LMFDB - Embedded newform 33.7.b.a.23.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1026 x^{18} + 441321 x^{16} + 103808124 x^{14} + 14594358456 x^{12} + 1256133373152 x^{10} + \cdots + 32\!\cdots\!64 $ x^20 + 1026x^18 + 441321x^16 + 103808124x^14 + 14594358456x^12 + 1256133373152x^10 + 64843235559312x^8 + 1864534894961472x^6 + 25120735435348224x^4 + 103653954147713024*x^2 + 32367107232497664
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{17}\cdot 11^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.19
Root			$14.5373i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.5373i q^{2} +(-26.2741 + 6.21862i) q^{3} -147.333 q^{4} +220.756i q^{5} +(-90.4019 - 381.955i) q^{6} +126.134 q^{7} -1211.44i q^{8} +(651.658 - 326.777i) q^{9} +O(q^{10})$	\(q+14.5373i q^{2} +(-26.2741 + 6.21862i) q^{3} -147.333 q^{4} +220.756i q^{5} +(-90.4019 - 381.955i) q^{6} +126.134 q^{7} -1211.44i q^{8} +(651.658 - 326.777i) q^{9} -3209.19 q^{10} +401.312i q^{11} +(3871.04 - 916.208i) q^{12} +1708.06 q^{13} +1833.65i q^{14} +(-1372.79 - 5800.16i) q^{15} +8181.71 q^{16} +5011.77i q^{17} +(4750.46 + 9473.34i) q^{18} -6950.39 q^{19} -32524.6i q^{20} +(-3314.07 + 784.381i) q^{21} -5833.99 q^{22} -10992.7i q^{23} +(7533.47 + 31829.4i) q^{24} -33108.0 q^{25} +24830.5i q^{26} +(-15089.6 + 12638.2i) q^{27} -18583.8 q^{28} -12667.2i q^{29} +(84318.6 - 19956.7i) q^{30} +9409.63 q^{31} +41408.0i q^{32} +(-2495.60 - 10544.1i) q^{33} -72857.6 q^{34} +27844.9i q^{35} +(-96010.7 + 48145.1i) q^{36} +85665.0 q^{37} -101040. i q^{38} +(-44877.7 + 10621.8i) q^{39} +267432. q^{40} +103017. i q^{41} +(-11402.8 - 48177.6i) q^{42} -75114.2 q^{43} -59126.5i q^{44} +(72137.9 + 143857. i) q^{45} +159805. q^{46} +14348.2i q^{47} +(-214967. + 50879.0i) q^{48} -101739. q^{49} -481301. i q^{50} +(-31166.3 - 131680. i) q^{51} -251653. q^{52} -15809.9i q^{53} +(-183725. - 219362. i) q^{54} -88591.8 q^{55} -152804. i q^{56} +(182615. - 43221.8i) q^{57} +184147. q^{58} +84825.4i q^{59} +(202258. + 854555. i) q^{60} +201587. q^{61} +136791. i q^{62} +(82196.4 - 41217.8i) q^{63} -78331.1 q^{64} +377063. i q^{65} +(153283. - 36279.3i) q^{66} +123382. q^{67} -738400. i q^{68} +(68359.6 + 288824. i) q^{69} -404789. q^{70} +39114.3i q^{71} +(-395870. - 789442. i) q^{72} -554508. q^{73} +1.24534e6i q^{74} +(869884. - 205886. i) q^{75} +1.02402e6 q^{76} +50619.2i q^{77} +(-154412. - 652401. i) q^{78} +86158.5 q^{79} +1.80616e6i q^{80} +(317874. - 425894. i) q^{81} -1.49759e6 q^{82} -495018. i q^{83} +(488272. - 115565. i) q^{84} -1.10638e6 q^{85} -1.09196e6i q^{86} +(78772.4 + 332819. i) q^{87} +486164. q^{88} +693910. i q^{89} +(-2.09129e6 + 1.04869e6i) q^{90} +215445. q^{91} +1.61959e6i q^{92} +(-247230. + 58514.9i) q^{93} -208583. q^{94} -1.53434e6i q^{95} +(-257501. - 1.08796e6i) q^{96} -1.46106e6 q^{97} -1.47901e6i q^{98} +(131140. + 261518. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$			14.5373i			1.81716i	0.417708	+	0.908581i	$0.362833\pi$
$2$			14.5373i			1.81716i	−0.417708	+	0.908581i	$0.637167\pi$
$3$	−26.2741	+	6.21862i	−0.973115	+	0.230319i
$3$	−26.2741	+	6.21862i	−0.973115	+	0.230319i
$4$	−147.333			−2.30208
$5$			220.756i			1.76604i	0.469331	+	0.883022i	$0.344495\pi$
$5$			220.756i			1.76604i	−0.469331	+	0.883022i	$0.655505\pi$
$6$	−90.4019	−	381.955i	−0.418527	−	1.76831i
$7$	126.134			0.367738			0.183869	−	0.982951i	$-0.441138\pi$
$7$	126.134			0.367738			0.183869	+	0.982951i	$0.441138\pi$
$8$		−	1211.44i		−	2.36609i
$9$	651.658	−	326.777i	0.893906	−	0.448254i
$10$	−3209.19			−3.20919
$11$			401.312i			0.301511i
$11$			401.312i			0.301511i
$12$	3871.04	−	916.208i	2.24019	−	0.530213i
$13$	1708.06			0.777450			0.388725	−	0.921354i	$-0.372916\pi$
$13$	1708.06			0.777450			0.388725	+	0.921354i	$0.372916\pi$
$14$			1833.65i			0.668241i
$15$	−1372.79	−	5800.16i	−0.406754	−	1.71856i
$16$	8181.71			1.99749
$17$			5011.77i			1.02010i	0.860143	+	0.510052i	$0.170374\pi$
$17$			5011.77i			1.02010i	−0.860143	+	0.510052i	$0.829626\pi$
$18$	4750.46	+	9473.34i	0.814551	+	1.62437i
$19$	−6950.39			−1.01332			−0.506662	−	0.862145i	$-0.669121\pi$
$19$	−6950.39			−1.01332			−0.506662	+	0.862145i	$0.669121\pi$
$20$		−	32524.6i		−	4.06557i
$21$	−3314.07	+	784.381i	−0.357852	+	0.0846972i
$22$	−5833.99			−0.547895
$23$		−	10992.7i		−	0.903487i	−0.892148	−	0.451743i	$-0.850802\pi$
$23$		−	10992.7i		−	0.903487i	0.892148	−	0.451743i	$-0.149198\pi$
$24$	7533.47	+	31829.4i	0.544956	+	2.30248i
$25$	−33108.0			−2.11891
$26$			24830.5i			1.41275i
$27$	−15089.6	+	12638.2i	−0.766632	+	0.642087i
$28$	−18583.8			−0.846563
$29$		−	12667.2i		−	0.519381i	−0.965692	−	0.259691i	$-0.916379\pi$
$29$		−	12667.2i		−	0.519381i	0.965692	−	0.259691i	$-0.0836206\pi$
$30$	84318.6	−	19956.7i	3.12291	−	0.739138i
$31$	9409.63			0.315855			0.157927	−	0.987451i	$-0.449519\pi$
$31$	9409.63			0.315855			0.157927	+	0.987451i	$0.449519\pi$
$32$			41408.0i			1.26367i
$33$	−2495.60	−	10544.1i	−0.0694438	−	0.293405i
$34$	−72857.6			−1.85370
$35$			27844.9i			0.649443i
$36$	−96010.7	+	48145.1i	−2.05784	+	1.03192i
$37$	85665.0			1.69121			0.845607	−	0.533806i	$-0.179239\pi$
$37$	85665.0			1.69121			0.845607	+	0.533806i	$0.179239\pi$
$38$		−	101040.i		−	1.84138i
$39$	−44877.7	+	10621.8i	−0.756548	+	0.179062i
$40$	267432.			4.17862
$41$			103017.i			1.49471i	0.664423	+	0.747357i	$0.268677\pi$
$41$			103017.i			1.49471i	−0.664423	+	0.747357i	$0.731323\pi$
$42$	−11402.8	−	48177.6i	−0.153909	−	0.650275i
$43$	−75114.2			−0.944749			−0.472374	−	0.881398i	$-0.656603\pi$
$43$	−75114.2			−0.944749			−0.472374	+	0.881398i	$0.656603\pi$
$44$		−	59126.5i		−	0.694103i
$45$	72137.9	+	143857.i	0.791637	+	1.57868i
$46$	159805.			1.64178
$47$			14348.2i			0.138198i	0.997610	+	0.0690991i	$0.0220125\pi$
$47$			14348.2i			0.138198i	−0.997610	+	0.0690991i	$0.977988\pi$
$48$	−214967.	+	50879.0i	−1.94379	+	0.460060i
$49$	−101739.			−0.864768
$50$		−	481301.i		−	3.85041i
$51$	−31166.3	−	131680.i	−0.234950	−	0.992679i
$52$	−251653.			−1.78975
$53$		−	15809.9i		−	0.106195i	−0.998589	−	0.0530973i	$-0.983091\pi$
$53$		−	15809.9i		−	0.106195i	0.998589	−	0.0530973i	$-0.0169093\pi$
$54$	−183725.	−	219362.i	−1.16678	−	1.39309i
$55$	−88591.8			−0.532483
$56$		−	152804.i		−	0.870102i
$57$	182615.	−	43221.8i	0.986082	−	0.233388i
$58$	184147.			0.943800
$59$			84825.4i			0.413019i	0.978445	+	0.206510i	$0.0662104\pi$
$59$			84825.4i			0.413019i	−0.978445	+	0.206510i	$0.933790\pi$
$60$	202258.	+	854555.i	0.936380	+	3.95627i
$61$	201587.			0.888124			0.444062	−	0.895996i	$-0.353537\pi$
$61$	201587.			0.888124			0.444062	+	0.895996i	$0.353537\pi$
$62$			136791.i			0.573960i
$63$	82196.4	−	41217.8i	0.328724	−	0.164840i
$64$	−78331.1			−0.298809
$65$			377063.i			1.37301i
$66$	153283.	−	36279.3i	0.533165	−	0.126191i
$67$	123382.			0.410229			0.205115	−	0.978738i	$-0.434243\pi$
$67$	123382.			0.410229			0.205115	+	0.978738i	$0.434243\pi$
$68$		−	738400.i		−	2.34836i
$69$	68359.6	+	288824.i	0.208090	+	0.879197i
$70$	−404789.			−1.18014
$71$			39114.3i			0.109285i	0.998506	+	0.0546425i	$0.0174019\pi$
$71$			39114.3i			0.109285i	−0.998506	+	0.0546425i	$0.982598\pi$
$72$	−395870.	−	789442.i	−1.06061	−	2.11506i
$73$	−554508.			−1.42541			−0.712704	−	0.701465i	$-0.752530\pi$
$73$	−554508.			−1.42541			−0.712704	+	0.701465i	$0.752530\pi$
$74$			1.24534e6i			3.07321i
$75$	869884.	−	205886.i	2.06195	−	0.488027i
$76$	1.02402e6			2.33275
$77$			50619.2i			0.110877i
$78$	−154412.	−	652401.i	−0.325384	−	1.37477i
$79$	86158.5			0.174750			0.0873749	−	0.996175i	$-0.472152\pi$
$79$	86158.5			0.174750			0.0873749	+	0.996175i	$0.472152\pi$
$80$			1.80616e6i			3.52765i
$81$	317874.	−	425894.i	0.598136	−	0.801394i
$82$	−1.49759e6			−2.71614
$83$		−	495018.i		−	0.865738i	−0.901457	−	0.432869i	$-0.857501\pi$
$83$		−	495018.i		−	0.865738i	0.901457	−	0.432869i	$-0.142499\pi$
$84$	488272.	−	115565.i	0.823803	−	0.194980i
$85$	−1.10638e6			−1.80155
$86$		−	1.09196e6i		−	1.71676i
$87$	78772.4	+	332819.i	0.119623	+	0.505418i
$88$	486164.			0.713403
$89$			693910.i			0.984313i	0.870507	+	0.492157i	$0.163791\pi$
$89$			693910.i			0.984313i	−0.870507	+	0.492157i	$0.836209\pi$
$90$	−2.09129e6	+	1.04869e6i	−2.86871	+	1.43853i
$91$	215445.			0.285898
$92$			1.61959e6i			2.07990i
$93$	−247230.	+	58514.9i	−0.307363	+	0.0727474i
$94$	−208583.			−0.251129
$95$		−	1.53434e6i		−	1.78958i
$96$	−257501.	−	1.08796e6i	−0.291048	−	1.22970i
$97$	−1.46106e6			−1.60086			−0.800429	−	0.599427i	$-0.795395\pi$
$97$	−1.46106e6			−1.60086			−0.800429	+	0.599427i	$0.795395\pi$
$98$		−	1.47901e6i		−	1.57142i
$99$	131140.	+	261518.i	0.135154	+	0.269523i
$100$	4.87791e6			4.87791
$101$			676095.i			0.656211i	0.944641	+	0.328106i	$0.106410\pi$
$101$			676095.i			0.656211i	−0.944641	+	0.328106i	$0.893590\pi$
$102$	1.91427e6	−	453074.i	1.80386	−	0.426942i
$103$	−549359.			−0.502741			−0.251371	−	0.967891i	$-0.580881\pi$
$103$	−549359.			−0.502741			−0.251371	+	0.967891i	$0.580881\pi$
$104$		−	2.06921e6i		−	1.83952i
$105$	−173156.	−	731599.i	−0.149579	−	0.631982i
$106$	229834.			0.192973
$107$			30965.6i			0.0252772i	0.999920	+	0.0126386i	$0.00402309\pi$
$107$			30965.6i			0.0252772i	−0.999920	+	0.0126386i	$0.995977\pi$
$108$	2.22320e6	−	1.86202e6i	1.76485	−	1.47813i
$109$	−339923.			−0.262483			−0.131241	−	0.991350i	$-0.541896\pi$
$109$	−339923.			−0.262483			−0.131241	+	0.991350i	$0.541896\pi$
$110$		−	1.28789e6i		−	0.967607i
$111$	−2.25077e6	+	532718.i	−1.64575	+	0.389519i
$112$	1.03199e6			0.734554
$113$			1.21825e6i			0.844310i	0.906524	+	0.422155i	$0.138726\pi$
$113$			1.21825e6i			0.844310i	−0.906524	+	0.422155i	$0.861274\pi$
$114$	628329.	+	2.65473e6i	0.424104	+	1.79187i
$115$	2.42671e6			1.59560
$116$			1.86630e6i			1.19566i
$117$	1.11307e6	−	558154.i	0.694967	−	0.348495i
$118$	−1.23313e6			−0.750523
$119$			632156.i			0.375132i
$120$	−7.02653e6	+	1.66306e6i	−4.06628	+	0.962416i
$121$	−161051.			−0.0909091
$122$			2.93053e6i			1.61386i
$123$	−640624.	−	2.70668e6i	−0.344261	−	1.45453i
$124$	−1.38635e6			−0.727123
$125$		−	3.85948e6i		−	1.97605i
$126$	599196.	+	1.19491e6i	0.299542	+	0.597344i
$127$	708350.			0.345809			0.172905	−	0.984939i	$-0.444685\pi$
$127$	708350.			0.345809			0.172905	+	0.984939i	$0.444685\pi$
$128$			1.51139e6i			0.720687i
$129$	1.97356e6	−	467106.i	0.919349	−	0.217594i
$130$	−5.48148e6			−2.49499
$131$			664516.i			0.295591i	0.989018	+	0.147796i	$0.0472178\pi$
$131$			664516.i			0.295591i	−0.989018	+	0.147796i	$0.952782\pi$
$132$	367685.	+	1.55350e6i	0.159865	+	0.675442i
$133$	−876683.			−0.372638
$134$			1.79364e6i			0.745453i
$135$	−2.78995e6	−	3.33112e6i	−1.13395	−	1.35391i
$136$	6.07145e6			2.41366
$137$			2.40014e6i			0.933415i	0.884412	+	0.466708i	$0.154560\pi$
$137$			2.40014e6i			0.933415i	−0.884412	+	0.466708i	$0.845440\pi$
$138$	−4.19872e6	+	993763.i	−1.59764	+	0.378134i
$139$	4.98305e6			1.85546			0.927729	−	0.373255i	$-0.121758\pi$
$139$	4.98305e6			1.85546			0.927729	+	0.373255i	$0.121758\pi$
$140$		−	4.10247e6i		−	1.49507i
$141$	−89225.7	−	376985.i	−0.0318297	−	0.134483i
$142$	−568617.			−0.198589
$143$			685463.i			0.234410i
$144$	5.33168e6	−	2.67360e6i	1.78557	−	0.895383i
$145$	2.79635e6			0.917250
$146$		−	8.06104e6i		−	2.59020i
$147$	2.67311e6	−	632677.i	0.841519	−	0.199173i
$148$	−1.26213e7			−3.89331
$149$			1.07892e6i			0.326159i	0.986613	+	0.163080i	$0.0521427\pi$
$149$			1.07892e6i			0.326159i	−0.986613	+	0.163080i	$0.947857\pi$
$150$	2.99303e6	+	1.26458e7i	0.886823	+	3.74689i
$151$	−2.25438e6			−0.654781			−0.327391	−	0.944889i	$-0.606169\pi$
$151$	−2.25438e6			−0.654781			−0.327391	+	0.944889i	$0.606169\pi$
$152$			8.41997e6i			2.39762i
$153$	1.63773e6	+	3.26596e6i	0.457266	+	0.911878i
$154$	−735866.			−0.201482
$155$			2.07723e6i			0.557814i
$156$	6.61197e6	−	1.56494e6i	1.74163	−	0.412214i
$157$	1.47246e6			0.380490			0.190245	−	0.981737i	$-0.439072\pi$
$157$	1.47246e6			0.380490			0.190245	+	0.981737i	$0.439072\pi$
$158$			1.25251e6i			0.317549i
$159$	98315.9	+	415392.i	0.0244586	+	0.103339i
$160$	−9.14105e6			−2.23170
$161$		−	1.38656e6i		−	0.332247i
$162$	6.19135e6	+	4.62103e6i	1.45626	+	1.08691i
$163$	−120445.			−0.0278117			−0.0139058	−	0.999903i	$-0.504427\pi$
$163$	−120445.			−0.0278117			−0.0139058	+	0.999903i	$0.504427\pi$
$164$		−	1.51778e7i		−	3.44095i
$165$	2.32767e6	−	550918.i	0.518167	−	0.122641i
$166$	7.19622e6			1.57319
$167$		−	5.10217e6i		−	1.09548i	−0.836647	−	0.547742i	$-0.815488\pi$
$167$		−	5.10217e6i		−	1.09548i	0.836647	−	0.547742i	$-0.184512\pi$
$168$	950229.	+	4.01478e6i	0.200401	+	0.846709i
$169$	−1.90935e6			−0.395571
$170$		−	1.60837e7i		−	3.27371i
$171$	−4.52928e6	+	2.27123e6i	−0.905817	+	0.454227i
$172$	1.10668e7			2.17489
$173$		−	494335.i		−	0.0954736i	−0.998860	−	0.0477368i	$-0.984799\pi$
$173$		−	494335.i		−	0.0954736i	0.998860	−	0.0477368i	$-0.0152009\pi$
$174$	−4.83829e6	+	1.14514e6i	−0.918426	+	0.217375i
$175$	−4.17606e6			−0.779206
$176$			3.28342e6i			0.602266i
$177$	−527497.	−	2.22871e6i	−0.0951262	−	0.401915i
$178$	−1.00876e7			−1.78866
$179$		−	3.23803e6i		−	0.564575i	−0.959330	−	0.282288i	$-0.908907\pi$
$179$		−	3.23803e6i		−	0.564575i	0.959330	−	0.282288i	$-0.0910933\pi$
$180$	−1.06283e7	−	2.11949e7i	−1.82241	−	3.63424i
$181$	1.07842e7			1.81867			0.909333	−	0.416070i	$-0.136593\pi$
$181$	1.07842e7			1.81867			0.909333	+	0.416070i	$0.136593\pi$
$182$			3.13198e6i			0.519524i
$183$	−5.29652e6	+	1.25359e6i	−0.864247	+	0.204552i
$184$	−1.33170e7			−2.13773
$185$			1.89110e7i			2.98676i
$186$	−850649.	−	3.59405e6i	−0.132194	−	0.558529i
$187$	−2.01128e6			−0.307573
$188$		−	2.11396e6i		−	0.318143i
$189$	−1.90332e6	+	1.59411e6i	−0.281920	+	0.236120i
$190$	2.23051e7			3.25195
$191$			1.15933e7i			1.66382i	0.554907	+	0.831912i	$0.312754\pi$
$191$			1.15933e7i			1.66382i	−0.554907	+	0.831912i	$0.687246\pi$
$192$	2.05808e6	−	487111.i	0.290776	−	0.0688215i
$193$	−2.40762e6			−0.334900			−0.167450	−	0.985881i	$-0.553553\pi$
$193$	−2.40762e6			−0.334900			−0.167450	+	0.985881i	$0.553553\pi$
$194$		−	2.12399e7i		−	2.90902i
$195$	−2.34481e6	−	9.90700e6i	−0.316231	−	1.33610i
$196$	1.49895e7			1.99077
$197$			6.85236e6i			0.896275i	0.893965	+	0.448138i	$0.147913\pi$
$197$			6.85236e6i			0.896275i	−0.893965	+	0.448138i	$0.852087\pi$
$198$	−3.80176e6	+	1.90641e6i	−0.489767	+	0.245596i
$199$	2.15825e6			0.273869			0.136934	−	0.990580i	$-0.456275\pi$
$199$	2.15825e6			0.273869			0.136934	+	0.990580i	$0.456275\pi$
$200$			4.01083e7i			5.01354i
$201$	−3.24174e6	+	767264.i	−0.399200	+	0.0944836i
$202$	−9.82860e6			−1.19244
$203$		−	1.59777e6i		−	0.190996i
$204$	4.59183e6	+	1.94008e7i	0.540873	+	2.28523i
$205$	−2.27416e7			−2.63973
$206$		−	7.98620e6i		−	0.913563i
$207$	−3.59217e6	−	7.16349e6i	−0.404992	−	0.807633i
$208$	1.39748e7			1.55295
$209$		−	2.78927e6i		−	0.305529i
$210$	1.06355e7	−	2.51723e6i	1.14841	−	0.271809i
$211$	1.22790e7			1.30712			0.653559	−	0.756875i	$-0.273275\pi$
$211$	1.22790e7			1.30712			0.653559	+	0.756875i	$0.273275\pi$
$212$			2.32932e6i			0.244468i
$213$	−243237.	−	1.02769e6i	−0.0251704	−	0.106347i
$214$	−450156.			−0.0459327
$215$		−	1.65819e7i		−	1.66847i
$216$	1.53104e7	+	1.82801e7i	1.51923	+	1.81392i
$217$	1.18688e6			0.116152
$218$		−	4.94156e6i		−	0.476974i
$219$	1.45692e7	−	3.44827e6i	1.38709	−	0.328299i
$220$	1.30525e7			1.22582
$221$			8.56040e6i			0.793080i
$222$	−7.74428e6	−	3.27202e7i	−0.707819	−	2.99059i
$223$	3.80146e6			0.342796			0.171398	−	0.985202i	$-0.445172\pi$
$223$	3.80146e6			0.342796			0.171398	+	0.985202i	$0.445172\pi$
$224$			5.22297e6i			0.464701i
$225$	−2.15751e7	+	1.08190e7i	−1.89411	+	0.949812i
$226$	−1.77101e7			−1.53425
$227$			1.49865e7i			1.28122i	0.767867	+	0.640609i	$0.221318\pi$
$227$			1.49865e7i			1.28122i	−0.767867	+	0.640609i	$0.778682\pi$
$228$	−2.69053e7	+	6.36801e6i	−2.27004	+	0.537278i
$229$	1.78353e7			1.48516			0.742579	−	0.669758i	$-0.233602\pi$
$229$	1.78353e7			1.48516			0.742579	+	0.669758i	$0.233602\pi$
$230$			3.52777e7i			2.89946i
$231$	−314781.	−	1.32997e6i	−0.0255372	−	0.107896i
$232$	−1.53455e7			−1.22890
$233$		−	1.05068e7i		−	0.830618i	−0.909680	−	0.415309i	$-0.863673\pi$
$233$		−	1.05068e7i		−	0.830618i	0.909680	−	0.415309i	$-0.136327\pi$
$234$	8.11406e6	+	1.61810e7i	0.633272	+	1.26287i
$235$	−3.16744e6			−0.244064
$236$		−	1.24976e7i		−	0.950803i
$237$	−2.26374e6	+	535787.i	−0.170052	+	0.0402482i
$238$	−9.18985e6			−0.681675
$239$		−	4.98570e6i		−	0.365201i	−0.983187	−	0.182601i	$-0.941548\pi$
$239$		−	4.98570e6i		−	0.365201i	0.983187	−	0.182601i	$-0.0584516\pi$
$240$	−1.12318e7	−	4.74552e7i	−0.812487	−	3.43281i
$241$	−1.26114e7			−0.900975			−0.450488	−	0.892783i	$-0.648750\pi$
$241$	−1.26114e7			−0.900975			−0.450488	+	0.892783i	$0.648750\pi$
$242$		−	2.34125e6i		−	0.165197i
$243$	−5.70339e6	+	1.31667e7i	−0.397479	+	0.917611i
$244$	−2.97005e7			−2.04453
$245$		−	2.24595e7i		−	1.52722i
$246$	3.93479e7	−	9.31295e6i	2.64311	−	0.625578i
$247$	−1.18717e7			−0.787809
$248$		−	1.13992e7i		−	0.747341i
$249$	3.07833e6	+	1.30062e7i	0.199396	+	0.842463i
$250$	5.61064e7			3.59081
$251$			5.42830e6i			0.343276i	0.985160	+	0.171638i	$0.0549059\pi$
$251$			5.42830e6i			0.343276i	−0.985160	+	0.171638i	$0.945094\pi$
$252$	−1.21102e7	+	6.07275e6i	−0.756748	+	0.379475i
$253$	4.41151e6			0.272412
$254$			1.02975e7i			0.628391i
$255$	2.90691e7	−	6.88013e6i	1.75312	−	0.414931i
$256$	−2.69847e7			−1.60842
$257$			2.11197e7i			1.24420i	0.782939	+	0.622098i	$0.213719\pi$
$257$			2.11197e7i			1.24420i	−0.782939	+	0.622098i	$0.786281\pi$
$258$	6.79046e6	+	2.86902e7i	0.395403	+	1.67061i
$259$	1.08053e7			0.621924
$260$		−	5.55539e7i		−	3.16078i
$261$	−4.13935e6	−	8.25467e6i	−0.232815	−	0.464278i
$262$	−9.66027e6			−0.537138
$263$		−	2.35095e7i		−	1.29234i	−0.763195	−	0.646168i	$-0.776370\pi$
$263$		−	2.35095e7i		−	1.29234i	0.763195	−	0.646168i	$-0.223630\pi$
$264$	−1.27735e7	+	3.02327e6i	−0.694223	+	0.164310i
$265$	3.49013e6			0.187544
$266$		−	1.27446e7i		−	0.677145i
$267$	−4.31516e6	−	1.82319e7i	−0.226706	−	0.957850i
$268$	−1.81782e7			−0.944380
$269$			3.22890e7i			1.65881i	0.558645	+	0.829407i	$0.311322\pi$
$269$			3.22890e7i			1.65881i	−0.558645	+	0.829407i	$0.688678\pi$
$270$	4.84255e7	−	4.05584e7i	2.46027	−	2.06058i
$271$	1.46324e7			0.735202			0.367601	−	0.929984i	$-0.380179\pi$
$271$	1.46324e7			0.735202			0.367601	+	0.929984i	$0.380179\pi$
$272$			4.10049e7i			2.03765i
$273$	−5.66062e6	+	1.33977e6i	−0.278212	+	0.0658479i
$274$	−3.48916e7			−1.69617
$275$		−	1.32866e7i		−	0.638877i
$276$	−1.00716e7	−	4.25533e7i	−0.479040	−	2.02398i
$277$	7.53384e6			0.354468			0.177234	−	0.984169i	$-0.443285\pi$
$277$	7.53384e6			0.354468			0.177234	+	0.984169i	$0.443285\pi$
$278$			7.24401e7i			3.37167i
$279$	6.13186e6	−	3.07485e6i	0.282345	−	0.141583i
$280$	3.37323e7			1.53664
$281$		−	6.11935e6i		−	0.275795i	−0.990447	−	0.137897i	$-0.955966\pi$
$281$		−	6.11935e6i		−	0.275795i	0.990447	−	0.137897i	$-0.0440344\pi$
$282$	5.48034e6	−	1.29710e6i	0.244377	−	0.0578397i
$283$	−2.05774e6			−0.0907887			−0.0453944	−	0.998969i	$-0.514454\pi$
$283$	−2.05774e6			−0.0907887			−0.0453944	+	0.998969i	$0.514454\pi$
$284$		−	5.76283e6i		−	0.251583i
$285$	9.54146e6	+	4.03134e7i	0.412174	+	1.74146i
$286$	−9.96479e6			−0.425961
$287$			1.29940e7i			0.549664i
$288$	1.35312e7	+	2.69839e7i	0.566447	+	1.12960i
$289$	−980295.			−0.0406128
$290$			4.06514e7i			1.66679i
$291$	3.83881e7	−	9.08577e6i	1.55782	−	0.368708i
$292$	8.16973e7			3.28140
$293$		−	3.43176e7i		−	1.36431i	−0.731206	−	0.682157i	$-0.761042\pi$
$293$		−	3.43176e7i		−	1.36431i	0.731206	−	0.682157i	$-0.238958\pi$
$294$	9.19741e6	+	3.88597e7i	0.361929	+	1.52918i
$295$	−1.87257e7			−0.729410
$296$		−	1.03778e8i		−	4.00156i
$297$	−5.07185e6	−	6.05564e6i	−0.193596	−	0.231148i
$298$	−1.56846e7			−0.592684
$299$		−	1.87762e7i		−	0.702416i
$300$	−1.28163e8	+	3.03338e7i	−4.74677	+	1.12348i
$301$	−9.47447e6			−0.347421
$302$		−	3.27726e7i		−	1.18984i
$303$	−4.20438e6	−	1.77638e7i	−0.151138	−	0.638569i
$304$	−5.68661e7			−2.02410
$305$			4.45015e7i			1.56847i
$306$	−4.74782e7	+	2.38082e7i	−1.65703	+	0.830927i
$307$	−1.02039e7			−0.352658			−0.176329	−	0.984331i	$-0.556422\pi$
$307$	−1.02039e7			−0.352658			−0.176329	+	0.984331i	$0.556422\pi$
$308$		−	7.45788e6i		−	0.255248i
$309$	1.44339e7	−	3.41625e6i	0.489225	−	0.115791i
$310$	−3.01973e7			−1.01364
$311$		−	2.78522e7i		−	0.925929i	−0.886377	−	0.462964i	$-0.846786\pi$
$311$		−	2.78522e7i		−	0.925929i	0.886377	−	0.462964i	$-0.153214\pi$
$312$	1.28676e7	+	5.43665e7i	0.423676	+	1.79006i
$313$	1.52192e7			0.496316			0.248158	−	0.968720i	$-0.420175\pi$
$313$	1.52192e7			0.496316			0.248158	+	0.968720i	$0.420175\pi$
$314$			2.14056e7i			0.691413i
$315$	9.09907e6	+	1.81453e7i	0.291115	+	0.580541i
$316$	−1.26940e7			−0.402288
$317$			1.66091e6i			0.0521396i	0.999660	+	0.0260698i	$0.00829921\pi$
$317$			1.66091e6i			0.0521396i	−0.999660	+	0.0260698i	$0.991701\pi$
$318$	−6.03867e6	+	1.42925e6i	−0.187785	+	0.0444453i
$319$	5.08349e6			0.156599
$320$		−	1.72920e7i		−	0.527711i
$321$	−192563.	−	813594.i	−0.00582182	−	0.0245976i
$322$	2.01568e7			0.603747
$323$		−	3.48338e7i		−	1.03370i
$324$	−4.68334e7	+	6.27482e7i	−1.37696	+	1.84487i
$325$	−5.65504e7			−1.64735
$326$		−	1.75095e6i		−	0.0505383i
$327$	8.93117e6	−	2.11385e6i	0.255426	−	0.0604548i
$328$	1.24799e8			3.53663
$329$			1.80979e6i			0.0508208i
$330$	8.00887e6	+	3.38380e7i	0.222858	+	0.941593i
$331$	−6.63322e7			−1.82911			−0.914557	−	0.404458i	$-0.867460\pi$
$331$	−6.63322e7			−1.82911			−0.914557	+	0.404458i	$0.867460\pi$
$332$			7.29325e7i			1.99300i
$333$	5.58243e7	−	2.79934e7i	1.51179	−	0.758093i
$334$	7.41718e7			1.99067
$335$			2.72372e7i			0.724483i
$336$	−2.71147e7	+	6.41758e6i	−0.714805	+	0.169182i
$337$	6.54478e7			1.71004			0.855018	−	0.518598i	$-0.173546\pi$
$337$	6.54478e7			1.71004			0.855018	+	0.518598i	$0.173546\pi$
$338$		−	2.77568e7i		−	0.718817i
$339$	−7.57585e6	−	3.20085e7i	−0.194461	−	0.821611i
$340$	1.63006e8			4.14731
$341$			3.77619e6i			0.0952338i
$342$	−3.30176e7	−	6.58435e7i	−0.825404	−	1.64602i
$343$	−2.76724e7			−0.685747
$344$			9.09961e7i			2.23536i
$345$	−6.37595e7	+	1.50908e7i	−1.55270	+	0.367497i
$346$	7.18630e6			0.173491
$347$		−	8.29148e7i		−	1.98447i	−0.124396	−	0.992233i	$-0.539699\pi$
$347$		−	8.29148e7i		−	1.98447i	0.124396	−	0.992233i	$-0.460301\pi$
$348$	−1.16058e7	−	4.90353e7i	−0.275383	−	1.16351i
$349$	−4.61399e7			−1.08543			−0.542713	−	0.839918i	$-0.682603\pi$
$349$	−4.61399e7			−1.08543			−0.542713	+	0.839918i	$0.682603\pi$
$350$		−	6.07086e7i		−	1.41594i
$351$	−2.57739e7	+	2.15868e7i	−0.596018	+	0.499190i
$352$	−1.66175e7			−0.381012
$353$		−	7.58340e6i		−	0.172401i	−0.996278	−	0.0862005i	$-0.972527\pi$
$353$		−	7.58340e6i		−	0.172401i	0.996278	−	0.0862005i	$-0.0274726\pi$
$354$	3.23995e7	−	7.66838e6i	0.730345	−	0.172860i
$355$	−8.63471e6			−0.193002
$356$		−	1.02236e8i		−	2.26597i
$357$	−3.93114e6	−	1.66093e7i	−0.0864000	−	0.365046i
$358$	4.70722e7			1.02593
$359$			6.70036e7i			1.44815i	0.689719	+	0.724077i	$0.257734\pi$
$359$			6.70036e7i			1.44815i	−0.689719	+	0.724077i	$0.742266\pi$
$360$	1.74274e8	−	8.73906e7i	3.73529	−	1.87308i
$361$	1.26209e6			0.0268268
$362$			1.56773e8i			3.30481i
$363$	4.23147e6	−	1.00151e6i	0.0884650	−	0.0209381i
$364$	−3.17421e7			−0.658161
$365$		−	1.22411e8i		−	2.51733i
$366$	−1.82239e7	−	7.69972e7i	−0.371704	−	1.57048i
$367$	−3.39588e7			−0.686996			−0.343498	−	0.939153i	$-0.611612\pi$
$367$	−3.39588e7			−0.686996			−0.343498	+	0.939153i	$0.611612\pi$
$368$		−	8.99393e7i		−	1.80471i
$369$	3.36637e7	+	6.71319e7i	0.670012	+	1.33613i
$370$	−2.74915e8			−5.42743
$371$		−	1.99417e6i		−	0.0390518i
$372$	3.64251e7	−	8.62118e6i	0.707574	−	0.167470i
$373$	8.39405e7			1.61750			0.808751	−	0.588151i	$-0.200144\pi$
$373$	8.39405e7			1.61750			0.808751	+	0.588151i	$0.200144\pi$
$374$		−	2.92386e7i		−	0.558910i
$375$	2.40006e7	+	1.01404e8i	0.455123	+	1.92293i
$376$	1.73819e7			0.326989
$377$		−	2.16363e7i		−	0.403793i
$378$	−2.31740e7	−	2.76691e7i	−0.429068	−	0.512295i
$379$	−5.79874e7			−1.06516			−0.532581	−	0.846379i	$-0.678778\pi$
$379$	−5.79874e7			−1.06516			−0.532581	+	0.846379i	$0.678778\pi$
$380$			2.26059e8i			4.11975i
$381$	−1.86113e7	+	4.40496e6i	−0.336512	+	0.0796465i
$382$	−1.68536e8			−3.02344
$383$			9.99137e7i			1.77840i	0.457522	+	0.889198i	$0.348737\pi$
$383$			9.99137e7i			1.77840i	−0.457522	+	0.889198i	$0.651263\pi$
$384$	−9.39876e6	−	3.97105e7i	−0.165988	−	0.701312i
$385$	−1.11745e7			−0.195814
$386$		−	3.50002e7i		−	0.608568i
$387$	−4.89487e7	+	2.45456e7i	−0.844517	+	0.423488i
$388$	2.15262e8			3.68530
$389$		−	7.71392e7i		−	1.31047i	−0.755426	−	0.655233i	$-0.772570\pi$
$389$		−	7.71392e7i		−	1.31047i	0.755426	−	0.655233i	$-0.227430\pi$
$390$	1.44021e8	−	3.40872e7i	2.42791	−	0.574643i
$391$	5.50930e7			0.921651
$392$			1.23251e8i			2.04612i
$393$	−4.13237e6	−	1.74596e7i	−0.0680804	−	0.287644i
$394$	−9.96148e7			−1.62868
$395$			1.90200e7i			0.308616i
$396$	−1.93212e7	−	3.85302e7i	−0.311135	−	0.620463i
$397$	−4.04893e7			−0.647096			−0.323548	−	0.946212i	$-0.604876\pi$
$397$	−4.04893e7			−0.647096			−0.323548	+	0.946212i	$0.604876\pi$
$398$			3.13751e7i			0.497664i
$399$	2.30341e7	−	5.45176e6i	0.362620	−	0.0858258i
$400$	−2.70880e8			−4.23251
$401$			1.15168e7i			0.178608i	0.996004	+	0.0893038i	$0.0284642\pi$
$401$			1.15168e7i			0.178608i	−0.996004	+	0.0893038i	$0.971536\pi$
$402$	−1.11539e7	−	4.71262e7i	−0.171692	−	0.725411i
$403$	1.60722e7			0.245561
$404$		−	9.96111e7i		−	1.51065i
$405$	9.40184e7	+	7.01725e7i	1.41530	+	1.05634i
$406$	2.32272e7			0.347072
$407$			3.43784e7i			0.509920i
$408$	−1.59522e8	+	3.77560e7i	−2.34877	+	0.555912i
$409$	6.74782e7			0.986264			0.493132	−	0.869954i	$-0.335852\pi$
$409$	6.74782e7			0.986264			0.493132	+	0.869954i	$0.335852\pi$
$410$		−	3.30602e8i		−	4.79682i
$411$	−1.49256e7	−	6.30615e7i	−0.214983	−	0.908320i
$412$	8.09387e7			1.15735
$413$			1.06994e7i			0.151883i
$414$	1.04138e8	−	5.22205e7i	1.46760	−	0.735936i
$415$	1.09278e8			1.52893
$416$			7.07273e7i			0.982442i
$417$	−1.30925e8	+	3.09877e7i	−1.80557	+	0.427347i
$418$	4.05485e7			0.555196
$419$			1.28510e8i			1.74701i	0.486812	+	0.873507i	$0.338160\pi$
$419$			1.28510e8i			1.74701i	−0.486812	+	0.873507i	$0.661840\pi$
$420$	2.55117e7	+	1.07789e8i	0.344343	+	1.45487i
$421$	4.47016e7			0.599069			0.299535	−	0.954085i	$-0.403169\pi$
$421$	4.47016e7			0.599069			0.299535	+	0.954085i	$0.403169\pi$
$422$			1.78503e8i			2.37525i
$423$	4.68865e6	+	9.35009e6i	0.0619479	+	0.123536i
$424$	−1.91527e7			−0.251266
$425$		−	1.65930e8i		−	2.16151i
$426$	1.49399e7	−	3.53601e6i	0.193250	−	0.0457388i
$427$	2.54271e7			0.326597
$428$		−	4.56226e6i		−	0.0581900i
$429$	−4.26264e6	−	1.80099e7i	−0.0539891	−	0.228108i
$430$	2.41056e8			3.03188
$431$			5.99179e7i			0.748384i	0.927351	+	0.374192i	$0.122080\pi$
$431$			5.99179e7i			0.748384i	−0.927351	+	0.374192i	$0.877920\pi$
$432$	−1.23459e8	+	1.03402e8i	−1.53134	+	1.28256i
$433$	8.55572e7			1.05388			0.526942	−	0.849901i	$-0.323338\pi$
$433$	8.55572e7			1.05388			0.526942	+	0.849901i	$0.323338\pi$
$434$			1.72540e7i			0.211067i
$435$	−7.34717e7	+	1.73894e7i	−0.892590	+	0.211260i
$436$	5.00819e7			0.604256
$437$			7.64038e7i			0.915526i
$438$	5.01285e7	+	2.11797e8i	0.596572	+	2.52056i
$439$	1.29812e8			1.53434			0.767171	−	0.641443i	$-0.221664\pi$
$439$	1.29812e8			1.53434			0.767171	+	0.641443i	$0.221664\pi$
$440$			1.07323e8i			1.25990i
$441$	−6.62991e7	+	3.32460e7i	−0.773022	+	0.387636i
$442$	−1.24445e8			−1.44116
$443$			1.42700e8i			1.64140i	0.571362	+	0.820698i	$0.306415\pi$
$443$			1.42700e8i			1.64140i	−0.571362	+	0.820698i	$0.693585\pi$
$444$	3.31613e8	−	7.84870e7i	3.78864	−	0.896703i
$445$	−1.53185e8			−1.73834
$446$			5.52630e7i			0.622916i
$447$	−6.70938e6	−	2.83476e7i	−0.0751207	−	0.317391i
$448$	−9.88024e6			−0.109884
$449$		−	2.37778e7i		−	0.262683i	−0.991337	−	0.131341i	$-0.958072\pi$
$449$		−	2.37778e7i		−	0.262683i	0.991337	−	0.131341i	$-0.0419284\pi$
$450$	−1.57278e8	−	3.13644e8i	−1.72596	−	3.44191i
$451$	−4.13420e7			−0.450673
$452$		−	1.79489e8i		−	1.94367i
$453$	5.92318e7	−	1.40191e7i	0.637178	−	0.150809i
$454$	−2.17863e8			−2.32818
$455$			4.75606e7i			0.504909i
$456$	−5.23606e7	−	2.21227e8i	−0.552217	−	2.33316i
$457$	−1.47699e8			−1.54749			−0.773745	−	0.633498i	$-0.781619\pi$
$457$	−1.47699e8			−1.54749			−0.773745	+	0.633498i	$0.781619\pi$
$458$			2.59276e8i			2.69877i
$459$	−6.33397e7	−	7.56257e7i	−0.654995	−	0.782045i
$460$	−3.57534e8			−3.67319
$461$			5.27217e7i			0.538130i	0.963122	+	0.269065i	$0.0867146\pi$
$461$			5.27217e7i			0.538130i	−0.963122	+	0.269065i	$0.913285\pi$
$462$	1.93342e7	−	4.57607e6i	0.196065	−	0.0464052i
$463$	5.00170e7			0.503935			0.251968	−	0.967736i	$-0.418922\pi$
$463$	5.00170e7			0.503935			0.251968	+	0.967736i	$0.418922\pi$
$464$		−	1.03639e8i		−	1.03746i
$465$	−1.29175e7	−	5.45773e7i	−0.128475	−	0.542817i
$466$	1.52740e8			1.50937
$467$		−	1.15176e8i		−	1.13087i	−0.824793	−	0.565435i	$-0.808708\pi$
$467$		−	1.15176e8i		−	1.13087i	0.824793	−	0.565435i	$-0.191292\pi$
$468$	−1.63992e8	+	8.22346e7i	−1.59987	+	0.802264i
$469$	1.55627e7			0.150857
$470$		−	4.60460e7i		−	0.443504i
$471$	−3.86875e7	+	9.15665e6i	−0.370261	+	0.0876343i
$472$	1.02761e8			0.977240
$473$		−	3.01442e7i		−	0.284853i
$474$	−7.78889e6	−	3.29086e7i	−0.0731376	−	0.309012i
$475$	2.30114e8			2.14715
$476$		−	9.31375e7i		−	0.863583i
$477$	−5.16632e6	−	1.03027e7i	−0.0476021	−	0.0949279i
$478$	7.24786e7			0.663630
$479$		−	7.35963e7i		−	0.669653i	−0.942280	−	0.334826i	$-0.891322\pi$
$479$		−	7.35963e7i		−	0.669653i	0.942280	−	0.334826i	$-0.108678\pi$
$480$	2.40173e8	−	5.68447e7i	2.17170	−	0.514004i
$481$	1.46321e8			1.31483
$482$		−	1.83336e8i		−	1.63722i
$483$	8.62249e6	+	3.64306e7i	0.0765228	+	0.323315i
$484$	2.37281e7			0.209280
$485$		−	3.22537e8i		−	2.82719i
$486$	−1.91409e8	−	8.29119e7i	−1.66745	−	0.722284i
$487$	−1.03965e8			−0.900123			−0.450062	−	0.892997i	$-0.648598\pi$
$487$	−1.03965e8			−0.900123			−0.450062	+	0.892997i	$0.648598\pi$
$488$		−	2.44210e8i		−	2.10138i
$489$	3.16459e6	−	749003.i	0.0270639	−	0.00640556i
$490$	3.26500e8			2.77521
$491$			2.11427e8i			1.78614i	0.449916	+	0.893071i	$0.351454\pi$
$491$			2.11427e8i			1.78614i	−0.449916	+	0.893071i	$0.648546\pi$
$492$	9.43851e7	+	3.98784e8i	0.792516	+	3.34844i
$493$	6.34851e7			0.529823
$494$		−	1.72582e8i		−	1.43158i
$495$	−5.77315e7	+	2.89498e7i	−0.475989	+	0.238688i
$496$	7.69869e7			0.630917
$497$			4.93366e6i			0.0401883i
$498$	−1.89074e8	+	4.47506e7i	−1.53089	+	0.362335i
$499$	−8.28166e7			−0.666524			−0.333262	−	0.942834i	$-0.608149\pi$
$499$	−8.28166e7			−0.666524			−0.333262	+	0.942834i	$0.608149\pi$
$500$			5.68629e8i			4.54903i
$501$	3.17285e7	+	1.34055e8i	0.252311	+	1.06603i
$502$	−7.89129e7			−0.623788
$503$		−	6.95806e7i		−	0.546744i	−0.961908	−	0.273372i	$-0.911861\pi$
$503$		−	6.95806e7i		−	0.546744i	0.961908	−	0.273372i	$-0.0881390\pi$
$504$	−4.99328e7	−	9.95758e7i	−0.390027	−	0.777790i
$505$	−1.49252e8			−1.15890
$506$			6.41314e7i			0.495016i
$507$	5.01664e7	−	1.18735e7i	0.384936	−	0.0911077i
$508$	−1.04363e8			−0.796080
$509$			4.47288e7i			0.339183i	0.985514	+	0.169591i	$0.0542448\pi$
$509$			4.47288e7i			0.339183i	−0.985514	+	0.169591i	$0.945755\pi$
$510$	1.00019e8	+	4.22586e8i	0.753998	+	3.18570i
$511$	−6.99424e7			−0.524177
$512$		−	2.95556e8i		−	2.20206i
$513$	1.04879e8	−	8.78404e7i	0.776847	−	0.650642i
$514$	−3.07024e8			−2.26091
$515$		−	1.21274e8i		−	0.887864i
$516$	−2.90770e8	+	6.88202e7i	−2.11642	+	0.500918i
$517$	−5.75808e6			−0.0416683
$518$			1.57080e8i			1.13014i
$519$	3.07408e6	+	1.29882e7i	0.0219894	+	0.0929068i
$520$	4.56789e8			3.24867
$521$		−	1.21590e8i		−	0.859773i	−0.902883	−	0.429887i	$-0.858554\pi$
$521$		−	1.21590e8i		−	0.859773i	0.902883	−	0.429887i	$-0.141446\pi$
$522$	1.20001e8	−	6.01750e7i	0.843669	−	0.423062i
$523$	2.07668e7			0.145166			0.0725831	−	0.997362i	$-0.476876\pi$
$523$	2.07668e7			0.145166			0.0725831	+	0.997362i	$0.476876\pi$
$524$		−	9.79052e7i		−	0.680475i
$525$	1.09722e8	−	2.59693e7i	0.758257	−	0.179466i
$526$	3.41764e8			2.34839
$527$			4.71589e7i			0.322205i
$528$	−2.04183e7	−	8.62689e7i	−0.138713	−	0.586074i
$529$	2.71959e7			0.183711
$530$			5.07370e7i			0.340798i
$531$	2.77190e7	+	5.52771e7i	0.185138	+	0.369200i
$532$	1.29164e8			0.857843
$533$			1.75959e8i			1.16207i
$534$	2.65042e8	−	6.27308e7i	1.74057	−	0.411962i
$535$	−6.83583e6			−0.0446406
$536$		−	1.49469e8i		−	0.970638i
$537$	2.01361e7	+	8.50764e7i	0.130033	+	0.549397i
$538$	−4.69395e8			−3.01434
$539$		−	4.08291e7i		−	0.260737i
$540$	4.11052e8	+	4.90784e8i	2.61045	+	3.11680i
$541$	−2.21324e8			−1.39777			−0.698886	−	0.715233i	$-0.746320\pi$
$541$	−2.21324e8			−1.39777			−0.698886	+	0.715233i	$0.746320\pi$
$542$			2.12715e8i			1.33598i
$543$	−2.83346e8	+	6.70629e7i	−1.76977	+	0.418874i
$544$	−2.07528e8			−1.28908
$545$		−	7.50399e7i		−	0.463556i
$546$	−1.94766e7	−	8.22901e7i	−0.119656	−	0.505556i
$547$	−2.31787e8			−1.41621			−0.708104	−	0.706109i	$-0.750449\pi$
$547$	−2.31787e8			−1.41621			−0.708104	+	0.706109i	$0.750449\pi$
$548$		−	3.53620e8i		−	2.14880i
$549$	1.31366e8	−	6.58741e7i	0.793899	−	0.398105i
$550$	1.93152e8			1.16094
$551$			8.80419e7i			0.526302i
$552$	3.49892e8	−	8.28133e7i	2.08026	−	0.492360i
$553$	1.08675e7			0.0642622
$554$			1.09522e8i			0.644126i
$555$	−1.17600e8	−	4.96871e8i	−0.687908	−	2.90646i
$556$	−7.34168e8			−4.27141
$557$		−	4.09324e7i		−	0.236865i	−0.992962	−	0.118433i	$-0.962213\pi$
$557$		−	4.09324e7i		−	0.236865i	0.992962	−	0.118433i	$-0.0377869\pi$
$558$	4.47001e7	+	8.91407e7i	0.257280	+	0.513066i
$559$	−1.28299e8			−0.734495
$560$			2.27819e8i			1.29725i
$561$	5.28447e7	−	1.25074e7i	0.299304	−	0.0708400i
$562$	8.89588e7			0.501164
$563$		−	2.01027e8i		−	1.12649i	−0.826289	−	0.563247i	$-0.809552\pi$
$563$		−	2.01027e8i		−	1.12649i	0.826289	−	0.563247i	$-0.190448\pi$
$564$	1.31459e7	+	5.55424e7i	0.0732745	+	0.309590i
$565$	−2.68936e8			−1.49109
$566$		−	2.99140e7i		−	0.164978i
$567$	4.00948e7	−	5.37198e7i	0.219958	−	0.294704i
$568$	4.73846e7			0.258578
$569$			6.61784e7i			0.359236i	0.983736	+	0.179618i	$0.0574861\pi$
$569$			6.61784e7i			0.359236i	−0.983736	+	0.179618i	$0.942514\pi$
$570$	−5.86048e8	+	1.38707e8i	−3.16452	+	0.748987i
$571$	2.62487e8			1.40994			0.704968	−	0.709239i	$-0.250961\pi$
$571$	2.62487e8			1.40994			0.704968	+	0.709239i	$0.250961\pi$
$572$		−	1.00991e8i		−	0.539630i
$573$	−7.20944e7	−	3.04604e8i	−0.383211	−	1.61909i
$574$	−1.88898e8			−0.998828
$575$			3.63948e8i			1.91441i
$576$	−5.10451e7	+	2.55968e7i	−0.267108	+	0.133943i
$577$	2.77384e8			1.44396			0.721978	−	0.691916i	$-0.243233\pi$
$577$	2.77384e8			1.44396			0.721978	+	0.691916i	$0.243233\pi$
$578$		−	1.42508e7i		−	0.0738001i
$579$	6.32580e7	−	1.49720e7i	0.325896	−	0.0771339i
$580$	−4.11995e8			−2.11158
$581$		−	6.24388e7i		−	0.318365i
$582$	1.32083e8	+	5.58059e8i	0.670003	+	2.83081i
$583$	6.34470e6			0.0320188
$584$			6.71751e8i			3.37264i
$585$	1.23216e8	+	2.45716e8i	0.615458	+	1.22734i
$586$	4.98886e8			2.47918
$587$			3.23706e8i			1.60043i	0.599715	+	0.800214i	$0.295281\pi$
$587$			3.23706e8i			1.60043i	−0.599715	+	0.800214i	$0.704719\pi$
$588$	−3.93837e8	+	9.32142e7i	−1.93724	+	0.458511i
$589$	−6.54007e7			−0.320064
$590$		−	2.72221e8i		−	1.32546i
$591$	−4.26122e7	−	1.80040e8i	−0.206429	−	0.872179i
$592$	7.00887e8			3.37818
$593$		−	1.77845e8i		−	0.852858i	−0.904521	−	0.426429i	$-0.859771\pi$
$593$		−	1.77845e8i		−	0.852858i	0.904521	−	0.426429i	$-0.140229\pi$
$594$	8.80326e7	−	7.37310e7i	0.420034	−	0.351796i
$595$	−1.39552e8			−0.662499
$596$		−	1.58960e8i		−	0.750844i
$597$	−5.67061e7	+	1.34213e7i	−0.266506	+	0.0630772i
$598$	2.72955e8			1.27640
$599$			2.78419e8i			1.29545i	0.761876	+	0.647723i	$0.224278\pi$
$599$			2.78419e8i			1.29545i	−0.761876	+	0.647723i	$0.775722\pi$
$600$	−2.49418e8	−	1.05381e9i	−1.15471	−	4.87875i
$601$	1.72457e8			0.794433			0.397217	−	0.917725i	$-0.369976\pi$
$601$	1.72457e8			0.794433			0.397217	+	0.917725i	$0.369976\pi$
$602$		−	1.37733e8i		−	0.631320i
$603$	8.04026e7	−	4.03183e7i	0.366706	−	0.183887i
$604$	3.32145e8			1.50736
$605$		−	3.55529e7i		−	0.160550i
$606$	2.58238e8	−	6.11203e7i	1.16038	−	0.274642i
$607$	2.51726e7			0.112554			0.0562772	−	0.998415i	$-0.482077\pi$
$607$	2.51726e7			0.112554			0.0562772	+	0.998415i	$0.482077\pi$
$608$		−	2.87802e8i		−	1.28051i
$609$	9.93590e6	+	4.19799e7i	0.0439901	+	0.185862i
$610$	−6.46932e8			−2.85016
$611$			2.45075e7i			0.107442i
$612$	−2.41292e8	−	4.81184e8i	−1.05266	−	2.09921i
$613$	3.01626e8			1.30945			0.654723	−	0.755869i	$-0.272785\pi$
$613$	3.01626e8			1.30945			0.654723	+	0.755869i	$0.272785\pi$
$614$		−	1.48338e8i		−	0.640836i
$615$	5.97516e8	−	1.41421e8i	2.56876	−	0.607981i
$616$	6.13220e7			0.262346
$617$		−	3.17718e8i		−	1.35265i	−0.736601	−	0.676327i	$-0.763571\pi$
$617$		−	3.17718e8i		−	1.35265i	0.736601	−	0.676327i	$-0.236429\pi$
$618$	4.96631e7	+	2.09830e8i	0.210411	+	0.889002i
$619$	2.43586e8			1.02702			0.513512	−	0.858083i	$-0.328344\pi$
$619$	2.43586e8			1.02702			0.513512	+	0.858083i	$0.328344\pi$
$620$		−	3.06045e8i		−	1.28413i
$621$	1.38928e8	+	1.65876e8i	0.580117	+	0.692642i
$622$	4.04895e8			1.68256
$623$			8.75259e7i			0.361970i
$624$	−3.67177e8	+	8.69042e7i	−1.51120	+	0.357674i
$625$	3.34688e8			1.37088
$626$			2.21246e8i			0.901886i
$627$	1.73454e7	+	7.32857e7i	0.0703692	+	0.297315i
$628$	−2.16942e8			−0.875919
$629$			4.29334e8i			1.72521i
$630$	−2.63784e8	+	1.32276e8i	−1.05494	+	0.529004i
$631$	−3.16702e8			−1.26056			−0.630279	−	0.776368i	$-0.717060\pi$
$631$	−3.16702e8			−1.26056			−0.630279	+	0.776368i	$0.717060\pi$
$632$		−	1.04376e8i		−	0.413474i
$633$	−3.22619e8	+	7.63583e7i	−1.27198	+	0.301054i
$634$	−2.41451e7			−0.0947461
$635$			1.56372e8i			0.610715i
$636$	−1.44852e7	−	6.12009e7i	−0.0563057	−	0.237896i
$637$	−1.73776e8			−0.672314
$638$			7.39002e7i			0.284566i
$639$	1.27817e7	+	2.54892e7i	0.0489875	+	0.0976906i
$640$	−3.33648e8			−1.27277
$641$			4.70022e7i			0.178461i	0.996011	+	0.0892306i	$0.0284408\pi$
$641$			4.70022e7i			0.178461i	−0.996011	+	0.0892306i	$0.971559\pi$
$642$	1.18275e7	−	2.79935e6i	0.0446978	−	0.0105792i
$643$	4.70410e8			1.76947			0.884736	−	0.466092i	$-0.154338\pi$
$643$	4.70410e8			1.76947			0.884736	+	0.466092i	$0.154338\pi$
$644$			2.04286e8i			0.764859i
$645$	1.03116e8	+	4.35674e8i	0.384280	+	1.62361i
$646$	5.06389e8			1.87840
$647$		−	4.87562e8i		−	1.80019i	−0.435699	−	0.900093i	$-0.643499\pi$
$647$		−	4.87562e8i		−	1.80019i	0.435699	−	0.900093i	$-0.356501\pi$
$648$	−5.15944e8	−	3.85085e8i	−1.89617	−	1.41524i
$649$	−3.40414e7			−0.124530
$650$		−	8.22091e8i		−	2.99350i
$651$	−3.11841e7	+	7.38074e6i	−0.113029	+	0.0267520i
$652$	1.77456e7			0.0640246
$653$		−	1.26180e8i		−	0.453158i	−0.973993	−	0.226579i	$-0.927246\pi$
$653$		−	1.26180e8i		−	0.453158i	0.973993	−	0.226579i	$-0.0727541\pi$
$654$	3.07297e7	+	1.29835e8i	0.109856	+	0.464151i
$655$	−1.46696e8			−0.522028
$656$			8.42857e8i			2.98567i
$657$	−3.61349e8	+	1.81200e8i	−1.27418	+	0.638945i
$658$	−2.63095e7			−0.0923497
$659$		−	2.54954e8i		−	0.890853i	−0.895319	−	0.445426i	$-0.853052\pi$
$659$		−	2.54954e8i		−	0.890853i	0.895319	−	0.445426i	$-0.146948\pi$
$660$	−3.42943e8	+	8.11685e7i	−1.19286	+	0.282329i
$661$	−9.89929e7			−0.342768			−0.171384	−	0.985204i	$-0.554824\pi$
$661$	−9.89929e7			−0.342768			−0.171384	+	0.985204i	$0.554824\pi$
$662$		−	9.64291e8i		−	3.32380i
$663$	−5.32338e7	−	2.24917e8i	−0.182662	−	0.771758i
$664$	−5.99683e8			−2.04841
$665$		−	1.93533e8i		−	0.658096i
$666$	4.06948e8	+	8.11534e8i	1.37758	+	2.74716i
$667$	−1.39247e8			−0.469254
$668$			7.51719e8i			2.52189i
$669$	−9.98800e7	+	2.36398e7i	−0.333580	+	0.0789525i
$670$	−3.95955e8			−1.31650
$671$			8.08993e7i			0.267779i
$672$	−3.24797e7	−	1.37229e8i	−0.107030	−	0.452208i
$673$	1.17086e8			0.384115			0.192058	−	0.981384i	$-0.438484\pi$
$673$	1.17086e8			0.384115			0.192058	+	0.981384i	$0.438484\pi$
$674$			9.51434e8i			3.10741i
$675$	4.99588e8	−	4.18426e8i	1.62443	−	1.36053i
$676$	2.81310e8			0.910637
$677$		−	1.77528e8i		−	0.572137i	−0.958209	−	0.286069i	$-0.907651\pi$
$677$		−	1.77528e8i		−	0.572137i	0.958209	−	0.286069i	$-0.0923485\pi$
$678$	4.65317e8	−	1.10132e8i	1.49300	−	0.353367i
$679$	−1.84290e8			−0.588697
$680$			1.34031e9i			4.26263i
$681$	−9.31954e7	−	3.93757e8i	−0.295089	−	1.24677i
$682$	−5.48957e7			−0.173055
$683$			9.07615e6i			0.0284865i	0.999899	+	0.0142433i	$0.00453393\pi$
$683$			9.07615e6i			0.0284865i	−0.999899	+	0.0142433i	$0.995466\pi$
$684$	6.67312e8	−	3.34627e8i	2.08526	−	1.04567i
$685$	−5.29844e8			−1.64845
$686$		−	4.02282e8i		−	1.24611i
$687$	−4.68605e8	+	1.10911e8i	−1.44523	+	0.342061i
$688$	−6.14563e8			−1.88713
$689$		−	2.70043e7i		−	0.0825609i
$690$	−2.19379e8	−	9.26891e8i	−0.667802	−	2.82151i
$691$	1.08052e8			0.327490			0.163745	−	0.986503i	$-0.447643\pi$
$691$	1.08052e8			0.327490			0.163745	+	0.986503i	$0.447643\pi$
$692$			7.28319e7i			0.219788i
$693$	1.65412e7	+	3.29864e7i	0.0497012	+	0.0991139i
$694$	1.20536e9			3.60610
$695$			1.10004e9i			3.27682i
$696$	4.03190e8	−	9.54279e7i	1.19586	−	0.283040i
$697$	−5.16299e8			−1.52476
$698$		−	6.70750e8i		−	1.97240i
$699$	6.53376e7	+	2.76056e8i	0.191307	+	0.808287i
$700$	6.15271e8			1.79379
$701$			2.46070e8i			0.714339i	0.934040	+	0.357169i	$0.116258\pi$
$701$			2.46070e8i			0.714339i	−0.934040	+	0.357169i	$0.883742\pi$
$702$	−3.13813e8	−	3.74684e8i	−0.907110	−	1.08306i
$703$	−5.95406e8			−1.71375
$704$		−	3.14352e7i		−	0.0900944i
$705$	8.32216e7	−	1.96971e7i	0.237503	−	0.0562127i
$706$	1.10242e8			0.313281
$707$			8.52788e7i			0.241314i
$708$	7.77177e7	+	3.28363e8i	0.218988	+	0.925240i
$709$	5.27089e7			0.147892			0.0739461	−	0.997262i	$-0.476441\pi$
$709$	5.27089e7			0.147892			0.0739461	+	0.997262i	$0.476441\pi$
$710$		−	1.25525e8i		−	0.350717i
$711$	5.61458e7	−	2.81546e7i	0.156210	−	0.0783323i
$712$	8.40629e8			2.32897
$713$		−	1.03438e8i		−	0.285371i
$714$	2.41455e8	−	5.71481e7i	0.663348	−	0.157003i
$715$	−1.51320e8			−0.413979
$716$			4.77069e8i			1.29970i
$717$	3.10042e7	+	1.30995e8i	0.0841129	+	0.355383i
$718$	−9.74051e8			−2.63153
$719$			4.86858e8i			1.30983i	0.755702	+	0.654916i	$0.227296\pi$
$719$			4.86858e8i			1.30983i	−0.755702	+	0.654916i	$0.772704\pi$
$720$	5.90212e8	+	1.17700e9i	1.58129	+	3.15339i
$721$	−6.92930e7			−0.184877
$722$			1.83474e7i			0.0487487i
$723$	3.31354e8	−	7.84256e7i	0.876753	−	0.207512i
$724$	−1.58887e9			−4.18671
$725$			4.19386e8i			1.10052i
$726$	1.45593e7	+	6.15142e7i	0.0380479	+	0.160755i
$727$	−2.01150e8			−0.523500			−0.261750	−	0.965136i	$-0.584300\pi$
$727$	−2.01150e8			−0.523500			−0.261750	+	0.965136i	$0.584300\pi$
$728$		−	2.60998e8i		−	0.676461i
$729$	6.79727e7	−	3.81411e8i	0.175450	−	0.984488i
$730$	1.77952e9			4.57440
$731$		−	3.76455e8i		−	0.963742i
$732$	7.80353e8	−	1.84696e8i	1.98956	−	0.470895i
$733$	−1.27098e7			−0.0322720			−0.0161360	−	0.999870i	$-0.505136\pi$
$733$	−1.27098e7			−0.0322720			−0.0161360	+	0.999870i	$0.505136\pi$
$734$		−	4.93669e8i		−	1.24838i
$735$	1.39667e8	+	5.90103e8i	0.351748	+	1.48616i
$736$	4.55187e8			1.14171
$737$			4.95145e7i			0.123689i
$738$	−9.75917e8	+	4.89379e8i	−2.42797	+	1.21752i
$739$	5.44744e8			1.34977			0.674884	−	0.737923i	$-0.264193\pi$
$739$	5.44744e8			1.34977			0.674884	+	0.737923i	$0.264193\pi$
$740$		−	2.78622e9i		−	6.87575i
$741$	3.11918e8	−	7.38254e7i	0.766629	−	0.181448i
$742$	2.89899e7			0.0709635
$743$			3.93734e7i			0.0959922i	0.998848	+	0.0479961i	$0.0152835\pi$
$743$			3.93734e7i			0.0959922i	−0.998848	+	0.0479961i	$0.984716\pi$
$744$	7.08872e7	+	2.99503e8i	0.172127	+	0.727249i
$745$	−2.38177e8			−0.576012
$746$			1.22027e9i			2.93927i
$747$	−1.61761e8	−	3.22582e8i	−0.388071	−	0.773889i
$748$	2.96328e8			0.708057
$749$			3.90583e6i			0.00929539i
$750$	−1.47414e9	+	3.48904e8i	−3.49427	+	0.827032i
$751$	3.21343e8			0.758663			0.379332	−	0.925261i	$-0.376154\pi$
$751$	3.21343e8			0.758663			0.379332	+	0.925261i	$0.376154\pi$
$752$			1.17393e8i			0.276049i
$753$	−3.37565e7	−	1.42624e8i	−0.0790630	−	0.334047i
$754$	3.14533e8			0.733757
$755$		−	4.97667e8i		−	1.15637i
$756$	2.80422e8	−	2.34865e8i	0.649002	−	0.543567i
$757$	4.04530e8			0.932530			0.466265	−	0.884645i	$-0.345599\pi$
$757$	4.04530e8			0.932530			0.466265	+	0.884645i	$0.345599\pi$
$758$		−	8.42980e8i		−	1.93557i
$759$	−1.15908e8	+	2.74335e7i	−0.265088	+	0.0627416i
$760$	−1.85876e9			−4.23430
$761$		−	8.72186e7i		−	0.197904i	−0.995092	−	0.0989521i	$-0.968451\pi$
$761$		−	8.72186e7i		−	0.197904i	0.995092	−	0.0989521i	$-0.0315491\pi$
$762$	−6.40362e7	−	2.70557e8i	−0.144731	−	0.611497i
$763$	−4.28759e7			−0.0965251
$764$		−	1.70808e9i		−	3.83026i
$765$	−7.20979e8	+	3.61539e8i	−1.61042	+	0.807552i
$766$	−1.45247e9			−3.23164
$767$			1.44887e8i			0.321102i
$768$	7.09000e8	−	1.67808e8i	1.56517	−	0.370449i
$769$	4.94555e8			1.08752			0.543758	−	0.839242i	$-0.317001\pi$
$769$	4.94555e8			1.08752			0.543758	+	0.839242i	$0.317001\pi$
$770$		−	1.62447e8i		−	0.355826i
$771$	−1.31335e8	−	5.54902e8i	−0.286562	−	1.21075i
$772$	3.54722e8			0.770967
$773$			1.72074e8i			0.372542i	0.982498	+	0.186271i	$0.0596403\pi$
$773$			1.72074e8i			0.372542i	−0.982498	+	0.186271i	$0.940360\pi$
$774$	−3.56827e8	−	7.11582e8i	−0.769546	−	1.53462i
$775$	−3.11534e8			−0.669269
$776$			1.76998e9i			3.78777i
$777$	−2.83900e8	+	6.71940e7i	−0.605204	+	0.143241i
$778$	1.12139e9			2.38133
$779$		−	7.16010e8i		−	1.51463i
$780$	3.45468e8	+	1.45963e9i	0.727989	+	3.07580i
$781$	−1.56970e7			−0.0329507
$782$			8.00904e8i			1.67479i
$783$	1.60090e8	+	1.91143e8i	0.333488	+	0.398174i
$784$	−8.32401e8			−1.72737
$785$			3.25053e8i			0.671963i
$786$	2.53815e8	−	6.00735e7i	0.522697	−	0.123713i
$787$	−2.46369e8			−0.505431			−0.252715	−	0.967541i	$-0.581324\pi$
$787$	−2.46369e8			−0.505431			−0.252715	+	0.967541i	$0.581324\pi$
$788$		−	1.00958e9i		−	2.06330i
$789$	1.46196e8	+	6.17690e8i	0.297650	+	1.25759i
$790$	−2.76499e8			−0.560805
$791$			1.53663e8i			0.310485i
$792$	3.16812e8	−	1.58867e8i	0.637715	−	0.319786i
$793$	3.44323e8			0.690472
$794$		−	5.88605e8i		−	1.17588i
$795$	−9.17000e7	+	2.17038e7i	−0.182502	+	0.0431950i
$796$	−3.17982e8			−0.630468
$797$			1.23150e7i			0.0243253i	0.999926	+	0.0121626i	$0.00387159\pi$
$797$			1.23150e7i			0.0243253i	−0.999926	+	0.0121626i	$0.996128\pi$
$798$	7.92538e7	+	3.34853e8i	0.155959	+	0.658940i
$799$	−7.19097e7			−0.140977
$800$		−	1.37094e9i		−	2.67761i
$801$	2.26754e8	+	4.52192e8i	0.441223	+	0.879884i
$802$	−1.67424e8			−0.324559
$803$		−	2.22530e8i		−	0.429776i
$804$	4.77616e8	−	1.13043e8i	0.918990	−	0.217509i
$805$	3.06091e8			0.586763
$806$			2.33646e8i			0.446225i
$807$	−2.00793e8	−	8.48365e8i	−0.382057	−	1.61422i
$808$	8.19047e8			1.55265
$809$		−	1.61781e8i		−	0.305550i	−0.988261	−	0.152775i	$-0.951179\pi$
$809$		−	1.61781e8i		−	0.305550i	0.988261	−	0.152775i	$-0.0488209\pi$
$810$	−1.02012e9	+	1.36677e9i	−1.91953	+	2.57183i
$811$	−9.04677e8			−1.69602			−0.848010	−	0.529980i	$-0.822199\pi$
$811$	−9.04677e8			−1.69602			−0.848010	+	0.529980i	$0.822199\pi$
$812$			2.35404e8i			0.439689i
$813$	−3.84452e8	+	9.09930e7i	−0.715436	+	0.169331i
$814$	−4.99769e8			−0.926607
$815$		−	2.65890e7i		−	0.0491166i
$816$	−2.54994e8	−	1.07737e9i	−0.469309	−	1.98287i
$817$	5.22073e8			0.957337
$818$			9.80950e8i			1.79220i
$819$	1.40396e8	−	7.04024e7i	0.255566	−	0.128155i
$820$	3.35059e9			6.07687
$821$		−	6.21457e8i		−	1.12301i	−0.827475	−	0.561503i	$-0.810223\pi$
$821$		−	6.21457e8i		−	1.12301i	0.827475	−	0.561503i	$-0.189777\pi$
$822$	9.16744e8	−	2.16977e8i	1.65057	−	0.390660i
$823$	1.52145e8			0.272935			0.136467	−	0.990645i	$-0.456425\pi$
$823$	1.52145e8			0.272935			0.136467	+	0.990645i	$0.456425\pi$
$824$			6.65514e8i			1.18953i
$825$	8.26245e7	+	3.49095e8i	0.147146	+	0.621700i
$826$	−1.55540e8			−0.275996
$827$			4.20731e7i			0.0743854i	0.999308	+	0.0371927i	$0.0118415\pi$
$827$			4.20731e7i			0.0743854i	−0.999308	+	0.0371927i	$0.988158\pi$
$828$	5.29246e8	+	1.05542e9i	0.932323	+	1.85923i
$829$	6.69117e8			1.17446			0.587230	−	0.809420i	$-0.300218\pi$
$829$	6.69117e8			1.17446			0.587230	+	0.809420i	$0.300218\pi$
$830$			1.58861e9i			2.77832i
$831$	−1.97945e8	+	4.68501e7i	−0.344938	+	0.0816408i
$832$	−1.33794e8			−0.232309
$833$		−	5.09893e8i		−	0.882154i
$834$	−4.50477e8	−	1.90330e9i	−0.776560	−	3.28102i
$835$	1.12633e9			1.93467
$836$			4.10952e8i			0.703352i
$837$	−1.41988e8	+	1.18921e8i	−0.242144	+	0.202806i
$838$	−1.86819e9			−3.17461
$839$			1.93911e7i			0.0328335i	0.999865	+	0.0164167i	$0.00522585\pi$
$839$			1.93911e7i			0.0328335i	−0.999865	+	0.0164167i	$0.994774\pi$
$840$	−8.86286e8	+	2.09768e8i	−1.49533	+	0.353917i
$841$	4.34366e8			0.730243
$842$			6.49841e8i			1.08861i
$843$	3.80539e7	+	1.60780e8i	0.0635208	+	0.268380i
$844$	−1.80910e9			−3.00909
$845$		−	4.21499e8i		−	0.698597i
$846$	−1.35925e8	+	6.81603e7i	−0.224485	+	0.112569i
$847$	−2.03141e7			−0.0334308
$848$		−	1.29352e8i		−	0.212122i
$849$	5.40654e7	−	1.27963e7i	0.0883479	−	0.0209104i
$850$	2.41217e9			3.92782
$851$		−	9.41692e8i		−	1.52799i
$852$	3.58369e7	+	1.51413e8i	0.0579444	+	0.244819i
$853$	1.59238e8			0.256567			0.128283	−	0.991738i	$-0.459053\pi$
$853$	1.59238e8			0.256567			0.128283	+	0.991738i	$0.459053\pi$
$854$			3.69641e8i			0.593480i
$855$	−5.01387e8	−	9.99863e8i	−0.802185	−	1.59971i
$856$	3.75129e7			0.0598080
$857$		−	3.00646e8i		−	0.477653i	−0.971062	−	0.238827i	$-0.923237\pi$
$857$		−	3.00646e8i		−	0.477653i	0.971062	−	0.238827i	$-0.0767628\pi$
$858$	2.61816e8	−	6.19672e7i	0.414509	−	0.0981070i
$859$	1.14200e9			1.80172			0.900858	−	0.434113i	$-0.142938\pi$
$859$	1.14200e9			1.80172			0.900858	+	0.434113i	$0.142938\pi$
$860$			2.44306e9i			3.84095i
$861$	−8.08047e7	−	3.41406e8i	−0.126598	−	0.534886i
$862$	−8.71044e8			−1.35994
$863$			1.34281e8i			0.208920i	0.994529	+	0.104460i	$0.0333115\pi$
$863$			1.34281e8i			0.208920i	−0.994529	+	0.104460i	$0.966689\pi$
$864$	−5.23323e8	−	6.24831e8i	−0.811387	−	0.968772i
$865$	1.09127e8			0.168611
$866$			1.24377e9i			1.91508i
$867$	2.57564e7	−	6.09608e6i	0.0395210	−	0.00935392i
$868$	−1.74866e8			−0.267391
$869$			3.45764e7i			0.0526891i
$870$	−2.52796e8	−	1.06808e9i	−0.383894	−	1.62198i
$871$	2.10743e8			0.318933
$872$			4.11795e8i			0.621058i
$873$	−9.52111e8	+	4.77441e8i	−1.43102	+	0.717591i
$874$	−1.11070e9			−1.66366
$875$		−	4.86812e8i		−	0.726670i
$876$	−2.14652e9	+	5.08044e8i	−3.19318	+	0.755769i
$877$	2.90097e8			0.430075			0.215038	−	0.976606i	$-0.431013\pi$
$877$	2.90097e8			0.430075			0.215038	+	0.976606i	$0.431013\pi$
$878$			1.88712e9i			2.78815i
$879$	2.13408e8	+	9.01665e8i	0.314228	+	1.32763i
$880$	−7.24833e8			−1.06363
$881$			6.85229e8i			1.00209i	0.865420	+	0.501047i	$0.167052\pi$
$881$			6.85229e8i			1.00209i	−0.865420	+	0.501047i	$0.832948\pi$
$882$	−4.83308e8	−	9.63810e8i	−0.704398	−	1.40471i
$883$	−7.49126e8			−1.08811			−0.544055	−	0.839050i	$-0.683112\pi$
$883$	−7.49126e8			−1.08811			−0.544055	+	0.839050i	$0.683112\pi$
$884$		−	1.26123e9i		−	1.82573i
$885$	4.92001e8	−	1.16448e8i	0.709800	−	0.167997i
$886$	−2.07448e9			−2.98268
$887$		−	9.12381e7i		−	0.130739i	−0.997861	−	0.0653696i	$-0.979177\pi$
$887$		−	9.12381e7i		−	0.130739i	0.997861	−	0.0653696i	$-0.0208226\pi$
$888$	6.45355e8	+	2.72667e9i	0.921636	+	3.89398i
$889$	8.93472e7			0.127167
$890$		−	2.22689e9i		−	3.15885i
$891$	1.70916e8	+	1.27567e8i	0.241629	+	0.180345i
$892$	−5.60081e8			−0.789144
$893$		−	9.97253e7i		−	0.140040i
$894$	4.12098e8	−	9.75363e7i	0.576750	−	0.136507i
$895$	7.14813e8			0.997065
$896$			1.90638e8i			0.265024i
$897$	1.16762e8	+	4.93328e8i	0.161780	+	0.683532i
$898$	3.45664e8			0.477338
$899$		−	1.19194e8i		−	0.164049i
$900$	3.17873e9	−	1.59399e9i	4.36039	−	2.18654i
$901$	7.92357e7			0.108329
$902$		−	6.01001e8i		−	0.818946i
$903$	2.48933e8	−	5.89181e7i	0.338080	−	0.0800176i
$904$	1.47584e9			1.99771
$905$			2.38068e9i			3.21184i
$906$	2.03800e8	+	8.61071e8i	0.274044	+	1.15786i
$907$	−8.57017e8			−1.14860			−0.574299	−	0.818646i	$-0.694725\pi$
$907$	−8.57017e8			−1.14860			−0.574299	+	0.818646i	$0.694725\pi$
$908$		−	2.20801e9i		−	2.94947i
$909$	2.20932e8	+	4.40582e8i	0.294149	+	0.586591i
$910$	−6.91403e8			−0.917502
$911$		−	4.15062e8i		−	0.548981i	−0.961590	−	0.274491i	$-0.911491\pi$
$911$		−	4.15062e8i		−	0.548981i	0.961590	−	0.274491i	$-0.0885092\pi$
$912$	1.49411e9	−	3.53629e8i	1.96969	−	0.466190i
$913$	1.98656e8			0.261030
$914$		−	2.14714e9i		−	2.81204i
$915$	−2.76738e8	−	1.16924e9i	−0.361248	−	1.52630i
$916$	−2.62772e9			−3.41895
$917$			8.38183e7i			0.108700i
$918$	1.09939e9	−	9.20789e8i	1.42110	−	1.19023i
$919$	1.16986e9			1.50726			0.753628	−	0.657301i	$-0.228302\pi$
$919$	1.16986e9			1.50726			0.753628	+	0.657301i	$0.228302\pi$
$920$		−	2.93980e9i		−	3.77533i
$921$	2.68100e8	−	6.34545e7i	0.343176	−	0.0812238i
$922$	−7.66432e8			−0.977869
$923$			6.68095e7i			0.0849637i
$924$	4.63777e7	+	1.95949e8i	0.0587886	+	0.248386i
$925$	−2.83620e9			−3.58354
$926$			7.27112e8i			0.915732i
$927$	−3.57994e8	+	1.79518e8i	−0.449404	+	0.225356i
$928$	5.24523e8			0.656328
$929$			9.44517e7i			0.117805i	0.998264	+	0.0589023i	$0.0187601\pi$
$929$			9.44517e7i			0.117805i	−0.998264	+	0.0589023i	$0.981240\pi$
$930$	7.93407e8	−	1.87785e8i	0.986387	−	0.233460i
$931$	7.07127e8			0.876291
$932$			1.54800e9i			1.91215i
$933$	1.73202e8	+	7.31791e8i	0.213259	+	0.901035i
$934$	1.67435e9			2.05498
$935$		−	4.44002e8i		−	0.543188i
$936$	−6.76169e8	−	1.34841e9i	−0.824571	−	1.64435i
$937$	−1.10636e9			−1.34487			−0.672433	−	0.740158i	$-0.734751\pi$
$937$	−1.10636e9			−1.34487			−0.672433	+	0.740158i	$0.734751\pi$
$938$			2.26239e8i			0.274132i
$939$	−3.99870e8	+	9.46422e7i	−0.482972	+	0.114311i
$940$	4.66668e8			0.561855
$941$		−	1.42824e9i		−	1.71409i	−0.515243	−	0.857044i	$-0.672298\pi$
$941$		−	1.42824e9i		−	1.71409i	0.515243	−	0.857044i	$-0.327702\pi$
$942$	−1.33113e8	−	5.62412e8i	−0.159246	−	0.672824i
$943$	1.13244e9			1.35045
$944$			6.94018e8i			0.825001i
$945$	−3.51909e8	−	4.20168e8i	−0.416998	−	0.497884i
$946$	4.38215e8			0.517623
$947$		−	8.24347e7i		−	0.0970644i	−0.998822	−	0.0485322i	$-0.984546\pi$
$947$		−	8.24347e7i		−	0.0970644i	0.998822	−	0.0485322i	$-0.0154543\pi$
$948$	3.33523e8	−	7.89391e7i	0.391472	−	0.0926546i
$949$	−9.47131e8			−1.10818
$950$			3.34523e9i			3.90172i
$951$	−1.03285e7	−	4.36388e7i	−0.0120087	−	0.0507378i
$952$	7.65818e8			0.887595
$953$		−	5.89021e8i		−	0.680538i	−0.940328	−	0.340269i	$-0.889482\pi$
$953$		−	5.89021e8i		−	0.680538i	0.940328	−	0.340269i	$-0.110518\pi$
$954$	1.49773e8	−	7.51044e7i	0.172499	−	0.0865008i
$955$	−2.55929e9			−2.93839
$956$			7.34558e8i			0.840723i
$957$	−1.33564e8	+	3.16123e7i	−0.152389	+	0.0360678i
$958$	1.06989e9			1.21687
$959$			3.02740e8i			0.343253i
$960$	1.07533e8	+	4.54333e8i	0.121542	+	0.513523i
$961$	−7.98962e8			−0.900236
$962$			2.12711e9i			2.38927i
$963$	1.01189e7	+	2.01790e7i	0.0113306	+	0.0225954i
$964$	1.85808e9			2.07412
$965$		−	5.31495e8i		−	0.591449i
$966$	−5.29603e8	+	1.25348e8i	−0.587515	+	0.139054i
$967$	5.86488e8			0.648604			0.324302	−	0.945954i	$-0.394871\pi$
$967$	5.86488e8			0.648604			0.324302	+	0.945954i	$0.394871\pi$
$968$			1.95103e8i			0.215099i
$969$	2.16618e8	+	9.15227e8i	0.238080	+	1.00591i
$970$	4.68882e9			5.13746
$971$		−	1.40827e9i		−	1.53825i	−0.639098	−	0.769125i	$-0.720692\pi$
$971$		−	1.40827e9i		−	1.53825i	0.639098	−	0.769125i	$-0.279308\pi$
$972$	8.40298e8	−	1.93989e9i	0.915028	−	2.11241i
$973$	6.28534e8			0.682323
$974$		−	1.51138e9i		−	1.63567i
$975$	1.48581e9	−	3.51666e8i	1.60306	−	0.379416i
$976$	1.64933e9			1.77402
$977$			5.36961e6i			0.00575783i	0.999996	+	0.00287892i	$0.000916389\pi$
$977$			5.36961e6i			0.00575783i	−0.999996	+	0.00287892i	$0.999084\pi$
$978$	1.08885e7	+	4.60046e7i	0.0116399	+	0.0491796i
$979$	−2.78474e8			−0.296782
$980$			3.30902e9i			3.51578i
$981$	−2.21513e8	+	1.11079e8i	−0.234635	+	0.117659i
$982$	−3.07358e9			−3.24571
$983$			9.59942e8i			1.01061i	0.862940	+	0.505306i	$0.168620\pi$
$983$			9.59942e8i			1.01061i	−0.862940	+	0.505306i	$0.831380\pi$
$984$	−3.27898e9	+	7.76076e8i	−3.44154	+	0.814553i
$985$	−1.51270e9			−1.58286
$986$			9.22901e8i			0.962774i
$987$	−1.12544e7	−	4.75507e7i	−0.0117050	−	0.0494545i
$988$	1.74909e9			1.81360
$989$			8.25709e8i			0.853568i
$990$	−4.20852e8	−	8.39260e8i	−0.433734	−	0.864950i
$991$	4.76438e8			0.489537			0.244769	−	0.969582i	$-0.421288\pi$
$991$	4.76438e8			0.489537			0.244769	+	0.969582i	$0.421288\pi$
$992$			3.89634e8i			0.399137i
$993$	1.74282e9	−	4.12495e8i	1.77994	−	0.421280i
$994$	−7.17221e7			−0.0730287
$995$			4.76446e8i			0.483665i
$996$	−4.53539e8	−	1.91624e9i	−0.459026	−	1.93942i
$997$	−6.28492e8			−0.634182			−0.317091	−	0.948395i	$-0.602706\pi$
$997$	−6.28492e8			−0.634182			−0.317091	+	0.948395i	$0.602706\pi$
$998$		−	1.20393e9i		−	1.21118i
$999$	−1.29265e9	+	1.08265e9i	−1.29654	+	1.08591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.19	yes	20
3.2	odd	2	inner	33.7.b.a.23.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.2	✓	20	3.2	odd	2	inner
33.7.b.a.23.19	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+14.5373i q^{2} +(-26.2741 + 6.21862i) q^{3} -147.333 q^{4} +220.756i q^{5} +(-90.4019 - 381.955i) q^{6} +126.134 q^{7} -1211.44i q^{8} +(651.658 - 326.777i) q^{9} +O(q^{10})\)	\(q+14.5373i q^{2} +(-26.2741 + 6.21862i) q^{3} -147.333 q^{4} +220.756i q^{5} +(-90.4019 - 381.955i) q^{6} +126.134 q^{7} -1211.44i q^{8} +(651.658 - 326.777i) q^{9} -3209.19 q^{10} +401.312i q^{11} +(3871.04 - 916.208i) q^{12} +1708.06 q^{13} +1833.65i q^{14} +(-1372.79 - 5800.16i) q^{15} +8181.71 q^{16} +5011.77i q^{17} +(4750.46 + 9473.34i) q^{18} -6950.39 q^{19} -32524.6i q^{20} +(-3314.07 + 784.381i) q^{21} -5833.99 q^{22} -10992.7i q^{23} +(7533.47 + 31829.4i) q^{24} -33108.0 q^{25} +24830.5i q^{26} +(-15089.6 + 12638.2i) q^{27} -18583.8 q^{28} -12667.2i q^{29} +(84318.6 - 19956.7i) q^{30} +9409.63 q^{31} +41408.0i q^{32} +(-2495.60 - 10544.1i) q^{33} -72857.6 q^{34} +27844.9i q^{35} +(-96010.7 + 48145.1i) q^{36} +85665.0 q^{37} -101040. i q^{38} +(-44877.7 + 10621.8i) q^{39} +267432. q^{40} +103017. i q^{41} +(-11402.8 - 48177.6i) q^{42} -75114.2 q^{43} -59126.5i q^{44} +(72137.9 + 143857. i) q^{45} +159805. q^{46} +14348.2i q^{47} +(-214967. + 50879.0i) q^{48} -101739. q^{49} -481301. i q^{50} +(-31166.3 - 131680. i) q^{51} -251653. q^{52} -15809.9i q^{53} +(-183725. - 219362. i) q^{54} -88591.8 q^{55} -152804. i q^{56} +(182615. - 43221.8i) q^{57} +184147. q^{58} +84825.4i q^{59} +(202258. + 854555. i) q^{60} +201587. q^{61} +136791. i q^{62} +(82196.4 - 41217.8i) q^{63} -78331.1 q^{64} +377063. i q^{65} +(153283. - 36279.3i) q^{66} +123382. q^{67} -738400. i q^{68} +(68359.6 + 288824. i) q^{69} -404789. q^{70} +39114.3i q^{71} +(-395870. - 789442. i) q^{72} -554508. q^{73} +1.24534e6i q^{74} +(869884. - 205886. i) q^{75} +1.02402e6 q^{76} +50619.2i q^{77} +(-154412. - 652401. i) q^{78} +86158.5 q^{79} +1.80616e6i q^{80} +(317874. - 425894. i) q^{81} -1.49759e6 q^{82} -495018. i q^{83} +(488272. - 115565. i) q^{84} -1.10638e6 q^{85} -1.09196e6i q^{86} +(78772.4 + 332819. i) q^{87} +486164. q^{88} +693910. i q^{89} +(-2.09129e6 + 1.04869e6i) q^{90} +215445. q^{91} +1.61959e6i q^{92} +(-247230. + 58514.9i) q^{93} -208583. q^{94} -1.53434e6i q^{95} +(-257501. - 1.08796e6i) q^{96} -1.46106e6 q^{97} -1.47901e6i q^{98} +(131140. + 261518. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Introduction

L-functions

Modular forms

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