LMFDB - Embedded newform 189.3.k.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	189.19
Dual form			189.3.k.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41697 - 2.45427i) q^{2} +(-2.01561 + 3.49114i) q^{4} +2.39855i q^{5} +(0.0107242 - 6.99999i) q^{7} +0.0884848 q^{8} +O(q^{10})$	\(q+(-1.41697 - 2.45427i) q^{2} +(-2.01561 + 3.49114i) q^{4} +2.39855i q^{5} +(0.0107242 - 6.99999i) q^{7} +0.0884848 q^{8} +(5.88667 - 3.39867i) q^{10} -11.3906 q^{11} +(-13.4628 + 7.77278i) q^{13} +(-17.1950 + 9.89246i) q^{14} +(7.93707 + 13.7474i) q^{16} +(-10.4807 + 6.05105i) q^{17} +(-13.8576 - 8.00071i) q^{19} +(-8.37367 - 4.83454i) q^{20} +(16.1401 + 27.9555i) q^{22} +16.0566 q^{23} +19.2470 q^{25} +(38.1529 + 22.0276i) q^{26} +(24.4163 + 14.1467i) q^{28} +(-16.2339 + 28.1180i) q^{29} +(-36.7194 - 21.1999i) q^{31} +(22.6701 - 39.2658i) q^{32} +(29.7018 + 17.1483i) q^{34} +(16.7898 + 0.0257224i) q^{35} +(-3.61406 + 6.25973i) q^{37} +45.3471i q^{38} +0.212235i q^{40} +(7.55990 - 4.36471i) q^{41} +(-22.2113 + 38.4711i) q^{43} +(22.9590 - 39.7661i) q^{44} +(-22.7518 - 39.4072i) q^{46} +(22.8382 - 13.1856i) q^{47} +(-48.9998 - 0.150138i) q^{49} +(-27.2724 - 47.2372i) q^{50} -62.6676i q^{52} +(-34.0624 - 58.9979i) q^{53} -27.3208i q^{55} +(0.000948925 - 0.619393i) q^{56} +92.0120 q^{58} +(-82.4104 - 47.5797i) q^{59} +(-42.8184 + 24.7212i) q^{61} +120.159i q^{62} -64.9952 q^{64} +(-18.6434 - 32.2913i) q^{65} +(40.9350 - 70.9015i) q^{67} -48.7863i q^{68} +(-23.7275 - 41.2431i) q^{70} +112.881 q^{71} +(58.8056 - 33.9514i) q^{73} +20.4840 q^{74} +(55.8633 - 32.2527i) q^{76} +(-0.122154 + 79.7339i) q^{77} +(-68.4439 - 118.548i) q^{79} +(-32.9738 + 19.0374i) q^{80} +(-21.4243 - 12.3693i) q^{82} +(-18.8674 - 10.8931i) q^{83} +(-14.5137 - 25.1385i) q^{85} +125.891 q^{86} -1.00789 q^{88} +(-93.9050 - 54.2161i) q^{89} +(54.2650 + 94.3232i) q^{91} +(-32.3639 + 56.0559i) q^{92} +(-64.7220 - 37.3673i) q^{94} +(19.1901 - 33.2382i) q^{95} +(96.5982 + 55.7710i) q^{97} +(69.0628 + 120.471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.41697	−	2.45427i	−0.708485	−	1.22713i	−0.965419	−	0.260704i	$-0.916045\pi$
$2$	−1.41697	−	2.45427i	−0.708485	−	1.22713i	0.256934	−	0.966429i	$-0.417288\pi$
$3$		0			0
$3$		0			0
$4$	−2.01561	+	3.49114i	−0.503903	+	0.872785i
$5$			2.39855i			0.479709i	0.970809	+	0.239855i	$0.0770998\pi$
$5$			2.39855i			0.479709i	−0.970809	+	0.239855i	$0.922900\pi$
$6$		0			0
$7$	0.0107242	−	6.99999i	0.00153202	−	0.999999i
$7$	0.0107242	−	6.99999i	0.00153202	−	0.999999i
$8$	0.0884848			0.0110606
$9$		0			0
$10$	5.88667	−	3.39867i	0.588667	−	0.339867i
$11$	−11.3906			−1.03551			−0.517753	−	0.855530i	$-0.673231\pi$
$11$	−11.3906			−1.03551			−0.517753	+	0.855530i	$0.673231\pi$
$12$		0			0
$13$	−13.4628	+	7.77278i	−1.03560	+	0.597906i	−0.918585	−	0.395224i	$-0.870667\pi$
$13$	−13.4628	+	7.77278i	−1.03560	+	0.597906i	−0.117019	+	0.993130i	$0.537334\pi$
$14$	−17.1950	+	9.89246i	−1.22822	+	0.706604i
$15$		0			0
$16$	7.93707	+	13.7474i	0.496067	+	0.859213i
$17$	−10.4807	+	6.05105i	−0.616513	+	0.355944i	−0.775510	−	0.631335i	$-0.782507\pi$
$17$	−10.4807	+	6.05105i	−0.616513	+	0.355944i	0.158997	+	0.987279i	$0.449174\pi$
$18$		0			0
$19$	−13.8576	−	8.00071i	−0.729350	−	0.421090i	0.0888345	−	0.996046i	$-0.471686\pi$
$19$	−13.8576	−	8.00071i	−0.729350	−	0.421090i	−0.818184	+	0.574956i	$0.805019\pi$
$20$	−8.37367	−	4.83454i	−0.418683	−	0.241727i
$21$		0			0
$22$	16.1401	+	27.9555i	0.733641	+	1.27070i
$23$	16.0566			0.698114			0.349057	−	0.937102i	$-0.386502\pi$
$23$	16.0566			0.698114			0.349057	+	0.937102i	$0.386502\pi$
$24$		0			0
$25$	19.2470			0.769879
$26$	38.1529	+	22.0276i	1.46742	+	0.847215i
$27$		0			0
$28$	24.4163	+	14.1467i	0.872012	+	0.505239i
$29$	−16.2339	+	28.1180i	−0.559791	+	0.969586i	0.437723	+	0.899110i	$0.355785\pi$
$29$	−16.2339	+	28.1180i	−0.559791	+	0.969586i	−0.997513	+	0.0704760i	$0.977548\pi$
$30$		0			0
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.227445	−	0.973791i	$-0.573037\pi$
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.957050	+	0.289922i	$0.906371\pi$
$32$	22.6701	−	39.2658i	0.708442	−	1.22706i
$33$		0			0
$34$	29.7018	+	17.1483i	0.873581	+	0.504362i
$35$	16.7898	+	0.0257224i	0.479709	+	0.000734926i
$36$		0			0
$37$	−3.61406	+	6.25973i	−0.0976772	+	0.169182i	−0.910723	−	0.413018i	$-0.864475\pi$
$37$	−3.61406	+	6.25973i	−0.0976772	+	0.169182i	0.813046	+	0.582200i	$0.197808\pi$
$38$			45.3471i			1.19335i
$39$		0			0
$40$			0.212235i			0.00530587i
$41$	7.55990	−	4.36471i	0.184388	−	0.106456i	−0.404965	−	0.914332i	$-0.632716\pi$
$41$	7.55990	−	4.36471i	0.184388	−	0.106456i	0.589353	+	0.807876i	$0.299383\pi$
$42$		0			0
$43$	−22.2113	+	38.4711i	−0.516542	+	0.894676i	0.483274	+	0.875469i	$0.339448\pi$
$43$	−22.2113	+	38.4711i	−0.516542	+	0.894676i	−0.999816	+	0.0192072i	$0.993886\pi$
$44$	22.9590	−	39.7661i	0.521795	−	0.903775i
$45$		0			0
$46$	−22.7518	−	39.4072i	−0.494603	−	0.856678i
$47$	22.8382	−	13.1856i	0.485919	−	0.280545i	−0.236961	−	0.971519i	$-0.576151\pi$
$47$	22.8382	−	13.1856i	0.485919	−	0.280545i	0.722880	+	0.690974i	$0.242818\pi$
$48$		0			0
$49$	−48.9998	−	0.150138i	−0.999995	−	0.00306404i
$50$	−27.2724	−	47.2372i	−0.545448	−	0.944744i
$51$		0			0
$52$		−	62.6676i		−	1.20515i
$53$	−34.0624	−	58.9979i	−0.642688	−	1.11317i	−0.984830	−	0.173520i	$-0.944486\pi$
$53$	−34.0624	−	58.9979i	−0.642688	−	1.11317i	0.342143	−	0.939648i	$-0.388847\pi$
$54$		0			0
$55$		−	27.3208i		−	0.496742i
$56$	0.000948925	−	0.619393i	1.69451e−5	−	0.0110606i
$57$		0			0
$58$	92.0120			1.58641
$59$	−82.4104	−	47.5797i	−1.39679	−	0.806435i	−0.402732	−	0.915318i	$-0.631939\pi$
$59$	−82.4104	−	47.5797i	−1.39679	−	0.806435i	−0.994055	+	0.108883i	$0.965273\pi$
$60$		0			0
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	−0.808070	−	0.589087i	$-0.799488\pi$
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	0.106129	+	0.994352i	$0.466154\pi$
$62$			120.159i			1.93804i
$63$		0			0
$64$	−64.9952			−1.01555
$65$	−18.6434	−	32.2913i	−0.286821	−	0.496789i
$66$		0			0
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	−0.380107	−	0.924943i	$-0.624113\pi$
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	0.991077	−	0.133289i	$-0.0425539\pi$
$68$		−	48.7863i		−	0.717445i
$69$		0			0
$70$	−23.7275	−	41.2431i	−0.338965	−	0.589187i
$71$	112.881			1.58987			0.794936	−	0.606694i	$-0.207504\pi$
$71$	112.881			1.58987			0.794936	+	0.606694i	$0.207504\pi$
$72$		0			0
$73$	58.8056	−	33.9514i	0.805556	−	0.465088i	−0.0398541	−	0.999206i	$-0.512689\pi$
$73$	58.8056	−	33.9514i	0.805556	−	0.465088i	0.845410	+	0.534117i	$0.179356\pi$
$74$	20.4840			0.276811
$75$		0			0
$76$	55.8633	−	32.2527i	0.735043	−	0.424377i
$77$	−0.122154	+	79.7339i	−0.00158642	+	1.03551i
$78$		0			0
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.865671	−	0.500613i	$-0.833108\pi$
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.000707812	−	1.00000i	$-0.500225\pi$
$80$	−32.9738	+	19.0374i	−0.412172	+	0.237968i
$81$		0			0
$82$	−21.4243	−	12.3693i	−0.261272	−	0.150846i
$83$	−18.8674	−	10.8931i	−0.227318	−	0.131242i	0.382016	−	0.924156i	$-0.375230\pi$
$83$	−18.8674	−	10.8931i	−0.227318	−	0.131242i	−0.609334	+	0.792913i	$0.708563\pi$
$84$		0			0
$85$	−14.5137	−	25.1385i	−0.170750	−	0.295747i
$86$	125.891			1.46385
$87$		0			0
$88$	−1.00789			−0.0114533
$89$	−93.9050	−	54.2161i	−1.05511	−	0.609169i	−0.131036	−	0.991378i	$-0.541830\pi$
$89$	−93.9050	−	54.2161i	−1.05511	−	0.609169i	−0.924076	+	0.382208i	$0.875164\pi$
$90$		0			0
$91$	54.2650	+	94.3232i	0.596319	+	1.03652i
$92$	−32.3639	+	56.0559i	−0.351782	+	0.609304i
$93$		0			0
$94$	−64.7220	−	37.3673i	−0.688532	−	0.397524i
$95$	19.1901	−	33.2382i	0.202001	−	0.349876i
$96$		0			0
$97$	96.5982	+	55.7710i	0.995857	+	0.574959i	0.907020	−	0.421088i	$-0.138351\pi$
$97$	96.5982	+	55.7710i	0.995857	+	0.574959i	0.0888375	+	0.996046i	$0.471685\pi$
$98$	69.0628	+	120.471i	0.704722	+	1.22930i
$99$		0			0
$100$	−38.7944	+	67.1939i	−0.387944	+	0.671939i
$101$		−	76.8626i		−	0.761016i	−0.924778	−	0.380508i	$-0.875749\pi$
$101$		−	76.8626i		−	0.761016i	0.924778	−	0.380508i	$-0.124251\pi$
$102$		0			0
$103$			150.781i			1.46389i	0.681362	+	0.731946i	$0.261388\pi$
$103$			150.781i			1.46389i	−0.681362	+	0.731946i	$0.738612\pi$
$104$	−1.19126	+	0.687773i	−0.0114544	+	0.00661320i
$105$		0			0
$106$	−96.5310	+	167.197i	−0.910669	+	1.57733i
$107$	38.3022	−	66.3413i	0.357964	−	0.620013i	−0.629656	−	0.776874i	$-0.716804\pi$
$107$	38.3022	−	66.3413i	0.357964	−	0.620013i	0.987621	+	0.156861i	$0.0501376\pi$
$108$		0			0
$109$	12.5985	+	21.8212i	0.115582	+	0.200195i	0.918012	−	0.396552i	$-0.129793\pi$
$109$	12.5985	+	21.8212i	0.115582	+	0.200195i	−0.802430	+	0.596746i	$0.796460\pi$
$110$	−67.0525	+	38.7128i	−0.609568	+	0.351934i
$111$		0			0
$112$	96.3168	−	55.4120i	0.859972	−	0.494750i
$113$	−37.0748	−	64.2154i	−0.328095	−	0.568277i	0.654039	−	0.756461i	$-0.273073\pi$
$113$	−37.0748	−	64.2154i	−0.328095	−	0.568277i	−0.982134	+	0.188184i	$0.939740\pi$
$114$		0			0
$115$			38.5125i			0.334892i
$116$	−65.4426	−	113.350i	−0.564160	−	0.977154i
$117$		0			0
$118$			269.676i			2.28539i
$119$	42.2449	+	73.4299i	0.354999	+	0.617058i
$120$		0			0
$121$	8.74506			0.0722732
$122$	121.345	+	70.0585i	0.994629	+	0.574250i
$123$		0			0
$124$	148.024	−	85.4617i	1.19374	−	0.689207i
$125$			106.128i			0.849027i
$126$		0			0
$127$	52.2864			0.411704			0.205852	−	0.978583i	$-0.434003\pi$
$127$	52.2864			0.411704			0.205852	+	0.978583i	$0.434003\pi$
$128$	1.41571	+	2.45209i	0.0110603	+	0.0191569i
$129$		0			0
$130$	−52.8342	+	91.5116i	−0.406417	+	0.703935i
$131$			186.539i			1.42396i	0.702198	+	0.711982i	$0.252202\pi$
$131$			186.539i			1.42396i	−0.702198	+	0.711982i	$0.747798\pi$
$132$		0			0
$133$	−56.1535	+	96.9176i	−0.422207	+	0.728704i
$134$	−232.015			−1.73145
$135$		0			0
$136$	−0.927385	+	0.535426i	−0.00681901	+	0.00393696i
$137$	153.374			1.11952			0.559760	−	0.828655i	$-0.310893\pi$
$137$	153.374			1.11952			0.559760	+	0.828655i	$0.310893\pi$
$138$		0			0
$139$	−79.0232	+	45.6241i	−0.568513	+	0.328231i	−0.756555	−	0.653930i	$-0.773119\pi$
$139$	−79.0232	+	45.6241i	−0.568513	+	0.328231i	0.188043	+	0.982161i	$0.439786\pi$
$140$	−33.9315	+	58.5637i	−0.242368	+	0.418312i
$141$		0			0
$142$	−159.949	−	277.040i	−1.12640	−	1.95098i
$143$	153.349	−	88.5364i	1.07237	−	0.619135i
$144$		0			0
$145$	−67.4423	−	38.9378i	−0.465119	−	0.268537i
$146$	−166.652	−	96.2164i	−1.14145	−	0.659016i
$147$		0			0
$148$	−14.5691	−	25.2344i	−0.0984396	−	0.170502i
$149$	−112.412			−0.754445			−0.377223	−	0.926123i	$-0.623121\pi$
$149$	−112.412			−0.754445			−0.377223	+	0.926123i	$0.623121\pi$
$150$		0			0
$151$	28.1969			0.186734			0.0933671	−	0.995632i	$-0.470237\pi$
$151$	28.1969			0.186734			0.0933671	+	0.995632i	$0.470237\pi$
$152$	−1.22619	−	0.707942i	−0.00806705	−	0.00465751i
$153$		0			0
$154$	195.861	−	112.681i	1.27183	−	0.731693i
$155$	50.8490	−	88.0731i	0.328058	−	0.568214i
$156$		0			0
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	0.471462	−	0.881886i	$-0.343726\pi$
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	−0.528005	+	0.849241i	$0.677060\pi$
$158$	−193.966	+	335.959i	−1.22763	+	2.12632i
$159$		0			0
$160$	94.1810	+	54.3754i	0.588631	+	0.339846i
$161$	0.172194	−	112.396i	0.00106953	−	0.698113i
$162$		0			0
$163$	88.8411	−	153.877i	0.545037	−	0.944033i	−0.453567	−	0.891222i	$-0.649849\pi$
$163$	88.8411	−	153.877i	0.545037	−	0.944033i	0.998605	−	0.0528105i	$-0.0168179\pi$
$164$			35.1903i			0.214575i
$165$		0			0
$166$			61.7409i			0.371933i
$167$	−53.9725	+	31.1611i	−0.323189	+	0.186593i	−0.652813	−	0.757519i	$-0.726411\pi$
$167$	−53.9725	+	31.1611i	−0.323189	+	0.186593i	0.329624	+	0.944112i	$0.393078\pi$
$168$		0			0
$169$	36.3322	−	62.9292i	0.214983	−	0.372362i
$170$	−41.1311	+	71.2411i	−0.241947	+	0.419065i
$171$		0			0
$172$	−89.5387	−	155.086i	−0.520574	−	0.901660i
$173$	−76.2216	+	44.0066i	−0.440587	+	0.254373i	−0.703847	−	0.710352i	$-0.748536\pi$
$173$	−76.2216	+	44.0066i	−0.440587	+	0.254373i	0.263259	+	0.964725i	$0.415203\pi$
$174$		0			0
$175$	0.206408	−	134.729i	0.00117947	−	0.769878i
$176$	−90.4077	−	156.591i	−0.513680	−	0.889720i
$177$		0			0
$178$			307.290i			1.72635i
$179$	6.47603	+	11.2168i	0.0361789	+	0.0626638i	0.883548	−	0.468341i	$-0.155148\pi$
$179$	6.47603	+	11.2168i	0.0361789	+	0.0626638i	−0.847369	+	0.531005i	$0.821815\pi$
$180$		0			0
$181$		−	225.852i		−	1.24780i	−0.781503	−	0.623901i	$-0.785547\pi$
$181$		−	225.852i		−	1.24780i	0.781503	−	0.623901i	$-0.214453\pi$
$182$	154.602	−	266.834i	0.849462	−	1.46612i
$183$		0			0
$184$	1.42077			0.00772156
$185$	−15.0143	−	8.66848i	−0.0811581	−	0.0468567i
$186$		0			0
$187$	119.381	−	68.9249i	0.638404	−	0.368582i
$188$			106.308i			0.565470i
$189$		0			0
$190$	−108.767			−0.572459
$191$	51.9453	+	89.9718i	0.271965	+	0.471057i	0.969365	−	0.245625i	$-0.0789933\pi$
$191$	51.9453	+	89.9718i	0.271965	+	0.471057i	−0.697400	+	0.716682i	$0.745660\pi$
$192$		0			0
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	−0.995996	−	0.0893998i	$-0.971505\pi$
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	0.575420	+	0.817858i	$0.304838\pi$
$194$		−	316.103i		−	1.62940i
$195$		0			0
$196$	99.2887	−	170.763i	0.506575	−	0.871237i
$197$	−301.595			−1.53094			−0.765470	−	0.643472i	$-0.777493\pi$
$197$	−301.595			−1.53094			−0.765470	+	0.643472i	$0.777493\pi$
$198$		0			0
$199$	50.0571	−	28.9005i	0.251543	−	0.145229i	−0.368927	−	0.929458i	$-0.620275\pi$
$199$	50.0571	−	28.9005i	0.251543	−	0.145229i	0.620471	+	0.784230i	$0.286942\pi$
$200$	1.70307			0.00851533
$201$		0			0
$202$	−188.641	+	108.912i	−0.933868	+	0.539169i
$203$	196.652	+	113.939i	0.968727	+	0.561276i
$204$		0			0
$205$	10.4690	+	18.1328i	0.0510681	+	0.0884526i
$206$	370.056	−	213.652i	1.79639	−	1.03715i
$207$		0			0
$208$	−213.711	−	123.386i	−1.02746	−	0.593202i
$209$	157.846	+	91.1327i	0.755246	+	0.436042i
$210$		0			0
$211$	−21.2197	−	36.7535i	−0.100567	−	0.174187i	0.811351	−	0.584559i	$-0.198732\pi$
$211$	−21.2197	−	36.7535i	−0.100567	−	0.174187i	−0.911918	+	0.410371i	$0.865399\pi$
$212$	274.627			1.29541
$213$		0			0
$214$	−217.092			−1.01445
$215$	−92.2747	−	53.2748i	−0.429185	−	0.247790i
$216$		0			0
$217$	−148.793	+	256.808i	−0.685683	+	1.18345i
$218$	35.7034	−	61.8400i	0.163777	−	0.283670i
$219$		0			0
$220$	95.3808	+	55.0681i	0.433549	+	0.250310i
$221$	94.0670	−	162.929i	0.425642	−	0.737234i
$222$		0			0
$223$	166.212	+	95.9625i	0.745345	+	0.430325i	0.824009	−	0.566576i	$-0.191732\pi$
$223$	166.212	+	95.9625i	0.745345	+	0.430325i	−0.0786645	+	0.996901i	$0.525066\pi$
$224$	−274.618	−	159.112i	−1.22597	−	0.710321i
$225$		0			0
$226$	−105.068	+	181.983i	−0.464901	+	0.805233i
$227$			224.779i			0.990216i	0.868831	+	0.495108i	$0.164872\pi$
$227$			224.779i			0.990216i	−0.868831	+	0.495108i	$0.835128\pi$
$228$		0			0
$229$		−	160.148i		−	0.699338i	−0.936873	−	0.349669i	$-0.886294\pi$
$229$		−	160.148i		−	0.699338i	0.936873	−	0.349669i	$-0.113706\pi$
$230$	94.5200	−	54.5712i	0.410957	−	0.237266i
$231$		0			0
$232$	−1.43646	+	2.48802i	−0.00619162	+	0.0107242i
$233$	−123.299	+	213.560i	−0.529180	+	0.916566i	0.470241	+	0.882538i	$0.344167\pi$
$233$	−123.299	+	213.560i	−0.529180	+	0.916566i	−0.999421	+	0.0340281i	$0.989166\pi$
$234$		0			0
$235$	31.6263	+	54.7784i	0.134580	+	0.233100i
$236$	332.215	−	191.804i	1.40769	−	0.812730i
$237$		0			0
$238$	120.357	−	207.728i	0.505700	−	0.872808i
$239$	110.141	+	190.769i	0.460839	+	0.798197i	0.999003	−	0.0446434i	$-0.0142152\pi$
$239$	110.141	+	190.769i	0.460839	+	0.798197i	−0.538164	+	0.842840i	$0.680882\pi$
$240$		0			0
$241$			263.598i			1.09377i	0.837209	+	0.546883i	$0.184186\pi$
$241$			263.598i			1.09377i	−0.837209	+	0.546883i	$0.815814\pi$
$242$	−12.3915	−	21.4627i	−0.0512045	−	0.0886889i
$243$		0			0
$244$		−	199.313i		−	0.816858i
$245$	0.360113	−	117.528i	0.00146985	−	0.479707i
$246$		0			0
$247$	248.751			1.00709
$248$	−3.24911	−	1.87587i	−0.0131012	−	0.00756400i
$249$		0			0
$250$	260.467	−	150.381i	1.04187	−	0.601523i
$251$			23.0003i			0.0916348i	0.998950	+	0.0458174i	$0.0145892\pi$
$251$			23.0003i			0.0916348i	−0.998950	+	0.0458174i	$0.985411\pi$
$252$		0			0
$253$	−182.894			−0.722901
$254$	−74.0883	−	128.325i	−0.291686	−	0.505215i
$255$		0			0
$256$	−125.978	+	218.201i	−0.492103	+	0.852347i
$257$			17.8170i			0.0693270i	0.999399	+	0.0346635i	$0.0110359\pi$
$257$			17.8170i			0.0693270i	−0.999399	+	0.0346635i	$0.988964\pi$
$258$		0			0
$259$	43.7793	+	25.3655i	0.169032	+	0.0979363i
$260$	150.311			0.578120
$261$		0			0
$262$	457.817	−	264.321i	1.74739	−	1.00886i
$263$	363.008			1.38026			0.690130	−	0.723685i	$-0.257553\pi$
$263$	363.008			1.38026			0.690130	+	0.723685i	$0.257553\pi$
$264$		0			0
$265$	141.509	−	81.7004i	0.533997	−	0.308303i
$266$	317.429	+	0.486310i	1.19334	+	0.00182823i
$267$		0			0
$268$	165.018	+	285.820i	0.615740	+	1.06649i
$269$	−169.879	+	98.0794i	−0.631519	+	0.364607i	−0.781340	−	0.624106i	$-0.785463\pi$
$269$	−169.879	+	98.0794i	−0.631519	+	0.364607i	0.149821	+	0.988713i	$0.452130\pi$
$270$		0			0
$271$	−82.5249	−	47.6458i	−0.304520	−	0.175815i	0.339952	−	0.940443i	$-0.389589\pi$
$271$	−82.5249	−	47.6458i	−0.304520	−	0.175815i	−0.644472	+	0.764628i	$0.722923\pi$
$272$	−166.372	−	96.0552i	−0.611663	−	0.353144i
$273$		0			0
$274$	−217.327	−	376.421i	−0.793163	−	1.37380i
$275$	−219.234			−0.797214
$276$		0			0
$277$	−215.451			−0.777801			−0.388901	−	0.921280i	$-0.627145\pi$
$277$	−215.451			−0.777801			−0.388901	+	0.921280i	$0.627145\pi$
$278$	223.947	+	129.296i	0.805566	+	0.465093i
$279$		0			0
$280$	1.48564	+	0.00227604i	0.00530587	+	8.12872e-6i
$281$	−101.916	+	176.523i	−0.362689	+	0.628196i	−0.988402	−	0.151857i	$-0.951475\pi$
$281$	−101.916	+	176.523i	−0.362689	+	0.628196i	0.625713	+	0.780053i	$0.284808\pi$
$282$		0			0
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	0.304233	−	0.952598i	$-0.401600\pi$
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	−0.672857	+	0.739773i	$0.734933\pi$
$284$	−227.524	+	394.083i	−0.801141	+	1.38762i
$285$		0			0
$286$	−434.583	−	250.907i	−1.51952	−	0.877297i
$287$	−30.4719	−	52.9661i	−0.106174	−	0.184551i
$288$		0			0
$289$	−71.2696	+	123.442i	−0.246607	+	0.427137i
$290$			220.695i			0.761018i
$291$		0			0
$292$			273.732i			0.937437i
$293$	−151.688	+	87.5769i	−0.517705	+	0.298897i	−0.735995	−	0.676987i	$-0.763285\pi$
$293$	−151.688	+	87.5769i	−0.517705	+	0.298897i	0.218290	+	0.975884i	$0.429952\pi$
$294$		0			0
$295$	114.122	−	197.665i	0.386854	−	0.670051i
$296$	−0.319789	+	0.553891i	−0.00108037	+	0.00187125i
$297$		0			0
$298$	159.285	+	275.890i	0.534513	+	0.925804i
$299$	−216.168	+	124.805i	−0.722969	+	0.417406i
$300$		0			0
$301$	269.059	+	155.891i	0.893884	+	0.517912i
$302$	−39.9541	−	69.2026i	−0.132298	−	0.229148i
$303$		0			0
$304$		−	254.009i		−	0.835555i
$305$	−59.2950	−	102.702i	−0.194410	−	0.336728i
$306$		0			0
$307$			18.3665i			0.0598259i	0.999553	+	0.0299129i	$0.00952300\pi$
$307$			18.3665i			0.0598259i	−0.999553	+	0.0299129i	$0.990477\pi$
$308$	−278.116	−	161.139i	−0.902974	−	0.523179i
$309$		0			0
$310$	−288.206			−0.929698
$311$	−353.193	−	203.916i	−1.13567	−	0.655679i	−0.190315	−	0.981723i	$-0.560951\pi$
$311$	−353.193	−	203.916i	−1.13567	−	0.655679i	−0.945355	+	0.326044i	$0.894284\pi$
$312$		0			0
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.939952	−	0.341307i	$-0.889130\pi$
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.174396	+	0.984676i	$0.555797\pi$
$314$			29.0495i			0.0925145i
$315$		0			0
$316$	551.826			1.74628
$317$	−148.273	−	256.817i	−0.467739	−	0.810149i	0.531581	−	0.847007i	$-0.321598\pi$
$317$	−148.273	−	256.817i	−0.467739	−	0.810149i	−0.999320	+	0.0368589i	$0.988265\pi$
$318$		0			0
$319$	184.914	−	320.280i	0.579667	−	1.00401i
$320$		−	155.894i		−	0.487169i
$321$		0			0
$322$	−276.094	+	158.840i	−0.857435	+	0.493290i
$323$	193.651			0.599539
$324$		0			0
$325$	−259.119	+	149.602i	−0.797289	+	0.460315i
$326$	−503.541			−1.54460
$327$		0			0
$328$	0.668937	−	0.386211i	0.00203944	−	0.00117747i
$329$	−92.0543	−	160.008i	−0.279800	−	0.486348i
$330$		0			0
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	−0.916241	−	0.400627i	$-0.868792\pi$
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	0.111167	−	0.993802i	$-0.464541\pi$
$332$	76.0588	−	43.9126i	0.229093	−	0.132267i
$333$		0			0
$334$	152.955	+	88.3086i	0.457949	+	0.264397i
$335$	170.061	+	98.1846i	0.507644	+	0.293088i
$336$		0			0
$337$	149.044	+	258.152i	0.442267	+	0.766029i	0.997857	−	0.0654274i	$-0.0208411\pi$
$337$	149.044	+	258.152i	0.442267	+	0.766029i	−0.555590	+	0.831456i	$0.687508\pi$
$338$	−205.926			−0.609250
$339$		0			0
$340$	117.016			0.344165
$341$	418.255	+	241.479i	1.22655	+	0.708151i
$342$		0			0
$343$	−1.57645	+	342.996i	−0.00459605	+	0.999989i
$344$	−1.96536	+	3.40411i	−0.00571326	+	0.00989566i
$345$		0			0
$346$	216.008	+	124.712i	0.624300	+	0.360439i
$347$	−90.4019	+	156.581i	−0.260524	+	0.451241i	−0.966381	−	0.257113i	$-0.917229\pi$
$347$	−90.4019	+	156.581i	−0.260524	+	0.451241i	0.705857	+	0.708354i	$0.250562\pi$
$348$		0			0
$349$	151.888	+	87.6925i	0.435209	+	0.251268i	0.701563	−	0.712607i	$-0.252486\pi$
$349$	151.888	+	87.6925i	0.435209	+	0.251268i	−0.266354	+	0.963875i	$0.585819\pi$
$350$	−330.952	+	190.400i	−0.945578	+	0.544000i
$351$		0			0
$352$	−258.226	+	447.260i	−0.733596	+	1.27063i
$353$			39.3099i			0.111359i	0.998449	+	0.0556797i	$0.0177326\pi$
$353$			39.3099i			0.111359i	−0.998449	+	0.0556797i	$0.982267\pi$
$354$		0			0
$355$			270.750i			0.762676i
$356$	378.552	−	218.557i	1.06335	−	0.613924i
$357$		0			0
$358$	18.3527	−	31.7878i	0.0512645	−	0.0887927i
$359$	123.823	−	214.468i	0.344912	−	0.597405i	−0.640426	−	0.768020i	$-0.721242\pi$
$359$	123.823	−	214.468i	0.344912	−	0.597405i	0.985338	+	0.170615i	$0.0545755\pi$
$360$		0			0
$361$	−52.4771	−	90.8930i	−0.145366	−	0.251781i
$362$	−554.302	+	320.026i	−1.53122	+	0.884050i
$363$		0			0
$364$	−438.673	−	0.672057i	−1.20514	−	0.00184631i
$365$	81.4341	+	141.048i	0.223107	+	0.386433i
$366$		0			0
$367$		−	396.795i		−	1.08119i	−0.841284	−	0.540593i	$-0.818200\pi$
$367$		−	396.795i		−	1.08119i	0.841284	−	0.540593i	$-0.181800\pi$
$368$	127.442	+	220.737i	0.346311	+	0.599828i
$369$		0			0
$370$			49.1319i			0.132789i
$371$	−413.350	+	237.804i	−1.11415	+	0.640981i
$372$		0			0
$373$	373.141			1.00038			0.500189	−	0.865916i	$-0.333264\pi$
$373$	373.141			1.00038			0.500189	+	0.865916i	$0.333264\pi$
$374$	−338.320	−	195.329i	−0.904599	−	0.522271i
$375$		0			0
$376$	2.02083	−	1.16673i	0.00537455	−	0.00310300i
$377$		−	504.731i		−	1.33881i
$378$		0			0
$379$	548.285			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$379$	548.285			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$380$	77.3595	+	133.991i	0.203578	+	0.352607i
$381$		0			0
$382$	147.210	−	254.975i	0.385366	−	0.667474i
$383$		−	4.66627i		−	0.0121835i	−0.999981	−	0.00609174i	$-0.998061\pi$
$383$		−	4.66627i		−	0.0121835i	0.999981	−	0.00609174i	$-0.00193907\pi$
$384$		0			0
$385$	−191.245	−	0.292993i	−0.496741	−	0.000761020i
$386$	460.068			1.19189
$387$		0			0
$388$	−389.409	+	224.825i	−1.00363	+	0.579447i
$389$	672.626			1.72912			0.864558	−	0.502533i	$-0.167599\pi$
$389$	672.626			1.72912			0.864558	+	0.502533i	$0.167599\pi$
$390$		0			0
$391$	−168.285	+	97.1594i	−0.430397	+	0.248490i
$392$	−4.33574	−	0.0132849i	−0.0110606	−	3.38902e-5i
$393$		0			0
$394$	427.351	+	740.194i	1.08465	+	1.87867i
$395$	284.344	−	164.166i	0.719858	−	0.415610i
$396$		0			0
$397$	92.0332	+	53.1354i	0.231822	+	0.133842i	0.611412	−	0.791312i	$-0.290602\pi$
$397$	92.0332	+	53.1354i	0.231822	+	0.133842i	−0.379591	+	0.925155i	$0.623935\pi$
$398$	−141.859	−	81.9023i	−0.356429	−	0.205785i
$399$		0			0
$400$	152.765	+	264.596i	0.381911	+	0.661490i
$401$	298.393			0.744122			0.372061	−	0.928208i	$-0.378651\pi$
$401$	298.393			0.744122			0.372061	+	0.928208i	$0.378651\pi$
$402$		0			0
$403$	659.130			1.63556
$404$	268.338	+	154.925i	0.664204	+	0.383478i
$405$		0			0
$406$	0.986752	−	644.083i	0.00243042	−	1.58641i
$407$	41.1662	−	71.3019i	0.101145	−	0.175189i
$408$		0			0
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.401661	−	0.915789i	$-0.631567\pi$
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.993927	+	0.110046i	$0.964900\pi$
$410$	29.6684	−	51.3872i	0.0723620	−	0.125335i
$411$		0			0
$412$	−526.398	−	303.916i	−1.27766	−	0.737660i
$413$	−333.941	+	576.362i	−0.808574	+	1.39555i
$414$		0			0
$415$	26.1276	−	45.2544i	0.0629582	−	0.109047i
$416$			704.840i			1.69433i
$417$		0			0
$418$		−	516.529i		−	1.23572i
$419$	485.296	−	280.186i	1.15822	−	0.668701i	0.207346	−	0.978268i	$-0.433517\pi$
$419$	485.296	−	280.186i	1.15822	−	0.668701i	0.950878	+	0.309566i	$0.100184\pi$
$420$		0			0
$421$	57.9969	−	100.454i	0.137760	−	0.238607i	−0.788889	−	0.614536i	$-0.789343\pi$
$421$	57.9969	−	100.454i	0.137760	−	0.238607i	0.926648	+	0.375929i	$0.122676\pi$
$422$	−60.1353	+	104.157i	−0.142501	+	0.246818i
$423$		0			0
$424$	−3.01401	−	5.22042i	−0.00710851	−	0.0123123i
$425$	−201.722	+	116.464i	−0.474641	+	0.274034i
$426$		0			0
$427$	172.589	+	299.993i	0.404190	+	0.702561i
$428$	154.405	+	267.437i	0.360759	+	0.624852i
$429$		0			0
$430$			301.955i			0.702222i
$431$	−161.254	−	279.299i	−0.374138	−	0.648027i	0.616059	−	0.787700i	$-0.288728\pi$
$431$	−161.254	−	279.299i	−0.374138	−	0.648027i	−0.990198	+	0.139673i	$0.955395\pi$
$432$		0			0
$433$			117.316i			0.270937i	0.990782	+	0.135468i	$0.0432539\pi$
$433$			117.316i			0.270937i	−0.990782	+	0.135468i	$0.956746\pi$
$434$	841.110	+	1.28860i	1.93804	+	0.00296913i
$435$		0			0
$436$	−101.575			−0.232969
$437$	−222.507	−	128.464i	−0.509169	−	0.293969i
$438$		0			0
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	−0.698393	−	0.715714i	$-0.746101\pi$
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	0.270630	+	0.962683i	$0.412768\pi$
$440$		−	2.41748i		−	0.00549427i
$441$		0			0
$442$	−533.160			−1.20625
$443$	−74.8709	−	129.680i	−0.169009	−	0.292732i	0.769063	−	0.639173i	$-0.220723\pi$
$443$	−74.8709	−	129.680i	−0.169009	−	0.292732i	−0.938072	+	0.346441i	$0.887390\pi$
$444$		0			0
$445$	130.040	−	225.235i	0.292224	−	0.506147i
$446$		−	543.904i		−	1.21952i
$447$		0			0
$448$	−0.697019	+	454.966i	−0.00155585	+	1.01555i
$449$	263.767			0.587455			0.293727	−	0.955889i	$-0.405104\pi$
$449$	263.767			0.587455			0.293727	+	0.955889i	$0.405104\pi$
$450$		0			0
$451$	−86.1116	+	49.7166i	−0.190935	+	0.110236i
$452$	298.913			0.661312
$453$		0			0
$454$	551.668	−	318.505i	1.21513	−	0.701554i
$455$	−226.239	+	130.157i	−0.497228	+	0.286060i
$456$		0			0
$457$	109.396	+	189.480i	0.239379	+	0.414617i	0.960536	−	0.278154i	$-0.0897227\pi$
$457$	109.396	+	189.480i	0.239379	+	0.414617i	−0.721157	+	0.692772i	$0.756389\pi$
$458$	−393.047	+	226.926i	−0.858180	+	0.495471i
$459$		0			0
$460$	−134.453	−	77.6263i	−0.292289	−	0.168753i
$461$	−334.892	−	193.350i	−0.726446	−	0.419414i	0.0906743	−	0.995881i	$-0.471098\pi$
$461$	−334.892	−	193.350i	−0.726446	−	0.419414i	−0.817121	+	0.576467i	$0.804431\pi$
$462$		0			0
$463$	241.881	+	418.950i	0.522421	+	0.904860i	0.999660	+	0.0260863i	$0.00830447\pi$
$463$	241.881	+	418.950i	0.522421	+	0.904860i	−0.477238	+	0.878774i	$0.658362\pi$
$464$	−515.399			−1.11077
$465$		0			0
$466$	698.843			1.49966
$467$	100.042	+	57.7593i	0.214223	+	0.123682i	0.603272	−	0.797535i	$-0.293863\pi$
$467$	100.042	+	57.7593i	0.214223	+	0.123682i	−0.389049	+	0.921217i	$0.627196\pi$
$468$		0			0
$469$	−495.871	−	287.305i	−1.05729	−	0.612591i
$470$	89.6272	−	155.239i	0.190696	−	0.330295i
$471$		0			0
$472$	−7.29207	−	4.21008i	−0.0154493	−	0.00891966i
$473$	252.999	−	438.208i	0.534882	−	0.926443i
$474$		0			0
$475$	−266.718	−	153.990i	−0.561511	−	0.324189i
$476$	−341.504	−	0.523192i	−0.717444	−	0.00109914i
$477$		0			0
$478$	312.132	−	540.628i	0.652996	−	1.13102i
$479$		−	455.647i		−	0.951246i	−0.879649	−	0.475623i	$-0.842223\pi$
$479$		−	455.647i		−	0.951246i	0.879649	−	0.475623i	$-0.157777\pi$
$480$		0			0
$481$		−	112.365i		−	0.233607i
$482$	646.939	−	373.510i	1.34220	−	0.774918i
$483$		0			0
$484$	−17.6267	+	30.5303i	−0.0364187	+	0.0630790i
$485$	−133.769	+	231.695i	−0.275813	+	0.477722i
$486$		0			0
$487$	−162.334	−	281.171i	−0.333335	−	0.577354i	0.649828	−	0.760081i	$-0.274841\pi$
$487$	−162.334	−	281.171i	−0.333335	−	0.577354i	−0.983164	+	0.182727i	$0.941507\pi$
$488$	−3.78878	+	2.18745i	−0.00776389	+	0.00448248i
$489$		0			0
$490$	−288.956	+	165.650i	−0.589706	+	0.338062i
$491$	155.221	+	268.850i	0.316132	+	0.547557i	0.979678	−	0.200579i	$-0.0642824\pi$
$491$	155.221	+	268.850i	0.316132	+	0.547557i	−0.663545	+	0.748136i	$0.730949\pi$
$492$		0			0
$493$		−	392.929i		−	0.797017i
$494$	−352.473	−	610.501i	−0.713508	−	1.23583i
$495$		0			0
$496$		−	673.061i		−	1.35698i
$497$	1.21055	−	790.165i	0.00243572	−	1.58987i
$498$		0			0
$499$	−774.220			−1.55154			−0.775771	−	0.631014i	$-0.782639\pi$
$499$	−774.220			−1.55154			−0.775771	+	0.631014i	$0.782639\pi$
$500$	−370.509	−	213.914i	−0.741019	−	0.427827i
$501$		0			0
$502$	56.4489	−	32.5908i	0.112448	−	0.0649219i
$503$			106.472i			0.211674i	0.994384	+	0.105837i	$0.0337521\pi$
$503$			106.472i			0.211674i	−0.994384	+	0.105837i	$0.966248\pi$
$504$		0			0
$505$	184.359			0.365067
$506$	259.155	+	448.870i	0.512165	+	0.887096i
$507$		0			0
$508$	−105.389	+	182.539i	−0.207459	+	0.359329i
$509$			338.626i			0.665276i	0.943055	+	0.332638i	$0.107939\pi$
$509$			338.626i			0.665276i	−0.943055	+	0.332638i	$0.892061\pi$
$510$		0			0
$511$	−237.029	−	412.003i	−0.463853	−	0.806268i
$512$	725.356			1.41671
$513$		0			0
$514$	43.7277	−	25.2462i	0.0850734	−	0.0491172i
$515$	−361.655			−0.702243
$516$		0			0
$517$	−260.140	+	150.192i	−0.503172	+	0.290506i
$518$	0.219674	−	143.388i	0.000424081	−	0.276811i
$519$		0			0
$520$	−1.64966	−	2.85729i	−0.00317241	−	0.00549478i
$521$	84.1424	−	48.5796i	0.161502	−	0.0932431i	−0.417071	−	0.908874i	$-0.636943\pi$
$521$	84.1424	−	48.5796i	0.161502	−	0.0932431i	0.578573	+	0.815631i	$0.303610\pi$
$522$		0			0
$523$	513.773	+	296.627i	0.982357	+	0.567164i	0.902981	−	0.429681i	$-0.141374\pi$
$523$	513.773	+	296.627i	0.982357	+	0.567164i	0.0793761	+	0.996845i	$0.474707\pi$
$524$	−651.235	−	375.990i	−1.24281	−	0.717539i
$525$		0			0
$526$	−514.372	−	890.919i	−0.977894	−	1.69376i
$527$	513.128			0.973677
$528$		0			0
$529$	−271.185			−0.512637
$530$	−401.029	−	231.534i	−0.756658	−	0.436857i
$531$		0			0
$532$	−225.169	−	391.388i	−0.423251	−	0.735692i
$533$	−67.8519	+	117.523i	−0.127302	+	0.220493i
$534$		0			0
$535$	159.123	+	91.8696i	0.297426	+	0.171719i
$536$	3.62213	−	6.27371i	0.00675770	−	0.0117047i
$537$		0			0
$538$	481.426	+	277.951i	0.894843	+	0.516638i
$539$	558.135	+	1.71016i	1.03550	+	0.00317283i
$540$		0			0
$541$	289.077	−	500.696i	0.534338	−	0.925500i	−0.464857	−	0.885386i	$-0.653894\pi$
$541$	289.077	−	500.696i	0.534338	−	0.925500i	0.999195	−	0.0401146i	$-0.0127723\pi$
$542$			270.051i			0.498249i
$543$		0			0
$544$			548.713i			1.00866i
$545$	−52.3392	+	30.2181i	−0.0960352	+	0.0554460i
$546$		0			0
$547$	110.283	−	191.016i	0.201615	−	0.349207i	−0.747434	−	0.664336i	$-0.768714\pi$
$547$	110.283	−	191.016i	0.201615	−	0.349207i	0.949049	+	0.315129i	$0.102048\pi$
$548$	−309.143	+	535.451i	−0.564129	+	0.977101i
$549$		0			0
$550$	310.648	+	538.058i	0.564815	+	0.978288i
$551$	449.928	−	259.766i	0.816566	−	0.471445i
$552$		0			0
$553$	−830.572	+	477.836i	−1.50194	+	0.864079i
$554$	305.288	+	528.774i	0.551061	+	0.954465i
$555$		0			0
$556$		−	367.842i		−	0.661586i
$557$	−179.797	−	311.417i	−0.322795	−	0.559098i	0.658268	−	0.752783i	$-0.271289\pi$
$557$	−179.797	−	311.417i	−0.322795	−	0.559098i	−0.981064	+	0.193686i	$0.937956\pi$
$558$		0			0
$559$		−	690.574i		−	1.23537i
$560$	132.908	+	231.020i	0.237336	+	0.412536i
$561$		0			0
$562$	577.646			1.02784
$563$	−854.592	−	493.399i	−1.51792	−	0.876374i	−0.999778	−	0.0210827i	$-0.993289\pi$
$563$	−854.592	−	493.399i	−1.51792	−	0.876374i	−0.518147	−	0.855292i	$-0.673378\pi$
$564$		0			0
$565$	154.024	−	88.9255i	0.272608	−	0.157390i
$566$			341.373i			0.603133i
$567$		0			0
$568$	9.98825			0.0175849
$569$	41.8937	+	72.5620i	0.0736269	+	0.127525i	0.900488	−	0.434880i	$-0.143209\pi$
$569$	41.8937	+	72.5620i	0.0736269	+	0.127525i	−0.826861	+	0.562406i	$0.809876\pi$
$570$		0			0
$571$	175.350	−	303.715i	0.307093	−	0.531901i	−0.670632	−	0.741790i	$-0.733977\pi$
$571$	175.350	−	303.715i	0.307093	−	0.531901i	0.977725	+	0.209889i	$0.0673103\pi$
$572$			713.820i			1.24794i
$573$		0			0
$574$	−86.8150	+	149.837i	−0.151246	+	0.261041i
$575$	309.041			0.537463
$576$		0			0
$577$	−652.529	+	376.738i	−1.13090	+	0.652925i	−0.944161	−	0.329485i	$-0.893125\pi$
$577$	−652.529	+	376.738i	−1.13090	+	0.652925i	−0.186738	+	0.982410i	$0.559792\pi$
$578$	403.947			0.698871
$579$		0			0
$580$	271.875	−	156.967i	0.468750	−	0.270633i
$581$	−76.4541	+	131.955i	−0.131590	+	0.227117i
$582$		0			0
$583$	387.991	+	672.019i	0.665507	+	1.15269i
$584$	5.20340	−	3.00419i	0.00890994	−	0.00514416i
$585$		0			0
$586$	429.874	+	248.188i	0.733573	+	0.423528i
$587$	112.348	+	64.8642i	0.191394	+	0.110501i	0.592635	−	0.805471i	$-0.298088\pi$
$587$	112.348	+	64.8642i	0.191394	+	0.110501i	−0.401241	+	0.915972i	$0.631421\pi$
$588$		0			0
$589$	339.229	+	587.562i	0.575941	+	0.997559i
$590$	−646.830			−1.09632
$591$		0			0
$592$	−114.740			−0.193818
$593$	−435.912	−	251.674i	−0.735096	−	0.424408i	0.0851878	−	0.996365i	$-0.472851\pi$
$593$	−435.912	−	251.674i	−0.735096	−	0.424408i	−0.820283	+	0.571957i	$0.806184\pi$
$594$		0			0
$595$	−176.125	+	101.326i	−0.296008	+	0.170296i
$596$	226.580	−	392.447i	0.380167	−	0.658469i
$597$		0			0
$598$	612.607	+	353.689i	1.02443	+	0.591453i
$599$	−141.278	+	244.701i	−0.235857	+	0.408516i	−0.959521	−	0.281636i	$-0.909123\pi$
$599$	−141.278	+	244.701i	−0.235857	+	0.408516i	0.723664	+	0.690152i	$0.242456\pi$
$600$		0			0
$601$	−159.905	−	92.3214i	−0.266065	−	0.153613i	0.361033	−	0.932553i	$-0.382424\pi$
$601$	−159.905	−	92.3214i	−0.266065	−	0.153613i	−0.627098	+	0.778940i	$0.715758\pi$
$602$	1.35008	−	881.236i	0.00224265	−	1.46385i
$603$		0			0
$604$	−56.8339	+	98.4392i	−0.0940959	+	0.162979i
$605$			20.9754i			0.0346702i
$606$		0			0
$607$		−	1045.66i		−	1.72267i	−0.508040	−	0.861333i	$-0.669630\pi$
$607$		−	1045.66i		−	1.72267i	0.508040	−	0.861333i	$-0.330370\pi$
$608$	−628.310	+	362.755i	−1.03340	+	0.596636i
$609$		0			0
$610$	−168.038	+	291.051i	−0.275473	+	0.477133i
$611$	−204.978	+	355.032i	−0.335479	+	0.581067i
$612$		0			0
$613$	−52.6647	−	91.2179i	−0.0859131	−	0.148806i	0.819867	−	0.572554i	$-0.194047\pi$
$613$	−52.6647	−	91.2179i	−0.0859131	−	0.148806i	−0.905780	+	0.423748i	$0.860714\pi$
$614$	45.0764	−	26.0248i	0.0734143	−	0.0423857i
$615$		0			0
$616$	−0.0108088	+	7.05524i	−1.75468e−5	+	0.0114533i
$617$	−269.908	−	467.495i	−0.437452	−	0.757690i	0.560040	−	0.828466i	$-0.310786\pi$
$617$	−269.908	−	467.495i	−0.437452	−	0.757690i	−0.997492	+	0.0707759i	$0.977452\pi$
$618$		0			0
$619$			1117.89i			1.80596i	0.429678	+	0.902982i	$0.358627\pi$
$619$			1117.89i			1.80596i	−0.429678	+	0.902982i	$0.641373\pi$
$620$	204.984	+	355.042i	0.330619	+	0.572649i
$621$		0			0
$622$			1155.77i			1.85816i
$623$	−380.519	+	656.753i	−0.610785	+	1.05418i
$624$		0			0
$625$	226.620			0.362593
$626$	988.452	+	570.683i	1.57900	+	0.911635i
$627$		0			0
$628$	35.7862	−	20.6612i	0.0569845	−	0.0329000i
$629$		−	87.4754i		−	0.139071i
$630$		0			0
$631$	−710.879			−1.12659			−0.563296	−	0.826255i	$-0.690467\pi$
$631$	−710.879			−1.12659			−0.563296	+	0.826255i	$0.690467\pi$
$632$	−6.05625	−	10.4897i	−0.00958268	−	0.0165977i
$633$		0			0
$634$	−420.198	+	727.805i	−0.662773	+	1.14796i
$635$			125.411i			0.197498i
$636$		0			0
$637$	660.843	−	378.843i	1.03743	−	0.594730i
$638$	−1048.07			−1.64274
$639$		0			0
$640$	−5.88145	+	3.39566i	−0.00918977	+	0.00530571i
$641$	−1070.78			−1.67048			−0.835240	−	0.549885i	$-0.814672\pi$
$641$	−1070.78			−1.67048			−0.835240	+	0.549885i	$0.814672\pi$
$642$		0			0
$643$	−664.371	+	383.575i	−1.03324	+	0.596539i	−0.917910	−	0.396788i	$-0.870125\pi$
$643$	−664.371	+	383.575i	−1.03324	+	0.596539i	−0.115326	+	0.993328i	$0.536791\pi$
$644$	392.044	+	227.148i	0.608764	+	0.352715i
$645$		0			0
$646$	−274.398	−	475.271i	−0.424764	−	0.735713i
$647$	−14.8163	+	8.55422i	−0.0229001	+	0.0132214i	−0.511406	−	0.859339i	$-0.670875\pi$
$647$	−14.8163	+	8.55422i	−0.0229001	+	0.0132214i	0.488506	+	0.872560i	$0.337542\pi$
$648$		0			0
$649$	938.701	+	541.959i	1.44638	+	0.835068i
$650$	734.328	+	423.965i	1.12974	+	0.652253i
$651$		0			0
$652$	358.138	+	620.314i	0.549292	+	0.951402i
$653$	968.287			1.48283			0.741414	−	0.671048i	$-0.234155\pi$
$653$	968.287			1.48283			0.741414	+	0.671048i	$0.234155\pi$
$654$		0			0
$655$	−447.423			−0.683088
$656$	120.007	+	69.2860i	0.182937	+	0.105619i
$657$		0			0
$658$	−262.265	+	452.653i	−0.398579	+	0.687923i
$659$	−470.849	+	815.535i	−0.714490	+	1.23753i	0.248665	+	0.968589i	$0.420008\pi$
$659$	−470.849	+	815.535i	−0.714490	+	1.23753i	−0.963156	+	0.268944i	$0.913325\pi$
$660$		0			0
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	0.503595	−	0.863940i	$-0.332010\pi$
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	−0.496396	+	0.868096i	$0.665344\pi$
$662$	−755.187	+	1308.02i	−1.14077	+	1.97586i
$663$		0			0
$664$	−1.66948	−	0.963876i	−0.00251428	−	0.00145162i
$665$	−232.461	−	134.687i	−0.349566	−	0.202537i
$666$		0			0
$667$	−260.662	+	451.480i	−0.390798	+	0.676881i
$668$		−	251.234i		−	0.376099i
$669$		0			0
$670$		−	556.499i		−	0.830595i
$671$	487.726	−	281.589i	0.726864	−	0.419655i
$672$		0			0
$673$	329.366	−	570.479i	0.489400	−	0.847666i	−0.510525	−	0.859863i	$-0.670549\pi$
$673$	329.366	−	570.479i	0.489400	−	0.847666i	0.999926	+	0.0121964i	$0.00388233\pi$
$674$	422.382	−	731.587i	0.626679	−	1.08544i
$675$		0			0
$676$	146.463	+	253.681i	0.216661	+	0.375268i
$677$	730.516	−	421.763i	1.07905	−	0.622989i	0.148409	−	0.988926i	$-0.452585\pi$
$677$	730.516	−	421.763i	1.07905	−	0.622989i	0.930639	+	0.365937i	$0.119252\pi$
$678$		0			0
$679$	391.432	−	675.588i	0.576484	−	0.994975i
$680$	−1.28424	−	2.22438i	−0.00188860	−	0.00327114i
$681$		0			0
$682$		−	1368.68i		−	2.00686i
$683$	290.414	+	503.012i	0.425203	+	0.736474i	0.996439	−	0.0843121i	$-0.0268693\pi$
$683$	290.414	+	503.012i	0.425203	+	0.736474i	−0.571236	+	0.820786i	$0.693536\pi$
$684$		0			0
$685$			367.875i			0.537044i
$686$	844.038	−	482.147i	1.23038	−	0.702838i
$687$		0			0
$688$	−705.170			−1.02496
$689$	917.155	+	529.520i	1.33114	+	0.768534i
$690$		0			0
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.995718	−	0.0924390i	$-0.970534\pi$
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.417805	+	0.908537i	$0.637200\pi$
$692$		−	354.801i		−	0.512718i
$693$		0			0
$694$	512.388			0.738311
$695$	−109.432	−	189.541i	−0.157455	−	0.272721i
$696$		0			0
$697$	−52.8222	+	91.4907i	−0.0757851	+	0.131264i
$698$		−	497.031i		−	0.712078i
$699$		0			0
$700$	469.941	+	272.281i	0.671344	+	0.388973i
$701$	−352.754			−0.503216			−0.251608	−	0.967829i	$-0.580959\pi$
$701$	−352.754			−0.503216			−0.251608	+	0.967829i	$0.580959\pi$
$702$		0			0
$703$	100.165	−	57.8301i	0.142482	−	0.0822618i
$704$	740.332			1.05161
$705$		0			0
$706$	96.4769	−	55.7009i	0.136653	−	0.0788965i
$707$	−538.038	−	0.824287i	−0.761015	−	0.00116589i
$708$		0			0
$709$	396.038	+	685.959i	0.558587	+	0.967502i	0.997615	+	0.0690279i	$0.0219898\pi$
$709$	396.038	+	685.959i	0.558587	+	0.967502i	−0.439027	+	0.898474i	$0.644677\pi$
$710$	664.492	−	383.645i	0.935905	−	0.540345i
$711$		0			0
$712$	−8.30917	−	4.79730i	−0.0116702	−	0.00673778i
$713$	−589.589	−	340.399i	−0.826913	−	0.477418i
$714$		0			0
$715$	212.359	+	367.816i	0.297005	+	0.514428i
$716$	−52.2126			−0.0729227
$717$		0			0
$718$	−701.816			−0.977460
$719$	−473.277	−	273.247i	−0.658244	−	0.380037i	0.133364	−	0.991067i	$-0.457422\pi$
$719$	−473.277	−	273.247i	−0.658244	−	0.380037i	−0.791608	+	0.611030i	$0.790756\pi$
$720$		0			0
$721$	1055.47	+	1.61700i	1.46389	+	0.00224272i
$722$	−148.717	+	257.586i	−0.205979	+	0.356767i
$723$		0			0
$724$	788.483	+	455.231i	1.08906	+	0.628772i
$725$	−312.454	+	541.186i	−0.430971	+	0.746464i
$726$		0			0
$727$	−113.839	−	65.7248i	−0.156587	−	0.0904055i	0.419659	−	0.907682i	$-0.362150\pi$
$727$	−113.839	−	65.7248i	−0.156587	−	0.0904055i	−0.576246	+	0.817276i	$0.695483\pi$
$728$	4.80163	+	8.34617i	0.00659565	+	0.0114645i
$729$		0			0
$730$	230.779	−	399.722i	0.316136	−	0.547564i
$731$		−	537.607i		−	0.735440i
$732$		0			0
$733$		−	1279.26i		−	1.74524i	−0.488400	−	0.872620i	$-0.662419\pi$
$733$		−	1279.26i		−	1.74524i	0.488400	−	0.872620i	$-0.337581\pi$
$734$	−973.840	+	562.247i	−1.32676	+	0.766004i
$735$		0			0
$736$	364.006	−	630.477i	0.494573	−	0.856626i
$737$	−466.273	+	807.609i	−0.632664	+	1.09581i
$738$		0			0
$739$	9.93656	+	17.2106i	0.0134460	+	0.0232891i	0.872670	−	0.488310i	$-0.162387\pi$
$739$	9.93656	+	17.2106i	0.0134460	+	0.0232891i	−0.859224	+	0.511599i	$0.829053\pi$
$740$	60.5258	−	34.9446i	0.0817916	−	0.0472224i
$741$		0			0
$742$	1169.34	+	677.509i	1.57593	+	0.913085i
$743$	−729.663	−	1263.81i	−0.982050	−	1.70096i	−0.654374	−	0.756171i	$-0.727068\pi$
$743$	−729.663	−	1263.81i	−0.982050	−	1.70096i	−0.327677	−	0.944790i	$-0.606266\pi$
$744$		0			0
$745$		−	269.626i		−	0.361914i
$746$	−528.729	−	915.786i	−0.708753	−	1.22760i
$747$		0			0
$748$			555.703i			0.742919i
$749$	−463.978	−	268.826i	−0.619463	−	0.358914i
$750$		0			0
$751$	−989.823			−1.31801			−0.659003	−	0.752140i	$-0.729022\pi$
$751$	−989.823			−1.31801			−0.659003	+	0.752140i	$0.729022\pi$
$752$	362.536	+	209.310i	0.482096	+	0.278338i
$753$		0			0
$754$	−1238.74	+	715.189i	−1.64290	+	0.948527i
$755$			67.6315i			0.0895781i
$756$		0			0
$757$	−499.688			−0.660089			−0.330045	−	0.943965i	$-0.607064\pi$
$757$	−499.688			−0.660089			−0.330045	+	0.943965i	$0.607064\pi$
$758$	−776.903	−	1345.64i	−1.02494	−	1.77525i
$759$		0			0
$760$	1.69803	−	2.94108i	0.00223425	−	0.00386984i
$761$			685.947i			0.901376i	0.892682	+	0.450688i	$0.148821\pi$
$761$			685.947i			0.901376i	−0.892682	+	0.450688i	$0.851179\pi$
$762$		0			0
$763$	152.883	−	87.9553i	0.200371	−	0.115276i
$764$	−418.806			−0.548175
$765$		0			0
$766$	−11.4523	+	6.61197i	−0.0149507	+	0.00863182i
$767$	1479.30			1.92869
$768$		0			0
$769$	586.160	−	338.420i	0.762237	−	0.440078i	−0.0678613	−	0.997695i	$-0.521618\pi$
$769$	586.160	−	338.420i	0.762237	−	0.440078i	0.830098	+	0.557617i	$0.188284\pi$
$770$	270.270	+	469.782i	0.351000	+	0.610107i
$771$		0			0
$772$	−327.219	−	566.759i	−0.423858	−	0.734144i
$773$	−437.359	+	252.509i	−0.565794	+	0.326661i	−0.755468	−	0.655186i	$-0.772590\pi$
$773$	−437.359	+	252.509i	−0.565794	+	0.326661i	0.189674	+	0.981847i	$0.439257\pi$
$774$		0			0
$775$	−706.737	−	408.035i	−0.911918	−	0.526496i
$776$	8.54747	+	4.93489i	0.0110148	+	0.00635939i
$777$		0			0
$778$	−953.091	−	1650.80i	−1.22505	−	2.12185i
$779$	−139.683			−0.179311
$780$		0			0
$781$	−1285.78			−1.64632
$782$	476.910	+	275.344i	0.609859	+	0.352102i
$783$		0			0
$784$	−386.850	−	674.811i	−0.493432	−	0.860729i
$785$	12.2932	−	21.2925i	0.0156602	−	0.0271242i
$786$		0			0
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	0.489776	−	0.871848i	$-0.337079\pi$
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	−0.510155	+	0.860083i	$0.670412\pi$
$788$	607.898	−	1052.91i	0.771445	−	1.33618i
$789$		0			0
$790$	−805.814	−	465.237i	−1.02002	−	0.588907i
$791$	−449.905	+	258.834i	−0.568779	+	0.327224i
$792$		0			0
$793$	384.305	−	665.636i	0.484622	−	0.839389i
$794$		−	301.165i		−	0.379301i
$795$		0			0
$796$			233.009i			0.292724i
$797$	615.232	−	355.205i	0.771935	−	0.445677i	−0.0616293	−	0.998099i	$-0.519630\pi$
$797$	615.232	−	355.205i	0.771935	−	0.445677i	0.833565	+	0.552422i	$0.186296\pi$
$798$		0			0
$799$	−159.574	+	276.390i	−0.199717	+	0.345920i
$800$	436.332	−	755.749i	0.545415	−	0.944686i
$801$		0			0
$802$	−422.814	−	732.336i	−0.527200	−	0.913137i
$803$	−669.829	+	386.726i	−0.834159	+	0.481602i
$804$		0			0
$805$	269.588	+	0.413015i	0.334891	+	0.000513062i
$806$	−933.967	−	1617.68i	−1.15877	−	2.00705i
$807$		0			0
$808$		−	6.80118i		−	0.00841730i
$809$	565.769	+	979.941i	0.699344	+	1.21130i	0.968694	+	0.248257i	$0.0798576\pi$
$809$	565.769	+	979.941i	0.699344	+	1.21130i	−0.269351	+	0.963042i	$0.586809\pi$
$810$		0			0
$811$			199.736i			0.246283i	0.992389	+	0.123142i	$0.0392970\pi$
$811$			199.736i			0.246283i	−0.992389	+	0.123142i	$0.960703\pi$
$812$	−794.150	+	456.882i	−0.978018	+	0.562663i
$813$		0			0
$814$	−233.325			−0.286640
$815$	369.082	+	213.090i	0.452861	+	0.261460i
$816$		0			0
$817$	615.592	−	355.412i	0.753479	−	0.435021i
$818$			1867.84i			2.28343i
$819$		0			0
$820$	−84.4055			−0.102934
$821$	196.680	+	340.660i	0.239562	+	0.414933i	0.960589	−	0.277974i	$-0.0896630\pi$
$821$	196.680	+	340.660i	0.239562	+	0.414933i	−0.721027	+	0.692907i	$0.756330\pi$
$822$		0			0
$823$	424.378	−	735.045i	0.515648	−	0.893128i	−0.484187	−	0.874965i	$-0.660885\pi$
$823$	424.378	−	735.045i	0.515648	−	0.893128i	0.999835	−	0.0181639i	$-0.00578208\pi$
$824$			13.3418i			0.0161915i
$825$		0			0
$826$	1887.73	+	2.89205i	2.28539	+	0.00350127i
$827$	−495.009			−0.598559			−0.299280	−	0.954165i	$-0.596746\pi$
$827$	−495.009			−0.598559			−0.299280	+	0.954165i	$0.596746\pi$
$828$		0			0
$829$	820.334	−	473.620i	0.989546	−	0.571315i	0.0844077	−	0.996431i	$-0.473100\pi$
$829$	820.334	−	473.620i	0.989546	−	0.571315i	0.905139	+	0.425116i	$0.139767\pi$
$830$	−148.088			−0.178420
$831$		0			0
$832$	875.021	−	505.193i	1.05171	−	0.607204i
$833$	514.462	−	294.927i	0.617601	−	0.354053i
$834$		0			0
$835$	−74.7412	−	129.456i	−0.0895105	−	0.155037i
$836$	−636.314	+	367.376i	−0.761142	+	0.439445i
$837$		0			0
$838$	−1375.30	−	794.030i	−1.64117	−	0.947530i
$839$	787.270	+	454.531i	0.938343	+	0.541753i	0.889441	−	0.457051i	$-0.151094\pi$
$839$	787.270	+	454.531i	0.938343	+	0.541753i	0.0489028	+	0.998804i	$0.484428\pi$
$840$		0			0
$841$	−106.581	−	184.604i	−0.126731	−	0.219505i
$842$	−328.720			−0.390403
$843$		0			0
$844$	171.082			0.202704
$845$	150.939	+	87.1444i	0.178625	+	0.103129i
$846$		0			0
$847$	0.0937834	−	61.2154i	0.000110724	−	0.0722732i
$848$	540.712	−	936.540i	0.637632	−	1.10441i
$849$		0			0
$850$	571.669	+	330.053i	0.672552	+	0.388298i
$851$	−58.0295	+	100.510i	−0.0681898	+	0.118108i
$852$		0			0
$853$	768.763	+	443.845i	0.901246	+	0.520335i	0.877604	−	0.479386i	$-0.159141\pi$
$853$	768.763	+	443.845i	0.901246	+	0.520335i	0.0236417	+	0.999720i	$0.492474\pi$
$854$	491.710	−	848.661i	0.575773	−	0.993749i
$855$		0			0
$856$	3.38916	−	5.87020i	0.00395930	−	0.00685771i
$857$			175.131i			0.204354i	0.994766	+	0.102177i	$0.0325808\pi$
$857$			175.131i			0.204354i	−0.994766	+	0.102177i	$0.967419\pi$
$858$		0			0
$859$			1377.03i			1.60306i	0.597953	+	0.801531i	$0.295981\pi$
$859$			1377.03i			1.60306i	−0.597953	+	0.801531i	$0.704019\pi$
$860$	371.980	−	214.763i	0.432535	−	0.249724i
$861$		0			0
$862$	−456.983	+	791.518i	−0.530143	+	0.918235i
$863$	761.374	−	1318.74i	0.882241	−	1.52809i	0.0333969	−	0.999442i	$-0.489367\pi$
$863$	761.374	−	1318.74i	0.882241	−	1.52809i	0.848844	−	0.528644i	$-0.177299\pi$
$864$		0			0
$865$	−105.552	−	182.821i	−0.122025	−	0.211354i
$866$	287.924	−	166.233i	0.332475	−	0.191955i
$867$		0			0
$868$	−596.644	−	1037.08i	−0.687377	−	1.19480i
$869$	779.616	+	1350.33i	0.897141	+	1.55389i
$870$		0			0
$871$			1272.72i			1.46121i
$872$	1.11477	+	1.93085i	0.00127841	+	0.00221427i
$873$		0			0
$874$			728.121i			0.833091i
$875$	742.898	+	1.13814i	0.849026	+	0.00130073i
$876$		0			0
$877$	−719.054			−0.819902			−0.409951	−	0.912108i	$-0.634454\pi$
$877$	−719.054			−0.819902			−0.409951	+	0.912108i	$0.634454\pi$
$878$	532.180	+	307.254i	0.606128	+	0.349948i
$879$		0			0
$880$	375.590	−	216.847i	0.426807	−	0.246417i
$881$			1065.56i			1.20949i	0.796418	+	0.604747i	$0.206726\pi$
$881$			1065.56i			1.20949i	−0.796418	+	0.604747i	$0.793274\pi$
$882$		0			0
$883$	−378.403			−0.428543			−0.214271	−	0.976774i	$-0.568738\pi$
$883$	−378.403			−0.428543			−0.214271	+	0.976774i	$0.568738\pi$
$884$	379.205	+	656.802i	0.428965	+	0.742989i
$885$		0			0
$886$	−212.180	+	367.506i	−0.239481	+	0.414793i
$887$		−	1758.17i		−	1.98216i	−0.133277	−	0.991079i	$-0.542550\pi$
$887$		−	1758.17i		−	1.98216i	0.133277	−	0.991079i	$-0.457450\pi$
$888$		0			0
$889$	0.560727	−	366.004i	0.000630739	−	0.411703i
$890$	−737.050			−0.828146
$891$		0			0
$892$	−670.037	+	386.846i	−0.751163	+	0.433684i
$893$	−421.978			−0.472539
$894$		0			0
$895$	−26.9040	+	15.5331i	−0.0300604	+	0.0173554i
$896$	17.1798	−	9.88369i	0.0191739	−	0.0110309i
$897$		0			0
$898$	−373.750	−	647.355i	−0.416203	−	0.720885i
$899$	1192.20	−	688.317i	1.32614	−	0.765647i
$900$		0			0
$901$	713.998	+	412.227i	0.792451	+	0.457522i
$902$	244.035	+	140.894i	0.270549	+	0.156202i
$903$		0			0
$904$	−3.28055	−	5.68209i	−0.00362893	−	0.00628549i
$905$	541.717			0.598583
$906$		0			0
$907$	742.349			0.818467			0.409233	−	0.912430i	$-0.365796\pi$
$907$	742.349			0.818467			0.409233	+	0.912430i	$0.365796\pi$
$908$	−784.736	−	453.067i	−0.864246	−	0.498973i
$909$		0			0
$910$	640.014	+	370.820i	0.703312	+	0.407495i
$911$	−394.703	+	683.645i	−0.433263	+	0.750434i	−0.997152	−	0.0754169i	$-0.975971\pi$
$911$	−394.703	+	683.645i	−0.433263	+	0.750434i	0.563889	+	0.825851i	$0.309305\pi$
$912$		0			0
$913$	214.911	+	124.079i	0.235390	+	0.135902i
$914$	310.023	−	536.975i	0.339193	−	0.587500i
$915$		0			0
$916$	559.101	+	322.797i	0.610372	+	0.352398i
$917$	1305.77	+	2.00048i	1.42396	+	0.00218154i
$918$		0			0
$919$	213.779	−	370.276i	0.232621	−	0.402912i	−0.725957	−	0.687740i	$-0.758603\pi$
$919$	213.779	−	370.276i	0.232621	−	0.402912i	0.958579	+	0.284828i	$0.0919363\pi$
$920$			3.40778i			0.00370410i
$921$		0			0
$922$			1095.88i			1.18859i
$923$	−1519.70	+	877.398i	−1.64648	+	0.950594i
$924$		0			0
$925$	−69.5596	+	120.481i	−0.0751996	+	0.130250i
$926$	685.477	−	1187.28i	0.740256	−	1.28216i
$927$		0			0
$928$	736.051	+	1274.88i	0.793159	+	1.37379i
$929$	978.107	−	564.711i	1.05286	−	0.607869i	0.129412	−	0.991591i	$-0.458691\pi$
$929$	978.107	−	564.711i	1.05286	−	0.607869i	0.923449	+	0.383722i	$0.125358\pi$
$930$		0			0
$931$	677.820	+	394.114i	0.728056	+	0.423323i
$932$	−497.045	−	860.908i	−0.533310	−	0.923721i
$933$		0			0
$934$		−	327.373i		−	0.350507i
$935$	165.320	+	286.342i	0.176812	+	0.306248i
$936$		0			0
$937$		−	736.130i		−	0.785625i	−0.919619	−	0.392812i	$-0.871502\pi$
$937$		−	736.130i		−	0.785625i	0.919619	−	0.392812i	$-0.128498\pi$
$938$	−2.48816	+	1624.10i	−0.00265263	+	1.73145i
$939$		0			0
$940$	−254.986			−0.271261
$941$	−75.0157	−	43.3103i	−0.0797191	−	0.0460259i	0.459611	−	0.888121i	$-0.347989\pi$
$941$	−75.0157	−	43.3103i	−0.0797191	−	0.0460259i	−0.539330	+	0.842095i	$0.681322\pi$
$942$		0			0
$943$	121.386	−	70.0825i	0.128724	−	0.0743187i
$944$		−	1510.57i		−	1.60018i
$945$		0			0
$946$	−1433.97			−1.51582
$947$	293.684	+	508.676i	0.310121	+	0.537145i	0.978388	−	0.206776i	$-0.0662972\pi$
$947$	293.684	+	508.676i	0.310121	+	0.537145i	−0.668268	+	0.743921i	$0.732964\pi$
$948$		0			0
$949$	−527.794	+	914.166i	−0.556158	+	0.963294i
$950$			872.795i			0.918731i
$951$		0			0
$952$	3.73803	+	6.49743i	0.00392651	+	0.00682503i
$953$	396.549			0.416106			0.208053	−	0.978118i	$-0.433287\pi$
$953$	396.549			0.416106			0.208053	+	0.978118i	$0.433287\pi$
$954$		0			0
$955$	−215.802	+	124.593i	−0.225970	+	0.130464i
$956$	−888.002			−0.928873
$957$		0			0
$958$	−1118.28	+	645.638i	−1.16730	+	0.673944i
$959$	1.64481	−	1073.62i	0.00171513	−	1.11952i
$960$		0			0
$961$	418.375	+	724.646i	0.435353	+	0.754054i
$962$	−275.774	+	159.218i	−0.286667	+	0.165507i
$963$		0			0
$964$	−920.257	−	531.311i	−0.954624	−	0.551152i
$965$	−337.217	−	194.693i	−0.349448	−	0.201754i
$966$		0			0
$967$	−163.959	−	283.985i	−0.169554	−	0.293676i	0.768709	−	0.639598i	$-0.220899\pi$
$967$	−163.959	−	283.985i	−0.169554	−	0.293676i	−0.938263	+	0.345922i	$0.887566\pi$
$968$	0.773805			0.000799386
$969$		0			0
$970$	758.189			0.781638
$971$	−900.251	−	519.760i	−0.927138	−	0.535283i	−0.0412328	−	0.999150i	$-0.513129\pi$
$971$	−900.251	−	519.760i	−0.927138	−	0.535283i	−0.885905	+	0.463866i	$0.846462\pi$
$972$		0			0
$973$	318.521	+	553.651i	0.327359	+	0.569015i
$974$	−460.046	+	796.823i	−0.472326	+	0.818093i
$975$		0			0
$976$	−679.705	−	392.428i	−0.696419	−	0.402078i
$977$	743.417	−	1287.64i	0.760918	−	1.31795i	−0.181460	−	0.983398i	$-0.558082\pi$
$977$	743.417	−	1287.64i	0.760918	−	1.31795i	0.942378	−	0.334550i	$-0.108584\pi$
$978$		0			0
$979$	1069.63	+	617.552i	1.09258	+	0.630799i
$980$	409.582	+	238.148i	0.417941	+	0.243009i
$981$		0			0
$982$	439.887	−	761.906i	0.447950	−	0.775872i
$983$			1106.95i			1.12609i	0.826426	+	0.563045i	$0.190370\pi$
$983$			1106.95i			1.12609i	−0.826426	+	0.563045i	$0.809630\pi$
$984$		0			0
$985$		−	723.390i		−	0.734406i
$986$	−964.353	+	556.769i	−0.978046	+	0.564675i
$987$		0			0
$988$	−501.386	+	868.425i	−0.507475	+	0.878973i
$989$	−356.638	+	617.716i	−0.360605	+	0.624586i
$990$		0			0
$991$	−543.503	−	941.374i	−0.548439	−	0.949924i	−0.998382	−	0.0568665i	$-0.981889\pi$
$991$	−543.503	−	941.374i	−0.548439	−	0.949924i	0.449943	−	0.893057i	$-0.351444\pi$
$992$	−1664.87	+	961.211i	−1.67829	+	0.968963i
$993$		0			0
$994$	−1940.99	+	1116.67i	−1.95271	+	1.12341i
$995$	69.3191	+	120.064i	0.0696675	+	0.120668i
$996$		0			0
$997$		−	827.392i		−	0.829882i	−0.909848	−	0.414941i	$-0.863802\pi$
$997$		−	827.392i		−	0.829882i	0.909848	−	0.414941i	$-0.136198\pi$
$998$	1097.05	+	1900.14i	1.09925	+	1.90395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.19.3		28
3.2	odd	2		63.3.k.a.61.12	yes	28
7.3	odd	6		189.3.t.a.73.12		28
9.4	even	3		189.3.t.a.145.12		28
9.5	odd	6		63.3.t.a.40.3	yes	28
21.2	odd	6		441.3.l.a.97.12		28
21.5	even	6		441.3.l.b.97.12		28
21.11	odd	6		441.3.t.a.178.3		28
21.17	even	6		63.3.t.a.52.3	yes	28
21.20	even	2		441.3.k.b.313.12		28
63.5	even	6		441.3.l.a.391.12		28
63.23	odd	6		441.3.l.b.391.12		28
63.31	odd	6	inner	189.3.k.a.10.3		28
63.32	odd	6		441.3.k.b.31.12		28
63.41	even	6		441.3.t.a.166.3		28
63.59	even	6		63.3.k.a.31.12	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.12	✓	28	63.59	even	6
63.3.k.a.61.12	yes	28	3.2	odd	2
63.3.t.a.40.3	yes	28	9.5	odd	6
63.3.t.a.52.3	yes	28	21.17	even	6
189.3.k.a.10.3		28	63.31	odd	6	inner
189.3.k.a.19.3		28	1.1	even	1	trivial
189.3.t.a.73.12		28	7.3	odd	6
189.3.t.a.145.12		28	9.4	even	3
441.3.k.b.31.12		28	63.32	odd	6
441.3.k.b.313.12		28	21.20	even	2
441.3.l.a.97.12		28	21.2	odd	6
441.3.l.a.391.12		28	63.5	even	6
441.3.l.b.97.12		28	21.5	even	6
441.3.l.b.391.12		28	63.23	odd	6
441.3.t.a.166.3		28	63.41	even	6
441.3.t.a.178.3		28	21.11	odd	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41697 - 2.45427i) q^{2} +(-2.01561 + 3.49114i) q^{4} +2.39855i q^{5} +(0.0107242 - 6.99999i) q^{7} +0.0884848 q^{8} +O(q^{10})\)	\(q+(-1.41697 - 2.45427i) q^{2} +(-2.01561 + 3.49114i) q^{4} +2.39855i q^{5} +(0.0107242 - 6.99999i) q^{7} +0.0884848 q^{8} +(5.88667 - 3.39867i) q^{10} -11.3906 q^{11} +(-13.4628 + 7.77278i) q^{13} +(-17.1950 + 9.89246i) q^{14} +(7.93707 + 13.7474i) q^{16} +(-10.4807 + 6.05105i) q^{17} +(-13.8576 - 8.00071i) q^{19} +(-8.37367 - 4.83454i) q^{20} +(16.1401 + 27.9555i) q^{22} +16.0566 q^{23} +19.2470 q^{25} +(38.1529 + 22.0276i) q^{26} +(24.4163 + 14.1467i) q^{28} +(-16.2339 + 28.1180i) q^{29} +(-36.7194 - 21.1999i) q^{31} +(22.6701 - 39.2658i) q^{32} +(29.7018 + 17.1483i) q^{34} +(16.7898 + 0.0257224i) q^{35} +(-3.61406 + 6.25973i) q^{37} +45.3471i q^{38} +0.212235i q^{40} +(7.55990 - 4.36471i) q^{41} +(-22.2113 + 38.4711i) q^{43} +(22.9590 - 39.7661i) q^{44} +(-22.7518 - 39.4072i) q^{46} +(22.8382 - 13.1856i) q^{47} +(-48.9998 - 0.150138i) q^{49} +(-27.2724 - 47.2372i) q^{50} -62.6676i q^{52} +(-34.0624 - 58.9979i) q^{53} -27.3208i q^{55} +(0.000948925 - 0.619393i) q^{56} +92.0120 q^{58} +(-82.4104 - 47.5797i) q^{59} +(-42.8184 + 24.7212i) q^{61} +120.159i q^{62} -64.9952 q^{64} +(-18.6434 - 32.2913i) q^{65} +(40.9350 - 70.9015i) q^{67} -48.7863i q^{68} +(-23.7275 - 41.2431i) q^{70} +112.881 q^{71} +(58.8056 - 33.9514i) q^{73} +20.4840 q^{74} +(55.8633 - 32.2527i) q^{76} +(-0.122154 + 79.7339i) q^{77} +(-68.4439 - 118.548i) q^{79} +(-32.9738 + 19.0374i) q^{80} +(-21.4243 - 12.3693i) q^{82} +(-18.8674 - 10.8931i) q^{83} +(-14.5137 - 25.1385i) q^{85} +125.891 q^{86} -1.00789 q^{88} +(-93.9050 - 54.2161i) q^{89} +(54.2650 + 94.3232i) q^{91} +(-32.3639 + 56.0559i) q^{92} +(-64.7220 - 37.3673i) q^{94} +(19.1901 - 33.2382i) q^{95} +(96.5982 + 55.7710i) q^{97} +(69.0628 + 120.471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

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