LMFDB - Embedded newform 76.3.b.b.39.9

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			39.9
Root			$0.711746 + 1.86907i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.b.39.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +O(q^{10})$	\(q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +(3.54430 - 9.30745i) q^{10} -13.4463i q^{11} +(-11.8382 + 13.2898i) q^{12} +14.1766 q^{13} +(22.9201 + 8.72803i) q^{14} -22.1571i q^{15} +(1.84237 + 15.8936i) q^{16} -5.89478 q^{17} +(-7.68520 + 20.1816i) q^{18} +4.35890i q^{19} +(-14.8736 - 13.2491i) q^{20} +54.5630 q^{21} +(-25.1320 - 9.57032i) q^{22} +0.906592i q^{23} +(16.4137 + 31.5855i) q^{24} -0.202335 q^{25} +(10.0901 - 26.4969i) q^{26} +7.99863i q^{27} +(32.6266 - 36.6271i) q^{28} -10.3853 q^{29} +(-41.4131 - 15.7702i) q^{30} +43.2608i q^{31} +(31.0175 + 7.86868i) q^{32} -59.8285 q^{33} +(-4.19559 + 11.0178i) q^{34} +61.0656i q^{35} +(32.2508 + 28.7283i) q^{36} -1.61331 q^{37} +(8.14708 + 3.10243i) q^{38} -63.0779i q^{39} +(-35.3497 + 18.3698i) q^{40} +69.3758 q^{41} +(38.8350 - 101.982i) q^{42} -32.0147i q^{43} +(-35.7752 + 40.1617i) q^{44} -53.7694 q^{45} +(1.69448 + 0.645264i) q^{46} +38.9732i q^{47} +(70.7178 - 8.19753i) q^{48} -101.377 q^{49} +(-0.144011 + 0.378179i) q^{50} +26.2286i q^{51} +(-42.3430 - 37.7182i) q^{52} -8.31560 q^{53} +(14.9500 + 5.69299i) q^{54} -66.9586i q^{55} +(-45.2367 - 87.0505i) q^{56} +19.3947 q^{57} +(-7.39169 + 19.4108i) q^{58} +20.9242i q^{59} +(-58.9512 + 66.1795i) q^{60} -118.329 q^{61} +(80.8574 + 30.7907i) q^{62} -132.410i q^{63} +(36.7837 - 52.3733i) q^{64} +70.5953 q^{65} +(-42.5827 + 111.824i) q^{66} +57.4499i q^{67} +(17.6067 + 15.6837i) q^{68} +4.03384 q^{69} +(114.136 + 43.4632i) q^{70} +11.3393i q^{71} +(76.6496 - 39.8318i) q^{72} -23.5952 q^{73} +(-1.14827 + 3.01539i) q^{74} +0.900282i q^{75} +(11.5973 - 13.0193i) q^{76} +164.889 q^{77} +(-117.897 - 44.8955i) q^{78} -0.286369i q^{79} +(9.17448 + 79.1456i) q^{80} -61.5894 q^{81} +(49.3780 - 129.668i) q^{82} -24.9311i q^{83} +(-162.971 - 145.171i) q^{84} -29.3544 q^{85} +(-59.8376 - 22.7863i) q^{86} +46.2089i q^{87} +(49.6022 + 95.4512i) q^{88} -43.7018 q^{89} +(-38.2702 + 100.499i) q^{90} +173.845i q^{91} +(2.41208 - 2.70784i) q^{92} +192.487 q^{93} +(72.8436 + 27.7390i) q^{94} +21.7061i q^{95} +(35.0113 - 138.011i) q^{96} +115.905 q^{97} +(-72.1549 + 189.481i) q^{98} +145.188i 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 $

$2$	0.711746	−	1.86907i	0.355873	−	0.934534i
$2$	0.711746	−	1.86907i	0.355873	−	0.934534i
$3$		−	4.44946i		−	1.48315i	−0.670869	−	0.741576i	$-0.734079\pi$
$3$		−	4.44946i		−	1.48315i	0.670869	−	0.741576i	$-0.265921\pi$
$4$	−2.98683	−	2.66060i	−0.746709	−	0.665151i
$5$	4.97973			0.995945			0.497973	−	0.867193i	$-0.334078\pi$
$5$	4.97973			0.995945			0.497973	+	0.867193i	$0.334078\pi$
$6$	−8.31634	−	3.16688i	−1.38606	−	0.527814i
$7$			12.2628i			1.75183i	0.482461	+	0.875917i	$0.339743\pi$
$7$			12.2628i			1.75183i	−0.482461	+	0.875917i	$0.660257\pi$
$8$	−7.09872	+	3.68892i	−0.887340	+	0.461116i
$9$	−10.7977			−1.19974
$10$	3.54430	−	9.30745i	0.354430	−	0.930745i
$11$		−	13.4463i		−	1.22239i	−0.791481	−	0.611193i	$-0.790690\pi$
$11$		−	13.4463i		−	1.22239i	0.791481	−	0.611193i	$-0.209310\pi$
$12$	−11.8382	+	13.2898i	−0.986520	+	1.10748i
$13$	14.1766			1.09050			0.545252	−	0.838272i	$-0.316434\pi$
$13$	14.1766			1.09050			0.545252	+	0.838272i	$0.316434\pi$
$14$	22.9201	+	8.72803i	1.63715	+	0.623431i
$15$		−	22.1571i		−	1.47714i
$16$	1.84237	+	15.8936i	0.115148	+	0.993348i
$17$	−5.89478			−0.346752			−0.173376	−	0.984856i	$-0.555468\pi$
$17$	−5.89478			−0.346752			−0.173376	+	0.984856i	$0.555468\pi$
$18$	−7.68520	+	20.1816i	−0.426955	+	1.12120i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−14.8736	−	13.2491i	−0.743681	−	0.662454i
$21$	54.5630			2.59824
$22$	−25.1320	−	9.57032i	−1.14236	−	0.435014i
$23$			0.906592i			0.0394171i	0.999806	+	0.0197085i	$0.00627383\pi$
$23$			0.906592i			0.0394171i	−0.999806	+	0.0197085i	$0.993726\pi$
$24$	16.4137	+	31.5855i	0.683905	+	1.31606i
$25$	−0.202335			−0.00809341
$26$	10.0901	−	26.4969i	0.388081	−	1.01911i
$27$			7.99863i			0.296246i
$28$	32.6266	−	36.6271i	1.16524	−	1.30811i
$29$	−10.3853			−0.358114			−0.179057	−	0.983839i	$-0.557305\pi$
$29$	−10.3853			−0.358114			−0.179057	+	0.983839i	$0.557305\pi$
$30$	−41.4131	−	15.7702i	−1.38044	−	0.525674i
$31$			43.2608i			1.39551i	0.716337	+	0.697755i	$0.245817\pi$
$31$			43.2608i			1.39551i	−0.716337	+	0.697755i	$0.754183\pi$
$32$	31.0175	+	7.86868i	0.969296	+	0.245896i
$33$	−59.8285			−1.81299
$34$	−4.19559	+	11.0178i	−0.123400	+	0.324052i
$35$			61.0656i			1.74473i
$36$	32.2508	+	28.7283i	0.895857	+	0.798009i
$37$	−1.61331			−0.0436030			−0.0218015	−	0.999762i	$-0.506940\pi$
$37$	−1.61331			−0.0436030			−0.0218015	+	0.999762i	$0.506940\pi$
$38$	8.14708	+	3.10243i	0.214397	+	0.0816429i
$39$		−	63.0779i		−	1.61738i
$40$	−35.3497	+	18.3698i	−0.883742	+	0.459246i
$41$	69.3758			1.69209			0.846047	−	0.533109i	$-0.178976\pi$
$41$	69.3758			1.69209			0.846047	+	0.533109i	$0.178976\pi$
$42$	38.8350	−	101.982i	0.924643	−	2.42814i
$43$		−	32.0147i		−	0.744527i	−0.928127	−	0.372264i	$-0.878582\pi$
$43$		−	32.0147i		−	0.744527i	0.928127	−	0.372264i	$-0.121418\pi$
$44$	−35.7752	+	40.1617i	−0.813072	+	0.912767i
$45$	−53.7694			−1.19488
$46$	1.69448	+	0.645264i	0.0368366	+	0.0140275i
$47$			38.9732i			0.829217i	0.910000	+	0.414609i	$0.136082\pi$
$47$			38.9732i			0.829217i	−0.910000	+	0.414609i	$0.863918\pi$
$48$	70.7178	−	8.19753i	1.47329	−	0.170782i
$49$	−101.377			−2.06893
$50$	−0.144011	+	0.378179i	−0.00288023	+	0.00756357i
$51$			26.2286i			0.514286i
$52$	−42.3430	−	37.7182i	−0.814289	−	0.725350i
$53$	−8.31560			−0.156898			−0.0784491	−	0.996918i	$-0.524997\pi$
$53$	−8.31560			−0.156898			−0.0784491	+	0.996918i	$0.524997\pi$
$54$	14.9500	+	5.69299i	0.276852	+	0.105426i
$55$		−	66.9586i		−	1.21743i
$56$	−45.2367	−	87.0505i	−0.807798	−	1.55447i
$57$	19.3947			0.340258
$58$	−7.39169	+	19.4108i	−0.127443	+	0.334669i
$59$			20.9242i			0.354648i	0.984153	+	0.177324i	$0.0567440\pi$
$59$			20.9242i			0.354648i	−0.984153	+	0.177324i	$0.943256\pi$
$60$	−58.9512	+	66.1795i	−0.982520	+	1.10299i
$61$	−118.329			−1.93983			−0.969913	−	0.243453i	$-0.921720\pi$
$61$	−118.329			−1.93983			−0.969913	+	0.243453i	$0.921720\pi$
$62$	80.8574	+	30.7907i	1.30415	+	0.496624i
$63$		−	132.410i		−	2.10175i
$64$	36.7837	−	52.3733i	0.574745	−	0.818333i
$65$	70.5953			1.08608
$66$	−42.5827	+	111.824i	−0.645193	+	1.69430i
$67$			57.4499i			0.857462i	0.903432	+	0.428731i	$0.141039\pi$
$67$			57.4499i			0.857462i	−0.903432	+	0.428731i	$0.858961\pi$
$68$	17.6067	+	15.6837i	0.258923	+	0.230642i
$69$	4.03384			0.0584615
$70$	114.136	+	43.4632i	1.63051	+	0.620903i
$71$			11.3393i			0.159709i	0.996807	+	0.0798545i	$0.0254456\pi$
$71$			11.3393i			0.159709i	−0.996807	+	0.0798545i	$0.974554\pi$
$72$	76.6496	−	39.8318i	1.06458	−	0.553219i
$73$	−23.5952			−0.323222			−0.161611	−	0.986855i	$-0.551669\pi$
$73$	−23.5952			−0.323222			−0.161611	+	0.986855i	$0.551669\pi$
$74$	−1.14827	+	3.01539i	−0.0155171	+	0.0407485i
$75$			0.900282i			0.0120038i
$76$	11.5973	−	13.0193i	0.152596	−	0.171307i
$77$	164.889			2.14142
$78$	−117.897	−	44.8955i	−1.51150	−	0.575583i
$79$		−	0.286369i		−	0.00362492i	−0.999998	−	0.00181246i	$-0.999423\pi$
$79$		−	0.286369i		−	0.00362492i	0.999998	−	0.00181246i	$-0.000576925\pi$
$80$	9.17448	+	79.1456i	0.114681	+	0.989320i
$81$	−61.5894			−0.760363
$82$	49.3780	−	129.668i	0.602170	−	1.58132i
$83$		−	24.9311i		−	0.300375i	−0.988658	−	0.150188i	$-0.952012\pi$
$83$		−	24.9311i		−	0.300375i	0.988658	−	0.150188i	$-0.0479878\pi$
$84$	−162.971	−	145.171i	−1.94013	−	1.72822i
$85$	−29.3544			−0.345346
$86$	−59.8376	−	22.7863i	−0.695786	−	0.264957i
$87$			46.2089i			0.531137i
$88$	49.6022	+	95.4512i	0.563662	+	1.08467i
$89$	−43.7018			−0.491031			−0.245515	−	0.969393i	$-0.578957\pi$
$89$	−43.7018			−0.491031			−0.245515	+	0.969393i	$0.578957\pi$
$90$	−38.2702	+	100.499i	−0.425224	+	1.11665i
$91$			173.845i			1.91038i
$92$	2.41208	−	2.70784i	0.0262183	−	0.0294331i
$93$	192.487			2.06975
$94$	72.8436	+	27.7390i	0.774932	+	0.295096i
$95$			21.7061i			0.228485i
$96$	35.0113	−	138.011i	0.364702	−	1.43761i
$97$	115.905			1.19490			0.597448	−	0.801908i	$-0.296182\pi$
$97$	115.905			1.19490			0.597448	+	0.801908i	$0.296182\pi$
$98$	−72.1549	+	189.481i	−0.736275	+	1.93348i
$99$			145.188i			1.46655i
$100$	0.604342	+	0.538334i	0.00604342	+	0.00538334i
$101$	−10.3010			−0.101990			−0.0509950	−	0.998699i	$-0.516239\pi$
$101$	−10.3010			−0.101990			−0.0509950	+	0.998699i	$0.516239\pi$
$102$	49.0230	+	18.6681i	0.480618	+	0.183021i
$103$		−	110.807i		−	1.07579i	−0.843011	−	0.537897i	$-0.819219\pi$
$103$		−	110.807i		−	1.07579i	0.843011	−	0.537897i	$-0.180781\pi$
$104$	−100.635	+	52.2962i	−0.967648	+	0.502848i
$105$	271.709			2.58770
$106$	−5.91860	+	15.5424i	−0.0558358	+	0.146627i
$107$		−	29.6484i		−	0.277088i	−0.990356	−	0.138544i	$-0.955758\pi$
$107$		−	29.6484i		−	0.277088i	0.990356	−	0.138544i	$-0.0442422\pi$
$108$	21.2812	−	23.8906i	0.197048	−	0.221209i
$109$	−1.00851			−0.00925235			−0.00462617	−	0.999989i	$-0.501473\pi$
$109$	−1.00851			−0.00925235			−0.00462617	+	0.999989i	$0.501473\pi$
$110$	−125.150	−	47.6576i	−1.13773	−	0.433251i
$111$			7.17835i			0.0646698i
$112$	−194.900	+	22.5927i	−1.74018	+	0.201720i
$113$	−59.0375			−0.522456			−0.261228	−	0.965277i	$-0.584127\pi$
$113$	−59.0375			−0.522456			−0.261228	+	0.965277i	$0.584127\pi$
$114$	13.8041	−	36.2501i	0.121089	−	0.317983i
$115$			4.51458i			0.0392572i
$116$	31.0192	+	27.6312i	0.267407	+	0.238200i
$117$	−153.074			−1.30832
$118$	39.1088	+	14.8927i	0.331431	+	0.126210i
$119$		−	72.2868i		−	0.607452i
$120$	81.7358	+	157.287i	0.681131	+	1.31072i
$121$	−59.8017			−0.494229
$122$	−84.2205	+	221.166i	−0.690332	+	1.81283i
$123$		−	308.685i		−	2.50963i
$124$	115.100	−	129.213i	0.928225	−	1.04204i
$125$	−125.501			−1.00401
$126$	−247.484	−	94.2424i	−1.96416	−	0.747955i
$127$		−	209.454i		−	1.64925i	−0.565681	−	0.824624i	$-0.691387\pi$
$127$		−	209.454i		−	1.64925i	0.565681	−	0.824624i	$-0.308613\pi$
$128$	−71.7086	−	106.028i	−0.560224	−	0.828341i
$129$	−142.448			−1.10425
$130$	50.2460	−	131.948i	0.386507	−	1.01498i
$131$		−	46.0795i		−	0.351752i	−0.984412	−	0.175876i	$-0.943724\pi$
$131$		−	46.0795i		−	0.351752i	0.984412	−	0.175876i	$-0.0562758\pi$
$132$	178.698	+	159.180i	1.35377	+	1.20591i
$133$	−53.4525			−0.401899
$134$	107.378	+	40.8898i	0.801327	+	0.305147i
$135$			39.8310i			0.295044i
$136$	41.8454	−	21.7454i	0.307687	−	0.159893i
$137$	206.272			1.50564			0.752819	−	0.658228i	$-0.228694\pi$
$137$	206.272			1.50564			0.752819	+	0.658228i	$0.228694\pi$
$138$	2.87107	−	7.53953i	0.0208049	−	0.0546343i
$139$		−	125.355i		−	0.901835i	−0.892566	−	0.450918i	$-0.851097\pi$
$139$		−	125.355i		−	0.901835i	0.892566	−	0.450918i	$-0.148903\pi$
$140$	162.471	−	182.393i	1.16051	−	1.30281i
$141$	173.410			1.22986
$142$	21.1940	+	8.07073i	0.149253	+	0.0568361i
$143$		−	190.621i		−	1.33302i
$144$	−19.8933	−	171.613i	−0.138148	−	1.19176i
$145$	−51.7159			−0.356661
$146$	−16.7938	+	44.1011i	−0.115026	+	0.302062i
$147$			451.074i			3.06853i
$148$	4.81869	+	4.29238i	0.0325587	+	0.0290026i
$149$	−170.871			−1.14679			−0.573394	−	0.819280i	$-0.694374\pi$
$149$	−170.871			−1.14679			−0.573394	+	0.819280i	$0.694374\pi$
$150$	1.68269	+	0.640772i	0.0112179	+	0.00427182i
$151$			131.745i			0.872482i	0.899830	+	0.436241i	$0.143690\pi$
$151$			131.745i			0.872482i	−0.899830	+	0.436241i	$0.856310\pi$
$152$	−16.0796	−	30.9426i	−0.105787	−	0.203570i
$153$	63.6499			0.416012
$154$	117.359	−	308.189i	0.762074	−	2.00123i
$155$			215.427i			1.38985i
$156$	−167.825	+	188.403i	−1.07580	+	1.20771i
$157$	−3.40126			−0.0216641			−0.0108320	−	0.999941i	$-0.503448\pi$
$157$	−3.40126			−0.0216641			−0.0108320	+	0.999941i	$0.503448\pi$
$158$	−0.535243	−	0.203822i	−0.00338761	−	0.00129001i
$159$			36.9999i			0.232704i
$160$	154.459	+	39.1839i	0.965366	+	0.244899i
$161$	−11.1174			−0.0690522
$162$	−43.8360	+	115.115i	−0.270593	+	0.710585i
$163$			170.519i			1.04613i	0.852293	+	0.523064i	$0.175211\pi$
$163$			170.519i			1.04613i	−0.852293	+	0.523064i	$0.824789\pi$
$164$	−207.214	−	184.582i	−1.26350	−	1.12550i
$165$	−297.930			−1.80563
$166$	−46.5980	−	17.7446i	−0.280711	−	0.106895i
$167$		−	245.186i		−	1.46818i	−0.679053	−	0.734089i	$-0.737610\pi$
$167$		−	245.186i		−	1.46818i	0.679053	−	0.734089i	$-0.262390\pi$
$168$	−387.327	+	201.279i	−2.30552	+	1.19809i
$169$	31.9746			0.189199
$170$	−20.8929	+	54.8654i	−0.122899	+	0.322738i
$171$		−	47.0659i		−	0.275239i
$172$	−85.1784	+	95.6225i	−0.495223	+	0.555945i
$173$	62.3081			0.360162			0.180081	−	0.983652i	$-0.442364\pi$
$173$	62.3081			0.360162			0.180081	+	0.983652i	$0.442364\pi$
$174$	86.3676	+	32.8890i	0.496366	+	0.189017i
$175$		−	2.48121i		−	0.0141783i
$176$	213.709	−	24.7729i	1.21426	−	0.140755i
$177$	93.1014			0.525997
$178$	−31.1046	+	81.6816i	−0.174745	+	0.458885i
$179$		−	129.080i		−	0.721115i	−0.932737	−	0.360557i	$-0.882586\pi$
$179$		−	129.080i		−	0.721115i	0.932737	−	0.360557i	$-0.117414\pi$
$180$	160.600	+	143.059i	0.892224	+	0.794773i
$181$	−198.677			−1.09766			−0.548831	−	0.835933i	$-0.684927\pi$
$181$	−198.677			−1.09766			−0.548831	+	0.835933i	$0.684927\pi$
$182$	324.928	+	123.733i	1.78532	+	0.679854i
$183$			526.501i			2.87706i
$184$	−3.34435	−	6.43565i	−0.0181758	−	0.0349763i
$185$	−8.03384			−0.0434261
$186$	137.002	−	359.771i	0.736569	−	1.93426i
$187$			79.2628i			0.423865i
$188$	103.692	−	116.407i	0.551555	−	0.619184i
$189$	−98.0860			−0.518973
$190$	40.5702	+	15.4492i	0.213528	+	0.0813118i
$191$			380.217i			1.99067i	0.0965041	+	0.995333i	$0.469234\pi$
$191$			380.217i			1.99067i	−0.0965041	+	0.995333i	$0.530766\pi$
$192$	−233.033	−	163.667i	−1.21371	−	0.852434i
$193$	−264.689			−1.37145			−0.685724	−	0.727862i	$-0.740514\pi$
$193$	−264.689			−1.37145			−0.685724	+	0.727862i	$0.740514\pi$
$194$	82.4948	−	216.634i	0.425231	−	1.11667i
$195$		−	314.111i		−	1.61082i
$196$	302.797	+	269.725i	1.54488	+	1.37615i
$197$	125.565			0.637386			0.318693	−	0.947858i	$-0.396756\pi$
$197$	125.565			0.637386			0.318693	+	0.947858i	$0.396756\pi$
$198$	271.367	+	103.337i	1.37054	+	0.521904i
$199$			14.4081i			0.0724026i	0.999345	+	0.0362013i	$0.0115258\pi$
$199$			14.4081i			0.0724026i	−0.999345	+	0.0362013i	$0.988474\pi$
$200$	1.43632	−	0.746400i	0.00718161	−	0.00373200i
$201$	255.621			1.27175
$202$	−7.33168	+	19.2532i	−0.0362955	+	0.0953131i
$203$		−	127.353i		−	0.627356i
$204$	69.7839	−	78.3405i	0.342078	−	0.384022i
$205$	345.473			1.68523
$206$	−207.105	−	78.8663i	−1.00537	−	0.382846i
$207$		−	9.78908i		−	0.0472902i
$208$	26.1184	+	225.316i	0.125569	+	1.08325i
$209$	58.6109			0.280435
$210$	193.388	−	507.842i	0.920893	−	2.41830i
$211$			81.1242i			0.384475i	0.981348	+	0.192237i	$0.0615744\pi$
$211$			81.1242i			0.384475i	−0.981348	+	0.192237i	$0.938426\pi$
$212$	24.8373	+	22.1245i	0.117157	+	0.104361i
$213$	50.4539			0.236873
$214$	−55.4148	−	21.1021i	−0.258948	−	0.0986080i
$215$		−	159.424i		−	0.741508i
$216$	−29.5063	−	56.7800i	−0.136603	−	0.262871i
$217$	−530.500			−2.44470
$218$	−0.717800	+	1.88497i	−0.00329266	+	0.00864664i
$219$			104.986i			0.479388i
$220$	−178.150	+	199.994i	−0.809775	+	0.909066i
$221$	−83.5677			−0.378134
$222$	13.4168	+	5.10916i	0.0604362	+	0.0230142i
$223$		−	181.944i		−	0.815892i	−0.913006	−	0.407946i	$-0.866245\pi$
$223$		−	181.944i		−	0.815892i	0.913006	−	0.407946i	$-0.133755\pi$
$224$	−96.4924	+	380.363i	−0.430770	+	1.69805i
$225$	2.18475			0.00970999
$226$	−42.0197	+	110.345i	−0.185928	+	0.488253i
$227$		−	423.077i		−	1.86377i	−0.362748	−	0.931887i	$-0.618162\pi$
$227$		−	423.077i		−	1.86377i	0.362748	−	0.931887i	$-0.381838\pi$
$228$	−57.9289	−	51.6017i	−0.254074	−	0.226323i
$229$	360.509			1.57427			0.787137	−	0.616778i	$-0.211562\pi$
$229$	360.509			1.57427			0.787137	+	0.616778i	$0.211562\pi$
$230$	8.43806	+	3.21324i	0.0366872	+	0.0139706i
$231$		−	733.668i		−	3.17605i
$232$	73.7223	−	38.3106i	0.317769	−	0.165132i
$233$	2.13039			0.00914329			0.00457164	−	0.999990i	$-0.498545\pi$
$233$	2.13039			0.00914329			0.00457164	+	0.999990i	$0.498545\pi$
$234$	−108.950	+	286.105i	−0.465596	+	1.22267i
$235$			194.076i			0.825855i
$236$	55.6711	−	62.4972i	0.235894	−	0.264819i
$237$	−1.27419			−0.00537631
$238$	−135.109	−	51.4499i	−0.567685	−	0.216176i
$239$			228.926i			0.957847i	0.877857	+	0.478924i	$0.158973\pi$
$239$			228.926i			0.957847i	−0.877857	+	0.478924i	$0.841027\pi$
$240$	352.155	−	40.8214i	1.46731	−	0.170089i
$241$	245.133			1.01715			0.508575	−	0.861017i	$-0.330172\pi$
$241$	245.133			1.01715			0.508575	+	0.861017i	$0.330172\pi$
$242$	−42.5636	+	111.774i	−0.175883	+	0.461874i
$243$			346.027i			1.42398i
$244$	353.430	+	314.828i	1.44848	+	1.29028i
$245$	−504.831			−2.06054
$246$	−576.953	−	219.705i	−2.34534	−	0.893110i
$247$			61.7942i			0.250179i
$248$	−159.586	−	307.096i	−0.643491	−	1.23829i
$249$	−110.930			−0.445502
$250$	−89.3246	+	234.569i	−0.357299	+	0.938278i
$251$		−	178.193i		−	0.709934i	−0.934879	−	0.354967i	$-0.884492\pi$
$251$		−	178.193i		−	0.709934i	0.934879	−	0.354967i	$-0.115508\pi$
$252$	−352.291	+	395.487i	−1.39798	+	1.56939i
$253$	12.1903			0.0481829
$254$	−391.485	−	149.078i	−1.54128	−	0.586923i
$255$			130.611i			0.512201i
$256$	−249.211	+	58.5636i	−0.973482	+	0.228764i
$257$	−239.267			−0.930998			−0.465499	−	0.885048i	$-0.654125\pi$
$257$	−239.267			−0.930998			−0.465499	+	0.885048i	$0.654125\pi$
$258$	−101.387	+	266.245i	−0.392972	+	1.03196i
$259$		−	19.7838i		−	0.0763852i
$260$	−210.857	−	187.826i	−0.810987	−	0.722409i
$261$	112.137			0.429643
$262$	−86.1257	−	32.7969i	−0.328724	−	0.125179i
$263$		−	39.7564i		−	0.151165i	−0.997140	−	0.0755825i	$-0.975918\pi$
$263$		−	39.7564i		−	0.151165i	0.997140	−	0.0755825i	$-0.0240816\pi$
$264$	424.706	−	220.703i	1.60873	−	0.835996i
$265$	−41.4094			−0.156262
$266$	−38.0446	+	99.9064i	−0.143025	+	0.375588i
$267$			194.449i			0.728274i
$268$	152.852	−	171.593i	0.570342	−	0.640274i
$269$	−25.6332			−0.0952905			−0.0476453	−	0.998864i	$-0.515172\pi$
$269$	−25.6332			−0.0952905			−0.0476453	+	0.998864i	$0.515172\pi$
$270$	74.4468	+	28.3495i	0.275729	+	0.104998i
$271$			53.7535i			0.198353i	0.995070	+	0.0991763i	$0.0316208\pi$
$271$			53.7535i			0.198353i	−0.995070	+	0.0991763i	$0.968379\pi$
$272$	−10.8604	−	93.6892i	−0.0399278	−	0.344446i
$273$	773.515			2.83339
$274$	146.813	−	385.537i	0.535816	−	1.40707i
$275$			2.72065i			0.00989328i
$276$	−12.0484	−	10.7325i	−0.0436537	−	0.0388857i
$277$	353.449			1.27599			0.637995	−	0.770040i	$-0.279764\pi$
$277$	353.449			1.27599			0.637995	+	0.770040i	$0.279764\pi$
$278$	−234.297	−	89.2210i	−0.842796	−	0.320939i
$279$		−	467.116i		−	1.67425i
$280$	−225.266	−	433.488i	−0.804523	−	1.54817i
$281$	221.272			0.787445			0.393722	−	0.919229i	$-0.371187\pi$
$281$	221.272			0.787445			0.393722	+	0.919229i	$0.371187\pi$
$282$	123.424	−	324.115i	0.437673	−	1.14934i
$283$		−	81.0003i		−	0.286220i	−0.989707	−	0.143110i	$-0.954290\pi$
$283$		−	81.0003i		−	0.286220i	0.989707	−	0.143110i	$-0.0457103\pi$
$284$	30.1695	−	33.8687i	0.106231	−	0.119256i
$285$	96.5804			0.338879
$286$	−356.285	−	135.674i	−1.24575	−	0.474385i
$287$			850.745i			2.96427i
$288$	−334.916	−	84.9634i	−1.16290	−	0.295012i
$289$	−254.252			−0.879763
$290$	−36.8086	+	96.6606i	−0.126926	+	0.333312i
$291$		−	515.714i		−	1.77221i
$292$	70.4750	+	62.7776i	0.241353	+	0.214992i
$293$	517.659			1.76675			0.883377	−	0.468664i	$-0.155264\pi$
$293$	517.659			1.76675			0.883377	+	0.468664i	$0.155264\pi$
$294$	843.089	+	321.050i	2.86765	+	1.09201i
$295$			104.197i			0.353210i
$296$	11.4524	−	5.95138i	0.0386906	−	0.0201060i
$297$	107.552			0.362127
$298$	−121.617	+	319.371i	−0.408111	+	1.07171i
$299$			12.8524i			0.0429845i
$300$	2.39529	−	2.68899i	0.00798432	−	0.00896331i
$301$	392.591			1.30429
$302$	246.240	+	93.7688i	0.815364	+	0.310493i
$303$			45.8338i			0.151267i
$304$	−69.2785	+	8.03069i	−0.227890	+	0.0264167i
$305$	−589.248			−1.93196
$306$	45.3026	−	118.966i	0.148048	−	0.388778i
$307$			249.101i			0.811405i	0.914005	+	0.405703i	$0.132973\pi$
$307$			249.101i			0.811405i	−0.914005	+	0.405703i	$0.867027\pi$
$308$	−492.497	−	438.705i	−1.59902	−	1.42437i
$309$	−493.030			−1.59557
$310$	402.648	+	153.329i	1.29886	+	0.494610i
$311$		−	252.481i		−	0.811835i	−0.913910	−	0.405917i	$-0.866952\pi$
$311$		−	252.481i		−	0.811835i	0.913910	−	0.405917i	$-0.133048\pi$
$312$	232.690	+	447.773i	0.745801	+	1.43517i
$313$	−595.875			−1.90376			−0.951878	−	0.306478i	$-0.900849\pi$
$313$	−595.875			−1.90376			−0.951878	+	0.306478i	$0.900849\pi$
$314$	−2.42083	+	6.35719i	−0.00770966	+	0.0202458i
$315$		−	659.366i		−	2.09322i
$316$	−0.761914	+	0.855337i	−0.00241112	+	0.00270676i
$317$	491.836			1.55153			0.775766	−	0.631020i	$-0.217364\pi$
$317$	491.836			1.55153			0.775766	+	0.631020i	$0.217364\pi$
$318$	69.1554	+	26.3345i	0.217470	+	0.0828130i
$319$			139.643i			0.437753i
$320$	183.173	−	260.805i	0.572414	−	0.815014i
$321$	−131.919			−0.410963
$322$	−7.91277	+	20.7792i	−0.0245738	+	0.0645316i
$323$		−	25.6948i		−	0.0795504i
$324$	183.957	+	163.865i	0.567770	+	0.505756i
$325$	−2.86842			−0.00882590
$326$	318.711	+	121.366i	0.977643	+	0.372289i
$327$			4.48730i			0.0137226i
$328$	−492.480	+	255.922i	−1.50146	+	0.780251i
$329$	−477.923			−1.45265
$330$	−212.050	+	556.851i	−0.642576	+	1.68743i
$331$			413.971i			1.25067i	0.780358	+	0.625333i	$0.215037\pi$
$331$			413.971i			1.25067i	−0.780358	+	0.625333i	$0.784963\pi$
$332$	−66.3319	+	74.4652i	−0.199795	+	0.224293i
$333$	17.4200			0.0523122
$334$	−458.269	−	174.510i	−1.37206	−	0.522485i
$335$			286.085i			0.853985i
$336$	100.525	+	867.201i	0.299182	+	2.58096i
$337$	393.328			1.16715			0.583573	−	0.812061i	$-0.301654\pi$
$337$	393.328			1.16715			0.583573	+	0.812061i	$0.301654\pi$
$338$	22.7578	−	59.7627i	0.0673307	−	0.176813i
$339$			262.685i			0.774882i
$340$	87.6768	+	78.1005i	0.257873	+	0.229707i
$341$	581.696			1.70585
$342$	−87.9695	−	33.4990i	−0.257221	−	0.0979503i
$343$		−	642.295i		−	1.87258i
$344$	118.100	+	227.263i	0.343313	+	0.660649i
$345$	20.0874			0.0582244
$346$	44.3475	−	116.458i	0.128172	−	0.336584i
$347$		−	476.716i		−	1.37382i	−0.726742	−	0.686911i	$-0.758966\pi$
$347$		−	476.716i		−	1.37382i	0.726742	−	0.686911i	$-0.241034\pi$
$348$	122.944	−	138.018i	0.353286	−	0.396605i
$349$	−118.794			−0.340383			−0.170191	−	0.985411i	$-0.554439\pi$
$349$	−118.794			−0.340383			−0.170191	+	0.985411i	$0.554439\pi$
$350$	−4.63754	−	1.76599i	−0.0132501	−	0.00504568i
$351$			113.393i			0.323057i
$352$	105.804	−	417.069i	0.300580	−	1.18485i
$353$	297.291			0.842185			0.421092	−	0.907018i	$-0.361647\pi$
$353$	297.291			0.842185			0.421092	+	0.907018i	$0.361647\pi$
$354$	66.2646	−	174.013i	0.187188	−	0.491562i
$355$			56.4668i			0.159061i
$356$	130.530	+	116.273i	0.366657	+	0.326610i
$357$	−321.637			−0.900944
$358$	−241.259	−	91.8719i	−0.673907	−	0.256625i
$359$			212.978i			0.593252i	0.954994	+	0.296626i	$0.0958615\pi$
$359$			212.978i			0.593252i	−0.954994	+	0.296626i	$0.904139\pi$
$360$	381.694	−	198.351i	1.06026	−	0.550976i
$361$	−19.0000			−0.0526316
$362$	−141.407	+	371.341i	−0.390628	+	1.02580i
$363$			266.085i			0.733017i
$364$	462.532	−	519.246i	1.27069	−	1.42650i
$365$	−117.498			−0.321912
$366$	984.067	+	374.735i	2.68871	+	1.02387i
$367$			326.797i			0.890456i	0.895417	+	0.445228i	$0.146877\pi$
$367$			326.797i			0.890456i	−0.895417	+	0.445228i	$0.853123\pi$
$368$	−14.4090	+	1.67028i	−0.0391549	+	0.00453879i
$369$	−749.097			−2.03007
$370$	−5.71805	+	15.0158i	−0.0154542	+	0.0405832i
$371$		−	101.973i		−	0.274860i
$372$	−574.927	−	512.132i	−1.54550	−	1.37670i
$373$	235.813			0.632205			0.316103	−	0.948725i	$-0.397626\pi$
$373$	235.813			0.632205			0.316103	+	0.948725i	$0.397626\pi$
$374$	148.148	+	56.4150i	0.396116	+	0.150842i
$375$			558.410i			1.48909i
$376$	−143.769	−	276.660i	−0.382365	−	0.735798i
$377$	−147.228			−0.390524
$378$	−69.8123	+	183.329i	−0.184689	+	0.484998i
$379$		−	471.811i		−	1.24489i	−0.782666	−	0.622443i	$-0.786140\pi$
$379$		−	471.811i		−	1.24489i	0.782666	−	0.622443i	$-0.213860\pi$
$380$	57.7514	−	64.8326i	0.151977	−	0.170612i
$381$	−931.959			−2.44609
$382$	710.652	+	270.618i	1.86034	+	0.708424i
$383$		−	131.099i		−	0.342294i	−0.985246	−	0.171147i	$-0.945253\pi$
$383$		−	131.099i		−	0.342294i	0.985246	−	0.171147i	$-0.0547473\pi$
$384$	−471.766	+	319.064i	−1.22856	+	0.830897i
$385$	821.104			2.13274
$386$	−188.392	+	494.722i	−0.488061	+	1.28166i
$387$			345.684i			0.893239i
$388$	−346.189	−	308.377i	−0.892239	−	0.794786i
$389$	20.4959			0.0526887			0.0263444	−	0.999653i	$-0.491613\pi$
$389$	20.4959			0.0526887			0.0263444	+	0.999653i	$0.491613\pi$
$390$	−587.095	−	223.567i	−1.50537	−	0.573249i
$391$		−	5.34417i		−	0.0136679i
$392$	719.650	−	373.973i	1.83584	−	0.954014i
$393$	−205.029			−0.521702
$394$	89.3704	−	234.690i	0.226828	−	0.595659i
$395$		−	1.42604i		−	0.00361022i
$396$	386.288	−	433.653i	0.975475	−	1.09508i
$397$	9.07740			0.0228650			0.0114325	−	0.999935i	$-0.496361\pi$
$397$	9.07740			0.0228650			0.0114325	+	0.999935i	$0.496361\pi$
$398$	26.9298	+	10.2549i	0.0676628	+	0.0257661i
$399$			237.835i			0.596077i
$400$	−0.372776	−	3.21583i	−0.000931939	−	0.00803958i
$401$	−336.682			−0.839606			−0.419803	−	0.907615i	$-0.637901\pi$
$401$	−336.682			−0.839606			−0.419803	+	0.907615i	$0.637901\pi$
$402$	181.937	−	477.773i	0.452580	−	1.18849i
$403$			613.289i			1.52181i
$404$	30.7673	+	27.4068i	0.0761568	+	0.0678387i
$405$	−306.698			−0.757280
$406$	−238.032	−	90.6432i	−0.586286	−	0.223259i
$407$			21.6930i			0.0532997i
$408$	−96.7553	−	186.189i	−0.237145	−	0.456347i
$409$	75.6667			0.185004			0.0925020	−	0.995712i	$-0.470514\pi$
$409$	75.6667			0.185004			0.0925020	+	0.995712i	$0.470514\pi$
$410$	245.889	−	645.712i	0.599729	−	1.57491i
$411$		−	917.800i		−	2.23309i
$412$	−294.813	+	330.961i	−0.715565	+	0.803304i
$413$	−256.591			−0.621285
$414$	−18.2965	−	6.96734i	−0.0441944	−	0.0168293i
$415$		−	124.150i		−	0.299157i
$416$	439.721	+	111.551i	1.05702	+	0.268151i
$417$	−557.762			−1.33756
$418$	41.7160	−	109.548i	0.0997992	−	0.262076i
$419$			619.532i			1.47860i	0.673378	+	0.739298i	$0.264843\pi$
$419$			619.532i			1.47860i	−0.673378	+	0.739298i	$0.735157\pi$
$420$	−811.549	−	722.910i	−1.93226	−	1.72121i
$421$	−18.4384			−0.0437967			−0.0218983	−	0.999760i	$-0.506971\pi$
$421$	−18.4384			−0.0437967			−0.0218983	+	0.999760i	$0.506971\pi$
$422$	151.627	+	57.7398i	0.359305	+	0.136824i
$423$		−	420.820i		−	0.994846i
$424$	59.0301	−	30.6756i	0.139222	−	0.0723482i
$425$	1.19272			0.00280641
$426$	35.9104	−	94.3018i	0.0842966	−	0.221366i
$427$		−	1451.05i		−	3.39825i
$428$	−78.8826	+	88.5548i	−0.184305	+	0.206904i
$429$	−848.162			−1.97707
$430$	−297.975	−	113.470i	−0.692965	−	0.263883i
$431$			496.147i			1.15115i	0.817748	+	0.575577i	$0.195222\pi$
$431$			496.147i			1.15115i	−0.817748	+	0.575577i	$0.804778\pi$
$432$	−127.127	+	14.7364i	−0.294275	+	0.0341121i
$433$	623.687			1.44039			0.720193	−	0.693774i	$-0.244053\pi$
$433$	623.687			1.44039			0.720193	+	0.693774i	$0.244053\pi$
$434$	−377.582	+	991.542i	−0.870004	+	2.28466i
$435$			230.108i			0.528983i
$436$	3.01224	+	2.68324i	0.00690881	+	0.00615421i
$437$	−3.95174			−0.00904289
$438$	196.226	+	74.7233i	0.448004	+	0.170601i
$439$			105.337i			0.239947i	0.992777	+	0.119974i	$0.0382810\pi$
$439$			105.337i			0.239947i	−0.992777	+	0.119974i	$0.961719\pi$
$440$	247.005	+	475.321i	0.561376	+	1.08027i
$441$	1094.64			2.48217
$442$	−59.4790	+	156.194i	−0.134568	+	0.353380i
$443$			113.329i			0.255821i	0.991786	+	0.127911i	$0.0408271\pi$
$443$			113.329i			0.255821i	−0.991786	+	0.127911i	$0.959173\pi$
$444$	19.0987	−	21.4405i	0.0430152	−	0.0482895i
$445$	−217.623			−0.489040
$446$	−340.066	−	129.498i	−0.762479	−	0.290354i
$447$			760.285i			1.70086i
$448$	642.246	+	451.072i	1.43358	+	1.00686i
$449$	413.979			0.922003			0.461001	−	0.887399i	$-0.347490\pi$
$449$	413.979			0.922003			0.461001	+	0.887399i	$0.347490\pi$
$450$	1.55499	−	4.08345i	0.00345553	−	0.00907432i
$451$		−	932.845i		−	2.06839i
$452$	176.335	+	157.076i	0.390122	+	0.347512i
$453$	586.192			1.29402
$454$	−790.760	−	301.123i	−1.74176	−	0.663267i
$455$			865.700i			1.90264i
$456$	−137.678	+	71.5457i	−0.301925	+	0.156898i
$457$	320.223			0.700707			0.350353	−	0.936618i	$-0.386061\pi$
$457$	320.223			0.700707			0.350353	+	0.936618i	$0.386061\pi$
$458$	256.591	−	673.816i	0.560242	−	1.47121i
$459$		−	47.1502i		−	0.102724i
$460$	12.0115	−	13.4843i	0.0261120	−	0.0293137i
$461$	−460.179			−0.998218			−0.499109	−	0.866539i	$-0.666339\pi$
$461$	−460.179			−0.998218			−0.499109	+	0.866539i	$0.666339\pi$
$462$	−1371.28	−	522.185i	−2.96813	−	1.13027i
$463$		−	323.224i		−	0.698108i	−0.937103	−	0.349054i	$-0.886503\pi$
$463$		−	323.224i		−	0.698108i	0.937103	−	0.349054i	$-0.113497\pi$
$464$	−19.1335	−	165.059i	−0.0412360	−	0.355732i
$465$	958.533			2.06136
$466$	1.51629	−	3.98184i	0.00325385	−	0.00854472i
$467$		−	523.352i		−	1.12067i	−0.828267	−	0.560334i	$-0.810673\pi$
$467$		−	523.352i		−	1.12067i	0.828267	−	0.560334i	$-0.189327\pi$
$468$	457.206	+	407.268i	0.976935	+	0.870232i
$469$	−704.500			−1.50213
$470$	362.741	+	138.133i	0.771790	+	0.293900i
$471$			15.1338i			0.0321311i
$472$	−77.1879	−	148.535i	−0.163534	−	0.314693i
$473$	−430.477			−0.910100
$474$	−0.906897	+	2.38154i	−0.00191328	+	0.00502435i
$475$		−	0.881959i		−	0.00185676i
$476$	−192.327	+	215.909i	−0.404048	+	0.453590i
$477$	89.7891			0.188237
$478$	427.878	+	162.937i	0.895141	+	0.340872i
$479$		−	458.055i		−	0.956274i	−0.878285	−	0.478137i	$-0.841312\pi$
$479$		−	458.055i		−	0.956274i	0.878285	−	0.478137i	$-0.158688\pi$
$480$	174.347	−	687.256i	0.363223	−	1.43178i
$481$	−22.8712			−0.0475492
$482$	174.473	−	458.171i	0.361977	−	0.950562i
$483$			49.4664i			0.102415i
$484$	178.618	+	159.109i	0.369045	+	0.328737i
$485$	577.174			1.19005
$486$	646.748	+	246.283i	1.33076	+	0.506756i
$487$		−	49.8747i		−	0.102412i	−0.998688	−	0.0512060i	$-0.983693\pi$
$487$		−	49.8747i		−	0.102412i	0.998688	−	0.0512060i	$-0.0163065\pi$
$488$	839.987	−	436.508i	1.72128	−	0.894484i
$489$	758.716			1.55157
$490$	−359.312	+	943.565i	−0.733289	+	1.92564i
$491$		−	381.364i		−	0.776709i	−0.921510	−	0.388354i	$-0.873044\pi$
$491$		−	381.364i		−	0.776709i	0.921510	−	0.388354i	$-0.126956\pi$
$492$	−821.288	+	921.990i	−1.66928	+	1.87396i
$493$	61.2191			0.124177
$494$	115.498	+	43.9817i	0.233801	+	0.0890319i
$495$			722.997i			1.46060i
$496$	−687.569	+	79.7022i	−1.38623	+	0.160690i
$497$	−139.053			−0.279784
$498$	−78.9540	+	207.336i	−0.158542	+	0.416337i
$499$			191.567i			0.383903i	0.981404	+	0.191951i	$0.0614816\pi$
$499$			191.567i			0.383903i	−0.981404	+	0.191951i	$0.938518\pi$
$500$	374.850	+	333.908i	0.749700	+	0.667816i
$501$	−1090.94			−2.17753
$502$	−333.056	−	126.829i	−0.663458	−	0.252646i
$503$			393.811i			0.782925i	0.920194	+	0.391463i	$0.128031\pi$
$503$			393.811i			0.782925i	−0.920194	+	0.391463i	$0.871969\pi$
$504$	488.451	+	939.942i	0.969148	+	1.86496i
$505$	−51.2961			−0.101576
$506$	8.67638	−	22.7845i	0.0171470	−	0.0450286i
$507$		−	142.270i		−	0.280611i
$508$	−557.276	+	625.606i	−1.09700	+	1.23151i
$509$	−711.118			−1.39709			−0.698544	−	0.715567i	$-0.746168\pi$
$509$	−711.118			−1.39709			−0.698544	+	0.715567i	$0.746168\pi$
$510$	244.121	+	92.9620i	0.478669	+	0.182278i
$511$		−	289.345i		−	0.566232i
$512$	−67.9159	+	507.476i	−0.132648	+	0.991163i
$513$	−34.8652			−0.0679634
$514$	−170.297	+	447.206i	−0.331317	+	0.870050i
$515$		−	551.787i		−	1.07143i
$516$	425.468	+	378.997i	0.824551	+	0.734491i
$517$	524.044			1.01362
$518$	−36.9772	−	14.0810i	−0.0713846	−	0.0271834i
$519$		−	277.237i		−	0.534176i
$520$	−501.137	+	260.421i	−0.963724	+	0.500809i
$521$	401.456			0.770549			0.385274	−	0.922802i	$-0.374107\pi$
$521$	401.456			0.770549			0.385274	+	0.922802i	$0.374107\pi$
$522$	79.8130	−	209.592i	0.152898	−	0.401516i
$523$			83.5113i			0.159677i	0.996808	+	0.0798387i	$0.0254405\pi$
$523$			83.5113i			0.159677i	−0.996808	+	0.0798387i	$0.974559\pi$
$524$	−122.599	+	137.632i	−0.233968	+	0.262656i
$525$	−11.0400			−0.0210286
$526$	−74.3074	−	28.2965i	−0.141269	−	0.0537956i
$527$		−	255.013i		−	0.483896i
$528$	−110.226	−	950.889i	−0.208761	−	1.80093i
$529$	528.178			0.998446
$530$	−29.4730	+	77.3970i	−0.0556094	+	0.146032i
$531$		−	225.933i		−	0.425486i
$532$	159.654	+	142.216i	0.300101	+	0.267323i
$533$	983.510			1.84523
$534$	363.439	+	138.398i	0.680597	+	0.259173i
$535$		−	147.641i		−	0.275964i
$536$	−211.928	−	407.821i	−0.395389	−	0.760860i
$537$	−574.334			−1.06952
$538$	−18.2443	+	47.9101i	−0.0339113	+	0.0890523i
$539$			1363.15i			2.52903i
$540$	105.975	−	118.969i	0.196249	−	0.220312i
$541$	315.779			0.583694			0.291847	−	0.956465i	$-0.405730\pi$
$541$	315.779			0.583694			0.291847	+	0.956465i	$0.405730\pi$
$542$	100.469	+	38.2589i	0.185367	+	0.0705883i
$543$			884.004i			1.62800i
$544$	−182.841	−	46.3842i	−0.336105	−	0.0852650i
$545$	−5.02208			−0.00921483
$546$	550.546	−	1445.75i	1.00833	−	2.64790i
$547$		−	115.726i		−	0.211564i	−0.994389	−	0.105782i	$-0.966265\pi$
$547$		−	115.726i		−	0.211564i	0.994389	−	0.105782i	$-0.0337346\pi$
$548$	−616.101	−	548.809i	−1.12427	−	1.00148i
$549$	1277.68			2.32729
$550$	5.08508	+	1.93641i	0.00924561	+	0.00352075i
$551$		−	45.2684i		−	0.0821569i
$552$	−28.6351	+	14.8805i	−0.0518752	+	0.0269575i
$553$	3.51170			0.00635027
$554$	251.566	−	660.621i	0.454091	−	1.19246i
$555$			35.7462i			0.0644076i
$556$	−333.520	+	374.415i	−0.599857	+	0.673408i
$557$	−597.571			−1.07284			−0.536419	−	0.843952i	$-0.680223\pi$
$557$	−597.571			−1.07284			−0.536419	+	0.843952i	$0.680223\pi$
$558$	−873.071	−	332.468i	−1.56464	−	0.595820i
$559$		−	453.857i		−	0.811910i
$560$	−970.551	+	112.505i	−1.73313	+	0.200902i
$561$	352.676			0.628656
$562$	157.490	−	413.573i	0.280230	−	0.735894i
$563$			622.336i			1.10539i	0.833383	+	0.552696i	$0.186401\pi$
$563$			622.336i			1.10539i	−0.833383	+	0.552696i	$0.813599\pi$
$564$	−517.946	−	461.375i	−0.918344	−	0.818040i
$565$	−293.991			−0.520337
$566$	−151.395	−	57.6516i	−0.267482	−	0.101858i
$567$		−	755.261i		−	1.33203i
$568$	−41.8300	−	80.4948i	−0.0736443	−	0.141716i
$569$	497.207			0.873826			0.436913	−	0.899504i	$-0.356072\pi$
$569$	497.207			0.873826			0.436913	+	0.899504i	$0.356072\pi$
$570$	68.7408	−	180.515i	0.120598	−	0.316694i
$571$			623.096i			1.09124i	0.838034	+	0.545619i	$0.183705\pi$
$571$			623.096i			1.09124i	−0.838034	+	0.545619i	$0.816295\pi$
$572$	−507.168	+	569.355i	−0.886658	+	0.995376i
$573$	1691.76			2.95246
$574$	1590.10	+	605.514i	2.77021	+	1.05490i
$575$		−	0.183436i		−	0.000319019i
$576$	−397.178	+	565.509i	−0.689545	+	0.981787i
$577$	−934.139			−1.61896			−0.809479	−	0.587148i	$-0.800251\pi$
$577$	−934.139			−1.61896			−0.809479	+	0.587148i	$0.800251\pi$
$578$	−180.963	+	475.214i	−0.313084	+	0.822169i
$579$			1177.72i			2.03406i
$580$	154.467	+	137.596i	0.266322	+	0.237234i
$581$	305.727			0.526208
$582$	−963.904	−	367.057i	−1.65619	−	0.630682i
$583$			111.814i			0.191790i
$584$	167.496	−	87.0410i	0.286808	−	0.149043i
$585$	−762.265			−1.30302
$586$	368.442	−	967.540i	0.628740	−	1.65109i
$587$		−	778.304i		−	1.32590i	−0.748663	−	0.662951i	$-0.769304\pi$
$587$		−	778.304i		−	1.32590i	0.748663	−	0.662951i	$-0.230696\pi$
$588$	1200.13	−	1347.28i	2.04104	−	2.29130i
$589$	−188.569			−0.320152
$590$	194.751	+	74.1617i	0.330087	+	0.125698i
$591$		−	558.696i		−	0.945340i
$592$	−2.97231	−	25.6412i	−0.00502079	−	0.0433129i
$593$	−1012.64			−1.70766			−0.853832	−	0.520549i	$-0.825727\pi$
$593$	−1012.64			−1.70766			−0.853832	+	0.520549i	$0.825727\pi$
$594$	76.5494	−	201.021i	0.128871	−	0.338420i
$595$		−	359.969i		−	0.604989i
$596$	510.365	+	454.621i	0.856317	+	0.762788i
$597$	64.1083			0.107384
$598$	24.0219	+	9.14761i	0.0401705	+	0.0152970i
$599$		−	37.3119i		−	0.0622903i	−0.999515	−	0.0311452i	$-0.990085\pi$
$599$		−	37.3119i		−	0.0622903i	0.999515	−	0.0311452i	$-0.00991541\pi$
$600$	−3.32107	−	6.39085i	−0.00553512	−	0.0106514i
$601$	−181.988			−0.302808			−0.151404	−	0.988472i	$-0.548379\pi$
$601$	−181.988			−0.302808			−0.151404	+	0.988472i	$0.548379\pi$
$602$	279.425	−	733.779i	0.464161	−	1.21890i
$603$		−	620.325i		−	1.02873i
$604$	350.521	−	393.500i	0.580332	−	0.651490i
$605$	−297.796			−0.492225
$606$	85.6665	+	32.6220i	0.141364	+	0.0538317i
$607$			218.379i			0.359767i	0.983688	+	0.179884i	$0.0575721\pi$
$607$			218.379i			0.359767i	−0.983688	+	0.179884i	$0.942428\pi$
$608$	−34.2988	+	135.202i	−0.0564125	+	0.222372i
$609$	−566.653			−0.930464
$610$	−419.395	+	1101.34i	−0.687532	+	1.80548i
$611$			552.506i			0.904265i
$612$	−190.112	−	169.347i	−0.310640	−	0.276711i
$613$	641.406			1.04634			0.523170	−	0.852229i	$-0.324749\pi$
$613$	641.406			1.04634			0.523170	+	0.852229i	$0.324749\pi$
$614$	465.588	+	177.297i	0.758286	+	0.288757i
$615$		−	1537.17i		−	2.49946i
$616$	−1170.50	+	608.264i	−1.90017	+	0.987442i
$617$	−223.015			−0.361450			−0.180725	−	0.983534i	$-0.557844\pi$
$617$	−223.015			−0.361450			−0.180725	+	0.983534i	$0.557844\pi$
$618$	−350.912	+	921.506i	−0.567819	+	1.49111i
$619$			126.536i			0.204420i	0.994763	+	0.102210i	$0.0325914\pi$
$619$			126.536i			0.204420i	−0.994763	+	0.102210i	$0.967409\pi$
$620$	573.166	−	643.445i	0.924461	−	1.03781i
$621$	−7.25150			−0.0116771
$622$	−471.903	−	179.702i	−0.758687	−	0.288910i
$623$		−	535.908i		−	0.860205i
$624$	1002.53	−	116.213i	1.60663	−	0.186238i
$625$	−619.901			−0.991841
$626$	−424.112	+	1113.73i	−0.677495	+	1.77912i
$627$		−	260.786i		−	0.415927i
$628$	10.1590	+	9.04941i	0.0161768	+	0.0144099i
$629$	9.51011			0.0151194
$630$	−1232.40	−	469.301i	−1.95619	−	0.744922i
$631$			250.558i			0.397081i	0.980093	+	0.198541i	$0.0636202\pi$
$631$			250.558i			0.397081i	−0.980093	+	0.198541i	$0.936380\pi$
$632$	1.05639	+	2.03285i	0.00167151	+	0.00321654i
$633$	360.959			0.570235
$634$	350.062	−	919.275i	0.552149	−	1.44996i
$635$		−	1043.03i		−	1.64256i
$636$	98.4421	−	110.513i	0.154783	−	0.173762i
$637$	−1437.18			−2.25617
$638$	261.003	+	99.3906i	0.409095	+	0.155785i
$639$		−	122.438i		−	0.191609i
$640$	−357.089	−	527.989i	−0.557952	−	0.824982i
$641$	−744.927			−1.16213			−0.581067	−	0.813856i	$-0.697364\pi$
$641$	−744.927			−1.16213			−0.581067	+	0.813856i	$0.697364\pi$
$642$	−93.8929	+	246.566i	−0.146251	+	0.384059i
$643$			1161.89i			1.80699i	0.428604	+	0.903493i	$0.359006\pi$
$643$			1161.89i			1.80699i	−0.428604	+	0.903493i	$0.640994\pi$
$644$	33.2058	+	29.5790i	0.0515619	+	0.0459301i
$645$	−709.351			−1.09977
$646$	−48.0253	−	18.2882i	−0.0743425	−	0.0283098i
$647$		−	550.347i		−	0.850614i	−0.905049	−	0.425307i	$-0.860166\pi$
$647$		−	550.347i		−	0.850614i	0.905049	−	0.425307i	$-0.139834\pi$
$648$	437.206	−	227.199i	0.674701	−	0.350615i
$649$	281.352			0.433517
$650$	−2.04158	+	5.36127i	−0.00314090	+	0.00824810i
$651$			2360.44i			3.62587i
$652$	453.683	−	509.312i	0.695833	−	0.781153i
$653$	−170.874			−0.261675			−0.130838	−	0.991404i	$-0.541767\pi$
$653$	−170.874			−0.261675			−0.130838	+	0.991404i	$0.541767\pi$
$654$	8.38708	+	3.19382i	0.0128243	+	0.00488352i
$655$		−	229.463i		−	0.350326i
$656$	127.816	+	1102.63i	0.194841	+	1.68084i
$657$	254.773			0.387783
$658$	−340.160	+	893.270i	−0.516960	+	1.35755i
$659$		−	933.406i		−	1.41640i	−0.706013	−	0.708199i	$-0.749508\pi$
$659$		−	933.406i		−	1.41640i	0.706013	−	0.708199i	$-0.250492\pi$
$660$	889.867	+	792.673i	1.34828	+	1.20102i
$661$	−498.493			−0.754150			−0.377075	−	0.926183i	$-0.623070\pi$
$661$	−498.493			−0.754150			−0.377075	+	0.926183i	$0.623070\pi$
$662$	773.740	+	294.642i	1.16879	+	0.445079i
$663$			371.831i			0.560831i
$664$	91.9691	+	176.979i	0.138508	+	0.266535i
$665$	−266.179			−0.400269
$666$	12.3986	−	32.5591i	0.0186165	−	0.0488876i
$667$		−	9.41523i		−	0.0141158i
$668$	−652.342	+	732.329i	−0.976560	+	1.09630i
$669$	−809.551			−1.21009
$670$	534.712	+	203.620i	0.798078	+	0.303910i
$671$			1591.09i			2.37122i
$672$	1692.41	+	429.339i	2.51846	+	0.638897i
$673$	779.779			1.15866			0.579331	−	0.815093i	$-0.303314\pi$
$673$	779.779			1.15866			0.579331	+	0.815093i	$0.303314\pi$
$674$	279.950	−	735.157i	0.415356	−	1.09074i
$675$		−	1.61841i		−	0.00239764i
$676$	−95.5028	−	85.0718i	−0.141276	−	0.125846i
$677$	910.302			1.34461			0.672306	−	0.740273i	$-0.265304\pi$
$677$	910.302			1.34461			0.672306	+	0.740273i	$0.265304\pi$
$678$	490.976	+	186.965i	0.724154	+	0.275760i
$679$			1421.32i			2.09326i
$680$	208.379	−	108.286i	0.306439	−	0.159244i
$681$	−1882.46			−2.76426
$682$	414.020	−	1087.23i	0.607067	−	1.59418i
$683$		−	93.5131i		−	0.136915i	−0.997654	−	0.0684576i	$-0.978192\pi$
$683$		−	93.5131i		−	0.136915i	0.997654	−	0.0684576i	$-0.0218078\pi$
$684$	−125.224	+	140.578i	−0.183076	+	0.205524i
$685$	1027.18			1.49953
$686$	−1200.49	−	457.151i	−1.74999	−	0.666401i
$687$		−	1604.07i		−	2.33489i
$688$	508.827	−	58.9827i	0.739575	−	0.0857307i
$689$	−117.887			−0.171098
$690$	14.2972	−	37.5448i	0.0207205	−	0.0544127i
$691$			663.683i			0.960468i	0.877140	+	0.480234i	$0.159448\pi$
$691$			663.683i			0.960468i	−0.877140	+	0.480234i	$0.840552\pi$
$692$	−186.104	−	165.777i	−0.268936	−	0.239562i
$693$	−1780.42			−2.56915
$694$	−891.015	−	339.301i	−1.28388	−	0.488906i
$695$		−	624.234i		−	0.898179i
$696$	−170.461	−	328.024i	−0.244916	−	0.471299i
$697$	−408.956			−0.586737
$698$	−84.5509	+	222.033i	−0.121133	+	0.318099i
$699$		−	9.47906i		−	0.0135609i
$700$	−6.60151	+	7.41095i	−0.00943073	+	0.0105871i
$701$	959.216			1.36835			0.684177	−	0.729316i	$-0.260162\pi$
$701$	959.216			1.36835			0.684177	+	0.729316i	$0.260162\pi$
$702$	211.939	+	80.7070i	0.301908	+	0.114967i
$703$		−	7.03225i		−	0.0100032i
$704$	−704.225	−	494.603i	−1.00032	−	0.702560i
$705$	863.532			1.22487
$706$	211.596	−	555.658i	0.299711	−	0.787051i
$707$		−	126.319i		−	0.178670i
$708$	−278.079	−	247.706i	−0.392766	−	0.349867i
$709$	825.957			1.16496			0.582480	−	0.812845i	$-0.302082\pi$
$709$	825.957			1.16496			0.582480	+	0.812845i	$0.302082\pi$
$710$	105.540	+	40.1900i	0.148648	+	0.0566056i
$711$			3.09212i			0.00434897i
$712$	310.227	−	161.212i	0.435711	−	0.226422i
$713$	−39.2199			−0.0550069
$714$	−228.924	+	601.162i	−0.320622	+	0.841963i
$715$		−	949.243i		−	1.32761i
$716$	−343.430	+	385.539i	−0.479650	+	0.538463i
$717$	1018.59			1.42063
$718$	398.070	+	151.586i	0.554414	+	0.211122i
$719$		−	1019.44i		−	1.41786i	−0.705281	−	0.708928i	$-0.749179\pi$
$719$		−	1019.44i		−	1.41786i	0.705281	−	0.708928i	$-0.250821\pi$
$720$	−99.0630	−	854.588i	−0.137587	−	1.18693i
$721$	1358.81			1.88461
$722$	−13.5232	+	35.5123i	−0.0187302	+	0.0491860i
$723$		−	1090.71i		−	1.50859i
$724$	593.415	+	528.601i	0.819634	+	0.730111i
$725$	2.10131			0.00289836
$726$	497.331	+	189.385i	0.685030	+	0.260861i
$727$			227.791i			0.313330i	0.987652	+	0.156665i	$0.0500742\pi$
$727$			227.791i			0.313330i	−0.987652	+	0.156665i	$0.949926\pi$
$728$	−641.301	−	1234.08i	−0.880907	−	1.69516i
$729$	985.328			1.35162
$730$	−83.6286	+	219.611i	−0.114560	+	0.300837i
$731$			188.720i			0.258166i
$732$	1400.81	−	1572.57i	1.91368	−	2.14832i
$733$	−998.335			−1.36198			−0.680992	−	0.732291i	$-0.738451\pi$
$733$	−998.335			−1.36198			−0.680992	+	0.732291i	$0.738451\pi$
$734$	610.807	+	232.597i	0.832162	+	0.316889i
$735$			2246.23i			3.05609i
$736$	−7.13369	+	28.1202i	−0.00969251	+	0.0382068i
$737$	772.486			1.04815
$738$	−533.167	+	1400.11i	−0.722448	+	1.89717i
$739$			614.741i			0.831856i	0.909398	+	0.415928i	$0.136543\pi$
$739$			614.741i			0.831856i	−0.909398	+	0.415928i	$0.863457\pi$
$740$	23.9957	+	21.3749i	0.0324267	+	0.0288850i
$741$	274.950			0.371053
$742$	−190.594	−	72.5788i	−0.256866	−	0.0978151i
$743$		−	156.926i		−	0.211206i	−0.994408	−	0.105603i	$-0.966323\pi$
$743$		−	156.926i		−	0.211206i	0.994408	−	0.105603i	$-0.0336772\pi$
$744$	−1366.41	+	710.070i	−1.83657	+	0.954395i
$745$	−850.893			−1.14214
$746$	167.839	−	440.750i	0.224985	−	0.590817i
$747$			269.198i			0.360372i
$748$	210.887	−	236.745i	0.281934	−	0.316504i
$749$	363.573			0.485412
$750$	1043.71	+	397.446i	1.39161	+	0.529928i
$751$		−	766.925i		−	1.02120i	−0.859817	−	0.510602i	$-0.829422\pi$
$751$		−	766.925i		−	1.02120i	0.859817	−	0.510602i	$-0.170578\pi$
$752$	−619.424	+	71.8030i	−0.823702	+	0.0954827i
$753$	−792.864			−1.05294
$754$	−104.789	+	275.179i	−0.138977	+	0.364958i
$755$			656.053i			0.868944i
$756$	292.967	+	260.968i	0.387522	+	0.345196i
$757$	163.896			0.216507			0.108253	−	0.994123i	$-0.465474\pi$
$757$	163.896			0.216507			0.108253	+	0.994123i	$0.465474\pi$
$758$	−881.848	−	335.810i	−1.16339	−	0.443021i
$759$		−	54.2401i		−	0.0714626i
$760$	−80.0722	−	154.086i	−0.105358	−	0.202744i
$761$	−512.227			−0.673098			−0.336549	−	0.941666i	$-0.609260\pi$
$761$	−512.227			−0.673098			−0.336549	+	0.941666i	$0.609260\pi$
$762$	−663.318	+	1741.89i	−0.870496	+	2.28595i
$763$		−	12.3672i		−	0.0162086i
$764$	1011.61	−	1135.65i	1.32409	−	1.48645i
$765$	316.959			0.414326
$766$	−245.032	−	93.3089i	−0.319886	−	0.121813i
$767$			296.633i			0.386745i
$768$	260.576	+	1108.86i	0.339292	+	1.44382i
$769$	1124.70			1.46255			0.731275	−	0.682083i	$-0.238926\pi$
$769$	1124.70			1.46255			0.731275	+	0.682083i	$0.238926\pi$
$770$	584.417	−	1534.70i	0.758983	−	1.99312i
$771$			1064.61i			1.38081i
$772$	790.583	+	704.234i	1.02407	+	0.912220i
$773$	669.217			0.865740			0.432870	−	0.901456i	$-0.357501\pi$
$773$	669.217			0.865740			0.432870	+	0.901456i	$0.357501\pi$
$774$	646.106	+	246.039i	0.834763	+	0.317880i
$775$		−	8.75319i		−	0.0112944i
$776$	−822.776	+	427.564i	−1.06028	+	0.550985i
$777$	−88.0270			−0.113291
$778$	14.5879	−	38.3083i	0.0187505	−	0.0492394i
$779$			302.402i			0.388193i
$780$	−835.725	+	938.197i	−1.07144	+	1.20282i
$781$	152.472			0.195226
$782$	−9.98861	−	3.80369i	−0.0127732	−	0.00486405i
$783$		−	83.0681i		−	0.106090i
$784$	−186.774	−	1611.25i	−0.238232	−	2.05516i
$785$	−16.9373			−0.0215762
$786$	−145.928	+	383.213i	−0.185660	+	0.487548i
$787$			1456.58i			1.85080i	0.378995	+	0.925399i	$0.376270\pi$
$787$			1456.58i			1.85080i	−0.378995	+	0.925399i	$0.623730\pi$
$788$	−375.042	−	334.079i	−0.475942	−	0.423958i
$789$	−176.894			−0.224201
$790$	−2.66536	−	1.01498i	−0.00337388	−	0.00128478i
$791$		−	723.968i		−	0.915257i
$792$	−535.588	−	1030.65i	−0.676248	−	1.30133i
$793$	−1677.50			−2.11539
$794$	6.46080	−	16.9663i	0.00813703	−	0.0213681i
$795$			184.249i			0.231760i
$796$	38.3343	−	43.0347i	0.0481587	−	0.0540637i
$797$	−672.133			−0.843329			−0.421665	−	0.906752i	$-0.638554\pi$
$797$	−672.133			−0.843329			−0.421665	+	0.906752i	$0.638554\pi$
$798$	444.529	+	169.278i	0.557054	+	0.212128i
$799$		−	229.739i		−	0.287533i
$800$	−6.27593	−	1.59211i	−0.00784491	−	0.00199014i
$801$	471.877			0.589110
$802$	−239.632	+	629.282i	−0.298793	+	0.784641i
$803$			317.267i			0.395103i
$804$	−763.498	−	680.106i	−0.949624	−	0.845903i
$805$	−55.3616			−0.0687722
$806$	1146.28	+	436.506i	1.42218	+	0.541571i
$807$			114.054i			0.141330i
$808$	73.1238	−	37.9996i	0.0904998	−	0.0470291i
$809$	517.842			0.640102			0.320051	−	0.947400i	$-0.396300\pi$
$809$	517.842			0.640102			0.320051	+	0.947400i	$0.396300\pi$
$810$	−218.291	+	573.240i	−0.269496	+	0.707704i
$811$		−	264.166i		−	0.325729i	−0.986648	−	0.162865i	$-0.947927\pi$
$811$		−	264.166i		−	0.325729i	0.986648	−	0.162865i	$-0.0520734\pi$
$812$	−338.837	+	380.383i	−0.417286	+	0.468452i
$813$	239.174			0.294187
$814$	40.5456	+	15.4399i	0.0498104	+	0.0189679i
$815$			849.137i			1.04189i
$816$	−416.866	+	48.3227i	−0.510865	+	0.0592190i
$817$	139.549			0.170806
$818$	53.8555	−	141.426i	0.0658380	−	0.172893i
$819$		−	1877.12i		−	2.29196i
$820$	−1031.87	−	919.166i	−1.25838	−	1.12093i
$821$	−876.553			−1.06766			−0.533832	−	0.845590i	$-0.679249\pi$
$821$	−876.553			−1.06766			−0.533832	+	0.845590i	$0.679249\pi$
$822$	−1715.43	−	653.240i	−2.08690	−	0.794696i
$823$			560.045i			0.680492i	0.940337	+	0.340246i	$0.110510\pi$
$823$			560.045i			0.680492i	−0.940337	+	0.340246i	$0.889490\pi$
$824$	408.758	+	786.586i	0.496065	+	0.954595i
$825$	12.1054			0.0146732
$826$	−182.627	+	479.585i	−0.221098	+	0.580612i
$827$		−	445.217i		−	0.538352i	−0.963091	−	0.269176i	$-0.913249\pi$
$827$		−	445.217i		−	0.538352i	0.963091	−	0.269176i	$-0.0867513\pi$
$828$	−26.0449	+	29.2384i	−0.0314552	+	0.0353120i
$829$	−376.283			−0.453900			−0.226950	−	0.973906i	$-0.572875\pi$
$829$	−376.283			−0.453900			−0.226950	+	0.973906i	$0.572875\pi$
$830$	−232.045	−	88.3634i	−0.279573	−	0.106462i
$831$		−	1572.66i		−	1.89249i
$832$	521.466	−	742.473i	0.626762	−	0.892395i
$833$	597.598			0.717404
$834$	−396.985	+	1042.50i	−0.476001	+	1.25000i
$835$		−	1220.96i		−	1.46222i
$836$	−175.061	−	155.940i	−0.209403	−	0.186531i
$837$	−346.027			−0.413414
$838$	1157.95	+	440.949i	1.38180	+	0.526193i
$839$			756.891i			0.902135i	0.892490	+	0.451068i	$0.148957\pi$
$839$			756.891i			0.902135i	−0.892490	+	0.451068i	$0.851043\pi$
$840$	−1928.78	+	1002.31i	−2.29617	+	1.19323i
$841$	−733.146			−0.871755
$842$	−13.1235	+	34.4626i	−0.0155861	+	0.0409295i
$843$		−	984.540i		−	1.16790i
$844$	215.839	−	242.305i	0.255734	−	0.287091i
$845$	159.225			0.188432
$846$	−786.541	−	299.517i	−0.929718	−	0.354039i
$847$		−	733.339i		−	0.865808i
$848$	−15.3204	−	132.165i	−0.0180665	−	0.155855i
$849$	−360.407			−0.424508
$850$	0.848916	−	2.22928i	0.000998725	−	0.00262268i
$851$		−	1.46261i		−	0.00171870i
$852$	−150.697	−	134.238i	−0.176875	−	0.157556i
$853$	−688.346			−0.806971			−0.403486	−	0.914986i	$-0.632201\pi$
$853$	−688.346			−0.806971			−0.403486	+	0.914986i	$0.632201\pi$
$854$	−2712.12	−	1032.78i	−3.17578	−	1.20935i
$855$		−	234.375i		−	0.274123i
$856$	109.371	+	210.466i	0.127769	+	0.245871i
$857$	1311.51			1.53035			0.765176	−	0.643822i	$-0.222652\pi$
$857$	1311.51			1.53035			0.765176	+	0.643822i	$0.222652\pi$
$858$	−603.676	+	1585.27i	−0.703585	+	1.84764i
$859$		−	947.410i		−	1.10292i	−0.834201	−	0.551461i	$-0.814071\pi$
$859$		−	947.410i		−	1.10292i	0.834201	−	0.551461i	$-0.185929\pi$
$860$	−424.165	+	476.174i	−0.493215	+	0.553691i
$861$	3785.35			4.39646
$862$	927.333	+	353.131i	1.07579	+	0.409664i
$863$		−	1271.16i		−	1.47295i	−0.676463	−	0.736477i	$-0.736488\pi$
$863$		−	1271.16i		−	1.47295i	0.676463	−	0.736477i	$-0.263512\pi$
$864$	−62.9387	+	248.097i	−0.0728457	+	0.287150i
$865$	310.277			0.358702
$866$	443.907	−	1165.71i	0.512594	−	1.34609i
$867$			1131.28i			1.30482i
$868$	1584.52	+	1411.45i	1.82548	+	1.62610i
$869$	−3.85059			−0.00443106
$870$	430.087	+	163.778i	0.494353	+	0.188251i
$871$			814.442i			0.935065i
$872$	7.15910	−	3.72030i	0.00820998	−	0.00426640i
$873$	−1251.50			−1.43356
$874$	−2.81264	+	7.38608i	−0.00321812	+	0.00845090i
$875$		−	1539.00i		−	1.75885i
$876$	279.326	−	313.576i	0.318865	−	0.357963i
$877$	−797.891			−0.909796			−0.454898	−	0.890543i	$-0.650324\pi$
$877$	−797.891			−0.909796			−0.454898	+	0.890543i	$0.650324\pi$
$878$	196.882	+	74.9731i	0.224239	+	0.0853908i
$879$		−	2303.30i		−	2.62036i
$880$	1064.21	−	123.362i	1.20933	−	0.140185i
$881$	−440.769			−0.500305			−0.250153	−	0.968206i	$-0.580481\pi$
$881$	−440.769			−0.500305			−0.250153	+	0.968206i	$0.580481\pi$
$882$	779.105	−	2045.95i	0.883339	−	2.31968i
$883$			148.904i			0.168634i	0.996439	+	0.0843170i	$0.0268708\pi$
$883$			148.904i			0.168634i	−0.996439	+	0.0843170i	$0.973129\pi$
$884$	249.603	+	222.341i	0.282356	+	0.251517i
$885$	463.620			0.523864
$886$	211.819	+	80.6613i	0.239074	+	0.0910399i
$887$			607.820i			0.685254i	0.939472	+	0.342627i	$0.111317\pi$
$887$			607.820i			0.685254i	−0.939472	+	0.342627i	$0.888683\pi$
$888$	−26.4804	−	50.9571i	−0.0298203	−	0.0573841i
$889$	2568.51			2.88921
$890$	−154.892	+	406.752i	−0.174036	+	0.457025i
$891$			828.147i			0.929458i
$892$	−484.081	+	543.436i	−0.542691	+	0.609234i
$893$	−169.880			−0.190236
$894$	1421.03	+	541.130i	1.58951	+	0.605291i
$895$		−	642.781i		−	0.718191i
$896$	1300.20	−	879.352i	1.45112	−	0.981420i
$897$	57.1860			0.0637525
$898$	294.648	−	773.756i	0.328116	−	0.861643i
$899$		−	449.276i		−	0.499751i
$900$	−6.52548	−	5.81275i	−0.00725054	−	0.00645861i
$901$	49.0187			0.0544047
$902$	−1743.55	−	663.949i	−1.93298	−	0.736085i
$903$		−	1746.82i		−	1.93446i
$904$	419.091	−	217.785i	0.463596	−	0.240913i
$905$	−989.356			−1.09321
$906$	417.220	−	1095.63i	0.460508	−	1.20931i
$907$		−	131.690i		−	0.145193i	−0.997361	−	0.0725966i	$-0.976871\pi$
$907$		−	131.690i		−	0.145193i	0.997361	−	0.0725966i	$-0.0231286\pi$
$908$	−1125.64	+	1263.66i	−1.23969	+	1.39170i
$909$	111.227			0.122361
$910$	1618.05	+	616.158i	1.77808	+	0.677097i
$911$			645.749i			0.708835i	0.935087	+	0.354417i	$0.115321\pi$
$911$			645.749i			0.708835i	−0.935087	+	0.354417i	$0.884679\pi$
$912$	35.7322	+	308.252i	0.0391801	+	0.337995i
$913$	−335.230			−0.367175
$914$	227.917	−	598.519i	0.249363	−	0.654835i
$915$			2621.83i			2.86539i
$916$	−1076.78	−	959.171i	−1.17552	−	1.04713i
$917$	565.066			0.616211
$918$	−88.1270	−	33.5590i	−0.0959989	−	0.0365566i
$919$		−	745.172i		−	0.810851i	−0.914128	−	0.405425i	$-0.867123\pi$
$919$		−	745.172i		−	0.810851i	0.914128	−	0.405425i	$-0.132877\pi$
$920$	−16.6540	−	32.0478i	−0.0181021	−	0.0348345i
$921$	1108.37			1.20344
$922$	−327.530	+	860.105i	−0.355239	+	0.932869i
$923$			160.753i			0.174163i
$924$	−1952.00	+	2191.34i	−2.11255	+	2.37159i
$925$	0.326429			0.000352897
$926$	−604.128	−	230.054i	−0.652406	−	0.248438i
$927$			1196.45i			1.29067i
$928$	−322.126	−	81.7185i	−0.347118	−	0.0880588i
$929$	156.417			0.168372			0.0841859	−	0.996450i	$-0.473171\pi$
$929$	156.417			0.168372			0.0841859	+	0.996450i	$0.473171\pi$
$930$	682.232	−	1791.56i	0.733583	−	1.92641i
$931$		−	441.894i		−	0.474644i
$932$	−6.36311	−	5.66812i	−0.00682737	−	0.00608167i
$933$	−1123.40			−1.20407
$934$	−978.180	−	372.494i	−1.04730	−	0.398815i
$935$			394.707i			0.422146i
$936$	1086.63	−	564.677i	1.16093	−	0.603288i
$937$	−1489.44			−1.58959			−0.794793	−	0.606880i	$-0.792421\pi$
$937$	−1489.44			−1.58959			−0.794793	+	0.606880i	$0.792421\pi$
$938$	−501.425	+	1316.76i	−0.534568	+	1.40379i
$939$			2651.32i			2.82356i
$940$	516.359	−	579.673i	0.549318	−	0.616673i
$941$	−985.993			−1.04781			−0.523907	−	0.851775i	$-0.675526\pi$
$941$	−985.993			−1.04781			−0.523907	+	0.851775i	$0.675526\pi$
$942$	28.2860	+	10.7714i	0.0300276	+	0.0114346i
$943$			62.8956i			0.0666974i
$944$	−332.561	+	38.5501i	−0.352289	+	0.0408370i
$945$	−488.441			−0.516869
$946$	−306.391	+	804.592i	−0.323880	+	0.850520i
$947$			1612.77i			1.70304i	0.524326	+	0.851518i	$0.324317\pi$
$947$			1612.77i			1.70304i	−0.524326	+	0.851518i	$0.675683\pi$
$948$	3.80578	+	3.39010i	0.00401454	+	0.00357606i
$949$	−334.499			−0.352475
$950$	−1.64844	−	0.627731i	−0.00173520	−	0.000660769i
$951$		−	2188.40i		−	2.30116i
$952$	266.661	+	513.144i	0.280106	+	0.539017i
$953$	−1434.39			−1.50513			−0.752565	−	0.658518i	$-0.771184\pi$
$953$	−1434.39			−1.50513			−0.752565	+	0.658518i	$0.771184\pi$
$954$	63.9070	−	167.822i	0.0669885	−	0.175914i
$955$			1893.38i			1.98259i
$956$	609.080	−	683.763i	0.637113	−	0.715233i
$957$	621.337			0.649255
$958$	−856.137	−	326.019i	−0.893671	−	0.340312i
$959$			2529.48i			2.63763i
$960$	−1160.44	−	815.018i	−1.20879	−	0.848978i
$961$	−910.496			−0.947447
$962$	−16.2785	+	42.7478i	−0.0169215	+	0.0444364i
$963$			320.133i			0.332433i
$964$	−732.173	−	652.203i	−0.759516	−	0.676559i
$965$	−1318.08			−1.36589
$966$	92.4561	+	35.2075i	0.0957102	+	0.0364467i
$967$		−	920.021i		−	0.951418i	−0.879603	−	0.475709i	$-0.842192\pi$
$967$		−	920.021i		−	0.951418i	0.879603	−	0.475709i	$-0.157808\pi$
$968$	424.516	−	220.604i	0.438549	−	0.227897i
$969$	−114.328			−0.117985
$970$	410.802	−	1078.78i	0.423507	−	1.11214i
$971$		−	345.002i		−	0.355306i	−0.984093	−	0.177653i	$-0.943150\pi$
$971$		−	345.002i		−	0.355306i	0.984093	−	0.177653i	$-0.0568504\pi$
$972$	920.641	−	1033.53i	0.947162	−	1.06330i
$973$	1537.21			1.57987
$974$	−93.2192	−	35.4981i	−0.0957076	−	0.0364457i
$975$			12.7629i			0.0130901i
$976$	−218.006	−	1880.68i	−0.223367	−	1.92692i
$977$	254.828			0.260827			0.130413	−	0.991460i	$-0.458370\pi$
$977$	254.828			0.260827			0.130413	+	0.991460i	$0.458370\pi$
$978$	540.013	−	1418.09i	0.552161	−	1.44999i
$979$			587.625i			0.600230i
$980$	1507.85	+	1343.16i	1.53862	+	1.37057i
$981$	10.8895			0.0111004
$982$	−712.795	−	271.434i	−0.725861	−	0.276410i
$983$			712.458i			0.724779i	0.932027	+	0.362390i	$0.118039\pi$
$983$			712.458i			0.724779i	−0.932027	+	0.362390i	$0.881961\pi$
$984$	1138.71	+	2191.27i	1.15723	+	2.22690i
$985$	625.279			0.634801
$986$	43.5724	−	114.423i	0.0441911	−	0.116047i
$987$			2126.50i			2.15450i
$988$	164.410	−	184.569i	0.166407	−	0.186811i
$989$	29.0243			0.0293471
$990$	1351.33	+	514.590i	1.36498	+	0.519788i
$991$			1719.28i			1.73490i	0.497526	+	0.867449i	$0.334242\pi$
$991$			1719.28i			1.73490i	−0.497526	+	0.867449i	$0.665758\pi$
$992$	−340.405	+	1341.84i	−0.343151	+	1.35266i
$993$	1841.94			1.85493
$994$	−98.9701	+	259.899i	−0.0995675	+	0.261467i
$995$			71.7485i			0.0721091i
$996$	331.330	+	295.141i	0.332660	+	0.296326i
$997$	488.006			0.489475			0.244737	−	0.969589i	$-0.421298\pi$
$997$	488.006			0.489475			0.244737	+	0.969589i	$0.421298\pi$
$998$	358.053	+	136.347i	0.358770	+	0.136621i
$999$		−	12.9043i		−	0.0129172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.b.39.9	✓	14
3.2	odd	2		684.3.g.b.343.6		14
4.3	odd	2	inner	76.3.b.b.39.10	yes	14
8.3	odd	2		1216.3.d.d.191.3		14
8.5	even	2		1216.3.d.d.191.12		14
12.11	even	2		684.3.g.b.343.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.9	✓	14	1.1	even	1	trivial
76.3.b.b.39.10	yes	14	4.3	odd	2	inner
684.3.g.b.343.5		14	12.11	even	2
684.3.g.b.343.6		14	3.2	odd	2
1216.3.d.d.191.3		14	8.3	odd	2
1216.3.d.d.191.12		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)

\(f(q)\)	\(=\)	\(q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +O(q^{10})\)	\(q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +(3.54430 - 9.30745i) q^{10} -13.4463i q^{11} +(-11.8382 + 13.2898i) q^{12} +14.1766 q^{13} +(22.9201 + 8.72803i) q^{14} -22.1571i q^{15} +(1.84237 + 15.8936i) q^{16} -5.89478 q^{17} +(-7.68520 + 20.1816i) q^{18} +4.35890i q^{19} +(-14.8736 - 13.2491i) q^{20} +54.5630 q^{21} +(-25.1320 - 9.57032i) q^{22} +0.906592i q^{23} +(16.4137 + 31.5855i) q^{24} -0.202335 q^{25} +(10.0901 - 26.4969i) q^{26} +7.99863i q^{27} +(32.6266 - 36.6271i) q^{28} -10.3853 q^{29} +(-41.4131 - 15.7702i) q^{30} +43.2608i q^{31} +(31.0175 + 7.86868i) q^{32} -59.8285 q^{33} +(-4.19559 + 11.0178i) q^{34} +61.0656i q^{35} +(32.2508 + 28.7283i) q^{36} -1.61331 q^{37} +(8.14708 + 3.10243i) q^{38} -63.0779i q^{39} +(-35.3497 + 18.3698i) q^{40} +69.3758 q^{41} +(38.8350 - 101.982i) q^{42} -32.0147i q^{43} +(-35.7752 + 40.1617i) q^{44} -53.7694 q^{45} +(1.69448 + 0.645264i) q^{46} +38.9732i q^{47} +(70.7178 - 8.19753i) q^{48} -101.377 q^{49} +(-0.144011 + 0.378179i) q^{50} +26.2286i q^{51} +(-42.3430 - 37.7182i) q^{52} -8.31560 q^{53} +(14.9500 + 5.69299i) q^{54} -66.9586i q^{55} +(-45.2367 - 87.0505i) q^{56} +19.3947 q^{57} +(-7.39169 + 19.4108i) q^{58} +20.9242i q^{59} +(-58.9512 + 66.1795i) q^{60} -118.329 q^{61} +(80.8574 + 30.7907i) q^{62} -132.410i q^{63} +(36.7837 - 52.3733i) q^{64} +70.5953 q^{65} +(-42.5827 + 111.824i) q^{66} +57.4499i q^{67} +(17.6067 + 15.6837i) q^{68} +4.03384 q^{69} +(114.136 + 43.4632i) q^{70} +11.3393i q^{71} +(76.6496 - 39.8318i) q^{72} -23.5952 q^{73} +(-1.14827 + 3.01539i) q^{74} +0.900282i q^{75} +(11.5973 - 13.0193i) q^{76} +164.889 q^{77} +(-117.897 - 44.8955i) q^{78} -0.286369i q^{79} +(9.17448 + 79.1456i) q^{80} -61.5894 q^{81} +(49.3780 - 129.668i) q^{82} -24.9311i q^{83} +(-162.971 - 145.171i) q^{84} -29.3544 q^{85} +(-59.8376 - 22.7863i) q^{86} +46.2089i q^{87} +(49.6022 + 95.4512i) q^{88} -43.7018 q^{89} +(-38.2702 + 100.499i) q^{90} +173.845i q^{91} +(2.41208 - 2.70784i) q^{92} +192.487 q^{93} +(72.8436 + 27.7390i) q^{94} +21.7061i q^{95} +(35.0113 - 138.011i) q^{96} +115.905 q^{97} +(-72.1549 + 189.481i) q^{98} +145.188i 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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