LMFDB - Embedded newform 567.3.r.c.134.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,3,Mod(134,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("567.134");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	567.r (of order $6$, 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:	$15.4496309892$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.39033114624.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 6x^{6} - 30x^{5} + 34x^{4} - 102x^{3} + 486x^{2} - 730x + 373 $ x^8 - 2x^7 + 6x^6 - 30x^5 + 34x^4 - 102x^3 + 486x^2 - 730*x + 373
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.4
Root			$2.10277 - 0.136187i$ of defining polynomial
Character	$\chi$	$=$	567.134
Dual form			567.3.r.c.512.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.03622 - 1.75296i) q^{2} +(4.14575 - 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(-1.32288 - 2.29129i) q^{7} -15.0457i q^{8} +O(q^{10})$	\(q+(3.03622 - 1.75296i) q^{2} +(4.14575 - 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(-1.32288 - 2.29129i) q^{7} -15.0457i q^{8} +4.35425 q^{10} +(6.07244 - 3.50592i) q^{11} +(5.82288 - 10.0855i) q^{13} +(-8.03308 - 4.63790i) q^{14} +(-9.79150 - 16.9594i) q^{16} -4.52791i q^{17} +16.2288 q^{19} +(8.91815 - 5.14889i) q^{20} +(12.2915 - 21.2895i) q^{22} +(-22.1386 - 12.7817i) q^{23} +(-11.7288 - 20.3148i) q^{25} -40.8291i q^{26} -21.9373 q^{28} +(-8.22359 + 4.74789i) q^{29} +(-14.3542 + 24.8623i) q^{31} +(-7.33853 - 4.23690i) q^{32} +(-7.93725 - 13.7477i) q^{34} -3.28594i q^{35} -33.0405 q^{37} +(49.2741 - 28.4484i) q^{38} +(9.34313 - 16.1828i) q^{40} +(58.1922 + 33.5973i) q^{41} +(12.0627 + 20.8933i) q^{43} -58.1388i q^{44} -89.6235 q^{46} +(28.5921 - 16.5076i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-71.2222 - 41.1201i) q^{50} +(-48.2804 - 83.6241i) q^{52} +15.1877i q^{53} +8.70850 q^{55} +(-34.4740 + 19.9036i) q^{56} +(-16.6458 + 28.8313i) q^{58} +(80.0173 + 46.1980i) q^{59} +(28.7601 + 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(12.5259 - 7.23183i) q^{65} +(-7.58301 + 13.1342i) q^{67} +(-32.5133 - 18.7716i) q^{68} +(-5.76013 - 9.97684i) q^{70} +70.5584i q^{71} -76.7895 q^{73} +(-100.318 + 57.9188i) q^{74} +(67.2804 - 116.533i) q^{76} +(-16.0662 - 9.27580i) q^{77} +(-63.6235 - 110.199i) q^{79} -24.3215i q^{80} +235.579 q^{82} +(-64.3321 + 37.1422i) q^{83} +(2.81176 - 4.87011i) q^{85} +(73.2503 + 42.2911i) q^{86} +(-52.7490 - 91.3640i) q^{88} +127.377i q^{89} -30.8118 q^{91} +(-183.562 + 105.980i) q^{92} +(57.8745 - 100.242i) q^{94} +(17.4553 + 10.0778i) q^{95} +(11.5830 + 20.0624i) q^{97} +24.5415i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4}+O(q^{10}) $ 8 * q + 12 * q^4	$ 8 q + 12 q^{4} + 56 q^{10} + 36 q^{13} - 36 q^{16} + 24 q^{19} + 56 q^{22} + 12 q^{25} - 112 q^{28} - 136 q^{31} + 32 q^{37} - 84 q^{40} + 160 q^{43} - 336 q^{46} - 28 q^{49} - 164 q^{52} + 112 q^{55} - 112 q^{58} + 156 q^{61} + 8 q^{64} + 24 q^{67} + 28 q^{70} - 64 q^{73} + 316 q^{76} - 128 q^{79} + 784 q^{82} - 168 q^{85} - 168 q^{88} - 56 q^{91} + 336 q^{94} + 8 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 + 56 * q^10 + 36 * q^13 - 36 * q^16 + 24 * q^19 + 56 * q^22 + 12 * q^25 - 112 * q^28 - 136 * q^31 + 32 * q^37 - 84 * q^40 + 160 * q^43 - 336 * q^46 - 28 * q^49 - 164 * q^52 + 112 * q^55 - 112 * q^58 + 156 * q^61 + 8 * q^64 + 24 * q^67 + 28 * q^70 - 64 * q^73 + 316 * q^76 - 128 * q^79 + 784 * q^82 - 168 * q^85 - 168 * q^88 - 56 * q^91 + 336 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.03622	−	1.75296i	1.51811	−	0.876481i	0.518337	−	0.855177i	$-0.326551\pi$
$2$	3.03622	−	1.75296i	1.51811	−	0.876481i	0.999773	−	0.0213043i	$-0.00678187\pi$
$3$		0			0
$3$		0			0
$4$	4.14575	−	7.18065i	1.03644	−	1.79516i
$5$	1.07558	+	0.620984i	0.215115	+	0.124197i	0.603686	−	0.797222i	$-0.293698\pi$
$5$	1.07558	+	0.620984i	0.215115	+	0.124197i	−0.388571	+	0.921419i	$0.627031\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$8$		−	15.0457i		−	1.88071i
$9$		0			0
$10$	4.35425			0.435425
$11$	6.07244	−	3.50592i	0.552040	−	0.318720i	−0.197904	−	0.980221i	$-0.563414\pi$
$11$	6.07244	−	3.50592i	0.552040	−	0.318720i	0.749944	+	0.661501i	$0.230080\pi$
$12$		0			0
$13$	5.82288	−	10.0855i	0.447914	−	0.775809i	−0.550337	−	0.834943i	$-0.685501\pi$
$13$	5.82288	−	10.0855i	0.447914	−	0.775809i	0.998250	+	0.0591340i	$0.0188339\pi$
$14$	−8.03308	−	4.63790i	−0.573791	−	0.331279i
$15$		0			0
$16$	−9.79150	−	16.9594i	−0.611969	−	1.05996i
$17$		−	4.52791i		−	0.266348i	−0.991093	−	0.133174i	$-0.957483\pi$
$17$		−	4.52791i		−	0.266348i	0.991093	−	0.133174i	$-0.0425169\pi$
$18$		0			0
$19$	16.2288			0.854145			0.427073	−	0.904217i	$-0.359545\pi$
$19$	16.2288			0.854145			0.427073	+	0.904217i	$0.359545\pi$
$20$	8.91815	−	5.14889i	0.445907	−	0.257445i
$21$		0			0
$22$	12.2915	−	21.2895i	0.558705	−	0.967705i
$23$	−22.1386	−	12.7817i	−0.962548	−	0.555727i	−0.0655916	−	0.997847i	$-0.520893\pi$
$23$	−22.1386	−	12.7817i	−0.962548	−	0.555727i	−0.896956	+	0.442119i	$0.854227\pi$
$24$		0			0
$25$	−11.7288	−	20.3148i	−0.469150	−	0.812592i
$26$		−	40.8291i		−	1.57035i
$27$		0			0
$28$	−21.9373			−0.783473
$29$	−8.22359	+	4.74789i	−0.283572	+	0.163720i	−0.635039	−	0.772480i	$-0.719016\pi$
$29$	−8.22359	+	4.74789i	−0.283572	+	0.163720i	0.351467	+	0.936200i	$0.385683\pi$
$30$		0			0
$31$	−14.3542	+	24.8623i	−0.463040	+	0.802009i	−0.999111	−	0.0421640i	$-0.986575\pi$
$31$	−14.3542	+	24.8623i	−0.463040	+	0.802009i	0.536070	+	0.844173i	$0.319908\pi$
$32$	−7.33853	−	4.23690i	−0.229329	−	0.132403i
$33$		0			0
$34$	−7.93725	−	13.7477i	−0.233449	−	0.404345i
$35$		−	3.28594i		−	0.0938840i
$36$		0			0
$37$	−33.0405			−0.892987			−0.446493	−	0.894787i	$-0.647327\pi$
$37$	−33.0405			−0.892987			−0.446493	+	0.894787i	$0.647327\pi$
$38$	49.2741	−	28.4484i	1.29669	−	0.748642i
$39$		0			0
$40$	9.34313	−	16.1828i	0.233578	−	0.404570i
$41$	58.1922	+	33.5973i	1.41932	+	0.819446i	0.996239	−	0.0866449i	$-0.0276146\pi$
$41$	58.1922	+	33.5973i	1.41932	+	0.819446i	0.423083	+	0.906091i	$0.360948\pi$
$42$		0			0
$43$	12.0627	+	20.8933i	0.280529	+	0.485890i	0.971515	−	0.236978i	$-0.0761568\pi$
$43$	12.0627	+	20.8933i	0.280529	+	0.485890i	−0.690986	+	0.722868i	$0.742823\pi$
$44$		−	58.1388i		−	1.32134i
$45$		0			0
$46$	−89.6235			−1.94834
$47$	28.5921	−	16.5076i	0.608342	−	0.351226i	−0.163974	−	0.986465i	$-0.552431\pi$
$47$	28.5921	−	16.5076i	0.608342	−	0.351226i	0.772316	+	0.635238i	$0.219098\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	−71.2222	−	41.1201i	−1.42444	−	0.822403i
$51$		0			0
$52$	−48.2804	−	83.6241i	−0.928469	−	1.60816i
$53$			15.1877i			0.286561i	0.989682	+	0.143281i	$0.0457651\pi$
$53$			15.1877i			0.286561i	−0.989682	+	0.143281i	$0.954235\pi$
$54$		0			0
$55$	8.70850			0.158336
$56$	−34.4740	+	19.9036i	−0.615607	+	0.355421i
$57$		0			0
$58$	−16.6458	+	28.8313i	−0.286996	+	0.497091i
$59$	80.0173	+	46.1980i	1.35623	+	0.783017i	0.989113	−	0.147160i	$-0.0470131\pi$
$59$	80.0173	+	46.1980i	1.35623	+	0.783017i	0.367112	+	0.930177i	$0.380346\pi$
$60$		0			0
$61$	28.7601	+	49.8140i	0.471478	+	0.816623i	0.999468	−	0.0326275i	$-0.0103875\pi$
$61$	28.7601	+	49.8140i	0.471478	+	0.816623i	−0.527990	+	0.849251i	$0.677054\pi$
$62$			100.650i			1.62338i
$63$		0			0
$64$	48.6235			0.759743
$65$	12.5259	−	7.23183i	0.192706	−	0.111259i
$66$		0			0
$67$	−7.58301	+	13.1342i	−0.113179	+	0.196032i	−0.917050	−	0.398771i	$-0.869437\pi$
$67$	−7.58301	+	13.1342i	−0.113179	+	0.196032i	0.803871	+	0.594803i	$0.202770\pi$
$68$	−32.5133	−	18.7716i	−0.478137	−	0.276053i
$69$		0			0
$70$	−5.76013	−	9.97684i	−0.0822876	−	0.142526i
$71$			70.5584i			0.993781i	0.867813	+	0.496890i	$0.165525\pi$
$71$			70.5584i			0.993781i	−0.867813	+	0.496890i	$0.834475\pi$
$72$		0			0
$73$	−76.7895			−1.05191			−0.525956	−	0.850512i	$-0.676292\pi$
$73$	−76.7895			−1.05191			−0.525956	+	0.850512i	$0.676292\pi$
$74$	−100.318	+	57.9188i	−1.35565	+	0.782686i
$75$		0			0
$76$	67.2804	−	116.533i	0.885268	−	1.53333i
$77$	−16.0662	−	9.27580i	−0.208651	−	0.120465i
$78$		0			0
$79$	−63.6235	−	110.199i	−0.805361	−	1.39493i	−0.916047	−	0.401071i	$-0.868638\pi$
$79$	−63.6235	−	110.199i	−0.805361	−	1.39493i	0.110686	−	0.993855i	$-0.464695\pi$
$80$		−	24.3215i		−	0.304019i
$81$		0			0
$82$	235.579			2.87292
$83$	−64.3321	+	37.1422i	−0.775086	+	0.447496i	−0.834686	−	0.550726i	$-0.814351\pi$
$83$	−64.3321	+	37.1422i	−0.775086	+	0.447496i	0.0596000	+	0.998222i	$0.481017\pi$
$84$		0			0
$85$	2.81176	−	4.87011i	0.0330796	−	0.0572955i
$86$	73.2503	+	42.2911i	0.851747	+	0.491757i
$87$		0			0
$88$	−52.7490	−	91.3640i	−0.599421	−	1.03823i
$89$			127.377i			1.43121i	0.698507	+	0.715603i	$0.253848\pi$
$89$			127.377i			1.43121i	−0.698507	+	0.715603i	$0.746152\pi$
$90$		0			0
$91$	−30.8118			−0.338591
$92$	−183.562	+	105.980i	−1.99524	+	1.15195i
$93$		0			0
$94$	57.8745	−	100.242i	0.615686	−	1.06640i
$95$	17.4553	+	10.0778i	0.183740	+	0.106082i
$96$		0			0
$97$	11.5830	+	20.0624i	0.119412	+	0.206828i	0.919535	−	0.393008i	$-0.128566\pi$
$97$	11.5830	+	20.0624i	0.119412	+	0.206828i	−0.800123	+	0.599837i	$0.795232\pi$
$98$			24.5415i			0.250423i
$99$		0			0
$100$	−194.498			−1.94498
$101$	116.833	−	67.4535i	1.15676	−	0.667857i	0.206236	−	0.978502i	$-0.433879\pi$
$101$	116.833	−	67.4535i	1.15676	−	0.667857i	0.950526	+	0.310646i	$0.100545\pi$
$102$		0			0
$103$	59.8745	−	103.706i	0.581306	−	1.00685i	−0.414019	−	0.910268i	$-0.635875\pi$
$103$	59.8745	−	103.706i	0.581306	−	1.00685i	0.995325	−	0.0965831i	$-0.0307914\pi$
$104$	−151.743	−	87.6091i	−1.45907	−	0.842396i
$105$		0			0
$106$	26.6235	+	46.1133i	0.251165	+	0.435031i
$107$			77.8544i			0.727611i	0.931475	+	0.363806i	$0.118523\pi$
$107$			77.8544i			0.727611i	−0.931475	+	0.363806i	$0.881477\pi$
$108$		0			0
$109$	−36.5385			−0.335216			−0.167608	−	0.985854i	$-0.553604\pi$
$109$	−36.5385			−0.335216			−0.167608	+	0.985854i	$0.553604\pi$
$110$	26.4409	−	15.2657i	0.240372	−	0.138779i
$111$		0			0
$112$	−25.9059	+	44.8703i	−0.231303	+	0.400628i
$113$	18.8444	+	10.8798i	0.166764	+	0.0962815i	0.581059	−	0.813861i	$-0.302638\pi$
$113$	18.8444	+	10.8798i	0.166764	+	0.0962815i	−0.414295	+	0.910143i	$0.635972\pi$
$114$		0			0
$115$	−15.8745	−	27.4955i	−0.138039	−	0.239091i
$116$			78.7343i			0.678744i
$117$		0			0
$118$	323.933			2.74520
$119$	−10.3747	+	5.98986i	−0.0871827	+	0.0503350i
$120$		0			0
$121$	−35.9170	+	62.2101i	−0.296835	+	0.514133i
$122$	174.644	+	100.831i	1.43151	+	0.826482i
$123$		0			0
$124$	119.018	+	206.146i	0.959825	+	1.66247i
$125$		−	60.1827i		−	0.481462i
$126$		0			0
$127$	−15.4170			−0.121394			−0.0606968	−	0.998156i	$-0.519332\pi$
$127$	−15.4170			−0.121394			−0.0606968	+	0.998156i	$0.519332\pi$
$128$	176.986	−	102.183i	1.38270	−	0.798303i
$129$		0			0
$130$	25.3542	−	43.9148i	0.195033	−	0.337807i
$131$	158.578	+	91.5550i	1.21052	+	0.698893i	0.962872	−	0.269957i	$-0.0870095\pi$
$131$	158.578	+	91.5550i	1.21052	+	0.698893i	0.247646	+	0.968850i	$0.420343\pi$
$132$		0			0
$133$	−21.4686	−	37.1848i	−0.161418	−	0.279585i
$134$			53.1709i			0.396798i
$135$		0			0
$136$	−68.1255			−0.500923
$137$	−28.5921	+	16.5076i	−0.208701	+	0.120494i	−0.600708	−	0.799469i	$-0.705114\pi$
$137$	−28.5921	+	16.5076i	−0.208701	+	0.120494i	0.392006	+	0.919962i	$0.371781\pi$
$138$		0			0
$139$	−32.3209	+	55.9815i	−0.232525	+	0.402744i	−0.958550	−	0.284923i	$-0.908032\pi$
$139$	−32.3209	+	55.9815i	−0.232525	+	0.402744i	0.726026	+	0.687667i	$0.241365\pi$
$140$	−23.5952	−	13.6227i	−0.168537	−	0.0973050i
$141$		0			0
$142$	123.686	+	214.231i	0.871030	+	1.50867i
$143$		−	81.6582i		−	0.571037i
$144$		0			0
$145$	−11.7935			−0.0813343
$146$	−233.150	+	134.609i	−1.59692	+	0.921980i
$147$		0			0
$148$	−136.978	+	237.252i	−0.925525	+	1.60306i
$149$	169.512	+	97.8680i	1.13767	+	0.656832i	0.945852	−	0.324599i	$-0.105229\pi$
$149$	169.512	+	97.8680i	1.13767	+	0.656832i	0.191815	+	0.981431i	$0.438563\pi$
$150$		0			0
$151$	−51.1255	−	88.5519i	−0.338579	−	0.586437i	0.645586	−	0.763687i	$-0.276613\pi$
$151$	−51.1255	−	88.5519i	−0.338579	−	0.586437i	−0.984166	+	0.177251i	$0.943280\pi$
$152$		−	244.173i		−	1.60640i
$153$		0			0
$154$	−65.0405			−0.422341
$155$	−30.8782	+	17.8275i	−0.199214	+	0.115016i
$156$		0			0
$157$	−52.3614	+	90.6926i	−0.333512	+	0.577660i	−0.983198	−	0.182543i	$-0.941567\pi$
$157$	−52.3614	+	90.6926i	−0.333512	+	0.577660i	0.649686	+	0.760203i	$0.274901\pi$
$158$	−386.350	−	223.059i	−2.44525	−	1.41177i
$159$		0			0
$160$	−5.26210	−	9.11422i	−0.0328881	−	0.0569639i
$161$			67.6345i			0.420090i
$162$		0			0
$163$	−70.9595			−0.435334			−0.217667	−	0.976023i	$-0.569845\pi$
$163$	−70.9595			−0.435334			−0.217667	+	0.976023i	$0.569845\pi$
$164$	482.501	−	278.572i	2.94208	−	1.69861i
$165$		0			0
$166$	−130.218	+	225.544i	−0.784444	+	1.35870i
$167$	−179.260	−	103.496i	−1.07341	−	0.619735i	−0.144301	−	0.989534i	$-0.546093\pi$
$167$	−179.260	−	103.496i	−1.07341	−	0.619735i	−0.929112	+	0.369799i	$0.879427\pi$
$168$		0			0
$169$	16.6882	+	28.9049i	0.0987470	+	0.171035i
$170$		−	19.7156i		−	0.115974i
$171$		0			0
$172$	200.037			1.16300
$173$	−93.9323	+	54.2318i	−0.542961	+	0.313479i	−0.746278	−	0.665634i	$-0.768161\pi$
$173$	−93.9323	+	54.2318i	−0.542961	+	0.313479i	0.203317	+	0.979113i	$0.434828\pi$
$174$		0			0
$175$	−31.0314	+	53.7479i	−0.177322	+	0.307131i
$176$	−118.917	−	68.6565i	−0.675662	−	0.390094i
$177$		0			0
$178$	223.288	+	386.745i	1.25442	+	2.17273i
$179$		−	159.357i		−	0.890261i	−0.895466	−	0.445131i	$-0.853157\pi$
$179$		−	159.357i		−	0.890261i	0.895466	−	0.445131i	$-0.146843\pi$
$180$		0			0
$181$	−233.889			−1.29220			−0.646102	−	0.763251i	$-0.723602\pi$
$181$	−233.889			−1.29220			−0.646102	+	0.763251i	$0.723602\pi$
$182$	−93.5513	+	54.0118i	−0.514018	+	0.296768i
$183$		0			0
$184$	−192.310	+	333.090i	−1.04516	+	1.81027i
$185$	−35.5376	−	20.5176i	−0.192095	−	0.110906i
$186$		0			0
$187$	−15.8745	−	27.4955i	−0.0848904	−	0.147035i
$188$		−	273.746i		−	1.45610i
$189$		0			0
$190$	70.6640			0.371916
$191$	249.597	−	144.105i	1.30679	−	0.754476i	0.325232	−	0.945634i	$-0.394558\pi$
$191$	249.597	−	144.105i	1.30679	−	0.754476i	0.981559	+	0.191158i	$0.0612244\pi$
$192$		0			0
$193$	−38.5608	+	66.7892i	−0.199797	+	0.346058i	−0.948462	−	0.316890i	$-0.897362\pi$
$193$	−38.5608	+	66.7892i	−0.199797	+	0.346058i	0.748666	+	0.662948i	$0.230695\pi$
$194$	70.3371	+	40.6091i	0.362562	+	0.209325i
$195$		0			0
$196$	29.0203	+	50.2646i	0.148063	+	0.256452i
$197$			136.433i			0.692554i	0.938132	+	0.346277i	$0.112554\pi$
$197$			136.433i			0.692554i	−0.938132	+	0.346277i	$0.887446\pi$
$198$		0			0
$199$	86.5830			0.435090			0.217545	−	0.976050i	$-0.430195\pi$
$199$	86.5830			0.435090			0.217545	+	0.976050i	$0.430195\pi$
$200$	−305.650	+	176.467i	−1.52825	+	0.882336i
$201$		0			0
$202$	236.487	−	409.607i	1.17073	−	2.02776i
$203$	21.7576	+	12.5617i	0.107180	+	0.0618805i
$204$		0			0
$205$	41.7268	+	72.2729i	0.203545	+	0.352551i
$206$		−	419.831i		−	2.03801i
$207$		0			0
$208$	−228.059			−1.09644
$209$	98.5481	−	56.8968i	0.471522	−	0.272233i
$210$		0			0
$211$	−9.70850	+	16.8156i	−0.0460118	+	0.0796948i	−0.888114	−	0.459623i	$-0.847985\pi$
$211$	−9.70850	+	16.8156i	−0.0460118	+	0.0796948i	0.842102	+	0.539318i	$0.181318\pi$
$212$	109.058	+	62.9646i	0.514424	+	0.297003i
$213$		0			0
$214$	136.476	+	236.383i	0.637737	+	1.10459i
$215$			29.9631i			0.139363i
$216$		0			0
$217$	75.9555			0.350026
$218$	−110.939	+	64.0507i	−0.508895	+	0.293810i
$219$		0			0
$220$	36.1033	−	62.5327i	0.164106	−	0.284239i
$221$	−45.6663	−	26.3655i	−0.206635	−	0.119301i
$222$		0			0
$223$	−87.5203	−	151.590i	−0.392468	−	0.679774i	0.600307	−	0.799770i	$-0.295045\pi$
$223$	−87.5203	−	151.590i	−0.392468	−	0.679774i	−0.992774	+	0.119996i	$0.961712\pi$
$224$			22.4196i			0.100087i
$225$		0			0
$226$	76.2876			0.337556
$227$	153.784	−	88.7870i	0.677461	−	0.391132i	−0.121437	−	0.992599i	$-0.538750\pi$
$227$	153.784	−	88.7870i	0.677461	−	0.391132i	0.798898	+	0.601467i	$0.205417\pi$
$228$		0			0
$229$	−20.4059	+	35.3440i	−0.0891087	+	0.154341i	−0.907135	−	0.420841i	$-0.861735\pi$
$229$	−20.4059	+	35.3440i	−0.0891087	+	0.154341i	0.818026	+	0.575181i	$0.195069\pi$
$230$	−96.3970	−	55.6548i	−0.419117	−	0.241977i
$231$		0			0
$232$	71.4353	+	123.730i	0.307911	+	0.533317i
$233$		−	387.696i		−	1.66393i	−0.554828	−	0.831965i	$-0.687216\pi$
$233$		−	387.696i		−	1.66393i	0.554828	−	0.831965i	$-0.312784\pi$
$234$		0			0
$235$	41.0039			0.174485
$236$	663.463	−	383.051i	2.81129	−	1.62310i
$237$		0			0
$238$	−21.0000	+	36.3731i	−0.0882353	+	0.152828i
$239$	−42.8881	−	24.7615i	−0.179448	−	0.103604i	0.407585	−	0.913167i	$-0.366371\pi$
$239$	−42.8881	−	24.7615i	−0.179448	−	0.103604i	−0.587033	+	0.809563i	$0.699704\pi$
$240$		0			0
$241$	−162.624	−	281.672i	−0.674786	−	1.16876i	−0.976531	−	0.215376i	$-0.930902\pi$
$241$	−162.624	−	281.672i	−0.674786	−	1.16876i	0.301745	−	0.953389i	$-0.402431\pi$
$242$			251.845i			1.04068i
$243$		0			0
$244$	476.929			1.95463
$245$	−7.52904	+	4.34689i	−0.0307308	+	0.0177424i
$246$		0			0
$247$	94.4980	−	163.675i	0.382583	−	0.662653i
$248$	374.070	+	215.969i	1.50835	+	0.870845i
$249$		0			0
$250$	−105.498	−	182.728i	−0.421992	−	0.730912i
$251$			263.732i			1.05073i	0.850878	+	0.525364i	$0.176071\pi$
$251$			263.732i			1.05073i	−0.850878	+	0.525364i	$0.823929\pi$
$252$		0			0
$253$	−179.247			−0.708486
$254$	−46.8094	+	27.0254i	−0.184289	+	0.106399i
$255$		0			0
$256$	260.998	−	452.062i	1.01952	−	1.76587i
$257$	−130.926	−	75.5904i	−0.509442	−	0.294126i	0.223162	−	0.974781i	$-0.428362\pi$
$257$	−130.926	−	75.5904i	−0.509442	−	0.294126i	−0.732604	+	0.680655i	$0.761695\pi$
$258$		0			0
$259$	43.7085	+	75.7053i	0.168759	+	0.292299i
$260$		−	119.925i		−	0.461252i
$261$		0			0
$262$	641.970			2.45027
$263$	−99.0641	+	57.1947i	−0.376670	+	0.217470i	−0.676368	−	0.736564i	$-0.736447\pi$
$263$	−99.0641	+	57.1947i	−0.376670	+	0.217470i	0.299699	+	0.954034i	$0.403114\pi$
$264$		0			0
$265$	−9.43135	+	16.3356i	−0.0355900	+	0.0616437i
$266$	−130.367	−	75.2674i	−0.490101	−	0.282960i
$267$		0			0
$268$	62.8745	+	108.902i	0.234606	+	0.406350i
$269$		−	4.76170i		−	0.0177015i	−0.999961	−	0.00885074i	$-0.997183\pi$
$269$		−	4.76170i		−	0.0177015i	0.999961	−	0.00885074i	$-0.00281731\pi$
$270$		0			0
$271$	−518.701			−1.91402			−0.957012	−	0.290048i	$-0.906329\pi$
$271$	−518.701			−1.91402			−0.957012	+	0.290048i	$0.906329\pi$
$272$	−76.7905	+	44.3350i	−0.282318	+	0.162996i
$273$		0			0
$274$	−57.8745	+	100.242i	−0.211221	+	0.365845i
$275$	−142.444	−	82.2403i	−0.517979	−	0.299055i
$276$		0			0
$277$	60.5425	+	104.863i	0.218565	+	0.378566i	0.954369	−	0.298628i	$-0.0965291\pi$
$277$	60.5425	+	104.863i	0.218565	+	0.378566i	−0.735805	+	0.677194i	$0.763196\pi$
$278$			226.629i			0.815213i
$279$		0			0
$280$	−49.4392			−0.176569
$281$	−352.694	+	203.628i	−1.25514	+	0.724654i	−0.972125	−	0.234463i	$-0.924667\pi$
$281$	−352.694	+	203.628i	−1.25514	+	0.724654i	−0.283012	+	0.959116i	$0.591334\pi$
$282$		0			0
$283$	199.317	−	345.227i	0.704300	−	1.21988i	−0.262643	−	0.964893i	$-0.584594\pi$
$283$	199.317	−	345.227i	0.704300	−	1.21988i	0.966943	−	0.254991i	$-0.0820724\pi$
$284$	506.656	+	292.518i	1.78400	+	1.02999i
$285$		0			0
$286$	−143.144	−	247.932i	−0.500503	−	0.866896i
$287$		−	177.780i		−	0.619443i
$288$		0			0
$289$	268.498			0.929059
$290$	−35.8076	+	20.6735i	−0.123474	+	0.0712880i
$291$		0			0
$292$	−318.350	+	551.399i	−1.09024	+	1.88835i
$293$	2.19473	+	1.26713i	0.00749056	+	0.00432468i	0.503741	−	0.863855i	$-0.331957\pi$
$293$	2.19473	+	1.26713i	0.00749056	+	0.00432468i	−0.496250	+	0.868180i	$0.665290\pi$
$294$		0			0
$295$	57.3765	+	99.3790i	0.194497	+	0.336878i
$296$			497.117i			1.67945i
$297$		0			0
$298$	686.235			2.30280
$299$	−257.821	+	148.853i	−0.862276	+	0.497835i
$300$		0			0
$301$	31.9150	−	55.2784i	0.106030	−	0.183649i
$302$	−310.456	−	179.242i	−1.02800	−	0.593517i
$303$		0			0
$304$	−158.904	−	275.230i	−0.522710	−	0.905361i
$305$			71.4384i			0.234224i
$306$		0			0
$307$	86.2366			0.280901			0.140451	−	0.990088i	$-0.455145\pi$
$307$	86.2366			0.280901			0.140451	+	0.990088i	$0.455145\pi$
$308$	−133.213	+	76.9103i	−0.432509	+	0.249709i
$309$		0			0
$310$	−62.5020	+	108.257i	−0.201619	+	0.349215i
$311$	131.442	+	75.8884i	0.422645	+	0.244014i	0.696208	−	0.717840i	$-0.254869\pi$
$311$	131.442	+	75.8884i	0.422645	+	0.244014i	−0.273564	+	0.961854i	$0.588202\pi$
$312$		0			0
$313$	−159.059	−	275.498i	−0.508175	−	0.880185i	−0.999955	−	0.00946567i	$-0.996987\pi$
$313$	−159.059	−	275.498i	−0.508175	−	0.880185i	0.491780	−	0.870719i	$-0.336346\pi$
$314$			367.150i			1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$	−315.251	+	182.010i	−0.994482	+	0.574164i	−0.906611	−	0.421967i	$-0.861340\pi$
$317$	−315.251	+	182.010i	−0.994482	+	0.574164i	−0.0878710	+	0.996132i	$0.528006\pi$
$318$		0			0
$319$	−33.2915	+	57.6626i	−0.104362	+	0.180760i
$320$	52.2983	+	30.1945i	0.163432	+	0.0943577i
$321$		0			0
$322$	118.561	+	205.353i	0.368201	+	0.637743i
$323$		−	73.4823i		−	0.227500i
$324$		0			0
$325$	−273.180			−0.840555
$326$	−215.449	+	124.389i	−0.660885	+	0.381562i
$327$		0			0
$328$	505.494	−	875.541i	1.54114	−	2.66933i
$329$	−75.6475	−	43.6751i	−0.229932	−	0.132751i
$330$		0			0
$331$	−77.1843	−	133.687i	−0.233185	−	0.403889i	0.725559	−	0.688160i	$-0.241582\pi$
$331$	−77.1843	−	133.687i	−0.233185	−	0.403889i	−0.958744	+	0.284272i	$0.908248\pi$
$332$			615.929i			1.85521i
$333$		0			0
$334$	−725.697			−2.17274
$335$	−16.3122	+	9.41786i	−0.0486932	+	0.0281130i
$336$		0			0
$337$	−201.520	+	349.043i	−0.597983	+	1.03574i	0.395136	+	0.918623i	$0.370698\pi$
$337$	−201.520	+	349.043i	−0.597983	+	1.03574i	−0.993118	+	0.117114i	$0.962636\pi$
$338$	101.338	+	58.5077i	0.299817	+	0.173100i
$339$		0			0
$340$	−23.3137	−	40.3806i	−0.0685698	−	0.118766i
$341$			201.300i			0.590321i
$342$		0			0
$343$	18.5203			0.0539949
$344$	314.354	−	181.492i	0.913819	−	0.527594i
$345$		0			0
$346$	−190.133	+	329.319i	−0.549516	+	0.951790i
$347$	−408.108	−	235.621i	−1.17610	−	0.679023i	−0.220993	−	0.975275i	$-0.570930\pi$
$347$	−408.108	−	235.621i	−1.17610	−	0.679023i	−0.955110	+	0.296252i	$0.904263\pi$
$348$		0			0
$349$	182.258	+	315.680i	0.522230	+	0.904528i	0.999666	+	0.0258617i	$0.00823297\pi$
$349$	182.258	+	315.680i	0.522230	+	0.904528i	−0.477436	+	0.878667i	$0.658434\pi$
$350$			217.587i			0.621678i
$351$		0			0
$352$	−59.4170			−0.168798
$353$	74.7744	−	43.1710i	0.211825	−	0.122297i	−0.390334	−	0.920673i	$-0.627640\pi$
$353$	74.7744	−	43.1710i	0.211825	−	0.122297i	0.602159	+	0.798376i	$0.294307\pi$
$354$		0			0
$355$	−43.8157	+	75.8910i	−0.123425	+	0.213778i
$356$	914.652	+	528.075i	2.56925	+	1.48336i
$357$		0			0
$358$	−279.346	−	483.842i	−0.780297	−	1.35151i
$359$		−	372.068i		−	1.03640i	−0.855259	−	0.518200i	$-0.826602\pi$
$359$		−	372.068i		−	1.03640i	0.855259	−	0.518200i	$-0.173398\pi$
$360$		0			0
$361$	−97.6275			−0.270436
$362$	−710.138	+	409.998i	−1.96171	+	1.13259i
$363$		0			0
$364$	−127.738	+	221.249i	−0.350928	+	0.607826i
$365$	−82.5930	−	47.6851i	−0.226282	−	0.130644i
$366$		0			0
$367$	80.8928	+	140.110i	0.220416	+	0.381772i	0.954934	−	0.296817i	$-0.0959251\pi$
$367$	80.8928	+	140.110i	0.220416	+	0.381772i	−0.734518	+	0.678589i	$0.762592\pi$
$368$			500.609i			1.36035i
$369$		0			0
$370$	−143.867			−0.388829
$371$	34.7995	−	20.0915i	0.0937991	−	0.0541549i
$372$		0			0
$373$	−189.125	+	327.575i	−0.507039	+	0.878217i	0.492928	+	0.870070i	$0.335927\pi$
$373$	−189.125	+	327.575i	−0.507039	+	0.878217i	−0.999967	+	0.00814693i	$0.997407\pi$
$374$	−96.3970	−	55.6548i	−0.257746	−	0.148810i
$375$		0			0
$376$	−248.369	−	430.187i	−0.660555	−	1.14411i
$377$			110.586i			0.293330i
$378$		0			0
$379$	−50.7974			−0.134030			−0.0670151	−	0.997752i	$-0.521348\pi$
$379$	−50.7974			−0.134030			−0.0670151	+	0.997752i	$0.521348\pi$
$380$	144.730	−	83.5602i	0.380870	−	0.219895i
$381$		0			0
$382$	505.221	−	875.068i	1.32257	−	2.29075i
$383$	98.1910	+	56.6906i	0.256373	+	0.148017i	0.622679	−	0.782477i	$-0.286044\pi$
$383$	98.1910	+	56.6906i	0.256373	+	0.148017i	−0.366306	+	0.930495i	$0.619378\pi$
$384$		0			0
$385$	−11.5203	−	19.9537i	−0.0299228	−	0.0518277i
$386$			270.382i			0.700472i
$387$		0			0
$388$	192.081			0.495054
$389$	628.374	−	362.792i	1.61536	−	0.932628i	0.627259	−	0.778811i	$-0.284177\pi$
$389$	628.374	−	362.792i	1.61536	−	0.932628i	0.988099	−	0.153817i	$-0.0491565\pi$
$390$		0			0
$391$	−57.8745	+	100.242i	−0.148017	+	0.256372i
$392$	91.2096	+	52.6599i	0.232678	+	0.134336i
$393$		0			0
$394$	239.162	+	414.241i	0.607010	+	1.05137i
$395$		−	158.037i		−	0.400093i
$396$		0			0
$397$	−94.3464			−0.237648			−0.118824	−	0.992915i	$-0.537912\pi$
$397$	−94.3464			−0.237648			−0.118824	+	0.992915i	$0.537912\pi$
$398$	262.885	−	151.777i	0.660515	−	0.381349i
$399$		0			0
$400$	−229.684	+	397.825i	−0.574211	+	0.994562i
$401$	−586.875	−	338.833i	−1.46353	−	0.844969i	−0.464357	−	0.885648i	$-0.653715\pi$
$401$	−586.875	−	338.833i	−1.46353	−	0.844969i	−0.999172	+	0.0406787i	$0.987048\pi$
$402$		0			0
$403$	167.166	+	289.540i	0.414804	+	0.718462i
$404$		−	1118.58i		−	2.76877i
$405$		0			0
$406$	88.0810			0.216948
$407$	−200.637	+	115.838i	−0.492964	+	0.284613i
$408$		0			0
$409$	−8.68233	+	15.0382i	−0.0212282	+	0.0367683i	−0.876444	−	0.481503i	$-0.840091\pi$
$409$	−8.68233	+	15.0382i	−0.0212282	+	0.0367683i	0.855216	+	0.518271i	$0.173424\pi$
$410$	253.383	+	146.291i	0.618008	+	0.356807i
$411$		0			0
$412$	−496.450	−	859.876i	−1.20497	−	2.08708i
$413$		−	244.457i		−	0.591905i
$414$		0			0
$415$	−92.2589			−0.222311
$416$	−85.4626	+	49.3419i	−0.205439	+	0.118610i
$417$		0			0
$418$	199.476	−	345.502i	0.477215	−	0.826560i
$419$	117.841	+	68.0355i	0.281243	+	0.162376i	0.633986	−	0.773344i	$-0.281418\pi$
$419$	117.841	+	68.0355i	0.281243	+	0.162376i	−0.352743	+	0.935720i	$0.614751\pi$
$420$		0			0
$421$	−211.996	−	367.188i	−0.503554	−	0.872180i	−0.999992	−	0.00410821i	$-0.998692\pi$
$421$	−211.996	−	367.188i	−0.503554	−	0.872180i	0.496438	−	0.868072i	$-0.334641\pi$
$422$			68.0745i			0.161314i
$423$		0			0
$424$	228.510			0.538938
$425$	−91.9836	+	53.1068i	−0.216432	+	0.124957i
$426$		0			0
$427$	76.0922	−	131.795i	0.178202	−	0.308654i
$428$	559.045	+	322.765i	1.30618	+	0.754124i
$429$		0			0
$430$	52.5242	+	90.9746i	0.122149	+	0.211569i
$431$		−	340.244i		−	0.789430i	−0.918804	−	0.394715i	$-0.870843\pi$
$431$		−	340.244i		−	0.789430i	0.918804	−	0.394715i	$-0.129157\pi$
$432$		0			0
$433$	159.166			0.367589			0.183794	−	0.982965i	$-0.441162\pi$
$433$	159.166			0.367589			0.183794	+	0.982965i	$0.441162\pi$
$434$	230.618	−	133.147i	0.531377	−	0.306791i
$435$		0			0
$436$	−151.480	+	262.371i	−0.347431	+	0.601767i
$437$	−359.282	−	207.432i	−0.822155	−	0.474672i
$438$		0			0
$439$	−64.0366	−	110.915i	−0.145869	−	0.252653i	0.783828	−	0.620978i	$-0.213265\pi$
$439$	−64.0366	−	110.915i	−0.145869	−	0.252653i	−0.929697	+	0.368326i	$0.879931\pi$
$440$		−	131.025i		−	0.297785i
$441$		0			0
$442$	−184.871			−0.418259
$443$	170.901	−	98.6700i	0.385782	−	0.222731i	−0.294549	−	0.955636i	$-0.595169\pi$
$443$	170.901	−	98.6700i	0.385782	−	0.222731i	0.680331	+	0.732905i	$0.261836\pi$
$444$		0			0
$445$	−79.0993	+	137.004i	−0.177751	+	0.307874i
$446$	−531.461	−	306.839i	−1.19162	−	0.687981i
$447$		0			0
$448$	−64.3229	−	111.410i	−0.143578	−	0.248684i
$449$		−	148.101i		−	0.329847i	−0.986306	−	0.164923i	$-0.947262\pi$
$449$		−	148.101i		−	0.329847i	0.986306	−	0.164923i	$-0.0527377\pi$
$450$		0			0
$451$	471.158			1.04470
$452$	156.248	−	90.2100i	0.345682	−	0.199580i
$453$		0			0
$454$	311.280	−	539.153i	0.685640	−	1.18756i
$455$	−33.1404	−	19.1336i	−0.0728361	−	0.0420519i
$456$		0			0
$457$	61.1072	+	105.841i	0.133714	+	0.231599i	0.925105	−	0.379710i	$-0.123976\pi$
$457$	61.1072	+	105.841i	0.133714	+	0.231599i	−0.791392	+	0.611310i	$0.790643\pi$
$458$			143.083i			0.312408i
$459$		0			0
$460$	−263.247			−0.572276
$461$	−521.424	+	301.044i	−1.13107	+	0.653025i	−0.944204	−	0.329361i	$-0.893167\pi$
$461$	−521.424	+	301.044i	−1.13107	+	0.653025i	−0.186868	+	0.982385i	$0.559834\pi$
$462$		0			0
$463$	318.531	−	551.711i	0.687971	−	1.19160i	−0.284522	−	0.958670i	$-0.591835\pi$
$463$	318.531	−	551.711i	0.687971	−	1.19160i	0.972493	−	0.232932i	$-0.0748318\pi$
$464$	161.043	+	92.9780i	0.347075	+	0.200384i
$465$		0			0
$466$	−679.616	−	1177.13i	−1.45840	−	2.52603i
$467$			767.706i			1.64391i	0.569553	+	0.821955i	$0.307116\pi$
$467$			767.706i			1.64391i	−0.569553	+	0.821955i	$0.692884\pi$
$468$		0			0
$469$	40.1255			0.0855554
$470$	124.497	−	71.8783i	0.264887	−	0.152933i
$471$		0			0
$472$	695.080	−	1203.91i	1.47263	−	2.55067i
$473$	146.501	+	84.5821i	0.309726	+	0.178821i
$474$		0			0
$475$	−190.343	−	329.684i	−0.400722	−	0.694072i
$476$			99.3299i			0.208676i
$477$		0			0
$478$	−173.624			−0.363229
$479$	−341.089	+	196.928i	−0.712085	+	0.411122i	−0.811832	−	0.583890i	$-0.801530\pi$
$479$	−341.089	+	196.928i	−0.712085	+	0.411122i	0.0997478	+	0.995013i	$0.468196\pi$
$480$		0			0
$481$	−192.391	+	333.231i	−0.399981	+	0.692787i
$482$	−987.521	−	570.146i	−2.04880	−	1.18287i
$483$		0			0
$484$	297.806	+	515.815i	0.615301	+	1.06573i
$485$			28.7715i			0.0593226i
$486$		0			0
$487$	573.409			1.17743			0.588716	−	0.808340i	$-0.299634\pi$
$487$	573.409			1.17743			0.588716	+	0.808340i	$0.299634\pi$
$488$	749.486	−	432.716i	1.53583	−	0.886713i
$489$		0			0
$490$	−15.2399	+	26.3962i	−0.0311018	+	0.0538699i
$491$	−147.914	−	85.3979i	−0.301250	−	0.173927i	0.341754	−	0.939789i	$-0.388979\pi$
$491$	−147.914	−	85.3979i	−0.301250	−	0.173927i	−0.643004	+	0.765863i	$0.722312\pi$
$492$		0			0
$493$	21.4980	+	37.2357i	0.0436066	+	0.0755288i
$494$		−	662.606i		−	1.34131i
$495$		0			0
$496$	562.199			1.13347
$497$	161.670	−	93.3400i	0.325291	−	0.187807i
$498$		0			0
$499$	423.907	−	734.229i	0.849513	−	1.47140i	−0.0321299	−	0.999484i	$-0.510229\pi$
$499$	423.907	−	734.229i	0.849513	−	1.47140i	0.881643	−	0.471917i	$-0.156438\pi$
$500$	−432.151	−	249.503i	−0.864302	−	0.499005i
$501$		0			0
$502$	462.313	+	800.750i	0.920942	+	1.59512i
$503$		−	197.624i		−	0.392891i	−0.980515	−	0.196445i	$-0.937060\pi$
$503$		−	197.624i		−	0.392891i	0.980515	−	0.196445i	$-0.0629398\pi$
$504$		0			0
$505$	167.550			0.331783
$506$	−544.233	+	314.213i	−1.07556	+	0.620975i
$507$		0			0
$508$	−63.9150	+	110.704i	−0.125817	+	0.217921i
$509$	425.606	+	245.724i	0.836162	+	0.482758i	0.855958	−	0.517046i	$-0.172968\pi$
$509$	425.606	+	245.724i	0.836162	+	0.482758i	−0.0197959	+	0.999804i	$0.506302\pi$
$510$		0			0
$511$	101.583	+	175.947i	0.198793	+	0.344319i
$512$		−	1012.62i		−	1.97777i
$513$		0			0
$514$	−530.029			−1.03118
$515$	128.799	−	74.3623i	0.250096	−	0.144393i
$516$		0			0
$517$	115.749	−	200.483i	0.223886	−	0.387782i
$518$	265.417	+	153.239i	0.512388	+	0.295828i
$519$		0			0
$520$	−108.808	−	188.461i	−0.209246	−	0.362424i
$521$		−	870.010i		−	1.66988i	−0.550338	−	0.834942i	$-0.685501\pi$
$521$		−	870.010i		−	1.66988i	0.550338	−	0.834942i	$-0.314499\pi$
$522$		0			0
$523$	798.707			1.52716			0.763582	−	0.645710i	$-0.223439\pi$
$523$	798.707			1.52716			0.763582	+	0.645710i	$0.223439\pi$
$524$	1314.85	−	759.129i	2.50925	−	1.44872i
$525$		0			0
$526$	−200.520	+	347.311i	−0.381217	+	0.660288i
$527$	112.574	+	64.9947i	0.213613	+	0.123330i
$528$		0			0
$529$	62.2451	+	107.812i	0.117666	+	0.203803i
$530$			66.1312i			0.124776i
$531$		0			0
$532$	−356.014			−0.669200
$533$	677.692	−	391.266i	1.27147	−	0.734082i
$534$		0			0
$535$	−48.3464	+	83.7384i	−0.0903671	+	0.156520i
$536$	197.612	+	114.091i	0.368680	+	0.212857i
$537$		0			0
$538$	−8.34707	−	14.4576i	−0.0155150	−	0.0268728i
$539$			49.0829i			0.0910630i
$540$		0			0
$541$	−736.243			−1.36089			−0.680446	−	0.732798i	$-0.738214\pi$
$541$	−736.243			−1.36089			−0.680446	+	0.732798i	$0.738214\pi$
$542$	−1574.89	+	909.262i	−2.90570	+	1.67761i
$543$		0			0
$544$	−19.1843	+	33.2282i	−0.0352653	+	0.0610812i
$545$	−39.3000	−	22.6899i	−0.0721101	−	0.0416328i
$546$		0			0
$547$	114.476	+	198.278i	0.209279	+	0.362482i	0.951488	−	0.307687i	$-0.0995549\pi$
$547$	114.476	+	198.278i	0.209279	+	0.362482i	−0.742208	+	0.670169i	$0.766222\pi$
$548$			273.746i			0.499537i
$549$		0			0
$550$	−576.656			−1.04847
$551$	−133.459	+	77.0524i	−0.242212	+	0.139841i
$552$		0			0
$553$	−168.332	+	291.560i	−0.304398	+	0.527233i
$554$	367.641	+	212.257i	0.663611	+	0.383136i
$555$		0			0
$556$	267.989	+	464.170i	0.481994	+	0.834839i
$557$		−	906.288i		−	1.62709i	−0.581503	−	0.813544i	$-0.697535\pi$
$557$		−	906.288i		−	1.62709i	0.581503	−	0.813544i	$-0.302465\pi$
$558$		0			0
$559$	280.959			0.502611
$560$	−55.7275	+	32.1743i	−0.0995134	+	0.0574541i
$561$		0			0
$562$	−713.903	+	1236.52i	−1.27029	+	2.20021i
$563$	−397.173	−	229.308i	−0.705459	−	0.407297i	0.103919	−	0.994586i	$-0.466862\pi$
$563$	−397.173	−	229.308i	−0.705459	−	0.407297i	−0.809377	+	0.587289i	$0.800195\pi$
$564$		0			0
$565$	13.5124	+	23.4041i	0.0239157	+	0.0414233i
$566$		−	1397.58i		−	2.46922i
$567$		0			0
$568$	1061.60			1.86901
$569$	500.067	−	288.714i	0.878853	−	0.507406i	0.00857275	−	0.999963i	$-0.497271\pi$
$569$	500.067	−	288.714i	0.878853	−	0.507406i	0.870280	+	0.492557i	$0.163938\pi$
$570$		0			0
$571$	51.5608	−	89.3059i	0.0902991	−	0.156403i	−0.817338	−	0.576159i	$-0.804551\pi$
$571$	51.5608	−	89.3059i	0.0902991	−	0.156403i	0.907637	+	0.419756i	$0.137884\pi$
$572$	−586.359	−	338.535i	−1.02510	−	0.591844i
$573$		0			0
$574$	−311.642	−	539.779i	−0.542930	−	0.940382i
$575$			599.655i			1.04288i
$576$		0			0
$577$	−676.583			−1.17259			−0.586294	−	0.810099i	$-0.699414\pi$
$577$	−676.583			−1.17259			−0.586294	+	0.810099i	$0.699414\pi$
$578$	815.219	−	470.667i	1.41041	−	0.814302i
$579$		0			0
$580$	−48.8928	+	84.6848i	−0.0842979	+	0.146008i
$581$	170.207	+	98.2690i	0.292955	+	0.169138i
$582$		0			0
$583$	53.2470	+	92.2266i	0.0913328	+	0.158193i
$584$			1155.35i			1.97834i
$585$		0			0
$586$	8.88492			0.0151620
$587$	−137.424	+	79.3415i	−0.234112	+	0.135164i	−0.612467	−	0.790496i	$-0.709823\pi$
$587$	−137.424	+	79.3415i	−0.234112	+	0.135164i	0.378356	+	0.925660i	$0.376490\pi$
$588$		0			0
$589$	−232.952	+	403.484i	−0.395504	+	0.685032i
$590$	348.415	+	201.158i	0.590534	+	0.340945i
$591$		0			0
$592$	323.516	+	560.347i	0.546480	+	0.946532i
$593$			935.371i			1.57735i	0.614807	+	0.788677i	$0.289234\pi$
$593$			935.371i			1.57735i	−0.614807	+	0.788677i	$0.710766\pi$
$594$		0			0
$595$	−14.8784			−0.0250058
$596$	1405.51	−	811.472i	2.35824	−	1.36153i
$597$		0			0
$598$	−521.867	+	903.900i	−0.872687	+	1.51154i
$599$	63.8836	+	36.8832i	0.106650	+	0.0615747i	0.552376	−	0.833595i	$-0.313721\pi$
$599$	63.8836	+	36.8832i	0.106650	+	0.0615747i	−0.445726	+	0.895169i	$0.647054\pi$
$600$		0			0
$601$	467.140	+	809.110i	0.777271	+	1.34627i	0.933509	+	0.358553i	$0.116730\pi$
$601$	467.140	+	809.110i	0.777271	+	1.34627i	−0.156238	+	0.987719i	$0.549937\pi$
$602$		−	223.783i		−	0.371733i
$603$		0			0
$604$	−847.814			−1.40367
$605$	−77.2630	+	44.6078i	−0.127707	+	0.0737319i
$606$		0			0
$607$	90.8039	−	157.277i	0.149595	−	0.259105i	−0.781483	−	0.623926i	$-0.785536\pi$
$607$	90.8039	−	157.277i	0.149595	−	0.259105i	0.931078	+	0.364821i	$0.118870\pi$
$608$	−119.095	−	68.7596i	−0.195880	−	0.113091i
$609$		0			0
$610$	125.229	+	216.903i	0.205293	+	0.355578i
$611$		−	384.488i		−	0.629276i
$612$		0			0
$613$	−897.940			−1.46483			−0.732414	−	0.680859i	$-0.761606\pi$
$613$	−897.940			−1.46483			−0.732414	+	0.680859i	$0.761606\pi$
$614$	261.833	−	151.170i	0.426439	−	0.246204i
$615$		0			0
$616$	−139.561	+	241.726i	−0.226560	+	0.392413i
$617$	1012.98	+	584.843i	1.64178	+	0.947882i	0.980201	+	0.198006i	$0.0634467\pi$
$617$	1012.98	+	584.843i	1.64178	+	0.947882i	0.661579	+	0.749876i	$0.269887\pi$
$618$		0			0
$619$	−604.483	−	1047.00i	−0.976548	−	1.69143i	−0.674730	−	0.738064i	$-0.735740\pi$
$619$	−604.483	−	1047.00i	−0.976548	−	1.69143i	−0.301817	−	0.953366i	$-0.597593\pi$
$620$			295.634i			0.476829i
$621$		0			0
$622$	532.118			0.855495
$623$	291.858	−	168.504i	0.468472	−	0.270472i
$624$		0			0
$625$	−255.846	+	443.139i	−0.409354	+	0.709022i
$626$	−965.875	−	557.648i	−1.54293	−	0.890812i
$627$		0			0
$628$	434.155	+	751.978i	0.691329	+	1.19742i
$629$			149.604i			0.237845i
$630$		0			0
$631$	901.223			1.42825			0.714123	−	0.700020i	$-0.246826\pi$
$631$	901.223			1.42825			0.714123	+	0.700020i	$0.246826\pi$
$632$	−1658.02	+	957.259i	−2.62345	+	1.51465i
$633$		0			0
$634$	−638.114	+	1105.25i	−1.00649	+	1.74329i
$635$	−16.5822	−	9.57371i	−0.0261136	−	0.0150767i
$636$		0			0
$637$	40.7601	+	70.5986i	0.0639876	+	0.110830i
$638$			233.435i			0.365886i
$639$		0			0
$640$	253.816			0.396587
$641$	−457.806	+	264.315i	−0.714206	+	0.412347i	−0.812616	−	0.582799i	$-0.801958\pi$
$641$	−457.806	+	264.315i	−0.714206	+	0.412347i	0.0984103	+	0.995146i	$0.468624\pi$
$642$		0			0
$643$	−16.7196	+	28.9592i	−0.0260025	+	0.0450377i	−0.878734	−	0.477312i	$-0.841611\pi$
$643$	−16.7196	+	28.9592i	−0.0260025	+	0.0450377i	0.852731	+	0.522350i	$0.174944\pi$
$644$	485.660	+	280.396i	0.754131	+	0.435397i
$645$		0			0
$646$	−128.812	−	223.109i	−0.199399	−	0.345369i
$647$			786.308i			1.21531i	0.794200	+	0.607657i	$0.207890\pi$
$647$			786.308i			1.21531i	−0.794200	+	0.607657i	$0.792110\pi$
$648$		0			0
$649$	647.867			0.998254
$650$	−829.435	+	478.875i	−1.27605	+	0.736730i
$651$		0			0
$652$	−294.180	+	509.535i	−0.451197	+	0.781496i
$653$	−334.119	−	192.904i	−0.511668	−	0.295412i	0.221851	−	0.975081i	$-0.428790\pi$
$653$	−334.119	−	192.904i	−0.511668	−	0.295412i	−0.733519	+	0.679669i	$0.762123\pi$
$654$		0			0
$655$	113.708	+	196.949i	0.173601	+	0.300685i
$656$		−	1315.87i		−	2.00590i
$657$		0			0
$658$	−306.243			−0.465415
$659$	84.2282	−	48.6292i	0.127812	−	0.0737924i	−0.434731	−	0.900560i	$-0.643156\pi$
$659$	84.2282	−	48.6292i	0.127812	−	0.0737924i	0.562543	+	0.826768i	$0.309823\pi$
$660$		0			0
$661$	480.752	−	832.687i	0.727311	−	1.25974i	−0.230705	−	0.973024i	$-0.574103\pi$
$661$	480.752	−	832.687i	0.727311	−	1.25974i	0.958016	−	0.286715i	$-0.0925633\pi$
$662$	−468.697	−	270.602i	−0.708001	−	0.408765i
$663$		0			0
$664$	558.829	+	967.921i	0.841610	+	1.45771i
$665$		−	53.3267i		−	0.0801906i
$666$		0			0
$667$	242.745			0.363936
$668$	−1486.33	+	858.136i	−2.22505	+	1.28463i
$669$		0			0
$670$	−33.0183	+	57.1894i	−0.0492810	+	0.0853572i
$671$	349.288	+	201.662i	0.520549	+	0.300539i
$672$		0			0
$673$	544.903	+	943.800i	0.809663	+	1.40238i	0.913098	+	0.407741i	$0.133683\pi$
$673$	544.903	+	943.800i	0.809663	+	1.40238i	−0.103435	+	0.994636i	$0.532983\pi$
$674$			1413.03i			2.09648i
$675$		0			0
$676$	276.741			0.409380
$677$	−1084.75	+	626.279i	−1.60229	+	0.925080i	−0.611258	+	0.791432i	$0.709336\pi$
$677$	−1084.75	+	626.279i	−1.60229	+	0.925080i	−0.991029	+	0.133649i	$0.957331\pi$
$678$		0			0
$679$	30.6458	−	53.0800i	0.0451337	−	0.0781738i
$680$	−73.2742	−	42.3049i	−0.107756	−	0.0622130i
$681$		0			0
$682$	352.871	+	611.190i	0.517406	+	0.896173i
$683$		−	341.097i		−	0.499409i	−0.968322	−	0.249705i	$-0.919666\pi$
$683$		−	341.097i		−	0.499409i	0.968322	−	0.249705i	$-0.0803335\pi$
$684$		0			0
$685$	−41.0039			−0.0598598
$686$	56.2316	−	32.4653i	0.0819702	−	0.0473255i
$687$		0			0
$688$	236.225	−	409.153i	0.343350	−	0.594700i
$689$	153.176	+	88.4363i	0.222317	+	0.128355i
$690$		0			0
$691$	391.833	+	678.675i	0.567053	+	0.982164i	0.996855	+	0.0792411i	$0.0252497\pi$
$691$	391.833	+	678.675i	0.567053	+	0.982164i	−0.429803	+	0.902923i	$0.641417\pi$
$692$			899.327i			1.29961i
$693$		0			0
$694$	−1652.14			−2.38060
$695$	−69.5272	+	40.1416i	−0.100039	+	0.0577576i
$696$		0			0
$697$	152.125	−	263.489i	0.218258	−	0.378033i
$698$	1106.75	+	638.983i	1.58560	+	0.915449i
$699$		0			0
$700$	257.297	+	445.651i	0.367567	+	0.636644i
$701$			1331.76i			1.89979i	0.312562	+	0.949897i	$0.398813\pi$
$701$			1331.76i			1.89979i	−0.312562	+	0.949897i	$0.601187\pi$
$702$		0			0
$703$	−536.207			−0.762740
$704$	295.263	−	170.470i	0.419408	−	0.242145i
$705$		0			0
$706$	151.354	−	262.153i	0.214383	−	0.371322i
$707$	−309.111	−	178.465i	−0.437215	−	0.252426i
$708$		0			0
$709$	−381.982	−	661.612i	−0.538761	−	0.933162i	−0.998971	−	0.0453517i	$-0.985559\pi$
$709$	−381.982	−	661.612i	−0.538761	−	0.933162i	0.460210	−	0.887810i	$-0.347774\pi$
$710$			307.229i			0.432717i
$711$		0			0
$712$	1916.48			2.69168
$713$	635.566	−	366.944i	0.891397	−	0.514648i
$714$		0			0
$715$	50.7085	−	87.8297i	0.0709210	−	0.122839i
$716$	−1144.29	−	660.654i	−1.59816	−	0.922701i
$717$		0			0
$718$	−652.221	−	1129.68i	−0.908386	−	1.57337i
$719$			623.715i			0.867476i	0.901039	+	0.433738i	$0.142806\pi$
$719$			623.715i			0.867476i	−0.901039	+	0.433738i	$0.857194\pi$
$720$		0			0
$721$	−316.826			−0.439426
$722$	−296.418	+	171.137i	−0.410552	+	0.237032i
$723$		0			0
$724$	−969.645	+	1679.47i	−1.33929	+	2.31972i
$725$	192.905	+	111.374i	0.266076	+	0.153619i
$726$		0			0
$727$	−339.247	−	587.593i	−0.466640	−	0.808244i	0.532634	−	0.846346i	$-0.321202\pi$
$727$	−339.247	−	587.593i	−0.466640	−	0.808244i	−0.999274	+	0.0381019i	$0.987869\pi$
$728$			463.584i			0.636791i
$729$		0			0
$730$	−334.361			−0.458028
$731$	94.6029	−	54.6190i	0.129416	−	0.0747182i
$732$		0			0
$733$	197.483	−	342.051i	0.269417	−	0.466645i	−0.699294	−	0.714834i	$-0.746502\pi$
$733$	197.483	−	342.051i	0.269417	−	0.466645i	0.968712	+	0.248189i	$0.0798355\pi$
$734$	491.217	+	283.604i	0.669232	+	0.386381i
$735$		0			0
$736$	108.310	+	187.598i	0.147160	+	0.254889i
$737$			106.342i			0.144290i
$738$		0			0
$739$	292.199			0.395397			0.197699	−	0.980263i	$-0.436653\pi$
$739$	292.199			0.395397			0.197699	+	0.980263i	$0.436653\pi$
$740$	−294.660	+	170.122i	−0.398189	+	0.229895i
$741$		0			0
$742$	70.4392	−	122.004i	0.0949316	−	0.164426i
$743$	332.079	+	191.726i	0.446943	+	0.258043i	0.706538	−	0.707675i	$-0.250256\pi$
$743$	332.079	+	191.726i	0.446943	+	0.258043i	−0.259595	+	0.965718i	$0.583589\pi$
$744$		0			0
$745$	121.549	+	210.529i	0.163153	+	0.282589i
$746$			1326.12i			1.77764i
$747$		0			0
$748$	−263.247			−0.351935
$749$	178.387	−	102.992i	0.238167	−	0.137506i
$750$		0			0
$751$	348.166	−	603.041i	0.463603	−	0.802984i	−0.535534	−	0.844514i	$-0.679890\pi$
$751$	348.166	−	603.041i	0.463603	−	0.802984i	0.999137	+	0.0415293i	$0.0132230\pi$
$752$	−559.918	−	323.269i	−0.744572	−	0.429879i
$753$		0			0
$754$	193.852	+	335.762i	0.257099	+	0.445308i
$755$		−	126.993i		−	0.168202i
$756$		0			0
$757$	967.357			1.27788			0.638941	−	0.769256i	$-0.279373\pi$
$757$	967.357			1.27788			0.638941	+	0.769256i	$0.279373\pi$
$758$	−154.232	+	89.0459i	−0.203472	+	0.117475i
$759$		0			0
$760$	151.627	−	262.626i	0.199510	−	0.345561i
$761$	77.6876	+	44.8529i	0.102086	+	0.0589395i	0.550174	−	0.835050i	$-0.314561\pi$
$761$	77.6876	+	44.8529i	0.102086	+	0.0589395i	−0.448088	+	0.893990i	$0.647895\pi$
$762$		0			0
$763$	48.3360	+	83.7203i	0.0633499	+	0.109725i
$764$		−	2389.69i		−	3.12787i
$765$		0			0
$766$	397.506			0.518937
$767$	931.861	−	538.010i	1.21494	−	0.701448i
$768$		0			0
$769$	−463.110	+	802.130i	−0.602223	+	1.04308i	0.390260	+	0.920705i	$0.372385\pi$
$769$	−463.110	+	802.130i	−0.602223	+	1.04308i	−0.992484	+	0.122377i	$0.960948\pi$
$770$	−69.9561	−	40.3892i	−0.0908520	−	0.0524534i
$771$		0			0
$772$	319.727	+	553.783i	0.414154	+	0.717336i
$773$			424.125i			0.548674i	0.961634	+	0.274337i	$0.0884584\pi$
$773$			424.125i			0.548674i	−0.961634	+	0.274337i	$0.911542\pi$
$774$		0			0
$775$	673.430			0.868942
$776$	301.852	−	174.274i	0.388984	−	0.224580i
$777$		0			0
$778$	1271.92	−	2203.03i	1.63486	−	2.83166i
$779$	944.387	+	545.242i	1.21231	+	0.699926i
$780$		0			0
$781$	247.373	+	428.462i	0.316738	+	0.548607i
$782$			405.807i			0.518935i
$783$		0			0
$784$	137.081			0.174848
$785$	−112.637	+	65.0313i	−0.143487	+	0.0828424i
$786$		0			0
$787$	77.9444	−	135.004i	0.0990399	−	0.171542i	−0.812248	−	0.583313i	$-0.801756\pi$
$787$	77.9444	−	135.004i	0.0990399	−	0.171542i	0.911288	+	0.411771i	$0.135090\pi$
$788$	979.679	+	565.618i	1.24325	+	0.717789i
$789$		0			0
$790$	−277.033	−	479.835i	−0.350674	−	0.607386i
$791$		−	57.5705i		−	0.0727820i
$792$		0			0
$793$	669.867			0.844725
$794$	−286.456	+	165.386i	−0.360776	+	0.208294i
$795$		0			0
$796$	358.952	−	621.722i	0.450944	−	0.781058i
$797$	622.838	+	359.595i	0.781478	+	0.451186i	0.836954	−	0.547274i	$-0.184334\pi$
$797$	622.838	+	359.595i	0.781478	+	0.451186i	−0.0554761	+	0.998460i	$0.517668\pi$
$798$		0			0
$799$	−74.7451	−	129.462i	−0.0935483	−	0.162030i
$800$			198.774i			0.248468i
$801$		0			0
$802$	−2375.84			−2.96240
$803$	−466.300	+	269.218i	−0.580697	+	0.335266i
$804$		0			0
$805$	−42.0000	+	72.7461i	−0.0521739	+	0.0903679i
$806$	1015.11	+	586.071i	1.25944	+	0.727136i
$807$		0			0
$808$	−1014.88	−	1757.83i	−1.25604	−	2.17553i
$809$		−	212.244i		−	0.262353i	−0.991359	−	0.131176i	$-0.958125\pi$
$809$		−	212.244i		−	0.262353i	0.991359	−	0.131176i	$-0.0418755\pi$
$810$		0			0
$811$	1058.66			1.30538			0.652690	−	0.757625i	$-0.273641\pi$
$811$	1058.66			1.30538			0.652690	+	0.757625i	$0.273641\pi$
$812$	180.403	−	104.156i	0.222171	−	0.128271i
$813$		0			0
$814$	−406.118	+	703.416i	−0.498916	+	0.864148i
$815$	−76.3224	−	44.0647i	−0.0936471	−	0.0540672i
$816$		0			0
$817$	195.763	+	339.072i	0.239612	+	0.415021i
$818$			60.8792i			0.0744244i
$819$		0			0
$820$	691.956			0.843848
$821$	708.903	−	409.286i	0.863463	−	0.498521i	−0.00170721	−	0.999999i	$-0.500543\pi$
$821$	708.903	−	409.286i	0.863463	−	0.498521i	0.865171	+	0.501478i	$0.167210\pi$
$822$		0			0
$823$	−103.425	+	179.137i	−0.125668	+	0.217664i	−0.921994	−	0.387204i	$-0.873441\pi$
$823$	−103.425	+	179.137i	−0.125668	+	0.217664i	0.796326	+	0.604868i	$0.206774\pi$
$824$	−1560.32	−	900.853i	−1.89360	−	1.09327i
$825$		0			0
$826$	−428.523	−	742.224i	−0.518794	−	0.898577i
$827$		−	438.639i		−	0.530398i	−0.964194	−	0.265199i	$-0.914562\pi$
$827$		−	438.639i		−	0.530398i	0.964194	−	0.265199i	$-0.0854376\pi$
$828$		0			0
$829$	654.804			0.789872			0.394936	−	0.918709i	$-0.370767\pi$
$829$	654.804			0.789872			0.394936	+	0.918709i	$0.370767\pi$
$830$	−280.118	+	161.726i	−0.337492	+	0.194851i
$831$		0			0
$832$	283.129	−	490.393i	0.340299	−	0.589415i
$833$	27.4490	+	15.8477i	0.0329520	+	0.0190248i
$834$		0			0
$835$	−128.539	−	222.635i	−0.153938	−	0.266629i
$836$		−	943.520i		−	1.12861i
$837$		0			0
$838$	477.055			0.569278
$839$	44.1422	−	25.4855i	0.0526129	−	0.0303761i	−0.473463	−	0.880814i	$-0.656996\pi$
$839$	44.1422	−	25.4855i	0.0526129	−	0.0303761i	0.526076	+	0.850438i	$0.323663\pi$
$840$		0			0
$841$	−375.415	+	650.238i	−0.446391	+	0.773172i
$842$	−1287.33	−	743.242i	−1.52890	−	0.882710i
$843$		0			0
$844$	80.4980	+	139.427i	0.0953768	+	0.165197i
$845$			41.4525i			0.0490563i
$846$		0			0
$847$	190.055			0.224386
$848$	257.575	−	148.711i	0.303744	−	0.175366i
$849$		0			0
$850$	−186.188	+	322.487i	−0.219045	+	0.379397i
$851$	731.471	+	422.315i	0.859543	+	0.496257i
$852$		0			0
$853$	441.971	+	765.516i	0.518137	+	0.897439i	0.999778	+	0.0210706i	$0.00670748\pi$
$853$	441.971	+	765.516i	0.518137	+	0.897439i	−0.481641	+	0.876368i	$0.659959\pi$
$854$		−	533.547i		−	0.624762i
$855$		0			0
$856$	1171.37			1.36843
$857$	−481.961	+	278.260i	−0.562382	+	0.324691i	−0.754101	−	0.656759i	$-0.771927\pi$
$857$	−481.961	+	278.260i	−0.562382	+	0.324691i	0.191719	+	0.981450i	$0.438594\pi$
$858$		0			0
$859$	321.539	−	556.922i	0.374318	−	0.648338i	−0.615907	−	0.787819i	$-0.711210\pi$
$859$	321.539	−	556.922i	0.374318	−	0.648338i	0.990225	+	0.139481i	$0.0445435\pi$
$860$	215.155	+	124.220i	0.250180	+	0.144441i
$861$		0			0
$862$	−596.435	−	1033.06i	−0.691920	−	1.19844i
$863$		−	204.892i		−	0.237419i	−0.992929	−	0.118709i	$-0.962124\pi$
$863$		−	204.892i		−	0.237419i	0.992929	−	0.118709i	$-0.0378757\pi$
$864$		0			0
$865$	−134.708			−0.155732
$866$	483.263	−	279.012i	0.558040	−	0.322185i
$867$		0			0
$868$	314.893	−	545.410i	0.362780	−	0.628353i
$869$	−772.700	−	446.118i	−0.889183	−	0.513370i
$870$		0			0
$871$	88.3098	+	152.957i	0.101389	+	0.175611i
$872$			549.747i			0.630444i
$873$		0			0
$874$	−1454.48			−1.66416
$875$	−137.896	+	79.6143i	−0.157595	+	0.0909877i
$876$		0			0
$877$	103.605	−	179.450i	0.118136	−	0.204617i	−0.800893	−	0.598807i	$-0.795641\pi$
$877$	103.605	−	179.450i	0.118136	−	0.204617i	0.919029	+	0.394190i	$0.128975\pi$
$878$	−388.858	−	224.507i	−0.442891	−	0.255703i
$879$		0			0
$880$	−85.2693	−	147.691i	−0.0968969	−	0.167830i
$881$			1391.37i			1.57931i	0.613552	+	0.789654i	$0.289740\pi$
$881$			1391.37i			1.57931i	−0.613552	+	0.789654i	$0.710260\pi$
$882$		0			0
$883$	−1091.99			−1.23668			−0.618342	−	0.785909i	$-0.712195\pi$
$883$	−1091.99			−1.23668			−0.618342	+	0.785909i	$0.712195\pi$
$884$	−378.642	+	218.609i	−0.428328	+	0.247296i
$885$		0			0
$886$	345.929	−	599.167i	0.390439	−	0.676261i
$887$	129.426	+	74.7243i	0.145915	+	0.0842439i	0.571180	−	0.820825i	$-0.306486\pi$
$887$	129.426	+	74.7243i	0.145915	+	0.0842439i	−0.425265	+	0.905069i	$0.639819\pi$
$888$		0			0
$889$	20.3948	+	35.3248i	0.0229412	+	0.0397354i
$890$			554.632i			0.623183i
$891$		0			0
$892$	−1451.35			−1.62707
$893$	464.014	−	267.898i	0.519612	−	0.299998i
$894$		0			0
$895$	98.9581	−	171.400i	0.110568	−	0.191509i
$896$	−468.260	−	270.350i	−0.522612	−	0.301730i
$897$		0			0
$898$	−259.616	−	449.667i	−0.289104	−	0.500743i
$899$		−	272.610i		−	0.303237i
$900$		0			0
$901$	68.7687			0.0763249
$902$	1430.54	−	825.922i	1.58596	−	0.915657i
$903$		0			0
$904$	163.694	−	283.527i	0.181078	−	0.313636i
$905$	−251.565	−	145.241i	−0.277973	−	0.160488i
$906$		0			0
$907$	−296.859	−	514.174i	−0.327297	−	0.566896i	0.654677	−	0.755909i	$-0.272805\pi$
$907$	−296.859	−	514.174i	−0.327297	−	0.566896i	−0.981975	+	0.189013i	$0.939471\pi$
$908$		−	1472.35i		−	1.62154i
$909$		0			0
$910$	−134.162			−0.147431
$911$	−981.854	+	566.874i	−1.07778	+	0.622254i	−0.930296	−	0.366811i	$-0.880450\pi$
$911$	−981.854	+	566.874i	−1.07778	+	0.622254i	−0.147480	+	0.989065i	$0.547116\pi$
$912$		0			0
$913$	−260.435	+	451.087i	−0.285252	+	0.494071i
$914$	371.070	+	214.237i	0.405984	+	0.234395i
$915$		0			0
$916$	169.195	+	293.055i	0.184711	+	0.319929i
$917$		−	484.464i		−	0.528314i
$918$		0			0
$919$	−684.988			−0.745363			−0.372681	−	0.927959i	$-0.621562\pi$
$919$	−684.988			−0.745363			−0.372681	+	0.927959i	$0.621562\pi$
$920$	−413.688	+	238.843i	−0.449661	+	0.259612i
$921$		0			0
$922$	−1055.44	+	1828.07i	−1.14473	+	1.98273i
$923$	711.618	+	410.853i	0.770984	+	0.445128i
$924$		0			0
$925$	387.524	+	671.212i	0.418945	+	0.725634i
$926$		−	2233.49i		−	2.41197i
$927$		0			0
$928$	80.4654			0.0867084
$929$	166.551	−	96.1584i	0.179280	−	0.103507i	−0.407674	−	0.913127i	$-0.633660\pi$
$929$	166.551	−	96.1584i	0.179280	−	0.103507i	0.586954	+	0.809620i	$0.300327\pi$
$930$		0			0
$931$	−56.8006	+	98.3816i	−0.0610104	+	0.105673i
$932$	−2783.91	−	1607.29i	−2.98702	−	1.72456i
$933$		0			0
$934$	1345.76	+	2330.92i	1.44086	+	2.49563i
$935$		−	39.4313i		−	0.0421725i
$936$		0			0
$937$	−1270.28			−1.35569			−0.677844	−	0.735206i	$-0.737086\pi$
$937$	−1270.28			−1.35569			−0.677844	+	0.735206i	$0.737086\pi$
$938$	121.830	−	70.3385i	0.129883	−	0.0749877i
$939$		0			0
$940$	169.992	−	294.435i	0.180843	−	0.313229i
$941$	135.923	+	78.4754i	0.144446	+	0.0833957i	0.570481	−	0.821311i	$-0.306757\pi$
$941$	135.923	+	78.4754i	0.144446	+	0.0833957i	−0.426035	+	0.904706i	$0.640090\pi$
$942$		0			0
$943$	−858.863	−	1487.59i	−0.910777	−	1.57751i
$944$		−	1809.39i		−	1.91673i
$945$		0			0
$946$	593.077			0.626931
$947$	−762.055	+	439.973i	−0.804704	+	0.464596i	−0.845114	−	0.534587i	$-0.820467\pi$
$947$	−762.055	+	439.973i	−0.804704	+	0.464596i	0.0404090	+	0.999183i	$0.487134\pi$
$948$		0			0
$949$	−447.136	+	774.462i	−0.471165	+	0.816082i
$950$	−1155.85	−	667.329i	−1.21668	−	0.702451i
$951$		0			0
$952$	90.1216	+	156.095i	0.0946655	+	0.163965i
$953$		−	563.276i		−	0.591056i	−0.955334	−	0.295528i	$-0.904505\pi$
$953$		−	563.276i		−	0.591056i	0.955334	−	0.295528i	$-0.0954955\pi$
$954$		0			0
$955$	357.948			0.374814
$956$	−355.607	+	205.310i	−0.371974	+	0.214759i
$957$		0			0
$958$	−690.413	+	1195.83i	−0.720682	+	1.24826i
$959$	75.6475	+	43.6751i	0.0788816	+	0.0455423i
$960$		0			0
$961$	68.4111	+	118.491i	0.0711874	+	0.123300i
$962$			1349.02i			1.40230i
$963$		0			0
$964$	−2696.79			−2.79750
$965$	−82.9501	+	47.8913i	−0.0859587	+	0.0496283i
$966$		0			0
$967$	−118.838	+	205.833i	−0.122893	+	0.212858i	−0.920908	−	0.389781i	$-0.872551\pi$
$967$	−118.838	+	205.833i	−0.122893	+	0.212858i	0.798014	+	0.602639i	$0.205884\pi$
$968$	935.993	+	540.396i	0.966935	+	0.558260i
$969$		0			0
$970$	50.4353	+	87.3565i	0.0519951	+	0.0900582i
$971$			1355.00i			1.39546i	0.716359	+	0.697732i	$0.245808\pi$
$971$			1355.00i			1.39546i	−0.716359	+	0.697732i	$0.754192\pi$
$972$		0			0
$973$	171.026			0.175772
$974$	1741.00	−	1005.16i	1.78747	−	1.03200i
$975$		0			0
$976$	563.210	−	975.508i	0.577059	−	0.999496i
$977$	−427.579	−	246.863i	−0.437645	−	0.252674i	0.264953	−	0.964261i	$-0.414643\pi$
$977$	−427.579	−	246.863i	−0.437645	−	0.252674i	−0.702598	+	0.711587i	$0.747977\pi$
$978$		0			0
$979$	446.575	+	773.491i	0.456154	+	0.790083i
$980$			72.0845i			0.0735556i
$981$		0			0
$982$	−598.797			−0.609773
$983$	1331.99	−	769.026i	1.35503	−	0.782325i	0.366078	−	0.930584i	$-0.380700\pi$
$983$	1331.99	−	769.026i	1.35503	−	0.782325i	0.988949	+	0.148259i	$0.0473670\pi$
$984$		0			0
$985$	−84.7229	+	146.744i	−0.0860130	+	0.148979i
$986$	130.545	+	75.3705i	0.132399	+	0.0764406i
$987$		0			0
$988$	−783.531	−	1357.11i	−0.793047	−	1.37360i
$989$		−	616.731i		−	0.623590i
$990$		0			0
$991$	1514.73			1.52849			0.764243	−	0.644929i	$-0.223113\pi$
$991$	1514.73			1.52849			0.764243	+	0.644929i	$0.223113\pi$
$992$	210.678	−	121.635i	0.212377	−	0.122616i
$993$		0			0
$994$	327.243	−	566.802i	0.329218	−	0.570223i
$995$	93.1267	+	53.7667i	0.0935946	+	0.0540369i
$996$		0			0
$997$	−913.216	−	1581.74i	−0.915964	−	1.58650i	−0.805484	−	0.592618i	$-0.798094\pi$
$997$	−913.216	−	1581.74i	−0.915964	−	1.58650i	−0.110481	−	0.993878i	$-0.535239\pi$
$998$		−	2972.37i		−	2.97833i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.r.c.134.4		8
3.2	odd	2	inner	567.3.r.c.134.1		8
9.2	odd	6	inner	567.3.r.c.512.4		8
9.4	even	3		21.3.b.a.8.4	yes	4
9.5	odd	6		21.3.b.a.8.1	✓	4
9.7	even	3	inner	567.3.r.c.512.1		8
36.23	even	6		336.3.d.c.113.1		4
36.31	odd	6		336.3.d.c.113.2		4
45.4	even	6		525.3.c.a.176.1		4
45.13	odd	12		525.3.f.a.449.8		8
45.14	odd	6		525.3.c.a.176.4		4
45.22	odd	12		525.3.f.a.449.1		8
45.23	even	12		525.3.f.a.449.2		8
45.32	even	12		525.3.f.a.449.7		8
63.4	even	3		147.3.h.e.128.1		8
63.5	even	6		147.3.h.c.116.1		8
63.13	odd	6		147.3.b.f.50.4		4
63.23	odd	6		147.3.h.e.116.1		8
63.31	odd	6		147.3.h.c.128.1		8
63.32	odd	6		147.3.h.e.128.4		8
63.40	odd	6		147.3.h.c.116.4		8
63.41	even	6		147.3.b.f.50.1		4
63.58	even	3		147.3.h.e.116.4		8
63.59	even	6		147.3.h.c.128.4		8
72.5	odd	6		1344.3.d.f.449.1		4
72.13	even	6		1344.3.d.f.449.2		4
72.59	even	6		1344.3.d.b.449.4		4
72.67	odd	6		1344.3.d.b.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	9.5	odd	6
21.3.b.a.8.4	yes	4	9.4	even	3
147.3.b.f.50.1		4	63.41	even	6
147.3.b.f.50.4		4	63.13	odd	6
147.3.h.c.116.1		8	63.5	even	6
147.3.h.c.116.4		8	63.40	odd	6
147.3.h.c.128.1		8	63.31	odd	6
147.3.h.c.128.4		8	63.59	even	6
147.3.h.e.116.1		8	63.23	odd	6
147.3.h.e.116.4		8	63.58	even	3
147.3.h.e.128.1		8	63.4	even	3
147.3.h.e.128.4		8	63.32	odd	6
336.3.d.c.113.1		4	36.23	even	6
336.3.d.c.113.2		4	36.31	odd	6
525.3.c.a.176.1		4	45.4	even	6
525.3.c.a.176.4		4	45.14	odd	6
525.3.f.a.449.1		8	45.22	odd	12
525.3.f.a.449.2		8	45.23	even	12
525.3.f.a.449.7		8	45.32	even	12
525.3.f.a.449.8		8	45.13	odd	12
567.3.r.c.134.1		8	3.2	odd	2	inner
567.3.r.c.134.4		8	1.1	even	1	trivial
567.3.r.c.512.1		8	9.7	even	3	inner
567.3.r.c.512.4		8	9.2	odd	6	inner
1344.3.d.b.449.3		4	72.67	odd	6
1344.3.d.b.449.4		4	72.59	even	6
1344.3.d.f.449.1		4	72.5	odd	6
1344.3.d.f.449.2		4	72.13	even	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.03622 - 1.75296i) q^{2} +(4.14575 - 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(-1.32288 - 2.29129i) q^{7} -15.0457i q^{8} +O(q^{10})\)	\(q+(3.03622 - 1.75296i) q^{2} +(4.14575 - 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(-1.32288 - 2.29129i) q^{7} -15.0457i q^{8} +4.35425 q^{10} +(6.07244 - 3.50592i) q^{11} +(5.82288 - 10.0855i) q^{13} +(-8.03308 - 4.63790i) q^{14} +(-9.79150 - 16.9594i) q^{16} -4.52791i q^{17} +16.2288 q^{19} +(8.91815 - 5.14889i) q^{20} +(12.2915 - 21.2895i) q^{22} +(-22.1386 - 12.7817i) q^{23} +(-11.7288 - 20.3148i) q^{25} -40.8291i q^{26} -21.9373 q^{28} +(-8.22359 + 4.74789i) q^{29} +(-14.3542 + 24.8623i) q^{31} +(-7.33853 - 4.23690i) q^{32} +(-7.93725 - 13.7477i) q^{34} -3.28594i q^{35} -33.0405 q^{37} +(49.2741 - 28.4484i) q^{38} +(9.34313 - 16.1828i) q^{40} +(58.1922 + 33.5973i) q^{41} +(12.0627 + 20.8933i) q^{43} -58.1388i q^{44} -89.6235 q^{46} +(28.5921 - 16.5076i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-71.2222 - 41.1201i) q^{50} +(-48.2804 - 83.6241i) q^{52} +15.1877i q^{53} +8.70850 q^{55} +(-34.4740 + 19.9036i) q^{56} +(-16.6458 + 28.8313i) q^{58} +(80.0173 + 46.1980i) q^{59} +(28.7601 + 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(12.5259 - 7.23183i) q^{65} +(-7.58301 + 13.1342i) q^{67} +(-32.5133 - 18.7716i) q^{68} +(-5.76013 - 9.97684i) q^{70} +70.5584i q^{71} -76.7895 q^{73} +(-100.318 + 57.9188i) q^{74} +(67.2804 - 116.533i) q^{76} +(-16.0662 - 9.27580i) q^{77} +(-63.6235 - 110.199i) q^{79} -24.3215i q^{80} +235.579 q^{82} +(-64.3321 + 37.1422i) q^{83} +(2.81176 - 4.87011i) q^{85} +(73.2503 + 42.2911i) q^{86} +(-52.7490 - 91.3640i) q^{88} +127.377i q^{89} -30.8118 q^{91} +(-183.562 + 105.980i) q^{92} +(57.8745 - 100.242i) q^{94} +(17.4553 + 10.0778i) q^{95} +(11.5830 + 20.0624i) q^{97} +24.5415i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4}+O(q^{10}) \) 8 * q + 12 * q^4	\( 8 q + 12 q^{4} + 56 q^{10} + 36 q^{13} - 36 q^{16} + 24 q^{19} + 56 q^{22} + 12 q^{25} - 112 q^{28} - 136 q^{31} + 32 q^{37} - 84 q^{40} + 160 q^{43} - 336 q^{46} - 28 q^{49} - 164 q^{52} + 112 q^{55} - 112 q^{58} + 156 q^{61} + 8 q^{64} + 24 q^{67} + 28 q^{70} - 64 q^{73} + 316 q^{76} - 128 q^{79} + 784 q^{82} - 168 q^{85} - 168 q^{88} - 56 q^{91} + 336 q^{94} + 8 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 + 56 * q^10 + 36 * q^13 - 36 * q^16 + 24 * q^19 + 56 * q^22 + 12 * q^25 - 112 * q^28 - 136 * q^31 + 32 * q^37 - 84 * q^40 + 160 * q^43 - 336 * q^46 - 28 * q^49 - 164 * q^52 + 112 * q^55 - 112 * q^58 + 156 * q^61 + 8 * q^64 + 24 * q^67 + 28 * q^70 - 64 * q^73 + 316 * q^76 - 128 * q^79 + 784 * q^82 - 168 * q^85 - 168 * q^88 - 56 * q^91 + 336 * q^94 + 8 * q^97

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