LMFDB - Embedded newform 76.3.b.b.39.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.b (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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.3
Root			$-1.89728 + 0.632718i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.b.39.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +O(q^{10})$	\(q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +(-10.9903 - 3.66514i) q^{10} +8.07883i q^{11} +(12.8296 - 17.0963i) q^{12} -14.0396 q^{13} +(-3.71745 + 11.1472i) q^{14} -30.9544i q^{15} +(4.47149 + 15.3625i) q^{16} +29.9906 q^{17} +(37.1016 + 12.3729i) q^{18} -4.35890i q^{19} +(18.5327 + 13.9076i) q^{20} -31.3962 q^{21} +(5.11162 - 15.3278i) q^{22} +8.74865i q^{23} +(-35.1585 + 24.3189i) q^{24} +8.55515 q^{25} +(26.6370 + 8.88309i) q^{26} +56.4036i q^{27} +(14.1061 - 18.7973i) q^{28} +13.4473 q^{29} +(-19.5854 + 58.7291i) q^{30} -7.65793i q^{31} +(1.23646 - 31.9761i) q^{32} +43.1708 q^{33} +(-56.9006 - 18.9756i) q^{34} -34.0341i q^{35} +(-62.5635 - 46.9497i) q^{36} +25.1221 q^{37} +(-2.75796 + 8.27005i) q^{38} +75.0232i q^{39} +(-26.3622 - 38.1125i) q^{40} +49.6861 q^{41} +(59.5673 + 19.8649i) q^{42} -47.2402i q^{43} +(-19.3963 + 25.8469i) q^{44} -113.277 q^{45} +(5.53543 - 16.5986i) q^{46} +46.8391i q^{47} +(82.0925 - 23.8943i) q^{48} +14.4801 q^{49} +(-16.2315 - 5.41300i) q^{50} -160.261i q^{51} +(-44.9173 - 33.7074i) q^{52} -14.1940 q^{53} +(35.6876 - 107.013i) q^{54} +46.7981i q^{55} +(-38.6565 + 26.7385i) q^{56} -23.2927 q^{57} +(-25.5133 - 8.50835i) q^{58} +100.107i q^{59} +(74.3179 - 99.0334i) q^{60} -31.1928 q^{61} +(-4.84532 + 14.5292i) q^{62} +114.894i q^{63} +(-22.5778 + 59.8853i) q^{64} -81.3267 q^{65} +(-81.9071 - 27.3150i) q^{66} +34.5861i q^{67} +(95.9501 + 72.0041i) q^{68} +46.7502 q^{69} +(-21.5340 + 64.5722i) q^{70} -66.0243i q^{71} +(88.9944 + 128.662i) q^{72} -27.5063 q^{73} +(-47.6636 - 15.8952i) q^{74} -45.7162i q^{75} +(10.4652 - 13.9456i) q^{76} +47.4661 q^{77} +(47.4686 - 142.340i) q^{78} +40.9739i q^{79} +(25.9019 + 88.9899i) q^{80} +125.408 q^{81} +(-94.2684 - 31.4373i) q^{82} -87.8564i q^{83} +(-100.447 - 75.3787i) q^{84} +173.726 q^{85} +(-29.8898 + 89.6279i) q^{86} -71.8584i q^{87} +(53.1541 - 36.7663i) q^{88} +28.6482 q^{89} +(214.918 + 71.6723i) q^{90} +82.4875i q^{91} +(-21.0045 + 27.9899i) q^{92} -40.9217 q^{93} +(29.6360 - 88.8669i) q^{94} -25.2497i q^{95} +(-170.871 - 6.60728i) q^{96} +9.35629 q^{97} +(-27.4728 - 9.16182i) q^{98} -157.983i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.89728	−	0.632718i	−0.948639	−	0.316359i
$2$	−1.89728	−	0.632718i	−0.948639	−	0.316359i
$3$		−	5.34370i		−	1.78123i	−0.454754	−	0.890617i	$-0.650273\pi$
$3$		−	5.34370i		−	1.78123i	0.454754	−	0.890617i	$-0.349727\pi$
$4$	3.19934	+	2.40089i	0.799834	+	0.600222i
$5$	5.79268			1.15854			0.579268	−	0.815137i	$-0.303338\pi$
$5$	5.79268			1.15854			0.579268	+	0.815137i	$0.303338\pi$
$6$	−3.38106	+	10.1385i	−0.563510	+	1.68975i
$7$		−	5.87536i		−	0.839338i	−0.907677	−	0.419669i	$-0.862146\pi$
$7$		−	5.87536i		−	0.839338i	0.907677	−	0.419669i	$-0.137854\pi$
$8$	−4.55095	−	6.57943i	−0.568868	−	0.822429i
$9$	−19.5551			−2.17279
$10$	−10.9903	−	3.66514i	−1.09903	−	0.366514i
$11$			8.07883i			0.734439i	0.930134	+	0.367219i	$0.119690\pi$
$11$			8.07883i			0.734439i	−0.930134	+	0.367219i	$0.880310\pi$
$12$	12.8296	−	17.0963i	1.06914	−	1.42469i
$13$	−14.0396			−1.07997			−0.539983	−	0.841676i	$-0.681569\pi$
$13$	−14.0396			−1.07997			−0.539983	+	0.841676i	$0.681569\pi$
$14$	−3.71745	+	11.1472i	−0.265532	+	0.796229i
$15$		−	30.9544i		−	2.06362i
$16$	4.47149	+	15.3625i	0.279468	+	0.960155i
$17$	29.9906			1.76415			0.882077	−	0.471104i	$-0.156145\pi$
$17$	29.9906			1.76415			0.882077	+	0.471104i	$0.156145\pi$
$18$	37.1016	+	12.3729i	2.06120	+	0.687383i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	18.5327	+	13.9076i	0.926636	+	0.695378i
$21$	−31.3962			−1.49506
$22$	5.11162	−	15.3278i	0.232346	−	0.696718i
$23$			8.74865i			0.380376i	0.981748	+	0.190188i	$0.0609098\pi$
$23$			8.74865i			0.380376i	−0.981748	+	0.190188i	$0.939090\pi$
$24$	−35.1585	+	24.3189i	−1.46494	+	1.01329i
$25$	8.55515			0.342206
$26$	26.6370	+	8.88309i	1.02450	+	0.341657i
$27$			56.4036i			2.08902i
$28$	14.1061	−	18.7973i	0.503789	−	0.671331i
$29$	13.4473			0.463700			0.231850	−	0.972752i	$-0.425522\pi$
$29$	13.4473			0.463700			0.231850	+	0.972752i	$0.425522\pi$
$30$	−19.5854	+	58.7291i	−0.652846	+	1.95764i
$31$		−	7.65793i		−	0.247030i	−0.992343	−	0.123515i	$-0.960583\pi$
$31$		−	7.65793i		−	0.247030i	0.992343	−	0.123515i	$-0.0394167\pi$
$32$	1.23646	−	31.9761i	0.0386394	−	0.999253i
$33$	43.1708			1.30821
$34$	−56.9006	−	18.9756i	−1.67355	−	0.558107i
$35$		−	34.0341i		−	0.972403i
$36$	−62.5635	−	46.9497i	−1.73787	−	1.30416i
$37$	25.1221			0.678975			0.339488	−	0.940611i	$-0.389746\pi$
$37$	25.1221			0.678975			0.339488	+	0.940611i	$0.389746\pi$
$38$	−2.75796	+	8.27005i	−0.0725778	+	0.217633i
$39$			75.0232i			1.92367i
$40$	−26.3622	−	38.1125i	−0.659054	−	0.952813i
$41$	49.6861			1.21186			0.605928	−	0.795519i	$-0.292802\pi$
$41$	49.6861			1.21186			0.605928	+	0.795519i	$0.292802\pi$
$42$	59.5673	+	19.8649i	1.41827	+	0.472975i
$43$		−	47.2402i		−	1.09861i	−0.835622	−	0.549305i	$-0.814892\pi$
$43$		−	47.2402i		−	1.09861i	0.835622	−	0.549305i	$-0.185108\pi$
$44$	−19.3963	+	25.8469i	−0.440826	+	0.587429i
$45$	−113.277			−2.51726
$46$	5.53543	−	16.5986i	0.120336	−	0.360840i
$47$			46.8391i			0.996577i	0.867011	+	0.498289i	$0.166038\pi$
$47$			46.8391i			0.996577i	−0.867011	+	0.498289i	$0.833962\pi$
$48$	82.0925	−	23.8943i	1.71026	−	0.497798i
$49$	14.4801			0.295512
$50$	−16.2315	−	5.41300i	−0.324630	−	0.108260i
$51$		−	160.261i		−	3.14237i
$52$	−44.9173	−	33.7074i	−0.863793	−	0.648219i
$53$	−14.1940			−0.267811			−0.133906	−	0.990994i	$-0.542752\pi$
$53$	−14.1940			−0.267811			−0.133906	+	0.990994i	$0.542752\pi$
$54$	35.6876	−	107.013i	0.660881	−	1.98173i
$55$			46.7981i			0.850874i
$56$	−38.6565	+	26.7385i	−0.690295	+	0.477473i
$57$	−23.2927			−0.408643
$58$	−25.5133	−	8.50835i	−0.439884	−	0.146696i
$59$			100.107i			1.69673i	0.529415	+	0.848363i	$0.322411\pi$
$59$			100.107i			1.69673i	−0.529415	+	0.848363i	$0.677589\pi$
$60$	74.3179	−	99.0334i	1.23863	−	1.65056i
$61$	−31.1928			−0.511357			−0.255678	−	0.966762i	$-0.582299\pi$
$61$	−31.1928			−0.511357			−0.255678	+	0.966762i	$0.582299\pi$
$62$	−4.84532	+	14.5292i	−0.0781503	+	0.234343i
$63$			114.894i			1.82371i
$64$	−22.5778	+	59.8853i	−0.352778	+	0.935707i
$65$	−81.3267			−1.25118
$66$	−81.9071	−	27.3150i	−1.24102	−	0.413863i
$67$			34.5861i			0.516210i	0.966117	+	0.258105i	$0.0830981\pi$
$67$			34.5861i			0.516210i	−0.966117	+	0.258105i	$0.916902\pi$
$68$	95.9501	+	72.0041i	1.41103	+	1.05888i
$69$	46.7502			0.677539
$70$	−21.5340	+	64.5722i	−0.307629	+	0.922460i
$71$		−	66.0243i		−	0.929919i	−0.885332	−	0.464960i	$-0.846069\pi$
$71$		−	66.0243i		−	0.929919i	0.885332	−	0.464960i	$-0.153931\pi$
$72$	88.9944	+	128.662i	1.23603	+	1.78697i
$73$	−27.5063			−0.376798			−0.188399	−	0.982093i	$-0.560330\pi$
$73$	−27.5063			−0.376798			−0.188399	+	0.982093i	$0.560330\pi$
$74$	−47.6636	−	15.8952i	−0.644103	−	0.214800i
$75$		−	45.7162i		−	0.609549i
$76$	10.4652	−	13.9456i	0.137700	−	0.183494i
$77$	47.4661			0.616442
$78$	47.4686	−	142.340i	0.608571	−	1.82487i
$79$			40.9739i			0.518657i	0.965789	+	0.259329i	$0.0835013\pi$
$79$			40.9739i			0.518657i	−0.965789	+	0.259329i	$0.916499\pi$
$80$	25.9019	+	88.9899i	0.323774	+	1.11237i
$81$	125.408			1.54824
$82$	−94.2684	−	31.4373i	−1.14961	−	0.383382i
$83$		−	87.8564i		−	1.05851i	−0.848463	−	0.529255i	$-0.822471\pi$
$83$		−	87.8564i		−	1.05851i	0.848463	−	0.529255i	$-0.177529\pi$
$84$	−100.447	−	75.3787i	−1.19580	−	0.897365i
$85$	173.726			2.04384
$86$	−29.8898	+	89.6279i	−0.347555	+	1.04219i
$87$		−	71.8584i		−	0.825958i
$88$	53.1541	−	36.7663i	0.604024	−	0.417799i
$89$	28.6482			0.321890			0.160945	−	0.986963i	$-0.448546\pi$
$89$	28.6482			0.321890			0.160945	+	0.986963i	$0.448546\pi$
$90$	214.918	+	71.6723i	2.38797	+	0.796359i
$91$			82.4875i			0.906457i
$92$	−21.0045	+	27.9899i	−0.228310	+	0.304238i
$93$	−40.9217			−0.440018
$94$	29.6360	−	88.8669i	0.315276	−	0.945393i
$95$		−	25.2497i		−	0.265786i
$96$	−170.871	−	6.60728i	−1.77990	−	0.0688258i
$97$	9.35629			0.0964566			0.0482283	−	0.998836i	$-0.484642\pi$
$97$	9.35629			0.0964566			0.0482283	+	0.998836i	$0.484642\pi$
$98$	−27.4728	−	9.16182i	−0.280334	−	0.0934879i
$99$		−	157.983i		−	1.59578i
$100$	27.3708	+	20.5399i	0.273708	+	0.205399i
$101$	−86.6846			−0.858263			−0.429132	−	0.903242i	$-0.641180\pi$
$101$	−86.6846			−0.858263			−0.429132	+	0.903242i	$0.641180\pi$
$102$	−101.400	+	304.060i	−0.994118	+	2.98098i
$103$			139.602i			1.35536i	0.735358	+	0.677679i	$0.237014\pi$
$103$			139.602i			1.35536i	−0.735358	+	0.677679i	$0.762986\pi$
$104$	63.8933	+	92.3723i	0.614359	+	0.888195i
$105$	−181.868			−1.73208
$106$	26.9300	+	8.98081i	0.254057	+	0.0847246i
$107$		−	53.5627i		−	0.500586i	−0.968170	−	0.250293i	$-0.919473\pi$
$107$		−	53.5627i		−	0.500586i	0.968170	−	0.250293i	$-0.0805269\pi$
$108$	−135.419	+	180.454i	−1.25388	+	1.67087i
$109$	−154.519			−1.41760			−0.708802	−	0.705408i	$-0.750764\pi$
$109$	−154.519			−1.41760			−0.708802	+	0.705408i	$0.750764\pi$
$110$	29.6100	−	88.7890i	0.269182	−	0.807173i
$111$		−	134.245i		−	1.20941i
$112$	90.2602	−	26.2716i	0.805894	−	0.234568i
$113$	−66.0050			−0.584115			−0.292057	−	0.956401i	$-0.594340\pi$
$113$	−66.0050			−0.584115			−0.292057	+	0.956401i	$0.594340\pi$
$114$	44.1927	+	14.7377i	0.387655	+	0.129278i
$115$			50.6782i			0.440680i
$116$	43.0224	+	32.2854i	0.370883	+	0.278323i
$117$	274.546			2.34654
$118$	63.3394	−	189.931i	0.536775	−	1.60958i
$119$		−	176.206i		−	1.48072i
$120$	−203.662	+	140.872i	−1.69718	+	1.17393i
$121$	55.7325			0.460600
$122$	59.1814	+	19.7362i	0.485093	+	0.161772i
$123$		−	265.508i		−	2.15860i
$124$	18.3858	−	24.5003i	0.148273	−	0.197583i
$125$	−95.2598			−0.762078
$126$	72.6953	−	217.985i	0.576947	−	1.73004i
$127$			222.988i			1.75581i	0.478833	+	0.877906i	$0.341060\pi$
$127$			222.988i			1.75581i	−0.478833	+	0.877906i	$0.658940\pi$
$128$	80.7268	−	99.3337i	0.630678	−	0.776044i
$129$	−252.438			−1.95688
$130$	154.299	+	51.4569i	1.18692	+	0.395822i
$131$			199.333i			1.52163i	0.648971	+	0.760813i	$0.275200\pi$
$131$			199.333i			1.52163i	−0.648971	+	0.760813i	$0.724800\pi$
$132$	138.118	+	103.648i	1.04635	+	0.785214i
$133$	−25.6101			−0.192557
$134$	21.8833	−	65.6195i	0.163308	−	0.489698i
$135$			326.728i			2.42021i
$136$	−136.486	−	197.321i	−1.00357	−	1.45089i
$137$	−6.01427			−0.0438998			−0.0219499	−	0.999759i	$-0.506987\pi$
$137$	−6.01427			−0.0438998			−0.0219499	+	0.999759i	$0.506987\pi$
$138$	−88.6982	−	29.5797i	−0.642740	−	0.214346i
$139$		−	77.3080i		−	0.556172i	−0.960556	−	0.278086i	$-0.910300\pi$
$139$		−	77.3080i		−	0.556172i	0.960556	−	0.278086i	$-0.0897001\pi$
$140$	81.7120	−	108.887i	0.583657	−	0.777761i
$141$	250.294			1.77514
$142$	−41.7748	+	125.266i	−0.294188	+	0.882158i
$143$		−	113.423i		−	0.793169i
$144$	−87.4406	−	300.416i	−0.607227	−	2.08622i
$145$	77.8959			0.537213
$146$	52.1870	+	17.4037i	0.357445	+	0.119203i
$147$		−	77.3773i		−	0.526376i
$148$	80.3740	+	60.3153i	0.543067	+	0.407536i
$149$	250.996			1.68454			0.842270	−	0.539056i	$-0.181219\pi$
$149$	250.996			1.68454			0.842270	+	0.539056i	$0.181219\pi$
$150$	−28.9255	+	86.7363i	−0.192836	+	0.578242i
$151$		−	62.0159i		−	0.410701i	−0.978688	−	0.205351i	$-0.934167\pi$
$151$		−	62.0159i		−	0.410701i	0.978688	−	0.205351i	$-0.0658335\pi$
$152$	−28.6791	+	19.8371i	−0.188678	+	0.130507i
$153$	−586.471			−3.83315
$154$	−90.0564	−	30.0326i	−0.584782	−	0.195017i
$155$		−	44.3600i		−	0.286193i
$156$	−180.122	+	240.024i	−1.15463	+	1.53862i
$157$	−100.150			−0.637898			−0.318949	−	0.947772i	$-0.603330\pi$
$157$	−100.150			−0.637898			−0.318949	+	0.947772i	$0.603330\pi$
$158$	25.9250	−	77.7390i	0.164082	−	0.492019i
$159$			75.8485i			0.477035i
$160$	7.16242	−	185.227i	0.0447651	−	1.15767i
$161$	51.4015			0.319264
$162$	−237.933	−	79.3476i	−1.46872	−	0.489800i
$163$		−	187.915i		−	1.15285i	−0.817150	−	0.576425i	$-0.804447\pi$
$163$		−	187.915i		−	1.15285i	0.817150	−	0.576425i	$-0.195553\pi$
$164$	158.963	+	119.291i	0.969284	+	0.727382i
$165$	250.075			1.51561
$166$	−55.5883	+	166.688i	−0.334869	+	1.00414i
$167$			24.2604i			0.145272i	0.997359	+	0.0726361i	$0.0231412\pi$
$167$			24.2604i			0.145272i	−0.997359	+	0.0726361i	$0.976859\pi$
$168$	142.882	+	206.569i	0.850490	+	1.22958i
$169$	28.1093			0.166327
$170$	−329.607	−	109.920i	−1.93886	−	0.646587i
$171$			85.2389i			0.498473i
$172$	113.418	−	151.137i	0.659410	−	0.878706i
$173$	−250.771			−1.44954			−0.724772	−	0.688989i	$-0.758055\pi$
$173$	−250.771			−1.44954			−0.724772	+	0.688989i	$0.758055\pi$
$174$	−45.4661	+	136.335i	−0.261299	+	0.783537i
$175$		−	50.2646i		−	0.287226i
$176$	−124.111	+	36.1244i	−0.705175	+	0.205252i
$177$	534.941			3.02227
$178$	−54.3537	−	18.1263i	−0.305358	−	0.101833i
$179$			62.4162i			0.348694i	0.984684	+	0.174347i	$0.0557815\pi$
$179$			62.4162i			0.348694i	−0.984684	+	0.174347i	$0.944219\pi$
$180$	−362.410	−	271.965i	−2.01339	−	1.51091i
$181$	−66.6789			−0.368392			−0.184196	−	0.982890i	$-0.558968\pi$
$181$	−66.6789			−0.368392			−0.184196	+	0.982890i	$0.558968\pi$
$182$	52.1914	−	156.502i	0.286766	−	0.859900i
$183$			166.685i			0.910846i
$184$	57.5612	−	39.8147i	0.312832	−	0.216384i
$185$	145.524			0.786617
$186$	77.6399	+	25.8919i	0.417419	+	0.139204i
$187$			242.289i			1.29566i
$188$	−112.455	+	149.854i	−0.598167	+	0.797096i
$189$	331.392			1.75339
$190$	−15.9760	+	47.9057i	−0.0840840	+	0.252135i
$191$			218.487i			1.14391i	0.820285	+	0.571955i	$0.193815\pi$
$191$			218.487i			1.14391i	−0.820285	+	0.571955i	$0.806185\pi$
$192$	320.009	+	120.649i	1.66671	+	0.628380i
$193$	61.9485			0.320977			0.160488	−	0.987038i	$-0.448693\pi$
$193$	61.9485			0.320977			0.160488	+	0.987038i	$0.448693\pi$
$194$	−17.7515	−	5.91990i	−0.0915025	−	0.0305149i
$195$			434.586i			2.22864i
$196$	46.3267	+	34.7651i	0.236361	+	0.177373i
$197$	−355.348			−1.80380			−0.901898	−	0.431950i	$-0.857826\pi$
$197$	−355.348			−1.80380			−0.901898	+	0.431950i	$0.857826\pi$
$198$	−99.9585	+	299.737i	−0.504841	+	1.51382i
$199$			208.471i			1.04759i	0.851843	+	0.523797i	$0.175485\pi$
$199$			208.471i			1.04759i	−0.851843	+	0.523797i	$0.824515\pi$
$200$	−38.9340	−	56.2880i	−0.194670	−	0.281440i
$201$	184.818			0.919491
$202$	164.465	+	54.8469i	0.814183	+	0.271519i
$203$		−	79.0078i		−	0.389201i
$204$	384.768	−	512.729i	1.88612	−	2.51338i
$205$	287.816			1.40398
$206$	88.3286	−	264.864i	0.428780	−	1.28575i
$207$		−	171.081i		−	0.826479i
$208$	−62.7777	−	215.682i	−0.301816	−	1.03694i
$209$	35.2148			0.168492
$210$	345.055	+	115.071i	1.64312	+	0.547959i
$211$		−	275.150i		−	1.30403i	−0.758206	−	0.652015i	$-0.773924\pi$
$211$		−	275.150i		−	1.30403i	0.758206	−	0.652015i	$-0.226076\pi$
$212$	−45.4114	−	34.0782i	−0.214205	−	0.160746i
$213$	−352.814			−1.65640
$214$	−33.8901	+	101.623i	−0.158365	+	0.474876i
$215$		−	273.648i		−	1.27278i
$216$	371.103	−	256.690i	1.71807	−	1.18838i
$217$	−44.9932			−0.207342
$218$	293.165	+	97.7669i	1.34479	+	0.448472i
$219$			146.985i			0.671165i
$220$	−112.357	+	149.723i	−0.510713	+	0.680558i
$221$	−421.055			−1.90523
$222$	−84.9392	+	254.700i	−0.382609	+	1.14730i
$223$			237.911i			1.06687i	0.845842	+	0.533434i	$0.179099\pi$
$223$			237.911i			1.06687i	−0.845842	+	0.533434i	$0.820901\pi$
$224$	−187.871	−	7.26466i	−0.838711	−	0.0324315i
$225$	−167.297			−0.743543
$226$	125.230	+	41.7626i	0.554114	+	0.184790i
$227$		−	157.067i		−	0.691924i	−0.938249	−	0.345962i	$-0.887553\pi$
$227$		−	157.067i		−	0.691924i	0.938249	−	0.345962i	$-0.112447\pi$
$228$	−74.5210	−	55.9230i	−0.326847	−	0.245276i
$229$	−177.569			−0.775412			−0.387706	−	0.921783i	$-0.626732\pi$
$229$	−177.569			−0.775412			−0.387706	+	0.921783i	$0.626732\pi$
$230$	32.0650	−	96.1506i	0.139413	−	0.418046i
$231$		−	253.644i		−	1.09803i
$232$	−61.1979	−	88.4756i	−0.263784	−	0.381360i
$233$	75.5890			0.324416			0.162208	−	0.986757i	$-0.448138\pi$
$233$	75.5890			0.324416			0.162208	+	0.986757i	$0.448138\pi$
$234$	−520.890	−	173.710i	−2.22602	−	0.742351i
$235$			271.324i			1.15457i
$236$	−240.345	+	320.275i	−1.01841	+	1.35710i
$237$	218.952			0.923850
$238$	−111.489	+	334.312i	−0.468440	+	1.40467i
$239$		−	1.99543i		−	0.00834909i	−0.999991	−	0.00417454i	$-0.998671\pi$
$239$		−	1.99543i		−	0.00834909i	0.999991	−	0.00417454i	$-0.00132880\pi$
$240$	475.536	−	138.412i	1.98140	−	0.576717i
$241$	−64.6551			−0.268278			−0.134139	−	0.990962i	$-0.542827\pi$
$241$	−64.6551			−0.268278			−0.134139	+	0.990962i	$0.542827\pi$
$242$	−105.740	−	35.2630i	−0.436943	−	0.145715i
$243$		−	162.508i		−	0.668758i
$244$	−99.7961	−	74.8903i	−0.409000	−	0.306927i
$245$	83.8785			0.342361
$246$	−167.992	+	503.742i	−0.682893	+	2.04773i
$247$			61.1970i			0.247761i
$248$	−50.3848	+	34.8508i	−0.203165	+	0.140528i
$249$	−469.478			−1.88545
$250$	180.734	+	60.2726i	0.722937	+	0.241090i
$251$			245.790i			0.979245i	0.871935	+	0.489622i	$0.162865\pi$
$251$			245.790i			0.979245i	−0.871935	+	0.489622i	$0.837135\pi$
$252$	−275.847	+	367.583i	−1.09463	+	1.45866i
$253$	−70.6789			−0.279363
$254$	141.089	−	423.071i	0.555467	−	1.66563i
$255$		−	928.341i		−	3.64055i
$256$	−216.012	+	137.386i	−0.843795	+	0.536665i
$257$	276.853			1.07725			0.538625	−	0.842546i	$-0.318944\pi$
$257$	276.853			1.07725			0.538625	+	0.842546i	$0.318944\pi$
$258$	478.945	+	159.722i	1.85638	+	0.619078i
$259$		−	147.601i		−	0.569890i
$260$	−260.191	−	195.256i	−1.00074	−	0.750985i
$261$	−262.964			−1.00752
$262$	126.122	−	378.190i	0.481380	−	1.44347i
$263$		−	95.4157i		−	0.362797i	−0.983410	−	0.181399i	$-0.941938\pi$
$263$		−	95.4157i		−	0.362797i	0.983410	−	0.181399i	$-0.0580624\pi$
$264$	−196.468	−	284.040i	−0.744198	−	1.07591i
$265$	−82.2213			−0.310269
$266$	48.5895	+	16.2040i	0.182667	+	0.0609173i
$267$		−	153.088i		−	0.573362i
$268$	−83.0373	+	110.653i	−0.309841	+	0.412882i
$269$	−128.844			−0.478974			−0.239487	−	0.970900i	$-0.576979\pi$
$269$	−128.844			−0.478974			−0.239487	+	0.970900i	$0.576979\pi$
$270$	206.727	−	619.894i	0.765654	−	2.29590i
$271$		−	317.491i		−	1.17155i	−0.810472	−	0.585777i	$-0.800789\pi$
$271$		−	317.491i		−	1.17155i	0.810472	−	0.585777i	$-0.199211\pi$
$272$	134.103	+	460.730i	0.493025	+	1.69386i
$273$	440.789			1.61461
$274$	11.4107	+	3.80534i	0.0416450	+	0.0138881i
$275$			69.1156i			0.251329i
$276$	149.570	+	112.242i	0.541919	+	0.406674i
$277$	−29.1910			−0.105383			−0.0526913	−	0.998611i	$-0.516780\pi$
$277$	−29.1910			−0.105383			−0.0526913	+	0.998611i	$0.516780\pi$
$278$	−48.9142	+	146.675i	−0.175950	+	0.527607i
$279$			149.752i			0.536746i
$280$	−223.925	+	154.887i	−0.799732	+	0.553169i
$281$	204.530			0.727866			0.363933	−	0.931425i	$-0.381434\pi$
$281$	204.530			0.727866			0.363933	+	0.931425i	$0.381434\pi$
$282$	−474.878	−	158.366i	−1.68397	−	0.561581i
$283$		−	502.549i		−	1.77579i	−0.460044	−	0.887896i	$-0.652166\pi$
$283$		−	502.549i		−	1.77579i	0.460044	−	0.887896i	$-0.347834\pi$
$284$	158.517	−	211.234i	0.558158	−	0.743781i
$285$	−134.927			−0.473428
$286$	−71.7649	+	215.195i	−0.250926	+	0.752432i
$287$		−	291.924i		−	1.01716i
$288$	−24.1792	+	625.297i	−0.0839555	+	2.17117i
$289$	610.438			2.11224
$290$	−147.790	−	49.2862i	−0.509622	−	0.169952i
$291$		−	49.9972i		−	0.171812i
$292$	−88.0017	−	66.0394i	−0.301376	−	0.226162i
$293$	239.563			0.817623			0.408811	−	0.912619i	$-0.365943\pi$
$293$	239.563			0.817623			0.408811	+	0.912619i	$0.365943\pi$
$294$	−48.9580	+	146.806i	−0.166524	+	0.499341i
$295$			579.887i			1.96572i
$296$	−114.329	−	165.289i	−0.386248	−	0.558409i
$297$	−455.675			−1.53426
$298$	−476.210	−	158.810i	−1.59802	−	0.532919i
$299$		−	122.827i		−	0.410794i
$300$	109.759	−	146.261i	0.365864	−	0.487538i
$301$	−277.554			−0.922105
$302$	−39.2386	+	117.661i	−0.129929	+	0.389608i
$303$			463.217i			1.52877i
$304$	66.9635	−	19.4908i	0.220275	−	0.0641144i
$305$	−180.690			−0.592425
$306$	1112.70	+	371.071i	3.63627	+	1.21265i
$307$		−	310.436i		−	1.01119i	−0.862771	−	0.505595i	$-0.831273\pi$
$307$		−	310.436i		−	1.01119i	0.862771	−	0.505595i	$-0.168727\pi$
$308$	151.860	+	113.961i	0.493051	+	0.370002i
$309$	745.990			2.41421
$310$	−28.0674	+	84.1632i	−0.0905399	+	0.271494i
$311$		−	219.552i		−	0.705956i	−0.935632	−	0.352978i	$-0.885169\pi$
$311$		−	219.552i		−	0.705956i	0.935632	−	0.352978i	$-0.114831\pi$
$312$	493.610	−	341.427i	1.58208	−	1.09432i
$313$	322.681			1.03093			0.515465	−	0.856911i	$-0.327619\pi$
$313$	322.681			1.03093			0.515465	+	0.856911i	$0.327619\pi$
$314$	190.013	+	63.3668i	0.605136	+	0.201805i
$315$			665.542i			2.11283i
$316$	−98.3738	+	131.089i	−0.311309	+	0.414840i
$317$	−53.6396			−0.169210			−0.0846050	−	0.996415i	$-0.526963\pi$
$317$	−53.6396			−0.169210			−0.0846050	+	0.996415i	$0.526963\pi$
$318$	47.9908	−	143.906i	0.150914	−	0.452534i
$319$			108.638i			0.340559i
$320$	−130.786	+	346.896i	−0.408706	+	1.08405i
$321$	−286.223			−0.891661
$322$	−97.5231	−	32.5227i	−0.302867	−	0.101002i
$323$		−	130.726i		−	0.404725i
$324$	401.221	+	301.089i	1.23834	+	0.929288i
$325$	−120.111			−0.369571
$326$	−118.897	+	356.526i	−0.364715	+	1.09364i
$327$			825.702i			2.52508i
$328$	−226.119	−	326.906i	−0.689387	−	0.996665i
$329$	275.197			0.836465
$330$	−474.462	−	158.227i	−1.43776	−	0.479476i
$331$			165.098i			0.498786i	0.968402	+	0.249393i	$0.0802310\pi$
$331$			165.098i			0.498786i	−0.968402	+	0.249393i	$0.919769\pi$
$332$	210.933	−	281.082i	0.635341	−	0.846632i
$333$	−491.266			−1.47527
$334$	15.3500	−	46.0288i	0.0459582	−	0.137811i
$335$			200.346i			0.598048i
$336$	−140.388	−	482.323i	−0.417821	−	1.43549i
$337$	−374.211			−1.11042			−0.555210	−	0.831710i	$-0.687362\pi$
$337$	−374.211			−1.11042			−0.555210	+	0.831710i	$0.687362\pi$
$338$	−53.3312	−	17.7853i	−0.157785	−	0.0526191i
$339$			352.711i			1.04045i
$340$	555.808	+	417.097i	1.63473	+	1.22676i
$341$	61.8671			0.181429
$342$	53.9322	−	161.722i	0.157697	−	0.472871i
$343$		−	372.969i		−	1.08737i
$344$	−310.814	+	214.988i	−0.903529	+	0.624965i
$345$	270.809			0.784954
$346$	475.783	+	158.667i	1.37509	+	0.458577i
$347$			442.710i			1.27582i	0.770110	+	0.637911i	$0.220201\pi$
$347$			442.710i			1.27582i	−0.770110	+	0.637911i	$0.779799\pi$
$348$	172.524	−	229.899i	0.495758	−	0.660629i
$349$	−163.363			−0.468090			−0.234045	−	0.972226i	$-0.575196\pi$
$349$	−163.363			−0.468090			−0.234045	+	0.972226i	$0.575196\pi$
$350$	−31.8033	+	95.3660i	−0.0908667	+	0.272474i
$351$		−	791.881i		−	2.25607i
$352$	258.329	+	9.98915i	0.733890	+	0.0283783i
$353$	410.271			1.16224			0.581120	−	0.813818i	$-0.302615\pi$
$353$	410.271			1.16224			0.581120	+	0.813818i	$0.302615\pi$
$354$	−1014.93	−	338.467i	−2.86704	−	0.956121i
$355$		−	382.457i		−	1.07734i
$356$	91.6553	+	68.7812i	0.257459	+	0.193206i
$357$	−941.592			−2.63751
$358$	39.4919	−	118.421i	0.110313	−	0.330785i
$359$			124.552i			0.346941i	0.984839	+	0.173470i	$0.0554981\pi$
$359$			124.552i			0.346941i	−0.984839	+	0.173470i	$0.944502\pi$
$360$	515.516	+	745.296i	1.43199	+	2.07027i
$361$	−19.0000			−0.0526316
$362$	126.508	+	42.1890i	0.349471	+	0.116544i
$363$		−	297.818i		−	0.820436i
$364$	−198.043	+	263.905i	−0.544075	+	0.725015i
$365$	−159.335			−0.436534
$366$	105.465	−	316.248i	0.288155	−	0.864065i
$367$		−	288.749i		−	0.786782i	−0.919371	−	0.393391i	$-0.871302\pi$
$367$		−	288.749i		−	0.786782i	0.919371	−	0.393391i	$-0.128698\pi$
$368$	−134.401	+	39.1195i	−0.365220	+	0.106303i
$369$	−971.619			−2.63311
$370$	−276.100	−	92.0758i	−0.746216	−	0.248854i
$371$			83.3950i			0.224784i
$372$	−130.922	−	98.2484i	−0.351942	−	0.264109i
$373$	380.740			1.02075			0.510376	−	0.859952i	$-0.329506\pi$
$373$	380.740			1.02075			0.510376	+	0.859952i	$0.329506\pi$
$374$	153.301	−	459.690i	0.409895	−	1.22912i
$375$			509.040i			1.35744i
$376$	308.175	−	213.162i	0.819614	−	0.566921i
$377$	−188.794			−0.500780
$378$	−628.742	−	209.677i	−1.66334	−	0.554702i
$379$			176.366i			0.465345i	0.972555	+	0.232673i	$0.0747471\pi$
$379$			176.366i			0.465345i	−0.972555	+	0.232673i	$0.925253\pi$
$380$	60.6217	−	80.7823i	0.159531	−	0.212585i
$381$	1191.58			3.12751
$382$	138.241	−	414.530i	0.361886	−	1.08516i
$383$		−	389.993i		−	1.01826i	−0.860690	−	0.509129i	$-0.829968\pi$
$383$		−	389.993i		−	1.01826i	0.860690	−	0.509129i	$-0.170032\pi$
$384$	−530.809	−	431.380i	−1.38232	−	1.12339i
$385$	274.956			0.714171
$386$	−117.534	−	39.1960i	−0.304491	−	0.101544i
$387$			923.790i			2.38705i
$388$	29.9339	+	22.4634i	0.0771493	+	0.0578953i
$389$	5.08380			0.0130689			0.00653445	−	0.999979i	$-0.497920\pi$
$389$	5.08380			0.0130689			0.00653445	+	0.999979i	$0.497920\pi$
$390$	274.970	−	824.530i	0.705052	−	2.11418i
$391$			262.378i			0.671043i
$392$	−65.8981	−	95.2707i	−0.168107	−	0.243038i
$393$	1065.18			2.71037
$394$	674.194	+	224.835i	1.71115	+	0.570647i
$395$			237.349i			0.600883i
$396$	379.298	−	505.439i	0.957824	−	1.27636i
$397$	320.541			0.807409			0.403705	−	0.914889i	$-0.367722\pi$
$397$	320.541			0.807409			0.403705	+	0.914889i	$0.367722\pi$
$398$	131.904	−	395.528i	0.331416	−	0.993789i
$399$			136.853i			0.342990i
$400$	38.2543	+	131.428i	0.0956356	+	0.328571i
$401$	−428.362			−1.06823			−0.534117	−	0.845410i	$-0.679356\pi$
$401$	−428.362			−1.06823			−0.534117	+	0.845410i	$0.679356\pi$
$402$	−350.651	−	116.938i	−0.872266	−	0.290890i
$403$			107.514i			0.266784i
$404$	−277.333	−	208.120i	−0.686468	−	0.515148i
$405$	726.446			1.79369
$406$	−49.9897	+	149.900i	−0.123127	+	0.369211i
$407$			202.957i			0.498666i
$408$	−1054.43	+	729.339i	−2.58438	+	1.78760i
$409$	109.550			0.267849			0.133925	−	0.990992i	$-0.457242\pi$
$409$	109.550			0.267849			0.133925	+	0.990992i	$0.457242\pi$
$410$	−546.067	−	182.106i	−1.33187	−	0.444162i
$411$			32.1385i			0.0781957i
$412$	−335.168	+	446.633i	−0.813515	+	1.08406i
$413$	588.164			1.42413
$414$	−108.246	+	324.589i	−0.261464	+	0.784031i
$415$		−	508.924i		−	1.22632i
$416$	−17.3594	+	448.930i	−0.0417292	+	1.07916i
$417$	−413.111			−0.990673
$418$	−66.8123	−	22.2810i	−0.159838	−	0.0533039i
$419$			305.115i			0.728199i	0.931360	+	0.364099i	$0.118623\pi$
$419$			305.115i			0.728199i	−0.931360	+	0.364099i	$0.881377\pi$
$420$	−581.857	−	436.645i	−1.38537	−	1.03963i
$421$	−721.115			−1.71286			−0.856431	−	0.516261i	$-0.827323\pi$
$421$	−721.115			−1.71286			−0.856431	+	0.516261i	$0.827323\pi$
$422$	−174.093	+	522.037i	−0.412542	+	1.23705i
$423$		−	915.946i		−	2.16536i
$424$	64.5962	+	93.3885i	0.152349	+	0.220256i
$425$	256.574			0.603704
$426$	669.386	+	223.232i	1.57133	+	0.524018i
$427$			183.269i			0.429201i
$428$	128.598	−	171.365i	0.300462	−	0.400386i
$429$	−606.100			−1.41282
$430$	−173.142	+	519.186i	−0.402656	+	1.20741i
$431$			275.396i			0.638971i	0.947591	+	0.319485i	$0.103510\pi$
$431$			275.396i			0.638971i	−0.947591	+	0.319485i	$0.896490\pi$
$432$	−866.499	+	252.208i	−2.00578	+	0.583815i
$433$	−445.559			−1.02900			−0.514502	−	0.857489i	$-0.672023\pi$
$433$	−445.559			−1.02900			−0.514502	+	0.857489i	$0.672023\pi$
$434$	85.3646	+	28.4680i	0.196693	+	0.0655945i
$435$		−	416.253i		−	0.956903i
$436$	−494.357	−	370.982i	−1.13385	−	0.850876i
$437$	38.1345			0.0872643
$438$	93.0002	−	278.872i	0.212329	−	0.636694i
$439$		−	501.542i		−	1.14246i	−0.820788	−	0.571232i	$-0.806466\pi$
$439$		−	501.542i		−	1.14246i	0.820788	−	0.571232i	$-0.193534\pi$
$440$	307.905	−	212.975i	0.699783	−	0.484035i
$441$	−283.160			−0.642087
$442$	798.859	+	266.409i	1.80737	+	0.602736i
$443$		−	297.237i		−	0.670964i	−0.942047	−	0.335482i	$-0.891101\pi$
$443$		−	297.237i		−	0.670964i	0.942047	−	0.335482i	$-0.108899\pi$
$444$	322.307	−	429.495i	0.725916	−	0.967330i
$445$	165.950			0.372922
$446$	150.531	−	451.384i	0.337513	−	1.01207i
$447$		−	1341.25i		−	3.00056i
$448$	351.848	+	132.653i	0.785374	+	0.296100i
$449$	−286.813			−0.638782			−0.319391	−	0.947623i	$-0.603478\pi$
$449$	−286.813			−0.638782			−0.319391	+	0.947623i	$0.603478\pi$
$450$	317.409	+	105.852i	0.705354	+	0.235227i
$451$			401.405i			0.890034i
$452$	−211.172	−	158.470i	−0.467195	−	0.350598i
$453$	−331.395			−0.731555
$454$	−99.3789	+	297.999i	−0.218896	+	0.656386i
$455$			477.824i			1.05016i
$456$	106.004	+	153.252i	0.232464	+	0.336080i
$457$	254.383			0.556637			0.278318	−	0.960489i	$-0.410223\pi$
$457$	254.383			0.556637			0.278318	+	0.960489i	$0.410223\pi$
$458$	336.899	+	112.351i	0.735587	+	0.245309i
$459$			1691.58i			3.68536i
$460$	−121.673	+	162.136i	−0.264505	+	0.352470i
$461$	−77.6648			−0.168470			−0.0842351	−	0.996446i	$-0.526845\pi$
$461$	−77.6648			−0.168470			−0.0842351	+	0.996446i	$0.526845\pi$
$462$	−160.485	+	481.234i	−0.347371	+	1.04163i
$463$		−	543.071i		−	1.17294i	−0.809971	−	0.586470i	$-0.800517\pi$
$463$		−	543.071i		−	1.17294i	0.809971	−	0.586470i	$-0.199483\pi$
$464$	60.1295	+	206.584i	0.129589	+	0.445224i
$465$	−237.046			−0.509777
$466$	−143.413	−	47.8265i	−0.307754	−	0.102632i
$467$		−	384.665i		−	0.823694i	−0.911253	−	0.411847i	$-0.864884\pi$
$467$		−	384.665i		−	0.823694i	0.911253	−	0.411847i	$-0.135116\pi$
$468$	878.364	+	659.153i	1.87685	+	1.40845i
$469$	203.206			0.433275
$470$	171.672	−	514.778i	0.365259	−	1.09527i
$471$			535.172i			1.13625i
$472$	658.646	−	455.581i	1.39544	−	0.965213i
$473$	381.646			0.806862
$474$	−415.414	−	138.535i	−0.876401	−	0.292268i
$475$		−	37.2910i		−	0.0785074i
$476$	423.050	−	563.742i	0.888761	−	1.18433i
$477$	277.566			0.581899
$478$	−1.26255	+	3.78589i	−0.00264131	+	0.00792027i
$479$		−	661.184i		−	1.38034i	−0.723646	−	0.690171i	$-0.757535\pi$
$479$		−	661.184i		−	1.38034i	0.723646	−	0.690171i	$-0.242465\pi$
$480$	−989.800	−	38.2738i	−2.06208	−	0.0797372i
$481$	−352.703			−0.733270
$482$	122.669	+	40.9085i	0.254500	+	0.0848724i
$483$		−	274.674i		−	0.568684i
$484$	178.307	+	133.808i	0.368403	+	0.276462i
$485$	54.1980			0.111748
$486$	−102.822	+	308.323i	−0.211568	+	0.634410i
$487$		−	626.822i		−	1.28711i	−0.765401	−	0.643554i	$-0.777459\pi$
$487$		−	626.822i		−	1.28711i	0.765401	−	0.643554i	$-0.222541\pi$
$488$	141.957	+	205.231i	0.290895	+	0.420555i
$489$	−1004.16			−2.05350
$490$	−159.141	−	53.0715i	−0.324778	−	0.108309i
$491$			973.335i			1.98235i	0.132555	+	0.991176i	$0.457682\pi$
$491$			973.335i			1.98235i	−0.132555	+	0.991176i	$0.542318\pi$
$492$	637.454	−	849.448i	1.29564	−	1.72652i
$493$	403.293			0.818039
$494$	38.7205	−	116.108i	0.0783815	−	0.235036i
$495$		−	915.143i		−	1.84877i
$496$	117.645	−	34.2424i	0.237187	−	0.0690370i
$497$	−387.917			−0.780516
$498$	890.731	+	297.047i	1.78862	+	0.596481i
$499$		−	171.966i		−	0.344621i	−0.985043	−	0.172311i	$-0.944877\pi$
$499$		−	171.966i		−	0.344621i	0.985043	−	0.172311i	$-0.0551233\pi$
$500$	−304.768	−	228.708i	−0.609536	−	0.457416i
$501$	129.641			0.258764
$502$	155.516	−	466.333i	0.309793	−	0.928950i
$503$			806.197i			1.60278i	0.598145	+	0.801388i	$0.295905\pi$
$503$			806.197i			1.60278i	−0.598145	+	0.801388i	$0.704095\pi$
$504$	755.935	−	522.875i	1.49987	−	1.03745i
$505$	−502.136			−0.994329
$506$	134.098	+	44.7198i	0.265015	+	0.0883791i
$507$		−	150.208i		−	0.296268i
$508$	−535.369	+	713.414i	−1.05388	+	1.40436i
$509$	944.065			1.85475			0.927373	−	0.374139i	$-0.122062\pi$
$509$	944.065			1.85475			0.927373	+	0.374139i	$0.122062\pi$
$510$	−587.378	+	1761.32i	−1.15172	+	3.45357i
$511$			161.609i			0.316261i
$512$	496.761	−	123.986i	0.970236	−	0.242160i
$513$	245.857			0.479254
$514$	−525.268	−	175.170i	−1.02192	−	0.340798i
$515$			808.669i			1.57023i
$516$	−807.633	−	606.074i	−1.56518	−	1.17456i
$517$	−378.405			−0.731925
$518$	−93.3901	+	280.041i	−0.180290	+	0.540620i
$519$			1340.05i			2.58198i
$520$	370.113	+	535.083i	0.711757	+	1.02901i
$521$	168.936			0.324253			0.162126	−	0.986770i	$-0.448165\pi$
$521$	168.936			0.324253			0.162126	+	0.986770i	$0.448165\pi$
$522$	498.916	+	166.382i	0.955778	+	0.318740i
$523$		−	391.361i		−	0.748300i	−0.927368	−	0.374150i	$-0.877935\pi$
$523$		−	391.361i		−	0.748300i	0.927368	−	0.374150i	$-0.122065\pi$
$524$	−478.576	+	637.733i	−0.913313	+	1.21705i
$525$	−268.599			−0.511617
$526$	−60.3712	+	181.030i	−0.114774	+	0.344164i
$527$		−	229.666i		−	0.435799i
$528$	193.038	+	663.211i	0.365602	+	1.25608i
$529$	452.461			0.855314
$530$	155.997	+	52.0230i	0.294334	+	0.0981565i
$531$		−	1957.60i		−	3.68664i
$532$	−81.9354	−	61.4870i	−0.154014	−	0.115577i
$533$	−697.571			−1.30876
$534$	−96.8614	+	290.450i	−0.181388	+	0.543914i
$535$		−	310.272i		−	0.579947i
$536$	227.557	−	157.399i	0.424546	−	0.293656i
$537$	333.534			0.621106
$538$	244.453	+	81.5220i	0.454374	+	0.151528i
$539$			116.982i			0.217036i
$540$	−784.436	+	1045.31i	−1.45266	+	1.93576i
$541$	−561.849			−1.03854			−0.519269	−	0.854611i	$-0.673796\pi$
$541$	−561.849			−1.03854			−0.519269	+	0.854611i	$0.673796\pi$
$542$	−200.883	+	602.370i	−0.370632	+	1.11138i
$543$			356.312i			0.656192i
$544$	37.0822	−	958.984i	0.0681659	−	1.76284i
$545$	−895.078			−1.64234
$546$	−836.299	−	278.895i	−1.53168	−	0.510797i
$547$		−	630.789i		−	1.15318i	−0.817034	−	0.576590i	$-0.804383\pi$
$547$		−	630.789i		−	1.15318i	0.817034	−	0.576590i	$-0.195617\pi$
$548$	−19.2417	−	14.4396i	−0.0351125	−	0.0263496i
$549$	609.979			1.11107
$550$	43.7307	−	131.132i	0.0795103	−	0.238421i
$551$		−	58.6154i		−	0.106380i
$552$	−212.758	−	307.590i	−0.385431	−	0.557228i
$553$	240.737			0.435329
$554$	55.3834	+	18.4697i	0.0999700	+	0.0333387i
$555$		−	777.638i		−	1.40115i
$556$	185.608	−	247.334i	0.333827	−	0.444845i
$557$	123.847			0.222346			0.111173	−	0.993801i	$-0.464539\pi$
$557$	123.847			0.222346			0.111173	+	0.993801i	$0.464539\pi$
$558$	94.7509	−	284.121i	0.169804	−	0.509178i
$559$			663.232i			1.18646i
$560$	522.848	−	152.183i	0.933658	−	0.271756i
$561$	1294.72			2.30788
$562$	−388.051	−	129.410i	−0.690483	−	0.230267i
$563$			935.582i			1.66178i	0.556437	+	0.830890i	$0.312168\pi$
$563$			935.582i			1.66178i	−0.556437	+	0.830890i	$0.687832\pi$
$564$	800.775	+	600.928i	1.41981	+	1.06548i
$565$	−382.346			−0.676718
$566$	−317.972	+	953.476i	−0.561788	+	1.68459i
$567$		−	736.815i		−	1.29950i
$568$	−434.402	+	300.473i	−0.764792	+	0.529001i
$569$	373.028			0.655586			0.327793	−	0.944750i	$-0.393695\pi$
$569$	373.028			0.655586			0.327793	+	0.944750i	$0.393695\pi$
$570$	255.994	+	85.3707i	0.449112	+	0.149773i
$571$			435.521i			0.762733i	0.924424	+	0.381367i	$0.124546\pi$
$571$			435.521i			0.762733i	−0.924424	+	0.381367i	$0.875454\pi$
$572$	272.316	−	362.879i	0.476077	−	0.634404i
$573$	1167.53			2.03757
$574$	−184.706	+	553.861i	−0.321787	+	0.964915i
$575$			74.8460i			0.130167i
$576$	441.512	−	1171.07i	0.766514	−	2.03310i
$577$	−807.758			−1.39993			−0.699964	−	0.714178i	$-0.746801\pi$
$577$	−807.758			−1.39993			−0.699964	+	0.714178i	$0.746801\pi$
$578$	−1158.17	−	386.235i	−2.00376	−	0.668227i
$579$		−	331.034i		−	0.571735i
$580$	249.215	+	187.019i	0.429681	+	0.322447i
$581$	−516.188			−0.888448
$582$	−31.6342	+	94.8587i	−0.0543542	+	0.162987i
$583$		−	114.671i		−	0.196691i
$584$	125.179	+	180.975i	0.214348	+	0.309889i
$585$	1590.36			2.71856
$586$	−454.519	−	151.576i	−0.775629	−	0.258662i
$587$		−	311.402i		−	0.530498i	−0.964180	−	0.265249i	$-0.914546\pi$
$587$		−	311.402i		−	0.530498i	0.964180	−	0.265249i	$-0.0854542\pi$
$588$	185.774	−	247.556i	0.315942	−	0.421013i
$589$	−33.3802			−0.0566726
$590$	366.905	−	1100.21i	0.621873	−	1.86476i
$591$			1898.87i			3.21298i
$592$	112.333	+	385.938i	0.189752	+	0.651922i
$593$	−1048.73			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$593$	−1048.73			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$594$	864.542	+	288.314i	1.45546	+	0.485377i
$595$		−	1020.70i		−	1.71547i
$596$	803.021	+	602.614i	1.34735	+	1.01110i
$597$	1114.01			1.86601
$598$	−77.7151	+	233.038i	−0.129958	+	0.389695i
$599$			20.9544i			0.0349822i	0.999847	+	0.0174911i	$0.00556788\pi$
$599$			20.9544i			0.0349822i	−0.999847	+	0.0174911i	$0.994432\pi$
$600$	−300.786	+	208.052i	−0.501310	+	0.346753i
$601$	4.04669			0.00673326			0.00336663	−	0.999994i	$-0.498928\pi$
$601$	4.04669			0.00673326			0.00336663	+	0.999994i	$0.498928\pi$
$602$	526.597	+	175.613i	0.874745	+	0.291716i
$603$		−	676.336i		−	1.12162i
$604$	148.893	−	198.410i	0.246512	−	0.328493i
$605$	322.841			0.533621
$606$	293.086	−	878.851i	0.483640	−	1.45025i
$607$			718.845i			1.18426i	0.805843	+	0.592129i	$0.201712\pi$
$607$			718.845i			1.18426i	−0.805843	+	0.592129i	$0.798288\pi$
$608$	−139.381	−	5.38961i	−0.229244	−	0.00886449i
$609$	−422.194			−0.693258
$610$	342.819	+	114.326i	0.561998	+	0.187419i
$611$		−	657.601i		−	1.07627i
$612$	−1876.32	−	1408.05i	−3.06588	−	2.30074i
$613$	−568.157			−0.926847			−0.463424	−	0.886137i	$-0.653379\pi$
$613$	−568.157			−0.926847			−0.463424	+	0.886137i	$0.653379\pi$
$614$	−196.418	+	588.983i	−0.319899	+	0.959255i
$615$		−	1538.00i		−	2.50082i
$616$	−216.015	−	312.300i	−0.350674	−	0.506980i
$617$	344.297			0.558017			0.279009	−	0.960289i	$-0.409994\pi$
$617$	344.297			0.558017			0.279009	+	0.960289i	$0.409994\pi$
$618$	−1415.35	−	472.002i	−2.29021	−	0.763757i
$619$		−	269.442i		−	0.435286i	−0.976028	−	0.217643i	$-0.930163\pi$
$619$		−	269.442i		−	0.435286i	0.976028	−	0.217643i	$-0.0698368\pi$
$620$	106.503	−	141.922i	0.171779	−	0.228907i
$621$	−493.455			−0.794614
$622$	−138.915	+	416.552i	−0.223336	+	0.669698i
$623$		−	168.319i		−	0.270175i
$624$	−1152.54	+	335.466i	−1.84702	+	0.537605i
$625$	−765.688			−1.22510
$626$	−612.216	−	204.166i	−0.977980	−	0.326144i
$627$		−	188.177i		−	0.300123i
$628$	−320.414	−	240.449i	−0.510213	−	0.382880i
$629$	753.427			1.19782
$630$	421.101	−	1262.72i	0.668414	−	2.00432i
$631$		−	916.217i		−	1.45201i	−0.687691	−	0.726004i	$-0.741375\pi$
$631$		−	916.217i		−	1.45201i	0.687691	−	0.726004i	$-0.258625\pi$
$632$	269.585	−	186.470i	0.426559	−	0.295048i
$633$	−1470.32			−2.32278
$634$	101.769	+	33.9387i	0.160519	+	0.0535311i
$635$			1291.70i			2.03417i
$636$	−182.104	+	242.665i	−0.286327	+	0.381549i
$637$	−203.294			−0.319143
$638$	68.7375	−	206.117i	0.107739	−	0.323068i
$639$			1291.11i			2.02052i
$640$	467.625	−	575.408i	0.730664	−	0.899075i
$641$	809.161			1.26234			0.631171	−	0.775644i	$-0.282575\pi$
$641$	809.161			1.26234			0.631171	+	0.775644i	$0.282575\pi$
$642$	543.045	+	181.099i	0.845864	+	0.282085i
$643$			611.403i			0.950859i	0.879754	+	0.475430i	$0.157707\pi$
$643$			611.403i			0.950859i	−0.879754	+	0.475430i	$0.842293\pi$
$644$	164.451	+	123.409i	0.255358	+	0.191629i
$645$	−1462.29			−2.26712
$646$	−82.7128	+	248.024i	−0.128038	+	0.383938i
$647$		−	375.179i		−	0.579875i	−0.957046	−	0.289938i	$-0.906365\pi$
$647$		−	375.179i		−	0.579875i	0.957046	−	0.289938i	$-0.0936345\pi$
$648$	−570.723	−	825.110i	−0.880745	−	1.27332i
$649$	−808.746			−1.24614
$650$	227.883	+	75.9961i	0.350590	+	0.116917i
$651$			240.430i			0.369324i
$652$	451.161	−	601.202i	0.691965	−	0.922088i
$653$	122.859			0.188146			0.0940729	−	0.995565i	$-0.470011\pi$
$653$	122.859			0.188146			0.0940729	+	0.995565i	$0.470011\pi$
$654$	522.437	−	1566.59i	0.798833	−	2.39539i
$655$			1154.67i			1.76286i
$656$	222.171	+	763.302i	0.338675	+	1.16357i
$657$	537.889			0.818704
$658$	−522.125	−	174.122i	−0.793504	−	0.264623i
$659$		−	104.791i		−	0.159015i	−0.996834	−	0.0795074i	$-0.974665\pi$
$659$		−	104.791i		−	0.159015i	0.996834	−	0.0795074i	$-0.0253347\pi$
$660$	800.073	+	600.401i	1.21223	+	0.909699i
$661$	−1185.52			−1.79352			−0.896762	−	0.442514i	$-0.854087\pi$
$661$	−1185.52			−1.79352			−0.896762	+	0.442514i	$0.854087\pi$
$662$	104.461	−	313.237i	0.157795	−	0.473168i
$663$			2249.99i			3.39366i
$664$	−578.045	+	399.830i	−0.870549	+	0.602153i
$665$	−148.351			−0.223085
$666$	932.069	+	310.833i	1.39950	+	0.466716i
$667$			117.646i			0.176381i
$668$	−58.2466	+	77.6173i	−0.0871955	+	0.116194i
$669$	1271.33			1.90034
$670$	126.763	−	380.113i	0.189198	−	0.567332i
$671$		−	252.001i		−	0.375560i
$672$	−38.8202	+	1003.93i	−0.0577681	+	1.49394i
$673$	86.7624			0.128919			0.0644594	−	0.997920i	$-0.479468\pi$
$673$	86.7624			0.128919			0.0644594	+	0.997920i	$0.479468\pi$
$674$	709.983	+	236.770i	1.05339	+	0.351291i
$675$			482.541i			0.714875i
$676$	89.9310	+	67.4872i	0.133034	+	0.0998332i
$677$	−566.786			−0.837202			−0.418601	−	0.908170i	$-0.637479\pi$
$677$	−566.786			−0.837202			−0.418601	+	0.908170i	$0.637479\pi$
$678$	223.167	−	669.191i	0.329154	−	0.987007i
$679$		−	54.9716i		−	0.0809597i
$680$	−790.618	−	1143.02i	−1.16267	−	1.68091i
$681$	−839.317			−1.23248
$682$	−117.379	−	39.1445i	−0.172110	−	0.0573966i
$683$		−	192.839i		−	0.282341i	−0.989985	−	0.141170i	$-0.954913\pi$
$683$		−	192.839i		−	0.282341i	0.989985	−	0.141170i	$-0.0450865\pi$
$684$	−204.649	+	272.708i	−0.299194	+	0.398696i
$685$	−34.8387			−0.0508595
$686$	−235.984	+	707.626i	−0.344000	+	1.03152i
$687$			948.878i			1.38119i
$688$	725.727	−	211.234i	1.05484	−	0.307026i
$689$	199.278			0.289227
$690$	−513.800	−	171.346i	−0.744638	−	0.248327i
$691$			639.216i			0.925059i	0.886604	+	0.462530i	$0.153058\pi$
$691$			639.216i			0.925059i	−0.886604	+	0.462530i	$0.846942\pi$
$692$	−802.301	−	602.073i	−1.15939	−	0.870048i
$693$	−928.206			−1.33940
$694$	280.111	−	839.945i	0.403618	−	1.21029i
$695$		−	447.820i		−	0.644346i
$696$	−472.787	+	327.024i	−0.679292	+	0.469861i
$697$	1490.12			2.13790
$698$	309.946	+	103.363i	0.444049	+	0.148085i
$699$		−	403.925i		−	0.577861i
$700$	120.680	−	160.813i	0.172399	−	0.229733i
$701$	109.111			0.155650			0.0778250	−	0.996967i	$-0.475202\pi$
$701$	109.111			0.155650			0.0778250	+	0.996967i	$0.475202\pi$
$702$	−501.038	+	1502.42i	−0.713729	+	2.14020i
$703$		−	109.505i		−	0.155768i
$704$	−483.803	−	182.402i	−0.687220	−	0.259094i
$705$	1449.88			2.05656
$706$	−778.398	−	259.586i	−1.10255	−	0.367685i
$707$			509.304i			0.720373i
$708$	1711.46	+	1284.33i	2.41731	+	1.81403i
$709$	1381.83			1.94898			0.974489	−	0.224434i	$-0.0720532\pi$
$709$	1381.83			1.94898			0.974489	+	0.224434i	$0.0720532\pi$
$710$	−241.988	+	725.628i	−0.340828	+	1.02201i
$711$		−	801.251i		−	1.12694i
$712$	−130.377	−	188.489i	−0.183113	−	0.264732i
$713$	66.9966			0.0939644
$714$	1786.46	+	595.762i	2.50205	+	0.834401i
$715$		−	657.024i		−	0.918915i
$716$	−149.854	+	199.690i	−0.209294	+	0.278897i
$717$	−10.6630			−0.0148717
$718$	78.8062	−	236.309i	0.109758	−	0.329122i
$719$		−	844.528i		−	1.17459i	−0.809374	−	0.587293i	$-0.800194\pi$
$719$		−	844.528i		−	1.17459i	0.809374	−	0.587293i	$-0.199806\pi$
$720$	−506.516	−	1740.21i	−0.703494	−	2.41696i
$721$	820.211			1.13760
$722$	36.0483	+	12.0216i	0.0499284	+	0.0166505i
$723$			345.498i			0.477867i
$724$	−213.328	−	160.088i	−0.294652	−	0.221117i
$725$	115.044			0.158681
$726$	−188.435	+	565.044i	−0.259552	+	0.778298i
$727$			926.186i			1.27398i	0.770871	+	0.636992i	$0.219821\pi$
$727$			926.186i			1.27398i	−0.770871	+	0.636992i	$0.780179\pi$
$728$	542.721	−	375.396i	0.745496	−	0.515654i
$729$	260.272			0.357026
$730$	302.303	+	100.814i	0.414113	+	0.138102i
$731$		−	1416.76i		−	1.93812i
$732$	−400.191	+	533.281i	−0.546710	+	0.728526i
$733$	108.418			0.147910			0.0739551	−	0.997262i	$-0.476438\pi$
$733$	108.418			0.147910			0.0739551	+	0.997262i	$0.476438\pi$
$734$	−182.697	+	547.837i	−0.248906	+	0.746372i
$735$		−	448.222i		−	0.609826i
$736$	279.748	+	10.8174i	0.380092	+	0.0146975i
$737$	−279.415			−0.379125
$738$	1843.43	+	614.761i	2.49788	+	0.833010i
$739$			209.058i			0.282893i	0.989946	+	0.141447i	$0.0451753\pi$
$739$			209.058i			0.282893i	−0.989946	+	0.141447i	$0.954825\pi$
$740$	465.581	+	349.387i	0.629163	+	0.472145i
$741$	327.019			0.441321
$742$	52.7655	−	158.224i	0.0711126	−	0.213239i
$743$		−	862.421i		−	1.16073i	−0.814357	−	0.580364i	$-0.802910\pi$
$743$		−	862.421i		−	1.16073i	0.814357	−	0.580364i	$-0.197090\pi$
$744$	186.233	+	269.242i	0.250313	+	0.361884i
$745$	1453.94			1.95160
$746$	−722.371	−	240.901i	−0.968325	−	0.322924i
$747$			1718.04i			2.29993i
$748$	−581.709	+	775.164i	−0.777685	+	1.03632i
$749$	−314.700			−0.420161
$750$	322.079	−	965.791i	0.429438	−	1.28772i
$751$			167.423i			0.222933i	0.993768	+	0.111467i	$0.0355548\pi$
$751$			167.423i			0.222933i	−0.993768	+	0.111467i	$0.964445\pi$
$752$	−719.565	+	209.441i	−0.956869	+	0.278512i
$753$	1313.43			1.74426
$754$	358.195	+	119.454i	0.475060	+	0.158426i
$755$		−	359.238i		−	0.475812i
$756$	1060.23	+	795.633i	1.40242	+	1.05243i
$757$	347.592			0.459171			0.229586	−	0.973288i	$-0.426263\pi$
$757$	347.592			0.459171			0.229586	+	0.973288i	$0.426263\pi$
$758$	111.590	−	334.615i	0.147216	−	0.441445i
$759$			377.687i			0.497611i
$760$	−166.129	+	114.910i	−0.218590	+	0.151197i
$761$	1395.24			1.83343			0.916714	−	0.399544i	$-0.130832\pi$
$761$	1395.24			1.83343			0.916714	+	0.399544i	$0.130832\pi$
$762$	−2260.76	−	753.936i	−2.96688	−	0.989417i
$763$			907.854i			1.18985i
$764$	−524.562	+	699.012i	−0.686599	+	0.914937i
$765$	−3397.24			−4.44084
$766$	−246.756	+	739.925i	−0.322135	+	0.965960i
$767$		−	1405.46i		−	1.83241i
$768$	734.152	+	1154.30i	0.955926	+	1.50300i
$769$	1104.80			1.43667			0.718333	−	0.695700i	$-0.244906\pi$
$769$	1104.80			1.43667			0.718333	+	0.695700i	$0.244906\pi$
$770$	−521.668	−	173.970i	−0.677490	−	0.225934i
$771$		−	1479.42i		−	1.91883i
$772$	198.194	+	148.731i	0.256728	+	0.192657i
$773$	−1508.32			−1.95125			−0.975627	−	0.219436i	$-0.929578\pi$
$773$	−1508.32			−1.95125			−0.975627	+	0.219436i	$0.929578\pi$
$774$	584.499	−	1752.69i	0.755166	−	2.26445i
$775$		−	65.5148i		−	0.0845352i
$776$	−42.5800	−	61.5591i	−0.0548711	−	0.0793287i
$777$	−788.738			−1.01511
$778$	−9.64539	−	3.21661i	−0.0123977	−	0.00413447i
$779$		−	216.577i		−	0.278019i
$780$	−1043.39	+	1390.38i	−1.33768	+	1.78254i
$781$	533.399			0.682969
$782$	166.011	−	497.804i	0.212290	−	0.636578i
$783$			758.476i			0.968679i
$784$	64.7476	+	222.450i	0.0825862	+	0.283737i
$785$	−580.137			−0.739028
$786$	−2020.94	−	673.956i	−2.57117	−	0.857451i
$787$			964.500i			1.22554i	0.790261	+	0.612770i	$0.209945\pi$
$787$			964.500i			1.22554i	−0.790261	+	0.612770i	$0.790055\pi$
$788$	−1136.88	−	853.149i	−1.44274	−	1.08268i
$789$	−509.873			−0.646227
$790$	150.175	−	450.317i	0.190095	−	0.570022i
$791$			387.803i			0.490270i
$792$	−1039.44	+	718.971i	−1.31242	+	0.907791i
$793$	437.933			0.552248
$794$	−608.157	−	202.812i	−0.765940	−	0.255431i
$795$			439.366i			0.552662i
$796$	−500.516	+	666.969i	−0.628789	+	0.837901i
$797$	−237.493			−0.297984			−0.148992	−	0.988838i	$-0.547603\pi$
$797$	−237.493			−0.297984			−0.148992	+	0.988838i	$0.547603\pi$
$798$	86.5893	−	259.648i	0.108508	−	0.325373i
$799$			1404.74i			1.75812i
$800$	10.5781	−	273.560i	0.0132226	−	0.341950i
$801$	−560.221			−0.699402
$802$	812.722	+	271.032i	1.01337	+	0.337946i
$803$		−	222.218i		−	0.276735i
$804$	591.294	+	443.726i	0.735440	+	0.551899i
$805$	297.753			0.369879
$806$	68.0261	−	203.984i	0.0843996	−	0.253082i
$807$			688.504i			0.853165i
$808$	394.497	+	570.335i	0.488239	+	0.705860i
$809$	−1195.19			−1.47736			−0.738681	−	0.674056i	$-0.764551\pi$
$809$	−1195.19			−1.47736			−0.738681	+	0.674056i	$0.764551\pi$
$810$	−1378.27	−	459.635i	−1.70157	−	0.567451i
$811$		−	1407.36i		−	1.73534i	−0.497140	−	0.867670i	$-0.665616\pi$
$811$		−	1407.36i		−	1.73534i	0.497140	−	0.867670i	$-0.334384\pi$
$812$	189.689	−	252.772i	0.233607	−	0.311296i
$813$	−1696.58			−2.08681
$814$	128.415	−	385.066i	0.157758	−	0.473054i
$815$		−	1088.53i		−	1.33562i
$816$	2462.01	−	716.605i	3.01716	−	0.878193i
$817$	−205.915			−0.252038
$818$	−207.848	−	69.3145i	−0.254092	−	0.0847366i
$819$		−	1613.06i		−	1.96954i
$820$	920.819	+	691.013i	1.12295	+	0.842699i
$821$	336.476			0.409836			0.204918	−	0.978779i	$-0.434307\pi$
$821$	336.476			0.409836			0.204918	+	0.978779i	$0.434307\pi$
$822$	20.3346	−	60.9756i	0.0247379	−	0.0741796i
$823$		−	260.242i		−	0.316211i	−0.987422	−	0.158106i	$-0.949461\pi$
$823$		−	260.242i		−	0.316211i	0.987422	−	0.158106i	$-0.0505386\pi$
$824$	918.500	−	635.320i	1.11468	−	0.771020i
$825$	369.333			0.447676
$826$	−1115.91	−	372.142i	−1.35098	−	0.450535i
$827$			424.028i			0.512730i	0.966580	+	0.256365i	$0.0825249\pi$
$827$			424.028i			0.512730i	−0.966580	+	0.256365i	$0.917475\pi$
$828$	410.747	−	547.346i	0.496071	−	0.661046i
$829$	1148.21			1.38506			0.692529	−	0.721390i	$-0.256496\pi$
$829$	1148.21			1.38506			0.692529	+	0.721390i	$0.256496\pi$
$830$	−322.005	+	965.570i	−0.387958	+	1.16334i
$831$			155.988i			0.187711i
$832$	316.982	−	840.763i	0.380988	−	1.01053i
$833$	434.267			0.521329
$834$	783.786	+	261.383i	0.939792	+	0.313409i
$835$			140.533i			0.168303i
$836$	112.664	+	84.5467i	0.134765	+	0.101132i
$837$	431.935			0.516051
$838$	193.052	−	578.889i	0.230372	−	0.690798i
$839$		−	1071.72i		−	1.27737i	−0.769467	−	0.638686i	$-0.779478\pi$
$839$		−	1071.72i		−	1.27737i	0.769467	−	0.638686i	$-0.220522\pi$
$840$	827.672	+	1196.59i	0.985324	+	1.42451i
$841$	−660.170			−0.784982
$842$	1368.16	+	456.263i	1.62489	+	0.541880i
$843$		−	1092.95i		−	1.29650i
$844$	660.604	−	880.297i	0.782706	−	1.04301i
$845$	162.828			0.192696
$846$	−579.536	+	1737.81i	−0.685031	+	2.05414i
$847$		−	327.449i		−	0.386599i
$848$	−63.4683	−	218.055i	−0.0748447	−	0.257140i
$849$	−2685.47			−3.16310
$850$	−486.793	−	162.339i	−0.572698	−	0.190987i
$851$			219.784i			0.258266i
$852$	−1128.77	−	847.066i	−1.32485	−	0.994209i
$853$	−11.0568			−0.0129622			−0.00648110	−	0.999979i	$-0.502063\pi$
$853$	−11.0568			−0.0129622			−0.00648110	+	0.999979i	$0.502063\pi$
$854$	115.958	−	347.712i	0.135782	−	0.407157i
$855$			493.762i			0.577499i
$856$	−352.412	+	243.761i	−0.411696	+	0.284767i
$857$	−612.058			−0.714187			−0.357094	−	0.934069i	$-0.616232\pi$
$857$	−612.058			−0.714187			−0.357094	+	0.934069i	$0.616232\pi$
$858$	1149.94	+	383.490i	1.34026	+	0.446959i
$859$		−	1496.82i		−	1.74252i	−0.490826	−	0.871258i	$-0.663305\pi$
$859$		−	1496.82i		−	1.74252i	0.490826	−	0.871258i	$-0.336695\pi$
$860$	656.997	−	875.490i	0.763950	−	1.01801i
$861$	−1559.95			−1.81179
$862$	174.248	−	522.504i	0.202144	−	0.606153i
$863$		−	482.163i		−	0.558706i	−0.960189	−	0.279353i	$-0.909880\pi$
$863$		−	482.163i		−	0.558706i	0.960189	−	0.279353i	$-0.0901199\pi$
$864$	1803.57	+	69.7408i	2.08746	+	0.0807185i
$865$	−1452.64			−1.67935
$866$	845.350	+	281.913i	0.976154	+	0.325535i
$867$		−	3262.00i		−	3.76240i
$868$	−143.948	−	108.023i	−0.165839	−	0.124451i
$869$	−331.021			−0.380922
$870$	−263.371	+	789.747i	−0.302725	+	0.907756i
$871$		−	485.574i		−	0.557490i
$872$	703.207	+	1016.65i	0.806430	+	1.16588i
$873$	−182.964			−0.209580
$874$	−72.3518	−	24.1284i	−0.0827824	−	0.0276069i
$875$			559.686i			0.639641i
$876$	−352.895	+	470.255i	−0.402848	+	0.536821i
$877$	321.889			0.367034			0.183517	−	0.983017i	$-0.441252\pi$
$877$	321.889			0.367034			0.183517	+	0.983017i	$0.441252\pi$
$878$	−317.335	+	951.565i	−0.361429	+	1.08379i
$879$		−	1280.16i		−	1.45638i
$880$	−718.934	+	209.257i	−0.816971	+	0.237792i
$881$	1053.56			1.19587			0.597934	−	0.801545i	$-0.295988\pi$
$881$	1053.56			1.19587			0.597934	+	0.801545i	$0.295988\pi$
$882$	537.234	+	179.161i	0.609109	+	0.203130i
$883$			152.797i			0.173043i	0.996250	+	0.0865213i	$0.0275751\pi$
$883$			152.797i			0.173043i	−0.996250	+	0.0865213i	$0.972425\pi$
$884$	−1347.10	−	1010.91i	−1.52387	−	1.14356i
$885$	3098.74			3.50140
$886$	−188.067	+	563.941i	−0.212266	+	0.636503i
$887$			1486.18i			1.67551i	0.546044	+	0.837756i	$0.316133\pi$
$887$			1486.18i			1.67551i	−0.546044	+	0.837756i	$0.683867\pi$
$888$	−883.255	+	610.941i	−0.994657	+	0.687997i
$889$	1310.14			1.47372
$890$	−314.854	−	105.000i	−0.353768	−	0.117977i
$891$			1013.15i			1.13709i
$892$	−571.198	+	761.158i	−0.640357	+	0.853317i
$893$	204.167			0.228631
$894$	−848.633	+	2544.72i	−0.949254	+	2.84645i
$895$			361.557i			0.403975i
$896$	−583.621	−	474.300i	−0.651363	−	0.529352i
$897$	−656.352			−0.731719
$898$	544.165	+	181.472i	0.605974	+	0.202085i
$899$		−	102.979i		−	0.114548i
$900$	−535.240	−	401.662i	−0.594711	−	0.446291i
$901$	−425.687			−0.472461
$902$	253.977	−	761.578i	0.281571	−	0.844322i
$903$			1483.16i			1.64248i
$904$	300.385	+	434.275i	0.332284	+	0.480393i
$905$	−386.249			−0.426795
$906$	628.748	+	209.679i	0.693982	+	0.231434i
$907$			805.225i			0.887790i	0.896079	+	0.443895i	$0.146404\pi$
$907$			805.225i			0.887790i	−0.896079	+	0.443895i	$0.853596\pi$
$908$	377.099	−	502.509i	0.415307	−	0.553424i
$909$	1695.13			1.86483
$910$	302.328	−	906.565i	0.332229	−	0.996226i
$911$			1424.24i			1.56339i	0.623664	+	0.781693i	$0.285643\pi$
$911$			1424.24i			1.56339i	−0.623664	+	0.781693i	$0.714357\pi$
$912$	−104.153	−	357.833i	−0.114203	−	0.392361i
$913$	709.776			0.777411
$914$	−482.635	−	160.953i	−0.528047	−	0.176097i
$915$			965.552i			1.05525i
$916$	−568.104	−	426.324i	−0.620201	−	0.465419i
$917$	1171.15			1.27716
$918$	1070.29	−	3209.40i	1.16590	−	3.49607i
$919$			798.305i			0.868667i	0.900752	+	0.434334i	$0.143016\pi$
$919$			798.305i			0.868667i	−0.900752	+	0.434334i	$0.856984\pi$
$920$	333.433	−	230.634i	0.362428	−	0.250689i
$921$	−1658.88			−1.80117
$922$	147.352	+	49.1399i	0.159817	+	0.0532971i
$923$			926.952i			1.00428i
$924$	608.972	−	811.494i	0.659060	−	0.878240i
$925$	214.923			0.232349
$926$	−343.611	+	1030.36i	−0.371070	+	1.11270i
$927$		−	2729.93i		−	2.94491i
$928$	16.6271	−	429.992i	0.0179171	−	0.463354i
$929$	−1237.61			−1.33220			−0.666099	−	0.745864i	$-0.732037\pi$
$929$	−1237.61			−1.33220			−0.666099	+	0.745864i	$0.732037\pi$
$930$	449.743	+	149.984i	0.483595	+	0.161273i
$931$		−	63.1173i		−	0.0677951i
$932$	241.835	+	181.481i	0.259479	+	0.194722i
$933$	−1173.22			−1.25747
$934$	−243.385	+	729.817i	−0.260583	+	0.781388i
$935$			1403.50i			1.50107i
$936$	−1249.44	−	1806.35i	−1.33487	−	1.92987i
$937$	−1445.92			−1.54313			−0.771567	−	0.636148i	$-0.780527\pi$
$937$	−1445.92			−1.54313			−0.771567	+	0.636148i	$0.780527\pi$
$938$	−385.538	−	128.572i	−0.411022	−	0.137070i
$939$		−	1724.31i		−	1.83633i
$940$	−651.418	+	868.057i	−0.692998	+	0.923465i
$941$	−165.774			−0.176168			−0.0880840	−	0.996113i	$-0.528074\pi$
$941$	−165.774			−0.176168			−0.0880840	+	0.996113i	$0.528074\pi$
$942$	338.613	−	1015.37i	0.359462	−	1.07789i
$943$			434.687i			0.460961i
$944$	−1537.89	+	447.626i	−1.62912	+	0.474181i
$945$	1919.65			2.03137
$946$	−724.088	−	241.474i	−0.765421	−	0.255258i
$947$		−	1229.50i		−	1.29831i	−0.760655	−	0.649156i	$-0.775122\pi$
$947$		−	1229.50i		−	1.29831i	0.760655	−	0.649156i	$-0.224878\pi$
$948$	700.502	+	525.680i	0.738927	+	0.554515i
$949$	386.176			0.406929
$950$	−23.5947	+	70.7515i	−0.0248365	+	0.0744752i
$951$			286.634i			0.301403i
$952$	−1159.33	+	801.904i	−1.21779	+	0.842336i
$953$	1664.37			1.74646			0.873229	−	0.487310i	$-0.162022\pi$
$953$	1664.37			1.74646			0.873229	+	0.487310i	$0.162022\pi$
$954$	−526.620	−	175.621i	−0.552013	−	0.184089i
$955$			1265.62i			1.32526i
$956$	4.79080	−	6.38405i	0.00501130	−	0.00667788i
$957$	580.531			0.606616
$958$	−418.343	+	1254.45i	−0.436684	+	1.30945i
$959$			35.3360i			0.0368467i
$960$	1853.71	+	698.881i	1.93095	+	0.728001i
$961$	902.356			0.938976
$962$	669.176	+	223.162i	0.695609	+	0.231977i
$963$			1047.43i			1.08767i
$964$	−206.853	−	155.230i	−0.214578	−	0.161027i
$965$	358.848			0.371863
$966$	−173.792	+	521.134i	−0.179908	+	0.539476i
$967$		−	70.9865i		−	0.0734090i	−0.999326	−	0.0367045i	$-0.988314\pi$
$967$		−	70.9865i		−	0.0734090i	0.999326	−	0.0367045i	$-0.0116860\pi$
$968$	−253.636	−	366.688i	−0.262020	−	0.378810i
$969$	−698.561			−0.720910
$970$	−102.829	−	34.2921i	−0.106009	−	0.0353527i
$971$		−	925.687i		−	0.953334i	−0.879084	−	0.476667i	$-0.841845\pi$
$971$		−	925.687i		−	0.953334i	0.879084	−	0.476667i	$-0.158155\pi$
$972$	390.164	−	519.918i	0.401403	−	0.534895i
$973$	−454.212			−0.466817
$974$	−396.602	+	1189.26i	−0.407188	+	1.22100i
$975$			641.835i			0.658292i
$976$	−139.478	−	479.198i	−0.142908	−	0.490982i
$977$	−720.813			−0.737782			−0.368891	−	0.929473i	$-0.620262\pi$
$977$	−720.813			−0.737782			−0.368891	+	0.929473i	$0.620262\pi$
$978$	1905.17	+	635.350i	1.94803	+	0.649642i
$979$			231.444i			0.236409i
$980$	268.356	+	201.383i	0.273832	+	0.205493i
$981$	3021.64			3.08016
$982$	615.847	−	1846.69i	0.627135	−	1.88054i
$983$		−	802.902i		−	0.816787i	−0.912806	−	0.408394i	$-0.866089\pi$
$983$		−	802.902i		−	0.816787i	0.912806	−	0.408394i	$-0.133911\pi$
$984$	−1746.89	+	1208.31i	−1.77529	+	1.22796i
$985$	−2058.42			−2.08976
$986$	−765.160	−	255.171i	−0.776024	−	0.258794i
$987$		−	1470.57i		−	1.48994i
$988$	−146.927	+	195.790i	−0.148712	+	0.198168i
$989$	413.289			0.417885
$990$	−579.028	+	1736.28i	−0.584877	+	1.75382i
$991$		−	117.656i		−	0.118725i	−0.998236	−	0.0593624i	$-0.981093\pi$
$991$		−	117.656i		−	0.118725i	0.998236	−	0.0593624i	$-0.0189068\pi$
$992$	−244.871	−	9.46874i	−0.246846	−	0.00954510i
$993$	882.235			0.888454
$994$	735.986	+	245.442i	0.740429	+	0.246923i
$995$			1207.61i			1.21368i
$996$	−1502.02	−	1127.16i	−1.50805	−	1.13169i
$997$	−1165.44			−1.16894			−0.584472	−	0.811414i	$-0.698698\pi$
$997$	−1165.44			−1.16894			−0.584472	+	0.811414i	$0.698698\pi$
$998$	−108.806	+	326.267i	−0.109024	+	0.326921i
$999$			1416.98i			1.41839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.b.39.3	✓	14
3.2	odd	2		684.3.g.b.343.12		14
4.3	odd	2	inner	76.3.b.b.39.4	yes	14
8.3	odd	2		1216.3.d.d.191.2		14
8.5	even	2		1216.3.d.d.191.13		14
12.11	even	2		684.3.g.b.343.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.3	✓	14	1.1	even	1	trivial
76.3.b.b.39.4	yes	14	4.3	odd	2	inner
684.3.g.b.343.11		14	12.11	even	2
684.3.g.b.343.12		14	3.2	odd	2
1216.3.d.d.191.2		14	8.3	odd	2
1216.3.d.d.191.13		14	8.5	even	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +O(q^{10})\)	\(q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +(-10.9903 - 3.66514i) q^{10} +8.07883i q^{11} +(12.8296 - 17.0963i) q^{12} -14.0396 q^{13} +(-3.71745 + 11.1472i) q^{14} -30.9544i q^{15} +(4.47149 + 15.3625i) q^{16} +29.9906 q^{17} +(37.1016 + 12.3729i) q^{18} -4.35890i q^{19} +(18.5327 + 13.9076i) q^{20} -31.3962 q^{21} +(5.11162 - 15.3278i) q^{22} +8.74865i q^{23} +(-35.1585 + 24.3189i) q^{24} +8.55515 q^{25} +(26.6370 + 8.88309i) q^{26} +56.4036i q^{27} +(14.1061 - 18.7973i) q^{28} +13.4473 q^{29} +(-19.5854 + 58.7291i) q^{30} -7.65793i q^{31} +(1.23646 - 31.9761i) q^{32} +43.1708 q^{33} +(-56.9006 - 18.9756i) q^{34} -34.0341i q^{35} +(-62.5635 - 46.9497i) q^{36} +25.1221 q^{37} +(-2.75796 + 8.27005i) q^{38} +75.0232i q^{39} +(-26.3622 - 38.1125i) q^{40} +49.6861 q^{41} +(59.5673 + 19.8649i) q^{42} -47.2402i q^{43} +(-19.3963 + 25.8469i) q^{44} -113.277 q^{45} +(5.53543 - 16.5986i) q^{46} +46.8391i q^{47} +(82.0925 - 23.8943i) q^{48} +14.4801 q^{49} +(-16.2315 - 5.41300i) q^{50} -160.261i q^{51} +(-44.9173 - 33.7074i) q^{52} -14.1940 q^{53} +(35.6876 - 107.013i) q^{54} +46.7981i q^{55} +(-38.6565 + 26.7385i) q^{56} -23.2927 q^{57} +(-25.5133 - 8.50835i) q^{58} +100.107i q^{59} +(74.3179 - 99.0334i) q^{60} -31.1928 q^{61} +(-4.84532 + 14.5292i) q^{62} +114.894i q^{63} +(-22.5778 + 59.8853i) q^{64} -81.3267 q^{65} +(-81.9071 - 27.3150i) q^{66} +34.5861i q^{67} +(95.9501 + 72.0041i) q^{68} +46.7502 q^{69} +(-21.5340 + 64.5722i) q^{70} -66.0243i q^{71} +(88.9944 + 128.662i) q^{72} -27.5063 q^{73} +(-47.6636 - 15.8952i) q^{74} -45.7162i q^{75} +(10.4652 - 13.9456i) q^{76} +47.4661 q^{77} +(47.4686 - 142.340i) q^{78} +40.9739i q^{79} +(25.9019 + 88.9899i) q^{80} +125.408 q^{81} +(-94.2684 - 31.4373i) q^{82} -87.8564i q^{83} +(-100.447 - 75.3787i) q^{84} +173.726 q^{85} +(-29.8898 + 89.6279i) q^{86} -71.8584i q^{87} +(53.1541 - 36.7663i) q^{88} +28.6482 q^{89} +(214.918 + 71.6723i) q^{90} +82.4875i q^{91} +(-21.0045 + 27.9899i) q^{92} -40.9217 q^{93} +(29.6360 - 88.8669i) q^{94} -25.2497i q^{95} +(-170.871 - 6.60728i) q^{96} +9.35629 q^{97} +(-27.4728 - 9.16182i) q^{98} -157.983i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

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