LMFDB - Embedded newform 28.3.c.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,3,Mod(15,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("28.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	28.c (of order $2$, degree $1$, 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:	$0.762944740209$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1539727.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{3} - 8x + 8 $ x^6 - 2x^5 + 3x^3 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.3
Root			$1.35935 + 0.390070i$ of defining polynomial
Character	$\chi$	$=$	28.15
Dual form			28.3.c.a.15.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.163664 - 1.99329i) q^{2} -1.56028i q^{3} +(-3.94643 + 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 + 0.255361i) q^{6} +2.64575i q^{7} +(1.94643 + 7.75960i) q^{8} +6.56553 q^{9} +O(q^{10})$	\(q+(-0.163664 - 1.99329i) q^{2} -1.56028i q^{3} +(-3.94643 + 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 + 0.255361i) q^{6} +2.64575i q^{7} +(1.94643 + 7.75960i) q^{8} +6.56553 q^{9} +(-0.562581 - 6.85178i) q^{10} +8.48389i q^{11} +(1.01802 + 6.15753i) q^{12} -18.5685 q^{13} +(5.27376 - 0.433013i) q^{14} -5.36333i q^{15} +(15.1486 - 5.14977i) q^{16} -8.87484 q^{17} +(-1.07454 - 13.0870i) q^{18} -30.3324i q^{19} +(-13.5655 + 2.24278i) q^{20} +4.12811 q^{21} +(16.9109 - 1.38850i) q^{22} +26.5293i q^{23} +(12.1071 - 3.03697i) q^{24} -13.1841 q^{25} +(3.03899 + 37.0124i) q^{26} -24.2866i q^{27} +(-1.72624 - 10.4413i) q^{28} +18.6245 q^{29} +(-10.6907 + 0.877783i) q^{30} +41.2544i q^{31} +(-12.7443 - 29.3527i) q^{32} +13.2372 q^{33} +(1.45249 + 17.6901i) q^{34} +9.09456i q^{35} +(-25.9104 + 4.28374i) q^{36} -3.49346 q^{37} +(-60.4613 + 4.96431i) q^{38} +28.9720i q^{39} +(6.69069 + 26.6730i) q^{40} +37.7556 q^{41} +(-0.675622 - 8.22853i) q^{42} -50.8159i q^{43} +(-5.53539 - 33.4811i) q^{44} +22.5685 q^{45} +(52.8807 - 4.34189i) q^{46} -51.9810i q^{47} +(-8.03507 - 23.6360i) q^{48} -7.00000 q^{49} +(2.15777 + 26.2799i) q^{50} +13.8472i q^{51} +(73.2792 - 12.1152i) q^{52} +15.3814 q^{53} +(-48.4102 + 3.97483i) q^{54} +29.1627i q^{55} +(-20.5300 + 5.14977i) q^{56} -47.3270 q^{57} +(-3.04816 - 37.1241i) q^{58} -38.3291i q^{59} +(3.49936 + 21.1660i) q^{60} -72.5744 q^{61} +(82.2320 - 6.75184i) q^{62} +17.3708i q^{63} +(-56.4228 + 30.2070i) q^{64} -63.8276 q^{65} +(-2.16645 - 26.3857i) q^{66} +32.0834i q^{67} +(35.0239 - 5.79047i) q^{68} +41.3932 q^{69} +(18.1281 - 1.48845i) q^{70} +50.6160i q^{71} +(12.7793 + 50.9459i) q^{72} -5.48756 q^{73} +(0.571752 + 6.96348i) q^{74} +20.5709i q^{75} +(19.7906 + 119.705i) q^{76} -22.4463 q^{77} +(57.7497 - 4.74166i) q^{78} -39.8894i q^{79} +(52.0721 - 17.7019i) q^{80} +21.1959 q^{81} +(-6.17922 - 75.2579i) q^{82} -4.28106i q^{83} +(-16.2913 + 2.69342i) q^{84} -30.5065 q^{85} +(-101.291 + 8.31672i) q^{86} -29.0594i q^{87} +(-65.8316 + 16.5133i) q^{88} +123.906 q^{89} +(-3.69364 - 44.9856i) q^{90} -49.1276i q^{91} +(-17.3093 - 104.696i) q^{92} +64.3683 q^{93} +(-103.613 + 8.50740i) q^{94} -104.265i q^{95} +(-45.7985 + 19.8846i) q^{96} -32.0177 q^{97} +(1.14565 + 13.9530i) q^{98} +55.7012i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) $ 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9	$ 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) $ 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9 - 28 * q^10 + 6 * q^12 + 12 * q^13 + 7 * q^14 + 17 * q^16 - 4 * q^17 + 43 * q^18 - 32 * q^20 + 52 * q^22 + 122 * q^24 - 30 * q^25 - 56 * q^26 - 35 * q^28 - 36 * q^29 - 64 * q^30 - 101 * q^32 + 80 * q^33 + 58 * q^34 - 131 * q^36 + 28 * q^37 - 190 * q^38 + 40 * q^40 - 20 * q^41 + 70 * q^42 + 164 * q^44 + 12 * q^45 + 120 * q^46 - 98 * q^48 - 42 * q^49 + 161 * q^50 + 292 * q^52 + 92 * q^53 - 44 * q^54 - 49 * q^56 + 160 * q^57 - 166 * q^58 - 176 * q^60 - 164 * q^61 + 148 * q^62 - 215 * q^64 - 136 * q^65 - 408 * q^66 + 62 * q^68 - 48 * q^69 + 84 * q^70 + 151 * q^72 - 132 * q^73 + 250 * q^74 - 78 * q^76 + 112 * q^77 + 248 * q^78 + 312 * q^80 - 218 * q^81 - 86 * q^82 - 98 * q^84 - 232 * q^85 - 164 * q^86 - 100 * q^88 + 348 * q^89 + 52 * q^90 - 104 * q^92 + 288 * q^93 - 276 * q^94 + 170 * q^96 + 252 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.163664	−	1.99329i	−0.0818318	−	0.996646i
$2$	−0.163664	−	1.99329i	−0.0818318	−	0.996646i
$3$		−	1.56028i		−	0.520093i	−0.965596	−	0.260046i	$-0.916262\pi$
$3$		−	1.56028i		−	0.520093i	0.965596	−	0.260046i	$-0.0837379\pi$
$4$	−3.94643	+	0.652459i	−0.986607	+	0.163115i
$5$	3.43742			0.687484			0.343742	−	0.939064i	$-0.388305\pi$
$5$	3.43742			0.687484			0.343742	+	0.939064i	$0.388305\pi$
$6$	−3.11009	+	0.255361i	−0.518349	+	0.0425602i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	1.94643	+	7.75960i	0.243304	+	0.969950i
$9$	6.56553			0.729503
$10$	−0.562581	−	6.85178i	−0.0562581	−	0.685178i
$11$			8.48389i			0.771263i	0.922653	+	0.385631i	$0.126016\pi$
$11$			8.48389i			0.771263i	−0.922653	+	0.385631i	$0.873984\pi$
$12$	1.01802	+	6.15753i	0.0848348	+	0.513127i
$13$	−18.5685			−1.42834			−0.714172	−	0.699970i	$-0.753197\pi$
$13$	−18.5685			−1.42834			−0.714172	+	0.699970i	$0.753197\pi$
$14$	5.27376	−	0.433013i	0.376697	−	0.0309295i
$15$		−	5.36333i		−	0.357556i
$16$	15.1486	−	5.14977i	0.946787	−	0.321860i
$17$	−8.87484			−0.522049			−0.261025	−	0.965332i	$-0.584060\pi$
$17$	−8.87484			−0.522049			−0.261025	+	0.965332i	$0.584060\pi$
$18$	−1.07454	−	13.0870i	−0.0596966	−	0.727057i
$19$		−	30.3324i		−	1.59644i	−0.602365	−	0.798221i	$-0.705775\pi$
$19$		−	30.3324i		−	1.59644i	0.602365	−	0.798221i	$-0.294225\pi$
$20$	−13.5655	+	2.24278i	−0.678276	+	0.112139i
$21$	4.12811			0.196577
$22$	16.9109	−	1.38850i	0.768676	−	0.0631138i
$23$			26.5293i			1.15345i	0.816938	+	0.576725i	$0.195670\pi$
$23$			26.5293i			1.15345i	−0.816938	+	0.576725i	$0.804330\pi$
$24$	12.1071	−	3.03697i	0.504464	−	0.126540i
$25$	−13.1841			−0.527366
$26$	3.03899	+	37.0124i	0.116884	+	1.42355i
$27$		−	24.2866i		−	0.899503i
$28$	−1.72624	−	10.4413i	−0.0616516	−	0.372902i
$29$	18.6245			0.642225			0.321112	−	0.947041i	$-0.395943\pi$
$29$	18.6245			0.642225			0.321112	+	0.947041i	$0.395943\pi$
$30$	−10.6907	+	0.877783i	−0.356356	+	0.0292594i
$31$			41.2544i			1.33079i	0.746493	+	0.665393i	$0.231736\pi$
$31$			41.2544i			1.33079i	−0.746493	+	0.665393i	$0.768264\pi$
$32$	−12.7443	−	29.3527i	−0.398258	−	0.917273i
$33$	13.2372			0.401128
$34$	1.45249	+	17.6901i	0.0427203	+	0.520298i
$35$			9.09456i			0.259844i
$36$	−25.9104	+	4.28374i	−0.719733	+	0.118993i
$37$	−3.49346			−0.0944178			−0.0472089	−	0.998885i	$-0.515033\pi$
$37$	−3.49346			−0.0944178			−0.0472089	+	0.998885i	$0.515033\pi$
$38$	−60.4613	+	4.96431i	−1.59109	+	0.130640i
$39$			28.9720i			0.742872i
$40$	6.69069	+	26.6730i	0.167267	+	0.666825i
$41$	37.7556			0.920868			0.460434	−	0.887694i	$-0.347694\pi$
$41$	37.7556			0.920868			0.460434	+	0.887694i	$0.347694\pi$
$42$	−0.675622	−	8.22853i	−0.0160862	−	0.195917i
$43$		−	50.8159i		−	1.18177i	−0.806757	−	0.590883i	$-0.798780\pi$
$43$		−	50.8159i		−	1.18177i	0.806757	−	0.590883i	$-0.201220\pi$
$44$	−5.53539	−	33.4811i	−0.125804	−	0.760933i
$45$	22.5685			0.501522
$46$	52.8807	−	4.34189i	1.14958	−	0.0943889i
$47$		−	51.9810i		−	1.10598i	−0.833188	−	0.552990i	$-0.813487\pi$
$47$		−	51.9810i		−	1.10598i	0.833188	−	0.552990i	$-0.186513\pi$
$48$	−8.03507	−	23.6360i	−0.167397	−	0.492417i
$49$	−7.00000			−0.142857
$50$	2.15777	+	26.2799i	0.0431553	+	0.525597i
$51$			13.8472i			0.271514i
$52$	73.2792	−	12.1152i	1.40921	−	0.232984i
$53$	15.3814			0.290215			0.145107	−	0.989416i	$-0.453647\pi$
$53$	15.3814			0.290215			0.145107	+	0.989416i	$0.453647\pi$
$54$	−48.4102	+	3.97483i	−0.896486	+	0.0736079i
$55$			29.1627i			0.530231i
$56$	−20.5300	+	5.14977i	−0.366607	+	0.0919601i
$57$	−47.3270			−0.830298
$58$	−3.04816	−	37.1241i	−0.0525544	−	0.640071i
$59$		−	38.3291i		−	0.649645i	−0.945775	−	0.324823i	$-0.894695\pi$
$59$		−	38.3291i		−	0.649645i	0.945775	−	0.324823i	$-0.105305\pi$
$60$	3.49936	+	21.1660i	0.0583226	+	0.352767i
$61$	−72.5744			−1.18974			−0.594872	−	0.803820i	$-0.702797\pi$
$61$	−72.5744			−1.18974			−0.594872	+	0.803820i	$0.702797\pi$
$62$	82.2320	−	6.75184i	1.32632	−	0.108901i
$63$			17.3708i			0.275726i
$64$	−56.4228	+	30.2070i	−0.881607	+	0.471985i
$65$	−63.8276			−0.981964
$66$	−2.16645	−	26.3857i	−0.0328251	−	0.399783i
$67$			32.0834i			0.478856i	0.970914	+	0.239428i	$0.0769599\pi$
$67$			32.0834i			0.478856i	−0.970914	+	0.239428i	$0.923040\pi$
$68$	35.0239	−	5.79047i	0.515058	−	0.0851539i
$69$	41.3932			0.599901
$70$	18.1281	−	1.48845i	0.258973	−	0.0212635i
$71$			50.6160i			0.712902i	0.934314	+	0.356451i	$0.116013\pi$
$71$			50.6160i			0.712902i	−0.934314	+	0.356451i	$0.883987\pi$
$72$	12.7793	+	50.9459i	0.177491	+	0.707582i
$73$	−5.48756			−0.0751720			−0.0375860	−	0.999293i	$-0.511967\pi$
$73$	−5.48756			−0.0751720			−0.0375860	+	0.999293i	$0.511967\pi$
$74$	0.571752	+	6.96348i	0.00772638	+	0.0941011i
$75$			20.5709i			0.274279i
$76$	19.7906	+	119.705i	0.260403	+	1.57506i
$77$	−22.4463			−0.291510
$78$	57.7497	−	4.74166i	0.740380	−	0.0607906i
$79$		−	39.8894i		−	0.504929i	−0.967606	−	0.252464i	$-0.918759\pi$
$79$		−	39.8894i		−	0.504929i	0.967606	−	0.252464i	$-0.0812410\pi$
$80$	52.0721	−	17.7019i	0.650901	−	0.221274i
$81$	21.1959			0.261678
$82$	−6.17922	−	75.2579i	−0.0753563	−	0.917779i
$83$		−	4.28106i		−	0.0515791i	−0.999667	−	0.0257895i	$-0.991790\pi$
$83$		−	4.28106i		−	0.0515791i	0.999667	−	0.0257895i	$-0.00820997\pi$
$84$	−16.2913	+	2.69342i	−0.193944	+	0.0320646i
$85$	−30.5065			−0.358901
$86$	−101.291	+	8.31672i	−1.17780	+	0.0967060i
$87$		−	29.0594i		−	0.334017i
$88$	−65.8316	+	16.5133i	−0.748087	+	0.187651i
$89$	123.906			1.39220			0.696099	−	0.717946i	$-0.254917\pi$
$89$	123.906			1.39220			0.696099	+	0.717946i	$0.254917\pi$
$90$	−3.69364	−	44.9856i	−0.0410404	−	0.499840i
$91$		−	49.1276i		−	0.539863i
$92$	−17.3093	−	104.696i	−0.188145	−	1.13800i
$93$	64.3683			0.692132
$94$	−103.613	+	8.50740i	−1.10227	+	0.0905043i
$95$		−	104.265i		−	1.09753i
$96$	−45.7985	+	19.8846i	−0.477067	+	0.207131i
$97$	−32.0177			−0.330079			−0.165040	−	0.986287i	$-0.552775\pi$
$97$	−32.0177			−0.330079			−0.165040	+	0.986287i	$0.552775\pi$
$98$	1.14565	+	13.9530i	0.0116903	+	0.142378i
$99$			55.7012i			0.562639i
$100$	52.0303	−	8.60212i	0.520303	−	0.0860212i
$101$	−0.718521			−0.00711407			−0.00355703	−	0.999994i	$-0.501132\pi$
$101$	−0.718521			−0.00711407			−0.00355703	+	0.999994i	$0.501132\pi$
$102$	27.6016	−	2.26629i	0.270604	−	0.0222185i
$103$			116.453i			1.13062i	0.824880	+	0.565308i	$0.191243\pi$
$103$			116.453i			1.13062i	−0.824880	+	0.565308i	$0.808757\pi$
$104$	−36.1422	−	144.084i	−0.347521	−	1.38542i
$105$	14.1900			0.135143
$106$	−2.51737	−	30.6596i	−0.0237488	−	0.289241i
$107$		−	37.9431i		−	0.354608i	−0.984156	−	0.177304i	$-0.943262\pi$
$107$		−	37.9431i		−	0.354608i	0.984156	−	0.177304i	$-0.0567377\pi$
$108$	15.8460	+	95.8452i	0.146722	+	0.887456i
$109$	88.2300			0.809450			0.404725	−	0.914438i	$-0.367367\pi$
$109$	88.2300			0.809450			0.404725	+	0.914438i	$0.367367\pi$
$110$	58.1298	−	4.77287i	0.528452	−	0.0433898i
$111$			5.45077i			0.0491060i
$112$	13.6250	+	40.0794i	0.121652	+	0.357852i
$113$	125.115			1.10721			0.553605	−	0.832780i	$-0.313252\pi$
$113$	125.115			1.10721			0.553605	+	0.832780i	$0.313252\pi$
$114$	7.74571	+	94.3366i	0.0679448	+	0.827514i
$115$			91.1925i			0.792978i
$116$	−73.5003	+	12.1517i	−0.633623	+	0.104756i
$117$	−121.912			−1.04198
$118$	−76.4011	+	6.27308i	−0.647467	+	0.0531617i
$119$		−	23.4806i		−	0.197316i
$120$	41.6173	−	10.4393i	0.346811	−	0.0869945i
$121$	49.0236			0.405154
$122$	11.8778	+	144.662i	0.0973589	+	1.18575i
$123$		−	58.9092i		−	0.478937i
$124$	−26.9168	−	162.807i	−0.217071	−	1.31296i
$125$	−131.255			−1.05004
$126$	34.6250	−	2.84296i	0.274802	−	0.0225632i
$127$		−	51.8936i		−	0.408611i	−0.978907	−	0.204305i	$-0.934506\pi$
$127$		−	51.8936i		−	0.408611i	0.978907	−	0.204305i	$-0.0654936\pi$
$128$	69.4458	+	107.523i	0.542545	+	0.840027i
$129$	−79.2870			−0.614628
$130$	10.4463	+	127.227i	0.0803559	+	0.978670i
$131$			242.670i			1.85245i	0.376976	+	0.926223i	$0.376964\pi$
$131$			242.670i			1.85245i	−0.376976	+	0.926223i	$0.623036\pi$
$132$	−52.2398	+	8.63675i	−0.395756	+	0.0654300i
$133$	80.2520			0.603398
$134$	63.9515	−	5.25088i	0.477250	−	0.0391857i
$135$		−	83.4831i		−	0.618393i
$136$	−17.2742	−	68.8652i	−0.127016	−	0.506362i
$137$	−270.560			−1.97489			−0.987444	−	0.157970i	$-0.949505\pi$
$137$	−270.560			−1.97489			−0.987444	+	0.157970i	$0.949505\pi$
$138$	−6.77456	−	82.5087i	−0.0490910	−	0.597889i
$139$			15.6948i			0.112912i	0.998405	+	0.0564562i	$0.0179801\pi$
$139$			15.6948i			0.112912i	−0.998405	+	0.0564562i	$0.982020\pi$
$140$	−5.93383	−	35.8910i	−0.0423845	−	0.256364i
$141$	−81.1049			−0.575212
$142$	100.893	−	8.28400i	0.710511	−	0.0583381i
$143$		−	157.533i		−	1.10163i
$144$	99.4585	−	33.8109i	0.690684	−	0.234798i
$145$	64.0203			0.441519
$146$	0.898114	+	10.9383i	0.00615147	+	0.0749199i
$147$			10.9220i			0.0742990i
$148$	13.7867	−	2.27934i	0.0931532	−	0.0154009i
$149$	24.4627			0.164179			0.0820895	−	0.996625i	$-0.473841\pi$
$149$	24.4627			0.164179			0.0820895	+	0.996625i	$0.473841\pi$
$150$	41.0039	−	3.36672i	0.273359	−	0.0224448i
$151$		−	189.391i		−	1.25425i	−0.778920	−	0.627124i	$-0.784232\pi$
$151$		−	189.391i		−	1.25425i	0.778920	−	0.627124i	$-0.215768\pi$
$152$	235.367	−	59.0398i	1.54847	−	0.388420i
$153$	−58.2680			−0.380837
$154$	3.67364	+	44.7420i	0.0238548	+	0.290532i
$155$			141.809i			0.914894i
$156$	−18.9030	−	114.336i	−0.121173	−	0.732923i
$157$	101.743			0.648047			0.324024	−	0.946049i	$-0.394964\pi$
$157$	101.743			0.648047			0.324024	+	0.946049i	$0.394964\pi$
$158$	−79.5112	+	6.52844i	−0.503235	+	0.0413192i
$159$		−	23.9992i		−	0.150939i
$160$	−43.8074	−	100.898i	−0.273796	−	0.630611i
$161$	−70.1900			−0.435963
$162$	−3.46901	−	42.2497i	−0.0214136	−	0.260801i
$163$			68.5832i			0.420756i	0.977620	+	0.210378i	$0.0674695\pi$
$163$			68.5832i			0.420756i	−0.977620	+	0.210378i	$0.932531\pi$
$164$	−149.000	+	24.6340i	−0.908535	+	0.150207i
$165$	45.5019			0.275769
$166$	−8.53341	+	0.700654i	−0.0514061	+	0.00422081i
$167$			55.7795i			0.334009i	0.985956	+	0.167004i	$0.0534094\pi$
$167$			55.7795i			0.334009i	−0.985956	+	0.167004i	$0.946591\pi$
$168$	8.03507	+	32.0325i	0.0478278	+	0.190670i
$169$	175.788			1.04017
$170$	4.99281	+	60.8085i	0.0293695	+	0.357697i
$171$		−	199.148i		−	1.16461i
$172$	33.1553	+	200.541i	0.192763	+	1.16594i
$173$	19.2284			0.111147			0.0555734	−	0.998455i	$-0.482301\pi$
$173$	19.2284			0.111147			0.0555734	+	0.998455i	$0.482301\pi$
$174$	−57.9240	+	4.75597i	−0.332896	+	0.0273332i
$175$		−	34.8820i		−	0.199326i
$176$	43.6901	+	128.519i	0.248239	+	0.730222i
$177$	−59.8041			−0.337876
$178$	−20.2788	−	246.980i	−0.113926	−	1.38753i
$179$			195.745i			1.09355i	0.837280	+	0.546774i	$0.184144\pi$
$179$			195.745i			1.09355i	−0.837280	+	0.546774i	$0.815856\pi$
$180$	−89.0649	+	14.7250i	−0.494805	+	0.0818056i
$181$	82.5482			0.456067			0.228034	−	0.973653i	$-0.426770\pi$
$181$	82.5482			0.456067			0.228034	+	0.973653i	$0.426770\pi$
$182$	−97.9256	+	8.04040i	−0.538053	+	0.0441780i
$183$			113.236i			0.618777i
$184$	−205.857	+	51.6375i	−1.11879	+	0.280638i
$185$	−12.0085			−0.0649107
$186$	−10.5348	−	128.305i	−0.0566384	−	0.689811i
$187$		−	75.2932i		−	0.402637i
$188$	33.9155	+	205.139i	0.180402	+	1.09117i
$189$	64.2562			0.339980
$190$	−207.831	+	17.0644i	−1.09385	+	0.0898127i
$191$		−	159.670i		−	0.835968i	−0.908454	−	0.417984i	$-0.862737\pi$
$191$		−	159.670i		−	0.835968i	0.908454	−	0.417984i	$-0.137263\pi$
$192$	47.1314	+	88.0354i	0.245476	+	0.458517i
$193$	106.455			0.551583			0.275791	−	0.961218i	$-0.411060\pi$
$193$	106.455			0.551583			0.275791	+	0.961218i	$0.411060\pi$
$194$	5.24013	+	63.8206i	0.0270110	+	0.328972i
$195$			99.5889i			0.510712i
$196$	27.6250	−	4.56721i	0.140944	−	0.0233021i
$197$	−177.868			−0.902881			−0.451441	−	0.892301i	$-0.649090\pi$
$197$	−177.868			−0.902881			−0.451441	+	0.892301i	$0.649090\pi$
$198$	111.029	−	9.11627i	0.560752	−	0.0460418i
$199$			267.633i			1.34489i	0.740148	+	0.672444i	$0.234756\pi$
$199$			267.633i			1.34489i	−0.740148	+	0.672444i	$0.765244\pi$
$200$	−25.6620	−	102.304i	−0.128310	−	0.511519i
$201$	50.0590			0.249050
$202$	0.117596	+	1.43222i	0.000582157	+	0.00709021i
$203$			49.2758i			0.242738i
$204$	−9.03475	−	54.6471i	−0.0442880	−	0.267878i
$205$	129.782			0.633082
$206$	232.126	−	19.0592i	1.12682	−	0.0925204i
$207$			174.179i			0.841445i
$208$	−281.286	+	95.6233i	−1.35234	+	0.459727i
$209$	257.337			1.23128
$210$	−2.32239	−	28.2849i	−0.0110590	−	0.134690i
$211$		−	162.784i		−	0.771487i	−0.922606	−	0.385744i	$-0.873945\pi$
$211$		−	162.784i		−	0.771487i	0.922606	−	0.385744i	$-0.126055\pi$
$212$	−60.7015	+	10.0357i	−0.286328	+	0.0473383i
$213$	78.9751			0.370775
$214$	−75.6317	+	6.20991i	−0.353419	+	0.0290183i
$215$		−	174.676i		−	0.812445i
$216$	188.454	−	47.2721i	0.872473	−	0.218852i
$217$	−109.149			−0.502990
$218$	−14.4401	−	175.868i	−0.0662388	−	0.806735i
$219$			8.56212i			0.0390965i
$220$	−19.0275	−	115.088i	−0.0864885	−	0.523129i
$221$	164.792			0.745666
$222$	10.8650	−	0.892093i	0.0489413	−	0.00401844i
$223$		−	317.727i		−	1.42479i	−0.701780	−	0.712393i	$-0.747611\pi$
$223$		−	317.727i		−	1.42479i	0.701780	−	0.712393i	$-0.252389\pi$
$224$	77.6601	−	33.7181i	0.346697	−	0.150527i
$225$	−86.5609			−0.384715
$226$	−20.4767	−	249.390i	−0.0906050	−	1.10350i
$227$			116.168i			0.511754i	0.966709	+	0.255877i	$0.0823642\pi$
$227$			116.168i			0.511754i	−0.966709	+	0.255877i	$0.917636\pi$
$228$	186.773	−	30.8789i	0.819178	−	0.135434i
$229$	−357.643			−1.56176			−0.780880	−	0.624681i	$-0.785229\pi$
$229$	−357.643			−1.56176			−0.780880	+	0.624681i	$0.785229\pi$
$230$	181.773	−	14.9249i	0.790319	−	0.0648908i
$231$			35.0224i			0.151612i
$232$	36.2513	+	144.519i	0.156256	+	0.622926i
$233$	−402.307			−1.72664			−0.863319	−	0.504658i	$-0.831618\pi$
$233$	−402.307			−1.72664			−0.863319	+	0.504658i	$0.831618\pi$
$234$	19.9525	+	243.006i	0.0852673	+	1.03849i
$235$		−	178.681i		−	0.760343i
$236$	25.0082	+	151.263i	0.105967	+	0.640945i
$237$	−62.2385			−0.262610
$238$	−46.8037	+	3.84292i	−0.196654	+	0.0161467i
$239$		−	241.476i		−	1.01036i	−0.863014	−	0.505179i	$-0.831426\pi$
$239$		−	241.476i		−	1.01036i	0.863014	−	0.505179i	$-0.168574\pi$
$240$	−27.6199	−	81.2470i	−0.115083	−	0.338529i
$241$	−116.678			−0.484143			−0.242071	−	0.970258i	$-0.577827\pi$
$241$	−116.678			−0.484143			−0.242071	+	0.970258i	$0.577827\pi$
$242$	−8.02338	−	97.7183i	−0.0331545	−	0.403795i
$243$		−	251.651i		−	1.03560i
$244$	286.410	−	47.3518i	1.17381	−	0.194065i
$245$	−24.0619			−0.0982120
$246$	−117.423	+	9.64130i	−0.477331	+	0.0391923i
$247$			563.226i			2.28027i
$248$	−320.117	+	80.2986i	−1.29080	+	0.323785i
$249$	−6.67965			−0.0268259
$250$	21.4817	+	261.629i	0.0859266	+	1.04652i
$251$			7.21755i			0.0287552i	0.999897	+	0.0143776i	$0.00457669\pi$
$251$			7.21755i			0.0287552i	−0.999897	+	0.0143776i	$0.995423\pi$
$252$	−11.3337	−	68.5525i	−0.0449750	−	0.272034i
$253$	−225.072			−0.889613
$254$	−103.439	+	8.49309i	−0.407240	+	0.0334374i
$255$			47.5987i			0.186662i
$256$	202.960	−	156.023i	0.792812	−	0.609466i
$257$	380.233			1.47951			0.739754	−	0.672878i	$-0.234942\pi$
$257$	380.233			1.47951			0.739754	+	0.672878i	$0.234942\pi$
$258$	12.9764	+	158.042i	0.0502961	+	0.612567i
$259$		−	9.24282i		−	0.0356866i
$260$	251.891	−	41.6449i	0.968812	−	0.160173i
$261$	122.280			0.468505
$262$	483.713	−	39.7163i	1.84623	−	0.151589i
$263$			313.354i			1.19146i	0.803184	+	0.595731i	$0.203137\pi$
$263$			313.354i			1.19146i	−0.803184	+	0.595731i	$0.796863\pi$
$264$	25.7653	+	102.716i	0.0975960	+	0.389075i
$265$	52.8723			0.199518
$266$	−13.1343	−	159.966i	−0.0493772	−	0.601375i
$267$		−	193.327i		−	0.724072i
$268$	−20.9331	−	126.615i	−0.0781085	−	0.472443i
$269$	−170.127			−0.632442			−0.316221	−	0.948686i	$-0.602414\pi$
$269$	−170.127			−0.632442			−0.316221	+	0.948686i	$0.602414\pi$
$270$	−166.406	+	13.6632i	−0.616319	+	0.0506043i
$271$			50.3103i			0.185647i	0.995683	+	0.0928234i	$0.0295892\pi$
$271$			50.3103i			0.185647i	−0.995683	+	0.0928234i	$0.970411\pi$
$272$	−134.441	+	45.7033i	−0.494270	+	0.168027i
$273$	−76.6527			−0.280779
$274$	44.2808	+	539.304i	0.161609	+	1.96826i
$275$		−	111.853i		−	0.406738i
$276$	−163.355	+	27.0074i	−0.591867	+	0.0978527i
$277$	58.9777			0.212916			0.106458	−	0.994317i	$-0.466049\pi$
$277$	58.9777			0.212916			0.106458	+	0.994317i	$0.466049\pi$
$278$	31.2844	−	2.56867i	0.112534	−	0.00923983i
$279$			270.857i			0.970812i
$280$	−70.5701	+	17.7019i	−0.252036	+	0.0632211i
$281$	325.523			1.15844			0.579222	−	0.815170i	$-0.303356\pi$
$281$	325.523			1.15844			0.579222	+	0.815170i	$0.303356\pi$
$282$	13.2739	+	161.666i	0.0470706	+	0.573283i
$283$			282.815i			0.999348i	0.866214	+	0.499674i	$0.166547\pi$
$283$			282.815i			0.999348i	−0.866214	+	0.499674i	$0.833453\pi$
$284$	−33.0249	−	199.753i	−0.116285	−	0.703354i
$285$	−162.683			−0.570817
$286$	−314.009	+	25.7824i	−1.09793	+	0.0901483i
$287$			99.8919i			0.348055i
$288$	−83.6728	−	192.716i	−0.290531	−	0.669154i
$289$	−210.237			−0.727464
$290$	−10.4778	−	127.611i	−0.0361303	−	0.440038i
$291$			49.9565i			0.171672i
$292$	21.6563	−	3.58041i	0.0741653	−	0.0122617i
$293$	47.5056			0.162135			0.0810676	−	0.996709i	$-0.474167\pi$
$293$	47.5056			0.162135			0.0810676	+	0.996709i	$0.474167\pi$
$294$	21.7706	−	1.78753i	0.0740498	−	0.00608002i
$295$		−	131.753i		−	0.446621i
$296$	−6.79976	−	27.1078i	−0.0229722	−	0.0915805i
$297$	206.045			0.693753
$298$	−4.00365	−	48.7613i	−0.0134351	−	0.163628i
$299$		−	492.610i		−	1.64752i
$300$	−13.4217	−	81.1818i	−0.0447390	−	0.270606i
$301$	134.446			0.446665
$302$	−377.512	+	30.9965i	−1.25004	+	0.102637i
$303$			1.12109i			0.00369998i
$304$	−156.205	−	459.493i	−0.513831	−	1.51149i
$305$	−249.469			−0.817930
$306$	9.53636	+	116.145i	0.0311646	+	0.379559i
$307$		−	349.978i		−	1.13999i	−0.821647	−	0.569997i	$-0.806945\pi$
$307$		−	349.978i		−	1.13999i	0.821647	−	0.569997i	$-0.193055\pi$
$308$	88.5826	−	14.6453i	0.287606	−	0.0475496i
$309$	181.700			0.588026
$310$	282.666	−	23.2089i	0.911825	−	0.0748674i
$311$		−	344.941i		−	1.10914i	−0.832138	−	0.554568i	$-0.812884\pi$
$311$		−	344.941i		−	1.10914i	0.832138	−	0.554568i	$-0.187116\pi$
$312$	−224.811	+	56.3919i	−0.720549	+	0.180743i
$313$	281.520			0.899424			0.449712	−	0.893174i	$-0.351527\pi$
$313$	281.520			0.899424			0.449712	+	0.893174i	$0.351527\pi$
$314$	−16.6517	−	202.804i	−0.0530309	−	0.645874i
$315$			59.7106i			0.189557i
$316$	26.0262	+	157.420i	0.0823613	+	0.498166i
$317$	525.202			1.65679			0.828394	−	0.560146i	$-0.189255\pi$
$317$	525.202			1.65679			0.828394	+	0.560146i	$0.189255\pi$
$318$	−47.8375	+	3.92780i	−0.150432	+	0.0123516i
$319$			158.008i			0.495324i
$320$	−193.949	+	103.834i	−0.606090	+	0.324482i
$321$	−59.2018			−0.184429
$322$	11.4876	+	139.909i	0.0356757	+	0.434501i
$323$			269.195i			0.833421i
$324$	−83.6483	+	13.8295i	−0.258174	+	0.0426836i
$325$	244.810			0.753260
$326$	136.706	−	11.2246i	0.419345	−	0.0344312i
$327$		−	137.663i		−	0.420989i
$328$	73.4885	+	292.968i	0.224050	+	0.893196i
$329$	137.529			0.418021
$330$	−7.44701	−	90.6987i	−0.0225667	−	0.274844i
$331$			177.187i			0.535309i	0.963515	+	0.267655i	$0.0862486\pi$
$331$			177.187i			0.535309i	−0.963515	+	0.267655i	$0.913751\pi$
$332$	2.79322	+	16.8949i	0.00841331	+	0.0508883i
$333$	−22.9364			−0.0688781
$334$	111.185	−	9.12907i	0.332889	−	0.0273326i
$335$			110.284i			0.329206i
$336$	62.5351	−	21.2588i	0.186116	−	0.0632702i
$337$	−111.377			−0.330495			−0.165247	−	0.986252i	$-0.552842\pi$
$337$	−111.377			−0.330495			−0.165247	+	0.986252i	$0.552842\pi$
$338$	−28.7702	−	350.398i	−0.0851188	−	1.03668i
$339$		−	195.214i		−	0.575852i
$340$	120.392	−	19.9043i	0.354094	−	0.0585420i
$341$	−349.997			−1.02639
$342$	−396.961	+	32.5933i	−1.16070	+	0.0953021i
$343$		−	18.5203i		−	0.0539949i
$344$	394.311	−	98.9095i	1.14625	−	0.287528i
$345$	142.286			0.412422
$346$	−3.14699	−	38.3278i	−0.00909534	−	0.110774i
$347$		−	52.1533i		−	0.150298i	−0.997172	−	0.0751488i	$-0.976057\pi$
$347$		−	52.1533i		−	0.150298i	0.997172	−	0.0751488i	$-0.0239432\pi$
$348$	18.9601	+	114.681i	0.0544830	+	0.329543i
$349$	−419.921			−1.20321			−0.601606	−	0.798793i	$-0.705472\pi$
$349$	−419.921			−1.20321			−0.601606	+	0.798793i	$0.705472\pi$
$350$	−69.5300	+	5.70891i	−0.198657	+	0.0163112i
$351$			450.965i			1.28480i
$352$	249.026	−	108.121i	0.707459	−	0.307162i
$353$	−198.456			−0.562198			−0.281099	−	0.959679i	$-0.590699\pi$
$353$	−198.456			−0.562198			−0.281099	+	0.959679i	$0.590699\pi$
$354$	9.78775	+	119.207i	0.0276490	+	0.336743i
$355$			173.989i			0.490108i
$356$	−488.985	+	80.8433i	−1.37355	+	0.227088i
$357$	−36.6363			−0.102623
$358$	390.177	−	32.0363i	1.08988	−	0.0894870i
$359$		−	234.090i		−	0.652063i	−0.945359	−	0.326031i	$-0.894289\pi$
$359$		−	234.090i		−	0.652063i	0.945359	−	0.326031i	$-0.105711\pi$
$360$	43.9279	+	175.122i	0.122022	+	0.486451i
$361$	−559.054			−1.54863
$362$	−13.5101	−	164.543i	−0.0373208	−	0.454538i
$363$		−	76.4905i		−	0.210718i
$364$	32.0537	+	193.878i	0.0880597	+	0.532633i
$365$	−18.8630			−0.0516796
$366$	225.713	−	18.5327i	0.616702	−	0.0506357i
$367$			369.480i			1.00676i	0.864066	+	0.503379i	$0.167910\pi$
$367$			369.480i			1.00676i	−0.864066	+	0.503379i	$0.832090\pi$
$368$	136.620	+	401.882i	0.371250	+	1.09207i
$369$	247.885			0.671776
$370$	1.96535	+	23.9364i	0.00531176	+	0.0646930i
$371$			40.6953i			0.109691i
$372$	−254.025	+	41.9977i	−0.682863	+	0.112897i
$373$	−280.481			−0.751960			−0.375980	−	0.926628i	$-0.622694\pi$
$373$	−280.481			−0.751960			−0.375980	+	0.926628i	$0.622694\pi$
$374$	−150.081	+	12.3228i	−0.401287	+	0.0329485i
$375$			204.794i			0.546118i
$376$	403.352	−	101.177i	1.07274	−	0.269089i
$377$	−345.829			−0.917318
$378$	−10.5164	−	128.081i	−0.0278212	−	0.338840i
$379$		−	259.908i		−	0.685772i	−0.939377	−	0.342886i	$-0.888596\pi$
$379$		−	259.908i		−	0.685772i	0.939377	−	0.342886i	$-0.111404\pi$
$380$	68.0288	+	411.475i	0.179023	+	1.08283i
$381$	−80.9685			−0.212516
$382$	−318.269	+	26.1322i	−0.833164	+	0.0684088i
$383$			412.996i			1.07832i	0.842203	+	0.539160i	$0.181258\pi$
$383$			412.996i			1.07832i	−0.842203	+	0.539160i	$0.818742\pi$
$384$	167.767	−	108.355i	0.436892	−	0.282174i
$385$	−77.1572			−0.200408
$386$	−17.4229	−	212.197i	−0.0451370	−	0.549733i
$387$		−	333.633i		−	0.862102i
$388$	126.356	−	20.8902i	0.325659	−	0.0538408i
$389$	348.842			0.896766			0.448383	−	0.893842i	$-0.352000\pi$
$389$	348.842			0.896766			0.448383	+	0.893842i	$0.352000\pi$
$390$	198.510	−	16.2991i	0.509000	−	0.0417925i
$391$		−	235.444i		−	0.602158i
$392$	−13.6250	−	54.3172i	−0.0347577	−	0.138564i
$393$	378.634			0.963444
$394$	29.1105	+	354.542i	0.0738844	+	0.899853i
$395$		−	137.116i		−	0.347130i
$396$	−36.3428	−	219.821i	−0.0917747	−	0.555103i
$397$	33.6988			0.0848836			0.0424418	−	0.999099i	$-0.486486\pi$
$397$	33.6988			0.0848836			0.0424418	+	0.999099i	$0.486486\pi$
$398$	533.470	−	43.8018i	1.34038	−	0.110055i
$399$		−	125.215i		−	0.313823i
$400$	−199.721	+	67.8953i	−0.499303	+	0.169738i
$401$	140.120			0.349426			0.174713	−	0.984619i	$-0.444100\pi$
$401$	140.120			0.349426			0.174713	+	0.984619i	$0.444100\pi$
$402$	−8.19284	−	99.7822i	−0.0203802	−	0.248214i
$403$		−	766.031i		−	1.90082i
$404$	2.83559	−	0.468805i	0.00701879	−	0.00116041i
$405$	72.8593			0.179900
$406$	98.2211	−	8.06466i	0.241924	−	0.0198637i
$407$		−	29.6381i		−	0.0728209i
$408$	−107.449	+	26.9526i	−0.263355	+	0.0660604i
$409$	−707.963			−1.73096			−0.865480	−	0.500943i	$-0.832987\pi$
$409$	−707.963			−1.73096			−0.865480	+	0.500943i	$0.832987\pi$
$410$	−21.2406	−	258.693i	−0.0518062	−	0.630958i
$411$			422.148i			1.02713i
$412$	−75.9811	−	459.575i	−0.184420	−	1.11547i
$413$	101.409			0.245543
$414$	347.190	−	28.5068i	0.838623	−	0.0688570i
$415$		−	14.7158i		−	0.0354598i
$416$	236.642	+	545.036i	0.568850	+	1.31018i
$417$	24.4883			0.0587250
$418$	−42.1167	−	512.947i	−0.100758	−	1.22715i
$419$			596.341i			1.42325i	0.702560	+	0.711625i	$0.252040\pi$
$419$			596.341i			1.42325i	−0.702560	+	0.711625i	$0.747960\pi$
$420$	−56.0000	+	9.25842i	−0.133333	+	0.0220439i
$421$	−162.813			−0.386728			−0.193364	−	0.981127i	$-0.561940\pi$
$421$	−162.813			−0.386728			−0.193364	+	0.981127i	$0.561940\pi$
$422$	−324.476	+	26.6418i	−0.768900	+	0.0631322i
$423$		−	341.283i		−	0.806815i
$424$	29.9388	+	119.353i	0.0706103	+	0.281494i
$425$	117.007			0.275311
$426$	−12.9254	−	157.420i	−0.0303412	−	0.369532i
$427$		−	192.014i		−	0.449681i
$428$	24.7563	+	149.740i	0.0578419	+	0.349859i
$429$	−245.795			−0.572950
$430$	−348.180	+	28.5880i	−0.809720	+	0.0664838i
$431$		−	386.832i		−	0.897522i	−0.893652	−	0.448761i	$-0.851865\pi$
$431$		−	386.832i		−	0.897522i	0.893652	−	0.448761i	$-0.148135\pi$
$432$	−125.070	−	367.907i	−0.289514	−	0.851637i
$433$	574.844			1.32758			0.663792	−	0.747918i	$-0.268946\pi$
$433$	574.844			1.32758			0.663792	+	0.747918i	$0.268946\pi$
$434$	17.8637	+	217.565i	0.0411606	+	0.501303i
$435$		−	99.8895i		−	0.229631i
$436$	−348.194	+	57.5665i	−0.798609	+	0.132033i
$437$	804.699			1.84142
$438$	17.0668	−	1.40131i	0.0389653	−	0.00319933i
$439$			295.206i			0.672450i	0.941782	+	0.336225i	$0.109150\pi$
$439$			295.206i			0.672450i	−0.941782	+	0.336225i	$0.890850\pi$
$440$	−226.291	+	56.7631i	−0.514297	+	0.129007i
$441$	−45.9587			−0.104215
$442$	−26.9705	−	328.479i	−0.0610192	−	0.743165i
$443$			426.510i			0.962776i	0.876508	+	0.481388i	$0.159867\pi$
$443$			426.510i			0.962776i	−0.876508	+	0.481388i	$0.840133\pi$
$444$	−3.55640	−	21.5111i	−0.00800992	−	0.0484483i
$445$	425.916			0.957114
$446$	−633.324	+	52.0004i	−1.42001	+	0.116593i
$447$		−	38.1686i		−	0.0853884i
$448$	−79.9203	−	149.281i	−0.178393	−	0.333216i
$449$	−458.779			−1.02178			−0.510889	−	0.859646i	$-0.670684\pi$
$449$	−458.779			−1.02178			−0.510889	+	0.859646i	$0.670684\pi$
$450$	14.1669	+	172.541i	0.0314819	+	0.383425i
$451$			320.314i			0.710231i
$452$	−493.756	+	81.6322i	−1.09238	+	0.180602i
$453$	−295.503			−0.652325
$454$	231.557	−	19.0125i	0.510038	−	0.0418778i
$455$		−	168.872i		−	0.371147i
$456$	−92.1186	−	367.239i	−0.202015	−	0.805348i
$457$	384.429			0.841202			0.420601	−	0.907246i	$-0.361819\pi$
$457$	384.429			0.841202			0.420601	+	0.907246i	$0.361819\pi$
$458$	58.5332	+	712.887i	0.127802	+	1.55652i
$459$			215.539i			0.469585i
$460$	−59.4994	−	359.885i	−0.129346	−	0.782358i
$461$	−48.0796			−0.104294			−0.0521471	−	0.998639i	$-0.516606\pi$
$461$	−48.0796			−0.104294			−0.0521471	+	0.998639i	$0.516606\pi$
$462$	69.8100	−	5.73190i	0.151104	−	0.0124067i
$463$		−	62.2803i		−	0.134515i	−0.997736	−	0.0672573i	$-0.978575\pi$
$463$		−	62.2803i		−	0.134515i	0.997736	−	0.0672573i	$-0.0214249\pi$
$464$	282.135	−	95.9119i	0.608050	−	0.206707i
$465$	221.261			0.475830
$466$	65.8430	+	801.915i	0.141294	+	1.72085i
$467$			358.971i			0.768674i	0.923193	+	0.384337i	$0.125570\pi$
$467$			358.971i			0.768674i	−0.923193	+	0.384337i	$0.874430\pi$
$468$	481.117	−	79.5425i	1.02803	−	0.169963i
$469$	−84.8846			−0.180991
$470$	−356.163	+	29.2435i	−0.757793	+	0.0622202i
$471$		−	158.748i		−	0.337045i
$472$	297.418	−	74.6048i	0.630124	−	0.158061i
$473$	431.117			0.911452
$474$	10.1862	+	124.060i	0.0214898	+	0.261729i
$475$			399.907i			0.841909i
$476$	15.3201	+	92.6646i	0.0321852	+	0.194673i
$477$	100.987			0.211713
$478$	−481.332	+	39.5208i	−1.00697	+	0.0826795i
$479$		−	196.744i		−	0.410740i	−0.978684	−	0.205370i	$-0.934160\pi$
$479$		−	196.744i		−	0.410740i	0.978684	−	0.205370i	$-0.0658398\pi$
$480$	−157.429	+	68.3517i	−0.327976	+	0.142399i
$481$	64.8682			0.134861
$482$	19.0960	+	232.574i	0.0396183	+	0.482519i
$483$			109.516i			0.226741i
$484$	−193.468	+	31.9859i	−0.399727	+	0.0660865i
$485$	−110.058			−0.226924
$486$	−501.613	+	41.1861i	−1.03213	+	0.0847450i
$487$		−	490.201i		−	1.00657i	−0.864120	−	0.503287i	$-0.832124\pi$
$487$		−	490.201i		−	1.00657i	0.864120	−	0.503287i	$-0.167876\pi$
$488$	−141.261	−	563.148i	−0.289469	−	1.15399i
$489$	107.009			0.218832
$490$	3.93806	+	47.9625i	0.00803687	+	0.0978826i
$491$			852.129i			1.73550i	0.497004	+	0.867748i	$0.334433\pi$
$491$			852.129i			1.73550i	−0.497004	+	0.867748i	$0.665567\pi$
$492$	38.4359	+	232.481i	0.0781217	+	0.472522i
$493$	−165.290			−0.335273
$494$	1122.67	−	92.1797i	2.27262	−	0.186599i
$495$			191.469i			0.386805i
$496$	212.450	+	624.945i	0.428327	+	1.25997i
$497$	−133.917			−0.269452
$498$	1.09322	+	13.3145i	0.00219521	+	0.0267359i
$499$		−	851.935i		−	1.70729i	−0.520859	−	0.853643i	$-0.674388\pi$
$499$		−	851.935i		−	1.70729i	0.520859	−	0.853643i	$-0.325612\pi$
$500$	517.988	−	85.6385i	1.03598	−	0.171277i
$501$	87.0315			0.173716
$502$	14.3867	−	1.18125i	0.0286587	−	0.00235309i
$503$		−	483.294i		−	0.960823i	−0.877043	−	0.480411i	$-0.840487\pi$
$503$		−	483.294i		−	0.960823i	0.877043	−	0.480411i	$-0.159513\pi$
$504$	−134.790	+	33.8109i	−0.267441	+	0.0670852i
$505$	−2.46986			−0.00489081
$506$	36.8361	+	448.634i	0.0727986	+	0.886629i
$507$		−	274.279i		−	0.540984i
$508$	33.8584	+	204.794i	0.0666505	+	0.403138i
$509$	−653.399			−1.28369			−0.641846	−	0.766833i	$-0.721831\pi$
$509$	−653.399			−1.28369			−0.641846	+	0.766833i	$0.721831\pi$
$510$	94.8782	−	7.79018i	0.186036	−	0.0152749i
$511$		−	14.5187i		−	0.0284124i
$512$	−344.217	−	379.023i	−0.672300	−	0.740279i
$513$	−736.670			−1.43600
$514$	−62.2304	−	757.916i	−0.121071	−	1.47455i
$515$			400.299i			0.777280i
$516$	312.900	−	51.7315i	0.606396	−	0.100255i
$517$	441.001			0.853001
$518$	−18.4236	+	1.51271i	−0.0355669	+	0.00292030i
$519$		−	30.0016i		−	0.0578066i
$520$	−124.236	−	495.277i	−0.238915	−	0.952456i
$521$	−70.1290			−0.134605			−0.0673023	−	0.997733i	$-0.521439\pi$
$521$	−70.1290			−0.134605			−0.0673023	+	0.997733i	$0.521439\pi$
$522$	−20.0128	−	243.739i	−0.0383386	−	0.466934i
$523$			288.438i			0.551507i	0.961228	+	0.275753i	$0.0889273\pi$
$523$			288.438i			0.551507i	−0.961228	+	0.275753i	$0.911073\pi$
$524$	−158.332	−	957.681i	−0.302161	−	1.82764i
$525$	−54.4256			−0.103668
$526$	624.607	−	51.2847i	1.18747	−	0.0974995i
$527$		−	366.126i		−	0.694736i
$528$	200.526	−	68.1687i	0.379783	−	0.129107i
$529$	−174.806			−0.330446
$530$	−8.65327	−	105.390i	−0.0163269	−	0.198849i
$531$		−	251.651i		−	0.473918i
$532$	−316.709	+	52.3611i	−0.595317	+	0.0984232i
$533$	−701.064			−1.31532
$534$	−385.358	+	31.6407i	−0.721644	+	0.0592522i
$535$		−	130.426i		−	0.243788i
$536$	−248.954	+	62.4480i	−0.464467	+	0.116507i
$537$	305.417			0.568746
$538$	27.8436	+	339.112i	0.0517539	+	0.630321i
$539$		−	59.3872i		−	0.110180i
$540$	54.4693	+	329.460i	0.100869	+	0.610111i
$541$	−9.90711			−0.0183126			−0.00915630	−	0.999958i	$-0.502915\pi$
$541$	−9.90711			−0.0183126			−0.00915630	+	0.999958i	$0.502915\pi$
$542$	100.283	−	8.23397i	0.185024	−	0.0151918i
$543$		−	128.798i		−	0.237197i
$544$	113.103	+	260.501i	0.207910	+	0.478862i
$545$	303.284			0.556484
$546$	12.5453	+	152.791i	0.0229767	+	0.279838i
$547$			265.156i			0.484746i	0.970183	+	0.242373i	$0.0779257\pi$
$547$			265.156i			0.484746i	−0.970183	+	0.242373i	$0.922074\pi$
$548$	1067.74	−	176.529i	1.94844	−	0.322133i
$549$	−476.489			−0.867922
$550$	−222.955	+	18.3063i	−0.405374	+	0.0332841i
$551$		−	564.926i		−	1.02527i
$552$	80.5689	+	321.195i	0.145958	+	0.581874i
$553$	105.537			0.190845
$554$	−9.65251	−	117.560i	−0.0174233	−	0.212202i
$555$			18.7366i			0.0337596i
$556$	−10.2402	−	61.9385i	−0.0184177	−	0.111400i
$557$	−718.935			−1.29073			−0.645363	−	0.763876i	$-0.723294\pi$
$557$	−718.935			−1.29073			−0.645363	+	0.763876i	$0.723294\pi$
$558$	539.896	−	44.3294i	0.967556	−	0.0794434i
$559$			943.574i			1.68797i
$560$	46.8348	+	137.770i	0.0836336	+	0.246017i
$561$	−117.478			−0.209409
$562$	−53.2763	−	648.862i	−0.0947976	−	1.15456i
$563$		−	283.534i		−	0.503613i	−0.967778	−	0.251807i	$-0.918975\pi$
$563$		−	283.534i		−	0.503613i	0.967778	−	0.251807i	$-0.0810247\pi$
$564$	320.075	−	52.9176i	0.567508	−	0.0938256i
$565$	430.072			0.761189
$566$	563.734	−	46.2866i	0.995996	−	0.0817785i
$567$			56.0792i			0.0989051i
$568$	−392.760	+	98.5205i	−0.691479	+	0.173452i
$569$	31.4542			0.0552798			0.0276399	−	0.999618i	$-0.491201\pi$
$569$	31.4542			0.0552798			0.0276399	+	0.999618i	$0.491201\pi$
$570$	26.6253	+	324.274i	0.0467110	+	0.568902i
$571$			580.635i			1.01687i	0.861099	+	0.508437i	$0.169776\pi$
$571$			580.635i			1.01687i	−0.861099	+	0.508437i	$0.830224\pi$
$572$	102.784	+	621.693i	0.179692	+	1.08688i
$573$	−249.130			−0.434781
$574$	199.114	−	16.3487i	0.346888	−	0.0284820i
$575$		−	349.767i		−	0.608290i
$576$	−370.446	+	198.325i	−0.643135	+	0.344314i
$577$	909.096			1.57556			0.787778	−	0.615959i	$-0.211231\pi$
$577$	909.096			1.57556			0.787778	+	0.615959i	$0.211231\pi$
$578$	34.4082	+	419.064i	0.0595297	+	0.725025i
$579$		−	166.100i		−	0.286874i
$580$	−252.651	+	41.7706i	−0.435606	+	0.0720183i
$581$	11.3266			0.0194951
$582$	99.5780	−	8.17607i	0.171096	−	0.0140482i
$583$			130.494i			0.223832i
$584$	−10.6811	−	42.5813i	−0.0182896	−	0.0729131i
$585$	−419.062			−0.716346
$586$	−7.77495	−	94.6926i	−0.0132678	−	0.161591i
$587$		−	30.9295i		−	0.0526908i	−0.999653	−	0.0263454i	$-0.991613\pi$
$587$		−	30.9295i		−	0.0526908i	0.999653	−	0.0263454i	$-0.00838696\pi$
$588$	−7.12613	−	43.1027i	−0.0121193	−	0.0733039i
$589$	1251.34			2.12452
$590$	−262.622	+	21.5632i	−0.445123	+	0.0365478i
$591$			277.523i			0.469582i
$592$	−52.9210	+	17.9905i	−0.0893935	+	0.0303893i
$593$	−879.391			−1.48295			−0.741476	−	0.670979i	$-0.765874\pi$
$593$	−879.391			−1.48295			−0.741476	+	0.670979i	$0.765874\pi$
$594$	−33.7220	−	410.707i	−0.0567711	−	0.691426i
$595$		−	80.7127i		−	0.135652i
$596$	−96.5402	+	15.9609i	−0.161980	+	0.0267800i
$597$	417.582			0.699467
$598$	−981.915	+	80.6223i	−1.64200	+	0.134820i
$599$		−	252.069i		−	0.420816i	−0.977614	−	0.210408i	$-0.932521\pi$
$599$		−	252.069i		−	0.420816i	0.977614	−	0.210408i	$-0.0674793\pi$
$600$	−159.622	+	40.0399i	−0.266037	+	0.0667331i
$601$	−475.958			−0.791943			−0.395972	−	0.918263i	$-0.629592\pi$
$601$	−475.958			−0.791943			−0.395972	+	0.918263i	$0.629592\pi$
$602$	−22.0040	−	267.991i	−0.0365514	−	0.445167i
$603$			210.644i			0.349327i
$604$	123.570	+	747.420i	0.204586	+	1.23745i
$605$	168.515			0.278537
$606$	2.23467	−	0.183482i	0.00368757	−	0.000302776i
$607$		−	150.523i		−	0.247979i	−0.992284	−	0.123989i	$-0.960431\pi$
$607$		−	150.523i		−	0.247979i	0.992284	−	0.123989i	$-0.0395689\pi$
$608$	−890.339	+	386.564i	−1.46437	+	0.635796i
$609$	76.8841			0.126246
$610$	40.8289	+	497.264i	0.0669327	+	0.815187i
$611$			965.208i			1.57972i
$612$	229.951	−	38.0175i	0.375736	−	0.0621201i
$613$	184.999			0.301794			0.150897	−	0.988550i	$-0.451784\pi$
$613$	184.999			0.301794			0.150897	+	0.988550i	$0.451784\pi$
$614$	−697.608	+	57.2787i	−1.13617	+	0.0932877i
$615$		−	202.496i		−	0.329261i
$616$	−43.6901	−	174.174i	−0.0709254	−	0.282750i
$617$	−40.0241			−0.0648689			−0.0324345	−	0.999474i	$-0.510326\pi$
$617$	−40.0241			−0.0648689			−0.0324345	+	0.999474i	$0.510326\pi$
$618$	−29.7377	−	362.181i	−0.0481192	−	0.586053i
$619$			389.507i			0.629253i	0.949216	+	0.314626i	$0.101879\pi$
$619$			389.507i			0.629253i	−0.949216	+	0.314626i	$0.898121\pi$
$620$	−92.5242	−	559.637i	−0.149233	−	0.902641i
$621$	644.307			1.03753
$622$	−687.569	+	56.4544i	−1.10542	+	0.0907626i
$623$			327.823i			0.526201i
$624$	149.199	+	438.885i	0.239101	+	0.703342i
$625$	−121.575			−0.194519
$626$	−46.0745	−	561.151i	−0.0736015	−	0.896407i
$627$		−	401.517i		−	0.640378i
$628$	−401.523	+	66.3834i	−0.639368	+	0.105706i
$629$	31.0039			0.0492907
$630$	119.021	−	9.77245i	0.188922	−	0.0155118i
$631$		−	615.708i		−	0.975765i	−0.872909	−	0.487883i	$-0.837769\pi$
$631$		−	615.708i		−	0.975765i	0.872909	−	0.487883i	$-0.162231\pi$
$632$	309.526	−	77.6418i	0.489756	−	0.122851i
$633$	−253.988			−0.401245
$634$	−85.9565	−	1046.88i	−0.135578	−	1.65123i
$635$		−	178.380i		−	0.280913i
$636$	15.6585	+	94.7113i	0.0246203	+	0.148917i
$637$	129.979			0.204049
$638$	314.957	−	25.8602i	0.493663	−	0.0405333i
$639$			332.321i			0.520064i
$640$	238.714	+	369.603i	0.372991	+	0.577505i
$641$	975.771			1.52226			0.761132	−	0.648597i	$-0.224644\pi$
$641$	975.771			1.52226			0.761132	+	0.648597i	$0.224644\pi$
$642$	9.68919	+	118.007i	0.0150922	+	0.183811i
$643$		−	888.565i		−	1.38190i	−0.722900	−	0.690952i	$-0.757191\pi$
$643$		−	888.565i		−	1.38190i	0.722900	−	0.690952i	$-0.242809\pi$
$644$	277.000	−	45.7961i	0.430124	−	0.0711120i
$645$	−272.543			−0.422547
$646$	536.585	−	44.0575i	0.830626	−	0.0682004i
$647$			263.161i			0.406740i	0.979102	+	0.203370i	$0.0651894\pi$
$647$			263.161i			0.406740i	−0.979102	+	0.203370i	$0.934811\pi$
$648$	41.2564	+	164.472i	0.0636673	+	0.253815i
$649$	325.180			0.501047
$650$	−40.0664	−	487.977i	−0.0616407	−	0.750734i
$651$			170.303i			0.261601i
$652$	−44.7478	−	270.659i	−0.0686315	−	0.415121i
$653$	923.879			1.41482			0.707411	−	0.706803i	$-0.249863\pi$
$653$	923.879			1.41482			0.707411	+	0.706803i	$0.249863\pi$
$654$	−274.404	+	22.5305i	−0.419577	+	0.0344503i
$655$			834.160i			1.27353i
$656$	571.944	−	194.432i	0.871866	−	0.296391i
$657$	−36.0287			−0.0548383
$658$	−22.5085	−	274.135i	−0.0342074	−	0.416619i
$659$		−	1297.45i		−	1.96882i	−0.175881	−	0.984411i	$-0.556277\pi$
$659$		−	1297.45i		−	1.96882i	0.175881	−	0.984411i	$-0.443723\pi$
$660$	−179.570	+	29.6881i	−0.272076	+	0.0449820i
$661$	−597.632			−0.904133			−0.452067	−	0.891984i	$-0.649313\pi$
$661$	−597.632			−0.904133			−0.452067	+	0.891984i	$0.649313\pi$
$662$	353.186	−	28.9991i	0.533514	−	0.0438053i
$663$		−	257.122i		−	0.387816i
$664$	33.2193	−	8.33278i	0.0500291	−	0.0125494i
$665$	275.860			0.414827
$666$	3.75385	+	45.7189i	0.00563642	+	0.0686471i
$667$			494.096i			0.740774i
$668$	−36.3938	−	220.130i	−0.0544818	−	0.329535i
$669$	−495.743			−0.741022
$670$	219.828	−	18.0495i	0.328102	−	0.0269395i
$671$		−	615.713i		−	0.917605i
$672$	−52.6097	−	121.171i	−0.0782883	−	0.180315i
$673$	478.696			0.711287			0.355643	−	0.934622i	$-0.384262\pi$
$673$	478.696			0.711287			0.355643	+	0.934622i	$0.384262\pi$
$674$	18.2283	+	222.006i	0.0270450	+	0.329386i
$675$			320.198i			0.474367i
$676$	−693.736	+	114.695i	−1.02624	+	0.169667i
$677$	208.658			0.308210			0.154105	−	0.988054i	$-0.450751\pi$
$677$	208.658			0.308210			0.154105	+	0.988054i	$0.450751\pi$
$678$	−389.118	+	31.9494i	−0.573920	+	0.0471230i
$679$		−	84.7109i		−	0.124758i
$680$	−59.3788	−	236.719i	−0.0873218	−	0.348116i
$681$	181.255			0.266160
$682$	57.2819	+	697.647i	0.0839910	+	1.02294i
$683$		−	12.4224i		−	0.0181880i	−0.999959	−	0.00909400i	$-0.997105\pi$
$683$		−	12.4224i		−	0.0181880i	0.999959	−	0.00909400i	$-0.00289475\pi$
$684$	129.936	+	785.924i	0.189965	+	1.14901i
$685$	−930.027			−1.35770
$686$	−36.9163	+	3.03109i	−0.0538138	+	0.00441850i
$687$			558.023i			0.812261i
$688$	−261.690	−	769.790i	−0.380363	−	1.11888i
$689$	−285.609			−0.414527
$690$	−23.2870	−	283.617i	−0.0337493	−	0.411039i
$691$		−	914.850i		−	1.32395i	−0.749526	−	0.661975i	$-0.769718\pi$
$691$		−	914.850i		−	1.32395i	0.749526	−	0.661975i	$-0.230282\pi$
$692$	−75.8834	+	12.5457i	−0.109658	+	0.0181297i
$693$	−147.372			−0.212657
$694$	−103.957	+	8.53560i	−0.149794	+	0.0122991i
$695$			53.9497i			0.0776255i
$696$	225.490	−	56.5621i	0.323979	−	0.0812674i
$697$	−335.075			−0.480738
$698$	68.7258	+	837.026i	0.0984611	+	1.19918i
$699$			627.711i			0.898012i
$700$	22.7591	+	137.659i	0.0325129	+	0.196656i
$701$	338.736			0.483218			0.241609	−	0.970374i	$-0.422325\pi$
$701$	338.736			0.483218			0.241609	+	0.970374i	$0.422325\pi$
$702$	898.904	−	73.8065i	1.28049	−	0.105137i
$703$			105.965i			0.150732i
$704$	−256.273	−	478.685i	−0.364024	−	0.679951i
$705$	−278.792			−0.395449
$706$	32.4800	+	395.581i	0.0460057	+	0.560313i
$707$		−	1.90103i		−	0.00268886i
$708$	236.012	−	39.0197i	0.333351	−	0.0551126i
$709$	−665.756			−0.939006			−0.469503	−	0.882931i	$-0.655567\pi$
$709$	−665.756			−0.939006			−0.469503	+	0.882931i	$0.655567\pi$
$710$	346.810	−	28.4756i	0.488465	−	0.0401065i
$711$		−	261.895i		−	0.368347i
$712$	241.173	+	961.458i	0.338727	+	1.35036i
$713$	−1094.45			−1.53499
$714$	5.99603	+	73.0269i	0.00839780	+	0.102279i
$715$		−	541.507i		−	0.757352i
$716$	−127.716	−	772.494i	−0.178374	−	1.07890i
$717$	−376.769			−0.525480
$718$	−466.611	+	38.3121i	−0.649876	+	0.0533595i
$719$		−	517.776i		−	0.720134i	−0.932926	−	0.360067i	$-0.882754\pi$
$719$		−	517.776i		−	0.720134i	0.932926	−	0.360067i	$-0.117246\pi$
$720$	341.881	−	116.222i	0.474834	−	0.161420i
$721$	−308.107			−0.427333
$722$	91.4969	+	1114.36i	0.126727	+	1.54343i
$723$			182.051i			0.251799i
$724$	−325.771	+	53.8593i	−0.449959	+	0.0743913i
$725$	−245.548			−0.338687
$726$	−152.468	+	12.5187i	−0.210011	+	0.0172434i
$727$			428.891i			0.589946i	0.955506	+	0.294973i	$0.0953106\pi$
$727$			428.891i			0.589946i	−0.955506	+	0.294973i	$0.904689\pi$
$728$	381.210	−	95.6233i	0.523641	−	0.131351i
$729$	−201.882			−0.276930
$730$	3.08719	+	37.5996i	0.00422903	+	0.0515062i
$731$			450.983i			0.616940i
$732$	−73.8820	−	446.879i	−0.100932	−	0.610490i
$733$	758.896			1.03533			0.517665	−	0.855584i	$-0.326802\pi$
$733$	758.896			1.03533			0.517665	+	0.855584i	$0.326802\pi$
$734$	736.482	−	60.4705i	1.00338	−	0.0823849i
$735$			37.5433i			0.0510794i
$736$	778.709	−	338.097i	1.05803	−	0.459371i
$737$	−272.192			−0.369324
$738$	−40.5698	−	494.108i	−0.0549727	−	0.669523i
$739$			1100.00i			1.48849i	0.667906	+	0.744246i	$0.267191\pi$
$739$			1100.00i			1.48849i	−0.667906	+	0.744246i	$0.732809\pi$
$740$	47.3906	−	7.83504i	0.0640413	−	0.0105879i
$741$	878.790			1.18595
$742$	81.1176	−	6.66034i	0.109323	−	0.00897620i
$743$			1056.59i			1.42205i	0.703165	+	0.711027i	$0.251769\pi$
$743$			1056.59i			1.42205i	−0.703165	+	0.711027i	$0.748231\pi$
$744$	125.288	+	499.472i	0.168398	+	0.671334i
$745$	84.0885			0.112870
$746$	45.9046	+	559.081i	0.0615343	+	0.749438i
$747$		−	28.1074i		−	0.0376271i
$748$	49.1257	+	297.139i	0.0656761	+	0.397245i
$749$	100.388			0.134029
$750$	408.215	−	33.5174i	0.544287	−	0.0446898i
$751$			42.1730i			0.0561557i	0.999606	+	0.0280779i	$0.00893864\pi$
$751$			42.1730i			0.0561557i	−0.999606	+	0.0280779i	$0.991061\pi$
$752$	−267.690	−	787.439i	−0.355971	−	1.04713i
$753$	11.2614			0.0149554
$754$	56.5996	+	689.338i	0.0750658	+	0.914242i
$755$		−	651.018i		−	0.862275i
$756$	−253.583	+	41.9245i	−0.335427	+	0.0554558i
$757$	−931.250			−1.23018			−0.615092	−	0.788455i	$-0.710881\pi$
$757$	−931.250			−1.23018			−0.615092	+	0.788455i	$0.710881\pi$
$758$	−518.072	+	42.5374i	−0.683472	+	0.0561180i
$759$			351.175i			0.462681i
$760$	809.056	−	202.945i	1.06455	−	0.267032i
$761$	−423.281			−0.556217			−0.278108	−	0.960550i	$-0.589707\pi$
$761$	−423.281			−0.556217			−0.278108	+	0.960550i	$0.589707\pi$
$762$	13.2516	+	161.394i	0.0173905	+	0.211803i
$763$			233.435i			0.305943i
$764$	104.178	+	630.126i	0.136359	+	0.824772i
$765$	−200.292			−0.261819
$766$	823.223	−	67.5925i	1.07470	−	0.0882409i
$767$			711.713i			0.927917i
$768$	−243.440	−	316.674i	−0.316979	−	0.412336i
$769$	600.534			0.780928			0.390464	−	0.920618i	$-0.372315\pi$
$769$	600.534			0.780928			0.390464	+	0.920618i	$0.372315\pi$
$770$	12.6278	+	153.797i	0.0163998	+	0.199736i
$771$		−	593.270i		−	0.769481i
$772$	−420.119	+	69.4578i	−0.544196	+	0.0899713i
$773$	120.049			0.155303			0.0776516	−	0.996981i	$-0.475258\pi$
$773$	120.049			0.155303			0.0776516	+	0.996981i	$0.475258\pi$
$774$	−665.029	+	54.6037i	−0.859210	+	0.0705474i
$775$		−	543.903i		−	0.701811i
$776$	−62.3201	−	248.445i	−0.0803095	−	0.320160i
$777$	−14.4214			−0.0185603
$778$	−57.0928	−	695.344i	−0.0733840	−	0.893758i
$779$		−	1145.22i		−	1.47011i
$780$	−64.9777	−	393.021i	−0.0833047	−	0.503873i
$781$	−429.421			−0.549835
$782$	−469.308	+	38.5336i	−0.600138	+	0.0492757i
$783$		−	452.326i		−	0.577683i
$784$	−106.040	+	36.0484i	−0.135255	+	0.0459800i
$785$	349.735			0.445522
$786$	−61.9685	−	754.727i	−0.0788404	−	0.960213i
$787$		−	1277.61i		−	1.62339i	−0.584081	−	0.811696i	$-0.698545\pi$
$787$		−	1277.61i		−	1.62339i	0.584081	−	0.811696i	$-0.301455\pi$
$788$	701.942	−	116.051i	0.890789	−	0.147273i
$789$	488.920			0.619671
$790$	−273.313	+	22.4410i	−0.345966	+	0.0284063i
$791$			331.022i			0.418486i
$792$	−432.219	+	108.418i	−0.545732	+	0.136892i
$793$	1347.60			1.69936
$794$	−5.51527	−	67.1715i	−0.00694618	−	0.0845989i
$795$		−	82.4955i		−	0.103768i
$796$	−174.619	−	1056.19i	−0.219371	−	1.32688i
$797$	84.2194			0.105670			0.0528352	−	0.998603i	$-0.483174\pi$
$797$	84.2194			0.105670			0.0528352	+	0.998603i	$0.483174\pi$
$798$	−249.591	+	20.4932i	−0.312771	+	0.0256807i
$799$			461.323i			0.577376i
$800$	168.022	+	386.991i	0.210028	+	0.483739i
$801$	813.506			1.01561
$802$	−22.9326	−	279.300i	−0.0285942	−	0.348254i
$803$		−	46.5559i		−	0.0579774i
$804$	−197.554	+	32.6614i	−0.245714	+	0.0406237i
$805$	−241.273			−0.299718
$806$	−1526.92	+	125.371i	−1.89445	+	0.155548i
$807$			265.445i			0.328928i
$808$	−1.39855	−	5.57544i	−0.00173088	−	0.00690029i
$809$	1224.02			1.51300			0.756501	−	0.653993i	$-0.226907\pi$
$809$	1224.02			1.51300			0.756501	+	0.653993i	$0.226907\pi$
$810$	−11.9244	−	145.230i	−0.0147215	−	0.179296i
$811$		−	346.748i		−	0.427556i	−0.976882	−	0.213778i	$-0.931423\pi$
$811$		−	346.748i		−	0.427556i	0.976882	−	0.213778i	$-0.0685769\pi$
$812$	−32.1505	−	194.464i	−0.0395942	−	0.239487i
$813$	78.4981			0.0965536
$814$	−59.0774	+	4.85068i	−0.0725767	+	0.00595907i
$815$			235.749i			0.289263i
$816$	71.3100	+	209.766i	0.0873897	+	0.257066i
$817$	−1541.37			−1.88662
$818$	115.868	+	1411.18i	0.141648	+	1.72515i
$819$		−	322.549i		−	0.393832i
$820$	−512.174	+	84.6773i	−0.624603	+	0.103265i
$821$	−1288.46			−1.56938			−0.784690	−	0.619888i	$-0.787178\pi$
$821$	−1288.46			−1.56938			−0.784690	+	0.619888i	$0.787178\pi$
$822$	841.465	−	69.0904i	1.02368	−	0.0840515i
$823$		−	496.071i		−	0.602759i	−0.953504	−	0.301379i	$-0.902553\pi$
$823$		−	496.071i		−	0.602759i	0.953504	−	0.301379i	$-0.0974471\pi$
$824$	−903.633	+	226.668i	−1.09664	+	0.275083i
$825$	−174.522			−0.211541
$826$	−16.5970	−	202.138i	−0.0200932	−	0.244719i
$827$		−	2.15878i		−	0.00261037i	−0.999999	−	0.00130519i	$-0.999585\pi$
$827$		−	2.15878i		−	0.00261037i	0.999999	−	0.00130519i	$-0.000415453\pi$
$828$	−113.645	−	687.386i	−0.137252	−	0.830176i
$829$	501.082			0.604442			0.302221	−	0.953238i	$-0.402272\pi$
$829$	501.082			0.604442			0.302221	+	0.953238i	$0.402272\pi$
$830$	−29.3329	+	2.40844i	−0.0353408	+	0.00290174i
$831$		−	92.0217i		−	0.110736i
$832$	1047.69	−	560.898i	1.25924	−	0.674157i
$833$	62.1239			0.0745785
$834$	−4.00785	−	48.8124i	−0.00480557	−	0.0585280i
$835$			191.737i			0.229626i
$836$	−1015.56	+	167.902i	−1.21479	+	0.200839i
$837$	1001.93			1.19704
$838$	1188.68	−	97.5994i	1.41848	−	0.116467i
$839$			1576.56i			1.87909i	0.342424	+	0.939546i	$0.388752\pi$
$839$			1576.56i			1.87909i	−0.342424	+	0.939546i	$0.611248\pi$
$840$	27.6199	+	110.109i	0.0328808	+	0.131082i
$841$	−494.127			−0.587547
$842$	26.6465	+	324.533i	0.0316467	+	0.385431i
$843$		−	507.907i		−	0.602499i
$844$	106.210	+	642.415i	0.125841	+	0.761155i
$845$	604.258			0.715099
$846$	−680.277	+	55.8556i	−0.804109	+	0.0660232i
$847$			129.704i			0.153134i
$848$	233.006	−	79.2105i	0.274772	−	0.0934086i
$849$	441.271			0.519754
$850$	−19.1498	−	233.230i	−0.0225292	−	0.274388i
$851$		−	92.6791i		−	0.108906i
$852$	−311.670	+	51.5280i	−0.365809	+	0.0604789i
$853$	1502.12			1.76098			0.880490	−	0.474065i	$-0.157214\pi$
$853$	1502.12			1.76098			0.880490	+	0.474065i	$0.157214\pi$
$854$	−382.740	+	31.4257i	−0.448173	+	0.0367982i
$855$		−	684.556i		−	0.800650i
$856$	294.423	−	73.8535i	0.343953	−	0.0862775i
$857$	−112.940			−0.131786			−0.0658929	−	0.997827i	$-0.520990\pi$
$857$	−112.940			−0.131786			−0.0658929	+	0.997827i	$0.520990\pi$
$858$	40.2278	+	489.942i	0.0468855	+	0.571028i
$859$			7.56729i			0.00880941i	0.999990	+	0.00440471i	$0.00140207\pi$
$859$			7.56729i			0.00880941i	−0.999990	+	0.00440471i	$0.998598\pi$
$860$	113.969	+	689.345i	0.132522	+	0.801564i
$861$	155.859			0.181021
$862$	−771.069	+	63.3104i	−0.894512	+	0.0734459i
$863$			1013.78i			1.17472i	0.809327	+	0.587358i	$0.199832\pi$
$863$			1013.78i			1.17472i	−0.809327	+	0.587358i	$0.800168\pi$
$864$	−712.878	+	309.514i	−0.825090	+	0.358234i
$865$	66.0960			0.0764116
$866$	−94.0810	−	1145.83i	−0.108639	−	1.32313i
$867$			328.029i			0.378349i
$868$	430.748	−	71.2151i	0.496253	−	0.0820450i
$869$	338.417			0.389433
$870$	−199.109	+	16.3483i	−0.228861	+	0.0187911i
$871$		−	595.739i		−	0.683972i
$872$	171.733	+	684.630i	0.196942	+	0.785126i
$873$	−210.213			−0.240794
$874$	−131.700	−	1604.00i	−0.150686	−	1.83524i
$875$		−	347.268i		−	0.396878i
$876$	−5.58643	−	33.7898i	−0.00637721	−	0.0385728i
$877$	−1231.12			−1.40378			−0.701890	−	0.712285i	$-0.747660\pi$
$877$	−1231.12			−1.40378			−0.701890	+	0.712285i	$0.747660\pi$
$878$	588.431	−	48.3144i	0.670195	−	0.0550278i
$879$		−	74.1220i		−	0.0843254i
$880$	150.181	+	441.774i	0.170660	+	0.502016i
$881$	1270.31			1.44189			0.720945	−	0.692992i	$-0.243708\pi$
$881$	1270.31			1.44189			0.720945	+	0.692992i	$0.243708\pi$
$882$	7.52177	+	91.6091i	0.00852808	+	0.103865i
$883$			1407.95i			1.59451i	0.603646	+	0.797253i	$0.293714\pi$
$883$			1407.95i			1.59451i	−0.603646	+	0.797253i	$0.706286\pi$
$884$	−650.341	+	107.520i	−0.735680	+	0.121629i
$885$	−205.572			−0.232284
$886$	850.159	−	69.8042i	0.959547	−	0.0787857i
$887$			1721.23i			1.94051i	0.242093	+	0.970253i	$0.422166\pi$
$887$			1721.23i			1.94051i	−0.242093	+	0.970253i	$0.577834\pi$
$888$	−42.2958	+	10.6095i	−0.0476304	+	0.0119477i
$889$	137.298			0.154440
$890$	−69.7069	−	848.974i	−0.0783224	−	0.953904i
$891$			179.824i			0.201823i
$892$	207.304	+	1253.89i	0.232404	+	1.40570i
$893$	−1576.71			−1.76563
$894$	−76.0812	+	6.24681i	−0.0851020	+	0.00698749i
$895$			672.858i			0.751796i
$896$	−284.480	+	183.736i	−0.317500	+	0.205063i
$897$	−768.608			−0.856865
$898$	75.0854	+	914.480i	0.0836140	+	1.01835i
$899$			768.342i			0.854663i
$900$	341.606	−	56.4774i	0.379563	−	0.0627527i
$901$	−136.507			−0.151506
$902$	638.480	−	52.4238i	0.707849	−	0.0581195i
$903$		−	209.774i		−	0.232308i
$904$	243.527	+	970.840i	0.269388	+	1.07394i
$905$	283.753			0.313539
$906$	48.3632	+	589.025i	0.0533810	+	0.650138i
$907$		−	1181.35i		−	1.30248i	−0.758871	−	0.651241i	$-0.774249\pi$
$907$		−	1181.35i		−	1.30248i	0.758871	−	0.651241i	$-0.225751\pi$
$908$	−75.7950	−	458.449i	−0.0834746	−	0.504900i
$909$	−4.71747			−0.00518974
$910$	−336.611	+	27.6382i	−0.369903	+	0.0303717i
$911$		−	1286.03i		−	1.41166i	−0.708379	−	0.705832i	$-0.750573\pi$
$911$		−	1286.03i		−	1.41166i	0.708379	−	0.705832i	$-0.249427\pi$
$912$	−716.938	+	243.723i	−0.786116	+	0.267240i
$913$	36.3201			0.0397810
$914$	−62.9171	−	766.280i	−0.0688371	−	0.838381i
$915$			389.241i			0.425400i
$916$	1411.41	−	233.347i	1.54084	−	0.254746i
$917$	−642.046			−0.700159
$918$	429.633	−	35.2760i	0.468010	−	0.0384270i
$919$		−	1618.74i		−	1.76142i	−0.473659	−	0.880708i	$-0.657067\pi$
$919$		−	1618.74i		−	1.76142i	0.473659	−	0.880708i	$-0.342933\pi$
$920$	−707.617	+	177.500i	−0.769149	+	0.192934i
$921$	−546.063			−0.592902
$922$	7.86889	+	95.8368i	0.00853459	+	0.103944i
$923$		−	939.863i		−	1.01827i
$924$	−22.8507	−	138.214i	−0.0247302	−	0.149582i
$925$	46.0583			0.0497927
$926$	−124.143	+	10.1930i	−0.134064	+	0.0110076i
$927$			764.579i			0.824788i
$928$	−237.356	−	546.681i	−0.255771	−	0.589096i
$929$	−551.019			−0.593131			−0.296566	−	0.955012i	$-0.595841\pi$
$929$	−551.019			−0.593131			−0.296566	+	0.955012i	$0.595841\pi$
$930$	−36.2124	−	441.038i	−0.0389380	−	0.474234i
$931$			212.327i			0.228063i
$932$	1587.67	−	262.489i	1.70351	−	0.281640i
$933$	−538.205			−0.576854
$934$	715.533	−	58.7504i	0.766096	−	0.0629020i
$935$		−	258.814i		−	0.276807i
$936$	−237.293	−	945.988i	−0.253518	−	1.01067i
$937$	−1710.84			−1.82587			−0.912934	−	0.408108i	$-0.866189\pi$
$937$	−1710.84			−1.82587			−0.912934	+	0.408108i	$0.866189\pi$
$938$	13.8925	+	169.200i	0.0148108	+	0.180384i
$939$		−	439.249i		−	0.467784i
$940$	116.582	+	705.150i	0.124023	+	0.750160i
$941$	32.9788			0.0350466			0.0175233	−	0.999846i	$-0.494422\pi$
$941$	32.9788			0.0350466			0.0175233	+	0.999846i	$0.494422\pi$
$942$	−316.431	+	25.9813i	−0.335914	+	0.0275810i
$943$			1001.63i			1.06217i
$944$	−197.386	−	580.632i	−0.209095	−	0.615076i
$945$	220.876			0.233731
$946$	−70.5581	−	859.342i	−0.0745858	−	0.908395i
$947$		−	1186.26i		−	1.25265i	−0.779560	−	0.626327i	$-0.784557\pi$
$947$		−	1186.26i		−	1.25265i	0.779560	−	0.626327i	$-0.215443\pi$
$948$	245.620	−	40.6081i	0.259093	−	0.0428355i
$949$	101.896			0.107372
$950$	797.131	−	65.4502i	0.839085	−	0.0688950i
$951$		−	819.461i		−	0.861684i
$952$	182.200	−	45.7033i	0.191387	−	0.0480077i
$953$	572.985			0.601244			0.300622	−	0.953743i	$-0.402806\pi$
$953$	572.985			0.601244			0.300622	+	0.953743i	$0.402806\pi$
$954$	−16.5279	−	201.296i	−0.0173248	−	0.211003i
$955$		−	548.852i		−	0.574715i
$956$	157.553	+	952.966i	0.164804	+	0.996827i
$957$	246.537			0.257615
$958$	−392.169	+	32.1999i	−0.409362	+	0.0336116i
$959$		−	715.833i		−	0.746437i
$960$	162.010	+	302.614i	0.168761	+	0.315223i
$961$	−740.921			−0.770990
$962$	−10.6166	−	129.301i	−0.0110359	−	0.134409i
$963$		−	249.117i		−	0.258688i
$964$	460.463	−	76.1278i	0.477658	−	0.0789708i
$965$	365.932			0.379204
$966$	218.298	−	17.9238i	0.225981	−	0.0185547i
$967$			717.087i			0.741558i	0.928721	+	0.370779i	$0.120909\pi$
$967$			717.087i			0.741558i	−0.928721	+	0.370779i	$0.879091\pi$
$968$	95.4209	+	380.404i	0.0985753	+	0.392979i
$969$	420.020			0.433457
$970$	18.0125	+	219.378i	0.0185696	+	0.226163i
$971$			675.604i			0.695782i	0.937535	+	0.347891i	$0.113102\pi$
$971$			675.604i			0.695782i	−0.937535	+	0.347891i	$0.886898\pi$
$972$	164.192	+	993.121i	0.168922	+	1.02173i
$973$	−41.5246			−0.0426769
$974$	−977.114	+	80.2281i	−1.00320	+	0.0823697i
$975$		−	381.971i		−	0.391765i
$976$	−1099.40	+	373.741i	−1.12643	+	0.382931i
$977$	582.678			0.596395			0.298197	−	0.954504i	$-0.403615\pi$
$977$	582.678			0.596395			0.298197	+	0.954504i	$0.403615\pi$
$978$	−17.5135	−	213.300i	−0.0179074	−	0.218098i
$979$			1051.20i			1.07375i
$980$	94.9587	−	15.6994i	0.0968966	−	0.0160198i
$981$	579.277			0.590496
$982$	1698.54	−	139.462i	1.72968	−	0.142019i
$983$			448.087i			0.455837i	0.973680	+	0.227918i	$0.0731919\pi$
$983$			448.087i			0.455837i	−0.973680	+	0.227918i	$0.926808\pi$
$984$	457.112	−	114.663i	0.464545	−	0.116527i
$985$	−611.406			−0.620716
$986$	27.0519	+	329.470i	0.0274360	+	0.334149i
$987$		−	214.583i		−	0.217410i
$988$	−367.482	−	2222.73i	−0.371946	−	2.24973i
$989$	1348.11			1.36311
$990$	381.653	−	31.3364i	0.385508	−	0.0316530i
$991$		−	872.154i		−	0.880075i	−0.897979	−	0.440037i	$-0.854965\pi$
$991$		−	872.154i		−	0.880075i	0.897979	−	0.440037i	$-0.145035\pi$
$992$	1210.93	−	525.756i	1.22069	−	0.529996i
$993$	276.462			0.278410
$994$	21.9174	+	266.937i	0.0220497	+	0.268548i
$995$			919.966i			0.924589i
$996$	26.3608	−	4.35820i	0.0264666	−	0.00437570i
$997$	−1176.24			−1.17978			−0.589888	−	0.807485i	$-0.700828\pi$
$997$	−1176.24			−1.17978			−0.589888	+	0.807485i	$0.700828\pi$
$998$	−1698.16	+	139.431i	−1.70156	+	0.139710i
$999$			84.8441i			0.0849290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.3.c.a.15.3	✓	6
3.2	odd	2		252.3.g.a.127.4		6
4.3	odd	2	inner	28.3.c.a.15.4	yes	6
7.2	even	3		196.3.g.k.67.2		12
7.3	odd	6		196.3.g.j.79.6		12
7.4	even	3		196.3.g.k.79.6		12
7.5	odd	6		196.3.g.j.67.2		12
7.6	odd	2		196.3.c.g.99.3		6
8.3	odd	2		448.3.d.d.127.3		6
8.5	even	2		448.3.d.d.127.4		6
12.11	even	2		252.3.g.a.127.3		6
16.3	odd	4		1792.3.g.g.127.5		12
16.5	even	4		1792.3.g.g.127.6		12
16.11	odd	4		1792.3.g.g.127.8		12
16.13	even	4		1792.3.g.g.127.7		12
28.3	even	6		196.3.g.j.79.2		12
28.11	odd	6		196.3.g.k.79.2		12
28.19	even	6		196.3.g.j.67.6		12
28.23	odd	6		196.3.g.k.67.6		12
28.27	even	2		196.3.c.g.99.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.c.a.15.3	✓	6	1.1	even	1	trivial
28.3.c.a.15.4	yes	6	4.3	odd	2	inner
196.3.c.g.99.3		6	7.6	odd	2
196.3.c.g.99.4		6	28.27	even	2
196.3.g.j.67.2		12	7.5	odd	6
196.3.g.j.67.6		12	28.19	even	6
196.3.g.j.79.2		12	28.3	even	6
196.3.g.j.79.6		12	7.3	odd	6
196.3.g.k.67.2		12	7.2	even	3
196.3.g.k.67.6		12	28.23	odd	6
196.3.g.k.79.2		12	28.11	odd	6
196.3.g.k.79.6		12	7.4	even	3
252.3.g.a.127.3		6	12.11	even	2
252.3.g.a.127.4		6	3.2	odd	2
448.3.d.d.127.3		6	8.3	odd	2
448.3.d.d.127.4		6	8.5	even	2
1792.3.g.g.127.5		12	16.3	odd	4
1792.3.g.g.127.6		12	16.5	even	4
1792.3.g.g.127.7		12	16.13	even	4
1792.3.g.g.127.8		12	16.11	odd	4

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.163664 - 1.99329i) q^{2} -1.56028i q^{3} +(-3.94643 + 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 + 0.255361i) q^{6} +2.64575i q^{7} +(1.94643 + 7.75960i) q^{8} +6.56553 q^{9} +O(q^{10})\)	\(q+(-0.163664 - 1.99329i) q^{2} -1.56028i q^{3} +(-3.94643 + 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 + 0.255361i) q^{6} +2.64575i q^{7} +(1.94643 + 7.75960i) q^{8} +6.56553 q^{9} +(-0.562581 - 6.85178i) q^{10} +8.48389i q^{11} +(1.01802 + 6.15753i) q^{12} -18.5685 q^{13} +(5.27376 - 0.433013i) q^{14} -5.36333i q^{15} +(15.1486 - 5.14977i) q^{16} -8.87484 q^{17} +(-1.07454 - 13.0870i) q^{18} -30.3324i q^{19} +(-13.5655 + 2.24278i) q^{20} +4.12811 q^{21} +(16.9109 - 1.38850i) q^{22} +26.5293i q^{23} +(12.1071 - 3.03697i) q^{24} -13.1841 q^{25} +(3.03899 + 37.0124i) q^{26} -24.2866i q^{27} +(-1.72624 - 10.4413i) q^{28} +18.6245 q^{29} +(-10.6907 + 0.877783i) q^{30} +41.2544i q^{31} +(-12.7443 - 29.3527i) q^{32} +13.2372 q^{33} +(1.45249 + 17.6901i) q^{34} +9.09456i q^{35} +(-25.9104 + 4.28374i) q^{36} -3.49346 q^{37} +(-60.4613 + 4.96431i) q^{38} +28.9720i q^{39} +(6.69069 + 26.6730i) q^{40} +37.7556 q^{41} +(-0.675622 - 8.22853i) q^{42} -50.8159i q^{43} +(-5.53539 - 33.4811i) q^{44} +22.5685 q^{45} +(52.8807 - 4.34189i) q^{46} -51.9810i q^{47} +(-8.03507 - 23.6360i) q^{48} -7.00000 q^{49} +(2.15777 + 26.2799i) q^{50} +13.8472i q^{51} +(73.2792 - 12.1152i) q^{52} +15.3814 q^{53} +(-48.4102 + 3.97483i) q^{54} +29.1627i q^{55} +(-20.5300 + 5.14977i) q^{56} -47.3270 q^{57} +(-3.04816 - 37.1241i) q^{58} -38.3291i q^{59} +(3.49936 + 21.1660i) q^{60} -72.5744 q^{61} +(82.2320 - 6.75184i) q^{62} +17.3708i q^{63} +(-56.4228 + 30.2070i) q^{64} -63.8276 q^{65} +(-2.16645 - 26.3857i) q^{66} +32.0834i q^{67} +(35.0239 - 5.79047i) q^{68} +41.3932 q^{69} +(18.1281 - 1.48845i) q^{70} +50.6160i q^{71} +(12.7793 + 50.9459i) q^{72} -5.48756 q^{73} +(0.571752 + 6.96348i) q^{74} +20.5709i q^{75} +(19.7906 + 119.705i) q^{76} -22.4463 q^{77} +(57.7497 - 4.74166i) q^{78} -39.8894i q^{79} +(52.0721 - 17.7019i) q^{80} +21.1959 q^{81} +(-6.17922 - 75.2579i) q^{82} -4.28106i q^{83} +(-16.2913 + 2.69342i) q^{84} -30.5065 q^{85} +(-101.291 + 8.31672i) q^{86} -29.0594i q^{87} +(-65.8316 + 16.5133i) q^{88} +123.906 q^{89} +(-3.69364 - 44.9856i) q^{90} -49.1276i q^{91} +(-17.3093 - 104.696i) q^{92} +64.3683 q^{93} +(-103.613 + 8.50740i) q^{94} -104.265i q^{95} +(-45.7985 + 19.8846i) q^{96} -32.0177 q^{97} +(1.14565 + 13.9530i) q^{98} +55.7012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) \) 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9	\( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) \) 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9 - 28 * q^10 + 6 * q^12 + 12 * q^13 + 7 * q^14 + 17 * q^16 - 4 * q^17 + 43 * q^18 - 32 * q^20 + 52 * q^22 + 122 * q^24 - 30 * q^25 - 56 * q^26 - 35 * q^28 - 36 * q^29 - 64 * q^30 - 101 * q^32 + 80 * q^33 + 58 * q^34 - 131 * q^36 + 28 * q^37 - 190 * q^38 + 40 * q^40 - 20 * q^41 + 70 * q^42 + 164 * q^44 + 12 * q^45 + 120 * q^46 - 98 * q^48 - 42 * q^49 + 161 * q^50 + 292 * q^52 + 92 * q^53 - 44 * q^54 - 49 * q^56 + 160 * q^57 - 166 * q^58 - 176 * q^60 - 164 * q^61 + 148 * q^62 - 215 * q^64 - 136 * q^65 - 408 * q^66 + 62 * q^68 - 48 * q^69 + 84 * q^70 + 151 * q^72 - 132 * q^73 + 250 * q^74 - 78 * q^76 + 112 * q^77 + 248 * q^78 + 312 * q^80 - 218 * q^81 - 86 * q^82 - 98 * q^84 - 232 * q^85 - 164 * q^86 - 100 * q^88 + 348 * q^89 + 52 * q^90 - 104 * q^92 + 288 * q^93 - 276 * q^94 + 170 * q^96 + 252 * q^97 + 7 * q^98

Introduction

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