LMFDB - Embedded newform 112.3.r.b.95.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(79,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("112.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.259470000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 14x^{4} - x^{3} + 176x^{2} - 91x + 49 $ x^6 - x^5 + 14x^4 - x^3 + 176x^2 - 91*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.3
Root			$1.94170 - 3.36313i$ of defining polynomial
Character	$\chi$	$=$	112.95
Dual form			112.3.r.b.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.54043 + 1.46672i) q^{3} +(3.38341 + 5.86024i) q^{5} +(-5.88341 + 3.79282i) q^{7} +(-0.197460 - 0.342011i) q^{9} +(-8.19066 - 4.72888i) q^{11} +23.9286 q^{13} +19.8501i q^{15} +(1.69746 - 2.94009i) q^{17} +(-2.89021 + 1.66866i) q^{19} +(-20.5094 + 1.00610i) q^{21} +(26.7830 - 15.4632i) q^{23} +(-10.3949 + 18.0045i) q^{25} -27.5595i q^{27} -11.6051 q^{29} +(13.0289 + 7.52225i) q^{31} +(-13.8719 - 24.0268i) q^{33} +(-42.1328 - 21.6455i) q^{35} +(-24.8813 - 43.0957i) q^{37} +(60.7889 + 35.0965i) q^{39} -2.67236 q^{41} -44.7593i q^{43} +(1.33618 - 2.31433i) q^{45} +(-69.5720 + 40.1674i) q^{47} +(20.2290 - 44.6294i) q^{49} +(8.62457 - 4.97940i) q^{51} +(-38.4864 + 66.6604i) q^{53} -63.9990i q^{55} -9.78984 q^{57} +(-7.57526 - 4.37358i) q^{59} +(-25.9758 - 44.9914i) q^{61} +(2.45893 + 1.26326i) q^{63} +(80.9601 + 140.227i) q^{65} +(100.164 + 57.8299i) q^{67} +90.7208 q^{69} +122.338i q^{71} +(-12.9622 + 22.4512i) q^{73} +(-52.8152 + 30.4929i) q^{75} +(66.1248 - 3.24377i) q^{77} +(0.0203900 - 0.0117722i) q^{79} +(38.6449 - 66.9349i) q^{81} -107.921i q^{83} +22.9728 q^{85} +(-29.4819 - 17.0214i) q^{87} +(7.08206 + 12.2665i) q^{89} +(-140.782 + 90.7567i) q^{91} +(22.0661 + 38.2196i) q^{93} +(-19.5575 - 11.2915i) q^{95} -57.3654 q^{97} +3.73507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - q^{5} - 14 q^{7} + 14 q^{9} + 33 q^{11} + 28 q^{13} - 5 q^{17} - 63 q^{19} + 29 q^{21} + 33 q^{23} - 32 q^{25} - 100 q^{29} + 69 q^{31} - 71 q^{33} - 189 q^{35} + 15 q^{37} + 246 q^{39}+ \cdots + 124 q^{97}+O(q^{100}) $ 6 * q - 3 * q^3 - q^5 - 14 * q^7 + 14 * q^9 + 33 * q^11 + 28 * q^13 - 5 * q^17 - 63 * q^19 + 29 * q^21 + 33 * q^23 - 32 * q^25 - 100 * q^29 + 69 * q^31 - 71 * q^33 - 189 * q^35 + 15 * q^37 + 246 * q^39 + 124 * q^41 - 62 * q^45 - 171 * q^47 - 122 * q^49 + 225 * q^51 - 97 * q^53 + 2 * q^57 - 27 * q^59 - 89 * q^61 - 414 * q^63 + 142 * q^65 + 309 * q^67 + 538 * q^69 + 123 * q^73 - 408 * q^75 + 181 * q^77 + 201 * q^79 - 203 * q^81 - 130 * q^85 + 270 * q^87 + 91 * q^89 - 212 * q^91 - 123 * q^93 + 321 * q^95 + 124 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.54043	+	1.46672i	0.846812	+	0.488907i	0.859574	−	0.511012i	$-0.170729\pi$
$3$	2.54043	+	1.46672i	0.846812	+	0.488907i	−0.0127622	+	0.999919i	$0.504062\pi$
$4$		0			0
$5$	3.38341	+	5.86024i	0.676682	+	1.17205i	0.975974	+	0.217886i	$0.0699161\pi$
$5$	3.38341	+	5.86024i	0.676682	+	1.17205i	−0.299292	+	0.954161i	$0.596751\pi$
$6$		0			0
$7$	−5.88341	+	3.79282i	−0.840487	+	0.541832i
$7$	−5.88341	+	3.79282i	−0.840487	+	0.541832i
$8$		0			0
$9$	−0.197460	−	0.342011i	−0.0219400	−	0.0380012i
$10$		0			0
$11$	−8.19066	−	4.72888i	−0.744606	−	0.429898i	0.0791358	−	0.996864i	$-0.474784\pi$
$11$	−8.19066	−	4.72888i	−0.744606	−	0.429898i	−0.823742	+	0.566965i	$0.808117\pi$
$12$		0			0
$13$	23.9286			1.84066			0.920329	−	0.391145i	$-0.127921\pi$
$13$	23.9286			1.84066			0.920329	+	0.391145i	$0.127921\pi$
$14$		0			0
$15$			19.8501i			1.32334i
$16$		0			0
$17$	1.69746	−	2.94009i	0.0998506	−	0.172946i	−0.811772	−	0.583974i	$-0.801497\pi$
$17$	1.69746	−	2.94009i	0.0998506	−	0.172946i	0.911623	+	0.411028i	$0.134830\pi$
$18$		0			0
$19$	−2.89021	+	1.66866i	−0.152116	+	0.0878243i	−0.574126	−	0.818767i	$-0.694658\pi$
$19$	−2.89021	+	1.66866i	−0.152116	+	0.0878243i	0.422010	+	0.906591i	$0.361325\pi$
$20$		0			0
$21$	−20.5094	+	1.00610i	−0.976639	+	0.0479093i
$22$		0			0
$23$	26.7830	−	15.4632i	1.16448	−	0.672313i	0.212107	−	0.977247i	$-0.431968\pi$
$23$	26.7830	−	15.4632i	1.16448	−	0.672313i	0.952374	+	0.304934i	$0.0986343\pi$
$24$		0			0
$25$	−10.3949	+	18.0045i	−0.415797	+	0.720181i
$26$		0			0
$27$		−	27.5595i		−	1.02072i
$28$		0			0
$29$	−11.6051			−0.400175			−0.200088	−	0.979778i	$-0.564123\pi$
$29$	−11.6051			−0.400175			−0.200088	+	0.979778i	$0.564123\pi$
$30$		0			0
$31$	13.0289	+	7.52225i	0.420288	+	0.242653i	0.695200	−	0.718816i	$-0.255316\pi$
$31$	13.0289	+	7.52225i	0.420288	+	0.242653i	−0.274913	+	0.961469i	$0.588649\pi$
$32$		0			0
$33$	−13.8719	−	24.0268i	−0.420361	−	0.728086i
$34$		0			0
$35$	−42.1328	−	21.6455i	−1.20379	−	0.618443i
$36$		0			0
$37$	−24.8813	−	43.0957i	−0.672468	−	1.16475i	−0.977202	−	0.212312i	$-0.931901\pi$
$37$	−24.8813	−	43.0957i	−0.672468	−	1.16475i	0.304734	−	0.952438i	$-0.401433\pi$
$38$		0			0
$39$	60.7889	+	35.0965i	1.55869	+	0.899911i
$40$		0			0
$41$	−2.67236			−0.0651794			−0.0325897	−	0.999469i	$-0.510375\pi$
$41$	−2.67236			−0.0651794			−0.0325897	+	0.999469i	$0.510375\pi$
$42$		0			0
$43$		−	44.7593i		−	1.04091i	−0.853888	−	0.520456i	$-0.825762\pi$
$43$		−	44.7593i		−	1.04091i	0.853888	−	0.520456i	$-0.174238\pi$
$44$		0			0
$45$	1.33618	−	2.31433i	0.0296928	−	0.0514295i
$46$		0			0
$47$	−69.5720	+	40.1674i	−1.48026	+	0.854626i	−0.999750	−	0.0223661i	$-0.992880\pi$
$47$	−69.5720	+	40.1674i	−1.48026	+	0.854626i	−0.480505	+	0.876992i	$0.659547\pi$
$48$		0			0
$49$	20.2290	−	44.6294i	0.412837	−	0.910805i
$50$		0			0
$51$	8.62457	−	4.97940i	0.169109	−	0.0976353i
$52$		0			0
$53$	−38.4864	+	66.6604i	−0.726159	+	1.25774i	0.232337	+	0.972635i	$0.425363\pi$
$53$	−38.4864	+	66.6604i	−0.726159	+	1.25774i	−0.958495	+	0.285108i	$0.907970\pi$
$54$		0			0
$55$		−	63.9990i		−	1.16362i
$56$		0			0
$57$	−9.78984			−0.171752
$58$		0			0
$59$	−7.57526	−	4.37358i	−0.128394	−	0.0741285i	0.434427	−	0.900707i	$-0.356951\pi$
$59$	−7.57526	−	4.37358i	−0.128394	−	0.0741285i	−0.562821	+	0.826578i	$0.690284\pi$
$60$		0			0
$61$	−25.9758	−	44.9914i	−0.425833	−	0.737564i	0.570665	−	0.821183i	$-0.306685\pi$
$61$	−25.9758	−	44.9914i	−0.425833	−	0.737564i	−0.996498	+	0.0836191i	$0.973352\pi$
$62$		0			0
$63$	2.45893	+	1.26326i	0.0390306	+	0.0200518i
$64$		0			0
$65$	80.9601	+	140.227i	1.24554	+	2.15734i
$66$		0			0
$67$	100.164	+	57.8299i	1.49499	+	0.863133i	0.999983	−	0.00575564i	$-0.00183209\pi$
$67$	100.164	+	57.8299i	1.49499	+	0.863133i	0.495007	+	0.868889i	$0.335165\pi$
$68$		0			0
$69$	90.7208			1.31479
$70$		0			0
$71$			122.338i			1.72306i	0.507703	+	0.861532i	$0.330495\pi$
$71$			122.338i			1.72306i	−0.507703	+	0.861532i	$0.669505\pi$
$72$		0			0
$73$	−12.9622	+	22.4512i	−0.177564	+	0.307550i	−0.941046	−	0.338279i	$-0.890155\pi$
$73$	−12.9622	+	22.4512i	−0.177564	+	0.307550i	0.763481	+	0.645830i	$0.223488\pi$
$74$		0			0
$75$	−52.8152	+	30.4929i	−0.704203	+	0.406572i
$76$		0			0
$77$	66.1248	−	3.24377i	0.858764	−	0.0421269i
$78$		0			0
$79$	0.0203900	−	0.0117722i	0.000258101	−	0.000149015i	−0.499871	−	0.866100i	$-0.666619\pi$
$79$	0.0203900	−	0.0117722i	0.000258101	−	0.000149015i	0.500129	+	0.865951i	$0.333286\pi$
$80$		0			0
$81$	38.6449	−	66.9349i	0.477097	−	0.826357i
$82$		0			0
$83$		−	107.921i		−	1.30025i	−0.759827	−	0.650126i	$-0.774716\pi$
$83$		−	107.921i		−	1.30025i	0.759827	−	0.650126i	$-0.225284\pi$
$84$		0			0
$85$	22.9728			0.270268
$86$		0			0
$87$	−29.4819	−	17.0214i	−0.338873	−	0.195648i
$88$		0			0
$89$	7.08206	+	12.2665i	0.0795737	+	0.137826i	0.903066	−	0.429502i	$-0.141311\pi$
$89$	7.08206	+	12.2665i	0.0795737	+	0.137826i	−0.823492	+	0.567327i	$0.807977\pi$
$90$		0			0
$91$	−140.782	+	90.7567i	−1.54705	+	0.997327i
$92$		0			0
$93$	22.0661	+	38.2196i	0.237270	+	0.410963i
$94$		0			0
$95$	−19.5575	−	11.2915i	−0.205868	−	0.118858i
$96$		0			0
$97$	−57.3654			−0.591395			−0.295698	−	0.955282i	$-0.595552\pi$
$97$	−57.3654			−0.591395			−0.295698	+	0.955282i	$0.595552\pi$
$98$		0			0
$99$			3.73507i			0.0377279i
$100$		0			0
$101$	−55.5221	+	96.1671i	−0.549724	+	0.952150i	0.448569	+	0.893748i	$0.351934\pi$
$101$	−55.5221	+	96.1671i	−0.549724	+	0.952150i	−0.998293	+	0.0584018i	$0.981400\pi$
$102$		0			0
$103$	56.9619	−	32.8869i	0.553028	−	0.319291i	−0.197315	−	0.980340i	$-0.563222\pi$
$103$	56.9619	−	32.8869i	0.553028	−	0.319291i	0.750342	+	0.661050i	$0.229889\pi$
$104$		0			0
$105$	−75.2878	−	116.786i	−0.717026	−	1.11225i
$106$		0			0
$107$	−27.3754	+	15.8052i	−0.255845	+	0.147712i	−0.622438	−	0.782669i	$-0.713858\pi$
$107$	−27.3754	+	15.8052i	−0.255845	+	0.147712i	0.366593	+	0.930382i	$0.380524\pi$
$108$		0			0
$109$	23.8940	−	41.3857i	0.219211	−	0.379685i	−0.735356	−	0.677681i	$-0.762985\pi$
$109$	23.8940	−	41.3857i	0.219211	−	0.379685i	0.954567	+	0.297996i	$0.0963183\pi$
$110$		0			0
$111$		−	145.976i		−	1.31510i
$112$		0			0
$113$	−74.7609			−0.661601			−0.330800	−	0.943701i	$-0.607319\pi$
$113$	−74.7609			−0.661601			−0.330800	+	0.943701i	$0.607319\pi$
$114$		0			0
$115$	181.236	+	104.637i	1.57597	+	0.909884i
$116$		0			0
$117$	−4.72494	−	8.18384i	−0.0403841	−	0.0699473i
$118$		0			0
$119$	1.16437	+	23.7359i	0.00978464	+	0.199461i
$120$		0			0
$121$	−15.7754	−	27.3237i	−0.130375	−	0.225816i
$122$		0			0
$123$	−6.78895	−	3.91960i	−0.0551947	−	0.0318667i
$124$		0			0
$125$	28.4894			0.227915
$126$		0			0
$127$		−	61.4397i		−	0.483777i	−0.970304	−	0.241889i	$-0.922233\pi$
$127$		−	61.4397i		−	0.483777i	0.970304	−	0.241889i	$-0.0777669\pi$
$128$		0			0
$129$	65.6493	−	113.708i	0.508910	−	0.881457i
$130$		0			0
$131$	96.0026	−	55.4271i	0.732845	−	0.423108i	−0.0866174	−	0.996242i	$-0.527606\pi$
$131$	96.0026	−	55.4271i	0.732845	−	0.423108i	0.819462	+	0.573134i	$0.194272\pi$
$132$		0			0
$133$	10.6753	−	20.7795i	0.0802657	−	0.156236i
$134$		0			0
$135$	161.505	−	93.2449i	1.19633	−	0.690703i
$136$		0			0
$137$	−98.6449	+	170.858i	−0.720036	+	1.24714i	0.240949	+	0.970538i	$0.422541\pi$
$137$	−98.6449	+	170.858i	−0.720036	+	1.24714i	−0.960985	+	0.276601i	$0.910792\pi$
$138$		0			0
$139$			82.8378i			0.595955i	0.954573	+	0.297978i	$0.0963121\pi$
$139$			82.8378i			0.595955i	−0.954573	+	0.297978i	$0.903688\pi$
$140$		0			0
$141$	−235.657			−1.67133
$142$		0			0
$143$	−195.991	−	113.155i	−1.37056	−	0.791296i
$144$		0			0
$145$	−39.2647	−	68.0085i	−0.270791	−	0.469024i
$146$		0			0
$147$	116.849	−	83.7079i	0.794894	−	0.569441i
$148$		0			0
$149$	−98.0534	−	169.833i	−0.658076	−	1.13982i	−0.981113	−	0.193435i	$-0.938037\pi$
$149$	−98.0534	−	169.833i	−0.658076	−	1.13982i	0.323037	−	0.946386i	$-0.395296\pi$
$150$		0			0
$151$	−95.5484	−	55.1649i	−0.632771	−	0.365330i	0.149054	−	0.988829i	$-0.452377\pi$
$151$	−95.5484	−	55.1649i	−0.632771	−	0.365330i	−0.781824	+	0.623499i	$0.785711\pi$
$152$		0			0
$153$	−1.34072			−0.00876290
$154$		0			0
$155$			101.803i			0.656796i
$156$		0			0
$157$	−37.4906	+	64.9356i	−0.238793	+	0.413602i	−0.960368	−	0.278734i	$-0.910085\pi$
$157$	−37.4906	+	64.9356i	−0.238793	+	0.413602i	0.721575	+	0.692336i	$0.243419\pi$
$158$		0			0
$159$	−195.544	+	112.898i	−1.22984	+	0.710048i
$160$		0			0
$161$	−98.9265	+	192.560i	−0.614450	+	1.19602i
$162$		0			0
$163$	−30.1762	+	17.4222i	−0.185130	+	0.106885i	−0.589701	−	0.807622i	$-0.700754\pi$
$163$	−30.1762	+	17.4222i	−0.185130	+	0.106885i	0.404571	+	0.914507i	$0.367421\pi$
$164$		0			0
$165$	93.8686	−	162.585i	0.568901	−	0.985365i
$166$		0			0
$167$			103.266i			0.618357i	0.951004	+	0.309178i	$0.100054\pi$
$167$			103.266i			0.618357i	−0.951004	+	0.309178i	$0.899946\pi$
$168$		0			0
$169$	403.576			2.38802
$170$		0			0
$171$	1.14140	+	0.658989i	0.00667486	+	0.00385373i
$172$		0			0
$173$	17.6565	+	30.5819i	0.102061	+	0.176774i	0.912533	−	0.409002i	$-0.134123\pi$
$173$	17.6565	+	30.5819i	0.102061	+	0.176774i	−0.810473	+	0.585776i	$0.800790\pi$
$174$		0			0
$175$	−7.13039	−	145.354i	−0.0407451	−	0.830595i
$176$		0			0
$177$	−12.8296	−	22.2216i	−0.0724838	−	0.125546i
$178$		0			0
$179$	105.728	+	61.0420i	0.590658	+	0.341017i	0.765358	−	0.643605i	$-0.222562\pi$
$179$	105.728	+	61.0420i	0.590658	+	0.341017i	−0.174700	+	0.984622i	$0.555895\pi$
$180$		0			0
$181$	22.7013			0.125422			0.0627109	−	0.998032i	$-0.480025\pi$
$181$	22.7013			0.125422			0.0627109	+	0.998032i	$0.480025\pi$
$182$		0			0
$183$		−	152.397i		−	0.832770i
$184$		0			0
$185$	168.367	−	291.621i	0.910094	−	1.57633i
$186$		0			0
$187$	−27.8067	+	16.0542i	−0.148699	+	0.0858512i
$188$		0			0
$189$	104.528	+	162.144i	0.553059	+	0.857902i
$190$		0			0
$191$	−175.202	+	101.153i	−0.917290	+	0.529598i	−0.882770	−	0.469806i	$-0.844324\pi$
$191$	−175.202	+	101.153i	−0.917290	+	0.529598i	−0.0345208	+	0.999404i	$0.510990\pi$
$192$		0			0
$193$	−137.775	+	238.634i	−0.713861	+	1.23644i	0.249536	+	0.968366i	$0.419722\pi$
$193$	−137.775	+	238.634i	−0.713861	+	1.23644i	−0.963397	+	0.268079i	$0.913611\pi$
$194$		0			0
$195$			474.984i			2.43581i
$196$		0			0
$197$	194.605			0.987842			0.493921	−	0.869507i	$-0.335563\pi$
$197$	194.605			0.987842			0.493921	+	0.869507i	$0.335563\pi$
$198$		0			0
$199$	145.739	+	84.1424i	0.732357	+	0.422826i	0.819284	−	0.573388i	$-0.194371\pi$
$199$	145.739	+	84.1424i	0.732357	+	0.422826i	−0.0869270	+	0.996215i	$0.527705\pi$
$200$		0			0
$201$	169.641	+	293.826i	0.843984	+	1.46182i
$202$		0			0
$203$	68.2774	−	44.0160i	0.336342	−	0.216828i
$204$		0			0
$205$	−9.04167	−	15.6606i	−0.0441057	−	0.0763934i
$206$		0			0
$207$	−10.5772	−	6.10673i	−0.0510975	−	0.0295011i
$208$		0			0
$209$	31.5636			0.151022
$210$		0			0
$211$		−	222.522i		−	1.05461i	−0.849677	−	0.527304i	$-0.823203\pi$
$211$		−	222.522i		−	1.05461i	0.849677	−	0.527304i	$-0.176797\pi$
$212$		0			0
$213$	−179.435	+	310.791i	−0.842418	+	1.45911i
$214$		0			0
$215$	262.300	−	151.439i	1.22000	−	0.704367i
$216$		0			0
$217$	−105.185	+	5.15988i	−0.484724	+	0.0237783i
$218$		0			0
$219$	−65.8592	+	38.0238i	−0.300727	+	0.173625i
$220$		0			0
$221$	40.6178	−	70.3521i	0.183791	−	0.318335i
$222$		0			0
$223$			265.253i			1.18948i	0.803919	+	0.594738i	$0.202744\pi$
$223$			265.253i			1.18948i	−0.803919	+	0.594738i	$0.797256\pi$
$224$		0			0
$225$	8.21034			0.0364904
$226$		0			0
$227$	−198.715	−	114.728i	−0.875398	−	0.505411i	−0.00625983	−	0.999980i	$-0.501993\pi$
$227$	−198.715	−	114.728i	−0.875398	−	0.505411i	−0.869138	+	0.494569i	$0.835326\pi$
$228$		0			0
$229$	−18.1520	−	31.4402i	−0.0792665	−	0.137294i	0.823667	−	0.567073i	$-0.191924\pi$
$229$	−18.1520	−	31.4402i	−0.0792665	−	0.137294i	−0.902934	+	0.429780i	$0.858591\pi$
$230$		0			0
$231$	172.744	+	88.7461i	0.747808	+	0.384182i
$232$		0			0
$233$	−56.6431	−	98.1087i	−0.243103	−	0.421067i	0.718493	−	0.695534i	$-0.244832\pi$
$233$	−56.6431	−	98.1087i	−0.243103	−	0.421067i	−0.961597	+	0.274466i	$0.911499\pi$
$234$		0			0
$235$	−470.781	−	271.806i	−2.00332	−	1.15662i
$236$		0			0
$237$	0.0690659			0.000291417
$238$		0			0
$239$			125.206i			0.523873i	0.965085	+	0.261936i	$0.0843611\pi$
$239$			125.206i			0.523873i	−0.965085	+	0.261936i	$0.915639\pi$
$240$		0			0
$241$	140.071	−	242.611i	0.581209	−	1.00668i	−0.414127	−	0.910219i	$-0.635913\pi$
$241$	140.071	−	242.611i	0.581209	−	1.00668i	0.995336	−	0.0964645i	$-0.0307534\pi$
$242$		0			0
$243$	−18.4551	+	10.6550i	−0.0759468	+	0.0438479i
$244$		0			0
$245$	329.982	−	32.4528i	1.34687	−	0.132461i
$246$		0			0
$247$	−69.1585	+	39.9287i	−0.279994	+	0.161654i
$248$		0			0
$249$	158.290	−	274.166i	0.635702	−	1.10107i
$250$		0			0
$251$		−	128.827i		−	0.513255i	−0.966510	−	0.256627i	$-0.917389\pi$
$251$		−	128.827i		−	0.513255i	0.966510	−	0.256627i	$-0.0826113\pi$
$252$		0			0
$253$	−292.495			−1.15610
$254$		0			0
$255$	58.3609	+	33.6947i	0.228866	+	0.132136i
$256$		0			0
$257$	23.4200	+	40.5647i	0.0911285	+	0.157839i	0.907986	−	0.419000i	$-0.137619\pi$
$257$	23.4200	+	40.5647i	0.0911285	+	0.157839i	−0.816858	+	0.576839i	$0.804286\pi$
$258$		0			0
$259$	309.841	+	159.179i	1.19630	+	0.614592i
$260$		0			0
$261$	2.29154	+	3.96907i	0.00877986	+	0.0152072i
$262$		0			0
$263$	−185.429	−	107.057i	−0.705052	−	0.407062i	0.104174	−	0.994559i	$-0.466780\pi$
$263$	−185.429	−	107.057i	−0.705052	−	0.407062i	−0.809226	+	0.587497i	$0.800113\pi$
$264$		0			0
$265$	−520.861			−1.96551
$266$		0			0
$267$			41.5496i			0.155616i
$268$		0			0
$269$	32.3713	−	56.0687i	0.120339	−	0.208434i	−0.799562	−	0.600583i	$-0.794935\pi$
$269$	32.3713	−	56.0687i	0.120339	−	0.208434i	0.919902	+	0.392149i	$0.128268\pi$
$270$		0			0
$271$	230.972	−	133.352i	0.852297	−	0.492074i	−0.00912848	−	0.999958i	$-0.502906\pi$
$271$	230.972	−	133.352i	0.852297	−	0.492074i	0.861425	+	0.507885i	$0.169572\pi$
$272$		0			0
$273$	−490.761	+	24.0744i	−1.79766	+	0.0881847i
$274$		0			0
$275$	170.283	−	98.3127i	0.619209	−	0.357501i
$276$		0			0
$277$	162.249	−	281.024i	0.585737	−	1.01453i	−0.409046	−	0.912514i	$-0.634139\pi$
$277$	162.249	−	281.024i	0.585737	−	1.01453i	0.994783	−	0.102012i	$-0.0325281\pi$
$278$		0			0
$279$		−	5.94138i		−	0.0212953i
$280$		0			0
$281$	−298.659			−1.06284			−0.531422	−	0.847107i	$-0.678342\pi$
$281$	−298.659			−1.06284			−0.531422	+	0.847107i	$0.678342\pi$
$282$		0			0
$283$	−229.716	−	132.627i	−0.811717	−	0.468645i	0.0358346	−	0.999358i	$-0.488591\pi$
$283$	−229.716	−	132.627i	−0.811717	−	0.468645i	−0.847552	+	0.530713i	$0.821924\pi$
$284$		0			0
$285$	−33.1230	−	57.3708i	−0.116221	−	0.201301i
$286$		0			0
$287$	15.7226	−	10.1358i	0.0547825	−	0.0353163i
$288$		0			0
$289$	138.737	+	240.300i	0.480060	+	0.831488i
$290$		0			0
$291$	−145.733	−	84.1390i	−0.500801	−	0.289137i
$292$		0			0
$293$	−437.504			−1.49319			−0.746594	−	0.665280i	$-0.768312\pi$
$293$	−437.504			−1.49319			−0.746594	+	0.665280i	$0.768312\pi$
$294$		0			0
$295$		−	59.1904i		−	0.200646i
$296$		0			0
$297$	−130.325	+	225.730i	−0.438806	+	0.760034i
$298$		0			0
$299$	640.880	−	370.012i	2.14341	−	1.23750i
$300$		0			0
$301$	169.764	+	263.337i	0.564000	+	0.874874i
$302$		0			0
$303$	−282.101	+	162.871i	−0.931025	+	0.537528i
$304$		0			0
$305$	175.773	−	304.449i	0.576306	−	0.998192i
$306$		0			0
$307$		−	338.398i		−	1.10227i	−0.834415	−	0.551137i	$-0.814194\pi$
$307$		−	338.398i		−	1.10227i	0.834415	−	0.551137i	$-0.185806\pi$
$308$		0			0
$309$	192.944			0.624414
$310$		0			0
$311$	320.421	+	184.995i	1.03029	+	0.594841i	0.917069	−	0.398729i	$-0.130548\pi$
$311$	320.421	+	184.995i	1.03029	+	0.594841i	0.113225	+	0.993569i	$0.463882\pi$
$312$		0			0
$313$	23.1807	+	40.1501i	0.0740597	+	0.128275i	0.900677	−	0.434489i	$-0.143071\pi$
$313$	23.1807	+	40.1501i	0.0740597	+	0.128275i	−0.826617	+	0.562764i	$0.809738\pi$
$314$		0			0
$315$	0.916550	+	18.6840i	0.00290968	+	0.0593144i
$316$		0			0
$317$	−205.697	−	356.277i	−0.648885	−	1.12390i	−0.983390	−	0.181508i	$-0.941902\pi$
$317$	−205.697	−	356.277i	−0.648885	−	1.12390i	0.334504	−	0.942394i	$-0.391431\pi$
$318$		0			0
$319$	95.0533	+	54.8790i	0.297973	+	0.172035i
$320$		0			0
$321$	−92.7273			−0.288870
$322$		0			0
$323$			11.3299i			0.0350772i
$324$		0			0
$325$	−248.735	+	430.822i	−0.765340	+	1.32561i
$326$		0			0
$327$	121.402	−	70.0917i	0.371261	−	0.214348i
$328$		0			0
$329$	256.973	−	500.195i	0.781072	−	1.52035i
$330$		0			0
$331$	−171.730	+	99.1486i	−0.518823	+	0.299543i	−0.736453	−	0.676489i	$-0.763501\pi$
$331$	−171.730	+	99.1486i	−0.518823	+	0.299543i	0.217630	+	0.976031i	$0.430167\pi$
$332$		0			0
$333$	−9.82615	+	17.0194i	−0.0295080	+	0.0511093i
$334$		0			0
$335$			782.649i			2.33627i
$336$		0			0
$337$	372.293			1.10473			0.552364	−	0.833603i	$-0.313726\pi$
$337$	372.293			1.10473			0.552364	+	0.833603i	$0.313726\pi$
$338$		0			0
$339$	−189.925	−	109.653i	−0.560251	−	0.323461i
$340$		0			0
$341$	−71.1437	−	123.224i	−0.208633	−	0.361362i
$342$		0			0
$343$	50.2559	+	339.298i	0.146519	+	0.989208i
$344$		0			0
$345$	306.946	+	531.645i	0.889697	+	1.54100i
$346$		0			0
$347$	25.8710	+	14.9367i	0.0745563	+	0.0430451i	0.536815	−	0.843700i	$-0.319627\pi$
$347$	25.8710	+	14.9367i	0.0745563	+	0.0430451i	−0.462258	+	0.886745i	$0.652961\pi$
$348$		0			0
$349$	491.816			1.40922			0.704608	−	0.709597i	$-0.251123\pi$
$349$	491.816			1.40922			0.704608	+	0.709597i	$0.251123\pi$
$350$		0			0
$351$		−	659.458i		−	1.87880i
$352$		0			0
$353$	209.599	−	363.036i	0.593764	−	1.02843i	−0.399956	−	0.916535i	$-0.630974\pi$
$353$	209.599	−	363.036i	0.593764	−	1.02843i	0.993720	−	0.111896i	$-0.0356922\pi$
$354$		0			0
$355$	−716.927	+	413.918i	−2.01951	+	1.16597i
$356$		0			0
$357$	−31.8559	+	62.0073i	−0.0892323	+	0.173690i
$358$		0			0
$359$	−246.329	+	142.218i	−0.686154	+	0.396151i	−0.802170	−	0.597096i	$-0.796321\pi$
$359$	−246.329	+	142.218i	−0.686154	+	0.396151i	0.116016	+	0.993247i	$0.462988\pi$
$360$		0			0
$361$	−174.931	+	302.990i	−0.484574	+	0.839306i
$362$		0			0
$363$		−	92.5522i		−	0.254965i
$364$		0			0
$365$	−175.426			−0.480618
$366$		0			0
$367$	−127.579	−	73.6575i	−0.347626	−	0.200702i	0.316013	−	0.948755i	$-0.397656\pi$
$367$	−127.579	−	73.6575i	−0.347626	−	0.200702i	−0.663639	+	0.748053i	$0.730989\pi$
$368$		0			0
$369$	0.527684	+	0.913976i	0.00143004	+	0.00247690i
$370$		0			0
$371$	−26.3997	−	538.163i	−0.0711583	−	1.45057i
$372$		0			0
$373$	1.17126	+	2.02868i	0.00314010	+	0.00543881i	0.867591	−	0.497278i	$-0.165667\pi$
$373$	1.17126	+	2.02868i	0.00314010	+	0.00543881i	−0.864451	+	0.502717i	$0.832334\pi$
$374$		0			0
$375$	72.3754	+	41.7860i	0.193001	+	0.111429i
$376$		0			0
$377$	−277.693			−0.736586
$378$		0			0
$379$			440.261i			1.16164i	0.814033	+	0.580819i	$0.197268\pi$
$379$			440.261i			1.16164i	−0.814033	+	0.580819i	$0.802732\pi$
$380$		0			0
$381$	90.1149	−	156.084i	0.236522	−	0.409668i
$382$		0			0
$383$	−38.8014	+	22.4020i	−0.101309	+	0.0584909i	−0.549799	−	0.835297i	$-0.685296\pi$
$383$	−38.8014	+	22.4020i	−0.101309	+	0.0584909i	0.448489	+	0.893788i	$0.351962\pi$
$384$		0			0
$385$	242.737	+	376.532i	0.630485	+	0.978006i
$386$		0			0
$387$	−15.3082	+	8.83818i	−0.0395560	+	0.0228377i
$388$		0			0
$389$	−94.3414	+	163.404i	−0.242523	+	0.420062i	−0.961432	−	0.275042i	$-0.911308\pi$
$389$	−94.3414	+	163.404i	−0.242523	+	0.420062i	0.718909	+	0.695104i	$0.244642\pi$
$390$		0			0
$391$		−	104.993i		−	0.268523i
$392$		0			0
$393$	325.185			0.827442
$394$		0			0
$395$	0.137975	+	0.0796601i	0.000349305	+	0.000201671i
$396$		0			0
$397$	189.387	+	328.029i	0.477046	+	0.826269i	0.999654	−	0.0263048i	$-0.00837405\pi$
$397$	189.387	+	328.029i	0.477046	+	0.826269i	−0.522608	+	0.852573i	$0.675041\pi$
$398$		0			0
$399$	57.5976	−	37.1311i	0.144355	−	0.0930604i
$400$		0			0
$401$	127.223	+	220.356i	0.317264	+	0.549517i	0.979916	−	0.199410i	$-0.0639026\pi$
$401$	127.223	+	220.356i	0.317264	+	0.549517i	−0.662652	+	0.748927i	$0.730569\pi$
$402$		0			0
$403$	311.763	+	179.997i	0.773606	+	0.446642i
$404$		0			0
$405$	523.006			1.29137
$406$		0			0
$407$			470.643i			1.15637i
$408$		0			0
$409$	150.973	−	261.492i	0.369126	−	0.639345i	−0.620303	−	0.784362i	$-0.712990\pi$
$409$	150.973	−	261.492i	0.369126	−	0.639345i	0.989429	+	0.145017i	$0.0463238\pi$
$410$		0			0
$411$	−501.202	+	289.369i	−1.21947	+	0.704061i
$412$		0			0
$413$	61.1566	−	3.00005i	0.148079	−	0.00726405i
$414$		0			0
$415$	632.442	−	365.140i	1.52396	−	0.879856i
$416$		0			0
$417$	−121.500	+	210.444i	−0.291367	+	0.504662i
$418$		0			0
$419$			100.704i			0.240344i	0.992753	+	0.120172i	$0.0383446\pi$
$419$			100.704i			0.240344i	−0.992753	+	0.120172i	$0.961655\pi$
$420$		0			0
$421$	−226.449			−0.537883			−0.268942	−	0.963156i	$-0.586674\pi$
$421$	−226.449			−0.537883			−0.268942	+	0.963156i	$0.586674\pi$
$422$		0			0
$423$	27.4754	+	15.8629i	0.0649537	+	0.0375010i
$424$		0			0
$425$	35.2899	+	61.1240i	0.0830351	+	0.143821i
$426$		0			0
$427$	323.471	+	166.181i	0.757542	+	0.389183i
$428$		0			0
$429$	−331.935	−	574.927i	−0.773740	−	1.34016i
$430$		0			0
$431$	628.951	+	363.125i	1.45928	+	0.842518i	0.998976	−	0.0452414i	$-0.0144057\pi$
$431$	628.951	+	363.125i	1.45928	+	0.842518i	0.460308	+	0.887759i	$0.347739\pi$
$432$		0			0
$433$	−4.54373			−0.0104936			−0.00524680	−	0.999986i	$-0.501670\pi$
$433$	−4.54373			−0.0104936			−0.00524680	+	0.999986i	$0.501670\pi$
$434$		0			0
$435$		−	230.362i		−	0.529567i
$436$		0			0
$437$	−51.6057	+	89.3837i	−0.118091	+	0.204539i
$438$		0			0
$439$	−374.387	+	216.153i	−0.852818	+	0.492375i	−0.861601	−	0.507587i	$-0.830538\pi$
$439$	−374.387	+	216.153i	−0.852818	+	0.492375i	0.00878248	+	0.999961i	$0.497204\pi$
$440$		0			0
$441$	−19.2582	+	1.89399i	−0.0436694	+	0.00429476i
$442$		0			0
$443$	332.942	−	192.224i	0.751561	−	0.433914i	−0.0746967	−	0.997206i	$-0.523799\pi$
$443$	332.942	−	192.224i	0.751561	−	0.433914i	0.826258	+	0.563292i	$0.190466\pi$
$444$		0			0
$445$	−47.9230	+	83.0051i	−0.107692	+	0.186528i
$446$		0			0
$447$		−	575.268i		−	1.28695i
$448$		0			0
$449$	98.6049			0.219610			0.109805	−	0.993953i	$-0.464977\pi$
$449$	98.6049			0.219610			0.109805	+	0.993953i	$0.464977\pi$
$450$		0			0
$451$	21.8884	+	12.6373i	0.0485330	+	0.0280205i
$452$		0			0
$453$	−161.823	−	280.286i	−0.357225	−	0.618732i
$454$		0			0
$455$	−1008.18	−	517.946i	−2.21577	−	1.13834i
$456$		0			0
$457$	−129.739	−	224.714i	−0.283893	−	0.491717i	0.688447	−	0.725286i	$-0.258293\pi$
$457$	−129.739	−	224.714i	−0.283893	−	0.491717i	−0.972340	+	0.233570i	$0.924959\pi$
$458$		0			0
$459$	−81.0272	−	46.7811i	−0.176530	−	0.101920i
$460$		0			0
$461$	444.260			0.963688			0.481844	−	0.876257i	$-0.339967\pi$
$461$	444.260			0.963688			0.481844	+	0.876257i	$0.339967\pi$
$462$		0			0
$463$		−	270.748i		−	0.584769i	−0.956301	−	0.292385i	$-0.905551\pi$
$463$		−	270.748i		−	0.584769i	0.956301	−	0.292385i	$-0.0944487\pi$
$464$		0			0
$465$	−149.317	+	258.625i	−0.321112	+	0.556183i
$466$		0			0
$467$	507.985	−	293.285i	1.08776	−	0.628020i	0.154783	−	0.987948i	$-0.450532\pi$
$467$	507.985	−	293.285i	1.08776	−	0.628020i	0.932980	+	0.359928i	$0.117199\pi$
$468$		0			0
$469$	−808.647	+	39.6684i	−1.72419	+	0.0845808i
$470$		0			0
$471$	−190.485	+	109.976i	−0.404426	+	0.233496i
$472$		0			0
$473$	−211.661	+	366.608i	−0.447487	+	0.775070i
$474$		0			0
$475$		−	69.3824i		−	0.146068i
$476$		0			0
$477$	30.3981			0.0637278
$478$		0			0
$479$	62.3189	+	35.9798i	0.130102	+	0.0751145i	0.563638	−	0.826022i	$-0.309401\pi$
$479$	62.3189	+	35.9798i	0.130102	+	0.0751145i	−0.433536	+	0.901136i	$0.642734\pi$
$480$		0			0
$481$	−595.374	−	1031.22i	−1.23778	−	2.14391i
$482$		0			0
$483$	−533.747	+	344.088i	−1.10507	+	0.712397i
$484$		0			0
$485$	−194.091	−	336.175i	−0.400187	−	0.693144i
$486$		0			0
$487$	−653.899	−	377.529i	−1.34271	−	0.775214i	−0.355505	−	0.934674i	$-0.615691\pi$
$487$	−653.899	−	377.529i	−1.34271	−	0.775214i	−0.987204	+	0.159461i	$0.949024\pi$
$488$		0			0
$489$	−102.214			−0.209027
$490$		0			0
$491$			259.760i			0.529042i	0.964380	+	0.264521i	$0.0852139\pi$
$491$			259.760i			0.529042i	−0.964380	+	0.264521i	$0.914786\pi$
$492$		0			0
$493$	−19.6992	+	34.1199i	−0.0399577	+	0.0692088i
$494$		0			0
$495$	−21.8884	+	12.6373i	−0.0442189	+	0.0255298i
$496$		0			0
$497$	−464.004	−	719.762i	−0.933610	−	1.44821i
$498$		0			0
$499$	288.135	−	166.355i	0.577426	−	0.333377i	−0.182684	−	0.983172i	$-0.558479\pi$
$499$	288.135	−	166.355i	0.577426	−	0.333377i	0.760110	+	0.649795i	$0.225145\pi$
$500$		0			0
$501$	−151.462	+	262.340i	−0.302319	+	0.523632i
$502$		0			0
$503$		−	705.652i		−	1.40289i	−0.712725	−	0.701443i	$-0.752539\pi$
$503$		−	705.652i		−	1.40289i	0.712725	−	0.701443i	$-0.247461\pi$
$504$		0			0
$505$	−751.416			−1.48795
$506$		0			0
$507$	1025.26	+	591.933i	2.02221	+	1.16752i
$508$		0			0
$509$	318.419	+	551.517i	0.625577	+	1.08353i	0.988429	+	0.151684i	$0.0484698\pi$
$509$	318.419	+	551.517i	0.625577	+	1.08353i	−0.362852	+	0.931847i	$0.618197\pi$
$510$		0			0
$511$	−8.89141	−	181.253i	−0.0174000	−	0.354702i
$512$		0			0
$513$	45.9874	+	79.6525i	0.0896440	+	0.155268i
$514$		0			0
$515$	385.451	+	222.540i	0.748448	+	0.432116i
$516$		0			0
$517$	759.788			1.46961
$518$		0			0
$519$			103.588i			0.199592i
$520$		0			0
$521$	89.8671	−	155.654i	0.172490	−	0.298761i	−0.766800	−	0.641886i	$-0.778152\pi$
$521$	89.8671	−	155.654i	0.172490	−	0.298761i	0.939290	+	0.343125i	$0.111486\pi$
$522$		0			0
$523$	160.112	−	92.4406i	0.306141	−	0.176751i	−0.339057	−	0.940766i	$-0.610108\pi$
$523$	160.112	−	92.4406i	0.306141	−	0.176751i	0.645198	+	0.764015i	$0.276775\pi$
$524$		0			0
$525$	195.080	−	379.721i	0.371580	−	0.723278i
$526$		0			0
$527$	44.2322	−	25.5375i	0.0839320	−	0.0484582i
$528$		0			0
$529$	213.721	−	370.176i	0.404009	−	0.699765i
$530$		0			0
$531$			3.45443i			0.00650552i
$532$		0			0
$533$	−63.9456			−0.119973
$534$		0			0
$535$	−185.245	−	106.951i	−0.346251	−	0.199908i
$536$		0			0
$537$	179.063	+	310.146i	0.333451	+	0.577554i
$538$		0			0
$539$	−376.736	+	269.884i	−0.698954	+	0.500713i
$540$		0			0
$541$	186.923	+	323.760i	0.345514	+	0.598447i	0.985447	−	0.169983i	$-0.0543714\pi$
$541$	186.923	+	323.760i	0.345514	+	0.598447i	−0.639933	+	0.768430i	$0.721038\pi$
$542$		0			0
$543$	57.6713	+	33.2965i	0.106209	+	0.0613195i
$544$		0			0
$545$	323.373			0.593345
$546$		0			0
$547$			686.108i			1.25431i	0.778895	+	0.627155i	$0.215781\pi$
$547$			686.108i			1.25431i	−0.778895	+	0.627155i	$0.784219\pi$
$548$		0			0
$549$	−10.2584	+	17.7680i	−0.0186856	+	0.0323643i
$550$		0			0
$551$	33.5411	−	19.3649i	0.0608731	−	0.0351451i
$552$		0			0
$553$	−0.0753130	+	0.146596i	−0.000136190	+	0.000265092i
$554$		0			0
$555$	855.453	−	493.896i	1.54136	−	0.889903i
$556$		0			0
$557$	−194.523	+	336.923i	−0.349233	+	0.604889i	−0.986113	−	0.166073i	$-0.946891\pi$
$557$	−194.523	+	336.923i	−0.349233	+	0.604889i	0.636881	+	0.770963i	$0.280224\pi$
$558$		0			0
$559$		−	1071.02i		−	1.91597i
$560$		0			0
$561$	−94.1880			−0.167893
$562$		0			0
$563$	−767.717	−	443.242i	−1.36362	−	0.787286i	−0.373515	−	0.927624i	$-0.621848\pi$
$563$	−767.717	−	443.242i	−1.36362	−	0.787286i	−0.990104	+	0.140338i	$0.955181\pi$
$564$		0			0
$565$	−252.947	−	438.116i	−0.447693	−	0.775427i
$566$		0			0
$567$	26.5084	+	540.378i	0.0467521	+	0.953048i
$568$		0			0
$569$	74.8405	+	129.628i	0.131530	+	0.227817i	0.924267	−	0.381748i	$-0.124678\pi$
$569$	74.8405	+	129.628i	0.131530	+	0.227817i	−0.792737	+	0.609564i	$0.791344\pi$
$570$		0			0
$571$	376.443	+	217.340i	0.659270	+	0.380630i	0.791999	−	0.610523i	$-0.209041\pi$
$571$	376.443	+	217.340i	0.659270	+	0.380630i	−0.132729	+	0.991152i	$0.542374\pi$
$572$		0			0
$573$	−593.454			−1.03570
$574$		0			0
$575$			642.955i			1.11818i
$576$		0			0
$577$	−269.546	+	466.867i	−0.467151	+	0.809129i	−0.999296	−	0.0375243i	$-0.988053\pi$
$577$	−269.546	+	466.867i	−0.467151	+	0.809129i	0.532145	+	0.846653i	$0.321386\pi$
$578$		0			0
$579$	−700.018	+	404.156i	−1.20901	+	0.698024i
$580$		0			0
$581$	409.324	+	634.943i	0.704517	+	1.09284i
$582$		0			0
$583$	630.458	−	363.995i	1.08140	−	0.624349i
$584$		0			0
$585$	31.9728	−	55.3785i	0.0546544	−	0.0946642i
$586$		0			0
$587$		−	467.257i		−	0.796008i	−0.917384	−	0.398004i	$-0.869703\pi$
$587$		−	467.257i		−	0.796008i	0.917384	−	0.398004i	$-0.130297\pi$
$588$		0			0
$589$	−50.2084			−0.0852434
$590$		0			0
$591$	494.381	+	285.431i	0.836516	+	0.482963i
$592$		0			0
$593$	514.015	+	890.300i	0.866805	+	1.50135i	0.865244	+	0.501351i	$0.167163\pi$
$593$	514.015	+	890.300i	0.866805	+	1.50135i	0.00156081	+	0.999999i	$0.499503\pi$
$594$		0			0
$595$	−135.158	+	87.1318i	−0.227157	+	0.146440i
$596$		0			0
$597$	246.827	+	427.517i	0.413445	+	0.716109i
$598$		0			0
$599$	125.950	+	72.7170i	0.210266	+	0.121397i	0.601435	−	0.798922i	$-0.294596\pi$
$599$	125.950	+	72.7170i	0.210266	+	0.121397i	−0.391169	+	0.920319i	$0.627929\pi$
$600$		0			0
$601$	888.535			1.47843			0.739214	−	0.673471i	$-0.235197\pi$
$601$	888.535			1.47843			0.739214	+	0.673471i	$0.235197\pi$
$602$		0			0
$603$		−	45.6765i		−	0.0757487i
$604$		0			0
$605$	106.749	−	184.895i	0.176445	−	0.305611i
$606$		0			0
$607$	−992.716	+	573.145i	−1.63545	+	0.944226i	−0.653074	+	0.757294i	$0.726521\pi$
$607$	−992.716	+	573.145i	−1.63545	+	0.944226i	−0.982373	+	0.186931i	$0.940146\pi$
$608$		0			0
$609$	238.014	−	11.6758i	0.390827	−	0.0191721i
$610$		0			0
$611$	−1664.76	+	961.148i	−2.72464	+	1.57307i
$612$		0			0
$613$	287.236	−	497.508i	0.468575	−	0.811595i	−0.530780	−	0.847509i	$-0.678101\pi$
$613$	287.236	−	497.508i	0.468575	−	0.811595i	0.999355	+	0.0359145i	$0.0114344\pi$
$614$		0			0
$615$		−	53.0464i		−	0.0862544i
$616$		0			0
$617$	−282.236			−0.457432			−0.228716	−	0.973493i	$-0.573453\pi$
$617$	−282.236			−0.457432			−0.228716	+	0.973493i	$0.573453\pi$
$618$		0			0
$619$	350.617	+	202.429i	0.566424	+	0.327025i	0.755720	−	0.654895i	$-0.227287\pi$
$619$	350.617	+	202.429i	0.566424	+	0.327025i	−0.189296	+	0.981920i	$0.560620\pi$
$620$		0			0
$621$	−426.157	−	738.126i	−0.686244	−	1.18861i
$622$		0			0
$623$	−88.1912	−	45.3078i	−0.141559	−	0.0727252i
$624$		0			0
$625$	356.264	+	617.068i	0.570023	+	0.987308i
$626$		0			0
$627$	80.1853	+	46.2950i	0.127887	+	0.0738357i
$628$		0			0
$629$	−168.940			−0.268585
$630$		0			0
$631$		−	112.125i		−	0.177694i	−0.996045	−	0.0888472i	$-0.971682\pi$
$631$		−	112.125i		−	0.177694i	0.996045	−	0.0888472i	$-0.0283183\pi$
$632$		0			0
$633$	326.378	−	565.304i	0.515605	−	0.893055i
$634$		0			0
$635$	360.051	−	207.876i	0.567010	−	0.327363i
$636$		0			0
$637$	484.051	−	1067.92i	0.759892	−	1.67648i
$638$		0			0
$639$	41.8408	−	24.1568i	0.0654786	−	0.0378041i
$640$		0			0
$641$	−65.1233	+	112.797i	−0.101596	+	0.175970i	−0.912343	−	0.409428i	$-0.865728\pi$
$641$	−65.1233	+	112.797i	−0.101596	+	0.175970i	0.810746	+	0.585398i	$0.199062\pi$
$642$		0			0
$643$			376.192i			0.585058i	0.956257	+	0.292529i	$0.0944968\pi$
$643$			376.192i			0.585058i	−0.956257	+	0.292529i	$0.905503\pi$
$644$		0			0
$645$	888.474			1.37748
$646$		0			0
$647$	−1105.04	−	637.994i	−1.70794	−	0.986080i	−0.937105	−	0.349047i	$-0.886506\pi$
$647$	−1105.04	−	637.994i	−1.70794	−	0.986080i	−0.770836	−	0.637034i	$-0.780161\pi$
$648$		0			0
$649$	41.3643	+	71.6450i	0.0637354	+	0.110393i
$650$		0			0
$651$	−274.784	−	141.169i	−0.422095	−	0.216849i
$652$		0			0
$653$	447.669	+	775.386i	0.685558	+	1.18742i	0.973261	+	0.229701i	$0.0737749\pi$
$653$	447.669	+	775.386i	0.685558	+	1.18742i	−0.287703	+	0.957720i	$0.592892\pi$
$654$		0			0
$655$	649.632	+	375.065i	0.991805	+	0.572619i
$656$		0			0
$657$	10.2381			0.0155831
$658$		0			0
$659$		−	587.884i		−	0.892086i	−0.895012	−	0.446043i	$-0.852833\pi$
$659$		−	587.884i		−	0.892086i	0.895012	−	0.446043i	$-0.147167\pi$
$660$		0			0
$661$	−50.5886	+	87.6220i	−0.0765335	+	0.132560i	−0.901752	−	0.432254i	$-0.857719\pi$
$661$	−50.5886	+	87.6220i	−0.0765335	+	0.132560i	0.825219	+	0.564813i	$0.191052\pi$
$662$		0			0
$663$	206.374	−	119.150i	0.311272	−	0.179713i
$664$		0			0
$665$	157.892	−	7.74542i	0.237431	−	0.0116472i
$666$		0			0
$667$	−310.819	+	179.452i	−0.465996	+	0.269043i
$668$		0			0
$669$	−389.052	+	673.859i	−0.581543	+	1.00726i
$670$		0			0
$671$			491.346i			0.732259i
$672$		0			0
$673$	1227.95			1.82460			0.912298	−	0.409528i	$-0.134306\pi$
$673$	1227.95			1.82460			0.912298	+	0.409528i	$0.134306\pi$
$674$		0			0
$675$	496.195	+	286.478i	0.735104	+	0.424412i
$676$		0			0
$677$	−166.350	−	288.127i	−0.245717	−	0.425594i	0.716616	−	0.697468i	$-0.245690\pi$
$677$	−166.350	−	288.127i	−0.245717	−	0.425594i	−0.962333	+	0.271874i	$0.912357\pi$
$678$		0			0
$679$	337.504	−	217.577i	0.497060	−	0.320437i
$680$		0			0
$681$	−336.549	−	582.920i	−0.494198	−	0.855976i
$682$		0			0
$683$	1020.33	+	589.087i	1.49389	+	0.862499i	0.999975	−	0.00700950i	$-0.00223121\pi$
$683$	1020.33	+	589.087i	1.49389	+	0.862499i	0.493917	+	0.869509i	$0.335565\pi$
$684$		0			0
$685$	−1335.02			−1.94894
$686$		0			0
$687$		−	106.496i		−	0.155016i
$688$		0			0
$689$	−920.924	+	1595.09i	−1.33661	+	2.31508i
$690$		0			0
$691$	−158.888	+	91.7338i	−0.229939	+	0.132755i	−0.610544	−	0.791983i	$-0.709049\pi$
$691$	−158.888	+	91.7338i	−0.229939	+	0.132755i	0.380605	+	0.924738i	$0.375716\pi$
$692$		0			0
$693$	−14.1664	−	21.9749i	−0.0204422	−	0.0317098i
$694$		0			0
$695$	−485.449	+	280.274i	−0.698488	+	0.403272i
$696$		0			0
$697$	−4.53622	+	7.85696i	−0.00650820	+	0.0112725i
$698$		0			0
$699$		−	332.318i		−	0.475420i
$700$		0			0
$701$	−1021.59			−1.45733			−0.728664	−	0.684872i	$-0.759858\pi$
$701$	−1021.59			−1.45733			−0.728664	+	0.684872i	$0.759858\pi$
$702$		0			0
$703$	143.824	+	83.0370i	0.204587	+	0.118118i
$704$		0			0
$705$	−797.326	−	1381.01i	−1.13096	−	1.95888i
$706$		0			0
$707$	−38.0854	−	776.376i	−0.0538690	−	1.09813i
$708$		0			0
$709$	235.749	+	408.329i	0.332509	+	0.575923i	0.983003	−	0.183589i	$-0.0587714\pi$
$709$	235.749	+	408.329i	0.332509	+	0.575923i	−0.650494	+	0.759511i	$0.725438\pi$
$710$		0			0
$711$	−0.00805243	−	0.00464907i	−1.13255e−5	−	6.53878e-6i
$712$		0			0
$713$	465.272			0.652556
$714$		0			0
$715$		−	1531.40i		−	2.14182i
$716$		0			0
$717$	−183.642	+	318.077i	−0.256125	+	0.443622i
$718$		0			0
$719$	491.275	−	283.638i	0.683275	−	0.394489i	−0.117813	−	0.993036i	$-0.537588\pi$
$719$	491.275	−	283.638i	0.683275	−	0.394489i	0.801088	+	0.598547i	$0.204255\pi$
$720$		0			0
$721$	−210.396	+	409.533i	−0.291811	+	0.568008i
$722$		0			0
$723$	711.684	−	410.891i	0.984349	−	0.568314i
$724$		0			0
$725$	120.634	−	208.944i	0.166392	−	0.288199i
$726$		0			0
$727$			514.680i			0.707951i	0.935255	+	0.353976i	$0.115170\pi$
$727$			514.680i			0.707951i	−0.935255	+	0.353976i	$0.884830\pi$
$728$		0			0
$729$	−758.120			−1.03994
$730$		0			0
$731$	−131.596	−	75.9771i	−0.180022	−	0.103936i
$732$		0			0
$733$	269.215	+	466.294i	0.367278	+	0.636144i	0.989139	−	0.146984i	$-0.0469564\pi$
$733$	269.215	+	466.294i	0.367278	+	0.636144i	−0.621861	+	0.783128i	$0.713623\pi$
$734$		0			0
$735$	885.897	+	401.547i	1.20530	+	0.546323i
$736$		0			0
$737$	−546.942	−	947.331i	−0.742119	−	1.28539i
$738$		0			0
$739$	−504.372	−	291.199i	−0.682506	−	0.394045i	0.118292	−	0.992979i	$-0.462258\pi$
$739$	−504.372	−	291.199i	−0.682506	−	0.394045i	−0.800799	+	0.598934i	$0.795591\pi$
$740$		0			0
$741$	−234.257			−0.316136
$742$		0			0
$743$			734.391i			0.988413i	0.869344	+	0.494207i	$0.164541\pi$
$743$			734.391i			0.988413i	−0.869344	+	0.494207i	$0.835459\pi$
$744$		0			0
$745$	663.510	−	1149.23i	0.890617	−	1.54259i
$746$		0			0
$747$	−36.9101	+	21.3101i	−0.0494112	+	0.0285276i
$748$		0			0
$749$	101.115	−	196.819i	0.134999	−	0.262775i
$750$		0			0
$751$	190.323	−	109.883i	0.253426	−	0.146316i	−0.367906	−	0.929863i	$-0.619925\pi$
$751$	190.323	−	109.883i	0.253426	−	0.146316i	0.621332	+	0.783547i	$0.286592\pi$
$752$		0			0
$753$	188.953	−	327.276i	0.250934	−	0.434630i
$754$		0			0
$755$		−	746.582i		−	0.988850i
$756$		0			0
$757$	−38.5398			−0.0509112			−0.0254556	−	0.999676i	$-0.508104\pi$
$757$	−38.5398			−0.0509112			−0.0254556	+	0.999676i	$0.508104\pi$
$758$		0			0
$759$	−743.063	−	429.008i	−0.979003	−	0.565228i
$760$		0			0
$761$	386.969	+	670.250i	0.508501	+	0.880749i	0.999952	+	0.00984360i	$0.00313336\pi$
$761$	386.969	+	670.250i	0.508501	+	0.880749i	−0.491451	+	0.870905i	$0.663533\pi$
$762$		0			0
$763$	16.3901	+	334.115i	0.0214811	+	0.437896i
$764$		0			0
$765$	−4.53622	−	7.85696i	−0.00592970	−	0.0102705i
$766$		0			0
$767$	−181.265	−	104.653i	−0.236330	−	0.136445i
$768$		0			0
$769$	−1159.88			−1.50830			−0.754150	−	0.656702i	$-0.771951\pi$
$769$	−1159.88			−1.50830			−0.754150	+	0.656702i	$0.771951\pi$
$770$		0			0
$771$			137.403i			0.178213i
$772$		0			0
$773$	654.351	−	1133.37i	0.846509	−	1.46620i	−0.0377957	−	0.999285i	$-0.512034\pi$
$773$	654.351	−	1133.37i	0.846509	−	1.46620i	0.884304	−	0.466911i	$-0.154633\pi$
$774$		0			0
$775$	−270.869	+	156.386i	−0.349509	+	0.201789i
$776$		0			0
$777$	553.660	+	858.836i	0.712561	+	1.10532i
$778$		0			0
$779$	7.72366	−	4.45926i	0.00991484	−	0.00572434i
$780$		0			0
$781$	578.520	−	1002.03i	0.740742	−	1.28300i
$782$		0			0
$783$			319.830i			0.408467i
$784$		0			0
$785$	−507.384			−0.646349
$786$		0			0
$787$	387.858	+	223.930i	0.492831	+	0.284536i	0.725748	−	0.687961i	$-0.241494\pi$
$787$	387.858	+	223.930i	0.492831	+	0.284536i	−0.232917	+	0.972497i	$0.574827\pi$
$788$		0			0
$789$	−314.046	−	543.944i	−0.398031	−	0.689410i
$790$		0			0
$791$	439.849	−	283.555i	0.556067	−	0.358476i
$792$		0			0
$793$	−621.563	−	1076.58i	−0.783812	−	1.35760i
$794$		0			0
$795$	−1323.21	−	763.958i	−1.66442	−	0.960953i
$796$		0			0
$797$	−761.194			−0.955074			−0.477537	−	0.878612i	$-0.658470\pi$
$797$	−761.194			−0.955074			−0.477537	+	0.878612i	$0.658470\pi$
$798$		0			0
$799$			272.730i			0.341340i
$800$		0			0
$801$	2.79685	−	4.84429i	0.00349170	−	0.00604780i
$802$		0			0
$803$	212.338	−	122.593i	0.264431	−	0.152669i
$804$		0			0
$805$	−1463.15	+	71.7754i	−1.81758	+	0.0891620i
$806$		0			0
$807$	164.474	−	94.9593i	0.203810	−	0.117670i
$808$		0			0
$809$	−492.156	+	852.439i	−0.608351	+	1.05369i	0.383162	+	0.923681i	$0.374835\pi$
$809$	−492.156	+	852.439i	−0.608351	+	1.05369i	−0.991512	+	0.130013i	$0.958498\pi$
$810$		0			0
$811$			124.916i			0.154027i	0.997030	+	0.0770136i	$0.0245385\pi$
$811$			124.916i			0.154027i	−0.997030	+	0.0770136i	$0.975462\pi$
$812$		0			0
$813$	782.360			0.962313
$814$		0			0
$815$	−204.197	−	117.893i	−0.250548	−	0.144654i
$816$		0			0
$817$	74.6880	+	129.363i	0.0914174	+	0.158340i
$818$		0			0
$819$	58.8386	+	30.2280i	0.0718420	+	0.0369084i
$820$		0			0
$821$	434.046	+	751.790i	0.528680	+	0.915700i	0.999441	+	0.0334394i	$0.0106461\pi$
$821$	434.046	+	751.790i	0.528680	+	0.915700i	−0.470761	+	0.882261i	$0.656021\pi$
$822$		0			0
$823$	−171.529	−	99.0320i	−0.208419	−	0.120331i	0.392158	−	0.919898i	$-0.371729\pi$
$823$	−171.529	−	99.0320i	−0.208419	−	0.120331i	−0.600576	+	0.799567i	$0.705062\pi$
$824$		0			0
$825$	576.789			0.699138
$826$		0			0
$827$			494.720i			0.598211i	0.954220	+	0.299105i	$0.0966882\pi$
$827$			494.720i			0.598211i	−0.954220	+	0.299105i	$0.903312\pi$
$828$		0			0
$829$	−174.683	+	302.560i	−0.210715	+	0.364970i	−0.951939	−	0.306289i	$-0.900913\pi$
$829$	−174.683	+	302.560i	−0.210715	+	0.364970i	0.741223	+	0.671259i	$0.234246\pi$
$830$		0			0
$831$	824.366	−	475.948i	0.992017	−	0.572741i
$832$		0			0
$833$	−96.8765	−	135.232i	−0.116298	−	0.162343i
$834$		0			0
$835$	−605.161	+	349.390i	−0.724744	+	0.418431i
$836$		0			0
$837$	207.309	−	359.070i	0.247681	−	0.428996i
$838$		0			0
$839$			1216.12i			1.44949i	0.689016	+	0.724746i	$0.258043\pi$
$839$			1216.12i			1.44949i	−0.689016	+	0.724746i	$0.741957\pi$
$840$		0			0
$841$	−706.322			−0.839860
$842$		0			0
$843$	−758.724	−	438.050i	−0.900029	−	0.519632i
$844$		0			0
$845$	1365.46	+	2365.05i	1.61593	+	2.79888i
$846$		0			0
$847$	196.447	+	100.924i	0.231932	+	0.119154i
$848$		0			0
$849$	−389.052	−	673.858i	−0.458248	−	0.793708i
$850$		0			0
$851$	−1332.80	−	769.490i	−1.56615	−	0.904218i
$852$		0			0
$853$	849.999			0.996482			0.498241	−	0.867039i	$-0.333980\pi$
$853$	849.999			0.996482			0.498241	+	0.867039i	$0.333980\pi$
$854$		0			0
$855$			8.91851i			0.0104310i
$856$		0			0
$857$	−279.499	+	484.107i	−0.326137	+	0.564886i	−0.981742	−	0.190219i	$-0.939080\pi$
$857$	−279.499	+	484.107i	−0.326137	+	0.564886i	0.655605	+	0.755104i	$0.272414\pi$
$858$		0			0
$859$	1021.83	−	589.951i	1.18955	−	0.686788i	0.231347	−	0.972871i	$-0.425687\pi$
$859$	1021.83	−	589.951i	1.18955	−	0.686788i	0.958205	+	0.286083i	$0.0923534\pi$
$860$		0			0
$861$	54.8085	−	2.68865i	0.0636568	−	0.00312270i
$862$		0			0
$863$	711.505	−	410.788i	0.824456	−	0.476000i	−0.0274949	−	0.999622i	$-0.508753\pi$
$863$	711.505	−	410.788i	0.824456	−	0.476000i	0.851951	+	0.523622i	$0.175420\pi$
$864$		0			0
$865$	−119.478	+	206.942i	−0.138125	+	0.239240i
$866$		0			0
$867$			813.955i			0.938818i
$868$		0			0
$869$	−0.222677			−0.000256245
$870$		0			0
$871$	2396.79	+	1383.79i	2.75177	+	1.58873i
$872$		0			0
$873$	11.3274	+	19.6196i	0.0129752	+	0.0224738i
$874$		0			0
$875$	−167.615	+	108.055i	−0.191560	+	0.123492i
$876$		0			0
$877$	−325.399	−	563.608i	−0.371037	−	0.642654i	0.618689	−	0.785636i	$-0.287664\pi$
$877$	−325.399	−	563.608i	−0.371037	−	0.642654i	−0.989725	+	0.142982i	$0.954331\pi$
$878$		0			0
$879$	−1111.45	−	641.696i	−1.26445	−	0.730030i
$880$		0			0
$881$	1592.49			1.80760			0.903799	−	0.427958i	$-0.140767\pi$
$881$	1592.49			1.80760			0.903799	+	0.427958i	$0.140767\pi$
$882$		0			0
$883$		−	1548.91i		−	1.75414i	−0.480363	−	0.877070i	$-0.659495\pi$
$883$		−	1548.91i		−	1.75414i	0.480363	−	0.877070i	$-0.340505\pi$
$884$		0			0
$885$	86.8158	−	150.369i	0.0980970	−	0.169909i
$886$		0			0
$887$	159.831	−	92.2784i	0.180193	−	0.104034i	−0.407191	−	0.913343i	$-0.633492\pi$
$887$	159.831	−	92.2784i	0.180193	−	0.104034i	0.587383	+	0.809309i	$0.300158\pi$
$888$		0			0
$889$	233.030	+	361.475i	0.262126	+	0.406609i
$890$		0			0
$891$	−633.054	+	365.494i	−0.710499	+	0.410207i
$892$		0			0
$893$	134.052	−	232.184i	0.150114	−	0.260005i
$894$		0			0
$895$			826.120i			0.923039i
$896$		0			0
$897$	2170.82			2.42009
$898$		0			0
$899$	−151.202	−	87.2963i	−0.168189	−	0.0971038i
$900$		0			0
$901$	130.658	+	226.307i	0.145015	+	0.251173i
$902$		0			0
$903$	45.0321	+	917.987i	0.0498695	+	1.01660i
$904$		0			0
$905$	76.8079	+	133.035i	0.0848706	+	0.147000i
$906$		0			0
$907$	7.24397	+	4.18231i	0.00798673	+	0.00461114i	0.503988	−	0.863711i	$-0.331866\pi$
$907$	7.24397	+	4.18231i	0.00798673	+	0.00461114i	−0.496001	+	0.868322i	$0.665199\pi$
$908$		0			0
$909$	43.8537			0.0482438
$910$		0			0
$911$			1048.88i			1.15135i	0.817679	+	0.575674i	$0.195260\pi$
$911$			1048.88i			1.15135i	−0.817679	+	0.575674i	$0.804740\pi$
$912$		0			0
$913$	−510.345	+	883.943i	−0.558976	+	0.968175i
$914$		0			0
$915$	893.082	−	515.621i	0.976046	−	0.563520i
$916$		0			0
$917$	−354.598	+	690.221i	−0.386693	+	0.752695i
$918$		0			0
$919$	−837.967	+	483.800i	−0.911824	+	0.526442i	−0.881018	−	0.473083i	$-0.843141\pi$
$919$	−837.967	+	483.800i	−0.911824	+	0.526442i	−0.0308066	+	0.999525i	$0.509808\pi$
$920$		0			0
$921$	496.335	−	859.678i	0.538909	−	0.933418i
$922$		0			0
$923$			2927.36i			3.17157i
$924$		0			0
$925$	1034.56			1.11844
$926$		0			0
$927$	−22.4954	−	12.9877i	−0.0242669	−	0.0140105i
$928$		0			0
$929$	−61.8348	−	107.101i	−0.0665606	−	0.115286i	0.830825	−	0.556534i	$-0.187869\pi$
$929$	−61.8348	−	107.101i	−0.0665606	−	0.115286i	−0.897385	+	0.441248i	$0.854536\pi$
$930$		0			0
$931$	16.0054	+	162.744i	0.0171916	+	0.174805i
$932$		0			0
$933$	542.673	+	939.938i	0.581643	+	1.00744i
$934$		0			0
$935$	−188.163	−	108.636i	−0.201243	−	0.116188i
$936$		0			0
$937$	49.6952			0.0530365			0.0265183	−	0.999648i	$-0.491558\pi$
$937$	49.6952			0.0530365			0.0265183	+	0.999648i	$0.491558\pi$
$938$		0			0
$939$			135.998i			0.144833i
$940$		0			0
$941$	852.751	−	1477.01i	0.906217	−	1.56961i	0.0869428	−	0.996213i	$-0.472290\pi$
$941$	852.751	−	1477.01i	0.906217	−	1.56961i	0.819275	−	0.573401i	$-0.194376\pi$
$942$		0			0
$943$	−71.5738	+	41.3232i	−0.0759001	+	0.0438210i
$944$		0			0
$945$	−596.538	+	1161.16i	−0.631257	+	1.22874i
$946$		0			0
$947$	501.920	−	289.783i	0.530010	−	0.306002i	−0.211010	−	0.977484i	$-0.567675\pi$
$947$	501.920	−	289.783i	0.530010	−	0.306002i	0.741021	+	0.671482i	$0.234342\pi$
$948$		0			0
$949$	−310.167	+	537.224i	−0.326835	+	0.566095i
$950$		0			0
$951$		−	1206.80i		−	1.26898i
$952$		0			0
$953$	−696.869			−0.731237			−0.365619	−	0.930765i	$-0.619143\pi$
$953$	−696.869			−0.731237			−0.365619	+	0.930765i	$0.619143\pi$
$954$		0			0
$955$	−1185.56	−	684.485i	−1.24143	−	0.716739i
$956$		0			0
$957$	160.984	+	278.833i	0.168218	+	0.291362i
$958$		0			0
$959$	−67.6654	−	1379.37i	−0.0705583	−	1.43834i
$960$		0			0
$961$	−367.331	−	636.237i	−0.382239	−	0.662057i
$962$		0			0
$963$	10.8111	+	6.24180i	0.0112265	+	0.00648162i
$964$		0			0
$965$	−1864.60			−1.93223
$966$		0			0
$967$		−	811.681i		−	0.839380i	−0.907667	−	0.419690i	$-0.862139\pi$
$967$		−	811.681i		−	0.839380i	0.907667	−	0.419690i	$-0.137861\pi$
$968$		0			0
$969$	−16.6179	+	28.7830i	−0.0171495	+	0.0297038i
$970$		0			0
$971$	−413.161	+	238.539i	−0.425500	+	0.245663i	−0.697428	−	0.716655i	$-0.745672\pi$
$971$	−413.161	+	238.539i	−0.425500	+	0.245663i	0.271927	+	0.962318i	$0.412339\pi$
$972$		0			0
$973$	−314.189	−	487.369i	−0.322907	−	0.500893i
$974$		0			0
$975$	−1263.79	+	729.651i	−1.29620	+	0.748360i
$976$		0			0
$977$	809.641	−	1402.34i	0.828701	−	1.43535i	−0.0703565	−	0.997522i	$-0.522414\pi$
$977$	809.641	−	1402.34i	0.828701	−	1.43535i	0.899058	−	0.437830i	$-0.144253\pi$
$978$		0			0
$979$		−	133.961i		−	0.136834i
$980$		0			0
$981$	−18.8725			−0.0192380
$982$		0			0
$983$	−1088.06	−	628.189i	−1.10687	−	0.639053i	−0.168855	−	0.985641i	$-0.554007\pi$
$983$	−1088.06	−	628.189i	−1.10687	−	0.639053i	−0.938018	+	0.346588i	$0.887340\pi$
$984$		0			0
$985$	658.428	+	1140.43i	0.668455	+	1.15780i
$986$		0			0
$987$	1386.47	−	893.807i	1.40473	−	0.905579i
$988$		0			0
$989$	−692.121	−	1198.79i	−0.699819	−	1.21212i
$990$		0			0
$991$	−1002.15	−	578.591i	−1.01125	−	0.583846i	−0.0996932	−	0.995018i	$-0.531786\pi$
$991$	−1002.15	−	578.591i	−1.01125	−	0.583846i	−0.911558	+	0.411172i	$0.865119\pi$
$992$		0			0
$993$	−581.693			−0.585794
$994$		0			0
$995$			1138.75i			1.14448i
$996$		0			0
$997$	123.032	−	213.098i	0.123403	−	0.213740i	−0.797705	−	0.603048i	$-0.793953\pi$
$997$	123.032	−	213.098i	0.123403	−	0.213740i	0.921107	+	0.389309i	$0.127286\pi$
$998$		0			0
$999$	−1187.69	+	685.716i	−1.18888	+	0.686402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.r.b.95.3	yes	6
3.2	odd	2		1008.3.cd.j.991.1		6
4.3	odd	2		112.3.r.c.95.1	yes	6
7.2	even	3		112.3.r.c.79.1	yes	6
7.3	odd	6		784.3.d.k.687.5		6
7.4	even	3		784.3.d.l.687.2		6
7.5	odd	6		784.3.r.p.79.3		6
7.6	odd	2		784.3.r.q.655.1		6
8.3	odd	2		448.3.r.d.319.3		6
8.5	even	2		448.3.r.e.319.1		6
12.11	even	2		1008.3.cd.k.991.1		6
21.2	odd	6		1008.3.cd.k.415.1		6
28.3	even	6		784.3.d.k.687.2		6
28.11	odd	6		784.3.d.l.687.5		6
28.19	even	6		784.3.r.q.79.1		6
28.23	odd	6	inner	112.3.r.b.79.3	✓	6
28.27	even	2		784.3.r.p.655.3		6
56.37	even	6		448.3.r.d.191.3		6
56.51	odd	6		448.3.r.e.191.1		6
84.23	even	6		1008.3.cd.j.415.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.r.b.79.3	✓	6	28.23	odd	6	inner
112.3.r.b.95.3	yes	6	1.1	even	1	trivial
112.3.r.c.79.1	yes	6	7.2	even	3
112.3.r.c.95.1	yes	6	4.3	odd	2
448.3.r.d.191.3		6	56.37	even	6
448.3.r.d.319.3		6	8.3	odd	2
448.3.r.e.191.1		6	56.51	odd	6
448.3.r.e.319.1		6	8.5	even	2
784.3.d.k.687.2		6	28.3	even	6
784.3.d.k.687.5		6	7.3	odd	6
784.3.d.l.687.2		6	7.4	even	3
784.3.d.l.687.5		6	28.11	odd	6
784.3.r.p.79.3		6	7.5	odd	6
784.3.r.p.655.3		6	28.27	even	2
784.3.r.q.79.1		6	28.19	even	6
784.3.r.q.655.1		6	7.6	odd	2
1008.3.cd.j.415.1		6	84.23	even	6
1008.3.cd.j.991.1		6	3.2	odd	2
1008.3.cd.k.415.1		6	21.2	odd	6
1008.3.cd.k.991.1		6	12.11	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.54043 + 1.46672i) q^{3} +(3.38341 + 5.86024i) q^{5} +(-5.88341 + 3.79282i) q^{7} +(-0.197460 - 0.342011i) q^{9} +(-8.19066 - 4.72888i) q^{11} +23.9286 q^{13} +19.8501i q^{15} +(1.69746 - 2.94009i) q^{17} +(-2.89021 + 1.66866i) q^{19} +(-20.5094 + 1.00610i) q^{21} +(26.7830 - 15.4632i) q^{23} +(-10.3949 + 18.0045i) q^{25} -27.5595i q^{27} -11.6051 q^{29} +(13.0289 + 7.52225i) q^{31} +(-13.8719 - 24.0268i) q^{33} +(-42.1328 - 21.6455i) q^{35} +(-24.8813 - 43.0957i) q^{37} +(60.7889 + 35.0965i) q^{39} -2.67236 q^{41} -44.7593i q^{43} +(1.33618 - 2.31433i) q^{45} +(-69.5720 + 40.1674i) q^{47} +(20.2290 - 44.6294i) q^{49} +(8.62457 - 4.97940i) q^{51} +(-38.4864 + 66.6604i) q^{53} -63.9990i q^{55} -9.78984 q^{57} +(-7.57526 - 4.37358i) q^{59} +(-25.9758 - 44.9914i) q^{61} +(2.45893 + 1.26326i) q^{63} +(80.9601 + 140.227i) q^{65} +(100.164 + 57.8299i) q^{67} +90.7208 q^{69} +122.338i q^{71} +(-12.9622 + 22.4512i) q^{73} +(-52.8152 + 30.4929i) q^{75} +(66.1248 - 3.24377i) q^{77} +(0.0203900 - 0.0117722i) q^{79} +(38.6449 - 66.9349i) q^{81} -107.921i q^{83} +22.9728 q^{85} +(-29.4819 - 17.0214i) q^{87} +(7.08206 + 12.2665i) q^{89} +(-140.782 + 90.7567i) q^{91} +(22.0661 + 38.2196i) q^{93} +(-19.5575 - 11.2915i) q^{95} -57.3654 q^{97} +3.73507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - q^{5} - 14 q^{7} + 14 q^{9} + 33 q^{11} + 28 q^{13} - 5 q^{17} - 63 q^{19} + 29 q^{21} + 33 q^{23} - 32 q^{25} - 100 q^{29} + 69 q^{31} - 71 q^{33} - 189 q^{35} + 15 q^{37} + 246 q^{39}+ \cdots + 124 q^{97}+O(q^{100}) \) 6 * q - 3 * q^3 - q^5 - 14 * q^7 + 14 * q^9 + 33 * q^11 + 28 * q^13 - 5 * q^17 - 63 * q^19 + 29 * q^21 + 33 * q^23 - 32 * q^25 - 100 * q^29 + 69 * q^31 - 71 * q^33 - 189 * q^35 + 15 * q^37 + 246 * q^39 + 124 * q^41 - 62 * q^45 - 171 * q^47 - 122 * q^49 + 225 * q^51 - 97 * q^53 + 2 * q^57 - 27 * q^59 - 89 * q^61 - 414 * q^63 + 142 * q^65 + 309 * q^67 + 538 * q^69 + 123 * q^73 - 408 * q^75 + 181 * q^77 + 201 * q^79 - 203 * q^81 - 130 * q^85 + 270 * q^87 + 91 * q^89 - 212 * q^91 - 123 * q^93 + 321 * q^95 + 124 * q^97

Introduction

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