LMFDB - Embedded newform 136.3.t.a.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	136.97
Dual form			136.3.t.a.129.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30540 + 1.54042i) q^{3} +(5.10009 + 1.01447i) q^{5} +(-1.70555 + 0.339255i) q^{7} +(-0.502166 + 1.21234i) q^{9} +O(q^{10})$	\(q+(-2.30540 + 1.54042i) q^{3} +(5.10009 + 1.01447i) q^{5} +(-1.70555 + 0.339255i) q^{7} +(-0.502166 + 1.21234i) q^{9} +(-7.03331 + 10.5261i) q^{11} +(7.79731 + 7.79731i) q^{13} +(-13.3205 + 5.51752i) q^{15} +(-3.27621 + 16.6813i) q^{17} +(5.87515 + 14.1839i) q^{19} +(3.40939 - 3.40939i) q^{21} +(5.68800 + 3.80060i) q^{23} +(1.88474 + 0.780685i) q^{25} +(-5.57813 - 28.0431i) q^{27} +(8.05543 - 40.4974i) q^{29} +(2.61189 + 3.90897i) q^{31} -35.1012i q^{33} -9.04262 q^{35} +(22.6769 - 15.1522i) q^{37} +(-29.9871 - 5.96480i) q^{39} +(28.9062 - 5.74980i) q^{41} +(13.6306 - 32.9071i) q^{43} +(-3.79097 + 5.67358i) q^{45} +(13.6173 + 13.6173i) q^{47} +(-42.4763 + 17.5943i) q^{49} +(-18.1433 - 43.5039i) q^{51} +(16.1037 + 38.8777i) q^{53} +(-46.5489 + 46.5489i) q^{55} +(-35.3937 - 23.6493i) q^{57} +(68.7830 + 28.4908i) q^{59} +(-8.57149 - 43.0918i) q^{61} +(0.445178 - 2.23806i) q^{63} +(31.8568 + 47.6771i) q^{65} -120.452i q^{67} -18.9676 q^{69} +(35.3204 - 23.6003i) q^{71} +(-39.8798 - 7.93258i) q^{73} +(-5.54767 + 1.10350i) q^{75} +(8.42464 - 20.3389i) q^{77} +(-60.9820 + 91.2660i) q^{79} +(47.7071 + 47.7071i) q^{81} +(130.045 - 53.8664i) q^{83} +(-33.6317 + 81.7526i) q^{85} +(43.8120 + 105.772i) q^{87} +(-89.1222 + 89.1222i) q^{89} +(-15.9440 - 10.6534i) q^{91} +(-12.0429 - 4.98834i) q^{93} +(15.5746 + 78.2990i) q^{95} +(24.4520 - 122.928i) q^{97} +(-9.22927 - 13.8126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.30540	+	1.54042i	−0.768468	+	0.513474i	−0.876925	−	0.480628i	$-0.840409\pi$
$3$	−2.30540	+	1.54042i	−0.768468	+	0.513474i	0.108457	+	0.994101i	$0.465409\pi$
$4$		0			0
$5$	5.10009	+	1.01447i	1.02002	+	0.202894i	0.676648	−	0.736307i	$-0.263432\pi$
$5$	5.10009	+	1.01447i	1.02002	+	0.202894i	0.343369	+	0.939201i	$0.388432\pi$
$6$		0			0
$7$	−1.70555	+	0.339255i	−0.243650	+	0.0484650i	−0.315405	−	0.948957i	$-0.602140\pi$
$7$	−1.70555	+	0.339255i	−0.243650	+	0.0484650i	0.0717544	+	0.997422i	$0.477140\pi$
$8$		0			0
$9$	−0.502166	+	1.21234i	−0.0557962	+	0.134704i
$10$		0			0
$11$	−7.03331	+	10.5261i	−0.639392	+	0.956918i	0.360318	+	0.932830i	$0.382668\pi$
$11$	−7.03331	+	10.5261i	−0.639392	+	0.956918i	−0.999710	+	0.0240883i	$0.992332\pi$
$12$		0			0
$13$	7.79731	+	7.79731i	0.599793	+	0.599793i	0.940257	−	0.340464i	$-0.110584\pi$
$13$	7.79731	+	7.79731i	0.599793	+	0.599793i	−0.340464	+	0.940257i	$0.610584\pi$
$14$		0			0
$15$	−13.3205	+	5.51752i	−0.888031	+	0.367834i
$16$		0			0
$17$	−3.27621	+	16.6813i	−0.192718	+	0.981254i
$17$	−3.27621	+	16.6813i	−0.192718	+	0.981254i
$18$		0			0
$19$	5.87515	+	14.1839i	0.309218	+	0.746519i	0.999731	+	0.0231985i	$0.00738497\pi$
$19$	5.87515	+	14.1839i	0.309218	+	0.746519i	−0.690513	+	0.723320i	$0.742615\pi$
$20$		0			0
$21$	3.40939	−	3.40939i	0.162352	−	0.162352i
$22$		0			0
$23$	5.68800	+	3.80060i	0.247304	+	0.165243i	0.673044	−	0.739602i	$-0.264986\pi$
$23$	5.68800	+	3.80060i	0.247304	+	0.165243i	−0.425740	+	0.904845i	$0.639986\pi$
$24$		0			0
$25$	1.88474	+	0.780685i	0.0753896	+	0.0312274i
$26$		0			0
$27$	−5.57813	−	28.0431i	−0.206597	−	1.03863i
$28$		0			0
$29$	8.05543	−	40.4974i	0.277773	−	1.39646i	−0.549890	−	0.835237i	$-0.685330\pi$
$29$	8.05543	−	40.4974i	0.277773	−	1.39646i	0.827664	−	0.561224i	$-0.189670\pi$
$30$		0			0
$31$	2.61189	+	3.90897i	0.0842546	+	0.126096i	0.871203	−	0.490923i	$-0.163340\pi$
$31$	2.61189	+	3.90897i	0.0842546	+	0.126096i	−0.786948	+	0.617019i	$0.788340\pi$
$32$		0			0
$33$		−	35.1012i		−	1.06367i
$34$		0			0
$35$	−9.04262			−0.258361
$36$		0			0
$37$	22.6769	−	15.1522i	0.612889	−	0.409519i	−0.210016	−	0.977698i	$-0.567352\pi$
$37$	22.6769	−	15.1522i	0.612889	−	0.409519i	0.822905	+	0.568178i	$0.192352\pi$
$38$		0			0
$39$	−29.9871	−	5.96480i	−0.768900	−	0.152944i
$40$		0			0
$41$	28.9062	−	5.74980i	0.705030	−	0.140239i	0.170461	−	0.985364i	$-0.445474\pi$
$41$	28.9062	−	5.74980i	0.705030	−	0.140239i	0.534568	+	0.845125i	$0.320474\pi$
$42$		0			0
$43$	13.6306	−	32.9071i	0.316990	−	0.765282i	−0.682421	−	0.730960i	$-0.739073\pi$
$43$	13.6306	−	32.9071i	0.316990	−	0.765282i	0.999411	−	0.0343221i	$-0.0109272\pi$
$44$		0			0
$45$	−3.79097	+	5.67358i	−0.0842437	+	0.126080i
$46$		0			0
$47$	13.6173	+	13.6173i	0.289729	+	0.289729i	0.836973	−	0.547244i	$-0.184323\pi$
$47$	13.6173	+	13.6173i	0.289729	+	0.289729i	−0.547244	+	0.836973i	$0.684323\pi$
$48$		0			0
$49$	−42.4763	+	17.5943i	−0.866863	+	0.359066i
$50$		0			0
$51$	−18.1433	−	43.5039i	−0.355750	−	0.853018i
$52$		0			0
$53$	16.1037	+	38.8777i	0.303843	+	0.733541i	0.999879	+	0.0155349i	$0.00494512\pi$
$53$	16.1037	+	38.8777i	0.303843	+	0.733541i	−0.696037	+	0.718006i	$0.745055\pi$
$54$		0			0
$55$	−46.5489	+	46.5489i	−0.846344	+	0.846344i
$56$		0			0
$57$	−35.3937	−	23.6493i	−0.620942	−	0.414900i
$58$		0			0
$59$	68.7830	+	28.4908i	1.16581	+	0.482896i	0.879806	−	0.475332i	$-0.157672\pi$
$59$	68.7830	+	28.4908i	1.16581	+	0.482896i	0.286007	+	0.958228i	$0.407672\pi$
$60$		0			0
$61$	−8.57149	−	43.0918i	−0.140516	−	0.706423i	−0.985234	−	0.171211i	$-0.945232\pi$
$61$	−8.57149	−	43.0918i	−0.140516	−	0.706423i	0.844718	−	0.535212i	$-0.179768\pi$
$62$		0			0
$63$	0.445178	−	2.23806i	0.00706632	−	0.0355248i
$64$		0			0
$65$	31.8568	+	47.6771i	0.490105	+	0.733494i
$66$		0			0
$67$		−	120.452i		−	1.79779i	−0.438161	−	0.898896i	$-0.644370\pi$
$67$		−	120.452i		−	1.79779i	0.438161	−	0.898896i	$-0.355630\pi$
$68$		0			0
$69$	−18.9676			−0.274893
$70$		0			0
$71$	35.3204	−	23.6003i	0.497470	−	0.332399i	−0.281393	−	0.959592i	$-0.590797\pi$
$71$	35.3204	−	23.6003i	0.497470	−	0.332399i	0.778863	+	0.627194i	$0.215797\pi$
$72$		0			0
$73$	−39.8798	−	7.93258i	−0.546298	−	0.108666i	−0.0857774	−	0.996314i	$-0.527337\pi$
$73$	−39.8798	−	7.93258i	−0.546298	−	0.108666i	−0.460521	+	0.887649i	$0.652337\pi$
$74$		0			0
$75$	−5.54767	+	1.10350i	−0.0739689	+	0.0147133i
$76$		0			0
$77$	8.42464	−	20.3389i	0.109411	−	0.264141i
$78$		0			0
$79$	−60.9820	+	91.2660i	−0.771924	+	1.15527i	0.212103	+	0.977247i	$0.431969\pi$
$79$	−60.9820	+	91.2660i	−0.771924	+	1.15527i	−0.984027	+	0.178019i	$0.943031\pi$
$80$		0			0
$81$	47.7071	+	47.7071i	0.588977	+	0.588977i
$82$		0			0
$83$	130.045	−	53.8664i	1.56681	−	0.648992i	0.580551	−	0.814224i	$-0.302837\pi$
$83$	130.045	−	53.8664i	1.56681	−	0.648992i	0.986255	+	0.165231i	$0.0528370\pi$
$84$		0			0
$85$	−33.6317	+	81.7526i	−0.395667	+	0.961795i
$86$		0			0
$87$	43.8120	+	105.772i	0.503586	+	1.21576i
$88$		0			0
$89$	−89.1222	+	89.1222i	−1.00137	+	1.00137i	−0.00137423	+	0.999999i	$0.500437\pi$
$89$	−89.1222	+	89.1222i	−1.00137	+	1.00137i	−0.999999	+	0.00137423i	$0.999563\pi$
$90$		0			0
$91$	−15.9440	−	10.6534i	−0.175209	−	0.117071i
$92$		0			0
$93$	−12.0429	−	4.98834i	−0.129494	−	0.0536381i
$94$		0			0
$95$	15.5746	+	78.2990i	0.163944	+	0.824201i
$96$		0			0
$97$	24.4520	−	122.928i	0.252082	−	1.26730i	−0.622574	−	0.782561i	$-0.713913\pi$
$97$	24.4520	−	122.928i	0.252082	−	1.26730i	0.874657	−	0.484743i	$-0.161087\pi$
$98$		0			0
$99$	−9.22927	−	13.8126i	−0.0932250	−	0.139521i
$100$		0			0
$101$			136.980i			1.35624i	0.734953	+	0.678118i	$0.237204\pi$
$101$			136.980i			1.35624i	−0.734953	+	0.678118i	$0.762796\pi$
$102$		0			0
$103$	22.0660			0.214233			0.107117	−	0.994246i	$-0.465838\pi$
$103$	22.0660			0.214233			0.107117	+	0.994246i	$0.465838\pi$
$104$		0			0
$105$	20.8469	−	13.9294i	0.198542	−	0.132661i
$106$		0			0
$107$	60.6631	+	12.0666i	0.566944	+	0.112772i	0.470236	−	0.882541i	$-0.344169\pi$
$107$	60.6631	+	12.0666i	0.566944	+	0.112772i	0.0967081	+	0.995313i	$0.469169\pi$
$108$		0			0
$109$	−183.962	+	36.5923i	−1.68772	+	0.335709i	−0.943286	−	0.331982i	$-0.892283\pi$
$109$	−183.962	+	36.5923i	−1.68772	+	0.335709i	−0.744438	+	0.667691i	$0.767283\pi$
$110$		0			0
$111$	−28.9386	+	69.8639i	−0.260708	+	0.629405i
$112$		0			0
$113$	7.53437	−	11.2760i	0.0666758	−	0.0997874i	−0.796633	−	0.604463i	$-0.793388\pi$
$113$	7.53437	−	11.2760i	0.0666758	−	0.0997874i	0.863309	+	0.504675i	$0.168388\pi$
$114$		0			0
$115$	25.1537	+	25.1537i	0.218728	+	0.218728i
$116$		0			0
$117$	−13.3685	+	5.53741i	−0.114261	+	0.0473283i
$118$		0			0
$119$	−0.0714813	−	29.5623i	−0.000600683	−	0.248423i
$120$		0			0
$121$	−15.0265	−	36.2772i	−0.124186	−	0.299812i
$122$		0			0
$123$	−57.7833	+	57.7833i	−0.469783	+	0.469783i
$124$		0			0
$125$	−99.2708	−	66.3306i	−0.794166	−	0.530645i
$126$		0			0
$127$	82.8548	+	34.3196i	0.652400	+	0.270233i	0.684236	−	0.729260i	$-0.260136\pi$
$127$	82.8548	+	34.3196i	0.652400	+	0.270233i	−0.0318366	+	0.999493i	$0.510136\pi$
$128$		0			0
$129$	19.2668	+	96.8610i	0.149355	+	0.750860i
$130$		0			0
$131$	42.6919	−	214.626i	0.325892	−	1.63837i	−0.376383	−	0.926464i	$-0.622832\pi$
$131$	42.6919	−	214.626i	0.325892	−	1.63837i	0.702275	−	0.711906i	$-0.252168\pi$
$132$		0			0
$133$	−14.8323	−	22.1981i	−0.111521	−	0.166903i
$134$		0			0
$135$		−	148.681i		−	1.10134i
$136$		0			0
$137$	207.423			1.51404			0.757019	−	0.653392i	$-0.226655\pi$
$137$	207.423			1.51404			0.757019	+	0.653392i	$0.226655\pi$
$138$		0			0
$139$	−79.3172	+	52.9980i	−0.570627	+	0.381281i	−0.807151	−	0.590345i	$-0.798992\pi$
$139$	−79.3172	+	52.9980i	−0.570627	+	0.381281i	0.236524	+	0.971626i	$0.423992\pi$
$140$		0			0
$141$	−52.3696	−	10.4170i	−0.371416	−	0.0738792i
$142$		0			0
$143$	−136.916	+	27.2343i	−0.957456	+	0.190450i
$144$		0			0
$145$	82.1668	−	198.368i	0.566667	−	1.36806i
$146$		0			0
$147$	70.8224	−	105.993i	0.481785	−	0.721042i
$148$		0			0
$149$	134.018	+	134.018i	0.899453	+	0.899453i	0.995388	−	0.0959347i	$-0.0305840\pi$
$149$	134.018	+	134.018i	0.899453	+	0.899453i	−0.0959347	+	0.995388i	$0.530584\pi$
$150$		0			0
$151$	29.3818	−	12.1703i	0.194581	−	0.0805982i	−0.283265	−	0.959042i	$-0.591418\pi$
$151$	29.3818	−	12.1703i	0.194581	−	0.0805982i	0.477846	+	0.878443i	$0.341418\pi$
$152$		0			0
$153$	−18.5782	−	12.3487i	−0.121426	−	0.0807102i
$154$		0			0
$155$	9.35534	+	22.5858i	0.0603570	+	0.145715i
$156$		0			0
$157$	60.1557	−	60.1557i	0.383157	−	0.383157i	−0.489081	−	0.872238i	$-0.662668\pi$
$157$	60.1557	−	60.1557i	0.383157	−	0.383157i	0.872238	+	0.489081i	$0.162668\pi$
$158$		0			0
$159$	−97.0134	−	64.8223i	−0.610147	−	0.407687i
$160$		0			0
$161$	−10.9905	−	4.55243i	−0.0682642	−	0.0282760i
$162$		0			0
$163$	27.3641	+	137.568i	0.167878	+	0.843978i	0.969300	+	0.245880i	$0.0790769\pi$
$163$	27.3641	+	137.568i	0.167878	+	0.843978i	−0.801423	+	0.598099i	$0.795923\pi$
$164$		0			0
$165$	35.6091	−	179.019i	0.215813	−	1.08496i
$166$		0			0
$167$	−169.962	−	254.366i	−1.01774	−	1.52315i	−0.842552	−	0.538615i	$-0.818948\pi$
$167$	−169.962	−	254.366i	−1.01774	−	1.52315i	−0.175184	−	0.984536i	$-0.556052\pi$
$168$		0			0
$169$		−	47.4039i		−	0.280496i
$170$		0			0
$171$	−20.1459			−0.117812
$172$		0			0
$173$	242.131	−	161.787i	1.39960	−	0.935182i	0.399772	−	0.916615i	$-0.369089\pi$
$173$	242.131	−	161.787i	1.39960	−	0.935182i	0.999828	−	0.0185674i	$-0.00591053\pi$
$174$		0			0
$175$	−3.47937	−	0.692090i	−0.0198821	−	0.00395480i
$176$		0			0
$177$	−202.460	+	40.2719i	−1.14384	+	0.227525i
$178$		0			0
$179$	−37.9878	+	91.7108i	−0.212223	+	0.512351i	−0.993764	−	0.111502i	$-0.964434\pi$
$179$	−37.9878	+	91.7108i	−0.212223	+	0.512351i	0.781542	+	0.623853i	$0.214434\pi$
$180$		0			0
$181$	123.016	−	184.106i	0.679646	−	1.01716i	−0.317966	−	0.948102i	$-0.603000\pi$
$181$	123.016	−	184.106i	0.679646	−	1.01716i	0.997612	−	0.0690606i	$-0.0220002\pi$
$182$		0			0
$183$	86.1402	+	86.1402i	0.470712	+	0.470712i
$184$		0			0
$185$	131.026	−	54.2726i	0.708247	−	0.293365i
$186$		0			0
$187$	−152.547	−	151.811i	−0.815757	−	0.811822i
$188$		0			0
$189$	19.0276	+	45.9366i	0.100675	+	0.243051i
$190$		0			0
$191$	−147.902	+	147.902i	−0.774357	+	0.774357i	−0.978865	−	0.204508i	$-0.934441\pi$
$191$	−147.902	+	147.902i	−0.774357	+	0.774357i	0.204508	+	0.978865i	$0.434441\pi$
$192$		0			0
$193$	−106.643	−	71.2567i	−0.552556	−	0.369206i	0.247726	−	0.968830i	$-0.420317\pi$
$193$	−106.643	−	71.2567i	−0.552556	−	0.369206i	−0.800282	+	0.599624i	$0.795317\pi$
$194$		0			0
$195$	−146.886	−	60.8420i	−0.753259	−	0.312010i
$196$		0			0
$197$	42.4827	+	213.575i	0.215648	+	1.08414i	0.925199	+	0.379483i	$0.123898\pi$
$197$	42.4827	+	213.575i	0.215648	+	1.08414i	−0.709551	+	0.704654i	$0.751102\pi$
$198$		0			0
$199$	−34.8779	+	175.343i	−0.175266	+	0.881121i	0.788635	+	0.614861i	$0.210788\pi$
$199$	−34.8779	+	175.343i	−0.175266	+	0.881121i	−0.963901	+	0.266260i	$0.914212\pi$
$200$		0			0
$201$	185.547	+	277.691i	0.923119	+	1.38155i
$202$		0			0
$203$			71.8032i			0.353710i
$204$		0			0
$205$	153.257			0.747596
$206$		0			0
$207$	−7.46392	+	4.98723i	−0.0360576	+	0.0240929i
$208$		0			0
$209$	−190.622	−	37.9171i	−0.912069	−	0.181422i
$210$		0			0
$211$	−228.993	+	45.5496i	−1.08528	+	0.215875i	−0.705149	−	0.709059i	$-0.749120\pi$
$211$	−228.993	+	45.5496i	−1.08528	+	0.215875i	−0.380127	+	0.924934i	$0.624120\pi$
$212$		0			0
$213$	−45.0732	+	108.816i	−0.211611	+	0.510875i
$214$		0			0
$215$	102.900	−	154.001i	0.478606	−	0.716285i
$216$		0			0
$217$	−5.78085	−	5.78085i	−0.0266399	−	0.0266399i
$218$		0			0
$219$	104.158	−	43.1439i	0.475609	−	0.197004i
$220$		0			0
$221$	−155.615	+	104.524i	−0.704141	+	0.472958i
$222$		0			0
$223$	135.546	+	327.238i	0.607832	+	1.46744i	0.865353	+	0.501163i	$0.167094\pi$
$223$	135.546	+	327.238i	0.607832	+	1.46744i	−0.257521	+	0.966273i	$0.582906\pi$
$224$		0			0
$225$	−1.89290	+	1.89290i	−0.00841291	+	0.00841291i
$226$		0			0
$227$	106.365	+	71.0706i	0.468567	+	0.313086i	0.767343	−	0.641237i	$-0.221578\pi$
$227$	106.365	+	71.0706i	0.468567	+	0.313086i	−0.298776	+	0.954323i	$0.596578\pi$
$228$		0			0
$229$	−63.6254	−	26.3545i	−0.277840	−	0.115085i	0.239412	−	0.970918i	$-0.423045\pi$
$229$	−63.6254	−	26.3545i	−0.277840	−	0.115085i	−0.517253	+	0.855833i	$0.673045\pi$
$230$		0			0
$231$	11.9082	+	59.8668i	0.0515509	+	0.259164i
$232$		0			0
$233$	−41.4903	+	208.586i	−0.178070	+	0.895217i	0.783654	+	0.621197i	$0.213353\pi$
$233$	−41.4903	+	208.586i	−0.178070	+	0.895217i	−0.961724	+	0.274020i	$0.911647\pi$
$234$		0			0
$235$	55.6350	+	83.2636i	0.236745	+	0.354313i
$236$		0			0
$237$		−	304.343i		−	1.28415i
$238$		0			0
$239$	362.320			1.51598			0.757991	−	0.652265i	$-0.226181\pi$
$239$	362.320			1.51598			0.757991	+	0.652265i	$0.226181\pi$
$240$		0			0
$241$	263.742	−	176.227i	1.09437	−	0.731233i	0.128874	−	0.991661i	$-0.458864\pi$
$241$	263.742	−	176.227i	1.09437	−	0.731233i	0.965493	+	0.260428i	$0.0838638\pi$
$242$		0			0
$243$	68.9151	+	13.7081i	0.283601	+	0.0564118i
$244$		0			0
$245$	−234.482	+	46.6413i	−0.957068	+	0.190373i
$246$		0			0
$247$	−64.7856	+	156.406i	−0.262290	+	0.633224i
$248$		0			0
$249$	−216.829	+	324.508i	−0.870799	+	1.30324i
$250$		0			0
$251$	160.188	+	160.188i	0.638199	+	0.638199i	0.950111	−	0.311912i	$-0.100969\pi$
$251$	160.188	+	160.188i	0.638199	+	0.638199i	−0.311912	+	0.950111i	$0.600969\pi$
$252$		0			0
$253$	−80.0109	+	33.1416i	−0.316249	+	0.130995i
$254$		0			0
$255$	−48.3988	−	240.279i	−0.189799	−	0.942272i
$256$		0			0
$257$	−123.520	−	298.203i	−0.480621	−	1.16032i	−0.959314	−	0.282340i	$-0.908889\pi$
$257$	−123.520	−	298.203i	−0.480621	−	1.16032i	0.478693	−	0.877982i	$-0.341111\pi$
$258$		0			0
$259$	−33.5361	+	33.5361i	−0.129483	+	0.129483i
$260$		0			0
$261$	45.0513	+	30.1023i	0.172610	+	0.115334i
$262$		0			0
$263$	−266.395	−	110.345i	−1.01291	−	0.419561i	−0.186395	−	0.982475i	$-0.559680\pi$
$263$	−266.395	−	110.345i	−1.01291	−	0.419561i	−0.826516	+	0.562914i	$0.809680\pi$
$264$		0			0
$265$	42.6898	+	214.616i	0.161094	+	0.809873i
$266$		0			0
$267$	68.1769	−	342.748i	0.255344	−	1.28370i
$268$		0			0
$269$	183.078	+	273.996i	0.680588	+	1.01857i	0.997538	+	0.0701295i	$0.0223412\pi$
$269$	183.078	+	273.996i	0.680588	+	1.01857i	−0.316950	+	0.948442i	$0.602659\pi$
$270$		0			0
$271$		−	296.270i		−	1.09325i	−0.837379	−	0.546623i	$-0.815913\pi$
$271$		−	296.270i		−	1.09325i	0.837379	−	0.546623i	$-0.184087\pi$
$272$		0			0
$273$	53.1681			0.194755
$274$		0			0
$275$	−21.4735	+	14.3482i	−0.0780856	+	0.0521751i
$276$		0			0
$277$	227.914	+	45.3350i	0.822796	+	0.163664i	0.588496	−	0.808500i	$-0.299720\pi$
$277$	227.914	+	45.3350i	0.822796	+	0.163664i	0.234300	+	0.972164i	$0.424720\pi$
$278$		0			0
$279$	−6.05059	+	1.20354i	−0.0216867	+	0.00431375i
$280$		0			0
$281$	−53.8026	+	129.891i	−0.191468	+	0.462245i	−0.990237	−	0.139393i	$-0.955485\pi$
$281$	−53.8026	+	129.891i	−0.191468	+	0.462245i	0.798769	+	0.601638i	$0.205485\pi$
$282$		0			0
$283$	−142.247	+	212.887i	−0.502639	+	0.752252i	−0.992852	−	0.119350i	$-0.961919\pi$
$283$	−142.247	+	212.887i	−0.502639	+	0.752252i	0.490213	+	0.871602i	$0.336919\pi$
$284$		0			0
$285$	−156.519	−	156.519i	−0.549191	−	0.549191i
$286$		0			0
$287$	−47.3504	+	19.6132i	−0.164984	+	0.0683385i
$288$		0			0
$289$	−267.533	−	109.303i	−0.925719	−	0.378211i
$290$		0			0
$291$	132.990	+	321.066i	0.457010	+	1.10332i
$292$		0			0
$293$	14.5324	−	14.5324i	0.0495987	−	0.0495987i	−0.681872	−	0.731471i	$-0.738834\pi$
$293$	14.5324	−	14.5324i	0.0495987	−	0.0495987i	0.731471	+	0.681872i	$0.238834\pi$
$294$		0			0
$295$	321.896	+	215.084i	1.09117	+	0.729098i
$296$		0			0
$297$	334.418	+	138.520i	1.12598	+	0.466398i
$298$		0			0
$299$	14.7166	+	73.9855i	0.0492195	+	0.247443i
$300$		0			0
$301$	−12.0837	+	60.7490i	−0.0401453	+	0.201824i
$302$		0			0
$303$	−211.007	−	315.794i	−0.696391	−	1.04222i
$304$		0			0
$305$		−	228.467i		−	0.749073i
$306$		0			0
$307$	−68.4872			−0.223085			−0.111543	−	0.993760i	$-0.535579\pi$
$307$	−68.4872			−0.223085			−0.111543	+	0.993760i	$0.535579\pi$
$308$		0			0
$309$	−50.8711	+	33.9910i	−0.164631	+	0.110003i
$310$		0			0
$311$	−255.325	−	50.7872i	−0.820979	−	0.163303i	−0.233308	−	0.972403i	$-0.574955\pi$
$311$	−255.325	−	50.7872i	−0.820979	−	0.163303i	−0.587671	+	0.809100i	$0.699955\pi$
$312$		0			0
$313$	−357.074	+	71.0263i	−1.14081	+	0.226921i	−0.729109	−	0.684398i	$-0.760065\pi$
$313$	−357.074	+	71.0263i	−1.14081	+	0.226921i	−0.411701	+	0.911319i	$0.635065\pi$
$314$		0			0
$315$	4.54090	−	10.9627i	0.0144155	−	0.0348022i
$316$		0			0
$317$	125.093	−	187.215i	0.394616	−	0.590585i	−0.579959	−	0.814646i	$-0.696931\pi$
$317$	125.093	−	187.215i	0.394616	−	0.590585i	0.974575	+	0.224061i	$0.0719314\pi$
$318$		0			0
$319$	369.623	+	369.623i	1.15869	+	1.15869i
$320$		0			0
$321$	−158.440	+	65.6282i	−0.493584	+	0.204449i
$322$		0			0
$323$	−255.854	+	51.5359i	−0.792117	+	0.159554i
$324$		0			0
$325$	8.60866	+	20.7831i	0.0264882	+	0.0639481i
$326$		0			0
$327$	367.739	−	367.739i	1.12458	−	1.12458i
$328$		0			0
$329$	−27.8447	−	18.6052i	−0.0846343	−	0.0565508i
$330$		0			0
$331$	−409.631	−	169.675i	−1.23756	−	0.512612i	−0.334606	−	0.942358i	$-0.608603\pi$
$331$	−409.631	−	169.675i	−1.23756	−	0.512612i	−0.902950	+	0.429746i	$0.858603\pi$
$332$		0			0
$333$	6.98201	+	35.1009i	0.0209670	+	0.105408i
$334$		0			0
$335$	122.195	−	614.316i	0.364761	−	1.83378i
$336$		0			0
$337$	9.47181	+	14.1756i	0.0281063	+	0.0420640i	0.845257	−	0.534360i	$-0.179448\pi$
$337$	9.47181	+	14.1756i	0.0281063	+	0.0420640i	−0.817150	+	0.576424i	$0.804448\pi$
$338$		0			0
$339$			37.6018i			0.110920i
$340$		0			0
$341$	−59.5165			−0.174535
$342$		0			0
$343$	137.325	−	91.7579i	0.400366	−	0.267516i
$344$		0			0
$345$	−96.7366	−	19.2421i	−0.280396	−	0.0557742i
$346$		0			0
$347$	305.555	−	60.7786i	0.880562	−	0.175155i	0.265952	−	0.963986i	$-0.414314\pi$
$347$	305.555	−	60.7786i	0.880562	−	0.175155i	0.614609	+	0.788832i	$0.289314\pi$
$348$		0			0
$349$	167.196	−	403.646i	0.479070	−	1.15658i	−0.480975	−	0.876734i	$-0.659717\pi$
$349$	167.196	−	403.646i	0.479070	−	1.15658i	0.960046	−	0.279844i	$-0.0902827\pi$
$350$		0			0
$351$	175.167	−	262.155i	0.499050	−	0.746882i
$352$		0			0
$353$	−281.753	−	281.753i	−0.798168	−	0.798168i	0.184639	−	0.982806i	$-0.440888\pi$
$353$	−281.753	−	281.753i	−0.798168	−	0.798168i	−0.982806	+	0.184639i	$0.940888\pi$
$354$		0			0
$355$	204.079	−	84.5322i	0.574870	−	0.238119i
$356$		0			0
$357$	45.7032	+	68.0429i	0.128020	+	0.190596i
$358$		0			0
$359$	−75.1021	−	181.313i	−0.209198	−	0.505049i	0.784099	−	0.620635i	$-0.213125\pi$
$359$	−75.1021	−	181.313i	−0.209198	−	0.505049i	−0.993297	+	0.115586i	$0.963125\pi$
$360$		0			0
$361$	88.6011	−	88.6011i	0.245432	−	0.245432i
$362$		0			0
$363$	90.5244	+	60.4865i	0.249379	+	0.166629i
$364$		0			0
$365$	−195.343	−	80.9137i	−0.535186	−	0.221681i
$366$		0			0
$367$	−102.050	−	513.038i	−0.278064	−	1.39792i	−0.827067	−	0.562103i	$-0.809992\pi$
$367$	−102.050	−	513.038i	−0.278064	−	1.39792i	0.549003	−	0.835821i	$-0.315008\pi$
$368$		0			0
$369$	−7.54502	+	37.9314i	−0.0204472	+	0.102795i
$370$		0			0
$371$	−40.6551	−	60.8446i	−0.109582	−	0.164002i
$372$		0			0
$373$		−	46.0668i		−	0.123504i	−0.998092	−	0.0617518i	$-0.980331\pi$
$373$		−	46.0668i		−	0.123504i	0.998092	−	0.0617518i	$-0.0196687\pi$
$374$		0			0
$375$	331.036			0.882763
$376$		0			0
$377$	378.581	−	252.960i	1.00419	−	0.670981i
$378$		0			0
$379$	484.664	+	96.4056i	1.27880	+	0.254368i	0.787332	−	0.616529i	$-0.211462\pi$
$379$	484.664	+	96.4056i	1.27880	+	0.254368i	0.491464	+	0.870898i	$0.336462\pi$
$380$		0			0
$381$	−243.880	+	48.5108i	−0.640106	+	0.127325i
$382$		0			0
$383$	−31.8846	+	76.9762i	−0.0832496	+	0.200982i	−0.960023	−	0.279922i	$-0.909691\pi$
$383$	−31.8846	+	76.9762i	−0.0832496	+	0.200982i	0.876773	+	0.480904i	$0.159691\pi$
$384$		0			0
$385$	63.5996	−	95.1835i	0.165194	−	0.247230i
$386$		0			0
$387$	33.0497	+	33.0497i	0.0853996	+	0.0853996i
$388$		0			0
$389$	−682.498	+	282.700i	−1.75449	+	0.726736i	−0.757204	+	0.653179i	$0.773435\pi$
$389$	−682.498	+	282.700i	−1.75449	+	0.726736i	−0.997291	+	0.0735569i	$0.976565\pi$
$390$		0			0
$391$	−82.0341	+	82.4318i	−0.209806	+	0.210823i
$392$		0			0
$393$	232.193	+	560.564i	0.590822	+	1.42637i
$394$		0			0
$395$	−403.600	+	403.600i	−1.02177	+	1.02177i
$396$		0			0
$397$	−357.350	−	238.774i	−0.900126	−	0.601445i	0.0170817	−	0.999854i	$-0.494562\pi$
$397$	−357.350	−	238.774i	−0.900126	−	0.601445i	−0.917208	+	0.398409i	$0.869562\pi$
$398$		0			0
$399$	68.3889	+	28.3276i	0.171401	+	0.0709965i
$400$		0			0
$401$	−48.6564	−	244.612i	−0.121338	−	0.610005i	−0.992824	−	0.119585i	$-0.961843\pi$
$401$	−48.6564	−	244.612i	−0.121338	−	0.610005i	0.871486	−	0.490420i	$-0.163157\pi$
$402$		0			0
$403$	−10.1137	+	50.8452i	−0.0250961	+	0.126167i
$404$		0			0
$405$	194.913	+	291.708i	0.481267	+	0.720266i
$406$		0			0
$407$			345.270i			0.848328i
$408$		0			0
$409$	−136.456			−0.333634			−0.166817	−	0.985988i	$-0.553349\pi$
$409$	−136.456			−0.333634			−0.166817	+	0.985988i	$0.553349\pi$
$410$		0			0
$411$	−478.194	+	319.519i	−1.16349	+	0.777419i
$412$		0			0
$413$	−126.979	−	25.2576i	−0.307454	−	0.0611564i
$414$		0			0
$415$	717.886	−	142.796i	1.72985	−	0.344088i
$416$		0			0
$417$	101.219	−	244.364i	0.242731	−	0.586004i
$418$		0			0
$419$	−212.212	+	317.597i	−0.506472	+	0.757988i	−0.993307	−	0.115505i	$-0.963151\pi$
$419$	−212.212	+	317.597i	−0.506472	+	0.757988i	0.486835	+	0.873494i	$0.338151\pi$
$420$		0			0
$421$	520.220	+	520.220i	1.23568	+	1.23568i	0.961751	+	0.273927i	$0.0883226\pi$
$421$	520.220	+	520.220i	1.23568	+	1.23568i	0.273927	+	0.961751i	$0.411677\pi$
$422$		0			0
$423$	−23.3468	+	9.67058i	−0.0551935	+	0.0228619i
$424$		0			0
$425$	−19.1977	+	28.8823i	−0.0451710	+	0.0679583i
$426$		0			0
$427$	29.2382	+	70.5873i	0.0684736	+	0.165310i
$428$		0			0
$429$	273.695	−	273.695i	0.637983	−	0.637983i
$430$		0			0
$431$	−220.308	−	147.205i	−0.511155	−	0.341543i	0.273096	−	0.961987i	$-0.411952\pi$
$431$	−220.308	−	147.205i	−0.511155	−	0.341543i	−0.784251	+	0.620444i	$0.786952\pi$
$432$		0			0
$433$	609.180	+	252.331i	1.40688	+	0.582750i	0.951528	−	0.307561i	$-0.0995129\pi$
$433$	609.180	+	252.331i	1.40688	+	0.582750i	0.455353	+	0.890311i	$0.349513\pi$
$434$		0			0
$435$	116.143	+	583.890i	0.266995	+	1.34228i
$436$		0			0
$437$	−20.4893	+	103.007i	−0.0468863	+	0.235714i
$438$		0			0
$439$	−165.242	−	247.303i	−0.376406	−	0.563332i	0.594105	−	0.804388i	$-0.297506\pi$
$439$	−165.242	−	247.303i	−0.376406	−	0.563332i	−0.970511	+	0.241056i	$0.922506\pi$
$440$		0			0
$441$		−	60.3308i		−	0.136804i
$442$		0			0
$443$	−584.733			−1.31994			−0.659970	−	0.751292i	$-0.729431\pi$
$443$	−584.733			−1.31994			−0.659970	+	0.751292i	$0.729431\pi$
$444$		0			0
$445$	−544.943	+	364.119i	−1.22459	+	0.818245i
$446$		0			0
$447$	−515.411	−	102.522i	−1.15305	−	0.229355i
$448$		0			0
$449$	−76.6982	+	15.2562i	−0.170820	+	0.0339782i	−0.279759	−	0.960070i	$-0.590255\pi$
$449$	−76.6982	+	15.2562i	−0.170820	+	0.0339782i	0.108939	+	0.994048i	$0.465255\pi$
$450$		0			0
$451$	−142.783	+	344.710i	−0.316593	+	0.764323i
$452$		0			0
$453$	−48.9894	+	73.3178i	−0.108144	+	0.161849i
$454$		0			0
$455$	−70.5081	−	70.5081i	−0.154963	−	0.154963i
$456$		0			0
$457$	569.359	−	235.836i	1.24586	−	0.516053i	0.340321	−	0.940309i	$-0.389464\pi$
$457$	569.359	−	235.836i	1.24586	−	0.516053i	0.905542	+	0.424256i	$0.139464\pi$
$458$		0			0
$459$	486.072	−	1.17532i	1.05898	−	0.00256060i
$460$		0			0
$461$	−115.450	−	278.722i	−0.250435	−	0.604603i	0.747804	−	0.663919i	$-0.231108\pi$
$461$	−115.450	−	278.722i	−0.250435	−	0.604603i	−0.998239	+	0.0593159i	$0.981108\pi$
$462$		0			0
$463$	−640.400	+	640.400i	−1.38315	+	1.38315i	−0.544193	+	0.838960i	$0.683164\pi$
$463$	−640.400	+	640.400i	−1.38315	+	1.38315i	−0.838960	+	0.544193i	$0.816836\pi$
$464$		0			0
$465$	−56.3594	−	37.6582i	−0.121203	−	0.0809853i
$466$		0			0
$467$	−350.667	−	145.251i	−0.750892	−	0.311030i	−0.0257866	−	0.999667i	$-0.508209\pi$
$467$	−350.667	−	145.251i	−0.750892	−	0.311030i	−0.725106	+	0.688638i	$0.758209\pi$
$468$		0			0
$469$	40.8640	+	205.437i	0.0871301	+	0.438032i
$470$		0			0
$471$	−46.0180	+	231.348i	−0.0977028	+	0.491185i
$472$		0			0
$473$	250.515	+	374.923i	0.529631	+	0.792649i
$474$		0			0
$475$			31.3195i			0.0659358i
$476$		0			0
$477$	−55.2195			−0.115764
$478$		0			0
$479$	93.9177	−	62.7538i	0.196070	−	0.131010i	−0.453660	−	0.891175i	$-0.649882\pi$
$479$	93.9177	−	62.7538i	0.196070	−	0.131010i	0.649730	+	0.760165i	$0.274882\pi$
$480$		0			0
$481$	294.965	+	58.6723i	0.613234	+	0.121980i
$482$		0			0
$483$	32.3503	−	6.43487i	0.0669778	−	0.0133227i
$484$		0			0
$485$	249.414	−	602.140i	0.514257	−	1.24153i
$486$		0			0
$487$	−24.1593	+	36.1569i	−0.0496083	+	0.0742441i	−0.855445	−	0.517894i	$-0.826716\pi$
$487$	−24.1593	+	36.1569i	−0.0496083	+	0.0742441i	0.805836	+	0.592138i	$0.201716\pi$
$488$		0			0
$489$	−274.999	−	274.999i	−0.562369	−	0.562369i
$490$		0			0
$491$	303.412	−	125.678i	0.617948	−	0.255962i	−0.0516746	−	0.998664i	$-0.516456\pi$
$491$	303.412	−	125.678i	0.617948	−	0.255962i	0.669623	+	0.742702i	$0.266456\pi$
$492$		0			0
$493$	649.158	+	267.053i	1.31675	+	0.541690i
$494$		0			0
$495$	−33.0576	−	79.8082i	−0.0667831	−	0.161229i
$496$		0			0
$497$	−52.2341	+	52.2341i	−0.105099	+	0.105099i
$498$		0			0
$499$	−67.0818	−	44.8226i	−0.134432	−	0.0898248i	0.486536	−	0.873661i	$-0.338260\pi$
$499$	−67.0818	−	44.8226i	−0.134432	−	0.0898248i	−0.620968	+	0.783836i	$0.713260\pi$
$500$		0			0
$501$	783.662	+	324.603i	1.56419	+	0.647911i
$502$		0			0
$503$	−79.9626	−	401.999i	−0.158971	−	0.799203i	−0.975175	−	0.221438i	$-0.928925\pi$
$503$	−79.9626	−	401.999i	−0.158971	−	0.799203i	0.816203	−	0.577765i	$-0.196075\pi$
$504$		0			0
$505$	−138.962	+	698.609i	−0.275172	+	1.38338i
$506$		0			0
$507$	73.0219	+	109.285i	0.144027	+	0.215552i
$508$		0			0
$509$			87.4398i			0.171787i	0.996304	+	0.0858937i	$0.0273745\pi$
$509$			87.4398i			0.171787i	−0.996304	+	0.0858937i	$0.972625\pi$
$510$		0			0
$511$	70.7082			0.138372
$512$		0			0
$513$	364.988	−	243.877i	0.711477	−	0.475394i
$514$		0			0
$515$	112.539	+	22.3853i	0.218522	+	0.0434667i
$516$		0			0
$517$	−239.111	+	47.5622i	−0.462498	+	0.0919965i
$518$		0			0
$519$	−308.989	+	745.966i	−0.595355	+	1.43731i
$520$		0			0
$521$	−33.3785	+	49.9545i	−0.0640662	+	0.0958819i	−0.862119	−	0.506705i	$-0.830863\pi$
$521$	−33.3785	+	49.9545i	−0.0640662	+	0.0958819i	0.798053	+	0.602587i	$0.205863\pi$
$522$		0			0
$523$	−610.564	−	610.564i	−1.16743	−	1.16743i	−0.982811	−	0.184615i	$-0.940896\pi$
$523$	−610.564	−	610.564i	−1.16743	−	1.16743i	−0.184615	−	0.982811i	$-0.559104\pi$
$524$		0			0
$525$	9.08746	−	3.76415i	0.0173094	−	0.00716981i
$526$		0			0
$527$	−73.7639	+	30.7632i	−0.139970	+	0.0583742i
$528$		0			0
$529$	−184.531	−	445.497i	−0.348829	−	0.842149i
$530$		0			0
$531$	−69.0809	+	69.0809i	−0.130096	+	0.130096i
$532$		0			0
$533$	270.224	+	180.558i	0.506986	+	0.338757i
$534$		0			0
$535$	297.146	+	123.082i	0.555412	+	0.230059i
$536$		0			0
$537$	−53.6959	−	269.948i	−0.0999924	−	0.502696i
$538$		0			0
$539$	113.550	−	570.855i	0.210668	−	1.05910i
$540$		0			0
$541$	−512.191	−	766.548i	−0.946749	−	1.41691i	−0.908614	−	0.417637i	$-0.862858\pi$
$541$	−512.191	−	766.548i	−0.946749	−	1.41691i	−0.0381350	−	0.999273i	$-0.512142\pi$
$542$		0			0
$543$			613.936i			1.13064i
$544$		0			0
$545$	−975.343			−1.78962
$546$		0			0
$547$	158.508	−	105.911i	0.289776	−	0.193622i	−0.402182	−	0.915560i	$-0.631748\pi$
$547$	158.508	−	105.911i	0.289776	−	0.193622i	0.691958	+	0.721937i	$0.256748\pi$
$548$		0			0
$549$	56.5460	+	11.2477i	0.102998	+	0.0204876i
$550$		0			0
$551$	621.736	−	123.671i	1.12838	−	0.224448i
$552$		0			0
$553$	73.0454	−	176.347i	0.132089	−	0.318892i
$554$		0			0
$555$	−218.464	+	326.955i	−0.393629	+	0.589108i
$556$		0			0
$557$	91.3389	+	91.3389i	0.163984	+	0.163984i	0.784329	−	0.620345i	$-0.213007\pi$
$557$	91.3389	+	91.3389i	0.163984	+	0.163984i	−0.620345	+	0.784329i	$0.713007\pi$
$558$		0			0
$559$	362.869	−	150.305i	0.649139	−	0.268882i
$560$		0			0
$561$	585.534	+	114.999i	1.04373	+	0.204989i
$562$		0			0
$563$	−215.095	−	519.286i	−0.382052	−	0.922356i	−0.991569	−	0.129582i	$-0.958636\pi$
$563$	−215.095	−	519.286i	−0.382052	−	0.922356i	0.609516	−	0.792774i	$-0.291364\pi$
$564$		0			0
$565$	49.8651	−	49.8651i	0.0882568	−	0.0882568i
$566$		0			0
$567$	−97.5518	−	65.1820i	−0.172049	−	0.114960i
$568$		0			0
$569$	292.748	+	121.260i	0.514495	+	0.213111i	0.624797	−	0.780787i	$-0.285182\pi$
$569$	292.748	+	121.260i	0.514495	+	0.213111i	−0.110302	+	0.993898i	$0.535182\pi$
$570$		0			0
$571$	−176.710	−	888.382i	−0.309475	−	1.55584i	−0.752051	−	0.659105i	$-0.770935\pi$
$571$	−176.710	−	888.382i	−0.309475	−	1.55584i	0.442576	−	0.896731i	$-0.354065\pi$
$572$		0			0
$573$	113.143	−	568.806i	0.197456	−	0.992681i
$574$		0			0
$575$	7.75333	+	11.6037i	0.0134840	+	0.0201803i
$576$		0			0
$577$			178.801i			0.309881i	0.987924	+	0.154941i	$0.0495186\pi$
$577$			178.801i			0.309881i	−0.987924	+	0.154941i	$0.950481\pi$
$578$		0			0
$579$	355.621			0.614199
$580$		0			0
$581$	−203.524	+	135.990i	−0.350299	+	0.234062i
$582$		0			0
$583$	−522.492	−	103.930i	−0.896213	−	0.178268i
$584$		0			0
$585$	−73.7981	+	14.6793i	−0.126151	+	0.0250929i
$586$		0			0
$587$	46.2911	−	111.757i	0.0788605	−	0.190386i	−0.879532	−	0.475840i	$-0.842144\pi$
$587$	46.2911	−	111.757i	0.0788605	−	0.190386i	0.958393	+	0.285454i	$0.0921442\pi$
$588$		0			0
$589$	−40.0991	+	60.0125i	−0.0680799	+	0.101889i
$590$		0			0
$591$	−426.935	−	426.935i	−0.722394	−	0.722394i
$592$		0			0
$593$	−225.895	+	93.5687i	−0.380936	+	0.157789i	−0.564931	−	0.825138i	$-0.691097\pi$
$593$	−225.895	+	93.5687i	−0.380936	+	0.157789i	0.183995	+	0.982927i	$0.441097\pi$
$594$		0			0
$595$	29.6255	−	150.843i	0.0497908	−	0.253517i
$596$		0			0
$597$	−189.694	−	457.963i	−0.317746	−	0.767107i
$598$		0			0
$599$	−289.979	+	289.979i	−0.484106	+	0.484106i	−0.906440	−	0.422334i	$-0.861211\pi$
$599$	−289.979	+	289.979i	−0.484106	+	0.484106i	0.422334	+	0.906440i	$0.361211\pi$
$600$		0			0
$601$	−391.059	−	261.298i	−0.650681	−	0.434771i	0.185934	−	0.982562i	$-0.440469\pi$
$601$	−391.059	−	261.298i	−0.650681	−	0.434771i	−0.836615	+	0.547791i	$0.815469\pi$
$602$		0			0
$603$	146.028	+	60.4869i	0.242170	+	0.100310i
$604$		0			0
$605$	−39.8344	−	200.261i	−0.0658420	−	0.331010i
$606$		0			0
$607$	−146.290	+	735.449i	−0.241005	+	1.21161i	0.650820	+	0.759232i	$0.274425\pi$
$607$	−146.290	+	735.449i	−0.241005	+	1.21161i	−0.891825	+	0.452381i	$0.850575\pi$
$608$		0			0
$609$	−110.607	−	165.535i	−0.181621	−	0.271815i
$610$		0			0
$611$			212.356i			0.347555i
$612$		0			0
$613$	187.538			0.305935			0.152968	−	0.988231i	$-0.451117\pi$
$613$	187.538			0.305935			0.152968	+	0.988231i	$0.451117\pi$
$614$		0			0
$615$	−353.319	+	236.081i	−0.574503	+	0.383871i
$616$		0			0
$617$	−24.9869	−	4.97020i	−0.0404974	−	0.00805542i	0.174800	−	0.984604i	$-0.444072\pi$
$617$	−24.9869	−	4.97020i	−0.0404974	−	0.00805542i	−0.215297	+	0.976549i	$0.569072\pi$
$618$		0			0
$619$	1068.19	−	212.476i	1.72567	−	0.343257i	0.770077	−	0.637951i	$-0.220218\pi$
$619$	1068.19	−	212.476i	1.72567	−	0.343257i	0.955591	+	0.294695i	$0.0952179\pi$
$620$		0			0
$621$	74.8523	−	180.710i	0.120535	−	0.290998i
$622$		0			0
$623$	121.767	−	182.238i	0.195453	−	0.292516i
$624$		0			0
$625$	−475.062	−	475.062i	−0.760099	−	0.760099i
$626$		0			0
$627$	497.870	−	206.224i	0.794051	−	0.328907i
$628$		0			0
$629$	178.465	+	427.922i	0.283728	+	0.680322i
$630$		0			0
$631$	186.096	+	449.276i	0.294923	+	0.712007i	0.999996	+	0.00287204i	$0.000914200\pi$
$631$	186.096	+	449.276i	0.294923	+	0.712007i	−0.705073	+	0.709135i	$0.749086\pi$
$632$		0			0
$633$	457.756	−	457.756i	0.723153	−	0.723153i
$634$		0			0
$635$	387.750	+	259.087i	0.610631	+	0.408010i
$636$		0			0
$637$	−468.389	−	194.013i	−0.735304	−	0.304573i
$638$		0			0
$639$	10.8748	+	54.6714i	0.0170185	+	0.0855578i
$640$		0			0
$641$	−101.983	+	512.704i	−0.159100	+	0.799851i	0.815994	+	0.578060i	$0.196190\pi$
$641$	−101.983	+	512.704i	−0.159100	+	0.799851i	−0.975094	+	0.221791i	$0.928810\pi$
$642$		0			0
$643$	−327.462	−	490.082i	−0.509272	−	0.762180i	0.484358	−	0.874870i	$-0.339053\pi$
$643$	−327.462	−	490.082i	−0.509272	−	0.762180i	−0.993630	+	0.112690i	$0.964053\pi$
$644$		0			0
$645$			513.545i			0.796194i
$646$		0			0
$647$	151.691			0.234453			0.117226	−	0.993105i	$-0.462600\pi$
$647$	151.691			0.234453			0.117226	+	0.993105i	$0.462600\pi$
$648$		0			0
$649$	−783.669	+	523.631i	−1.20750	+	0.806828i
$650$		0			0
$651$	22.2321	+	4.42225i	0.0341508	+	0.00679301i
$652$		0			0
$653$	688.097	−	136.871i	1.05375	−	0.209603i	0.362324	−	0.932052i	$-0.381984\pi$
$653$	688.097	−	136.871i	1.05375	−	0.209603i	0.691424	+	0.722449i	$0.256984\pi$
$654$		0			0
$655$	435.464	−	1051.30i	0.664831	−	1.60504i
$656$		0			0
$657$	29.6432	−	44.3642i	0.0451191	−	0.0675254i
$658$		0			0
$659$	323.420	+	323.420i	0.490774	+	0.490774i	0.908550	−	0.417776i	$-0.137190\pi$
$659$	323.420	+	323.420i	0.490774	+	0.490774i	−0.417776	+	0.908550i	$0.637190\pi$
$660$		0			0
$661$	−696.804	+	288.626i	−1.05417	+	0.436650i	−0.841377	−	0.540448i	$-0.818255\pi$
$661$	−696.804	+	288.626i	−1.05417	+	0.436650i	−0.212789	+	0.977098i	$0.568255\pi$
$662$		0			0
$663$	197.745	−	480.682i	0.298258	−	0.725011i
$664$		0			0
$665$	−53.1267	−	128.259i	−0.0798898	−	0.192871i
$666$		0			0
$667$	199.734	−	199.734i	0.299451	−	0.299451i
$668$		0			0
$669$	−816.574	−	545.617i	−1.22059	−	0.815571i
$670$		0			0
$671$	513.874	+	212.854i	0.765834	+	0.317219i
$672$		0			0
$673$	28.0268	+	140.900i	0.0416446	+	0.209361i	0.996005	−	0.0892953i	$-0.0284615\pi$
$673$	28.0268	+	140.900i	0.0416446	+	0.209361i	−0.954361	+	0.298657i	$0.903461\pi$
$674$		0			0
$675$	11.3795	−	57.2088i	0.0168586	−	0.0847537i
$676$		0			0
$677$	−134.761	−	201.684i	−0.199056	−	0.297909i	0.718490	−	0.695537i	$-0.244833\pi$
$677$	−134.761	−	201.684i	−0.199056	−	0.297909i	−0.917547	+	0.397628i	$0.869833\pi$
$678$		0			0
$679$			217.956i			0.320996i
$680$		0			0
$681$	−354.692			−0.520840
$682$		0			0
$683$	423.582	−	283.028i	0.620178	−	0.414390i	−0.205400	−	0.978678i	$-0.565849\pi$
$683$	423.582	−	283.028i	0.620178	−	0.414390i	0.825578	+	0.564288i	$0.190849\pi$
$684$		0			0
$685$	1057.88	+	210.425i	1.54435	+	0.307189i
$686$		0			0
$687$	187.279	−	37.2522i	0.272605	−	0.0542244i
$688$		0			0
$689$	−177.576	+	428.707i	−0.257730	+	0.622216i
$690$		0			0
$691$	38.5508	−	57.6954i	0.0557899	−	0.0834955i	−0.802526	−	0.596617i	$-0.796511\pi$
$691$	38.5508	−	57.6954i	0.0557899	−	0.0834955i	0.858316	+	0.513122i	$0.171511\pi$
$692$		0			0
$693$	20.4270	+	20.4270i	0.0294762	+	0.0294762i
$694$		0			0
$695$	−458.289	+	189.830i	−0.659409	+	0.273136i
$696$		0			0
$697$	1.21149	+	501.031i	0.00173815	+	0.718840i
$698$		0			0
$699$	−225.658	−	544.786i	−0.322830	−	0.779380i
$700$		0			0
$701$	802.519	−	802.519i	1.14482	−	1.14482i	0.157264	−	0.987557i	$-0.449733\pi$
$701$	802.519	−	802.519i	1.14482	−	1.14482i	0.987557	−	0.157264i	$-0.0502672\pi$
$702$		0			0
$703$	348.147	+	232.624i	0.495230	+	0.330902i
$704$		0			0
$705$	−256.522	−	106.255i	−0.363861	−	0.150716i
$706$		0			0
$707$	−46.4711	−	233.626i	−0.0657300	−	0.330447i
$708$		0			0
$709$	−129.636	+	651.724i	−0.182843	+	0.919216i	0.775008	+	0.631951i	$0.217746\pi$
$709$	−129.636	+	651.724i	−0.182843	+	0.919216i	−0.957851	+	0.287264i	$0.907254\pi$
$710$		0			0
$711$	−80.0220	−	119.761i	−0.112548	−	0.168441i
$712$		0			0
$713$			32.1610i			0.0451066i
$714$		0			0
$715$	−725.913			−1.01526
$716$		0			0
$717$	−835.293	+	558.125i	−1.16498	+	0.778417i
$718$		0			0
$719$	−109.728	−	21.8263i	−0.152613	−	0.0303565i	0.118193	−	0.992991i	$-0.462290\pi$
$719$	−109.728	−	21.8263i	−0.152613	−	0.0303565i	−0.270805	+	0.962634i	$0.587290\pi$
$720$		0			0
$721$	−37.6348	+	7.48602i	−0.0521980	+	0.0103828i
$722$		0			0
$723$	−336.569	+	812.549i	−0.465517	+	1.12386i
$724$		0			0
$725$	46.7981	−	70.0383i	0.0645491	−	0.0966045i
$726$		0			0
$727$	113.388	+	113.388i	0.155968	+	0.155968i	0.780777	−	0.624810i	$-0.214823\pi$
$727$	113.388	+	113.388i	0.155968	+	0.155968i	−0.624810	+	0.780777i	$0.714823\pi$
$728$		0			0
$729$	−740.984	+	306.926i	−1.01644	+	0.421023i
$730$		0			0
$731$	504.277	+	335.187i	0.689846	+	0.458532i
$732$		0			0
$733$	151.534	+	365.835i	0.206731	+	0.499093i	0.992905	−	0.118913i	$-0.0379409\pi$
$733$	151.534	+	365.835i	0.206731	+	0.499093i	−0.786174	+	0.618006i	$0.787941\pi$
$734$		0			0
$735$	468.727	−	468.727i	0.637724	−	0.637724i
$736$		0			0
$737$	1267.89	+	847.177i	1.72034	+	1.14949i
$738$		0			0
$739$	−863.550	−	357.694i	−1.16854	−	0.484025i	−0.287830	−	0.957682i	$-0.592934\pi$
$739$	−863.550	−	357.694i	−1.16854	−	0.484025i	−0.880709	+	0.473657i	$0.842934\pi$
$740$		0			0
$741$	−91.5746	−	460.377i	−0.123582	−	0.621291i
$742$		0			0
$743$	−282.800	+	1421.73i	−0.380619	+	1.91350i	0.0254825	+	0.999675i	$0.491888\pi$
$743$	−282.800	+	1421.73i	−0.380619	+	1.91350i	−0.406102	+	0.913828i	$0.633112\pi$
$744$		0			0
$745$	547.548	+	819.464i	0.734964	+	1.09995i
$746$		0			0
$747$			184.708i			0.247266i
$748$		0			0
$749$	−107.558			−0.143602
$750$		0			0
$751$	−629.047	+	420.316i	−0.837613	+	0.559675i	−0.898754	−	0.438454i	$-0.855526\pi$
$751$	−629.047	+	420.316i	−0.837613	+	0.559675i	0.0611408	+	0.998129i	$0.480526\pi$
$752$		0			0
$753$	−616.054	−	122.541i	−0.818133	−	0.162737i
$754$		0			0
$755$	162.196	−	32.2628i	0.214829	−	0.0427322i
$756$		0			0
$757$	−198.961	+	480.335i	−0.262828	+	0.634524i	−0.999111	−	0.0421498i	$-0.986579\pi$
$757$	−198.961	+	480.335i	−0.262828	+	0.634524i	0.736283	+	0.676674i	$0.236579\pi$
$758$		0			0
$759$	133.405	−	199.655i	0.175765	−	0.263050i
$760$		0			0
$761$	−150.677	−	150.677i	−0.197999	−	0.197999i	0.601143	−	0.799142i	$-0.294712\pi$
$761$	−150.677	−	150.677i	−0.197999	−	0.197999i	−0.799142	+	0.601143i	$0.794712\pi$
$762$		0			0
$763$	301.342	−	124.820i	0.394944	−	0.163591i
$764$		0			0
$765$	−82.2229	−	81.8262i	−0.107481	−	0.106962i
$766$		0			0
$767$	314.170	+	758.474i	0.409609	+	0.988884i
$768$		0			0
$769$	−525.065	+	525.065i	−0.682789	+	0.682789i	−0.960628	−	0.277839i	$-0.910382\pi$
$769$	−525.065	+	525.065i	−0.682789	+	0.682789i	0.277839	+	0.960628i	$0.410382\pi$
$770$		0			0
$771$	744.121	+	497.206i	0.965137	+	0.644884i
$772$		0			0
$773$	89.3690	+	37.0178i	0.115613	+	0.0478885i	0.439740	−	0.898125i	$-0.355071\pi$
$773$	89.3690	+	37.0178i	0.115613	+	0.0478885i	−0.324127	+	0.946014i	$0.605071\pi$
$774$		0			0
$775$	1.87106	+	9.40646i	0.00241427	+	0.0121374i
$776$		0			0
$777$	25.6545	−	128.974i	0.0330174	−	0.165990i
$778$		0			0
$779$	251.383	+	376.221i	0.322699	+	0.482953i
$780$		0			0
$781$			537.774i			0.688571i
$782$		0			0
$783$	−1180.61			−1.50780
$784$		0			0
$785$	367.825	−	245.773i	0.468567	−	0.313087i
$786$		0			0
$787$	530.825	+	105.588i	0.674492	+	0.134165i	0.520440	−	0.853898i	$-0.325768\pi$
$787$	530.825	+	105.588i	0.674492	+	0.134165i	0.154052	+	0.988063i	$0.450768\pi$
$788$		0			0
$789$	784.126	−	155.972i	0.993822	−	0.197684i
$790$		0			0
$791$	−9.02482	+	21.7878i	−0.0114094	+	0.0275447i
$792$		0			0
$793$	269.166	−	402.835i	0.339427	−	0.507988i
$794$		0			0
$795$	−429.017	−	429.017i	−0.539643	−	0.539643i
$796$		0			0
$797$	−1292.05	+	535.184i	−1.62114	+	0.671499i	−0.994198	−	0.107566i	$-0.965694\pi$
$797$	−1292.05	+	535.184i	−1.62114	+	0.671499i	−0.626943	+	0.779065i	$0.715694\pi$
$798$		0			0
$799$	−271.767	+	182.541i	−0.340134	+	0.228462i
$800$		0			0
$801$	−63.2919	−	152.800i	−0.0790161	−	0.190762i
$802$		0			0
$803$	363.986	−	363.986i	0.453283	−	0.453283i
$804$		0			0
$805$	−51.4344	−	34.3674i	−0.0638937	−	0.0426924i
$806$		0			0
$807$	−844.138	−	349.653i	−1.04602	−	0.433275i
$808$		0			0
$809$	−54.8854	−	275.927i	−0.0678435	−	0.341072i	0.931924	−	0.362655i	$-0.118130\pi$
$809$	−54.8854	−	275.927i	−0.0678435	−	0.341072i	−0.999767	+	0.0215825i	$0.993130\pi$
$810$		0			0
$811$	−25.8410	+	129.911i	−0.0318631	+	0.160187i	−0.993441	−	0.114345i	$-0.963523\pi$
$811$	−25.8410	+	129.911i	−0.0318631	+	0.160187i	0.961578	+	0.274532i	$0.0885229\pi$
$812$		0			0
$813$	456.380	+	683.021i	0.561353	+	0.840124i
$814$		0			0
$815$			729.371i			0.894934i
$816$		0			0
$817$	546.831			0.669316
$818$		0			0
$819$	20.9221	−	13.9797i	0.0255459	−	0.0170692i
$820$		0			0
$821$	989.530	+	196.830i	1.20527	+	0.239744i	0.756556	−	0.653929i	$-0.226881\pi$
$821$	989.530	+	196.830i	1.20527	+	0.239744i	0.448718	+	0.893673i	$0.351881\pi$
$822$		0			0
$823$	618.239	−	122.975i	0.751201	−	0.149423i	0.195383	−	0.980727i	$-0.437405\pi$
$823$	618.239	−	122.975i	0.751201	−	0.149423i	0.555818	+	0.831304i	$0.312405\pi$
$824$		0			0
$825$	27.4029	−	66.1565i	0.0332157	−	0.0801897i
$826$		0			0
$827$	−318.696	+	476.963i	−0.385364	+	0.576739i	−0.972544	−	0.232718i	$-0.925238\pi$
$827$	−318.696	+	476.963i	−0.385364	+	0.576739i	0.587180	+	0.809457i	$0.300238\pi$
$828$		0			0
$829$	−358.145	−	358.145i	−0.432021	−	0.432021i	0.457295	−	0.889315i	$-0.348818\pi$
$829$	−358.145	−	358.145i	−0.432021	−	0.432021i	−0.889315	+	0.457295i	$0.848818\pi$
$830$		0			0
$831$	−595.269	+	246.569i	−0.716329	+	0.296713i
$832$		0			0
$833$	−154.334	−	766.203i	−0.185275	−	0.919812i
$834$		0			0
$835$	−608.774	−	1469.71i	−0.729071	−	1.76013i
$836$		0			0
$837$	95.0504	−	95.0504i	0.113561	−	0.113561i
$838$		0			0
$839$	608.319	+	406.466i	0.725053	+	0.484465i	0.862508	−	0.506043i	$-0.168892\pi$
$839$	608.319	+	406.466i	0.725053	+	0.484465i	−0.137456	+	0.990508i	$0.543892\pi$
$840$		0			0
$841$	−798.165	−	330.611i	−0.949067	−	0.393116i
$842$		0			0
$843$	−76.0500	−	382.329i	−0.0902136	−	0.453534i
$844$		0			0
$845$	48.0898	−	241.764i	0.0569110	−	0.286111i
$846$		0			0
$847$	37.9357	+	56.7749i	0.0447884	+	0.0670305i
$848$		0			0
$849$		−	709.911i		−	0.836173i
$850$		0			0
$851$	186.574			0.219240
$852$		0			0
$853$	780.372	−	521.428i	0.914856	−	0.611287i	−0.00651184	−	0.999979i	$-0.502073\pi$
$853$	780.372	−	521.428i	0.914856	−	0.611287i	0.921368	+	0.388691i	$0.127073\pi$
$854$		0			0
$855$	−102.746	−	20.4374i	−0.120171	−	0.0239034i
$856$		0			0
$857$	767.480	−	152.661i	0.895542	−	0.178134i	0.274199	−	0.961673i	$-0.411587\pi$
$857$	767.480	−	152.661i	0.895542	−	0.178134i	0.621343	+	0.783539i	$0.286587\pi$
$858$		0			0
$859$	−24.9899	+	60.3309i	−0.0290918	+	0.0702339i	−0.937758	−	0.347290i	$-0.887102\pi$
$859$	−24.9899	+	60.3309i	−0.0290918	+	0.0702339i	0.908666	+	0.417524i	$0.137102\pi$
$860$		0			0
$861$	78.9491	−	118.156i	0.0916947	−	0.137231i
$862$		0			0
$863$	−437.927	−	437.927i	−0.507447	−	0.507447i	0.406295	−	0.913742i	$-0.366821\pi$
$863$	−437.927	−	437.927i	−0.507447	−	0.507447i	−0.913742	+	0.406295i	$0.866821\pi$
$864$		0			0
$865$	1399.01	−	579.491i	1.61736	−	0.669932i
$866$		0			0
$867$	785.144	−	160.126i	0.905587	−	0.184689i
$868$		0			0
$869$	−531.769	−	1283.80i	−0.611933	−	1.47734i
$870$		0			0
$871$	939.203	−	939.203i	1.07830	−	1.07830i
$872$		0			0
$873$	136.752	+	91.3745i	0.156646	+	0.104667i
$874$		0			0
$875$	191.814	+	79.4521i	0.219216	+	0.0908024i
$876$		0			0
$877$	19.2893	+	96.9736i	0.0219946	+	0.110574i	0.990223	−	0.139493i	$-0.0445473\pi$
$877$	19.2893	+	96.9736i	0.0219946	+	0.110574i	−0.968228	+	0.250067i	$0.919547\pi$
$878$		0			0
$879$	−11.1170	+	55.8891i	−0.0126474	+	0.0635826i
$880$		0			0
$881$	−316.179	−	473.196i	−0.358887	−	0.537112i	0.607462	−	0.794349i	$-0.292188\pi$
$881$	−316.179	−	473.196i	−0.358887	−	0.537112i	−0.966348	+	0.257237i	$0.917188\pi$
$882$		0			0
$883$		−	1695.85i		−	1.92055i	−0.279055	−	0.960275i	$-0.590021\pi$
$883$		−	1695.85i		−	1.92055i	0.279055	−	0.960275i	$-0.409979\pi$
$884$		0			0
$885$	−1073.42			−1.21290
$886$		0			0
$887$	−247.890	+	165.635i	−0.279470	+	0.186736i	−0.687403	−	0.726276i	$-0.741250\pi$
$887$	−247.890	+	165.635i	−0.279470	+	0.186736i	0.407933	+	0.913012i	$0.366250\pi$
$888$		0			0
$889$	−152.956	−	30.4249i	−0.172054	−	0.0342237i
$890$		0			0
$891$	−837.709	+	166.631i	−0.940190	+	0.187015i
$892$		0			0
$893$	−113.142	+	273.149i	−0.126699	+	0.305878i
$894$		0			0
$895$	−286.779	+	429.195i	−0.320424	+	0.479548i
$896$		0			0
$897$	−147.897	−	147.897i	−0.164879	−	0.164879i
$898$		0			0
$899$	179.343	−	74.2863i	0.199492	−	0.0826322i
$900$		0			0
$901$	−701.290	+	141.259i	−0.778346	+	0.156780i
$902$		0			0
$903$	−65.7212	−	158.665i	−0.0727809	−	0.175709i
$904$		0			0
$905$	814.163	−	814.163i	0.899627	−	0.899627i
$906$		0			0
$907$	−290.635	−	194.196i	−0.320436	−	0.214108i	0.384940	−	0.922941i	$-0.374222\pi$
$907$	−290.635	−	194.196i	−0.320436	−	0.214108i	−0.705376	+	0.708833i	$0.749222\pi$
$908$		0			0
$909$	−166.066	−	68.7866i	−0.182690	−	0.0756728i
$910$		0			0
$911$	184.882	+	929.465i	0.202944	+	1.02027i	0.939149	+	0.343510i	$0.111616\pi$
$911$	184.882	+	929.465i	0.202944	+	1.02027i	−0.736205	+	0.676759i	$0.763384\pi$
$912$		0			0
$913$	−347.644	+	1747.72i	−0.380771	+	1.91427i
$914$		0			0
$915$	351.936	+	526.709i	0.384629	+	0.575639i
$916$		0			0
$917$			380.540i			0.414983i
$918$		0			0
$919$	294.203			0.320134			0.160067	−	0.987106i	$-0.448829\pi$
$919$	294.203			0.320134			0.160067	+	0.987106i	$0.448829\pi$
$920$		0			0
$921$	157.891	−	105.499i	0.171434	−	0.114548i
$922$		0			0
$923$	459.423	+	91.3849i	0.497749	+	0.0990085i
$924$		0			0
$925$	54.5692	−	10.8545i	0.0589937	−	0.0117346i
$926$		0			0
$927$	−11.0808	+	26.7514i	−0.0119534	+	0.0288581i
$928$		0			0
$929$	−188.122	+	281.545i	−0.202500	+	0.303062i	−0.918795	−	0.394735i	$-0.870836\pi$
$929$	−188.122	+	281.545i	−0.202500	+	0.303062i	0.716295	+	0.697797i	$0.245836\pi$
$930$		0			0
$931$	−499.109	−	499.109i	−0.536100	−	0.536100i
$932$		0			0
$933$	666.860	−	276.222i	0.714748	−	0.296058i
$934$		0			0
$935$	−623.993	−	929.001i	−0.667373	−	0.993584i
$936$		0			0
$937$	−215.542	−	520.365i	−0.230034	−	0.555352i	0.766147	−	0.642666i	$-0.222172\pi$
$937$	−215.542	−	520.365i	−0.230034	−	0.555352i	−0.996181	+	0.0873141i	$0.972172\pi$
$938$		0			0
$939$	713.788	−	713.788i	0.760157	−	0.760157i
$940$		0			0
$941$	921.387	+	615.651i	0.979157	+	0.654252i	0.938630	−	0.344927i	$-0.112096\pi$
$941$	921.387	+	615.651i	0.979157	+	0.654252i	0.0405273	+	0.999178i	$0.487096\pi$
$942$		0			0
$943$	186.271	+	77.1560i	0.197530	+	0.0818198i
$944$		0			0
$945$	50.4409	+	253.583i	0.0533766	+	0.268342i
$946$		0			0
$947$	−162.201	+	815.439i	−0.171279	+	0.861076i	0.795597	+	0.605827i	$0.207158\pi$
$947$	−162.201	+	815.439i	−0.171279	+	0.861076i	−0.966875	+	0.255249i	$0.917842\pi$
$948$		0			0
$949$	−249.102	−	372.808i	−0.262489	−	0.392843i
$950$		0			0
$951$			624.303i			0.656471i
$952$		0			0
$953$	1379.52			1.44755			0.723776	−	0.690035i	$-0.242405\pi$
$953$	1379.52			1.44755			0.723776	+	0.690035i	$0.242405\pi$
$954$		0			0
$955$	−904.357	+	604.272i	−0.946970	+	0.632745i
$956$		0			0
$957$	−1421.50	−	282.755i	−1.48538	−	0.295460i
$958$		0			0
$959$	−353.771	+	70.3694i	−0.368896	+	0.0733779i
$960$		0			0
$961$	359.301	−	867.429i	0.373882	−	0.902631i
$962$		0			0
$963$	−45.0917	+	67.4845i	−0.0468242	+	0.0700774i
$964$		0			0
$965$	−471.602	−	471.602i	−0.488707	−	0.488707i
$966$		0			0
$967$	−1485.06	+	615.133i	−1.53574	+	0.636125i	−0.980669	−	0.195676i	$-0.937310\pi$
$967$	−1485.06	+	615.133i	−1.53574	+	0.636125i	−0.555074	+	0.831801i	$0.687310\pi$
$968$		0			0
$969$	510.459	−	512.933i	0.526789	−	0.529343i
$970$		0			0
$971$	36.0265	+	86.9758i	0.0371025	+	0.0895734i	0.941345	−	0.337447i	$-0.109563\pi$
$971$	36.0265	+	86.9758i	0.0371025	+	0.0895734i	−0.904242	+	0.427020i	$0.859563\pi$
$972$		0			0
$973$	117.300	−	117.300i	0.120555	−	0.120555i
$974$		0			0
$975$	−51.8612	−	34.6526i	−0.0531910	−	0.0355411i
$976$		0			0
$977$	−37.2053	−	15.4109i	−0.0380812	−	0.0157737i	0.363562	−	0.931570i	$-0.381561\pi$
$977$	−37.2053	−	15.4109i	−0.0380812	−	0.0157737i	−0.401643	+	0.915796i	$0.631561\pi$
$978$		0			0
$979$	−311.285	−	1564.93i	−0.317962	−	1.59850i
$980$		0			0
$981$	48.0173	−	241.399i	0.0489472	−	0.246074i
$982$		0			0
$983$	−446.498	−	668.231i	−0.454220	−	0.679788i	0.531714	−	0.846924i	$-0.321548\pi$
$983$	−446.498	−	668.231i	−0.454220	−	0.679788i	−0.985934	+	0.167136i	$0.946548\pi$
$984$		0			0
$985$			1132.35i			1.14959i
$986$		0			0
$987$	92.8531			0.0940761
$988$		0			0
$989$	202.597	−	135.371i	0.204851	−	0.136877i
$990$		0			0
$991$	686.047	+	136.463i	0.692278	+	0.137703i	0.528676	−	0.848824i	$-0.322689\pi$
$991$	686.047	+	136.463i	0.692278	+	0.137703i	0.163602	+	0.986526i	$0.447689\pi$
$992$		0			0
$993$	1205.73	−	239.836i	1.21423	−	0.241526i
$994$		0			0
$995$	−355.761	+	858.882i	−0.357548	+	0.863198i
$996$		0			0
$997$	236.294	−	353.639i	0.237005	−	0.354703i	−0.693833	−	0.720136i	$-0.744079\pi$
$997$	236.294	−	353.639i	0.237005	−	0.354703i	0.930837	+	0.365433i	$0.119079\pi$
$998$		0			0
$999$	−551.410	−	551.410i	−0.551962	−	0.551962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.97.2	✓	32
4.3	odd	2		272.3.bh.f.97.3		32
17.10	odd	16	inner	136.3.t.a.129.2	yes	32
68.27	even	16		272.3.bh.f.129.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.97.2	✓	32	1.1	even	1	trivial
136.3.t.a.129.2	yes	32	17.10	odd	16	inner
272.3.bh.f.97.3		32	4.3	odd	2
272.3.bh.f.129.3		32	68.27	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30540 + 1.54042i) q^{3} +(5.10009 + 1.01447i) q^{5} +(-1.70555 + 0.339255i) q^{7} +(-0.502166 + 1.21234i) q^{9} +O(q^{10})\)	\(q+(-2.30540 + 1.54042i) q^{3} +(5.10009 + 1.01447i) q^{5} +(-1.70555 + 0.339255i) q^{7} +(-0.502166 + 1.21234i) q^{9} +(-7.03331 + 10.5261i) q^{11} +(7.79731 + 7.79731i) q^{13} +(-13.3205 + 5.51752i) q^{15} +(-3.27621 + 16.6813i) q^{17} +(5.87515 + 14.1839i) q^{19} +(3.40939 - 3.40939i) q^{21} +(5.68800 + 3.80060i) q^{23} +(1.88474 + 0.780685i) q^{25} +(-5.57813 - 28.0431i) q^{27} +(8.05543 - 40.4974i) q^{29} +(2.61189 + 3.90897i) q^{31} -35.1012i q^{33} -9.04262 q^{35} +(22.6769 - 15.1522i) q^{37} +(-29.9871 - 5.96480i) q^{39} +(28.9062 - 5.74980i) q^{41} +(13.6306 - 32.9071i) q^{43} +(-3.79097 + 5.67358i) q^{45} +(13.6173 + 13.6173i) q^{47} +(-42.4763 + 17.5943i) q^{49} +(-18.1433 - 43.5039i) q^{51} +(16.1037 + 38.8777i) q^{53} +(-46.5489 + 46.5489i) q^{55} +(-35.3937 - 23.6493i) q^{57} +(68.7830 + 28.4908i) q^{59} +(-8.57149 - 43.0918i) q^{61} +(0.445178 - 2.23806i) q^{63} +(31.8568 + 47.6771i) q^{65} -120.452i q^{67} -18.9676 q^{69} +(35.3204 - 23.6003i) q^{71} +(-39.8798 - 7.93258i) q^{73} +(-5.54767 + 1.10350i) q^{75} +(8.42464 - 20.3389i) q^{77} +(-60.9820 + 91.2660i) q^{79} +(47.7071 + 47.7071i) q^{81} +(130.045 - 53.8664i) q^{83} +(-33.6317 + 81.7526i) q^{85} +(43.8120 + 105.772i) q^{87} +(-89.1222 + 89.1222i) q^{89} +(-15.9440 - 10.6534i) q^{91} +(-12.0429 - 4.98834i) q^{93} +(15.5746 + 78.2990i) q^{95} +(24.4520 - 122.928i) q^{97} +(-9.22927 - 13.8126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

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Database

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