160i	0.775661	+	1.34348i	0.934422	+	0.356167i	$0.115917\pi$
$593$	18.8886	+	32.7160i	0.775661	+	1.34348i	−0.158761	+	0.987317i	$0.550750\pi$
$594$	−11.2291			−0.460737
$595$	12.1582			0.498437
$596$	15.7937	−	27.3555i	0.646936	−	1.12053i
$597$	−2.66440	−	4.61488i	−0.109047	−	0.188874i
$598$	−107.096			−4.37946
$599$	7.41451	−	12.8423i	0.302949	−	0.524723i	−0.673854	−	0.738865i	$-0.735362\pi$
$599$	7.41451	−	12.8423i	0.302949	−	0.524723i	0.976803	+	0.214142i	$0.0686956\pi$
$600$	7.93171			0.323811
$601$	−9.98129	−	17.2881i	−0.407145	−	0.705196i	0.587423	−	0.809280i	$-0.300142\pi$
$601$	−9.98129	−	17.2881i	−0.407145	−	0.705196i	−0.994569	+	0.104084i	$0.966809\pi$
$602$	−120.738			−4.92091
$603$	−7.76558	−	2.58761i	−0.316239	−	0.105376i
$604$	−6.64171			−0.270247
$605$	3.50888	+	6.07756i	0.142656	+	0.247088i
$606$	9.18808			0.373240
$607$	−14.5374	+	25.1796i	−0.590056	+	1.02201i	0.404168	+	0.914685i	$0.367561\pi$
$607$	−14.5374	+	25.1796i	−0.590056	+	1.02201i	−0.994224	+	0.107322i	$0.965772\pi$
$608$	14.2966			0.579804
$609$	7.74782	+	13.4196i	0.313958	+	0.543791i
$610$	−1.98202	+	3.43296i	−0.0802497	+	0.138996i
$611$	28.8321			1.16642
$612$	13.1997			0.533568
$613$	−12.4702	−	21.5990i	−0.503667	−	0.872377i	−0.999991	−	0.00423952i	$-0.998651\pi$
$613$	−12.4702	−	21.5990i	−0.503667	−	0.872377i	0.496324	−	0.868137i	$-0.334683\pi$
$614$	−42.8103	+	74.1497i	−1.72768	+	2.99244i
$615$	1.52306	−	2.63801i	0.0614156	−	0.106375i
$616$	77.5016	+	134.237i	3.12263	+	5.40855i
$617$	−15.9787			−0.643280			−0.321640	−	0.946862i	$-0.604234\pi$
$617$	−15.9787			−0.643280			−0.321640	+	0.946862i	$0.604234\pi$
$618$	−30.5233			−1.22783
$619$	−8.31197	−	14.3968i	−0.334086	−	0.578654i	0.649223	−	0.760598i	$-0.275094\pi$
$619$	−8.31197	−	14.3968i	−0.334086	−	0.578654i	−0.983309	+	0.181944i	$0.941761\pi$
$620$	25.1689	+	43.5937i	1.01081	+	1.75077i
$621$	4.31870	+	7.48021i	0.173304	+	0.300171i
$622$	0.137310	+	0.237828i	0.00550564	+	0.00953605i
$623$	−11.6811	+	20.2323i	−0.467994	+	0.810589i
$624$	25.7460	−	44.5934i	1.03066	−	1.78516i
$625$	1.00000			0.0400000
$626$	−38.3107	−	66.3561i	−1.53120	−	2.65212i
$627$	−4.59747			−0.183605
$628$	36.3887			1.45207
$629$	3.54796	−	6.14525i	0.141466	−	0.245027i
$630$	−12.1792			−0.485231
$631$	−6.30138	−	10.9143i	−0.250854	−	0.434492i	0.712907	−	0.701258i	$-0.247378\pi$
$631$	−6.30138	−	10.9143i	−0.250854	−	0.434492i	−0.963761	+	0.266767i	$0.914045\pi$
$632$	33.7022	−	58.3739i	1.34060	−	2.32199i
$633$	−3.51937	−	6.09574i	−0.139883	−	0.242284i
$634$	−32.7916	+	56.7967i	−1.30232	+	2.25568i
$635$	−5.31057	+	9.19817i	−0.210743	+	0.365018i
$636$	28.2088	−	48.8590i	1.11855	−	1.93738i
$637$	−33.2674	+	57.6208i	−1.31810	+	2.28302i
$638$	18.8974	−	32.7313i	0.748155	−	1.29584i
$639$	3.23228	−	5.59848i	0.127867	−	0.221472i
$640$	−3.92479	−	6.79793i	−0.155141	−	0.268712i
$641$	−19.7908	+	34.2786i	−0.781688	+	1.35392i	0.149269	+	0.988797i	$0.452308\pi$
$641$	−19.7908	+	34.2786i	−0.781688	+	1.35392i	−0.930958	+	0.365127i	$0.881026\pi$
$642$	−3.66645	−	6.35048i	−0.144703	−	0.250633i
$643$	25.7420			1.01517			0.507583	−	0.861603i	$-0.330539\pi$
$643$	25.7420			1.01517			0.507583	+	0.861603i	$0.330539\pi$
$644$	99.3795	−	172.130i	3.91610	−	6.78289i
$645$	−9.91345			−0.390342
$646$	7.56674			0.297709
$647$	2.01542	+	3.49082i	0.0792345	+	0.137238i	0.902920	−	0.429809i	$-0.141419\pi$
$647$	2.01542	+	3.49082i	0.0792345	+	0.137238i	−0.823685	+	0.567047i	$0.808086\pi$
$648$	−7.93171			−0.311587
$649$	24.7120	−	42.8024i	0.970029	−	1.68014i
$650$	6.19952	−	10.7379i	0.243165	−	0.421174i
$651$	−23.1829	−	40.1539i	−0.908608	−	1.57375i
$652$	8.55203	+	14.8125i	0.334923	+	0.580104i
$653$	10.7601	+	18.6370i	0.421073	+	0.729320i	0.996045	−	0.0888531i	$-0.0283202\pi$
$653$	10.7601	+	18.6370i	0.421073	+	0.729320i	−0.574971	+	0.818174i	$0.694987\pi$
$654$	−9.88567	−	17.1225i	−0.386560	−	0.669542i
$655$	−11.3739			−0.444417
$656$	−33.4652			−1.30660
$657$	3.63150	+	6.28994i	0.141678	+	0.245394i
$658$	−37.4604	+	64.8834i	−1.46036	+	2.52942i
$659$	−3.02557	+	5.24044i	−0.117860	+	0.204139i	−0.918919	−	0.394446i	$-0.870937\pi$
$659$	−3.02557	+	5.24044i	−0.117860	+	0.204139i	0.801060	+	0.598584i	$0.204270\pi$
$660$	10.6082	+	18.3739i	0.412922	+	0.715203i
$661$	19.4900			0.758072			0.379036	−	0.925382i	$-0.376256\pi$
$661$	19.4900			0.758072			0.379036	+	0.925382i	$0.376256\pi$
$662$	82.5975			3.21024
$663$	6.18882	−	10.7193i	0.240354	−	0.416305i
$664$	0.799407	+	1.38461i	0.0310230	+	0.0537334i
$665$	−4.98645			−0.193366
$666$	−3.55409	+	6.15587i	−0.137718	+	0.238535i
$667$	−29.0716			−1.12566
$668$	3.57290	+	6.18845i	0.138240	+	0.239438i
$669$	−2.70570			−0.104608
$670$	4.34340	+	21.2137i	0.167800	+	0.819555i
$671$	−6.36053			−0.245545
$672$	30.3850	+	52.6283i	1.17213	+	2.03018i
$673$	−10.2713			−0.395930			−0.197965	−	0.980209i	$-0.563433\pi$
$673$	−10.2713			−0.395930			−0.197965	+	0.980209i	$0.563433\pi$
$674$	21.6985	−	37.5829i	0.835794	−	1.44764i
$675$	−1.00000			−0.0384900
$676$	−22.4116	−	38.8180i	−0.861984	−	1.49300i
$677$	−7.44707	+	12.8987i	−0.286214	+	0.495737i	−0.972903	−	0.231214i	$-0.925730\pi$
$677$	−7.44707	+	12.8987i	−0.286214	+	0.495737i	0.686689	+	0.726952i	$0.259064\pi$
$678$	−54.3899			−2.08883
$679$	23.8731			0.916164
$680$	−10.4733	−	18.1402i	−0.401631	−	0.695645i
$681$	2.62310	−	4.54334i	0.100517	−	0.174101i
$682$	−56.5444	+	97.9377i	−2.16520	+	3.75023i
$683$	4.74035	+	8.21052i	0.181384	+	0.314167i	0.942352	−	0.334623i	$-0.108609\pi$
$683$	4.74035	+	8.21052i	0.181384	+	0.314167i	−0.760968	+	0.648790i	$0.775276\pi$
$684$	−5.41363			−0.206995
$685$	−16.2753			−0.621848
$686$	−43.8188	−	75.8963i	−1.67301	−	2.89774i
$687$	−8.53971	−	14.7912i	−0.325810	−	0.564320i
$688$	54.4555	+	94.3197i	2.07610	+	3.59591i
$689$	−26.4519	−	45.8160i	−1.00774	−	1.74545i
$690$	11.4248	−	19.7883i	0.434935	−	0.753329i
$691$	−16.6911	+	28.9098i	−0.634959	+	1.09978i	0.351564	+	0.936164i	$0.385650\pi$
$691$	−16.6911	+	28.9098i	−0.634959	+	1.09978i	−0.986524	+	0.163618i	$0.947683\pi$
$692$	−56.0934			−2.13235
$693$	−9.77111	−	16.9241i	−0.371174	−	0.642892i
$694$	79.1277			3.00365
$695$	1.34050			0.0508482
$696$	13.3482	−	23.1198i	0.505962	−	0.876353i
$697$	−8.04436			−0.304702
$698$	43.9814	+	76.1779i	1.66472	+	2.88338i
$699$	−6.64923	+	11.5168i	−0.251497	+	0.435605i
$700$	11.5057	+	19.9285i	0.434875	+	0.753226i
$701$	4.65316	−	8.05951i	0.175748	−	0.304404i	−0.764672	−	0.644419i	$-0.777099\pi$
$701$	4.65316	−	8.05951i	0.175748	−	0.304404i	0.940420	+	0.340016i	$0.110432\pi$
$702$	−6.19952	+	10.7379i	−0.233986	+	0.405275i
$703$	−1.45513	+	2.52036i	−0.0548813	+	0.0950571i
$704$	27.4773	−	47.5920i	1.03559	−	1.79369i
$705$	−3.07577	+	5.32739i	−0.115840	+	0.200641i
$706$	13.3519	−	23.1261i	0.502504	−	0.870363i
$707$	7.99508	+	13.8479i	0.300686	+	0.520803i
$708$	29.0989	−	50.4008i	1.09360	−	1.89418i
$709$	−1.13932	−	1.97336i	−0.0427881	−	0.0741112i	0.843838	−	0.536598i	$-0.180291\pi$
$709$	−1.13932	−	1.97336i	−0.0427881	−	0.0741112i	−0.886626	+	0.462486i	$0.846957\pi$
$710$	−17.1015			−0.641809
$711$	−4.24905	+	7.35957i	−0.159352	+	0.276005i
$712$	40.2492			1.50840
$713$	86.9875			3.25771
$714$	16.0818	+	27.8545i	0.601845	+	1.04243i
$715$	19.8950			0.744029
$716$	−43.4845	+	75.3174i	−1.62509	+	2.81474i
$717$	1.53772	−	2.66341i	0.0574272	−	0.0994668i
$718$	−44.6212	−	77.2861i	−1.66525	−	2.88429i
$719$	−6.28235	−	10.8813i	−0.234292	−	0.405806i	0.724775	−	0.688986i	$-0.241944\pi$
$719$	−6.28235	−	10.8813i	−0.234292	−	0.405806i	−0.959067	+	0.283180i	$0.908611\pi$
$720$	5.49310	+	9.51432i	0.204716	+	0.354578i
$721$	−26.5601	−	46.0035i	−0.989151	−	1.71326i
$722$	47.1597			1.75510
$723$	−10.6166			−0.394834
$724$	−54.7439	−	94.8192i	−2.03454	−	3.52393i
$725$	1.68289	−	2.91485i	0.0625010	−	0.108255i
$726$	−9.28248	+	16.0777i	−0.344505	+	0.596701i
$727$	16.2208	+	28.0953i	0.601596	+	1.04200i	0.992579	+	0.121597i	$0.0388017\pi$
$727$	16.2208	+	28.0953i	0.601596	+	1.04200i	−0.390983	+	0.920398i	$0.627865\pi$
$728$	171.152			6.34333
$729$	1.00000			0.0370370
$730$	9.60685	−	16.6396i	0.355566	−	0.615858i
$731$	13.0900	+	22.6726i	0.484151	+	0.838575i
$732$	−7.48967			−0.276826
$733$	23.3361	−	40.4193i	0.861939	−	1.49292i	−0.00811531	−	0.999967i	$-0.502583\pi$
$733$	23.3361	−	40.4193i	0.861939	−	1.49292i	0.870055	−	0.492955i	$-0.164083\pi$
$734$	27.6454			1.02041
$735$	−7.09783	−	12.2938i	−0.261808	−	0.453464i
$736$	−114.011			−4.20252
$737$	−25.9936	+	23.0548i	−0.957487	+	0.849234i
$738$	8.05827			0.296629
$739$	7.56530	+	13.1035i	0.278294	+	0.482020i	0.970961	−	0.239238i	$-0.0768976\pi$
$739$	7.56530	+	13.1035i	0.278294	+	0.482020i	−0.692667	+	0.721258i	$0.743564\pi$
$740$	13.4302			0.493705
$741$	−2.53823	+	4.39634i	−0.0932442	+	0.161504i
$742$	137.472			5.04674
$743$	−18.7176	−	32.4198i	−0.686680	−	1.18937i	−0.972906	−	0.231203i	$-0.925734\pi$
$743$	−18.7176	−	32.4198i	−0.686680	−	1.18937i	0.286225	−	0.958162i	$-0.407599\pi$
$744$	−39.9402	+	69.1784i	−1.46428	+	2.53620i
$745$	6.31967			0.231535
$746$	83.0810			3.04181
$747$	−0.100786	−	0.174567i	−0.00368758	−	0.00638707i
$748$	28.0147	−	48.5228i	1.02432	−	1.77417i
$749$	6.38078	−	11.0518i	0.233149	−	0.403825i
$750$	1.32271	+	2.29101i	0.0482986	+	0.0836557i
$751$	−1.54468			−0.0563660			−0.0281830	−	0.999603i	$-0.508972\pi$
$751$	−1.54468			−0.0563660			−0.0281830	+	0.999603i	$0.508972\pi$
$752$	67.5820			2.46446
$753$	12.1770	+	21.0912i	0.443754	+	0.768605i
$754$	−20.8662	−	36.1414i	−0.759904	−	1.31619i
$755$	−0.664400	−	1.15077i	−0.0241800	−	0.0418810i
$756$	−11.5057	−	19.9285i	−0.418459	−	0.724792i
$757$	4.41876	−	7.65351i	0.160602	−	0.278172i	−0.774482	−	0.632595i	$-0.781990\pi$
$757$	4.41876	−	7.65351i	0.160602	−	0.278172i	0.935085	+	0.354424i	$0.115323\pi$
$758$	−10.7099	+	18.5500i	−0.388999	+	0.673767i
$759$	36.6635			1.33080
$760$	4.29541	+	7.43987i	0.155811	+	0.269873i
$761$	−21.1413			−0.766371			−0.383185	−	0.923671i	$-0.625173\pi$
$761$	−21.1413			−0.766371			−0.383185	+	0.923671i	$0.625173\pi$
$762$	−28.0974			−1.01786
$763$	17.2042	−	29.7985i	0.622833	−	1.07878i
$764$	92.4210			3.34367
$765$	1.32043	+	2.28705i	0.0477402	+	0.0826885i
$766$	38.9901	−	67.5329i	1.40877	−	2.44006i
$767$	−27.2866	−	47.2618i	−0.985262	−	1.70652i
$768$	−2.56379	+	4.44061i	−0.0925127	+	0.160237i
$769$	2.11431	−	3.66208i	0.0762438	−	0.132058i	−0.825383	−	0.564574i	$-0.809041\pi$
$769$	2.11431	−	3.66208i	0.0762438	−	0.132058i	0.901626	+	0.432516i	$0.142374\pi$
$770$	−25.8487	+	44.7713i	−0.931524	+	1.61345i
$771$	0.363705	−	0.629955i	0.0130985	−	0.0226873i
$772$	23.7194	−	41.0832i	0.853680	−	1.47862i
$773$	6.04389	−	10.4683i	0.217384	−	0.376519i	−0.736624	−	0.676303i	$-0.763581\pi$
$773$	6.04389	−	10.4683i	0.217384	−	0.376519i	0.954007	+	0.299783i	$0.0969144\pi$
$774$	−13.1126	−	22.7118i	−0.471324	−	0.816357i
$775$	−5.03551	+	8.72176i	−0.180881	+	0.313295i
$776$	−20.5646	−	35.6190i	−0.738228	−	1.27865i
$777$	−12.3705			−0.443789
$778$	−31.6081	+	54.7469i	−1.13321	+	1.96277i
$779$	3.29925			0.118208
$780$	23.4268			0.838813
$781$	−13.7202	−	23.7640i	−0.490947	−	0.850345i
$782$	−60.3426			−2.15785
$783$	−1.68289	+	2.91485i	−0.0601416	+	0.104168i
$784$	−77.9782	+	135.062i	−2.78493	+	4.82365i
$785$	3.64013	+	6.30488i	0.129922	+	0.225031i
$786$	−15.0445	−	26.0578i	−0.536618	−	0.929450i
$787$	−18.7396	−	32.4579i	−0.667994	−	1.15700i	−0.978464	−	0.206416i	$-0.933820\pi$
$787$	−18.7396	−	32.4579i	−0.667994	−	1.15700i	0.310470	−	0.950583i	$-0.399513\pi$
$788$	−43.3746	−	75.1270i	−1.54516	−	2.67629i
$789$	8.11617			0.288943
$790$	22.4811			0.799841
$791$	−47.3278	−	81.9742i	−1.68278	−	2.91467i
$792$	−16.8340	+	29.1573i	−0.598170	+	1.03606i
$793$	−3.51160	+	6.08227i	−0.124701	+	0.215988i
$794$	−38.8047	−	67.2117i	−1.37713	−	2.38525i
$795$	11.2874			0.400323
$796$	−26.6348			−0.944046
$797$	18.5310	−	32.0967i	0.656402	−	1.13692i	−0.325138	−	0.945667i	$-0.605411\pi$
$797$	18.5310	−	32.0967i	0.656402	−	1.13692i	0.981540	−	0.191256i	$-0.0612560\pi$
$798$	−6.59564	−	11.4240i	−0.233483	−	0.404405i
$799$	16.2453			0.574719
$800$	6.59987	−	11.4313i	0.233340	−	0.404158i
$801$	−5.07447			−0.179298
$802$	−21.3942	−	37.0558i	−0.755455	−	1.30849i
$803$	30.8295			1.08795
$804$	−30.6081	+	27.1475i	−1.07946	+	0.957420i
$805$	39.7655			1.40155
$806$	62.4355	+	108.141i	2.19920	+	3.80912i
$807$	−8.67585			−0.305404
$808$	13.7742	−	23.8576i	0.484574	−	0.839307i
$809$	53.3784			1.87668			0.938342	−	0.345707i	$-0.112361\pi$
$809$	53.3784			1.87668			0.938342	+	0.345707i	$0.112361\pi$
$810$	−1.32271	−	2.29101i	−0.0464754	−	0.0804977i
$811$	9.21739	−	15.9650i	0.323666	−	0.560607i	−0.657575	−	0.753389i	$-0.728418\pi$
$811$	9.21739	−	15.9650i	0.323666	−	0.560607i	0.981242	+	0.192782i	$0.0617511\pi$
$812$	77.4515			2.71801
$813$	21.7510			0.762841
$814$	15.0862	+	26.1300i	0.528771	+	0.915857i
$815$	−1.71100	+	2.96353i	−0.0599336	+	0.103808i
$816$	14.5065	−	25.1260i	0.507829	−	0.879585i
$817$	−5.36862	−	9.29873i	−0.187824	−	0.325321i
$818$	−50.4200			−1.76289
$819$	−21.5782			−0.754005
$820$	−7.61266	−	13.1855i	−0.265846	−	0.460458i
$821$	10.7073	+	18.5456i	0.373688	+	0.647247i	0.990130	−	0.140154i	$-0.0447596\pi$
$821$	10.7073	+	18.5456i	0.373688	+	0.647247i	−0.616441	+	0.787401i	$0.711426\pi$
$822$	−21.5276	−	37.2868i	−0.750860	−	1.30053i
$823$	10.4263	+	18.0589i	0.363439	+	0.629495i	0.988524	−	0.151061i	$-0.0482691\pi$
$823$	10.4263	+	18.0589i	0.363439	+	0.629495i	−0.625085	+	0.780556i	$0.714936\pi$
$824$	−45.7587	+	79.2563i	−1.59408	+	2.76102i
$825$	−2.12237	+	3.67605i	−0.0738913	+	0.127984i
$826$	141.810			4.93419
$827$	−8.80648	−	15.2533i	−0.306231	−	0.530408i	0.671303	−	0.741183i	$-0.265735\pi$
$827$	−8.80648	−	15.2533i	−0.306231	−	0.530408i	−0.977535	+	0.210774i	$0.932401\pi$
$828$	43.1721			1.50033
$829$	−19.5524			−0.679084			−0.339542	−	0.940591i	$-0.610272\pi$
$829$	−19.5524			−0.679084			−0.339542	+	0.940591i	$0.610272\pi$
$830$	−0.266622	+	0.461804i	−0.00925460	+	0.0160294i
$831$	−12.5690			−0.436013
$832$	−30.3400	−	52.5504i	−1.05185	−	1.82186i
$833$	−18.7444	+	32.4662i	−0.649454	+	1.12489i
$834$	1.77310	+	3.07110i	0.0613974	+	0.106343i
$835$	−0.714827	+	1.23812i	−0.0247376	+	0.0428468i
$836$	−11.4897	+	19.9007i	−0.397380	+	0.688282i
$837$	5.03551	−	8.72176i	0.174053	−	0.301468i
$838$	1.92784	−	3.33912i	0.0665963	−	0.115348i
$839$	−4.29384	+	7.43715i	−0.148240	+	0.256759i	−0.930577	−	0.366096i	$-0.880694\pi$
$839$	−4.29384	+	7.43715i	−0.148240	+	0.256759i	0.782337	+	0.622855i	$0.214027\pi$
$840$	−18.2583	+	31.6243i	−0.629971	+	1.09114i
$841$	8.83575	+	15.3040i	0.304681	+	0.527723i
$842$	−49.7574	+	86.1823i	−1.71475	+	2.97004i
$843$	−7.46770	−	12.9344i	−0.257201	−	0.445486i
$844$	−35.1816			−1.21100
$845$	4.48387	−	7.76628i	0.154250	−	0.267168i
$846$	−16.2734			−0.559492
$847$	−32.3089			−1.11015
$848$	−62.0028	−	107.392i	−2.12918	−	3.68785i
$849$	−15.8375			−0.543543
$850$	3.49310	−	6.05022i	0.119812	−	0.207521i
$851$	11.6042	−	20.0991i	0.397788	−	0.688990i
$852$	−16.1558	−	27.9827i	−0.553490	−	0.958672i
$853$	22.2303	+	38.5040i	0.761151	+	1.31835i	0.942257	+	0.334889i	$0.108699\pi$
$853$	22.2303	+	38.5040i	0.761151	+	1.31835i	−0.181106	+	0.983464i	$0.557968\pi$
$854$	−9.12497	−	15.8049i	−0.312250	−	0.540833i
$855$	−0.541550	−	0.937991i	−0.0185206	−	0.0320786i
$856$	−21.9860			−0.751468
$857$	−4.60764			−0.157394			−0.0786970	−	0.996899i	$-0.525076\pi$
$857$	−4.60764			−0.157394			−0.0786970	+	0.996899i	$0.525076\pi$
$858$	26.3153	+	45.5795i	0.898390	+	1.55606i
$859$	10.4718	−	18.1377i	0.357293	−	0.618850i	−0.630214	−	0.776421i	$-0.717033\pi$
$859$	10.4718	−	18.1377i	0.357293	−	0.618850i	0.987508	+	0.157571i	$0.0503663\pi$
$860$	−24.7751	+	42.9117i	−0.844823	+	1.46328i
$861$	7.01197	+	12.1451i	0.238967	+	0.413904i
$862$	−45.8212			−1.56068
$863$	17.4843			0.595173			0.297586	−	0.954695i	$-0.403818\pi$
$863$	17.4843			0.595173			0.297586	+	0.954695i	$0.403818\pi$
$864$	−6.59987	+	11.4313i	−0.224532	+	0.388901i
$865$	−5.61128	−	9.71902i	−0.190789	−	0.330457i
$866$	−1.68743			−0.0573413
$867$	−5.01293	+	8.68266i	−0.170248	+	0.294878i
$868$	−231.749			−7.86606
$869$	18.0361	+	31.2394i	0.611832	+	1.05972i
$870$	8.90393			0.301871
$871$	7.69532	+	37.5848i	0.260746	+	1.27351i
$872$	−59.2799			−2.00747
$873$	2.59271	+	4.49071i	0.0877500	+	0.151988i
$874$	24.7484			0.837127
$875$	−2.30194	+	3.98707i	−0.0778197	+	0.134788i
$876$	36.3024			1.22655
$877$	7.79774	+	13.5061i	0.263311	+	0.456068i	0.967120	−	0.254322i	$-0.0818522\pi$
$877$	7.79774	+	13.5061i	0.263311	+	0.456068i	−0.703809	+	0.710389i	$0.748519\pi$
$878$	−15.4559	+	26.7704i	−0.521611	+	0.903456i
$879$	20.3924			0.687819
$880$	46.6335			1.57201
$881$	10.3657	+	17.9539i	0.349229	+	0.604882i	0.986113	−	0.166077i	$-0.0531102\pi$
$881$	10.3657	+	17.9539i	0.349229	+	0.604882i	−0.636884	+	0.770960i	$0.719777\pi$
$882$	18.7768	−	32.5224i	0.632247	−	1.09508i
$883$	12.4358	−	21.5394i	0.418498	−	0.724860i	−0.577291	−	0.816539i	$-0.695890\pi$
$883$	12.4358	−	21.5394i	0.418498	−	0.724860i	0.995789	+	0.0916791i	$0.0292234\pi$
$884$	−30.9334	−	53.5782i	−1.04040	−	1.80203i
$885$	11.6436			0.391395
$886$	2.35201			0.0790174
$887$	−7.89761	−	13.6791i	−0.265176	−	0.459298i	0.702434	−	0.711749i	$-0.252097\pi$
$887$	−7.89761	−	13.6791i	−0.265176	−	0.459298i	−0.967610	+	0.252451i	$0.918763\pi$
$888$	10.6561	+	18.4570i	0.357597	+	0.619376i
$889$	−24.4492	−	42.3472i	−0.819999	−	1.42028i
$890$	6.71207	+	11.6256i	0.224989	+	0.389692i
$891$	2.12237	−	3.67605i	0.0711020	−	0.123152i
$892$	−6.76191	+	11.7120i	−0.226405	+	0.392146i
$893$	−6.66273			−0.222960
$894$	8.35910	+	14.4784i	0.279570	+	0.484230i
$895$	−17.3998			−0.581612
$896$	36.1385			1.20730
$897$	20.2416	−	35.0596i	0.675849	−	1.17060i
$898$	−32.6351			−1.08905
$899$	16.9484	+	29.3555i	0.565262	+	0.979062i
$900$	−2.49914	+	4.32863i	−0.0833046	+	0.144288i
$901$	−14.9042	−	25.8148i	−0.496531	−	0.860017i
$902$	17.1026	−	29.6226i	0.569455	−	0.986324i
$903$	22.8201	−	39.5256i	0.759407	−	1.31533i
$904$	−81.5379	+	141.228i	−2.71191	+	4.69717i
$905$	10.9526	−	18.9704i	0.364075	−	0.630597i
$906$	1.75762	−	3.04429i	0.0583930	−	0.101140i
$907$	−15.6113	+	27.0396i	−0.518365	+	0.897835i	0.481407	+	0.876497i	$0.340126\pi$
$907$	−15.6113	+	27.0396i	−0.518365	+	0.897835i	−0.999772	+	0.0213381i	$0.993207\pi$
$908$	−13.1110	−	22.7089i	−0.435103	−	0.753620i
$909$	−1.73660	+	3.00788i	−0.0575993	+	0.0997649i
$910$	28.5418	+	49.4359i	0.946152	+	1.63878i
$911$	21.0250			0.696588			0.348294	−	0.937385i	$-0.386761\pi$
$911$	21.0250			0.696588			0.348294	+	0.937385i	$0.386761\pi$
$912$	−5.94957	+	10.3050i	−0.197010	+	0.341231i
$913$	−0.855622			−0.0283169
$914$	43.3377			1.43348
$915$	−0.749226	−	1.29770i	−0.0247686	−	0.0429005i
$916$	−85.3676			−2.82062
$917$	26.1821	−	45.3488i	0.864610	−	1.49755i
$918$	−3.49310	+	6.05022i	−0.115289	+	0.199687i
$919$	−28.8892	−	50.0376i	−0.952968	−	1.65059i	−0.738952	−	0.673758i	$-0.764679\pi$
$919$	−28.8892	−	50.0376i	−0.952968	−	1.65059i	−0.214015	−	0.976830i	$-0.568654\pi$
$920$	−34.2547	−	59.3309i	−1.12934	−	1.95608i
$921$	−16.1828	−	28.0294i	−0.533241	−	0.923600i
$922$	8.72235	+	15.1075i	0.287255	+	0.497541i
$923$	−30.2993			−0.997312
$924$	−97.6774			−3.21335
$925$	1.34349	+	2.32699i	0.0441736	+	0.0765109i
$926$	−8.04336	+	13.9315i	−0.264321	+	0.457818i
$927$	5.76908	−	9.99234i	0.189481	−	0.328191i
$928$	−22.2137	−	38.4753i	−0.729201	−	1.26301i
$929$	7.74725			0.254179			0.127090	−	0.991891i	$-0.459436\pi$
$929$	7.74725			0.254179			0.127090	+	0.991891i	$0.459436\pi$
$930$	−26.6421			−0.873630
$931$	7.68766	−	13.3154i	0.251953	−	0.436395i
$932$	33.2347	+	57.5641i	1.08864	+	1.88558i
$933$	−0.103810			−0.00339857
$934$	−23.6143	+	40.9011i	−0.772682	+	1.33832i
$935$	11.2097			0.366598
$936$	18.5879	+	32.1951i	0.607563	+	1.05233i
$937$	−11.5459			−0.377189			−0.188594	−	0.982055i	$-0.560393\pi$
$937$	−11.5459			−0.377189			−0.188594	+	0.982055i	$0.560393\pi$
$938$	−94.5786	−	31.5151i	−3.08810	−	1.02900i
$939$	28.9638			0.945196
$940$	15.3735	+	26.6278i	0.501430	+	0.868502i
$941$	−13.3787			−0.436133			−0.218067	−	0.975934i	$-0.569975\pi$
$941$	−13.3787			−0.436133			−0.218067	+	0.975934i	$0.569975\pi$
$942$	−9.62968	+	16.6791i	−0.313752	+	0.543434i
$943$	−26.3105			−0.856789
$944$	−63.9593	−	110.781i	−2.08170	−	3.60561i
$945$	2.30194	−	3.98707i	0.0748820	−	0.129699i
$946$	−111.319			−3.61930
$947$	−7.56085			−0.245695			−0.122847	−	0.992426i	$-0.539203\pi$
$947$	−7.56085			−0.245695			−0.122847	+	0.992426i	$0.539203\pi$
$948$	21.2379	+	36.7851i	0.689775	+	1.19473i
$949$	17.0207	−	29.4808i	0.552516	−	0.956986i
$950$	−1.43263	+	2.48139i	−0.0464806	+	0.0805068i
$951$	−12.3956	−	21.4698i	−0.401954	−	0.696205i
$952$	96.4351			3.12548
$953$	28.0544			0.908772			0.454386	−	0.890805i	$-0.349859\pi$
$953$	28.0544			0.908772			0.454386	+	0.890805i	$0.349859\pi$
$954$	14.9300	+	25.8595i	0.483376	+	0.837232i
$955$	9.24529	+	16.0133i	0.299171	+	0.518179i
$956$	−7.68594	−	13.3124i	−0.248581	−	0.430555i
$957$	7.14343	+	12.3728i	0.230914	+	0.399955i
$958$	44.1132	−	76.4062i	1.42523	−	2.46857i
$959$	37.4648	−	64.8909i	1.20980	−	2.09544i
$960$	12.9465			0.417847
$961$	−35.2127	−	60.9902i	−1.13589	−	1.96743i
$962$	33.3159			1.07415
$963$	2.77192			0.0893238
$964$	−26.5322	+	45.9552i	−0.854545	+	1.48012i
$965$	9.49104			0.305527
$966$	52.5984	+	91.1031i	1.69232	+	2.93119i
$967$	−18.5273	+	32.0902i	−0.595798	+	1.03195i	0.397636	+	0.917543i	$0.369831\pi$
$967$	−18.5273	+	32.0902i	−0.595798	+	1.03195i	−0.993434	+	0.114409i	$0.963503\pi$
$968$	27.8314	+	48.2054i	0.894536	+	1.54938i
$969$	−1.43016	+	2.47710i	−0.0459432	+	0.0795760i
$970$	6.85883	−	11.8798i	0.220224	−	0.381439i
$971$	−17.6582	+	30.5848i	−0.566677	+	0.981514i	0.430214	+	0.902727i	$0.358438\pi$
$971$	−17.6582	+	30.5848i	−0.566677	+	0.981514i	−0.996891	+	0.0787869i	$0.974895\pi$
$972$	2.49914	−	4.32863i	0.0801599	−	0.138841i
$973$	−3.08575	+	5.34468i	−0.0989247	+	0.171343i
$974$	−8.87691	+	15.3753i	−0.284435	+	0.492655i
$975$	2.34349	+	4.05904i	0.0750517	+	0.129993i
$976$	−8.23114	+	14.2567i	−0.263472	+	0.456347i
$977$	−10.1577	−	17.5937i	−0.324975	−	0.562873i	0.656533	−	0.754298i	$-0.272022\pi$
$977$	−10.1577	−	17.5937i	−0.324975	−	0.562873i	−0.981507	+	0.191425i	$0.938689\pi$
$978$	−9.05263			−0.289471
$979$	−10.7699	+	18.6540i	−0.344207	+	0.596184i
$980$	−70.9538			−2.26654
$981$	7.47378			0.238620
$982$	20.7750	+	35.9833i	0.662956	+	1.14827i
$983$	33.4793			1.06782			0.533912	−	0.845540i	$-0.320721\pi$
$983$	33.4793			1.06782			0.533912	+	0.845540i	$0.320721\pi$
$984$	12.0805	−	20.9240i	0.385111	−	0.667031i
$985$	8.67792	−	15.0306i	0.276502	−	0.478915i
$986$	−11.7570	−	20.3637i	−0.374419	−	0.648513i
$987$	−14.1605	−	24.5266i	−0.450733	−	0.780692i
$988$	12.6868	+	21.9741i	0.403620	+	0.699090i
$989$	42.8132	+	74.1547i	1.36138	+	2.35798i
$990$	−11.2291			−0.356885
$991$	16.1836			0.514089			0.257045	−	0.966400i	$-0.417251\pi$
$991$	16.1836			0.514089			0.257045	+	0.966400i	$0.417251\pi$
$992$	66.4674	+	115.125i	2.11034	+	3.65522i
$993$	−15.6114	+	27.0397i	−0.495412	+	0.858079i
$994$	39.3666	−	68.1850i	1.24863	−	2.16270i
$995$	−2.66440	−	4.61488i	−0.0844672	−	0.146301i
$996$	−1.00751			−0.0319243
$997$	19.2374			0.609253			0.304627	−	0.952472i	$-0.401468\pi$
$997$	19.2374			0.609253			0.304627	+	0.952472i	$0.401468\pi$
$998$	16.7701	−	29.0467i	0.530849	−	0.919457i
$999$	−1.34349	−	2.32699i	−0.0425061	−	0.0736227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1005.2.i.c.841.6	yes	12
67.29	even	3	inner	1005.2.i.c.766.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1005.2.i.c.766.6	✓	12	67.29	even	3	inner
1005.2.i.c.841.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1005 = 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1005.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32271 + 2.29101i) q^{2} -1.00000 q^{3} +(-2.49914 + 4.32863i) q^{4} -1.00000 q^{5} +(-1.32271 - 2.29101i) q^{6} +(2.30194 - 3.98707i) q^{7} -7.93171 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.32271 + 2.29101i) q^{2} -1.00000 q^{3} +(-2.49914 + 4.32863i) q^{4} -1.00000 q^{5} +(-1.32271 - 2.29101i) q^{6} +(2.30194 - 3.98707i) q^{7} -7.93171 q^{8} +1.00000 q^{9} +(-1.32271 - 2.29101i) q^{10} +(2.12237 - 3.67605i) q^{11} +(2.49914 - 4.32863i) q^{12} +(-2.34349 - 4.05904i) q^{13} +12.1792 q^{14} +1.00000 q^{15} +(-5.49310 - 9.51432i) q^{16} +(-1.32043 - 2.28705i) q^{17} +(1.32271 + 2.29101i) q^{18} +(0.541550 + 0.937991i) q^{19} +(2.49914 - 4.32863i) q^{20} +(-2.30194 + 3.98707i) q^{21} +11.2291 q^{22} +(-4.31870 - 7.48021i) q^{23} +7.93171 q^{24} +1.00000 q^{25} +(6.19952 - 10.7379i) q^{26} -1.00000 q^{27} +(11.5057 + 19.9285i) q^{28} +(1.68289 - 2.91485i) q^{29} +(1.32271 + 2.29101i) q^{30} +(-5.03551 + 8.72176i) q^{31} +(6.59987 - 11.4313i) q^{32} +(-2.12237 + 3.67605i) q^{33} +(3.49310 - 6.05022i) q^{34} +(-2.30194 + 3.98707i) q^{35} +(-2.49914 + 4.32863i) q^{36} +(1.34349 + 2.32699i) q^{37} +(-1.43263 + 2.48139i) q^{38} +(2.34349 + 4.05904i) q^{39} +7.93171 q^{40} +(1.52306 - 2.63801i) q^{41} -12.1792 q^{42} -9.91345 q^{43} +(10.6082 + 18.3739i) q^{44} -1.00000 q^{45} +(11.4248 - 19.7883i) q^{46} +(-3.07577 + 5.32739i) q^{47} +(5.49310 + 9.51432i) q^{48} +(-7.09783 - 12.2938i) q^{49} +(1.32271 + 2.29101i) q^{50} +(1.32043 + 2.28705i) q^{51} +23.4268 q^{52} +11.2874 q^{53} +(-1.32271 - 2.29101i) q^{54} +(-2.12237 + 3.67605i) q^{55} +(-18.2583 + 31.6243i) q^{56} +(-0.541550 - 0.937991i) q^{57} +8.90393 q^{58} +11.6436 q^{59} +(-2.49914 + 4.32863i) q^{60} +(-0.749226 - 1.29770i) q^{61} -26.6421 q^{62} +(2.30194 - 3.98707i) q^{63} +12.9465 q^{64} +(2.34349 + 4.05904i) q^{65} -11.2291 q^{66} +(-7.76558 - 2.58761i) q^{67} +13.1997 q^{68} +(4.31870 + 7.48021i) q^{69} -12.1792 q^{70} +(3.23228 - 5.59848i) q^{71} -7.93171 q^{72} +(3.63150 + 6.28994i) q^{73} +(-3.55409 + 6.15587i) q^{74} -1.00000 q^{75} -5.41363 q^{76} +(-9.77111 - 16.9241i) q^{77} +(-6.19952 + 10.7379i) q^{78} +(-4.24905 + 7.35957i) q^{79} +(5.49310 + 9.51432i) q^{80} +1.00000 q^{81} +8.05827 q^{82} +(-0.100786 - 0.174567i) q^{83} +(-11.5057 - 19.9285i) q^{84} +(1.32043 + 2.28705i) q^{85} +(-13.1126 - 22.7118i) q^{86} +(-1.68289 + 2.91485i) q^{87} +(-16.8340 + 29.1573i) q^{88} -5.07447 q^{89} +(-1.32271 - 2.29101i) q^{90} -21.5782 q^{91} +43.1721 q^{92} +(5.03551 - 8.72176i) q^{93} -16.2734 q^{94} +(-0.541550 - 0.937991i) q^{95} +(-6.59987 + 11.4313i) q^{96} +(2.59271 + 4.49071i) q^{97} +(18.7768 - 32.5224i) q^{98} +(2.12237 - 3.67605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 12 q^{3} - 9 q^{4} - 12 q^{5} + q^{6} + 10 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - q^2 - 12 * q^3 - 9 * q^4 - 12 * q^5 + q^6 + 10 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - q^{2} - 12 q^{3} - 9 q^{4} - 12 q^{5} + q^{6} + 10 q^{7} - 12 q^{8} + 12 q^{9} + q^{10} + 9 q^{12} - 12 q^{13} + 34 q^{14} + 12 q^{15} - 7 q^{16} - 8 q^{17} - q^{18} + 8 q^{19} + 9 q^{20} - 10 q^{21} + 6 q^{22} - 2 q^{23} + 12 q^{24} + 12 q^{25} + 21 q^{26} - 12 q^{27} + 15 q^{28} - 2 q^{29} - q^{30} - 24 q^{31} + 11 q^{32} - 17 q^{34} - 10 q^{35} - 9 q^{36} - 3 q^{38} + 12 q^{39} + 12 q^{40} + 10 q^{41} - 34 q^{42} - 32 q^{43} - q^{44} - 12 q^{45} - 5 q^{46} + 2 q^{47} + 7 q^{48} - 12 q^{49} - q^{50} + 8 q^{51} + 58 q^{52} - 16 q^{53} + q^{54} - 38 q^{56} - 8 q^{57} - 38 q^{58} - 32 q^{59} - 9 q^{60} - 22 q^{61} - 38 q^{62} + 10 q^{63} - 8 q^{64} + 12 q^{65} - 6 q^{66} + 22 q^{68} + 2 q^{69} - 34 q^{70} + 16 q^{71} - 12 q^{72} + 20 q^{73} - 23 q^{74} - 12 q^{75} - 46 q^{76} - 28 q^{77} - 21 q^{78} + 4 q^{79} + 7 q^{80} + 12 q^{81} + 74 q^{82} - 2 q^{83} - 15 q^{84} + 8 q^{85} - 4 q^{86} + 2 q^{87} - 64 q^{88} - 72 q^{89} + q^{90} - 40 q^{91} + 146 q^{92} + 24 q^{93} - 90 q^{94} - 8 q^{95} - 11 q^{96} + 28 q^{97} + 54 q^{98}+O(q^{100}) \) 12 * q - q^2 - 12 * q^3 - 9 * q^4 - 12 * q^5 + q^6 + 10 * q^7 - 12 * q^8 + 12 * q^9 + q^10 + 9 * q^12 - 12 * q^13 + 34 * q^14 + 12 * q^15 - 7 * q^16 - 8 * q^17 - q^18 + 8 * q^19 + 9 * q^20 - 10 * q^21 + 6 * q^22 - 2 * q^23 + 12 * q^24 + 12 * q^25 + 21 * q^26 - 12 * q^27 + 15 * q^28 - 2 * q^29 - q^30 - 24 * q^31 + 11 * q^32 - 17 * q^34 - 10 * q^35 - 9 * q^36 - 3 * q^38 + 12 * q^39 + 12 * q^40 + 10 * q^41 - 34 * q^42 - 32 * q^43 - q^44 - 12 * q^45 - 5 * q^46 + 2 * q^47 + 7 * q^48 - 12 * q^49 - q^50 + 8 * q^51 + 58 * q^52 - 16 * q^53 + q^54 - 38 * q^56 - 8 * q^57 - 38 * q^58 - 32 * q^59 - 9 * q^60 - 22 * q^61 - 38 * q^62 + 10 * q^63 - 8 * q^64 + 12 * q^65 - 6 * q^66 + 22 * q^68 + 2 * q^69 - 34 * q^70 + 16 * q^71 - 12 * q^72 + 20 * q^73 - 23 * q^74 - 12 * q^75 - 46 * q^76 - 28 * q^77 - 21 * q^78 + 4 * q^79 + 7 * q^80 + 12 * q^81 + 74 * q^82 - 2 * q^83 - 15 * q^84 + 8 * q^85 - 4 * q^86 + 2 * q^87 - 64 * q^88 - 72 * q^89 + q^90 - 40 * q^91 + 146 * q^92 + 24 * q^93 - 90 * q^94 - 8 * q^95 - 11 * q^96 + 28 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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