LMFDB - Embedded newform 349.3.d.a.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,3,Mod(136,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("349.136");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	349.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.50956122617$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			136.2
Character	$\chi$	$=$	349.136
Dual form			349.3.d.a.213.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.62430 + 2.62430i) q^{2} +3.62850i q^{3} -9.77395i q^{4} -2.36293i q^{5} +(-9.52228 - 9.52228i) q^{6} +(3.10965 + 3.10965i) q^{7} +(15.1526 + 15.1526i) q^{8} -4.16599 q^{9} +O(q^{10})$	\(q+(-2.62430 + 2.62430i) q^{2} +3.62850i q^{3} -9.77395i q^{4} -2.36293i q^{5} +(-9.52228 - 9.52228i) q^{6} +(3.10965 + 3.10965i) q^{7} +(15.1526 + 15.1526i) q^{8} -4.16599 q^{9} +(6.20105 + 6.20105i) q^{10} +(7.13579 - 7.13579i) q^{11} +35.4648 q^{12} +(5.81992 + 5.81992i) q^{13} -16.3213 q^{14} +8.57389 q^{15} -40.4343 q^{16} +19.0468i q^{17} +(10.9328 - 10.9328i) q^{18} -6.89113 q^{19} -23.0952 q^{20} +(-11.2833 + 11.2833i) q^{21} +37.4530i q^{22} -7.26590 q^{23} +(-54.9812 + 54.9812i) q^{24} +19.4166 q^{25} -30.5465 q^{26} +17.5402i q^{27} +(30.3935 - 30.3935i) q^{28} +51.7706i q^{29} +(-22.5005 + 22.5005i) q^{30} -8.11432 q^{31} +(45.5015 - 45.5015i) q^{32} +(25.8922 + 25.8922i) q^{33} +(-49.9847 - 49.9847i) q^{34} +(7.34788 - 7.34788i) q^{35} +40.7182i q^{36} -41.5845i q^{37} +(18.0844 - 18.0844i) q^{38} +(-21.1176 + 21.1176i) q^{39} +(35.8046 - 35.8046i) q^{40} +0.783957 q^{41} -59.2219i q^{42} +(9.10585 - 9.10585i) q^{43} +(-69.7448 - 69.7448i) q^{44} +9.84396i q^{45} +(19.0679 - 19.0679i) q^{46} +(34.4228 + 34.4228i) q^{47} -146.716i q^{48} -29.6602i q^{49} +(-50.9550 + 50.9550i) q^{50} -69.1114 q^{51} +(56.8836 - 56.8836i) q^{52} +(12.3743 + 12.3743i) q^{53} +(-46.0308 - 46.0308i) q^{54} +(-16.8614 - 16.8614i) q^{55} +94.2384i q^{56} -25.0044i q^{57} +(-135.862 - 135.862i) q^{58} +(13.4518 + 13.4518i) q^{59} -83.8008i q^{60} +(-40.3733 - 40.3733i) q^{61} +(21.2944 - 21.2944i) q^{62} +(-12.9548 - 12.9548i) q^{63} +77.0823i q^{64} +(13.7521 - 13.7521i) q^{65} -135.898 q^{66} -20.8242 q^{67} +186.163 q^{68} -26.3643i q^{69} +38.5661i q^{70} +(-74.8356 + 74.8356i) q^{71} +(-63.1257 - 63.1257i) q^{72} +54.7468i q^{73} +(109.130 + 109.130i) q^{74} +70.4529i q^{75} +67.3535i q^{76} +44.3796 q^{77} -110.838i q^{78} +(94.7057 + 94.7057i) q^{79} +95.5434i q^{80} -101.138 q^{81} +(-2.05734 + 2.05734i) q^{82} +18.6532i q^{83} +(110.283 + 110.283i) q^{84} +45.0063 q^{85} +47.7931i q^{86} -187.849 q^{87} +216.252 q^{88} +(9.04776 - 9.04776i) q^{89} +(-25.8335 - 25.8335i) q^{90} +36.1958i q^{91} +71.0166i q^{92} -29.4428i q^{93} -180.672 q^{94} +16.2833i q^{95} +(165.102 + 165.102i) q^{96} +(-90.7206 - 90.7206i) q^{97} +(77.8374 + 77.8374i) q^{98} +(-29.7277 + 29.7277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9}+O(q^{10}) $ 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9	$ 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9} - 16 q^{10} + 8 q^{11} + 32 q^{12} + 22 q^{13} + 56 q^{14} + 32 q^{15} - 436 q^{16} - 112 q^{18} - 52 q^{19} - 72 q^{20} + 50 q^{21} + 200 q^{23} + 144 q^{24} - 408 q^{25} + 72 q^{26} - 84 q^{28} - 6 q^{30} + 68 q^{31} - 130 q^{32} + 146 q^{33} + 62 q^{34} - 60 q^{35} + 2 q^{38} + 64 q^{39} - 218 q^{40} + 144 q^{41} - 180 q^{43} + 32 q^{44} + 122 q^{46} - 100 q^{47} + 56 q^{50} - 172 q^{51} + 296 q^{52} - 188 q^{53} - 540 q^{54} + 160 q^{55} - 140 q^{58} + 202 q^{59} + 62 q^{61} + 424 q^{62} + 362 q^{63} + 206 q^{65} - 268 q^{66} + 252 q^{67} - 404 q^{68} + 12 q^{71} + 664 q^{72} - 68 q^{74} - 884 q^{77} + 50 q^{79} + 1284 q^{81} - 666 q^{82} - 742 q^{84} + 1240 q^{85} + 220 q^{87} + 60 q^{88} + 48 q^{89} + 298 q^{90} + 940 q^{94} - 1588 q^{96} + 180 q^{97} + 704 q^{98} - 26 q^{99}+O(q^{100}) $ 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9 - 16 * q^10 + 8 * q^11 + 32 * q^12 + 22 * q^13 + 56 * q^14 + 32 * q^15 - 436 * q^16 - 112 * q^18 - 52 * q^19 - 72 * q^20 + 50 * q^21 + 200 * q^23 + 144 * q^24 - 408 * q^25 + 72 * q^26 - 84 * q^28 - 6 * q^30 + 68 * q^31 - 130 * q^32 + 146 * q^33 + 62 * q^34 - 60 * q^35 + 2 * q^38 + 64 * q^39 - 218 * q^40 + 144 * q^41 - 180 * q^43 + 32 * q^44 + 122 * q^46 - 100 * q^47 + 56 * q^50 - 172 * q^51 + 296 * q^52 - 188 * q^53 - 540 * q^54 + 160 * q^55 - 140 * q^58 + 202 * q^59 + 62 * q^61 + 424 * q^62 + 362 * q^63 + 206 * q^65 - 268 * q^66 + 252 * q^67 - 404 * q^68 + 12 * q^71 + 664 * q^72 - 68 * q^74 - 884 * q^77 + 50 * q^79 + 1284 * q^81 - 666 * q^82 - 742 * q^84 + 1240 * q^85 + 220 * q^87 + 60 * q^88 + 48 * q^89 + 298 * q^90 + 940 * q^94 - 1588 * q^96 + 180 * q^97 + 704 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.62430	+	2.62430i	−1.31215	+	1.31215i	−0.392326	+	0.919826i	$0.628330\pi$
$2$	−2.62430	+	2.62430i	−1.31215	+	1.31215i	−0.919826	+	0.392326i	$0.871670\pi$
$3$			3.62850i			1.20950i	0.796416	+	0.604750i	$0.206727\pi$
$3$			3.62850i			1.20950i	−0.796416	+	0.604750i	$0.793273\pi$
$4$		−	9.77395i		−	2.44349i
$5$		−	2.36293i		−	0.472586i	−0.971682	−	0.236293i	$-0.924067\pi$
$5$		−	2.36293i		−	0.472586i	0.971682	−	0.236293i	$-0.0759326\pi$
$6$	−9.52228	−	9.52228i	−1.58705	−	1.58705i
$7$	3.10965	+	3.10965i	0.444235	+	0.444235i	0.893433	−	0.449197i	$-0.148290\pi$
$7$	3.10965	+	3.10965i	0.444235	+	0.444235i	−0.449197	+	0.893433i	$0.648290\pi$
$8$	15.1526	+	15.1526i	1.89408	+	1.89408i
$9$	−4.16599			−0.462888
$10$	6.20105	+	6.20105i	0.620105	+	0.620105i
$11$	7.13579	−	7.13579i	0.648708	−	0.648708i	−0.303973	−	0.952681i	$-0.598313\pi$
$11$	7.13579	−	7.13579i	0.648708	−	0.648708i	0.952681	+	0.303973i	$0.0983132\pi$
$12$	35.4648			2.95540
$13$	5.81992	+	5.81992i	0.447686	+	0.447686i	0.894585	−	0.446898i	$-0.147471\pi$
$13$	5.81992	+	5.81992i	0.447686	+	0.447686i	−0.446898	+	0.894585i	$0.647471\pi$
$14$	−16.3213			−1.16581
$15$	8.57389			0.571593
$16$	−40.4343			−2.52714
$17$			19.0468i			1.12040i	0.828357	+	0.560201i	$0.189276\pi$
$17$			19.0468i			1.12040i	−0.828357	+	0.560201i	$0.810724\pi$
$18$	10.9328	−	10.9328i	0.607380	−	0.607380i
$19$	−6.89113			−0.362691			−0.181345	−	0.983419i	$-0.558045\pi$
$19$	−6.89113			−0.362691			−0.181345	+	0.983419i	$0.558045\pi$
$20$	−23.0952			−1.15476
$21$	−11.2833	+	11.2833i	−0.537302	+	0.537302i
$22$			37.4530i			1.70241i
$23$	−7.26590			−0.315909			−0.157954	−	0.987446i	$-0.550490\pi$
$23$	−7.26590			−0.315909			−0.157954	+	0.987446i	$0.550490\pi$
$24$	−54.9812	+	54.9812i	−2.29088	+	2.29088i
$25$	19.4166			0.776662
$26$	−30.5465			−1.17487
$27$			17.5402i			0.649636i
$28$	30.3935	−	30.3935i	1.08548	−	1.08548i
$29$			51.7706i			1.78519i	0.450858	+	0.892596i	$0.351118\pi$
$29$			51.7706i			1.78519i	−0.450858	+	0.892596i	$0.648882\pi$
$30$	−22.5005	+	22.5005i	−0.750017	+	0.750017i
$31$	−8.11432			−0.261752			−0.130876	−	0.991399i	$-0.541779\pi$
$31$	−8.11432			−0.261752			−0.130876	+	0.991399i	$0.541779\pi$
$32$	45.5015	−	45.5015i	1.42192	−	1.42192i
$33$	25.8922	+	25.8922i	0.784612	+	0.784612i
$34$	−49.9847	−	49.9847i	−1.47014	−	1.47014i
$35$	7.34788	−	7.34788i	0.209939	−	0.209939i
$36$			40.7182i			1.13106i
$37$		−	41.5845i		−	1.12391i	−0.827169	−	0.561953i	$-0.810050\pi$
$37$		−	41.5845i		−	1.12391i	0.827169	−	0.561953i	$-0.189950\pi$
$38$	18.0844	−	18.0844i	0.475906	−	0.475906i
$39$	−21.1176	+	21.1176i	−0.541476	+	0.541476i
$40$	35.8046	−	35.8046i	0.895114	−	0.895114i
$41$	0.783957			0.0191209			0.00956045	−	0.999954i	$-0.496957\pi$
$41$	0.783957			0.0191209			0.00956045	+	0.999954i	$0.496957\pi$
$42$		−	59.2219i		−	1.41004i
$43$	9.10585	−	9.10585i	0.211764	−	0.211764i	−0.593252	−	0.805016i	$-0.702156\pi$
$43$	9.10585	−	9.10585i	0.211764	−	0.211764i	0.805016	+	0.593252i	$0.202156\pi$
$44$	−69.7448	−	69.7448i	−1.58511	−	1.58511i
$45$			9.84396i			0.218755i
$46$	19.0679	−	19.0679i	0.414521	−	0.414521i
$47$	34.4228	+	34.4228i	0.732401	+	0.732401i	0.971095	−	0.238694i	$-0.0767194\pi$
$47$	34.4228	+	34.4228i	0.732401	+	0.732401i	−0.238694	+	0.971095i	$0.576719\pi$
$48$		−	146.716i		−	3.05658i
$49$		−	29.6602i		−	0.605310i
$50$	−50.9550	+	50.9550i	−1.01910	+	1.01910i
$51$	−69.1114			−1.35512
$52$	56.8836	−	56.8836i	1.09392	−	1.09392i
$53$	12.3743	+	12.3743i	0.233478	+	0.233478i	0.814143	−	0.580665i	$-0.197207\pi$
$53$	12.3743	+	12.3743i	0.233478	+	0.233478i	−0.580665	+	0.814143i	$0.697207\pi$
$54$	−46.0308	−	46.0308i	−0.852422	−	0.852422i
$55$	−16.8614	−	16.8614i	−0.306571	−	0.306571i
$56$			94.2384i			1.68283i
$57$		−	25.0044i		−	0.438674i
$58$	−135.862	−	135.862i	−2.34244	−	2.34244i
$59$	13.4518	+	13.4518i	0.227996	+	0.227996i	0.811855	−	0.583859i	$-0.198458\pi$
$59$	13.4518	+	13.4518i	0.227996	+	0.227996i	−0.583859	+	0.811855i	$0.698458\pi$
$60$		−	83.8008i		−	1.39668i
$61$	−40.3733	−	40.3733i	−0.661857	−	0.661857i	0.293961	−	0.955818i	$-0.405027\pi$
$61$	−40.3733	−	40.3733i	−0.661857	−	0.661857i	−0.955818	+	0.293961i	$0.905027\pi$
$62$	21.2944	−	21.2944i	0.343459	−	0.343459i
$63$	−12.9548	−	12.9548i	−0.205631	−	0.205631i
$64$			77.0823i			1.20441i
$65$	13.7521	−	13.7521i	0.211570	−	0.211570i
$66$	−135.898			−2.05906
$67$	−20.8242			−0.310810			−0.155405	−	0.987851i	$-0.549668\pi$
$67$	−20.8242			−0.310810			−0.155405	+	0.987851i	$0.549668\pi$
$68$	186.163			2.73769
$69$		−	26.3643i		−	0.382092i
$70$			38.5661i			0.550945i
$71$	−74.8356	+	74.8356i	−1.05402	+	1.05402i	−0.0555679	+	0.998455i	$0.517697\pi$
$71$	−74.8356	+	74.8356i	−1.05402	+	1.05402i	−0.998455	+	0.0555679i	$0.982303\pi$
$72$	−63.1257	−	63.1257i	−0.876745	−	0.876745i
$73$			54.7468i			0.749956i	0.927034	+	0.374978i	$0.122350\pi$
$73$			54.7468i			0.749956i	−0.927034	+	0.374978i	$0.877650\pi$
$74$	109.130	+	109.130i	1.47474	+	1.47474i
$75$			70.4529i			0.939372i
$76$			67.3535i			0.886230i
$77$	44.3796			0.576358
$78$		−	110.838i		−	1.42100i
$79$	94.7057	+	94.7057i	1.19881	+	1.19881i	0.974524	+	0.224282i	$0.0720036\pi$
$79$	94.7057	+	94.7057i	1.19881	+	1.19881i	0.224282	+	0.974524i	$0.427996\pi$
$80$			95.5434i			1.19429i
$81$	−101.138			−1.24862
$82$	−2.05734	+	2.05734i	−0.0250895	+	0.0250895i
$83$			18.6532i			0.224737i	0.993667	+	0.112369i	$0.0358437\pi$
$83$			18.6532i			0.224737i	−0.993667	+	0.112369i	$0.964156\pi$
$84$	110.283	+	110.283i	1.31289	+	1.31289i
$85$	45.0063			0.529486
$86$			47.7931i			0.555733i
$87$	−187.849			−2.15919
$88$	216.252			2.45740
$89$	9.04776	−	9.04776i	0.101660	−	0.101660i	−0.654447	−	0.756108i	$-0.727099\pi$
$89$	9.04776	−	9.04776i	0.101660	−	0.101660i	0.756108	+	0.654447i	$0.227099\pi$
$90$	−25.8335	−	25.8335i	−0.287039	−	0.287039i
$91$			36.1958i			0.397756i
$92$			71.0166i			0.771919i
$93$		−	29.4428i		−	0.316589i
$94$	−180.672			−1.92204
$95$			16.2833i			0.171403i
$96$	165.102	+	165.102i	1.71981	+	1.71981i
$97$	−90.7206	−	90.7206i	−0.935264	−	0.935264i	0.0627641	−	0.998028i	$-0.480008\pi$
$97$	−90.7206	−	90.7206i	−0.935264	−	0.935264i	−0.998028	+	0.0627641i	$0.980008\pi$
$98$	77.8374	+	77.8374i	0.794259	+	0.794259i
$99$	−29.7277	+	29.7277i	−0.300279	+	0.300279i
$100$		−	189.776i		−	1.89776i
$101$	−100.049	+	100.049i	−0.990586	+	0.990586i	−0.999956	−	0.00936966i	$-0.997018\pi$
$101$	−100.049	+	100.049i	−0.990586	+	0.990586i	0.00936966	+	0.999956i	$0.497018\pi$
$102$	181.369	−	181.369i	1.77813	−	1.77813i
$103$	−55.3261	+	55.3261i	−0.537147	+	0.537147i	−0.922690	−	0.385543i	$-0.874014\pi$
$103$	−55.3261	+	55.3261i	−0.537147	+	0.537147i	0.385543	+	0.922690i	$0.374014\pi$
$104$			176.374i			1.69590i
$105$	26.6618	+	26.6618i	0.253922	+	0.253922i
$106$	−64.9480			−0.612717
$107$	60.3115	−	60.3115i	0.563659	−	0.563659i	−0.366686	−	0.930345i	$-0.619508\pi$
$107$	60.3115	−	60.3115i	0.563659	−	0.563659i	0.930345	+	0.366686i	$0.119508\pi$
$108$	171.437			1.58738
$109$		−	157.615i		−	1.44601i	−0.690844	−	0.723004i	$-0.742761\pi$
$109$		−	157.615i		−	1.44601i	0.690844	−	0.723004i	$-0.257239\pi$
$110$	88.4988			0.804534
$111$	150.889			1.35936
$112$	−125.736	−	125.736i	−1.12265	−	1.12265i
$113$	13.2248	+	13.2248i	0.117033	+	0.117033i	0.763198	−	0.646165i	$-0.223628\pi$
$113$	13.2248	+	13.2248i	0.117033	+	0.117033i	−0.646165	+	0.763198i	$0.723628\pi$
$114$	65.6192	+	65.6192i	0.575607	+	0.575607i
$115$			17.1688i			0.149294i
$116$	506.003			4.36209
$117$	−24.2458	−	24.2458i	−0.207229	−	0.207229i
$118$	−70.6030			−0.598331
$119$	−59.2289	+	59.2289i	−0.497722	+	0.497722i
$120$	129.917	+	129.917i	1.08264	+	1.08264i
$121$			19.1610i			0.158356i
$122$	211.903			1.73691
$123$			2.84459i			0.0231267i
$124$			79.3090i			0.639588i
$125$		−	104.953i		−	0.839626i
$126$	67.9945			0.539639
$127$	107.007	+	107.007i	0.842576	+	0.842576i	0.989193	−	0.146617i	$-0.0468386\pi$
$127$	107.007	+	107.007i	0.842576	+	0.842576i	−0.146617	+	0.989193i	$0.546839\pi$
$128$	−20.2815	−	20.2815i	−0.158450	−	0.158450i
$129$	33.0406	+	33.0406i	0.256128	+	0.256128i
$130$			72.1793i			0.555225i
$131$	−79.0231	+	79.0231i	−0.603230	+	0.603230i	−0.941168	−	0.337938i	$-0.890270\pi$
$131$	−79.0231	+	79.0231i	−0.603230	+	0.603230i	0.337938	+	0.941168i	$0.390270\pi$
$132$	253.069	−	253.069i	1.91719	−	1.91719i
$133$	−21.4290	−	21.4290i	−0.161120	−	0.161120i
$134$	54.6491	−	54.6491i	0.407829	−	0.407829i
$135$	41.4462			0.307009
$136$	−288.609	+	288.609i	−2.12212	+	2.12212i
$137$	−39.1963	−	39.1963i	−0.286105	−	0.286105i	0.549433	−	0.835538i	$-0.314844\pi$
$137$	−39.1963	−	39.1963i	−0.286105	−	0.286105i	−0.835538	+	0.549433i	$0.814844\pi$
$138$	69.1880	+	69.1880i	0.501362	+	0.501362i
$139$			78.4344i			0.564276i	0.959374	+	0.282138i	$0.0910436\pi$
$139$			78.4344i			0.564276i	−0.959374	+	0.282138i	$0.908956\pi$
$140$	−71.8178	−	71.8178i	−0.512984	−	0.512984i
$141$	−124.903	+	124.903i	−0.885838	+	0.885838i
$142$		−	392.783i		−	2.76608i
$143$	83.0595			0.580836
$144$	168.449			1.16978
$145$	122.330			0.843657
$146$	−143.672	−	143.672i	−0.984057	−	0.984057i
$147$	107.622			0.732122
$148$	−406.445			−2.74625
$149$	−103.352	+	103.352i	−0.693634	+	0.693634i	−0.963030	−	0.269395i	$-0.913176\pi$
$149$	−103.352	+	103.352i	−0.693634	+	0.693634i	0.269395	+	0.963030i	$0.413176\pi$
$150$	−184.890	−	184.890i	−1.23260	−	1.23260i
$151$	136.231			0.902192			0.451096	−	0.892475i	$-0.351033\pi$
$151$	136.231			0.902192			0.451096	+	0.892475i	$0.351033\pi$
$152$	−104.418	−	104.418i	−0.686964	−	0.686964i
$153$		−	79.3490i		−	0.518621i
$154$	−116.465	+	116.465i	−0.756269	+	0.756269i
$155$			19.1736i			0.123701i
$156$	206.402	+	206.402i	1.32309	+	1.32309i
$157$		−	29.7157i		−	0.189272i	−0.995512	−	0.0946361i	$-0.969831\pi$
$157$		−	29.7157i		−	0.189272i	0.995512	−	0.0946361i	$-0.0301688\pi$
$158$	−497.073			−3.14603
$159$	−44.9002	+	44.9002i	−0.282391	+	0.282391i
$160$	−107.517	−	107.517i	−0.671980	−	0.671980i
$161$	−22.5944	−	22.5944i	−0.140338	−	0.140338i
$162$	265.418	−	265.418i	1.63838	−	1.63838i
$163$	−7.41912	+	7.41912i	−0.0455161	+	0.0455161i	−0.729498	−	0.683982i	$-0.760246\pi$
$163$	−7.41912	+	7.41912i	−0.0455161	+	0.0455161i	0.683982	+	0.729498i	$0.260246\pi$
$164$		−	7.66236i		−	0.0467217i
$165$	61.1815	−	61.1815i	0.370797	−	0.370797i
$166$	−48.9516	−	48.9516i	−0.294889	−	0.294889i
$167$	−165.941	+	165.941i	−0.993660	+	0.993660i	−0.999980	−	0.00632003i	$-0.997988\pi$
$167$	−165.941	+	165.941i	−0.993660	+	0.993660i	0.00632003	+	0.999980i	$0.497988\pi$
$168$	−341.944			−2.03538
$169$		−	101.257i		−	0.599154i
$170$	−118.110	+	118.110i	−0.694767	+	0.694767i
$171$	28.7084			0.167885
$172$	−89.0001	−	89.0001i	−0.517443	−	0.517443i
$173$	134.439	+	134.439i	0.777103	+	0.777103i	0.979337	−	0.202234i	$-0.0648201\pi$
$173$	134.439	+	134.439i	0.777103	+	0.777103i	−0.202234	+	0.979337i	$0.564820\pi$
$174$	492.974	−	492.974i	2.83318	−	2.83318i
$175$	60.3786	+	60.3786i	0.345021	+	0.345021i
$176$	−288.531	+	288.531i	−1.63938	+	1.63938i
$177$	−48.8097	+	48.8097i	−0.275761	+	0.275761i
$178$			47.4882i			0.266787i
$179$	123.173	+	123.173i	0.688115	+	0.688115i	0.961815	−	0.273700i	$-0.0882477\pi$
$179$	123.173	+	123.173i	0.688115	+	0.688115i	−0.273700	+	0.961815i	$0.588248\pi$
$180$	96.2144			0.534524
$181$			65.9482i			0.364355i	0.983266	+	0.182177i	$0.0583145\pi$
$181$			65.9482i			0.364355i	−0.983266	+	0.182177i	$0.941686\pi$
$182$	−94.9888	−	94.9888i	−0.521917	−	0.521917i
$183$	146.494	−	146.494i	0.800515	−	0.800515i
$184$	−110.097	−	110.097i	−0.598355	−	0.598355i
$185$	−98.2614			−0.531142
$186$	77.2669	+	77.2669i	0.415413	+	0.415413i
$187$	135.914	+	135.914i	0.726814	+	0.726814i
$188$	336.447	−	336.447i	1.78961	−	1.78961i
$189$	−54.5437	+	54.5437i	−0.288591	+	0.288591i
$190$	−42.7322	−	42.7322i	−0.224906	−	0.224906i
$191$		−	323.146i		−	1.69186i	−0.533291	−	0.845932i	$-0.679045\pi$
$191$		−	323.146i		−	1.69186i	0.533291	−	0.845932i	$-0.320955\pi$
$192$	−279.693			−1.45673
$193$	−152.459	+	152.459i	−0.789941	+	0.789941i	−0.981484	−	0.191543i	$-0.938651\pi$
$193$	−152.459	+	152.459i	−0.789941	+	0.789941i	0.191543	+	0.981484i	$0.438651\pi$
$194$	476.157			2.45442
$195$	49.8994	+	49.8994i	0.255894	+	0.255894i
$196$	−289.897			−1.47907
$197$	274.278	−	274.278i	1.39227	−	1.39227i	0.572062	−	0.820210i	$-0.306144\pi$
$197$	274.278	−	274.278i	1.39227	−	1.39227i	0.820210	−	0.572062i	$-0.193856\pi$
$198$		−	156.029i		−	0.788025i
$199$	204.654	−	204.654i	1.02841	−	1.02841i	0.0288301	−	0.999584i	$-0.490822\pi$
$199$	204.654	−	204.654i	1.02841	−	1.02841i	0.999584	−	0.0288301i	$-0.00917818\pi$
$200$	294.211	+	294.211i	1.47106	+	1.47106i
$201$		−	75.5607i		−	0.375924i
$202$		−	525.119i		−	2.59960i
$203$	−160.988	+	160.988i	−0.793045	+	0.793045i
$204$			675.491i			3.31123i
$205$		−	1.85244i		−	0.00903628i
$206$		−	290.385i		−	1.40964i
$207$	30.2697			0.146231
$208$	−235.324	−	235.324i	−1.13137	−	1.13137i
$209$	−49.1736	+	49.1736i	−0.235280	+	0.235280i
$210$	−139.937			−0.666367
$211$	−150.097	+	150.097i	−0.711362	+	0.711362i	−0.966820	−	0.255458i	$-0.917774\pi$
$211$	−150.097	+	150.097i	−0.711362	+	0.711362i	0.255458	+	0.966820i	$0.417774\pi$
$212$	120.946	−	120.946i	0.570500	−	0.570500i
$213$	−271.541	−	271.541i	−1.27484	−	1.27484i
$214$			316.551i			1.47921i
$215$	−21.5165	−	21.5165i	−0.100077	−	0.100077i
$216$	−265.779	+	265.779i	−1.23046	+	1.23046i
$217$	−25.2327	−	25.2327i	−0.116280	−	0.116280i
$218$	413.630	+	413.630i	1.89738	+	1.89738i
$219$	−198.649			−0.907071
$220$	−164.802	+	164.802i	−0.749101	+	0.749101i
$221$	−110.851	+	110.851i	−0.501589	+	0.501589i
$222$	−395.980	+	395.980i	−1.78369	+	1.78369i
$223$			109.865i			0.492670i	0.969185	+	0.246335i	$0.0792263\pi$
$223$			109.865i			0.492670i	−0.969185	+	0.246335i	$0.920774\pi$
$224$	282.987			1.26333
$225$	−80.8893			−0.359508
$226$	−69.4117			−0.307131
$227$			63.7895i			0.281011i	0.990080	+	0.140506i	$0.0448728\pi$
$227$			63.7895i			0.281011i	−0.990080	+	0.140506i	$0.955127\pi$
$228$	−244.392			−1.07189
$229$	277.750	−	277.750i	1.21288	−	1.21288i	0.242807	−	0.970075i	$-0.421932\pi$
$229$	277.750	−	277.750i	1.21288	−	1.21288i	0.970075	−	0.242807i	$-0.0780683\pi$
$230$	−45.0562	−	45.0562i	−0.195897	−	0.195897i
$231$			161.031i			0.697104i
$232$	−784.459	+	784.459i	−3.38129	+	3.38129i
$233$		−	138.809i		−	0.595745i	−0.954606	−	0.297873i	$-0.903723\pi$
$233$		−	138.809i		−	0.595745i	0.954606	−	0.297873i	$-0.0962771\pi$
$234$	127.257			0.543832
$235$	81.3388	−	81.3388i	0.346122	−	0.346122i
$236$	131.477	−	131.477i	0.557105	−	0.557105i
$237$	−343.639	+	343.639i	−1.44996	+	1.44996i
$238$		−	310.869i		−	1.30617i
$239$		−	377.670i		−	1.58021i	−0.612972	−	0.790104i	$-0.710026\pi$
$239$		−	377.670i		−	1.58021i	0.612972	−	0.790104i	$-0.289974\pi$
$240$	−346.679			−1.44450
$241$		−	154.397i		−	0.640650i	−0.947308	−	0.320325i	$-0.896208\pi$
$241$		−	154.397i		−	0.640650i	0.947308	−	0.320325i	$-0.103792\pi$
$242$	−50.2844	−	50.2844i	−0.207787	−	0.207787i
$243$		−	209.119i		−	0.860572i
$244$	−394.606	+	394.606i	−1.61724	+	1.61724i
$245$	−70.0850			−0.286061
$246$	−7.46506	−	7.46506i	−0.0303458	−	0.0303458i
$247$	−40.1058	−	40.1058i	−0.162372	−	0.162372i
$248$	−122.953	−	122.953i	−0.495778	−	0.495778i
$249$	−67.6830			−0.271819
$250$	275.429	+	275.429i	1.10172	+	1.10172i
$251$	130.923	−	130.923i	0.521607	−	0.521607i	−0.396450	−	0.918056i	$-0.629758\pi$
$251$	130.923	−	130.923i	0.521607	−	0.521607i	0.918056	+	0.396450i	$0.129758\pi$
$252$	−126.619	+	126.619i	−0.502457	+	0.502457i
$253$	−51.8480	+	51.8480i	−0.204933	+	0.204933i
$254$	−561.639			−2.21118
$255$			163.305i			0.640413i
$256$	−201.879			−0.788591
$257$	321.017			1.24909			0.624546	−	0.780988i	$-0.285284\pi$
$257$	321.017			1.24909			0.624546	+	0.780988i	$0.285284\pi$
$258$	−173.417			−0.672159
$259$	129.313	−	129.313i	0.499278	−	0.499278i
$260$	−134.412	−	134.412i	−0.516970	−	0.516970i
$261$		−	215.676i		−	0.826344i
$262$		−	414.761i		−	1.58306i
$263$	88.4884			0.336458			0.168229	−	0.985748i	$-0.446195\pi$
$263$	88.4884			0.336458			0.168229	+	0.985748i	$0.446195\pi$
$264$			784.668i			2.97223i
$265$	29.2397	−	29.2397i	0.110338	−	0.110338i
$266$	112.472			0.422828
$267$	32.8298	+	32.8298i	0.122958	+	0.122958i
$268$			203.535i			0.759459i
$269$	374.632			1.39269			0.696343	−	0.717709i	$-0.254809\pi$
$269$	374.632			1.39269			0.696343	+	0.717709i	$0.254809\pi$
$270$	−108.768	+	108.768i	−0.402843	+	0.402843i
$271$	359.926			1.32814			0.664070	−	0.747670i	$-0.268828\pi$
$271$	359.926			1.32814			0.664070	+	0.747670i	$0.268828\pi$
$272$		−	770.145i		−	2.83141i
$273$	−131.336			−0.481086
$274$	205.726			0.750826
$275$	138.552	−	138.552i	0.503827	−	0.503827i
$276$	−257.683			−0.933636
$277$	281.961	−	281.961i	1.01791	−	1.01791i	0.0180738	−	0.999837i	$-0.494247\pi$
$277$	281.961	−	281.961i	1.01791	−	1.01791i	0.999837	−	0.0180738i	$-0.00575339\pi$
$278$	−205.836	−	205.836i	−0.740416	−	0.740416i
$279$	33.8042			0.121162
$280$	222.679			0.795282
$281$		−	139.286i		−	0.495681i	−0.968801	−	0.247841i	$-0.920279\pi$
$281$		−	139.286i		−	0.495681i	0.968801	−	0.247841i	$-0.0797209\pi$
$282$		−	655.568i		−	2.32471i
$283$			165.422i			0.584531i	0.956337	+	0.292265i	$0.0944090\pi$
$283$			165.422i			0.584531i	−0.956337	+	0.292265i	$0.905591\pi$
$284$	731.440	+	731.440i	2.57549	+	2.57549i
$285$	−59.0838			−0.207311
$286$	−217.973	+	217.973i	−0.762145	+	0.762145i
$287$	2.43783	+	2.43783i	0.00849418	+	0.00849418i
$288$	−189.559	+	189.559i	−0.658191	+	0.658191i
$289$	−73.7815			−0.255299
$290$	−321.032	+	321.032i	−1.10701	+	1.10701i
$291$	329.180	−	329.180i	1.13120	−	1.13120i
$292$	535.092			1.83251
$293$	−400.377			−1.36647			−0.683237	−	0.730197i	$-0.739428\pi$
$293$	−400.377			−1.36647			−0.683237	+	0.730197i	$0.739428\pi$
$294$	−282.433	+	282.433i	−0.960656	+	0.960656i
$295$	31.7856	−	31.7856i	0.107748	−	0.107748i
$296$	630.114	−	630.114i	2.12876	−	2.12876i
$297$	125.163	+	125.163i	0.421424	+	0.421424i
$298$		−	542.452i		−	1.82031i
$299$	−42.2870	−	42.2870i	−0.141428	−	0.141428i
$300$	688.603			2.29534
$301$	56.6320			0.188146
$302$	−357.512	+	357.512i	−1.18381	+	1.18381i
$303$	−363.028	−	363.028i	−1.19811	−	1.19811i
$304$	278.638			0.916571
$305$	−95.3993	+	95.3993i	−0.312784	+	0.312784i
$306$	208.236	+	208.236i	0.680509	+	0.680509i
$307$	98.7956			0.321810			0.160905	−	0.986970i	$-0.448559\pi$
$307$	98.7956			0.321810			0.160905	+	0.986970i	$0.448559\pi$
$308$		−	433.763i		−	1.40832i
$309$	−200.751	−	200.751i	−0.649679	−	0.649679i
$310$	−50.3173	−	50.3173i	−0.162314	−	0.162314i
$311$	−334.979	−	334.979i	−1.07710	−	1.07710i	−0.996768	−	0.0803366i	$-0.974400\pi$
$311$	−334.979	−	334.979i	−1.07710	−	1.07710i	−0.0803366	−	0.996768i	$-0.525600\pi$
$312$	−639.973			−2.05119
$313$	110.060			0.351629			0.175814	−	0.984423i	$-0.443744\pi$
$313$	110.060			0.351629			0.175814	+	0.984423i	$0.443744\pi$
$314$	77.9831	+	77.9831i	0.248354	+	0.248354i
$315$	−30.6112	+	30.6112i	−0.0971785	+	0.0971785i
$316$	925.649	−	925.649i	2.92927	−	2.92927i
$317$	18.7013	+	18.7013i	0.0589945	+	0.0589945i	0.735989	−	0.676994i	$-0.236718\pi$
$317$	18.7013	+	18.7013i	0.0589945	+	0.0589945i	−0.676994	+	0.735989i	$0.736718\pi$
$318$		−	235.664i		−	0.741081i
$319$	369.424	+	369.424i	1.15807	+	1.15807i
$320$	182.140			0.569188
$321$	218.840	+	218.840i	0.681745	+	0.681745i
$322$	118.589			0.368289
$323$		−	131.254i		−	0.406359i
$324$			988.522i			3.05099i
$325$	113.003	+	113.003i	0.347701	+	0.347701i
$326$		−	38.9400i		−	0.119448i
$327$	571.905			1.74895
$328$	11.8790	+	11.8790i	0.0362164	+	0.0362164i
$329$			214.086i			0.650716i
$330$			321.118i			0.973084i
$331$	47.8081	+	47.8081i	0.144435	+	0.144435i	0.775627	−	0.631192i	$-0.217434\pi$
$331$	47.8081	+	47.8081i	0.144435	+	0.144435i	−0.631192	+	0.775627i	$0.717434\pi$
$332$	182.315			0.549142
$333$			173.241i			0.520243i
$334$		−	870.961i		−	2.60767i
$335$			49.2062i			0.146884i
$336$	456.234	−	456.234i	1.35784	−	1.35784i
$337$			486.566i			1.44381i	0.691990	+	0.721907i	$0.256734\pi$
$337$			486.566i			1.44381i	−0.691990	+	0.721907i	$0.743266\pi$
$338$	265.729	+	265.729i	0.786181	+	0.786181i
$339$	−47.9861	+	47.9861i	−0.141552	+	0.141552i
$340$		−	439.890i		−	1.29379i
$341$	−57.9021	+	57.9021i	−0.169801	+	0.169801i
$342$	−75.3396	+	75.3396i	−0.220291	+	0.220291i
$343$	244.605	−	244.605i	0.713135	−	0.713135i
$344$	275.955			0.802194
$345$	−62.2971			−0.180571
$346$	−705.617			−2.03936
$347$	−409.116	−	409.116i	−1.17901	−	1.17901i	−0.979997	−	0.199011i	$-0.936227\pi$
$347$	−409.116	−	409.116i	−1.17901	−	1.17901i	−0.199011	−	0.979997i	$-0.563773\pi$
$348$			1836.03i			5.27595i
$349$	−264.498	+	227.688i	−0.757874	+	0.652401i
$349$	−264.498	+	227.688i	−0.757874	+	0.652401i
$350$	−316.904			−0.905439
$351$	−102.082	+	102.082i	−0.290833	+	0.290833i
$352$		−	649.378i		−	1.84482i
$353$			82.3864i			0.233389i	0.993168	+	0.116695i	$0.0372299\pi$
$353$			82.3864i			0.233389i	−0.993168	+	0.116695i	$0.962770\pi$
$354$		−	256.183i		−	0.723681i
$355$	176.831	+	176.831i	0.498117	+	0.498117i
$356$	−88.4324	−	88.4324i	−0.248406	−	0.248406i
$357$	−214.912	−	214.912i	−0.601994	−	0.601994i
$358$	−646.484			−1.80582
$359$	484.337	+	484.337i	1.34913	+	1.34913i	0.886611	+	0.462517i	$0.153053\pi$
$359$	484.337	+	484.337i	1.34913	+	1.34913i	0.462517	+	0.886611i	$0.346947\pi$
$360$	−149.162	+	149.162i	−0.414338	+	0.414338i
$361$	−313.512			−0.868455
$362$	−173.068	−	173.068i	−0.478089	−	0.478089i
$363$	−69.5258			−0.191531
$364$	353.776			0.971912
$365$	129.363			0.354419
$366$			768.891i			2.10080i
$367$	−297.464	+	297.464i	−0.810529	+	0.810529i	−0.984713	−	0.174184i	$-0.944271\pi$
$367$	−297.464	+	297.464i	−0.810529	+	0.810529i	0.174184	+	0.984713i	$0.444271\pi$
$368$	293.792			0.798347
$369$	−3.26596			−0.00885084
$370$	257.868	−	257.868i	0.696940	−	0.696940i
$371$			76.9595i			0.207438i
$372$	−287.772			−0.773582
$373$	475.656	−	475.656i	1.27522	−	1.27522i	0.331903	−	0.943313i	$-0.392309\pi$
$373$	475.656	−	475.656i	1.27522	−	1.27522i	0.943313	−	0.331903i	$-0.107691\pi$
$374$	−713.360			−1.90738
$375$	380.823			1.01553
$376$			1043.19i			2.77444i
$377$	−301.301	+	301.301i	−0.799206	+	0.799206i
$378$		−	286.279i		−	0.757351i
$379$	−38.6738	+	38.6738i	−0.102042	+	0.102042i	−0.756285	−	0.654243i	$-0.772987\pi$
$379$	−38.6738	+	38.6738i	−0.102042	+	0.102042i	0.654243	+	0.756285i	$0.272987\pi$
$380$	159.152			0.418820
$381$	−388.275	+	388.275i	−1.01910	+	1.01910i
$382$	848.033	+	848.033i	2.21998	+	2.21998i
$383$	201.352	+	201.352i	0.525722	+	0.525722i	0.919294	−	0.393572i	$-0.128761\pi$
$383$	201.352	+	201.352i	0.525722	+	0.525722i	−0.393572	+	0.919294i	$0.628761\pi$
$384$	73.5915	−	73.5915i	0.191645	−	0.191645i
$385$		−	104.866i		−	0.272379i
$386$		−	800.195i		−	2.07304i
$387$	−37.9349	+	37.9349i	−0.0980231	+	0.0980231i
$388$	−886.699	+	886.699i	−2.28531	+	2.28531i
$389$	305.920	−	305.920i	0.786426	−	0.786426i	−0.194480	−	0.980906i	$-0.562302\pi$
$389$	305.920	−	305.920i	0.786426	−	0.786426i	0.980906	+	0.194480i	$0.0623020\pi$
$390$	−261.902			−0.671545
$391$		−	138.392i		−	0.353945i
$392$	449.429	−	449.429i	1.14650	−	1.14650i
$393$	−286.735	−	286.735i	−0.729606	−	0.729606i
$394$			1439.58i			3.65375i
$395$	223.783	−	223.783i	0.566539	−	0.566539i
$396$	290.557	+	290.557i	0.733729	+	0.733729i
$397$			52.4968i			0.132234i	0.997812	+	0.0661169i	$0.0210610\pi$
$397$			52.4968i			0.132234i	−0.997812	+	0.0661169i	$0.978939\pi$
$398$			1074.15i			2.69887i
$399$	77.7549	−	77.7549i	0.194874	−	0.194874i
$400$	−785.094			−1.96274
$401$	234.914	−	234.914i	0.585819	−	0.585819i	−0.350677	−	0.936496i	$-0.614049\pi$
$401$	234.914	−	234.914i	0.585819	−	0.585819i	0.936496	+	0.350677i	$0.114049\pi$
$402$	198.294	+	198.294i	0.493269	+	0.493269i
$403$	−47.2247	−	47.2247i	−0.117183	−	0.117183i
$404$	977.876	+	977.876i	2.42049	+	2.42049i
$405$			238.983i			0.590082i
$406$		−	844.964i		−	2.08119i
$407$	−296.738	−	296.738i	−0.729087	−	0.729087i
$408$	−1047.22	−	1047.22i	−2.56671	−	2.56671i
$409$		−	315.585i		−	0.771601i	−0.922582	−	0.385801i	$-0.873925\pi$
$409$		−	315.585i		−	0.771601i	0.922582	−	0.385801i	$-0.126075\pi$
$410$	4.86136	+	4.86136i	0.0118570	+	0.0118570i
$411$	142.224	−	142.224i	0.346043	−	0.346043i
$412$	540.755	+	540.755i	1.31251	+	1.31251i
$413$			83.6604i			0.202568i
$414$	−79.4370	+	79.4370i	−0.191877	+	0.191877i
$415$	44.0762			0.106208
$416$	529.630			1.27315
$417$	−284.599			−0.682491
$418$		−	258.093i		−	0.617448i
$419$			645.905i			1.54154i	0.637114	+	0.770770i	$0.280128\pi$
$419$			645.905i			1.54154i	−0.637114	+	0.770770i	$0.719872\pi$
$420$	260.591	−	260.591i	0.620454	−	0.620454i
$421$	550.110	+	550.110i	1.30668	+	1.30668i	0.923800	+	0.382876i	$0.125066\pi$
$421$	550.110	+	550.110i	1.30668	+	1.30668i	0.382876	+	0.923800i	$0.374934\pi$
$422$		−	787.803i		−	1.86683i
$423$	−143.405	−	143.405i	−0.339020	−	0.339020i
$424$			375.006i			0.884449i
$425$			369.824i			0.870173i
$426$	1425.21			3.34557
$427$		−	251.093i		−	0.588040i
$428$	−589.481	−	589.481i	−1.37729	−	1.37729i
$429$			301.381i			0.702520i
$430$	112.932			0.262632
$431$	−52.3427	+	52.3427i	−0.121445	+	0.121445i	−0.765217	−	0.643772i	$-0.777368\pi$
$431$	−52.3427	+	52.3427i	−0.121445	+	0.121445i	0.643772	+	0.765217i	$0.277368\pi$
$432$		−	709.224i		−	1.64172i
$433$	−465.977	−	465.977i	−1.07616	−	1.07616i	−0.996850	−	0.0793091i	$-0.974729\pi$
$433$	−465.977	−	465.977i	−1.07616	−	1.07616i	−0.0793091	−	0.996850i	$-0.525271\pi$
$434$	132.436			0.305153
$435$			443.875i			1.02040i
$436$	−1540.52			−3.53330
$437$	50.0703			0.114577
$438$	521.314	−	521.314i	1.19022	−	1.19022i
$439$	−575.799	−	575.799i	−1.31162	−	1.31162i	−0.920224	−	0.391392i	$-0.871994\pi$
$439$	−575.799	−	575.799i	−1.31162	−	1.31162i	−0.391392	−	0.920224i	$-0.628006\pi$
$440$		−	510.988i		−	1.16134i
$441$			123.564i			0.280191i
$442$		−	581.814i		−	1.31632i
$443$	−103.524			−0.233688			−0.116844	−	0.993150i	$-0.537278\pi$
$443$	−103.524			−0.233688			−0.116844	+	0.993150i	$0.537278\pi$
$444$		−	1474.78i		−	3.32159i
$445$	−21.3792	−	21.3792i	−0.0480432	−	0.0480432i
$446$	−288.320	−	288.320i	−0.646457	−	0.646457i
$447$	−375.011	−	375.011i	−0.838950	−	0.838950i
$448$	−239.699	+	239.699i	−0.535042	+	0.535042i
$449$		−	699.185i		−	1.55721i	−0.627517	−	0.778603i	$-0.715929\pi$
$449$		−	699.185i		−	1.55721i	0.627517	−	0.778603i	$-0.284071\pi$
$450$	212.278	−	212.278i	0.471729	−	0.471729i
$451$	5.59415	−	5.59415i	0.0124039	−	0.0124039i
$452$	129.258	−	129.258i	0.285970	−	0.285970i
$453$			494.314i			1.09120i
$454$	−167.403	−	167.403i	−0.368729	−	0.368729i
$455$	85.5282			0.187974
$456$	378.882	−	378.882i	0.830882	−	0.830882i
$457$	71.2560			0.155921			0.0779606	−	0.996956i	$-0.475159\pi$
$457$	71.2560			0.155921			0.0779606	+	0.996956i	$0.475159\pi$
$458$			1457.80i			3.18297i
$459$	−334.085			−0.727853
$460$	167.807			0.364798
$461$	−176.734	−	176.734i	−0.383372	−	0.383372i	0.488944	−	0.872315i	$-0.337382\pi$
$461$	−176.734	−	176.734i	−0.383372	−	0.383372i	−0.872315	+	0.488944i	$0.837382\pi$
$462$	−422.595	−	422.595i	−0.914707	−	0.914707i
$463$	−1.36695	−	1.36695i	−0.00295238	−	0.00295238i	0.705629	−	0.708581i	$-0.250665\pi$
$463$	−1.36695	−	1.36695i	−0.00295238	−	0.00295238i	−0.708581	+	0.705629i	$0.750665\pi$
$464$		−	2093.31i		−	4.51143i
$465$	−69.5713			−0.149616
$466$	364.276	+	364.276i	0.781709	+	0.781709i
$467$	412.526			0.883353			0.441676	−	0.897174i	$-0.354384\pi$
$467$	412.526			0.883353			0.441676	+	0.897174i	$0.354384\pi$
$468$	−236.977	+	236.977i	−0.506361	+	0.506361i
$469$	−64.7560	−	64.7560i	−0.138072	−	0.138072i
$470$			426.915i			0.908331i
$471$	107.823			0.228925
$472$			407.658i			0.863683i
$473$		−	129.955i		−	0.274746i
$474$		−	1803.63i		−	3.80512i
$475$	−133.802			−0.281688
$476$	578.900	+	578.900i	1.21618	+	1.21618i
$477$	−51.5514	−	51.5514i	−0.108074	−	0.108074i
$478$	991.121	+	991.121i	2.07347	+	2.07347i
$479$			378.487i			0.790161i	0.918647	+	0.395080i	$0.129283\pi$
$479$			378.487i			0.790161i	−0.918647	+	0.395080i	$0.870717\pi$
$480$	390.125	−	390.125i	0.812760	−	0.812760i
$481$	242.019	−	242.019i	0.503157	−	0.503157i
$482$	405.184	+	405.184i	0.840631	+	0.840631i
$483$	81.9837	−	81.9837i	0.169738	−	0.169738i
$484$	187.279			0.386940
$485$	−214.367	+	214.367i	−0.441993	+	0.441993i
$486$	548.792	+	548.792i	1.12920	+	1.12920i
$487$	591.231	+	591.231i	1.21403	+	1.21403i	0.969691	+	0.244335i	$0.0785697\pi$
$487$	591.231	+	591.231i	1.21403	+	1.21403i	0.244335	+	0.969691i	$0.421430\pi$
$488$		−	1223.52i		−	2.50721i
$489$	−26.9202	−	26.9202i	−0.0550516	−	0.0550516i
$490$	183.924	−	183.924i	0.375356	−	0.375356i
$491$		−	106.060i		−	0.216007i	−0.994150	−	0.108004i	$-0.965554\pi$
$491$		−	106.060i		−	0.216007i	0.994150	−	0.108004i	$-0.0344458\pi$
$492$	27.8028			0.0565098
$493$	−986.065			−2.00013
$494$	210.500			0.426113
$495$	70.2444	+	70.2444i	0.141908	+	0.141908i
$496$	328.097			0.661485
$497$	−465.425			−0.936468
$498$	177.621	−	177.621i	0.356669	−	0.356669i
$499$	−607.175	−	607.175i	−1.21678	−	1.21678i	−0.968752	−	0.248032i	$-0.920216\pi$
$499$	−607.175	−	607.175i	−1.21678	−	1.21678i	−0.248032	−	0.968752i	$-0.579784\pi$
$500$	−1025.81			−2.05162
$501$	−602.117	−	602.117i	−1.20183	−	1.20183i
$502$			687.165i			1.36885i
$503$	−328.895	+	328.895i	−0.653867	+	0.653867i	−0.953922	−	0.300055i	$-0.902995\pi$
$503$	−328.895	+	328.895i	−0.653867	+	0.653867i	0.300055	+	0.953922i	$0.402995\pi$
$504$		−	392.597i		−	0.778962i
$505$	236.409	+	236.409i	0.468138	+	0.468138i
$506$		−	272.130i		−	0.537806i
$507$	367.411			0.724676
$508$	1045.88	−	1045.88i	2.05882	−	2.05882i
$509$	−208.536	−	208.536i	−0.409697	−	0.409697i	0.471936	−	0.881633i	$-0.343555\pi$
$509$	−208.536	−	208.536i	−0.409697	−	0.409697i	−0.881633	+	0.471936i	$0.843555\pi$
$510$	−428.563	−	428.563i	−0.840320	−	0.840320i
$511$	−170.243	+	170.243i	−0.333157	+	0.333157i
$512$	610.919	−	610.919i	1.19320	−	1.19320i
$513$		−	120.872i		−	0.235617i
$514$	−842.446	+	842.446i	−1.63900	+	1.63900i
$515$	130.732	+	130.732i	0.253848	+	0.253848i
$516$	322.937	−	322.937i	0.625846	−	0.625846i
$517$	491.268			0.950228
$518$			678.714i			1.31026i
$519$	−487.811	+	487.811i	−0.939906	+	0.939906i
$520$	416.760			0.801461
$521$	−423.461	−	423.461i	−0.812786	−	0.812786i	0.172265	−	0.985051i	$-0.444891\pi$
$521$	−423.461	−	423.461i	−0.812786	−	0.812786i	−0.985051	+	0.172265i	$0.944891\pi$
$522$	565.999	+	565.999i	1.08429	+	1.08429i
$523$	458.964	−	458.964i	0.877560	−	0.877560i	−0.115722	−	0.993282i	$-0.536918\pi$
$523$	458.964	−	458.964i	0.877560	−	0.877560i	0.993282	+	0.115722i	$0.0369182\pi$
$524$	772.368	+	772.368i	1.47398	+	1.47398i
$525$	−219.084	+	219.084i	−0.417302	+	0.417302i
$526$	−232.221	+	232.221i	−0.441484	+	0.441484i
$527$		−	154.552i		−	0.293268i
$528$	−1046.93	−	1046.93i	−1.98283	−	1.98283i
$529$	−476.207			−0.900202
$530$			153.468i			0.289562i
$531$	−56.0400	−	56.0400i	−0.105537	−	0.105537i
$532$	−209.446	+	209.446i	−0.393695	+	0.393695i
$533$	4.56257	+	4.56257i	0.00856017	+	0.00856017i
$534$	−172.311			−0.322679
$535$	−142.512	−	142.512i	−0.266377	−	0.266377i
$536$	−315.541	−	315.541i	−0.588697	−	0.588697i
$537$	−446.931	+	446.931i	−0.832274	+	0.832274i
$538$	−983.150	+	983.150i	−1.82742	+	1.82742i
$539$	−211.649	−	211.649i	−0.392670	−	0.392670i
$540$		−	405.093i		−	0.750173i
$541$	551.457			1.01933			0.509665	−	0.860373i	$-0.329769\pi$
$541$	551.457			1.01933			0.509665	+	0.860373i	$0.329769\pi$
$542$	−944.555	+	944.555i	−1.74272	+	1.74272i
$543$	−239.293			−0.440687
$544$	866.659	+	866.659i	1.59312	+	1.59312i
$545$	−372.433			−0.683364
$546$	344.667	−	344.667i	0.631258	−	0.631258i
$547$		−	841.451i		−	1.53830i	−0.639068	−	0.769151i	$-0.720680\pi$
$547$		−	841.451i		−	1.53830i	0.639068	−	0.769151i	$-0.279320\pi$
$548$	−383.103	+	383.103i	−0.699093	+	0.699093i
$549$	168.195	+	168.195i	0.306366	+	0.306366i
$550$			727.208i			1.32220i
$551$		−	356.757i		−	0.647473i
$552$	399.488	−	399.488i	0.723710	−	0.723710i
$553$			589.002i			1.06510i
$554$			1479.90i			2.67131i
$555$		−	356.541i		−	0.642416i
$556$	766.614			1.37880
$557$	−122.179	−	122.179i	−0.219352	−	0.219352i	0.588873	−	0.808226i	$-0.299572\pi$
$557$	−122.179	−	122.179i	−0.219352	−	0.219352i	−0.808226	+	0.588873i	$0.799572\pi$
$558$	−88.7126	+	88.7126i	−0.158983	+	0.158983i
$559$	105.991			0.189608
$560$	−297.106	+	297.106i	−0.530547	+	0.530547i
$561$	−493.164	+	493.164i	−0.879080	+	0.879080i
$562$	365.530	+	365.530i	0.650409	+	0.650409i
$563$		−	668.592i		−	1.18755i	−0.804630	−	0.593776i	$-0.797637\pi$
$563$		−	668.592i		−	1.18755i	0.804630	−	0.593776i	$-0.202363\pi$
$564$	1220.80	+	1220.80i	2.16453	+	2.16453i
$565$	31.2492	−	31.2492i	0.0553084	−	0.0553084i
$566$	−434.118	−	434.118i	−0.766993	−	0.766993i
$567$	−314.505	−	314.505i	−0.554682	−	0.554682i
$568$	−2267.91			−3.99280
$569$	536.795	−	536.795i	0.943401	−	0.943401i	−0.0550810	−	0.998482i	$-0.517542\pi$
$569$	536.795	−	536.795i	0.943401	−	0.943401i	0.998482	+	0.0550810i	$0.0175417\pi$
$570$	155.054	−	155.054i	0.272024	−	0.272024i
$571$	−500.307	+	500.307i	−0.876194	+	0.876194i	−0.993138	−	0.116944i	$-0.962690\pi$
$571$	−500.307	+	500.307i	−0.876194	+	0.876194i	0.116944	+	0.993138i	$0.462690\pi$
$572$		−	811.819i		−	1.41926i
$573$	1172.53			2.04631
$574$	−12.7952			−0.0222913
$575$	−141.079			−0.245354
$576$		−	321.124i		−	0.557508i
$577$	−358.443			−0.621218			−0.310609	−	0.950538i	$-0.600533\pi$
$577$	−358.443			−0.621218			−0.310609	+	0.950538i	$0.600533\pi$
$578$	193.625	−	193.625i	0.334992	−	0.334992i
$579$	−553.195	−	553.195i	−0.955433	−	0.955433i
$580$		−	1195.65i		−	2.06147i
$581$	−58.0048	+	58.0048i	−0.0998362	+	0.0998362i
$582$			1727.74i			2.96862i
$583$	176.601			0.302918
$584$	−829.556	+	829.556i	−1.42047	+	1.42047i
$585$	−57.2911	+	57.2911i	−0.0979335	+	0.0979335i
$586$	1050.71	−	1050.71i	1.79302	−	1.79302i
$587$			795.907i			1.35589i	0.735113	+	0.677945i	$0.237129\pi$
$587$			795.907i			1.35589i	−0.735113	+	0.677945i	$0.762871\pi$
$588$		−	1051.89i		−	1.78893i
$589$	55.9168			0.0949351
$590$			166.830i			0.282763i
$591$	995.216	+	995.216i	1.68395	+	1.68395i
$592$			1681.44i			2.84027i
$593$	−545.191	+	545.191i	−0.919379	+	0.919379i	−0.996984	−	0.0776056i	$-0.975273\pi$
$593$	−545.191	+	545.191i	−0.919379	+	0.919379i	0.0776056	+	0.996984i	$0.475273\pi$
$594$	−656.932			−1.10595
$595$	139.954	+	139.954i	0.235216	+	0.235216i
$596$	1010.15	+	1010.15i	1.69489	+	1.69489i
$597$	742.588	+	742.588i	1.24387	+	1.24387i
$598$	221.948			0.371150
$599$	510.362	+	510.362i	0.852024	+	0.852024i	0.990382	−	0.138358i	$-0.0441826\pi$
$599$	510.362	+	510.362i	0.852024	+	0.852024i	−0.138358	+	0.990382i	$0.544183\pi$
$600$	−1067.55	+	1067.55i	−1.77924	+	1.77924i
$601$	−465.290	+	465.290i	−0.774192	+	0.774192i	−0.978836	−	0.204644i	$-0.934396\pi$
$601$	−465.290	+	465.290i	−0.774192	+	0.774192i	0.204644	+	0.978836i	$0.434396\pi$
$602$	−148.619	+	148.619i	−0.246876	+	0.246876i
$603$	86.7537			0.143870
$604$		−	1331.51i		−	2.20449i
$605$	45.2762			0.0748367
$606$	1905.39			3.14421
$607$	577.309			0.951085			0.475543	−	0.879693i	$-0.342252\pi$
$607$	577.309			0.951085			0.475543	+	0.879693i	$0.342252\pi$
$608$	−313.556	+	313.556i	−0.515718	+	0.515718i
$609$	−584.145	−	584.145i	−0.959187	−	0.959187i
$610$		−	500.713i		−	0.820842i
$611$			400.676i			0.655772i
$612$	−775.553			−1.26724
$613$			45.7191i			0.0745825i	0.999304	+	0.0372913i	$0.0118729\pi$
$613$			45.7191i			0.0745825i	−0.999304	+	0.0372913i	$0.988127\pi$
$614$	−259.270	+	259.270i	−0.422263	+	0.422263i
$615$	6.72156			0.0109294
$616$	672.466	+	672.466i	1.09166	+	1.09166i
$617$			440.137i			0.713351i	0.934228	+	0.356675i	$0.116090\pi$
$617$			440.137i			0.713351i	−0.934228	+	0.356675i	$0.883910\pi$
$618$	1053.66			1.70495
$619$	663.010	−	663.010i	1.07110	−	1.07110i	0.0738272	−	0.997271i	$-0.476479\pi$
$619$	663.010	−	663.010i	1.07110	−	1.07110i	0.997271	−	0.0738272i	$-0.0235213\pi$
$620$	187.402			0.302261
$621$		−	127.445i		−	0.205226i
$622$	1758.18			2.82665
$623$	56.2707			0.0903221
$624$	853.874	−	853.874i	1.36839	−	1.36839i
$625$	237.416			0.379866
$626$	−288.830	+	288.830i	−0.461390	+	0.461390i
$627$	−178.426	−	178.426i	−0.284572	−	0.284572i
$628$	−290.440			−0.462484
$629$	792.053			1.25923
$630$		−	160.666i		−	0.255026i
$631$		−	370.620i		−	0.587353i	−0.955905	−	0.293677i	$-0.905121\pi$
$631$		−	370.620i		−	0.587353i	0.955905	−	0.293677i	$-0.0948789\pi$
$632$			2870.07i			4.54126i
$633$	−544.628	−	544.628i	−0.860392	−	0.860392i
$634$	−98.1556			−0.154820
$635$	252.851	−	252.851i	0.398190	−	0.398190i
$636$	438.852	+	438.852i	0.690019	+	0.690019i
$637$	172.620	−	172.620i	0.270989	−	0.270989i
$638$	−1938.96			−3.03912
$639$	311.765	−	311.765i	0.487895	−	0.487895i
$640$	−47.9239	+	47.9239i	−0.0748811	+	0.0748811i
$641$	−452.228			−0.705504			−0.352752	−	0.935717i	$-0.614754\pi$
$641$	−452.228			−0.705504			−0.352752	+	0.935717i	$0.614754\pi$
$642$	−1148.61			−1.78911
$643$	135.697	−	135.697i	0.211038	−	0.211038i	−0.593670	−	0.804708i	$-0.702322\pi$
$643$	135.697	−	135.697i	0.211038	−	0.211038i	0.804708	+	0.593670i	$0.202322\pi$
$644$	−220.836	+	220.836i	−0.342914	+	0.342914i
$645$	78.0726	−	78.0726i	0.121043	−	0.121043i
$646$	344.451	+	344.451i	0.533205	+	0.533205i
$647$			388.071i			0.599800i	0.953971	+	0.299900i	$0.0969533\pi$
$647$			388.071i			0.599800i	−0.953971	+	0.299900i	$0.903047\pi$
$648$	−1532.51	−	1532.51i	−2.36499	−	2.36499i
$649$	191.978			0.295806
$650$	−593.108			−0.912474
$651$	91.5567	−	91.5567i	0.140640	−	0.140640i
$652$	72.5141	+	72.5141i	0.111218	+	0.111218i
$653$	−557.383			−0.853572			−0.426786	−	0.904353i	$-0.640354\pi$
$653$	−557.383			−0.853572			−0.426786	+	0.904353i	$0.640354\pi$
$654$	−1500.85	+	1500.85i	−2.29488	+	2.29488i
$655$	186.726	+	186.726i	0.285078	+	0.285078i
$656$	−31.6987			−0.0483212
$657$		−	228.075i		−	0.347146i
$658$	−561.826	−	561.826i	−0.853839	−	0.853839i
$659$	−124.900	−	124.900i	−0.189529	−	0.189529i	0.605963	−	0.795492i	$-0.292788\pi$
$659$	−124.900	−	124.900i	−0.189529	−	0.189529i	−0.795492	+	0.605963i	$0.792788\pi$
$660$	−597.985	−	597.985i	−0.906037	−	0.906037i
$661$	−521.215			−0.788525			−0.394263	−	0.918998i	$-0.629000\pi$
$661$	−521.215			−0.788525			−0.394263	+	0.918998i	$0.629000\pi$
$662$	−250.926			−0.379042
$663$	−402.223	−	402.223i	−0.606671	−	0.606671i
$664$	−282.644	+	282.644i	−0.425669	+	0.425669i
$665$	−50.6352	+	50.6352i	−0.0761431	+	0.0761431i
$666$	−454.637	−	454.637i	−0.682638	−	0.682638i
$667$		−	376.160i		−	0.563958i
$668$	1621.90	+	1621.90i	2.42800	+	2.42800i
$669$	−398.646			−0.595883
$670$	−129.132	−	129.132i	−0.192735	−	0.192735i
$671$	−576.190			−0.858704
$672$			1026.82i			1.52800i
$673$			159.575i			0.237109i	0.992948	+	0.118555i	$0.0378261\pi$
$673$			159.575i			0.237109i	−0.992948	+	0.118555i	$0.962174\pi$
$674$	−1276.90	−	1276.90i	−1.89450	−	1.89450i
$675$			340.570i			0.504548i
$676$	−989.680			−1.46402
$677$	−73.3708	−	73.3708i	−0.108376	−	0.108376i	0.650839	−	0.759216i	$-0.274417\pi$
$677$	−73.3708	−	73.3708i	−0.108376	−	0.108376i	−0.759216	+	0.650839i	$0.774417\pi$
$678$		−	251.860i		−	0.371475i
$679$		−	564.218i		−	0.830954i
$680$	681.963	+	681.963i	1.00289	+	1.00289i
$681$	−231.460			−0.339883
$682$		−	303.905i		−	0.445609i
$683$		−	1183.11i		−	1.73222i	−0.499850	−	0.866112i	$-0.666611\pi$
$683$		−	1183.11i		−	1.73222i	0.499850	−	0.866112i	$-0.333389\pi$
$684$		−	280.594i		−	0.410226i
$685$	−92.6183	+	92.6183i	−0.135209	+	0.135209i
$686$			1283.84i			1.87148i
$687$	1007.82	+	1007.82i	1.46698	+	1.46698i
$688$	−368.189	+	368.189i	−0.535158	+	0.535158i
$689$			144.035i			0.209050i
$690$	163.486	−	163.486i	0.236937	−	0.236937i
$691$	24.2006	−	24.2006i	0.0350225	−	0.0350225i	−0.689379	−	0.724401i	$-0.742116\pi$
$691$	24.2006	−	24.2006i	0.0350225	−	0.0350225i	0.724401	+	0.689379i	$0.242116\pi$
$692$	1314.00	−	1314.00i	1.89884	−	1.89884i
$693$	−184.885			−0.266789
$694$	2147.29			3.09408
$695$	185.335			0.266669
$696$	−2846.41	−	2846.41i	−4.08966	−	4.08966i
$697$			14.9319i			0.0214231i
$698$	96.6000	−	1291.65i	0.138395	−	1.85050i
$699$	503.667			0.720553
$700$	590.137	−	590.137i	0.843053	−	0.843053i
$701$		−	901.693i		−	1.28630i	−0.765742	−	0.643148i	$-0.777628\pi$
$701$		−	901.693i		−	1.28630i	0.765742	−	0.643148i	$-0.222372\pi$
$702$		−	535.791i		−	0.763235i
$703$			286.564i			0.407630i
$704$	550.043	+	550.043i	0.781311	+	0.781311i
$705$	295.138	+	295.138i	0.418635	+	0.418635i
$706$	−216.207	−	216.207i	−0.306242	−	0.306242i
$707$	−622.235			−0.880107
$708$	477.063	+	477.063i	0.673818	+	0.673818i
$709$	220.966	−	220.966i	0.311658	−	0.311658i	−0.533894	−	0.845552i	$-0.679272\pi$
$709$	220.966	−	220.966i	0.311658	−	0.311658i	0.845552	+	0.533894i	$0.179272\pi$
$710$	−928.119			−1.30721
$711$	−394.543	−	394.543i	−0.554913	−	0.554913i
$712$	274.194			0.385104
$713$	58.9579			0.0826899
$714$	1127.99			1.57982
$715$		−	196.264i		−	0.274495i
$716$	1203.88	−	1203.88i	1.68140	−	1.68140i
$717$	1370.37			1.91126
$718$	−2542.09			−3.54052
$719$	−385.160	+	385.160i	−0.535688	+	0.535688i	−0.922259	−	0.386572i	$-0.873659\pi$
$719$	−385.160	+	385.160i	−0.535688	+	0.535688i	0.386572	+	0.922259i	$0.373659\pi$
$720$		−	398.033i		−	0.552824i
$721$	−344.089			−0.477239
$722$	822.752	−	822.752i	1.13955	−	1.13955i
$723$	560.228			0.774866
$724$	644.574			0.890296
$725$			1005.21i			1.38649i
$726$	182.457	−	182.457i	0.251318	−	0.251318i
$727$			345.333i			0.475011i	0.971386	+	0.237505i	$0.0763298\pi$
$727$			345.333i			0.475011i	−0.971386	+	0.237505i	$0.923670\pi$
$728$	−548.461	+	548.461i	−0.753380	+	0.753380i
$729$	−151.458			−0.207762
$730$	−339.488	+	339.488i	−0.465052	+	0.465052i
$731$	173.438	+	173.438i	0.237261	+	0.237261i
$732$	−1431.83	−	1431.83i	−1.95605	−	1.95605i
$733$	756.048	−	756.048i	1.03144	−	1.03144i	0.0319539	−	0.999489i	$-0.489827\pi$
$733$	756.048	−	756.048i	1.03144	−	1.03144i	0.999489	−	0.0319539i	$-0.0101730\pi$
$734$		−	1561.27i		−	2.12708i
$735$		−	254.303i		−	0.345991i
$736$	−330.609	+	330.609i	−0.449197	+	0.449197i
$737$	−148.597	+	148.597i	−0.201625	+	0.201625i
$738$	8.57088	−	8.57088i	0.0116137	−	0.0116137i
$739$	1401.26			1.89615			0.948077	−	0.318040i	$-0.103025\pi$
$739$	1401.26			1.89615			0.948077	+	0.318040i	$0.103025\pi$
$740$			960.401i			1.29784i
$741$	145.524	−	145.524i	0.196389	−	0.196389i
$742$	−201.965	−	201.965i	−0.272190	−	0.272190i
$743$		−	360.203i		−	0.484796i	−0.970177	−	0.242398i	$-0.922066\pi$
$743$		−	360.203i		−	0.484796i	0.970177	−	0.242398i	$-0.0779340\pi$
$744$	446.135	−	446.135i	0.599644	−	0.599644i
$745$	244.213	+	244.213i	0.327802	+	0.327802i
$746$			2496.53i			3.34656i
$747$		−	77.7091i		−	0.104028i
$748$	1328.42	−	1328.42i	1.77596	−	1.77596i
$749$	375.095			0.500794
$750$	−999.395	+	999.395i	−1.33253	+	1.33253i
$751$	482.281	+	482.281i	0.642185	+	0.642185i	0.951092	−	0.308907i	$-0.0999631\pi$
$751$	482.281	+	482.281i	0.642185	+	0.642185i	−0.308907	+	0.951092i	$0.599963\pi$
$752$	−1391.86	−	1391.86i	−1.85088	−	1.85088i
$753$	475.055	+	475.055i	0.630883	+	0.630883i
$754$		−	1581.41i		−	2.09736i
$755$		−	321.905i		−	0.426364i
$756$	533.108	+	533.108i	0.705169	+	0.705169i
$757$	−511.651	−	511.651i	−0.675893	−	0.675893i	0.283176	−	0.959068i	$-0.408612\pi$
$757$	−511.651	−	511.651i	−0.675893	−	0.675893i	−0.959068	+	0.283176i	$0.908612\pi$
$758$		−	202.984i		−	0.267788i
$759$	−188.130	−	188.130i	−0.247866	−	0.247866i
$760$	−246.734	+	246.734i	−0.324650	+	0.324650i
$761$	−1015.13	−	1015.13i	−1.33394	−	1.33394i	−0.901814	−	0.432124i	$-0.857764\pi$
$761$	−1015.13	−	1015.13i	−1.33394	−	1.33394i	−0.432124	−	0.901814i	$-0.642236\pi$
$762$		−	2037.90i		−	2.67442i
$763$	490.127	−	490.127i	0.642368	−	0.642368i
$764$	−3158.41			−4.13405
$765$	−187.496			−0.245093
$766$	−1056.82			−1.37966
$767$			156.576i			0.204141i
$768$		−	732.518i		−	0.953800i
$769$	331.755	−	331.755i	0.431411	−	0.431411i	−0.457697	−	0.889108i	$-0.651326\pi$
$769$	331.755	−	331.755i	0.431411	−	0.431411i	0.889108	+	0.457697i	$0.151326\pi$
$770$	275.200	+	275.200i	0.357402	+	0.357402i
$771$			1164.81i			1.51078i
$772$	1490.12	+	1490.12i	1.93021	+	1.93021i
$773$			126.140i			0.163183i	0.996666	+	0.0815915i	$0.0260003\pi$
$773$			126.140i			0.163183i	−0.996666	+	0.0815915i	$0.974000\pi$
$774$		−	199.106i		−	0.257242i
$775$	−157.552			−0.203293
$776$		−	2749.31i		−	3.54292i
$777$	469.212	+	469.212i	0.603877	+	0.603877i
$778$			1605.65i			2.06382i
$779$	−5.40235			−0.00693498
$780$	487.714	−	487.714i	0.625275	−	0.625275i
$781$			1068.02i			1.36751i
$782$	363.184	+	363.184i	0.464429	+	0.464429i
$783$	−908.065			−1.15973
$784$			1199.29i			1.52971i
$785$	−70.2162			−0.0894475
$786$	1504.96			1.91471
$787$	800.257	−	800.257i	1.01684	−	1.01684i	0.0169892	−	0.999856i	$-0.494592\pi$
$787$	800.257	−	800.257i	1.01684	−	1.01684i	0.999856	−	0.0169892i	$-0.00540809\pi$
$788$	−2680.78	−	2680.78i	−3.40200	−	3.40200i
$789$			321.080i			0.406945i
$790$			1174.55i			1.48677i
$791$			82.2487i			0.103981i
$792$	−900.903			−1.13750
$793$		−	469.939i		−	0.592609i
$794$	−137.768	−	137.768i	−0.173511	−	0.173511i
$795$	106.096	+	106.096i	0.133454	+	0.133454i
$796$	−2000.28	−	2000.28i	−2.51292	−	2.51292i
$797$	286.646	−	286.646i	0.359656	−	0.359656i	−0.504030	−	0.863686i	$-0.668150\pi$
$797$	286.646	−	286.646i	0.359656	−	0.359656i	0.863686	+	0.504030i	$0.168150\pi$
$798$			408.105i			0.511410i
$799$	−655.646	+	655.646i	−0.820583	+	0.820583i
$800$	883.482	−	883.482i	1.10435	−	1.10435i
$801$	−37.6929	+	37.6929i	−0.0470573	+	0.0470573i
$802$			1232.97i			1.53737i
$803$	390.662	+	390.662i	0.486503	+	0.486503i
$804$	−738.526			−0.918565
$805$	−53.3890	+	53.3890i	−0.0663217	+	0.0663217i
$806$	247.864			0.307524
$807$			1359.35i			1.68445i
$808$	−3032.01			−3.75249
$809$	−144.264			−0.178324			−0.0891621	−	0.996017i	$-0.528419\pi$
$809$	−144.264			−0.178324			−0.0891621	+	0.996017i	$0.528419\pi$
$810$	−627.165	−	627.165i	−0.774277	−	0.774277i
$811$	−307.437	−	307.437i	−0.379084	−	0.379084i	0.491688	−	0.870772i	$-0.336380\pi$
$811$	−307.437	−	307.437i	−0.379084	−	0.379084i	−0.870772	+	0.491688i	$0.836380\pi$
$812$	1573.49	+	1573.49i	1.93779	+	1.93779i
$813$			1305.99i			1.60638i
$814$	1557.46			1.91335
$815$	17.5309	+	17.5309i	0.0215103	+	0.0215103i
$816$	2794.47			3.42459
$817$	−62.7496	+	62.7496i	−0.0768049	+	0.0768049i
$818$	828.191	+	828.191i	1.01246	+	1.01246i
$819$		−	150.792i		−	0.184117i
$820$	−18.1056			−0.0220800
$821$		−	444.514i		−	0.541430i	−0.962660	−	0.270715i	$-0.912740\pi$
$821$		−	444.514i		−	0.541430i	0.962660	−	0.270715i	$-0.0872600\pi$
$822$			746.477i			0.908123i
$823$			1097.01i			1.33294i	0.745532	+	0.666470i	$0.232196\pi$
$823$			1097.01i			1.33294i	−0.745532	+	0.666470i	$0.767804\pi$
$824$	−1676.67			−2.03479
$825$	502.737	+	502.737i	0.609378	+	0.609378i
$826$	−219.550	−	219.550i	−0.265800	−	0.265800i
$827$	118.006	+	118.006i	0.142692	+	0.142692i	0.774844	−	0.632152i	$-0.217828\pi$
$827$	118.006	+	118.006i	0.142692	+	0.142692i	−0.632152	+	0.774844i	$0.717828\pi$
$828$		−	295.855i		−	0.357312i
$829$	489.656	−	489.656i	0.590659	−	0.590659i	−0.347150	−	0.937809i	$-0.612851\pi$
$829$	489.656	−	489.656i	0.590659	−	0.590659i	0.937809	+	0.347150i	$0.112851\pi$
$830$	−115.669	+	115.669i	−0.139361	+	0.139361i
$831$	1023.10	+	1023.10i	1.23116	+	1.23116i
$832$	−448.613	+	448.613i	−0.539198	+	0.539198i
$833$	564.933			0.678191
$834$	746.874	−	746.874i	0.895533	−	0.895533i
$835$	392.108	+	392.108i	0.469590	+	0.469590i
$836$	480.620	+	480.620i	0.574905	+	0.574905i
$837$		−	142.327i		−	0.170044i
$838$	−1695.05	−	1695.05i	−2.02274	−	2.02274i
$839$	675.961	−	675.961i	0.805675	−	0.805675i	−0.178301	−	0.983976i	$-0.557060\pi$
$839$	675.961	−	675.961i	0.805675	−	0.805675i	0.983976	+	0.178301i	$0.0570601\pi$
$840$			807.990i			0.961893i
$841$	−1839.19			−2.18691
$842$	−2887.31			−3.42911
$843$	505.400			0.599526
$844$	1467.04	+	1467.04i	1.73820	+	1.73820i
$845$	−239.263			−0.283152
$846$	752.678			0.889691
$847$	−59.5840	+	59.5840i	−0.0703471	+	0.0703471i
$848$	−500.347	−	500.347i	−0.590032	−	0.590032i
$849$	−600.234			−0.706989
$850$	−970.530	−	970.530i	−1.14180	−	1.14180i
$851$			302.149i			0.355052i
$852$	−2654.03	+	2654.03i	−3.11505	+	3.11505i
$853$		−	1461.81i		−	1.71373i	−0.515539	−	0.856866i	$-0.672408\pi$
$853$		−	1461.81i		−	1.71373i	0.515539	−	0.856866i	$-0.327592\pi$
$854$	658.945	+	658.945i	0.771598	+	0.771598i
$855$		−	67.8360i		−	0.0793403i
$856$	1827.75			2.13522
$857$	256.701	−	256.701i	0.299534	−	0.299534i	−0.541297	−	0.840831i	$-0.682067\pi$
$857$	256.701	−	256.701i	0.299534	−	0.299534i	0.840831	+	0.541297i	$0.182067\pi$
$858$	−790.916	−	790.916i	−0.921814	−	0.921814i
$859$	−116.811	−	116.811i	−0.135985	−	0.135985i	0.635838	−	0.771823i	$-0.280655\pi$
$859$	−116.811	−	116.811i	−0.135985	−	0.135985i	−0.771823	+	0.635838i	$0.780655\pi$
$860$	−210.301	+	210.301i	−0.244536	+	0.244536i
$861$	−8.84566	+	8.84566i	−0.0102737	+	0.0102737i
$862$		−	274.726i		−	0.318708i
$863$	302.333	−	302.333i	0.350328	−	0.350328i	−0.509903	−	0.860232i	$-0.670319\pi$
$863$	302.333	−	302.333i	0.350328	−	0.350328i	0.860232	+	0.509903i	$0.170319\pi$
$864$	798.104	+	798.104i	0.923731	+	0.923731i
$865$	317.670	−	317.670i	0.367248	−	0.367248i
$866$	2445.73			2.82417
$867$		−	267.716i		−	0.308785i
$868$	−246.623	+	246.623i	−0.284128	+	0.284128i
$869$	1351.60			1.55535
$870$	−1164.86	−	1164.86i	−1.33892	−	1.33892i
$871$	−121.195	−	121.195i	−0.139145	−	0.139145i
$872$	2388.28	−	2388.28i	2.73885	−	2.73885i
$873$	377.942	+	377.942i	0.432923	+	0.432923i
$874$	−131.400	+	131.400i	−0.150343	+	0.150343i
$875$	326.367	−	326.367i	0.372991	−	0.372991i
$876$			1941.58i			2.21642i
$877$	19.0525	+	19.0525i	0.0217246	+	0.0217246i	0.717886	−	0.696161i	$-0.245110\pi$
$877$	19.0525	+	19.0525i	0.0217246	+	0.0217246i	−0.696161	+	0.717886i	$0.745110\pi$
$878$	3022.15			3.44208
$879$		−	1452.77i		−	1.65275i
$880$	681.778	+	681.778i	0.774747	+	0.774747i
$881$	−1021.90	+	1021.90i	−1.15993	+	1.15993i	−0.175440	+	0.984490i	$0.556135\pi$
$881$	−1021.90	+	1021.90i	−1.15993	+	1.15993i	−0.984490	+	0.175440i	$0.943865\pi$
$882$	−324.270	−	324.270i	−0.367653	−	0.367653i
$883$	−495.511			−0.561168			−0.280584	−	0.959829i	$-0.590528\pi$
$883$	−495.511			−0.561168			−0.280584	+	0.959829i	$0.590528\pi$
$884$	1083.45	+	1083.45i	1.22563	+	1.22563i
$885$	115.334	+	115.334i	0.130321	+	0.130321i
$886$	271.678	−	271.678i	0.306635	−	0.306635i
$887$	826.994	−	826.994i	0.932350	−	0.932350i	−0.0655024	−	0.997852i	$-0.520865\pi$
$887$	826.994	−	826.994i	0.932350	−	0.932350i	0.997852	+	0.0655024i	$0.0208650\pi$
$888$	2286.37	+	2286.37i	2.57474	+	2.57474i
$889$			665.509i			0.748604i
$890$	112.211			0.126080
$891$	−721.703	+	721.703i	−0.809992	+	0.809992i
$892$	1073.82			1.20383
$893$	−237.212	−	237.212i	−0.265635	−	0.265635i
$894$	1968.29			2.20166
$895$	291.048	−	291.048i	0.325194	−	0.325194i
$896$		−	126.137i		−	0.140778i
$897$	153.438	−	153.438i	0.171057	−	0.171057i
$898$	1834.87	+	1834.87i	2.04329	+	2.04329i
$899$		−	420.083i		−	0.467278i
$900$			790.608i			0.878453i
$901$	−235.692	+	235.692i	−0.261589	+	0.261589i
$902$			29.3615i			0.0325516i
$903$			205.489i			0.227562i
$904$			400.779i			0.443340i
$905$	155.831			0.172189
$906$	−1297.23	−	1297.23i	−1.43182	−	1.43182i
$907$	378.043	−	378.043i	0.416806	−	0.416806i	−0.467295	−	0.884101i	$-0.654772\pi$
$907$	378.043	−	378.043i	0.416806	−	0.416806i	0.884101	+	0.467295i	$0.154772\pi$
$908$	623.475			0.686647
$909$	416.805	−	416.805i	0.458531	−	0.458531i
$910$	−224.452	+	224.452i	−0.246651	+	0.246651i
$911$	807.482	+	807.482i	0.886368	+	0.886368i	0.994172	−	0.107804i	$-0.0343818\pi$
$911$	807.482	+	807.482i	0.886368	+	0.886368i	−0.107804	+	0.994172i	$0.534382\pi$
$912$			1011.04i			1.10859i
$913$	133.105	+	133.105i	0.145789	+	0.145789i
$914$	−186.997	+	186.997i	−0.204592	+	0.204592i
$915$	−346.156	−	346.156i	−0.378313	−	0.378313i
$916$	−2714.71	−	2714.71i	−2.96366	−	2.96366i
$917$	−491.468			−0.535952
$918$	876.740	−	876.740i	0.955054	−	0.955054i
$919$	799.038	−	799.038i	0.869465	−	0.869465i	−0.122949	−	0.992413i	$-0.539235\pi$
$919$	799.038	−	799.038i	0.869465	−	0.869465i	0.992413	+	0.122949i	$0.0392350\pi$
$920$	−260.152	+	260.152i	−0.282774	+	0.282774i
$921$			358.480i			0.389229i
$922$	927.610			1.00608
$923$	−871.075			−0.943744
$924$	1573.91			1.70337
$925$		−	807.428i		−	0.872895i
$926$	7.17459			0.00774794
$927$	230.488	−	230.488i	0.248639	−	0.248639i
$928$	2355.64	+	2355.64i	2.53840	+	2.53840i
$929$		−	460.876i		−	0.496099i	−0.968747	−	0.248050i	$-0.920210\pi$
$929$		−	460.876i		−	0.496099i	0.968747	−	0.248050i	$-0.0797896\pi$
$930$	182.576	−	182.576i	0.196319	−	0.196319i
$931$			204.392i			0.219540i
$932$	−1356.71			−1.45570
$933$	1215.47	−	1215.47i	1.30276	−	1.30276i
$934$	−1082.59	+	1082.59i	−1.15909	+	1.15909i
$935$	321.156	−	321.156i	0.343482	−	0.343482i
$936$		−	734.773i		−	0.785014i
$937$		−	112.535i		−	0.120101i	−0.998195	−	0.0600504i	$-0.980874\pi$
$937$		−	112.535i		−	0.120101i	0.998195	−	0.0600504i	$-0.0191262\pi$
$938$	339.879			0.362344
$939$			399.352i			0.425295i
$940$	−795.001	−	795.001i	−0.845746	−	0.845746i
$941$		−	682.155i		−	0.724925i	−0.931998	−	0.362463i	$-0.881936\pi$
$941$		−	682.155i		−	0.724925i	0.931998	−	0.362463i	$-0.118064\pi$
$942$	−282.962	+	282.962i	−0.300384	+	0.300384i
$943$	−5.69616			−0.00604046
$944$	−543.912	−	543.912i	−0.576178	−	0.576178i
$945$	128.883	+	128.883i	0.136384	+	0.136384i
$946$	341.041	+	341.041i	0.360509	+	0.360509i
$947$	1806.39			1.90749			0.953743	−	0.300624i	$-0.0971948\pi$
$947$	1806.39			1.90749			0.953743	+	0.300624i	$0.0971948\pi$
$948$	3358.71	+	3358.71i	3.54295	+	3.54295i
$949$	−318.622	+	318.622i	−0.335745	+	0.335745i
$950$	351.137	−	351.137i	0.369618	−	0.369618i
$951$	−67.8575	+	67.8575i	−0.0713538	+	0.0713538i
$952$	−1794.94			−1.88544
$953$			364.330i			0.382298i	0.981561	+	0.191149i	$0.0612214\pi$
$953$			364.330i			0.382298i	−0.981561	+	0.191149i	$0.938779\pi$
$954$	270.573			0.283620
$955$	−763.572			−0.799552
$956$	−3691.33			−3.86122
$957$	−1340.45	+	1340.45i	−1.40068	+	1.40068i
$958$	−993.265	−	993.265i	−1.03681	−	1.03681i
$959$		−	243.773i		−	0.254195i
$960$			660.895i			0.688433i
$961$	−895.158			−0.931486
$962$			1270.26i			1.32044i
$963$	−251.257	+	251.257i	−0.260911	+	0.260911i
$964$	−1509.07			−1.56542
$965$	360.249	+	360.249i	0.373315	+	0.373315i
$966$			430.300i			0.445445i
$967$	539.289			0.557693			0.278847	−	0.960336i	$-0.410048\pi$
$967$	539.289			0.557693			0.278847	+	0.960336i	$0.410048\pi$
$968$	−290.339	+	290.339i	−0.299937	+	0.299937i
$969$	476.255			0.491491
$970$		−	1125.13i		−	1.15992i
$971$	0.0467432			4.81392e−5			2.40696e−5	−	1.00000i	$-0.499992\pi$
$971$	0.0467432			4.81392e−5			2.40696e−5		1.00000i	$0.499992\pi$
$972$	−2043.92			−2.10280
$973$	−243.903	+	243.903i	−0.250671	+	0.250671i
$974$	−3103.14			−3.18597
$975$	−410.031	+	410.031i	−0.420544	+	0.420544i
$976$	1632.46	+	1632.46i	1.67261	+	1.67261i
$977$	−162.032			−0.165846			−0.0829231	−	0.996556i	$-0.526426\pi$
$977$	−162.032			−0.165846			−0.0829231	+	0.996556i	$0.526426\pi$
$978$	141.294			0.144472
$979$		−	129.126i		−	0.131896i
$980$			685.008i			0.698987i
$981$			656.623i			0.669340i
$982$	278.333	+	278.333i	0.283435	+	0.283435i
$983$	−9.60738			−0.00977353			−0.00488676	−	0.999988i	$-0.501556\pi$
$983$	−9.60738			−0.00977353			−0.00488676	+	0.999988i	$0.501556\pi$
$984$	−43.1029	+	43.1029i	−0.0438037	+	0.0438037i
$985$	−648.099	−	648.099i	−0.657969	−	0.657969i
$986$	2587.73	−	2587.73i	2.62448	−	2.62448i
$987$	−776.809			−0.787041
$988$	−391.992	+	391.992i	−0.396753	+	0.396753i
$989$	−66.1622	+	66.1622i	−0.0668981	+	0.0668981i
$990$	−368.686			−0.372410
$991$	−1459.61			−1.47286			−0.736432	−	0.676511i	$-0.763491\pi$
$991$	−1459.61			−1.47286			−0.736432	+	0.676511i	$0.763491\pi$
$992$	−369.213	+	369.213i	−0.372191	+	0.372191i
$993$	−173.471	+	173.471i	−0.174694	+	0.174694i
$994$	1221.42	−	1221.42i	1.22879	−	1.22879i
$995$	−483.584	−	483.584i	−0.486015	−	0.486015i
$996$			661.531i			0.664187i
$997$	664.890	+	664.890i	0.666891	+	0.666891i	0.956995	−	0.290104i	$-0.0936899\pi$
$997$	664.890	+	664.890i	0.666891	+	0.666891i	−0.290104	+	0.956995i	$0.593690\pi$
$998$	3186.82			3.19321
$999$	729.400			0.730130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.3.d.a.136.2	✓	116
349.213	odd	4	inner	349.3.d.a.213.2	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.3.d.a.136.2	✓	116	1.1	even	1	trivial
349.3.d.a.213.2	yes	116	349.213	odd	4	inner

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	349.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.62430 + 2.62430i) q^{2} +3.62850i q^{3} -9.77395i q^{4} -2.36293i q^{5} +(-9.52228 - 9.52228i) q^{6} +(3.10965 + 3.10965i) q^{7} +(15.1526 + 15.1526i) q^{8} -4.16599 q^{9} +O(q^{10})\)	\(q+(-2.62430 + 2.62430i) q^{2} +3.62850i q^{3} -9.77395i q^{4} -2.36293i q^{5} +(-9.52228 - 9.52228i) q^{6} +(3.10965 + 3.10965i) q^{7} +(15.1526 + 15.1526i) q^{8} -4.16599 q^{9} +(6.20105 + 6.20105i) q^{10} +(7.13579 - 7.13579i) q^{11} +35.4648 q^{12} +(5.81992 + 5.81992i) q^{13} -16.3213 q^{14} +8.57389 q^{15} -40.4343 q^{16} +19.0468i q^{17} +(10.9328 - 10.9328i) q^{18} -6.89113 q^{19} -23.0952 q^{20} +(-11.2833 + 11.2833i) q^{21} +37.4530i q^{22} -7.26590 q^{23} +(-54.9812 + 54.9812i) q^{24} +19.4166 q^{25} -30.5465 q^{26} +17.5402i q^{27} +(30.3935 - 30.3935i) q^{28} +51.7706i q^{29} +(-22.5005 + 22.5005i) q^{30} -8.11432 q^{31} +(45.5015 - 45.5015i) q^{32} +(25.8922 + 25.8922i) q^{33} +(-49.9847 - 49.9847i) q^{34} +(7.34788 - 7.34788i) q^{35} +40.7182i q^{36} -41.5845i q^{37} +(18.0844 - 18.0844i) q^{38} +(-21.1176 + 21.1176i) q^{39} +(35.8046 - 35.8046i) q^{40} +0.783957 q^{41} -59.2219i q^{42} +(9.10585 - 9.10585i) q^{43} +(-69.7448 - 69.7448i) q^{44} +9.84396i q^{45} +(19.0679 - 19.0679i) q^{46} +(34.4228 + 34.4228i) q^{47} -146.716i q^{48} -29.6602i q^{49} +(-50.9550 + 50.9550i) q^{50} -69.1114 q^{51} +(56.8836 - 56.8836i) q^{52} +(12.3743 + 12.3743i) q^{53} +(-46.0308 - 46.0308i) q^{54} +(-16.8614 - 16.8614i) q^{55} +94.2384i q^{56} -25.0044i q^{57} +(-135.862 - 135.862i) q^{58} +(13.4518 + 13.4518i) q^{59} -83.8008i q^{60} +(-40.3733 - 40.3733i) q^{61} +(21.2944 - 21.2944i) q^{62} +(-12.9548 - 12.9548i) q^{63} +77.0823i q^{64} +(13.7521 - 13.7521i) q^{65} -135.898 q^{66} -20.8242 q^{67} +186.163 q^{68} -26.3643i q^{69} +38.5661i q^{70} +(-74.8356 + 74.8356i) q^{71} +(-63.1257 - 63.1257i) q^{72} +54.7468i q^{73} +(109.130 + 109.130i) q^{74} +70.4529i q^{75} +67.3535i q^{76} +44.3796 q^{77} -110.838i q^{78} +(94.7057 + 94.7057i) q^{79} +95.5434i q^{80} -101.138 q^{81} +(-2.05734 + 2.05734i) q^{82} +18.6532i q^{83} +(110.283 + 110.283i) q^{84} +45.0063 q^{85} +47.7931i q^{86} -187.849 q^{87} +216.252 q^{88} +(9.04776 - 9.04776i) q^{89} +(-25.8335 - 25.8335i) q^{90} +36.1958i q^{91} +71.0166i q^{92} -29.4428i q^{93} -180.672 q^{94} +16.2833i q^{95} +(165.102 + 165.102i) q^{96} +(-90.7206 - 90.7206i) q^{97} +(77.8374 + 77.8374i) q^{98} +(-29.7277 + 29.7277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9}+O(q^{10}) \) 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9	\( 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9} - 16 q^{10} + 8 q^{11} + 32 q^{12} + 22 q^{13} + 56 q^{14} + 32 q^{15} - 436 q^{16} - 112 q^{18} - 52 q^{19} - 72 q^{20} + 50 q^{21} + 200 q^{23} + 144 q^{24} - 408 q^{25} + 72 q^{26} - 84 q^{28} - 6 q^{30} + 68 q^{31} - 130 q^{32} + 146 q^{33} + 62 q^{34} - 60 q^{35} + 2 q^{38} + 64 q^{39} - 218 q^{40} + 144 q^{41} - 180 q^{43} + 32 q^{44} + 122 q^{46} - 100 q^{47} + 56 q^{50} - 172 q^{51} + 296 q^{52} - 188 q^{53} - 540 q^{54} + 160 q^{55} - 140 q^{58} + 202 q^{59} + 62 q^{61} + 424 q^{62} + 362 q^{63} + 206 q^{65} - 268 q^{66} + 252 q^{67} - 404 q^{68} + 12 q^{71} + 664 q^{72} - 68 q^{74} - 884 q^{77} + 50 q^{79} + 1284 q^{81} - 666 q^{82} - 742 q^{84} + 1240 q^{85} + 220 q^{87} + 60 q^{88} + 48 q^{89} + 298 q^{90} + 940 q^{94} - 1588 q^{96} + 180 q^{97} + 704 q^{98} - 26 q^{99}+O(q^{100}) \) 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9 - 16 * q^10 + 8 * q^11 + 32 * q^12 + 22 * q^13 + 56 * q^14 + 32 * q^15 - 436 * q^16 - 112 * q^18 - 52 * q^19 - 72 * q^20 + 50 * q^21 + 200 * q^23 + 144 * q^24 - 408 * q^25 + 72 * q^26 - 84 * q^28 - 6 * q^30 + 68 * q^31 - 130 * q^32 + 146 * q^33 + 62 * q^34 - 60 * q^35 + 2 * q^38 + 64 * q^39 - 218 * q^40 + 144 * q^41 - 180 * q^43 + 32 * q^44 + 122 * q^46 - 100 * q^47 + 56 * q^50 - 172 * q^51 + 296 * q^52 - 188 * q^53 - 540 * q^54 + 160 * q^55 - 140 * q^58 + 202 * q^59 + 62 * q^61 + 424 * q^62 + 362 * q^63 + 206 * q^65 - 268 * q^66 + 252 * q^67 - 404 * q^68 + 12 * q^71 + 664 * q^72 - 68 * q^74 - 884 * q^77 + 50 * q^79 + 1284 * q^81 - 666 * q^82 - 742 * q^84 + 1240 * q^85 + 220 * q^87 + 60 * q^88 + 48 * q^89 + 298 * q^90 + 940 * q^94 - 1588 * q^96 + 180 * q^97 + 704 * q^98 - 26 * q^99

Introduction

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