LMFDB - Embedded newform 33.7.b.a.23.17

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			23.17
Root			$11.1144i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.1144i q^{2} +(-19.8885 + 18.2606i) q^{3} -59.5295 q^{4} -223.873i q^{5} +(-202.955 - 221.048i) q^{6} -152.100 q^{7} +49.6872i q^{8} +(62.1023 - 726.350i) q^{9} +O(q^{10})$	\(q+11.1144i q^{2} +(-19.8885 + 18.2606i) q^{3} -59.5295 q^{4} -223.873i q^{5} +(-202.955 - 221.048i) q^{6} -152.100 q^{7} +49.6872i q^{8} +(62.1023 - 726.350i) q^{9} +2488.21 q^{10} +401.312i q^{11} +(1183.95 - 1087.04i) q^{12} -1707.54 q^{13} -1690.50i q^{14} +(4088.05 + 4452.49i) q^{15} -4362.13 q^{16} -8377.54i q^{17} +(8072.93 + 690.229i) q^{18} +2284.74 q^{19} +13327.1i q^{20} +(3025.04 - 2777.44i) q^{21} -4460.33 q^{22} -14576.3i q^{23} +(-907.317 - 988.202i) q^{24} -34494.2 q^{25} -18978.2i q^{26} +(12028.5 + 15580.0i) q^{27} +9054.46 q^{28} +22114.1i q^{29} +(-49486.7 + 45436.2i) q^{30} -25055.8 q^{31} -45302.4i q^{32} +(-7328.18 - 7981.47i) q^{33} +93111.2 q^{34} +34051.2i q^{35} +(-3696.92 + 43239.2i) q^{36} -47629.7 q^{37} +25393.5i q^{38} +(33960.3 - 31180.6i) q^{39} +11123.6 q^{40} +17524.1i q^{41} +(30869.6 + 33621.5i) q^{42} +369.278 q^{43} -23889.9i q^{44} +(-162610. - 13903.0i) q^{45} +162007. q^{46} -11698.2i q^{47} +(86756.0 - 79655.0i) q^{48} -94514.5 q^{49} -383382. i q^{50} +(152979. + 166616. i) q^{51} +101649. q^{52} -191066. i q^{53} +(-173162. + 133689. i) q^{54} +89842.9 q^{55} -7557.44i q^{56} +(-45440.0 + 41720.7i) q^{57} -245785. q^{58} +141415. i q^{59} +(-243360. - 265055. i) q^{60} +178218. q^{61} -278480. i q^{62} +(-9445.79 + 110478. i) q^{63} +224332. q^{64} +382271. i q^{65} +(88709.1 - 81448.2i) q^{66} -60692.5 q^{67} +498710. i q^{68} +(266172. + 289901. i) q^{69} -378458. q^{70} +609914. i q^{71} +(36090.3 + 3085.69i) q^{72} +218017. q^{73} -529374. i q^{74} +(686037. - 629884. i) q^{75} -136009. q^{76} -61039.7i q^{77} +(346553. + 377447. i) q^{78} -571814. q^{79} +976563. i q^{80} +(-523728. - 90216.1i) q^{81} -194769. q^{82} -772199. i q^{83} +(-180079. + 165340. i) q^{84} -1.87551e6 q^{85} +4104.30i q^{86} +(-403817. - 439816. i) q^{87} -19940.0 q^{88} +808766. i q^{89} +(154524. - 1.80731e6i) q^{90} +259717. q^{91} +867720. i q^{92} +(498322. - 457534. i) q^{93} +130018. q^{94} -511492. i q^{95} +(827248. + 900995. i) q^{96} +377714. q^{97} -1.05047e6i q^{98} +(291493. + 24922.4i) 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 $

$2$			11.1144i			1.38930i	0.719349	+	0.694649i	$0.244440\pi$
$2$			11.1144i			1.38930i	−0.719349	+	0.694649i	$0.755560\pi$
$3$	−19.8885	+	18.2606i	−0.736610	+	0.676318i
$3$	−19.8885	+	18.2606i	−0.736610	+	0.676318i
$4$	−59.5295			−0.930148
$5$		−	223.873i		−	1.79099i	−0.445076	−	0.895493i	$-0.646823\pi$
$5$		−	223.873i		−	1.79099i	0.445076	−	0.895493i	$-0.353177\pi$
$6$	−202.955	−	221.048i	−0.939607	−	1.02337i
$7$	−152.100			−0.443441			−0.221721	−	0.975110i	$-0.571167\pi$
$7$	−152.100			−0.443441			−0.221721	+	0.975110i	$0.571167\pi$
$8$			49.6872i			0.0970453i
$9$	62.1023	−	726.350i	0.0851884	−	0.996365i
$10$	2488.21			2.48821
$11$			401.312i			0.301511i
$11$			401.312i			0.301511i
$12$	1183.95	−	1087.04i	0.685156	−	0.629076i
$13$	−1707.54			−0.777212			−0.388606	−	0.921404i	$-0.627043\pi$
$13$	−1707.54			−0.777212			−0.388606	+	0.921404i	$0.627043\pi$
$14$		−	1690.50i		−	0.616072i
$15$	4088.05	+	4452.49i	1.21128	+	1.31926i
$16$	−4362.13			−1.06497
$17$		−	8377.54i		−	1.70518i	−0.522582	−	0.852589i	$-0.675031\pi$
$17$		−	8377.54i		−	1.70518i	0.522582	−	0.852589i	$-0.324969\pi$
$18$	8072.93	+	690.229i	1.38425	+	0.118352i
$19$	2284.74			0.333101			0.166551	−	0.986033i	$-0.446737\pi$
$19$	2284.74			0.333101			0.166551	+	0.986033i	$0.446737\pi$
$20$			13327.1i			1.66588i
$21$	3025.04	−	2777.44i	0.326643	−	0.299907i
$22$	−4460.33			−0.418889
$23$		−	14576.3i		−	1.19802i	−0.800741	−	0.599010i	$-0.795561\pi$
$23$		−	14576.3i		−	1.19802i	0.800741	−	0.599010i	$-0.204439\pi$
$24$	−907.317	−	988.202i	−0.0656334	−	0.0714845i
$25$	−34494.2			−2.20763
$26$		−	18978.2i		−	1.07978i
$27$	12028.5	+	15580.0i	0.611109	+	0.791547i
$28$	9054.46			0.412466
$29$			22114.1i			0.906725i	0.891326	+	0.453362i	$0.149776\pi$
$29$			22114.1i			0.906725i	−0.891326	+	0.453362i	$0.850224\pi$
$30$	−49486.7	+	45436.2i	−1.83284	+	1.68282i
$31$	−25055.8			−0.841053			−0.420527	−	0.907280i	$-0.638155\pi$
$31$	−25055.8			−0.841053			−0.420527	+	0.907280i	$0.638155\pi$
$32$		−	45302.4i		−	1.38252i
$33$	−7328.18	−	7981.47i	−0.203917	−	0.222096i
$34$	93111.2			2.36900
$35$			34051.2i			0.794197i
$36$	−3696.92	+	43239.2i	−0.0792378	+	0.926767i
$37$	−47629.7			−0.940313			−0.470157	−	0.882583i	$-0.655803\pi$
$37$	−47629.7			−0.940313			−0.470157	+	0.882583i	$0.655803\pi$
$38$			25393.5i			0.462777i
$39$	33960.3	−	31180.6i	0.572502	−	0.525643i
$40$	11123.6			0.173807
$41$			17524.1i			0.254263i	0.991886	+	0.127131i	$0.0405770\pi$
$41$			17524.1i			0.254263i	−0.991886	+	0.127131i	$0.959423\pi$
$42$	30869.6	+	33621.5i	0.416661	+	0.453805i
$43$	369.278			0.00464460			0.00232230	−	0.999997i	$-0.499261\pi$
$43$	369.278			0.00464460			0.00232230	+	0.999997i	$0.499261\pi$
$44$		−	23889.9i		−	0.280450i
$45$	−162610.	−	13903.0i	−1.78447	−	0.152571i
$46$	162007.			1.66441
$47$		−	11698.2i		−	0.112674i	−0.998412	−	0.0563372i	$-0.982058\pi$
$47$		−	11698.2i		−	0.112674i	0.998412	−	0.0563372i	$-0.0179422\pi$
$48$	86756.0	−	79655.0i	0.784469	−	0.720260i
$49$	−94514.5			−0.803360
$50$		−	383382.i		−	3.06705i
$51$	152979.	+	166616.i	1.15324	+	1.25605i
$52$	101649.			0.722922
$53$		−	191066.i		−	1.28338i	−0.766963	−	0.641691i	$-0.778233\pi$
$53$		−	191066.i		−	1.28338i	0.766963	−	0.641691i	$-0.221767\pi$
$54$	−173162.	+	133689.i	−1.09969	+	0.849012i
$55$	89842.9			0.540002
$56$		−	7557.44i		−	0.0430339i
$57$	−45440.0	+	41720.7i	−0.245366	+	0.225282i
$58$	−245785.			−1.25971
$59$			141415.i			0.688557i	0.938868	+	0.344278i	$0.111876\pi$
$59$			141415.i			0.688557i	−0.938868	+	0.344278i	$0.888124\pi$
$60$	−243360.	−	265055.i	−1.12667	−	1.22710i
$61$	178218.			0.785167			0.392584	−	0.919716i	$-0.371581\pi$
$61$	178218.			0.785167			0.392584	+	0.919716i	$0.371581\pi$
$62$		−	278480.i		−	1.16847i
$63$	−9445.79	+	110478.i	−0.0377761	+	0.441830i
$64$	224332.			0.855757
$65$			382271.i			1.39198i
$66$	88709.1	−	81448.2i	0.308558	−	0.283302i
$67$	−60692.5			−0.201795			−0.100897	−	0.994897i	$-0.532171\pi$
$67$	−60692.5			−0.201795			−0.100897	+	0.994897i	$0.532171\pi$
$68$			498710.i			1.58607i
$69$	266172.	+	289901.i	0.810242	+	0.882474i
$70$	−378458.			−1.10338
$71$			609914.i			1.70409i	0.523465	+	0.852047i	$0.324639\pi$
$71$			609914.i			1.70409i	−0.523465	+	0.852047i	$0.675361\pi$
$72$	36090.3	+	3085.69i	0.0966925	+	0.00826713i
$73$	218017.			0.560430			0.280215	−	0.959937i	$-0.409594\pi$
$73$	218017.			0.560430			0.280215	+	0.959937i	$0.409594\pi$
$74$		−	529374.i		−	1.30637i
$75$	686037.	−	629884.i	1.62616	−	1.49306i
$76$	−136009.			−0.309833
$77$		−	61039.7i		−	0.133703i
$78$	346553.	+	377447.i	0.730274	+	0.795376i
$79$	−571814.			−1.15978			−0.579888	−	0.814697i	$-0.696904\pi$
$79$	−571814.			−1.15978			−0.579888	+	0.814697i	$0.696904\pi$
$80$			976563.i			1.90735i
$81$	−523728.	−	90216.1i	−0.985486	−	0.169757i
$82$	−194769.			−0.353247
$83$		−	772199.i		−	1.35050i	−0.737588	−	0.675251i	$-0.764035\pi$
$83$		−	772199.i		−	1.35050i	0.737588	−	0.675251i	$-0.235965\pi$
$84$	−180079.	+	165340.i	−0.303827	+	0.278958i
$85$	−1.87551e6			−3.05395
$86$			4104.30i			0.00645273i
$87$	−403817.	−	439816.i	−0.613234	−	0.667902i
$88$	−19940.0			−0.0292602
$89$			808766.i			1.14724i	0.819123	+	0.573618i	$0.194461\pi$
$89$			808766.i			1.14724i	−0.819123	+	0.573618i	$0.805539\pi$
$90$	154524.	−	1.80731e6i	0.211967	−	2.47917i
$91$	259717.			0.344648
$92$			867720.i			1.11434i
$93$	498322.	−	457534.i	0.619528	−	0.568819i
$94$	130018.			0.156538
$95$		−	511492.i		−	0.596579i
$96$	827248.	+	900995.i	0.935022	+	1.01838i
$97$	377714.			0.413854			0.206927	−	0.978356i	$-0.433654\pi$
$97$	377714.			0.413854			0.206927	+	0.978356i	$0.433654\pi$
$98$		−	1.05047e6i		−	1.11611i
$99$	291493.	+	24922.4i	0.300415	+	0.0256853i
$100$	2.05342e6			2.05342
$101$			171966.i			0.166908i	0.996512	+	0.0834542i	$0.0265952\pi$
$101$			171966.i			0.166908i	−0.996512	+	0.0834542i	$0.973405\pi$
$102$	−1.85184e6	+	1.70026e6i	−1.74503	+	1.60220i
$103$	1.37654e6			1.25973			0.629863	−	0.776706i	$-0.283111\pi$
$103$	1.37654e6			1.25973			0.629863	+	0.776706i	$0.283111\pi$
$104$		−	84842.6i		−	0.0754248i
$105$	−621795.	−	677226.i	−0.537130	−	0.585014i
$106$	2.12358e6			1.78300
$107$			48577.3i			0.0396535i	0.999803	+	0.0198268i	$0.00631147\pi$
$107$			48577.3i			0.0396535i	−0.999803	+	0.0198268i	$0.993689\pi$
$108$	−716047.	−	927470.i	−0.568422	−	0.736256i
$109$	1.93483e6			1.49404			0.747022	−	0.664800i	$-0.231483\pi$
$109$	1.93483e6			1.49404			0.747022	+	0.664800i	$0.231483\pi$
$110$			998548.i			0.750224i
$111$	947281.	−	869746.i	0.692644	−	0.635951i
$112$	663482.			0.472253
$113$		−	2.00243e6i		−	1.38778i	−0.720080	−	0.693891i	$-0.755895\pi$
$113$		−	2.00243e6i		−	1.38778i	0.720080	−	0.693891i	$-0.244105\pi$
$114$	−463700.	−	505038.i	−0.312984	−	0.340886i
$115$	−3.26325e6			−2.14564
$116$		−	1.31644e6i		−	0.843388i
$117$	−106042.	+	1.24027e6i	−0.0662095	+	0.774387i
$118$	−1.57174e6			−0.956610
$119$			1.27423e6i			0.756147i
$120$	−221232.	+	203124.i	−0.128028	+	0.117549i
$121$	−161051.			−0.0909091
$122$			1.98078e6i			1.09083i
$123$	−319999.	−	348527.i	−0.171963	−	0.187293i
$124$	1.49156e6			0.782304
$125$			4.22431e6i			2.16284i
$126$	−1.22790e6	−	104984.i	−0.613833	−	0.0524822i
$127$	68618.0			0.0334986			0.0167493	−	0.999860i	$-0.494668\pi$
$127$	68618.0			0.0334986			0.0167493	+	0.999860i	$0.494668\pi$
$128$		−	406044.i		−	0.193617i
$129$	−7344.38	+	6743.23i	−0.00342126	+	0.00314122i
$130$	−4.24871e6			−1.93387
$131$		−	3.94189e6i		−	1.75344i	−0.481002	−	0.876720i	$-0.659727\pi$
$131$		−	3.94189e6i		−	1.75344i	0.481002	−	0.876720i	$-0.340273\pi$
$132$	436243.	+	475133.i	0.189673	+	0.206582i
$133$	−347510.			−0.147711
$134$		−	674559.i		−	0.280353i
$135$	3.48795e6	−	2.69285e6i	1.41765	−	1.09449i
$136$	416256.			0.165479
$137$		−	955976.i		−	0.371779i	−0.982571	−	0.185890i	$-0.940483\pi$
$137$		−	955976.i		−	0.371779i	0.982571	−	0.185890i	$-0.0595167\pi$
$138$	−3.22206e6	+	2.95834e6i	−1.22602	+	1.12567i
$139$	−1.58125e6			−0.588783			−0.294392	−	0.955685i	$-0.595117\pi$
$139$	−1.58125e6			−0.588783			−0.294392	+	0.955685i	$0.595117\pi$
$140$		−	2.02705e6i		−	0.738721i
$141$	213616.	+	232659.i	0.0762037	+	0.0829971i
$142$	−6.77882e6			−2.36750
$143$		−	685254.i		−	0.234338i
$144$	−270898.	+	3.16843e6i	−0.0907233	+	1.06110i
$145$	4.95076e6			1.62393
$146$			2.42312e6i			0.778604i
$147$	1.87975e6	−	1.72589e6i	0.591763	−	0.543326i
$148$	2.83537e6			0.874630
$149$		−	757821.i		−	0.229091i	−0.993418	−	0.114545i	$-0.963459\pi$
$149$		−	757821.i		−	0.229091i	0.993418	−	0.114545i	$-0.0365412\pi$
$150$	7.00077e6	+	7.62487e6i	2.07430	+	2.25922i
$151$	2.87435e6			0.834851			0.417425	−	0.908711i	$-0.362932\pi$
$151$	2.87435e6			0.834851			0.417425	+	0.908711i	$0.362932\pi$
$152$			113522.i			0.0323259i
$153$	−6.08502e6	−	520265.i	−1.69898	−	0.145261i
$154$	678418.			0.185753
$155$			5.60932e6i			1.50631i
$156$	−2.02164e6	+	1.85616e6i	−0.532512	+	0.488925i
$157$	2.92235e6			0.755151			0.377575	−	0.925979i	$-0.376758\pi$
$157$	2.92235e6			0.755151			0.377575	+	0.925979i	$0.376758\pi$
$158$		−	6.35536e6i		−	1.61127i
$159$	3.48898e6	+	3.80001e6i	0.867974	+	0.945352i
$160$	−1.01420e7			−2.47607
$161$			2.21706e6i			0.531252i
$162$	1.00270e6	−	5.82091e6i	0.235844	−	1.36913i
$163$	−2.44305e6			−0.564118			−0.282059	−	0.959397i	$-0.591017\pi$
$163$	−2.44305e6			−0.564118			−0.282059	+	0.959397i	$0.591017\pi$
$164$		−	1.04320e6i		−	0.236502i
$165$	−1.78684e6	+	1.64058e6i	−0.397771	+	0.365213i
$166$	8.58251e6			1.87625
$167$			7.78475e6i			1.67146i	0.549143	+	0.835728i	$0.314954\pi$
$167$			7.78475e6i			1.67146i	−0.549143	+	0.835728i	$0.685046\pi$
$168$	138003.	+	150306.i	0.0291046	+	0.0316992i
$169$	−1.91113e6			−0.395941
$170$		−	2.08451e7i		−	4.24284i
$171$	141888.	−	1.65952e6i	0.0283764	−	0.331890i
$172$	−21982.9			−0.00432016
$173$		−	5.99187e6i		−	1.15724i	−0.815597	−	0.578621i	$-0.803591\pi$
$173$		−	5.99187e6i		−	1.15724i	0.815597	−	0.578621i	$-0.196409\pi$
$174$	4.88828e6	−	4.48817e6i	0.927915	−	0.851965i
$175$	5.24658e6			0.978954
$176$		−	1.75057e6i		−	0.321101i
$177$	−2.58232e6	−	2.81253e6i	−0.465683	−	0.507198i
$178$	−8.98893e6			−1.59385
$179$		−	6.37429e6i		−	1.11141i	−0.831381	−	0.555703i	$-0.812449\pi$
$179$		−	6.37429e6i		−	1.11141i	0.831381	−	0.555703i	$-0.187551\pi$
$180$	9.68010e6	+	827641.i	1.65983	+	0.141914i
$181$	−1.20464e6			−0.203152			−0.101576	−	0.994828i	$-0.532389\pi$
$181$	−1.20464e6			−0.203152			−0.101576	+	0.994828i	$0.532389\pi$
$182$			2.88659e6i			0.478819i
$183$	−3.54448e6	+	3.25437e6i	−0.578362	+	0.531023i
$184$	724256.			0.116262
$185$			1.06630e7i			1.68409i
$186$	5.08520e6	+	5.53854e6i	0.790259	+	0.860709i
$187$	3.36200e6			0.514130
$188$			696387.i			0.104804i
$189$	−1.82953e6	−	2.36973e6i	−0.270991	−	0.351005i
$190$	5.68492e6			0.828826
$191$		−	3.44802e6i		−	0.494845i	−0.968908	−	0.247423i	$-0.920416\pi$
$191$		−	3.44802e6i		−	0.494845i	0.968908	−	0.247423i	$-0.0795836\pi$
$192$	−4.46161e6	+	4.09643e6i	−0.630359	+	0.578764i
$193$	−1.17928e7			−1.64038			−0.820188	−	0.572094i	$-0.806131\pi$
$193$	−1.17928e7			−1.64038			−0.820188	+	0.572094i	$0.806131\pi$
$194$			4.19805e6i			0.574967i
$195$	−6.98050e6	−	7.60279e6i	−0.941418	−	1.02534i
$196$	5.62640e6			0.747243
$197$			7.55975e6i			0.988801i	0.869234	+	0.494400i	$0.164612\pi$
$197$			7.55975e6i			0.988801i	−0.869234	+	0.494400i	$0.835388\pi$
$198$	−276997.	+	3.23976e6i	−0.0356845	+	0.417366i
$199$	3.63951e6			0.461831			0.230916	−	0.972974i	$-0.425828\pi$
$199$	3.63951e6			0.461831			0.230916	+	0.972974i	$0.425828\pi$
$200$		−	1.71392e6i		−	0.214240i
$201$	1.20708e6	−	1.10828e6i	0.148644	−	0.136478i
$202$	−1.91129e6			−0.231885
$203$		−	3.36357e6i		−	0.402079i
$204$	−9.10674e6	−	9.91859e6i	−1.07269	−	1.16831i
$205$	3.92316e6			0.455381
$206$			1.52994e7i			1.75014i
$207$	−1.05875e7	−	905223.i	−1.19367	−	0.102057i
$208$	7.44849e6			0.827710
$209$			916893.i			0.100434i
$210$	7.52695e6	−	6.91086e6i	0.812758	−	0.746233i
$211$	−1.44916e6			−0.154266			−0.0771330	−	0.997021i	$-0.524577\pi$
$211$	−1.44916e6			−0.154266			−0.0771330	+	0.997021i	$0.524577\pi$
$212$			1.13741e7i			1.19373i
$213$	−1.11374e7	−	1.21303e7i	−1.15251	−	1.25525i
$214$	−539906.			−0.0550905
$215$		−	82671.5i		−	0.00831841i
$216$	−774127.	+	597660.i	−0.0768159	+	0.0593052i
$217$	3.81100e6			0.372958
$218$			2.15044e7i			2.07567i
$219$	−4.33602e6	+	3.98111e6i	−0.412818	+	0.379029i
$220$	−5.34830e6			−0.502282
$221$			1.43049e7i			1.32529i
$222$	9.66669e6	+	1.05284e7i	0.883525	+	0.962289i
$223$	6.13185e6			0.552939			0.276469	−	0.961023i	$-0.410836\pi$
$223$	6.13185e6			0.552939			0.276469	+	0.961023i	$0.410836\pi$
$224$			6.89051e6i			0.613066i
$225$	−2.14217e6	+	2.50549e7i	−0.188064	+	2.19960i
$226$	2.22557e7			1.92804
$227$		−	1.45984e7i		−	1.24804i	−0.781408	−	0.624021i	$-0.785498\pi$
$227$		−	1.45984e7i		−	1.24804i	0.781408	−	0.624021i	$-0.214502\pi$
$228$	2.70502e6	−	2.48361e6i	0.228226	−	0.209546i
$229$	−5.75742e6			−0.479426			−0.239713	−	0.970844i	$-0.577053\pi$
$229$	−5.75742e6			−0.479426			−0.239713	+	0.970844i	$0.577053\pi$
$230$		−	3.62689e7i		−	2.98093i
$231$	1.11462e6	+	1.21399e6i	0.0904255	+	0.0984867i
$232$	−1.09879e6			−0.0879933
$233$		−	4.22333e6i		−	0.333878i	−0.985967	−	0.166939i	$-0.946612\pi$
$233$		−	4.22333e6i		−	0.333878i	0.985967	−	0.166939i	$-0.0533883\pi$
$234$	−1.37848e7	−	1.17859e6i	−1.07585	−	0.0919846i
$235$	−2.61891e6			−0.201798
$236$		−	8.41836e6i		−	0.640460i
$237$	1.13725e7	−	1.04417e7i	0.854302	−	0.784377i
$238$	−1.41622e7			−1.05051
$239$		−	528802.i		−	0.0387346i	−0.999812	−	0.0193673i	$-0.993835\pi$
$239$		−	528802.i		−	0.0387346i	0.999812	−	0.0193673i	$-0.00616520\pi$
$240$	−1.78326e7	−	1.94224e7i	−1.28998	−	1.40497i
$241$	−1.21855e7			−0.870547			−0.435274	−	0.900298i	$-0.643348\pi$
$241$	−1.21855e7			−0.870547			−0.435274	+	0.900298i	$0.643348\pi$
$242$		−	1.78998e6i		−	0.126300i
$243$	1.20635e7	−	7.76931e6i	0.840729	−	0.541457i
$244$	−1.06092e7			−0.730322
$245$			2.11593e7i			1.43881i
$246$	3.87366e6	−	3.55659e6i	0.260205	−	0.238907i
$247$	−3.90128e6			−0.258890
$248$		−	1.24495e6i		−	0.0816202i
$249$	1.41008e7	+	1.53579e7i	0.913368	+	0.994793i
$250$	−4.69505e7			−3.00483
$251$		−	9.76595e6i		−	0.617580i	−0.951130	−	0.308790i	$-0.900076\pi$
$251$		−	9.76595e6i		−	0.617580i	0.951130	−	0.308790i	$-0.0999240\pi$
$252$	562303.	−	6.57671e6i	0.0351373	−	0.410967i
$253$	5.84964e6			0.361217
$254$			762647.i			0.0465396i
$255$	3.73009e7	−	3.42478e7i	2.24957	−	2.06544i
$256$	1.88702e7			1.12475
$257$			1.65625e7i			0.975724i	0.872921	+	0.487862i	$0.162223\pi$
$257$			1.65625e7i			0.975724i	−0.872921	+	0.487862i	$0.837777\pi$
$258$	−74946.9	−	81628.2i	−0.00436410	−	0.00475315i
$259$	7.24450e6			0.416974
$260$		−	2.27564e7i		−	1.29474i
$261$	1.60626e7	+	1.37334e6i	0.903429	+	0.0772424i
$262$	4.38117e7			2.43605
$263$			2.89217e7i			1.58985i	0.606706	+	0.794926i	$0.292491\pi$
$263$			2.89217e7i			1.58985i	−0.606706	+	0.794926i	$0.707509\pi$
$264$	396577.	−	364117.i	0.0215534	−	0.0197892i
$265$	−4.27745e7			−2.29852
$266$		−	3.86236e6i		−	0.205214i
$267$	−1.47685e7	−	1.60851e7i	−0.775896	−	0.845066i
$268$	3.61299e6			0.187699
$269$			2.36746e6i			0.121626i	0.998149	+	0.0608128i	$0.0193693\pi$
$269$			2.36746e6i			0.121626i	−0.998149	+	0.0608128i	$0.980631\pi$
$270$	2.99293e7	+	3.87664e7i	1.52057	+	1.96954i
$271$	5.80859e6			0.291852			0.145926	−	0.989296i	$-0.453384\pi$
$271$	5.80859e6			0.291852			0.145926	+	0.989296i	$0.453384\pi$
$272$			3.65439e7i			1.81597i
$273$	−5.16537e6	+	4.74258e6i	−0.253871	+	0.233092i
$274$	1.06251e7			0.516512
$275$		−	1.38429e7i		−	0.665625i
$276$	−1.58451e7	−	1.72576e7i	−0.753645	−	0.820831i
$277$	1.68591e7			0.793223			0.396612	−	0.917986i	$-0.370186\pi$
$277$	1.68591e7			0.793223			0.396612	+	0.917986i	$0.370186\pi$
$278$		−	1.75746e7i		−	0.817995i
$279$	−1.55602e6	+	1.81993e7i	−0.0716480	+	0.837996i
$280$	−1.69191e6			−0.0770731
$281$		−	2.75913e7i		−	1.24352i	−0.783207	−	0.621760i	$-0.786418\pi$
$281$		−	2.75913e7i		−	1.24352i	0.783207	−	0.621760i	$-0.213582\pi$
$282$	−2.58586e6	+	2.37421e6i	−0.115308	+	0.105870i
$283$	3.22024e7			1.42078			0.710392	−	0.703806i	$-0.248517\pi$
$283$	3.22024e7			1.42078			0.710392	+	0.703806i	$0.248517\pi$
$284$		−	3.63079e7i		−	1.58506i
$285$	9.34015e6	+	1.01728e7i	0.403477	+	0.439446i
$286$	7.61617e6			0.325566
$287$		−	2.66542e6i		−	0.112751i
$288$	−3.29054e7	−	2.81338e6i	−1.37749	−	0.117775i
$289$	−4.60456e7			−1.90763
$290$			5.50246e7i			2.25612i
$291$	−7.51214e6	+	6.89727e6i	−0.304849	+	0.279897i
$292$	−1.29784e7			−0.521283
$293$		−	3.95679e7i		−	1.57304i	−0.617564	−	0.786520i	$-0.711881\pi$
$293$		−	3.95679e7i		−	1.57304i	0.617564	−	0.786520i	$-0.288119\pi$
$294$	1.91822e7	+	2.08922e7i	0.754842	+	0.822135i
$295$	3.16590e7			1.23319
$296$		−	2.36658e6i		−	0.0912529i
$297$	−6.25244e6	+	4.82716e6i	−0.238660	+	0.184256i
$298$	8.42271e6			0.318275
$299$			2.48896e7i			0.931116i
$300$	−4.08394e7	+	3.74967e7i	−1.51257	+	1.38877i
$301$	−56167.4			−0.00205961
$302$			3.19466e7i			1.15986i
$303$	−3.14020e6	−	3.42014e6i	−0.112883	−	0.122946i
$304$	−9.96634e6			−0.354744
$305$		−	3.98982e7i		−	1.40622i
$306$	5.78242e6	−	6.76313e7i	0.201811	−	2.36039i
$307$	−2.18276e7			−0.754380			−0.377190	−	0.926136i	$-0.623110\pi$
$307$	−2.18276e7			−0.754380			−0.377190	+	0.926136i	$0.623110\pi$
$308$			3.63366e6i			0.124363i
$309$	−2.73772e7	+	2.51364e7i	−0.927927	+	0.851976i
$310$	−6.23442e7			−2.09272
$311$		−	3.75226e7i		−	1.24742i	−0.781657	−	0.623708i	$-0.785625\pi$
$311$		−	3.75226e7i		−	1.24742i	0.781657	−	0.623708i	$-0.214375\pi$
$312$	1.54928e6	+	1.68739e6i	0.0510111	+	0.0555586i
$313$	9.67362e6			0.315469			0.157734	−	0.987482i	$-0.449581\pi$
$313$	9.67362e6			0.315469			0.157734	+	0.987482i	$0.449581\pi$
$314$			3.24801e7i			1.04913i
$315$	2.47331e7	+	2.11466e6i	0.791310	+	0.0676564i
$316$	3.40398e7			1.07876
$317$			5.43885e6i			0.170738i	0.996349	+	0.0853688i	$0.0272069\pi$
$317$			5.43885e6i			0.170738i	−0.996349	+	0.0853688i	$0.972793\pi$
$318$	−4.22348e7	+	3.87778e7i	−1.31337	+	1.20587i
$319$	−8.87465e6			−0.273388
$320$		−	5.02218e7i		−	1.53265i
$321$	−887049.	−	966127.i	−0.0268184	−	0.0292092i
$322$	−2.46413e7			−0.738067
$323$		−	1.91405e7i		−	0.567997i
$324$	3.11772e7	+	5.37051e6i	0.916648	+	0.157900i
$325$	5.89001e7			1.71580
$326$		−	2.71530e7i		−	0.783728i
$327$	−3.84808e7	+	3.53311e7i	−1.10053	+	1.01045i
$328$	−870721.			−0.0246750
$329$			1.77930e6i			0.0499645i
$330$	−1.82341e7	−	1.98596e7i	−0.507390	−	0.552622i
$331$	1.13623e7			0.313317			0.156658	−	0.987653i	$-0.449928\pi$
$331$	1.13623e7			0.313317			0.156658	+	0.987653i	$0.449928\pi$
$332$			4.59686e7i			1.25617i
$333$	−2.95791e6	+	3.45958e7i	−0.0801038	+	0.936895i
$334$	−8.65226e7			−2.32215
$335$			1.35874e7i			0.361412i
$336$	−1.31956e7	+	1.21156e7i	−0.347866	+	0.319393i
$337$	−7.24058e7			−1.89184			−0.945918	−	0.324405i	$-0.894836\pi$
$337$	−7.24058e7			−1.89184			−0.945918	+	0.324405i	$0.894836\pi$
$338$		−	2.12411e7i		−	0.550080i
$339$	3.65655e7	+	3.98252e7i	0.938582	+	1.02225i
$340$	1.11648e8			2.84062
$341$		−	1.00552e7i		−	0.253587i
$342$	1.84446e7	+	1.57700e6i	0.461095	+	0.0394232i
$343$	3.22702e7			0.799684
$344$			18348.4i			0.000450736i
$345$	6.49009e7	−	5.95888e7i	1.58050	−	1.45113i
$346$	6.65959e7			1.60775
$347$		−	3.81191e6i		−	0.0912335i	−0.998959	−	0.0456168i	$-0.985475\pi$
$347$		−	3.81191e6i		−	0.0912335i	0.998959	−	0.0456168i	$-0.0145253\pi$
$348$	2.40390e7	+	2.61820e7i	0.570398	+	0.621248i
$349$	−2.57867e7			−0.606625			−0.303312	−	0.952891i	$-0.598093\pi$
$349$	−2.57867e7			−0.606625			−0.303312	+	0.952891i	$0.598093\pi$
$350$			5.83125e7i			1.36006i
$351$	−2.05390e7	−	2.66034e7i	−0.474961	−	0.615200i
$352$	1.81804e7			0.416845
$353$			2.60339e7i			0.591855i	0.955210	+	0.295928i	$0.0956287\pi$
$353$			2.60339e7i			0.591855i	−0.955210	+	0.295928i	$0.904371\pi$
$354$	3.12595e7	−	2.87009e7i	0.704649	−	0.646972i
$355$	1.36543e8			3.05201
$356$		−	4.81454e7i		−	1.06710i
$357$	−2.32681e7	−	2.53424e7i	−0.511395	−	0.556985i
$358$	7.08463e7			1.54407
$359$		−	3.44066e7i		−	0.743633i	−0.928306	−	0.371817i	$-0.878735\pi$
$359$		−	3.44066e7i		−	0.743633i	0.928306	−	0.371817i	$-0.121265\pi$
$360$	690803.	−	8.07964e6i	0.0148063	−	0.173175i
$361$	−4.18258e7			−0.889044
$362$		−	1.33888e7i		−	0.282239i
$363$	3.20306e6	−	2.94088e6i	0.0669645	−	0.0614834i
$364$	−1.54608e7			−0.320574
$365$		−	4.88081e7i		−	1.00372i
$366$	−3.61703e7	−	3.93948e7i	−0.737749	−	0.803517i
$367$	−7.52031e7			−1.52138			−0.760690	−	0.649116i	$-0.775139\pi$
$367$	−7.52031e7			−1.52138			−0.760690	+	0.649116i	$0.775139\pi$
$368$			6.35837e7i			1.27586i
$369$	1.27286e7	+	1.08828e6i	0.253339	+	0.0216602i
$370$	−1.18513e8			−2.33970
$371$			2.90612e7i			0.569105i
$372$	−2.96648e7	+	2.72367e7i	−0.576253	+	0.529086i
$373$	5.84527e7			1.12636			0.563182	−	0.826333i	$-0.309577\pi$
$373$	5.84527e7			1.12636			0.563182	+	0.826333i	$0.309577\pi$
$374$			3.73666e7i			0.714280i
$375$	−7.71383e7	−	8.40150e7i	−1.46277	−	1.59317i
$376$	581250.			0.0109345
$377$		−	3.77606e7i		−	0.704718i
$378$	2.63380e7	−	2.03341e7i	0.487650	−	0.376487i
$379$	−7.41271e7			−1.36163			−0.680816	−	0.732455i	$-0.738374\pi$
$379$	−7.41271e7			−1.36163			−0.680816	+	0.732455i	$0.738374\pi$
$380$			3.04489e7i			0.554907i
$381$	−1.36471e6	+	1.25300e6i	−0.0246754	+	0.0226557i
$382$	3.83226e7			0.687488
$383$			3.96990e7i			0.706615i	0.935507	+	0.353308i	$0.114943\pi$
$383$			3.96990e7i			0.706615i	−0.935507	+	0.353308i	$0.885057\pi$
$384$	7.41460e6	+	8.07560e6i	0.130947	+	0.142620i
$385$	−1.36651e7			−0.239459
$386$		−	1.31069e8i		−	2.27897i
$387$	22933.0	−	268225.i	0.000395666	−	0.00462771i
$388$	−2.24851e7			−0.384946
$389$		−	4.42946e7i		−	0.752491i	−0.926520	−	0.376246i	$-0.877215\pi$
$389$		−	4.42946e7i		−	0.752491i	0.926520	−	0.376246i	$-0.122785\pi$
$390$	8.45003e7	−	7.75839e7i	1.42451	−	1.30791i
$391$	−1.22114e8			−2.04284
$392$		−	4.69616e6i		−	0.0779622i
$393$	7.19812e7	+	7.83982e7i	1.18588	+	1.29160i
$394$	−8.40219e7			−1.37374
$395$			1.28014e8i			2.07714i
$396$	−1.73524e7	−	1.48362e6i	−0.279431	−	0.0238911i
$397$	−4.58210e7			−0.732307			−0.366153	−	0.930554i	$-0.619325\pi$
$397$	−4.58210e7			−0.732307			−0.366153	+	0.930554i	$0.619325\pi$
$398$			4.04509e7i			0.641621i
$399$	6.91145e6	−	6.34574e6i	0.108805	−	0.0998995i
$400$	1.50468e8			2.35106
$401$		−	4.73886e7i		−	0.734921i	−0.930039	−	0.367460i	$-0.880227\pi$
$401$		−	4.73886e7i		−	0.734921i	0.930039	−	0.367460i	$-0.119773\pi$
$402$	1.23178e7	+	1.34159e7i	0.189608	+	0.206511i
$403$	4.27837e7			0.653677
$404$		−	1.02370e7i		−	0.155250i
$405$	−2.01970e7	+	1.17249e8i	−0.304033	+	1.76499i
$406$	3.73840e7			0.558608
$407$		−	1.91143e7i		−	0.283515i
$408$	−8.27870e6	+	7.60108e6i	−0.121894	+	0.111917i
$409$	6.54573e7			0.956728			0.478364	−	0.878162i	$-0.341230\pi$
$409$	6.54573e7			0.956728			0.478364	+	0.878162i	$0.341230\pi$
$410$			4.36035e7i			0.632660i
$411$	1.74567e7	+	1.90129e7i	0.251441	+	0.273856i
$412$	−8.19445e7			−1.17173
$413$		−	2.15093e7i		−	0.305335i
$414$	1.00610e7	−	1.17674e8i	0.141788	−	1.65836i
$415$	−1.72875e8			−2.41873
$416$			7.73554e7i			1.07451i
$417$	3.14486e7	−	2.88745e7i	0.433704	−	0.398205i
$418$	−1.01907e7			−0.139532
$419$			2.18240e7i			0.296683i	0.988936	+	0.148341i	$0.0473934\pi$
$419$			2.18240e7i			0.296683i	−0.988936	+	0.148341i	$0.952607\pi$
$420$	3.70151e7	+	4.03149e7i	0.499610	+	0.544149i
$421$	1.35012e8			1.80937			0.904684	−	0.426084i	$-0.140107\pi$
$421$	1.35012e8			1.80937			0.904684	+	0.426084i	$0.140107\pi$
$422$		−	1.61066e7i		−	0.214321i
$423$	−8.49698e6	−	726485.i	−0.112265	−	0.00959855i
$424$	9.49353e6			0.124546
$425$			2.88976e8i			3.76440i
$426$	1.34820e8	−	1.23785e8i	1.74392	−	1.60118i
$427$	−2.71070e7			−0.348176
$428$		−	2.89178e6i		−	0.0368836i
$429$	1.25131e7	+	1.36286e7i	0.158487	+	0.172616i
$430$	918842.			0.0115567
$431$			2.09818e7i			0.262067i	0.991378	+	0.131033i	$0.0418295\pi$
$431$			2.09818e7i			0.262067i	−0.991378	+	0.131033i	$0.958171\pi$
$432$	−5.24697e7	−	6.79620e7i	−0.650814	−	0.842976i
$433$	−3.95681e7			−0.487395			−0.243698	−	0.969851i	$-0.578360\pi$
$433$	−3.95681e7			−0.487395			−0.243698	+	0.969851i	$0.578360\pi$
$434$			4.23569e7i			0.518150i
$435$	−9.84629e7	+	9.04037e7i	−1.19620	+	1.09829i
$436$	−1.15179e8			−1.38968
$437$		−	3.33031e7i		−	0.399062i
$438$	−4.42476e7	−	4.81922e7i	−0.526584	−	0.573528i
$439$	4.83647e7			0.571656			0.285828	−	0.958281i	$-0.407731\pi$
$439$	4.83647e7			0.571656			0.285828	+	0.958281i	$0.407731\pi$
$440$			4.46404e6i			0.0524047i
$441$	−5.86957e6	+	6.86506e7i	−0.0684369	+	0.800439i
$442$	−1.58991e8			−1.84122
$443$		−	3.60643e7i		−	0.414826i	−0.978253	−	0.207413i	$-0.933496\pi$
$443$		−	3.60643e7i		−	0.414826i	0.978253	−	0.207413i	$-0.0665044\pi$
$444$	−5.63912e7	+	5.17755e7i	−0.644261	+	0.591528i
$445$	1.81061e8			2.05468
$446$			6.81517e7i			0.768196i
$447$	1.38383e7	+	1.50719e7i	0.154938	+	0.168751i
$448$	−3.41209e7			−0.379478
$449$		−	1.63001e8i		−	1.80074i	−0.435120	−	0.900372i	$-0.643294\pi$
$449$		−	1.63001e8i		−	1.80074i	0.435120	−	0.900372i	$-0.356706\pi$
$450$	−2.78469e8	−	2.38089e7i	−3.05590	−	0.261277i
$451$	−7.03260e6			−0.0766631
$452$			1.19203e8i			1.29084i
$453$	−5.71664e7	+	5.24873e7i	−0.614959	+	0.564625i
$454$	1.62253e8			1.73390
$455$		−	5.81436e7i		−	0.617260i
$456$	−2.07298e6	−	2.25779e6i	−0.0218626	−	0.0238116i
$457$	8.09988e7			0.848652			0.424326	−	0.905509i	$-0.360511\pi$
$457$	8.09988e7			0.848652			0.424326	+	0.905509i	$0.360511\pi$
$458$		−	6.39902e7i		−	0.666066i
$459$	1.30522e8	−	1.00769e8i	1.34973	−	1.04205i
$460$	1.94259e8			1.99576
$461$		−	1.17032e8i		−	1.19454i	−0.802039	−	0.597271i	$-0.796252\pi$
$461$		−	1.17032e8i		−	1.19454i	0.802039	−	0.597271i	$-0.203748\pi$
$462$	−1.34927e7	+	1.23883e7i	−0.136827	+	0.125628i
$463$	7.01116e7			0.706394			0.353197	−	0.935549i	$-0.385095\pi$
$463$	7.01116e7			0.706394			0.353197	+	0.935549i	$0.385095\pi$
$464$		−	9.64646e7i		−	0.965637i
$465$	−1.02430e8	−	1.11561e8i	−1.01875	−	1.10957i
$466$	4.69397e7			0.463856
$467$			4.05567e7i			0.398210i	0.979978	+	0.199105i	$0.0638034\pi$
$467$			4.05567e7i			0.398210i	−0.979978	+	0.199105i	$0.936197\pi$
$468$	6.31262e6	−	7.38325e7i	0.0615846	−	0.720294i
$469$	9.23135e6			0.0894843
$470$		−	2.91076e7i		−	0.280358i
$471$	−5.81211e7	+	5.33639e7i	−0.556252	+	0.510722i
$472$	−7.02651e6			−0.0668212
$473$			148196.i			0.00140040i
$474$	1.16053e8	+	1.26398e8i	1.08973	+	1.18688i
$475$	−7.88103e7			−0.735364
$476$		−	7.58541e7i		−	0.703328i
$477$	−1.38781e8	−	1.18656e7i	−1.27872	−	0.109329i
$478$	5.87731e6			0.0538140
$479$			1.63724e8i			1.48972i	0.667220	+	0.744861i	$0.267484\pi$
$479$			1.63724e8i			1.48972i	−0.667220	+	0.744861i	$0.732516\pi$
$480$	2.01709e8	−	1.85199e8i	1.82390	−	1.67461i
$481$	8.13294e7			0.730823
$482$		−	1.35434e8i		−	1.20945i
$483$	−4.04849e7	−	4.40940e7i	−0.359295	−	0.391325i
$484$	9.58728e6			0.0845589
$485$		−	8.45599e7i		−	0.741207i
$486$	8.63511e7	+	1.34079e8i	0.752244	+	1.16802i
$487$	−1.17125e8			−1.01406			−0.507031	−	0.861928i	$-0.669257\pi$
$487$	−1.17125e8			−1.01406			−0.507031	+	0.861928i	$0.669257\pi$
$488$			8.85515e6i			0.0761968i
$489$	4.85886e7	−	4.46116e7i	0.415535	−	0.381523i
$490$	−2.35172e8			−1.99893
$491$			7.27786e7i			0.614836i	0.951575	+	0.307418i	$0.0994649\pi$
$491$			7.27786e7i			0.614836i	−0.951575	+	0.307418i	$0.900535\pi$
$492$	1.90494e7	+	2.07476e7i	0.159951	+	0.174210i
$493$	1.85262e8			1.54613
$494$		−	4.33603e7i		−	0.359676i
$495$	5.57945e6	−	6.52574e7i	0.0460019	−	0.538039i
$496$	1.09297e8			0.895699
$497$		−	9.27682e7i		−	0.755666i
$498$	−1.70693e8	+	1.56722e8i	−1.38206	+	1.26894i
$499$	−6.21305e7			−0.500038			−0.250019	−	0.968241i	$-0.580437\pi$
$499$	−6.21305e7			−0.500038			−0.250019	+	0.968241i	$0.580437\pi$
$500$		−	2.51471e8i		−	2.01177i
$501$	−1.42154e8	−	1.54827e8i	−1.13044	−	1.23121i
$502$	1.08542e8			0.858002
$503$			1.20870e8i			0.949758i	0.880051	+	0.474879i	$0.157508\pi$
$503$			1.20870e8i			0.949758i	−0.880051	+	0.474879i	$0.842492\pi$
$504$	−5.48935e6	−	469335.i	−0.0428775	−	0.00366599i
$505$	3.84986e7			0.298931
$506$			6.50152e7i			0.501837i
$507$	3.80095e7	−	3.48984e7i	0.291654	−	0.267782i
$508$	−4.08479e6			−0.0311587
$509$			1.01461e8i			0.769386i	0.923045	+	0.384693i	$0.125693\pi$
$509$			1.01461e8i			0.769386i	−0.923045	+	0.384693i	$0.874307\pi$
$510$	3.80643e8	+	4.14577e8i	2.86951	+	3.12532i
$511$	−3.31605e7			−0.248518
$512$			1.83743e8i			1.36899i
$513$	2.74819e7	+	3.55963e7i	0.203561	+	0.263665i
$514$	−1.84082e8			−1.35557
$515$		−	3.08170e8i		−	2.25615i
$516$	437207.	−	401421.i	0.00318228	−	0.00292180i
$517$	4.69462e6			0.0339726
$518$			8.05181e7i			0.579301i
$519$	1.09415e8	+	1.19169e8i	0.782663	+	0.852435i
$520$	−1.89940e7			−0.135085
$521$		−	3.69258e7i		−	0.261106i	−0.991441	−	0.130553i	$-0.958325\pi$
$521$		−	3.69258e7i		−	0.261106i	0.991441	−	0.130553i	$-0.0416752\pi$
$522$	−1.52638e7	+	1.78526e8i	−0.107313	+	1.25513i
$523$	5.29022e7			0.369802			0.184901	−	0.982757i	$-0.440804\pi$
$523$	5.29022e7			0.369802			0.184901	+	0.982757i	$0.440804\pi$
$524$			2.34659e8i			1.63096i
$525$	−1.04346e8	+	9.58056e7i	−0.721107	+	0.662084i
$526$	−3.21447e8			−2.20878
$527$			2.09906e8i			1.43415i
$528$	3.19665e7	+	3.48162e7i	0.217167	+	0.236526i
$529$	−6.44330e7			−0.435252
$530$		−	4.75413e8i		−	3.19333i
$531$	1.02717e8	+	8.78221e6i	0.686054	+	0.0586570i
$532$	2.06871e7			0.137393
$533$		−	2.99229e7i		−	0.197616i
$534$	1.78776e8	−	1.64143e8i	1.17405	−	1.07795i
$535$	1.08751e7			0.0710189
$536$		−	3.01564e6i		−	0.0195832i
$537$	1.16398e8	+	1.26775e8i	0.751664	+	0.818673i
$538$	−2.63128e7			−0.168974
$539$		−	3.79297e7i		−	0.242222i
$540$	−2.07636e8	+	1.60304e8i	−1.31862	+	1.01803i
$541$	5.10829e6			0.0322614			0.0161307	−	0.999870i	$-0.494865\pi$
$541$	5.10829e6			0.0322614			0.0161307	+	0.999870i	$0.494865\pi$
$542$			6.45589e7i			0.405469i
$543$	2.39584e7	−	2.19974e7i	0.149644	−	0.137395i
$544$	−3.79522e8			−2.35744
$545$		−	4.33156e8i		−	2.67581i
$546$	−5.27109e7	−	5.74099e7i	−0.323834	−	0.352703i
$547$	1.21777e7			0.0744051			0.0372025	−	0.999308i	$-0.488155\pi$
$547$	1.21777e7			0.0744051			0.0372025	+	0.999308i	$0.488155\pi$
$548$			5.69088e7i			0.345810i
$549$	1.10678e7	−	1.29449e8i	0.0668872	−	0.782313i
$550$	1.53855e8			0.924751
$551$			5.05250e7i			0.302031i
$552$	−1.44043e7	+	1.32253e7i	−0.0856399	+	0.0786302i
$553$	8.69732e7			0.514292
$554$			1.87379e8i			1.10202i
$555$	−1.94713e8	−	2.12071e8i	−1.13898	−	1.24052i
$556$	9.41308e7			0.547656
$557$		−	9.83837e7i		−	0.569321i	−0.958628	−	0.284661i	$-0.908119\pi$
$557$		−	9.83837e7i		−	0.569321i	0.958628	−	0.284661i	$-0.0918809\pi$
$558$	−2.02274e8	−	1.72943e7i	−1.16423	−	0.0995404i
$559$	−630555.			−0.00360984
$560$		−	1.48536e8i		−	0.845798i
$561$	−6.68651e7	+	6.13921e7i	−0.378714	+	0.347716i
$562$	3.06660e8			1.72762
$563$			1.30849e8i			0.733241i	0.930371	+	0.366621i	$0.119485\pi$
$563$			1.30849e8i			0.733241i	−0.930371	+	0.366621i	$0.880515\pi$
$564$	−1.27164e7	−	1.38501e7i	−0.0708807	−	0.0771996i
$565$	−4.48290e8			−2.48550
$566$			3.57909e8i			1.97389i
$567$	7.96592e7	+	1.37219e7i	0.437005	+	0.0752775i
$568$	−3.03049e7			−0.165374
$569$			1.98182e7i			0.107579i	0.998552	+	0.0537894i	$0.0171300\pi$
$569$			1.98182e7i			0.107579i	−0.998552	+	0.0537894i	$0.982870\pi$
$570$	−1.13064e8	+	1.03810e8i	−0.610522	+	0.560550i
$571$	5.56664e7			0.299009			0.149505	−	0.988761i	$-0.452232\pi$
$571$	5.56664e7			0.299009			0.149505	+	0.988761i	$0.452232\pi$
$572$			4.07928e7i			0.217969i
$573$	6.29628e7	+	6.85758e7i	0.334673	+	0.364508i
$574$	2.96244e7			0.156644
$575$			5.02798e8i			2.64478i
$576$	1.39315e7	−	1.62943e8i	0.0729006	−	0.852647i
$577$	−2.75709e8			−1.43524			−0.717619	−	0.696436i	$-0.754768\pi$
$577$	−2.75709e8			−1.43524			−0.717619	+	0.696436i	$0.754768\pi$
$578$		−	5.11768e8i		−	2.65027i
$579$	2.34540e8	−	2.15343e8i	1.20832	−	1.10942i
$580$	−2.94716e8			−1.51050
$581$			1.17452e8i			0.598868i
$582$	−7.66589e7	−	8.34928e7i	−0.388860	−	0.423526i
$583$	7.66770e7			0.386954
$584$			1.08326e7i			0.0543871i
$585$	2.77663e8	+	2.37399e7i	1.38692	+	0.118580i
$586$	4.39772e8			2.18542
$587$		−	1.51403e8i		−	0.748551i	−0.927318	−	0.374276i	$-0.877891\pi$
$587$		−	1.51403e8i		−	0.748551i	0.927318	−	0.374276i	$-0.122109\pi$
$588$	−1.11900e8	+	1.02741e8i	−0.550427	+	0.505374i
$589$	−5.72461e7			−0.280156
$590$			3.51871e8i			1.71327i
$591$	−1.38045e8	−	1.50352e8i	−0.668744	−	0.728360i
$592$	2.07767e8			1.00141
$593$		−	2.01359e8i		−	0.965622i	−0.875725	−	0.482811i	$-0.839616\pi$
$593$		−	2.01359e8i		−	0.965622i	0.875725	−	0.482811i	$-0.160384\pi$
$594$	−5.36509e7	−	6.94920e7i	−0.255987	−	0.331570i
$595$	2.85265e8			1.35425
$596$			4.51127e7i			0.213088i
$597$	−7.23842e7	+	6.64595e7i	−0.340190	+	0.312345i
$598$	−2.76632e8			−1.29360
$599$			1.30657e8i			0.607928i	0.952684	+	0.303964i	$0.0983102\pi$
$599$			1.30657e8i			0.607928i	−0.952684	+	0.303964i	$0.901690\pi$
$600$	3.12972e7	+	3.40872e7i	0.144894	+	0.157811i
$601$	−1.17913e8			−0.543175			−0.271587	−	0.962414i	$-0.587549\pi$
$601$	−1.17913e8			−0.543175			−0.271587	+	0.962414i	$0.587549\pi$
$602$		−	624265.i		−	0.00286141i
$603$	−3.76914e6	+	4.40840e7i	−0.0171906	+	0.201061i
$604$	−1.71109e8			−0.776535
$605$			3.60550e7i			0.162817i
$606$	3.80127e7	−	3.49014e7i	0.170809	−	0.156828i
$607$	1.18988e8			0.532030			0.266015	−	0.963969i	$-0.414293\pi$
$607$	1.18988e8			0.532030			0.266015	+	0.963969i	$0.414293\pi$
$608$		−	1.03504e8i		−	0.460519i
$609$	6.14207e7	+	6.68962e7i	0.271933	+	0.296176i
$610$	4.43444e8			1.95366
$611$			1.99751e7i			0.0875719i
$612$	3.62238e8	+	3.09711e7i	1.58030	+	0.135115i
$613$	1.34137e8			0.582327			0.291164	−	0.956673i	$-0.405958\pi$
$613$	1.34137e8			0.582327			0.291164	+	0.956673i	$0.405958\pi$
$614$		−	2.42600e8i		−	1.04806i
$615$	−7.80257e7	+	7.16393e7i	−0.335438	+	0.307982i
$616$	3.03289e6			0.0129752
$617$		−	2.83802e8i		−	1.20826i	−0.796887	−	0.604129i	$-0.793521\pi$
$617$		−	2.83802e8i		−	1.20826i	0.796887	−	0.604129i	$-0.206479\pi$
$618$	−2.79375e8	−	3.04281e8i	−1.18365	−	1.28917i
$619$	−3.44461e8			−1.45234			−0.726170	−	0.687515i	$-0.758702\pi$
$619$	−3.44461e8			−1.45234			−0.726170	+	0.687515i	$0.758702\pi$
$620$		−	3.33920e8i		−	1.40109i
$621$	2.27099e8	−	1.75330e8i	0.948289	−	0.732121i
$622$	4.17040e8			1.73303
$623$		−	1.23014e8i		−	0.508732i
$624$	−1.48139e8	+	1.36014e8i	−0.609699	+	0.559795i
$625$	4.06737e8			1.66599
$626$			1.07516e8i			0.438280i
$627$	−1.67430e7	−	1.82356e7i	−0.0679252	−	0.0739805i
$628$	−1.73966e8			−0.702402
$629$			3.99020e8i			1.60340i
$630$	−2.35031e7	+	2.74893e8i	−0.0939949	+	1.09937i
$631$	4.21058e8			1.67592			0.837961	−	0.545730i	$-0.183748\pi$
$631$	4.21058e8			1.67592			0.837961	+	0.545730i	$0.183748\pi$
$632$		−	2.84118e7i		−	0.112551i
$633$	2.88216e7	−	2.64626e7i	0.113634	−	0.104333i
$634$	−6.04495e7			−0.237205
$635$		−	1.53617e7i		−	0.0599955i
$636$	−2.07697e8	−	2.26213e8i	−0.807344	−	0.879317i
$637$	1.61387e8			0.624381
$638$		−	9.86362e7i		−	0.379817i
$639$	4.43011e8	+	3.78771e7i	1.69790	+	0.145169i
$640$	−9.09024e7			−0.346765
$641$			3.15955e8i			1.19964i	0.800135	+	0.599820i	$0.204761\pi$
$641$			3.15955e8i			1.19964i	−0.800135	+	0.599820i	$0.795239\pi$
$642$	1.07379e7	−	9.85900e6i	0.0405802	−	0.0372587i
$643$	−5.49484e7			−0.206691			−0.103346	−	0.994645i	$-0.532955\pi$
$643$	−5.49484e7			−0.206691			−0.103346	+	0.994645i	$0.532955\pi$
$644$		−	1.31981e8i		−	0.494143i
$645$	1.50963e6	+	1.64421e6i	0.00562589	+	0.00612742i
$646$	2.12735e8			0.789117
$647$			1.14477e8i			0.422676i	0.977413	+	0.211338i	$0.0677820\pi$
$647$			1.14477e8i			0.422676i	−0.977413	+	0.211338i	$0.932218\pi$
$648$	4.48258e6	−	2.60225e7i	0.0164742	−	0.0956367i
$649$	−5.67515e7			−0.207608
$650$			6.54638e8i			2.38375i
$651$	−7.57950e7	+	6.95911e7i	−0.274724	+	0.252238i
$652$	1.45434e8			0.524713
$653$			1.88098e8i			0.675532i	0.941230	+	0.337766i	$0.109671\pi$
$653$			1.88098e8i			0.675532i	−0.941230	+	0.337766i	$0.890329\pi$
$654$	−3.92683e8	−	4.27690e8i	−1.40381	−	1.52896i
$655$	−8.82484e8			−3.14038
$656$		−	7.64422e7i		−	0.270783i
$657$	1.35394e7	−	1.58357e8i	0.0477421	−	0.558393i
$658$	−1.97758e7			−0.0694156
$659$			4.71856e8i			1.64874i	0.566049	+	0.824372i	$0.308471\pi$
$659$			4.71856e8i			1.64874i	−0.566049	+	0.824372i	$0.691529\pi$
$660$	1.06369e8	−	9.76631e7i	0.369986	−	0.339702i
$661$	−2.94797e8			−1.02075			−0.510374	−	0.859953i	$-0.670493\pi$
$661$	−2.94797e8			−1.02075			−0.510374	+	0.859953i	$0.670493\pi$
$662$			1.26285e8i			0.435290i
$663$	−2.61217e8	−	2.84503e8i	−0.896314	−	0.976218i
$664$	3.83684e7			0.131060
$665$			7.77982e7i			0.264548i
$666$	−3.84511e8	−	3.28754e7i	−1.30163	−	0.111288i
$667$	3.22342e8			1.08627
$668$		−	4.63422e8i		−	1.55470i
$669$	−1.21953e8	+	1.11971e8i	−0.407300	+	0.373962i
$670$	−1.51016e8			−0.502109
$671$			7.15210e7i			0.236737i
$672$	−1.25825e8	−	1.37042e8i	−0.414628	−	0.451591i
$673$	−2.05510e8			−0.674198			−0.337099	−	0.941469i	$-0.609446\pi$
$673$	−2.05510e8			−0.674198			−0.337099	+	0.941469i	$0.609446\pi$
$674$		−	8.04746e8i		−	2.62832i
$675$	−4.14912e8	−	5.37420e8i	−1.34910	−	1.74744i
$676$	1.13769e8			0.368284
$677$		−	3.91154e8i		−	1.26061i	−0.776347	−	0.630306i	$-0.782930\pi$
$677$		−	3.91154e8i		−	1.26061i	0.776347	−	0.630306i	$-0.217070\pi$
$678$	−4.42633e8	+	4.06403e8i	−1.42022	+	1.30397i
$679$	−5.74504e7			−0.183520
$680$		−	9.31886e7i		−	0.296371i
$681$	2.66576e8	+	2.90341e8i	0.844073	+	0.919320i
$682$	1.11757e8			0.352308
$683$		−	4.51729e8i		−	1.41780i	−0.705308	−	0.708901i	$-0.749191\pi$
$683$		−	4.51729e8i		−	1.41780i	0.705308	−	0.708901i	$-0.250809\pi$
$684$	−8.44651e6	+	9.87905e7i	−0.0263942	+	0.308707i
$685$	−2.14017e8			−0.665851
$686$			3.58663e8i			1.11100i
$687$	1.14506e8	−	1.05134e8i	0.353150	−	0.324244i
$688$	−1.61084e6			−0.00494637
$689$			3.26252e8i			0.997460i
$690$	6.62292e8	+	7.21334e8i	2.01605	+	2.19578i
$691$	1.72968e8			0.524243			0.262121	−	0.965035i	$-0.415578\pi$
$691$	1.72968e8			0.524243			0.262121	+	0.965035i	$0.415578\pi$
$692$			3.56693e8i			1.07641i
$693$	−4.43362e7	−	3.79071e6i	−0.133217	−	0.0113899i
$694$	4.23670e7			0.126751
$695$			3.53999e8i			1.05450i
$696$	2.18532e7	−	2.00645e7i	0.0648168	−	0.0595115i
$697$	1.46808e8			0.433563
$698$		−	2.86604e8i		−	0.842783i
$699$	7.71205e7	+	8.39956e7i	0.225808	+	0.245938i
$700$	−3.12326e8			−0.910572
$701$			2.18124e8i			0.633213i	0.948557	+	0.316607i	$0.102544\pi$
$701$			2.18124e8i			0.633213i	−0.948557	+	0.316607i	$0.897456\pi$
$702$	2.95681e8	−	2.28278e8i	0.854696	−	0.659862i
$703$	−1.08822e8			−0.313220
$704$			9.00269e7i			0.258021i
$705$	5.20861e7	−	4.78228e7i	0.148647	−	0.136480i
$706$	−2.89351e8			−0.822263
$707$		−	2.61561e7i		−	0.0740141i
$708$	1.53724e8	+	1.67428e8i	0.433154	+	0.471769i
$709$	3.00081e7			0.0841977			0.0420988	−	0.999113i	$-0.486596\pi$
$709$	3.00081e7			0.0841977			0.0420988	+	0.999113i	$0.486596\pi$
$710$			1.51760e9i			4.24015i
$711$	−3.55110e7	+	4.15337e8i	−0.0987994	+	1.15556i
$712$	−4.01853e7			−0.111334
$713$			3.65221e8i			1.00760i
$714$	2.81665e8	−	2.58611e8i	0.773818	−	0.710480i
$715$	−1.53410e8			−0.419696
$716$			3.79458e8i			1.03377i
$717$	9.65624e6	+	1.05171e7i	0.0261969	+	0.0285323i
$718$	3.82408e8			1.03313
$719$			1.04257e8i			0.280492i	0.990117	+	0.140246i	$0.0447893\pi$
$719$			1.04257e8i			0.280492i	−0.990117	+	0.140246i	$0.955211\pi$
$720$	7.09327e8	+	6.06469e7i	1.90042	+	0.162484i
$721$	−2.09372e8			−0.558615
$722$		−	4.64868e8i		−	1.23515i
$723$	2.42351e8	−	2.22514e8i	0.641254	−	0.588767i
$724$	7.17115e7			0.188961
$725$		−	7.62808e8i		−	2.00171i
$726$	3.26861e7	+	3.56000e7i	0.0854188	+	0.0930337i
$727$	−5.58249e8			−1.45286			−0.726431	−	0.687239i	$-0.758822\pi$
$727$	−5.58249e8			−1.45286			−0.726431	+	0.687239i	$0.758822\pi$
$728$			1.29046e7i			0.0334465i
$729$	−9.80531e7	+	3.74807e8i	−0.253092	+	0.967442i
$730$	5.42472e8			1.39447
$731$		−	3.09364e6i		−	0.00791987i
$732$	2.11001e8	−	1.93731e8i	0.537962	−	0.493930i
$733$	5.34961e8			1.35834			0.679172	−	0.733979i	$-0.262339\pi$
$733$	5.34961e8			1.35834			0.679172	+	0.733979i	$0.262339\pi$
$734$		−	8.35836e8i		−	2.11365i
$735$	−3.86380e8	−	4.20825e8i	−0.973090	−	1.05984i
$736$	−6.60342e8			−1.65629
$737$		−	2.43566e7i		−	0.0608435i
$738$	−1.20956e7	+	1.41470e8i	−0.0300925	+	0.351963i
$739$	−1.81159e8			−0.448876			−0.224438	−	0.974488i	$-0.572055\pi$
$739$	−1.81159e8			−0.448876			−0.224438	+	0.974488i	$0.572055\pi$
$740$		−	6.34763e8i		−	1.56645i
$741$	7.75904e7	−	7.12396e7i	0.190701	−	0.175092i
$742$	−3.22997e8			−0.790656
$743$		−	7.79442e7i		−	0.190028i	−0.995476	−	0.0950139i	$-0.969710\pi$
$743$		−	7.79442e7i		−	0.190028i	0.995476	−	0.0950139i	$-0.0302896\pi$
$744$	2.27336e7	+	2.47602e7i	0.0552012	+	0.0601223i
$745$	−1.69656e8			−0.410298
$746$			6.49666e8i			1.56485i
$747$	−5.60887e8	−	4.79554e7i	−1.34559	−	0.115047i
$748$	−2.00138e8			−0.478217
$749$		−	7.38862e6i		−	0.0175840i
$750$	9.33774e8	−	8.57344e8i	2.21339	−	2.03222i
$751$	1.65937e8			0.391763			0.195881	−	0.980628i	$-0.437243\pi$
$751$	1.65937e8			0.391763			0.195881	+	0.980628i	$0.437243\pi$
$752$			5.10290e7i			0.119995i
$753$	1.78332e8	+	1.94230e8i	0.417680	+	0.454915i
$754$	4.19686e8			0.979062
$755$		−	6.43490e8i		−	1.49521i
$756$	1.08911e8	+	1.41069e8i	0.252062	+	0.326486i
$757$	−6.79943e8			−1.56742			−0.783709	−	0.621128i	$-0.786675\pi$
$757$	−6.79943e8			−1.56742			−0.783709	+	0.621128i	$0.786675\pi$
$758$		−	8.23877e8i		−	1.89171i
$759$	−1.16340e8	+	1.06818e8i	−0.266076	+	0.244297i
$760$	2.54146e7			0.0578952
$761$			1.10198e8i			0.250045i	0.992154	+	0.125022i	$0.0399003\pi$
$761$			1.10198e8i			0.250045i	−0.992154	+	0.125022i	$0.960100\pi$
$762$	−1.39264e7	−	1.51679e7i	−0.0314755	−	0.0342815i
$763$	−2.94288e8			−0.662521
$764$			2.05259e8i			0.460279i
$765$	−1.16473e8	+	1.36227e9i	−0.260161	+	3.04285i
$766$	−4.41229e8			−0.981699
$767$		−	2.41471e8i		−	0.535155i
$768$	−3.75299e8	+	3.44580e8i	−0.828501	+	0.760688i
$769$	4.61738e8			1.01535			0.507676	−	0.861548i	$-0.330505\pi$
$769$	4.61738e8			1.01535			0.507676	+	0.861548i	$0.330505\pi$
$770$		−	1.51880e8i		−	0.332680i
$771$	−3.02441e8	−	3.29403e8i	−0.659900	−	0.718728i
$772$	7.02017e8			1.52579
$773$		−	6.91258e8i		−	1.49659i	−0.663369	−	0.748293i	$-0.730874\pi$
$773$		−	6.91258e8i		−	1.49659i	0.663369	−	0.748293i	$-0.269126\pi$
$774$	2.98116e6	+	254886.i	0.00642927	+	0.000549698i
$775$	8.64280e8			1.85673
$776$			1.87675e7i			0.0401626i
$777$	−1.44082e8	+	1.32289e8i	−0.307147	+	0.282007i
$778$	4.92307e8			1.04543
$779$			4.00379e7i			0.0846953i
$780$	4.15545e8	+	4.52590e8i	0.875658	+	0.953721i
$781$	−2.44766e8			−0.513804
$782$		−	1.35722e9i		−	2.83811i
$783$	−3.44538e8	+	2.65999e8i	−0.717715	+	0.554107i
$784$	4.12284e8			0.855556
$785$		−	6.54236e8i		−	1.35246i
$786$	−8.71347e8	+	8.00027e8i	−1.79442	+	1.64754i
$787$	9.33030e8			1.91413			0.957065	−	0.289873i	$-0.0936130\pi$
$787$	9.33030e8			1.91413			0.957065	+	0.289873i	$0.0936130\pi$
$788$		−	4.50028e8i		−	0.919731i
$789$	−5.28127e8	−	5.75209e8i	−1.07525	−	1.17110i
$790$	−1.42280e9			−2.88577
$791$			3.04570e8i			0.615400i
$792$	−1.23832e6	+	1.44834e7i	−0.00249263	+	0.0291539i
$793$	−3.04314e8			−0.610242
$794$		−	5.09272e8i		−	1.01739i
$795$	8.50720e8	−	7.81088e8i	1.69311	−	1.55453i
$796$	−2.16658e8			−0.429571
$797$			7.09892e8i			1.40222i	0.713052	+	0.701111i	$0.247312\pi$
$797$			7.09892e8i			1.40222i	−0.713052	+	0.701111i	$0.752688\pi$
$798$	7.05290e7	+	7.68164e7i	0.138790	+	0.151163i
$799$	−9.80021e7			−0.192130
$800$			1.56267e9i			3.05209i
$801$	5.87447e8	+	5.02263e7i	1.14307	+	0.0977312i
$802$	5.26695e8			1.02102
$803$			8.74927e7i			0.168976i
$804$	−7.18568e7	+	6.59753e7i	−0.138261	+	0.126944i
$805$	4.96341e8			0.951464
$806$			4.75514e8i			0.908152i
$807$	−4.32311e7	−	4.70851e7i	−0.0822576	−	0.0895906i
$808$	−8.54450e6			−0.0161977
$809$		−	6.14863e8i		−	1.16127i	−0.814164	−	0.580634i	$-0.802805\pi$
$809$		−	6.14863e8i		−	1.16127i	0.814164	−	0.580634i	$-0.197195\pi$
$810$	−1.30315e9	−	2.24477e8i	−2.45210	−	0.422392i
$811$	5.15240e8			0.965933			0.482967	−	0.875639i	$-0.339559\pi$
$811$	5.15240e8			0.965933			0.482967	+	0.875639i	$0.339559\pi$
$812$			2.00231e8i			0.373993i
$813$	−1.15524e8	+	1.06068e8i	−0.214981	+	0.197385i
$814$	2.12444e8			0.393887
$815$			5.46934e8i			1.01033i
$816$	−6.67313e8	−	7.26802e8i	−1.22817	−	1.33766i
$817$	843705.			0.00154712
$818$			7.27518e8i			1.32918i
$819$	1.61290e7	−	1.88645e8i	0.0293600	−	0.343395i
$820$	−2.33544e8			−0.423572
$821$		−	4.81895e8i		−	0.870809i	−0.900235	−	0.435404i	$-0.856605\pi$
$821$		−	4.81895e8i		−	0.870809i	0.900235	−	0.435404i	$-0.143395\pi$
$822$	−2.11317e8	+	1.94020e8i	−0.380468	+	0.349326i
$823$	5.40502e8			0.969611			0.484805	−	0.874622i	$-0.338890\pi$
$823$	5.40502e8			0.969611			0.484805	+	0.874622i	$0.338890\pi$
$824$			6.83963e7i			0.122251i
$825$	2.52780e8	+	2.75314e8i	0.450174	+	0.490306i
$826$	2.39062e8			0.424201
$827$		−	2.58475e8i		−	0.456985i	−0.973546	−	0.228492i	$-0.926620\pi$
$827$		−	2.58475e8i		−	0.456985i	0.973546	−	0.228492i	$-0.0733796\pi$
$828$	6.30268e8	+	5.38874e7i	1.11029	+	0.0949285i
$829$	6.48832e8			1.13886			0.569428	−	0.822041i	$-0.307165\pi$
$829$	6.48832e8			1.13886			0.569428	+	0.822041i	$0.307165\pi$
$830$		−	1.92139e9i		−	3.36033i
$831$	−3.35302e8	+	3.07857e8i	−0.584296	+	0.536471i
$832$	−3.83054e8			−0.665105
$833$			7.91799e8i			1.36987i
$834$	3.20922e8	+	3.49532e8i	0.553225	+	0.602543i
$835$	1.74280e9			2.99355
$836$		−	5.45822e7i		−	0.0934183i
$837$	−3.01383e8	−	3.90370e8i	−0.513975	−	0.665733i
$838$	−2.42560e8			−0.412181
$839$			7.91463e8i			1.34012i	0.742306	+	0.670061i	$0.233732\pi$
$839$			7.91463e8i			1.34012i	−0.742306	+	0.670061i	$0.766268\pi$
$840$	3.36495e7	−	3.08952e7i	0.0567728	−	0.0521259i
$841$	1.05789e8			0.177850
$842$			1.50058e9i			2.51375i
$843$	5.03833e8	+	5.48749e8i	0.841015	+	0.915990i
$844$	8.62679e7			0.143490
$845$			4.27851e8i			0.709125i
$846$	8.07443e6	−	9.44387e7i	0.0133352	−	0.155969i
$847$	2.44959e7			0.0403129
$848$			8.33454e8i			1.36677i
$849$	−6.40456e8	+	5.88034e8i	−1.04656	+	0.960902i
$850$	−3.21179e9			−5.22987
$851$			6.94265e8i			1.12651i
$852$	6.63003e8	+	7.22108e8i	1.07200	+	1.16757i
$853$	−5.12457e8			−0.825678			−0.412839	−	0.910804i	$-0.635463\pi$
$853$	−5.12457e8			−0.825678			−0.412839	+	0.910804i	$0.635463\pi$
$854$		−	3.01278e8i		−	0.483720i
$855$	−3.71522e8	−	3.17649e7i	−0.594411	−	0.0508216i
$856$	−2.41367e6			−0.00384818
$857$		−	2.32653e8i		−	0.369630i	−0.982773	−	0.184815i	$-0.940831\pi$
$857$		−	2.32653e8i		−	0.369630i	0.982773	−	0.184815i	$-0.0591686\pi$
$858$	−1.51474e8	+	1.39076e8i	−0.239815	+	0.220186i
$859$	3.09980e8			0.489050			0.244525	−	0.969643i	$-0.421368\pi$
$859$	3.09980e8			0.489050			0.244525	+	0.969643i	$0.421368\pi$
$860$			4.92139e6i			0.00773735i
$861$	4.86720e7	+	5.30110e7i	0.0762553	+	0.0830533i
$862$	−2.33200e8			−0.364089
$863$		−	4.95427e8i		−	0.770810i	−0.922748	−	0.385405i	$-0.874062\pi$
$863$		−	4.95427e8i		−	0.770810i	0.922748	−	0.385405i	$-0.125938\pi$
$864$	7.05812e8	−	5.44918e8i	1.09433	−	0.844869i
$865$	−1.34142e9			−2.07260
$866$		−	4.39775e8i		−	0.677137i
$867$	9.15776e8	−	8.40819e8i	1.40518	−	1.29017i
$868$	−2.26867e8			−0.346906
$869$		−	2.29476e8i		−	0.349685i
$870$	−1.00478e9	−	1.09435e9i	−1.52586	−	1.66188i
$871$	1.03635e8			0.156838
$872$			9.61362e7i			0.144990i
$873$	2.34569e7	−	2.74352e8i	0.0352556	−	0.412350i
$874$	3.70143e8			0.554416
$875$		−	6.42519e8i		−	0.959095i
$876$	2.58121e8	−	2.36994e8i	0.383982	−	0.352553i
$877$	−2.65556e8			−0.393692			−0.196846	−	0.980434i	$-0.563070\pi$
$877$	−2.65556e8			−0.393692			−0.196846	+	0.980434i	$0.563070\pi$
$878$			5.37544e8i			0.794200i
$879$	7.22532e8	+	7.86945e8i	1.06388	+	1.15872i
$880$	−3.91906e8			−0.575088
$881$		−	8.43976e8i		−	1.23425i	−0.786866	−	0.617124i	$-0.788298\pi$
$881$		−	8.43976e8i		−	1.23425i	0.786866	−	0.617124i	$-0.211702\pi$
$882$	−7.63009e8	−	6.52366e7i	−1.11205	−	0.0950792i
$883$	1.08658e8			0.157826			0.0789131	−	0.996881i	$-0.474855\pi$
$883$	1.08658e8			0.157826			0.0789131	+	0.996881i	$0.474855\pi$
$884$		−	8.51566e8i		−	1.23271i
$885$	−6.29650e8	+	5.78112e8i	−0.908384	+	0.834032i
$886$	4.00832e8			0.576317
$887$		−	3.00810e8i		−	0.431044i	−0.976499	−	0.215522i	$-0.930855\pi$
$887$		−	3.00810e8i		−	0.431044i	0.976499	−	0.215522i	$-0.0691453\pi$
$888$	4.32152e7	+	4.70677e7i	0.0617160	+	0.0672178i
$889$	−1.04368e7			−0.0148547
$890$			2.01238e9i			2.85457i
$891$	3.62048e7	−	2.10178e8i	0.0511838	−	0.297135i
$892$	−3.65026e8			−0.514315
$893$		−	2.67273e7i		−	0.0375320i
$894$	−1.67515e8	+	1.53804e8i	−0.234445	+	0.215255i
$895$	−1.42703e9			−1.99051
$896$			6.17595e7i			0.0858578i
$897$	−4.54498e8	−	4.95015e8i	−0.629730	−	0.685869i
$898$	1.81166e9			2.50177
$899$		−	5.54087e8i		−	0.762604i
$900$	1.27522e8	−	1.49150e9i	0.174928	−	2.04596i
$901$	−1.60066e9			−2.18839
$902$		−	7.81631e7i		−	0.106508i
$903$	1.11708e6	−	1.02565e6i	0.00151713	−	0.00139295i
$904$	9.94950e7			0.134678
$905$			2.69686e8i			0.363842i
$906$	−5.83364e8	−	6.35370e8i	−0.784432	−	0.854362i
$907$	−6.39801e8			−0.857478			−0.428739	−	0.903428i	$-0.641042\pi$
$907$	−6.39801e8			−0.857478			−0.428739	+	0.903428i	$0.641042\pi$
$908$			8.69038e8i			1.16086i
$909$	1.24907e8	+	1.06795e7i	0.166302	+	0.0142187i
$910$	6.46231e8			0.857558
$911$		−	9.09529e8i		−	1.20299i	−0.798877	−	0.601494i	$-0.794572\pi$
$911$		−	9.09529e8i		−	1.20299i	0.798877	−	0.601494i	$-0.205428\pi$
$912$	1.98215e8	−	1.81991e8i	0.261308	−	0.239920i
$913$	3.09892e8			0.407191
$914$			9.00251e8i			1.17903i
$915$	7.28565e8	+	7.93515e8i	0.951054	+	1.03584i
$916$	3.42736e8			0.445937
$917$			5.99563e8i			0.777548i
$918$	1.11998e9	+	1.45067e9i	1.44772	+	1.87517i
$919$	9.30422e8			1.19876			0.599382	−	0.800463i	$-0.295413\pi$
$919$	9.30422e8			1.19876			0.599382	+	0.800463i	$0.295413\pi$
$920$		−	1.62141e8i		−	0.208224i
$921$	4.34117e8	−	3.98584e8i	0.555684	−	0.510201i
$922$	1.30074e9			1.65957
$923$		−	1.04145e9i		−	1.32444i
$924$	−6.63527e7	−	7.22679e7i	−0.0841091	−	0.0916072i
$925$	1.64295e9			2.07586
$926$			7.79247e8i			0.981391i
$927$	8.54862e7	−	9.99848e8i	0.107314	−	1.25515i
$928$	1.00182e9			1.25356
$929$		−	5.50577e7i		−	0.0686706i	−0.999410	−	0.0343353i	$-0.989069\pi$
$929$		−	5.50577e7i		−	0.0686706i	0.999410	−	0.0343353i	$-0.0109314\pi$
$930$	1.23993e9	−	1.13844e9i	1.54152	−	1.41534i
$931$	−2.15941e8			−0.267600
$932$			2.51413e8i			0.310556i
$933$	6.85184e8	+	7.46267e8i	0.843650	+	0.918860i
$934$	−4.50762e8			−0.553232
$935$		−	7.52662e8i		−	0.920800i
$936$	−6.16254e7	−	5.26892e6i	−0.0751506	−	0.00642531i
$937$	−3.36067e8			−0.408515			−0.204257	−	0.978917i	$-0.565478\pi$
$937$	−3.36067e8			−0.408515			−0.204257	+	0.978917i	$0.565478\pi$
$938$			1.02601e8i			0.124320i
$939$	−1.92394e8	+	1.76646e8i	−0.232377	+	0.213357i
$940$	1.55902e8			0.187702
$941$		−	1.36803e8i		−	0.164183i	−0.996625	−	0.0820913i	$-0.973840\pi$
$941$		−	1.36803e8i		−	0.164183i	0.996625	−	0.0820913i	$-0.0261599\pi$
$942$	−5.93106e8	−	6.45980e8i	−0.709545	−	0.772799i
$943$	2.55436e8			0.304612
$944$		−	6.16871e8i		−	0.733294i
$945$	−5.30518e8	+	4.09583e8i	−0.628644	+	0.485341i
$946$	−1.64710e6			−0.00194557
$947$			3.64404e8i			0.429075i	0.976716	+	0.214538i	$0.0688244\pi$
$947$			3.64404e8i			0.429075i	−0.976716	+	0.214538i	$0.931176\pi$
$948$	−6.77000e8	+	6.21587e8i	−0.794627	+	0.729586i
$949$	−3.72271e8			−0.435573
$950$		−	8.75928e8i		−	1.02164i
$951$	−9.93166e7	−	1.08170e8i	−0.115473	−	0.125767i
$952$	−6.33127e7			−0.0733804
$953$		−	1.21646e9i		−	1.40546i	−0.711455	−	0.702731i	$-0.751964\pi$
$953$		−	1.21646e9i		−	1.40546i	0.711455	−	0.702731i	$-0.248036\pi$
$954$	1.31879e8	−	1.54246e9i	0.151891	−	1.77652i
$955$	−7.71919e8			−0.886261
$956$			3.14793e7i			0.0360290i
$957$	1.76503e8	−	1.62056e8i	0.201380	−	0.184897i
$958$	−1.81969e9			−2.06967
$959$			1.45404e8i			0.164862i
$960$	9.17080e8	+	9.98836e8i	1.03656	+	1.12896i
$961$	−2.59710e8			−0.292630
$962$			9.03926e8i			1.01533i
$963$	3.52841e7	+	3.01676e6i	0.0395094	+	0.00337802i
$964$	7.25397e8			0.809738
$965$			2.64008e9i			2.93789i
$966$	4.90077e8	−	4.49964e8i	0.543667	−	0.499168i
$967$	−1.23870e9			−1.36989			−0.684945	−	0.728595i	$-0.740174\pi$
$967$	−1.23870e9			−1.36989			−0.684945	+	0.728595i	$0.740174\pi$
$968$		−	8.00217e6i		−	0.00882230i
$969$	3.49517e8	+	3.80675e8i	0.384146	+	0.418392i
$970$	9.39831e8			1.02976
$971$			5.60634e8i			0.612381i	0.951970	+	0.306190i	$0.0990544\pi$
$971$			5.60634e8i			0.612381i	−0.951970	+	0.306190i	$0.900946\pi$
$972$	−7.18136e8	+	4.62503e8i	−0.782002	+	0.503635i
$973$	2.40508e8			0.261091
$974$		−	1.30178e9i		−	1.40883i
$975$	−1.17143e9	+	1.07555e9i	−1.26387	+	1.16042i
$976$	−7.77410e8			−0.836182
$977$			6.18408e8i			0.663119i	0.943434	+	0.331560i	$0.107575\pi$
$977$			6.18408e8i			0.663119i	−0.943434	+	0.331560i	$0.892425\pi$
$978$	4.95830e8	+	5.40032e8i	0.530049	+	0.577302i
$979$	−3.24567e8			−0.345905
$980$		−	1.25960e9i		−	1.33830i
$981$	1.20157e8	−	1.40536e9i	0.127275	−	1.48861i
$982$	−8.08889e8			−0.854190
$983$			2.55022e8i			0.268483i	0.990949	+	0.134242i	$0.0428598\pi$
$983$			2.55022e8i			0.268483i	−0.990949	+	0.134242i	$0.957140\pi$
$984$	1.73173e7	−	1.58999e7i	0.0181759	−	0.0166881i
$985$	1.69243e9			1.77093
$986$			2.05907e9i			2.14803i
$987$	−3.24911e7	−	3.53876e7i	−0.0337919	−	0.0368043i
$988$	2.32241e8			0.240806
$989$		−	5.38271e6i		−	0.00556432i
$990$	7.25295e8	+	6.20122e7i	0.747497	+	0.0639104i
$991$	−1.59278e9			−1.63657			−0.818284	−	0.574814i	$-0.805074\pi$
$991$	−1.59278e9			−1.63657			−0.818284	+	0.574814i	$0.805074\pi$
$992$			1.13509e9i			1.16277i
$993$	−2.25979e8	+	2.07483e8i	−0.230792	+	0.211902i
$994$	1.03106e9			1.04985
$995$		−	8.14788e8i		−	0.827133i
$996$	−8.39413e8	−	9.14245e8i	−0.849567	−	0.925304i
$997$	8.94078e8			0.902173			0.451087	−	0.892480i	$-0.351037\pi$
$997$	8.94078e8			0.902173			0.451087	+	0.892480i	$0.351037\pi$
$998$		−	6.90542e8i		−	0.694702i
$999$	−5.72911e8	−	7.42071e8i	−0.574634	−	0.744302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.17	yes	20
3.2	odd	2	inner	33.7.b.a.23.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.4	✓	20	3.2	odd	2	inner
33.7.b.a.23.17	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)

\(f(q)\)	\(=\)	\(q+11.1144i q^{2} +(-19.8885 + 18.2606i) q^{3} -59.5295 q^{4} -223.873i q^{5} +(-202.955 - 221.048i) q^{6} -152.100 q^{7} +49.6872i q^{8} +(62.1023 - 726.350i) q^{9} +O(q^{10})\)	\(q+11.1144i q^{2} +(-19.8885 + 18.2606i) q^{3} -59.5295 q^{4} -223.873i q^{5} +(-202.955 - 221.048i) q^{6} -152.100 q^{7} +49.6872i q^{8} +(62.1023 - 726.350i) q^{9} +2488.21 q^{10} +401.312i q^{11} +(1183.95 - 1087.04i) q^{12} -1707.54 q^{13} -1690.50i q^{14} +(4088.05 + 4452.49i) q^{15} -4362.13 q^{16} -8377.54i q^{17} +(8072.93 + 690.229i) q^{18} +2284.74 q^{19} +13327.1i q^{20} +(3025.04 - 2777.44i) q^{21} -4460.33 q^{22} -14576.3i q^{23} +(-907.317 - 988.202i) q^{24} -34494.2 q^{25} -18978.2i q^{26} +(12028.5 + 15580.0i) q^{27} +9054.46 q^{28} +22114.1i q^{29} +(-49486.7 + 45436.2i) q^{30} -25055.8 q^{31} -45302.4i q^{32} +(-7328.18 - 7981.47i) q^{33} +93111.2 q^{34} +34051.2i q^{35} +(-3696.92 + 43239.2i) q^{36} -47629.7 q^{37} +25393.5i q^{38} +(33960.3 - 31180.6i) q^{39} +11123.6 q^{40} +17524.1i q^{41} +(30869.6 + 33621.5i) q^{42} +369.278 q^{43} -23889.9i q^{44} +(-162610. - 13903.0i) q^{45} +162007. q^{46} -11698.2i q^{47} +(86756.0 - 79655.0i) q^{48} -94514.5 q^{49} -383382. i q^{50} +(152979. + 166616. i) q^{51} +101649. q^{52} -191066. i q^{53} +(-173162. + 133689. i) q^{54} +89842.9 q^{55} -7557.44i q^{56} +(-45440.0 + 41720.7i) q^{57} -245785. q^{58} +141415. i q^{59} +(-243360. - 265055. i) q^{60} +178218. q^{61} -278480. i q^{62} +(-9445.79 + 110478. i) q^{63} +224332. q^{64} +382271. i q^{65} +(88709.1 - 81448.2i) q^{66} -60692.5 q^{67} +498710. i q^{68} +(266172. + 289901. i) q^{69} -378458. q^{70} +609914. i q^{71} +(36090.3 + 3085.69i) q^{72} +218017. q^{73} -529374. i q^{74} +(686037. - 629884. i) q^{75} -136009. q^{76} -61039.7i q^{77} +(346553. + 377447. i) q^{78} -571814. q^{79} +976563. i q^{80} +(-523728. - 90216.1i) q^{81} -194769. q^{82} -772199. i q^{83} +(-180079. + 165340. i) q^{84} -1.87551e6 q^{85} +4104.30i q^{86} +(-403817. - 439816. i) q^{87} -19940.0 q^{88} +808766. i q^{89} +(154524. - 1.80731e6i) q^{90} +259717. q^{91} +867720. i q^{92} +(498322. - 457534. i) q^{93} +130018. q^{94} -511492. i q^{95} +(827248. + 900995. i) q^{96} +377714. q^{97} -1.05047e6i q^{98} +(291493. + 24922.4i) 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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Database

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