LMFDB - Embedded newform 416.2.bd.a.83.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.11
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22104 + 0.713478i) q^{2} +(2.00588 + 0.830863i) q^{3} +(0.981898 - 1.74238i) q^{4} +(-1.19939 + 2.89559i) q^{5} +(-3.04207 + 0.416631i) q^{6} -2.39832i q^{7} +(0.0442070 + 2.82808i) q^{8} +(1.21190 + 1.21190i) q^{9} +O(q^{10})$	\(q+(-1.22104 + 0.713478i) q^{2} +(2.00588 + 0.830863i) q^{3} +(0.981898 - 1.74238i) q^{4} +(-1.19939 + 2.89559i) q^{5} +(-3.04207 + 0.416631i) q^{6} -2.39832i q^{7} +(0.0442070 + 2.82808i) q^{8} +(1.21190 + 1.21190i) q^{9} +(-0.601429 - 4.39139i) q^{10} +(5.82672 + 2.41351i) q^{11} +(3.41724 - 2.67918i) q^{12} +(-2.78085 + 2.29496i) q^{13} +(1.71115 + 2.92845i) q^{14} +(-4.81168 + 4.81168i) q^{15} +(-2.07175 - 3.42167i) q^{16} -2.90755 q^{17} +(-2.34445 - 0.615119i) q^{18} +(2.83528 + 6.84496i) q^{19} +(3.86753 + 4.93297i) q^{20} +(1.99267 - 4.81074i) q^{21} +(-8.83666 + 1.21024i) q^{22} +(1.87173 + 1.87173i) q^{23} +(-2.26107 + 5.70952i) q^{24} +(-3.41038 - 3.41038i) q^{25} +(1.75814 - 4.78633i) q^{26} +(-1.06858 - 2.57979i) q^{27} +(-4.17877 - 2.35490i) q^{28} +(0.0945097 - 0.228167i) q^{29} +(2.44224 - 9.30830i) q^{30} +(-4.03840 - 4.03840i) q^{31} +(4.97099 + 2.69986i) q^{32} +(9.68240 + 9.68240i) q^{33} +(3.55025 - 2.07447i) q^{34} +(6.94455 + 2.87653i) q^{35} +(3.30155 - 0.921625i) q^{36} +(4.45287 + 1.84444i) q^{37} +(-8.34573 - 6.33509i) q^{38} +(-7.48486 + 2.29291i) q^{39} +(-8.24199 - 3.26398i) q^{40} +0.944082 q^{41} +(0.999215 + 7.29585i) q^{42} +(-1.90544 - 4.60013i) q^{43} +(9.92648 - 7.78252i) q^{44} +(-4.96272 + 2.05562i) q^{45} +(-3.62091 - 0.950028i) q^{46} +(-5.54962 - 5.54962i) q^{47} +(-1.31275 - 8.58480i) q^{48} +1.24807 q^{49} +(6.59745 + 1.73099i) q^{50} +(-5.83219 - 2.41577i) q^{51} +(1.26817 + 7.09871i) q^{52} +(1.55309 + 3.74950i) q^{53} +(3.14541 + 2.38763i) q^{54} +(-13.9771 + 13.9771i) q^{55} +(6.78264 - 0.106023i) q^{56} +16.0859i q^{57} +(0.0473914 + 0.346032i) q^{58} +(-2.77880 + 6.70861i) q^{59} +(3.65918 + 13.1083i) q^{60} +(1.58815 - 3.83412i) q^{61} +(7.81237 + 2.04975i) q^{62} +(2.90652 - 2.90652i) q^{63} +(-7.99609 + 0.250042i) q^{64} +(-3.30993 - 10.8048i) q^{65} +(-18.7308 - 4.91446i) q^{66} +(-3.69601 + 1.53094i) q^{67} +(-2.85492 + 5.06605i) q^{68} +(2.19932 + 5.30962i) q^{69} +(-10.5319 + 1.44242i) q^{70} +9.26853 q^{71} +(-3.37378 + 3.48093i) q^{72} -4.25060i q^{73} +(-6.75311 + 0.924883i) q^{74} +(-4.00725 - 9.67436i) q^{75} +(14.7105 + 1.78093i) q^{76} +(5.78835 - 13.9743i) q^{77} +(7.50340 - 8.14003i) q^{78} +8.02110 q^{79} +(12.3926 - 1.89502i) q^{80} -11.2043i q^{81} +(-1.15277 + 0.673582i) q^{82} +(-3.21611 - 7.76437i) q^{83} +(-6.42552 - 8.19564i) q^{84} +(3.48730 - 8.41908i) q^{85} +(5.60872 + 4.25748i) q^{86} +(0.379150 - 0.379150i) q^{87} +(-6.56801 + 16.5851i) q^{88} +5.73652 q^{89} +(4.59305 - 6.05080i) q^{90} +(5.50405 + 6.66937i) q^{91} +(5.09911 - 1.42341i) q^{92} +(-4.74519 - 11.4559i) q^{93} +(10.7359 + 2.81680i) q^{94} -23.2208 q^{95} +(7.72799 + 9.54581i) q^{96} +(8.77970 - 8.77970i) q^{97} +(-1.52395 + 0.890470i) q^{98} +(4.13647 + 9.98633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.22104	+	0.713478i	−0.863409	+	0.504505i
$2$	−1.22104	+	0.713478i	−0.863409	+	0.504505i
$3$	2.00588	+	0.830863i	1.15810	+	0.479699i	0.877240	−	0.480052i	$-0.159382\pi$
$3$	2.00588	+	0.830863i	1.15810	+	0.479699i	0.280855	+	0.959750i	$0.409382\pi$
$4$	0.981898	−	1.74238i	0.490949	−	0.871188i
$5$	−1.19939	+	2.89559i	−0.536385	+	1.29495i	0.390845	+	0.920457i	$0.372183\pi$
$5$	−1.19939	+	2.89559i	−0.536385	+	1.29495i	−0.927230	+	0.374492i	$0.877817\pi$
$6$	−3.04207	+	0.416631i	−1.24192	+	0.170089i
$7$		−	2.39832i		−	0.906479i	−0.891389	−	0.453240i	$-0.850268\pi$
$7$		−	2.39832i		−	0.906479i	0.891389	−	0.453240i	$-0.149732\pi$
$8$	0.0442070	+	2.82808i	0.0156295	+	0.999878i
$9$	1.21190	+	1.21190i	0.403967	+	0.403967i
$10$	−0.601429	−	4.39139i	−0.190189	−	1.38868i
$11$	5.82672	+	2.41351i	1.75682	+	0.727699i	0.996986	+	0.0775836i	$0.0247205\pi$
$11$	5.82672	+	2.41351i	1.75682	+	0.727699i	0.759835	+	0.650116i	$0.225280\pi$
$12$	3.41724	−	2.67918i	0.986474	−	0.773411i
$13$	−2.78085	+	2.29496i	−0.771270	+	0.636508i
$13$	−2.78085	+	2.29496i	−0.771270	+	0.636508i
$14$	1.71115	+	2.92845i	0.457323	+	0.782662i
$15$	−4.81168	+	4.81168i	−1.24237	+	1.24237i
$16$	−2.07175	−	3.42167i	−0.517938	−	0.855418i
$17$	−2.90755			−0.705184			−0.352592	−	0.935777i	$-0.614700\pi$
$17$	−2.90755			−0.705184			−0.352592	+	0.935777i	$0.614700\pi$
$18$	−2.34445	−	0.615119i	−0.552592	−	0.144985i
$19$	2.83528	+	6.84496i	0.650457	+	1.57034i	0.812116	+	0.583495i	$0.198315\pi$
$19$	2.83528	+	6.84496i	0.650457	+	1.57034i	−0.161659	+	0.986847i	$0.551685\pi$
$20$	3.86753	+	4.93297i	0.864806	+	1.10305i
$21$	1.99267	−	4.81074i	0.434837	−	1.04979i
$22$	−8.83666	+	1.21024i	−1.88398	+	0.258024i
$23$	1.87173	+	1.87173i	0.390283	+	0.390283i	0.874788	−	0.484505i	$-0.161000\pi$
$23$	1.87173	+	1.87173i	0.390283	+	0.390283i	−0.484505	+	0.874788i	$0.661000\pi$
$24$	−2.26107	+	5.70952i	−0.461540	+	1.16545i
$25$	−3.41038	−	3.41038i	−0.682076	−	0.682076i
$26$	1.75814	−	4.78633i	0.344800	−	0.938676i
$27$	−1.06858	−	2.57979i	−0.205649	−	0.496481i
$28$	−4.17877	−	2.35490i	−0.789714	−	0.445035i
$29$	0.0945097	−	0.228167i	0.0175500	−	0.0423695i	−0.914862	−	0.403768i	$-0.867700\pi$
$29$	0.0945097	−	0.228167i	0.0175500	−	0.0423695i	0.932412	+	0.361398i	$0.117700\pi$
$30$	2.44224	−	9.30830i	0.445891	−	1.69946i
$31$	−4.03840	−	4.03840i	−0.725318	−	0.725318i	0.244365	−	0.969683i	$-0.421420\pi$
$31$	−4.03840	−	4.03840i	−0.725318	−	0.725318i	−0.969683	+	0.244365i	$0.921420\pi$
$32$	4.97099	+	2.69986i	0.878755	+	0.477273i
$33$	9.68240	+	9.68240i	1.68549	+	1.68549i
$34$	3.55025	−	2.07447i	0.608862	−	0.355769i
$35$	6.94455	+	2.87653i	1.17384	+	0.486222i
$36$	3.30155	−	0.921625i	0.550258	−	0.153604i
$37$	4.45287	+	1.84444i	0.732047	+	0.303224i	0.717393	−	0.696669i	$-0.245335\pi$
$37$	4.45287	+	1.84444i	0.732047	+	0.303224i	0.0146539	+	0.999893i	$0.495335\pi$
$38$	−8.34573	−	6.33509i	−1.35386	−	1.02769i
$39$	−7.48486	+	2.29291i	−1.19854	+	0.367159i
$40$	−8.24199	−	3.26398i	−1.30317	−	0.516080i
$41$	0.944082			0.147441			0.0737204	−	0.997279i	$-0.476513\pi$
$41$	0.944082			0.147441			0.0737204	+	0.997279i	$0.476513\pi$
$42$	0.999215	+	7.29585i	0.154182	+	1.12577i
$43$	−1.90544	−	4.60013i	−0.290576	−	0.701513i	0.709418	−	0.704788i	$-0.248958\pi$
$43$	−1.90544	−	4.60013i	−0.290576	−	0.701513i	−0.999995	+	0.00327430i	$0.998958\pi$
$44$	9.92648	−	7.78252i	1.49647	−	1.17326i
$45$	−4.96272	+	2.05562i	−0.739798	+	0.306434i
$46$	−3.62091	−	0.950028i	−0.533874	−	0.140074i
$47$	−5.54962	−	5.54962i	−0.809496	−	0.809496i	0.175062	−	0.984557i	$-0.443988\pi$
$47$	−5.54962	−	5.54962i	−0.809496	−	0.809496i	−0.984557	+	0.175062i	$0.943988\pi$
$48$	−1.31275	−	8.58480i	−0.189479	−	1.23911i
$49$	1.24807			0.178296
$50$	6.59745	+	1.73099i	0.933021	+	0.244799i
$51$	−5.83219	−	2.41577i	−0.816670	−	0.338276i
$52$	1.26817	+	7.09871i	0.175864	+	0.984414i
$53$	1.55309	+	3.74950i	0.213334	+	0.515033i	0.993932	−	0.110001i	$-0.0350853\pi$
$53$	1.55309	+	3.74950i	0.213334	+	0.515033i	−0.780598	+	0.625034i	$0.785085\pi$
$54$	3.14541	+	2.38763i	0.428036	+	0.324915i
$55$	−13.9771	+	13.9771i	−1.88467	+	1.88467i
$56$	6.78264	−	0.106023i	0.906368	−	0.0141679i
$57$			16.0859i			2.13063i
$58$	0.0473914	+	0.346032i	0.00622279	+	0.0454362i
$59$	−2.77880	+	6.70861i	−0.361768	+	0.873386i	0.633273	+	0.773928i	$0.281711\pi$
$59$	−2.77880	+	6.70861i	−0.361768	+	0.873386i	−0.995042	+	0.0994579i	$0.968289\pi$
$60$	3.65918	+	13.1083i	0.472398	+	1.69228i
$61$	1.58815	−	3.83412i	0.203341	−	0.490909i	−0.789006	−	0.614385i	$-0.789404\pi$
$61$	1.58815	−	3.83412i	0.203341	−	0.490909i	0.992348	+	0.123476i	$0.0394042\pi$
$62$	7.81237	+	2.04975i	0.992172	+	0.260319i
$63$	2.90652	−	2.90652i	0.366187	−	0.366187i
$64$	−7.99609	+	0.250042i	−0.999511	+	0.0312553i
$65$	−3.30993	−	10.8048i	−0.410547	−	1.34017i
$66$	−18.7308	−	4.91446i	−2.30560	−	0.604928i
$67$	−3.69601	+	1.53094i	−0.451540	+	0.187034i	−0.596851	−	0.802352i	$-0.703582\pi$
$67$	−3.69601	+	1.53094i	−0.451540	+	0.187034i	0.145311	+	0.989386i	$0.453582\pi$
$68$	−2.85492	+	5.06605i	−0.346209	+	0.614348i
$69$	2.19932	+	5.30962i	0.264767	+	0.639203i
$70$	−10.5319	+	1.44242i	−1.25881	+	0.172402i
$71$	9.26853			1.09997			0.549986	−	0.835174i	$-0.314633\pi$
$71$	9.26853			1.09997			0.549986	+	0.835174i	$0.314633\pi$
$72$	−3.37378	+	3.48093i	−0.397604	+	0.410231i
$73$		−	4.25060i		−	0.497495i	−0.968568	−	0.248748i	$-0.919981\pi$
$73$		−	4.25060i		−	0.497495i	0.968568	−	0.248748i	$-0.0800190\pi$
$74$	−6.75311	+	0.924883i	−0.785033	+	0.107515i
$75$	−4.00725	−	9.67436i	−0.462718	−	1.11710i
$76$	14.7105	+	1.78093i	1.68740	+	0.204287i
$77$	5.78835	−	13.9743i	0.659644	−	1.59252i
$78$	7.50340	−	8.14003i	0.849593	−	0.921676i
$79$	8.02110			0.902444			0.451222	−	0.892412i	$-0.350988\pi$
$79$	8.02110			0.902444			0.451222	+	0.892412i	$0.350988\pi$
$80$	12.3926	−	1.89502i	1.38554	−	0.211870i
$81$		−	11.2043i		−	1.24492i
$82$	−1.15277	+	0.673582i	−0.127302	+	0.0743847i
$83$	−3.21611	−	7.76437i	−0.353014	−	0.852250i	−0.996245	−	0.0865784i	$-0.972407\pi$
$83$	−3.21611	−	7.76437i	−0.353014	−	0.852250i	0.643231	−	0.765672i	$-0.277593\pi$
$84$	−6.42552	−	8.19564i	−0.701081	−	0.894218i
$85$	3.48730	−	8.41908i	0.378250	−	0.913177i
$86$	5.60872	+	4.25748i	0.604803	+	0.459095i
$87$	0.379150	−	0.379150i	0.0406492	−	0.0406492i
$88$	−6.56801	+	16.5851i	−0.700152	+	1.76798i
$89$	5.73652			0.608070			0.304035	−	0.952661i	$-0.401666\pi$
$89$	5.73652			0.608070			0.304035	+	0.952661i	$0.401666\pi$
$90$	4.59305	−	6.05080i	0.484150	−	0.637810i
$91$	5.50405	+	6.66937i	0.576981	+	0.699140i
$92$	5.09911	−	1.42341i	0.531619	−	0.148401i
$93$	−4.74519	−	11.4559i	−0.492053	−	1.18792i
$94$	10.7359	+	2.81680i	1.10732	+	0.290531i
$95$	−23.2208			−2.38241
$96$	7.72799	+	9.54581i	0.788735	+	0.974265i
$97$	8.77970	−	8.77970i	0.891443	−	0.891443i	−0.103216	−	0.994659i	$-0.532913\pi$
$97$	8.77970	−	8.77970i	0.891443	−	0.891443i	0.994659	+	0.103216i	$0.0329133\pi$
$98$	−1.52395	+	0.890470i	−0.153942	+	0.0899511i
$99$	4.13647	+	9.98633i	0.415731	+	1.00366i
$100$	−9.29080	+	2.59352i	−0.929080	+	0.259352i
$101$	0.493312	+	1.19096i	0.0490864	+	0.118505i	0.946521	−	0.322643i	$-0.104571\pi$
$101$	0.493312	+	1.19096i	0.0490864	+	0.118505i	−0.897434	+	0.441148i	$0.854571\pi$
$102$	8.84497	−	1.21138i	0.875782	−	0.119944i
$103$	14.0713	−	14.0713i	1.38648	−	1.38648i	0.553904	−	0.832581i	$-0.313138\pi$
$103$	14.0713	−	14.0713i	1.38648	−	1.38648i	0.832581	−	0.553904i	$-0.186862\pi$
$104$	−6.61327	−	7.76303i	−0.648485	−	0.761228i
$105$	11.5399	+	11.5399i	1.12618	+	1.12618i
$106$	−4.57158	−	3.47020i	−0.444031	−	0.337056i
$107$	11.5830	−	4.79785i	1.11978	−	0.463826i	0.255482	−	0.966814i	$-0.417766\pi$
$107$	11.5830	−	4.79785i	1.11978	−	0.463826i	0.864294	+	0.502988i	$0.167766\pi$
$108$	−5.54421	−	0.671214i	−0.533492	−	0.0645876i
$109$	−5.42429	+	2.24682i	−0.519553	+	0.215206i	−0.627021	−	0.779003i	$-0.715726\pi$
$109$	−5.42429	+	2.24682i	−0.519553	+	0.215206i	0.107468	+	0.994209i	$0.465726\pi$
$110$	7.09428	−	27.0389i	0.676413	−	2.57806i
$111$	7.39944	+	7.39944i	0.702324	+	0.702324i
$112$	−8.20626	+	4.96872i	−0.775419	+	0.469500i
$113$		−	19.2360i		−	1.80957i	−0.425872	−	0.904783i	$-0.640033\pi$
$113$		−	19.2360i		−	1.80957i	0.425872	−	0.904783i	$-0.359967\pi$
$114$	−11.4769	−	19.6416i	−1.07491	−	1.83960i
$115$	−7.66472	+	3.17483i	−0.714739	+	0.296054i
$116$	−0.304753	−	0.388708i	−0.0282956	−	0.0360906i
$117$	−6.15138	−	0.588853i	−0.568696	−	0.0544395i
$118$	−1.39341	−	10.1741i	−0.128274	−	0.936603i
$119$			6.97323i			0.639235i
$120$	−13.8205	−	13.3951i	−1.26164	−	1.22280i
$121$	20.3474	+	20.3474i	1.84977	+	1.84977i
$122$	0.796367	+	5.81474i	0.0720997	+	0.526442i
$123$	1.89372	+	0.784402i	0.170751	+	0.0707272i
$124$	−11.0017	+	3.07112i	−0.987983	+	0.275794i
$125$	−0.512513	+	0.212290i	−0.0458406	+	0.0189878i
$126$	−1.47525	+	5.62273i	−0.131426	+	0.500913i
$127$	−8.88320			−0.788257			−0.394128	−	0.919055i	$-0.628953\pi$
$127$	−8.88320			−0.788257			−0.394128	+	0.919055i	$0.628953\pi$
$128$	9.58518	−	6.01035i	0.847218	−	0.531245i
$129$		−	10.8105i		−	0.951808i
$130$	11.7506	+	10.8316i	1.03059	+	0.949990i
$131$	8.00910	+	3.31748i	0.699758	+	0.289849i	0.704059	−	0.710141i	$-0.251369\pi$
$131$	8.00910	+	3.31748i	0.699758	+	0.289849i	−0.00430095	+	0.999991i	$0.501369\pi$
$132$	26.3775	−	7.36326i	2.29587	−	0.640890i
$133$	16.4164	−	6.79989i	1.42348	−	0.589626i
$134$	3.42070	−	4.50637i	0.295504	−	0.389291i
$135$	8.75167			0.753224
$136$	−0.128534	−	8.22279i	−0.0110217	−	0.705098i
$137$			3.56204i			0.304326i	0.988355	+	0.152163i	$0.0486238\pi$
$137$			3.56204i			0.304326i	−0.988355	+	0.152163i	$0.951376\pi$
$138$	−6.47376	−	4.91412i	−0.551083	−	0.418317i
$139$	−14.9975	+	6.21215i	−1.27207	+	0.526908i	−0.913592	−	0.406631i	$-0.866703\pi$
$139$	−14.9975	+	6.21215i	−1.27207	+	0.526908i	−0.358476	+	0.933539i	$0.616703\pi$
$140$	11.8308	−	9.27557i	0.999888	−	0.783929i
$141$	−6.52090	−	15.7429i	−0.549159	−	1.32579i
$142$	−11.3173	+	6.61289i	−0.949725	+	0.554942i
$143$	−21.7422	+	6.66049i	−1.81817	+	0.556978i
$144$	1.63597	−	6.65748i	0.136331	−	0.554790i
$145$	0.547323	+	0.547323i	0.0454527	+	0.0454527i
$146$	3.03271	+	5.19017i	0.250989	+	0.429542i
$147$	2.50348	+	1.03697i	0.206483	+	0.0855282i
$148$	7.58596	−	5.94752i	0.623562	−	0.488883i
$149$	−10.4386	−	4.32382i	−0.855166	−	0.354222i	−0.0883511	−	0.996089i	$-0.528160\pi$
$149$	−10.4386	−	4.32382i	−0.855166	−	0.354222i	−0.766815	+	0.641868i	$0.778160\pi$
$150$	11.7955	+	8.95374i	0.963097	+	0.731070i
$151$	−5.04265			−0.410365			−0.205183	−	0.978724i	$-0.565779\pi$
$151$	−5.04265			−0.410365			−0.205183	+	0.978724i	$0.565779\pi$
$152$	−19.2328	+	8.32099i	−1.55998	+	0.674921i
$153$	−3.52366	−	3.52366i	−0.284871	−	0.284871i
$154$	2.90254	+	21.1931i	0.233893	+	1.70779i
$155$	16.5372	−	6.84993i	1.32830	−	0.550200i
$156$	−3.35425	+	15.2928i	−0.268555	+	1.22441i
$157$	8.40889	−	20.3009i	0.671103	−	1.62018i	−0.108638	−	0.994081i	$-0.534649\pi$
$157$	8.40889	−	20.3009i	0.671103	−	1.62018i	0.779740	−	0.626103i	$-0.215351\pi$
$158$	−9.79411	+	5.72288i	−0.779178	+	0.455288i
$159$			8.81144i			0.698793i
$160$	−13.7799	+	11.1558i	−1.08939	+	0.881941i
$161$	4.48901	−	4.48901i	0.353783	−	0.353783i
$162$	7.99399	+	13.6809i	0.628067	+	1.07487i
$163$	−2.72128	−	6.56975i	−0.213147	−	0.514583i	0.780756	−	0.624835i	$-0.214834\pi$
$163$	−2.72128	−	6.56975i	−0.213147	−	0.514583i	−0.993904	+	0.110253i	$0.964834\pi$
$164$	0.926992	−	1.64495i	0.0723859	−	0.128449i
$165$	−39.6493	+	16.4233i	−3.08669	+	1.27855i
$166$	9.46672	+	7.18602i	0.734760	+	0.557743i
$167$			20.0856i			1.55427i	0.629336	+	0.777133i	$0.283327\pi$
$167$			20.0856i			1.55427i	−0.629336	+	0.777133i	$0.716673\pi$
$168$	13.6932	+	5.42277i	1.05646	+	0.418376i
$169$	2.46630	−	12.7639i	0.189716	−	0.981839i
$170$	1.74869	+	12.7682i	0.134118	+	0.979274i
$171$	−4.85934	+	11.7315i	−0.371603	+	0.897129i
$172$	−9.88611	−	1.19687i	−0.753808	−	0.0912605i
$173$	−4.12613	+	9.96136i	−0.313704	+	0.757348i	0.685858	+	0.727736i	$0.259427\pi$
$173$	−4.12613	+	9.96136i	−0.313704	+	0.757348i	−0.999561	+	0.0296123i	$0.990573\pi$
$174$	−0.192444	+	0.733475i	−0.0145891	+	0.0556046i
$175$	−8.17917	+	8.17917i	−0.618287	+	0.618287i
$176$	−3.81330	−	24.9373i	−0.287438	−	1.87972i
$177$	−11.1479	+	11.1479i	−0.837924	+	0.837924i
$178$	−7.00455	+	4.09288i	−0.525013	+	0.306775i
$179$	2.76851	+	1.14675i	0.206928	+	0.0857124i	0.483740	−	0.875212i	$-0.339278\pi$
$179$	2.76851	+	1.14675i	0.206928	+	0.0857124i	−0.276812	+	0.960924i	$0.589278\pi$
$180$	−1.29121	+	10.6653i	−0.0962410	+	0.794947i
$181$	−6.55352	+	2.71456i	−0.487119	+	0.201771i	−0.612705	−	0.790311i	$-0.709919\pi$
$181$	−6.55352	+	2.71456i	−0.487119	+	0.201771i	0.125586	+	0.992083i	$0.459919\pi$
$182$	−11.4791	−	4.21658i	−0.850890	−	0.312554i
$183$	6.37126	−	6.37126i	0.470977	−	0.470977i
$184$	−5.21067	+	5.37616i	−0.384136	+	0.396335i
$185$	−10.6815	+	10.6815i	−0.785318	+	0.785318i
$186$	13.9676	+	10.6026i	1.02416	+	0.777418i
$187$	−16.9415	−	7.01738i	−1.23888	−	0.513162i
$188$	−15.1187	+	4.22037i	−1.10264	+	0.307802i
$189$	−6.18716	+	2.56280i	−0.450049	+	0.186417i
$190$	28.3537	−	16.5676i	2.05699	−	1.20194i
$191$		−	5.02721i		−	0.363756i	−0.983321	−	0.181878i	$-0.941782\pi$
$191$		−	5.02721i		−	0.363756i	0.983321	−	0.181878i	$-0.0582177\pi$
$192$	−16.2469	−	6.14210i	−1.17252	−	0.443268i
$193$	−6.41936	−	6.41936i	−0.462076	−	0.462076i	0.437260	−	0.899335i	$-0.355949\pi$
$193$	−6.41936	−	6.41936i	−0.462076	−	0.462076i	−0.899335	+	0.437260i	$0.855949\pi$
$194$	−4.45628	+	16.9845i	−0.319942	+	1.21942i
$195$	2.33796	−	24.4232i	0.167425	−	1.74898i
$196$	1.22548	−	2.17461i	0.0875341	−	0.155329i
$197$	6.08283	−	14.6853i	0.433384	−	1.04628i	−0.544805	−	0.838563i	$-0.683396\pi$
$197$	6.08283	−	14.6853i	0.433384	−	1.04628i	0.978189	−	0.207718i	$-0.0666037\pi$
$198$	−12.1758	−	9.24247i	−0.865299	−	0.656833i
$199$	0.100352	−	0.100352i	0.00711376	−	0.00711376i	−0.703541	−	0.710655i	$-0.748399\pi$
$199$	0.100352	−	0.100352i	0.00711376	−	0.00711376i	0.710655	+	0.703541i	$0.248399\pi$
$200$	9.49406	−	9.79559i	0.671332	−	0.692653i
$201$	−8.68576			−0.612646
$202$	−1.45208	−	1.10225i	−0.102168	−	0.0775539i
$203$	−0.547216	−	0.226664i	−0.0384070	−	0.0159087i
$204$	−9.93581	+	7.78983i	−0.695646	+	0.545398i
$205$	−1.13233	+	2.73368i	−0.0790851	+	0.190928i
$206$	−7.14210	+	27.2212i	−0.497614	+	1.89659i
$207$			4.53671i			0.315323i
$208$	13.6138	+	4.76058i	0.943951	+	0.330087i
$209$			46.7266i			3.23215i
$210$	−22.3243	−	5.85728i	−1.54052	−	0.404191i
$211$	6.87306	−	16.5930i	0.473161	−	1.14231i	−0.489597	−	0.871949i	$-0.662856\pi$
$211$	6.87306	−	16.5930i	0.473161	−	1.14231i	0.962758	−	0.270363i	$-0.0871437\pi$
$212$	8.05801	+	0.975551i	0.553427	+	0.0670011i
$213$	18.5916	+	7.70088i	1.27387	+	0.527655i
$214$	−10.7202	+	14.1226i	−0.732821	+	0.965404i
$215$	15.6055			1.06428
$216$	7.24862	−	3.13609i	0.493206	−	0.213384i
$217$	−9.68537	+	9.68537i	−0.657486	+	0.657486i
$218$	5.02025	−	6.61358i	0.340014	−	0.447928i
$219$	3.53166	−	8.52619i	0.238648	−	0.576147i
$220$	10.6293	+	38.0773i	0.716624	+	2.56717i
$221$	8.08547	−	6.67271i	0.543888	−	0.448855i
$222$	−14.3144	−	3.75570i	−0.960718	−	0.252066i
$223$	12.7401	+	12.7401i	0.853138	+	0.853138i	0.990518	−	0.137380i	$-0.0438682\pi$
$223$	12.7401	+	12.7401i	0.853138	+	0.853138i	−0.137380	+	0.990518i	$0.543868\pi$
$224$	6.47513	−	11.9220i	0.432638	−	0.796573i
$225$		−	8.26608i		−	0.551072i
$226$	13.7244	+	23.4880i	0.912936	+	1.56240i
$227$	−25.9579	+	10.7521i	−1.72289	+	0.713643i	−0.723151	+	0.690690i	$0.757307\pi$
$227$	−25.9579	+	10.7521i	−1.72289	+	0.713643i	−0.999737	+	0.0229538i	$0.992693\pi$
$228$	28.0277	+	15.7947i	1.85618	+	1.04603i
$229$	7.15781	+	2.96486i	0.473001	+	0.195924i	0.606433	−	0.795134i	$-0.292600\pi$
$229$	7.15781	+	2.96486i	0.473001	+	0.195924i	−0.133432	+	0.991058i	$0.542600\pi$
$230$	7.09379	−	9.34522i	0.467750	−	0.616205i
$231$	23.2215	−	23.2215i	1.52786	−	1.52786i
$232$	0.649452	+	0.257195i	0.0426386	+	0.0168857i
$233$	−9.47365	+	9.47365i	−0.620639	+	0.620639i	−0.945695	−	0.325056i	$-0.894617\pi$
$233$	−9.47365	+	9.47365i	−0.620639	+	0.620639i	0.325056	+	0.945695i	$0.394617\pi$
$234$	7.93125	−	3.66986i	0.518482	−	0.239906i
$235$	22.7256	−	9.41327i	1.48246	−	0.614054i
$236$	8.96042	+	11.4289i	0.583274	+	0.743956i
$237$	16.0894	+	6.66443i	1.04512	+	0.432901i
$238$	−4.97525	−	8.51462i	−0.322497	−	0.551921i
$239$	−19.7013	+	19.7013i	−1.27437	+	1.27437i	−0.330603	+	0.943770i	$0.607252\pi$
$239$	−19.7013	+	19.7013i	−1.27437	+	1.27437i	−0.943770	+	0.330603i	$0.892748\pi$
$240$	26.4326	+	6.49538i	1.70622	+	0.419275i
$241$	2.50179	−	2.50179i	0.161155	−	0.161155i	−0.621923	−	0.783078i	$-0.713648\pi$
$241$	2.50179	−	2.50179i	0.161155	−	0.161155i	0.783078	+	0.621923i	$0.213648\pi$
$242$	−39.3626	−	10.3277i	−2.53032	−	0.663888i
$243$	6.10344	−	14.7350i	0.391536	−	0.945252i
$244$	−5.12109	−	6.53187i	−0.327844	−	0.418160i
$245$	−1.49693	+	3.61390i	−0.0956352	+	0.230884i
$246$	−2.87196	+	0.393334i	−0.183110	+	0.0250781i
$247$	−23.5934	−	12.5280i	−1.50121	−	0.797137i
$248$	11.2424	−	11.5994i	0.713893	−	0.736566i
$249$		−	18.2465i		−	1.15633i
$250$	0.474337	−	0.624883i	0.0299997	−	0.0395211i
$251$	14.5719	−	6.03588i	0.919770	−	0.380981i	0.127981	−	0.991777i	$-0.459150\pi$
$251$	14.5719	−	6.03588i	0.919770	−	0.380981i	0.791788	+	0.610795i	$0.209150\pi$
$252$	−2.21035	−	7.91817i	−0.139239	−	0.498798i
$253$	6.38862	+	15.4235i	0.401649	+	0.969666i
$254$	10.8468	−	6.33797i	0.680588	−	0.397680i
$255$	13.9902	−	13.9902i	0.876100	−	0.876100i
$256$	−7.41568	+	14.1777i	−0.463480	+	0.886107i
$257$		−	8.56324i		−	0.534160i	−0.963674	−	0.267080i	$-0.913941\pi$
$257$		−	8.56324i		−	0.534160i	0.963674	−	0.267080i	$-0.0860588\pi$
$258$	7.71303	+	13.2001i	0.480192	+	0.821800i
$259$	4.42355	−	10.6794i	0.274866	−	0.663585i
$260$	−22.0760	−	4.84204i	−1.36910	−	0.300291i
$261$	0.391052	−	0.161979i	0.0242055	−	0.0100262i
$262$	−12.1464	+	1.66353i	−0.750408	+	0.102773i
$263$	19.1394	+	19.1394i	1.18019	+	1.18019i	0.979696	+	0.200490i	$0.0642533\pi$
$263$	19.1394	+	19.1394i	1.18019	+	1.18019i	0.200490	+	0.979696i	$0.435747\pi$
$264$	−26.9546	+	27.8107i	−1.65894	+	1.71163i
$265$	−12.7198			−0.781370
$266$	−15.1936	+	20.0157i	−0.931578	+	1.22724i
$267$	11.5068	+	4.76626i	0.704203	+	0.291690i
$268$	−0.961635	+	7.94307i	−0.0587412	+	0.485200i
$269$	11.0805	+	4.58970i	0.675590	+	0.279839i	0.693982	−	0.719992i	$-0.255855\pi$
$269$	11.0805	+	4.58970i	0.675590	+	0.279839i	−0.0183918	+	0.999831i	$0.505855\pi$
$270$	−10.6862	+	6.24413i	−0.650340	+	0.380006i
$271$	−10.5883	−	10.5883i	−0.643194	−	0.643194i	0.308145	−	0.951339i	$-0.400292\pi$
$271$	−10.5883	−	10.5883i	−0.643194	−	0.643194i	−0.951339	+	0.308145i	$0.900292\pi$
$272$	6.02372	+	9.94868i	0.365242	+	0.603227i
$273$	5.49913	+	17.9511i	0.332822	+	1.08645i
$274$	−2.54144	−	4.34941i	−0.153534	−	0.262758i
$275$	−11.6403	−	28.1023i	−0.701939	−	1.69463i
$276$	11.4109	+	1.38147i	0.686853	+	0.0831545i
$277$	−5.09082	+	2.10869i	−0.305878	+	0.126699i	−0.530343	−	0.847783i	$-0.677937\pi$
$277$	−5.09082	+	2.10869i	−0.305878	+	0.126699i	0.224465	+	0.974482i	$0.427937\pi$
$278$	13.8803	−	18.2857i	0.832487	−	1.09670i
$279$		−	9.78828i		−	0.586009i
$280$	−7.82806	+	19.7669i	−0.467816	+	1.18130i
$281$	15.5337			0.926662			0.463331	−	0.886185i	$-0.346654\pi$
$281$	15.5337			0.926662			0.463331	+	0.886185i	$0.346654\pi$
$282$	19.1945	+	14.5702i	1.14302	+	0.867643i
$283$	−20.8035	+	8.61707i	−1.23664	+	0.512232i	−0.902662	−	0.430350i	$-0.858390\pi$
$283$	−20.8035	+	8.61707i	−1.23664	+	0.512232i	−0.333975	+	0.942582i	$0.608390\pi$
$284$	9.10075	−	16.1493i	0.540030	−	0.958283i
$285$	−46.5782	−	19.2933i	−2.75905	−	1.14284i
$286$	21.7960	−	23.6453i	1.28883	−	1.39818i
$287$		−	2.26421i		−	0.133652i
$288$	2.75238	+	9.29631i	0.162186	+	0.547790i
$289$	−8.54616			−0.502715
$290$	−1.05881	−	0.277803i	−0.0621754	−	0.0163131i
$291$	24.9057	−	10.3163i	1.46000	−	0.604752i
$292$	−7.40615	−	4.17366i	−0.433412	−	0.244245i
$293$	−9.22618	−	3.82161i	−0.538999	−	0.223261i	0.0965404	−	0.995329i	$-0.469222\pi$
$293$	−9.22618	−	3.82161i	−0.538999	−	0.223261i	−0.635540	+	0.772068i	$0.719222\pi$
$294$	−3.79672	+	0.519985i	−0.221429	+	0.0303261i
$295$	−16.0925	−	16.0925i	−0.936943	−	0.936943i
$296$	−5.01937	+	12.6746i	−0.291745	+	0.736696i
$297$		−	17.6107i		−	1.02188i
$298$	15.8310	−	2.16816i	0.917065	−	0.125598i
$299$	−9.50057	−	0.909461i	−0.549432	−	0.0525955i
$300$	−20.7911	−	2.51709i	−1.20037	−	0.145324i
$301$	−11.0326	+	4.56984i	−0.635907	+	0.263401i
$302$	6.15730	−	3.59782i	0.354313	−	0.207031i
$303$			2.79880i			0.160787i
$304$	17.5472	−	23.8825i	1.00640	−	1.36975i
$305$	9.19725	+	9.19725i	0.526633	+	0.526633i
$306$	6.81660	+	1.78849i	0.389679	+	0.102241i
$307$	−28.7677	+	11.9160i	−1.64186	+	0.680080i	−0.996484	−	0.0837872i	$-0.973298\pi$
$307$	−28.7677	+	11.9160i	−1.64186	+	0.680080i	−0.645374	+	0.763867i	$0.723298\pi$
$308$	−18.6650	−	23.8068i	−1.06353	−	1.35652i
$309$	39.9166	−	16.5340i	2.27078	−	0.940586i
$310$	−15.3054	+	20.1630i	−0.869286	+	1.14518i
$311$	6.50763	+	6.50763i	0.369014	+	0.369014i	0.867117	−	0.498104i	$-0.165970\pi$
$311$	6.50763	+	6.50763i	0.369014	+	0.369014i	−0.498104	+	0.867117i	$0.665970\pi$
$312$	−6.81542	−	21.0664i	−0.385847	−	1.19265i
$313$	−19.6891	+	19.6891i	−1.11289	+	1.11289i	−0.120137	+	0.992757i	$0.538334\pi$
$313$	−19.6891	+	19.6891i	−1.11289	+	1.11289i	−0.992757	+	0.120137i	$0.961666\pi$
$314$	4.21659	+	30.7878i	0.237956	+	1.73746i
$315$	4.93004	+	11.9022i	0.277776	+	0.670611i
$316$	7.87590	−	13.9758i	0.443054	−	0.786199i
$317$	−4.01104	−	9.68351i	−0.225282	−	0.543880i	0.770310	−	0.637670i	$-0.220102\pi$
$317$	−4.01104	−	9.68351i	−0.225282	−	0.543880i	−0.995592	+	0.0937903i	$0.970102\pi$
$318$	−6.28677	−	10.7592i	−0.352545	−	0.603344i
$319$	1.10136	−	1.10136i	0.0616645	−	0.0616645i
$320$	8.86644	−	23.4533i	0.495649	−	1.31108i
$321$	27.2206			1.51930
$322$	−2.27847	+	8.68409i	−0.126974	+	0.483945i
$323$	−8.24370	−	19.9021i	−0.458692	−	1.10738i
$324$	−19.5220	−	11.0014i	−1.08456	−	0.611191i
$325$	17.3104	+	1.65708i	0.960211	+	0.0919181i
$326$	8.01018	+	6.08038i	0.443643	+	0.336761i
$327$	−12.7473			−0.704926
$328$	0.0417351	+	2.66994i	0.00230443	+	0.147423i
$329$	−13.3098	+	13.3098i	−0.733791	+	0.733791i
$330$	36.6959	−	48.3425i	2.02004	−	2.66116i
$331$	−1.13652	+	2.74381i	−0.0624690	+	0.150814i	−0.952032	−	0.306000i	$-0.901009\pi$
$331$	−1.13652	+	2.74381i	−0.0624690	+	0.150814i	0.889563	+	0.456813i	$0.151009\pi$
$332$	−16.6863	−	2.02015i	−0.915782	−	0.110870i
$333$	3.16116	+	7.63170i	0.173230	+	0.418215i
$334$	−14.3306	−	24.5254i	−0.784136	−	1.34197i
$335$		−	12.5383i		−	0.685043i
$336$	−20.5891	+	3.14839i	−1.12323	+	0.171759i
$337$	−8.78902			−0.478768			−0.239384	−	0.970925i	$-0.576946\pi$
$337$	−8.78902			−0.478768			−0.239384	+	0.970925i	$0.576946\pi$
$338$	6.09531	+	17.3449i	0.331541	+	0.943441i
$339$	15.9824	−	38.5850i	0.868047	−	2.09565i
$340$	−11.2450	−	14.3429i	−0.609848	−	0.777851i
$341$	−13.7839	−	33.2773i	−0.746441	−	1.80207i
$342$	−2.43669	−	17.7917i	−0.131761	−	0.962065i
$343$		−	19.7815i		−	1.06810i
$344$	12.9253	−	5.59209i	0.696886	−	0.301505i
$345$	−18.0123			−0.969752
$346$	−2.06902	−	15.1072i	−0.111231	−	0.812166i
$347$	8.22941	+	19.8676i	0.441778	+	1.06655i	0.975325	+	0.220776i	$0.0708588\pi$
$347$	8.22941	+	19.8676i	0.441778	+	1.06655i	−0.533547	+	0.845771i	$0.679141\pi$
$348$	−0.288336	−	1.03291i	−0.0154564	−	0.0553698i
$349$	13.0592	−	5.40930i	0.699043	−	0.289553i	−0.00471912	−	0.999989i	$-0.501502\pi$
$349$	13.0592	−	5.40930i	0.699043	−	0.289553i	0.703762	+	0.710436i	$0.251502\pi$
$350$	4.15147	−	15.8228i	0.221905	−	0.845764i
$351$	8.89210	+	4.72166i	0.474625	+	0.252024i
$352$	22.4484	+	27.7288i	1.19650	+	1.47795i
$353$	−11.5113	+	11.5113i	−0.612686	+	0.612686i	−0.943645	−	0.330959i	$-0.892628\pi$
$353$	−11.5113	+	11.5113i	−0.612686	+	0.612686i	0.330959	+	0.943645i	$0.392628\pi$
$354$	5.65827	−	21.5658i	0.300734	−	1.14621i
$355$	−11.1166	+	26.8379i	−0.590009	+	1.42441i
$356$	5.63268	−	9.99518i	0.298531	−	0.529744i
$357$	−5.79379	+	13.9875i	−0.306640	+	0.740295i
$358$	−4.19866	+	0.575034i	−0.221906	+	0.0303915i
$359$			0.408626i			0.0215665i	0.999942	+	0.0107832i	$0.00343248\pi$
$359$			0.408626i			0.0215665i	−0.999942	+	0.0107832i	$0.996568\pi$
$360$	−6.03286	−	13.9441i	−0.317960	−	0.734918i
$361$	−25.3797	+	25.3797i	−1.33577	+	1.33577i
$362$	6.06536	−	7.99038i	0.318788	−	0.419965i
$363$	23.9086	+	57.7205i	1.25488	+	3.02954i
$364$	17.0250	−	3.04148i	0.892351	−	0.159417i
$365$	12.3080	+	5.09814i	0.644231	+	0.266849i
$366$	−3.23383	+	12.3253i	−0.169035	+	0.644256i
$367$	−6.37559			−0.332803			−0.166402	−	0.986058i	$-0.553215\pi$
$367$	−6.37559			−0.332803			−0.166402	+	0.986058i	$0.553215\pi$
$368$	2.52669	−	10.2822i	0.131713	−	0.535998i
$369$	1.14413	+	1.14413i	0.0595612	+	0.0595612i
$370$	5.42156	−	20.6636i	0.281853	−	1.07425i
$371$	8.99249	−	3.72481i	0.466867	−	0.193382i
$372$	−24.6198	−	2.98062i	−1.27648	−	0.154538i
$373$	2.11429	+	5.10434i	0.109474	+	0.264293i	0.969117	−	0.246602i	$-0.0793141\pi$
$373$	2.11429	+	5.10434i	0.109474	+	0.264293i	−0.859643	+	0.510895i	$0.829314\pi$
$374$	25.6930	−	3.51883i	1.32855	−	0.181954i
$375$	−1.20442			−0.0621962
$376$	15.4495	−	15.9401i	0.796745	−	0.822049i
$377$	0.260816	+	0.851394i	0.0134327	+	0.0438490i
$378$	5.72629	−	7.54370i	0.294528	−	0.388006i
$379$	9.52085	+	3.94366i	0.489053	+	0.202572i	0.613563	−	0.789646i	$-0.289736\pi$
$379$	9.52085	+	3.94366i	0.489053	+	0.202572i	−0.124510	+	0.992218i	$0.539736\pi$
$380$	−22.8005	+	40.4594i	−1.16964	+	2.07553i
$381$	−17.8186	−	7.38072i	−0.912876	−	0.378126i
$382$	3.58681	+	6.13845i	0.183517	+	0.314070i
$383$	−9.01786	−	9.01786i	−0.460791	−	0.460791i	0.438124	−	0.898915i	$-0.355643\pi$
$383$	−9.01786	−	9.01786i	−0.460791	−	0.460791i	−0.898915	+	0.438124i	$0.855643\pi$
$384$	24.2205	−	4.09207i	1.23600	−	0.208823i
$385$	33.5214	+	33.5214i	1.70841	+	1.70841i
$386$	12.4184	+	3.25825i	0.632080	+	0.165841i
$387$	3.26570	−	7.88410i	0.166005	−	0.400771i
$388$	−6.67677	−	23.9183i	−0.338962	−	1.21427i
$389$	−3.01630	−	7.28199i	−0.152932	−	0.369212i	0.828782	−	0.559572i	$-0.189034\pi$
$389$	−3.01630	−	7.28199i	−0.152932	−	0.369212i	−0.981714	+	0.190360i	$0.939034\pi$
$390$	14.5707	+	31.4899i	0.737814	+	1.59455i
$391$	−5.44215	−	5.44215i	−0.275221	−	0.275221i
$392$	0.0551735	+	3.52964i	0.00278668	+	0.178274i
$393$	13.3089	+	13.3089i	0.671346	+	0.671346i
$394$	3.05020	+	22.2713i	0.153667	+	1.12201i
$395$	−9.62045	+	23.2258i	−0.484057	+	1.16862i
$396$	21.4615	+	2.59826i	1.07848	+	0.130568i
$397$	6.37836	+	15.3987i	0.320121	+	0.772839i	0.999246	+	0.0388174i	$0.0123591\pi$
$397$	6.37836	+	15.3987i	0.320121	+	0.772839i	−0.679126	+	0.734022i	$0.737641\pi$
$398$	−0.0509352	+	0.194133i	−0.00255315	+	0.00973101i
$399$	38.5791			1.93137
$400$	−4.60373	+	18.7347i	−0.230187	+	0.936733i
$401$	−10.4675	+	10.4675i	−0.522720	+	0.522720i	−0.918392	−	0.395672i	$-0.870512\pi$
$401$	−10.4675	+	10.4675i	−0.522720	+	0.522720i	0.395672	+	0.918392i	$0.370512\pi$
$402$	10.6057	−	6.19710i	0.528964	−	0.309083i
$403$	20.4982	+	1.96223i	1.02109	+	0.0977456i
$404$	2.55948	+	0.309866i	0.127339	+	0.0154164i
$405$	32.4430	+	13.4383i	1.61210	+	0.667755i
$406$	0.829895	−	0.113660i	0.0411870	−	0.00564083i
$407$	21.4940	+	21.4940i	1.06542	+	1.06542i
$408$	6.57418	−	16.6007i	0.325470	−	0.821858i
$409$		−	29.2348i		−	1.44557i	−0.691074	−	0.722784i	$-0.742862\pi$
$409$		−	29.2348i		−	1.44557i	0.691074	−	0.722784i	$-0.257138\pi$
$410$	−0.567799	−	4.14583i	−0.0280416	−	0.204748i
$411$	−2.95957	+	7.14503i	−0.145985	+	0.352438i
$412$	−10.7009	−	38.3340i	−0.527196	−	1.88858i
$413$	16.0894	+	6.66444i	0.791706	+	0.327935i
$414$	−3.23684	−	5.53952i	−0.159082	−	0.272252i
$415$	26.3398			1.29297
$416$	−20.0197	+	3.90031i	−0.981546	+	0.191228i
$417$	−35.2446			−1.72593
$418$	−33.3384	−	57.0553i	−1.63064	−	2.79066i
$419$	−2.02823	−	0.840122i	−0.0990858	−	0.0410427i	0.332590	−	0.943072i	$-0.392078\pi$
$419$	−2.02823	−	0.840122i	−0.0990858	−	0.0410427i	−0.431676	+	0.902029i	$0.642078\pi$
$420$	31.4380	−	8.77588i	1.53402	−	0.428219i
$421$	−1.43520	+	3.46487i	−0.0699472	+	0.168867i	−0.954987	−	0.296648i	$-0.904131\pi$
$421$	−1.43520	+	3.46487i	−0.0699472	+	0.168867i	0.885040	+	0.465516i	$0.154131\pi$
$422$	3.44646	+	25.1646i	0.167771	+	1.22499i
$423$		−	13.4512i		−	0.654019i
$424$	−10.5352	+	4.55803i	−0.511636	+	0.221357i
$425$	9.91584	+	9.91584i	0.480989	+	0.480989i
$426$	−28.1955	+	3.86156i	−1.36608	+	0.187093i
$427$	−9.19545	−	3.80888i	−0.444999	−	0.184325i
$428$	3.01370	−	24.8930i	0.145673	−	1.20325i
$429$	−49.1461	−	4.70461i	−2.37280	−	0.227141i
$430$	−19.0550	+	11.1342i	−0.918912	+	0.536937i
$431$	5.70433	−	5.70433i	0.274768	−	0.274768i	−0.556248	−	0.831016i	$-0.687760\pi$
$431$	5.70433	−	5.70433i	0.274768	−	0.274768i	0.831016	+	0.556248i	$0.187760\pi$
$432$	−6.61335	+	9.00103i	−0.318185	+	0.433062i
$433$	6.59654			0.317010			0.158505	−	0.987358i	$-0.449333\pi$
$433$	6.59654			0.317010			0.158505	+	0.987358i	$0.449333\pi$
$434$	4.91596	−	18.7366i	0.235974	−	0.899384i
$435$	0.643114	+	1.55262i	0.0308350	+	0.0744422i
$436$	−1.41130	+	11.6573i	−0.0675891	+	0.558284i
$437$	−7.50506	+	18.1188i	−0.359016	+	0.866740i
$438$	1.77093	+	12.9306i	0.0846185	+	0.617849i
$439$	−1.13820	−	1.13820i	−0.0543236	−	0.0543236i	0.679423	−	0.733747i	$-0.262230\pi$
$439$	−1.13820	−	1.13820i	−0.0543236	−	0.0543236i	−0.733747	+	0.679423i	$0.762230\pi$
$440$	−40.1461	−	38.9104i	−1.91389	−	1.85498i
$441$	1.51254	+	1.51254i	0.0720255	+	0.0720255i
$442$	−5.11188	+	13.9165i	−0.243147	+	0.661940i
$443$	2.03223	+	4.90624i	0.0965541	+	0.233102i	0.964775	−	0.263075i	$-0.0847366\pi$
$443$	2.03223	+	4.90624i	0.0965541	+	0.233102i	−0.868221	+	0.496177i	$0.834737\pi$
$444$	20.1581	−	5.62712i	0.956661	−	0.267051i
$445$	−6.88035	+	16.6106i	−0.326160	+	0.787419i
$446$	−24.6460	−	6.46643i	−1.16702	−	0.306194i
$447$	−17.3461	−	17.3461i	−0.820444	−	0.820444i
$448$	0.599681	+	19.1772i	0.0283323	+	0.906036i
$449$	−11.6724	−	11.6724i	−0.550855	−	0.550855i	0.375833	−	0.926688i	$-0.377357\pi$
$449$	−11.6724	−	11.6724i	−0.550855	−	0.550855i	−0.926688	+	0.375833i	$0.877357\pi$
$450$	5.89766	+	10.0932i	0.278019	+	0.475800i
$451$	5.50090	+	2.27855i	0.259027	+	0.107293i
$452$	−33.5163	−	18.8877i	−1.57647	−	0.888405i
$453$	−10.1150	−	4.18975i	−0.475242	−	0.196852i
$454$	24.0244	−	31.6492i	1.12752	−	1.48537i
$455$	−25.9133	+	7.93828i	−1.21483	+	0.372152i
$456$	−45.4922	+	0.711110i	−2.13037	+	0.0333008i
$457$	22.7495			1.06418			0.532088	−	0.846689i	$-0.321407\pi$
$457$	22.7495			1.06418			0.532088	+	0.846689i	$0.321407\pi$
$458$	−10.8554	+	1.48671i	−0.507238	+	0.0694695i
$459$	3.10696	+	7.50087i	0.145020	+	0.350110i
$460$	−1.99422	+	16.4722i	−0.0929810	+	0.768020i
$461$	−10.4948	+	4.34707i	−0.488790	+	0.202463i	−0.613446	−	0.789737i	$-0.710217\pi$
$461$	−10.4948	+	4.34707i	−0.488790	+	0.202463i	0.124656	+	0.992200i	$0.460217\pi$
$462$	−11.7864	+	44.9225i	−0.548355	+	2.08998i
$463$	7.30883	+	7.30883i	0.339670	+	0.339670i	0.856243	−	0.516573i	$-0.172793\pi$
$463$	7.30883	+	7.30883i	0.339670	+	0.339670i	−0.516573	+	0.856243i	$0.672793\pi$
$464$	−0.976512	+	0.149324i	−0.0453334	+	0.00693218i
$465$	38.8630			1.80223
$466$	4.80850	−	18.3270i	0.222750	−	0.848981i
$467$	−0.649861	−	0.269181i	−0.0300720	−	0.0124562i	0.367597	−	0.929985i	$-0.380181\pi$
$467$	−0.649861	−	0.269181i	−0.0300720	−	0.0124562i	−0.397669	+	0.917529i	$0.630181\pi$
$468$	−7.06603	+	10.1398i	−0.326628	+	0.468714i
$469$	3.67168	+	8.86422i	0.169542	+	0.409311i
$470$	−21.0328	+	27.7083i	−0.970173	+	1.27809i
$471$	33.7344	−	33.7344i	1.55440	−	1.55440i
$472$	−19.0953	−	7.56209i	−0.878934	−	0.348074i
$473$		−	31.4024i		−	1.44389i
$474$	−24.4007	+	3.34184i	−1.12076	+	0.153496i
$475$	13.6745	−	33.0133i	0.627431	−	1.51475i
$476$	12.1500	+	6.84700i	0.556894	+	0.313832i
$477$	−2.66182	+	6.42621i	−0.121877	+	0.294236i
$478$	9.99973	−	38.1127i	0.457377	−	1.74323i
$479$	−16.2750	+	16.2750i	−0.743625	+	0.743625i	−0.973274	−	0.229649i	$-0.926242\pi$
$479$	−16.2750	+	16.2750i	−0.743625	+	0.743625i	0.229649	+	0.973274i	$0.426242\pi$
$480$	−36.9097	+	10.9279i	−1.68469	+	0.498790i
$481$	−16.6157	+	5.09004i	−0.757610	+	0.232086i
$482$	−1.26983	+	4.83978i	−0.0578390	+	0.220446i
$483$	12.7342	−	5.27466i	0.579424	−	0.240005i
$484$	55.4320	−	15.4738i	2.51964	−	0.703355i
$485$	14.8921	+	35.9527i	0.676216	+	1.63253i
$486$	3.06054	+	22.3468i	0.138829	+	1.01367i
$487$	33.9323			1.53762			0.768810	−	0.639477i	$-0.220849\pi$
$487$	33.9323			1.53762			0.768810	+	0.639477i	$0.220849\pi$
$488$	10.9134	+	4.32191i	0.494027	+	0.195644i
$489$		−	15.4391i		−	0.698182i
$490$	−0.750626	−	5.48076i	−0.0339098	−	0.247595i
$491$	−4.92763	−	11.8963i	−0.222381	−	0.536875i	0.772832	−	0.634611i	$-0.218840\pi$
$491$	−4.92763	−	11.8963i	−0.222381	−	0.536875i	−0.995212	+	0.0977365i	$0.968840\pi$
$492$	3.22616	−	2.52936i	0.145446	−	0.114032i
$493$	−0.274792	+	0.663406i	−0.0123760	+	0.0298783i
$494$	37.7471	−	1.53615i	1.69832	−	0.0691148i
$495$	−33.8776			−1.52268
$496$	−5.45151	+	22.1846i	−0.244780	+	0.996120i
$497$		−	22.2289i		−	0.997102i
$498$	13.0185	+	22.2798i	0.583373	+	0.998383i
$499$	3.11063	+	7.50973i	0.139251	+	0.336182i	0.978085	−	0.208206i	$-0.0667623\pi$
$499$	3.11063	+	7.50973i	0.139251	+	0.336182i	−0.838834	+	0.544387i	$0.816762\pi$
$500$	−0.133347	+	1.10144i	−0.00596344	+	0.0492578i
$501$	−16.6883	+	40.2892i	−0.745580	+	1.79999i
$502$	−13.4865	+	17.7668i	−0.601930	+	0.792971i
$503$	−11.4329	+	11.4329i	−0.509769	+	0.509769i	−0.914456	−	0.404686i	$-0.867381\pi$
$503$	−11.4329	+	11.4329i	−0.509769	+	0.509769i	0.404686	+	0.914456i	$0.367381\pi$
$504$	8.34837	+	8.09140i	0.371866	+	0.360419i
$505$	−4.04021			−0.179787
$506$	−18.8051	−	14.2746i	−0.835989	−	0.634584i
$507$	15.5522	−	23.5537i	0.690696	−	1.04606i
$508$	−8.72240	+	15.4779i	−0.386994	+	0.686720i
$509$	−2.20452	−	5.32219i	−0.0977138	−	0.235902i	0.867462	−	0.497503i	$-0.165750\pi$
$509$	−2.20452	−	5.32219i	−0.0977138	−	0.235902i	−0.965176	+	0.261601i	$0.915750\pi$
$510$	−7.10095	+	27.0643i	−0.314435	+	1.19843i
$511$	−10.1943			−0.450969
$512$	−1.06062	−	22.6025i	−0.0468734	−	0.998901i
$513$	14.6288	−	14.6288i	0.645879	−	0.645879i
$514$	6.10968	+	10.4561i	0.269486	+	0.461198i
$515$	23.8677	+	57.6217i	1.05174	+	2.53912i
$516$	−18.8359	−	10.6148i	−0.829204	−	0.467289i
$517$	−18.9420	−	45.7301i	−0.833070	−	2.01121i
$518$	2.21816	+	16.1961i	0.0974605	+	0.711616i
$519$	−16.5530	+	16.5530i	−0.726598	+	0.726598i
$520$	30.4105	−	9.83841i	1.33359	−	0.431443i
$521$	−17.7626	−	17.7626i	−0.778192	−	0.778192i	0.201331	−	0.979523i	$-0.435473\pi$
$521$	−17.7626	−	17.7626i	−0.778192	−	0.778192i	−0.979523	+	0.201331i	$0.935473\pi$
$522$	−0.361923	+	0.476790i	−0.0158409	+	0.0208685i
$523$	0.773760	−	0.320502i	0.0338341	−	0.0140146i	−0.365702	−	0.930732i	$-0.619171\pi$
$523$	0.773760	−	0.320502i	0.0338341	−	0.0140146i	0.399536	+	0.916717i	$0.369171\pi$
$524$	13.6444	−	10.6974i	0.596059	−	0.467320i
$525$	−23.2022	+	9.61067i	−1.01263	+	0.419444i
$526$	−37.0256	−	9.71450i	−1.61439	−	0.423573i
$527$	11.7418	+	11.7418i	0.511483	+	0.511483i
$528$	13.0705	−	53.1895i	0.568819	−	2.31478i
$529$		−	15.9932i		−	0.695358i
$530$	15.5314	−	9.07529i	0.674642	−	0.394205i
$531$	−11.4978	+	4.76254i	−0.498961	+	0.206677i
$532$	4.27125	−	35.2804i	0.185182	−	1.52960i
$533$	−2.62535	+	2.16663i	−0.113717	+	0.0938473i
$534$	−17.4509	+	2.39002i	−0.755174	+	0.103426i
$535$			39.2943i			1.69884i
$536$	−4.49301	−	10.3849i	−0.194068	−	0.448561i
$537$	4.60050	+	4.60050i	0.198526	+	0.198526i
$538$	−16.8044	+	2.30148i	−0.724491	+	0.0992238i
$539$	7.27215	+	3.01222i	0.313234	+	0.129746i
$540$	8.59325	−	15.2487i	0.369795	−	0.656200i
$541$	29.5885	−	12.2560i	1.27211	−	0.526925i	0.358504	−	0.933528i	$-0.383287\pi$
$541$	29.5885	−	12.2560i	1.27211	−	0.526925i	0.913605	+	0.406603i	$0.133287\pi$
$542$	20.4833	+	5.37427i	0.879834	+	0.230844i
$543$	−15.4010			−0.660920
$544$	−14.4534	−	7.84998i	−0.619684	−	0.336565i
$545$		−	18.4014i		−	0.788228i
$546$	−19.5224	−	17.9955i	−0.835480	−	0.770138i
$547$	−5.84533	−	2.42122i	−0.249928	−	0.103524i	0.254202	−	0.967151i	$-0.418187\pi$
$547$	−5.84533	−	2.42122i	−0.249928	−	0.103524i	−0.504131	+	0.863627i	$0.668187\pi$
$548$	6.20642	+	3.49756i	0.265125	+	0.149408i
$549$	6.57125	−	2.72190i	0.280454	−	0.116168i
$550$	34.2637	+	26.0090i	1.46101	+	1.10903i
$551$	1.82975			0.0779501
$552$	−14.9188	+	6.45457i	−0.634987	+	0.274725i
$553$		−	19.2371i		−	0.818046i
$554$	4.71162	−	6.20699i	0.200177	−	0.263710i
$555$	−30.3006	+	12.5509i	−1.28619	+	0.532757i
$556$	−3.90207	+	32.2309i	−0.165484	+	1.36690i
$557$	10.7633	+	25.9850i	0.456057	+	1.10102i	0.969980	+	0.243183i	$0.0781916\pi$
$557$	10.7633	+	25.9850i	0.456057	+	1.10102i	−0.513923	+	0.857836i	$0.671808\pi$
$558$	6.98372	+	11.9519i	0.295644	+	0.505965i
$559$	15.8559	+	8.41939i	0.670632	+	0.356102i
$560$	−4.54486	−	29.7214i	−0.192056	−	1.25596i
$561$	−28.1521	−	28.1521i	−1.18858	−	1.18858i
$562$	−18.9673	+	11.0829i	−0.800088	+	0.467506i
$563$	−42.0620	−	17.4227i	−1.77270	−	0.734277i	−0.994313	−	0.106495i	$-0.966037\pi$
$563$	−42.0620	−	17.4227i	−1.77270	−	0.734277i	−0.778389	−	0.627783i	$-0.783963\pi$
$564$	−33.8328	−	4.09600i	−1.42462	−	0.172473i
$565$	55.6995	+	23.0715i	2.34330	+	0.970625i
$566$	19.2538	−	25.3646i	0.809300	−	1.06616i
$567$	−26.8714			−1.12849
$568$	0.409734	+	26.2122i	0.0171921	+	1.09984i
$569$	24.8519	+	24.8519i	1.04184	+	1.04184i	0.999085	+	0.0427589i	$0.0136147\pi$
$569$	24.8519	+	24.8519i	1.04184	+	1.04184i	0.0427589	+	0.999085i	$0.486385\pi$
$570$	70.6394	−	9.67453i	2.95876	−	0.405221i
$571$	−14.1085	+	5.84392i	−0.590422	+	0.244561i	−0.657832	−	0.753165i	$-0.728526\pi$
$571$	−14.1085	+	5.84392i	−0.590422	+	0.244561i	0.0674104	+	0.997725i	$0.478526\pi$
$572$	−9.74350	+	44.4229i	−0.407396	+	1.85742i
$573$	4.17692	−	10.0840i	0.174494	−	0.421265i
$574$	1.61546	+	2.76470i	0.0674282	+	0.115396i
$575$		−	12.7666i		−	0.532405i
$576$	−9.99349	−	9.38744i	−0.416396	−	0.391143i
$577$	27.0530	−	27.0530i	1.12623	−	1.12623i	0.135447	−	0.990785i	$-0.456753\pi$
$577$	27.0530	−	27.0530i	1.12623	−	1.12623i	0.990785	−	0.135447i	$-0.0432471\pi$
$578$	10.4352	−	6.09750i	0.434049	−	0.253622i
$579$	−7.54286	−	18.2101i	−0.313470	−	0.756785i
$580$	1.49106	−	0.416228i	0.0619128	−	0.0172829i
$581$	−18.6214	+	7.71325i	−0.772547	+	0.319999i
$582$	−23.0506	+	30.3663i	−0.955476	+	1.25873i
$583$			25.5956i			1.06006i
$584$	12.0210	−	0.187906i	0.497434	−	0.00777562i
$585$	9.08301	−	17.1056i	0.375536	−	0.707231i
$586$	13.9922	−	1.91632i	0.578013	−	0.0791626i
$587$	−12.0551	+	29.1036i	−0.497568	+	1.20124i	0.453222	+	0.891398i	$0.350275\pi$
$587$	−12.0551	+	29.1036i	−0.497568	+	1.20124i	−0.950790	+	0.309837i	$0.899725\pi$
$588$	4.26496	−	3.34380i	0.175884	−	0.137896i
$589$	16.1927	−	39.0927i	0.667209	−	1.61079i
$590$	31.1313	+	8.16802i	1.28166	+	0.336272i
$591$	24.4029	−	24.4029i	1.00380	−	1.00380i
$592$	−2.91418	−	19.0575i	−0.119772	−	0.783257i
$593$	2.22104	−	2.22104i	0.0912070	−	0.0912070i	−0.660031	−	0.751238i	$-0.729457\pi$
$593$	2.22104	−	2.22104i	0.0912070	−	0.0912070i	0.751238	+	0.660031i	$0.229457\pi$
$594$	12.5649	+	21.5035i	0.515543	+	0.882299i
$595$	−20.1916	−	8.36365i	−0.827776	−	0.342876i
$596$	−17.7834	+	13.9425i	−0.728437	+	0.571106i
$597$	0.284673	−	0.117915i	0.0116509	−	0.00482595i
$598$	12.2495	−	5.66796i	0.500919	−	0.231780i
$599$	4.70961	−	4.70961i	0.192429	−	0.192429i	−0.604316	−	0.796745i	$-0.706553\pi$
$599$	4.70961	−	4.70961i	0.192429	−	0.192429i	0.796745	+	0.604316i	$0.206553\pi$
$600$	27.1827	−	11.7605i	1.10973	−	0.480121i
$601$	19.9255	−	19.9255i	0.812779	−	0.812779i	−0.172271	−	0.985050i	$-0.555110\pi$
$601$	19.9255	−	19.9255i	0.812779	−	0.812779i	0.985050	+	0.172271i	$0.0551105\pi$
$602$	10.2108	−	13.4515i	0.416160	−	0.548242i
$603$	−6.33454	−	2.62385i	−0.257963	−	0.106852i
$604$	−4.95137	+	8.78620i	−0.201468	+	0.357505i
$605$	−83.3225	+	34.5133i	−3.38754	+	1.40317i
$606$	−1.99688	−	3.41746i	−0.0811177	−	0.138825i
$607$		−	16.6296i		−	0.674973i	−0.941330	−	0.337487i	$-0.890423\pi$
$607$		−	16.6296i		−	0.674973i	0.941330	−	0.337487i	$-0.109577\pi$
$608$	−4.38632	+	41.6811i	−0.177889	+	1.69039i
$609$	−0.909323	−	0.909323i	−0.0368476	−	0.0368476i
$610$	−17.7923	−	4.66821i	−0.720388	−	0.189010i
$611$	28.1689	+	2.69652i	1.13959	+	0.109090i
$612$	−9.59942	+	2.67967i	−0.388033	+	0.108319i
$613$	2.95524	−	7.13459i	0.119361	−	0.288163i	−0.852895	−	0.522083i	$-0.825155\pi$
$613$	2.95524	−	7.13459i	0.119361	−	0.288163i	0.972256	+	0.233919i	$0.0751552\pi$
$614$	26.6248	−	35.0750i	1.07449	−	1.41551i
$615$	−4.54262	+	4.54262i	−0.183176	+	0.183176i
$616$	39.7764	+	15.7522i	1.60264	+	0.634673i
$617$	−24.8576			−1.00073			−0.500365	−	0.865815i	$-0.666801\pi$
$617$	−24.8576			−1.00073			−0.500365	+	0.865815i	$0.666801\pi$
$618$	−36.9433	+	48.6684i	−1.48608	+	1.95773i
$619$	−20.8214	−	8.62452i	−0.836884	−	0.346649i	−0.0772596	−	0.997011i	$-0.524617\pi$
$619$	−20.8214	−	8.62452i	−0.836884	−	0.346649i	−0.759624	+	0.650362i	$0.774617\pi$
$620$	4.30268	−	35.5399i	0.172800	−	1.42732i
$621$	2.82857	−	6.82878i	0.113507	−	0.274029i
$622$	−12.5892	−	3.30305i	−0.504779	−	0.132440i
$623$		−	13.7580i		−	0.551203i
$624$	23.3524	+	20.8604i	0.934843	+	0.835084i
$625$		−	25.8537i		−	1.03415i
$626$	9.99353	−	38.0890i	0.399422	−	1.52234i
$627$	−38.8234	+	93.7280i	−1.55046	+	3.74313i
$628$	−27.1151	−	34.5848i	−1.08201	−	1.38008i
$629$	−12.9469	−	5.36279i	−0.516228	−	0.213829i
$630$	−14.5117	−	11.0156i	−0.578161	−	0.438872i
$631$	25.2915			1.00684			0.503420	−	0.864042i	$-0.332075\pi$
$631$	25.2915			1.00684			0.503420	+	0.864042i	$0.332075\pi$
$632$	0.354589	+	22.6843i	0.0141048	+	0.902334i
$633$	27.5731	−	27.5731i	1.09593	−	1.09593i
$634$	11.8066	+	8.96220i	0.468901	+	0.355934i
$635$	10.6545	−	25.7221i	0.422809	−	1.02075i
$636$	15.3529	+	8.65194i	0.608780	+	0.343072i
$637$	−3.47070	+	2.86427i	−0.137514	+	0.113487i
$638$	−0.559014	+	2.13061i	−0.0221316	+	0.0843517i
$639$	11.2325	+	11.2325i	0.444352	+	0.444352i
$640$	5.90712	+	34.9636i	0.233499	+	1.38206i
$641$			44.1449i			1.74362i	0.489847	+	0.871809i	$0.337053\pi$
$641$			44.1449i			1.74362i	−0.489847	+	0.871809i	$0.662947\pi$
$642$	−33.2375	+	19.4213i	−1.31178	+	0.766496i
$643$	−6.05068	+	2.50627i	−0.238615	+	0.0988378i	−0.498787	−	0.866725i	$-0.666221\pi$
$643$	−6.05068	+	2.50627i	−0.238615	+	0.0988378i	0.260171	+	0.965562i	$0.416221\pi$
$644$	−3.41380	−	12.2293i	−0.134522	−	0.481902i
$645$	31.3027	+	12.9660i	1.23254	+	0.510536i
$646$	24.2656	+	18.4196i	0.954718	+	0.724709i
$647$	35.1448	−	35.1448i	1.38169	−	1.38169i	0.540057	−	0.841629i	$-0.318403\pi$
$647$	35.1448	−	35.1448i	1.38169	−	1.38169i	0.841629	−	0.540057i	$-0.181597\pi$
$648$	31.6865	−	0.495307i	1.24476	−	0.0194575i
$649$	−32.3825	+	32.3825i	−1.27112	+	1.27112i
$650$	−22.3191	+	10.3273i	−0.875428	+	0.405069i
$651$	−27.4749	+	11.3805i	−1.07683	+	0.446036i
$652$	−14.1190	−	1.70933i	−0.552943	−	0.0669425i
$653$	−7.12342	−	2.95062i	−0.278761	−	0.115467i	0.238923	−	0.971039i	$-0.423206\pi$
$653$	−7.12342	−	2.95062i	−0.278761	−	0.115467i	−0.517684	+	0.855572i	$0.673206\pi$
$654$	15.5650	−	9.09490i	0.608639	−	0.355639i
$655$	−19.2121	+	19.2121i	−0.750680	+	0.750680i
$656$	−1.95591	−	3.23034i	−0.0763653	−	0.126124i
$657$	5.15130	−	5.15130i	0.200972	−	0.200972i
$658$	6.75559	−	25.7480i	0.263360	−	1.00376i
$659$	10.4079	−	25.1268i	0.405432	−	0.978801i	−0.580891	−	0.813981i	$-0.697296\pi$
$659$	10.4079	−	25.1268i	0.405432	−	0.978801i	0.986324	−	0.164819i	$-0.0527041\pi$
$660$	−10.3160	+	85.2100i	−0.401551	+	3.31679i
$661$	9.72994	−	23.4902i	0.378451	−	0.913661i	−0.613806	−	0.789457i	$-0.710362\pi$
$661$	9.72994	−	23.4902i	0.378451	−	0.913661i	0.992257	−	0.124204i	$-0.0396377\pi$
$662$	−0.569904	−	4.16120i	−0.0221499	−	0.161730i
$663$	21.7626	−	6.66675i	0.845189	−	0.258915i
$664$	21.8161	−	9.43865i	0.846629	−	0.366291i
$665$			55.6910i			2.15960i
$666$	−9.30496	−	7.06323i	−0.360560	−	0.273695i
$667$	0.603964	−	0.250170i	0.0233856	−	0.00968662i
$668$	34.9966	+	19.7220i	1.35406	+	0.763066i
$669$	14.9698	+	36.1403i	0.578766	+	1.39726i
$670$	8.94584	+	15.3099i	0.345608	+	0.591472i
$671$	18.5074	−	18.5074i	0.714468	−	0.714468i
$672$	22.8939	−	18.5342i	0.883151	−	0.714972i
$673$		−	15.9178i		−	0.613585i	−0.951776	−	0.306793i	$-0.900744\pi$
$673$		−	15.9178i		−	0.613585i	0.951776	−	0.306793i	$-0.0992558\pi$
$674$	10.7318	−	6.27077i	0.413373	−	0.241541i
$675$	−5.15378	+	12.4423i	−0.198369	+	0.478906i
$676$	−19.8179	−	16.8301i	−0.762226	−	0.647311i
$677$	−0.322826	+	0.133719i	−0.0124072	+	0.00513924i	−0.388878	−	0.921289i	$-0.627137\pi$
$677$	−0.322826	+	0.133719i	−0.0124072	+	0.00513924i	0.376471	+	0.926428i	$0.377137\pi$
$678$	8.01431	+	58.5171i	0.307788	+	2.24734i
$679$	−21.0565	−	21.0565i	−0.808074	−	0.808074i
$680$	23.9640	+	9.49018i	0.918977	+	0.363932i
$681$	−61.0020			−2.33760
$682$	40.5734	+	30.7985i	1.55364	+	1.17934i
$683$	−4.38400	−	1.81591i	−0.167749	−	0.0694839i	0.297229	−	0.954806i	$-0.403938\pi$
$683$	−4.38400	−	1.81591i	−0.167749	−	0.0694839i	−0.464978	+	0.885322i	$0.653938\pi$
$684$	15.6693	+	19.9859i	0.599130	+	0.764181i
$685$	−10.3142	−	4.27229i	−0.394086	−	0.163236i
$686$	14.1137	+	24.1541i	0.538862	+	0.922207i
$687$	11.8943	+	11.8943i	0.453796	+	0.453796i
$688$	−11.7925	+	16.0501i	−0.449587	+	0.611905i
$689$	−12.9239	−	6.86252i	−0.492360	−	0.261441i
$690$	21.9939	−	12.8514i	0.837292	−	0.489245i
$691$	13.5230	+	32.6473i	0.514437	+	1.24196i	0.941277	+	0.337634i	$0.109627\pi$
$691$	13.5230	+	32.6473i	0.514437	+	1.24196i	−0.426840	+	0.904327i	$0.640373\pi$
$692$	13.3050	+	16.9703i	0.505780	+	0.645114i
$693$	23.9504	−	9.92058i	0.909800	−	0.376852i
$694$	−24.2235	−	18.3877i	−0.919513	−	0.697986i
$695$		−	50.8774i		−	1.92989i
$696$	1.08903	+	1.05551i	0.0412795	+	0.0400089i
$697$	−2.74496			−0.103973
$698$	−12.0864	+	15.9224i	−0.457479	+	0.602673i
$699$	−26.8743	+	11.1317i	−1.01648	+	0.421039i
$700$	6.22009	+	22.2823i	0.235097	+	0.842192i
$701$	28.3089	+	11.7259i	1.06921	+	0.442882i	0.846712	−	0.532051i	$-0.178579\pi$
$701$	28.3089	+	11.7259i	1.06921	+	0.442882i	0.222499	+	0.974933i	$0.428579\pi$
$702$	−14.2264	+	0.578959i	−0.536943	+	0.0218514i
$703$			35.7092i			1.34680i
$704$	−47.1944	−	17.8417i	−1.77871	−	0.672434i
$705$	53.4060			2.01139
$706$	5.84276	−	22.2689i	0.219895	−	0.838102i
$707$	2.85630	−	1.18312i	0.107422	−	0.0444958i
$708$	8.47771	+	30.3698i	0.318612	+	1.14137i
$709$	11.7106	+	4.85069i	0.439801	+	0.182172i	0.591586	−	0.806242i	$-0.298502\pi$
$709$	11.7106	+	4.85069i	0.439801	+	0.182172i	−0.151785	+	0.988414i	$0.548502\pi$
$710$	−5.57437	−	40.7017i	−0.209202	−	1.52751i
$711$	9.72077	+	9.72077i	0.364557	+	0.364557i
$712$	0.253595	+	16.2234i	0.00950386	+	0.607996i
$713$		−	15.1176i		−	0.566159i
$714$	−2.90527	−	21.2130i	−0.108727	−	0.793878i
$715$	6.79135	−	70.9450i	0.253982	−	2.65319i
$716$	4.71647	−	3.69779i	0.176263	−	0.138193i
$717$	−55.8876	+	23.1494i	−2.08716	+	0.864530i
$718$	−0.291546	−	0.498951i	−0.0108804	−	0.0186207i
$719$			7.01089i			0.261462i	0.991418	+	0.130731i	$0.0417324\pi$
$719$			7.01089i			0.261462i	−0.991418	+	0.130731i	$0.958268\pi$
$720$	17.3152	+	12.7220i	0.645299	+	0.474122i
$721$	−33.7474	−	33.7474i	−1.25682	−	1.25682i
$722$	12.8819	−	49.0976i	0.479413	−	1.82722i
$723$	7.09694	−	2.93965i	0.263938	−	0.109327i
$724$	−1.70511	+	14.0841i	−0.0633698	+	0.523432i
$725$	−1.10045	+	0.455821i	−0.0408696	+	0.0169288i
$726$	−70.3757	−	53.4210i	−2.61189	−	1.98264i
$727$	−5.01376	−	5.01376i	−0.185950	−	0.185950i	0.607993	−	0.793943i	$-0.291975\pi$
$727$	−5.01376	−	5.01376i	−0.185950	−	0.185950i	−0.793943	+	0.607993i	$0.791975\pi$
$728$	−18.6182	+	15.8607i	−0.690037	+	0.587838i
$729$	0.717732	−	0.717732i	0.0265827	−	0.0265827i
$730$	−18.6660	+	2.55644i	−0.690861	+	0.0946179i
$731$	5.54015	+	13.3751i	0.204910	+	0.494696i
$732$	−4.84521	−	17.3571i	−0.179084	−	0.641535i
$733$	17.2885	+	41.7381i	0.638565	+	1.54163i	0.828592	+	0.559853i	$0.189142\pi$
$733$	17.2885	+	41.7381i	0.638565	+	1.54163i	−0.190027	+	0.981779i	$0.560858\pi$
$734$	7.78488	−	4.54884i	0.287345	−	0.167901i
$735$	−6.00531	+	6.00531i	−0.221509	+	0.221509i
$736$	4.25094	+	14.3578i	0.156692	+	0.529235i
$737$	−25.2305			−0.929379
$738$	−2.21335	−	0.580723i	−0.0814746	−	0.0213767i
$739$	−14.8787	−	35.9205i	−0.547324	−	1.32136i	−0.919462	−	0.393179i	$-0.871375\pi$
$739$	−14.8787	−	35.9205i	−0.547324	−	1.32136i	0.372138	−	0.928177i	$-0.378625\pi$
$740$	8.12304	+	29.0993i	0.298609	+	1.06971i
$741$	−36.9165	−	44.7325i	−1.35616	−	1.64329i
$742$	−8.32265	+	10.9641i	−0.305534	+	0.402505i
$743$	−50.8040			−1.86382			−0.931909	−	0.362692i	$-0.881858\pi$
$743$	−50.8040			−1.86382			−0.931909	+	0.362692i	$0.881858\pi$
$744$	32.1884	−	13.9262i	1.18009	−	0.510560i
$745$	25.0401	−	25.0401i	0.917397	−	0.917397i
$746$	−6.22348	−	4.72413i	−0.227858	−	0.172963i
$747$	5.51204	−	13.3072i	0.201675	−	0.486887i
$748$	−28.8617	+	22.6281i	−1.05529	+	0.827364i
$749$	−11.5068	−	27.7798i	−0.420449	−	1.01505i
$750$	1.47066	−	0.859330i	0.0537007	−	0.0313783i
$751$		−	20.7002i		−	0.755362i	−0.925936	−	0.377681i	$-0.876722\pi$
$751$		−	20.7002i		−	0.755362i	0.925936	−	0.377681i	$-0.123278\pi$
$752$	−7.49154	+	30.4864i	−0.273188	+	1.11173i
$753$	34.2445			1.24794
$754$	−0.925919	−	0.853504i	−0.0337200	−	0.0310828i
$755$	6.04813	−	14.6015i	0.220114	−	0.531402i
$756$	−1.60979	+	13.2968i	−0.0585473	+	0.483599i
$757$	8.78378	+	21.2059i	0.319252	+	0.770743i	0.999294	+	0.0375694i	$0.0119615\pi$
$757$	8.78378	+	21.2059i	0.319252	+	0.770743i	−0.680042	+	0.733173i	$0.738038\pi$
$758$	−14.4391	+	1.97753i	−0.524452	+	0.0718271i
$759$			36.2457i			1.31564i
$760$	−1.02652	−	65.6704i	−0.0372359	−	2.38212i
$761$	−27.3504			−0.991451			−0.495726	−	0.868479i	$-0.665098\pi$
$761$	−27.3504			−0.991451			−0.495726	+	0.868479i	$0.665098\pi$
$762$	27.0233	−	3.70102i	0.978952	−	0.134074i
$763$	5.38858	+	13.0092i	0.195080	+	0.470964i
$764$	−8.75930	−	4.93621i	−0.316900	−	0.178586i
$765$	14.4293	−	5.97683i	0.521694	−	0.216093i
$766$	17.4452	+	4.57716i	0.630322	+	0.165379i
$767$	−7.66857	−	25.0329i	−0.276896	−	0.903885i
$768$	−26.6547	+	22.2774i	−0.961818	+	0.803866i
$769$	−5.90601	+	5.90601i	−0.212976	+	0.212976i	−0.805531	−	0.592554i	$-0.798120\pi$

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22104 + 0.713478i) q^{2} +(2.00588 + 0.830863i) q^{3} +(0.981898 - 1.74238i) q^{4} +(-1.19939 + 2.89559i) q^{5} +(-3.04207 + 0.416631i) q^{6} -2.39832i q^{7} +(0.0442070 + 2.82808i) q^{8} +(1.21190 + 1.21190i) q^{9} +O(q^{10})\)	\(q+(-1.22104 + 0.713478i) q^{2} +(2.00588 + 0.830863i) q^{3} +(0.981898 - 1.74238i) q^{4} +(-1.19939 + 2.89559i) q^{5} +(-3.04207 + 0.416631i) q^{6} -2.39832i q^{7} +(0.0442070 + 2.82808i) q^{8} +(1.21190 + 1.21190i) q^{9} +(-0.601429 - 4.39139i) q^{10} +(5.82672 + 2.41351i) q^{11} +(3.41724 - 2.67918i) q^{12} +(-2.78085 + 2.29496i) q^{13} +(1.71115 + 2.92845i) q^{14} +(-4.81168 + 4.81168i) q^{15} +(-2.07175 - 3.42167i) q^{16} -2.90755 q^{17} +(-2.34445 - 0.615119i) q^{18} +(2.83528 + 6.84496i) q^{19} +(3.86753 + 4.93297i) q^{20} +(1.99267 - 4.81074i) q^{21} +(-8.83666 + 1.21024i) q^{22} +(1.87173 + 1.87173i) q^{23} +(-2.26107 + 5.70952i) q^{24} +(-3.41038 - 3.41038i) q^{25} +(1.75814 - 4.78633i) q^{26} +(-1.06858 - 2.57979i) q^{27} +(-4.17877 - 2.35490i) q^{28} +(0.0945097 - 0.228167i) q^{29} +(2.44224 - 9.30830i) q^{30} +(-4.03840 - 4.03840i) q^{31} +(4.97099 + 2.69986i) q^{32} +(9.68240 + 9.68240i) q^{33} +(3.55025 - 2.07447i) q^{34} +(6.94455 + 2.87653i) q^{35} +(3.30155 - 0.921625i) q^{36} +(4.45287 + 1.84444i) q^{37} +(-8.34573 - 6.33509i) q^{38} +(-7.48486 + 2.29291i) q^{39} +(-8.24199 - 3.26398i) q^{40} +0.944082 q^{41} +(0.999215 + 7.29585i) q^{42} +(-1.90544 - 4.60013i) q^{43} +(9.92648 - 7.78252i) q^{44} +(-4.96272 + 2.05562i) q^{45} +(-3.62091 - 0.950028i) q^{46} +(-5.54962 - 5.54962i) q^{47} +(-1.31275 - 8.58480i) q^{48} +1.24807 q^{49} +(6.59745 + 1.73099i) q^{50} +(-5.83219 - 2.41577i) q^{51} +(1.26817 + 7.09871i) q^{52} +(1.55309 + 3.74950i) q^{53} +(3.14541 + 2.38763i) q^{54} +(-13.9771 + 13.9771i) q^{55} +(6.78264 - 0.106023i) q^{56} +16.0859i q^{57} +(0.0473914 + 0.346032i) q^{58} +(-2.77880 + 6.70861i) q^{59} +(3.65918 + 13.1083i) q^{60} +(1.58815 - 3.83412i) q^{61} +(7.81237 + 2.04975i) q^{62} +(2.90652 - 2.90652i) q^{63} +(-7.99609 + 0.250042i) q^{64} +(-3.30993 - 10.8048i) q^{65} +(-18.7308 - 4.91446i) q^{66} +(-3.69601 + 1.53094i) q^{67} +(-2.85492 + 5.06605i) q^{68} +(2.19932 + 5.30962i) q^{69} +(-10.5319 + 1.44242i) q^{70} +9.26853 q^{71} +(-3.37378 + 3.48093i) q^{72} -4.25060i q^{73} +(-6.75311 + 0.924883i) q^{74} +(-4.00725 - 9.67436i) q^{75} +(14.7105 + 1.78093i) q^{76} +(5.78835 - 13.9743i) q^{77} +(7.50340 - 8.14003i) q^{78} +8.02110 q^{79} +(12.3926 - 1.89502i) q^{80} -11.2043i q^{81} +(-1.15277 + 0.673582i) q^{82} +(-3.21611 - 7.76437i) q^{83} +(-6.42552 - 8.19564i) q^{84} +(3.48730 - 8.41908i) q^{85} +(5.60872 + 4.25748i) q^{86} +(0.379150 - 0.379150i) q^{87} +(-6.56801 + 16.5851i) q^{88} +5.73652 q^{89} +(4.59305 - 6.05080i) q^{90} +(5.50405 + 6.66937i) q^{91} +(5.09911 - 1.42341i) q^{92} +(-4.74519 - 11.4559i) q^{93} +(10.7359 + 2.81680i) q^{94} -23.2208 q^{95} +(7.72799 + 9.54581i) q^{96} +(8.77970 - 8.77970i) q^{97} +(-1.52395 + 0.890470i) q^{98} +(4.13647 + 9.98633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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