LMFDB - Embedded newform 192.3.i.b.113.7

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.7
Root			$1.28499 - 1.53258i$ of defining polynomial
Character	$\chi$	$=$	192.113
Dual form			192.3.i.b.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06336 - 2.17774i) q^{3} +(-3.17955 + 3.17955i) q^{5} -6.03979i q^{7} +(-0.485128 - 8.98692i) q^{9} +O(q^{10})$	\(q+(2.06336 - 2.17774i) q^{3} +(-3.17955 + 3.17955i) q^{5} -6.03979i q^{7} +(-0.485128 - 8.98692i) q^{9} +(13.0097 - 13.0097i) q^{11} +(6.39520 - 6.39520i) q^{13} +(0.363700 + 13.4848i) q^{15} -4.39848i q^{17} +(3.21075 - 3.21075i) q^{19} +(-13.1531 - 12.4622i) q^{21} -34.0396 q^{23} +4.78097i q^{25} +(-20.5722 - 17.4867i) q^{27} +(27.9597 + 27.9597i) q^{29} +7.90993 q^{31} +(-1.48814 - 55.1754i) q^{33} +(19.2038 + 19.2038i) q^{35} +(20.0443 + 20.0443i) q^{37} +(-0.731530 - 27.1227i) q^{39} -45.1067 q^{41} +(36.0095 + 36.0095i) q^{43} +(30.1168 + 27.0318i) q^{45} -5.08935i q^{47} +12.5209 q^{49} +(-9.57876 - 9.07563i) q^{51} +(20.7687 - 20.7687i) q^{53} +82.7299i q^{55} +(-0.367268 - 13.6171i) q^{57} +(39.0656 - 39.0656i) q^{59} +(-49.8322 + 49.8322i) q^{61} +(-54.2791 + 2.93007i) q^{63} +40.6677i q^{65} +(-44.9162 + 44.9162i) q^{67} +(-70.2358 + 74.1295i) q^{69} -46.6947 q^{71} +97.3523i q^{73} +(10.4117 + 9.86483i) q^{75} +(-78.5758 - 78.5758i) q^{77} +40.1637 q^{79} +(-80.5293 + 8.71960i) q^{81} +(35.5451 + 35.5451i) q^{83} +(13.9852 + 13.9852i) q^{85} +(118.580 - 3.19823i) q^{87} +69.6795 q^{89} +(-38.6257 - 38.6257i) q^{91} +(16.3210 - 17.2258i) q^{93} +20.4174i q^{95} +61.0939 q^{97} +(-123.228 - 110.606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3}+O(q^{10}) $ 20 * q + 6 * q^3	$ 20 q + 6 q^{3} + 92 q^{13} + 116 q^{15} + 52 q^{19} + 48 q^{21} - 18 q^{27} + 80 q^{31} + 60 q^{33} - 116 q^{37} - 172 q^{43} + 60 q^{45} - 364 q^{49} - 128 q^{51} - 244 q^{61} - 296 q^{63} - 356 q^{67} - 20 q^{69} + 146 q^{75} - 384 q^{79} - 188 q^{81} + 48 q^{85} - 136 q^{91} - 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) $ 20 * q + 6 * q^3 + 92 * q^13 + 116 * q^15 + 52 * q^19 + 48 * q^21 - 18 * q^27 + 80 * q^31 + 60 * q^33 - 116 * q^37 - 172 * q^43 + 60 * q^45 - 364 * q^49 - 128 * q^51 - 244 * q^61 - 296 * q^63 - 356 * q^67 - 20 * q^69 + 146 * q^75 - 384 * q^79 - 188 * q^81 + 48 * q^85 - 136 * q^91 - 132 * q^93 + 472 * q^97 + 452 * 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
$3$	2.06336	−	2.17774i	0.687785	−	0.725914i
$3$	2.06336	−	2.17774i	0.687785	−	0.725914i
$4$		0			0
$5$	−3.17955	+	3.17955i	−0.635909	+	0.635909i	−0.949544	−	0.313634i	$-0.898453\pi$
$5$	−3.17955	+	3.17955i	−0.635909	+	0.635909i	0.313634	+	0.949544i	$0.398453\pi$
$6$		0			0
$7$		−	6.03979i		−	0.862827i	−0.902154	−	0.431414i	$-0.858015\pi$
$7$		−	6.03979i		−	0.862827i	0.902154	−	0.431414i	$-0.141985\pi$
$8$		0			0
$9$	−0.485128	−	8.98692i	−0.0539031	−	0.998546i
$10$		0			0
$11$	13.0097	−	13.0097i	1.18270	−	1.18270i	0.203657	−	0.979042i	$-0.434717\pi$
$11$	13.0097	−	13.0097i	1.18270	−	1.18270i	0.979042	−	0.203657i	$-0.0652828\pi$
$12$		0			0
$13$	6.39520	−	6.39520i	0.491939	−	0.491939i	−0.416978	−	0.908917i	$-0.636911\pi$
$13$	6.39520	−	6.39520i	0.491939	−	0.491939i	0.908917	+	0.416978i	$0.136911\pi$
$14$		0			0
$15$	0.363700	+	13.4848i	0.0242466	+	0.898985i
$16$		0			0
$17$		−	4.39848i		−	0.258734i	−0.991597	−	0.129367i	$-0.958705\pi$
$17$		−	4.39848i		−	0.258734i	0.991597	−	0.129367i	$-0.0412945\pi$
$18$		0			0
$19$	3.21075	−	3.21075i	0.168987	−	0.168987i	−0.617547	−	0.786534i	$-0.711874\pi$
$19$	3.21075	−	3.21075i	0.168987	−	0.168987i	0.786534	+	0.617547i	$0.211874\pi$
$20$		0			0
$21$	−13.1531	−	12.4622i	−0.626339	−	0.593440i
$22$		0			0
$23$	−34.0396			−1.47998			−0.739992	−	0.672616i	$-0.765171\pi$
$23$	−34.0396			−1.47998			−0.739992	+	0.672616i	$0.765171\pi$
$24$		0			0
$25$			4.78097i			0.191239i
$26$		0			0
$27$	−20.5722	−	17.4867i	−0.761933	−	0.647656i
$28$		0			0
$29$	27.9597	+	27.9597i	0.964128	+	0.964128i	0.999378	−	0.0352510i	$-0.0112231\pi$
$29$	27.9597	+	27.9597i	0.964128	+	0.964128i	−0.0352510	+	0.999378i	$0.511223\pi$
$30$		0			0
$31$	7.90993			0.255159			0.127580	−	0.991828i	$-0.459279\pi$
$31$	7.90993			0.255159			0.127580	+	0.991828i	$0.459279\pi$
$32$		0			0
$33$	−1.48814	−	55.1754i	−0.0450952	−	1.67198i
$34$		0			0
$35$	19.2038	+	19.2038i	0.548680	+	0.548680i
$36$		0			0
$37$	20.0443	+	20.0443i	0.541736	+	0.541736i	0.924038	−	0.382301i	$-0.124868\pi$
$37$	20.0443	+	20.0443i	0.541736	+	0.541736i	−0.382301	+	0.924038i	$0.624868\pi$
$38$		0			0
$39$	−0.731530	−	27.1227i	−0.0187572	−	0.695453i
$40$		0			0
$41$	−45.1067			−1.10016			−0.550081	−	0.835111i	$-0.685403\pi$
$41$	−45.1067			−1.10016			−0.550081	+	0.835111i	$0.685403\pi$
$42$		0			0
$43$	36.0095	+	36.0095i	0.837431	+	0.837431i	0.988520	−	0.151089i	$-0.0482782\pi$
$43$	36.0095	+	36.0095i	0.837431	+	0.837431i	−0.151089	+	0.988520i	$0.548278\pi$
$44$		0			0
$45$	30.1168	+	27.0318i	0.669262	+	0.600707i
$46$		0			0
$47$		−	5.08935i		−	0.108284i	−0.998533	−	0.0541421i	$-0.982758\pi$
$47$		−	5.08935i		−	0.108284i	0.998533	−	0.0541421i	$-0.0172424\pi$
$48$		0			0
$49$	12.5209			0.255529
$50$		0			0
$51$	−9.57876	−	9.07563i	−0.187819	−	0.177953i
$52$		0			0
$53$	20.7687	−	20.7687i	0.391863	−	0.391863i	−0.483488	−	0.875351i	$-0.660630\pi$
$53$	20.7687	−	20.7687i	0.391863	−	0.391863i	0.875351	+	0.483488i	$0.160630\pi$
$54$		0			0
$55$			82.7299i			1.50418i
$56$		0			0
$57$	−0.367268	−	13.6171i	−0.00644331	−	0.238896i
$58$		0			0
$59$	39.0656	−	39.0656i	0.662129	−	0.662129i	−0.293753	−	0.955881i	$-0.594904\pi$
$59$	39.0656	−	39.0656i	0.662129	−	0.662129i	0.955881	+	0.293753i	$0.0949043\pi$
$60$		0			0
$61$	−49.8322	+	49.8322i	−0.816921	+	0.816921i	−0.985661	−	0.168739i	$-0.946030\pi$
$61$	−49.8322	+	49.8322i	−0.816921	+	0.816921i	0.168739	+	0.985661i	$0.446030\pi$
$62$		0			0
$63$	−54.2791	+	2.93007i	−0.861573	+	0.0465090i
$64$		0			0
$65$			40.6677i			0.625657i
$66$		0			0
$67$	−44.9162	+	44.9162i	−0.670390	+	0.670390i	−0.957806	−	0.287416i	$-0.907204\pi$
$67$	−44.9162	+	44.9162i	−0.670390	+	0.670390i	0.287416	+	0.957806i	$0.407204\pi$
$68$		0			0
$69$	−70.2358	+	74.1295i	−1.01791	+	1.07434i
$70$		0			0
$71$	−46.6947			−0.657672			−0.328836	−	0.944387i	$-0.606656\pi$
$71$	−46.6947			−0.657672			−0.328836	+	0.944387i	$0.606656\pi$
$72$		0			0
$73$			97.3523i			1.33359i	0.745240	+	0.666797i	$0.232335\pi$
$73$			97.3523i			1.33359i	−0.745240	+	0.666797i	$0.767665\pi$
$74$		0			0
$75$	10.4117	+	9.86483i	0.138823	+	0.131531i
$76$		0			0
$77$	−78.5758	−	78.5758i	−1.02047	−	1.02047i
$78$		0			0
$79$	40.1637			0.508402			0.254201	−	0.967151i	$-0.418188\pi$
$79$	40.1637			0.508402			0.254201	+	0.967151i	$0.418188\pi$
$80$		0			0
$81$	−80.5293	+	8.71960i	−0.994189	+	0.107649i
$82$		0			0
$83$	35.5451	+	35.5451i	0.428254	+	0.428254i	0.888033	−	0.459779i	$-0.152071\pi$
$83$	35.5451	+	35.5451i	0.428254	+	0.428254i	−0.459779	+	0.888033i	$0.652071\pi$
$84$		0			0
$85$	13.9852	+	13.9852i	0.164531	+	0.164531i
$86$		0			0
$87$	118.580	−	3.19823i	1.36299	−	0.0367613i
$88$		0			0
$89$	69.6795			0.782916			0.391458	−	0.920196i	$-0.371971\pi$
$89$	69.6795			0.782916			0.391458	+	0.920196i	$0.371971\pi$
$90$		0			0
$91$	−38.6257	−	38.6257i	−0.424458	−	0.424458i
$92$		0			0
$93$	16.3210	−	17.2258i	0.175495	−	0.185224i
$94$		0			0
$95$			20.4174i			0.214920i
$96$		0			0
$97$	61.0939			0.629834			0.314917	−	0.949119i	$-0.398023\pi$
$97$	61.0939			0.629834			0.314917	+	0.949119i	$0.398023\pi$
$98$		0			0
$99$	−123.228	−	110.606i	−1.24473	−	1.11723i
$100$		0			0
$101$	104.036	−	104.036i	1.03006	−	1.03006i	0.0305280	−	0.999534i	$-0.490281\pi$
$101$	104.036	−	104.036i	1.03006	−	1.03006i	0.999534	−	0.0305280i	$-0.00971886\pi$
$102$		0			0
$103$		−	57.2961i		−	0.556272i	−0.960542	−	0.278136i	$-0.910283\pi$
$103$		−	57.2961i		−	0.556272i	0.960542	−	0.278136i	$-0.0897167\pi$
$104$		0			0
$105$	81.4452	−	2.19667i	0.775668	−	0.0209207i
$106$		0			0
$107$	−92.4468	+	92.4468i	−0.863989	+	0.863989i	−0.991799	−	0.127810i	$-0.959205\pi$
$107$	−92.4468	+	92.4468i	−0.863989	+	0.863989i	0.127810	+	0.991799i	$0.459205\pi$
$108$		0			0
$109$	75.3749	−	75.3749i	0.691513	−	0.691513i	−0.271052	−	0.962565i	$-0.587371\pi$
$109$	75.3749	−	75.3749i	0.691513	−	0.691513i	0.962565	+	0.271052i	$0.0873714\pi$
$110$		0			0
$111$	85.0096	−	2.29281i	0.765853	−	0.0206559i
$112$		0			0
$113$			112.254i			0.993401i	0.867922	+	0.496701i	$0.165455\pi$
$113$			112.254i			0.993401i	−0.867922	+	0.496701i	$0.834545\pi$
$114$		0			0
$115$	108.231	−	108.231i	0.941135	−	0.941135i
$116$		0			0
$117$	−60.5756	−	54.3707i	−0.517740	−	0.464706i
$118$		0			0
$119$	−26.5659			−0.223243
$120$		0			0
$121$		−	217.504i		−	1.79756i
$122$		0			0
$123$	−93.0711	+	98.2307i	−0.756676	+	0.798624i
$124$		0			0
$125$	−94.6900	−	94.6900i	−0.757520	−	0.757520i
$126$		0			0
$127$	−93.6335			−0.737272			−0.368636	−	0.929574i	$-0.620175\pi$
$127$	−93.6335			−0.737272			−0.368636	+	0.929574i	$0.620175\pi$
$128$		0			0
$129$	152.720	−	4.11903i	1.18388	−	0.0319305i
$130$		0			0
$131$	81.5208	+	81.5208i	0.622296	+	0.622296i	0.946118	−	0.323822i	$-0.104968\pi$
$131$	81.5208	+	81.5208i	0.622296	+	0.622296i	−0.323822	+	0.946118i	$0.604968\pi$
$132$		0			0
$133$	−19.3922	−	19.3922i	−0.145806	−	0.145806i
$134$		0			0
$135$	121.010	−	9.81037i	0.896371	−	0.0726694i
$136$		0			0
$137$	−24.5510			−0.179205			−0.0896023	−	0.995978i	$-0.528560\pi$
$137$	−24.5510			−0.179205			−0.0896023	+	0.995978i	$0.528560\pi$
$138$		0			0
$139$	−3.06917	−	3.06917i	−0.0220804	−	0.0220804i	0.695980	−	0.718061i	$-0.254970\pi$
$139$	−3.06917	−	3.06917i	−0.0220804	−	0.0220804i	−0.718061	+	0.695980i	$0.754970\pi$
$140$		0			0
$141$	−11.0833	−	10.5011i	−0.0786050	−	0.0744762i
$142$		0			0
$143$		−	166.399i		−	1.16363i
$144$		0			0
$145$	−177.798			−1.22620
$146$		0			0
$147$	25.8351	−	27.2674i	0.175749	−	0.185492i
$148$		0			0
$149$	5.86344	−	5.86344i	0.0393519	−	0.0393519i	−0.687157	−	0.726509i	$-0.741142\pi$
$149$	5.86344	−	5.86344i	0.0393519	−	0.0393519i	0.726509	+	0.687157i	$0.241142\pi$
$150$		0			0
$151$		−	179.561i		−	1.18914i	−0.804043	−	0.594571i	$-0.797322\pi$
$151$		−	179.561i		−	1.18914i	0.804043	−	0.594571i	$-0.202678\pi$
$152$		0			0
$153$	−39.5288	+	2.13382i	−0.258358	+	0.0139466i
$154$		0			0
$155$	−25.1500	+	25.1500i	−0.162258	+	0.162258i
$156$		0			0
$157$	−14.8689	+	14.8689i	−0.0947067	+	0.0947067i	−0.752873	−	0.658166i	$-0.771332\pi$
$157$	−14.8689	+	14.8689i	−0.0947067	+	0.0947067i	0.658166	+	0.752873i	$0.271332\pi$
$158$		0			0
$159$	−2.37568	−	88.0822i	−0.0149414	−	0.553976i
$160$		0			0
$161$			205.592i			1.27697i
$162$		0			0
$163$	−66.1190	+	66.1190i	−0.405638	+	0.405638i	−0.880214	−	0.474577i	$-0.842601\pi$
$163$	−66.1190	+	66.1190i	−0.405638	+	0.405638i	0.474577	+	0.880214i	$0.342601\pi$
$164$		0			0
$165$	180.164	+	170.701i	1.09191	+	1.03455i
$166$		0			0
$167$	158.709			0.950353			0.475176	−	0.879891i	$-0.342384\pi$
$167$	158.709			0.950353			0.475176	+	0.879891i	$0.342384\pi$
$168$		0			0
$169$			87.2028i			0.515993i
$170$		0			0
$171$	−30.4123	−	27.2971i	−0.177850	−	0.159632i
$172$		0			0
$173$	76.9955	+	76.9955i	0.445061	+	0.445061i	0.893709	−	0.448648i	$-0.148094\pi$
$173$	76.9955	+	76.9955i	0.445061	+	0.445061i	−0.448648	+	0.893709i	$0.648094\pi$
$174$		0			0
$175$	28.8760			0.165006
$176$		0			0
$177$	−4.46861	−	165.681i	−0.0252464	−	0.936051i
$178$		0			0
$179$	−101.360	−	101.360i	−0.566257	−	0.566257i	0.364821	−	0.931078i	$-0.381130\pi$
$179$	−101.360	−	101.360i	−0.566257	−	0.566257i	−0.931078	+	0.364821i	$0.881130\pi$
$180$		0			0
$181$	−212.373	−	212.373i	−1.17333	−	1.17333i	−0.981411	−	0.191920i	$-0.938529\pi$
$181$	−212.373	−	212.373i	−1.17333	−	1.17333i	−0.191920	−	0.981411i	$-0.561471\pi$
$182$		0			0
$183$	5.70017	+	211.343i	0.0311485	+	1.15488i
$184$		0			0
$185$	−127.463			−0.688991
$186$		0			0
$187$	−57.2229	−	57.2229i	−0.306005	−	0.306005i
$188$		0			0
$189$	−105.616	+	124.252i	−0.558815	+	0.657416i
$190$		0			0
$191$		−	36.3314i		−	0.190217i	−0.995467	−	0.0951083i	$-0.969680\pi$
$191$		−	36.3314i		−	0.190217i	0.995467	−	0.0951083i	$-0.0303197\pi$
$192$		0			0
$193$	47.1090			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$193$	47.1090			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$194$		0			0
$195$	88.5638	+	83.9119i	0.454173	+	0.430317i
$196$		0			0
$197$	−32.2783	+	32.2783i	−0.163849	+	0.163849i	−0.784269	−	0.620420i	$-0.786962\pi$
$197$	−32.2783	+	32.2783i	−0.163849	+	0.163849i	0.620420	+	0.784269i	$0.286962\pi$
$198$		0			0
$199$			118.181i			0.593874i	0.954897	+	0.296937i	$0.0959651\pi$
$199$			118.181i			0.593874i	−0.954897	+	0.296937i	$0.904035\pi$
$200$		0			0
$201$	5.13784	+	190.494i	0.0255614	+	0.947731i
$202$		0			0
$203$	168.871	−	168.871i	0.831875	−	0.831875i
$204$		0			0
$205$	143.419	−	143.419i	0.699604	−	0.699604i
$206$		0			0
$207$	16.5136	+	305.911i	0.0797756	+	1.47783i
$208$		0			0
$209$		−	83.5416i		−	0.399721i
$210$		0			0
$211$	−63.8884	+	63.8884i	−0.302789	+	0.302789i	−0.842104	−	0.539315i	$-0.818683\pi$
$211$	−63.8884	+	63.8884i	−0.302789	+	0.302789i	0.539315	+	0.842104i	$0.318683\pi$
$212$		0			0
$213$	−96.3478	+	101.689i	−0.452337	+	0.477413i
$214$		0			0
$215$	−228.988			−1.06506
$216$		0			0
$217$		−	47.7743i		−	0.220158i
$218$		0			0
$219$	212.008	+	200.872i	0.968075	+	0.917226i
$220$		0			0
$221$	−28.1292	−	28.1292i	−0.127281	−	0.127281i
$222$		0			0
$223$	42.8886			0.192326			0.0961628	−	0.995366i	$-0.469343\pi$
$223$	42.8886			0.192326			0.0961628	+	0.995366i	$0.469343\pi$
$224$		0			0
$225$	42.9661	−	2.31938i	0.190961	−	0.0103084i
$226$		0			0
$227$	−23.0035	−	23.0035i	−0.101337	−	0.101337i	0.654621	−	0.755958i	$-0.272828\pi$
$227$	−23.0035	−	23.0035i	−0.101337	−	0.101337i	−0.755958	+	0.654621i	$0.772828\pi$
$228$		0			0
$229$	241.282	+	241.282i	1.05363	+	1.05363i	0.998478	+	0.0551571i	$0.0175660\pi$
$229$	241.282	+	241.282i	1.05363	+	1.05363i	0.0551571	+	0.998478i	$0.482434\pi$
$230$		0			0
$231$	−333.248	+	8.98807i	−1.44263	+	0.0389094i
$232$		0			0
$233$	240.310			1.03137			0.515687	−	0.856777i	$-0.327537\pi$
$233$	240.310			1.03137			0.515687	+	0.856777i	$0.327537\pi$
$234$		0			0
$235$	16.1818	+	16.1818i	0.0688589	+	0.0688589i
$236$		0			0
$237$	82.8721	−	87.4663i	0.349671	−	0.369056i
$238$		0			0
$239$			218.171i			0.912851i	0.889762	+	0.456425i	$0.150870\pi$
$239$			218.171i			0.912851i	−0.889762	+	0.456425i	$0.849130\pi$
$240$		0			0
$241$	−88.9611			−0.369133			−0.184567	−	0.982820i	$-0.559088\pi$
$241$	−88.9611			−0.369133			−0.184567	+	0.982820i	$0.559088\pi$
$242$		0			0
$243$	−147.172	+	193.364i	−0.605644	+	0.795736i
$244$		0			0
$245$	−39.8109	+	39.8109i	−0.162493	+	0.162493i
$246$		0			0
$247$		−	41.0667i		−	0.166262i
$248$		0			0
$249$	150.750	−	4.06591i	0.605423	−	0.0163289i
$250$		0			0
$251$	169.225	−	169.225i	0.674205	−	0.674205i	−0.284478	−	0.958683i	$-0.591820\pi$
$251$	169.225	−	169.225i	0.674205	−	0.674205i	0.958683	+	0.284478i	$0.0918201\pi$
$252$		0			0
$253$	−442.845	+	442.845i	−1.75038	+	1.75038i
$254$		0			0
$255$	59.3125	−	1.59973i	0.232598	−	0.00627343i
$256$		0			0
$257$		−	393.109i		−	1.52961i	−0.644262	−	0.764804i	$-0.722836\pi$
$257$		−	393.109i		−	1.52961i	0.644262	−	0.764804i	$-0.277164\pi$
$258$		0			0
$259$	121.063	−	121.063i	0.467425	−	0.467425i
$260$		0			0
$261$	237.707	−	264.835i	0.910756	−	1.01470i
$262$		0			0
$263$	−179.865			−0.683897			−0.341948	−	0.939719i	$-0.611087\pi$
$263$	−179.865			−0.683897			−0.341948	+	0.939719i	$0.611087\pi$
$264$		0			0
$265$			132.070i			0.498378i
$266$		0			0
$267$	143.774	−	151.744i	0.538478	−	0.568330i
$268$		0			0
$269$	290.530	+	290.530i	1.08004	+	1.08004i	0.996505	+	0.0835324i	$0.0266202\pi$
$269$	290.530	+	290.530i	1.08004	+	1.08004i	0.0835324	+	0.996505i	$0.473380\pi$
$270$		0			0
$271$	−496.550			−1.83229			−0.916144	−	0.400849i	$-0.868715\pi$
$271$	−496.550			−1.83229			−0.916144	+	0.400849i	$0.868715\pi$
$272$		0			0
$273$	−163.815	+	4.41829i	−0.600056	+	0.0161842i
$274$		0			0
$275$	62.1989	+	62.1989i	0.226178	+	0.226178i
$276$		0			0
$277$	−93.0101	−	93.0101i	−0.335776	−	0.335776i	0.518999	−	0.854775i	$-0.326305\pi$
$277$	−93.0101	−	93.0101i	−0.335776	−	0.335776i	−0.854775	+	0.518999i	$0.826305\pi$
$278$		0			0
$279$	−3.83733	−	71.0859i	−0.0137539	−	0.254788i
$280$		0			0
$281$	−300.875			−1.07073			−0.535365	−	0.844621i	$-0.679826\pi$
$281$	−300.875			−1.07073			−0.535365	+	0.844621i	$0.679826\pi$
$282$		0			0
$283$	−101.469	−	101.469i	−0.358549	−	0.358549i	0.504729	−	0.863278i	$-0.331592\pi$
$283$	−101.469	−	101.469i	−0.358549	−	0.358549i	−0.863278	+	0.504729i	$0.831592\pi$
$284$		0			0
$285$	44.4639	+	42.1284i	0.156014	+	0.147819i
$286$		0			0
$287$			272.435i			0.949250i
$288$		0			0
$289$	269.653			0.933057
$290$		0			0
$291$	126.058	−	133.047i	0.433190	−	0.457205i
$292$		0			0
$293$	−321.104	+	321.104i	−1.09592	+	1.09592i	−0.101037	+	0.994883i	$0.532216\pi$
$293$	−321.104	+	321.104i	−1.09592	+	1.09592i	−0.994883	+	0.101037i	$0.967784\pi$
$294$		0			0
$295$			248.422i			0.842107i
$296$		0			0
$297$	−495.135	+	40.1409i	−1.66712	+	0.135155i
$298$		0			0
$299$	−217.690	+	217.690i	−0.728061	+	0.728061i
$300$		0			0
$301$	217.490	−	217.490i	0.722558	−	0.722558i
$302$		0			0
$303$	−11.9004	−	441.228i	−0.0392753	−	1.45620i
$304$		0			0
$305$		−	316.888i		−	1.03898i
$306$		0			0
$307$	−94.2282	+	94.2282i	−0.306932	+	0.306932i	−0.843718	−	0.536786i	$-0.819638\pi$
$307$	−94.2282	+	94.2282i	−0.306932	+	0.306932i	0.536786	+	0.843718i	$0.319638\pi$
$308$		0			0
$309$	−124.776	−	118.222i	−0.403806	−	0.382596i
$310$		0			0
$311$	245.712			0.790070			0.395035	−	0.918666i	$-0.370732\pi$
$311$	245.712			0.790070			0.395035	+	0.918666i	$0.370732\pi$
$312$		0			0
$313$		−	353.841i		−	1.13048i	−0.824925	−	0.565242i	$-0.808783\pi$
$313$		−	353.841i		−	1.13048i	0.824925	−	0.565242i	$-0.191217\pi$
$314$		0			0
$315$	163.267	−	181.899i	0.518307	−	0.577458i
$316$		0			0
$317$	234.024	+	234.024i	0.738245	+	0.738245i	0.972238	−	0.233994i	$-0.0751795\pi$
$317$	234.024	+	234.024i	0.738245	+	0.738245i	−0.233994	+	0.972238i	$0.575179\pi$
$318$		0			0
$319$	727.494			2.28055
$320$		0			0
$321$	10.5747	+	392.076i	0.0329431	+	1.22142i
$322$		0			0
$323$	−14.1224	−	14.1224i	−0.0437226	−	0.0437226i
$324$		0			0
$325$	30.5752	+	30.5752i	0.0940777	+	0.0940777i
$326$		0			0
$327$	−8.62193	−	319.673i	−0.0263668	−	0.977592i
$328$		0			0
$329$	−30.7386			−0.0934305
$330$		0			0
$331$	32.5392	+	32.5392i	0.0983058	+	0.0983058i	0.754549	−	0.656243i	$-0.227856\pi$
$331$	32.5392	+	32.5392i	0.0983058	+	0.0983058i	−0.656243	+	0.754549i	$0.727856\pi$
$332$		0			0
$333$	170.412	−	189.860i	0.511748	−	0.570150i
$334$		0			0
$335$		−	285.626i		−	0.852615i
$336$		0			0
$337$	−185.573			−0.550660			−0.275330	−	0.961350i	$-0.588787\pi$
$337$	−185.573			−0.550660			−0.275330	+	0.961350i	$0.588787\pi$
$338$		0			0
$339$	244.461	+	231.621i	0.721124	+	0.683247i
$340$		0			0
$341$	102.906	−	102.906i	0.301776	−	0.301776i
$342$		0			0
$343$		−	371.574i		−	1.08330i
$344$		0			0
$345$	−12.3802	−	459.016i	−0.0358846	−	1.33048i
$346$		0			0
$347$	−51.9585	+	51.9585i	−0.149736	+	0.149736i	−0.778000	−	0.628264i	$-0.783766\pi$
$347$	−51.9585	+	51.9585i	−0.149736	+	0.149736i	0.628264	+	0.778000i	$0.283766\pi$
$348$		0			0
$349$	378.719	−	378.719i	1.08515	−	1.08515i	0.0891344	−	0.996020i	$-0.471590\pi$
$349$	378.719	−	378.719i	1.08515	−	1.08515i	0.996020	−	0.0891344i	$-0.0284101\pi$
$350$		0			0
$351$	−243.394	+	19.7322i	−0.693431	+	0.0562170i
$352$		0			0
$353$		−	326.435i		−	0.924744i	−0.886686	−	0.462372i	$-0.846998\pi$
$353$		−	326.435i		−	0.924744i	0.886686	−	0.462372i	$-0.153002\pi$
$354$		0			0
$355$	148.468	−	148.468i	0.418220	−	0.418220i
$356$		0			0
$357$	−54.8149	+	57.8537i	−0.153543	+	0.162055i
$358$		0			0
$359$	254.927			0.710103			0.355051	−	0.934847i	$-0.384463\pi$
$359$	254.927			0.710103			0.355051	+	0.934847i	$0.384463\pi$
$360$		0			0
$361$			340.382i			0.942887i
$362$		0			0
$363$	−473.668	−	448.789i	−1.30487	−	1.23633i
$364$		0			0
$365$	−309.536	−	309.536i	−0.848045	−	0.848045i
$366$		0			0
$367$	124.247			0.338548			0.169274	−	0.985569i	$-0.445858\pi$
$367$	124.247			0.338548			0.169274	+	0.985569i	$0.445858\pi$
$368$		0			0
$369$	21.8825	+	405.370i	0.0593021	+	1.09856i
$370$		0			0
$371$	−125.439	−	125.439i	−0.338110	−	0.338110i
$372$		0			0
$373$	−201.674	−	201.674i	−0.540680	−	0.540680i	0.383048	−	0.923728i	$-0.374874\pi$
$373$	−201.674	−	201.674i	−0.540680	−	0.540680i	−0.923728	+	0.383048i	$0.874874\pi$
$374$		0			0
$375$	−401.589	+	10.8313i	−1.07091	+	0.0288835i
$376$		0			0
$377$	357.616			0.948583
$378$		0			0
$379$	227.541	+	227.541i	0.600372	+	0.600372i	0.940411	−	0.340040i	$-0.110440\pi$
$379$	227.541	+	227.541i	0.600372	+	0.600372i	−0.340040	+	0.940411i	$0.610440\pi$
$380$		0			0
$381$	−193.199	+	203.910i	−0.507084	+	0.535196i
$382$		0			0
$383$			128.933i			0.336641i	0.985732	+	0.168320i	$0.0538343\pi$
$383$			128.933i			0.336641i	−0.985732	+	0.168320i	$0.946166\pi$
$384$		0			0
$385$	499.671			1.29785
$386$		0			0
$387$	306.145	−	341.084i	0.791073	−	0.881353i
$388$		0			0
$389$	107.474	−	107.474i	0.276283	−	0.276283i	−0.555340	−	0.831623i	$-0.687412\pi$
$389$	107.474	−	107.474i	0.276283	−	0.276283i	0.831623	+	0.555340i	$0.187412\pi$
$390$		0			0
$391$			149.723i			0.382922i
$392$		0			0
$393$	345.738	−	9.32494i	0.879739	−	0.0237276i
$394$		0			0
$395$	−127.702	+	127.702i	−0.323297	+	0.323297i
$396$		0			0
$397$	−259.306	+	259.306i	−0.653163	+	0.653163i	−0.953753	−	0.300591i	$-0.902816\pi$
$397$	−259.306	+	259.306i	−0.653163	+	0.653163i	0.300591	+	0.953753i	$0.402816\pi$
$398$		0			0
$399$	−82.2444	+	2.21822i	−0.206126	+	0.00555946i
$400$		0			0
$401$			335.810i			0.837431i	0.908117	+	0.418716i	$0.137520\pi$
$401$			335.810i			0.837431i	−0.908117	+	0.418716i	$0.862480\pi$
$402$		0			0
$403$	50.5856	−	50.5856i	0.125523	−	0.125523i
$404$		0			0
$405$	228.322	−	283.771i	0.563759	−	0.700669i
$406$		0			0
$407$	521.539			1.28142
$408$		0			0
$409$			66.3618i			0.162254i	0.996704	+	0.0811269i	$0.0258519\pi$
$409$			66.3618i			0.162254i	−0.996704	+	0.0811269i	$0.974148\pi$
$410$		0			0
$411$	−50.6575	+	53.4658i	−0.123254	+	0.130087i
$412$		0			0
$413$	−235.948	−	235.948i	−0.571303	−	0.571303i
$414$		0			0
$415$	−226.035			−0.544662
$416$		0			0
$417$	−13.0167	+	0.351074i	−0.0312150	+	0.000841904i
$418$		0			0
$419$	−371.566	−	371.566i	−0.886792	−	0.886792i	0.107422	−	0.994214i	$-0.465740\pi$
$419$	−371.566	−	371.566i	−0.886792	−	0.886792i	−0.994214	+	0.107422i	$0.965740\pi$
$420$		0			0
$421$	487.629	+	487.629i	1.15826	+	1.15826i	0.984849	+	0.173416i	$0.0554806\pi$
$421$	487.629	+	487.629i	1.15826	+	1.15826i	0.173416	+	0.984849i	$0.444519\pi$
$422$		0			0
$423$	−45.7376	+	2.46899i	−0.108127	+	0.00583685i
$424$		0			0
$425$	21.0290			0.0494800
$426$		0			0
$427$	300.976	+	300.976i	0.704862	+	0.704862i
$428$		0			0
$429$	−362.375	−	343.341i	−0.844696	−	0.800328i
$430$		0			0
$431$			505.901i			1.17378i	0.809665	+	0.586892i	$0.199649\pi$
$431$			505.901i			1.17378i	−0.809665	+	0.586892i	$0.800351\pi$
$432$		0			0
$433$	−758.226			−1.75110			−0.875550	−	0.483128i	$-0.839500\pi$
$433$	−758.226			−1.75110			−0.875550	+	0.483128i	$0.839500\pi$
$434$		0			0
$435$	−366.861	+	387.199i	−0.843359	+	0.890113i
$436$		0			0
$437$	−109.293	+	109.293i	−0.250097	+	0.250097i
$438$		0			0
$439$			145.760i			0.332026i	0.986124	+	0.166013i	$0.0530895\pi$
$439$			145.760i			0.332026i	−0.986124	+	0.166013i	$0.946911\pi$
$440$		0			0
$441$	−6.07425	−	112.525i	−0.0137738	−	0.255158i
$442$		0			0
$443$	−607.046	+	607.046i	−1.37031	+	1.37031i	−0.510323	+	0.859983i	$0.670474\pi$
$443$	−607.046	+	607.046i	−1.37031	+	1.37031i	−0.859983	+	0.510323i	$0.829526\pi$
$444$		0			0
$445$	−221.549	+	221.549i	−0.497864	+	0.497864i
$446$		0			0
$447$	−0.670702	−	24.8674i	−0.00150045	−	0.0556318i
$448$		0			0
$449$			190.654i			0.424620i	0.977202	+	0.212310i	$0.0680986\pi$
$449$			190.654i			0.424620i	−0.977202	+	0.212310i	$0.931901\pi$
$450$		0			0
$451$	−586.824	+	586.824i	−1.30116	+	1.30116i
$452$		0			0
$453$	−391.037	−	370.497i	−0.863216	−	0.817875i
$454$		0			0
$455$	245.624			0.539834
$456$		0			0
$457$			128.091i			0.280287i	0.990131	+	0.140143i	$0.0447563\pi$
$457$			128.091i			0.280287i	−0.990131	+	0.140143i	$0.955244\pi$
$458$		0			0
$459$	−76.9150	+	90.4863i	−0.167571	+	0.197138i
$460$		0			0
$461$	−74.2060	−	74.2060i	−0.160968	−	0.160968i	0.622028	−	0.782995i	$-0.286309\pi$
$461$	−74.2060	−	74.2060i	−0.160968	−	0.160968i	−0.782995	+	0.622028i	$0.786309\pi$
$462$		0			0
$463$	−620.192			−1.33951			−0.669753	−	0.742584i	$-0.733600\pi$
$463$	−620.192			−1.33951			−0.669753	+	0.742584i	$0.733600\pi$
$464$		0			0
$465$	2.87684	+	106.664i	0.00618675	+	0.229384i
$466$		0			0
$467$	−331.708	−	331.708i	−0.710296	−	0.710296i	0.256301	−	0.966597i	$-0.417496\pi$
$467$	−331.708	−	331.708i	−0.710296	−	0.710296i	−0.966597	+	0.256301i	$0.917496\pi$
$468$		0			0
$469$	271.284	+	271.284i	0.578431	+	0.578431i
$470$		0			0
$471$	1.70082	+	63.0607i	0.00361108	+	0.133887i
$472$		0			0
$473$	936.946			1.98086
$474$		0			0
$475$	15.3505	+	15.3505i	0.0323168	+	0.0323168i
$476$		0			0
$477$	−196.722	−	176.571i	−0.412415	−	0.370170i
$478$		0			0
$479$		−	867.941i		−	1.81198i	−0.423294	−	0.905992i	$-0.639126\pi$
$479$		−	867.941i		−	1.81198i	0.423294	−	0.905992i	$-0.360874\pi$
$480$		0			0
$481$	256.374			0.533002
$482$		0			0
$483$	447.727	+	424.210i	0.926970	+	0.878281i
$484$		0			0
$485$	−194.251	+	194.251i	−0.400517	+	0.400517i
$486$		0			0
$487$			815.778i			1.67511i	0.546354	+	0.837554i	$0.316015\pi$
$487$			815.778i			1.67511i	−0.546354	+	0.837554i	$0.683985\pi$
$488$		0			0
$489$	7.56317	+	280.417i	0.0154666	+	0.573450i
$490$		0			0
$491$	337.746	−	337.746i	0.687874	−	0.687874i	−0.273888	−	0.961762i	$-0.588310\pi$
$491$	337.746	−	337.746i	0.687874	−	0.687874i	0.961762	+	0.273888i	$0.0883098\pi$
$492$		0			0
$493$	122.980	−	122.980i	0.249453	−	0.249453i
$494$		0			0
$495$	743.486	−	40.1345i	1.50199	−	0.0810799i
$496$		0			0
$497$			282.026i			0.567457i
$498$		0			0
$499$	515.289	−	515.289i	1.03264	−	1.03264i	0.0331940	−	0.999449i	$-0.489432\pi$
$499$	515.289	−	515.289i	1.03264	−	1.03264i	0.999449	−	0.0331940i	$-0.0105679\pi$
$500$		0			0
$501$	327.473	−	345.627i	0.653639	−	0.689875i
$502$		0			0
$503$	196.781			0.391215			0.195607	−	0.980682i	$-0.437332\pi$
$503$	196.781			0.391215			0.195607	+	0.980682i	$0.437332\pi$
$504$		0			0
$505$			661.576i			1.31005i
$506$		0			0
$507$	189.905	+	179.930i	0.374567	+	0.354892i
$508$		0			0
$509$	29.3054	+	29.3054i	0.0575744	+	0.0575744i	0.735308	−	0.677733i	$-0.237038\pi$
$509$	29.3054	+	29.3054i	0.0575744	+	0.0575744i	−0.677733	+	0.735308i	$0.737038\pi$
$510$		0			0
$511$	587.988			1.15066
$512$		0			0
$513$	−122.197	+	9.90664i	−0.238202	+	0.0193112i
$514$		0			0
$515$	182.175	+	182.175i	0.353739	+	0.353739i
$516$		0			0
$517$	−66.2109	−	66.2109i	−0.128068	−	0.128068i
$518$		0			0
$519$	326.546	−	8.80731i	0.629182	−	0.0169698i
$520$		0			0
$521$	−770.641			−1.47916			−0.739578	−	0.673071i	$-0.764975\pi$
$521$	−770.641			−1.47916			−0.739578	+	0.673071i	$0.764975\pi$
$522$		0			0
$523$	−258.725	−	258.725i	−0.494694	−	0.494694i	0.415087	−	0.909782i	$-0.363751\pi$
$523$	−258.725	−	258.725i	−0.494694	−	0.494694i	−0.909782	+	0.415087i	$0.863751\pi$
$524$		0			0
$525$	59.5815	−	62.8846i	0.113489	−	0.119780i
$526$		0			0
$527$		−	34.7917i		−	0.0660183i
$528$		0			0
$529$	629.695			1.19035
$530$		0			0
$531$	−370.031	−	332.127i	−0.696857	−	0.625475i
$532$		0			0
$533$	−288.466	+	288.466i	−0.541212	+	0.541212i
$534$		0			0
$535$		−	587.878i		−	1.09884i
$536$		0			0
$537$	−429.878	+	11.5943i	−0.800517	+	0.0215909i
$538$		0			0
$539$	162.894	−	162.894i	0.302214	−	0.302214i
$540$		0			0
$541$	−122.667	+	122.667i	−0.226742	+	0.226742i	−0.811330	−	0.584588i	$-0.801256\pi$
$541$	−122.667	+	122.667i	−0.226742	+	0.226742i	0.584588	+	0.811330i	$0.301256\pi$
$542$		0			0
$543$	−900.694	+	24.2927i	−1.65874	+	0.0447380i
$544$		0			0
$545$			479.316i			0.879479i
$546$		0			0
$547$	−334.075	+	334.075i	−0.610740	+	0.610740i	−0.943139	−	0.332399i	$-0.892142\pi$
$547$	−334.075	+	334.075i	−0.610740	+	0.610740i	0.332399	+	0.943139i	$0.392142\pi$
$548$		0			0
$549$	472.013	+	423.663i	0.859768	+	0.771699i
$550$		0			0
$551$	179.543			0.325849
$552$		0			0
$553$		−	242.581i		−	0.438663i
$554$		0			0
$555$	−263.002	+	277.582i	−0.473878	+	0.500148i
$556$		0			0
$557$	159.480	+	159.480i	0.286320	+	0.286320i	0.835623	−	0.549303i	$-0.185107\pi$
$557$	159.480	+	159.480i	0.286320	+	0.286320i	−0.549303	+	0.835623i	$0.685107\pi$
$558$		0			0
$559$	460.576			0.823929
$560$		0			0
$561$	−242.688	+	6.54557i	−0.432599	+	0.0116677i
$562$		0			0
$563$	341.226	+	341.226i	0.606086	+	0.606086i	0.941921	−	0.335835i	$-0.109018\pi$
$563$	341.226	+	341.226i	0.606086	+	0.606086i	−0.335835	+	0.941921i	$0.609018\pi$
$564$		0			0
$565$	−356.918	−	356.918i	−0.631713	−	0.631713i
$566$		0			0
$567$	52.6646	+	486.380i	0.0928828	+	0.857813i
$568$		0			0
$569$	−882.975			−1.55180			−0.775901	−	0.630855i	$-0.782704\pi$
$569$	−882.975			−1.55180			−0.775901	+	0.630855i	$0.782704\pi$
$570$		0			0
$571$	−370.112	−	370.112i	−0.648181	−	0.648181i	0.304372	−	0.952553i	$-0.401553\pi$
$571$	−370.112	−	370.112i	−0.648181	−	0.648181i	−0.952553	+	0.304372i	$0.901553\pi$
$572$		0			0
$573$	−79.1204	−	74.9645i	−0.138081	−	0.130828i
$574$		0			0
$575$		−	162.742i		−	0.283030i
$576$		0			0
$577$	−698.607			−1.21076			−0.605378	−	0.795938i	$-0.706978\pi$
$577$	−698.607			−1.21076			−0.605378	+	0.795938i	$0.706978\pi$
$578$		0			0
$579$	97.2025	−	102.591i	0.167880	−	0.177187i
$580$		0			0
$581$	214.685	−	214.685i	0.369509	−	0.369509i
$582$		0			0
$583$		−	540.389i		−	0.926911i
$584$		0			0
$585$	365.477	−	19.7290i	0.624747	−	0.0337248i
$586$		0			0
$587$	−196.072	+	196.072i	−0.334024	+	0.334024i	−0.854112	−	0.520088i	$-0.825899\pi$
$587$	−196.072	+	196.072i	−0.334024	+	0.334024i	0.520088	+	0.854112i	$0.325899\pi$
$588$		0			0
$589$	25.3968	−	25.3968i	0.0431185	−	0.0431185i
$590$		0			0
$591$	3.69222	+	136.895i	0.00624742	+	0.231633i
$592$		0			0
$593$		−	774.011i		−	1.30525i	−0.757683	−	0.652623i	$-0.773669\pi$
$593$		−	774.011i		−	1.30525i	0.757683	−	0.652623i	$-0.226331\pi$
$594$		0			0
$595$	84.4675	−	84.4675i	0.141962	−	0.141962i
$596$		0			0
$597$	257.368	+	243.849i	0.431102	+	0.408458i
$598$		0			0
$599$	−783.533			−1.30807			−0.654034	−	0.756465i	$-0.726925\pi$
$599$	−783.533			−1.30807			−0.654034	+	0.756465i	$0.726925\pi$
$600$		0			0
$601$		−	797.210i		−	1.32647i	−0.748410	−	0.663236i	$-0.769182\pi$
$601$		−	797.210i		−	1.32647i	0.748410	−	0.663236i	$-0.230818\pi$
$602$		0			0
$603$	425.448	+	381.868i	0.705552	+	0.633280i
$604$		0			0
$605$	691.565	+	691.565i	1.14308	+	1.14308i
$606$		0			0
$607$	−433.576			−0.714293			−0.357146	−	0.934048i	$-0.616250\pi$
$607$	−433.576			−0.714293			−0.357146	+	0.934048i	$0.616250\pi$
$608$		0			0
$609$	−19.3167	−	716.197i	−0.0317186	−	1.17602i
$610$		0			0
$611$	−32.5475	−	32.5475i	−0.0532692	−	0.0532692i
$612$		0			0
$613$	−493.642	−	493.642i	−0.805289	−	0.805289i	0.178628	−	0.983917i	$-0.442834\pi$
$613$	−493.642	−	493.642i	−0.805289	−	0.805289i	−0.983917	+	0.178628i	$0.942834\pi$
$614$		0			0
$615$	−16.4053	−	608.253i	−0.0266752	−	0.989029i
$616$		0			0
$617$	685.069			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$617$	685.069			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$618$		0			0
$619$	379.995	+	379.995i	0.613885	+	0.613885i	0.943956	−	0.330071i	$-0.107073\pi$
$619$	379.995	+	379.995i	0.613885	+	0.613885i	−0.330071	+	0.943956i	$0.607073\pi$
$620$		0			0
$621$	700.269	+	595.241i	1.12765	+	0.958520i
$622$		0			0
$623$		−	420.850i		−	0.675521i
$624$		0			0
$625$	482.618			0.772189
$626$		0			0
$627$	−181.932	−	172.376i	−0.290163	−	0.274922i
$628$		0			0
$629$	88.1642	−	88.1642i	0.140166	−	0.140166i
$630$		0			0
$631$			489.285i			0.775412i	0.921783	+	0.387706i	$0.126732\pi$
$631$			489.285i			0.775412i	−0.921783	+	0.387706i	$0.873268\pi$
$632$		0			0
$633$	7.30802	+	270.957i	0.0115451	+	0.428052i
$634$		0			0
$635$	297.712	−	297.712i	0.468838	−	0.468838i
$636$		0			0
$637$	80.0739	−	80.0739i	0.125705	−	0.125705i
$638$		0			0
$639$	22.6529	+	419.641i	0.0354505	+	0.656716i
$640$		0			0
$641$		−	492.158i		−	0.767797i	−0.923375	−	0.383898i	$-0.874581\pi$
$641$		−	492.158i		−	0.767797i	0.923375	−	0.383898i	$-0.125419\pi$
$642$		0			0
$643$	169.985	−	169.985i	0.264362	−	0.264362i	−0.562462	−	0.826823i	$-0.690146\pi$
$643$	169.985	−	169.985i	0.264362	−	0.264362i	0.826823	+	0.562462i	$0.190146\pi$
$644$		0			0
$645$	−472.483	+	498.677i	−0.732532	+	0.773142i
$646$		0			0
$647$	−1003.50			−1.55101			−0.775503	−	0.631343i	$-0.782504\pi$
$647$	−1003.50			−1.55101			−0.775503	+	0.631343i	$0.782504\pi$
$648$		0			0
$649$		−	1016.46i		−	1.56620i
$650$		0			0
$651$	−104.040	−	98.5754i	−0.159816	−	0.151422i
$652$		0			0
$653$	−407.090	−	407.090i	−0.623415	−	0.623415i	0.322988	−	0.946403i	$-0.395313\pi$
$653$	−407.090	−	407.090i	−0.623415	−	0.623415i	−0.946403	+	0.322988i	$0.895313\pi$
$654$		0			0
$655$	−518.398			−0.791448
$656$		0			0
$657$	874.897	−	47.2283i	1.33165	−	0.0718848i
$658$		0			0
$659$	635.355	+	635.355i	0.964119	+	0.964119i	0.999378	−	0.0352587i	$-0.0112255\pi$
$659$	635.355	+	635.355i	0.964119	+	0.964119i	−0.0352587	+	0.999378i	$0.511226\pi$
$660$		0			0
$661$	−196.325	−	196.325i	−0.297013	−	0.297013i	0.542830	−	0.839843i	$-0.317353\pi$
$661$	−196.325	−	196.325i	−0.297013	−	0.297013i	−0.839843	+	0.542830i	$0.817353\pi$
$662$		0			0
$663$	−119.299	+	3.21762i	−0.179937	+	0.00485312i
$664$		0			0
$665$	123.317			0.185439
$666$		0			0
$667$	−951.737	−	951.737i	−1.42689	−	1.42689i
$668$		0			0
$669$	88.4944	−	93.4003i	0.132279	−	0.139612i
$670$		0			0
$671$			1296.60i			1.93234i
$672$		0			0
$673$	−489.653			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$673$	−489.653			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$674$		0			0
$675$	83.6034	−	98.3549i	0.123857	−	0.145711i
$676$		0			0
$677$	832.940	−	832.940i	1.23034	−	1.23034i	0.266507	−	0.963833i	$-0.414131\pi$
$677$	832.940	−	832.940i	1.23034	−	1.23034i	0.963833	−	0.266507i	$-0.0858695\pi$
$678$		0			0
$679$		−	368.994i		−	0.543438i
$680$		0			0
$681$	−97.5600	+	2.63131i	−0.143260	+	0.00386388i
$682$		0			0
$683$	773.804	−	773.804i	1.13295	−	1.13295i	0.143264	−	0.989684i	$-0.454240\pi$
$683$	773.804	−	773.804i	1.13295	−	1.13295i	0.989684	−	0.143264i	$-0.0457599\pi$
$684$		0			0
$685$	78.0611	−	78.0611i	0.113958	−	0.113958i
$686$		0			0
$687$	1023.30	−	27.5996i	1.48952	−	0.0401741i
$688$		0			0
$689$		−	265.640i		−	0.385545i
$690$		0			0
$691$	840.306	−	840.306i	1.21607	−	1.21607i	0.247077	−	0.968996i	$-0.420530\pi$
$691$	840.306	−	840.306i	1.21607	−	1.21607i	0.968996	−	0.247077i	$-0.0794699\pi$
$692$		0			0
$693$	−668.035	+	744.274i	−0.963975	+	1.07399i
$694$		0			0
$695$	19.5171			0.0280822
$696$		0			0
$697$			198.401i			0.284650i
$698$		0			0
$699$	495.845	−	523.334i	0.709364	−	0.748689i
$700$		0			0
$701$	−529.432	−	529.432i	−0.755253	−	0.755253i	0.220201	−	0.975454i	$-0.429329\pi$
$701$	−529.432	−	529.432i	−0.755253	−	0.755253i	−0.975454	+	0.220201i	$0.929329\pi$
$702$		0			0
$703$	128.714			0.183092
$704$		0			0
$705$	68.6288	−	1.85100i	0.0973458	−	0.00262553i
$706$		0			0
$707$	−628.357	−	628.357i	−0.888765	−	0.888765i
$708$		0			0
$709$	−56.2182	−	56.2182i	−0.0792923	−	0.0792923i	0.666348	−	0.745641i	$-0.267856\pi$
$709$	−56.2182	−	56.2182i	−0.0792923	−	0.0792923i	−0.745641	+	0.666348i	$0.767856\pi$
$710$		0			0
$711$	−19.4845	−	360.948i	−0.0274044	−	0.507663i
$712$		0			0
$713$	−269.251			−0.377631
$714$		0			0
$715$	529.074	+	529.074i	0.739964	+	0.739964i
$716$		0			0
$717$	475.121	+	450.165i	0.662651	+	0.627845i
$718$		0			0
$719$			966.944i			1.34485i	0.740167	+	0.672423i	$0.234746\pi$
$719$			966.944i			1.34485i	−0.740167	+	0.672423i	$0.765254\pi$
$720$		0			0
$721$	−346.056			−0.479967
$722$		0			0
$723$	−183.558	+	193.734i	−0.253884	+	0.267959i
$724$		0			0
$725$	−133.674	+	133.674i	−0.184378	+	0.184378i
$726$		0			0
$727$		−	1338.18i		−	1.84069i	−0.391110	−	0.920344i	$-0.627909\pi$
$727$		−	1338.18i		−	1.84069i	0.391110	−	0.920344i	$-0.372091\pi$
$728$		0			0
$729$	117.429	+	719.480i	0.161083	+	0.986941i
$730$		0			0
$731$	158.387	−	158.387i	0.216672	−	0.216672i
$732$		0			0
$733$	757.046	−	757.046i	1.03280	−	1.03280i	0.0333615	−	0.999443i	$-0.489379\pi$
$733$	757.046	−	757.046i	1.03280	−	1.03280i	0.999443	−	0.0333615i	$-0.0106213\pi$
$734$		0			0
$735$	4.55386	+	168.842i	0.00619573	+	0.229717i
$736$		0			0
$737$			1168.69i			1.58574i
$738$		0			0
$739$	−495.335	+	495.335i	−0.670278	+	0.670278i	−0.957780	−	0.287502i	$-0.907175\pi$
$739$	−495.335	+	495.335i	−0.670278	+	0.670278i	0.287502	+	0.957780i	$0.407175\pi$
$740$		0			0
$741$	−89.4328	−	84.7353i	−0.120692	−	0.114353i
$742$		0			0
$743$	−1421.01			−1.91253			−0.956266	−	0.292500i	$-0.905513\pi$
$743$	−1421.01			−1.91253			−0.956266	+	0.292500i	$0.905513\pi$
$744$		0			0
$745$			37.2861i			0.0500485i
$746$		0			0
$747$	302.197	−	336.685i	0.404547	−	0.450716i
$748$		0			0
$749$	558.359	+	558.359i	0.745473	+	0.745473i
$750$		0			0
$751$	143.509			0.191090			0.0955452	−	0.995425i	$-0.469541\pi$
$751$	143.509			0.191090			0.0955452	+	0.995425i	$0.469541\pi$
$752$		0			0
$753$	−19.3572	−	717.702i	−0.0257068	−	0.953123i
$754$		0			0
$755$	570.921	+	570.921i	0.756187	+	0.756187i
$756$		0			0
$757$	651.883	+	651.883i	0.861140	+	0.861140i	0.991471	−	0.130331i	$-0.0416040\pi$
$757$	651.883	+	651.883i	0.861140	+	0.861140i	−0.130331	+	0.991471i	$0.541604\pi$
$758$		0			0
$759$	50.6558	+	1878.15i	0.0667402	+	2.47450i
$760$		0			0
$761$	−434.623			−0.571122			−0.285561	−	0.958361i	$-0.592180\pi$
$761$	−434.623			−0.571122			−0.285561	+	0.958361i	$0.592180\pi$
$762$		0			0
$763$	−455.249	−	455.249i	−0.596656	−	0.596656i
$764$		0			0
$765$	118.899	−	132.468i	0.155423	−	0.173161i
$766$		0			0
$767$		−	499.665i		−	0.651453i
$768$		0			0
$769$	17.1894			0.0223529			0.0111764	−	0.999938i	$-0.496442\pi$
$769$	17.1894			0.0223529			0.0111764	+	0.999938i	$0.496442\pi$
$770$		0			0
$771$	−856.091	−	811.125i	−1.11036	−	1.05204i
$772$		0			0
$773$	−553.125	+	553.125i	−0.715557	+	0.715557i	−0.967692	−	0.252135i	$-0.918867\pi$
$773$	−553.125	+	553.125i	−0.715557	+	0.715557i	0.252135	+	0.967692i	$0.418867\pi$
$774$		0			0
$775$			37.8171i			0.0487963i
$776$		0			0
$777$	−13.8481	−	513.440i	−0.0178225	−	0.660798i
$778$		0			0
$779$	−144.826	+	144.826i	−0.185913	+	0.185913i
$780$		0			0
$781$	−607.484	+	607.484i	−0.777828	+	0.777828i
$782$		0			0
$783$	−86.2686	−	1064.12i	−0.110177	−	1.35902i
$784$		0			0
$785$		−	94.5530i		−	0.120450i
$786$		0			0
$787$	−274.851	+	274.851i	−0.349239	+	0.349239i	−0.859826	−	0.510587i	$-0.829428\pi$
$787$	−274.851	+	274.851i	−0.349239	+	0.349239i	0.510587	+	0.859826i	$0.329428\pi$
$788$		0			0
$789$	−371.125	+	391.699i	−0.470374	+	0.496450i
$790$		0			0
$791$	677.993			0.857134
$792$		0			0
$793$			637.374i			0.803750i
$794$		0			0
$795$	287.615	+	272.508i	0.361780	+	0.342777i
$796$		0			0
$797$	−165.770	−	165.770i	−0.207993	−	0.207993i	0.595421	−	0.803414i	$-0.296985\pi$
$797$	−165.770	−	165.770i	−0.207993	−	0.207993i	−0.803414	+	0.595421i	$0.796985\pi$
$798$		0			0
$799$	−22.3854			−0.0280168
$800$		0			0
$801$	−33.8035	−	626.204i	−0.0422016	−	0.781778i
$802$		0			0
$803$	1266.52	+	1266.52i	1.57724	+	1.57724i
$804$		0			0
$805$	−653.690	−	653.690i	−0.812037	−	0.812037i
$806$		0			0
$807$	1232.17	−	33.2329i	1.52685	−	0.0411808i
$808$		0			0
$809$	−184.708			−0.228316			−0.114158	−	0.993463i	$-0.536417\pi$
$809$	−184.708			−0.228316			−0.114158	+	0.993463i	$0.536417\pi$
$810$		0			0
$811$	585.531	+	585.531i	0.721986	+	0.721986i	0.969010	−	0.247023i	$-0.0794524\pi$
$811$	585.531	+	585.531i	0.721986	+	0.721986i	−0.247023	+	0.969010i	$0.579452\pi$
$812$		0			0
$813$	−1024.56	+	1081.36i	−1.26022	+	1.33008i
$814$		0			0
$815$		−	420.457i		−	0.515898i
$816$		0			0
$817$	231.235			0.283029
$818$		0			0
$819$	−328.387	+	365.864i	−0.400961	+	0.446720i
$820$		0			0
$821$	659.299	−	659.299i	0.803044	−	0.803044i	−0.180526	−	0.983570i	$-0.557780\pi$
$821$	659.299	−	659.299i	0.803044	−	0.803044i	0.983570	+	0.180526i	$0.0577801\pi$
$822$		0			0
$823$			1397.61i			1.69819i	0.528237	+	0.849097i	$0.322853\pi$
$823$			1397.61i			1.69819i	−0.528237	+	0.849097i	$0.677147\pi$
$824$		0			0
$825$	263.792	−	7.11476i	0.319748	−	0.00862395i
$826$		0			0
$827$	78.1971	−	78.1971i	0.0945551	−	0.0945551i	−0.658247	−	0.752802i	$-0.728702\pi$
$827$	78.1971	−	78.1971i	0.0945551	−	0.0945551i	0.752802	+	0.658247i	$0.228702\pi$
$828$		0			0
$829$	−30.4254	+	30.4254i	−0.0367014	+	0.0367014i	−0.725219	−	0.688518i	$-0.758262\pi$
$829$	−30.4254	+	30.4254i	−0.0367014	+	0.0367014i	0.688518	+	0.725219i	$0.258262\pi$
$830$		0			0
$831$	−394.465	+	10.6392i	−0.474687	+	0.0128028i
$832$		0			0
$833$		−	55.0731i		−	0.0661141i
$834$		0			0
$835$	−504.622	+	504.622i	−0.604338	+	0.604338i
$836$		0			0
$837$	−162.725	−	138.319i	−0.194414	−	0.165255i
$838$		0			0
$839$	694.526			0.827802			0.413901	−	0.910322i	$-0.364166\pi$
$839$	694.526			0.827802			0.413901	+	0.910322i	$0.364166\pi$
$840$		0			0
$841$			722.489i			0.859084i
$842$		0			0
$843$	−620.812	+	655.228i	−0.736432	+	0.777258i
$844$		0			0
$845$	−277.265	−	277.265i	−0.328125	−	0.328125i
$846$		0			0
$847$	−1313.68			−1.55098
$848$		0			0
$849$	−430.341	+	11.6068i	−0.506880	+	0.0136711i
$850$		0			0
$851$	−682.298	−	682.298i	−0.801761	−	0.801761i
$852$		0			0
$853$	727.489	+	727.489i	0.852860	+	0.852860i	0.990484	−	0.137625i	$-0.0439468\pi$
$853$	727.489	+	727.489i	0.852860	+	0.852860i	−0.137625	+	0.990484i	$0.543947\pi$
$854$		0			0
$855$	183.490	−	9.90506i	0.214608	−	0.0115849i
$856$		0			0
$857$	−1275.44			−1.48826			−0.744128	−	0.668037i	$-0.767135\pi$
$857$	−1275.44			−1.48826			−0.744128	+	0.668037i	$0.767135\pi$
$858$		0			0
$859$	−2.20191	−	2.20191i	−0.00256334	−	0.00256334i	0.705824	−	0.708387i	$-0.250577\pi$
$859$	−2.20191	−	2.20191i	−0.00256334	−	0.00256334i	−0.708387	+	0.705824i	$0.750577\pi$
$860$		0			0
$861$	593.293	+	562.130i	0.689074	+	0.652880i
$862$		0			0
$863$		−	1311.55i		−	1.51976i	−0.650063	−	0.759880i	$-0.725258\pi$
$863$		−	1311.55i		−	1.51976i	0.650063	−	0.759880i	$-0.274742\pi$
$864$		0			0
$865$	−489.622			−0.566037
$866$		0			0
$867$	556.391	−	587.236i	0.641743	−	0.677319i
$868$		0			0
$869$	522.518	−	522.518i	0.601287	−	0.601287i
$870$		0			0
$871$			574.496i			0.659582i
$872$		0			0
$873$	−29.6383	−	549.046i	−0.0339500	−	0.628918i
$874$		0			0
$875$	−571.908	+	571.908i	−0.653609	+	0.653609i
$876$		0			0
$877$	−449.158	+	449.158i	−0.512152	+	0.512152i	−0.915185	−	0.403033i	$-0.867956\pi$
$877$	−449.158	+	449.158i	−0.512152	+	0.512152i	0.403033	+	0.915185i	$0.367956\pi$
$878$		0			0
$879$	36.7303	+	1361.84i	0.0417864	+	1.54930i
$880$		0			0
$881$			982.786i			1.11553i	0.829998	+	0.557767i	$0.188342\pi$
$881$			982.786i			1.11553i	−0.829998	+	0.557767i	$0.811658\pi$
$882$		0			0
$883$	−233.961	+	233.961i	−0.264962	+	0.264962i	−0.827066	−	0.562104i	$-0.809992\pi$
$883$	−233.961	+	233.961i	−0.264962	+	0.264962i	0.562104	+	0.827066i	$0.309992\pi$
$884$		0			0
$885$	540.999	+	512.582i	0.611298	+	0.579189i
$886$		0			0
$887$	−1421.57			−1.60267			−0.801334	−	0.598217i	$-0.795876\pi$
$887$	−1421.57			−1.60267			−0.801334	+	0.598217i	$0.795876\pi$
$888$		0			0
$889$			565.527i			0.636138i
$890$		0			0
$891$	−934.222	+	1161.10i	−1.04851	+	1.30314i
$892$		0			0
$893$	−16.3406	−	16.3406i	−0.0182986	−	0.0182986i
$894$		0			0
$895$	644.558			0.720176
$896$		0			0
$897$	24.9010	+	923.246i	0.0277603	+	1.02926i
$898$		0			0
$899$	221.159	+	221.159i	0.246006	+	0.246006i
$900$		0			0
$901$	−91.3508	−	91.3508i	−0.101388	−	0.101388i
$902$		0			0
$903$	−24.8781	−	922.396i	−0.0275505	−	1.02148i
$904$		0			0
$905$	1350.50			1.49226
$906$		0			0
$907$	358.736	+	358.736i	0.395519	+	0.395519i	0.876649	−	0.481130i	$-0.159774\pi$
$907$	358.736	+	358.736i	0.395519	+	0.395519i	−0.481130	+	0.876649i	$0.659774\pi$
$908$		0			0
$909$	−985.436	−	884.494i	−1.08409	−	0.973041i
$910$		0			0
$911$		−	353.455i		−	0.387986i	−0.981003	−	0.193993i	$-0.937856\pi$
$911$		−	353.455i		−	0.387986i	0.981003	−	0.193993i	$-0.0621439\pi$
$912$		0			0
$913$	924.862			1.01299
$914$		0			0
$915$	−690.100	−	653.852i	−0.754207	−	0.714592i
$916$		0			0
$917$	492.368	−	492.368i	0.536934	−	0.536934i
$918$		0			0
$919$		−	1519.58i		−	1.65351i	−0.562560	−	0.826757i	$-0.690183\pi$
$919$		−	1519.58i		−	1.65351i	0.562560	−	0.826757i	$-0.309817\pi$
$920$		0			0
$921$	10.7785	+	399.631i	0.0117030	+	0.433910i
$922$		0			0
$923$	−298.622	+	298.622i	−0.323534	+	0.323534i
$924$		0			0
$925$	−95.8309	+	95.8309i	−0.103601	+	0.103601i
$926$		0			0
$927$	−514.915	+	27.7959i	−0.555464	+	0.0299848i
$928$		0			0
$929$		−	95.2916i		−	0.102574i	−0.998684	−	0.0512872i	$-0.983668\pi$
$929$		−	95.2916i		−	0.102574i	0.998684	−	0.0512872i	$-0.0163324\pi$
$930$		0			0
$931$	40.2015	−	40.2015i	0.0431810	−	0.0431810i
$932$		0			0
$933$	506.991	−	535.097i	0.543398	−	0.573523i
$934$		0			0
$935$	363.886			0.389182
$936$		0			0
$937$		−	701.772i		−	0.748956i	−0.927236	−	0.374478i	$-0.877822\pi$
$937$		−	701.772i		−	0.748956i	0.927236	−	0.374478i	$-0.122178\pi$
$938$		0			0
$939$	−770.576	−	730.101i	−0.820634	−	0.777530i
$940$		0			0
$941$	−88.8345	−	88.8345i	−0.0944044	−	0.0944044i	0.658327	−	0.752732i	$-0.271264\pi$
$941$	−88.8345	−	88.8345i	−0.0944044	−	0.0944044i	−0.752732	+	0.658327i	$0.771264\pi$
$942$		0			0
$943$	1535.41			1.62822
$944$		0			0
$945$	−59.2526	−	730.875i	−0.0627012	−	0.773413i
$946$		0			0
$947$	−345.769	−	345.769i	−0.365120	−	0.365120i	0.500574	−	0.865694i	$-0.333122\pi$
$947$	−345.769	−	345.769i	−0.365120	−	0.365120i	−0.865694	+	0.500574i	$0.833122\pi$
$948$		0			0
$949$	622.588	+	622.588i	0.656046	+	0.656046i
$950$		0			0
$951$	992.517	−	26.7693i	1.04366	−	0.0281486i
$952$		0			0
$953$	1627.75			1.70803			0.854013	−	0.520251i	$-0.174162\pi$
$953$	1627.75			1.70803			0.854013	+	0.520251i	$0.174162\pi$
$954$		0			0
$955$	115.517	+	115.517i	0.120961	+	0.120961i
$956$		0			0
$957$	1501.08	−	1584.30i	1.56853	−	1.65548i
$958$		0			0
$959$			148.283i			0.154623i
$960$		0			0
$961$	−898.433			−0.934894
$962$		0			0
$963$	875.660	+	785.963i	0.909304	+	0.816161i
$964$		0			0
$965$	−149.785	+	149.785i	−0.155218	+	0.155218i
$966$		0			0
$967$			1444.31i			1.49360i	0.665049	+	0.746799i	$0.268410\pi$
$967$			1444.31i			1.49360i	−0.665049	+	0.746799i	$0.731590\pi$
$968$		0			0
$969$	−59.8945	+	1.61542i	−0.0618106	+	0.00166710i
$970$		0			0
$971$	165.972	−	165.972i	0.170929	−	0.170929i	−0.616458	−	0.787388i	$-0.711433\pi$
$971$	165.972	−	165.972i	0.170929	−	0.170929i	0.787388	+	0.616458i	$0.211433\pi$
$972$		0			0
$973$	−18.5371	+	18.5371i	−0.0190515	+	0.0190515i
$974$		0			0
$975$	129.673	−	3.49742i	0.132998	−	0.00358710i
$976$		0			0
$977$			1708.09i			1.74830i	0.485658	+	0.874149i	$0.338580\pi$
$977$			1708.09i			1.74830i	−0.485658	+	0.874149i	$0.661420\pi$
$978$		0			0
$979$	906.510	−	906.510i	0.925955	−	0.925955i
$980$		0			0
$981$	−713.955	−	640.822i	−0.727783	−	0.653233i
$982$		0			0
$983$	285.345			0.290279			0.145140	−	0.989411i	$-0.453637\pi$
$983$	285.345			0.290279			0.145140	+	0.989411i	$0.453637\pi$
$984$		0			0
$985$		−	205.261i		−	0.208386i
$986$		0			0
$987$	−63.4247	+	66.9408i	−0.0642601	+	0.0678225i
$988$		0			0
$989$	−1225.75	−	1225.75i	−1.23938	−	1.23938i
$990$		0			0
$991$	437.191			0.441162			0.220581	−	0.975369i	$-0.429205\pi$
$991$	437.191			0.441162			0.220581	+	0.975369i	$0.429205\pi$
$992$		0			0
$993$	138.002	−	3.72207i	0.138975	−	0.00374831i
$994$		0			0
$995$	−375.762	−	375.762i	−0.377650	−	0.377650i
$996$		0			0
$997$	−1029.10	−	1029.10i	−1.03220	−	1.03220i	−0.999464	−	0.0327341i	$-0.989579\pi$
$997$	−1029.10	−	1029.10i	−1.03220	−	1.03220i	−0.0327341	−	0.999464i	$-0.510421\pi$
$998$		0			0
$999$	−61.8458	−	762.862i	−0.0619077	−	0.763626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.3.i.b.113.7		20
3.2	odd	2	inner	192.3.i.b.113.8		20
4.3	odd	2		48.3.i.b.5.3	✓	20
8.3	odd	2		384.3.i.d.353.7		20
8.5	even	2		384.3.i.c.353.4		20
12.11	even	2		48.3.i.b.5.8	yes	20
16.3	odd	4		48.3.i.b.29.8	yes	20
16.5	even	4		384.3.i.c.161.3		20
16.11	odd	4		384.3.i.d.161.8		20
16.13	even	4	inner	192.3.i.b.17.8		20
24.5	odd	2		384.3.i.c.353.3		20
24.11	even	2		384.3.i.d.353.8		20
48.5	odd	4		384.3.i.c.161.4		20
48.11	even	4		384.3.i.d.161.7		20
48.29	odd	4	inner	192.3.i.b.17.7		20
48.35	even	4		48.3.i.b.29.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.3	✓	20	4.3	odd	2
48.3.i.b.5.8	yes	20	12.11	even	2
48.3.i.b.29.3	yes	20	48.35	even	4
48.3.i.b.29.8	yes	20	16.3	odd	4
192.3.i.b.17.7		20	48.29	odd	4	inner
192.3.i.b.17.8		20	16.13	even	4	inner
192.3.i.b.113.7		20	1.1	even	1	trivial
192.3.i.b.113.8		20	3.2	odd	2	inner
384.3.i.c.161.3		20	16.5	even	4
384.3.i.c.161.4		20	48.5	odd	4
384.3.i.c.353.3		20	24.5	odd	2
384.3.i.c.353.4		20	8.5	even	2
384.3.i.d.161.7		20	48.11	even	4
384.3.i.d.161.8		20	16.11	odd	4
384.3.i.d.353.7		20	8.3	odd	2
384.3.i.d.353.8		20	24.11	even	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)

\(f(q)\)	\(=\)	\(q+(2.06336 - 2.17774i) q^{3} +(-3.17955 + 3.17955i) q^{5} -6.03979i q^{7} +(-0.485128 - 8.98692i) q^{9} +O(q^{10})\)	\(q+(2.06336 - 2.17774i) q^{3} +(-3.17955 + 3.17955i) q^{5} -6.03979i q^{7} +(-0.485128 - 8.98692i) q^{9} +(13.0097 - 13.0097i) q^{11} +(6.39520 - 6.39520i) q^{13} +(0.363700 + 13.4848i) q^{15} -4.39848i q^{17} +(3.21075 - 3.21075i) q^{19} +(-13.1531 - 12.4622i) q^{21} -34.0396 q^{23} +4.78097i q^{25} +(-20.5722 - 17.4867i) q^{27} +(27.9597 + 27.9597i) q^{29} +7.90993 q^{31} +(-1.48814 - 55.1754i) q^{33} +(19.2038 + 19.2038i) q^{35} +(20.0443 + 20.0443i) q^{37} +(-0.731530 - 27.1227i) q^{39} -45.1067 q^{41} +(36.0095 + 36.0095i) q^{43} +(30.1168 + 27.0318i) q^{45} -5.08935i q^{47} +12.5209 q^{49} +(-9.57876 - 9.07563i) q^{51} +(20.7687 - 20.7687i) q^{53} +82.7299i q^{55} +(-0.367268 - 13.6171i) q^{57} +(39.0656 - 39.0656i) q^{59} +(-49.8322 + 49.8322i) q^{61} +(-54.2791 + 2.93007i) q^{63} +40.6677i q^{65} +(-44.9162 + 44.9162i) q^{67} +(-70.2358 + 74.1295i) q^{69} -46.6947 q^{71} +97.3523i q^{73} +(10.4117 + 9.86483i) q^{75} +(-78.5758 - 78.5758i) q^{77} +40.1637 q^{79} +(-80.5293 + 8.71960i) q^{81} +(35.5451 + 35.5451i) q^{83} +(13.9852 + 13.9852i) q^{85} +(118.580 - 3.19823i) q^{87} +69.6795 q^{89} +(-38.6257 - 38.6257i) q^{91} +(16.3210 - 17.2258i) q^{93} +20.4174i q^{95} +61.0939 q^{97} +(-123.228 - 110.606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3}+O(q^{10}) \) 20 * q + 6 * q^3	\( 20 q + 6 q^{3} + 92 q^{13} + 116 q^{15} + 52 q^{19} + 48 q^{21} - 18 q^{27} + 80 q^{31} + 60 q^{33} - 116 q^{37} - 172 q^{43} + 60 q^{45} - 364 q^{49} - 128 q^{51} - 244 q^{61} - 296 q^{63} - 356 q^{67} - 20 q^{69} + 146 q^{75} - 384 q^{79} - 188 q^{81} + 48 q^{85} - 136 q^{91} - 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) \) 20 * q + 6 * q^3 + 92 * q^13 + 116 * q^15 + 52 * q^19 + 48 * q^21 - 18 * q^27 + 80 * q^31 + 60 * q^33 - 116 * q^37 - 172 * q^43 + 60 * q^45 - 364 * q^49 - 128 * q^51 - 244 * q^61 - 296 * q^63 - 356 * q^67 - 20 * q^69 + 146 * q^75 - 384 * q^79 - 188 * q^81 + 48 * q^85 - 136 * q^91 - 132 * q^93 + 472 * q^97 + 452 * q^99

Introduction

L-functions

Modular forms

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Database

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