LMFDB - Embedded newform 76.3.b.b.39.10

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

$q$-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	$0.265921\pi$
$3$			4.44946i			1.48315i	−0.670869	+	0.741576i	$0.734079\pi$
$4$	−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	$-0.660257\pi$
$7$		−	12.2628i		−	1.75183i	0.482461	−	0.875917i	$-0.339743\pi$
$8$	−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	$0.209310\pi$
$11$			13.4463i			1.22239i	−0.791481	+	0.611193i	$0.790690\pi$
$12$	−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	$-0.993726\pi$
$23$		−	0.906592i		−	0.0394171i	0.999806	−	0.0197085i	$-0.00627383\pi$
$24$	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	$-0.754183\pi$
$31$		−	43.2608i		−	1.39551i	0.716337	−	0.697755i	$-0.245817\pi$
$32$	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	$0.121418\pi$
$43$			32.0147i			0.744527i	−0.928127	+	0.372264i	$0.878582\pi$
$44$	−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	$-0.863918\pi$
$47$		−	38.9732i		−	0.829217i	0.910000	−	0.414609i	$-0.136082\pi$
$48$	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	$-0.943256\pi$
$59$		−	20.9242i		−	0.354648i	0.984153	−	0.177324i	$-0.0567440\pi$
$60$	−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	$-0.858961\pi$
$67$		−	57.4499i		−	0.857462i	0.903432	−	0.428731i	$-0.141039\pi$
$68$	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	$-0.974554\pi$
$71$		−	11.3393i		−	0.159709i	0.996807	−	0.0798545i	$-0.0254456\pi$
$72$	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	$0.000576925\pi$
$79$			0.286369i			0.00362492i	−0.999998	+	0.00181246i	$0.999423\pi$
$80$	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	$0.0479878\pi$
$83$			24.9311i			0.300375i	−0.988658	+	0.150188i	$0.952012\pi$
$84$	−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	$0.180781\pi$
$103$			110.807i			1.07579i	−0.843011	+	0.537897i	$0.819219\pi$
$104$	−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	$0.0442422\pi$
$107$			29.6484i			0.277088i	−0.990356	+	0.138544i	$0.955758\pi$
$108$	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	$0.308613\pi$
$127$			209.454i			1.64925i	−0.565681	+	0.824624i	$0.691387\pi$
$128$	−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	$0.0562758\pi$
$131$			46.0795i			0.351752i	−0.984412	+	0.175876i	$0.943724\pi$
$132$	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	$0.148903\pi$
$139$			125.355i			0.901835i	−0.892566	+	0.450918i	$0.851097\pi$
$140$	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	$-0.856310\pi$
$151$		−	131.745i		−	0.872482i	0.899830	−	0.436241i	$-0.143690\pi$
$152$	−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	$-0.824789\pi$
$163$		−	170.519i		−	1.04613i	0.852293	−	0.523064i	$-0.175211\pi$
$164$	−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	$0.262390\pi$
$167$			245.186i			1.46818i	−0.679053	+	0.734089i	$0.737610\pi$
$168$	−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	$0.117414\pi$
$179$			129.080i			0.721115i	−0.932737	+	0.360557i	$0.882586\pi$
$180$	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	$-0.530766\pi$
$191$		−	380.217i		−	1.99067i	0.0965041	−	0.995333i	$-0.469234\pi$
$192$	−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	$-0.988474\pi$
$199$		−	14.4081i		−	0.0724026i	0.999345	−	0.0362013i	$-0.0115258\pi$
$200$	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	$-0.938426\pi$
$211$		−	81.1242i		−	0.384475i	0.981348	−	0.192237i	$-0.0615744\pi$
$212$	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	$0.133755\pi$
$223$			181.944i			0.815892i	−0.913006	+	0.407946i	$0.866245\pi$
$224$	−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	$0.381838\pi$
$227$			423.077i			1.86377i	−0.362748	+	0.931887i	$0.618162\pi$
$228$	−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	$-0.841027\pi$
$239$		−	228.926i		−	0.957847i	0.877857	−	0.478924i	$-0.158973\pi$
$240$	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	$0.115508\pi$
$251$			178.193i			0.709934i	−0.934879	+	0.354967i	$0.884492\pi$
$252$	−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	$0.0240816\pi$
$263$			39.7564i			0.151165i	−0.997140	+	0.0755825i	$0.975918\pi$
$264$	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	$-0.968379\pi$
$271$		−	53.7535i		−	0.198353i	0.995070	−	0.0991763i	$-0.0316208\pi$
$272$	−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	$0.0457103\pi$
$283$			81.0003i			0.286220i	−0.989707	+	0.143110i	$0.954290\pi$
$284$	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	$-0.867027\pi$
$307$		−	249.101i		−	0.811405i	0.914005	−	0.405703i	$-0.132973\pi$
$308$	−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	$0.133048\pi$
$311$			252.481i			0.811835i	−0.913910	+	0.405917i	$0.866952\pi$
$312$	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	$-0.784963\pi$
$331$		−	413.971i		−	1.25067i	0.780358	−	0.625333i	$-0.215037\pi$
$332$	−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	$0.241034\pi$
$347$			476.716i			1.37382i	−0.726742	+	0.686911i	$0.758966\pi$
$348$	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	$-0.904139\pi$
$359$		−	212.978i		−	0.593252i	0.954994	−	0.296626i	$-0.0958615\pi$
$360$	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	$-0.853123\pi$
$367$		−	326.797i		−	0.890456i	0.895417	−	0.445228i	$-0.146877\pi$
$368$	−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	$0.213860\pi$
$379$			471.811i			1.24489i	−0.782666	+	0.622443i	$0.786140\pi$
$380$	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	$0.0547473\pi$
$383$			131.099i			0.342294i	−0.985246	+	0.171147i	$0.945253\pi$
$384$	−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	$-0.735157\pi$
$419$		−	619.532i		−	1.47860i	0.673378	−	0.739298i	$-0.264843\pi$
$420$	−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	$-0.804778\pi$
$431$		−	496.147i		−	1.15115i	0.817748	−	0.575577i	$-0.195222\pi$
$432$	−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	$-0.961719\pi$
$439$		−	105.337i		−	0.239947i	0.992777	−	0.119974i	$-0.0382810\pi$
$440$	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	$-0.959173\pi$
$443$		−	113.329i		−	0.255821i	0.991786	−	0.127911i	$-0.0408271\pi$
$444$	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	$0.113497\pi$
$463$			323.224i			0.698108i	−0.937103	+	0.349054i	$0.886503\pi$
$464$	−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	$0.189327\pi$
$467$			523.352i			1.12067i	−0.828267	+	0.560334i	$0.810673\pi$
$468$	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	$0.158688\pi$
$479$			458.055i			0.956274i	−0.878285	+	0.478137i	$0.841312\pi$
$480$	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	$0.0163065\pi$
$487$			49.8747i			0.102412i	−0.998688	+	0.0512060i	$0.983693\pi$
$488$	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	$0.126956\pi$
$491$			381.364i			0.776709i	−0.921510	+	0.388354i	$0.873044\pi$
$492$	−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	$-0.938518\pi$
$499$		−	191.567i		−	0.383903i	0.981404	−	0.191951i	$-0.0614816\pi$
$500$	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	$-0.871969\pi$
$503$		−	393.811i		−	0.782925i	0.920194	−	0.391463i	$-0.128031\pi$
$504$	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	$-0.974559\pi$
$523$		−	83.5113i		−	0.159677i	0.996808	−	0.0798387i	$-0.0254405\pi$
$524$	−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	$0.0337346\pi$
$547$			115.726i			0.211564i	−0.994389	+	0.105782i	$0.966265\pi$
$548$	−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	$-0.813599\pi$
$563$		−	622.336i		−	1.10539i	0.833383	−	0.552696i	$-0.186401\pi$
$564$	−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	$-0.816295\pi$
$571$		−	623.096i		−	1.09124i	0.838034	−	0.545619i	$-0.183705\pi$
$572$	−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	$0.230696\pi$
$587$			778.304i			1.32590i	−0.748663	+	0.662951i	$0.769304\pi$
$588$	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	$0.00991541\pi$
$599$			37.3119i			0.0622903i	−0.999515	+	0.0311452i	$0.990085\pi$
$600$	−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	$-0.942428\pi$
$607$		−	218.379i		−	0.359767i	0.983688	−	0.179884i	$-0.0575721\pi$
$608$	−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	$-0.967409\pi$
$619$		−	126.536i		−	0.204420i	0.994763	−	0.102210i	$-0.0325914\pi$
$620$	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	$-0.936380\pi$
$631$		−	250.558i		−	0.397081i	0.980093	−	0.198541i	$-0.0636202\pi$
$632$	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	$-0.640994\pi$
$643$		−	1161.89i		−	1.80699i	0.428604	−	0.903493i	$-0.359006\pi$
$644$	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	$0.139834\pi$
$647$			550.347i			0.850614i	−0.905049	+	0.425307i	$0.860166\pi$
$648$	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	$0.250492\pi$
$659$			933.406i			1.41640i	−0.706013	+	0.708199i	$0.749508\pi$
$660$	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	$0.0218078\pi$
$683$			93.5131i			0.136915i	−0.997654	+	0.0684576i	$0.978192\pi$
$684$	−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	$-0.840552\pi$
$691$		−	663.683i		−	0.960468i	0.877140	−	0.480234i	$-0.159448\pi$
$692$	−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	$0.250821\pi$
$719$			1019.44i			1.41786i	−0.705281	+	0.708928i	$0.749179\pi$
$720$	−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	$-0.949926\pi$
$727$		−	227.791i		−	0.313330i	0.987652	−	0.156665i	$-0.0500742\pi$
$728$	−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	$-0.863457\pi$
$739$		−	614.741i		−	0.831856i	0.909398	−	0.415928i	$-0.136543\pi$
$740$	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	$0.0336772\pi$
$743$			156.926i			0.211206i	−0.994408	+	0.105603i	$0.966323\pi$
$744$	−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	$0.170578\pi$
$751$			766.925i			1.02120i	−0.859817	+	0.510602i	$0.829422\pi$
$752$	−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	$-0.623730\pi$
$787$		−	1456.58i		−	1.85080i	0.378995	−	0.925399i	$-0.376270\pi$
$788$	−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	$0.0520734\pi$
$811$			264.166i			0.325729i	−0.986648	+	0.162865i	$0.947927\pi$
$812$	−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	$-0.889490\pi$
$823$		−	560.045i		−	0.680492i	0.940337	−	0.340246i	$-0.110510\pi$
$824$	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	$0.0867513\pi$
$827$			445.217i			0.538352i	−0.963091	+	0.269176i	$0.913249\pi$
$828$	−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	$-0.851043\pi$
$839$		−	756.891i		−	0.902135i	0.892490	−	0.451068i	$-0.148957\pi$
$840$	−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	$0.185929\pi$
$859$			947.410i			1.10292i	−0.834201	+	0.551461i	$0.814071\pi$
$860$	−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	$0.263512\pi$
$863$			1271.16i			1.47295i	−0.676463	+	0.736477i	$0.736488\pi$
$864$	−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	$-0.973129\pi$
$883$		−	148.904i		−	0.168634i	0.996439	−	0.0843170i	$-0.0268708\pi$
$884$	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	$-0.888683\pi$
$887$		−	607.820i		−	0.685254i	0.939472	−	0.342627i	$-0.111317\pi$
$888$	−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	$0.0231286\pi$
$907$			131.690i			0.145193i	−0.997361	+	0.0725966i	$0.976871\pi$
$908$	−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	$-0.884679\pi$
$911$		−	645.749i		−	0.708835i	0.935087	−	0.354417i	$-0.115321\pi$
$912$	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	$0.132877\pi$
$919$			745.172i			0.810851i	−0.914128	+	0.405425i	$0.867123\pi$
$920$	−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	$-0.675683\pi$
$947$		−	1612.77i		−	1.70304i	0.524326	−	0.851518i	$-0.324317\pi$
$948$	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	$0.157808\pi$
$967$			920.021i			0.951418i	−0.879603	+	0.475709i	$0.842192\pi$
$968$	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	$0.0568504\pi$
$971$			345.002i			0.355306i	−0.984093	+	0.177653i	$0.943150\pi$
$972$	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	$-0.881961\pi$
$983$		−	712.458i		−	0.724779i	0.932027	−	0.362390i	$-0.118039\pi$
$984$	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	$-0.665758\pi$
$991$		−	1719.28i		−	1.73490i	0.497526	−	0.867449i	$-0.334242\pi$
$992$	−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.39.10	yes	14
3.2	odd	2		684.3.g.b.343.5		14
4.3	odd	2	inner	76.3.b.b.39.9	✓	14
8.3	odd	2		1216.3.d.d.191.12		14
8.5	even	2		1216.3.d.d.191.3		14
12.11	even	2		684.3.g.b.343.6		14

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
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

Introduction

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