LMFDB - Embedded newform 192.3.i.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,3,Mod(17,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("192.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	192.i (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.23162107572$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.3
Root			$-1.38255 + 0.297594i$ of defining polynomial
Character	$\chi$	$=$	192.113
Dual form			192.3.i.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737922 + 2.90783i) q^{3} +(-1.57472 + 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +O(q^{10})$	\(q+(-0.737922 + 2.90783i) q^{3} +(-1.57472 + 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +(1.19038 - 1.19038i) q^{11} +(-14.6458 + 14.6458i) q^{13} +(-3.41699 - 5.74103i) q^{15} -28.0726i q^{17} +(-12.5830 + 12.5830i) q^{19} +(-10.6012 - 2.69028i) q^{21} -29.2630 q^{23} +20.0405i q^{25} +(18.3166 - 19.8369i) q^{27} +(19.3557 + 19.3557i) q^{29} -11.6458 q^{31} +(2.58301 + 4.33981i) q^{33} +(-5.74103 - 5.74103i) q^{35} +(0.771243 + 0.771243i) q^{37} +(-31.7799 - 53.3948i) q^{39} +25.6919 q^{41} +(40.5830 + 40.5830i) q^{43} +(19.2154 - 5.69960i) q^{45} +50.2681i q^{47} +35.7085 q^{49} +(81.6304 + 20.7154i) q^{51} +(-46.2379 + 46.2379i) q^{53} +3.74902i q^{55} +(-27.3040 - 45.8745i) q^{57} +(22.7533 - 22.7533i) q^{59} +(12.7712 - 12.7712i) q^{61} +(15.6458 - 28.8413i) q^{63} -46.1259i q^{65} +(-10.6863 + 10.6863i) q^{67} +(21.5938 - 85.0919i) q^{69} +122.086 q^{71} -15.0405i q^{73} +(-58.2744 - 14.7883i) q^{75} +(4.33981 + 4.33981i) q^{77} +51.3948 q^{79} +(44.1660 + 67.8997i) q^{81} +(-37.8680 - 37.8680i) q^{83} +(44.2065 + 44.2065i) q^{85} +(-70.5659 + 42.0000i) q^{87} -5.45550 q^{89} +(-53.3948 - 53.3948i) q^{91} +(8.59366 - 33.8639i) q^{93} -39.6294i q^{95} -81.1660 q^{97} +(-14.5255 + 4.30849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3}+O(q^{10}) $ 8 * q - 4 * q^3	$ 8 q - 4 q^{3} - 96 q^{13} - 112 q^{15} - 16 q^{19} - 32 q^{21} + 68 q^{27} - 72 q^{31} - 64 q^{33} + 112 q^{37} + 240 q^{43} - 112 q^{45} + 328 q^{49} + 32 q^{51} + 208 q^{61} + 104 q^{63} + 232 q^{67} - 324 q^{75} + 136 q^{79} + 184 q^{81} - 112 q^{85} - 152 q^{91} + 64 q^{93} - 480 q^{97} - 160 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 96 * q^13 - 112 * q^15 - 16 * q^19 - 32 * q^21 + 68 * q^27 - 72 * q^31 - 64 * q^33 + 112 * q^37 + 240 * q^43 - 112 * q^45 + 328 * q^49 + 32 * q^51 + 208 * q^61 + 104 * q^63 + 232 * q^67 - 324 * q^75 + 136 * q^79 + 184 * q^81 - 112 * q^85 - 152 * q^91 + 64 * q^93 - 480 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.737922	+	2.90783i	−0.245974	+	0.969276i
$3$	−0.737922	+	2.90783i	−0.245974	+	0.969276i
$4$		0			0
$5$	−1.57472	+	1.57472i	−0.314944	+	0.314944i	−0.846821	−	0.531877i	$-0.821487\pi$
$5$	−1.57472	+	1.57472i	−0.314944	+	0.314944i	0.531877	+	0.846821i	$0.321487\pi$
$6$		0			0
$7$			3.64575i			0.520822i	0.965498	+	0.260411i	$0.0838580\pi$
$7$			3.64575i			0.520822i	−0.965498	+	0.260411i	$0.916142\pi$
$8$		0			0
$9$	−7.91094	−	4.29150i	−0.878994	−	0.476834i
$10$		0			0
$11$	1.19038	−	1.19038i	0.108216	−	0.108216i	−0.650926	−	0.759142i	$-0.725619\pi$
$11$	1.19038	−	1.19038i	0.108216	−	0.108216i	0.759142	+	0.650926i	$0.225619\pi$
$12$		0			0
$13$	−14.6458	+	14.6458i	−1.12660	+	1.12660i	−0.135870	+	0.990727i	$0.543383\pi$
$13$	−14.6458	+	14.6458i	−1.12660	+	1.12660i	−0.990727	+	0.135870i	$0.956617\pi$
$14$		0			0
$15$	−3.41699	−	5.74103i	−0.227800	−	0.382736i
$16$		0			0
$17$		−	28.0726i		−	1.65133i	−0.564159	−	0.825666i	$-0.690800\pi$
$17$		−	28.0726i		−	1.65133i	0.564159	−	0.825666i	$-0.309200\pi$
$18$		0			0
$19$	−12.5830	+	12.5830i	−0.662263	+	0.662263i	−0.955913	−	0.293650i	$-0.905130\pi$
$19$	−12.5830	+	12.5830i	−0.662263	+	0.662263i	0.293650	+	0.955913i	$0.405130\pi$
$20$		0			0
$21$	−10.6012	−	2.69028i	−0.504820	−	0.128109i
$22$		0			0
$23$	−29.2630			−1.27231			−0.636153	−	0.771563i	$-0.719475\pi$
$23$	−29.2630			−1.27231			−0.636153	+	0.771563i	$0.719475\pi$
$24$		0			0
$25$			20.0405i			0.801621i
$26$		0			0
$27$	18.3166	−	19.8369i	0.678393	−	0.734699i
$28$		0			0
$29$	19.3557	+	19.3557i	0.667437	+	0.667437i	0.957122	−	0.289685i	$-0.0935506\pi$
$29$	19.3557	+	19.3557i	0.667437	+	0.667437i	−0.289685	+	0.957122i	$0.593551\pi$
$30$		0			0
$31$	−11.6458			−0.375669			−0.187835	−	0.982201i	$-0.560147\pi$
$31$	−11.6458			−0.375669			−0.187835	+	0.982201i	$0.560147\pi$
$32$		0			0
$33$	2.58301	+	4.33981i	0.0782729	+	0.131510i
$34$		0			0
$35$	−5.74103	−	5.74103i	−0.164030	−	0.164030i
$36$		0			0
$37$	0.771243	+	0.771243i	0.0208444	+	0.0208444i	0.717452	−	0.696608i	$-0.245308\pi$
$37$	0.771243	+	0.771243i	0.0208444	+	0.0208444i	−0.696608	+	0.717452i	$0.745308\pi$
$38$		0			0
$39$	−31.7799	−	53.3948i	−0.814870	−	1.36910i
$40$		0			0
$41$	25.6919			0.626631			0.313316	−	0.949649i	$-0.398560\pi$
$41$	25.6919			0.626631			0.313316	+	0.949649i	$0.398560\pi$
$42$		0			0
$43$	40.5830	+	40.5830i	0.943791	+	0.943791i	0.998502	−	0.0547114i	$-0.0174239\pi$
$43$	40.5830	+	40.5830i	0.943791	+	0.943791i	−0.0547114	+	0.998502i	$0.517424\pi$
$44$		0			0
$45$	19.2154	−	5.69960i	0.427009	−	0.126658i
$46$		0			0
$47$			50.2681i			1.06953i	0.845000	+	0.534767i	$0.179601\pi$
$47$			50.2681i			1.06953i	−0.845000	+	0.534767i	$0.820399\pi$
$48$		0			0
$49$	35.7085			0.728745
$50$		0			0
$51$	81.6304	+	20.7154i	1.60060	+	0.406185i
$52$		0			0
$53$	−46.2379	+	46.2379i	−0.872414	+	0.872414i	−0.992735	−	0.120321i	$-0.961608\pi$
$53$	−46.2379	+	46.2379i	−0.872414	+	0.872414i	0.120321	+	0.992735i	$0.461608\pi$
$54$		0			0
$55$			3.74902i			0.0681639i
$56$		0			0
$57$	−27.3040	−	45.8745i	−0.479017	−	0.804816i
$58$		0			0
$59$	22.7533	−	22.7533i	0.385649	−	0.385649i	−0.487483	−	0.873132i	$-0.662085\pi$
$59$	22.7533	−	22.7533i	0.385649	−	0.385649i	0.873132	+	0.487483i	$0.162085\pi$
$60$		0			0
$61$	12.7712	−	12.7712i	0.209365	−	0.209365i	−0.594633	−	0.803997i	$-0.702703\pi$
$61$	12.7712	−	12.7712i	0.209365	−	0.209365i	0.803997	+	0.594633i	$0.202703\pi$
$62$		0			0
$63$	15.6458	−	28.8413i	0.248345	−	0.457799i
$64$		0			0
$65$		−	46.1259i		−	0.709629i
$66$		0			0
$67$	−10.6863	+	10.6863i	−0.159497	+	0.159497i	−0.782344	−	0.622847i	$-0.785976\pi$
$67$	−10.6863	+	10.6863i	−0.159497	+	0.159497i	0.622847	+	0.782344i	$0.285976\pi$
$68$		0			0
$69$	21.5938	−	85.0919i	0.312954	−	1.23322i
$70$		0			0
$71$	122.086			1.71952			0.859760	−	0.510699i	$-0.170613\pi$
$71$	122.086			1.71952			0.859760	+	0.510699i	$0.170613\pi$
$72$		0			0
$73$		−	15.0405i		−	0.206034i	−0.994680	−	0.103017i	$-0.967150\pi$
$73$		−	15.0405i		−	0.206034i	0.994680	−	0.103017i	$-0.0328497\pi$
$74$		0			0
$75$	−58.2744	−	14.7883i	−0.776992	−	0.197178i
$76$		0			0
$77$	4.33981	+	4.33981i	0.0563612	+	0.0563612i
$78$		0			0
$79$	51.3948			0.650567			0.325283	−	0.945617i	$-0.394540\pi$
$79$	51.3948			0.650567			0.325283	+	0.945617i	$0.394540\pi$
$80$		0			0
$81$	44.1660	+	67.8997i	0.545259	+	0.838267i
$82$		0			0
$83$	−37.8680	−	37.8680i	−0.456240	−	0.456240i	0.441179	−	0.897419i	$-0.354560\pi$
$83$	−37.8680	−	37.8680i	−0.456240	−	0.456240i	−0.897419	+	0.441179i	$0.854560\pi$
$84$		0			0
$85$	44.2065	+	44.2065i	0.520077	+	0.520077i
$86$		0			0
$87$	−70.5659	+	42.0000i	−0.811103	+	0.482759i
$88$		0			0
$89$	−5.45550			−0.0612977			−0.0306489	−	0.999530i	$-0.509757\pi$
$89$	−5.45550			−0.0612977			−0.0306489	+	0.999530i	$0.509757\pi$
$90$		0			0
$91$	−53.3948	−	53.3948i	−0.586756	−	0.586756i
$92$		0			0
$93$	8.59366	−	33.8639i	0.0924049	−	0.364127i
$94$		0			0
$95$		−	39.6294i		−	0.417152i
$96$		0			0
$97$	−81.1660			−0.836763			−0.418381	−	0.908271i	$-0.637402\pi$
$97$	−81.1660			−0.836763			−0.418381	+	0.908271i	$0.637402\pi$
$98$		0			0
$99$	−14.5255	+	4.30849i	−0.146722	+	0.0435201i
$100$		0			0
$101$	−32.4498	+	32.4498i	−0.321285	+	0.321285i	−0.849260	−	0.527975i	$-0.822952\pi$
$101$	−32.4498	+	32.4498i	−0.321285	+	0.321285i	0.527975	+	0.849260i	$0.322952\pi$
$102$		0			0
$103$			51.1882i			0.496973i	0.968635	+	0.248487i	$0.0799332\pi$
$103$			51.1882i			0.496973i	−0.968635	+	0.248487i	$0.920067\pi$
$104$		0			0
$105$	20.9304	−	12.4575i	0.199337	−	0.118643i
$106$		0			0
$107$	−85.4698	+	85.4698i	−0.798783	+	0.798783i	−0.982904	−	0.184121i	$-0.941056\pi$
$107$	−85.4698	+	85.4698i	−0.798783	+	0.798783i	0.184121	+	0.982904i	$0.441056\pi$
$108$		0			0
$109$	−52.8523	+	52.8523i	−0.484883	+	0.484883i	−0.906687	−	0.421804i	$-0.861397\pi$
$109$	−52.8523	+	52.8523i	−0.484883	+	0.484883i	0.421804	+	0.906687i	$0.361397\pi$
$110$		0			0
$111$	−2.81176	+	1.67353i	−0.0253312	+	0.0150768i
$112$		0			0
$113$			73.5045i			0.650483i	0.945631	+	0.325241i	$0.105446\pi$
$113$			73.5045i			0.650483i	−0.945631	+	0.325241i	$0.894554\pi$
$114$		0			0
$115$	46.0810	−	46.0810i	0.400705	−	0.400705i
$116$		0			0
$117$	178.714	−	53.0094i	1.52747	−	0.453072i
$118$		0			0
$119$	102.346			0.860049
$120$		0			0
$121$			118.166i			0.976579i
$122$		0			0
$123$	−18.9586	+	74.7076i	−0.154135	+	0.607379i
$124$		0			0
$125$	−70.9262	−	70.9262i	−0.567409	−	0.567409i
$126$		0			0
$127$	−73.9333			−0.582152			−0.291076	−	0.956700i	$-0.594013\pi$
$127$	−73.9333			−0.582152			−0.291076	+	0.956700i	$0.594013\pi$
$128$		0			0
$129$	−147.956	+	88.0614i	−1.14694	+	0.682646i
$130$		0			0
$131$	−158.430	−	158.430i	−1.20939	−	1.20939i	−0.971226	−	0.238161i	$-0.923455\pi$
$131$	−158.430	−	158.430i	−1.20939	−	1.20939i	−0.238161	−	0.971226i	$-0.576545\pi$
$132$		0			0
$133$	−45.8745	−	45.8745i	−0.344921	−	0.344921i
$134$		0			0
$135$	2.39398	+	60.0810i	0.0177332	+	0.445045i
$136$		0			0
$137$	100.734			0.735283			0.367642	−	0.929968i	$-0.380165\pi$
$137$	100.734			0.735283			0.367642	+	0.929968i	$0.380165\pi$
$138$		0			0
$139$	−18.2732	−	18.2732i	−0.131462	−	0.131462i	0.638314	−	0.769776i	$-0.279632\pi$
$139$	−18.2732	−	18.2732i	−0.131462	−	0.131462i	−0.769776	+	0.638314i	$0.779632\pi$
$140$		0			0
$141$	−146.171	−	37.0939i	−1.03667	−	0.263078i
$142$		0			0
$143$			34.8679i			0.243831i
$144$		0			0
$145$	−60.9595			−0.420410
$146$		0			0
$147$	−26.3501	+	103.834i	−0.179252	+	0.706355i
$148$		0			0
$149$	−44.9729	+	44.9729i	−0.301831	+	0.301831i	−0.841730	−	0.539899i	$-0.818463\pi$
$149$	−44.9729	+	44.9729i	−0.301831	+	0.301831i	0.539899	+	0.841730i	$0.318463\pi$
$150$		0			0
$151$			28.1033i			0.186114i	0.995661	+	0.0930572i	$0.0296639\pi$
$151$			28.1033i			0.186114i	−0.995661	+	0.0930572i	$0.970336\pi$
$152$		0			0
$153$	−120.474	+	222.081i	−0.787411	+	1.45151i
$154$		0			0
$155$	18.3388	−	18.3388i	0.118315	−	0.118315i
$156$		0			0
$157$	173.265	−	173.265i	1.10360	−	1.10360i	0.109628	−	0.993973i	$-0.465034\pi$
$157$	173.265	−	173.265i	1.10360	−	1.10360i	0.993973	−	0.109628i	$-0.0349660\pi$
$158$		0			0
$159$	−100.332	−	168.572i	−0.631019	−	1.06020i
$160$		0			0
$161$		−	106.686i		−	0.662644i
$162$		0			0
$163$	−51.9190	+	51.9190i	−0.318521	+	0.318521i	−0.848199	−	0.529678i	$-0.822313\pi$
$163$	−51.9190	+	51.9190i	−0.318521	+	0.318521i	0.529678	+	0.848199i	$0.322313\pi$
$164$		0			0
$165$	−10.9015	−	2.76648i	−0.0660697	−	0.0167666i
$166$		0			0
$167$	57.5333			0.344511			0.172255	−	0.985052i	$-0.444895\pi$
$167$	57.5333			0.344511			0.172255	+	0.985052i	$0.444895\pi$
$168$		0			0
$169$		−	259.996i		−	1.53844i
$170$		0			0
$171$	153.543	−	45.5434i	0.897915	−	0.266336i
$172$		0			0
$173$	−112.600	−	112.600i	−0.650868	−	0.650868i	0.302334	−	0.953202i	$-0.402234\pi$
$173$	−112.600	−	112.600i	−0.650868	−	0.650868i	−0.953202	+	0.302334i	$0.902234\pi$
$174$		0			0
$175$	−73.0627			−0.417501
$176$		0			0
$177$	49.3725	+	82.9529i	0.278941	+	0.468660i
$178$		0			0
$179$	22.4810	+	22.4810i	0.125592	+	0.125592i	0.767109	−	0.641517i	$-0.221695\pi$
$179$	22.4810	+	22.4810i	0.125592	+	0.125592i	−0.641517	+	0.767109i	$0.721695\pi$
$180$		0			0
$181$	−18.6013	−	18.6013i	−0.102770	−	0.102770i	0.653852	−	0.756622i	$-0.273152\pi$
$181$	−18.6013	−	18.6013i	−0.102770	−	0.102770i	−0.756622	+	0.653852i	$0.773152\pi$
$182$		0			0
$183$	27.7124	+	46.5608i	0.151434	+	0.254430i
$184$		0			0
$185$	−2.42898			−0.0131296
$186$		0			0
$187$	−33.4170	−	33.4170i	−0.178701	−	0.178701i
$188$		0			0
$189$	72.3203	+	66.7778i	0.382647	+	0.353322i
$190$		0			0
$191$			191.672i			1.00352i	0.865007	+	0.501760i	$0.167314\pi$
$191$			191.672i			1.00352i	−0.865007	+	0.501760i	$0.832686\pi$
$192$		0			0
$193$	48.6275			0.251956			0.125978	−	0.992033i	$-0.459793\pi$
$193$	48.6275			0.251956			0.125978	+	0.992033i	$0.459793\pi$
$194$		0			0
$195$	134.126	+	34.0373i	0.687827	+	0.174550i
$196$		0			0
$197$	136.258	−	136.258i	0.691667	−	0.691667i	−0.270932	−	0.962599i	$-0.587332\pi$
$197$	136.258	−	136.258i	0.691667	−	0.691667i	0.962599	+	0.270932i	$0.0873318\pi$
$198$		0			0
$199$		−	144.767i		−	0.727474i	−0.931502	−	0.363737i	$-0.881501\pi$
$199$		−	144.767i		−	0.727474i	0.931502	−	0.363737i	$-0.118499\pi$
$200$		0			0
$201$	−23.1882	−	38.9595i	−0.115364	−	0.193828i
$202$		0			0
$203$	−70.5659	+	70.5659i	−0.347615	+	0.347615i
$204$		0			0
$205$	−40.4575	+	40.4575i	−0.197354	+	0.197354i
$206$		0			0
$207$	231.498	+	125.582i	1.11835	+	0.606678i
$208$		0			0
$209$			29.9570i			0.143335i
$210$		0			0
$211$	196.354	−	196.354i	0.930589	−	0.930589i	−0.0671538	−	0.997743i	$-0.521392\pi$
$211$	196.354	−	196.354i	0.930589	−	0.930589i	0.997743	+	0.0671538i	$0.0213918\pi$
$212$		0			0
$213$	−90.0899	+	355.005i	−0.422957	+	1.66669i
$214$		0			0
$215$	−127.814			−0.594482
$216$		0			0
$217$		−	42.4575i		−	0.195657i
$218$		0			0
$219$	43.7353	+	11.0987i	0.199704	+	0.0506791i
$220$		0			0
$221$	411.145	+	411.145i	1.86038	+	1.86038i
$222$		0			0
$223$	375.261			1.68279			0.841393	−	0.540423i	$-0.181736\pi$
$223$	375.261			1.68279			0.841393	+	0.540423i	$0.181736\pi$
$224$		0			0
$225$	86.0039	−	158.539i	0.382240	−	0.704619i
$226$		0			0
$227$	181.108	+	181.108i	0.797834	+	0.797834i	0.982754	−	0.184920i	$-0.0592025\pi$
$227$	181.108	+	181.108i	0.797834	+	0.797834i	−0.184920	+	0.982754i	$0.559203\pi$
$228$		0			0
$229$	−153.937	−	153.937i	−0.672215	−	0.672215i	0.286011	−	0.958226i	$-0.407671\pi$
$229$	−153.937	−	153.937i	−0.672215	−	0.672215i	−0.958226	+	0.286011i	$0.907671\pi$
$230$		0			0
$231$	−15.8219	+	9.41699i	−0.0684930	+	0.0407662i
$232$		0			0
$233$	51.7790			0.222228			0.111114	−	0.993808i	$-0.464558\pi$
$233$	51.7790			0.222228			0.111114	+	0.993808i	$0.464558\pi$
$234$		0			0
$235$	−79.1581	−	79.1581i	−0.336843	−	0.336843i
$236$		0			0
$237$	−37.9253	+	149.447i	−0.160022	+	0.630579i
$238$		0			0
$239$		−	249.900i		−	1.04560i	−0.852454	−	0.522802i	$-0.824887\pi$
$239$		−	249.900i		−	1.04560i	0.852454	−	0.522802i	$-0.175113\pi$
$240$		0			0
$241$	442.531			1.83623			0.918113	−	0.396318i	$-0.129712\pi$
$241$	442.531			1.83623			0.918113	+	0.396318i	$0.129712\pi$
$242$		0			0
$243$	−230.032	+	78.3226i	−0.946632	+	0.322315i
$244$		0			0
$245$	−56.2309	+	56.2309i	−0.229514	+	0.229514i
$246$		0			0
$247$		−	368.575i		−	1.49221i
$248$		0			0
$249$	138.057	−	82.1699i	0.554446	−	0.330000i
$250$		0			0
$251$	43.3235	−	43.3235i	0.172603	−	0.172603i	−0.615519	−	0.788122i	$-0.711053\pi$
$251$	43.3235	−	43.3235i	0.172603	−	0.172603i	0.788122	+	0.615519i	$0.211053\pi$
$252$		0			0
$253$	−34.8340	+	34.8340i	−0.137684	+	0.137684i
$254$		0			0
$255$	−161.166	+	95.9241i	−0.632024	+	0.376173i
$256$		0			0
$257$		−	179.197i		−	0.697266i	−0.937259	−	0.348633i	$-0.886646\pi$
$257$		−	179.197i		−	0.697266i	0.937259	−	0.348633i	$-0.113354\pi$
$258$		0			0
$259$	−2.81176	+	2.81176i	−0.0108562	+	0.0108562i
$260$		0			0
$261$	−70.0567	−	236.186i	−0.268416	−	0.904929i
$262$		0			0
$263$	−419.478			−1.59497			−0.797486	−	0.603338i	$-0.793837\pi$
$263$	−419.478			−1.59497			−0.797486	+	0.603338i	$0.793837\pi$
$264$		0			0
$265$		−	145.624i		−	0.549523i
$266$		0			0
$267$	4.02573	−	15.8637i	0.0150777	−	0.0594145i
$268$		0			0
$269$	−33.7631	−	33.7631i	−0.125513	−	0.125513i	0.641560	−	0.767073i	$-0.278288\pi$
$269$	−33.7631	−	33.7631i	−0.125513	−	0.125513i	−0.767073	+	0.641560i	$0.778288\pi$
$270$		0			0
$271$	−329.269			−1.21502			−0.607508	−	0.794314i	$-0.707831\pi$
$271$	−329.269			−1.21502			−0.607508	+	0.794314i	$0.707831\pi$
$272$		0			0
$273$	194.664	−	115.862i	0.713055	−	0.424402i
$274$		0			0
$275$	23.8557	+	23.8557i	0.0867482	+	0.0867482i
$276$		0			0
$277$	251.265	+	251.265i	0.907095	+	0.907095i	0.996037	−	0.0889417i	$-0.0283485\pi$
$277$	251.265	+	251.265i	0.907095	+	0.907095i	−0.0889417	+	0.996037i	$0.528348\pi$
$278$		0			0
$279$	92.1289	+	49.9778i	0.330211	+	0.179132i
$280$		0			0
$281$	−171.809			−0.611421			−0.305711	−	0.952124i	$-0.598894\pi$
$281$	−171.809			−0.611421			−0.305711	+	0.952124i	$0.598894\pi$
$282$		0			0
$283$	193.476	+	193.476i	0.683660	+	0.683660i	0.960823	−	0.277163i	$-0.0893942\pi$
$283$	193.476	+	193.476i	0.683660	+	0.683660i	−0.277163	+	0.960823i	$0.589394\pi$
$284$		0			0
$285$	115.236	+	29.2434i	0.404335	+	0.102608i
$286$		0			0
$287$			93.6662i			0.326363i
$288$		0			0
$289$	−499.073			−1.72690
$290$		0			0
$291$	59.8942	−	236.017i	0.205822	−	0.811055i
$292$		0			0
$293$	−73.4937	+	73.4937i	−0.250832	+	0.250832i	−0.821312	−	0.570480i	$-0.806757\pi$
$293$	−73.4937	+	73.4937i	−0.250832	+	0.250832i	0.570480	+	0.821312i	$0.306757\pi$
$294$		0			0
$295$			71.6601i			0.242916i
$296$		0			0
$297$	−1.80968	−	45.4170i	−0.00609320	−	0.152919i
$298$		0			0
$299$	428.579	−	428.579i	1.43337	−	1.43337i
$300$		0			0
$301$	−147.956	+	147.956i	−0.491547	+	0.491547i
$302$		0			0
$303$	−70.4131	−	118.304i	−0.232386	−	0.390442i
$304$		0			0
$305$			40.2222i			0.131876i
$306$		0			0
$307$	−283.055	+	283.055i	−0.922003	+	0.922003i	−0.997171	−	0.0751680i	$-0.976051\pi$
$307$	−283.055	+	283.055i	−0.922003	+	0.922003i	0.0751680	+	0.997171i	$0.476051\pi$
$308$		0			0
$309$	−148.847	−	37.7729i	−0.481704	−	0.122242i
$310$		0			0
$311$	−54.0368			−0.173752			−0.0868759	−	0.996219i	$-0.527688\pi$
$311$	−54.0368			−0.173752			−0.0868759	+	0.996219i	$0.527688\pi$
$312$		0			0
$313$			490.280i			1.56639i	0.621777	+	0.783194i	$0.286411\pi$
$313$			490.280i			1.56639i	−0.621777	+	0.783194i	$0.713589\pi$
$314$		0			0
$315$	20.7793	+	70.0547i	0.0659661	+	0.222396i
$316$		0			0
$317$	−319.550	−	319.550i	−1.00804	−	1.00804i	−0.999967	−	0.00807607i	$-0.997429\pi$
$317$	−319.550	−	319.550i	−1.00804	−	1.00804i	−0.00807607	−	0.999967i	$-0.502571\pi$
$318$		0			0
$319$	46.0810			0.144455
$320$		0			0
$321$	−185.461	−	311.601i	−0.577762	−	0.970721i
$322$		0			0
$323$	353.238	+	353.238i	1.09362	+	1.09362i
$324$		0			0
$325$	−293.508	−	293.508i	−0.903103	−	0.903103i
$326$		0			0
$327$	−114.685	−	192.686i	−0.350717	−	0.589255i
$328$		0			0
$329$	−183.265			−0.557036
$330$		0			0
$331$	269.431	+	269.431i	0.813992	+	0.813992i	0.985230	−	0.171238i	$-0.0547766\pi$
$331$	269.431	+	269.431i	0.813992	+	0.813992i	−0.171238	+	0.985230i	$0.554777\pi$
$332$		0			0
$333$	−2.79147	−	9.41106i	−0.00838279	−	0.0282614i
$334$		0			0
$335$		−	33.6557i		−	0.100465i
$336$		0			0
$337$	143.041			0.424453			0.212226	−	0.977221i	$-0.431929\pi$
$337$	143.041			0.424453			0.212226	+	0.977221i	$0.431929\pi$
$338$		0			0
$339$	−213.739	−	54.2406i	−0.630497	−	0.160002i
$340$		0			0
$341$	−13.8628	+	13.8628i	−0.0406534	+	0.0406534i
$342$		0			0
$343$			308.826i			0.900368i
$344$		0			0
$345$	99.9916	+	168.000i	0.289831	+	0.486957i
$346$		0			0
$347$	−126.922	+	126.922i	−0.365770	+	0.365770i	−0.865932	−	0.500162i	$-0.833274\pi$
$347$	−126.922	+	126.922i	−0.365770	+	0.365770i	0.500162	+	0.865932i	$0.333274\pi$
$348$		0			0
$349$	195.893	−	195.893i	0.561297	−	0.561297i	−0.368378	−	0.929676i	$-0.620087\pi$
$349$	195.893	−	195.893i	0.561297	−	0.561297i	0.929676	+	0.368378i	$0.120087\pi$
$350$		0			0
$351$	22.2653	+	558.787i	0.0634340	+	1.59198i
$352$		0			0
$353$			291.488i			0.825745i	0.910789	+	0.412873i	$0.135475\pi$
$353$			291.488i			0.825745i	−0.910789	+	0.412873i	$0.864525\pi$
$354$		0			0
$355$	−192.251	+	192.251i	−0.541552	+	0.541552i
$356$		0			0
$357$	−75.5233	+	297.604i	−0.211550	+	0.833626i
$358$		0			0
$359$	40.3499			0.112395			0.0561976	−	0.998420i	$-0.482102\pi$
$359$	40.3499			0.112395			0.0561976	+	0.998420i	$0.482102\pi$
$360$		0			0
$361$			44.3360i			0.122814i
$362$		0			0
$363$	−343.607	−	87.1973i	−0.946575	−	0.240213i
$364$		0			0
$365$	23.6846	+	23.6846i	0.0648893	+	0.0648893i
$366$		0			0
$367$	−340.678			−0.928279			−0.464140	−	0.885762i	$-0.653636\pi$
$367$	−340.678			−0.928279			−0.464140	+	0.885762i	$0.653636\pi$
$368$		0			0
$369$	−203.247	−	110.257i	−0.550805	−	0.298799i
$370$		0			0
$371$	−168.572	−	168.572i	−0.454372	−	0.454372i
$372$		0			0
$373$	237.678	+	237.678i	0.637207	+	0.637207i	0.949866	−	0.312658i	$-0.101219\pi$
$373$	237.678	+	237.678i	0.637207	+	0.637207i	−0.312658	+	0.949866i	$0.601219\pi$
$374$		0			0
$375$	258.579	−	153.903i	0.689544	−	0.410409i
$376$		0			0
$377$	−566.957			−1.50386
$378$		0			0
$379$	−320.332	−	320.332i	−0.845203	−	0.845203i	0.144327	−	0.989530i	$-0.453898\pi$
$379$	−320.332	−	320.332i	−0.845203	−	0.845203i	−0.989530	+	0.144327i	$0.953898\pi$
$380$		0			0
$381$	54.5570	−	214.985i	0.143194	−	0.564266i
$382$		0			0
$383$		−	632.700i		−	1.65196i	−0.563702	−	0.825978i	$-0.690623\pi$
$383$		−	632.700i		−	1.65196i	0.563702	−	0.825978i	$-0.309377\pi$
$384$		0			0
$385$	−13.6680			−0.0355012
$386$		0			0
$387$	−146.888	−	495.212i	−0.379555	−	1.27962i
$388$		0			0
$389$	424.351	−	424.351i	1.09088	−	1.09088i	0.0954418	−	0.995435i	$-0.469574\pi$
$389$	424.351	−	424.351i	1.09088	−	1.09088i	0.995435	−	0.0954418i	$-0.0304264\pi$
$390$		0			0
$391$			821.490i			2.10100i
$392$		0			0
$393$	577.595	−	343.778i	1.46971	−	0.874752i
$394$		0			0
$395$	−80.9323	+	80.9323i	−0.204892	+	0.204892i
$396$		0			0
$397$	−445.678	+	445.678i	−1.12262	+	1.12262i	−0.131269	+	0.991347i	$0.541905\pi$
$397$	−445.678	+	445.678i	−1.12262	+	1.12262i	−0.991347	+	0.131269i	$0.958095\pi$
$398$		0			0
$399$	167.247	−	99.5434i	0.419166	−	0.249482i
$400$		0			0
$401$			555.896i			1.38627i	0.720806	+	0.693137i	$0.243772\pi$
$401$			555.896i			1.38627i	−0.720806	+	0.693137i	$0.756228\pi$
$402$		0			0
$403$	170.561	−	170.561i	0.423228	−	0.423228i
$404$		0			0
$405$	−176.472	−	37.3738i	−0.435733	−	0.0922811i
$406$		0			0
$407$	1.83614			0.00451140
$408$		0			0
$409$			44.8261i			0.109599i	0.998497	+	0.0547997i	$0.0174520\pi$
$409$			44.8261i			0.109599i	−0.998497	+	0.0547997i	$0.982548\pi$
$410$		0			0
$411$	−74.3337	+	292.917i	−0.180861	+	0.712693i
$412$		0			0
$413$	82.9529	+	82.9529i	0.200854	+	0.200854i
$414$		0			0
$415$	119.263			0.287380
$416$		0			0
$417$	66.6196	−	39.6512i	0.159759	−	0.0950868i
$418$		0			0
$419$	15.2026	+	15.2026i	0.0362830	+	0.0362830i	0.725016	−	0.688733i	$-0.241833\pi$
$419$	15.2026	+	15.2026i	0.0362830	+	0.0362830i	−0.688733	+	0.725016i	$0.741833\pi$
$420$		0			0
$421$	262.889	+	262.889i	0.624439	+	0.624439i	0.946663	−	0.322224i	$-0.104431\pi$
$421$	262.889	+	262.889i	0.624439	+	0.624439i	−0.322224	+	0.946663i	$0.604431\pi$
$422$		0			0
$423$	215.726	−	397.668i	0.509990	−	0.940113i
$424$		0			0
$425$	562.590			1.32374
$426$		0			0
$427$	46.5608	+	46.5608i	0.109042	+	0.109042i
$428$		0			0
$429$	−101.390	−	25.7298i	−0.236340	−	0.0599762i
$430$		0			0
$431$		−	163.103i		−	0.378430i	−0.981936	−	0.189215i	$-0.939406\pi$
$431$		−	163.103i		−	0.378430i	0.981936	−	0.189215i	$-0.0605943\pi$
$432$		0			0
$433$	−140.737			−0.325028			−0.162514	−	0.986706i	$-0.551960\pi$
$433$	−140.737			−0.325028			−0.162514	+	0.986706i	$0.551960\pi$
$434$		0			0
$435$	44.9833	−	177.260i	0.103410	−	0.407494i
$436$		0			0
$437$	368.217	−	368.217i	0.842601	−	0.842601i
$438$		0			0
$439$		−	434.893i		−	0.990644i	−0.868709	−	0.495322i	$-0.835050\pi$
$439$		−	434.893i		−	0.990644i	0.868709	−	0.495322i	$-0.164950\pi$
$440$		0			0
$441$	−282.488	−	153.243i	−0.640562	−	0.347490i
$442$		0			0
$443$	−260.367	+	260.367i	−0.587736	+	0.587736i	−0.937018	−	0.349282i	$-0.886426\pi$
$443$	−260.367	+	260.367i	−0.587736	+	0.587736i	0.349282	+	0.937018i	$0.386426\pi$
$444$		0			0
$445$	8.59088	−	8.59088i	0.0193053	−	0.0193053i
$446$		0			0
$447$	−97.5869	−	163.960i	−0.218315	−	0.366801i
$448$		0			0
$449$			98.9506i			0.220380i	0.993911	+	0.110190i	$0.0351459\pi$
$449$			98.9506i			0.220380i	−0.993911	+	0.110190i	$0.964854\pi$
$450$		0			0
$451$	30.5830	−	30.5830i	0.0678115	−	0.0678115i
$452$		0			0
$453$	−81.7195	−	20.7380i	−0.180396	−	0.0457793i
$454$		0			0
$455$	168.164			0.369590
$456$		0			0
$457$			14.4209i			0.0315556i	0.999876	+	0.0157778i	$0.00502245\pi$
$457$			14.4209i			0.0315556i	−0.999876	+	0.0157778i	$0.994978\pi$
$458$		0			0
$459$	−556.873	−	514.196i	−1.21323	−	1.12025i
$460$		0			0
$461$	−328.278	−	328.278i	−0.712099	−	0.712099i	0.254875	−	0.966974i	$-0.417966\pi$
$461$	−328.278	−	328.278i	−0.712099	−	0.712099i	−0.966974	+	0.254875i	$0.917966\pi$
$462$		0			0
$463$	848.427			1.83246			0.916228	−	0.400657i	$-0.131218\pi$
$463$	848.427			1.83246			0.916228	+	0.400657i	$0.131218\pi$
$464$		0			0
$465$	39.7935	+	66.8587i	0.0855774	+	0.143782i
$466$		0			0
$467$	56.0706	+	56.0706i	0.120066	+	0.120066i	0.764587	−	0.644521i	$-0.222943\pi$
$467$	56.0706	+	56.0706i	0.120066	+	0.120066i	−0.644521	+	0.764587i	$0.722943\pi$
$468$		0			0
$469$	−38.9595	−	38.9595i	−0.0830693	−	0.0830693i
$470$		0			0
$471$	375.970	+	631.682i	0.798237	+	1.34115i
$472$		0			0
$473$	96.6181			0.204267
$474$		0			0
$475$	−252.170	−	252.170i	−0.530884	−	0.530884i
$476$		0			0
$477$	564.216	−	167.355i	1.18284	−	0.350850i
$478$		0			0
$479$			648.794i			1.35448i	0.735764	+	0.677238i	$0.236823\pi$
$479$			648.794i			1.35448i	−0.735764	+	0.677238i	$0.763177\pi$
$480$		0			0
$481$	−22.5909			−0.0469665
$482$		0			0
$483$	310.224	+	78.7257i	0.642285	+	0.162993i
$484$		0			0
$485$	127.814	−	127.814i	0.263533	−	0.263533i
$486$		0			0
$487$			176.783i			0.363004i	0.983391	+	0.181502i	$0.0580959\pi$
$487$			176.783i			0.363004i	−0.983391	+	0.181502i	$0.941904\pi$
$488$		0			0
$489$	−112.659	−	189.284i	−0.230387	−	0.387083i
$490$		0			0
$491$	−317.369	+	317.369i	−0.646373	+	0.646373i	−0.952114	−	0.305742i	$-0.901096\pi$
$491$	−317.369	+	317.369i	−0.646373	+	0.646373i	0.305742	+	0.952114i	$0.401096\pi$
$492$		0			0
$493$	543.365	−	543.365i	1.10216	−	1.10216i
$494$		0			0
$495$	16.0889	−	29.6582i	0.0325029	−	0.0599156i
$496$		0			0
$497$			445.095i			0.895563i
$498$		0			0
$499$	374.391	−	374.391i	0.750282	−	0.750282i	−0.224250	−	0.974532i	$-0.571993\pi$
$499$	374.391	−	374.391i	0.750282	−	0.750282i	0.974532	+	0.224250i	$0.0719931\pi$
$500$		0			0
$501$	−42.4551	+	167.297i	−0.0847407	+	0.333926i
$502$		0			0
$503$	386.094			0.767583			0.383791	−	0.923420i	$-0.374618\pi$
$503$	386.094			0.767583			0.383791	+	0.923420i	$0.374618\pi$
$504$		0			0
$505$		−	102.199i		−	0.202374i
$506$		0			0
$507$	756.024	+	191.857i	1.49117	+	0.378416i
$508$		0			0
$509$	−41.6258	−	41.6258i	−0.0817796	−	0.0817796i	0.665034	−	0.746813i	$-0.268417\pi$
$509$	−41.6258	−	41.6258i	−0.0817796	−	0.0817796i	−0.746813	+	0.665034i	$0.768417\pi$
$510$		0			0
$511$	54.8340			0.107307
$512$		0			0
$513$	19.1294	+	480.086i	0.0372893	+	0.935839i
$514$		0			0
$515$	−80.6071	−	80.6071i	−0.156519	−	0.156519i
$516$		0			0
$517$	59.8379	+	59.8379i	0.115741	+	0.115741i
$518$		0			0
$519$	410.512	−	244.332i	0.790968	−	0.470775i
$520$		0			0
$521$	−233.704			−0.448569			−0.224284	−	0.974524i	$-0.572004\pi$
$521$	−233.704			−0.448569			−0.224284	+	0.974524i	$0.572004\pi$
$522$		0			0
$523$	219.506	+	219.506i	0.419705	+	0.419705i	0.885102	−	0.465397i	$-0.154088\pi$
$523$	219.506	+	219.506i	0.419705	+	0.419705i	−0.465397	+	0.885102i	$0.654088\pi$
$524$		0			0
$525$	53.9146	−	212.454i	0.102694	−	0.404674i
$526$		0			0
$527$			326.927i			0.620355i
$528$		0			0
$529$	327.324			0.618760
$530$		0			0
$531$	−277.646	+	82.3542i	−0.522873	+	0.155093i
$532$		0			0
$533$	−376.277	+	376.277i	−0.705961	+	0.705961i
$534$		0			0
$535$		−	269.182i		−	0.503143i
$536$		0			0
$537$	−81.9601	+	48.7817i	−0.152626	+	0.0908411i
$538$		0			0
$539$	42.5065	−	42.5065i	0.0788618	−	0.0788618i
$540$		0			0
$541$	80.5203	−	80.5203i	0.148836	−	0.148836i	−0.628762	−	0.777598i	$-0.716438\pi$
$541$	80.5203	−	80.5203i	0.148836	−	0.148836i	0.777598	+	0.628762i	$0.216438\pi$
$542$		0			0
$543$	67.8157	−	40.3631i	0.124891	−	0.0743335i
$544$		0			0
$545$		−	166.455i		−	0.305422i
$546$		0			0
$547$	−1.49803	+	1.49803i	−0.00273863	+	0.00273863i	−0.708475	−	0.705736i	$-0.750616\pi$
$547$	−1.49803	+	1.49803i	−0.00273863	+	0.00273863i	0.705736	+	0.708475i	$0.250616\pi$
$548$		0			0
$549$	−155.840	+	46.2247i	−0.283862	+	0.0841981i
$550$		0			0
$551$	−487.105			−0.884038
$552$		0			0
$553$			187.373i			0.338829i
$554$		0			0
$555$	1.79240	−	7.06307i	0.00322955	−	0.0127263i
$556$		0			0
$557$	322.326	+	322.326i	0.578682	+	0.578682i	0.934540	−	0.355858i	$-0.115811\pi$
$557$	322.326	+	322.326i	0.578682	+	0.578682i	−0.355858	+	0.934540i	$0.615811\pi$
$558$		0			0
$559$	−1188.74			−2.12654
$560$		0			0
$561$	121.830	−	72.5118i	0.217166	−	0.129255i
$562$		0			0
$563$	523.954	+	523.954i	0.930646	+	0.930646i	0.997746	−	0.0671003i	$-0.0213748\pi$
$563$	523.954	+	523.954i	0.930646	+	0.930646i	−0.0671003	+	0.997746i	$0.521375\pi$
$564$		0			0
$565$	−115.749	−	115.749i	−0.204866	−	0.204866i
$566$		0			0
$567$	−247.545	+	161.018i	−0.436588	+	0.283983i
$568$		0			0
$569$	767.880			1.34952			0.674762	−	0.738035i	$-0.264246\pi$
$569$	767.880			1.34952			0.674762	+	0.738035i	$0.264246\pi$
$570$		0			0
$571$	3.43922	+	3.43922i	0.00602316	+	0.00602316i	0.710112	−	0.704089i	$-0.248644\pi$
$571$	3.43922	+	3.43922i	0.00602316	+	0.00602316i	−0.704089	+	0.710112i	$0.748644\pi$
$572$		0			0
$573$	−557.350	−	141.439i	−0.972688	−	0.246840i
$574$		0			0
$575$		−	586.446i		−	1.01991i
$576$		0			0
$577$	−572.442			−0.992100			−0.496050	−	0.868294i	$-0.665217\pi$
$577$	−572.442			−0.992100			−0.496050	+	0.868294i	$0.665217\pi$
$578$		0			0
$579$	−35.8833	+	141.400i	−0.0619746	+	0.244215i
$580$		0			0
$581$	138.057	−	138.057i	0.237620	−	0.237620i
$582$		0			0
$583$			110.081i			0.188818i
$584$		0			0
$585$	−197.949	+	364.899i	−0.338375	+	0.623759i
$586$		0			0
$587$	446.694	−	446.694i	0.760977	−	0.760977i	−0.215522	−	0.976499i	$-0.569145\pi$
$587$	446.694	−	446.694i	0.760977	−	0.760977i	0.976499	+	0.215522i	$0.0691453\pi$
$588$		0			0
$589$	146.539	−	146.539i	0.248792	−	0.248792i
$590$		0			0
$591$	295.668	+	496.764i	0.500284	+	0.840548i
$592$		0			0
$593$		−	838.112i		−	1.41334i	−0.707542	−	0.706671i	$-0.750196\pi$
$593$		−	838.112i		−	1.41334i	0.707542	−	0.706671i	$-0.249804\pi$
$594$		0			0
$595$	−161.166	+	161.166i	−0.270867	+	0.270867i
$596$		0			0
$597$	420.959	+	106.827i	0.705123	+	0.178940i
$598$		0			0
$599$	−414.241			−0.691555			−0.345777	−	0.938317i	$-0.612385\pi$
$599$	−414.241			−0.691555			−0.345777	+	0.938317i	$0.612385\pi$
$600$		0			0
$601$		−	305.786i		−	0.508795i	−0.967100	−	0.254397i	$-0.918123\pi$
$601$		−	305.786i		−	0.508795i	0.967100	−	0.254397i	$-0.0818771\pi$
$602$		0			0
$603$	130.399	−	38.6783i	0.216250	−	0.0641431i
$604$		0			0
$605$	−186.078	−	186.078i	−0.307567	−	0.307567i
$606$		0			0
$607$	103.217			0.170044			0.0850222	−	0.996379i	$-0.472904\pi$
$607$	103.217			0.170044			0.0850222	+	0.996379i	$0.472904\pi$
$608$		0			0
$609$	−153.122	−	257.266i	−0.251431	−	0.422440i
$610$		0			0
$611$	−736.214	−	736.214i	−1.20493	−	1.20493i
$612$		0			0
$613$	−391.273	−	391.273i	−0.638292	−	0.638292i	0.311842	−	0.950134i	$-0.399054\pi$
$613$	−391.273	−	391.273i	−0.638292	−	0.638292i	−0.950134	+	0.311842i	$0.899054\pi$
$614$		0			0
$615$	−87.7891	−	147.498i	−0.142746	−	0.239834i
$616$		0			0
$617$	−713.373			−1.15620			−0.578098	−	0.815967i	$-0.696205\pi$
$617$	−713.373			−1.15620			−0.578098	+	0.815967i	$0.696205\pi$
$618$		0			0
$619$	399.763	+	399.763i	0.645821	+	0.645821i	0.951980	−	0.306159i	$-0.0990440\pi$
$619$	399.763	+	399.763i	0.645821	+	0.645821i	−0.306159	+	0.951980i	$0.599044\pi$
$620$		0			0
$621$	−535.999	+	580.487i	−0.863123	+	0.934761i
$622$		0			0
$623$		−	19.8894i		−	0.0319252i
$624$		0			0
$625$	−277.635			−0.444217
$626$		0			0
$627$	−87.1099	−	22.1059i	−0.138931	−	0.0352567i
$628$		0			0
$629$	21.6508	−	21.6508i	0.0344210	−	0.0344210i
$630$		0			0
$631$		−	934.242i		−	1.48057i	−0.672291	−	0.740287i	$-0.734690\pi$
$631$		−	934.242i		−	1.48057i	0.672291	−	0.740287i	$-0.265310\pi$
$632$		0			0
$633$	426.071	+	715.859i	0.673097	+	1.13090i
$634$		0			0
$635$	116.424	−	116.424i	0.183345	−	0.183345i
$636$		0			0
$637$	−522.978	+	522.978i	−0.821001	+	0.821001i
$638$		0			0
$639$	−965.814	−	523.932i	−1.51145	−	0.819925i
$640$		0			0
$641$		−	26.1836i		−	0.0408480i	−0.999791	−	0.0204240i	$-0.993498\pi$
$641$		−	26.1836i		−	0.0408480i	0.999791	−	0.0204240i	$-0.00650162\pi$
$642$		0			0
$643$	−625.336	+	625.336i	−0.972529	+	0.972529i	−0.999633	−	0.0271039i	$-0.991371\pi$
$643$	−625.336	+	625.336i	−0.972529	+	0.972529i	0.0271039	+	0.999633i	$0.491371\pi$
$644$		0			0
$645$	94.3165	−	371.660i	0.146227	−	0.576218i
$646$		0			0
$647$	−97.2591			−0.150323			−0.0751616	−	0.997171i	$-0.523947\pi$
$647$	−97.2591			−0.150323			−0.0751616	+	0.997171i	$0.523947\pi$
$648$		0			0
$649$		−	54.1699i		−	0.0834668i
$650$		0			0
$651$	123.459	+	31.3303i	0.189645	+	0.0481265i
$652$		0			0
$653$	129.213	+	129.213i	0.197875	+	0.197875i	0.799089	−	0.601213i	$-0.205316\pi$
$653$	129.213	+	129.213i	0.197875	+	0.197875i	−0.601213	+	0.799089i	$0.705316\pi$
$654$		0			0
$655$	498.965			0.761778
$656$		0			0
$657$	−64.5464	+	118.985i	−0.0982442	+	0.181103i
$658$		0			0
$659$	−3.10975	−	3.10975i	−0.00471889	−	0.00471889i	0.704743	−	0.709462i	$-0.251062\pi$
$659$	−3.10975	−	3.10975i	−0.00471889	−	0.00471889i	−0.709462	+	0.704743i	$0.751062\pi$
$660$		0			0
$661$	−22.3424	−	22.3424i	−0.0338010	−	0.0338010i	0.690004	−	0.723805i	$-0.257609\pi$
$661$	−22.3424	−	22.3424i	−0.0338010	−	0.0338010i	−0.723805	+	0.690004i	$0.757609\pi$
$662$		0			0
$663$	−1498.93	+	892.146i	−2.26083	+	1.34562i
$664$		0			0
$665$	144.479			0.217262
$666$		0			0
$667$	−566.405	−	566.405i	−0.849183	−	0.849183i
$668$		0			0
$669$	−276.914	+	1091.20i	−0.413922	+	1.63109i
$670$		0			0
$671$		−	30.4052i		−	0.0453132i
$672$		0			0
$673$	1085.74			1.61329			0.806643	−	0.591039i	$-0.201282\pi$
$673$	1085.74			1.61329			0.806643	+	0.591039i	$0.201282\pi$
$674$		0			0
$675$	397.541	+	367.074i	0.588950	+	0.543814i
$676$		0			0
$677$	−813.520	+	813.520i	−1.20165	+	1.20165i	−0.227991	+	0.973663i	$0.573216\pi$
$677$	−813.520	+	813.520i	−1.20165	+	1.20165i	−0.973663	+	0.227991i	$0.926784\pi$
$678$		0			0
$679$		−	295.911i		−	0.435804i
$680$		0			0
$681$	−660.276	+	392.988i	−0.969568	+	0.577075i
$682$		0			0
$683$	−427.362	+	427.362i	−0.625713	+	0.625713i	−0.946986	−	0.321273i	$-0.895889\pi$
$683$	−427.362	+	427.362i	−0.625713	+	0.625713i	0.321273	+	0.946986i	$0.395889\pi$
$684$		0			0
$685$	−158.627	+	158.627i	−0.231573	+	0.231573i
$686$		0			0
$687$	561.217	−	334.030i	0.816910	−	0.486215i
$688$		0			0
$689$		−	1354.38i		−	1.96572i
$690$		0			0
$691$	420.170	−	420.170i	0.608061	−	0.608061i	−0.334378	−	0.942439i	$-0.608526\pi$
$691$	420.170	−	420.170i	0.608061	−	0.608061i	0.942439	+	0.334378i	$0.108526\pi$
$692$		0			0
$693$	−15.7077	−	52.9563i	−0.0226662	−	0.0764161i
$694$		0			0
$695$	57.5504			0.0828063
$696$		0			0
$697$		−	721.239i		−	1.03478i
$698$		0			0
$699$	−38.2089	+	150.565i	−0.0546622	+	0.215400i
$700$		0			0
$701$	774.018	+	774.018i	1.10416	+	1.10416i	0.993903	+	0.110260i	$0.0351684\pi$
$701$	774.018	+	774.018i	1.10416	+	1.10416i	0.110260	+	0.993903i	$0.464832\pi$
$702$		0			0
$703$	−19.4091			−0.0276090
$704$		0			0
$705$	288.591	−	171.766i	0.409349	−	0.243639i
$706$		0			0
$707$	−118.304	−	118.304i	−0.167332	−	0.167332i
$708$		0			0
$709$	198.261	+	198.261i	0.279635	+	0.279635i	0.832963	−	0.553328i	$-0.186642\pi$
$709$	198.261	+	198.261i	0.279635	+	0.279635i	−0.553328	+	0.832963i	$0.686642\pi$
$710$		0			0
$711$	−406.581	−	220.561i	−0.571844	−	0.310212i
$712$		0			0
$713$	340.790			0.477966
$714$		0			0
$715$	−54.9072	−	54.9072i	−0.0767932	−	0.0767932i
$716$		0			0
$717$	726.665	+	184.406i	1.01348	+	0.257192i
$718$		0			0
$719$			639.218i			0.889037i	0.895770	+	0.444519i	$0.146625\pi$
$719$			639.218i			0.889037i	−0.895770	+	0.444519i	$0.853375\pi$
$720$		0			0
$721$	−186.620			−0.258834
$722$		0			0
$723$	−326.553	+	1286.80i	−0.451664	+	1.77981i
$724$		0			0
$725$	−387.898	+	387.898i	−0.535031	+	0.535031i
$726$		0			0
$727$			789.136i			1.08547i	0.839904	+	0.542734i	$0.182611\pi$
$727$			789.136i			1.08547i	−0.839904	+	0.542734i	$0.817389\pi$
$728$		0			0
$729$	−58.0032	−	726.689i	−0.0795654	−	0.996830i
$730$		0			0
$731$	1139.27	−	1139.27i	1.55851	−	1.55851i
$732$		0			0
$733$	−49.8641	+	49.8641i	−0.0680274	+	0.0680274i	−0.740302	−	0.672275i	$-0.765317\pi$
$733$	−49.8641	+	49.8641i	−0.0680274	+	0.0680274i	0.672275	+	0.740302i	$0.265317\pi$
$734$		0			0
$735$	−122.016	−	205.004i	−0.166008	−	0.278917i
$736$		0			0
$737$			25.4414i			0.0345202i
$738$		0			0
$739$	−157.593	+	157.593i	−0.213252	+	0.213252i	−0.805647	−	0.592395i	$-0.798182\pi$
$739$	−157.593	+	157.593i	−0.213252	+	0.213252i	0.592395	+	0.805647i	$0.298182\pi$
$740$		0			0
$741$	1071.75	+	271.980i	1.44636	+	0.367044i
$742$		0			0
$743$	1305.03			1.75643			0.878216	−	0.478265i	$-0.158734\pi$
$743$	1305.03			1.75643			0.878216	+	0.478265i	$0.158734\pi$
$744$		0			0
$745$		−	141.639i		−	0.190120i
$746$		0			0
$747$	137.061	+	462.082i	0.183482	+	0.618583i
$748$		0			0
$749$	−311.601	−	311.601i	−0.416023	−	0.416023i
$750$		0			0
$751$	−793.800			−1.05699			−0.528495	−	0.848936i	$-0.677244\pi$
$751$	−793.800			−1.05699			−0.528495	+	0.848936i	$0.677244\pi$
$752$		0			0
$753$	94.0079	+	157.947i	0.124844	+	0.209756i
$754$		0			0
$755$	−44.2548	−	44.2548i	−0.0586156	−	0.0586156i
$756$		0			0
$757$	−750.497	−	750.497i	−0.991409	−	0.991409i	0.00855438	−	0.999963i	$-0.497277\pi$
$757$	−750.497	−	750.497i	−0.991409	−	0.991409i	−0.999963	+	0.00855438i	$0.997277\pi$
$758$		0			0
$759$	−75.5865	−	126.996i	−0.0995870	−	0.167320i
$760$		0			0
$761$	−1055.45			−1.38692			−0.693462	−	0.720493i	$-0.743916\pi$
$761$	−1055.45			−1.38692			−0.693462	+	0.720493i	$0.743916\pi$
$762$		0			0
$763$	−192.686	−	192.686i	−0.252538	−	0.252538i
$764$		0			0
$765$	−160.003	−	539.428i	−0.209154	−	0.705134i
$766$		0			0
$767$			666.478i			0.868942i
$768$		0			0
$769$	883.681			1.14913			0.574565	−	0.818459i	$-0.305171\pi$
$769$	883.681			1.14913			0.574565	+	0.818459i	$0.305171\pi$
$770$		0			0
$771$	521.076	+	132.234i	0.675844	+	0.171509i
$772$		0			0
$773$	−894.518	+	894.518i	−1.15720	+	1.15720i	−0.172129	+	0.985074i	$0.555065\pi$
$773$	−894.518	+	894.518i	−1.15720	+	1.15720i	−0.985074	+	0.172129i	$0.944935\pi$
$774$		0			0
$775$		−	233.387i		−	0.301144i
$776$		0			0
$777$	−6.10126	−	10.2510i	−0.00785233	−	0.0131930i
$778$		0			0
$779$	−323.281	+	323.281i	−0.414995	+	0.414995i
$780$		0			0
$781$	145.328	−	145.328i	0.186079	−	0.186079i
$782$		0			0
$783$	738.486	−	29.4256i	0.943150	−	0.0375806i
$784$		0			0
$785$			545.689i			0.695145i
$786$		0			0
$787$	779.150	−	779.150i	0.990026	−	0.990026i	−0.00992500	−	0.999951i	$-0.503159\pi$
$787$	779.150	−	779.150i	0.990026	−	0.990026i	0.999951	+	0.00992500i	$0.00315928\pi$
$788$		0			0
$789$	309.542	−	1219.77i	0.392322	−	1.54597i
$790$		0			0
$791$	−267.979			−0.338785
$792$		0			0
$793$			374.089i			0.471739i
$794$		0			0
$795$	423.448	+	107.459i	0.532639	+	0.135168i
$796$		0			0
$797$	−149.801	−	149.801i	−0.187956	−	0.187956i	0.606856	−	0.794812i	$-0.292430\pi$
$797$	−149.801	−	149.801i	−0.187956	−	0.187956i	−0.794812	+	0.606856i	$0.792430\pi$
$798$		0			0
$799$	1411.16			1.76616
$800$		0			0
$801$	43.1581	+	23.4123i	0.0538803	+	0.0292288i
$802$		0			0
$803$	−17.9039	−	17.9039i	−0.0222962	−	0.0222962i
$804$		0			0
$805$	168.000	+	168.000i	0.208696	+	0.208696i
$806$		0			0
$807$	123.092	−	73.2628i	0.152530	−	0.0907841i
$808$		0			0
$809$	373.773			0.462019			0.231009	−	0.972951i	$-0.425797\pi$
$809$	373.773			0.462019			0.231009	+	0.972951i	$0.425797\pi$
$810$		0			0
$811$	239.150	+	239.150i	0.294883	+	0.294883i	0.839006	−	0.544123i	$-0.183137\pi$
$811$	239.150	+	239.150i	0.294883	+	0.294883i	−0.544123	+	0.839006i	$0.683137\pi$
$812$		0			0
$813$	242.975	−	957.459i	0.298862	−	1.17769i
$814$		0			0
$815$		−	163.516i		−	0.200633i
$816$		0			0
$817$	−1021.31			−1.25008
$818$		0			0
$819$	193.259	+	651.547i	0.235970	+	0.795539i
$820$		0			0
$821$	385.069	−	385.069i	0.469024	−	0.469024i	−0.432574	−	0.901598i	$-0.642395\pi$
$821$	385.069	−	385.069i	0.469024	−	0.469024i	0.901598	+	0.432574i	$0.142395\pi$
$822$		0			0
$823$		−	1270.78i		−	1.54408i	−0.635576	−	0.772038i	$-0.719237\pi$
$823$		−	1270.78i		−	1.54408i	0.635576	−	0.772038i	$-0.280763\pi$
$824$		0			0
$825$	−86.9721	+	51.7648i	−0.105421	+	0.0627452i
$826$		0			0
$827$	−113.766	+	113.766i	−0.137565	+	0.137565i	−0.772536	−	0.634971i	$-0.781012\pi$
$827$	−113.766	+	113.766i	−0.137565	+	0.137565i	0.634971	+	0.772536i	$0.281012\pi$
$828$		0			0
$829$	238.593	−	238.593i	0.287809	−	0.287809i	−0.548404	−	0.836213i	$-0.684765\pi$
$829$	238.593	−	238.593i	0.287809	−	0.287809i	0.836213	+	0.548404i	$0.184765\pi$
$830$		0			0
$831$	−916.051	+	545.222i	−1.10235	+	0.656104i
$832$		0			0
$833$		−	1002.43i		−	1.20340i
$834$		0			0
$835$	−90.5988	+	90.5988i	−0.108502	+	0.108502i
$836$		0			0
$837$	−213.311	+	231.015i	−0.254852	+	0.276004i
$838$		0			0
$839$	−65.2466			−0.0777671			−0.0388836	−	0.999244i	$-0.512380\pi$
$839$	−65.2466			−0.0777671			−0.0388836	+	0.999244i	$0.512380\pi$
$840$		0			0
$841$		−	91.7164i		−	0.109056i
$842$		0			0
$843$	126.782	−	499.592i	0.150394	−	0.592636i
$844$		0			0
$845$	409.421	+	409.421i	0.484522	+	0.484522i
$846$		0			0
$847$	−430.804			−0.508623
$848$		0			0
$849$	−705.365	+	419.825i	−0.830818	+	0.494493i
$850$		0			0
$851$	−22.5689	−	22.5689i	−0.0265205	−	0.0265205i
$852$		0			0
$853$	−245.067	−	245.067i	−0.287300	−	0.287300i	0.548712	−	0.836012i	$-0.315118\pi$
$853$	−245.067	−	245.067i	−0.287300	−	0.287300i	−0.836012	+	0.548712i	$0.815118\pi$
$854$		0			0
$855$	−170.070	+	313.506i	−0.198912	+	0.366674i
$856$		0			0
$857$	1408.63			1.64368			0.821841	−	0.569718i	$-0.192947\pi$
$857$	1408.63			1.64368			0.821841	+	0.569718i	$0.192947\pi$
$858$		0			0
$859$	50.1621	+	50.1621i	0.0583959	+	0.0583959i	0.735702	−	0.677306i	$-0.236853\pi$
$859$	50.1621	+	50.1621i	0.0583959	+	0.0583959i	−0.677306	+	0.735702i	$0.736853\pi$
$860$		0			0
$861$	−272.365	−	69.1184i	−0.316336	−	0.0802769i
$862$		0			0
$863$		−	1027.80i		−	1.19096i	−0.803370	−	0.595480i	$-0.796962\pi$
$863$		−	1027.80i		−	1.19096i	0.803370	−	0.595480i	$-0.203038\pi$
$864$		0			0
$865$	354.627			0.409974
$866$		0			0
$867$	368.277	−	1451.22i	0.424772	−	1.67384i
$868$		0			0
$869$	61.1791	−	61.1791i	0.0704017	−	0.0704017i
$870$		0			0
$871$		−	313.017i		−	0.359376i
$872$		0			0
$873$	642.100	+	348.324i	0.735509	+	0.398997i
$874$		0			0
$875$	258.579	−	258.579i	0.295519	−	0.295519i
$876$		0			0
$877$	600.071	−	600.071i	0.684231	−	0.684231i	−0.276720	−	0.960951i	$-0.589247\pi$
$877$	600.071	−	600.071i	0.684231	−	0.684231i	0.960951	+	0.276720i	$0.0892473\pi$
$878$		0			0
$879$	−159.474	−	267.940i	−0.181427	−	0.304823i
$880$		0			0
$881$			786.482i			0.892715i	0.894855	+	0.446358i	$0.147279\pi$
$881$			786.482i			0.892715i	−0.894855	+	0.446358i	$0.852721\pi$
$882$		0			0
$883$	390.413	−	390.413i	0.442144	−	0.442144i	−0.450588	−	0.892732i	$-0.648786\pi$
$883$	390.413	−	390.413i	0.442144	−	0.442144i	0.892732	+	0.450588i	$0.148786\pi$
$884$		0			0
$885$	−208.375	−	52.8796i	−0.235452	−	0.0597509i
$886$		0			0
$887$	1446.61			1.63090			0.815450	−	0.578827i	$-0.196489\pi$
$887$	1446.61			1.63090			0.815450	+	0.578827i	$0.196489\pi$
$888$		0			0
$889$		−	269.542i		−	0.303197i
$890$		0			0
$891$	133.400	+	28.2520i	0.149720	+	0.0317081i
$892$		0			0
$893$	−632.524	−	632.524i	−0.708313	−	0.708313i
$894$		0			0
$895$	−70.8025			−0.0791089
$896$		0			0
$897$	929.976	+	1562.49i	1.03676	+	1.74191i
$898$		0			0
$899$	−225.411	−	225.411i	−0.250736	−	0.250736i
$900$		0			0
$901$	1298.02	+	1298.02i	1.44064	+	1.44064i
$902$		0			0
$903$	−321.050	−	539.409i	−0.355537	−	0.597352i
$904$		0			0
$905$	58.5836			0.0647333
$906$		0			0
$907$	535.919	+	535.919i	0.590870	+	0.590870i	0.937866	−	0.346997i	$-0.112798\pi$
$907$	535.919	+	535.919i	0.590870	+	0.590870i	−0.346997	+	0.937866i	$0.612798\pi$
$908$		0			0
$909$	395.967	−	117.450i	0.435607	−	0.129208i
$910$		0			0
$911$			1580.22i			1.73460i	0.497786	+	0.867300i	$0.334146\pi$
$911$			1580.22i			1.73460i	−0.497786	+	0.867300i	$0.665854\pi$
$912$		0			0
$913$	−90.1542			−0.0987450
$914$		0			0
$915$	−116.959	−	29.6809i	−0.127825	−	0.0324381i
$916$		0			0
$917$	577.595	−	577.595i	0.629875	−	0.629875i
$918$		0			0
$919$			1486.86i			1.61791i	0.587869	+	0.808956i	$0.299967\pi$
$919$			1486.86i			1.61791i	−0.587869	+	0.808956i	$0.700033\pi$
$920$		0			0
$921$	−614.203	−	1031.95i	−0.666887	−	1.12046i
$922$		0			0
$923$	−1788.04	+	1788.04i	−1.93720	+	1.93720i
$924$		0			0
$925$	−15.4561	+	15.4561i	−0.0167093	+	0.0167093i
$926$		0			0
$927$	219.674	−	404.947i	0.236974	−	0.436836i
$928$		0			0
$929$			1091.41i			1.17482i	0.809290	+	0.587409i	$0.199852\pi$
$929$			1091.41i			1.17482i	−0.809290	+	0.587409i	$0.800148\pi$
$930$		0			0
$931$	−449.320	+	449.320i	−0.482621	+	0.482621i
$932$		0			0
$933$	39.8750	−	157.130i	0.0427384	−	0.168414i
$934$		0			0
$935$	105.245			0.112561
$936$		0			0
$937$			887.919i			0.947619i	0.880627	+	0.473809i	$0.157121\pi$
$937$			887.919i			0.947619i	−0.880627	+	0.473809i	$0.842879\pi$
$938$		0			0
$939$	−1425.65	−	361.788i	−1.51826	−	0.385291i
$940$		0			0
$941$	790.753	+	790.753i	0.840333	+	0.840333i	0.988902	−	0.148569i	$-0.0474667\pi$
$941$	790.753	+	790.753i	0.840333	+	0.840333i	−0.148569	+	0.988902i	$0.547467\pi$
$942$		0			0
$943$	−751.822			−0.797266
$944$		0			0
$945$	−219.041	+	8.72786i	−0.231789	+	0.00923583i
$946$		0			0
$947$	−1170.78	−	1170.78i	−1.23630	−	1.23630i	−0.961502	−	0.274796i	$-0.911390\pi$
$947$	−1170.78	−	1170.78i	−1.23630	−	1.23630i	−0.274796	−	0.961502i	$-0.588610\pi$
$948$		0			0
$949$	220.280	+	220.280i	0.232118	+	0.232118i
$950$		0			0
$951$	1165.00	−	693.393i	1.22503	−	0.729120i
$952$		0			0
$953$	1148.50			1.20514			0.602571	−	0.798065i	$-0.294143\pi$
$953$	1148.50			1.20514			0.602571	+	0.798065i	$0.294143\pi$
$954$		0			0
$955$	−301.830	−	301.830i	−0.316052	−	0.316052i
$956$		0			0
$957$	−34.0042	+	133.996i	−0.0355321	+	0.140016i
$958$		0			0
$959$			367.250i			0.382951i
$960$		0			0
$961$	−825.376			−0.858873
$962$		0			0
$963$	1042.94	−	309.353i	1.08301	−	0.321238i
$964$		0			0
$965$	−76.5746	+	76.5746i	−0.0793519	+	0.0793519i
$966$		0			0
$967$			1696.75i			1.75466i	0.479892	+	0.877328i	$0.340676\pi$
$967$			1696.75i			1.75466i	−0.479892	+	0.877328i	$0.659324\pi$
$968$		0			0
$969$	−1287.82	+	766.494i	−1.32902	+	0.791016i
$970$		0			0
$971$	−119.876	+	119.876i	−0.123457	+	0.123457i	−0.766136	−	0.642679i	$-0.777823\pi$
$971$	−119.876	+	119.876i	−0.123457	+	0.123457i	0.642679	+	0.766136i	$0.277823\pi$
$972$		0			0
$973$	66.6196	−	66.6196i	0.0684682	−	0.0684682i
$974$		0			0
$975$	1070.06	−	636.886i	1.09750	−	0.653217i
$976$		0			0
$977$		−	1408.74i		−	1.44190i	−0.692985	−	0.720952i	$-0.743705\pi$
$977$		−	1408.74i		−	1.44190i	0.692985	−	0.720952i	$-0.256295\pi$
$978$		0			0
$979$	−6.49409	+	6.49409i	−0.00663340	+	0.00663340i
$980$		0			0
$981$	644.927	−	191.296i	0.657418	−	0.195001i
$982$		0			0
$983$	−1288.34			−1.31062			−0.655309	−	0.755361i	$-0.727461\pi$
$983$	−1288.34			−1.31062			−0.655309	+	0.755361i	$0.727461\pi$
$984$		0			0
$985$			429.137i			0.435672i
$986$		0			0
$987$	135.235	−	532.903i	0.137016	−	0.539922i
$988$		0			0
$989$	−1187.58	−	1187.58i	−1.20079	−	1.20079i
$990$		0			0
$991$	1013.28			1.02248			0.511242	−	0.859437i	$-0.329185\pi$
$991$	1013.28			1.02248			0.511242	+	0.859437i	$0.329185\pi$
$992$		0			0
$993$	−982.280	+	584.641i	−0.989204	+	0.588762i
$994$		0			0
$995$	227.968	+	227.968i	0.229113	+	0.229113i
$996$		0			0
$997$	−537.885	−	537.885i	−0.539503	−	0.539503i	0.383880	−	0.923383i	$-0.374588\pi$
$997$	−537.885	−	537.885i	−0.539503	−	0.539503i	−0.923383	+	0.383880i	$0.874588\pi$
$998$		0			0
$999$	29.4256	−	1.17249i	0.0294551	−	0.00117366i

Twists

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

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

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.737922 + 2.90783i) q^{3} +(-1.57472 + 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +O(q^{10})\)	\(q+(-0.737922 + 2.90783i) q^{3} +(-1.57472 + 1.57472i) q^{5} +3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +(1.19038 - 1.19038i) q^{11} +(-14.6458 + 14.6458i) q^{13} +(-3.41699 - 5.74103i) q^{15} -28.0726i q^{17} +(-12.5830 + 12.5830i) q^{19} +(-10.6012 - 2.69028i) q^{21} -29.2630 q^{23} +20.0405i q^{25} +(18.3166 - 19.8369i) q^{27} +(19.3557 + 19.3557i) q^{29} -11.6458 q^{31} +(2.58301 + 4.33981i) q^{33} +(-5.74103 - 5.74103i) q^{35} +(0.771243 + 0.771243i) q^{37} +(-31.7799 - 53.3948i) q^{39} +25.6919 q^{41} +(40.5830 + 40.5830i) q^{43} +(19.2154 - 5.69960i) q^{45} +50.2681i q^{47} +35.7085 q^{49} +(81.6304 + 20.7154i) q^{51} +(-46.2379 + 46.2379i) q^{53} +3.74902i q^{55} +(-27.3040 - 45.8745i) q^{57} +(22.7533 - 22.7533i) q^{59} +(12.7712 - 12.7712i) q^{61} +(15.6458 - 28.8413i) q^{63} -46.1259i q^{65} +(-10.6863 + 10.6863i) q^{67} +(21.5938 - 85.0919i) q^{69} +122.086 q^{71} -15.0405i q^{73} +(-58.2744 - 14.7883i) q^{75} +(4.33981 + 4.33981i) q^{77} +51.3948 q^{79} +(44.1660 + 67.8997i) q^{81} +(-37.8680 - 37.8680i) q^{83} +(44.2065 + 44.2065i) q^{85} +(-70.5659 + 42.0000i) q^{87} -5.45550 q^{89} +(-53.3948 - 53.3948i) q^{91} +(8.59366 - 33.8639i) q^{93} -39.6294i q^{95} -81.1660 q^{97} +(-14.5255 + 4.30849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3}+O(q^{10}) \) 8 * q - 4 * q^3	\( 8 q - 4 q^{3} - 96 q^{13} - 112 q^{15} - 16 q^{19} - 32 q^{21} + 68 q^{27} - 72 q^{31} - 64 q^{33} + 112 q^{37} + 240 q^{43} - 112 q^{45} + 328 q^{49} + 32 q^{51} + 208 q^{61} + 104 q^{63} + 232 q^{67} - 324 q^{75} + 136 q^{79} + 184 q^{81} - 112 q^{85} - 152 q^{91} + 64 q^{93} - 480 q^{97} - 160 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 96 * q^13 - 112 * q^15 - 16 * q^19 - 32 * q^21 + 68 * q^27 - 72 * q^31 - 64 * q^33 + 112 * q^37 + 240 * q^43 - 112 * q^45 + 328 * q^49 + 32 * q^51 + 208 * q^61 + 104 * q^63 + 232 * q^67 - 324 * q^75 + 136 * q^79 + 184 * q^81 - 112 * q^85 - 152 * q^91 + 64 * q^93 - 480 * q^97 - 160 * q^99

Introduction

L-functions

Modular forms

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