LMFDB - Embedded newform 156.3.f.a.79.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			79.8
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25145 + 1.56009i) q^{2} +1.73205i q^{3} +(-0.867741 - 3.90474i) q^{4} +6.81265 q^{5} +(-2.70215 - 2.16758i) q^{6} -11.2335i q^{7} +(7.17767 + 3.53285i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.25145 + 1.56009i) q^{2} +1.73205i q^{3} +(-0.867741 - 3.90474i) q^{4} +6.81265 q^{5} +(-2.70215 - 2.16758i) q^{6} -11.2335i q^{7} +(7.17767 + 3.53285i) q^{8} -3.00000 q^{9} +(-8.52570 + 10.6283i) q^{10} -21.6848i q^{11} +(6.76322 - 1.50297i) q^{12} +3.60555 q^{13} +(17.5252 + 14.0581i) q^{14} +11.7999i q^{15} +(-14.4941 + 6.77661i) q^{16} +12.4717 q^{17} +(3.75435 - 4.68026i) q^{18} +18.7491i q^{19} +(-5.91161 - 26.6017i) q^{20} +19.4569 q^{21} +(33.8302 + 27.1375i) q^{22} +21.4197i q^{23} +(-6.11907 + 12.4321i) q^{24} +21.4122 q^{25} +(-4.51217 + 5.62497i) q^{26} -5.19615i q^{27} +(-43.8638 + 9.74774i) q^{28} -15.8535 q^{29} +(-18.4088 - 14.7669i) q^{30} +8.39825i q^{31} +(7.56650 - 31.0926i) q^{32} +37.5592 q^{33} +(-15.6078 + 19.4570i) q^{34} -76.5297i q^{35} +(2.60322 + 11.7142i) q^{36} -24.5135 q^{37} +(-29.2502 - 23.4636i) q^{38} +6.24500i q^{39} +(48.8990 + 24.0680i) q^{40} +55.7495 q^{41} +(-24.3494 + 30.3545i) q^{42} -0.733115i q^{43} +(-84.6737 + 18.8168i) q^{44} -20.4379 q^{45} +(-33.4166 - 26.8057i) q^{46} -16.3100i q^{47} +(-11.7374 - 25.1044i) q^{48} -77.1908 q^{49} +(-26.7963 + 33.4049i) q^{50} +21.6017i q^{51} +(-3.12868 - 14.0788i) q^{52} +57.0664 q^{53} +(8.10645 + 6.50273i) q^{54} -147.731i q^{55} +(39.6861 - 80.6302i) q^{56} -32.4744 q^{57} +(19.8399 - 24.7328i) q^{58} +14.3960i q^{59} +(46.0754 - 10.2392i) q^{60} -93.9673 q^{61} +(-13.1020 - 10.5100i) q^{62} +33.7004i q^{63} +(39.0380 + 50.7152i) q^{64} +24.5634 q^{65} +(-47.0035 + 58.5956i) q^{66} +13.0219i q^{67} +(-10.8222 - 48.6989i) q^{68} -37.1000 q^{69} +(119.393 + 95.7731i) q^{70} +115.800i q^{71} +(-21.5330 - 10.5985i) q^{72} +35.5392 q^{73} +(30.6775 - 38.2432i) q^{74} +37.0870i q^{75} +(73.2104 - 16.2694i) q^{76} -243.596 q^{77} +(-9.74274 - 7.81531i) q^{78} +48.5745i q^{79} +(-98.7429 + 46.1667i) q^{80} +9.00000 q^{81} +(-69.7678 + 86.9741i) q^{82} +31.4825i q^{83} +(-16.8836 - 75.9744i) q^{84} +84.9655 q^{85} +(1.14372 + 0.917458i) q^{86} -27.4591i q^{87} +(76.6091 - 155.647i) q^{88} +56.9132 q^{89} +(25.5771 - 31.8850i) q^{90} -40.5028i q^{91} +(83.6385 - 18.5868i) q^{92} -14.5462 q^{93} +(25.4450 + 20.4111i) q^{94} +127.731i q^{95} +(53.8539 + 13.1056i) q^{96} +15.6037 q^{97} +(96.6005 - 120.424i) q^{98} +65.0544i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.25145	+	1.56009i	−0.625726	+	0.780043i
$2$	−1.25145	+	1.56009i	−0.625726	+	0.780043i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−0.867741	−	3.90474i	−0.216935	−	0.976186i
$5$	6.81265			1.36253			0.681265	−	0.732037i	$-0.261430\pi$
$5$	6.81265			1.36253			0.681265	+	0.732037i	$0.261430\pi$
$6$	−2.70215	−	2.16758i	−0.450358	−	0.361263i
$7$		−	11.2335i		−	1.60478i	−0.596799	−	0.802391i	$-0.703561\pi$
$7$		−	11.2335i		−	1.60478i	0.596799	−	0.802391i	$-0.296439\pi$
$8$	7.17767	+	3.53285i	0.897209	+	0.441606i
$9$	−3.00000			−0.333333
$10$	−8.52570	+	10.6283i	−0.852570	+	1.06283i
$11$		−	21.6848i		−	1.97135i	−0.168665	−	0.985673i	$-0.553946\pi$
$11$		−	21.6848i		−	1.97135i	0.168665	−	0.985673i	$-0.446054\pi$
$12$	6.76322	−	1.50297i	0.563601	−	0.125248i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$	17.5252	+	14.0581i	1.25180	+	1.00415i
$15$			11.7999i			0.786657i
$16$	−14.4941	+	6.77661i	−0.905878	+	0.423538i
$17$	12.4717			0.733631			0.366816	−	0.930294i	$-0.380448\pi$
$17$	12.4717			0.733631			0.366816	+	0.930294i	$0.380448\pi$
$18$	3.75435	−	4.68026i	0.208575	−	0.260014i
$19$			18.7491i			0.986794i	0.869804	+	0.493397i	$0.164245\pi$
$19$			18.7491i			0.986794i	−0.869804	+	0.493397i	$0.835755\pi$
$20$	−5.91161	−	26.6017i	−0.295581	−	1.33008i
$21$	19.4569			0.926521
$22$	33.8302	+	27.1375i	1.53774	+	1.23352i
$23$			21.4197i			0.931292i	0.884971	+	0.465646i	$0.154178\pi$
$23$			21.4197i			0.931292i	−0.884971	+	0.465646i	$0.845822\pi$
$24$	−6.11907	+	12.4321i	−0.254961	+	0.518004i
$25$	21.4122			0.856488
$26$	−4.51217	+	5.62497i	−0.173545	+	0.216345i
$27$		−	5.19615i		−	0.192450i
$28$	−43.8638	+	9.74774i	−1.56656	+	0.348133i
$29$	−15.8535			−0.546673			−0.273336	−	0.961919i	$-0.588127\pi$
$29$	−15.8535			−0.546673			−0.273336	+	0.961919i	$0.588127\pi$
$30$	−18.4088	−	14.7669i	−0.613627	−	0.492231i
$31$			8.39825i			0.270911i	0.990783	+	0.135456i	$0.0432498\pi$
$31$			8.39825i			0.270911i	−0.990783	+	0.135456i	$0.956750\pi$
$32$	7.56650	−	31.0926i	0.236453	−	0.971643i
$33$	37.5592			1.13816
$34$	−15.6078	+	19.4570i	−0.459052	+	0.572264i
$35$		−	76.5297i		−	2.18656i
$36$	2.60322	+	11.7142i	0.0723117	+	0.325395i
$37$	−24.5135			−0.662527			−0.331264	−	0.943538i	$-0.607475\pi$
$37$	−24.5135			−0.662527			−0.331264	+	0.943538i	$0.607475\pi$
$38$	−29.2502	−	23.4636i	−0.769742	−	0.617462i
$39$			6.24500i			0.160128i
$40$	48.8990	+	24.0680i	1.22247	+	0.601701i
$41$	55.7495			1.35974			0.679872	−	0.733331i	$-0.262035\pi$
$41$	55.7495			1.35974			0.679872	+	0.733331i	$0.262035\pi$
$42$	−24.3494	+	30.3545i	−0.579748	+	0.722726i
$43$		−	0.733115i		−	0.0170492i	−0.999964	−	0.00852459i	$-0.997287\pi$
$43$		−	0.733115i		−	0.0170492i	0.999964	−	0.00852459i	$-0.00271350\pi$
$44$	−84.6737	+	18.8168i	−1.92440	+	0.427655i
$45$	−20.4379			−0.454177
$46$	−33.4166	−	26.8057i	−0.726448	−	0.582733i
$47$		−	16.3100i		−	0.347020i	−0.984832	−	0.173510i	$-0.944489\pi$
$47$		−	16.3100i		−	0.347020i	0.984832	−	0.173510i	$-0.0555110\pi$
$48$	−11.7374	−	25.1044i	−0.244530	−	0.523009i
$49$	−77.1908			−1.57532
$50$	−26.7963	+	33.4049i	−0.535926	+	0.668097i
$51$			21.6017i			0.423562i
$52$	−3.12868	−	14.0788i	−0.0601670	−	0.270745i
$53$	57.0664			1.07672			0.538362	−	0.842714i	$-0.319043\pi$
$53$	57.0664			1.07672			0.538362	+	0.842714i	$0.319043\pi$
$54$	8.10645	+	6.50273i	0.150119	+	0.120421i
$55$		−	147.731i		−	2.68602i
$56$	39.6861	−	80.6302i	0.708680	−	1.43982i
$57$	−32.4744			−0.569726
$58$	19.8399	−	24.7328i	0.342067	−	0.426428i
$59$			14.3960i			0.244000i	0.992530	+	0.122000i	$0.0389308\pi$
$59$			14.3960i			0.244000i	−0.992530	+	0.122000i	$0.961069\pi$
$60$	46.0754	−	10.2392i	0.767924	−	0.170654i
$61$	−93.9673			−1.54045			−0.770224	−	0.637774i	$-0.779855\pi$
$61$	−93.9673			−1.54045			−0.770224	+	0.637774i	$0.779855\pi$
$62$	−13.1020	−	10.5100i	−0.211323	−	0.169516i
$63$			33.7004i			0.534927i
$64$	39.0380	+	50.7152i	0.609969	+	0.792425i
$65$	24.5634			0.377898
$66$	−47.0035	+	58.5956i	−0.712174	+	0.887812i
$67$			13.0219i			0.194357i	0.995267	+	0.0971783i	$0.0309817\pi$
$67$			13.0219i			0.194357i	−0.995267	+	0.0971783i	$0.969018\pi$
$68$	−10.8222	−	48.6989i	−0.159150	−	0.716161i
$69$	−37.1000			−0.537681
$70$	119.393	+	95.7731i	1.70561	+	1.36819i
$71$			115.800i			1.63099i	0.578762	+	0.815496i	$0.303536\pi$
$71$			115.800i			1.63099i	−0.578762	+	0.815496i	$0.696464\pi$
$72$	−21.5330	−	10.5985i	−0.299070	−	0.147202i
$73$	35.5392			0.486839			0.243419	−	0.969921i	$-0.421731\pi$
$73$	35.5392			0.486839			0.243419	+	0.969921i	$0.421731\pi$
$74$	30.6775	−	38.2432i	0.414560	−	0.516800i
$75$			37.0870i			0.494493i
$76$	73.2104	−	16.2694i	0.963295	−	0.214070i
$77$	−243.596			−3.16358
$78$	−9.74274	−	7.81531i	−0.124907	−	0.100196i
$79$			48.5745i			0.614868i	0.951569	+	0.307434i	$0.0994702\pi$
$79$			48.5745i			0.614868i	−0.951569	+	0.307434i	$0.900530\pi$
$80$	−98.7429	+	46.1667i	−1.23429	+	0.577083i
$81$	9.00000			0.111111
$82$	−69.7678	+	86.9741i	−0.850827	+	1.06066i
$83$			31.4825i			0.379307i	0.981851	+	0.189653i	$0.0607364\pi$
$83$			31.4825i			0.379307i	−0.981851	+	0.189653i	$0.939264\pi$
$84$	−16.8836	−	75.9744i	−0.200995	−	0.904457i
$85$	84.9655			0.999594
$86$	1.14372	+	0.917458i	0.0132991	+	0.0106681i
$87$		−	27.4591i		−	0.315622i
$88$	76.6091	−	155.647i	0.870558	−	1.76871i
$89$	56.9132			0.639475			0.319737	−	0.947506i	$-0.396405\pi$
$89$	56.9132			0.639475			0.319737	+	0.947506i	$0.396405\pi$
$90$	25.5771	−	31.8850i	0.284190	−	0.354277i
$91$		−	40.5028i		−	0.445086i
$92$	83.6385	−	18.5868i	0.909114	−	0.202030i
$93$	−14.5462			−0.156411
$94$	25.4450	+	20.4111i	0.270691	+	0.217140i
$95$			127.731i			1.34454i
$96$	53.8539	+	13.1056i	0.560978	+	0.136516i
$97$	15.6037			0.160862			0.0804312	−	0.996760i	$-0.474370\pi$
$97$	15.6037			0.160862			0.0804312	+	0.996760i	$0.474370\pi$
$98$	96.6005	−	120.424i	0.985719	−	1.22882i
$99$			65.0544i			0.657116i
$100$	−18.5802	−	83.6091i	−0.185802	−	0.836091i
$101$	180.316			1.78530			0.892652	−	0.450746i	$-0.148842\pi$
$101$	180.316			1.78530			0.892652	+	0.450746i	$0.148842\pi$
$102$	−33.7005	−	27.0334i	−0.330397	−	0.265034i
$103$		−	169.697i		−	1.64754i	−0.566924	−	0.823770i	$-0.691867\pi$
$103$		−	169.697i		−	1.64754i	0.566924	−	0.823770i	$-0.308133\pi$
$104$	25.8795	+	12.7379i	0.248841	+	0.122479i
$105$	132.553			1.26241
$106$	−71.4158	+	89.0285i	−0.673734	+	0.839892i
$107$			59.2954i			0.554162i	0.960846	+	0.277081i	$0.0893671\pi$
$107$			59.2954i			0.554162i	−0.960846	+	0.277081i	$0.910633\pi$
$108$	−20.2896	+	4.50891i	−0.187867	+	0.0417492i
$109$	73.7243			0.676369			0.338185	−	0.941080i	$-0.390187\pi$
$109$	73.7243			0.676369			0.338185	+	0.941080i	$0.390187\pi$
$110$	230.473	+	184.878i	2.09521	+	1.68071i
$111$		−	42.4587i		−	0.382510i
$112$	76.1248	+	162.818i	0.679686	+	1.45374i
$113$	−86.2549			−0.763318			−0.381659	−	0.924303i	$-0.624647\pi$
$113$	−86.2549			−0.763318			−0.381659	+	0.924303i	$0.624647\pi$
$114$	40.6401	−	50.6628i	0.356492	−	0.444411i
$115$			145.925i			1.26891i
$116$	13.7567	+	61.9039i	0.118593	+	0.533654i
$117$	−10.8167			−0.0924500
$118$	−22.4590	−	18.0159i	−0.190330	−	0.152677i
$119$		−	140.101i		−	1.17732i
$120$	−41.6871	+	84.6955i	−0.347392	+	0.705796i
$121$	−349.231			−2.88621
$122$	117.595	−	146.597i	0.963897	−	1.20162i
$123$			96.5610i			0.785049i
$124$	32.7930	−	7.28751i	0.264460	−	0.0587702i
$125$	−24.4425			−0.195540
$126$	−52.5755	−	42.1744i	−0.417266	−	0.334717i
$127$		−	110.502i		−	0.870097i	−0.900407	−	0.435048i	$-0.856731\pi$
$127$		−	110.502i		−	0.870097i	0.900407	−	0.435048i	$-0.143269\pi$
$128$	−127.974	−	2.56493i	−0.999799	−	0.0200385i
$129$	1.26979			0.00984335
$130$	−30.7398	+	38.3210i	−0.236460	+	0.294777i
$131$			146.297i			1.11677i	0.829582	+	0.558385i	$0.188579\pi$
$131$			146.297i			1.11677i	−0.829582	+	0.558385i	$0.811421\pi$
$132$	−32.5917	−	146.659i	−0.246906	−	1.11105i
$133$	210.617			1.58359
$134$	−20.3153	−	16.2963i	−0.151607	−	0.121614i
$135$		−	35.3996i		−	0.262219i
$136$	89.5180	+	44.0607i	0.658221	+	0.323976i
$137$	−113.081			−0.825412			−0.412706	−	0.910864i	$-0.635416\pi$
$137$	−113.081			−0.825412			−0.412706	+	0.910864i	$0.635416\pi$
$138$	46.4289	−	57.8792i	0.336441	−	0.419415i
$139$			141.001i			1.01440i	0.861829	+	0.507199i	$0.169319\pi$
$139$			141.001i			1.01440i	−0.861829	+	0.507199i	$0.830681\pi$
$140$	−298.829	+	66.4079i	−2.13449	+	0.474342i
$141$	28.2497			0.200352
$142$	−180.659	−	144.919i	−1.27225	−	1.02055i
$143$		−	78.1857i		−	0.546753i
$144$	43.4822	−	20.3298i	0.301959	−	0.141179i
$145$	−108.004			−0.744858
$146$	−44.4756	+	55.4443i	−0.304627	+	0.379755i
$147$		−	133.698i		−	0.909513i
$148$	21.2714	+	95.7190i	0.143726	+	0.646750i
$149$	−65.4255			−0.439097			−0.219549	−	0.975602i	$-0.570458\pi$
$149$	−65.4255			−0.439097			−0.219549	+	0.975602i	$0.570458\pi$
$150$	−57.8589	−	46.4126i	−0.385726	−	0.309417i
$151$			149.878i			0.992570i	0.868160	+	0.496285i	$0.165303\pi$
$151$			149.878i			0.992570i	−0.868160	+	0.496285i	$0.834697\pi$
$152$	−66.2376	+	134.575i	−0.435774	+	0.885361i
$153$	−37.4152			−0.244544
$154$	304.848	−	380.030i	1.97953	−	2.46773i
$155$			57.2144i			0.369125i
$156$	24.3851	−	5.41904i	0.156315	−	0.0347374i
$157$	−100.641			−0.641024			−0.320512	−	0.947245i	$-0.603855\pi$
$157$	−100.641			−0.641024			−0.320512	+	0.947245i	$0.603855\pi$
$158$	−75.7805	−	60.7886i	−0.479623	−	0.384738i
$159$			98.8419i			0.621647i
$160$	51.5479	−	211.823i	0.322174	−	1.32389i
$161$	240.618			1.49452
$162$	−11.2631	+	14.0408i	−0.0695251	+	0.0866715i
$163$			63.1174i			0.387223i	0.981078	+	0.193612i	$0.0620201\pi$
$163$			63.1174i			0.387223i	−0.981078	+	0.193612i	$0.937980\pi$
$164$	−48.3761	−	217.688i	−0.294976	−	1.32736i
$165$	255.878			1.55077
$166$	−49.1154	−	39.3988i	−0.295876	−	0.237342i
$167$		−	147.074i		−	0.880685i	−0.897830	−	0.440343i	$-0.854857\pi$
$167$		−	147.074i		−	0.880685i	0.897830	−	0.440343i	$-0.145143\pi$
$168$	139.656	+	68.7383i	0.831283	+	0.409157i
$169$	13.0000			0.0769231
$170$	−106.330	+	132.554i	−0.625472	+	0.779727i
$171$		−	56.2473i		−	0.328931i
$172$	−2.86263	+	0.636154i	−0.0166432	+	0.00369857i
$173$	−47.8859			−0.276797			−0.138398	−	0.990377i	$-0.544195\pi$
$173$	−47.8859			−0.276797			−0.138398	+	0.990377i	$0.544195\pi$
$174$	42.8385	+	34.3637i	0.246198	+	0.197492i
$175$		−	240.533i		−	1.37448i
$176$	146.950	+	314.301i	0.834941	+	1.78580i
$177$	−24.9346			−0.140873
$178$	−71.2241	+	88.7896i	−0.400136	+	0.498818i
$179$			94.6143i			0.528572i	0.964444	+	0.264286i	$0.0851362\pi$
$179$			94.6143i			0.528572i	−0.964444	+	0.264286i	$0.914864\pi$
$180$	17.7348	+	79.8050i	0.0985269	+	0.443361i
$181$	−191.668			−1.05894			−0.529469	−	0.848330i	$-0.677609\pi$
$181$	−191.668			−1.05894			−0.529469	+	0.848330i	$0.677609\pi$
$182$	63.1879	+	50.6873i	0.347186	+	0.278502i
$183$		−	162.756i		−	0.889378i
$184$	−75.6725	+	153.744i	−0.411264	+	0.835563i
$185$	−167.002			−0.902713
$186$	18.2039	−	22.6933i	0.0978702	−	0.122007i
$187$		−	270.447i		−	1.44624i
$188$	−63.6862	+	14.1528i	−0.338757	+	0.0752810i
$189$	−58.3708			−0.308840
$190$	−199.271	−	159.849i	−1.04880	−	0.841311i
$191$		−	128.645i		−	0.673533i	−0.941588	−	0.336767i	$-0.890667\pi$
$191$		−	128.645i		−	0.673533i	0.941588	−	0.336767i	$-0.109333\pi$
$192$	−87.8413	+	67.6158i	−0.457507	+	0.352166i
$193$	−204.867			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$193$	−204.867			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$194$	−19.5272	+	24.3430i	−0.100656	+	0.125480i
$195$			42.5450i			0.218179i
$196$	66.9816	+	301.410i	0.341743	+	1.53781i
$197$	−80.2016			−0.407115			−0.203557	−	0.979063i	$-0.565250\pi$
$197$	−80.2016			−0.407115			−0.203557	+	0.979063i	$0.565250\pi$
$198$	−101.491	−	81.4125i	−0.512579	−	0.411174i
$199$		−	187.024i		−	0.939817i	−0.882715	−	0.469908i	$-0.844287\pi$
$199$		−	187.024i		−	0.939817i	0.882715	−	0.469908i	$-0.155713\pi$
$200$	153.690	+	75.6460i	0.768449	+	0.378230i
$201$	−22.5546			−0.112212
$202$	−225.656	+	281.308i	−1.11711	+	1.39262i
$203$			178.090i			0.877290i
$204$	84.3490	−	18.7447i	0.413475	−	0.0918855i
$205$	379.802			1.85269
$206$	264.741	+	212.367i	1.28515	+	1.03091i
$207$		−	64.2591i		−	0.310431i
$208$	−52.2590	+	24.4334i	−0.251245	+	0.117468i
$209$	406.571			1.94531
$210$	−165.884	+	206.795i	−0.789924	+	0.984736i
$211$			127.610i			0.604787i	0.953183	+	0.302393i	$0.0977856\pi$
$211$			127.610i			0.604787i	−0.953183	+	0.302393i	$0.902214\pi$
$212$	−49.5188	−	222.830i	−0.233579	−	1.05108i
$213$	−200.572			−0.941654
$214$	−92.5059	−	74.2053i	−0.432271	−	0.346754i
$215$		−	4.99446i		−	0.0232300i
$216$	18.3572	−	37.2963i	0.0849870	−	0.172668i
$217$	94.3415			0.434753
$218$	−92.2623	+	115.016i	−0.423222	+	0.527597i
$219$			61.5558i			0.281077i
$220$	−576.852	+	128.192i	−2.62205	+	0.582692i
$221$	44.9675			0.203473
$222$	66.2392	+	53.1349i	0.298375	+	0.239347i
$223$			103.522i			0.464224i	0.972689	+	0.232112i	$0.0745636\pi$
$223$			103.522i			0.464224i	−0.972689	+	0.232112i	$0.925436\pi$
$224$	−349.277	−	84.9980i	−1.55927	−	0.379455i
$225$	−64.2366			−0.285496
$226$	107.944	−	134.565i	0.477627	−	0.595421i
$227$			13.8072i			0.0608246i	0.999537	+	0.0304123i	$0.00968203\pi$
$227$			13.8072i			0.0608246i	−0.999537	+	0.0304123i	$0.990318\pi$
$228$	28.1793	+	126.804i	0.123594	+	0.556158i
$229$	206.691			0.902580			0.451290	−	0.892377i	$-0.350964\pi$
$229$	206.691			0.902580			0.451290	+	0.892377i	$0.350964\pi$
$230$	−227.656	−	182.618i	−0.989807	−	0.793991i
$231$		−	421.920i		−	1.82649i
$232$	−113.791	−	56.0080i	−0.490480	−	0.241414i
$233$	414.641			1.77957			0.889787	−	0.456377i	$-0.150853\pi$
$233$	414.641			1.77957			0.889787	+	0.456377i	$0.150853\pi$
$234$	13.5365	−	16.8749i	0.0578483	−	0.0721150i
$235$		−	111.114i		−	0.472826i
$236$	56.2126	−	12.4920i	0.238189	−	0.0529321i
$237$	−84.1336			−0.354994
$238$	218.569	+	175.329i	0.918359	+	0.736678i
$239$			243.190i			1.01753i	0.860905	+	0.508766i	$0.169898\pi$
$239$			243.190i			1.01753i	−0.860905	+	0.508766i	$0.830102\pi$
$240$	−79.9630	−	171.028i	−0.333179	−	0.712615i
$241$	293.890			1.21946			0.609730	−	0.792609i	$-0.291278\pi$
$241$	293.890			1.21946			0.609730	+	0.792609i	$0.291278\pi$
$242$	437.046	−	544.831i	1.80597	−	2.25137i
$243$			15.5885i			0.0641500i
$244$	81.5392	+	366.918i	0.334177	+	1.50376i
$245$	−525.874			−2.14642
$246$	−150.644	−	120.841i	−0.612372	−	0.491225i
$247$			67.6008i			0.273687i
$248$	−29.6697	+	60.2799i	−0.119636	+	0.243064i
$249$	−54.5292			−0.218993
$250$	30.5886	−	38.1324i	0.122354	−	0.152530i
$251$			218.275i			0.869621i	0.900522	+	0.434810i	$0.143185\pi$
$251$			218.275i			0.869621i	−0.900522	+	0.434810i	$0.856815\pi$
$252$	131.591	−	29.2432i	0.522188	−	0.116044i
$253$	464.482			1.83590
$254$	172.393	+	138.288i	0.678713	+	0.544442i
$255$			147.165i			0.577116i
$256$	164.155	−	196.441i	0.641231	−	0.767348i
$257$	126.480			0.492141			0.246070	−	0.969252i	$-0.420861\pi$
$257$	126.480			0.492141			0.246070	+	0.969252i	$0.420861\pi$
$258$	−1.58908	+	1.98099i	−0.00615924	+	0.00767824i
$259$			275.372i			1.06321i
$260$	−21.3146	−	95.9136i	−0.0819793	−	0.368899i
$261$	47.5605			0.182224
$262$	−228.236	−	183.083i	−0.871129	−	0.698791i
$263$		−	386.885i		−	1.47105i	−0.677500	−	0.735523i	$-0.736937\pi$
$263$		−	386.885i		−	1.47105i	0.677500	−	0.735523i	$-0.263063\pi$
$264$	269.588	+	132.691i	1.02117	+	0.502617i
$265$	388.773			1.46707
$266$	−263.577	+	328.581i	−0.990892	+	1.23527i
$267$			98.5766i			0.369201i
$268$	50.8471	−	11.2996i	0.189728	−	0.0421628i
$269$	−121.086			−0.450133			−0.225067	−	0.974343i	$-0.572260\pi$
$269$	−121.086			−0.450133			−0.225067	+	0.974343i	$0.572260\pi$
$270$	55.2264	+	44.3008i	0.204542	+	0.164077i
$271$			290.454i			1.07179i	0.844285	+	0.535894i	$0.180025\pi$
$271$			290.454i			1.07179i	−0.844285	+	0.535894i	$0.819975\pi$
$272$	−180.766	+	84.5161i	−0.664581	+	0.310721i
$273$	70.1530			0.256971
$274$	141.516	−	176.417i	0.516482	−	0.643857i
$275$		−	464.319i		−	1.68843i
$276$	32.1932	+	144.866i	0.116642	+	0.524877i
$277$	−511.453			−1.84640			−0.923201	−	0.384318i	$-0.874437\pi$
$277$	−511.453			−1.84640			−0.923201	+	0.384318i	$0.874437\pi$
$278$	−219.974	−	176.456i	−0.791274	−	0.634734i
$279$		−	25.1948i		−	0.0903038i
$280$	270.367	−	549.305i	0.965598	−	1.96180i
$281$	−24.4005			−0.0868347			−0.0434173	−	0.999057i	$-0.513825\pi$
$281$	−24.4005			−0.0868347			−0.0434173	+	0.999057i	$0.513825\pi$
$282$	−35.3531	+	44.0720i	−0.125366	+	0.156284i
$283$		−	231.220i		−	0.817034i	−0.912751	−	0.408517i	$-0.866046\pi$
$283$		−	231.220i		−	0.817034i	0.912751	−	0.408517i	$-0.133954\pi$
$284$	452.171	−	100.485i	1.59215	−	0.353820i
$285$	−221.237			−0.776269
$286$	121.976	+	97.8456i	0.426491	+	0.342117i
$287$		−	626.260i		−	2.18209i
$288$	−22.6995	+	93.2777i	−0.0788177	+	0.323881i
$289$	−133.456			−0.461785
$290$	135.162	−	168.496i	0.466076	−	0.581021i
$291$			27.0263i			0.0928739i
$292$	−30.8388	−	138.772i	−0.105612	−	0.475245i
$293$	452.853			1.54557			0.772787	−	0.634665i	$-0.218862\pi$
$293$	452.853			1.54557			0.772787	+	0.634665i	$0.218862\pi$
$294$	208.581	+	167.317i	0.709459	+	0.569105i
$295$			98.0748i			0.332457i
$296$	−175.950	−	86.6025i	−0.594426	−	0.292576i
$297$	−112.678			−0.379386
$298$	81.8768	−	102.069i	0.274754	−	0.342515i
$299$			77.2299i			0.258294i
$300$	144.815	−	32.1819i	0.482718	−	0.107273i
$301$	−8.23542			−0.0273602
$302$	−233.823	−	187.565i	−0.774248	−	0.621076i
$303$			312.316i			1.03075i
$304$	−127.055	−	271.750i	−0.417945	−	0.893915i
$305$	−640.166			−2.09891
$306$	46.8233	−	58.3709i	0.153017	−	0.190755i
$307$			274.652i			0.894632i	0.894376	+	0.447316i	$0.147620\pi$
$307$			274.652i			0.894632i	−0.894376	+	0.447316i	$0.852380\pi$
$308$	211.378	+	951.179i	0.686292	+	3.08824i
$309$	293.923			0.951207
$310$	−89.2594	−	71.6010i	−0.287933	−	0.230971i
$311$		−	320.665i		−	1.03108i	−0.856866	−	0.515539i	$-0.827592\pi$
$311$		−	320.665i		−	1.03108i	0.856866	−	0.515539i	$-0.172408\pi$
$312$	−22.0626	+	44.8246i	−0.0707135	+	0.143668i
$313$	117.403			0.375090			0.187545	−	0.982256i	$-0.439947\pi$
$313$	117.403			0.375090			0.187545	+	0.982256i	$0.439947\pi$
$314$	125.947	−	157.008i	0.401105	−	0.500026i
$315$			229.589i			0.728854i
$316$	189.671	−	42.1501i	0.600225	−	0.133386i
$317$	−323.537			−1.02062			−0.510311	−	0.859990i	$-0.670470\pi$
$317$	−323.537			−1.02062			−0.510311	+	0.859990i	$0.670470\pi$
$318$	−154.202	−	123.696i	−0.484912	−	0.388980i
$319$			343.780i			1.07768i
$320$	265.952	+	345.505i	0.831101	+	1.07970i
$321$	−102.703			−0.319946
$322$	−301.121	+	375.384i	−0.935159	+	1.16579i
$323$			233.834i			0.723943i
$324$	−7.80967	−	35.1427i	−0.0241039	−	0.108465i
$325$	77.2028			0.237547
$326$	−98.4686	−	78.9883i	−0.302051	−	0.242295i
$327$			127.694i			0.390502i
$328$	400.152	+	196.954i	1.21998	+	0.600471i
$329$	−183.217			−0.556892
$330$	−320.218	+	399.191i	−0.970359	+	1.20967i
$331$			28.9403i			0.0874329i	0.999044	+	0.0437165i	$0.0139198\pi$
$331$			28.9403i			0.0874329i	−0.999044	+	0.0437165i	$0.986080\pi$
$332$	122.931	−	27.3186i	0.370274	−	0.0822850i
$333$	73.5405			0.220842
$334$	229.449	+	184.056i	0.686973	+	0.551067i
$335$			88.7136i			0.264817i
$336$	−282.010	+	131.852i	−0.839315	+	0.392417i
$337$	582.263			1.72778			0.863892	−	0.503677i	$-0.168020\pi$
$337$	582.263			1.72778			0.863892	+	0.503677i	$0.168020\pi$
$338$	−16.2689	+	20.2811i	−0.0481327	+	0.0600033i
$339$		−	149.398i		−	0.440702i
$340$	−73.7281	−	331.769i	−0.216847	−	0.975790i
$341$	182.115			0.534060
$342$	87.7506	+	70.3907i	0.256581	+	0.205821i
$343$			316.680i			0.923266i
$344$	2.58998	−	5.26206i	0.00752902	−	0.0152967i
$345$	−252.749			−0.732607
$346$	59.9268	−	74.7061i	0.173199	−	0.215914i
$347$			251.966i			0.726126i	0.931764	+	0.363063i	$0.118269\pi$
$347$			251.966i			0.726126i	−0.931764	+	0.363063i	$0.881731\pi$
$348$	−107.221	+	23.8274i	−0.308105	+	0.0684694i
$349$	−63.4568			−0.181825			−0.0909123	−	0.995859i	$-0.528978\pi$
$349$	−63.4568			−0.181825			−0.0909123	+	0.995859i	$0.528978\pi$
$350$	375.253	+	301.015i	1.07215	+	0.860044i
$351$		−	18.7350i		−	0.0533761i
$352$	−674.237	−	164.078i	−1.91545	−	0.466131i
$353$	−34.3765			−0.0973839			−0.0486920	−	0.998814i	$-0.515505\pi$
$353$	−34.3765			−0.0973839			−0.0486920	+	0.998814i	$0.515505\pi$
$354$	31.2044	−	38.9001i	0.0881480	−	0.109887i
$355$			788.908i			2.22228i
$356$	−49.3859	−	222.232i	−0.138725	−	0.624246i
$357$	242.662			0.679725
$358$	−147.607	−	118.405i	−0.412309	−	0.330741i
$359$		−	234.212i		−	0.652400i	−0.945301	−	0.326200i	$-0.894232\pi$
$359$		−	234.212i		−	0.652400i	0.945301	−	0.326200i	$-0.105768\pi$
$360$	−146.697	−	72.2041i	−0.407491	−	0.200567i
$361$	9.47160			0.0262371
$362$	239.863	−	299.018i	0.662604	−	0.826017i
$363$		−	604.886i		−	1.66635i
$364$	−158.153	+	35.1460i	−0.434487	+	0.0965549i
$365$	242.116			0.663332
$366$	253.914	+	203.681i	0.693753	+	0.556506i
$367$		−	172.545i		−	0.470151i	−0.971977	−	0.235075i	$-0.924466\pi$
$367$		−	172.545i		−	0.470151i	0.971977	−	0.235075i	$-0.0755337\pi$
$368$	−145.153	−	310.458i	−0.394438	−	0.843637i
$369$	−167.249			−0.453248
$370$	208.995	−	260.538i	0.564851	−	0.704156i
$371$		−	641.053i		−	1.72791i
$372$	12.6223	+	56.7992i	0.0339310	+	0.152686i
$373$	45.7991			0.122786			0.0613929	−	0.998114i	$-0.480446\pi$
$373$	45.7991			0.122786			0.0613929	+	0.998114i	$0.480446\pi$
$374$	421.921	+	338.451i	1.12813	+	0.904950i
$375$		−	42.3356i		−	0.112895i
$376$	57.6206	−	117.068i	0.153246	−	0.311350i
$377$	−57.1606			−0.151620
$378$	73.0482	−	91.0635i	0.193249	−	0.240909i
$379$		−	556.312i		−	1.46784i	−0.679235	−	0.733921i	$-0.737688\pi$
$379$		−	556.312i		−	1.46784i	0.679235	−	0.733921i	$-0.262312\pi$
$380$	498.757	−	110.837i	1.31252	−	0.291677i
$381$	191.396			0.502351
$382$	200.697	+	160.993i	0.525385	+	0.421447i
$383$			115.797i			0.302341i	0.988508	+	0.151171i	$0.0483043\pi$
$383$			115.797i			0.302341i	−0.988508	+	0.151171i	$0.951696\pi$
$384$	4.44259	−	221.658i	0.0115693	−	0.577234i
$385$	−1659.53			−4.31047
$386$	256.382	−	319.611i	0.664201	−	0.828008i
$387$			2.19935i			0.00568306i
$388$	−13.5399	−	60.9283i	−0.0348967	−	0.157032i
$389$	−649.555			−1.66981			−0.834903	−	0.550397i	$-0.814476\pi$
$389$	−649.555			−1.66981			−0.834903	+	0.550397i	$0.814476\pi$
$390$	−66.3739	−	53.2430i	−0.170189	−	0.136520i
$391$			267.141i			0.683225i
$392$	−554.050	−	272.703i	−1.41339	−	0.695671i
$393$	−253.394			−0.644767
$394$	100.368	−	125.121i	0.254742	−	0.317567i
$395$			330.921i			0.837775i
$396$	254.021	−	56.4504i	0.641467	−	0.142552i
$397$	−272.073			−0.685321			−0.342661	−	0.939459i	$-0.611328\pi$
$397$	−272.073			−0.685321			−0.342661	+	0.939459i	$0.611328\pi$
$398$	291.773	+	234.051i	0.733098	+	0.588067i
$399$			364.800i			0.914285i
$400$	−310.349	+	145.102i	−0.775874	+	0.362755i
$401$	−193.106			−0.481562			−0.240781	−	0.970580i	$-0.577403\pi$
$401$	−193.106			−0.481562			−0.240781	+	0.970580i	$0.577403\pi$
$402$	28.2259	−	35.1871i	0.0702138	−	0.0875301i
$403$			30.2803i			0.0751373i
$404$	−156.467	−	704.087i	−0.387295	−	1.74279i
$405$	61.3138			0.151392
$406$	−277.836	−	222.871i	−0.684324	−	0.548943i
$407$			531.571i			1.30607i
$408$	−76.3154	+	155.050i	−0.187047	+	0.380024i
$409$	−573.972			−1.40336			−0.701678	−	0.712495i	$-0.747565\pi$
$409$	−573.972			−1.40336			−0.701678	+	0.712495i	$0.747565\pi$
$410$	−475.304	+	592.524i	−1.15928	+	1.44518i
$411$		−	195.863i		−	0.476552i
$412$	−662.622	+	147.253i	−1.60831	+	0.357409i
$413$	161.717			0.391566
$414$	100.250	+	80.4171i	0.242149	+	0.194244i
$415$			214.479i			0.516817i
$416$	27.2814	−	112.106i	0.0655803	−	0.269485i
$417$	−244.221			−0.585662
$418$	−508.803	+	634.285i	−1.21723	+	1.51743i
$419$		−	617.606i		−	1.47400i	−0.675893	−	0.737000i	$-0.736242\pi$
$419$		−	617.606i		−	1.47400i	0.675893	−	0.737000i	$-0.263758\pi$
$420$	−115.022	−	517.587i	−0.273862	−	1.23235i
$421$	95.4439			0.226708			0.113354	−	0.993555i	$-0.463841\pi$
$421$	95.4439			0.226708			0.113354	+	0.993555i	$0.463841\pi$
$422$	−199.083	−	159.698i	−0.471760	−	0.378430i
$423$			48.9299i			0.115673i
$424$	409.604	+	201.607i	0.966047	+	0.475488i
$425$	267.047			0.628346
$426$	251.006	−	312.910i	0.589217	−	0.734531i
$427$			1055.58i			2.47208i
$428$	231.533	−	51.4530i	0.540966	−	0.120217i
$429$	135.422			0.315668
$430$	7.79178	+	6.25032i	0.0181204	+	0.0145356i
$431$		−	3.15267i		−	0.00731479i	−0.999993	−	0.00365739i	$-0.998836\pi$
$431$		−	3.15267i		−	0.00731479i	0.999993	−	0.00365739i	$-0.00116419\pi$
$432$	35.2123	+	75.3133i	0.0815100	+	0.174336i
$433$	−2.36000			−0.00545035			−0.00272517	−	0.999996i	$-0.500867\pi$
$433$	−2.36000			−0.00545035			−0.00272517	+	0.999996i	$0.500867\pi$
$434$	−118.064	+	147.181i	−0.272036	+	0.339127i
$435$		−	187.069i		−	0.430044i
$436$	−63.9735	−	287.874i	−0.146728	−	0.660262i
$437$	−401.600			−0.918993
$438$	−96.0323	−	77.0340i	−0.219252	−	0.175877i
$439$		−	328.588i		−	0.748492i	−0.927329	−	0.374246i	$-0.877902\pi$
$439$		−	328.588i		−	0.748492i	0.927329	−	0.374246i	$-0.122098\pi$
$440$	521.911	−	1060.37i	1.18616	−	2.40992i
$441$	231.572			0.525107
$442$	−56.2746	+	70.1531i	−0.127318	+	0.158718i
$443$			110.026i			0.248366i	0.992259	+	0.124183i	$0.0396310\pi$
$443$			110.026i			0.248366i	−0.992259	+	0.124183i	$0.960369\pi$
$444$	−165.790	+	36.8431i	−0.373401	+	0.0829800i
$445$	387.730			0.871303
$446$	−161.503	−	129.553i	−0.362115	−	0.290477i
$447$		−	113.320i		−	0.253513i
$448$	569.708	−	438.532i	1.27167	−	0.978867i
$449$	75.2254			0.167540			0.0837699	−	0.996485i	$-0.473304\pi$
$449$	75.2254			0.167540			0.0837699	+	0.996485i	$0.473304\pi$
$450$	80.3889	−	100.215i	0.178642	−	0.222699i
$451$		−	1208.92i		−	2.68053i
$452$	74.8469	+	336.803i	0.165590	+	0.745140i
$453$	−259.596			−0.573061
$454$	−21.5404	−	17.2790i	−0.0474458	−	0.0380595i
$455$		−	275.932i		−	0.606443i
$456$	−233.090	−	114.727i	−0.511163	−	0.251594i
$457$	809.564			1.77147			0.885737	−	0.464187i	$-0.153654\pi$
$457$	809.564			1.77147			0.885737	+	0.464187i	$0.153654\pi$
$458$	−258.664	+	322.456i	−0.564768	+	0.704052i
$459$		−	64.8050i		−	0.141187i
$460$	569.800	−	126.625i	1.23869	−	0.275272i
$461$	106.573			0.231179			0.115589	−	0.993297i	$-0.463124\pi$
$461$	106.573			0.231179			0.115589	+	0.993297i	$0.463124\pi$
$462$	658.232	+	528.012i	1.42474	+	1.14288i
$463$		−	304.508i		−	0.657684i	−0.944385	−	0.328842i	$-0.893342\pi$
$463$		−	304.508i		−	0.657684i	0.944385	−	0.328842i	$-0.106658\pi$
$464$	229.782	−	107.433i	0.495219	−	0.231537i
$465$	−99.0982			−0.213114
$466$	−518.902	+	646.875i	−1.11352	+	1.38814i
$467$			820.612i			1.75720i	0.477558	+	0.878600i	$0.341522\pi$
$467$			820.612i			1.75720i	−0.477558	+	0.878600i	$0.658478\pi$
$468$	9.38605	+	42.2363i	0.0200557	+	0.0902484i
$469$	146.281			0.311900
$470$	173.348	+	139.054i	0.368825	+	0.295859i
$471$		−	174.315i		−	0.370095i
$472$	−50.8588	+	103.330i	−0.107752	+	0.218919i
$473$	−15.8975			−0.0336099
$474$	105.289	−	131.256i	0.222129	−	0.276911i
$475$			401.459i			0.845177i
$476$	−547.058	+	121.571i	−1.14928	+	0.255402i
$477$	−171.199			−0.358908
$478$	−379.398	−	304.341i	−0.793720	−	0.636696i
$479$		−	236.394i		−	0.493515i	−0.969077	−	0.246757i	$-0.920635\pi$
$479$		−	236.394i		−	0.493515i	0.969077	−	0.246757i	$-0.0793651\pi$
$480$	366.888	+	89.2835i	0.764350	+	0.186007i
$481$	−88.3847			−0.183752
$482$	−367.789	+	458.494i	−0.763047	+	0.951232i
$483$			416.762i			0.862861i
$484$	303.042	+	1363.66i	0.626120	+	2.81748i
$485$	106.302			0.219180
$486$	−24.3193	−	19.5082i	−0.0500398	−	0.0401403i
$487$		−	781.882i		−	1.60551i	−0.596310	−	0.802754i	$-0.703367\pi$
$487$		−	781.882i		−	1.60551i	0.596310	−	0.802754i	$-0.296633\pi$
$488$	−674.466	−	331.972i	−1.38210	−	0.680270i
$489$	−109.322			−0.223563
$490$	658.105	−	820.409i	1.34307	−	1.67430i
$491$			789.535i			1.60801i	0.594619	+	0.804007i	$0.297303\pi$
$491$			789.535i			1.60801i	−0.594619	+	0.804007i	$0.702697\pi$
$492$	377.046	−	83.7899i	0.766354	−	0.170305i
$493$	−197.721			−0.401056
$494$	−105.463	−	84.5991i	−0.213488	−	0.171253i
$495$			443.193i			0.895340i
$496$	−56.9117	−	121.725i	−0.114741	−	0.245413i
$497$	1300.84			2.61739
$498$	68.2407	−	85.0703i	0.137029	−	0.170824i
$499$		−	176.012i		−	0.352729i	−0.984325	−	0.176365i	$-0.943566\pi$
$499$		−	176.012i		−	0.352729i	0.984325	−	0.176365i	$-0.0564338\pi$
$500$	21.2097	+	95.4416i	0.0424195	+	0.190883i
$501$	254.740			0.508464
$502$	−340.528	−	273.160i	−0.678342	−	0.544144i
$503$			809.674i			1.60969i	0.593485	+	0.804845i	$0.297752\pi$
$503$			809.674i			1.60969i	−0.593485	+	0.804845i	$0.702248\pi$
$504$	−119.058	+	241.890i	−0.236227	+	0.479941i
$505$	1228.43			2.43253
$506$	−581.277	+	724.633i	−1.14877	+	1.43208i
$507$			22.5167i			0.0444116i
$508$	−431.483	+	95.8874i	−0.849376	+	0.188755i
$509$	457.195			0.898221			0.449111	−	0.893476i	$-0.351741\pi$
$509$	457.195			0.898221			0.449111	+	0.893476i	$0.351741\pi$
$510$	−229.590	−	184.169i	−0.450176	−	0.361116i
$511$		−	399.229i		−	0.781270i
$512$	101.033	+	501.933i	0.197330	+	0.980337i
$513$	97.4231			0.189909
$514$	−158.284	+	197.320i	−0.307945	+	0.383891i
$515$		−	1156.08i		−	2.24482i
$516$	−1.10185	−	4.95821i	−0.00213537	−	0.00960894i
$517$	−353.679			−0.684098
$518$	−429.604	−	344.614i	−0.829351	−	0.665279i
$519$		−	82.9408i		−	0.159809i
$520$	176.308	+	86.7785i	0.339053	+	0.166882i
$521$	−180.750			−0.346929			−0.173465	−	0.984840i	$-0.555496\pi$
$521$	−180.750			−0.346929			−0.173465	+	0.984840i	$0.555496\pi$
$522$	−59.5197	+	74.1985i	−0.114022	+	0.142143i
$523$		−	125.843i		−	0.240618i	−0.992736	−	0.120309i	$-0.961611\pi$
$523$		−	125.843i		−	0.240618i	0.992736	−	0.120309i	$-0.0383886\pi$
$524$	571.252	−	126.948i	1.09018	−	0.242267i
$525$	416.616			0.793554
$526$	603.574	+	484.168i	1.14748	+	0.920471i
$527$			104.741i			0.198749i
$528$	−544.385	+	254.524i	−1.03103	+	0.482053i
$529$	70.1962			0.132696
$530$	−486.531	+	606.520i	−0.917983	+	1.14438i
$531$		−	43.1880i		−	0.0813333i
$532$	−182.761	−	822.407i	−0.343536	−	1.54588i
$533$	201.008			0.377125
$534$	−153.788	−	123.364i	−0.287993	−	0.231018i
$535$			403.959i			0.755063i
$536$	−46.0043	+	93.4669i	−0.0858290	+	0.174379i
$537$	−163.877			−0.305171
$538$	151.533	−	188.904i	0.281660	−	0.351124i
$539$			1673.87i			3.10551i
$540$	−138.226	+	30.7176i	−0.255975	+	0.0568845i
$541$	236.115			0.436441			0.218221	−	0.975899i	$-0.429975\pi$
$541$	236.115			0.436441			0.218221	+	0.975899i	$0.429975\pi$
$542$	−453.134	−	363.490i	−0.836041	−	0.670645i
$543$		−	331.978i		−	0.611378i
$544$	94.3673	−	387.778i	0.173469	−	0.712828i
$545$	502.258			0.921573
$546$	−87.7930	+	109.445i	−0.160793	+	0.200448i
$547$		−	828.760i		−	1.51510i	−0.652777	−	0.757550i	$-0.726396\pi$
$547$		−	828.760i		−	1.51510i	0.652777	−	0.757550i	$-0.273604\pi$
$548$	98.1254	+	441.554i	0.179061	+	0.805756i
$549$	281.902			0.513482
$550$	724.379	+	581.073i	1.31705	+	1.05650i
$551$		−	297.239i		−	0.539453i
$552$	−266.292	−	131.069i	−0.482413	−	0.237443i
$553$	545.660			0.986728
$554$	640.059	−	797.911i	1.15534	−	1.44027i
$555$		−	289.256i		−	0.521182i
$556$	550.574	−	122.352i	0.990240	−	0.220058i
$557$	−328.828			−0.590355			−0.295178	−	0.955442i	$-0.595379\pi$
$557$	−328.828			−0.590355			−0.295178	+	0.955442i	$0.595379\pi$
$558$	39.3060	+	31.5300i	0.0704409	+	0.0565054i
$559$		−	2.64328i		−	0.00472859i
$560$	518.612	+	1109.23i	0.926093	+	1.98076i
$561$	468.428			0.834988
$562$	30.5361	−	38.0670i	0.0543347	−	0.0677348i
$563$		−	248.457i		−	0.441308i	−0.975352	−	0.220654i	$-0.929181\pi$
$563$		−	248.457i		−	0.441308i	0.975352	−	0.220654i	$-0.0708192\pi$
$564$	−24.5134	−	110.308i	−0.0434635	−	0.195581i
$565$	−587.624			−1.04004
$566$	360.724	+	289.361i	0.637322	+	0.511239i
$567$		−	101.101i		−	0.178309i
$568$	−409.105	+	831.178i	−0.720256	+	1.46334i
$569$	−661.140			−1.16193			−0.580966	−	0.813928i	$-0.697325\pi$
$569$	−661.140			−1.16193			−0.580966	+	0.813928i	$0.697325\pi$
$570$	276.867	−	345.148i	0.485731	−	0.605523i
$571$			578.642i			1.01338i	0.862127	+	0.506692i	$0.169132\pi$
$571$			578.642i			1.01338i	−0.862127	+	0.506692i	$0.830868\pi$
$572$	−305.295	+	67.8449i	−0.533733	+	0.118610i
$573$	222.819			0.388865
$574$	977.021	+	783.734i	1.70213	+	1.36539i
$575$			458.643i			0.797640i
$576$	−117.114	−	152.146i	−0.203323	−	0.264142i
$577$	−571.279			−0.990084			−0.495042	−	0.868869i	$-0.664847\pi$
$577$	−571.279			−0.990084			−0.495042	+	0.868869i	$0.664847\pi$
$578$	167.014	−	208.203i	0.288951	−	0.360212i
$579$		−	354.841i		−	0.612851i
$580$	93.7198	+	421.729i	0.161586	+	0.727120i
$581$	353.657			0.608704
$582$	−42.1634	−	33.8221i	−0.0724457	−	0.0581136i
$583$		−	1237.47i		−	2.12260i
$584$	255.089	+	125.555i	0.436796	+	0.214991i
$585$	−73.6901			−0.125966
$586$	−566.724	+	706.490i	−0.967105	+	1.20562i
$587$		−	1050.59i		−	1.78975i	−0.446314	−	0.894877i	$-0.647263\pi$
$587$		−	1050.59i		−	1.78975i	0.446314	−	0.894877i	$-0.352737\pi$
$588$	−522.058	+	116.016i	−0.887853	+	0.197305i
$589$	−157.460			−0.267334
$590$	−153.005	−	122.736i	−0.259331	−	0.208027i
$591$		−	138.913i		−	0.235048i
$592$	355.300	−	166.119i	0.600169	−	0.280606i
$593$	750.729			1.26599			0.632993	−	0.774158i	$-0.281826\pi$
$593$	750.729			1.26599			0.632993	+	0.774158i	$0.281826\pi$
$594$	141.011	−	175.787i	0.237391	−	0.295937i
$595$		−	954.458i		−	1.60413i
$596$	56.7724	+	255.470i	0.0952556	+	0.428641i
$597$	323.934			0.542603
$598$	−120.485	−	96.6494i	−0.201480	−	0.161621i
$599$			426.114i			0.711375i	0.934605	+	0.355688i	$0.115753\pi$
$599$			426.114i			0.711375i	−0.934605	+	0.355688i	$0.884247\pi$
$600$	−131.023	+	266.198i	−0.218371	+	0.443664i
$601$	−331.888			−0.552227			−0.276113	−	0.961125i	$-0.589046\pi$
$601$	−331.888			−0.552227			−0.276113	+	0.961125i	$0.589046\pi$
$602$	10.3062	−	12.8480i	0.0171200	−	0.0213422i
$603$		−	39.0657i		−	0.0647855i
$604$	585.236	−	130.055i	0.968933	−	0.215323i
$605$	−2379.19			−3.93255
$606$	−487.240	−	390.848i	−0.804027	−	0.644964i
$607$		−	39.2169i		−	0.0646078i	−0.999478	−	0.0323039i	$-0.989716\pi$
$607$		−	39.2169i		−	0.0646078i	0.999478	−	0.0323039i	$-0.0102844\pi$
$608$	582.957	+	141.865i	0.958812	+	0.233330i
$609$	−308.461			−0.506503
$610$	801.136	−	998.715i	1.31334	−	1.63724i
$611$		−	58.8064i		−	0.0962462i
$612$	32.4667	+	146.097i	0.0530501	+	0.238720i
$613$	924.717			1.50851			0.754256	−	0.656581i	$-0.227998\pi$
$613$	924.717			1.50851			0.754256	+	0.656581i	$0.227998\pi$
$614$	−428.481	−	343.714i	−0.697852	−	0.559794i
$615$			657.836i			1.06965i
$616$	−1748.45	−	860.586i	−2.83839	−	1.39705i
$617$	826.589			1.33969			0.669845	−	0.742501i	$-0.266360\pi$
$617$	826.589			1.33969			0.669845	+	0.742501i	$0.266360\pi$
$618$	−367.830	+	458.546i	−0.595195	+	0.741983i
$619$			1098.26i			1.77425i	0.461527	+	0.887126i	$0.347302\pi$
$619$			1098.26i			1.77425i	−0.461527	+	0.887126i	$0.652698\pi$
$620$	223.407	−	49.6472i	0.360335	−	0.0800762i
$621$	111.300			0.179227
$622$	500.266	+	401.297i	0.804286	+	0.645172i
$623$		−	639.333i		−	1.02622i
$624$	−42.3199	−	90.5153i	−0.0678204	−	0.145057i
$625$	−701.823			−1.12292
$626$	−146.924	+	183.159i	−0.234703	+	0.292586i
$627$			704.201i			1.12313i
$628$	87.3301	+	392.976i	0.139061	+	0.625758i
$629$	−305.726			−0.486051
$630$	−358.179	−	287.319i	−0.568538	−	0.456063i
$631$		−	580.160i		−	0.919429i	−0.888067	−	0.459714i	$-0.847952\pi$
$631$		−	580.160i		−	0.919429i	0.888067	−	0.459714i	$-0.152048\pi$
$632$	−171.606	+	348.652i	−0.271529	+	0.551665i
$633$	−221.027			−0.349174
$634$	404.891	−	504.746i	0.638629	−	0.796129i
$635$		−	752.813i		−	1.18553i
$636$	385.952	−	85.7691i	0.606843	−	0.134857i
$637$	−278.315			−0.436916
$638$	−536.327	−	430.224i	−0.840638	−	0.674333i
$639$		−	347.401i		−	0.543664i
$640$	−871.844	−	17.4740i	−1.36226	−	0.0273031i
$641$	−352.980			−0.550671			−0.275335	−	0.961348i	$-0.588789\pi$
$641$	−352.980			−0.550671			−0.275335	+	0.961348i	$0.588789\pi$
$642$	128.527	−	160.225i	0.200198	−	0.249572i
$643$		−	42.0303i		−	0.0653660i	−0.999466	−	0.0326830i	$-0.989595\pi$
$643$		−	42.0303i		−	0.0653660i	0.999466	−	0.0326830i	$-0.0104052\pi$
$644$	−208.794	−	939.550i	−0.324214	−	1.45893i
$645$	8.65065			0.0134119
$646$	−364.801	−	292.631i	−0.564707	−	0.452990i
$647$		−	470.882i		−	0.727792i	−0.931440	−	0.363896i	$-0.881446\pi$
$647$		−	470.882i		−	0.727792i	0.931440	−	0.363896i	$-0.118554\pi$
$648$	64.5991	+	31.7956i	0.0996899	+	0.0490673i
$649$	312.174			0.481008
$650$	−96.6155	+	120.443i	−0.148639	+	0.185297i
$651$			163.404i			0.251005i
$652$	246.457	−	54.7695i	0.378002	−	0.0840023i
$653$	222.311			0.340446			0.170223	−	0.985406i	$-0.445551\pi$
$653$	222.311			0.340446			0.170223	+	0.985406i	$0.445551\pi$
$654$	−199.214	−	159.803i	−0.304608	−	0.244347i
$655$			996.669i			1.52163i
$656$	−808.037	+	377.793i	−1.23176	+	0.575904i
$657$	−106.618			−0.162280
$658$	229.288	−	285.835i	0.348461	−	0.434400i
$659$			501.932i			0.761657i	0.924646	+	0.380829i	$0.124361\pi$
$659$			501.932i			0.761657i	−0.924646	+	0.380829i	$0.875639\pi$
$660$	−222.035	−	999.137i	−0.336417	−	1.51384i
$661$	−825.813			−1.24934			−0.624669	−	0.780889i	$-0.714766\pi$
$661$	−825.813			−1.24934			−0.624669	+	0.780889i	$0.714766\pi$
$662$	−45.1494	−	36.2174i	−0.0682015	−	0.0547090i
$663$			77.8859i			0.117475i
$664$	−111.223	+	225.971i	−0.167504	+	0.340318i
$665$	1434.86			2.15769
$666$	−92.0324	+	114.730i	−0.138187	+	0.172267i
$667$		−	339.577i		−	0.509112i
$668$	−574.288	+	127.622i	−0.859712	+	0.191052i
$669$	−179.305			−0.268020
$670$	−138.401	−	111.021i	−0.206568	−	0.165703i
$671$			2037.66i			3.03676i
$672$	147.221	−	604.966i	0.219079	−	0.900247i
$673$	1225.45			1.82088			0.910439	−	0.413642i	$-0.135744\pi$
$673$	1225.45			1.82088			0.910439	+	0.413642i	$0.135744\pi$
$674$	−728.674	+	908.381i	−1.08112	+	1.34775i
$675$		−	111.261i		−	0.164831i
$676$	−11.2806	−	50.7617i	−0.0166873	−	0.0750912i
$677$	−1078.34			−1.59281			−0.796407	−	0.604761i	$-0.793269\pi$
$677$	−1078.34			−1.59281			−0.796407	+	0.604761i	$0.793269\pi$
$678$	233.074	+	186.964i	0.343766	+	0.275758i
$679$		−	175.283i		−	0.258149i
$680$	609.855	+	300.170i	0.896845	+	0.441427i
$681$	−23.9148			−0.0351171
$682$	−227.907	+	284.115i	−0.334175	+	0.416590i
$683$		−	287.098i		−	0.420348i	−0.977664	−	0.210174i	$-0.932597\pi$
$683$		−	287.098i		−	0.420348i	0.977664	−	0.210174i	$-0.0674030\pi$
$684$	−219.631	+	48.8081i	−0.321098	+	0.0713568i
$685$	−770.385			−1.12465
$686$	−494.049	−	396.310i	−0.720187	−	0.577711i
$687$			357.999i			0.521105i
$688$	4.96804	+	10.6258i	0.00722098	+	0.0154445i
$689$	205.756			0.298630
$690$	316.304	−	394.311i	0.458411	−	0.571465i
$691$		−	918.379i		−	1.32906i	−0.747263	−	0.664529i	$-0.768632\pi$
$691$		−	918.379i		−	1.32906i	0.747263	−	0.664529i	$-0.231368\pi$
$692$	41.5525	+	186.982i	0.0600470	+	0.270205i
$693$	730.787			1.05453
$694$	−393.089	−	315.323i	−0.566410	−	0.454356i
$695$			960.592i			1.38215i
$696$	97.0087	−	197.092i	0.139380	−	0.283179i
$697$	695.293			0.997551
$698$	79.4131	−	98.9981i	0.113772	−	0.141831i
$699$			718.179i			1.02744i
$700$	−939.220	+	208.720i	−1.34174	+	0.298172i
$701$	357.022			0.509304			0.254652	−	0.967033i	$-0.418039\pi$
$701$	357.022			0.509304			0.254652	+	0.967033i	$0.418039\pi$
$702$	29.2282	+	23.4459i	0.0416356	+	0.0333988i
$703$		−	459.606i		−	0.653778i
$704$	1099.75	−	846.532i	1.56215	−	1.20246i
$705$	192.455			0.272986
$706$	43.0205	−	53.6304i	0.0609356	−	0.0759637i
$707$		−	2025.57i		−	2.86502i
$708$	21.6368	+	97.3631i	0.0305604	+	0.137519i
$709$	174.904			0.246691			0.123346	−	0.992364i	$-0.460638\pi$
$709$	174.904			0.246691			0.123346	+	0.992364i	$0.460638\pi$
$710$	−1230.77	−	987.280i	−1.73347	−	1.39053i
$711$		−	145.724i		−	0.204956i
$712$	408.505	+	201.066i	0.573742	+	0.282396i
$713$	−179.888			−0.252298
$714$	−303.679	+	378.573i	−0.425321	+	0.530215i
$715$		−	532.652i		−	0.744968i
$716$	369.445	−	82.1007i	0.515984	−	0.114666i
$717$	−421.218			−0.587473
$718$	365.390	+	293.104i	0.508900	+	0.408223i
$719$		−	419.087i		−	0.582875i	−0.956590	−	0.291437i	$-0.905867\pi$
$719$		−	419.087i		−	0.582875i	0.956590	−	0.291437i	$-0.0941335\pi$
$720$	296.229	−	138.500i	0.411429	−	0.192361i
$721$	−1906.28			−2.64394
$722$	−11.8532	+	14.7765i	−0.0164172	+	0.0204661i
$723$			509.032i			0.704056i
$724$	166.318	+	748.413i	0.229721	+	1.03372i
$725$	−339.458			−0.468218
$726$	943.675	+	756.986i	1.29983	+	1.04268i
$727$			1257.05i			1.72910i	0.502550	+	0.864548i	$0.332395\pi$
$727$			1257.05i			1.72910i	−0.502550	+	0.864548i	$0.667605\pi$
$728$	143.090	−	290.716i	0.196553	−	0.399335i
$729$	−27.0000			−0.0370370
$730$	−302.997	+	377.722i	−0.415064	+	0.517428i
$731$		−	9.14321i		−	0.0125078i
$732$	−635.521	+	141.230i	−0.868198	+	0.192937i
$733$	−426.806			−0.582273			−0.291136	−	0.956682i	$-0.594033\pi$
$733$	−426.806			−0.582273			−0.291136	+	0.956682i	$0.594033\pi$
$734$	269.186	+	215.932i	0.366738	+	0.294185i
$735$		−	910.840i		−	1.23924i
$736$	665.994	+	162.072i	0.904883	+	0.220207i
$737$	282.377			0.383144
$738$	209.303	−	260.922i	0.283609	−	0.353553i
$739$			757.308i			1.02477i	0.858755	+	0.512387i	$0.171239\pi$
$739$			757.308i			1.02477i	−0.858755	+	0.512387i	$0.828761\pi$
$740$	144.914	+	652.100i	0.195830	+	0.881216i
$741$	−117.088			−0.158014
$742$	1000.10	+	802.247i	1.34784	+	1.08120i
$743$			204.011i			0.274578i	0.990531	+	0.137289i	$0.0438389\pi$
$743$			204.011i			0.274578i	−0.990531	+	0.137289i	$0.956161\pi$
$744$	−104.408	−	51.3895i	−0.140333	−	0.0690719i
$745$	−445.721			−0.598283
$746$	−57.3154	+	71.4506i	−0.0768303	+	0.0957783i
$747$		−	94.4474i		−	0.126436i
$748$	−1056.03	+	234.678i	−1.41180	+	0.313741i
$749$	666.093			0.889309
$750$	66.0472	+	52.9810i	0.0880630	+	0.0706413i
$751$			2.41546i			0.00321632i	0.999999	+	0.00160816i	$0.000511893\pi$
$751$			2.41546i			0.00321632i	−0.999999	+	0.00160816i	$0.999488\pi$
$752$	110.526	+	236.397i	0.146976	+	0.314358i
$753$	−378.063			−0.502076
$754$	71.5337	−	89.1755i	0.0948723	−	0.118270i
$755$			1021.07i			1.35241i
$756$	50.6507	+	227.923i	0.0669983	+	0.301486i
$757$	−1213.94			−1.60362			−0.801812	−	0.597577i	$-0.796130\pi$
$757$	−1213.94			−1.60362			−0.801812	+	0.597577i	$0.796130\pi$
$758$	867.895	+	696.197i	1.14498	+	0.918466i
$759$			804.507i			1.05996i
$760$	−451.254	+	916.811i	−0.593755	+	1.20633i
$761$	173.545			0.228048			0.114024	−	0.993478i	$-0.463626\pi$
$761$	173.545			0.228048			0.114024	+	0.993478i	$0.463626\pi$
$762$	−239.522	+	298.594i	−0.314334	+	0.391855i
$763$		−	828.179i		−	1.08542i
$764$	−502.325	+	111.630i	−0.657494	+	0.146113i
$765$	−254.897			−0.333198
$766$	−180.653	−	144.914i	−0.235839	−	0.189182i
$767$			51.9055i			0.0676734i
$768$	340.246	+	284.325i	0.443029	+	0.370215i
$769$	−1241.50			−1.61444			−0.807218	−	0.590253i	$-0.799028\pi$
$769$	−1241.50			−1.61444			−0.807218	+	0.590253i	$0.799028\pi$
$770$	2076.82	−	2589.01i	2.69717	−	3.36236i
$771$			219.070i			0.284137i
$772$	177.772	+	799.955i	0.230274	+	1.03621i
$773$	−163.288			−0.211240			−0.105620	−	0.994407i	$-0.533683\pi$
$773$	−163.288			−0.211240			−0.105620	+	0.994407i	$0.533683\pi$
$774$	−3.43117	−	2.75237i	−0.00443303	−	0.00355604i
$775$			179.825i			0.232032i
$776$	111.998	+	55.1253i	0.144327	+	0.0710377i
$777$	−476.958			−0.613845
$778$	812.886	−	1013.36i	1.04484	−	1.30252i
$779$			1045.25i			1.34179i
$780$	166.127	−	36.9180i	0.212984	−	0.0473308i
$781$	2511.11			3.21525
$782$	−416.763	−	334.314i	−0.532945	−	0.427511i
$783$			82.3772i			0.105207i
$784$	1118.81	−	523.092i	1.42705	−	0.667209i
$785$	−685.630			−0.873414
$786$	317.110	−	395.316i	0.403447	−	0.502946i
$787$			399.493i			0.507615i	0.967255	+	0.253807i	$0.0816830\pi$
$787$			399.493i			0.507615i	−0.967255	+	0.253807i	$0.918317\pi$
$788$	69.5942	+	313.167i	0.0883175	+	0.397420i
$789$	670.105			0.849309
$790$	−516.266	−	414.132i	−0.653501	−	0.524217i
$791$			968.941i			1.22496i
$792$	−229.827	+	466.940i	−0.290186	+	0.589570i
$793$	−338.804			−0.427243
$794$	340.485	−	424.457i	0.428823	−	0.534580i
$795$			673.375i			0.847013i
$796$	−730.279	+	162.288i	−0.917436	+	0.203879i
$797$	232.557			0.291791			0.145896	−	0.989300i	$-0.453394\pi$
$797$	232.557			0.291791			0.145896	+	0.989300i	$0.453394\pi$
$798$	−569.119	−	456.529i	−0.713182	−	0.572092i
$799$		−	203.413i		−	0.254585i
$800$	162.015	−	665.760i	0.202519	−	0.832200i
$801$	−170.740			−0.213158
$802$	241.663	−	301.262i	0.301325	−	0.375639i
$803$		−	770.662i		−	0.959728i
$804$	19.5715	+	88.0698i	0.0243427	+	0.109540i
$805$	1639.24			2.03633
$806$	−47.2399	−	37.8944i	−0.0586104	−	0.0470153i
$807$		−	209.727i		−	0.259885i
$808$	1294.25	+	637.028i	1.60179	+	0.788401i
$809$	−552.211			−0.682585			−0.341293	−	0.939957i	$-0.610865\pi$
$809$	−552.211			−0.682585			−0.341293	+	0.939957i	$0.610865\pi$
$810$	−76.7313	+	95.6549i	−0.0947300	+	0.118092i
$811$			507.695i			0.626011i	0.949751	+	0.313005i	$0.101336\pi$
$811$			507.695i			0.626011i	−0.949751	+	0.313005i	$0.898664\pi$
$812$	695.395	−	154.536i	0.856398	−	0.190315i
$813$	−503.082			−0.618797
$814$	−829.297	−	665.235i	−1.01879	−	0.817242i
$815$			429.997i			0.527603i
$816$	−146.386	−	313.096i	−0.179395	−	0.383696i
$817$	13.7452			0.0168240
$818$	718.298	−	895.446i	0.878115	−	1.09468i
$819$			121.509i			0.148362i
$820$	−329.570	−	1483.03i	−0.401914	−	1.80857i
$821$	−528.853			−0.644158			−0.322079	−	0.946713i	$-0.604382\pi$
$821$	−528.853			−0.644158			−0.322079	+	0.946713i	$0.604382\pi$
$822$	305.563	+	245.113i	0.371731	+	0.298191i
$823$		−	1197.69i		−	1.45527i	−0.685964	−	0.727636i	$-0.740619\pi$
$823$		−	1197.69i		−	1.45527i	0.685964	−	0.727636i	$-0.259381\pi$
$824$	599.512	−	1218.03i	0.727563	−	1.47819i
$825$	804.225			0.974818
$826$	−202.381	+	252.292i	−0.245013	+	0.305439i
$827$		−	1507.56i		−	1.82293i	−0.411382	−	0.911463i	$-0.634954\pi$
$827$		−	1507.56i		−	1.82293i	0.411382	−	0.911463i	$-0.365046\pi$
$828$	−250.915	+	55.7603i	−0.303038	+	0.0673433i
$829$	−917.099			−1.10627			−0.553136	−	0.833091i	$-0.686569\pi$
$829$	−917.099			−1.10627			−0.553136	+	0.833091i	$0.686569\pi$
$830$	−334.606	−	268.410i	−0.403140	−	0.323386i
$831$		−	885.863i		−	1.06602i
$832$	140.754	+	182.856i	0.169175	+	0.219779i
$833$	−962.703			−1.15571
$834$	305.631	−	381.006i	0.366464	−	0.456842i
$835$		−	1001.97i		−	1.19996i
$836$	−352.798	−	1587.55i	−0.422007	−	1.89899i
$837$	43.6386			0.0521369
$838$	963.519	+	772.904i	1.14978	+	0.922320i
$839$			806.594i			0.961376i	0.876892	+	0.480688i	$0.159613\pi$
$839$			806.594i			0.961376i	−0.876892	+	0.480688i	$0.840387\pi$
$840$	951.424	+	468.290i	1.13265	+	0.557488i
$841$	−589.666			−0.701149
$842$	−119.443	+	148.901i	−0.141857	+	0.176842i
$843$		−	42.2630i		−	0.0501340i
$844$	498.284	−	110.732i	0.590384	−	0.131199i
$845$	88.5644			0.104810
$846$	−76.3349	−	61.2334i	−0.0902303	−	0.0723799i
$847$			3923.08i			4.63173i
$848$	−827.123	+	386.717i	−0.975381	+	0.456034i
$849$	400.486			0.471715
$850$	−334.196	+	416.617i	−0.393172	+	0.490137i
$851$		−	525.072i		−	0.617006i
$852$	174.045	+	783.184i	0.204278	+	0.919230i
$853$	−1130.05			−1.32480			−0.662399	−	0.749151i	$-0.730462\pi$
$853$	−1130.05			−1.32480			−0.662399	+	0.749151i	$0.730462\pi$
$854$	−1646.79	−	1321.00i	−1.92833	−	1.54684i
$855$		−	383.193i		−	0.448179i
$856$	−209.481	+	425.603i	−0.244721	+	0.497200i
$857$	−281.351			−0.328297			−0.164149	−	0.986436i	$-0.552488\pi$
$857$	−281.351			−0.328297			−0.164149	+	0.986436i	$0.552488\pi$
$858$	−169.474	+	211.269i	−0.197522	+	0.246235i
$859$			154.122i			0.179420i	0.995968	+	0.0897100i	$0.0285940\pi$
$859$			154.122i			0.179420i	−0.995968	+	0.0897100i	$0.971406\pi$
$860$	−19.5021	+	4.33389i	−0.0226768	+	0.00503941i
$861$	1084.71			1.25983
$862$	4.91844	+	3.94542i	0.00570585	+	0.00457705i
$863$		−	678.352i		−	0.786039i	−0.919530	−	0.393019i	$-0.871431\pi$
$863$		−	678.352i		−	0.786039i	0.919530	−	0.393019i	$-0.128569\pi$
$864$	−161.562	−	39.3167i	−0.186993	−	0.0455054i
$865$	−326.230			−0.377144
$866$	2.95343	−	3.68181i	0.00341042	−	0.00425151i
$867$		−	231.152i		−	0.266612i
$868$	−81.8640	−	368.379i	−0.0943133	−	0.424400i
$869$	1053.33			1.21212
$870$	291.844	+	234.108i	0.335453	+	0.269089i
$871$			46.9511i			0.0539048i
$872$	529.169	+	260.456i	0.606845	+	0.298689i
$873$	−46.8110			−0.0536208
$874$	502.583	−	626.531i	0.575037	−	0.716855i
$875$			274.574i			0.313799i
$876$	240.359	−	53.4144i	0.274383	−	0.0609754i
$877$	1196.44			1.36424			0.682121	−	0.731239i	$-0.261058\pi$
$877$	1196.44			1.36424			0.682121	+	0.731239i	$0.261058\pi$
$878$	512.626	+	411.212i	0.583856	+	0.468350i
$879$			784.365i			0.892338i
$880$	1001.12	+	2141.22i	1.13763	+	2.43321i
$881$	1501.00			1.70374			0.851871	−	0.523752i	$-0.175468\pi$
$881$	1501.00			1.70374			0.851871	+	0.523752i	$0.175468\pi$
$882$	−289.801	+	361.273i	−0.328573	+	0.409606i
$883$		−	1416.14i		−	1.60379i	−0.597467	−	0.801894i	$-0.703826\pi$
$883$		−	1416.14i		−	1.60379i	0.597467	−	0.801894i	$-0.296174\pi$
$884$	−39.0201	−	175.586i	−0.0441404	−	0.198627i
$885$	−169.871			−0.191944
$886$	−171.650	−	137.692i	−0.193736	−	0.155409i
$887$		−	264.906i		−	0.298654i	−0.988788	−	0.149327i	$-0.952289\pi$
$887$		−	264.906i		−	0.298654i	0.988788	−	0.149327i	$-0.0477108\pi$
$888$	150.000	−	304.754i	0.168919	−	0.343192i
$889$	−1241.32			−1.39632
$890$	−485.225	+	604.892i	−0.545197	+	0.679654i
$891$		−	195.163i		−	0.219039i
$892$	404.227	−	89.8303i	0.453169	−	0.100707i
$893$	305.797			0.342438
$894$	176.789	+	141.815i	0.197751	+	0.158629i
$895$			644.574i			0.720194i
$896$	−28.8131	+	1437.60i	−0.0321575	+	1.60446i
$897$	−133.766			−0.149126
$898$	−94.1409	+	117.358i	−0.104834	+	0.130688i
$899$		−	133.142i		−	0.148100i
$900$	55.7407	+	250.827i	0.0619341	+	0.278697i
$901$	711.717			0.789919
$902$	1886.02	+	1512.90i	2.09093	+	1.67727i
$903$		−	14.2642i		−	0.0157964i
$904$	−619.109	−	304.725i	−0.684856	−	0.337085i
$905$	−1305.76			−1.44283
$906$	324.872	−	404.993i	0.358579	−	0.447012i
$907$			1502.59i			1.65666i	0.560240	+	0.828330i	$0.310709\pi$
$907$			1502.59i			1.65666i	−0.560240	+	0.828330i	$0.689291\pi$
$908$	53.9135	−	11.9811i	0.0593762	−	0.0131950i
$909$	−540.947			−0.595102
$910$	430.477	+	345.315i	0.473052	+	0.379467i
$911$		−	1060.50i		−	1.16410i	−0.813151	−	0.582052i	$-0.802250\pi$
$911$		−	1060.50i		−	1.16410i	0.813151	−	0.582052i	$-0.197750\pi$
$912$	470.685	−	220.066i	0.516102	−	0.241301i
$913$	682.692			0.747745
$914$	−1013.13	+	1262.99i	−1.10846	+	1.38183i
$915$		−	1108.80i		−	1.21180i
$916$	−179.354	−	807.075i	−0.195801	−	0.881086i
$917$	1643.42			1.79217
$918$	101.101	+	81.1003i	0.110132	+	0.0883446i
$919$			747.698i			0.813599i	0.913517	+	0.406800i	$0.133355\pi$
$919$			747.698i			0.813599i	−0.913517	+	0.406800i	$0.866645\pi$
$920$	−515.530	+	1047.40i	−0.560359	+	1.13848i
$921$	−475.711			−0.516516
$922$	−133.371	+	166.264i	−0.144654	+	0.180329i
$923$			417.525i			0.452356i
$924$	−1647.49	+	366.117i	−1.78300	+	0.396231i
$925$	−524.888			−0.567447
$926$	475.058	+	381.076i	0.513022	+	0.411530i
$927$			509.090i			0.549180i
$928$	−119.955	+	492.926i	−0.129262	+	0.531171i
$929$	1369.57			1.47424			0.737120	−	0.675762i	$-0.236185\pi$
$929$	1369.57			1.47424			0.737120	+	0.675762i	$0.236185\pi$
$930$	124.017	−	154.602i	0.133351	−	0.166238i
$931$		−	1447.26i		−	1.55452i
$932$	−359.801	−	1619.07i	−0.386052	−	1.73719i
$933$	555.409			0.595294
$934$	−1280.23	−	1026.96i	−1.37069	−	1.09952i
$935$		−	1842.46i		−	1.97055i
$936$	−77.6384	−	38.2136i	−0.0829470	−	0.0408265i
$937$	−1398.58			−1.49261			−0.746306	−	0.665603i	$-0.768174\pi$
$937$	−1398.58			−1.49261			−0.746306	+	0.665603i	$0.768174\pi$
$938$	−183.063	+	228.211i	−0.195164	+	0.243295i
$939$			203.348i			0.216558i
$940$	−433.872	+	96.4182i	−0.461566	+	0.102573i
$941$	−127.702			−0.135709			−0.0678544	−	0.997695i	$-0.521615\pi$
$941$	−127.702			−0.135709			−0.0678544	+	0.997695i	$0.521615\pi$
$942$	271.946	+	218.146i	0.288690	+	0.231578i
$943$			1194.14i			1.26632i
$944$	−97.5560	−	208.656i	−0.103343	−	0.221034i
$945$	−397.660			−0.420804
$946$	19.8949	−	24.8014i	0.0210305	−	0.0262171i
$947$		−	724.498i		−	0.765046i	−0.923946	−	0.382523i	$-0.875055\pi$
$947$		−	724.498i		−	0.765046i	0.923946	−	0.382523i	$-0.124945\pi$
$948$	73.0061	+	328.520i	0.0770107	+	0.346540i
$949$	128.139			0.135025
$950$	−626.311	−	502.406i	−0.659275	−	0.528849i
$951$		−	560.383i		−	0.589256i
$952$	494.954	−	1005.60i	0.519910	−	1.05630i
$953$	1077.92			1.13108			0.565540	−	0.824721i	$-0.308668\pi$
$953$	1077.92			1.13108			0.565540	+	0.824721i	$0.308668\pi$
$954$	214.247	−	267.086i	0.224578	−	0.279964i
$955$		−	876.412i		−	0.917709i
$956$	949.596	−	211.026i	0.993301	−	0.220739i
$957$	−595.445			−0.622200
$958$	368.794	+	295.835i	0.384963	+	0.308805i
$959$			1270.30i			1.32461i
$960$	−598.432	+	460.643i	−0.623367	+	0.479836i
$961$	890.469			0.926607
$962$	110.609	−	137.888i	0.114978	−	0.143335i
$963$		−	177.886i		−	0.184721i
$964$	−255.020	−	1147.57i	−0.264544	−	1.19042i
$965$	−1395.69			−1.44631
$966$	−650.185	−	521.557i	−0.673069	−	0.539914i
$967$			91.9069i			0.0950434i	0.998870	+	0.0475217i	$0.0151323\pi$
$967$			91.9069i			0.0950434i	−0.998870	+	0.0475217i	$0.984868\pi$
$968$	−2506.67	−	1233.78i	−2.58953	−	1.27457i
$969$	−405.012			−0.417969
$970$	−133.032	+	165.841i	−0.137146	+	0.170970i
$971$		−	659.338i		−	0.679030i	−0.940601	−	0.339515i	$-0.889737\pi$
$971$		−	659.338i		−	0.679030i	0.940601	−	0.339515i	$-0.110263\pi$
$972$	60.8689	−	13.5267i	0.0626224	−	0.0139164i
$973$	1583.93			1.62789
$974$	1219.80	+	978.488i	1.25237	+	1.00461i
$975$			133.719i			0.137148i
$976$	1361.97	−	636.780i	1.39546	−	0.652438i
$977$	1141.60			1.16847			0.584236	−	0.811584i	$-0.301394\pi$
$977$	1141.60			1.16847			0.584236	+	0.811584i	$0.301394\pi$
$978$	136.812	−	170.553i	0.139889	−	0.174389i
$979$		−	1234.15i		−	1.26063i
$980$	456.322	+	2053.40i	0.465635	+	2.09531i
$981$	−221.173			−0.225456
$982$	−1231.74	−	988.065i	−1.25432	−	1.00618i
$983$		−	533.824i		−	0.543056i	−0.962430	−	0.271528i	$-0.912471\pi$
$983$		−	533.824i		−	0.543056i	0.962430	−	0.271528i	$-0.0875290\pi$
$984$	−341.135	+	693.083i	−0.346682	+	0.704353i
$985$	−546.385			−0.554706
$986$	247.438	−	308.461i	0.250951	−	0.312841i
$987$		−	317.342i		−	0.321522i
$988$	263.964	−	58.6600i	0.267170	−	0.0593724i
$989$	15.7031			0.0158778
$990$	−691.420	−	554.635i	−0.698404	−	0.560237i
$991$			1570.65i			1.58492i	0.609926	+	0.792458i	$0.291199\pi$
$991$			1570.65i			1.58492i	−0.609926	+	0.792458i	$0.708801\pi$
$992$	261.123	+	63.5453i	0.263229	+	0.0640578i
$993$	−50.1261			−0.0504794
$994$	−1627.94	+	2029.42i	−1.63777	+	2.04167i
$995$		−	1274.13i		−	1.28053i
$996$	47.3172	+	212.923i	0.0475073	+	0.213778i
$997$	810.574			0.813013			0.406507	−	0.913648i	$-0.366747\pi$
$997$	810.574			0.813013			0.406507	+	0.913648i	$0.366747\pi$
$998$	274.594	+	220.270i	0.275144	+	0.220712i
$999$			127.376i			0.127503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.8	yes	24
3.2	odd	2		468.3.f.b.235.17		24
4.3	odd	2	inner	156.3.f.a.79.7	✓	24
8.3	odd	2		2496.3.k.e.703.24		24
8.5	even	2		2496.3.k.e.703.23		24
12.11	even	2		468.3.f.b.235.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.7	✓	24	4.3	odd	2	inner
156.3.f.a.79.8	yes	24	1.1	even	1	trivial
468.3.f.b.235.17		24	3.2	odd	2
468.3.f.b.235.18		24	12.11	even	2
2496.3.k.e.703.23		24	8.5	even	2
2496.3.k.e.703.24		24	8.3	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25145 + 1.56009i) q^{2} +1.73205i q^{3} +(-0.867741 - 3.90474i) q^{4} +6.81265 q^{5} +(-2.70215 - 2.16758i) q^{6} -11.2335i q^{7} +(7.17767 + 3.53285i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.25145 + 1.56009i) q^{2} +1.73205i q^{3} +(-0.867741 - 3.90474i) q^{4} +6.81265 q^{5} +(-2.70215 - 2.16758i) q^{6} -11.2335i q^{7} +(7.17767 + 3.53285i) q^{8} -3.00000 q^{9} +(-8.52570 + 10.6283i) q^{10} -21.6848i q^{11} +(6.76322 - 1.50297i) q^{12} +3.60555 q^{13} +(17.5252 + 14.0581i) q^{14} +11.7999i q^{15} +(-14.4941 + 6.77661i) q^{16} +12.4717 q^{17} +(3.75435 - 4.68026i) q^{18} +18.7491i q^{19} +(-5.91161 - 26.6017i) q^{20} +19.4569 q^{21} +(33.8302 + 27.1375i) q^{22} +21.4197i q^{23} +(-6.11907 + 12.4321i) q^{24} +21.4122 q^{25} +(-4.51217 + 5.62497i) q^{26} -5.19615i q^{27} +(-43.8638 + 9.74774i) q^{28} -15.8535 q^{29} +(-18.4088 - 14.7669i) q^{30} +8.39825i q^{31} +(7.56650 - 31.0926i) q^{32} +37.5592 q^{33} +(-15.6078 + 19.4570i) q^{34} -76.5297i q^{35} +(2.60322 + 11.7142i) q^{36} -24.5135 q^{37} +(-29.2502 - 23.4636i) q^{38} +6.24500i q^{39} +(48.8990 + 24.0680i) q^{40} +55.7495 q^{41} +(-24.3494 + 30.3545i) q^{42} -0.733115i q^{43} +(-84.6737 + 18.8168i) q^{44} -20.4379 q^{45} +(-33.4166 - 26.8057i) q^{46} -16.3100i q^{47} +(-11.7374 - 25.1044i) q^{48} -77.1908 q^{49} +(-26.7963 + 33.4049i) q^{50} +21.6017i q^{51} +(-3.12868 - 14.0788i) q^{52} +57.0664 q^{53} +(8.10645 + 6.50273i) q^{54} -147.731i q^{55} +(39.6861 - 80.6302i) q^{56} -32.4744 q^{57} +(19.8399 - 24.7328i) q^{58} +14.3960i q^{59} +(46.0754 - 10.2392i) q^{60} -93.9673 q^{61} +(-13.1020 - 10.5100i) q^{62} +33.7004i q^{63} +(39.0380 + 50.7152i) q^{64} +24.5634 q^{65} +(-47.0035 + 58.5956i) q^{66} +13.0219i q^{67} +(-10.8222 - 48.6989i) q^{68} -37.1000 q^{69} +(119.393 + 95.7731i) q^{70} +115.800i q^{71} +(-21.5330 - 10.5985i) q^{72} +35.5392 q^{73} +(30.6775 - 38.2432i) q^{74} +37.0870i q^{75} +(73.2104 - 16.2694i) q^{76} -243.596 q^{77} +(-9.74274 - 7.81531i) q^{78} +48.5745i q^{79} +(-98.7429 + 46.1667i) q^{80} +9.00000 q^{81} +(-69.7678 + 86.9741i) q^{82} +31.4825i q^{83} +(-16.8836 - 75.9744i) q^{84} +84.9655 q^{85} +(1.14372 + 0.917458i) q^{86} -27.4591i q^{87} +(76.6091 - 155.647i) q^{88} +56.9132 q^{89} +(25.5771 - 31.8850i) q^{90} -40.5028i q^{91} +(83.6385 - 18.5868i) q^{92} -14.5462 q^{93} +(25.4450 + 20.4111i) q^{94} +127.731i q^{95} +(53.8539 + 13.1056i) q^{96} +15.6037 q^{97} +(96.6005 - 120.424i) q^{98} +65.0544i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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