LMFDB - Embedded newform 33.7.b.a.23.9

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			23.9
Root			$-2.50689i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50689i q^{2} +(23.0874 + 13.9990i) q^{3} +57.7155 q^{4} +201.357i q^{5} +(35.0940 - 57.8777i) q^{6} -481.867 q^{7} -305.128i q^{8} +(337.056 + 646.401i) q^{9} +O(q^{10})$	\(q-2.50689i q^{2} +(23.0874 + 13.9990i) q^{3} +57.7155 q^{4} +201.357i q^{5} +(35.0940 - 57.8777i) q^{6} -481.867 q^{7} -305.128i q^{8} +(337.056 + 646.401i) q^{9} +504.781 q^{10} +401.312i q^{11} +(1332.50 + 807.959i) q^{12} +552.107 q^{13} +1207.99i q^{14} +(-2818.80 + 4648.82i) q^{15} +2928.87 q^{16} -2698.35i q^{17} +(1620.46 - 844.964i) q^{18} +12145.9 q^{19} +11621.4i q^{20} +(-11125.1 - 6745.66i) q^{21} +1006.05 q^{22} -12453.3i q^{23} +(4271.48 - 7044.61i) q^{24} -24919.8 q^{25} -1384.07i q^{26} +(-1267.21 + 19642.2i) q^{27} -27811.2 q^{28} -20143.8i q^{29} +(11654.1 + 7066.43i) q^{30} +20739.8 q^{31} -26870.5i q^{32} +(-5617.96 + 9265.24i) q^{33} -6764.48 q^{34} -97027.5i q^{35} +(19453.4 + 37307.3i) q^{36} -15538.2 q^{37} -30448.5i q^{38} +(12746.7 + 7728.95i) q^{39} +61439.7 q^{40} +59542.8i q^{41} +(-16910.7 + 27889.4i) q^{42} -25066.0 q^{43} +23161.9i q^{44} +(-130158. + 67868.7i) q^{45} -31219.2 q^{46} +22475.9i q^{47} +(67619.9 + 41001.2i) q^{48} +114547. q^{49} +62471.2i q^{50} +(37774.2 - 62297.9i) q^{51} +31865.1 q^{52} -276472. i q^{53} +(49240.8 + 3176.77i) q^{54} -80807.0 q^{55} +147031. i q^{56} +(280418. + 170031. i) q^{57} -50498.3 q^{58} +245924. i q^{59} +(-162688. + 268309. i) q^{60} -23207.5 q^{61} -51992.5i q^{62} +(-162416. - 311480. i) q^{63} +120086. q^{64} +111171. i q^{65} +(23227.0 + 14083.6i) q^{66} +68142.9 q^{67} -155737. i q^{68} +(174334. - 287515. i) q^{69} -243238. q^{70} -572175. i q^{71} +(197235. - 102845. i) q^{72} -521489. q^{73} +38952.7i q^{74} +(-575333. - 348852. i) q^{75} +701007. q^{76} -193379. i q^{77} +(19375.7 - 31954.7i) q^{78} -468460. q^{79} +589749. i q^{80} +(-304227. + 435747. i) q^{81} +149268. q^{82} -92737.4i q^{83} +(-642089. - 389329. i) q^{84} +543333. q^{85} +62837.8i q^{86} +(281992. - 465067. i) q^{87} +122451. q^{88} +422007. i q^{89} +(170140. + 326291. i) q^{90} -266042. q^{91} -718751. i q^{92} +(478828. + 290336. i) q^{93} +56344.8 q^{94} +2.44567e6i q^{95} +(376161. - 620371. i) q^{96} +1.11090e6 q^{97} -287158. i q^{98} +(-259408. + 135265. 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 $

$2$		−	2.50689i		−	0.313362i	−0.987649	−	0.156681i	$-0.949921\pi$
$2$		−	2.50689i		−	0.313362i	0.987649	−	0.156681i	$-0.0500794\pi$
$3$	23.0874	+	13.9990i	0.855089	+	0.518481i
$3$	23.0874	+	13.9990i	0.855089	+	0.518481i
$4$	57.7155			0.901804
$5$			201.357i			1.61086i	0.592692	+	0.805429i	$0.298065\pi$
$5$			201.357i			1.61086i	−0.592692	+	0.805429i	$0.701935\pi$
$6$	35.0940	−	57.8777i	0.162472	−	0.267952i
$7$	−481.867			−1.40486			−0.702431	−	0.711752i	$-0.747902\pi$
$7$	−481.867			−1.40486			−0.702431	+	0.711752i	$0.747902\pi$
$8$		−	305.128i		−	0.595953i
$9$	337.056	+	646.401i	0.462354	+	0.886695i
$10$	504.781			0.504781
$11$			401.312i			0.301511i
$11$			401.312i			0.301511i
$12$	1332.50	+	807.959i	0.771123	+	0.467569i
$13$	552.107			0.251300			0.125650	−	0.992075i	$-0.459898\pi$
$13$	552.107			0.251300			0.125650	+	0.992075i	$0.459898\pi$
$14$			1207.99i			0.440230i
$15$	−2818.80	+	4648.82i	−0.835200	+	1.37743i
$16$	2928.87			0.715056
$17$		−	2698.35i		−	0.549227i	−0.961555	−	0.274614i	$-0.911450\pi$
$17$		−	2698.35i		−	0.549227i	0.961555	−	0.274614i	$-0.0885499\pi$
$18$	1620.46	−	844.964i	0.277856	−	0.144884i
$19$	12145.9			1.77080			0.885400	−	0.464830i	$-0.153885\pi$
$19$	12145.9			1.77080			0.885400	+	0.464830i	$0.153885\pi$
$20$			11621.4i			1.45268i
$21$	−11125.1	−	6745.66i	−1.20128	−	0.728394i
$22$	1006.05			0.0944821
$23$		−	12453.3i		−	1.02353i	−0.859124	−	0.511767i	$-0.828991\pi$
$23$		−	12453.3i		−	1.02353i	0.859124	−	0.511767i	$-0.171009\pi$
$24$	4271.48	−	7044.61i	0.308990	−	0.509593i
$25$	−24919.8			−1.59486
$26$		−	1384.07i		−	0.0787480i
$27$	−1267.21	+	19642.2i	−0.0643811	+	0.997925i
$28$	−27811.2			−1.26691
$29$		−	20143.8i		−	0.825936i	−0.910746	−	0.412968i	$-0.864492\pi$
$29$		−	20143.8i		−	0.825936i	0.910746	−	0.412968i	$-0.135508\pi$
$30$	11654.1	+	7066.43i	0.431633	+	0.261720i
$31$	20739.8			0.696177			0.348088	−	0.937462i	$-0.386831\pi$
$31$	20739.8			0.696177			0.348088	+	0.937462i	$0.386831\pi$
$32$		−	26870.5i		−	0.820024i
$33$	−5617.96	+	9265.24i	−0.156328	+	0.257819i
$34$	−6764.48			−0.172107
$35$		−	97027.5i		−	2.26303i
$36$	19453.4	+	37307.3i	0.416953	+	0.799626i
$37$	−15538.2			−0.306759			−0.153379	−	0.988167i	$-0.549016\pi$
$37$	−15538.2			−0.306759			−0.153379	+	0.988167i	$0.549016\pi$
$38$		−	30448.5i		−	0.554901i
$39$	12746.7	+	7728.95i	0.214884	+	0.130295i
$40$	61439.7			0.959996
$41$			59542.8i			0.863928i	0.901891	+	0.431964i	$0.142179\pi$
$41$			59542.8i			0.863928i	−0.901891	+	0.431964i	$0.857821\pi$
$42$	−16910.7	+	27889.4i	−0.228251	+	0.376436i
$43$	−25066.0			−0.315268			−0.157634	−	0.987498i	$-0.550387\pi$
$43$	−25066.0			−0.315268			−0.157634	+	0.987498i	$0.550387\pi$
$44$			23161.9i			0.271904i
$45$	−130158.	+	67868.7i	−1.42834	+	0.744787i
$46$	−31219.2			−0.320737
$47$			22475.9i			0.216483i	0.994125	+	0.108242i	$0.0345220\pi$
$47$			22475.9i			0.216483i	−0.994125	+	0.108242i	$0.965478\pi$
$48$	67619.9	+	41001.2i	0.611436	+	0.370743i
$49$	114547.			0.973635
$50$			62471.2i			0.499770i
$51$	37774.2	−	62297.9i	0.284764	−	0.469638i
$52$	31865.1			0.226624
$53$		−	276472.i		−	1.85705i	−0.371272	−	0.928524i	$-0.621078\pi$
$53$		−	276472.i		−	1.85705i	0.371272	−	0.928524i	$-0.378922\pi$
$54$	49240.8	+	3176.77i	0.312712	+	0.0201746i
$55$	−80807.0			−0.485692
$56$			147031.i			0.837231i
$57$	280418.	+	170031.i	1.51419	+	0.918127i
$58$	−50498.3			−0.258817
$59$			245924.i			1.19742i	0.800967	+	0.598708i	$0.204319\pi$
$59$			245924.i			1.19742i	−0.800967	+	0.598708i	$0.795681\pi$
$60$	−162688.	+	268309.i	−0.753187	+	1.24217i
$61$	−23207.5			−0.102244			−0.0511221	−	0.998692i	$-0.516280\pi$
$61$	−23207.5			−0.102244			−0.0511221	+	0.998692i	$0.516280\pi$
$62$		−	51992.5i		−	0.218155i
$63$	−162416.	−	311480.i	−0.649543	−	1.24568i
$64$	120086.			0.458091
$65$			111171.i			0.404809i
$66$	23227.0	+	14083.6i	0.0807906	+	0.0489872i
$67$	68142.9			0.226567			0.113283	−	0.993563i	$-0.463863\pi$
$67$	68142.9			0.226567			0.113283	+	0.993563i	$0.463863\pi$
$68$		−	155737.i		−	0.495295i
$69$	174334.	−	287515.i	0.530684	−	0.875213i
$70$	−243238.			−0.709148
$71$		−	572175.i		−	1.59865i	−0.600897	−	0.799326i	$-0.705190\pi$
$71$		−	572175.i		−	1.59865i	0.600897	−	0.799326i	$-0.294810\pi$
$72$	197235.	−	102845.i	0.528429	−	0.275541i
$73$	−521489.			−1.34053			−0.670265	−	0.742122i	$-0.733820\pi$
$73$	−521489.			−1.34053			−0.670265	+	0.742122i	$0.733820\pi$
$74$			38952.7i			0.0961264i
$75$	−575333.	−	348852.i	−1.36375	−	0.826908i
$76$	701007.			1.59692
$77$		−	193379.i		−	0.423582i
$78$	19375.7	−	31954.7i	0.0408294	−	0.0673365i
$79$	−468460.			−0.950149			−0.475074	−	0.879946i	$-0.657579\pi$
$79$	−468460.			−0.950149			−0.475074	+	0.879946i	$0.657579\pi$
$80$			589749.i			1.15185i
$81$	−304227.	+	435747.i	−0.572457	+	0.819935i
$82$	149268.			0.270722
$83$		−	92737.4i		−	0.162189i	−0.996706	−	0.0810944i	$-0.974158\pi$
$83$		−	92737.4i		−	0.162189i	0.996706	−	0.0810944i	$-0.0258415\pi$
$84$	−642089.	−	389329.i	−1.08332	−	0.656869i
$85$	543333.			0.884727
$86$			62837.8i			0.0987928i
$87$	281992.	−	465067.i	0.428232	−	0.706249i
$88$	122451.			0.179687
$89$			422007.i			0.598617i	0.954156	+	0.299309i	$0.0967560\pi$
$89$			422007.i			0.598617i	−0.954156	+	0.299309i	$0.903244\pi$
$90$	170140.	+	326291.i	0.233388	+	0.447587i
$91$	−266042.			−0.353042
$92$		−	718751.i		−	0.923028i
$93$	478828.	+	290336.i	0.595293	+	0.360955i
$94$	56344.8			0.0678375
$95$			2.44567e6i			2.85251i
$96$	376161.	−	620371.i	0.425167	−	0.701193i
$97$	1.11090e6			1.21720			0.608598	−	0.793479i	$-0.291732\pi$
$97$	1.11090e6			1.21720			0.608598	+	0.793479i	$0.291732\pi$
$98$		−	287158.i		−	0.305100i
$99$	−259408.	+	135265.i	−0.267349	+	0.139405i
$100$	−1.43826e6			−1.43826
$101$		−	239860.i		−	0.232805i	−0.993202	−	0.116403i	$-0.962864\pi$
$101$		−	239860.i		−	0.232805i	0.993202	−	0.116403i	$-0.0371363\pi$
$102$	−156174.	−	94696.0i	−0.147167	−	0.0892342i
$103$	759550.			0.695096			0.347548	−	0.937662i	$-0.387014\pi$
$103$	759550.			0.695096			0.347548	+	0.937662i	$0.387014\pi$
$104$		−	168463.i		−	0.149763i
$105$	1.35829e6	−	2.24011e6i	1.17334	−	1.93509i
$106$	−693086.			−0.581928
$107$			2.31959e6i			1.89347i	0.322009	+	0.946737i	$0.395642\pi$
$107$			2.31959e6i			1.89347i	−0.322009	+	0.946737i	$0.604358\pi$
$108$	−73137.8	+	1.13366e6i	−0.0580592	+	0.899933i
$109$	−1.26984e6			−0.980546			−0.490273	−	0.871569i	$-0.663103\pi$
$109$	−1.26984e6			−0.980546			−0.490273	+	0.871569i	$0.663103\pi$
$110$			202575.i			0.152197i
$111$	−358738.	−	217520.i	−0.262306	−	0.159049i
$112$	−1.41133e6			−1.00455
$113$			825684.i			0.572240i	0.958194	+	0.286120i	$0.0923656\pi$
$113$			825684.i			0.572240i	−0.958194	+	0.286120i	$0.907634\pi$
$114$	426249.	−	702977.i	0.287706	−	0.474490i
$115$	2.50757e6			1.64877
$116$		−	1.16261e6i		−	0.744833i
$117$	186091.	+	356883.i	0.116190	+	0.222827i
$118$	616506.			0.375225
$119$			1.30025e6i			0.771588i
$120$	1.41848e6	+	860094.i	0.820882	+	0.497740i
$121$	−161051.			−0.0909091
$122$			58178.7i			0.0320394i
$123$	−833540.	+	1.37469e6i	−0.447931	+	0.738736i
$124$	1.19701e6			0.627815
$125$		−	1.87157e6i		−	0.958243i
$126$	−780846.	+	407161.i	−0.390350	+	0.203542i
$127$	2.99803e6			1.46361			0.731804	−	0.681515i	$-0.238678\pi$
$127$	2.99803e6			1.46361			0.731804	+	0.681515i	$0.238678\pi$
$128$		−	2.02076e6i		−	0.963572i
$129$	−578708.	−	350899.i	−0.269582	−	0.163460i
$130$	278693.			0.126852
$131$		−	2.14096e6i		−	0.952347i	−0.879351	−	0.476173i	$-0.842024\pi$
$131$		−	2.14096e6i		−	0.952347i	0.879351	−	0.476173i	$-0.157976\pi$
$132$	−324243.	+	534748.i	−0.140977	+	0.232502i
$133$	−5.85272e6			−2.48773
$134$		−	170827.i		−	0.0709974i
$135$	−3.95509e6	−	255163.i	−1.60752	−	0.103709i
$136$	−823342.			−0.327313
$137$		−	1.28758e6i		−	0.500740i	−0.968150	−	0.250370i	$-0.919448\pi$
$137$		−	1.28758e6i		−	0.500740i	0.968150	−	0.250370i	$-0.0805522\pi$
$138$	−720771.	−	437038.i	−0.274258	−	0.166296i
$139$	−3.11413e6			−1.15956			−0.579779	−	0.814774i	$-0.696861\pi$
$139$	−3.11413e6			−1.15956			−0.579779	+	0.814774i	$0.696861\pi$
$140$		−	5.59999e6i		−	2.04081i
$141$	−314640.	+	518911.i	−0.112242	+	0.185112i
$142$	−1.43438e6			−0.500957
$143$			221567.i			0.0757699i
$144$	987193.	+	1.89322e6i	0.330609	+	0.634036i
$145$	4.05609e6			1.33047
$146$			1.30732e6i			0.420071i
$147$	2.64460e6	+	1.60355e6i	0.832545	+	0.504812i
$148$	−896797.			−0.276636
$149$		−	1.33075e6i		−	0.402287i	−0.979562	−	0.201144i	$-0.935534\pi$
$149$		−	1.33075e6i		−	0.402287i	0.979562	−	0.201144i	$-0.0644658\pi$
$150$	−874534.	+	1.44230e6i	−0.259121	+	0.427348i
$151$	5.93495e6			1.72380			0.861899	−	0.507081i	$-0.169275\pi$
$151$	5.93495e6			1.72380			0.861899	+	0.507081i	$0.169275\pi$
$152$		−	3.70606e6i		−	1.05531i
$153$	1.74422e6	−	909496.i	0.486997	−	0.253937i
$154$	−484781.			−0.132734
$155$			4.17611e6i			1.12144i
$156$	735683.	+	446080.i	0.193784	+	0.117500i
$157$	−4.99753e6			−1.29139			−0.645693	−	0.763597i	$-0.723431\pi$
$157$	−4.99753e6			−1.29139			−0.645693	+	0.763597i	$0.723431\pi$
$158$			1.17438e6i			0.297740i
$159$	3.87033e6	−	6.38302e6i	0.962845	−	1.58794i
$160$	5.41058e6			1.32094
$161$			6.00086e6i			1.43792i
$162$	1.09237e6	+	762666.i	0.256936	+	0.179386i
$163$	−2.20861e6			−0.509983			−0.254991	−	0.966943i	$-0.582073\pi$
$163$	−2.20861e6			−0.509983			−0.254991	+	0.966943i	$0.582073\pi$
$164$			3.43654e6i			0.779094i
$165$	−1.86562e6	−	1.13122e6i	−0.415310	−	0.251822i
$166$	−232483.			−0.0508238
$167$		−	1.04901e6i		−	0.225233i	−0.993639	−	0.112616i	$-0.964077\pi$
$167$		−	1.04901e6i		−	0.225233i	0.993639	−	0.112616i	$-0.0359231\pi$
$168$	−2.05829e6	+	3.39457e6i	−0.434089	+	0.715907i
$169$	−4.52199e6			−0.936848
$170$		−	1.36208e6i		−	0.277240i
$171$	4.09386e6	+	7.85113e6i	0.818737	+	1.57016i
$172$	−1.44670e6			−0.284310
$173$		−	5.02965e6i		−	0.971402i	−0.874125	−	0.485701i	$-0.838564\pi$
$173$		−	5.02965e6i		−	0.971402i	0.874125	−	0.485701i	$-0.161436\pi$
$174$	−1.16587e6	−	706925.i	−0.221311	−	0.134192i
$175$	1.20080e7			2.24056
$176$			1.17539e6i			0.215597i
$177$	−3.44269e6	+	5.67775e6i	−0.620838	+	1.02390i
$178$	1.05793e6			0.187584
$179$		−	2.80786e6i		−	0.489572i	−0.969577	−	0.244786i	$-0.921282\pi$
$179$		−	2.80786e6i		−	0.489572i	0.969577	−	0.244786i	$-0.0787177\pi$
$180$	−7.51211e6	+	3.91708e6i	−1.28808	+	0.671652i
$181$	−760944.			−0.128327			−0.0641634	−	0.997939i	$-0.520438\pi$
$181$	−760944.			−0.128327			−0.0641634	+	0.997939i	$0.520438\pi$
$182$			666940.i			0.110630i
$183$	−535801.	−	324882.i	−0.0874279	−	0.0530117i
$184$	−3.79986e6			−0.609978
$185$		−	3.12874e6i		−	0.494145i
$186$	727843.	−	1.20037e6i	0.113109	−	0.186542i
$187$	1.08288e6			0.165598
$188$			1.29721e6i			0.195225i
$189$	610629.	−	9.46492e6i	0.0904465	−	1.40195i
$190$	6.13103e6			0.893867
$191$			5.88975e6i			0.845272i	0.906299	+	0.422636i	$0.138895\pi$
$191$			5.88975e6i			0.845272i	−0.906299	+	0.422636i	$0.861105\pi$
$192$	2.77247e6	+	1.68108e6i	0.391709	+	0.237512i
$193$	−2.82471e6			−0.392918			−0.196459	−	0.980512i	$-0.562944\pi$
$193$	−2.82471e6			−0.392918			−0.196459	+	0.980512i	$0.562944\pi$
$194$		−	2.78491e6i		−	0.381423i
$195$	−1.55628e6	+	2.56665e6i	−0.209886	+	0.346148i
$196$	6.61115e6			0.878029
$197$		−	6.45234e6i		−	0.843954i	−0.906607	−	0.421977i	$-0.861336\pi$
$197$		−	6.45234e6i		−	0.843954i	0.906607	−	0.421977i	$-0.138664\pi$
$198$	339094.	+	650309.i	0.0436842	+	0.0837769i
$199$	−3.44258e6			−0.436843			−0.218421	−	0.975855i	$-0.570091\pi$
$199$	−3.44258e6			−0.436843			−0.218421	+	0.975855i	$0.570091\pi$
$200$			7.60371e6i			0.950464i
$201$	1.57324e6	+	953932.i	0.193735	+	0.117471i
$202$	−601303.			−0.0729523
$203$			9.70662e6i			1.16033i
$204$	2.18016e6	−	3.59556e6i	0.256801	−	0.423522i
$205$	−1.19894e7			−1.39167
$206$		−	1.90411e6i		−	0.217816i
$207$	8.04986e6	−	4.19748e6i	0.907564	−	0.473236i
$208$	1.61705e6			0.179694
$209$			4.87430e6i			0.533916i
$210$	−5.61573e6	−	3.40508e6i	−0.606385	−	0.367680i
$211$	−1.07715e7			−1.14664			−0.573321	−	0.819331i	$-0.694345\pi$
$211$	−1.07715e7			−1.14664			−0.573321	+	0.819331i	$0.694345\pi$
$212$		−	1.59567e7i		−	1.67469i
$213$	8.00988e6	−	1.32100e7i	0.828872	−	1.36699i
$214$	5.81496e6			0.593342
$215$		−	5.04722e6i		−	0.507851i
$216$	5.99337e6	+	386662.i	0.594716	+	0.0383681i
$217$	−9.99384e6			−0.978032
$218$			3.18334e6i			0.307266i
$219$	−1.20398e7	−	7.30032e6i	−1.14627	−	0.695040i
$220$	−4.66382e6			−0.437999
$221$		−	1.48978e6i		−	0.138021i
$222$	−545299.	+	899317.i	−0.0498398	+	0.0821966i
$223$	1.42533e6			0.128529			0.0642643	−	0.997933i	$-0.479530\pi$
$223$	1.42533e6			0.128529			0.0642643	+	0.997933i	$0.479530\pi$
$224$			1.29480e7i			1.15202i
$225$	−8.39936e6	−	1.61082e7i	−0.737392	−	1.41416i
$226$	2.06990e6			0.179318
$227$			1.12780e6i			0.0964175i	0.998837	+	0.0482088i	$0.0153513\pi$
$227$			1.12780e6i			0.0964175i	−0.998837	+	0.0482088i	$0.984649\pi$
$228$	1.61844e7	+	9.81340e6i	1.36550	+	0.827971i
$229$	6.66978e6			0.555399			0.277699	−	0.960668i	$-0.410428\pi$
$229$	6.66978e6			0.555399			0.277699	+	0.960668i	$0.410428\pi$
$230$		−	6.28622e6i		−	0.516661i
$231$	2.70711e6	−	4.46462e6i	0.219619	−	0.362200i
$232$	−6.14642e6			−0.492219
$233$		−	9.36350e6i		−	0.740236i	−0.928985	−	0.370118i	$-0.879317\pi$
$233$		−	9.36350e6i		−	0.740236i	0.928985	−	0.370118i	$-0.120683\pi$
$234$	894667.	−	466511.i	0.0698255	−	0.0364095i
$235$	−4.52569e6			−0.348724
$236$			1.41936e7i			1.07984i
$237$	−1.08155e7	−	6.55798e6i	−0.812462	−	0.492634i
$238$	3.25958e6			0.241786
$239$			1.29811e7i			0.950860i	0.879754	+	0.475430i	$0.157707\pi$
$239$			1.29811e7i			0.950860i	−0.879754	+	0.475430i	$0.842293\pi$
$240$	−8.25589e6	+	1.36158e7i	−0.597214	+	0.984937i
$241$	1.24968e7			0.892790			0.446395	−	0.894836i	$-0.352708\pi$
$241$	1.24968e7			0.892790			0.446395	+	0.894836i	$0.352708\pi$
$242$			403738.i			0.0284874i
$243$	−1.31238e7	+	5.80139e6i	−0.914623	+	0.404309i
$244$	−1.33943e6			−0.0922042
$245$			2.30649e7i			1.56839i
$246$	3.44620e6	+	2.08960e6i	0.231492	+	0.140364i
$247$	6.70585e6			0.445003
$248$		−	6.32829e6i		−	0.414889i
$249$	1.29823e6	−	2.14107e6i	0.0840919	−	0.138686i
$250$	−4.69182e6			−0.300277
$251$			1.65273e7i			1.04516i	0.852591	+	0.522579i	$0.175030\pi$
$251$			1.65273e7i			1.04516i	−0.852591	+	0.522579i	$0.824970\pi$
$252$	−9.37394e6	−	1.79772e7i	−0.585761	−	1.12336i
$253$	4.99767e6			0.308607
$254$		−	7.51575e6i		−	0.458639i
$255$	1.25441e7	+	7.60612e6i	0.756520	+	0.458714i
$256$	2.61967e6			0.156145
$257$		−	2.63674e7i		−	1.55335i	−0.629903	−	0.776674i	$-0.716905\pi$
$257$		−	2.63674e7i		−	1.55335i	0.629903	−	0.776674i	$-0.283095\pi$
$258$	−879666.	+	1.45076e6i	−0.0512222	+	0.0844767i
$259$	7.48737e6			0.430953
$260$			6.41628e6i			0.365059i
$261$	1.30209e7	−	6.78958e6i	0.732354	−	0.381875i
$262$	−5.36716e6			−0.298429
$263$			3.25172e7i			1.78750i	0.448568	+	0.893749i	$0.351934\pi$
$263$			3.25172e7i			1.78750i	−0.448568	+	0.893749i	$0.648066\pi$
$264$	2.82708e6	+	1.71420e6i	0.153648	+	0.0931641i
$265$	5.56696e7			2.99144
$266$			1.46722e7i			0.779559i
$267$	−5.90767e6	+	9.74304e6i	−0.310372	+	0.511871i
$268$	3.93290e6			0.204319
$269$		−	8.22286e6i		−	0.422441i	−0.977438	−	0.211220i	$-0.932256\pi$
$269$		−	8.22286e6i		−	0.422441i	0.977438	−	0.211220i	$-0.0677438\pi$
$270$	−639666.	+	9.91500e6i	−0.0324984	+	0.503734i
$271$	−6.86173e6			−0.344767			−0.172383	−	0.985030i	$-0.555147\pi$
$271$	−6.86173e6			−0.344767			−0.172383	+	0.985030i	$0.555147\pi$
$272$		−	7.90312e6i		−	0.392728i
$273$	−6.14223e6	−	3.72433e6i	−0.301883	−	0.183046i
$274$	−3.22782e6			−0.156913
$275$		−	1.00006e7i		−	0.480870i
$276$	1.00618e7	−	1.65941e7i	0.478573	−	0.789271i
$277$	−1.31363e7			−0.618064			−0.309032	−	0.951052i	$-0.600005\pi$
$277$	−1.31363e7			−0.618064			−0.309032	+	0.951052i	$0.600005\pi$
$278$			7.80679e6i			0.363361i
$279$	6.99048e6	+	1.34062e7i	0.321880	+	0.617297i
$280$	−2.96058e7			−1.34866
$281$			5.20327e6i			0.234508i	0.993102	+	0.117254i	$0.0374091\pi$
$281$			5.20327e6i			0.234508i	−0.993102	+	0.117254i	$0.962591\pi$
$282$	1.30085e6	+	788770.i	0.0580071	+	0.0351725i
$283$	−8.17964e6			−0.360890			−0.180445	−	0.983585i	$-0.557754\pi$
$283$	−8.17964e6			−0.360890			−0.180445	+	0.983585i	$0.557754\pi$
$284$		−	3.30234e7i		−	1.44167i
$285$	−3.42369e7	+	5.64641e7i	−1.47897	+	2.43915i
$286$	555445.			0.0237434
$287$		−	2.86917e7i		−	1.21370i
$288$	1.73691e7	−	9.05688e6i	0.727111	−	0.379141i
$289$	1.68565e7			0.698350
$290$		−	1.01682e7i		−	0.416917i
$291$	2.56478e7	+	1.55515e7i	1.04081	+	0.631093i
$292$	−3.00980e7			−1.20890
$293$		−	1.14315e7i		−	0.454464i	−0.973841	−	0.227232i	$-0.927032\pi$
$293$		−	1.14315e7i		−	0.454464i	0.973841	−	0.227232i	$-0.0729676\pi$
$294$	4.01992e6	−	6.62973e6i	0.158189	−	0.260888i
$295$	−4.95186e7			−1.92887
$296$			4.74115e6i			0.182814i
$297$	−7.88263e6	−	508547.i	−0.300886	−	0.0194116i
$298$	−3.33604e6			−0.126061
$299$		−	6.87558e6i		−	0.257215i
$300$	−3.32056e7	−	2.01341e7i	−1.22984	−	0.745709i
$301$	1.20785e7			0.442907
$302$		−	1.48783e7i		−	0.540172i
$303$	3.35779e6	−	5.53773e6i	0.120705	−	0.199069i
$304$	3.55738e7			1.26622
$305$		−	4.67300e6i		−	0.164701i
$306$	−2.28001e6	−	4.37257e6i	−0.0795743	−	0.152606i
$307$	8.81781e6			0.304751			0.152376	−	0.988323i	$-0.451308\pi$
$307$	8.81781e6			0.304751			0.152376	+	0.988323i	$0.451308\pi$
$308$		−	1.11610e7i		−	0.381988i
$309$	1.75360e7	+	1.06329e7i	0.594369	+	0.360394i
$310$	1.04691e7			0.351417
$311$		−	1.82310e7i		−	0.606079i	−0.952978	−	0.303039i	$-0.901999\pi$
$311$		−	1.82310e7i		−	0.606079i	0.952978	−	0.303039i	$-0.0980013\pi$
$312$	2.35832e6	−	3.88938e6i	0.0776494	−	0.128061i
$313$	−1.76949e7			−0.577053			−0.288526	−	0.957472i	$-0.593165\pi$
$313$	−1.76949e7			−0.577053			−0.288526	+	0.957472i	$0.593165\pi$
$314$			1.25283e7i			0.404671i
$315$	6.27187e7	−	3.27037e7i	2.00662	−	1.04632i
$316$	−2.70374e7			−0.856848
$317$		−	1.13314e6i		−	0.0355717i	−0.999842	−	0.0177859i	$-0.994338\pi$
$317$		−	1.13314e6i		−	0.0355717i	0.999842	−	0.0177859i	$-0.00566171\pi$
$318$	−1.60015e7	−	9.70250e6i	−0.497600	−	0.301719i
$319$	8.08392e6			0.249029
$320$			2.41802e7i			0.737920i
$321$	−3.24719e7	+	5.35532e7i	−0.981731	+	1.61909i
$322$	1.50435e7			0.450591
$323$		−	3.27740e7i		−	0.972571i
$324$	−1.75586e7	+	2.51493e7i	−0.516244	+	0.739421i
$325$	−1.37584e7			−0.400790
$326$			5.53674e6i			0.159809i
$327$	−2.93172e7	−	1.77764e7i	−0.838454	−	0.508395i
$328$	1.81682e7			0.514861
$329$		−	1.08304e7i		−	0.304129i
$330$	−2.83584e6	+	4.67692e6i	−0.0789115	+	0.130142i
$331$	2.06005e7			0.568058			0.284029	−	0.958816i	$-0.408329\pi$
$331$	2.06005e7			0.568058			0.284029	+	0.958816i	$0.408329\pi$
$332$		−	5.35239e6i		−	0.146263i
$333$	−5.23726e6	−	1.00439e7i	−0.141831	−	0.272001i
$334$	−2.62977e6			−0.0705793
$335$			1.37211e7i			0.364967i
$336$	−3.25838e7	−	1.97571e7i	−0.858983	−	0.520842i
$337$	−5.00319e7			−1.30725			−0.653623	−	0.756820i	$-0.726752\pi$
$337$	−5.00319e7			−1.30725			−0.653623	+	0.756820i	$0.726752\pi$
$338$			1.13361e7i			0.293572i
$339$	−1.15587e7	+	1.90629e7i	−0.296696	+	0.489316i
$340$	3.13587e7			0.797851
$341$			8.32312e6i			0.209905i
$342$	1.96820e7	−	1.02629e7i	0.492028	−	0.256561i
$343$	1.49465e6			0.0370388
$344$			7.64833e6i			0.187885i
$345$	5.78933e7	+	3.51035e7i	1.40984	+	0.854856i
$346$	−1.26088e7			−0.304400
$347$			2.62111e7i			0.627332i	0.949533	+	0.313666i	$0.101557\pi$
$347$			2.62111e7i			0.627332i	−0.949533	+	0.313666i	$0.898443\pi$
$348$	1.62753e7	−	2.68416e7i	0.386182	−	0.636898i
$349$	−5.18051e7			−1.21870			−0.609349	−	0.792902i	$-0.708569\pi$
$349$	−5.18051e7			−1.21870			−0.609349	+	0.792902i	$0.708569\pi$
$350$		−	3.01028e7i		−	0.702107i
$351$	−699638.	+	1.08446e7i	−0.0161790	+	0.250779i
$352$	1.07835e7			0.247247
$353$		−	2.26249e7i		−	0.514354i	−0.966364	−	0.257177i	$-0.917208\pi$
$353$		−	2.26249e7i		−	0.514354i	0.966364	−	0.257177i	$-0.0827923\pi$
$354$	1.42335e7	+	8.63046e6i	0.320850	+	0.194547i
$355$	1.15212e8			2.57520
$356$			2.43563e7i			0.539836i
$357$	−1.82022e7	+	3.00193e7i	−0.400054	+	0.659776i
$358$	−7.03901e6			−0.153413
$359$		−	2.17659e7i		−	0.470429i	−0.971944	−	0.235214i	$-0.924421\pi$
$359$		−	2.17659e7i		−	0.470429i	0.971944	−	0.235214i	$-0.0755792\pi$
$360$	2.07086e7	+	3.97147e7i	0.443858	+	0.851224i
$361$	1.00477e8			2.13573
$362$			1.90761e6i			0.0402127i
$363$	−3.71825e6	−	2.25455e6i	−0.0777354	−	0.0471347i
$364$	−1.53548e7			−0.318375
$365$		−	1.05006e8i		−	2.15940i
$366$	−814444.	+	1.34320e6i	−0.0166118	+	0.0273966i
$367$	−7.29532e7			−1.47586			−0.737932	−	0.674875i	$-0.764197\pi$
$367$	−7.29532e7			−1.47586			−0.737932	+	0.674875i	$0.764197\pi$
$368$		−	3.64742e7i		−	0.731884i
$369$	−3.84885e7	+	2.00693e7i	−0.766041	+	0.399441i
$370$	−7.84342e6			−0.154846
$371$			1.33223e8i			2.60890i
$372$	2.76358e7	+	1.67569e7i	0.536838	+	0.325511i
$373$	−9.19915e7			−1.77264			−0.886322	−	0.463070i	$-0.846748\pi$
$373$	−9.19915e7			−1.77264			−0.886322	+	0.463070i	$0.846748\pi$
$374$		−	2.71467e6i		−	0.0518921i
$375$	2.62001e7	−	4.32096e7i	0.496831	−	0.819383i
$376$	6.85803e6			0.129014
$377$		−	1.11215e7i		−	0.207558i
$378$	−2.37276e7	−	1.53078e6i	−0.439317	−	0.0283425i
$379$	−2.80473e7			−0.515197			−0.257598	−	0.966252i	$-0.582931\pi$
$379$	−2.80473e7			−0.515197			−0.257598	+	0.966252i	$0.582931\pi$
$380$			1.41153e8i			2.57240i
$381$	6.92168e7	+	4.19694e7i	1.25152	+	0.758854i
$382$	1.47650e7			0.264876
$383$			9.67561e7i			1.72219i	0.508441	+	0.861097i	$0.330222\pi$
$383$			9.67561e7i			1.72219i	−0.508441	+	0.861097i	$0.669778\pi$
$384$	2.82886e7	−	4.66540e7i	0.499594	−	0.823940i
$385$	3.89383e7			0.682330
$386$			7.08124e6i			0.123125i
$387$	−8.44864e6	−	1.62027e7i	−0.145765	−	0.279546i
$388$	6.41162e7			1.09767
$389$			5.61374e7i			0.953681i	0.878990	+	0.476841i	$0.158218\pi$
$389$			5.61374e7i			0.953681i	−0.878990	+	0.476841i	$0.841782\pi$
$390$	6.43431e6	+	3.90143e6i	0.108470	+	0.0657703i
$391$	−3.36035e7			−0.562153
$392$		−	3.49515e7i		−	0.580241i
$393$	2.99713e7	−	4.94292e7i	0.493774	−	0.814341i
$394$	−1.61753e7			−0.264463
$395$		−	9.43279e7i		−	1.53056i
$396$	−1.49719e7	+	7.80686e6i	−0.241096	+	0.125716i
$397$	6.12583e7			0.979025			0.489512	−	0.871996i	$-0.337175\pi$
$397$	6.12583e7			0.979025			0.489512	+	0.871996i	$0.337175\pi$
$398$			8.63019e6i			0.136890i
$399$	−1.35124e8	−	8.19322e7i	−2.12723	−	1.28984i
$400$	−7.29867e7			−1.14042
$401$			2.53009e7i			0.392377i	0.980566	+	0.196188i	$0.0628564\pi$
$401$			2.53009e7i			0.392377i	−0.980566	+	0.196188i	$0.937144\pi$
$402$	2.39141e6	−	3.94395e6i	0.0368108	−	0.0607091i
$403$	1.14506e7			0.174950
$404$		−	1.38436e7i		−	0.209945i
$405$	−8.77408e7	−	6.12584e7i	−1.32080	−	0.922148i
$406$	2.43335e7			0.363602
$407$		−	6.23568e6i		−	0.0924912i
$408$	−1.90088e7	−	1.15260e7i	−0.279882	−	0.169706i
$409$	−4.76857e7			−0.696977			−0.348488	−	0.937313i	$-0.613305\pi$
$409$	−4.76857e7			−0.696977			−0.348488	+	0.937313i	$0.613305\pi$
$410$			3.00561e7i			0.436095i
$411$	1.80248e7	−	2.97268e7i	0.259624	−	0.428177i
$412$	4.38378e7			0.626840
$413$		−	1.18503e8i		−	1.68220i
$414$	−1.05226e7	−	2.01801e7i	−0.148294	−	0.284396i
$415$	1.86734e7			0.261263
$416$		−	1.48354e7i		−	0.206072i
$417$	−7.18971e7	−	4.35947e7i	−0.991524	−	0.601209i
$418$	1.22193e7			0.167309
$419$		−	9.72912e7i		−	1.32261i	−0.750118	−	0.661304i	$-0.770003\pi$
$419$		−	9.72912e7i		−	1.32261i	0.750118	−	0.661304i	$-0.229997\pi$
$420$	7.83942e7	−	1.29289e8i	1.05812	−	1.74508i
$421$	2.57188e7			0.344671			0.172335	−	0.985038i	$-0.444869\pi$
$421$	2.57188e7			0.344671			0.172335	+	0.985038i	$0.444869\pi$
$422$			2.70029e7i			0.359314i
$423$	−1.45285e7	+	7.57565e6i	−0.191955	+	0.100092i
$424$	−8.43592e7			−1.10671
$425$			6.72423e7i			0.875943i
$426$	−3.31162e7	−	2.00799e7i	−0.428363	−	0.259737i
$427$	1.11829e7			0.143639
$428$			1.33876e8i			1.70754i
$429$	−3.10172e6	+	5.11541e6i	−0.0392853	+	0.0647900i
$430$	−1.26528e7			−0.159141
$431$			1.45977e8i			1.82328i	0.410987	+	0.911641i	$0.365184\pi$
$431$			1.45977e8i			1.82328i	−0.410987	+	0.911641i	$0.634816\pi$
$432$	−3.71150e6	+	5.75293e7i	−0.0460361	+	0.713572i
$433$	1.92900e7			0.237612			0.118806	−	0.992917i	$-0.462093\pi$
$433$	1.92900e7			0.237612			0.118806	+	0.992917i	$0.462093\pi$
$434$			2.50535e7i			0.306478i
$435$	9.36446e7	+	5.67812e7i	1.13767	+	0.689822i
$436$	−7.32891e7			−0.884260
$437$		−	1.51257e8i		−	1.81248i
$438$	−1.83011e7	+	3.01826e7i	−0.217799	+	0.359198i
$439$	1.26509e8			1.49530			0.747648	−	0.664096i	$-0.231183\pi$
$439$	1.26509e8			1.49530			0.747648	+	0.664096i	$0.231183\pi$
$440$			2.46565e7i			0.289450i
$441$	3.86088e7	+	7.40434e7i	0.450164	+	0.863318i
$442$	−3.73472e6			−0.0432505
$443$		−	1.15456e8i		−	1.32802i	−0.747722	−	0.664012i	$-0.768852\pi$
$443$		−	1.15456e8i		−	1.32802i	0.747722	−	0.664012i	$-0.231148\pi$
$444$	−2.07047e7	−	1.25543e7i	−0.236549	−	0.143431i
$445$	−8.49741e7			−0.964288
$446$		−	3.57314e6i		−	0.0402759i
$447$	1.86291e7	−	3.07235e7i	0.208578	−	0.343991i
$448$	−5.78655e7			−0.643555
$449$		−	2.02190e7i		−	0.223368i	−0.993744	−	0.111684i	$-0.964376\pi$
$449$		−	2.02190e7i		−	0.223368i	0.993744	−	0.111684i	$-0.0356244\pi$
$450$	−4.03814e7	+	2.10563e7i	−0.443143	+	0.231071i
$451$	−2.38952e7			−0.260484
$452$			4.76547e7i			0.516049i
$453$	1.37023e8	+	8.30833e7i	1.47400	+	0.893757i
$454$	2.82728e6			0.0302136
$455$		−	5.35696e7i		−	0.568701i
$456$	5.18811e7	−	8.55632e7i	0.547160	−	0.902387i
$457$	1.08985e8			1.14188			0.570939	−	0.820992i	$-0.306579\pi$
$457$	1.08985e8			1.14188			0.570939	+	0.820992i	$0.306579\pi$
$458$		−	1.67204e7i		−	0.174041i
$459$	5.30015e7	+	3.41939e6i	0.548088	+	0.0353598i
$460$	1.44726e8			1.48687
$461$			5.05116e7i			0.515570i	0.966202	+	0.257785i	$0.0829927\pi$
$461$			5.05116e7i			0.515570i	−0.966202	+	0.257785i	$0.917007\pi$
$462$	−1.11923e7	−	6.78644e6i	−0.113500	−	0.0688203i
$463$	−1.09491e8			−1.10315			−0.551574	−	0.834126i	$-0.685972\pi$
$463$	−1.09491e8			−1.10315			−0.551574	+	0.834126i	$0.685972\pi$
$464$		−	5.89984e7i		−	0.590590i
$465$	−5.84614e7	+	9.64155e7i	−0.581447	+	0.958933i
$466$	−2.34733e7			−0.231962
$467$			1.55417e7i			0.152598i	0.997085	+	0.0762988i	$0.0243103\pi$
$467$			1.55417e7i			0.152598i	−0.997085	+	0.0762988i	$0.975690\pi$
$468$	1.07403e7	+	2.05976e7i	0.104780	+	0.200946i
$469$	−3.28358e7			−0.318295
$470$			1.13454e7i			0.109277i
$471$	−1.15380e8	−	6.99604e7i	−1.10425	−	0.669560i
$472$	7.50383e7			0.713604
$473$		−	1.00593e7i		−	0.0950568i
$474$	−1.64402e7	+	2.71134e7i	−0.154373	+	0.254594i
$475$	−3.02673e8			−2.82419
$476$			7.50444e7i			0.695821i
$477$	1.78712e8	−	9.31865e7i	1.64664	−	0.858614i
$478$	3.25422e7			0.297963
$479$		−	1.55260e7i		−	0.141271i	−0.997502	−	0.0706353i	$-0.977497\pi$
$479$		−	1.55260e7i		−	0.141271i	0.997502	−	0.0706353i	$-0.0225027\pi$
$480$	1.24916e8	+	7.57427e7i	1.12952	+	0.684884i
$481$	−8.57877e6			−0.0770886
$482$		−	3.13283e7i		−	0.279766i
$483$	−8.40061e7	+	1.38544e8i	−0.745537	+	1.22955i
$484$	−9.29514e6			−0.0819822
$485$			2.23688e8i			1.96073i
$486$	1.45435e7	+	3.29001e7i	0.126695	+	0.286608i
$487$	−1.03886e8			−0.899439			−0.449719	−	0.893170i	$-0.648476\pi$
$487$	−1.03886e8			−0.899439			−0.449719	+	0.893170i	$0.648476\pi$
$488$			7.08125e6i			0.0609327i
$489$	−5.09910e7	−	3.09183e7i	−0.436081	−	0.264417i
$490$	5.78213e7			0.491473
$491$		−	9.74122e7i		−	0.822942i	−0.911423	−	0.411471i	$-0.865015\pi$
$491$		−	9.74122e7i		−	0.822942i	0.911423	−	0.411471i	$-0.134985\pi$
$492$	−4.81081e7	+	7.93408e7i	−0.403946	+	0.666195i
$493$	−5.43549e7			−0.453626
$494$		−	1.68109e7i		−	0.139447i
$495$	−2.72365e7	−	5.22337e7i	−0.224562	−	0.430661i
$496$	6.07441e7			0.497805
$497$			2.75713e8i			2.24589i
$498$	−5.36743e6	−	3.25453e6i	−0.0434588	−	0.0263512i
$499$	2.41483e8			1.94350			0.971751	−	0.236009i	$-0.0758394\pi$
$499$	2.41483e8			1.94350			0.971751	+	0.236009i	$0.0758394\pi$
$500$		−	1.08018e8i		−	0.864148i
$501$	1.46851e7	−	2.42190e7i	0.116779	−	0.192594i
$502$	4.14323e7			0.327513
$503$		−	1.50642e8i		−	1.18370i	−0.806049	−	0.591849i	$-0.798398\pi$
$503$		−	1.50642e8i		−	1.18370i	0.806049	−	0.591849i	$-0.201602\pi$
$504$	−9.50411e7	+	4.95578e7i	−0.742369	+	0.387097i
$505$	4.82975e7			0.375016
$506$		−	1.25286e7i		−	0.0967058i
$507$	−1.04401e8	−	6.33033e7i	−0.801088	−	0.485738i
$508$	1.73033e8			1.31989
$509$		−	7.28067e7i		−	0.552101i	−0.961143	−	0.276050i	$-0.910974\pi$
$509$		−	7.28067e7i		−	0.552101i	0.961143	−	0.276050i	$-0.0890256\pi$
$510$	1.90677e7	−	3.14468e7i	0.143744	−	0.237065i
$511$	2.51289e8			1.88326
$512$		−	1.35896e8i		−	1.01250i
$513$	−1.53915e7	+	2.38572e8i	−0.114006	+	1.76713i
$514$	−6.61004e7			−0.486760
$515$			1.52941e8i			1.11970i
$516$	−3.34004e7	−	2.02523e7i	−0.243110	−	0.147409i
$517$	−9.01985e6			−0.0652721
$518$		−	1.87701e7i		−	0.135044i
$519$	7.04100e7	−	1.16121e8i	0.503654	−	0.830635i
$520$	3.39213e7			0.241247
$521$		−	5.29956e7i		−	0.374737i	−0.982290	−	0.187368i	$-0.940004\pi$
$521$		−	5.29956e7i		−	0.374737i	0.982290	−	0.187368i	$-0.0599958\pi$
$522$	−1.70208e7	−	3.26421e7i	−0.119665	−	0.229492i
$523$	1.77033e8			1.23751			0.618755	−	0.785584i	$-0.287637\pi$
$523$	1.77033e8			1.23751			0.618755	+	0.785584i	$0.287637\pi$
$524$		−	1.23567e8i		−	0.858830i
$525$	2.77234e8	+	1.68100e8i	1.91588	+	1.16169i
$526$	8.15171e7			0.560133
$527$		−	5.59633e7i		−	0.382359i
$528$	−1.64543e7	+	2.71367e7i	−0.111783	+	0.184355i
$529$	−7.05000e6			−0.0476236
$530$		−	1.39558e8i		−	0.937404i
$531$	−1.58966e8	+	8.28903e7i	−1.06174	+	0.553630i
$532$	−3.37793e8			−2.24344
$533$			3.28740e7i			0.217106i
$534$	2.44248e7	+	1.48099e7i	0.160401	+	0.0972587i
$535$	−4.67066e8			−3.05012
$536$		−	2.07923e7i		−	0.135023i
$537$	3.93072e7	−	6.48262e7i	0.253834	−	0.418628i
$538$	−2.06138e7			−0.132377
$539$			4.59691e7i			0.293562i
$540$	−2.28270e8	−	1.47268e7i	−1.44967	−	0.0935251i
$541$	−1.13670e8			−0.717882			−0.358941	−	0.933360i	$-0.616862\pi$
$541$	−1.13670e8			−0.717882			−0.358941	+	0.933360i	$0.616862\pi$
$542$			1.72016e7i			0.108037i
$543$	−1.75682e7	−	1.06525e7i	−0.109731	−	0.0665350i
$544$	−7.25062e7			−0.450379
$545$		−	2.55691e8i		−	1.57952i
$546$	−9.33650e6	+	1.53979e7i	−0.0573596	+	0.0945985i
$547$	1.56149e7			0.0954064			0.0477032	−	0.998862i	$-0.484810\pi$
$547$	1.56149e7			0.0954064			0.0477032	+	0.998862i	$0.484810\pi$
$548$		−	7.43132e7i		−	0.451569i
$549$	−7.82223e6	−	1.50013e7i	−0.0472730	−	0.0906594i
$550$	−2.50704e7			−0.150686
$551$		−	2.44664e8i		−	1.46257i
$552$	−8.77290e7	−	5.31943e7i	−0.521586	−	0.316262i
$553$	2.25736e8			1.33483
$554$			3.29313e7i			0.193678i
$555$	4.37992e7	−	7.22344e7i	0.256205	−	0.422538i
$556$	−1.79733e8			−1.04569
$557$			2.75890e8i			1.59651i	0.602322	+	0.798253i	$0.294242\pi$
$557$			2.75890e8i			1.59651i	−0.602322	+	0.798253i	$0.705758\pi$
$558$	3.36080e7	−	1.75244e7i	0.193437	−	0.100865i
$559$	−1.38391e7			−0.0792269
$560$		−	2.84181e8i		−	1.61819i
$561$	2.50009e7	+	1.51592e7i	0.141601	+	0.0858596i
$562$	1.30440e7			0.0734858
$563$			1.77235e7i			0.0993173i	0.998766	+	0.0496587i	$0.0158133\pi$
$563$			1.77235e7i			0.0993173i	−0.998766	+	0.0496587i	$0.984187\pi$
$564$	−1.81596e7	+	2.99492e7i	−0.101221	+	0.166935i
$565$	−1.66257e8			−0.921798
$566$			2.05055e7i			0.113089i
$567$	1.46597e8	−	2.09972e8i	0.804223	−	1.15189i
$568$	−1.74587e8			−0.952722
$569$		−	2.25650e7i		−	0.122489i	−0.998123	−	0.0612446i	$-0.980493\pi$
$569$		−	2.25650e7i		−	0.122489i	0.998123	−	0.0612446i	$-0.0195070\pi$
$570$	1.41550e8	+	8.58283e7i	0.764336	+	0.463453i
$571$	2.54089e8			1.36483			0.682415	−	0.730965i	$-0.260930\pi$
$571$	2.54089e8			1.36483			0.682415	+	0.730965i	$0.260930\pi$
$572$			1.27878e7i			0.0683297i
$573$	−8.24506e7	+	1.35979e8i	−0.438258	+	0.722783i
$574$	−7.19272e7			−0.380327
$575$			3.10334e8i			1.63240i
$576$	4.04757e7	+	7.76236e7i	0.211800	+	0.406187i
$577$	9.72955e7			0.506483			0.253242	−	0.967403i	$-0.418503\pi$
$577$	9.72955e7			0.506483			0.253242	+	0.967403i	$0.418503\pi$
$578$		−	4.22574e7i		−	0.218836i
$579$	−6.52151e7	−	3.95431e7i	−0.335979	−	0.203720i
$580$	2.34099e8			1.19982
$581$			4.46871e7i			0.227853i
$582$	3.89860e7	−	6.42964e7i	0.197761	−	0.326150i
$583$	1.10951e8			0.559921
$584$			1.59121e8i			0.798893i
$585$	−7.18609e7	+	3.74708e7i	−0.358943	+	0.187165i
$586$	−2.86575e7			−0.142412
$587$			7.54426e7i			0.372995i	0.982455	+	0.186497i	$0.0597136\pi$
$587$			7.54426e7i			0.372995i	−0.982455	+	0.186497i	$0.940286\pi$
$588$	1.52634e8	+	9.25494e7i	0.750792	+	0.455241i
$589$	2.51904e8			1.23279
$590$			1.24138e8i			0.604434i
$591$	9.03263e7	−	1.48968e8i	0.437574	−	0.721656i
$592$	−4.55094e7			−0.219349
$593$		−	1.48416e8i		−	0.711730i	−0.934537	−	0.355865i	$-0.884186\pi$
$593$		−	1.48416e8i		−	0.711730i	0.934537	−	0.355865i	$-0.115814\pi$
$594$	−1.27487e6	+	1.97609e7i	−0.00608286	+	0.0942861i
$595$	−2.61814e8			−1.24292
$596$		−	7.68046e7i		−	0.362784i
$597$	−7.94803e7	−	4.81927e7i	−0.373539	−	0.226495i
$598$	−1.72364e7			−0.0806013
$599$			2.37749e8i			1.10621i	0.833111	+	0.553105i	$0.186557\pi$
$599$			2.37749e8i			1.10621i	−0.833111	+	0.553105i	$0.813443\pi$
$600$	−1.06444e8	+	1.75550e8i	−0.492798	+	0.812731i
$601$	−2.09401e7			−0.0964618			−0.0482309	−	0.998836i	$-0.515358\pi$
$601$	−2.09401e7			−0.0964618			−0.0482309	+	0.998836i	$0.515358\pi$
$602$		−	3.02795e7i		−	0.138790i
$603$	2.29680e7	+	4.40476e7i	0.104754	+	0.200896i
$604$	3.42538e8			1.55453
$605$		−	3.24288e7i		−	0.146442i
$606$	−1.38825e7	−	8.41763e6i	−0.0623807	−	0.0378244i
$607$	1.18347e8			0.529164			0.264582	−	0.964363i	$-0.414766\pi$
$607$	1.18347e8			0.529164			0.264582	+	0.964363i	$0.414766\pi$
$608$		−	3.26367e8i		−	1.45210i
$609$	−1.35883e8	+	2.24101e8i	−0.601607	+	0.992181i
$610$	−1.17147e7			−0.0516110
$611$			1.24091e7i			0.0544023i
$612$	1.00668e8	−	5.24920e7i	0.439176	−	0.229002i
$613$	−8.77684e7			−0.381028			−0.190514	−	0.981684i	$-0.561015\pi$
$613$	−8.77684e7			−0.381028			−0.190514	+	0.981684i	$0.561015\pi$
$614$		−	2.21053e7i		−	0.0954975i
$615$	−2.76804e8	−	1.67839e8i	−1.19000	−	0.721553i
$616$	−5.90053e7			−0.252435
$617$			2.73054e8i			1.16250i	0.813725	+	0.581250i	$0.197436\pi$
$617$			2.73054e8i			1.16250i	−0.813725	+	0.581250i	$0.802564\pi$
$618$	2.66557e7	−	4.39610e7i	0.112934	−	0.186252i
$619$	1.79024e8			0.754814			0.377407	−	0.926047i	$-0.376816\pi$
$619$	1.79024e8			0.754814			0.377407	+	0.926047i	$0.376816\pi$
$620$			2.41026e8i			1.01132i
$621$	2.44611e8	+	1.57810e7i	1.02141	+	0.0658963i
$622$	−4.57031e7			−0.189922
$623$		−	2.03351e8i		−	0.840974i
$624$	3.73335e7	+	2.26371e7i	0.153654	+	0.0931679i
$625$	−1.25174e7			−0.0512712
$626$			4.43593e7i			0.180826i
$627$	−6.82353e7	+	1.12535e8i	−0.276826	+	0.456546i
$628$	−2.88435e8			−1.16458
$629$			4.19276e7i			0.168480i
$630$	−8.19848e7	−	1.57229e8i	−0.327877	−	0.628798i
$631$	9.34078e7			0.371788			0.185894	−	0.982570i	$-0.440482\pi$
$631$	9.34078e7			0.371788			0.185894	+	0.982570i	$0.440482\pi$
$632$			1.42940e8i			0.566244i
$633$	−2.48685e8	−	1.50790e8i	−0.980480	−	0.594512i
$634$	−2.84065e6			−0.0111468
$635$			6.03676e8i			2.35767i
$636$	2.23378e8	−	3.68399e8i	0.868298	−	1.43201i
$637$	6.32423e7			0.244675
$638$		−	2.02655e7i		−	0.0780362i
$639$	3.69855e8	−	1.92855e8i	1.41752	−	0.739144i
$640$	4.06894e8			1.55218
$641$			2.20028e8i			0.835418i	0.908581	+	0.417709i	$0.137167\pi$
$641$			2.20028e8i			0.835418i	−0.908581	+	0.417709i	$0.862833\pi$
$642$	1.34252e8	+	8.14036e7i	0.507360	+	0.307637i
$643$	−3.09988e8			−1.16604			−0.583018	−	0.812459i	$-0.698128\pi$
$643$	−3.09988e8			−1.16604			−0.583018	+	0.812459i	$0.698128\pi$
$644$			3.46343e8i			1.29673i
$645$	7.06560e7	−	1.16527e8i	0.263312	−	0.434258i
$646$	−8.21609e7			−0.304767
$647$		−	1.21038e8i		−	0.446898i	−0.974716	−	0.223449i	$-0.928268\pi$
$647$		−	1.21038e8i		−	0.446898i	0.974716	−	0.223449i	$-0.0717316\pi$
$648$	1.32958e8	+	9.28282e7i	0.488642	+	0.341158i
$649$	−9.86922e7			−0.361035
$650$			3.44908e7i			0.125592i
$651$	−2.30732e8	−	1.39904e8i	−0.836304	−	0.507091i
$652$	−1.27471e8			−0.459905
$653$		−	6.60557e7i		−	0.237231i	−0.992940	−	0.118615i	$-0.962154\pi$
$653$		−	6.60557e7i		−	0.237231i	0.992940	−	0.118615i	$-0.0378455\pi$
$654$	−4.45636e7	+	7.34951e7i	−0.159311	+	0.262739i
$655$	4.31098e8			1.53410
$656$			1.74393e8i			0.617757i
$657$	−1.75771e8	−	3.37091e8i	−0.619800	−	1.18864i
$658$	−2.71507e7			−0.0953023
$659$			4.37820e8i			1.52982i	0.644140	+	0.764908i	$0.277215\pi$
$659$			4.37820e8i			1.52982i	−0.644140	+	0.764908i	$0.722785\pi$
$660$	−1.07675e8	−	6.52887e7i	−0.374528	−	0.227094i
$661$	1.82446e7			0.0631726			0.0315863	−	0.999501i	$-0.489944\pi$
$661$	1.82446e7			0.0631726			0.0315863	+	0.999501i	$0.489944\pi$
$662$		−	5.16432e7i		−	0.178008i
$663$	2.08554e7	−	3.43951e7i	0.0715613	−	0.118020i
$664$	−2.82968e7			−0.0966569
$665$		−	1.17849e9i		−	4.00738i
$666$	−2.51791e7	+	1.31293e7i	−0.0852348	+	0.0444444i
$667$	−2.50857e8			−0.845374
$668$		−	6.05443e7i		−	0.203116i
$669$	3.29071e7	+	1.99531e7i	0.109903	+	0.0666397i
$670$	3.43973e7			0.114367
$671$		−	9.31343e6i		−	0.0308278i
$672$	−1.81260e8	+	2.98937e8i	−0.597301	+	0.985079i
$673$	−2.31772e8			−0.760355			−0.380178	−	0.924913i	$-0.624137\pi$
$673$	−2.31772e8			−0.760355			−0.380178	+	0.924913i	$0.624137\pi$
$674$			1.25425e8i			0.409641i
$675$	3.15787e7	−	4.89478e8i	0.102679	−	1.59156i
$676$	−2.60989e8			−0.844854
$677$			4.60368e8i			1.48368i	0.670578	+	0.741839i	$0.266046\pi$
$677$			4.60368e8i			1.48368i	−0.670578	+	0.741839i	$0.733954\pi$
$678$	4.77886e7	+	2.89765e7i	0.153333	+	0.0929731i
$679$	−5.35307e8			−1.70999
$680$		−	1.65786e8i		−	0.527256i
$681$	−1.57881e7	+	2.60381e7i	−0.0499907	+	0.0824455i
$682$	2.08652e7			0.0657763
$683$			4.58897e8i			1.44030i	0.693819	+	0.720150i	$0.255927\pi$
$683$			4.58897e8i			1.44030i	−0.693819	+	0.720150i	$0.744073\pi$
$684$	2.36279e8	+	4.53132e8i	0.738340	+	1.41598i
$685$	2.59263e8			0.806621
$686$		−	3.74693e6i		−	0.0116066i
$687$	1.53988e8	+	9.33702e7i	0.474915	+	0.287964i
$688$	−7.34149e7			−0.225434
$689$		−	1.52642e8i		−	0.466677i
$690$	8.80008e7	−	1.45132e8i	0.267879	−	0.441791i
$691$	−3.46070e8			−1.04889			−0.524445	−	0.851444i	$-0.675727\pi$
$691$	−3.46070e8			−1.04889			−0.524445	+	0.851444i	$0.675727\pi$
$692$		−	2.90288e8i		−	0.876015i
$693$	1.25000e8	−	6.51796e7i	0.375588	−	0.195845i
$694$	6.57085e7			0.196582
$695$		−	6.27052e8i		−	1.86788i
$696$	−1.41905e8	−	8.60437e7i	−0.420891	−	0.255206i
$697$	1.60667e8			0.474493
$698$			1.29870e8i			0.381894i
$699$	1.31080e8	−	2.16179e8i	0.383799	−	0.632968i
$700$	6.93049e8			2.02055
$701$		−	5.38685e8i		−	1.56380i	−0.623405	−	0.781899i	$-0.714251\pi$
$701$		−	5.38685e8i		−	1.56380i	0.623405	−	0.781899i	$-0.285749\pi$
$702$	2.71862e7	+	1.75392e6i	0.0785846	+	0.00506988i
$703$	−1.88726e8			−0.543208
$704$			4.81919e7i			0.138120i
$705$	−1.04486e8	−	6.33551e7i	−0.298190	−	0.180807i
$706$	−5.67181e7			−0.161179
$707$			1.15581e8i			0.327059i
$708$	−1.98697e8	+	3.27694e8i	−0.559874	+	0.923355i
$709$	3.67958e8			1.03243			0.516214	−	0.856460i	$-0.327341\pi$
$709$	3.67958e8			1.03243			0.516214	+	0.856460i	$0.327341\pi$
$710$		−	2.88824e8i		−	0.806970i
$711$	−1.57897e8	−	3.02813e8i	−0.439305	−	0.842493i
$712$	1.28766e8			0.356748
$713$		−	2.58280e8i		−	0.712561i
$714$	7.52553e7	+	4.56309e7i	0.206749	+	0.125362i
$715$	−4.46141e7			−0.122055
$716$		−	1.62057e8i		−	0.441498i
$717$	−1.81722e8	+	2.99699e8i	−0.493003	+	0.813070i
$718$	−5.45649e7			−0.147414
$719$		−	2.27862e8i		−	0.613036i	−0.951865	−	0.306518i	$-0.900836\pi$
$719$		−	2.27862e8i		−	0.613036i	0.951865	−	0.306518i	$-0.0991639\pi$
$720$	−3.81214e8	+	1.98778e8i	−1.02134	+	0.532564i
$721$	−3.66002e8			−0.976513
$722$		−	2.51886e8i		−	0.669257i
$723$	2.88520e8	+	1.74943e8i	0.763415	+	0.462895i
$724$	−4.39183e7			−0.115726
$725$			5.01978e8i			1.31726i
$726$	−5.65192e6	+	9.32126e6i	−0.0147702	+	0.0243593i
$727$	2.64477e8			0.688312			0.344156	−	0.938912i	$-0.388165\pi$
$727$	2.64477e8			0.688312			0.344156	+	0.938912i	$0.388165\pi$
$728$			8.11770e7i			0.210397i
$729$	−3.84209e8	−	4.97816e7i	−0.991710	−	0.128495i
$730$	−2.63238e8			−0.676675
$731$			6.76369e7i			0.173153i
$732$	−3.09240e7	−	1.87507e7i	−0.0788428	−	0.0478062i
$733$	1.14273e7			0.0290157			0.0145079	−	0.999895i	$-0.495382\pi$
$733$	1.14273e7			0.0290157			0.0145079	+	0.999895i	$0.495382\pi$
$734$			1.82886e8i			0.462479i
$735$	−3.22886e8	+	5.32509e8i	−0.813180	+	1.34111i
$736$	−3.34628e8			−0.839323
$737$			2.73465e7i			0.0683124i
$738$	5.03115e7	+	9.64867e7i	0.125170	+	0.240048i
$739$	6.75961e8			1.67490			0.837449	−	0.546515i	$-0.184046\pi$
$739$	6.75961e8			1.67490			0.837449	+	0.546515i	$0.184046\pi$
$740$		−	1.80577e8i		−	0.445622i
$741$	1.54821e8	+	9.38751e7i	0.380517	+	0.230726i
$742$	3.33975e8			0.817528
$743$			3.32233e8i			0.809983i	0.914320	+	0.404992i	$0.132726\pi$
$743$			3.32233e8i			0.809983i	−0.914320	+	0.404992i	$0.867274\pi$
$744$	8.85897e7	−	1.46104e8i	0.215112	−	0.354767i
$745$	2.67955e8			0.648028
$746$			2.30613e8i			0.555479i
$747$	5.99456e7	−	3.12577e7i	0.143812	−	0.0749887i
$748$	6.24989e7			0.149337
$749$		−	1.11773e9i		−	2.66007i
$750$	−1.08322e8	−	6.56808e7i	−0.256763	−	0.155688i
$751$	−6.94853e8			−1.64049			−0.820244	−	0.572014i	$-0.806162\pi$
$751$	−6.94853e8			−1.64049			−0.820244	+	0.572014i	$0.806162\pi$
$752$			6.58290e7i			0.154797i
$753$	−2.31366e8	+	3.81573e8i	−0.541895	+	0.893703i
$754$	−2.78805e7			−0.0650408
$755$			1.19505e9i			2.77679i
$756$	3.52427e7	−	5.46272e8i	0.0815651	−	1.26428i
$757$	2.55328e8			0.588587			0.294293	−	0.955715i	$-0.404916\pi$
$757$	2.55328e8			0.588587			0.294293	+	0.955715i	$0.404916\pi$
$758$			7.03115e7i			0.161443i
$759$	1.15383e8	+	6.99624e7i	0.263887	+	0.160007i
$760$	7.46242e8			1.69996
$761$			3.90811e8i			0.886773i	0.896331	+	0.443386i	$0.146223\pi$
$761$			3.90811e8i			0.886773i	−0.896331	+	0.443386i	$0.853777\pi$
$762$	1.05213e8	−	1.73519e8i	0.237796	−	0.392177i
$763$	6.11892e8			1.37753
$764$			3.39930e8i			0.762270i
$765$	1.83134e8	+	3.51211e8i	0.409057	+	0.784483i
$766$	2.42557e8			0.539670
$767$			1.35776e8i			0.300911i
$768$	6.04814e7	+	3.66728e7i	0.133518	+	0.0809581i
$769$	−7.50739e8			−1.65086			−0.825430	−	0.564505i	$-0.809067\pi$
$769$	−7.50739e8			−1.65086			−0.825430	+	0.564505i	$0.809067\pi$
$770$		−	9.76141e7i		−	0.213816i
$771$	3.69118e8	−	6.08756e8i	0.805382	−	1.32825i
$772$	−1.63029e8			−0.354335
$773$		−	1.07200e8i		−	0.232089i	−0.993244	−	0.116044i	$-0.962978\pi$
$773$		−	1.07200e8i		−	0.232089i	0.993244	−	0.116044i	$-0.0370215\pi$
$774$	−4.06184e7	+	2.11799e7i	−0.0875991	+	0.0456773i
$775$	−5.16831e8			−1.11031
$776$		−	3.38967e8i		−	0.725391i
$777$	1.72864e8	+	1.04816e8i	0.368503	+	0.223441i
$778$	1.40730e8			0.298847
$779$			7.23202e8i			1.52984i
$780$	−8.98214e7	+	1.48135e8i	−0.189276	+	0.312158i
$781$	2.29621e8			0.482012
$782$			8.42405e7i			0.176157i
$783$	3.95667e8	+	2.55264e7i	0.824222	+	0.0531747i
$784$	3.35494e8			0.696203
$785$		−	1.00629e9i		−	2.08024i
$786$	−1.23914e8	−	7.51349e7i	−0.255183	−	0.154730i
$787$	−2.01391e8			−0.413157			−0.206579	−	0.978430i	$-0.566233\pi$
$787$	−2.01391e8			−0.413157			−0.206579	+	0.978430i	$0.566233\pi$
$788$		−	3.72400e8i		−	0.761081i
$789$	−4.55208e8	+	7.50737e8i	−0.926784	+	1.52847i
$790$	−2.36470e8			−0.479618
$791$		−	3.97870e8i		−	0.803918i
$792$	4.12730e7	+	7.91527e7i	0.0830788	+	0.159327i
$793$	−1.28130e7			−0.0256940
$794$		−	1.53568e8i		−	0.306789i
$795$	1.28527e9	+	7.79319e8i	2.55795	+	1.55101i
$796$	−1.98690e8			−0.393947
$797$			1.99086e8i			0.393248i	0.980479	+	0.196624i	$0.0629978\pi$
$797$			1.99086e8i			0.393248i	−0.980479	+	0.196624i	$0.937002\pi$
$798$	−2.05395e8	+	3.38742e8i	−0.404187	+	0.666592i
$799$	6.06480e7			0.118898
$800$			6.69608e8i			1.30783i
$801$	−2.72785e8	+	1.42240e8i	−0.530791	+	0.276773i
$802$	6.34267e7			0.122956
$803$		−	2.09280e8i		−	0.404185i
$804$	9.08004e7	+	5.50566e7i	0.174711	+	0.105936i
$805$	−1.20832e9			−2.31629
$806$		−	2.87054e7i		−	0.0548225i
$807$	1.15112e8	−	1.89844e8i	0.219028	−	0.361225i
$808$	−7.31878e7			−0.138741
$809$		−	4.43391e8i		−	0.837416i	−0.908121	−	0.418708i	$-0.862483\pi$
$809$		−	4.43391e8i		−	0.837416i	0.908121	−	0.418708i	$-0.137517\pi$
$810$	−1.53568e8	+	2.19957e8i	−0.288966	+	0.413888i
$811$	2.15942e8			0.404832			0.202416	−	0.979300i	$-0.435121\pi$
$811$	2.15942e8			0.404832			0.202416	+	0.979300i	$0.435121\pi$
$812$			5.60222e8i			1.04639i
$813$	−1.58419e8	−	9.60573e7i	−0.294806	−	0.178755i
$814$	−1.56322e7			−0.0289832
$815$		−	4.44719e8i		−	0.821510i
$816$	1.10636e8	−	1.82462e8i	0.203622	−	0.335817i
$817$	−3.04449e8			−0.558276
$818$			1.19543e8i			0.218406i
$819$	−8.96713e7	−	1.71970e8i	−0.163231	−	0.313041i
$820$	−6.91973e8			−1.25501
$821$		−	9.55614e8i		−	1.72684i	−0.504483	−	0.863422i	$-0.668317\pi$
$821$		−	9.55614e8i		−	1.72684i	0.504483	−	0.863422i	$-0.331683\pi$
$822$	−7.45221e7	−	4.51863e7i	−0.134174	−	0.0813563i
$823$	9.27043e8			1.66303			0.831515	−	0.555502i	$-0.187474\pi$
$823$	9.27043e8			1.66303			0.831515	+	0.555502i	$0.187474\pi$
$824$		−	2.31760e8i		−	0.414244i
$825$	1.39998e8	−	2.30888e8i	0.249322	−	0.411186i
$826$	−2.97074e8			−0.527138
$827$			4.68439e8i			0.828202i	0.910231	+	0.414101i	$0.135904\pi$
$827$			4.68439e8i			0.828202i	−0.910231	+	0.414101i	$0.864096\pi$
$828$	4.64601e8	−	2.42259e8i	0.818445	−	0.426766i
$829$	3.74038e6			0.00656526			0.00328263	−	0.999995i	$-0.498955\pi$
$829$	3.74038e6			0.00656526			0.00328263	+	0.999995i	$0.498955\pi$
$830$		−	4.68121e7i		−	0.0818699i
$831$	−3.03283e8	−	1.83895e8i	−0.528499	−	0.320455i
$832$	6.63003e7			0.115119
$833$		−	3.09089e8i		−	0.534747i
$834$	−1.09287e8	+	1.80239e8i	−0.188396	+	0.310706i
$835$	2.11226e8			0.362818
$836$			2.81322e8i			0.481488i
$837$	−2.62818e7	+	4.07375e8i	−0.0448206	+	0.694732i
$838$	−2.43899e8			−0.414455
$839$		−	8.72130e8i		−	1.47671i	−0.674412	−	0.738355i	$-0.735603\pi$
$839$		−	8.72130e8i		−	1.47671i	0.674412	−	0.738355i	$-0.264397\pi$
$840$	−6.83521e8	−	4.14451e8i	−1.15322	−	0.699255i
$841$	1.89053e8			0.317830
$842$		−	6.44743e7i		−	0.108007i
$843$	−7.28406e7	+	1.20130e8i	−0.121588	+	0.200525i
$844$	−6.21681e8			−1.03405
$845$		−	9.10535e8i		−	1.50913i
$846$	1.89914e7	+	3.64213e7i	0.0313650	+	0.0601512i
$847$	7.76052e7			0.127715
$848$		−	8.09749e8i		−	1.32789i
$849$	−1.88847e8	−	1.14507e8i	−0.308593	−	0.187115i
$850$	1.68569e8			0.274487
$851$			1.93503e8i			0.313978i
$852$	4.62294e8	−	7.62424e8i	0.747480	−	1.23276i
$853$	−5.00857e7			−0.0806987			−0.0403494	−	0.999186i	$-0.512847\pi$
$853$	−5.00857e7			−0.0806987			−0.0403494	+	0.999186i	$0.512847\pi$
$854$		−	2.80344e7i		−	0.0450109i
$855$	−1.58088e9	+	8.24328e8i	−2.52931	+	1.31887i
$856$	7.07770e8			1.12842
$857$			6.33937e8i			1.00717i	0.863945	+	0.503586i	$0.167986\pi$
$857$			6.33937e8i			1.00717i	−0.863945	+	0.503586i	$0.832014\pi$
$858$	1.28238e7	+	7.77567e6i	0.0203027	+	0.0123105i
$859$	8.95651e8			1.41306			0.706528	−	0.707685i	$-0.250260\pi$
$859$	8.95651e8			1.41306			0.706528	+	0.707685i	$0.250260\pi$
$860$		−	2.91303e8i		−	0.457983i
$861$	4.01656e8	−	6.62418e8i	0.629281	−	1.03782i
$862$	3.65950e8			0.571347
$863$			3.87060e8i			0.602207i	0.953592	+	0.301103i	$0.0973549\pi$
$863$			3.87060e8i			0.602207i	−0.953592	+	0.301103i	$0.902645\pi$
$864$	5.27796e8	+	3.40507e7i	0.818323	+	0.0527940i
$865$	1.01276e9			1.56479
$866$		−	4.83579e7i		−	0.0744585i
$867$	3.89172e8	+	2.35974e8i	0.597151	+	0.362081i
$868$	−5.76799e8			−0.881993
$869$		−	1.87999e8i		−	0.286481i
$870$	1.42345e8	−	2.34757e8i	0.216164	−	0.356501i
$871$	3.76222e7			0.0569363
$872$			3.87462e8i			0.584359i
$873$	3.74436e8	+	7.18088e8i	0.562776	+	1.07928i
$874$	−3.79186e8			−0.567961
$875$			9.01848e8i			1.34620i
$876$	−6.94884e8	−	4.21342e8i	−1.03371	−	0.626790i
$877$	4.26008e8			0.631566			0.315783	−	0.948831i	$-0.397733\pi$
$877$	4.26008e8			0.631566			0.315783	+	0.948831i	$0.397733\pi$
$878$		−	3.17144e8i		−	0.468568i
$879$	1.60029e8	−	2.63923e8i	0.235631	−	0.388607i
$880$	−2.36673e8			−0.347297
$881$			1.32566e9i			1.93867i	0.245750	+	0.969333i	$0.420966\pi$
$881$			1.32566e9i			1.93867i	−0.245750	+	0.969333i	$0.579034\pi$
$882$	1.85619e8	−	9.67883e7i	0.270531	−	0.141064i
$883$	−4.42207e8			−0.642308			−0.321154	−	0.947027i	$-0.604071\pi$
$883$	−4.42207e8			−0.642308			−0.321154	+	0.947027i	$0.604071\pi$
$884$		−	8.59834e7i		−	0.124468i
$885$	−1.14326e9	−	6.93211e8i	−1.64935	−	1.00008i
$886$	−2.89436e8			−0.416152
$887$			6.78447e8i			0.972176i	0.873910	+	0.486088i	$0.161577\pi$
$887$			6.78447e8i			0.972176i	−0.873910	+	0.486088i	$0.838423\pi$
$888$	−6.63713e7	+	1.09461e8i	−0.0947855	+	0.156322i
$889$	−1.44465e9			−2.05617
$890$			2.13021e8i			0.302171i
$891$	−1.74870e8	−	1.22090e8i	−0.247220	−	0.172602i
$892$	8.22634e7			0.115908
$893$			2.72991e8i			0.383348i
$894$	−7.70205e7	−	4.67012e7i	−0.107794	−	0.0653605i
$895$	5.65383e8			0.788631
$896$			9.73737e8i			1.35369i
$897$	9.62513e7	−	1.58739e8i	0.133361	−	0.219942i
$898$	−5.06869e7			−0.0699949
$899$		−	4.17777e8i		−	0.574997i
$900$	−4.84773e8	−	9.29690e8i	−0.664984	−	1.27529i
$901$	−7.46018e8			−1.01994
$902$			5.99028e7i			0.0816258i
$903$	2.78861e8	+	1.69087e8i	0.378725	+	0.229639i
$904$	2.51939e8			0.341028
$905$		−	1.53222e8i		−	0.206716i
$906$	2.08281e8	−	3.43501e8i	0.280069	−	0.461895i
$907$	−2.43515e7			−0.0326365			−0.0163183	−	0.999867i	$-0.505194\pi$
$907$	−2.43515e7			−0.0326365			−0.0163183	+	0.999867i	$0.505194\pi$
$908$			6.50917e7i			0.0869497i
$909$	1.55045e8	−	8.08462e7i	0.206427	−	0.107639i
$910$	−1.34293e8			−0.178209
$911$		−	9.00865e8i		−	1.19153i	−0.803159	−	0.595764i	$-0.796849\pi$
$911$		−	9.00865e8i		−	1.19153i	0.803159	−	0.595764i	$-0.203151\pi$
$912$	8.21306e8	+	4.97997e8i	1.08273	+	0.656512i
$913$	3.72166e7			0.0489018
$914$		−	2.73215e8i		−	0.357821i
$915$	6.54173e7	−	1.07887e8i	0.0853943	−	0.140834i
$916$	3.84949e8			0.500861
$917$			1.03166e9i			1.33791i
$918$	8.57204e6	−	1.32869e8i	0.0110804	−	0.171750i
$919$	−1.29317e9			−1.66613			−0.833064	−	0.553176i	$-0.813416\pi$
$919$	−1.29317e9			−1.66613			−0.833064	+	0.553176i	$0.813416\pi$
$920$		−	7.65130e8i		−	0.982589i
$921$	2.03580e8	+	1.23441e8i	0.260590	+	0.158008i
$922$	1.26627e8			0.161560
$923$		−	3.15902e8i		−	0.401742i
$924$	1.56242e8	−	2.57678e8i	0.198054	−	0.326634i
$925$	3.87209e8			0.489238
$926$			2.74481e8i			0.345684i
$927$	2.56011e8	+	4.90974e8i	0.321380	+	0.616338i
$928$	−5.41274e8			−0.677287
$929$			1.34045e9i			1.67188i	0.548823	+	0.835939i	$0.315076\pi$
$929$			1.34045e9i			1.67188i	−0.548823	+	0.835939i	$0.684924\pi$
$930$	2.41704e8	+	1.46556e8i	0.300493	+	0.182203i
$931$	1.39128e9			1.72411
$932$		−	5.40419e8i		−	0.667548i
$933$	2.55215e8	−	4.20906e8i	0.314240	−	0.518251i
$934$	3.89614e7			0.0478183
$935$			2.18046e8i			0.266755i
$936$	1.08895e8	−	5.67816e7i	0.132794	−	0.0692437i
$937$	1.54489e9			1.87793			0.938966	−	0.344011i	$-0.111786\pi$
$937$	1.54489e9			1.87793			0.938966	+	0.344011i	$0.111786\pi$
$938$			8.23160e7i			0.0997414i
$939$	−4.08530e8	−	2.47711e8i	−0.493432	−	0.299191i
$940$	−2.61202e8			−0.314480
$941$			1.23318e9i			1.47999i	0.672613	+	0.739995i	$0.265172\pi$
$941$			1.23318e9i			1.47999i	−0.672613	+	0.739995i	$0.734828\pi$
$942$	−1.75383e8	+	2.89245e8i	−0.209814	+	0.346030i
$943$	7.41507e8			0.884261
$944$			7.20279e8i			0.856219i
$945$	1.90583e9	+	1.22955e8i	2.25834	+	0.145697i
$946$	−2.52175e7			−0.0297872
$947$		−	1.41860e8i		−	0.167036i	−0.996506	−	0.0835180i	$-0.973384\pi$
$947$		−	1.41860e8i		−	0.167036i	0.996506	−	0.0835180i	$-0.0266156\pi$
$948$	−6.24224e8	−	3.78497e8i	−0.732682	−	0.444260i
$949$	−2.87918e8			−0.336876
$950$			7.58770e8i			0.884992i
$951$	1.58628e7	−	2.61612e7i	0.0184433	−	0.0304170i
$952$	3.96742e8			0.459830
$953$		−	1.05871e9i		−	1.22321i	−0.791165	−	0.611603i	$-0.790525\pi$
$953$		−	1.05871e9i		−	1.22321i	0.791165	−	0.611603i	$-0.209475\pi$
$954$	−2.33609e8	−	4.48011e8i	−0.269057	−	0.515993i
$955$	−1.18594e9			−1.36161
$956$			7.49208e8i			0.857490i
$957$	1.86637e8	+	1.13167e8i	0.212942	+	0.129117i
$958$	−3.89220e7			−0.0442688
$959$			6.20442e8i			0.703470i
$960$	−3.38498e8	+	5.58257e8i	−0.382598	+	0.630988i
$961$	−4.57364e8			−0.515338
$962$			2.15061e7i			0.0241566i
$963$	−1.49938e9	+	7.81831e8i	−1.67893	+	0.875455i
$964$	7.21262e8			0.805122
$965$		−	5.68775e8i		−	0.632935i
$966$	3.47316e8	+	2.10594e8i	0.385295	+	0.233623i
$967$	−4.62442e8			−0.511420			−0.255710	−	0.966753i	$-0.582309\pi$
$967$	−4.62442e8			−0.511420			−0.255710	+	0.966753i	$0.582309\pi$
$968$			4.91411e7i			0.0541775i
$969$	4.58803e8	−	7.56666e8i	0.504260	−	0.831635i
$970$	5.60763e8			0.614418
$971$		−	5.11976e8i		−	0.559232i	−0.960112	−	0.279616i	$-0.909793\pi$
$971$		−	5.11976e8i		−	0.559232i	0.960112	−	0.279616i	$-0.0902071\pi$
$972$	−7.57448e8	+	3.34830e8i	−0.824811	+	0.364607i
$973$	1.50060e9			1.62902
$974$			2.60432e8i			0.281850i
$975$	−3.17645e8	−	1.92604e8i	−0.342711	−	0.207802i
$976$	−6.79716e7			−0.0731103
$977$		−	2.74228e8i		−	0.294055i	−0.989132	−	0.147027i	$-0.953029\pi$
$977$		−	2.74228e8i		−	0.294055i	0.989132	−	0.147027i	$-0.0469705\pi$
$978$	−7.75089e7	+	1.27829e8i	−0.0828581	+	0.136651i
$979$	−1.69356e8			−0.180490
$980$			1.33120e9i			1.41438i
$981$	−4.28006e8	−	8.20823e8i	−0.453359	−	0.869445i
$982$	−2.44202e8			−0.257878
$983$			7.55863e8i			0.795760i	0.917437	+	0.397880i	$0.130254\pi$
$983$			7.55863e8i			0.795760i	−0.917437	+	0.397880i	$0.869746\pi$
$984$	4.19456e8	+	2.54336e8i	0.440252	+	0.266946i
$985$	1.29923e9			1.35949
$986$			1.36262e8i			0.142149i
$987$	1.51615e8	−	2.50046e8i	0.157685	−	0.260057i
$988$	3.87031e8			0.401306
$989$			3.12155e8i			0.322687i
$990$	−1.30944e8	+	6.82790e7i	−0.134953	+	0.0703691i
$991$	−1.46942e9			−1.50981			−0.754907	−	0.655832i	$-0.772318\pi$
$991$	−1.46942e9			−1.50981			−0.754907	+	0.655832i	$0.772318\pi$
$992$		−	5.57290e8i		−	0.570882i
$993$	4.75611e8	+	2.88386e8i	0.485740	+	0.294528i
$994$	6.91183e8			0.703775
$995$		−	6.93189e8i		−	0.703692i
$996$	7.49280e7	−	1.23573e8i	0.0758344	−	0.125067i
$997$	−1.49044e9			−1.50394			−0.751968	−	0.659199i	$-0.770895\pi$
$997$	−1.49044e9			−1.50394			−0.751968	+	0.659199i	$0.770895\pi$
$998$		−	6.05372e8i		−	0.609019i
$999$	1.96903e7	−	3.05205e8i	0.0197495	−	0.306122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.9	✓	20
3.2	odd	2	inner	33.7.b.a.23.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.9	✓	20	1.1	even	1	trivial
33.7.b.a.23.12	yes	20	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-2.50689i q^{2} +(23.0874 + 13.9990i) q^{3} +57.7155 q^{4} +201.357i q^{5} +(35.0940 - 57.8777i) q^{6} -481.867 q^{7} -305.128i q^{8} +(337.056 + 646.401i) q^{9} +O(q^{10})\)	\(q-2.50689i q^{2} +(23.0874 + 13.9990i) q^{3} +57.7155 q^{4} +201.357i q^{5} +(35.0940 - 57.8777i) q^{6} -481.867 q^{7} -305.128i q^{8} +(337.056 + 646.401i) q^{9} +504.781 q^{10} +401.312i q^{11} +(1332.50 + 807.959i) q^{12} +552.107 q^{13} +1207.99i q^{14} +(-2818.80 + 4648.82i) q^{15} +2928.87 q^{16} -2698.35i q^{17} +(1620.46 - 844.964i) q^{18} +12145.9 q^{19} +11621.4i q^{20} +(-11125.1 - 6745.66i) q^{21} +1006.05 q^{22} -12453.3i q^{23} +(4271.48 - 7044.61i) q^{24} -24919.8 q^{25} -1384.07i q^{26} +(-1267.21 + 19642.2i) q^{27} -27811.2 q^{28} -20143.8i q^{29} +(11654.1 + 7066.43i) q^{30} +20739.8 q^{31} -26870.5i q^{32} +(-5617.96 + 9265.24i) q^{33} -6764.48 q^{34} -97027.5i q^{35} +(19453.4 + 37307.3i) q^{36} -15538.2 q^{37} -30448.5i q^{38} +(12746.7 + 7728.95i) q^{39} +61439.7 q^{40} +59542.8i q^{41} +(-16910.7 + 27889.4i) q^{42} -25066.0 q^{43} +23161.9i q^{44} +(-130158. + 67868.7i) q^{45} -31219.2 q^{46} +22475.9i q^{47} +(67619.9 + 41001.2i) q^{48} +114547. q^{49} +62471.2i q^{50} +(37774.2 - 62297.9i) q^{51} +31865.1 q^{52} -276472. i q^{53} +(49240.8 + 3176.77i) q^{54} -80807.0 q^{55} +147031. i q^{56} +(280418. + 170031. i) q^{57} -50498.3 q^{58} +245924. i q^{59} +(-162688. + 268309. i) q^{60} -23207.5 q^{61} -51992.5i q^{62} +(-162416. - 311480. i) q^{63} +120086. q^{64} +111171. i q^{65} +(23227.0 + 14083.6i) q^{66} +68142.9 q^{67} -155737. i q^{68} +(174334. - 287515. i) q^{69} -243238. q^{70} -572175. i q^{71} +(197235. - 102845. i) q^{72} -521489. q^{73} +38952.7i q^{74} +(-575333. - 348852. i) q^{75} +701007. q^{76} -193379. i q^{77} +(19375.7 - 31954.7i) q^{78} -468460. q^{79} +589749. i q^{80} +(-304227. + 435747. i) q^{81} +149268. q^{82} -92737.4i q^{83} +(-642089. - 389329. i) q^{84} +543333. q^{85} +62837.8i q^{86} +(281992. - 465067. i) q^{87} +122451. q^{88} +422007. i q^{89} +(170140. + 326291. i) q^{90} -266042. q^{91} -718751. i q^{92} +(478828. + 290336. i) q^{93} +56344.8 q^{94} +2.44567e6i q^{95} +(376161. - 620371. i) q^{96} +1.11090e6 q^{97} -287158. i q^{98} +(-259408. + 135265. 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

Varieties

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Representations

Groups

Database

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