LMFDB - Embedded newform 48.3.i.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, 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:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.4
Root			$1.38255 + 0.297594i$ of defining polynomial
Character	$\chi$	$=$	48.29
Dual form			48.3.i.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68014 - 1.08495i) q^{2} +(0.737922 + 2.90783i) q^{3} +(1.64575 - 3.64575i) q^{4} +(-1.57472 - 1.57472i) q^{5} +(4.39467 + 4.08495i) q^{6} +3.64575i q^{7} +(-1.19038 - 7.91094i) q^{8} +(-7.91094 + 4.29150i) q^{9} +O(q^{10})$	\(q+(1.68014 - 1.08495i) q^{2} +(0.737922 + 2.90783i) q^{3} +(1.64575 - 3.64575i) q^{4} +(-1.57472 - 1.57472i) q^{5} +(4.39467 + 4.08495i) q^{6} +3.64575i q^{7} +(-1.19038 - 7.91094i) q^{8} +(-7.91094 + 4.29150i) q^{9} +(-4.35425 - 0.937254i) q^{10} +(-1.19038 - 1.19038i) q^{11} +(11.8157 + 2.09528i) q^{12} +(-14.6458 - 14.6458i) q^{13} +(3.95547 + 6.12538i) q^{14} +(3.41699 - 5.74103i) q^{15} +(-10.5830 - 12.0000i) q^{16} +28.0726i q^{17} +(-8.63542 + 15.7933i) q^{18} +(12.5830 + 12.5830i) q^{19} +(-8.33263 + 3.14944i) q^{20} +(-10.6012 + 2.69028i) q^{21} +(-3.29150 - 0.708497i) q^{22} +29.2630 q^{23} +(22.1253 - 9.29907i) q^{24} -20.0405i q^{25} +(-40.4969 - 8.71697i) q^{26} +(-18.3166 - 19.8369i) q^{27} +(13.2915 + 6.00000i) q^{28} +(19.3557 - 19.3557i) q^{29} +(-0.487722 - 13.3530i) q^{30} +11.6458 q^{31} +(-30.8004 - 8.67963i) q^{32} +(2.58301 - 4.33981i) q^{33} +(30.4575 + 47.1660i) q^{34} +(5.74103 - 5.74103i) q^{35} +(2.62631 + 35.9041i) q^{36} +(0.771243 - 0.771243i) q^{37} +(34.7932 + 7.48925i) q^{38} +(31.7799 - 53.3948i) q^{39} +(-10.5830 + 14.3320i) q^{40} +25.6919 q^{41} +(-14.8927 + 16.0219i) q^{42} +(-40.5830 + 40.5830i) q^{43} +(-6.29888 + 2.38075i) q^{44} +(19.2154 + 5.69960i) q^{45} +(49.1660 - 31.7490i) q^{46} +50.2681i q^{47} +(27.0845 - 39.6286i) q^{48} +35.7085 q^{49} +(-21.7430 - 33.6709i) q^{50} +(-81.6304 + 20.7154i) q^{51} +(-77.4980 + 29.2915i) q^{52} +(-46.2379 - 46.2379i) q^{53} +(-52.2966 - 13.4561i) q^{54} +3.74902i q^{55} +(28.8413 - 4.33981i) q^{56} +(-27.3040 + 45.8745i) q^{57} +(11.5203 - 53.5203i) q^{58} +(-22.7533 - 22.7533i) q^{59} +(-15.3069 - 21.9058i) q^{60} +(12.7712 + 12.7712i) q^{61} +(19.5665 - 12.6351i) q^{62} +(-15.6458 - 28.8413i) q^{63} +(-61.1660 + 18.8340i) q^{64} +46.1259i q^{65} +(-0.368683 - 10.0939i) q^{66} +(10.6863 + 10.6863i) q^{67} +(102.346 + 46.2006i) q^{68} +(21.5938 + 85.0919i) q^{69} +(3.41699 - 15.8745i) q^{70} -122.086 q^{71} +(43.3668 + 57.4745i) q^{72} +15.0405i q^{73} +(0.459035 - 2.13256i) q^{74} +(58.2744 - 14.7883i) q^{75} +(66.5830 - 25.1660i) q^{76} +(4.33981 - 4.33981i) q^{77} +(-4.53608 - 124.191i) q^{78} -51.3948 q^{79} +(-2.23137 + 35.5619i) q^{80} +(44.1660 - 67.8997i) q^{81} +(43.1660 - 27.8745i) q^{82} +(37.8680 - 37.8680i) q^{83} +(-7.63888 + 43.0770i) q^{84} +(44.2065 - 44.2065i) q^{85} +(-24.1545 + 112.216i) q^{86} +(70.5659 + 42.0000i) q^{87} +(-8.00000 + 10.8340i) q^{88} -5.45550 q^{89} +(38.4684 - 11.2717i) q^{90} +(53.3948 - 53.3948i) q^{91} +(48.1596 - 106.686i) q^{92} +(8.59366 + 33.8639i) q^{93} +(54.5385 + 84.4575i) q^{94} -39.6294i q^{95} +(2.51059 - 95.9672i) q^{96} -81.1660 q^{97} +(59.9953 - 38.7421i) q^{98} +(14.5255 + 4.30849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 8 q^{4} + 16 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 - 8 * q^4 + 16 * q^6	$ 8 q + 4 q^{3} - 8 q^{4} + 16 q^{6} - 56 q^{10} + 56 q^{12} - 96 q^{13} + 112 q^{15} - 64 q^{18} + 16 q^{19} - 32 q^{21} + 16 q^{22} - 48 q^{24} - 68 q^{27} + 64 q^{28} + 56 q^{30} + 72 q^{31} - 64 q^{33} + 32 q^{34} + 104 q^{36} + 112 q^{37} - 24 q^{42} - 240 q^{43} - 112 q^{45} + 224 q^{46} - 64 q^{48} + 328 q^{49} - 32 q^{51} - 112 q^{52} - 168 q^{54} - 56 q^{58} - 336 q^{60} + 208 q^{61} - 104 q^{63} - 320 q^{64} - 80 q^{66} - 232 q^{67} + 112 q^{70} + 160 q^{72} + 324 q^{75} + 448 q^{76} + 152 q^{78} - 136 q^{79} + 184 q^{81} + 176 q^{82} + 64 q^{84} - 112 q^{85} - 64 q^{88} + 392 q^{90} + 152 q^{91} + 64 q^{93} - 368 q^{94} + 512 q^{96} - 480 q^{97} + 160 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^4 + 16 * q^6 - 56 * q^10 + 56 * q^12 - 96 * q^13 + 112 * q^15 - 64 * q^18 + 16 * q^19 - 32 * q^21 + 16 * q^22 - 48 * q^24 - 68 * q^27 + 64 * q^28 + 56 * q^30 + 72 * q^31 - 64 * q^33 + 32 * q^34 + 104 * q^36 + 112 * q^37 - 24 * q^42 - 240 * q^43 - 112 * q^45 + 224 * q^46 - 64 * q^48 + 328 * q^49 - 32 * q^51 - 112 * q^52 - 168 * q^54 - 56 * q^58 - 336 * q^60 + 208 * q^61 - 104 * q^63 - 320 * q^64 - 80 * q^66 - 232 * q^67 + 112 * q^70 + 160 * q^72 + 324 * q^75 + 448 * q^76 + 152 * q^78 - 136 * q^79 + 184 * q^81 + 176 * q^82 + 64 * q^84 - 112 * q^85 - 64 * q^88 + 392 * q^90 + 152 * q^91 + 64 * q^93 - 368 * q^94 + 512 * q^96 - 480 * q^97 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.68014	−	1.08495i	0.840071	−	0.542477i
$2$	1.68014	−	1.08495i	0.840071	−	0.542477i
$3$	0.737922	+	2.90783i	0.245974	+	0.969276i
$3$	0.737922	+	2.90783i	0.245974	+	0.969276i
$4$	1.64575	−	3.64575i	0.411438	−	0.911438i
$5$	−1.57472	−	1.57472i	−0.314944	−	0.314944i	0.531877	−	0.846821i	$-0.321487\pi$
$5$	−1.57472	−	1.57472i	−0.314944	−	0.314944i	−0.846821	+	0.531877i	$0.821487\pi$
$6$	4.39467	+	4.08495i	0.732446	+	0.680826i
$7$			3.64575i			0.520822i	0.965498	+	0.260411i	$0.0838580\pi$
$7$			3.64575i			0.520822i	−0.965498	+	0.260411i	$0.916142\pi$
$8$	−1.19038	−	7.91094i	−0.148797	−	0.988868i
$9$	−7.91094	+	4.29150i	−0.878994	+	0.476834i
$10$	−4.35425	−	0.937254i	−0.435425	−	0.0937254i
$11$	−1.19038	−	1.19038i	−0.108216	−	0.108216i	0.650926	−	0.759142i	$-0.274381\pi$
$11$	−1.19038	−	1.19038i	−0.108216	−	0.108216i	−0.759142	+	0.650926i	$0.774381\pi$
$12$	11.8157	+	2.09528i	0.984638	+	0.174607i
$13$	−14.6458	−	14.6458i	−1.12660	−	1.12660i	−0.990727	−	0.135870i	$-0.956617\pi$
$13$	−14.6458	−	14.6458i	−1.12660	−	1.12660i	−0.135870	−	0.990727i	$-0.543383\pi$
$14$	3.95547	+	6.12538i	0.282534	+	0.437527i
$15$	3.41699	−	5.74103i	0.227800	−	0.382736i
$16$	−10.5830	−	12.0000i	−0.661438	−	0.750000i
$17$			28.0726i			1.65133i	0.564159	+	0.825666i	$0.309200\pi$
$17$			28.0726i			1.65133i	−0.564159	+	0.825666i	$0.690800\pi$
$18$	−8.63542	+	15.7933i	−0.479746	+	0.877408i
$19$	12.5830	+	12.5830i	0.662263	+	0.662263i	0.955913	−	0.293650i	$-0.0948699\pi$
$19$	12.5830	+	12.5830i	0.662263	+	0.662263i	−0.293650	+	0.955913i	$0.594870\pi$
$20$	−8.33263	+	3.14944i	−0.416632	+	0.157472i
$21$	−10.6012	+	2.69028i	−0.504820	+	0.128109i
$22$	−3.29150	−	0.708497i	−0.149614	−	0.0322044i
$23$	29.2630			1.27231			0.636153	−	0.771563i	$-0.280525\pi$
$23$	29.2630			1.27231			0.636153	+	0.771563i	$0.280525\pi$
$24$	22.1253	−	9.29907i	0.921886	−	0.387461i
$25$		−	20.0405i		−	0.801621i
$26$	−40.4969	−	8.71697i	−1.55757	−	0.335268i
$27$	−18.3166	−	19.8369i	−0.678393	−	0.734699i
$28$	13.2915	+	6.00000i	0.474697	+	0.214286i
$29$	19.3557	−	19.3557i	0.667437	−	0.667437i	−0.289685	−	0.957122i	$-0.593551\pi$
$29$	19.3557	−	19.3557i	0.667437	−	0.667437i	0.957122	+	0.289685i	$0.0935506\pi$
$30$	−0.487722	−	13.3530i	−0.0162574	−	0.445101i
$31$	11.6458			0.375669			0.187835	−	0.982201i	$-0.439853\pi$
$31$	11.6458			0.375669			0.187835	+	0.982201i	$0.439853\pi$
$32$	−30.8004	−	8.67963i	−0.962512	−	0.271238i
$33$	2.58301	−	4.33981i	0.0782729	−	0.131510i
$34$	30.4575	+	47.1660i	0.895809	+	1.38724i
$35$	5.74103	−	5.74103i	0.164030	−	0.164030i
$36$	2.62631	+	35.9041i	0.0729530	+	0.997335i
$37$	0.771243	−	0.771243i	0.0208444	−	0.0208444i	−0.696608	−	0.717452i	$-0.745308\pi$
$37$	0.771243	−	0.771243i	0.0208444	−	0.0208444i	0.717452	+	0.696608i	$0.245308\pi$
$38$	34.7932	+	7.48925i	0.915611	+	0.197086i
$39$	31.7799	−	53.3948i	0.814870	−	1.36910i
$40$	−10.5830	+	14.3320i	−0.264575	+	0.358301i
$41$	25.6919			0.626631			0.313316	−	0.949649i	$-0.398560\pi$
$41$	25.6919			0.626631			0.313316	+	0.949649i	$0.398560\pi$
$42$	−14.8927	+	16.0219i	−0.354589	+	0.381473i
$43$	−40.5830	+	40.5830i	−0.943791	+	0.943791i	−0.998502	−	0.0547114i	$-0.982576\pi$
$43$	−40.5830	+	40.5830i	−0.943791	+	0.943791i	0.0547114	+	0.998502i	$0.482576\pi$
$44$	−6.29888	+	2.38075i	−0.143156	+	0.0541080i
$45$	19.2154	+	5.69960i	0.427009	+	0.126658i
$46$	49.1660	−	31.7490i	1.06883	−	0.690196i
$47$			50.2681i			1.06953i	0.845000	+	0.534767i	$0.179601\pi$
$47$			50.2681i			1.06953i	−0.845000	+	0.534767i	$0.820399\pi$
$48$	27.0845	−	39.6286i	0.564261	−	0.825597i
$49$	35.7085			0.728745
$50$	−21.7430	−	33.6709i	−0.434861	−	0.673418i
$51$	−81.6304	+	20.7154i	−1.60060	+	0.406185i
$52$	−77.4980	+	29.2915i	−1.49035	+	0.563298i
$53$	−46.2379	−	46.2379i	−0.872414	−	0.872414i	0.120321	−	0.992735i	$-0.461608\pi$
$53$	−46.2379	−	46.2379i	−0.872414	−	0.872414i	−0.992735	+	0.120321i	$0.961608\pi$
$54$	−52.2966	−	13.4561i	−0.968455	−	0.249187i
$55$			3.74902i			0.0681639i
$56$	28.8413	−	4.33981i	0.515024	−	0.0774967i
$57$	−27.3040	+	45.8745i	−0.479017	+	0.804816i
$58$	11.5203	−	53.5203i	0.198625	−	0.922763i
$59$	−22.7533	−	22.7533i	−0.385649	−	0.385649i	0.487483	−	0.873132i	$-0.337915\pi$
$59$	−22.7533	−	22.7533i	−0.385649	−	0.385649i	−0.873132	+	0.487483i	$0.837915\pi$
$60$	−15.3069	−	21.9058i	−0.255114	−	0.365097i
$61$	12.7712	+	12.7712i	0.209365	+	0.209365i	0.803997	−	0.594633i	$-0.202703\pi$
$61$	12.7712	+	12.7712i	0.209365	+	0.209365i	−0.594633	+	0.803997i	$0.702703\pi$
$62$	19.5665	−	12.6351i	0.315589	−	0.203792i
$63$	−15.6458	−	28.8413i	−0.248345	−	0.457799i
$64$	−61.1660	+	18.8340i	−0.955719	+	0.294281i
$65$			46.1259i			0.709629i
$66$	−0.368683	−	10.0939i	−0.00558610	−	0.152939i
$67$	10.6863	+	10.6863i	0.159497	+	0.159497i	0.782344	−	0.622847i	$-0.214024\pi$
$67$	10.6863	+	10.6863i	0.159497	+	0.159497i	−0.622847	+	0.782344i	$0.714024\pi$
$68$	102.346	+	46.2006i	1.50509	+	0.679420i
$69$	21.5938	+	85.0919i	0.312954	+	1.23322i
$70$	3.41699	−	15.8745i	0.0488142	−	0.226779i
$71$	−122.086			−1.71952			−0.859760	−	0.510699i	$-0.829387\pi$
$71$	−122.086			−1.71952			−0.859760	+	0.510699i	$0.829387\pi$
$72$	43.3668	+	57.4745i	0.602317	+	0.798257i
$73$			15.0405i			0.206034i	0.994680	+	0.103017i	$0.0328497\pi$
$73$			15.0405i			0.206034i	−0.994680	+	0.103017i	$0.967150\pi$
$74$	0.459035	−	2.13256i	0.00620317	−	0.0288184i
$75$	58.2744	−	14.7883i	0.776992	−	0.197178i
$76$	66.5830	−	25.1660i	0.876092	−	0.331132i
$77$	4.33981	−	4.33981i	0.0563612	−	0.0563612i
$78$	−4.53608	−	124.191i	−0.0581549	−	1.59219i
$79$	−51.3948			−0.650567			−0.325283	−	0.945617i	$-0.605460\pi$
$79$	−51.3948			−0.650567			−0.325283	+	0.945617i	$0.605460\pi$
$80$	−2.23137	+	35.5619i	−0.0278921	+	0.444524i
$81$	44.1660	−	67.8997i	0.545259	−	0.838267i
$82$	43.1660	−	27.8745i	0.526415	−	0.339933i
$83$	37.8680	−	37.8680i	0.456240	−	0.456240i	−0.441179	−	0.897419i	$-0.645440\pi$
$83$	37.8680	−	37.8680i	0.456240	−	0.456240i	0.897419	+	0.441179i	$0.145440\pi$
$84$	−7.63888	+	43.0770i	−0.0909391	+	0.512821i
$85$	44.2065	−	44.2065i	0.520077	−	0.520077i
$86$	−24.1545	+	112.216i	−0.280866	+	1.30484i
$87$	70.5659	+	42.0000i	0.811103	+	0.482759i
$88$	−8.00000	+	10.8340i	−0.0909091	+	0.123114i
$89$	−5.45550			−0.0612977			−0.0306489	−	0.999530i	$-0.509757\pi$
$89$	−5.45550			−0.0612977			−0.0306489	+	0.999530i	$0.509757\pi$
$90$	38.4684	−	11.2717i	0.427427	−	0.125241i
$91$	53.3948	−	53.3948i	0.586756	−	0.586756i
$92$	48.1596	−	106.686i	0.523474	−	1.15963i
$93$	8.59366	+	33.8639i	0.0924049	+	0.364127i
$94$	54.5385	+	84.4575i	0.580197	+	0.898484i
$95$		−	39.6294i		−	0.417152i
$96$	2.51059	−	95.9672i	0.0261520	−	0.999658i
$97$	−81.1660			−0.836763			−0.418381	−	0.908271i	$-0.637402\pi$
$97$	−81.1660			−0.836763			−0.418381	+	0.908271i	$0.637402\pi$
$98$	59.9953	−	38.7421i	0.612197	−	0.395327i
$99$	14.5255	+	4.30849i	0.146722	+	0.0435201i
$100$	−73.0627	−	32.9817i	−0.730627	−	0.329817i
$101$	−32.4498	−	32.4498i	−0.321285	−	0.321285i	0.527975	−	0.849260i	$-0.322952\pi$
$101$	−32.4498	−	32.4498i	−0.321285	−	0.321285i	−0.849260	+	0.527975i	$0.822952\pi$
$102$	−114.675	+	123.370i	−1.12427	+	1.20951i
$103$			51.1882i			0.496973i	0.968635	+	0.248487i	$0.0799332\pi$
$103$			51.1882i			0.496973i	−0.968635	+	0.248487i	$0.920067\pi$
$104$	−98.4277	+	133.296i	−0.946421	+	1.28169i
$105$	20.9304	+	12.4575i	0.199337	+	0.118643i
$106$	−127.852	−	27.5203i	−1.20615	−	0.259625i
$107$	85.4698	+	85.4698i	0.798783	+	0.798783i	0.982904	−	0.184121i	$-0.0589438\pi$
$107$	85.4698	+	85.4698i	0.798783	+	0.798783i	−0.184121	+	0.982904i	$0.558944\pi$
$108$	−102.465	+	34.1313i	−0.948749	+	0.316030i
$109$	−52.8523	−	52.8523i	−0.484883	−	0.484883i	0.421804	−	0.906687i	$-0.361397\pi$
$109$	−52.8523	−	52.8523i	−0.484883	−	0.484883i	−0.906687	+	0.421804i	$0.861397\pi$
$110$	4.06751	+	6.29888i	0.0369773	+	0.0572625i
$111$	2.81176	+	1.67353i	0.0253312	+	0.0150768i
$112$	43.7490	−	38.5830i	0.390616	−	0.344491i
$113$		−	73.5045i		−	0.650483i	−0.945631	−	0.325241i	$-0.894554\pi$
$113$		−	73.5045i		−	0.650483i	0.945631	−	0.325241i	$-0.105446\pi$
$114$	3.89721	+	106.699i	0.0341860	+	0.935958i
$115$	−46.0810	−	46.0810i	−0.400705	−	0.400705i
$116$	−38.7113	−	102.421i	−0.333718	−	0.882936i
$117$	178.714	+	53.0094i	1.52747	+	0.453072i
$118$	−62.9150	−	13.5425i	−0.533178	−	0.114767i
$119$	−102.346			−0.860049
$120$	−49.4845	−	20.1977i	−0.412371	−	0.168314i
$121$		−	118.166i		−	0.976579i
$122$	35.3137	+	7.60129i	0.289457	+	0.0623057i
$123$	18.9586	+	74.7076i	0.154135	+	0.607379i
$124$	19.1660	−	42.4575i	0.154565	−	0.342399i
$125$	−70.9262	+	70.9262i	−0.567409	+	0.567409i
$126$	−57.5786	−	31.4826i	−0.456973	−	0.249862i
$127$	73.9333			0.582152			0.291076	−	0.956700i	$-0.405987\pi$
$127$	73.9333			0.582152			0.291076	+	0.956700i	$0.405987\pi$
$128$	−82.3336	+	98.0061i	−0.643231	+	0.765672i
$129$	−147.956	−	88.0614i	−1.14694	−	0.682646i
$130$	50.0445	+	77.4980i	0.384957	+	0.596139i
$131$	158.430	−	158.430i	1.20939	−	1.20939i	0.238161	−	0.971226i	$-0.423455\pi$
$131$	158.430	−	158.430i	1.20939	−	1.20939i	0.971226	−	0.238161i	$-0.0765447\pi$
$132$	−11.5709	−	16.5593i	−0.0876583	−	0.125449i
$133$	−45.8745	+	45.8745i	−0.344921	+	0.344921i
$134$	29.5486	+	6.36034i	0.220512	+	0.0474652i
$135$	−2.39398	+	60.0810i	−0.0177332	+	0.445045i
$136$	222.081	−	33.4170i	1.63295	−	0.245713i
$137$	100.734			0.735283			0.367642	−	0.929968i	$-0.380165\pi$
$137$	100.734			0.735283			0.367642	+	0.929968i	$0.380165\pi$
$138$	128.601	+	119.538i	0.931894	+	0.866218i
$139$	18.2732	−	18.2732i	0.131462	−	0.131462i	−0.638314	−	0.769776i	$-0.720368\pi$
$139$	18.2732	−	18.2732i	0.131462	−	0.131462i	0.769776	+	0.638314i	$0.220368\pi$
$140$	−11.4821	−	30.3787i	−0.0820148	−	0.216991i
$141$	−146.171	+	37.0939i	−1.03667	+	0.263078i
$142$	−205.122	+	132.458i	−1.44452	+	0.932799i
$143$			34.8679i			0.243831i
$144$	135.220	+	49.5143i	0.939025	+	0.343849i
$145$	−60.9595			−0.420410
$146$	16.3183	+	25.2702i	0.111769	+	0.173084i
$147$	26.3501	+	103.834i	0.179252	+	0.706355i
$148$	−1.54249	−	4.08104i	−0.0104222	−	0.0275746i
$149$	−44.9729	−	44.9729i	−0.301831	−	0.301831i	0.539899	−	0.841730i	$-0.318463\pi$
$149$	−44.9729	−	44.9729i	−0.301831	−	0.301831i	−0.841730	+	0.539899i	$0.818463\pi$
$150$	81.8646	−	88.0715i	0.545764	−	0.587144i
$151$			28.1033i			0.186114i	0.995661	+	0.0930572i	$0.0296639\pi$
$151$			28.1033i			0.186114i	−0.995661	+	0.0930572i	$0.970336\pi$
$152$	84.5649	−	114.522i	0.556348	−	0.753434i
$153$	−120.474	−	222.081i	−0.787411	−	1.45151i
$154$	2.58301	−	12.0000i	0.0167728	−	0.0779221i
$155$	−18.3388	−	18.3388i	−0.118315	−	0.118315i
$156$	−142.362	−	203.736i	−0.912578	−	1.30600i
$157$	173.265	+	173.265i	1.10360	+	1.10360i	0.993973	+	0.109628i	$0.0349660\pi$
$157$	173.265	+	173.265i	1.10360	+	1.10360i	0.109628	+	0.993973i	$0.465034\pi$
$158$	−86.3505	+	55.7609i	−0.546522	+	0.352917i
$159$	100.332	−	168.572i	0.631019	−	1.06020i
$160$	34.8340	+	62.1699i	0.217712	+	0.388562i
$161$			106.686i			0.662644i
$162$	0.537171	−	161.999i	0.00331587	−	0.999995i
$163$	51.9190	+	51.9190i	0.318521	+	0.318521i	0.848199	−	0.529678i	$-0.177687\pi$
$163$	51.9190	+	51.9190i	0.318521	+	0.318521i	−0.529678	+	0.848199i	$0.677687\pi$
$164$	42.2825	−	93.6662i	0.257820	−	0.571136i
$165$	−10.9015	+	2.76648i	−0.0660697	+	0.0167666i
$166$	22.5385	−	104.708i	0.135774	−	0.630774i
$167$	−57.5333			−0.344511			−0.172255	−	0.985052i	$-0.555105\pi$
$167$	−57.5333			−0.344511			−0.172255	+	0.985052i	$0.555105\pi$
$168$	33.9021	+	80.6632i	0.201798	+	0.480138i
$169$			259.996i			1.53844i
$170$	26.3112	−	122.235i	0.154772	−	0.719031i
$171$	−153.543	−	45.5434i	−0.897915	−	0.266336i
$172$	81.1660	+	214.745i	0.471895	+	1.24852i
$173$	−112.600	+	112.600i	−0.650868	+	0.650868i	−0.953202	−	0.302334i	$-0.902234\pi$
$173$	−112.600	+	112.600i	−0.650868	+	0.650868i	0.302334	+	0.953202i	$0.402234\pi$
$174$	164.129	−	5.99483i	0.943269	−	0.0344531i
$175$	73.0627			0.417501
$176$	−1.68676	+	26.8823i	−0.00958384	+	0.152740i
$177$	49.3725	−	82.9529i	0.278941	−	0.468660i
$178$	−9.16601	+	5.91896i	−0.0514944	+	0.0332526i
$179$	−22.4810	+	22.4810i	−0.125592	+	0.125592i	−0.767109	−	0.641517i	$-0.778305\pi$
$179$	−22.4810	+	22.4810i	−0.125592	+	0.125592i	0.641517	+	0.767109i	$0.278305\pi$
$180$	52.4031	−	60.6745i	0.291129	−	0.337081i
$181$	−18.6013	+	18.6013i	−0.102770	+	0.102770i	−0.756622	−	0.653852i	$-0.773152\pi$
$181$	−18.6013	+	18.6013i	−0.102770	+	0.102770i	0.653852	+	0.756622i	$0.273152\pi$
$182$	31.7799	−	147.642i	0.174615	−	0.811218i
$183$	−27.7124	+	46.5608i	−0.151434	+	0.254430i
$184$	−34.8340	−	231.498i	−0.189315	−	1.25814i
$185$	−2.42898			−0.0131296
$186$	51.1793	+	47.5724i	0.275157	+	0.255765i
$187$	33.4170	−	33.4170i	0.178701	−	0.178701i
$188$	183.265	+	82.7288i	0.974814	+	0.440047i
$189$	72.3203	−	66.7778i	0.382647	−	0.353322i
$190$	−42.9961	−	66.5830i	−0.226295	−	0.350437i
$191$			191.672i			1.00352i	0.865007	+	0.501760i	$0.167314\pi$
$191$			191.672i			1.00352i	−0.865007	+	0.501760i	$0.832686\pi$
$192$	−99.9018	−	163.962i	−0.520322	−	0.853970i
$193$	48.6275			0.251956			0.125978	−	0.992033i	$-0.459793\pi$
$193$	48.6275			0.251956			0.125978	+	0.992033i	$0.459793\pi$
$194$	−136.370	+	88.0614i	−0.702940	+	0.453925i
$195$	−134.126	+	34.0373i	−0.687827	+	0.174550i
$196$	58.7673	−	130.184i	0.299833	−	0.664206i
$197$	136.258	+	136.258i	0.691667	+	0.691667i	0.962599	−	0.270932i	$-0.0873318\pi$
$197$	136.258	+	136.258i	0.691667	+	0.691667i	−0.270932	+	0.962599i	$0.587332\pi$
$198$	29.0794	−	8.52061i	0.146866	−	0.0430334i
$199$		−	144.767i		−	0.727474i	−0.931502	−	0.363737i	$-0.881501\pi$
$199$		−	144.767i		−	0.727474i	0.931502	−	0.363737i	$-0.118499\pi$
$200$	−158.539	+	23.8557i	−0.792697	+	0.119279i
$201$	−23.1882	+	38.9595i	−0.115364	+	0.193828i
$202$	−89.7268	−	19.3137i	−0.444192	−	0.0956125i
$203$	70.5659	+	70.5659i	0.347615	+	0.347615i
$204$	−58.8201	+	331.697i	−0.288334	+	1.62596i
$205$	−40.4575	−	40.4575i	−0.197354	−	0.197354i
$206$	55.5369	+	86.0035i	0.269596	+	0.417493i
$207$	−231.498	+	125.582i	−1.11835	+	0.606678i
$208$	−20.7530	+	330.745i	−0.0997738	+	1.59012i
$209$		−	29.9570i		−	0.143335i
$210$	48.6818	−	1.77811i	0.231818	−	0.00846720i
$211$	−196.354	−	196.354i	−0.930589	−	0.930589i	0.0671538	−	0.997743i	$-0.478608\pi$
$211$	−196.354	−	196.354i	−0.930589	−	0.930589i	−0.997743	+	0.0671538i	$0.978608\pi$
$212$	−244.668	+	92.4759i	−1.15409	+	0.436207i
$213$	−90.0899	−	355.005i	−0.422957	−	1.66669i
$214$	236.332	+	50.8706i	1.10436	+	0.237713i
$215$	127.814			0.594482
$216$	−135.125	+	168.515i	−0.625577	+	0.780162i
$217$			42.4575i			0.195657i
$218$	−146.142	−	31.4570i	−0.670374	−	0.144298i
$219$	−43.7353	+	11.0987i	−0.199704	+	0.0506791i
$220$	13.6680	+	6.16995i	0.0621272	+	0.0280452i
$221$	411.145	−	411.145i	1.86038	−	1.86038i
$222$	6.53986	−	0.238869i	0.0294588	−	0.00107599i
$223$	−375.261			−1.68279			−0.841393	−	0.540423i	$-0.818264\pi$
$223$	−375.261			−1.68279			−0.841393	+	0.540423i	$0.818264\pi$
$224$	31.6438	−	112.291i	0.141267	−	0.501297i
$225$	86.0039	+	158.539i	0.382240	+	0.704619i
$226$	−79.7490	−	123.498i	−0.352872	−	0.546451i
$227$	−181.108	+	181.108i	−0.797834	+	0.797834i	−0.982754	−	0.184920i	$-0.940797\pi$
$227$	−181.108	+	181.108i	−0.797834	+	0.797834i	0.184920	+	0.982754i	$0.440797\pi$
$228$	122.312	+	175.041i	0.536454	+	0.767726i
$229$	−153.937	+	153.937i	−0.672215	+	0.672215i	−0.958226	−	0.286011i	$-0.907671\pi$
$229$	−153.937	+	153.937i	−0.672215	+	0.672215i	0.286011	+	0.958226i	$0.407671\pi$
$230$	−127.418	−	27.4269i	−0.553993	−	0.119247i
$231$	15.8219	+	9.41699i	0.0684930	+	0.0407662i
$232$	−176.162	−	130.081i	−0.759319	−	0.560694i
$233$	51.7790			0.222228			0.111114	−	0.993808i	$-0.464558\pi$
$233$	51.7790			0.222228			0.111114	+	0.993808i	$0.464558\pi$
$234$	357.778	−	104.833i	1.52896	−	0.448005i
$235$	79.1581	−	79.1581i	0.336843	−	0.336843i
$236$	−120.399	+	45.5066i	−0.510166	+	0.192825i
$237$	−37.9253	−	149.447i	−0.160022	−	0.630579i
$238$	−171.956	+	111.041i	−0.722502	+	0.466557i
$239$		−	249.900i		−	1.04560i	−0.852454	−	0.522802i	$-0.824887\pi$
$239$		−	249.900i		−	1.04560i	0.852454	−	0.522802i	$-0.175113\pi$
$240$	−105.054	+	19.7535i	−0.437727	+	0.0823061i
$241$	442.531			1.83623			0.918113	−	0.396318i	$-0.129712\pi$
$241$	442.531			1.83623			0.918113	+	0.396318i	$0.129712\pi$
$242$	−128.205	−	198.536i	−0.529771	−	0.820395i
$243$	230.032	+	78.3226i	0.946632	+	0.322315i
$244$	67.5791	−	25.5425i	0.276963	−	0.104682i
$245$	−56.2309	−	56.2309i	−0.229514	−	0.229514i
$246$	112.907	+	104.950i	0.458973	+	0.426627i
$247$		−	368.575i		−	1.49221i
$248$	−13.8628	−	92.1289i	−0.0558985	−	0.371487i
$249$	138.057	+	82.1699i	0.554446	+	0.330000i
$250$	−42.2144	+	196.118i	−0.168858	+	0.784470i
$251$	−43.3235	−	43.3235i	−0.172603	−	0.172603i	0.615519	−	0.788122i	$-0.288947\pi$
$251$	−43.3235	−	43.3235i	−0.172603	−	0.172603i	−0.788122	+	0.615519i	$0.788947\pi$
$252$	−130.897	+	9.57487i	−0.519434	+	0.0379955i
$253$	−34.8340	−	34.8340i	−0.137684	−	0.137684i
$254$	124.218	−	80.2142i	0.489049	−	0.315804i
$255$	161.166	+	95.9241i	0.632024	+	0.376173i
$256$	−32.0000	+	253.992i	−0.125000	+	0.992157i
$257$			179.197i			0.697266i	0.937259	+	0.348633i	$0.113354\pi$
$257$			179.197i			0.697266i	−0.937259	+	0.348633i	$0.886646\pi$
$258$	−344.129	+	12.5694i	−1.33383	+	0.0487184i
$259$	2.81176	+	2.81176i	0.0108562	+	0.0108562i
$260$	168.164	+	75.9118i	0.646783	+	0.291968i
$261$	−70.0567	+	236.186i	−0.268416	+	0.904929i
$262$	94.2954	−	438.073i	0.359906	−	1.67203i
$263$	419.478			1.59497			0.797486	−	0.603338i	$-0.206163\pi$
$263$	419.478			1.59497			0.797486	+	0.603338i	$0.206163\pi$
$264$	−37.4068	−	15.2680i	−0.141692	−	0.0578333i
$265$			145.624i			0.549523i
$266$	−27.3040	+	126.847i	−0.102646	+	0.476870i
$267$	−4.02573	−	15.8637i	−0.0150777	−	0.0594145i
$268$	56.5464	−	21.3725i	0.210994	−	0.0797483i
$269$	−33.7631	+	33.7631i	−0.125513	+	0.125513i	−0.767073	−	0.641560i	$-0.778288\pi$
$269$	−33.7631	+	33.7631i	−0.125513	+	0.125513i	0.641560	+	0.767073i	$0.278288\pi$
$270$	61.1629	+	103.542i	0.226529	+	0.383489i
$271$	329.269			1.21502			0.607508	−	0.794314i	$-0.292169\pi$
$271$	329.269			1.21502			0.607508	+	0.794314i	$0.292169\pi$
$272$	336.872	−	297.093i	1.23850	−	1.09225i
$273$	194.664	+	115.862i	0.713055	+	0.424402i
$274$	169.247	−	109.292i	0.617690	−	0.398874i
$275$	−23.8557	+	23.8557i	−0.0867482	+	0.0867482i
$276$	345.762	+	61.3143i	1.25276	+	0.222153i
$277$	251.265	−	251.265i	0.907095	−	0.907095i	−0.0889417	−	0.996037i	$-0.528348\pi$
$277$	251.265	−	251.265i	0.907095	−	0.907095i	0.996037	+	0.0889417i	$0.0283485\pi$
$278$	10.8760	−	50.5272i	0.0391223	−	0.181752i
$279$	−92.1289	+	49.9778i	−0.330211	+	0.179132i
$280$	−52.2510	−	38.5830i	−0.186611	−	0.137796i
$281$	−171.809			−0.611421			−0.305711	−	0.952124i	$-0.598894\pi$
$281$	−171.809			−0.611421			−0.305711	+	0.952124i	$0.598894\pi$
$282$	−205.343	+	220.912i	−0.728166	+	0.783375i
$283$	−193.476	+	193.476i	−0.683660	+	0.683660i	−0.960823	−	0.277163i	$-0.910606\pi$
$283$	−193.476	+	193.476i	−0.683660	+	0.683660i	0.277163	+	0.960823i	$0.410606\pi$
$284$	−200.923	+	445.095i	−0.707475	+	1.56724i
$285$	115.236	−	29.2434i	0.404335	−	0.102608i
$286$	37.8301	+	58.5830i	0.132273	+	0.204836i
$287$			93.6662i			0.326363i
$288$	280.909	−	63.5159i	0.975378	−	0.220541i
$289$	−499.073			−1.72690
$290$	−102.421	+	66.1382i	−0.353174	+	0.228063i
$291$	−59.8942	−	236.017i	−0.205822	−	0.811055i
$292$	54.8340	+	24.7530i	0.187788	+	0.0847704i
$293$	−73.4937	−	73.4937i	−0.250832	−	0.250832i	0.570480	−	0.821312i	$-0.306757\pi$
$293$	−73.4937	−	73.4937i	−0.250832	−	0.250832i	−0.821312	+	0.570480i	$0.806757\pi$
$294$	156.927	+	145.868i	0.533766	+	0.496148i
$295$			71.6601i			0.242916i
$296$	−7.01933	−	5.18319i	−0.0237140	−	0.0175108i
$297$	−1.80968	+	45.4170i	−0.00609320	+	0.152919i
$298$	−124.354	−	26.7673i	−0.417296	−	0.0898232i
$299$	−428.579	−	428.579i	−1.43337	−	1.43337i
$300$	41.9906	−	236.792i	0.139969	−	0.789306i
$301$	−147.956	−	147.956i	−0.491547	−	0.491547i
$302$	30.4907	+	47.2175i	0.100963	+	0.156349i
$303$	70.4131	−	118.304i	0.232386	−	0.390442i
$304$	17.8301	−	284.162i	0.0586515	−	0.934744i
$305$		−	40.2222i		−	0.131876i
$306$	−443.361	−	242.419i	−1.44889	−	0.792219i
$307$	283.055	+	283.055i	0.922003	+	0.922003i	0.997171	−	0.0751680i	$-0.0239493\pi$
$307$	283.055	+	283.055i	0.922003	+	0.922003i	−0.0751680	+	0.997171i	$0.523949\pi$
$308$	−8.67963	−	22.9641i	−0.0281806	−	0.0745589i
$309$	−148.847	+	37.7729i	−0.481704	+	0.122242i
$310$	−50.7085	−	10.9150i	−0.163576	−	0.0352098i
$311$	54.0368			0.173752			0.0868759	−	0.996219i	$-0.472312\pi$
$311$	54.0368			0.173752			0.0868759	+	0.996219i	$0.472312\pi$
$312$	−460.233	−	187.849i	−1.47511	−	0.602081i
$313$		−	490.280i		−	1.56639i	−0.621777	−	0.783194i	$-0.713589\pi$
$313$		−	490.280i		−	1.56639i	0.621777	−	0.783194i	$-0.286411\pi$
$314$	479.095	+	103.125i	1.52578	+	0.328425i
$315$	−20.7793	+	70.0547i	−0.0659661	+	0.222396i
$316$	−84.5830	+	187.373i	−0.267668	+	0.592951i
$317$	−319.550	+	319.550i	−1.00804	+	1.00804i	−0.00807607	+	0.999967i	$0.502571\pi$
$317$	−319.550	+	319.550i	−1.00804	+	1.00804i	−0.999967	+	0.00807607i	$0.997429\pi$
$318$	−14.3208	−	392.080i	−0.0450340	−	1.23296i
$319$	−46.0810			−0.144455
$320$	125.978	+	66.6610i	0.393680	+	0.208316i
$321$	−185.461	+	311.601i	−0.577762	+	0.970721i
$322$	115.749	+	179.247i	0.359469	+	0.556668i
$323$	−353.238	+	353.238i	−1.09362	+	1.09362i
$324$	−174.859	−	272.764i	−0.539688	−	0.841865i
$325$	−293.508	+	293.508i	−0.903103	+	0.903103i
$326$	143.561	+	30.9015i	0.440371	+	0.0947900i
$327$	114.685	−	192.686i	0.350717	−	0.589255i
$328$	−30.5830	−	203.247i	−0.0932409	−	0.619656i
$329$	−183.265			−0.557036
$330$	−15.3146	+	16.4757i	−0.0464077	+	0.0499264i
$331$	−269.431	+	269.431i	−0.813992	+	0.813992i	−0.985230	−	0.171238i	$-0.945223\pi$
$331$	−269.431	+	269.431i	−0.813992	+	0.813992i	0.171238	+	0.985230i	$0.445223\pi$
$332$	−75.7359	−	200.378i	−0.228120	−	0.603549i
$333$	−2.79147	+	9.41106i	−0.00838279	+	0.0282614i
$334$	−96.6640	+	62.4209i	−0.289413	+	0.186889i
$335$		−	33.6557i		−	0.100465i
$336$	144.476	+	98.7434i	0.429989	+	0.293879i
$337$	143.041			0.424453			0.212226	−	0.977221i	$-0.431929\pi$
$337$	143.041			0.424453			0.212226	+	0.977221i	$0.431929\pi$
$338$	282.084	+	436.830i	0.834567	+	1.29240i
$339$	213.739	−	54.2406i	0.630497	−	0.160002i
$340$	−88.4131	−	233.919i	−0.260038	−	0.687997i
$341$	−13.8628	−	13.8628i	−0.0406534	−	0.0406534i
$342$	−307.387	+	90.0681i	−0.898793	+	0.263357i
$343$			308.826i			0.900368i
$344$	369.359	+	272.741i	1.07372	+	0.792851i
$345$	99.9916	−	168.000i	0.289831	−	0.486957i
$346$	−67.0183	+	311.350i	−0.193694	+	0.899856i
$347$	126.922	+	126.922i	0.365770	+	0.365770i	0.865932	−	0.500162i	$-0.166726\pi$
$347$	126.922	+	126.922i	0.365770	+	0.365770i	−0.500162	+	0.865932i	$0.666726\pi$
$348$	269.256	−	188.144i	0.773723	−	0.540645i
$349$	195.893	+	195.893i	0.561297	+	0.561297i	0.929676	−	0.368378i	$-0.120087\pi$
$349$	195.893	+	195.893i	0.561297	+	0.561297i	−0.368378	+	0.929676i	$0.620087\pi$
$350$	122.756	−	79.2697i	0.350731	−	0.226485i
$351$	−22.2653	+	558.787i	−0.0634340	+	1.59198i
$352$	26.3320	+	46.9961i	0.0748069	+	0.133512i
$353$		−	291.488i		−	0.825745i	−0.910789	−	0.412873i	$-0.864525\pi$
$353$		−	291.488i		−	0.825745i	0.910789	−	0.412873i	$-0.135475\pi$
$354$	−7.04714	−	192.939i	−0.0199072	−	0.545027i
$355$	192.251	+	192.251i	0.541552	+	0.541552i
$356$	−8.97839	+	19.8894i	−0.0252202	+	0.0558691i
$357$	−75.5233	−	297.604i	−0.211550	−	0.833626i
$358$	−13.3804	+	62.1621i	−0.0373755	+	0.173637i
$359$	−40.3499			−0.112395			−0.0561976	−	0.998420i	$-0.517898\pi$
$359$	−40.3499			−0.112395			−0.0561976	+	0.998420i	$0.517898\pi$
$360$	22.2156	−	158.797i	0.0617101	−	0.441102i
$361$		−	44.3360i		−	0.122814i
$362$	−11.0713	+	51.4344i	−0.0305836	+	0.142084i
$363$	343.607	−	87.1973i	0.946575	−	0.240213i
$364$	−106.790	−	282.539i	−0.293378	−	0.776205i
$365$	23.6846	−	23.6846i	0.0648893	−	0.0648893i
$366$	3.95551	+	108.295i	0.0108074	+	0.295889i
$367$	340.678			0.928279			0.464140	−	0.885762i	$-0.346364\pi$
$367$	340.678			0.928279			0.464140	+	0.885762i	$0.346364\pi$
$368$	−309.691	−	351.156i	−0.841551	−	0.954229i
$369$	−203.247	+	110.257i	−0.550805	+	0.298799i
$370$	−4.08104	+	2.63533i	−0.0110298	+	0.00712253i
$371$	168.572	−	168.572i	0.454372	−	0.454372i
$372$	137.602	+	24.4012i	0.369898	+	0.0655945i
$373$	237.678	−	237.678i	0.637207	−	0.637207i	−0.312658	−	0.949866i	$-0.601219\pi$
$373$	237.678	−	237.678i	0.637207	−	0.637207i	0.949866	+	0.312658i	$0.101219\pi$
$374$	19.8894	−	92.4012i	0.0531802	−	0.247062i
$375$	−258.579	−	153.903i	−0.689544	−	0.410409i
$376$	397.668	−	59.8379i	1.05763	−	0.159143i
$377$	−566.957			−1.50386
$378$	49.0575	−	190.660i	0.129782	−	0.504393i
$379$	320.332	−	320.332i	0.845203	−	0.845203i	−0.144327	−	0.989530i	$-0.546102\pi$
$379$	320.332	−	320.332i	0.845203	−	0.845203i	0.989530	+	0.144327i	$0.0461017\pi$
$380$	−144.479	−	65.2201i	−0.380208	−	0.171632i
$381$	54.5570	+	214.985i	0.143194	+	0.564266i
$382$	207.956	+	322.037i	0.544386	+	0.843028i
$383$		−	632.700i		−	1.65196i	−0.563702	−	0.825978i	$-0.690623\pi$
$383$		−	632.700i		−	1.65196i	0.563702	−	0.825978i	$-0.309377\pi$
$384$	−345.741	−	167.091i	−0.900366	−	0.435133i
$385$	−13.6680			−0.0355012
$386$	81.7010	−	52.7585i	0.211661	−	0.136680i
$387$	146.888	−	495.212i	0.379555	−	1.27962i
$388$	−133.579	+	295.911i	−0.344276	+	0.762657i
$389$	424.351	+	424.351i	1.09088	+	1.09088i	0.995435	+	0.0954418i	$0.0304264\pi$
$389$	424.351	+	424.351i	1.09088	+	1.09088i	0.0954418	+	0.995435i	$0.469574\pi$
$390$	−188.422	+	202.708i	−0.483134	+	0.519765i
$391$			821.490i			2.10100i
$392$	−42.5065	−	282.488i	−0.108435	−	0.720632i
$393$	577.595	+	343.778i	1.46971	+	0.874752i
$394$	376.767	+	81.0993i	0.956262	+	0.205836i
$395$	80.9323	+	80.9323i	0.204892	+	0.204892i
$396$	39.6130	−	45.8656i	0.100033	−	0.115822i
$397$	−445.678	−	445.678i	−1.12262	−	1.12262i	−0.991347	−	0.131269i	$-0.958095\pi$
$397$	−445.678	−	445.678i	−1.12262	−	1.12262i	−0.131269	−	0.991347i	$-0.541905\pi$
$398$	−157.066	−	243.230i	−0.394638	−	0.611130i
$399$	−167.247	−	99.5434i	−0.419166	−	0.249482i
$400$	−240.486	+	212.089i	−0.601216	+	0.530222i
$401$		−	555.896i		−	1.38627i	−0.720806	−	0.693137i	$-0.756228\pi$
$401$		−	555.896i		−	1.38627i	0.720806	−	0.693137i	$-0.243772\pi$
$402$	3.30975	+	90.6156i	0.00823321	+	0.225412i
$403$	−170.561	−	170.561i	−0.423228	−	0.423228i
$404$	−171.708	+	64.8996i	−0.425020	+	0.160643i
$405$	−176.472	+	37.3738i	−0.435733	+	0.0922811i
$406$	195.122	+	42.0000i	0.480595	+	0.103448i
$407$	−1.83614			−0.00451140
$408$	261.049	+	621.115i	0.639827	+	1.52234i
$409$		−	44.8261i		−	0.109599i	−0.998497	−	0.0547997i	$-0.982548\pi$
$409$		−	44.8261i		−	0.109599i	0.998497	−	0.0547997i	$-0.0174520\pi$
$410$	−111.869	−	24.0798i	−0.272851	−	0.0587313i
$411$	74.3337	+	292.917i	0.180861	+	0.712693i
$412$	186.620	+	84.2431i	0.452960	+	0.204474i
$413$	82.9529	−	82.9529i	0.200854	−	0.200854i
$414$	−252.698	+	462.161i	−0.610383	+	1.11633i
$415$	−119.263			−0.287380
$416$	323.975	+	578.215i	0.778786	+	1.38994i
$417$	66.6196	+	39.6512i	0.159759	+	0.0950868i
$418$	−32.5020	−	50.3320i	−0.0777559	−	0.120412i
$419$	−15.2026	+	15.2026i	−0.0362830	+	0.0362830i	−0.725016	−	0.688733i	$-0.758167\pi$
$419$	−15.2026	+	15.2026i	−0.0362830	+	0.0362830i	0.688733	+	0.725016i	$0.258167\pi$
$420$	79.8632	−	55.8050i	0.190150	−	0.132869i
$421$	262.889	−	262.889i	0.624439	−	0.624439i	−0.322224	−	0.946663i	$-0.604431\pi$
$421$	262.889	−	262.889i	0.624439	−	0.624439i	0.946663	+	0.322224i	$0.104431\pi$
$422$	−542.938	−	116.868i	−1.28658	−	0.276938i
$423$	−215.726	−	397.668i	−0.509990	−	0.940113i
$424$	−310.745	+	420.826i	−0.732889	+	0.992514i
$425$	562.590			1.32374
$426$	−536.528	−	498.715i	−1.25945	−	1.17069i
$427$	−46.5608	+	46.5608i	−0.109042	+	0.109042i
$428$	452.263	−	170.940i	1.05669	−	0.399391i
$429$	−101.390	+	25.7298i	−0.236340	+	0.0599762i
$430$	214.745	−	138.672i	0.499407	−	0.322493i
$431$		−	163.103i		−	0.378430i	−0.981936	−	0.189215i	$-0.939406\pi$
$431$		−	163.103i		−	0.378430i	0.981936	−	0.189215i	$-0.0605943\pi$
$432$	−44.1977	+	429.733i	−0.102309	+	0.994753i
$433$	−140.737			−0.325028			−0.162514	−	0.986706i	$-0.551960\pi$
$433$	−140.737			−0.325028			−0.162514	+	0.986706i	$0.551960\pi$
$434$	46.0644	+	71.3346i	0.106139	+	0.164366i
$435$	−44.9833	−	177.260i	−0.103410	−	0.407494i
$436$	−279.668	+	105.705i	−0.641440	+	0.242442i
$437$	368.217	+	368.217i	0.842601	+	0.842601i
$438$	−61.4398	+	66.0982i	−0.140274	+	0.150909i
$439$		−	434.893i		−	0.990644i	−0.868709	−	0.495322i	$-0.835050\pi$
$439$		−	434.893i		−	0.990644i	0.868709	−	0.495322i	$-0.164950\pi$
$440$	29.6582	−	4.46274i	0.0674051	−	0.0101426i
$441$	−282.488	+	153.243i	−0.640562	+	0.347490i
$442$	244.708	−	1136.85i	0.553639	−	2.57207i
$443$	260.367	+	260.367i	0.587736	+	0.587736i	0.937018	−	0.349282i	$-0.113574\pi$
$443$	260.367	+	260.367i	0.587736	+	0.587736i	−0.349282	+	0.937018i	$0.613574\pi$
$444$	10.7287	−	7.49678i	0.0241638	−	0.0168846i
$445$	8.59088	+	8.59088i	0.0193053	+	0.0193053i
$446$	−630.492	+	407.141i	−1.41366	+	0.912873i
$447$	97.5869	−	163.960i	0.218315	−	0.366801i
$448$	−68.6640	−	222.996i	−0.153268	−	0.497759i
$449$		−	98.9506i		−	0.220380i	−0.993911	−	0.110190i	$-0.964854\pi$
$449$		−	98.9506i		−	0.220380i	0.993911	−	0.110190i	$-0.0351459\pi$
$450$	316.507	+	173.058i	0.703348	+	0.384574i
$451$	−30.5830	−	30.5830i	−0.0678115	−	0.0678115i
$452$	−267.979	−	120.970i	−0.592874	−	0.267633i
$453$	−81.7195	+	20.7380i	−0.180396	+	0.0457793i
$454$	−107.793	+	500.782i	−0.237431	+	1.10304i
$455$	−168.164			−0.369590
$456$	395.413	+	161.392i	0.867133	+	0.353930i
$457$		−	14.4209i		−	0.0315556i	−0.999876	−	0.0157778i	$-0.994978\pi$
$457$		−	14.4209i		−	0.0315556i	0.999876	−	0.0157778i	$-0.00502245\pi$
$458$	−91.6216	+	425.651i	−0.200047	+	0.929369i
$459$	556.873	−	514.196i	1.21323	−	1.12025i
$460$	−243.838	+	92.1621i	−0.530082	+	0.200352i
$461$	−328.278	+	328.278i	−0.712099	+	0.712099i	−0.966974	−	0.254875i	$-0.917966\pi$
$461$	−328.278	+	328.278i	−0.712099	+	0.712099i	0.254875	+	0.966974i	$0.417966\pi$
$462$	36.8000	−	1.34413i	0.0796537	−	0.00290936i
$463$	−848.427			−1.83246			−0.916228	−	0.400657i	$-0.868782\pi$
$463$	−848.427			−1.83246			−0.916228	+	0.400657i	$0.868782\pi$
$464$	−437.109	−	27.4269i	−0.942045	−	0.0591096i
$465$	39.7935	−	66.8587i	0.0855774	−	0.143782i
$466$	86.9961	−	56.1778i	0.186687	−	0.120553i
$467$	−56.0706	+	56.0706i	−0.120066	+	0.120066i	−0.764587	−	0.644521i	$-0.777057\pi$
$467$	−56.0706	+	56.0706i	−0.120066	+	0.120066i	0.644521	+	0.764587i	$0.277057\pi$
$468$	487.378	−	564.306i	1.04141	−	1.20578i
$469$	−38.9595	+	38.9595i	−0.0830693	+	0.0830693i
$470$	47.1140	−	218.880i	0.100242	−	0.465702i
$471$	−375.970	+	631.682i	−0.798237	+	1.34115i
$472$	−152.915	+	207.085i	−0.323973	+	0.438739i
$473$	96.6181			0.204267
$474$	−225.863	−	209.945i	−0.476505	−	0.442922i
$475$	252.170	−	252.170i	0.530884	−	0.530884i
$476$	−168.436	+	373.128i	−0.353857	+	0.783881i
$477$	564.216	+	167.355i	1.18284	+	0.350850i
$478$	−271.129	−	419.867i	−0.567216	−	0.878382i
$479$			648.794i			1.35448i	0.735764	+	0.677238i	$0.236823\pi$
$479$			648.794i			1.35448i	−0.735764	+	0.677238i	$0.763177\pi$
$480$	−155.075	+	147.168i	−0.323073	+	0.306600i
$481$	−22.5909			−0.0469665
$482$	743.514	−	480.125i	1.54256	−	0.996110i
$483$	−310.224	+	78.7257i	−0.642285	+	0.162993i
$484$	−430.804	−	194.472i	−0.890091	−	0.401801i
$485$	127.814	+	127.814i	0.263533	+	0.263533i
$486$	471.462	−	117.981i	0.970087	−	0.242759i
$487$			176.783i			0.363004i	0.983391	+	0.181502i	$0.0580959\pi$
$487$			176.783i			0.363004i	−0.983391	+	0.181502i	$0.941904\pi$
$488$	85.8300	−	116.235i	0.175881	−	0.238187i
$489$	−112.659	+	189.284i	−0.230387	+	0.387083i
$490$	−155.484	−	33.4679i	−0.317314	−	0.0683019i
$491$	317.369	+	317.369i	0.646373	+	0.646373i	0.952114	−	0.305742i	$-0.0989044\pi$
$491$	317.369	+	317.369i	0.646373	+	0.646373i	−0.305742	+	0.952114i	$0.598904\pi$
$492$	303.567	+	53.8318i	0.617005	+	0.109414i
$493$	543.365	+	543.365i	1.10216	+	1.10216i
$494$	−399.887	−	619.258i	−0.809488	−	1.25356i
$495$	−16.0889	−	29.6582i	−0.0325029	−	0.0599156i
$496$	−123.247	−	139.749i	−0.248482	−	0.281752i
$497$		−	445.095i		−	0.895563i
$498$	321.106	−	11.7285i	0.644791	−	0.0235511i
$499$	−374.391	−	374.391i	−0.750282	−	0.750282i	0.224250	−	0.974532i	$-0.428007\pi$
$499$	−374.391	−	374.391i	−0.750282	−	0.750282i	−0.974532	+	0.224250i	$0.928007\pi$
$500$	141.852	+	375.306i	0.283705	+	0.750612i
$501$	−42.4551	−	167.297i	−0.0847407	−	0.333926i
$502$	−119.793	−	25.7856i	−0.238632	−	0.0513657i
$503$	−386.094			−0.767583			−0.383791	−	0.923420i	$-0.625382\pi$
$503$	−386.094			−0.767583			−0.383791	+	0.923420i	$0.625382\pi$
$504$	−209.538	+	158.105i	−0.415750	+	0.313700i
$505$			102.199i			0.202374i
$506$	−96.3193	−	20.7328i	−0.190354	−	0.0409739i
$507$	−756.024	+	191.857i	−1.49117	+	0.378416i
$508$	121.676	−	269.542i	0.239519	−	0.530595i
$509$	−41.6258	+	41.6258i	−0.0817796	+	0.0817796i	−0.746813	−	0.665034i	$-0.768417\pi$
$509$	−41.6258	+	41.6258i	−0.0817796	+	0.0817796i	0.665034	+	0.746813i	$0.268417\pi$
$510$	374.855	−	13.6916i	0.735010	−	0.0268463i
$511$	−54.8340			−0.107307
$512$	221.805	+	461.461i	0.433213	+	0.901291i
$513$	19.1294	−	480.086i	0.0372893	−	0.935839i
$514$	194.421	+	301.077i	0.378251	+	0.585753i
$515$	80.6071	−	80.6071i	0.156519	−	0.156519i
$516$	−564.548	+	394.482i	−1.09408	+	0.764500i
$517$	59.8379	−	59.8379i	0.115741	−	0.115741i
$518$	7.77479	+	1.67353i	0.0150092	+	0.00323075i
$519$	−410.512	−	244.332i	−0.790968	−	0.470775i
$520$	364.899	−	54.9072i	0.701729	−	0.105591i
$521$	−233.704			−0.448569			−0.224284	−	0.974524i	$-0.572004\pi$
$521$	−233.704			−0.448569			−0.224284	+	0.974524i	$0.572004\pi$
$522$	138.546	+	472.835i	0.265414	+	0.905814i
$523$	−219.506	+	219.506i	−0.419705	+	0.419705i	−0.885102	−	0.465397i	$-0.845912\pi$
$523$	−219.506	+	219.506i	−0.419705	+	0.419705i	0.465397	+	0.885102i	$0.345912\pi$
$524$	−316.859	−	838.331i	−0.604693	−	1.59987i
$525$	53.9146	+	212.454i	0.102694	+	0.404674i
$526$	704.782	−	455.114i	1.33989	−	0.865235i
$527$			326.927i			0.620355i
$528$	−79.4137	+	14.9322i	−0.150405	+	0.0282807i
$529$	327.324			0.618760
$530$	157.995	+	244.668i	0.298103	+	0.461638i
$531$	277.646	+	82.3542i	0.522873	+	0.155093i
$532$	91.7490	+	242.745i	0.172461	+	0.456288i
$533$	−376.277	−	376.277i	−0.705961	−	0.705961i
$534$	−23.9751	−	22.2855i	−0.0448973	−	0.0417331i
$535$		−	269.182i		−	0.503143i
$536$	71.8178	−	97.2591i	0.133988	−	0.181454i
$537$	−81.9601	−	48.7817i	−0.152626	−	0.0908411i
$538$	−20.0954	+	93.3582i	−0.0373520	+	0.173528i
$539$	−42.5065	−	42.5065i	−0.0788618	−	0.0788618i
$540$	215.101	+	107.606i	0.398334	+	0.199271i
$541$	80.5203	+	80.5203i	0.148836	+	0.148836i	0.777598	−	0.628762i	$-0.216438\pi$
$541$	80.5203	+	80.5203i	0.148836	+	0.148836i	−0.628762	+	0.777598i	$0.716438\pi$
$542$	553.219	−	357.242i	1.02070	−	0.659118i
$543$	−67.8157	−	40.3631i	−0.124891	−	0.0743335i
$544$	243.660	−	864.648i	0.447905	−	1.58943i
$545$			166.455i			0.305422i
$546$	452.768	−	16.5374i	0.829245	−	0.0302883i
$547$	1.49803	+	1.49803i	0.00273863	+	0.00273863i	0.708475	−	0.705736i	$-0.249384\pi$
$547$	1.49803	+	1.49803i	0.00273863	+	0.00273863i	−0.705736	+	0.708475i	$0.749384\pi$
$548$	165.783	−	367.250i	0.302523	−	0.670165i
$549$	−155.840	−	46.2247i	−0.283862	−	0.0841981i
$550$	−14.1987	+	65.9634i	−0.0258157	+	0.119933i
$551$	487.105			0.884038
$552$	647.452	−	272.119i	1.17292	−	0.492969i
$553$		−	187.373i		−	0.338829i
$554$	149.550	−	694.773i	0.269946	−	1.25410i
$555$	−1.79240	−	7.06307i	−0.00322955	−	0.0127263i
$556$	−36.5464	−	96.6927i	−0.0657310	−	0.173908i
$557$	322.326	−	322.326i	0.578682	−	0.578682i	−0.355858	−	0.934540i	$-0.615811\pi$
$557$	322.326	−	322.326i	0.578682	−	0.578682i	0.934540	+	0.355858i	$0.115811\pi$
$558$	−100.566	+	183.925i	−0.180226	+	0.329615i
$559$	1188.74			2.12654
$560$	−129.650	−	8.13502i	−0.231518	−	0.0145268i
$561$	121.830	+	72.5118i	0.217166	+	0.129255i
$562$	−288.664	+	186.405i	−0.513637	+	0.331682i
$563$	−523.954	+	523.954i	−0.930646	+	0.930646i	−0.997746	−	0.0671003i	$-0.978625\pi$
$563$	−523.954	+	523.954i	−0.930646	+	0.930646i	0.0671003	+	0.997746i	$0.478625\pi$
$564$	−105.326	+	593.951i	−0.186748	+	1.05310i
$565$	−115.749	+	115.749i	−0.204866	+	0.204866i
$566$	−115.154	+	534.979i	−0.203453	+	0.945193i
$567$	247.545	+	161.018i	0.436588	+	0.283983i
$568$	145.328	+	965.814i	0.255859	+	1.70038i
$569$	767.880			1.34952			0.674762	−	0.738035i	$-0.264246\pi$
$569$	767.880			1.34952			0.674762	+	0.738035i	$0.264246\pi$
$570$	161.884	−	174.158i	0.284007	−	0.305541i
$571$	−3.43922	+	3.43922i	−0.00602316	+	0.00602316i	−0.710112	−	0.704089i	$-0.751356\pi$
$571$	−3.43922	+	3.43922i	−0.00602316	+	0.00602316i	0.704089	+	0.710112i	$0.251356\pi$
$572$	127.120	+	57.3839i	0.222237	+	0.100321i
$573$	−557.350	+	141.439i	−0.972688	+	0.246840i
$574$	101.624	+	157.373i	0.177044	+	0.274168i
$575$		−	586.446i		−	1.01991i
$576$	403.055	−	411.489i	0.699748	−	0.714390i
$577$	−572.442			−0.992100			−0.496050	−	0.868294i	$-0.665217\pi$
$577$	−572.442			−0.992100			−0.496050	+	0.868294i	$0.665217\pi$
$578$	−838.514	+	541.471i	−1.45072	+	0.936801i
$579$	35.8833	+	141.400i	0.0619746	+	0.244215i
$580$	−100.324	+	222.243i	−0.172973	+	0.383178i
$581$	138.057	+	138.057i	0.237620	+	0.237620i
$582$	−356.698	−	331.559i	−0.612883	−	0.569690i
$583$			110.081i			0.188818i
$584$	118.985	−	17.9039i	0.203741	−	0.0306573i
$585$	−197.949	−	364.899i	−0.338375	−	0.623759i
$586$	−203.217	−	43.7425i	−0.346787	−	0.0746460i
$587$	−446.694	−	446.694i	−0.760977	−	0.760977i	0.215522	−	0.976499i	$-0.430855\pi$
$587$	−446.694	−	446.694i	−0.760977	−	0.760977i	−0.976499	+	0.215522i	$0.930855\pi$
$588$	421.919	+	74.8194i	0.717550	+	0.127244i
$589$	146.539	+	146.539i	0.248792	+	0.248792i
$590$	77.7479	+	120.399i	0.131776	+	0.204066i
$591$	−295.668	+	496.764i	−0.500284	+	0.840548i
$592$	−17.4170	−	1.09285i	−0.0294206	−	0.00184603i
$593$			838.112i			1.41334i	0.707542	+	0.706671i	$0.249804\pi$
$593$			838.112i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$594$	46.2348	+	78.2704i	0.0778364	+	0.131768i
$595$	161.166	+	161.166i	0.270867	+	0.270867i
$596$	−237.974	+	89.9457i	−0.399285	+	0.150916i
$597$	420.959	−	106.827i	0.705123	−	0.178940i
$598$	−1185.06	−	255.085i	−1.98171	−	0.426564i
$599$	414.241			0.691555			0.345777	−	0.938317i	$-0.387615\pi$
$599$	414.241			0.691555			0.345777	+	0.938317i	$0.387615\pi$
$600$	−186.358	−	443.402i	−0.310597	−	0.739003i
$601$			305.786i			0.508795i	0.967100	+	0.254397i	$0.0818771\pi$
$601$			305.786i			0.508795i	−0.967100	+	0.254397i	$0.918123\pi$
$602$	−409.111	−	88.0614i	−0.679587	−	0.146281i
$603$	−130.399	−	38.6783i	−0.216250	−	0.0641431i
$604$	102.458	+	46.2510i	0.169632	+	0.0765745i
$605$	−186.078	+	186.078i	−0.307567	+	0.307567i
$606$	−10.0503	−	275.162i	−0.0165847	−	0.454063i
$607$	−103.217			−0.170044			−0.0850222	−	0.996379i	$-0.527096\pi$
$607$	−103.217			−0.170044			−0.0850222	+	0.996379i	$0.527096\pi$
$608$	−278.346	−	496.777i	−0.457805	−	0.817068i
$609$	−153.122	+	257.266i	−0.251431	+	0.422440i
$610$	−43.6393	−	67.5791i	−0.0715398	−	0.110785i
$611$	736.214	−	736.214i	1.20493	−	1.20493i
$612$	−1007.92	+	73.7274i	−1.64693	+	0.120470i
$613$	−391.273	+	391.273i	−0.638292	+	0.638292i	−0.950134	−	0.311842i	$-0.899054\pi$
$613$	−391.273	+	391.273i	−0.638292	+	0.638292i	0.311842	+	0.950134i	$0.399054\pi$
$614$	782.674	+	168.471i	1.27471	+	0.274382i
$615$	87.7891	−	147.498i	0.142746	−	0.239834i
$616$	−39.4980	−	29.1660i	−0.0641202	−	0.0473474i
$617$	−713.373			−1.15620			−0.578098	−	0.815967i	$-0.696205\pi$
$617$	−713.373			−1.15620			−0.578098	+	0.815967i	$0.696205\pi$
$618$	−209.102	+	224.956i	−0.338352	+	0.364006i
$619$	−399.763	+	399.763i	−0.645821	+	0.645821i	−0.951980	−	0.306159i	$-0.900956\pi$
$619$	−399.763	+	399.763i	−0.645821	+	0.645821i	0.306159	+	0.951980i	$0.400956\pi$
$620$	−97.0398	+	36.6776i	−0.156516	+	0.0591574i
$621$	−535.999	−	580.487i	−0.863123	−	0.934761i
$622$	90.7895	−	58.6275i	0.145964	−	0.0942564i
$623$		−	19.8894i		−	0.0319252i
$624$	−977.064	+	183.718i	−1.56581	+	0.294420i
$625$	−277.635			−0.444217
$626$	−531.931	−	823.739i	−0.849730	−	1.31588i
$627$	87.1099	−	22.1059i	0.138931	−	0.0352567i
$628$	916.834	−	346.531i	1.45993	−	0.551800i
$629$	21.6508	+	21.6508i	0.0344210	+	0.0344210i
$630$	41.0938	+	140.246i	0.0652283	+	0.222613i
$631$		−	934.242i		−	1.48057i	−0.672291	−	0.740287i	$-0.734690\pi$
$631$		−	934.242i		−	1.48057i	0.672291	−	0.740287i	$-0.265310\pi$
$632$	61.1791	+	406.581i	0.0968024	+	0.643324i
$633$	426.071	−	715.859i	0.673097	−	1.13090i
$634$	−190.192	+	883.586i	−0.299988	+	1.39367i
$635$	−116.424	−	116.424i	−0.183345	−	0.183345i
$636$	−449.450	−	643.213i	−0.706682	−	1.01134i
$637$	−522.978	−	522.978i	−0.821001	−	0.821001i
$638$	−77.4227	+	49.9958i	−0.121352	+	0.0783633i
$639$	965.814	−	523.932i	1.51145	−	0.819925i
$640$	283.984	−	24.6798i	0.443725	−	0.0385622i
$641$			26.1836i			0.0408480i	0.999791	+	0.0204240i	$0.00650162\pi$
$641$			26.1836i			0.0408480i	−0.999791	+	0.0204240i	$0.993498\pi$
$642$	26.4717	+	724.752i	0.0412331	+	1.12890i
$643$	625.336	+	625.336i	0.972529	+	0.972529i	0.999633	−	0.0271039i	$-0.00862850\pi$
$643$	625.336	+	625.336i	0.972529	+	0.972529i	−0.0271039	+	0.999633i	$0.508629\pi$
$644$	388.949	+	175.578i	0.603959	+	0.272637i
$645$	94.3165	+	371.660i	0.146227	+	0.576218i
$646$	−210.243	+	976.737i	−0.325454	+	1.51198i
$647$	97.2591			0.150323			0.0751616	−	0.997171i	$-0.476053\pi$
$647$	97.2591			0.150323			0.0751616	+	0.997171i	$0.476053\pi$
$648$	−589.724	−	268.569i	−0.910069	−	0.414458i
$649$			54.1699i			0.0834668i
$650$	−174.693	+	811.579i	−0.268758	+	1.24858i
$651$	−123.459	+	31.3303i	−0.189645	+	0.0481265i
$652$	274.729	−	103.838i	0.421364	−	0.159261i
$653$	129.213	−	129.213i	0.197875	−	0.197875i	−0.601213	−	0.799089i	$-0.705316\pi$
$653$	129.213	−	129.213i	0.197875	−	0.197875i	0.799089	+	0.601213i	$0.205316\pi$
$654$	−16.3694	−	448.168i	−0.0250297	−	0.685272i
$655$	−498.965			−0.761778
$656$	−271.897	−	308.303i	−0.414478	−	0.469974i
$657$	−64.5464	−	118.985i	−0.0982442	−	0.181103i
$658$	−307.911	+	198.834i	−0.467950	+	0.302179i
$659$	3.10975	−	3.10975i	0.00471889	−	0.00471889i	−0.704743	−	0.709462i	$-0.748938\pi$
$659$	3.10975	−	3.10975i	0.00471889	−	0.00471889i	0.709462	+	0.704743i	$0.248938\pi$
$660$	−7.85525	+	44.2971i	−0.0119019	+	0.0671168i
$661$	−22.3424	+	22.3424i	−0.0338010	+	0.0338010i	−0.723805	−	0.690004i	$-0.757609\pi$
$661$	−22.3424	+	22.3424i	−0.0338010	+	0.0338010i	0.690004	+	0.723805i	$0.257609\pi$
$662$	−160.362	+	745.003i	−0.242239	+	1.12538i
$663$	1498.93	+	892.146i	2.26083	+	1.34562i
$664$	−344.648	−	254.494i	−0.519049	−	0.383274i
$665$	144.479			0.217262
$666$	5.52050	+	18.8405i	0.00828903	+	0.0282891i
$667$	566.405	−	566.405i	0.849183	−	0.849183i
$668$	−94.6855	+	209.752i	−0.141745	+	0.314000i
$669$	−276.914	−	1091.20i	−0.413922	−	1.63109i
$670$	−36.5149	−	56.5464i	−0.0544999	−	0.0843976i
$671$		−	30.4052i		−	0.0453132i
$672$	349.872	+	9.15299i	0.520643	+	0.0136205i
$673$	1085.74			1.61329			0.806643	−	0.591039i	$-0.201282\pi$
$673$	1085.74			1.61329			0.806643	+	0.591039i	$0.201282\pi$
$674$	240.328	−	155.192i	0.356570	−	0.230256i
$675$	−397.541	+	367.074i	−0.588950	+	0.543814i
$676$	947.881	+	427.889i	1.40219	+	0.632972i
$677$	−813.520	−	813.520i	−1.20165	−	1.20165i	−0.973663	−	0.227991i	$-0.926784\pi$
$677$	−813.520	−	813.520i	−1.20165	−	1.20165i	−0.227991	−	0.973663i	$-0.573216\pi$
$678$	300.263	−	323.028i	0.442865	−	0.476443i
$679$		−	295.911i		−	0.435804i
$680$	−402.338	−	297.093i	−0.591673	−	0.436901i
$681$	−660.276	−	392.988i	−0.969568	−	0.577075i
$682$	−38.3320	−	8.25098i	−0.0562053	−	0.0120982i
$683$	427.362	+	427.362i	0.625713	+	0.625713i	0.946986	−	0.321273i	$-0.104111\pi$
$683$	427.362	+	427.362i	0.625713	+	0.625713i	−0.321273	+	0.946986i	$0.604111\pi$
$684$	−418.734	+	484.828i	−0.612185	+	0.708813i
$685$	−158.627	−	158.627i	−0.231573	−	0.231573i
$686$	335.062	+	518.872i	0.488429	+	0.756373i
$687$	−561.217	−	334.030i	−0.816910	−	0.486215i
$688$	916.486	+	57.5059i	1.33210	+	0.0835842i
$689$			1354.38i			1.96572i
$690$	−14.2722	−	390.750i	−0.0206844	−	0.566304i
$691$	−420.170	−	420.170i	−0.608061	−	0.608061i	0.334378	−	0.942439i	$-0.391474\pi$
$691$	−420.170	−	420.170i	−0.608061	−	0.608061i	−0.942439	+	0.334378i	$0.891474\pi$
$692$	225.200	+	595.824i	0.325434	+	0.861018i
$693$	−15.7077	+	52.9563i	−0.0226662	+	0.0764161i
$694$	350.952	+	75.5425i	0.505694	+	0.108851i
$695$	−57.5504			−0.0828063
$696$	248.260	−	608.239i	0.356695	−	0.873906i
$697$			721.239i			1.03478i
$698$	541.662	+	116.593i	0.776020	+	0.167039i
$699$	38.2089	+	150.565i	0.0546622	+	0.215400i
$700$	120.243	−	266.369i	0.171776	−	0.380527i
$701$	774.018	−	774.018i	1.10416	−	1.10416i	0.110260	−	0.993903i	$-0.464832\pi$
$701$	774.018	−	774.018i	1.10416	−	1.10416i	0.993903	−	0.110260i	$-0.0351684\pi$
$702$	568.849	+	962.997i	0.810326	+	1.37179i
$703$	19.4091			0.0276090
$704$	95.2301	+	50.3910i	0.135270	+	0.0715781i
$705$	288.591	+	171.766i	0.409349	+	0.243639i
$706$	−316.251	−	489.741i	−0.447948	−	0.693684i
$707$	118.304	−	118.304i	0.167332	−	0.167332i
$708$	−221.171	−	316.520i	−0.312388	−	0.447062i
$709$	198.261	−	198.261i	0.279635	−	0.279635i	−0.553328	−	0.832963i	$-0.686642\pi$
$709$	198.261	−	198.261i	0.279635	−	0.279635i	0.832963	+	0.553328i	$0.186642\pi$
$710$	531.592	+	114.425i	0.748722	+	0.161163i
$711$	406.581	−	220.561i	0.571844	−	0.310212i
$712$	6.49409	+	43.1581i	0.00912092	+	0.0606154i
$713$	340.790			0.477966
$714$	−449.777	−	418.078i	−0.629939	−	0.585544i
$715$	54.9072	−	54.9072i	0.0767932	−	0.0767932i
$716$	44.9620	+	118.958i	0.0627961	+	0.166143i
$717$	726.665	−	184.406i	1.01348	−	0.257192i
$718$	−67.7935	+	43.7777i	−0.0944199	+	0.0609718i
$719$			639.218i			0.889037i	0.895770	+	0.444519i	$0.146625\pi$
$719$			639.218i			0.889037i	−0.895770	+	0.444519i	$0.853375\pi$
$720$	−134.962	−	290.904i	−0.187447	−	0.404033i
$721$	−186.620			−0.258834
$722$	−48.1025	−	74.4907i	−0.0666239	−	0.103173i
$723$	326.553	+	1286.80i	0.451664	+	1.77981i
$724$	37.2026	+	98.4288i	0.0513848	+	0.135951i
$725$	−387.898	−	387.898i	−0.535031	−	0.535031i
$726$	482.703	−	519.301i	0.664880	−	0.715291i
$727$			789.136i			1.08547i	0.839904	+	0.542734i	$0.182611\pi$
$727$			789.136i			1.08547i	−0.839904	+	0.542734i	$0.817389\pi$
$728$	−485.963	−	358.843i	−0.667531	−	0.492916i
$729$	−58.0032	+	726.689i	−0.0795654	+	0.996830i
$730$	14.0968	−	65.4902i	0.0193107	−	0.0897125i
$731$	−1139.27	−	1139.27i	−1.55851	−	1.55851i
$732$	124.141	+	177.660i	0.169592	+	0.242705i
$733$	−49.8641	−	49.8641i	−0.0680274	−	0.0680274i	0.672275	−	0.740302i	$-0.265317\pi$
$733$	−49.8641	−	49.8641i	−0.0680274	−	0.0680274i	−0.740302	+	0.672275i	$0.765317\pi$
$734$	572.388	−	369.620i	0.779820	−	0.503570i
$735$	122.016	−	205.004i	0.166008	−	0.278917i
$736$	−901.312	−	253.992i	−1.22461	−	0.345098i
$737$		−	25.4414i		−	0.0345202i
$738$	−221.860	+	405.761i	−0.300624	+	0.549811i
$739$	157.593	+	157.593i	0.213252	+	0.213252i	0.805647	−	0.592395i	$-0.201818\pi$
$739$	157.593	+	157.593i	0.213252	+	0.213252i	−0.592395	+	0.805647i	$0.701818\pi$
$740$	−3.99750	+	8.85547i	−0.00540203	+	0.0119669i
$741$	1071.75	−	271.980i	1.44636	−	0.367044i
$742$	100.332	−	466.118i	0.135218	−	0.628191i
$743$	−1305.03			−1.75643			−0.878216	−	0.478265i	$-0.841266\pi$
$743$	−1305.03			−1.75643			−0.878216	+	0.478265i	$0.841266\pi$
$744$	257.665	−	108.295i	0.346324	−	0.145557i
$745$			141.639i			0.190120i
$746$	141.463	−	657.203i	0.189629	−	0.880970i
$747$	−137.061	+	462.082i	−0.183482	+	0.618583i
$748$	−66.8340	−	176.826i	−0.0893503	−	0.236399i
$749$	−311.601	+	311.601i	−0.416023	+	0.416023i
$750$	−601.427	+	21.9672i	−0.801903	+	0.0292896i
$751$	793.800			1.05699			0.528495	−	0.848936i	$-0.322756\pi$
$751$	793.800			1.05699			0.528495	+	0.848936i	$0.322756\pi$
$752$	603.217	−	531.987i	0.802150	−	0.707430i
$753$	94.0079	−	157.947i	0.124844	−	0.209756i
$754$	−952.567	+	615.122i	−1.26335	+	0.815811i
$755$	44.2548	−	44.2548i	0.0586156	−	0.0586156i
$756$	−124.434	−	373.562i	−0.164595	−	0.494129i
$757$	−750.497	+	750.497i	−0.991409	+	0.991409i	−0.999963	−	0.00855438i	$-0.997277\pi$
$757$	−750.497	+	750.497i	−0.991409	+	0.991409i	0.00855438	+	0.999963i	$0.497277\pi$
$758$	190.658	−	885.749i	0.251527	−	1.16853i
$759$	75.5865	−	126.996i	0.0995870	−	0.167320i
$760$	−313.506	+	47.1739i	−0.412508	+	0.0620709i
$761$	−1055.45			−1.38692			−0.693462	−	0.720493i	$-0.743916\pi$
$761$	−1055.45			−1.38692			−0.693462	+	0.720493i	$0.743916\pi$
$762$	324.913	+	302.014i	0.426395	+	0.396344i
$763$	192.686	−	192.686i	0.252538	−	0.252538i
$764$	698.790	+	315.445i	0.914646	+	0.412886i
$765$	−160.003	+	539.428i	−0.209154	+	0.705134i
$766$	−686.450	−	1063.02i	−0.896148	−	1.38776i
$767$			666.478i			0.868942i
$768$	−762.179	+	94.3759i	−0.992421	+	0.122885i
$769$	883.681			1.14913			0.574565	−	0.818459i	$-0.305171\pi$
$769$	883.681			1.14913			0.574565	+	0.818459i	$0.305171\pi$
$770$	−22.9641	+	14.8291i	−0.0298236	+	0.0192586i
$771$	−521.076	+	132.234i	−0.675844	+	0.171509i
$772$	80.0287	−	177.284i	0.103664	−	0.229642i
$773$	−894.518	−	894.518i	−1.15720	−	1.15720i	−0.985074	−	0.172129i	$-0.944935\pi$
$773$	−894.518	−	894.518i	−1.15720	−	1.15720i	−0.172129	−	0.985074i	$-0.555065\pi$
$774$	−290.490	−	991.392i	−0.375310	−	1.28087i
$775$		−	233.387i		−	0.301144i
$776$	96.6181	+	642.100i	0.124508	+	0.827448i
$777$	−6.10126	+	10.2510i	−0.00785233	+	0.0131930i
$778$	1173.37	+	252.569i	1.50819	+	0.324638i
$779$	323.281	+	323.281i	0.414995	+	0.414995i
$780$	−96.6468	+	545.008i	−0.123906	+	0.698728i
$781$	145.328	+	145.328i	0.186079	+	0.186079i
$782$	891.279	+	1380.22i	1.13974	+	1.76499i
$783$	−738.486	−	29.4256i	−0.943150	−	0.0375806i
$784$	−377.903	−	428.502i	−0.482019	−	0.546559i
$785$		−	545.689i		−	0.695145i
$786$	1343.42	−	49.0688i	1.70919	−	0.0624285i
$787$	−779.150	−	779.150i	−0.990026	−	0.990026i	0.00992500	−	0.999951i	$-0.496841\pi$
$787$	−779.150	−	779.150i	−0.990026	−	0.990026i	−0.999951	+	0.00992500i	$0.996841\pi$
$788$	721.011	−	272.517i	0.914989	−	0.345833i
$789$	309.542	+	1219.77i	0.392322	+	1.54597i
$790$	223.786	+	48.1699i	0.283273	+	0.0609746i
$791$	267.979			0.338785
$792$	16.7934	−	120.039i	0.0212038	−	0.151565i
$793$		−	374.089i		−	0.471739i
$794$	−1232.34	−	265.262i	−1.55207	−	0.334084i
$795$	−423.448	+	107.459i	−0.532639	+	0.135168i
$796$	−527.786	−	238.251i	−0.663047	−	0.299310i
$797$	−149.801	+	149.801i	−0.187956	+	0.187956i	−0.794812	−	0.606856i	$-0.792430\pi$
$797$	−149.801	+	149.801i	−0.187956	+	0.187956i	0.606856	+	0.794812i	$0.292430\pi$
$798$	−388.999	+	14.2082i	−0.487467	+	0.0178048i
$799$	−1411.16			−1.76616
$800$	−173.944	+	617.256i	−0.217430	+	0.771570i
$801$	43.1581	−	23.4123i	0.0538803	−	0.0292288i
$802$	−603.122	−	933.984i	−0.752022	−	1.16457i
$803$	17.9039	−	17.9039i	0.0222962	−	0.0222962i
$804$	103.875	+	148.656i	0.129197	+	0.184896i
$805$	168.000	−	168.000i	0.208696	−	0.208696i
$806$	−471.617	−	101.516i	−0.585132	−	0.125950i
$807$	−123.092	−	73.2628i	−0.152530	−	0.0907841i
$808$	−218.081	+	295.336i	−0.269902	+	0.365515i
$809$	373.773			0.462019			0.231009	−	0.972951i	$-0.425797\pi$
$809$	373.773			0.462019			0.231009	+	0.972951i	$0.425797\pi$
$810$	−255.949	+	254.257i	−0.315986	+	0.313898i
$811$	−239.150	+	239.150i	−0.294883	+	0.294883i	−0.839006	−	0.544123i	$-0.816863\pi$
$811$	−239.150	+	239.150i	−0.294883	+	0.294883i	0.544123	+	0.839006i	$0.316863\pi$
$812$	373.400	−	141.132i	0.459852	−	0.173808i
$813$	242.975	+	957.459i	0.298862	+	1.17769i
$814$	−3.08497	+	1.99213i	−0.00378989	+	0.00244733i
$815$		−	163.516i		−	0.200633i
$816$	1112.48	+	760.334i	1.36333	+	0.931782i
$817$	−1021.31			−1.25008
$818$	−48.6343	−	75.3142i	−0.0594551	−	0.0920712i
$819$	−193.259	+	651.547i	−0.235970	+	0.795539i
$820$	−214.081	+	80.9150i	−0.261074	+	0.0986769i
$821$	385.069	+	385.069i	0.469024	+	0.469024i	0.901598	−	0.432574i	$-0.142395\pi$
$821$	385.069	+	385.069i	0.469024	+	0.469024i	−0.432574	+	0.901598i	$0.642395\pi$
$822$	442.692	+	411.493i	0.538555	+	0.500600i
$823$		−	1270.78i		−	1.54408i	−0.635576	−	0.772038i	$-0.719237\pi$
$823$		−	1270.78i		−	1.54408i	0.635576	−	0.772038i	$-0.280763\pi$
$824$	404.947	−	60.9332i	0.491441	−	0.0739481i
$825$	−86.9721	−	51.7648i	−0.105421	−	0.0627452i
$826$	49.3725	−	229.373i	0.0597731	−	0.277691i
$827$	113.766	+	113.766i	0.137565	+	0.137565i	0.772536	−	0.634971i	$-0.218988\pi$
$827$	113.766	+	113.766i	0.137565	+	0.137565i	−0.634971	+	0.772536i	$0.718988\pi$
$828$	76.8537	+	1050.66i	0.0928185	+	1.26891i
$829$	238.593	+	238.593i	0.287809	+	0.287809i	0.836213	−	0.548404i	$-0.184765\pi$
$829$	238.593	+	238.593i	0.287809	+	0.287809i	−0.548404	+	0.836213i	$0.684765\pi$
$830$	−200.378	+	129.395i	−0.241420	+	0.155897i
$831$	916.051	+	545.222i	1.10235	+	0.656104i
$832$	1171.66	+	619.984i	1.40825	+	0.745173i
$833$			1002.43i			1.20340i
$834$	154.950	−	5.65957i	0.185791	−	0.00678606i
$835$	90.5988	+	90.5988i	0.108502	+	0.108502i
$836$	−109.216	−	49.3018i	−0.130641	−	0.0589734i
$837$	−213.311	−	231.015i	−0.254852	−	0.276004i
$838$	−9.04839	+	42.0366i	−0.0107976	+	0.0501630i
$839$	65.2466			0.0777671			0.0388836	−	0.999244i	$-0.487620\pi$
$839$	65.2466			0.0777671			0.0388836	+	0.999244i	$0.487620\pi$
$840$	73.6356	−	180.408i	0.0876615	−	0.214772i
$841$			91.7164i			0.109056i
$842$	156.468	−	726.913i	0.185829	−	0.863317i
$843$	−126.782	−	499.592i	−0.150394	−	0.592636i
$844$	−1039.01	+	392.708i	−1.23105	+	0.465294i
$845$	409.421	−	409.421i	0.484522	−	0.484522i
$846$	−793.901	−	434.086i	−0.938417	−	0.513104i
$847$	430.804			0.508623
$848$	−65.5189	+	1044.19i	−0.0772629	+	1.23136i
$849$	−705.365	−	419.825i	−0.830818	−	0.494493i
$850$	945.231	−	610.384i	1.11204	−	0.718099i
$851$	22.5689	−	22.5689i	0.0265205	−	0.0265205i
$852$	−1442.53	−	255.805i	−1.69310	−	0.300240i
$853$	−245.067	+	245.067i	−0.287300	+	0.287300i	−0.836012	−	0.548712i	$-0.815118\pi$
$853$	−245.067	+	245.067i	−0.287300	+	0.287300i	0.548712	+	0.836012i	$0.315118\pi$
$854$	−27.7124	+	128.745i	−0.0324501	+	0.150755i
$855$	170.070	+	313.506i	0.198912	+	0.366674i
$856$	574.405	−	777.887i	0.671034	−	0.908747i
$857$	1408.63			1.64368			0.821841	−	0.569718i	$-0.192947\pi$
$857$	1408.63			1.64368			0.821841	+	0.569718i	$0.192947\pi$
$858$	−142.434	+	153.233i	−0.166007	+	0.178593i
$859$	−50.1621	+	50.1621i	−0.0583959	+	0.0583959i	−0.735702	−	0.677306i	$-0.763147\pi$
$859$	−50.1621	+	50.1621i	−0.0583959	+	0.0583959i	0.677306	+	0.735702i	$0.263147\pi$
$860$	210.350	−	465.977i	0.244592	−	0.541834i
$861$	−272.365	+	69.1184i	−0.316336	+	0.0802769i
$862$	−176.959	−	274.037i	−0.205289	−	0.317908i
$863$		−	1027.80i		−	1.19096i	−0.803370	−	0.595480i	$-0.796962\pi$
$863$		−	1027.80i		−	1.19096i	0.803370	−	0.595480i	$-0.203038\pi$
$864$	391.982	+	769.965i	0.453683	+	0.891163i
$865$	354.627			0.409974
$866$	−236.458	+	152.693i	−0.273047	+	0.176320i
$867$	−368.277	−	1451.22i	−0.424772	−	1.67384i
$868$	154.790	+	69.8745i	0.178329	+	0.0805006i
$869$	61.1791	+	61.1791i	0.0704017	+	0.0704017i
$870$	−267.897	−	249.017i	−0.307928	−	0.286226i
$871$		−	313.017i		−	0.359376i
$872$	−355.197	+	481.025i	−0.407336	+	0.551635i
$873$	642.100	−	348.324i	0.735509	−	0.398997i
$874$	1018.15	+	219.158i	1.16494	+	0.250753i
$875$	−258.579	−	258.579i	−0.295519	−	0.295519i
$876$	−31.5142	+	177.714i	−0.0359751	+	0.202869i
$877$	600.071	+	600.071i	0.684231	+	0.684231i	0.960951	−	0.276720i	$-0.0892473\pi$
$877$	600.071	+	600.071i	0.684231	+	0.684231i	−0.276720	+	0.960951i	$0.589247\pi$
$878$	−471.839	−	730.681i	−0.537401	−	0.832211i
$879$	159.474	−	267.940i	0.181427	−	0.304823i
$880$	44.9882	−	39.6759i	0.0511229	−	0.0450862i
$881$		−	786.482i		−	0.892715i	−0.894855	−	0.446358i	$-0.852721\pi$
$881$		−	786.482i		−	0.892715i	0.894855	−	0.446358i	$-0.147279\pi$
$882$	−308.358	+	563.956i	−0.349612	+	0.639406i
$883$	−390.413	−	390.413i	−0.442144	−	0.442144i	0.450588	−	0.892732i	$-0.351214\pi$
$883$	−390.413	−	390.413i	−0.442144	−	0.442144i	−0.892732	+	0.450588i	$0.851214\pi$
$884$	−822.290	−	2175.57i	−0.930192	−	2.46106i
$885$	−208.375	+	52.8796i	−0.235452	+	0.0597509i
$886$	719.940	+	154.967i	0.812573	+	0.174907i
$887$	−1446.61			−1.63090			−0.815450	−	0.578827i	$-0.803511\pi$
$887$	−1446.61			−1.63090			−0.815450	+	0.578827i	$0.803511\pi$
$888$	9.89212	−	24.2358i	0.0111398	−	0.0272926i
$889$			269.542i			0.303197i
$890$	23.7546	+	5.11319i	0.0266906	+	0.00574515i
$891$	−133.400	+	28.2520i	−0.149720	+	0.0317081i
$892$	−617.587	+	1368.11i	−0.692362	+	1.53376i
$893$	−632.524	+	632.524i	−0.708313	+	0.708313i
$894$	−13.9290	−	381.353i	−0.0155805	−	0.426569i
$895$	70.8025			0.0791089
$896$	−357.306	−	300.168i	−0.398779	−	0.335009i
$897$	929.976	−	1562.49i	1.03676	−	1.74191i
$898$	−107.357	−	166.251i	−0.119551	−	0.185135i
$899$	225.411	−	225.411i	0.250736	−	0.250736i
$900$	719.536	−	52.6326i	0.799485	−	0.0584806i
$901$	1298.02	−	1298.02i	1.44064	−	1.44064i
$902$	−84.5649	−	18.2026i	−0.0937527	−	0.0201803i
$903$	321.050	−	539.409i	0.355537	−	0.597352i
$904$	−581.490	+	87.4980i	−0.643241	+	0.0967899i
$905$	58.5836			0.0647333
$906$	−114.801	+	123.505i	−0.126711	+	0.136319i
$907$	−535.919	+	535.919i	−0.590870	+	0.590870i	−0.937866	−	0.346997i	$-0.887202\pi$
$907$	−535.919	+	535.919i	−0.590870	+	0.590870i	0.346997	+	0.937866i	$0.387202\pi$
$908$	362.217	+	958.335i	0.398917	+	1.05544i
$909$	395.967	+	117.450i	0.435607	+	0.129208i
$910$	−282.539	+	182.450i	−0.310482	+	0.200494i
$911$			1580.22i			1.73460i	0.497786	+	0.867300i	$0.334146\pi$
$911$			1580.22i			1.73460i	−0.497786	+	0.867300i	$0.665854\pi$
$912$	839.452	−	157.843i	0.920452	−	0.173073i
$913$	−90.1542			−0.0987450
$914$	−15.6460	−	24.2292i	−0.0171182	−	0.0265090i
$915$	116.959	−	29.6809i	0.127825	−	0.0324381i
$916$	307.875	+	814.559i	0.336108	+	0.889257i
$917$	577.595	+	577.595i	0.629875	+	0.629875i
$918$	377.748	−	1468.10i	0.411490	−	1.59924i
$919$			1486.86i			1.61791i	0.587869	+	0.808956i	$0.299967\pi$
$919$			1486.86i			1.61791i	−0.587869	+	0.808956i	$0.700033\pi$
$920$	−309.691	+	419.398i	−0.336620	+	0.455868i
$921$	−614.203	+	1031.95i	−0.666887	+	1.12046i
$922$	−195.387	+	907.719i	−0.211916	+	0.984511i
$923$	1788.04	+	1788.04i	1.93720	+	1.93720i
$924$	60.3709	−	42.1846i	0.0653365	−	0.0456544i
$925$	−15.4561	−	15.4561i	−0.0167093	−	0.0167093i
$926$	−1425.48	+	920.504i	−1.53939	+	0.994065i
$927$	−219.674	−	404.947i	−0.236974	−	0.436836i
$928$	−764.162	+	428.162i	−0.823451	+	0.461382i
$929$		−	1091.41i		−	1.17482i	−0.809290	−	0.587409i	$-0.800148\pi$
$929$		−	1091.41i		−	1.17482i	0.809290	−	0.587409i	$-0.199852\pi$
$930$	−5.67989	−	155.506i	−0.00610740	−	0.167211i
$931$	449.320	+	449.320i	0.482621	+	0.482621i
$932$	85.2154	−	188.773i	0.0914328	−	0.202547i
$933$	39.8750	+	157.130i	0.0427384	+	0.168414i
$934$	−33.3725	+	155.041i	−0.0357308	+	0.165996i
$935$	−105.245			−0.112561
$936$	206.618	−	1476.90i	0.220745	−	1.57788i
$937$		−	887.919i		−	0.947619i	−0.880627	−	0.473809i	$-0.842879\pi$
$937$		−	887.919i		−	0.947619i	0.880627	−	0.473809i	$-0.157121\pi$
$938$	−23.1882	+	107.727i	−0.0247209	+	0.114847i
$939$	1425.65	−	361.788i	1.51826	−	0.385291i
$940$	−158.316	−	418.865i	−0.168422	−	0.445602i
$941$	790.753	−	790.753i	0.840333	−	0.840333i	−0.148569	−	0.988902i	$-0.547467\pi$
$941$	790.753	−	790.753i	0.840333	−	0.840333i	0.988902	+	0.148569i	$0.0474667\pi$
$942$	53.6637	+	1469.23i	0.0569678	+	1.55969i
$943$	751.822			0.797266
$944$	−32.2413	+	513.838i	−0.0341539	+	0.544320i
$945$	−219.041	−	8.72786i	−0.231789	−	0.00923583i
$946$	162.332	−	104.826i	0.171598	−	0.110810i
$947$	1170.78	−	1170.78i	1.23630	−	1.23630i	0.274796	−	0.961502i	$-0.411390\pi$
$947$	1170.78	−	1170.78i	1.23630	−	1.23630i	0.961502	−	0.274796i	$-0.0886105\pi$
$948$	−607.263	−	107.687i	−0.640573	−	0.113593i
$949$	220.280	−	220.280i	0.232118	−	0.232118i
$950$	150.089	−	697.274i	0.157988	−	0.733973i
$951$	−1165.00	−	693.393i	−1.22503	−	0.729120i
$952$	121.830	+	809.652i	0.127973	+	0.850475i
$953$	1148.50			1.20514			0.602571	−	0.798065i	$-0.294143\pi$
$953$	1148.50			1.20514			0.602571	+	0.798065i	$0.294143\pi$
$954$	1129.54	−	330.967i	1.18400	−	0.346926i
$955$	301.830	−	301.830i	0.316052	−	0.316052i
$956$	−911.072	−	411.273i	−0.953004	−	0.430201i
$957$	−34.0042	−	133.996i	−0.0355321	−	0.140016i
$958$	703.911	+	1090.07i	0.734771	+	1.13786i
$959$			367.250i			0.382951i
$960$	−100.877	+	415.512i	−0.105081	+	0.432825i
$961$	−825.376			−0.858873
$962$	−37.9559	+	24.5101i	−0.0394552	+	0.0254782i
$963$	−1042.94	−	309.353i	−1.08301	−	0.321238i
$964$	728.295	−	1613.36i	0.755493	−	1.67361i
$965$	−76.5746	−	76.5746i	−0.0793519	−	0.0793519i
$966$	−435.806	+	468.849i	−0.451145	+	0.485351i
$967$			1696.75i			1.75466i	0.479892	+	0.877328i	$0.340676\pi$
$967$			1696.75i			1.75466i	−0.479892	+	0.877328i	$0.659324\pi$
$968$	−934.804	+	140.662i	−0.965707	+	0.145312i
$969$	−1287.82	−	766.494i	−1.32902	−	0.791016i
$970$	353.417	+	76.0732i	0.364347	+	0.0784259i
$971$	119.876	+	119.876i	0.123457	+	0.123457i	0.766136	−	0.642679i	$-0.222177\pi$
$971$	119.876	+	119.876i	0.123457	+	0.123457i	−0.642679	+	0.766136i	$0.722177\pi$
$972$	664.120	−	709.739i	0.683251	−	0.730184i
$973$	66.6196	+	66.6196i	0.0684682	+	0.0684682i
$974$	191.801	+	297.021i	0.196921	+	0.304949i
$975$	−1070.06	−	636.886i	−1.09750	−	0.653217i
$976$	18.0968	−	288.413i	0.0185418	−	0.295505i
$977$			1408.74i			1.44190i	0.692985	+	0.720952i	$0.256295\pi$
$977$			1408.74i			1.44190i	−0.692985	+	0.720952i	$0.743705\pi$
$978$	16.0803	+	440.253i	0.0164421	+	0.450157i
$979$	6.49409	+	6.49409i	0.00663340	+	0.00663340i
$980$	−297.546	+	112.462i	−0.303618	+	0.114757i
$981$	644.927	+	191.296i	0.657418	+	0.195001i
$982$	877.555	+	188.894i	0.893641	+	0.192357i
$983$	1288.34			1.31062			0.655309	−	0.755361i	$-0.272539\pi$
$983$	1288.34			1.31062			0.655309	+	0.755361i	$0.272539\pi$
$984$	568.440	−	238.911i	0.577683	−	0.242795i
$985$		−	429.137i		−	0.435672i
$986$	1502.46	+	323.404i	1.52379	+	0.327996i
$987$	−135.235	−	532.903i	−0.137016	−	0.539922i
$988$	−1343.73	−	606.583i	−1.36005	−	0.613950i
$989$	−1187.58	+	1187.58i	−1.20079	+	1.20079i
$990$	−59.2095	−	32.3743i	−0.0598075	−	0.0327013i
$991$	−1013.28			−1.02248			−0.511242	−	0.859437i	$-0.670815\pi$
$991$	−1013.28			−1.02248			−0.511242	+	0.859437i	$0.670815\pi$
$992$	−358.694	−	101.081i	−0.361586	−	0.101896i
$993$	−982.280	−	584.641i	−0.989204	−	0.588762i
$994$	−482.907	−	747.822i	−0.485822	−	0.752336i
$995$	−227.968	+	227.968i	−0.229113	+	0.229113i
$996$	526.779	−	368.091i	0.528894	−	0.369569i
$997$	−537.885	+	537.885i	−0.539503	+	0.539503i	−0.923383	−	0.383880i	$-0.874588\pi$
$997$	−537.885	+	537.885i	−0.539503	+	0.539503i	0.383880	+	0.923383i	$0.374588\pi$
$998$	−1035.23	−	222.833i	−1.03730	−	0.223279i
$999$	−29.4256	−	1.17249i	−0.0294551	−	0.00117366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.i.a.29.4	yes	8
3.2	odd	2	inner	48.3.i.a.29.1	yes	8
4.3	odd	2		192.3.i.a.17.3		8
8.3	odd	2		384.3.i.b.161.2		8
8.5	even	2		384.3.i.a.161.3		8
12.11	even	2		192.3.i.a.17.1		8
16.3	odd	4		384.3.i.b.353.4		8
16.5	even	4	inner	48.3.i.a.5.1	✓	8
16.11	odd	4		192.3.i.a.113.1		8
16.13	even	4		384.3.i.a.353.1		8
24.5	odd	2		384.3.i.a.161.1		8
24.11	even	2		384.3.i.b.161.4		8
48.5	odd	4	inner	48.3.i.a.5.4	yes	8
48.11	even	4		192.3.i.a.113.3		8
48.29	odd	4		384.3.i.a.353.3		8
48.35	even	4		384.3.i.b.353.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.a.5.1	✓	8	16.5	even	4	inner
48.3.i.a.5.4	yes	8	48.5	odd	4	inner
48.3.i.a.29.1	yes	8	3.2	odd	2	inner
48.3.i.a.29.4	yes	8	1.1	even	1	trivial
192.3.i.a.17.1		8	12.11	even	2
192.3.i.a.17.3		8	4.3	odd	2
192.3.i.a.113.1		8	16.11	odd	4
192.3.i.a.113.3		8	48.11	even	4
384.3.i.a.161.1		8	24.5	odd	2
384.3.i.a.161.3		8	8.5	even	2
384.3.i.a.353.1		8	16.13	even	4
384.3.i.a.353.3		8	48.29	odd	4
384.3.i.b.161.2		8	8.3	odd	2
384.3.i.b.161.4		8	24.11	even	2
384.3.i.b.353.2		8	48.35	even	4
384.3.i.b.353.4		8	16.3	odd	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68014 - 1.08495i) q^{2} +(0.737922 + 2.90783i) q^{3} +(1.64575 - 3.64575i) q^{4} +(-1.57472 - 1.57472i) q^{5} +(4.39467 + 4.08495i) q^{6} +3.64575i q^{7} +(-1.19038 - 7.91094i) q^{8} +(-7.91094 + 4.29150i) q^{9} +O(q^{10})\)	\(q+(1.68014 - 1.08495i) q^{2} +(0.737922 + 2.90783i) q^{3} +(1.64575 - 3.64575i) q^{4} +(-1.57472 - 1.57472i) q^{5} +(4.39467 + 4.08495i) q^{6} +3.64575i q^{7} +(-1.19038 - 7.91094i) q^{8} +(-7.91094 + 4.29150i) q^{9} +(-4.35425 - 0.937254i) q^{10} +(-1.19038 - 1.19038i) q^{11} +(11.8157 + 2.09528i) q^{12} +(-14.6458 - 14.6458i) q^{13} +(3.95547 + 6.12538i) q^{14} +(3.41699 - 5.74103i) q^{15} +(-10.5830 - 12.0000i) q^{16} +28.0726i q^{17} +(-8.63542 + 15.7933i) q^{18} +(12.5830 + 12.5830i) q^{19} +(-8.33263 + 3.14944i) q^{20} +(-10.6012 + 2.69028i) q^{21} +(-3.29150 - 0.708497i) q^{22} +29.2630 q^{23} +(22.1253 - 9.29907i) q^{24} -20.0405i q^{25} +(-40.4969 - 8.71697i) q^{26} +(-18.3166 - 19.8369i) q^{27} +(13.2915 + 6.00000i) q^{28} +(19.3557 - 19.3557i) q^{29} +(-0.487722 - 13.3530i) q^{30} +11.6458 q^{31} +(-30.8004 - 8.67963i) q^{32} +(2.58301 - 4.33981i) q^{33} +(30.4575 + 47.1660i) q^{34} +(5.74103 - 5.74103i) q^{35} +(2.62631 + 35.9041i) q^{36} +(0.771243 - 0.771243i) q^{37} +(34.7932 + 7.48925i) q^{38} +(31.7799 - 53.3948i) q^{39} +(-10.5830 + 14.3320i) q^{40} +25.6919 q^{41} +(-14.8927 + 16.0219i) q^{42} +(-40.5830 + 40.5830i) q^{43} +(-6.29888 + 2.38075i) q^{44} +(19.2154 + 5.69960i) q^{45} +(49.1660 - 31.7490i) q^{46} +50.2681i q^{47} +(27.0845 - 39.6286i) q^{48} +35.7085 q^{49} +(-21.7430 - 33.6709i) q^{50} +(-81.6304 + 20.7154i) q^{51} +(-77.4980 + 29.2915i) q^{52} +(-46.2379 - 46.2379i) q^{53} +(-52.2966 - 13.4561i) q^{54} +3.74902i q^{55} +(28.8413 - 4.33981i) q^{56} +(-27.3040 + 45.8745i) q^{57} +(11.5203 - 53.5203i) q^{58} +(-22.7533 - 22.7533i) q^{59} +(-15.3069 - 21.9058i) q^{60} +(12.7712 + 12.7712i) q^{61} +(19.5665 - 12.6351i) q^{62} +(-15.6458 - 28.8413i) q^{63} +(-61.1660 + 18.8340i) q^{64} +46.1259i q^{65} +(-0.368683 - 10.0939i) q^{66} +(10.6863 + 10.6863i) q^{67} +(102.346 + 46.2006i) q^{68} +(21.5938 + 85.0919i) q^{69} +(3.41699 - 15.8745i) q^{70} -122.086 q^{71} +(43.3668 + 57.4745i) q^{72} +15.0405i q^{73} +(0.459035 - 2.13256i) q^{74} +(58.2744 - 14.7883i) q^{75} +(66.5830 - 25.1660i) q^{76} +(4.33981 - 4.33981i) q^{77} +(-4.53608 - 124.191i) q^{78} -51.3948 q^{79} +(-2.23137 + 35.5619i) q^{80} +(44.1660 - 67.8997i) q^{81} +(43.1660 - 27.8745i) q^{82} +(37.8680 - 37.8680i) q^{83} +(-7.63888 + 43.0770i) q^{84} +(44.2065 - 44.2065i) q^{85} +(-24.1545 + 112.216i) q^{86} +(70.5659 + 42.0000i) q^{87} +(-8.00000 + 10.8340i) q^{88} -5.45550 q^{89} +(38.4684 - 11.2717i) q^{90} +(53.3948 - 53.3948i) q^{91} +(48.1596 - 106.686i) q^{92} +(8.59366 + 33.8639i) q^{93} +(54.5385 + 84.4575i) q^{94} -39.6294i q^{95} +(2.51059 - 95.9672i) q^{96} -81.1660 q^{97} +(59.9953 - 38.7421i) q^{98} +(14.5255 + 4.30849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{4} + 16 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 - 8 * q^4 + 16 * q^6	\( 8 q + 4 q^{3} - 8 q^{4} + 16 q^{6} - 56 q^{10} + 56 q^{12} - 96 q^{13} + 112 q^{15} - 64 q^{18} + 16 q^{19} - 32 q^{21} + 16 q^{22} - 48 q^{24} - 68 q^{27} + 64 q^{28} + 56 q^{30} + 72 q^{31} - 64 q^{33} + 32 q^{34} + 104 q^{36} + 112 q^{37} - 24 q^{42} - 240 q^{43} - 112 q^{45} + 224 q^{46} - 64 q^{48} + 328 q^{49} - 32 q^{51} - 112 q^{52} - 168 q^{54} - 56 q^{58} - 336 q^{60} + 208 q^{61} - 104 q^{63} - 320 q^{64} - 80 q^{66} - 232 q^{67} + 112 q^{70} + 160 q^{72} + 324 q^{75} + 448 q^{76} + 152 q^{78} - 136 q^{79} + 184 q^{81} + 176 q^{82} + 64 q^{84} - 112 q^{85} - 64 q^{88} + 392 q^{90} + 152 q^{91} + 64 q^{93} - 368 q^{94} + 512 q^{96} - 480 q^{97} + 160 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^4 + 16 * q^6 - 56 * q^10 + 56 * q^12 - 96 * q^13 + 112 * q^15 - 64 * q^18 + 16 * q^19 - 32 * q^21 + 16 * q^22 - 48 * q^24 - 68 * q^27 + 64 * q^28 + 56 * q^30 + 72 * q^31 - 64 * q^33 + 32 * q^34 + 104 * q^36 + 112 * q^37 - 24 * q^42 - 240 * q^43 - 112 * q^45 + 224 * q^46 - 64 * q^48 + 328 * q^49 - 32 * q^51 - 112 * q^52 - 168 * q^54 - 56 * q^58 - 336 * q^60 + 208 * q^61 - 104 * q^63 - 320 * q^64 - 80 * q^66 - 232 * q^67 + 112 * q^70 + 160 * q^72 + 324 * q^75 + 448 * q^76 + 152 * q^78 - 136 * q^79 + 184 * q^81 + 176 * q^82 + 64 * q^84 - 112 * q^85 - 64 * q^88 + 392 * q^90 + 152 * q^91 + 64 * q^93 - 368 * q^94 + 512 * q^96 - 480 * q^97 + 160 * q^99

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